LMFDB - Embedded newform 1.48.a.a.1.3

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			1.3
Root			$129356.$ 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)

$f(q)$	$=$	$q+4.55092e6 q^{2} -2.21918e11 q^{3} -1.20027e14 q^{4} -3.08341e16 q^{5} -1.00993e18 q^{6} +1.11073e20 q^{7} -1.18672e21 q^{8} +2.26588e22 q^{9} +O(q^{10})$	\(q+4.55092e6 q^{2} -2.21918e11 q^{3} -1.20027e14 q^{4} -3.08341e16 q^{5} -1.00993e18 q^{6} +1.11073e20 q^{7} -1.18672e21 q^{8} +2.26588e22 q^{9} -1.40324e23 q^{10} -1.19449e24 q^{11} +2.66361e25 q^{12} -2.71503e24 q^{13} +5.05485e26 q^{14} +6.84264e27 q^{15} +1.14916e28 q^{16} +1.17417e29 q^{17} +1.03118e29 q^{18} -1.65620e30 q^{19} +3.70091e30 q^{20} -2.46491e31 q^{21} -5.43602e30 q^{22} +5.41759e31 q^{23} +2.63354e32 q^{24} +2.40198e32 q^{25} -1.23559e31 q^{26} +8.72142e32 q^{27} -1.33317e34 q^{28} -1.03639e34 q^{29} +3.11403e34 q^{30} -3.80854e34 q^{31} +2.19313e35 q^{32} +2.65078e35 q^{33} +5.34356e35 q^{34} -3.42483e36 q^{35} -2.71966e36 q^{36} +8.41184e36 q^{37} -7.53724e36 q^{38} +6.02513e35 q^{39} +3.65913e37 q^{40} +7.68510e37 q^{41} -1.12176e38 q^{42} -2.17109e38 q^{43} +1.43370e38 q^{44} -6.98663e38 q^{45} +2.46550e38 q^{46} +2.73873e39 q^{47} -2.55019e39 q^{48} +7.09387e39 q^{49} +1.09312e39 q^{50} -2.60570e40 q^{51} +3.25875e38 q^{52} +8.29394e39 q^{53} +3.96905e39 q^{54} +3.68309e40 q^{55} -1.31812e41 q^{56} +3.67541e41 q^{57} -4.71655e40 q^{58} +7.09596e40 q^{59} -8.21298e41 q^{60} -6.43092e41 q^{61} -1.73324e41 q^{62} +2.51678e42 q^{63} -6.19220e41 q^{64} +8.37153e40 q^{65} +1.20635e42 q^{66} +1.19612e43 q^{67} -1.40932e43 q^{68} -1.20226e43 q^{69} -1.55862e43 q^{70} +2.64034e43 q^{71} -2.68896e43 q^{72} +3.87700e43 q^{73} +3.82817e43 q^{74} -5.33042e43 q^{75} +1.98788e44 q^{76} -1.32675e44 q^{77} +2.74199e42 q^{78} -1.22812e44 q^{79} -3.54332e44 q^{80} -7.96015e44 q^{81} +3.49743e44 q^{82} +1.65007e45 q^{83} +2.95855e45 q^{84} -3.62045e45 q^{85} -9.88045e44 q^{86} +2.29995e45 q^{87} +1.41752e45 q^{88} -6.00200e45 q^{89} -3.17956e45 q^{90} -3.01566e44 q^{91} -6.50255e45 q^{92} +8.45183e45 q^{93} +1.24637e46 q^{94} +5.10674e46 q^{95} -4.86695e46 q^{96} -1.75152e46 q^{97} +3.22837e46 q^{98} -2.70656e46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.55092e6	0.383614	0.191807	−	0.981433i	$-0.438565\pi$
$2$	4.55092e6	0.383614	0.191807	+	0.981433i	$0.438565\pi$
$3$	−2.21918e11	−1.36095	−0.680476	−	0.732770i	$-0.738227\pi$
$3$	−2.21918e11	−1.36095	−0.680476	+	0.732770i	$0.738227\pi$
$4$	−1.20027e14	−0.852840
$5$	−3.08341e16	−1.15674	−0.578370	−	0.815774i	$-0.696311\pi$
$5$	−3.08341e16	−1.15674	−0.578370	+	0.815774i	$0.696311\pi$
$6$	−1.00993e18	−0.522081
$7$	1.11073e20	1.53393	0.766963	−	0.641691i	$-0.221767\pi$
$7$	1.11073e20	1.53393	0.766963	+	0.641691i	$0.221767\pi$
$8$	−1.18672e21	−0.710776
$9$	2.26588e22	0.852193
$10$	−1.40324e23	−0.443742
$11$	−1.19449e24	−0.402210	−0.201105	−	0.979570i	$-0.564453\pi$
$11$	−1.19449e24	−0.402210	−0.201105	+	0.979570i	$0.564453\pi$
$12$	2.66361e25	1.16068
$13$	−2.71503e24	−0.0180345	−0.00901727	−	0.999959i	$-0.502870\pi$
$13$	−2.71503e24	−0.0180345	−0.00901727	+	0.999959i	$0.502870\pi$
$14$	5.05485e26	0.588436
$15$	6.84264e27	1.57427
$16$	1.14916e28	0.580177
$17$	1.17417e29	1.42620	0.713102	−	0.701060i	$-0.247289\pi$
$17$	1.17417e29	1.42620	0.713102	+	0.701060i	$0.247289\pi$
$18$	1.03118e29	0.326913
$19$	−1.65620e30	−1.47368	−0.736840	−	0.676067i	$-0.763683\pi$
$19$	−1.65620e30	−1.47368	−0.736840	+	0.676067i	$0.763683\pi$
$20$	3.70091e30	0.986515
$21$	−2.46491e31	−2.08760
$22$	−5.43602e30	−0.154294
$23$	5.41759e31	0.541006	0.270503	−	0.962719i	$-0.412810\pi$
$23$	5.41759e31	0.541006	0.270503	+	0.962719i	$0.412810\pi$
$24$	2.63354e32	0.967332
$25$	2.40198e32	0.338048
$26$	−1.23559e31	−0.00691831
$27$	8.72142e32	0.201159
$28$	−1.33317e34	−1.30819
$29$	−1.03639e34	−0.445833	−0.222916	−	0.974838i	$-0.571558\pi$
$29$	−1.03639e34	−0.445833	−0.222916	+	0.974838i	$0.571558\pi$
$30$	3.11403e34	0.603912
$31$	−3.80854e34	−0.341789	−0.170895	−	0.985289i	$-0.554666\pi$
$31$	−3.80854e34	−0.341789	−0.170895	+	0.985289i	$0.554666\pi$
$32$	2.19313e35	0.933340
$33$	2.65078e35	0.547389
$34$	5.34356e35	0.547112
$35$	−3.42483e36	−1.77435
$36$	−2.71966e36	−0.726784
$37$	8.41184e36	1.18073	0.590365	−	0.807136i	$-0.298984\pi$
$37$	8.41184e36	1.18073	0.590365	+	0.807136i	$0.298984\pi$
$38$	−7.53724e36	−0.565324
$39$	6.02513e35	0.0245442
$40$	3.65913e37	0.822183
$41$	7.68510e37	0.966560	0.483280	−	0.875466i	$-0.339445\pi$
$41$	7.68510e37	0.966560	0.483280	+	0.875466i	$0.339445\pi$
$42$	−1.12176e38	−0.800834
$43$	−2.17109e38	−0.891597	−0.445799	−	0.895133i	$-0.647080\pi$
$43$	−2.17109e38	−0.891597	−0.445799	+	0.895133i	$0.647080\pi$
$44$	1.43370e38	0.343021
$45$	−6.98663e38	−0.985766
$46$	2.46550e38	0.207537
$47$	2.73873e39	1.39075	0.695375	−	0.718647i	$-0.255238\pi$
$47$	2.73873e39	1.39075	0.695375	+	0.718647i	$0.255238\pi$
$48$	−2.55019e39	−0.789593
$49$	7.09387e39	1.35293
$50$	1.09312e39	0.129680
$51$	−2.60570e40	−1.94100
$52$	3.25875e38	0.0153806
$53$	8.29394e39	0.250195	0.125097	−	0.992144i	$-0.460076\pi$
$53$	8.29394e39	0.250195	0.125097	+	0.992144i	$0.460076\pi$
$54$	3.96905e39	0.0771673
$55$	3.68309e40	0.465253
$56$	−1.31812e41	−1.09028
$57$	3.67541e41	2.00561
$58$	−4.71655e40	−0.171028
$59$	7.09596e40	0.172182	0.0860912	−	0.996287i	$-0.472562\pi$
$59$	7.09596e40	0.172182	0.0860912	+	0.996287i	$0.472562\pi$
$60$	−8.21298e41	−1.34260
$61$	−6.43092e41	−0.712889	−0.356444	−	0.934317i	$-0.616011\pi$
$61$	−6.43092e41	−0.712889	−0.356444	+	0.934317i	$0.616011\pi$
$62$	−1.73324e41	−0.131115
$63$	2.51678e42	1.30720
$64$	−6.19220e41	−0.222134
$65$	8.37153e40	0.0208613
$66$	1.20635e42	0.209986
$67$	1.19612e43	1.46223	0.731114	−	0.682255i	$-0.239001\pi$
$67$	1.19612e43	1.46223	0.731114	+	0.682255i	$0.239001\pi$
$68$	−1.40932e43	−1.21632
$69$	−1.20226e43	−0.736283
$70$	−1.55862e43	−0.680668
$71$	2.64034e43	0.826205	0.413103	−	0.910684i	$-0.364445\pi$
$71$	2.64034e43	0.826205	0.413103	+	0.910684i	$0.364445\pi$
$72$	−2.68896e43	−0.605718
$73$	3.87700e43	0.631552	0.315776	−	0.948834i	$-0.397735\pi$
$73$	3.87700e43	0.631552	0.315776	+	0.948834i	$0.397735\pi$
$74$	3.82817e43	0.452945
$75$	−5.33042e43	−0.460068
$76$	1.98788e44	1.25681
$77$	−1.32675e44	−0.616961
$78$	2.74199e42	0.00941549
$79$	−1.22812e44	−0.312612	−0.156306	−	0.987709i	$-0.549959\pi$
$79$	−1.22812e44	−0.312612	−0.156306	+	0.987709i	$0.549959\pi$
$80$	−3.54332e44	−0.671114
$81$	−7.96015e44	−1.12596
$82$	3.49743e44	0.370786
$83$	1.65007e45	1.31573	0.657867	−	0.753134i	$-0.271459\pi$
$83$	1.65007e45	1.31573	0.657867	+	0.753134i	$0.271459\pi$
$84$	2.95855e45	1.78039
$85$	−3.62045e45	−1.64975
$86$	−9.88045e44	−0.342029
$87$	2.29995e45	0.606757
$88$	1.41752e45	0.285881
$89$	−6.00200e45	−0.928177	−0.464089	−	0.885789i	$-0.653618\pi$
$89$	−6.00200e45	−0.928177	−0.464089	+	0.885789i	$0.653618\pi$
$90$	−3.17956e45	−0.378154
$91$	−3.01566e44	−0.0276637
$92$	−6.50255e45	−0.461391
$93$	8.45183e45	0.465159
$94$	1.24637e46	0.533512
$95$	5.10674e46	1.70466
$96$	−4.86695e46	−1.27023
$97$	−1.75152e46	−0.358328	−0.179164	−	0.983819i	$-0.557339\pi$
$97$	−1.75152e46	−0.358328	−0.179164	+	0.983819i	$0.557339\pi$
$98$	3.22837e46	0.519003
$99$	−2.70656e46	−0.342761
$100$	−2.88301e46	−0.288301
$101$	−2.93699e46	−0.232461	−0.116231	−	0.993222i	$-0.537081\pi$
$101$	−2.93699e46	−0.232461	−0.116231	+	0.993222i	$0.537081\pi$
$102$	−1.18583e47	−0.744594
$103$	−2.42094e46	−0.120868	−0.0604338	−	0.998172i	$-0.519248\pi$
$103$	−2.42094e46	−0.120868	−0.0604338	+	0.998172i	$0.519248\pi$
$104$	3.22197e45	0.0128185
$105$	7.60032e47	2.41481
$106$	3.77451e46	0.0959782
$107$	−3.58808e47	−0.731718	−0.365859	−	0.930670i	$-0.619225\pi$
$107$	−3.58808e47	−0.731718	−0.365859	+	0.930670i	$0.619225\pi$
$108$	−1.04680e47	−0.171556
$109$	−2.00272e47	−0.264301	−0.132150	−	0.991230i	$-0.542188\pi$
$109$	−2.00272e47	−0.264301	−0.132150	+	0.991230i	$0.542188\pi$
$110$	1.67615e47	0.178478
$111$	−1.86674e48	−1.60692
$112$	1.27640e48	0.889948
$113$	−4.99882e47	−0.282829	−0.141414	−	0.989950i	$-0.545165\pi$
$113$	−4.99882e47	−0.282829	−0.141414	+	0.989950i	$0.545165\pi$
$114$	1.67265e48	0.769380
$115$	−1.67046e48	−0.625803
$116$	1.24395e48	0.380224
$117$	−6.15192e46	−0.0153689
$118$	3.22932e47	0.0660516
$119$	1.30419e49	2.18769
$120$	−8.12028e48	−1.11895
$121$	−7.39295e48	−0.838227
$122$	−2.92666e48	−0.273474
$123$	−1.70546e49	−1.31544
$124$	4.57126e48	0.291492
$125$	1.45027e49	0.765706
$126$	1.14537e49	0.501461
$127$	8.93451e47	0.0324850	0.0162425	−	0.999868i	$-0.494830\pi$
$127$	8.93451e47	0.0324850	0.0162425	+	0.999868i	$0.494830\pi$
$128$	−3.36836e49	−1.01855
$129$	4.81804e49	1.21342
$130$	3.80982e47	0.00800269
$131$	8.86188e49	1.55471	0.777357	−	0.629060i	$-0.216560\pi$
$131$	8.86188e49	1.55471	0.777357	+	0.629060i	$0.216560\pi$
$132$	−3.18164e49	−0.466836
$133$	−1.83959e50	−2.26052
$134$	5.44343e49	0.560932
$135$	−2.68917e49	−0.232688
$136$	−1.39341e50	−1.01371
$137$	1.56850e50	0.960619	0.480310	−	0.877099i	$-0.340524\pi$
$137$	1.56850e50	0.960619	0.480310	+	0.877099i	$0.340524\pi$
$138$	−5.47140e49	−0.282449
$139$	2.09943e50	0.914648	0.457324	−	0.889300i	$-0.348808\pi$
$139$	2.09943e50	0.914648	0.457324	+	0.889300i	$0.348808\pi$
$140$	4.11071e50	1.51324
$141$	−6.07773e50	−1.89275
$142$	1.20160e50	0.316944
$143$	3.24306e48	0.00725368
$144$	2.60385e50	0.494422
$145$	3.19563e50	0.515713
$146$	1.76440e50	0.242272
$147$	−1.57426e51	−1.84128
$148$	−1.00964e51	−1.00697
$149$	1.17929e51	1.00402	0.502009	−	0.864862i	$-0.332594\pi$
$149$	1.17929e51	1.00402	0.502009	+	0.864862i	$0.332594\pi$
$150$	−2.42583e50	−0.176489
$151$	−1.05626e51	−0.657377	−0.328689	−	0.944438i	$-0.606607\pi$
$151$	−1.05626e51	−0.657377	−0.328689	+	0.944438i	$0.606607\pi$
$152$	1.96544e51	1.04746
$153$	2.66053e51	1.21540
$154$	−6.03795e50	−0.236675
$155$	1.17433e51	0.395361
$156$	−7.23176e49	−0.0209323
$157$	−2.43063e51	−0.605447	−0.302724	−	0.953078i	$-0.597896\pi$
$157$	−2.43063e51	−0.605447	−0.302724	+	0.953078i	$0.597896\pi$
$158$	−5.58909e50	−0.119922
$159$	−1.84057e51	−0.340503
$160$	−6.76231e51	−1.07963
$161$	6.01748e51	0.829863
$162$	−3.62260e51	−0.431934
$163$	8.76362e51	0.904222	0.452111	−	0.891962i	$-0.350671\pi$
$163$	8.76362e51	0.904222	0.452111	+	0.891962i	$0.350671\pi$
$164$	−9.22416e51	−0.824321
$165$	−8.17344e51	−0.633187
$166$	7.50936e51	0.504734
$167$	2.63045e52	1.53530	0.767648	−	0.640871i	$-0.221427\pi$
$167$	2.63045e52	1.53530	0.767648	+	0.640871i	$0.221427\pi$
$168$	2.92515e52	1.48382
$169$	−2.26567e52	−0.999675
$170$	−1.64764e52	−0.632867
$171$	−3.75275e52	−1.25586
$172$	2.60588e52	0.760390
$173$	−3.14535e52	−0.800913	−0.400456	−	0.916316i	$-0.631148\pi$
$173$	−3.14535e52	−0.800913	−0.400456	+	0.916316i	$0.631148\pi$
$174$	1.04669e52	0.232761
$175$	2.66795e52	0.518541
$176$	−1.37265e52	−0.233353
$177$	−1.57472e52	−0.234332
$178$	−2.73146e52	−0.356062
$179$	−5.75744e52	−0.657935	−0.328968	−	0.944341i	$-0.606701\pi$
$179$	−5.75744e52	−0.657935	−0.328968	+	0.944341i	$0.606701\pi$
$180$	8.38581e52	0.840701
$181$	1.66382e53	1.46440	0.732199	−	0.681091i	$-0.238494\pi$
$181$	1.66382e53	1.46440	0.732199	+	0.681091i	$0.238494\pi$
$182$	−1.37240e51	−0.0106122
$183$	1.42714e53	0.970208
$184$	−6.42915e52	−0.384534
$185$	−2.59371e53	−1.36580
$186$	3.84636e52	0.178442
$187$	−1.40253e53	−0.573634
$188$	−3.28720e53	−1.18609
$189$	9.68714e52	0.308563
$190$	2.32404e53	0.653934
$191$	−1.33768e53	−0.332713	−0.166356	−	0.986066i	$-0.553200\pi$
$191$	−1.33768e53	−0.332713	−0.166356	+	0.986066i	$0.553200\pi$
$192$	1.37416e53	0.302314
$193$	6.53394e53	1.27227	0.636134	−	0.771579i	$-0.280533\pi$
$193$	6.53394e53	1.27227	0.636134	+	0.771579i	$0.280533\pi$
$194$	−7.97105e52	−0.137460
$195$	−1.85779e52	−0.0283912
$196$	−8.51453e53	−1.15383
$197$	9.89833e53	1.19016	0.595081	−	0.803666i	$-0.297120\pi$
$197$	9.89833e53	1.19016	0.595081	+	0.803666i	$0.297120\pi$
$198$	−1.23174e53	−0.131488
$199$	1.17074e54	1.11023	0.555117	−	0.831772i	$-0.312673\pi$
$199$	1.17074e54	1.11023	0.555117	+	0.831772i	$0.312673\pi$
$200$	−2.85047e53	−0.240277
$201$	−2.65440e54	−1.99002
$202$	−1.33660e53	−0.0891754
$203$	−1.15115e54	−0.683875
$204$	3.12753e54	1.65536
$205$	−2.36963e54	−1.11806
$206$	−1.10175e53	−0.0463665
$207$	1.22756e54	0.461041
$208$	−3.11999e52	−0.0104632
$209$	1.97831e54	0.592729
$210$	3.45885e54	0.926357
$211$	1.13707e54	0.272364	0.136182	−	0.990684i	$-0.456517\pi$
$211$	1.13707e54	0.272364	0.136182	+	0.990684i	$0.456517\pi$
$212$	−9.95493e53	−0.213376
$213$	−5.85938e54	−1.12443
$214$	−1.63291e54	−0.280697
$215$	6.69435e54	1.03135
$216$	−1.03499e54	−0.142979
$217$	−4.23026e54	−0.524280
$218$	−9.11424e53	−0.101389
$219$	−8.60377e54	−0.859512
$220$	−4.42069e54	−0.396786
$221$	−3.18791e53	−0.0257210
$222$	−8.49539e54	−0.616437
$223$	2.34179e55	1.52892	0.764459	−	0.644672i	$-0.223006\pi$
$223$	2.34179e55	1.52892	0.764459	+	0.644672i	$0.223006\pi$
$224$	2.43597e55	1.43167
$225$	5.44259e54	0.288082
$226$	−2.27492e54	−0.108497
$227$	3.06780e55	1.31892	0.659462	−	0.751738i	$-0.270784\pi$
$227$	3.06780e55	1.31892	0.659462	+	0.751738i	$0.270784\pi$
$228$	−4.41146e55	−1.71046
$229$	−4.77257e55	−1.66962	−0.834811	−	0.550536i	$-0.814423\pi$
$229$	−4.77257e55	−1.66962	−0.834811	+	0.550536i	$0.814423\pi$
$230$	−7.60215e54	−0.240067
$231$	2.94430e55	0.839655
$232$	1.22991e55	0.316887
$233$	1.85272e55	0.431464	0.215732	−	0.976453i	$-0.430786\pi$
$233$	1.85272e55	0.431464	0.215732	+	0.976453i	$0.430786\pi$
$234$	−2.79969e53	−0.00589573
$235$	−8.44462e55	−1.60874
$236$	−8.51704e54	−0.146844
$237$	2.72543e55	0.425450
$238$	5.93526e55	0.839230
$239$	−6.05119e55	−0.775336	−0.387668	−	0.921799i	$-0.626719\pi$
$239$	−6.05119e55	−0.775336	−0.387668	+	0.921799i	$0.626719\pi$
$240$	7.86327e55	0.913354
$241$	3.35331e55	0.353242	0.176621	−	0.984279i	$-0.443483\pi$
$241$	3.35331e55	0.353242	0.176621	+	0.984279i	$0.443483\pi$
$242$	−3.36447e55	−0.321556
$243$	1.53461e56	1.33122
$244$	7.71881e55	0.607980
$245$	−2.18733e56	−1.56499
$246$	−7.76143e55	−0.504622
$247$	4.49663e54	0.0265771
$248$	4.51966e55	0.242936
$249$	−3.66181e56	−1.79065
$250$	6.60005e55	0.293736
$251$	3.39203e56	1.37444	0.687222	−	0.726448i	$-0.258830\pi$
$251$	3.39203e56	1.37444	0.687222	+	0.726448i	$0.258830\pi$
$252$	−3.02081e56	−1.11483
$253$	−6.47124e55	−0.217598
$254$	4.06603e54	0.0124617
$255$	8.03443e56	2.24523
$256$	−6.61439e55	−0.168597
$257$	−7.45663e56	−1.73426	−0.867130	−	0.498082i	$-0.834038\pi$
$257$	−7.45663e56	−1.73426	−0.867130	+	0.498082i	$0.834038\pi$
$258$	2.19265e56	0.465486
$259$	9.34329e56	1.81115
$260$	−1.00481e55	−0.0177913
$261$	−2.34834e56	−0.379935
$262$	4.03298e56	0.596410
$263$	−1.28505e57	−1.73764	−0.868819	−	0.495129i	$-0.835121\pi$
$263$	−1.28505e57	−1.73764	−0.868819	+	0.495129i	$0.835121\pi$
$264$	−3.14573e56	−0.389071
$265$	−2.55736e56	−0.289410
$266$	−8.37184e56	−0.867166
$267$	1.33195e57	1.26321
$268$	−1.43566e57	−1.24705
$269$	1.52143e57	1.21081	0.605403	−	0.795919i	$-0.293012\pi$
$269$	1.52143e57	1.21081	0.605403	+	0.795919i	$0.293012\pi$
$270$	−1.22382e56	−0.0892625
$271$	2.08539e56	0.139447	0.0697235	−	0.997566i	$-0.477788\pi$
$271$	2.08539e56	0.139447	0.0697235	+	0.997566i	$0.477788\pi$
$272$	1.34931e57	0.827450
$273$	6.69230e55	0.0376490
$274$	7.13813e56	0.368507
$275$	−2.86913e56	−0.135967
$276$	1.44303e57	0.627932
$277$	−4.91573e57	−1.96478	−0.982388	−	0.186853i	$-0.940171\pi$
$277$	−4.91573e57	−1.96478	−0.982388	+	0.186853i	$0.940171\pi$
$278$	9.55436e56	0.350872
$279$	−8.62969e56	−0.291270
$280$	4.06431e57	1.26117
$281$	2.99077e57	0.853462	0.426731	−	0.904379i	$-0.359665\pi$
$281$	2.99077e57	0.853462	0.426731	+	0.904379i	$0.359665\pi$
$282$	−2.76593e57	−0.726084
$283$	−2.40523e57	−0.580999	−0.290499	−	0.956875i	$-0.593821\pi$
$283$	−2.40523e57	−0.580999	−0.290499	+	0.956875i	$0.593821\pi$
$284$	−3.16910e57	−0.704621
$285$	−1.13328e58	−2.31997
$286$	1.47589e55	0.00278261
$287$	8.53607e57	1.48263
$288$	4.96937e57	0.795385
$289$	7.00882e57	1.03406
$290$	1.45430e57	0.197835
$291$	3.88695e57	0.487667
$292$	−4.65344e57	−0.538613
$293$	7.67134e57	0.819374	0.409687	−	0.912226i	$-0.365638\pi$
$293$	7.67134e57	0.819374	0.409687	+	0.912226i	$0.365638\pi$
$294$	−7.16433e57	−0.706339
$295$	−2.18797e57	−0.199170
$296$	−9.98248e57	−0.839235
$297$	−1.04176e57	−0.0809081
$298$	5.36684e57	0.385156
$299$	−1.47089e56	−0.00975679
$300$	6.39792e57	0.392364
$301$	−2.41149e58	−1.36764
$302$	−4.80698e57	−0.252179
$303$	6.51772e57	0.316369
$304$	−1.90324e58	−0.854994
$305$	1.98291e58	0.824627
$306$	1.21079e58	0.466245
$307$	1.66078e58	0.592325	0.296162	−	0.955138i	$-0.404293\pi$
$307$	1.66078e58	0.592325	0.296162	+	0.955138i	$0.404293\pi$
$308$	1.59246e58	0.526169
$309$	5.37251e57	0.164495
$310$	5.34427e57	0.151666
$311$	−2.17917e58	−0.573352	−0.286676	−	0.958028i	$-0.592550\pi$
$311$	−2.17917e58	−0.573352	−0.286676	+	0.958028i	$0.592550\pi$
$312$	−7.15013e56	−0.0174454
$313$	4.52774e58	1.02468	0.512342	−	0.858782i	$-0.328778\pi$
$313$	4.52774e58	1.02468	0.512342	+	0.858782i	$0.328778\pi$
$314$	−1.10616e58	−0.232258
$315$	−7.76026e58	−1.51209
$316$	1.47407e58	0.266608
$317$	−6.03868e58	−1.01403	−0.507014	−	0.861938i	$-0.669251\pi$
$317$	−6.03868e58	−1.01403	−0.507014	+	0.861938i	$0.669251\pi$
$318$	−8.37631e57	−0.130622
$319$	1.23796e58	0.179319
$320$	1.90931e58	0.256952
$321$	7.96260e58	0.995833
$322$	2.73851e58	0.318347
$323$	−1.94466e59	−2.10177
$324$	9.55429e58	0.960264
$325$	−6.52143e56	−0.00609655
$326$	3.98826e58	0.346872
$327$	4.44440e58	0.359701
$328$	−9.12004e58	−0.687007
$329$	3.04199e59	2.13331
$330$	−3.71967e58	−0.242900
$331$	−2.03088e57	−0.0123517	−0.00617585	−	0.999981i	$-0.501966\pi$
$331$	−2.03088e57	−0.0123517	−0.00617585	+	0.999981i	$0.501966\pi$
$332$	−1.98053e59	−1.12211
$333$	1.90602e59	1.00621
$334$	1.19710e59	0.588962
$335$	−3.68811e59	−1.69142
$336$	−2.83257e59	−1.21118
$337$	−1.81636e59	−0.724268	−0.362134	−	0.932126i	$-0.617952\pi$
$337$	−1.81636e59	−0.724268	−0.362134	+	0.932126i	$0.617952\pi$
$338$	−1.03109e59	−0.383489
$339$	1.10933e59	0.384917
$340$	4.34550e59	1.40697
$341$	4.54925e58	0.137471
$342$	−1.70785e59	−0.481765
$343$	2.05545e59	0.541370
$344$	2.57647e59	0.633726
$345$	3.70706e59	0.851689
$346$	−1.43142e59	−0.307241
$347$	1.01600e59	0.203776	0.101888	−	0.994796i	$-0.467512\pi$
$347$	1.01600e59	0.203776	0.101888	+	0.994796i	$0.467512\pi$
$348$	−2.76055e59	−0.517467
$349$	−4.81199e59	−0.843193	−0.421596	−	0.906784i	$-0.638530\pi$
$349$	−4.81199e59	−0.843193	−0.421596	+	0.906784i	$0.638530\pi$
$350$	1.21416e59	0.198920
$351$	−2.36789e57	−0.00362781
$352$	−2.61966e59	−0.375399
$353$	1.19790e60	1.60588	0.802941	−	0.596059i	$-0.203268\pi$
$353$	1.19790e60	1.60588	0.802941	+	0.596059i	$0.203268\pi$
$354$	−7.16644e58	−0.0898932
$355$	−8.14123e59	−0.955705
$356$	7.20400e59	0.791587
$357$	−2.89423e60	−2.97735
$358$	−2.62017e59	−0.252393
$359$	−8.62063e58	−0.0777713	−0.0388857	−	0.999244i	$-0.512381\pi$
$359$	−8.62063e58	−0.0777713	−0.0388857	+	0.999244i	$0.512381\pi$
$360$	8.29116e59	0.700658
$361$	1.47995e60	1.17173
$362$	7.57190e59	0.561764
$363$	1.64063e60	1.14079
$364$	3.61959e58	0.0235927
$365$	−1.19544e60	−0.730542
$366$	6.49479e59	0.372185
$367$	−2.19138e60	−1.17778	−0.588892	−	0.808212i	$-0.700435\pi$
$367$	−2.19138e60	−1.17778	−0.588892	+	0.808212i	$0.700435\pi$
$368$	6.22566e59	0.313879
$369$	1.74135e60	0.823696
$370$	−1.18038e60	−0.523940
$371$	9.21233e59	0.383780
$372$	−1.01444e60	−0.396706
$373$	1.32206e60	0.485393	0.242696	−	0.970102i	$-0.421968\pi$
$373$	1.32206e60	0.485393	0.242696	+	0.970102i	$0.421968\pi$
$374$	−6.38282e59	−0.220054
$375$	−3.21840e60	−1.04209
$376$	−3.25010e60	−0.988512
$377$	2.81384e58	0.00804039
$378$	4.40854e59	0.118369
$379$	6.08671e60	1.53589	0.767947	−	0.640513i	$-0.221278\pi$
$379$	6.08671e60	1.53589	0.767947	+	0.640513i	$0.221278\pi$
$380$	−6.12944e60	−1.45381
$381$	−1.98273e59	−0.0442106
$382$	−6.08770e59	−0.127633
$383$	3.42858e60	0.675995	0.337997	−	0.941147i	$-0.390250\pi$
$383$	3.42858e60	0.675995	0.337997	+	0.941147i	$0.390250\pi$
$384$	7.47499e60	1.38620
$385$	4.09092e60	0.713664
$386$	2.97355e60	0.488060
$387$	−4.91942e60	−0.759813
$388$	2.10229e60	0.305596
$389$	−5.62159e60	−0.769208	−0.384604	−	0.923082i	$-0.625662\pi$
$389$	−5.62159e60	−0.769208	−0.384604	+	0.923082i	$0.625662\pi$
$390$	−8.45468e58	−0.0108913
$391$	6.36118e60	0.771585
$392$	−8.41842e60	−0.961630
$393$	−1.96661e61	−2.11589
$394$	4.50466e60	0.456563
$395$	3.78680e60	0.361611
$396$	3.24860e60	0.292320
$397$	−1.94362e61	−1.64829	−0.824146	−	0.566377i	$-0.808345\pi$
$397$	−1.94362e61	−1.64829	−0.824146	+	0.566377i	$0.808345\pi$
$398$	5.32797e60	0.425902
$399$	4.08238e61	3.07646
$400$	2.76025e60	0.196128
$401$	−2.48633e61	−1.66597	−0.832984	−	0.553296i	$-0.813370\pi$
$401$	−2.48633e61	−1.66597	−0.832984	+	0.553296i	$0.813370\pi$
$402$	−1.20800e61	−0.763402
$403$	1.03403e59	0.00616401
$404$	3.52517e60	0.198252
$405$	2.45444e61	1.30244
$406$	−5.23881e60	−0.262344
$407$	−1.00478e61	−0.474902
$408$	3.09223e61	1.37961
$409$	1.77202e61	0.746397	0.373199	−	0.927751i	$-0.378261\pi$
$409$	1.77202e61	0.746397	0.373199	+	0.927751i	$0.378261\pi$
$410$	−1.07840e61	−0.428903
$411$	−3.48079e61	−1.30736
$412$	2.90578e60	0.103081
$413$	7.88170e60	0.264115
$414$	5.58653e60	0.176862
$415$	−5.08785e61	−1.52196
$416$	−5.95440e59	−0.0168324
$417$	−4.65902e61	−1.24479
$418$	9.00313e60	0.227379
$419$	6.32251e61	1.50959	0.754797	−	0.655958i	$-0.227735\pi$
$419$	6.32251e61	1.50959	0.754797	+	0.655958i	$0.227735\pi$
$420$	−9.12241e61	−2.05945
$421$	8.68512e61	1.85416	0.927078	−	0.374868i	$-0.122312\pi$
$421$	8.68512e61	1.85416	0.927078	+	0.374868i	$0.122312\pi$
$422$	5.17472e60	0.104483
$423$	6.20563e61	1.18519
$424$	−9.84256e60	−0.177832
$425$	2.82033e61	0.482126
$426$	−2.66656e61	−0.431346
$427$	−7.14301e61	−1.09352
$428$	4.30665e61	0.624038
$429$	−7.19694e59	−0.00987192
$430$	3.04655e61	0.395639
$431$	6.27735e61	0.771898	0.385949	−	0.922520i	$-0.373874\pi$
$431$	6.27735e61	0.771898	0.385949	+	0.922520i	$0.373874\pi$
$432$	1.00223e61	0.116708
$433$	−6.16297e61	−0.679711	−0.339855	−	0.940478i	$-0.610378\pi$
$433$	−6.16297e61	−0.679711	−0.339855	+	0.940478i	$0.610378\pi$
$434$	−1.92516e61	−0.201121
$435$	−7.09167e61	−0.701861
$436$	2.40380e61	0.225406
$437$	−8.97261e61	−0.797269
$438$	−3.91551e61	−0.329721
$439$	−1.66474e62	−1.32871	−0.664353	−	0.747419i	$-0.731293\pi$
$439$	−1.66474e62	−1.32871	−0.664353	+	0.747419i	$0.731293\pi$
$440$	−4.37079e61	−0.330691
$441$	1.60739e62	1.15296
$442$	−1.45079e60	−0.00986692
$443$	1.29305e62	0.833929	0.416965	−	0.908923i	$-0.363094\pi$
$443$	1.29305e62	0.833929	0.416965	+	0.908923i	$0.363094\pi$
$444$	2.24058e62	1.37044
$445$	1.85066e62	1.07366
$446$	1.06573e62	0.586515
$447$	−2.61705e62	−1.36642
$448$	−6.87786e61	−0.340738
$449$	−1.47587e62	−0.693839	−0.346920	−	0.937895i	$-0.612772\pi$
$449$	−1.47587e62	−0.693839	−0.346920	+	0.937895i	$0.612772\pi$
$450$	2.47688e61	0.110512
$451$	−9.17975e61	−0.388760
$452$	5.99991e61	0.241208
$453$	2.34404e62	0.894659
$454$	1.39613e62	0.505958
$455$	9.29851e60	0.0319997
$456$	−4.36167e62	−1.42554
$457$	−1.90700e62	−0.591998	−0.295999	−	0.955188i	$-0.595653\pi$
$457$	−1.90700e62	−0.591998	−0.295999	+	0.955188i	$0.595653\pi$
$458$	−2.17196e62	−0.640491
$459$	1.02404e62	0.286893
$460$	2.00500e62	0.533710
$461$	2.19785e61	0.0555939	0.0277970	−	0.999614i	$-0.491151\pi$
$461$	2.19785e61	0.0555939	0.0277970	+	0.999614i	$0.491151\pi$
$462$	1.33993e62	0.322104
$463$	−1.68005e62	−0.383857	−0.191929	−	0.981409i	$-0.561474\pi$
$463$	−1.68005e62	−0.383857	−0.191929	+	0.981409i	$0.561474\pi$
$464$	−1.19098e62	−0.258662
$465$	−2.60604e62	−0.538068
$466$	8.43157e61	0.165516
$467$	1.37225e62	0.256145	0.128073	−	0.991765i	$-0.459121\pi$
$467$	1.37225e62	0.256145	0.128073	+	0.991765i	$0.459121\pi$
$468$	7.38394e60	0.0131072
$469$	1.32856e63	2.24295
$470$	−3.84308e62	−0.617134
$471$	5.39400e62	0.823985
$472$	−8.42090e61	−0.122383
$473$	2.59334e62	0.358610
$474$	1.24032e62	0.163209
$475$	−3.97815e62	−0.498175
$476$	−1.56537e63	−1.86575
$477$	1.87931e62	0.213214
$478$	−2.75385e62	−0.297430
$479$	−1.62356e63	−1.66949	−0.834745	−	0.550637i	$-0.814385\pi$
$479$	−1.62356e63	−1.66949	−0.834745	+	0.550637i	$0.814385\pi$
$480$	1.50068e63	1.46933
$481$	−2.28384e61	−0.0212939
$482$	1.52606e62	0.135509
$483$	−1.33539e63	−1.12940
$484$	8.87351e62	0.714874
$485$	5.40066e62	0.414492
$486$	6.98388e62	0.510675
$487$	1.09889e62	0.0765640	0.0382820	−	0.999267i	$-0.487811\pi$
$487$	1.09889e62	0.0765640	0.0382820	+	0.999267i	$0.487811\pi$
$488$	7.63168e62	0.506704
$489$	−1.94481e63	−1.23060
$490$	−9.95438e62	−0.600352
$491$	2.66145e63	1.53004	0.765020	−	0.644007i	$-0.222729\pi$
$491$	2.66145e63	1.53004	0.765020	+	0.644007i	$0.222729\pi$
$492$	2.04701e63	1.12186
$493$	−1.21690e63	−0.635849
$494$	2.04638e61	0.0101954
$495$	8.34544e62	0.396485
$496$	−4.37661e62	−0.198298
$497$	2.93270e63	1.26734
$498$	−1.66646e63	−0.686919
$499$	−2.22266e63	−0.873997	−0.436999	−	0.899462i	$-0.643959\pi$
$499$	−2.22266e63	−0.873997	−0.436999	+	0.899462i	$0.643959\pi$
$500$	−1.74070e63	−0.653025
$501$	−5.83743e63	−2.08947
$502$	1.54369e63	0.527256
$503$	3.07975e63	1.00385	0.501924	−	0.864912i	$-0.332626\pi$
$503$	3.07975e63	1.00385	0.501924	+	0.864912i	$0.332626\pi$
$504$	−2.98671e63	−0.929127
$505$	9.05595e62	0.268897
$506$	−2.94501e62	−0.0834737
$507$	5.02793e63	1.36051
$508$	−1.07238e62	−0.0277046
$509$	−5.72771e63	−1.41291	−0.706453	−	0.707760i	$-0.749706\pi$
$509$	−5.72771e63	−1.41291	−0.706453	+	0.707760i	$0.749706\pi$
$510$	3.65641e63	0.861302
$511$	4.30631e63	0.968754
$512$	4.43953e63	0.953877
$513$	−1.44444e63	−0.296443
$514$	−3.39346e63	−0.665287
$515$	7.46476e62	0.139812
$516$	−5.78292e63	−1.03485
$517$	−3.27137e63	−0.559374
$518$	4.25206e63	0.694784
$519$	6.98009e63	1.09000
$520$	−9.93464e61	−0.0148277
$521$	1.17638e64	1.67826	0.839132	−	0.543928i	$-0.183064\pi$
$521$	1.17638e64	1.67826	0.839132	+	0.543928i	$0.183064\pi$
$522$	−1.06871e63	−0.145749
$523$	−6.38331e63	−0.832254	−0.416127	−	0.909306i	$-0.636613\pi$
$523$	−6.38331e63	−0.832254	−0.416127	+	0.909306i	$0.636613\pi$
$524$	−1.06366e64	−1.32592
$525$	−5.92066e63	−0.705710
$526$	−5.84816e63	−0.666583
$527$	−4.47188e63	−0.487461
$528$	3.04617e63	0.317582
$529$	−7.09283e63	−0.707313
$530$	−1.16383e63	−0.111022
$531$	1.60786e63	0.146733
$532$	2.20800e64	1.92786
$533$	−2.08652e62	−0.0174315
$534$	6.06161e63	0.484583
$535$	1.10635e64	0.846408
$536$	−1.41945e64	−1.03932
$537$	1.27768e64	0.895419
$538$	6.92393e63	0.464483
$539$	−8.47354e63	−0.544163
$540$	3.22772e63	0.198446
$541$	−7.64596e62	−0.0450087	−0.0225043	−	0.999747i	$-0.507164\pi$
$541$	−7.64596e62	−0.0450087	−0.0225043	+	0.999747i	$0.507164\pi$
$542$	9.49045e62	0.0534938
$543$	−3.69231e64	−1.99298
$544$	2.57511e64	1.33113
$545$	6.17521e63	0.305727
$546$	3.04561e62	0.0144427
$547$	−1.77108e64	−0.804519	−0.402259	−	0.915526i	$-0.631775\pi$
$547$	−1.77108e64	−0.804519	−0.402259	+	0.915526i	$0.631775\pi$
$548$	−1.88262e64	−0.819255
$549$	−1.45717e64	−0.607519
$550$	−1.30572e63	−0.0521587
$551$	1.71648e64	0.657015
$552$	1.42674e64	0.523332
$553$	−1.36411e64	−0.479523
$554$	−2.23711e64	−0.753716
$555$	5.75592e64	1.85879
$556$	−2.51988e64	−0.780049
$557$	1.48786e64	0.441535	0.220767	−	0.975327i	$-0.429144\pi$
$557$	1.48786e64	0.441535	0.220767	+	0.975327i	$0.429144\pi$
$558$	−3.92730e63	−0.111735
$559$	5.89456e62	0.0160795
$560$	−3.93568e64	−1.02944
$561$	3.11247e64	0.780689
$562$	1.36108e64	0.327400
$563$	4.11252e64	0.948770	0.474385	−	0.880317i	$-0.342670\pi$
$563$	4.11252e64	0.948770	0.474385	+	0.880317i	$0.342670\pi$
$564$	7.29489e64	1.61421
$565$	1.54134e64	0.327160
$566$	−1.09460e64	−0.222879
$567$	−8.84157e64	−1.72714
$568$	−3.13333e64	−0.587247
$569$	−5.04135e64	−0.906586	−0.453293	−	0.891362i	$-0.649751\pi$
$569$	−5.04135e64	−0.906586	−0.453293	+	0.891362i	$0.649751\pi$
$570$	−5.15746e64	−0.889973
$571$	1.68666e64	0.279305	0.139652	−	0.990201i	$-0.455402\pi$
$571$	1.68666e64	0.279305	0.139652	+	0.990201i	$0.455402\pi$
$572$	−3.89254e62	−0.00618623
$573$	2.96856e64	0.452806
$574$	3.88470e64	0.568759
$575$	1.30129e64	0.182886
$576$	−1.40308e64	−0.189301
$577$	−9.79059e63	−0.126817	−0.0634084	−	0.997988i	$-0.520197\pi$
$577$	−9.79059e63	−0.126817	−0.0634084	+	0.997988i	$0.520197\pi$
$578$	3.18966e64	0.396680
$579$	−1.45000e65	−1.73150
$580$	−3.83560e64	−0.439821
$581$	1.83279e65	2.01824
$582$	1.76892e64	0.187076
$583$	−9.90700e63	−0.100631
$584$	−4.60091e64	−0.448892
$585$	1.89689e63	0.0177778
$586$	3.49117e64	0.314323
$587$	2.78831e64	0.241183	0.120591	−	0.992702i	$-0.461521\pi$
$587$	2.78831e64	0.241183	0.120591	+	0.992702i	$0.461521\pi$
$588$	1.88953e65	1.57031
$589$	6.30770e64	0.503688
$590$	−9.95730e63	−0.0764046
$591$	−2.19662e65	−1.61975
$592$	9.66654e64	0.685032
$593$	1.49430e65	1.01778	0.508889	−	0.860832i	$-0.330056\pi$
$593$	1.49430e65	1.01778	0.508889	+	0.860832i	$0.330056\pi$
$594$	−4.74098e63	−0.0310375
$595$	−4.02134e65	−2.53059
$596$	−1.41546e65	−0.856267
$597$	−2.59809e65	−1.51098
$598$	−6.69390e62	−0.00374284
$599$	2.99285e65	1.60899	0.804496	−	0.593957i	$-0.202435\pi$
$599$	2.99285e65	1.60899	0.804496	+	0.593957i	$0.202435\pi$
$600$	6.32570e64	0.327005
$601$	−1.56472e65	−0.777831	−0.388916	−	0.921273i	$-0.627150\pi$
$601$	−1.56472e65	−0.777831	−0.388916	+	0.921273i	$0.627150\pi$
$602$	−1.09745e65	−0.524648
$603$	2.71025e65	1.24610
$604$	1.26780e65	0.560638
$605$	2.27955e65	0.969611
$606$	2.96616e64	0.121364
$607$	8.61159e64	0.338961	0.169480	−	0.985534i	$-0.445791\pi$
$607$	8.61159e64	0.338961	0.169480	+	0.985534i	$0.445791\pi$
$608$	−3.63226e65	−1.37544
$609$	2.55462e65	0.930721
$610$	9.02409e64	0.316339
$611$	−7.43572e63	−0.0250816
$612$	−3.19334e65	−1.03654
$613$	−1.58806e65	−0.496072	−0.248036	−	0.968751i	$-0.579785\pi$
$613$	−1.58806e65	−0.496072	−0.248036	+	0.968751i	$0.579785\pi$
$614$	7.55808e64	0.227224
$615$	5.25864e65	1.52163
$616$	1.57448e65	0.438521
$617$	−6.01082e65	−1.61151	−0.805753	−	0.592251i	$-0.798239\pi$
$617$	−6.01082e65	−1.61151	−0.805753	+	0.592251i	$0.798239\pi$
$618$	2.44499e64	0.0631026
$619$	3.62211e65	0.899978	0.449989	−	0.893034i	$-0.351428\pi$
$619$	3.62211e65	0.899978	0.449989	+	0.893034i	$0.351428\pi$
$620$	−1.40950e65	−0.337180
$621$	4.72491e64	0.108828
$622$	−9.91723e64	−0.219946
$623$	−6.66660e65	−1.42376
$624$	6.92383e63	0.0142399
$625$	−6.17847e65	−1.22377
$626$	2.06054e65	0.393083
$627$	−4.39022e65	−0.806677
$628$	2.91740e65	0.516350
$629$	9.87695e65	1.68396
$630$	−3.53164e65	−0.580060
$631$	9.92614e65	1.57069	0.785345	−	0.619059i	$-0.212486\pi$
$631$	9.92614e65	1.57069	0.785345	+	0.619059i	$0.212486\pi$
$632$	1.45743e65	0.222197
$633$	−2.52336e65	−0.370675
$634$	−2.74816e65	−0.388995
$635$	−2.75487e64	−0.0375768
$636$	2.20918e65	0.290395
$637$	−1.92601e64	−0.0243995
$638$	5.63386e64	0.0687891
$639$	5.98268e65	0.704086
$640$	1.03860e66	1.17820
$641$	−1.70256e66	−1.86183	−0.930915	−	0.365236i	$-0.880988\pi$
$641$	−1.70256e66	−1.86183	−0.930915	+	0.365236i	$0.880988\pi$
$642$	3.62372e65	0.382016
$643$	8.06741e65	0.819929	0.409964	−	0.912102i	$-0.365541\pi$
$643$	8.06741e65	0.819929	0.409964	+	0.912102i	$0.365541\pi$
$644$	−7.22257e65	−0.707740
$645$	−1.48560e66	−1.40361
$646$	−8.85001e65	−0.806268
$647$	−2.90914e65	−0.255573	−0.127786	−	0.991802i	$-0.540787\pi$
$647$	−2.90914e65	−0.255573	−0.127786	+	0.991802i	$0.540787\pi$
$648$	9.44644e65	0.800305
$649$	−8.47603e64	−0.0692536
$650$	−2.96785e63	−0.00233872
$651$	9.38770e65	0.713520
$652$	−1.05187e66	−0.771157
$653$	3.73213e65	0.263935	0.131967	−	0.991254i	$-0.457871\pi$
$653$	3.73213e65	0.263935	0.131967	+	0.991254i	$0.457871\pi$
$654$	2.02261e65	0.137986
$655$	−2.73248e66	−1.79840
$656$	8.83139e65	0.560775
$657$	8.78482e65	0.538204
$658$	1.38439e66	0.818368
$659$	7.84754e65	0.447637	0.223819	−	0.974631i	$-0.428148\pi$
$659$	7.84754e65	0.447637	0.223819	+	0.974631i	$0.428148\pi$
$660$	9.81030e65	0.540008
$661$	5.69856e65	0.302713	0.151356	−	0.988479i	$-0.451636\pi$
$661$	5.69856e65	0.302713	0.151356	+	0.988479i	$0.451636\pi$
$662$	−9.24239e63	−0.00473829
$663$	7.07454e64	0.0350050
$664$	−1.95817e66	−0.935192
$665$	5.67221e66	2.61483
$666$	8.67416e65	0.385996
$667$	−5.61476e65	−0.241198
$668$	−3.15723e66	−1.30936
$669$	−5.19686e66	−2.08079
$670$	−1.67843e66	−0.648852
$671$	7.68164e65	0.286731
$672$	−5.40587e66	−1.94844
$673$	4.43578e66	1.54389	0.771945	−	0.635689i	$-0.219284\pi$
$673$	4.43578e66	1.54389	0.771945	+	0.635689i	$0.219284\pi$
$674$	−8.26612e65	−0.277840
$675$	2.09487e65	0.0680013
$676$	2.71940e66	0.852563
$677$	3.52339e66	1.06691	0.533454	−	0.845829i	$-0.320894\pi$
$677$	3.52339e66	1.06691	0.533454	+	0.845829i	$0.320894\pi$
$678$	5.04846e65	0.147660
$679$	−1.94547e66	−0.549648
$680$	4.29645e66	1.17260
$681$	−6.80801e66	−1.79499
$682$	2.07033e65	0.0527359
$683$	−3.36076e66	−0.827087	−0.413543	−	0.910484i	$-0.635709\pi$
$683$	−3.36076e66	−0.827087	−0.413543	+	0.910484i	$0.635709\pi$
$684$	4.50430e66	1.07105
$685$	−4.83633e66	−1.11119
$686$	9.35418e65	0.207677
$687$	1.05912e67	2.27228
$688$	−2.49492e66	−0.517284
$689$	−2.25183e64	−0.00451214
$690$	1.68705e66	0.326720
$691$	2.04623e66	0.383020	0.191510	−	0.981491i	$-0.438662\pi$
$691$	2.04623e66	0.383020	0.191510	+	0.981491i	$0.438662\pi$
$692$	3.77525e66	0.683050
$693$	−3.00626e66	−0.525770
$694$	4.62376e65	0.0781714
$695$	−6.47341e66	−1.05801
$696$	−2.72939e66	−0.431268
$697$	9.02362e66	1.37851
$698$	−2.18990e66	−0.323461
$699$	−4.11151e66	−0.587203
$700$	−3.20225e66	−0.442233
$701$	−1.21798e67	−1.62655	−0.813275	−	0.581879i	$-0.802318\pi$
$701$	−1.21798e67	−1.62655	−0.813275	+	0.581879i	$0.802318\pi$
$702$	−1.07761e64	−0.00139168
$703$	−1.39317e67	−1.74002
$704$	7.39650e65	0.0893447
$705$	1.87401e67	2.18942
$706$	5.45153e66	0.616039
$707$	−3.26221e66	−0.356578
$708$	1.89008e66	0.199848
$709$	1.52742e67	1.56233	0.781166	−	0.624323i	$-0.214625\pi$
$709$	1.52742e67	1.56233	0.781166	+	0.624323i	$0.214625\pi$
$710$	−3.70501e66	−0.366622
$711$	−2.78278e66	−0.266405
$712$	7.12268e66	0.659726
$713$	−2.06331e66	−0.184910
$714$	−1.31714e67	−1.14215
$715$	−9.99969e64	−0.00839063
$716$	6.91046e66	0.561114
$717$	1.34287e67	1.05520
$718$	−3.92318e65	−0.0298342
$719$	5.76158e66	0.424045	0.212023	−	0.977265i	$-0.431995\pi$
$719$	5.76158e66	0.424045	0.212023	+	0.977265i	$0.431995\pi$
$720$	−8.02874e66	−0.571918
$721$	−2.68901e66	−0.185402
$722$	6.73515e66	0.449493
$723$	−7.44159e66	−0.480746
$724$	−1.99702e67	−1.24890
$725$	−2.48940e66	−0.150713
$726$	7.46638e66	0.437622
$727$	−7.68143e65	−0.0435896	−0.0217948	−	0.999762i	$-0.506938\pi$
$727$	−7.68143e65	−0.0435896	−0.0217948	+	0.999762i	$0.506938\pi$
$728$	3.57874e65	0.0196627
$729$	−1.28906e67	−0.685768
$730$	−5.44035e66	−0.280246
$731$	−2.54923e67	−1.27160
$732$	−1.71294e67	−0.827432
$733$	3.73856e67	1.74889	0.874443	−	0.485129i	$-0.161227\pi$
$733$	3.73856e67	1.74889	0.874443	+	0.485129i	$0.161227\pi$
$734$	−9.97281e66	−0.451814
$735$	4.85408e67	2.12988
$736$	1.18815e67	0.504942
$737$	−1.42874e67	−0.588124
$738$	7.92476e66	0.315981
$739$	−1.50450e67	−0.581095	−0.290548	−	0.956861i	$-0.593837\pi$
$739$	−1.50450e67	−0.581095	−0.290548	+	0.956861i	$0.593837\pi$
$740$	3.11315e67	1.16481
$741$	−9.97882e65	−0.0361702
$742$	4.19246e66	0.147223
$743$	5.97073e66	0.203138	0.101569	−	0.994829i	$-0.467614\pi$
$743$	5.97073e66	0.203138	0.101569	+	0.994829i	$0.467614\pi$
$744$	−1.00299e67	−0.330624
$745$	−3.63622e67	−1.16139
$746$	6.01659e66	0.186204
$747$	3.73887e67	1.12126
$748$	1.68341e67	0.489218
$749$	−3.98539e67	−1.12240
$750$	−1.46467e67	−0.399761
$751$	−1.14848e67	−0.303797	−0.151898	−	0.988396i	$-0.548539\pi$
$751$	−1.14848e67	−0.303797	−0.151898	+	0.988396i	$0.548539\pi$
$752$	3.14723e67	0.806881
$753$	−7.52752e67	−1.87055
$754$	1.28056e65	0.00308441
$755$	3.25690e67	0.760415
$756$	−1.16271e67	−0.263155
$757$	3.51013e66	0.0770141	0.0385070	−	0.999258i	$-0.487740\pi$
$757$	3.51013e66	0.0770141	0.0385070	+	0.999258i	$0.487740\pi$
$758$	2.77002e67	0.589191
$759$	1.43608e67	0.296141
$760$	−6.06026e67	−1.21163
$761$	2.99687e67	0.580937	0.290468	−	0.956885i	$-0.406189\pi$
$761$	2.99687e67	0.580937	0.290468	+	0.956885i	$0.406189\pi$
$762$	−9.02325e65	−0.0169598
$763$	−2.22448e67	−0.405418
$764$	1.60558e67	0.283751
$765$	−8.20350e67	−1.40590
$766$	1.56032e67	0.259321
$767$	−1.92657e65	−0.00310523
$768$	1.46785e67	0.229453
$769$	1.28547e68	1.94892	0.974461	−	0.224557i	$-0.0720935\pi$
$769$	1.28547e68	1.94892	0.974461	+	0.224557i	$0.0720935\pi$
$770$	1.86175e67	0.273772
$771$	1.65476e68	2.36025
$772$	−7.84247e67	−1.08504
$773$	6.24752e67	0.838474	0.419237	−	0.907877i	$-0.362298\pi$
$773$	6.24752e67	0.838474	0.419237	+	0.907877i	$0.362298\pi$
$774$	−2.23879e67	−0.291475
$775$	−9.14802e66	−0.115541
$776$	2.07856e67	0.254691
$777$	−2.07344e68	−2.46489
$778$	−2.55834e67	−0.295079
$779$	−1.27281e68	−1.42440
$780$	2.22985e66	0.0242132
$781$	−3.15385e67	−0.332308
$782$	2.89492e67	0.295991
$783$	−9.03883e66	−0.0896831
$784$	8.15198e67	0.784939
$785$	7.49461e67	0.700345
$786$	−8.94990e67	−0.811687
$787$	−3.00261e67	−0.264297	−0.132149	−	0.991230i	$-0.542188\pi$
$787$	−3.00261e67	−0.264297	−0.132149	+	0.991230i	$0.542188\pi$
$788$	−1.18806e68	−1.01502
$789$	2.85175e68	2.36484
$790$	1.72335e67	0.138719
$791$	−5.55233e67	−0.433839
$792$	3.21193e67	0.243626
$793$	1.74601e66	0.0128566
$794$	−8.84526e67	−0.632308
$795$	5.67524e67	0.393874
$796$	−1.40520e68	−0.946852
$797$	−2.46726e67	−0.161415	−0.0807077	−	0.996738i	$-0.525718\pi$
$797$	−2.46726e67	−0.161415	−0.0807077	+	0.996738i	$0.525718\pi$
$798$	1.85786e68	1.18017
$799$	3.21574e68	1.98349
$800$	5.26785e67	0.315514
$801$	−1.35998e68	−0.790986
$802$	−1.13151e68	−0.639089
$803$	−4.63103e67	−0.254017
$804$	3.18598e68	1.69717
$805$	−1.85543e68	−0.959936
$806$	4.70578e65	0.00236460
$807$	−3.37634e68	−1.64785
$808$	3.48538e67	0.165228
$809$	−2.87119e68	−1.32212	−0.661061	−	0.750332i	$-0.729894\pi$
$809$	−2.87119e68	−1.32212	−0.661061	+	0.750332i	$0.729894\pi$
$810$	1.11700e68	0.499636
$811$	4.03047e67	0.175132	0.0875661	−	0.996159i	$-0.472091\pi$
$811$	4.03047e67	0.175132	0.0875661	+	0.996159i	$0.472091\pi$
$812$	1.38169e68	0.583236
$813$	−4.62786e67	−0.189781
$814$	−4.57269e67	−0.182179
$815$	−2.70218e68	−1.04595
$816$	−2.99436e68	−1.12612
$817$	3.59575e68	1.31393
$818$	8.06431e67	0.286329
$819$	−6.83312e66	−0.0235748
$820$	2.84419e68	0.953526
$821$	2.55050e68	0.830923	0.415462	−	0.909611i	$-0.363620\pi$
$821$	2.55050e68	0.830923	0.415462	+	0.909611i	$0.363620\pi$
$822$	−1.58408e68	−0.501521
$823$	2.96708e68	0.912922	0.456461	−	0.889743i	$-0.349117\pi$
$823$	2.96708e68	0.912922	0.456461	+	0.889743i	$0.349117\pi$
$824$	2.87298e67	0.0859097
$825$	6.36712e67	0.185044
$826$	3.58690e67	0.101318
$827$	−5.78282e68	−1.58767	−0.793835	−	0.608133i	$-0.791919\pi$
$827$	−5.78282e68	−1.58767	−0.793835	+	0.608133i	$0.791919\pi$
$828$	−1.47340e68	−0.393194
$829$	−1.50860e68	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$829$	−1.50860e68	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$830$	−2.31544e68	−0.583846
$831$	1.09089e69	2.67397
$832$	1.68120e66	0.00400609
$833$	8.32942e68	1.92956
$834$	−2.12028e68	−0.477520
$835$	−8.11074e68	−1.77594
$836$	−2.37450e68	−0.505503
$837$	−3.32159e67	−0.0687539
$838$	2.87733e68	0.579102
$839$	5.78467e67	0.113207	0.0566034	−	0.998397i	$-0.481973\pi$
$839$	5.78467e67	0.113207	0.0566034	+	0.998397i	$0.481973\pi$
$840$	−9.01944e68	−1.71639
$841$	−4.32977e68	−0.801233
$842$	3.95253e68	0.711281
$843$	−6.63705e68	−1.16152
$844$	−1.36479e68	−0.232283
$845$	6.98598e68	1.15636
$846$	2.82413e68	0.454655
$847$	−8.21157e68	−1.28578
$848$	9.53104e67	0.145157
$849$	5.33764e68	0.790712
$850$	1.28351e68	0.184950
$851$	4.55719e68	0.638782
$852$	7.03281e68	0.958956
$853$	−6.70885e68	−0.889910	−0.444955	−	0.895553i	$-0.646780\pi$
$853$	−6.70885e68	−0.889910	−0.444955	+	0.895553i	$0.646780\pi$
$854$	−3.25073e68	−0.419489
$855$	1.15713e69	1.45270
$856$	4.25804e68	0.520087
$857$	1.18679e69	1.41034	0.705168	−	0.709040i	$-0.250871\pi$
$857$	1.18679e69	1.41034	0.705168	+	0.709040i	$0.250871\pi$
$858$	−3.27527e66	−0.00378701
$859$	−1.90685e67	−0.0214525	−0.0107262	−	0.999942i	$-0.503414\pi$
$859$	−1.90685e67	−0.0214525	−0.0107262	+	0.999942i	$0.503414\pi$
$860$	−8.03500e68	−0.879574
$861$	−1.89431e69	−2.01779
$862$	2.85677e68	0.296111
$863$	−8.52667e68	−0.860054	−0.430027	−	0.902816i	$-0.641496\pi$
$863$	−8.52667e68	−0.860054	−0.430027	+	0.902816i	$0.641496\pi$
$864$	1.91272e68	0.187749
$865$	9.69839e68	0.926448
$866$	−2.80472e68	−0.260747
$867$	−1.55538e69	−1.40731
$868$	5.07743e68	0.447127
$869$	1.46698e68	0.125736
$870$	−3.22736e68	−0.269244
$871$	−3.24749e67	−0.0263706
$872$	2.37667e68	0.187858
$873$	−3.96874e68	−0.305364
$874$	−4.08337e68	−0.305844
$875$	1.61085e69	1.17454
$876$	1.03268e69	0.733027
$877$	7.64441e67	0.0528267	0.0264134	−	0.999651i	$-0.491591\pi$
$877$	7.64441e67	0.0528267	0.0264134	+	0.999651i	$0.491591\pi$
$878$	−7.57608e68	−0.509711
$879$	−1.70241e69	−1.11513
$880$	4.23245e68	0.269929
$881$	−9.82470e68	−0.610078	−0.305039	−	0.952340i	$-0.598670\pi$
$881$	−9.82470e68	−0.610078	−0.305039	+	0.952340i	$0.598670\pi$
$882$	7.31509e68	0.442291
$883$	−1.96558e68	−0.115722	−0.0578609	−	0.998325i	$-0.518428\pi$
$883$	−1.96558e68	−0.115722	−0.0578609	+	0.998325i	$0.518428\pi$
$884$	3.82633e67	0.0219359
$885$	4.85551e68	0.271062
$886$	5.88459e68	0.319907
$887$	3.52341e69	1.86534	0.932670	−	0.360731i	$-0.117473\pi$
$887$	3.52341e69	1.86534	0.932670	+	0.360731i	$0.117473\pi$
$888$	2.21529e69	1.14216
$889$	9.92383e67	0.0498297
$890$	8.42222e68	0.411871
$891$	9.50829e68	0.452873
$892$	−2.81077e69	−1.30392
$893$	−4.53588e69	−2.04952
$894$	−1.19100e69	−0.524179
$895$	1.77525e69	0.761061
$896$	−3.74134e69	−1.56239
$897$	3.26417e67	0.0132785
$898$	−6.71657e68	−0.266167
$899$	3.94715e68	0.152381
$900$	−6.53256e68	−0.245688
$901$	9.73850e68	0.356829
$902$	−4.17763e68	−0.149134
$903$	5.35154e69	1.86130
$904$	5.93218e68	0.201028
$905$	−5.13022e69	−1.69393
$906$	1.06676e69	0.343204
$907$	1.85786e69	0.582428	0.291214	−	0.956658i	$-0.405941\pi$
$907$	1.85786e69	0.582428	0.291214	+	0.956658i	$0.405941\pi$
$908$	−3.68218e69	−1.12483
$909$	−6.65487e68	−0.198102
$910$	4.23168e67	0.0122755
$911$	1.88130e69	0.531835	0.265918	−	0.963996i	$-0.414325\pi$
$911$	1.88130e69	0.531835	0.265918	+	0.963996i	$0.414325\pi$
$912$	4.22362e69	1.16361
$913$	−1.97099e69	−0.529202
$914$	−8.67862e68	−0.227099
$915$	−4.40044e69	−1.12228
$916$	5.72835e69	1.42392
$917$	9.84316e69	2.38482
$918$	4.66035e68	0.110056
$919$	−3.45864e69	−0.796143	−0.398071	−	0.917354i	$-0.630320\pi$
$919$	−3.45864e69	−0.796143	−0.398071	+	0.917354i	$0.630320\pi$
$920$	1.98237e69	0.444806
$921$	−3.68557e69	−0.806126
$922$	1.00023e68	0.0213266
$923$	−7.16858e67	−0.0149002
$924$	−3.53395e69	−0.716092
$925$	2.02051e69	0.399144
$926$	−7.64579e68	−0.147253
$927$	−5.48557e68	−0.103002
$928$	−2.27295e69	−0.416113
$929$	−3.44629e69	−0.615153	−0.307576	−	0.951523i	$-0.599518\pi$
$929$	−3.44629e69	−0.615153	−0.307576	+	0.951523i	$0.599518\pi$
$930$	−1.18599e69	−0.206411
$931$	−1.17489e70	−1.99379
$932$	−2.22375e69	−0.367970
$933$	4.83597e69	0.780306
$934$	6.24500e68	0.0982609
$935$	4.32458e69	0.663546
$936$	7.30059e67	0.0109238
$937$	2.88144e69	0.420464	0.210232	−	0.977652i	$-0.432578\pi$
$937$	2.88144e69	0.420464	0.210232	+	0.977652i	$0.432578\pi$
$938$	6.04618e69	0.860428
$939$	−1.00479e70	−1.39455
$940$	1.01358e70	1.37200
$941$	3.65396e69	0.482400	0.241200	−	0.970475i	$-0.422459\pi$
$941$	3.65396e69	0.482400	0.241200	+	0.970475i	$0.422459\pi$
$942$	2.45477e69	0.316092
$943$	4.16347e69	0.522914
$944$	8.15438e68	0.0998962
$945$	−2.98694e69	−0.356927
$946$	1.18021e69	0.137568
$947$	−2.53356e69	−0.288075	−0.144038	−	0.989572i	$-0.546009\pi$
$947$	−2.53356e69	−0.288075	−0.144038	+	0.989572i	$0.546009\pi$
$948$	−3.27124e69	−0.362841
$949$	−1.05262e68	−0.0113898
$950$	−1.81043e69	−0.191107
$951$	1.34009e70	1.38004
$952$	−1.54770e70	−1.55496
$953$	−4.10317e69	−0.402195	−0.201097	−	0.979571i	$-0.564451\pi$
$953$	−4.10317e69	−0.402195	−0.201097	+	0.979571i	$0.564451\pi$
$954$	8.55258e68	0.0817919
$955$	4.12463e69	0.384862
$956$	7.26304e69	0.661238
$957$	−2.74725e69	−0.244044
$958$	−7.38870e69	−0.640440
$959$	1.74218e70	1.47352
$960$	−4.23710e69	−0.349699
$961$	−1.09660e70	−0.883180
$962$	−1.03936e68	−0.00816866
$963$	−8.13016e69	−0.623565
$964$	−4.02486e69	−0.301259
$965$	−2.01468e70	−1.47168
$966$	−6.07724e69	−0.433256
$967$	−2.82974e69	−0.196890	−0.0984451	−	0.995142i	$-0.531387\pi$
$967$	−2.82974e69	−0.196890	−0.0984451	+	0.995142i	$0.531387\pi$
$968$	8.77334e69	0.595791
$969$	4.31556e70	2.86041
$970$	2.45780e69	0.159005
$971$	−2.13025e70	−1.34517	−0.672587	−	0.740018i	$-0.734817\pi$
$971$	−2.13025e70	−1.34517	−0.672587	+	0.740018i	$0.734817\pi$
$972$	−1.84194e70	−1.13532
$973$	2.33190e70	1.40300
$974$	5.00098e68	0.0293711
$975$	1.44722e68	0.00829711
$976$	−7.39014e69	−0.413601
$977$	2.95878e70	1.61655	0.808277	−	0.588802i	$-0.200400\pi$
$977$	2.95878e70	1.61655	0.808277	+	0.588802i	$0.200400\pi$
$978$	−8.85066e69	−0.472077
$979$	7.16931e69	0.373322
$980$	2.62538e70	1.33469
$981$	−4.53793e69	−0.225235
$982$	1.21120e70	0.586945
$983$	−5.99760e69	−0.283772	−0.141886	−	0.989883i	$-0.545317\pi$
$983$	−5.99760e69	−0.283772	−0.141886	+	0.989883i	$0.545317\pi$
$984$	2.02390e70	0.934985
$985$	−3.05206e70	−1.37671
$986$	−5.53804e69	−0.243921
$987$	−6.75072e70	−2.90333
$988$	−5.39715e68	−0.0226661
$989$	−1.17621e70	−0.482359
$990$	3.79795e69	0.152097
$991$	3.56295e70	1.39341	0.696706	−	0.717357i	$-0.254648\pi$
$991$	3.56295e70	1.39341	0.696706	+	0.717357i	$0.254648\pi$
$992$	−8.35261e69	−0.319005
$993$	4.50689e68	0.0168101
$994$	1.33465e70	0.486169
$995$	−3.60988e70	−1.28425
$996$	4.39514e70	1.52714
$997$	−8.80387e69	−0.298770	−0.149385	−	0.988779i	$-0.547729\pi$
$997$	−8.80387e69	−0.298770	−0.149385	+	0.988779i	$0.547729\pi$
$998$	−1.01152e70	−0.335278
$999$	7.33632e69	0.237514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.48.a.a.1.3	✓	4
3.2	odd	2		9.48.a.c.1.2		4
4.3	odd	2		16.48.a.d.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.48.a.a.1.3	✓	4	1.1	even	1	trivial
9.48.a.c.1.2		4	3.2	odd	2
16.48.a.d.1.4		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)

\(f(q)\)	\(=\)	\(q+4.55092e6 q^{2} -2.21918e11 q^{3} -1.20027e14 q^{4} -3.08341e16 q^{5} -1.00993e18 q^{6} +1.11073e20 q^{7} -1.18672e21 q^{8} +2.26588e22 q^{9} +O(q^{10})\)	\(q+4.55092e6 q^{2} -2.21918e11 q^{3} -1.20027e14 q^{4} -3.08341e16 q^{5} -1.00993e18 q^{6} +1.11073e20 q^{7} -1.18672e21 q^{8} +2.26588e22 q^{9} -1.40324e23 q^{10} -1.19449e24 q^{11} +2.66361e25 q^{12} -2.71503e24 q^{13} +5.05485e26 q^{14} +6.84264e27 q^{15} +1.14916e28 q^{16} +1.17417e29 q^{17} +1.03118e29 q^{18} -1.65620e30 q^{19} +3.70091e30 q^{20} -2.46491e31 q^{21} -5.43602e30 q^{22} +5.41759e31 q^{23} +2.63354e32 q^{24} +2.40198e32 q^{25} -1.23559e31 q^{26} +8.72142e32 q^{27} -1.33317e34 q^{28} -1.03639e34 q^{29} +3.11403e34 q^{30} -3.80854e34 q^{31} +2.19313e35 q^{32} +2.65078e35 q^{33} +5.34356e35 q^{34} -3.42483e36 q^{35} -2.71966e36 q^{36} +8.41184e36 q^{37} -7.53724e36 q^{38} +6.02513e35 q^{39} +3.65913e37 q^{40} +7.68510e37 q^{41} -1.12176e38 q^{42} -2.17109e38 q^{43} +1.43370e38 q^{44} -6.98663e38 q^{45} +2.46550e38 q^{46} +2.73873e39 q^{47} -2.55019e39 q^{48} +7.09387e39 q^{49} +1.09312e39 q^{50} -2.60570e40 q^{51} +3.25875e38 q^{52} +8.29394e39 q^{53} +3.96905e39 q^{54} +3.68309e40 q^{55} -1.31812e41 q^{56} +3.67541e41 q^{57} -4.71655e40 q^{58} +7.09596e40 q^{59} -8.21298e41 q^{60} -6.43092e41 q^{61} -1.73324e41 q^{62} +2.51678e42 q^{63} -6.19220e41 q^{64} +8.37153e40 q^{65} +1.20635e42 q^{66} +1.19612e43 q^{67} -1.40932e43 q^{68} -1.20226e43 q^{69} -1.55862e43 q^{70} +2.64034e43 q^{71} -2.68896e43 q^{72} +3.87700e43 q^{73} +3.82817e43 q^{74} -5.33042e43 q^{75} +1.98788e44 q^{76} -1.32675e44 q^{77} +2.74199e42 q^{78} -1.22812e44 q^{79} -3.54332e44 q^{80} -7.96015e44 q^{81} +3.49743e44 q^{82} +1.65007e45 q^{83} +2.95855e45 q^{84} -3.62045e45 q^{85} -9.88045e44 q^{86} +2.29995e45 q^{87} +1.41752e45 q^{88} -6.00200e45 q^{89} -3.17956e45 q^{90} -3.01566e44 q^{91} -6.50255e45 q^{92} +8.45183e45 q^{93} +1.24637e46 q^{94} +5.10674e46 q^{95} -4.86695e46 q^{96} -1.75152e46 q^{97} +3.22837e46 q^{98} -2.70656e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5785560 q^{2} + 38461494960 q^{3} + 404807499161152 q^{4} - 31\!\cdots\!00 q^{5}+ \cdots - 17\!\cdots\!72 q^{9}+O(q^{10}) \) 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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