LMFDB - Embedded newform 1.50.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,50,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, 50, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 50);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 50 $
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:	$15.2066205099$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 27962089502x + 71708842875120 $ x^3 - x^2 - 27962089502*x + 71708842875120
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2565.11$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37650e7 q^{2} -2.01823e10 q^{3} +1.82457e12 q^{4} +2.93049e15 q^{5} -4.79631e17 q^{6} -2.24836e20 q^{7} -1.33351e22 q^{8} -2.38892e23 q^{9} +O(q^{10})$	\(q+2.37650e7 q^{2} -2.01823e10 q^{3} +1.82457e12 q^{4} +2.93049e15 q^{5} -4.79631e17 q^{6} -2.24836e20 q^{7} -1.33351e22 q^{8} -2.38892e23 q^{9} +6.96431e22 q^{10} +2.83247e25 q^{11} -3.68238e22 q^{12} -1.95503e27 q^{13} -5.34323e27 q^{14} -5.91440e25 q^{15} -3.17936e29 q^{16} -2.51820e30 q^{17} -5.67726e30 q^{18} +1.78906e30 q^{19} +5.34688e27 q^{20} +4.53770e30 q^{21} +6.73137e32 q^{22} +3.03017e33 q^{23} +2.69133e32 q^{24} -1.77550e34 q^{25} -4.64612e34 q^{26} +9.65098e33 q^{27} -4.10228e32 q^{28} +2.16603e35 q^{29} -1.40556e33 q^{30} +4.19094e36 q^{31} -4.87408e34 q^{32} -5.71657e35 q^{33} -5.98451e37 q^{34} -6.58881e35 q^{35} -4.35874e35 q^{36} +3.37729e38 q^{37} +4.25171e37 q^{38} +3.94568e37 q^{39} -3.90785e37 q^{40} -7.11635e38 q^{41} +1.07838e38 q^{42} -1.14021e40 q^{43} +5.16803e37 q^{44} -7.00072e38 q^{45} +7.20120e40 q^{46} +5.26318e40 q^{47} +6.41668e39 q^{48} -2.06372e41 q^{49} -4.21947e41 q^{50} +5.08230e40 q^{51} -3.56707e39 q^{52} +1.13392e42 q^{53} +2.29355e41 q^{54} +8.30054e40 q^{55} +2.99822e42 q^{56} -3.61074e40 q^{57} +5.14756e42 q^{58} -2.86886e43 q^{59} -1.07912e38 q^{60} -7.30250e43 q^{61} +9.95976e43 q^{62} +5.37115e43 q^{63} +1.77824e44 q^{64} -5.72919e42 q^{65} -1.35854e43 q^{66} -7.70219e44 q^{67} -4.59463e42 q^{68} -6.11558e43 q^{69} -1.56583e43 q^{70} +2.28512e44 q^{71} +3.18566e45 q^{72} -5.39611e45 q^{73} +8.02614e45 q^{74} +3.58336e44 q^{75} +3.26427e42 q^{76} -6.36842e45 q^{77} +9.37691e44 q^{78} -5.09606e46 q^{79} -9.31711e44 q^{80} +5.69719e46 q^{81} -1.69120e46 q^{82} +1.71355e47 q^{83} +8.27933e42 q^{84} -7.37958e45 q^{85} -2.70972e47 q^{86} -4.37153e45 q^{87} -3.77714e47 q^{88} +2.40065e47 q^{89} -1.66372e46 q^{90} +4.39560e47 q^{91} +5.52875e45 q^{92} -8.45826e46 q^{93} +1.25079e48 q^{94} +5.24284e45 q^{95} +9.83699e44 q^{96} +2.78383e48 q^{97} -4.90444e48 q^{98} -6.76655e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 24225168 q^{2} - 326954692404 q^{3} + 31502767984896 q^{4} + 63\!\cdots\!50 q^{5}+ \cdots + 34\!\cdots\!19 q^{9}+O(q^{10}) $ 3 * q - 24225168 * q^2 - 326954692404 * q^3 + 31502767984896 * q^4 + 63884035717079250 * q^5 + 8906136249246768576 * q^6 + 509391477498711192 * q^7 + 12774393005516465664000 * q^8 + 341625690512280455369319 * q^9	$ 3 q - 24225168 q^{2} - 326954692404 q^{3} + 31502767984896 q^{4} + 63\!\cdots\!50 q^{5}+ \cdots - 11\!\cdots\!52 q^{99}+O(q^{100}) $ 3 * q - 24225168 * q^2 - 326954692404 * q^3 + 31502767984896 * q^4 + 63884035717079250 * q^5 + 8906136249246768576 * q^6 + 509391477498711192 * q^7 + 12774393005516465664000 * q^8 + 341625690512280455369319 * q^9 - 1782704508900495946524000 * q^10 - 20839986192711815613370524 * q^11 - 101756595014280089890126848 * q^12 - 187524857197340618282341014 * q^13 - 9454369415029168241295938688 * q^14 - 204230679539215002884128467000 * q^15 - 958699697068386571735634214912 * q^16 - 3305035636247475259184114894538 * q^17 - 20227965712272756371678796043344 * q^18 - 45882942802931464757155696518660 * q^19 + 19614616637279540996591887296000 * q^20 + 617794442803555252870956383262816 * q^21 + 1789915191438262082177360193562944 * q^22 + 4533392548023086653463590407813576 * q^23 - 2513947703938508593953436558049280 * q^24 - 13921151905580403838435182832171875 * q^25 - 85826222237480824536590109710199264 * q^26 - 316454625615073819697154158592097800 * q^27 - 59263339345763305527729286468663296 * q^28 + 1118089919316361970349176934175494810 * q^29 + 5019197819712535273166303836165776000 * q^30 + 934226816157578575389156342339525216 * q^31 + 731728685735702515419064521056059392 * q^32 - 24487068877327908023713382739550873968 * q^33 - 44386547077569962679458968510685418528 * q^34 - 118496887985378726635932152589238374000 * q^35 + 37986811000754375090144064848875953408 * q^36 + 242135148519373130928922851818564983602 * q^37 + 1156029602765443663092741329710471492800 * q^38 + 1291017145684876237790670030697385259048 * q^39 + 521466322563622592824981612412298240000 * q^40 - 6211739675976490815696297371880432723714 * q^41 - 14577965575239226149151901656398676210176 * q^42 - 7795173962887472637660666233812713782844 * q^43 + 2342252938597505040255206661879982328832 * q^44 + 76758284157261249391010855229819118430250 * q^45 + 26787138361451470082912377308943265940096 * q^46 + 72757717838871152990888073123214445891472 * q^47 + 156517630976899733143320027855300206002176 * q^48 - 280157966384090888246597869444400847657429 * q^49 - 537697283161263679965664107392030595750000 * q^50 - 1538734957331600122304206020917586572488104 * q^51 - 123529799747407597799198092229890019578368 * q^52 - 155850890670432045962015052011776669693854 * q^53 + 8252737541190722285688590807826219494394240 * q^54 + 4640026560861316230546160030865773419591000 * q^55 + 6722101775263505338291028050795018900439040 * q^56 - 7909742361043655643598112535376781525014800 * q^57 - 16549417550295130349814323361508282251506400 * q^58 - 62596927936822013761436024025606581543386380 * q^59 - 8860237536153508564855019737671281942784000 * q^60 - 24037263967789435219196348055077866809754374 * q^61 + 188825800588885099392385526941761279238024704 * q^62 - 79613772299337773967480392108297858821089864 * q^63 + 514652981263254699809134733483815976080244736 * q^64 - 244975900670806240216695171564505814930314500 * q^65 + 520146826433507127417478540282210913545819392 * q^66 - 1019040852324305100821779153549119164107459188 * q^67 + 147929481309005416179289053660840704965292544 * q^68 - 4867866269191569039747093560336346164459611872 * q^69 + 2807457123724968989995337407321309803024672000 * q^70 - 3208129335291950593367863544185773469328334504 * q^71 + 10389376832262916146131931928642229401854259200 * q^72 + 5668108076325412165814435883536677392865317726 * q^73 + 10012493148932275797653251806650724700277983392 * q^74 - 12104818074938487392123628092507024931595687500 * q^75 + 753841821393723585433963960120373529551508480 * q^76 - 32043339793247959180079389483660528277811891936 * q^77 - 27771485354519690073790188371684714833523265408 * q^78 - 7871365395380306420112251724245018715125364240 * q^79 - 30434832804539714147732706266001913558351872000 * q^80 + 67270927730095597004530465543730351634592280043 * q^81 + 118639125705754411670909153459409940471487282784 * q^82 + 94164681901361229355849854653903786480577085116 * q^83 + 7700494417700399139591084235352419616317120512 * q^84 + 297863286656785614551226799130947646752077538500 * q^85 - 347916436657924446515600473690440815675104929984 * q^86 - 175500245979701689466461020645367234129141215000 * q^87 - 1057522149818049090984983413770258669302102016000 * q^88 + 367807201561165354579457777200332871192114777230 * q^89 - 2007318616781959003323900738484966136471887212000 * q^90 + 1613372397893666548508325640004129525440352221776 * q^91 + 467187868629171186038576611613065932844001728512 * q^92 + 5954871901405488350696717407304686000200433533312 * q^93 + 904097685092930858948295844890436017323554129152 * q^94 + 1475636199748052355599968141572624301097796705000 * q^95 - 2698554985048479483842995984936051823306493394944 * q^96 - 10431108583780665799950508389192126734793760399578 * q^97 - 2841886978251444216347516645227034756825518204176 * q^98 - 11387023179914295087805432025124514927226421923052 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.37650e7	1.00162	0.500810	−	0.865557i	$-0.333036\pi$
$2$	2.37650e7	1.00162	0.500810	+	0.865557i	$0.333036\pi$
$3$	−2.01823e10	−0.0412571	−0.0206286	−	0.999787i	$-0.506567\pi$
$3$	−2.01823e10	−0.0412571	−0.0206286	+	0.999787i	$0.506567\pi$
$4$	1.82457e12	0.00324108
$5$	2.93049e15	0.0219875	0.0109937	−	0.999940i	$-0.496501\pi$
$5$	2.93049e15	0.0219875	0.0109937	+	0.999940i	$0.496501\pi$
$6$	−4.79631e17	−0.0413239
$7$	−2.24836e20	−0.443572	−0.221786	−	0.975095i	$-0.571189\pi$
$7$	−2.24836e20	−0.443572	−0.221786	+	0.975095i	$0.571189\pi$
$8$	−1.33351e22	−0.998373
$9$	−2.38892e23	−0.998298
$10$	6.96431e22	0.0220231
$11$	2.83247e25	0.867051	0.433526	−	0.901141i	$-0.357269\pi$
$11$	2.83247e25	0.867051	0.433526	+	0.901141i	$0.357269\pi$
$12$	−3.68238e22	−0.000133718 0
$13$	−1.95503e27	−0.998942	−0.499471	−	0.866331i	$-0.666472\pi$
$13$	−1.95503e27	−0.998942	−0.499471	+	0.866331i	$0.666472\pi$
$14$	−5.34323e27	−0.444290
$15$	−5.91440e25	−0.000907141 0
$16$	−3.17936e29	−1.00323
$17$	−2.51820e30	−1.79925	−0.899627	−	0.436660i	$-0.856161\pi$
$17$	−2.51820e30	−1.79925	−0.899627	+	0.436660i	$0.856161\pi$
$18$	−5.67726e30	−0.999914
$19$	1.78906e30	0.0837843	0.0418922	−	0.999122i	$-0.486661\pi$
$19$	1.78906e30	0.0837843	0.0418922	+	0.999122i	$0.486661\pi$
$20$	5.34688e27	7.12632e−5 0
$21$	4.53770e30	0.0183005
$22$	6.73137e32	0.868455
$23$	3.03017e33	1.31564	0.657818	−	0.753177i	$-0.271480\pi$
$23$	3.03017e33	1.31564	0.657818	+	0.753177i	$0.271480\pi$
$24$	2.69133e32	0.0411900
$25$	−1.77550e34	−0.999517
$26$	−4.64612e34	−1.00056
$27$	9.65098e33	0.0824440
$28$	−4.10228e32	−0.00143765
$29$	2.16603e35	0.321302	0.160651	−	0.987011i	$-0.448641\pi$
$29$	2.16603e35	0.321302	0.160651	+	0.987011i	$0.448641\pi$
$30$	−1.40556e33	−0.000908610 0
$31$	4.19094e36	1.21325	0.606624	−	0.794989i	$-0.292523\pi$
$31$	4.19094e36	1.21325	0.606624	+	0.794989i	$0.292523\pi$
$32$	−4.87408e34	−0.00648213
$33$	−5.71657e35	−0.0357721
$34$	−5.98451e37	−1.80217
$35$	−6.58881e35	−0.00975303
$36$	−4.35874e35	−0.00323556
$37$	3.37729e38	1.28123	0.640614	−	0.767863i	$-0.278680\pi$
$37$	3.37729e38	1.28123	0.640614	+	0.767863i	$0.278680\pi$
$38$	4.25171e37	0.0839200
$39$	3.94568e37	0.0412135
$40$	−3.90785e37	−0.0219517
$41$	−7.11635e38	−0.218300	−0.109150	−	0.994025i	$-0.534813\pi$
$41$	−7.11635e38	−0.218300	−0.109150	+	0.994025i	$0.534813\pi$
$42$	1.07838e38	0.0183301
$43$	−1.14021e40	−1.08895	−0.544477	−	0.838776i	$-0.683272\pi$
$43$	−1.14021e40	−1.08895	−0.544477	+	0.838776i	$0.683272\pi$
$44$	5.16803e37	0.00281018
$45$	−7.00072e38	−0.0219501
$46$	7.20120e40	1.31777
$47$	5.26318e40	0.568658	0.284329	−	0.958727i	$-0.408229\pi$
$47$	5.26318e40	0.568658	0.284329	+	0.958727i	$0.408229\pi$
$48$	6.41668e39	0.0413904
$49$	−2.06372e41	−0.803244
$50$	−4.21947e41	−1.00113
$51$	5.08230e40	0.0742320
$52$	−3.56707e39	−0.00323765
$53$	1.13392e42	0.645390	0.322695	−	0.946503i	$-0.395411\pi$
$53$	1.13392e42	0.645390	0.322695	+	0.946503i	$0.395411\pi$
$54$	2.29355e41	0.0825775
$55$	8.30054e40	0.0190643
$56$	2.99822e42	0.442850
$57$	−3.61074e40	−0.00345670
$58$	5.14756e42	0.321822
$59$	−2.86886e43	−1.17987	−0.589935	−	0.807450i	$-0.700847\pi$
$59$	−2.86886e43	−1.17987	−0.589935	+	0.807450i	$0.700847\pi$
$60$	−1.07912e38	−2.94011e−6 0
$61$	−7.30250e43	−1.32706	−0.663530	−	0.748150i	$-0.730942\pi$
$61$	−7.30250e43	−1.32706	−0.663530	+	0.748150i	$0.730942\pi$
$62$	9.95976e43	1.21521
$63$	5.37115e43	0.442817
$64$	1.77824e44	0.996738
$65$	−5.72919e42	−0.0219642
$66$	−1.35854e43	−0.0358300
$67$	−7.70219e44	−1.40534	−0.702670	−	0.711516i	$-0.748009\pi$
$67$	−7.70219e44	−1.40534	−0.702670	+	0.711516i	$0.748009\pi$
$68$	−4.59463e42	−0.00583152
$69$	−6.11558e43	−0.0542793
$70$	−1.56583e43	−0.00976883
$71$	2.28512e44	0.100711	0.0503557	−	0.998731i	$-0.483964\pi$
$71$	2.28512e44	0.100711	0.0503557	+	0.998731i	$0.483964\pi$
$72$	3.18566e45	0.996674
$73$	−5.39611e45	−1.20412	−0.602061	−	0.798450i	$-0.705654\pi$
$73$	−5.39611e45	−1.20412	−0.602061	+	0.798450i	$0.705654\pi$
$74$	8.02614e45	1.28330
$75$	3.58336e44	0.0412372
$76$	3.26427e42	0.000271552 0
$77$	−6.36842e45	−0.384600
$78$	9.37691e44	0.0412802
$79$	−5.09606e46	−1.64199	−0.820996	−	0.570934i	$-0.806581\pi$
$79$	−5.09606e46	−1.64199	−0.820996	+	0.570934i	$0.806581\pi$
$80$	−9.31711e44	−0.0220585
$81$	5.69719e46	0.994896
$82$	−1.69120e46	−0.218653
$83$	1.71355e47	1.64621	0.823104	−	0.567891i	$-0.192240\pi$
$83$	1.71355e47	1.64621	0.823104	+	0.567891i	$0.192240\pi$
$84$	8.27933e42	5.93134e−5 0
$85$	−7.37958e45	−0.0395611
$86$	−2.70972e47	−1.09072
$87$	−4.37153e45	−0.0132560
$88$	−3.77714e47	−0.865641
$89$	2.40065e47	0.417133	0.208566	−	0.978008i	$-0.433120\pi$
$89$	2.40065e47	0.417133	0.208566	+	0.978008i	$0.433120\pi$
$90$	−1.66372e46	−0.0219856
$91$	4.39560e47	0.443103
$92$	5.52875e45	0.00426408
$93$	−8.45826e46	−0.0500551
$94$	1.25079e48	0.569578
$95$	5.24284e45	0.00184221
$96$	9.83699e44	0.000267434 0
$97$	2.78383e48	0.587131	0.293565	−	0.955939i	$-0.405158\pi$
$97$	2.78383e48	0.587131	0.293565	+	0.955939i	$0.405158\pi$
$98$	−4.90444e48	−0.804545
$99$	−6.76655e48	−0.865576
$100$	−3.23951e46	−0.00323951
$101$	−7.22373e48	−0.566093	−0.283047	−	0.959106i	$-0.591345\pi$
$101$	−7.22373e48	−0.566093	−0.283047	+	0.959106i	$0.591345\pi$
$102$	1.20781e48	0.0743522
$103$	2.04104e49	0.989325	0.494663	−	0.869085i	$-0.335292\pi$
$103$	2.04104e49	0.989325	0.494663	+	0.869085i	$0.335292\pi$
$104$	2.60705e49	0.997317
$105$	1.32977e46	0.000402382 0
$106$	2.69475e49	0.646435
$107$	−6.11487e49	−1.16543	−0.582713	−	0.812678i	$-0.698009\pi$
$107$	−6.11487e49	−1.16543	−0.582713	+	0.812678i	$0.698009\pi$
$108$	1.76088e46	0.000267208 0
$109$	−9.43074e49	−1.14182	−0.570908	−	0.821014i	$-0.693409\pi$
$109$	−9.43074e49	−1.14182	−0.570908	+	0.821014i	$0.693409\pi$
$110$	1.97262e48	0.0190952
$111$	−6.81614e48	−0.0528598
$112$	7.14836e49	0.445005
$113$	8.34560e49	0.417865	0.208932	−	0.977930i	$-0.433001\pi$
$113$	8.34560e49	0.417865	0.208932	+	0.977930i	$0.433001\pi$
$114$	−8.58091e47	−0.00346230
$115$	8.87991e48	0.0289275
$116$	3.95206e47	0.00104136
$117$	4.67040e50	0.997242
$118$	−6.81783e50	−1.18178
$119$	5.66183e50	0.798098
$120$	7.88693e47	0.000905665 0
$121$	−2.64900e50	−0.248222
$122$	−1.73544e51	−1.32921
$123$	1.43624e49	0.00900641
$124$	7.64664e48	0.00393223
$125$	−1.04087e50	−0.0439644
$126$	1.27645e51	0.443534
$127$	2.64505e51	0.757255	0.378627	−	0.925549i	$-0.376396\pi$
$127$	2.64505e51	0.757255	0.378627	+	0.925549i	$0.376396\pi$
$128$	4.25342e51	1.00483
$129$	2.30121e50	0.0449271
$130$	−1.36154e50	−0.0219998
$131$	−1.01829e52	−1.36372	−0.681858	−	0.731485i	$-0.738828\pi$
$131$	−1.01829e52	−1.36372	−0.681858	+	0.731485i	$0.738828\pi$
$132$	−1.04303e48	−0.000115940 0
$133$	−4.02246e50	−0.0371644
$134$	−1.83042e52	−1.40762
$135$	2.82821e49	0.00181274
$136$	3.35806e52	1.79633
$137$	−8.12665e51	−0.363294	−0.181647	−	0.983364i	$-0.558143\pi$
$137$	−8.12665e51	−0.363294	−0.181647	+	0.983364i	$0.558143\pi$
$138$	−1.45337e51	−0.0543672
$139$	1.99564e52	0.625490	0.312745	−	0.949837i	$-0.398752\pi$
$139$	1.99564e52	0.625490	0.312745	+	0.949837i	$0.398752\pi$
$140$	−1.20217e48	−3.16104e−5 0
$141$	−1.06223e51	−0.0234612
$142$	5.43058e51	0.100875
$143$	−5.53756e52	−0.866134
$144$	7.59525e52	1.00152
$145$	6.34753e50	0.00706462
$146$	−1.28238e53	−1.20607
$147$	4.16506e51	0.0331395
$148$	6.16209e50	0.00415256
$149$	−1.15349e53	−0.659101	−0.329550	−	0.944138i	$-0.606897\pi$
$149$	−1.15349e53	−0.659101	−0.329550	+	0.944138i	$0.606897\pi$
$150$	8.51584e51	0.0413040
$151$	1.93962e53	0.799434	0.399717	−	0.916639i	$-0.369108\pi$
$151$	1.93962e53	0.799434	0.399717	+	0.916639i	$0.369108\pi$
$152$	−2.38574e52	−0.0836480
$153$	6.01579e53	1.79619
$154$	−1.51345e53	−0.385222
$155$	1.22815e52	0.0266763
$156$	7.19916e49	0.000133576 0
$157$	−2.01540e53	−0.319758	−0.159879	−	0.987137i	$-0.551110\pi$
$157$	−2.01540e53	−0.319758	−0.159879	+	0.987137i	$0.551110\pi$
$158$	−1.21108e54	−1.64465
$159$	−2.28850e52	−0.0266270
$160$	−1.42835e50	−0.000142526 0
$161$	−6.81292e53	−0.583579
$162$	1.35394e54	0.996507
$163$	9.43838e53	0.597449	0.298725	−	0.954339i	$-0.403439\pi$
$163$	9.43838e53	0.597449	0.298725	+	0.954339i	$0.403439\pi$
$164$	−1.29842e51	−0.000707526 0
$165$	−1.67524e51	−0.000786538 0
$166$	4.07226e54	1.64887
$167$	−4.23487e54	−1.48008	−0.740042	−	0.672560i	$-0.765195\pi$
$167$	−4.23487e54	−1.48008	−0.740042	+	0.672560i	$0.765195\pi$
$168$	−6.05108e52	−0.0182707
$169$	−8.09806e51	−0.00211425
$170$	−1.75376e53	−0.0396251
$171$	−4.27393e53	−0.0836417
$172$	−2.08040e52	−0.00352938
$173$	−4.20690e54	−0.619202	−0.309601	−	0.950867i	$-0.600195\pi$
$173$	−4.20690e54	−0.619202	−0.309601	+	0.950867i	$0.600195\pi$
$174$	−1.03889e53	−0.0132775
$175$	3.99196e54	0.443357
$176$	−9.00546e54	−0.869853
$177$	5.79000e53	0.0486781
$178$	5.70515e54	0.417808
$179$	8.54114e54	0.545276	0.272638	−	0.962117i	$-0.412104\pi$
$179$	8.54114e54	0.545276	0.272638	+	0.962117i	$0.412104\pi$
$180$	−1.27733e51	−7.11419e−5 0
$181$	1.98261e55	0.964077	0.482039	−	0.876150i	$-0.339896\pi$
$181$	1.98261e55	0.964077	0.482039	+	0.876150i	$0.339896\pi$
$182$	1.04461e55	0.443820
$183$	1.47381e54	0.0547507
$184$	−4.04078e55	−1.31349
$185$	9.89714e53	0.0281710
$186$	−2.01010e54	−0.0501362
$187$	−7.13274e55	−1.56005
$188$	9.60302e52	0.00184306
$189$	−2.16989e54	−0.0365699
$190$	1.24596e53	0.00184519
$191$	1.39151e56	1.81204	0.906020	−	0.423236i	$-0.139106\pi$
$191$	1.39151e56	1.81204	0.906020	+	0.423236i	$0.139106\pi$
$192$	−3.58889e54	−0.0411225
$193$	−4.74055e53	−0.00478272	−0.00239136	−	0.999997i	$-0.500761\pi$
$193$	−4.74055e53	−0.00478272	−0.00239136	+	0.999997i	$0.500761\pi$
$194$	6.61576e55	0.588081
$195$	1.15628e53	0.000906181 0
$196$	−3.76540e53	−0.00260338
$197$	−3.08771e55	−0.188458	−0.0942289	−	0.995551i	$-0.530039\pi$
$197$	−3.08771e55	−0.188458	−0.0942289	+	0.995551i	$0.530039\pi$
$198$	−1.60807e56	−0.866977
$199$	−1.79305e56	−0.854461	−0.427231	−	0.904143i	$-0.640511\pi$
$199$	−1.79305e56	−0.854461	−0.427231	+	0.904143i	$0.640511\pi$
$200$	2.36765e56	0.997890
$201$	1.55447e55	0.0579803
$202$	−1.71672e56	−0.567010
$203$	−4.87001e55	−0.142520
$204$	9.27300e52	0.000240592 0
$205$	−2.08544e54	−0.00479986
$206$	4.85052e56	0.990927
$207$	−7.23884e56	−1.31340
$208$	6.21574e56	1.00217
$209$	5.06748e55	0.0726453
$210$	3.16020e53	0.000403034 0
$211$	9.93900e56	1.12829	0.564147	−	0.825674i	$-0.309205\pi$
$211$	9.93900e56	1.12829	0.564147	+	0.825674i	$0.309205\pi$
$212$	2.06891e54	0.00209176
$213$	−4.61188e54	−0.00415506
$214$	−1.45320e57	−1.16731
$215$	−3.34139e55	−0.0239434
$216$	−1.28697e56	−0.0823099
$217$	−9.42274e56	−0.538163
$218$	−2.24121e57	−1.14367
$219$	1.08906e56	0.0496786
$220$	1.51449e53	6.17889e−5 0
$221$	4.92316e57	1.79735
$222$	−1.61986e56	−0.0529454
$223$	1.44008e57	0.421615	0.210808	−	0.977528i	$-0.432391\pi$
$223$	1.44008e57	0.421615	0.210808	+	0.977528i	$0.432391\pi$
$224$	1.09587e55	0.00287529
$225$	4.24152e57	0.997815
$226$	1.98333e57	0.418541
$227$	−8.04692e57	−1.52404	−0.762020	−	0.647554i	$-0.775792\pi$
$227$	−8.04692e57	−1.52404	−0.762020	+	0.647554i	$0.775792\pi$
$228$	−6.58802e52	−1.12034e−5 0
$229$	−5.64510e57	−0.862388	−0.431194	−	0.902259i	$-0.641907\pi$
$229$	−5.64510e57	−0.862388	−0.431194	+	0.902259i	$0.641907\pi$
$230$	2.11031e56	0.0289744
$231$	1.28529e56	0.0158675
$232$	−2.88843e57	−0.320779
$233$	−5.26334e57	−0.526068	−0.263034	−	0.964787i	$-0.584723\pi$
$233$	−5.26334e57	−0.526068	−0.263034	+	0.964787i	$0.584723\pi$
$234$	1.10992e58	0.998857
$235$	1.54237e56	0.0125034
$236$	−5.23441e55	−0.00382405
$237$	1.02850e57	0.0677439
$238$	1.34553e58	0.799391
$239$	−2.01549e58	−1.08052	−0.540260	−	0.841498i	$-0.681674\pi$
$239$	−2.01549e58	−1.08052	−0.540260	+	0.841498i	$0.681674\pi$
$240$	1.88040e55	0.000910071 0
$241$	3.29787e58	1.44150	0.720751	−	0.693194i	$-0.243797\pi$
$241$	3.29787e58	1.44150	0.720751	+	0.693194i	$0.243797\pi$
$242$	−6.29534e57	−0.248624
$243$	−3.45929e57	−0.123491
$244$	−1.33239e56	−0.00430110
$245$	−6.04773e56	−0.0176613
$246$	3.41322e56	0.00902099
$247$	−3.49767e57	−0.0836957
$248$	−5.58867e58	−1.21127
$249$	−3.45834e57	−0.0679178
$250$	−2.47362e57	−0.0440355
$251$	−5.47917e58	−0.884522	−0.442261	−	0.896886i	$-0.645823\pi$
$251$	−5.47917e58	−0.884522	−0.442261	+	0.896886i	$0.645823\pi$
$252$	9.80002e55	0.00143520
$253$	8.58288e58	1.14072
$254$	6.28595e58	0.758481
$255$	1.48937e56	0.00163218
$256$	9.76530e56	0.00972313
$257$	1.54667e59	1.39970	0.699851	−	0.714289i	$-0.253250\pi$
$257$	1.54667e59	1.39970	0.699851	+	0.714289i	$0.253250\pi$
$258$	5.46882e57	0.0449998
$259$	−7.59338e58	−0.568317
$260$	−1.04533e55	−7.11878e−5 0
$261$	−5.17447e58	−0.320755
$262$	−2.41996e59	−1.36592
$263$	−7.50627e58	−0.385930	−0.192965	−	0.981206i	$-0.561810\pi$
$263$	−7.50627e58	−0.385930	−0.192965	+	0.981206i	$0.561810\pi$
$264$	7.62312e57	0.0357138
$265$	3.32294e57	0.0141905
$266$	−9.55938e57	−0.0372246
$267$	−4.84506e57	−0.0172097
$268$	−1.40531e57	−0.00455482
$269$	5.23133e59	1.54768	0.773840	−	0.633381i	$-0.218333\pi$
$269$	5.23133e59	1.54768	0.773840	+	0.633381i	$0.218333\pi$
$270$	6.72125e56	0.00181567
$271$	−5.44767e59	−1.34420	−0.672099	−	0.740461i	$-0.734607\pi$
$271$	−5.44767e59	−1.34420	−0.672099	+	0.740461i	$0.734607\pi$
$272$	8.00629e59	1.80507
$273$	−8.87132e57	−0.0182811
$274$	−1.93130e59	−0.363882
$275$	−5.02905e59	−0.866632
$276$	−1.11583e56	−0.000175924 0
$277$	6.08465e59	0.877973	0.438986	−	0.898494i	$-0.355338\pi$
$277$	6.08465e59	0.877973	0.438986	+	0.898494i	$0.355338\pi$
$278$	4.74264e59	0.626502
$279$	−1.00118e60	−1.21118
$280$	8.78626e57	0.00973716
$281$	−3.48884e59	−0.354304	−0.177152	−	0.984183i	$-0.556688\pi$
$281$	−3.48884e59	−0.354304	−0.177152	+	0.984183i	$0.556688\pi$
$282$	−2.52439e58	−0.0234992
$283$	−3.15433e59	−0.269240	−0.134620	−	0.990897i	$-0.542981\pi$
$283$	−3.15433e59	−0.269240	−0.134620	+	0.990897i	$0.542981\pi$
$284$	4.16934e56	0.000326414 0
$285$	−1.05812e56	−7.60042e−5 0
$286$	−1.31600e60	−0.867537
$287$	1.60001e59	0.0968315
$288$	1.16438e58	0.00647110
$289$	4.38252e60	2.23731
$290$	1.50849e58	0.00707606
$291$	−5.61839e58	−0.0242233
$292$	−9.84555e57	−0.00390266
$293$	1.34951e60	0.491949	0.245975	−	0.969276i	$-0.420892\pi$
$293$	1.34951e60	0.491949	0.245975	+	0.969276i	$0.420892\pi$
$294$	9.89826e58	0.0331932
$295$	−8.40716e58	−0.0259424
$296$	−4.50367e60	−1.27914
$297$	2.73361e59	0.0714832
$298$	−2.74128e60	−0.660168
$299$	−5.92407e60	−1.31424
$300$	6.53807e56	0.000133653 0
$301$	2.56361e60	0.483029
$302$	4.60952e60	0.800728
$303$	1.45791e59	0.0233554
$304$	−5.68809e59	−0.0840550
$305$	−2.13999e59	−0.0291787
$306$	1.42965e61	1.79910
$307$	−2.03285e60	−0.236164	−0.118082	−	0.993004i	$-0.537675\pi$
$307$	−2.03285e60	−0.236164	−0.118082	+	0.993004i	$0.537675\pi$
$308$	−1.16196e58	−0.00124652
$309$	−4.11928e59	−0.0408167
$310$	2.91870e59	0.0267195
$311$	−9.56098e60	−0.808859	−0.404430	−	0.914569i	$-0.632530\pi$
$311$	−9.56098e60	−0.808859	−0.404430	+	0.914569i	$0.632530\pi$
$312$	−5.26162e59	−0.0411464
$313$	2.13710e60	0.154521	0.0772607	−	0.997011i	$-0.475383\pi$
$313$	2.13710e60	0.154521	0.0772607	+	0.997011i	$0.475383\pi$
$314$	−4.78961e60	−0.320275
$315$	1.57401e59	0.00973643
$316$	−9.29810e58	−0.00532183
$317$	−9.54676e60	−0.505713	−0.252856	−	0.967504i	$-0.581370\pi$
$317$	−9.54676e60	−0.505713	−0.252856	+	0.967504i	$0.581370\pi$
$318$	−5.43862e59	−0.0266701
$319$	6.13521e60	0.278585
$320$	5.21112e59	0.0219158
$321$	1.23412e60	0.0480821
$322$	−1.61909e61	−0.584524
$323$	−4.50523e60	−0.150749
$324$	1.03949e59	0.00322454
$325$	3.47114e61	0.998459
$326$	2.24303e61	0.598417
$327$	1.90334e60	0.0471081
$328$	9.48975e60	0.217944
$329$	−1.18335e61	−0.252241
$330$	−3.98120e58	−0.000787811 0
$331$	6.84695e61	1.25809	0.629044	−	0.777369i	$-0.283446\pi$
$331$	6.84695e61	1.25809	0.629044	+	0.777369i	$0.283446\pi$
$332$	3.12649e59	0.00533549
$333$	−8.06809e61	−1.27905
$334$	−1.00642e62	−1.48248
$335$	−2.25712e60	−0.0308999
$336$	−1.44270e60	−0.0183596
$337$	−3.91949e61	−0.463764	−0.231882	−	0.972744i	$-0.574488\pi$
$337$	−3.91949e61	−0.463764	−0.231882	+	0.972744i	$0.574488\pi$
$338$	−1.92450e59	−0.00211767
$339$	−1.68433e60	−0.0172399
$340$	−1.34645e58	−0.000128221 0
$341$	1.18707e62	1.05195
$342$	−1.01570e61	−0.0837772
$343$	1.04166e62	0.799868
$344$	1.52049e62	1.08718
$345$	−1.79217e59	−0.00119347
$346$	−9.99768e61	−0.620205
$347$	1.22123e62	0.705869	0.352934	−	0.935648i	$-0.385184\pi$
$347$	1.22123e62	0.705869	0.352934	+	0.935648i	$0.385184\pi$
$348$	−7.97615e57	−4.29637e−5 0
$349$	−3.75761e62	−1.88664	−0.943320	−	0.331885i	$-0.892315\pi$
$349$	−3.75761e62	−1.88664	−0.943320	+	0.331885i	$0.892315\pi$
$350$	9.48689e61	0.444075
$351$	−1.88679e61	−0.0823568
$352$	−1.38057e60	−0.00562034
$353$	−2.12055e62	−0.805320	−0.402660	−	0.915350i	$-0.631914\pi$
$353$	−2.12055e62	−0.805320	−0.402660	+	0.915350i	$0.631914\pi$
$354$	1.37599e61	0.0487569
$355$	6.69652e59	0.00221439
$356$	4.38015e59	0.00135196
$357$	−1.14269e61	−0.0329272
$358$	2.02980e62	0.546159
$359$	1.19170e62	0.299471	0.149735	−	0.988726i	$-0.452158\pi$
$359$	1.19170e62	0.299471	0.149735	+	0.988726i	$0.452158\pi$
$360$	9.33555e60	0.0219144
$361$	−4.52759e62	−0.992980
$362$	4.71167e62	0.965638
$363$	5.34627e60	0.0102409
$364$	8.02007e59	0.00143613
$365$	−1.58133e61	−0.0264756
$366$	3.50250e61	0.0548393
$367$	1.19895e63	1.75583	0.877915	−	0.478816i	$-0.158934\pi$
$367$	1.19895e63	1.75583	0.877915	+	0.478816i	$0.158934\pi$
$368$	−9.63403e62	−1.31989
$369$	1.70004e62	0.217928
$370$	2.35205e61	0.0282166
$371$	−2.54945e62	−0.286277
$372$	−1.54326e59	−0.000162233 0
$373$	3.34334e62	0.329089	0.164545	−	0.986370i	$-0.447385\pi$
$373$	3.34334e62	0.329089	0.164545	+	0.986370i	$0.447385\pi$
$374$	−1.69510e63	−1.56257
$375$	2.10071e60	0.00181384
$376$	−7.01853e62	−0.567732
$377$	−4.23464e62	−0.320962
$378$	−5.15674e61	−0.0366291
$379$	9.52778e62	0.634353	0.317177	−	0.948366i	$-0.397265\pi$
$379$	9.52778e62	0.634353	0.317177	+	0.948366i	$0.397265\pi$
$380$	9.56591e57	5.97074e−6 0
$381$	−5.33830e61	−0.0312422
$382$	3.30691e63	1.81497
$383$	4.94161e62	0.254389	0.127195	−	0.991878i	$-0.459403\pi$
$383$	4.94161e62	0.254389	0.127195	+	0.991878i	$0.459403\pi$
$384$	−8.58437e61	−0.0414566
$385$	−1.86626e61	−0.00845638
$386$	−1.12659e61	−0.00479046
$387$	2.72388e63	1.08710
$388$	5.07927e60	0.00190294
$389$	−3.72484e63	−1.31021	−0.655107	−	0.755536i	$-0.727376\pi$
$389$	−3.72484e63	−1.31021	−0.655107	+	0.755536i	$0.727376\pi$
$390$	2.74790e60	0.000907649 0
$391$	−7.63060e63	−2.36716
$392$	2.75200e63	0.801937
$393$	2.05513e62	0.0562630
$394$	−7.33794e62	−0.188763
$395$	−1.49340e62	−0.0361033
$396$	−1.23460e61	−0.00280540
$397$	3.43967e63	0.734768	0.367384	−	0.930069i	$-0.380254\pi$
$397$	3.43967e63	0.734768	0.367384	+	0.930069i	$0.380254\pi$
$398$	−4.26118e63	−0.855845
$399$	8.11824e60	0.00153330
$400$	5.64496e63	1.00275
$401$	7.98650e63	1.33450	0.667251	−	0.744833i	$-0.267471\pi$
$401$	7.98650e63	1.33450	0.667251	+	0.744833i	$0.267471\pi$
$402$	3.69421e62	0.0580742
$403$	−8.19339e63	−1.21197
$404$	−1.31802e61	−0.00183475
$405$	1.66956e62	0.0218753
$406$	−1.15736e63	−0.142751
$407$	9.56609e63	1.11089
$408$	−6.77732e62	−0.0741113
$409$	−6.63092e63	−0.682893	−0.341447	−	0.939901i	$-0.610917\pi$
$409$	−6.63092e63	−0.682893	−0.341447	+	0.939901i	$0.610917\pi$
$410$	−4.95605e61	−0.00480763
$411$	1.64014e62	0.0149885
$412$	3.72401e61	0.00320648
$413$	6.45022e63	0.523357
$414$	−1.72031e64	−1.31552
$415$	5.02156e62	0.0361960
$416$	9.52895e61	0.00647528
$417$	−4.02766e62	−0.0258059
$418$	1.20428e63	0.0727630
$419$	−2.98385e64	−1.70033	−0.850165	−	0.526516i	$-0.823498\pi$
$419$	−2.98385e64	−1.70033	−0.850165	+	0.526516i	$0.823498\pi$
$420$	2.42625e58	1.30415e−6 0
$421$	2.66986e64	1.35387	0.676935	−	0.736043i	$-0.263308\pi$
$421$	2.66986e64	1.35387	0.676935	+	0.736043i	$0.263308\pi$
$422$	2.36200e64	1.13012
$423$	−1.25733e64	−0.567690
$424$	−1.51209e64	−0.644340
$425$	4.47107e64	1.79838
$426$	−1.09601e62	−0.00416179
$427$	1.64186e64	0.588646
$428$	−1.11570e62	−0.00377724
$429$	1.11760e63	0.0357342
$430$	−7.94081e62	−0.0239821
$431$	−2.10154e64	−0.599577	−0.299789	−	0.954006i	$-0.596916\pi$
$431$	−2.10154e64	−0.599577	−0.299789	+	0.954006i	$0.596916\pi$
$432$	−3.06840e63	−0.0827104
$433$	−5.87412e64	−1.49620	−0.748099	−	0.663587i	$-0.769033\pi$
$433$	−5.87412e64	−1.49620	−0.748099	+	0.663587i	$0.769033\pi$
$434$	−2.23931e64	−0.539034
$435$	−1.28107e61	−0.000291466 0
$436$	−1.72070e62	−0.00370072
$437$	5.42118e63	0.110230
$438$	2.58814e63	0.0497591
$439$	−4.26898e64	−0.776145	−0.388073	−	0.921629i	$-0.626859\pi$
$439$	−4.26898e64	−0.776145	−0.388073	+	0.921629i	$0.626859\pi$
$440$	−1.10689e63	−0.0190333
$441$	4.93007e64	0.801877
$442$	1.16999e65	1.80026
$443$	−6.85741e63	−0.0998317	−0.0499159	−	0.998753i	$-0.515895\pi$
$443$	−6.85741e63	−0.0998317	−0.0499159	+	0.998753i	$0.515895\pi$
$444$	−1.24365e61	−0.000171323 0
$445$	7.03510e62	0.00917170
$446$	3.42234e64	0.422298
$447$	2.32801e63	0.0271926
$448$	−3.99812e64	−0.442125
$449$	−8.88464e64	−0.930260	−0.465130	−	0.885242i	$-0.653992\pi$
$449$	−8.88464e64	−0.930260	−0.465130	+	0.885242i	$0.653992\pi$
$450$	1.00800e65	0.999431
$451$	−2.01569e64	−0.189277
$452$	1.52271e62	0.00135433
$453$	−3.91460e63	−0.0329823
$454$	−1.91235e65	−1.52651
$455$	1.28813e63	0.00974272
$456$	4.81497e62	0.00345108
$457$	2.63172e65	1.78769	0.893845	−	0.448376i	$-0.147997\pi$
$457$	2.63172e65	1.78769	0.893845	+	0.448376i	$0.147997\pi$
$458$	−1.34156e65	−0.863784
$459$	−2.43031e64	−0.148338
$460$	1.62020e61	9.37564e−5 0
$461$	−2.32881e65	−1.27779	−0.638897	−	0.769292i	$-0.720609\pi$
$461$	−2.32881e65	−1.27779	−0.638897	+	0.769292i	$0.720609\pi$
$462$	3.05449e63	0.0158932
$463$	2.55192e65	1.25931	0.629655	−	0.776875i	$-0.283196\pi$
$463$	2.55192e65	1.25931	0.629655	+	0.776875i	$0.283196\pi$
$464$	−6.88659e64	−0.322340
$465$	−2.47869e62	−0.00110059
$466$	−1.25083e65	−0.526919
$467$	2.96984e65	1.18705	0.593526	−	0.804815i	$-0.297735\pi$
$467$	2.96984e65	1.18705	0.593526	+	0.804815i	$0.297735\pi$
$468$	8.52145e62	0.00323214
$469$	1.73173e65	0.623369
$470$	3.66545e63	0.0125236
$471$	4.06754e63	0.0131923
$472$	3.82566e65	1.17795
$473$	−3.22963e65	−0.944179
$474$	2.44423e64	0.0678536
$475$	−3.17648e64	−0.0837438
$476$	1.03304e63	0.00258670
$477$	−2.70884e65	−0.644292
$478$	−4.78982e65	−1.08227
$479$	−2.69606e65	−0.578775	−0.289387	−	0.957212i	$-0.593452\pi$
$479$	−2.69606e65	−0.578775	−0.289387	+	0.957212i	$0.593452\pi$
$480$	2.88272e60	5.88021e−6 0
$481$	−6.60270e65	−1.27987
$482$	7.83737e65	1.44384
$483$	1.37500e64	0.0240768
$484$	−4.83327e62	−0.000804506 0
$485$	8.15799e63	0.0129095
$486$	−8.22101e64	−0.123691
$487$	6.61008e65	0.945686	0.472843	−	0.881147i	$-0.343228\pi$
$487$	6.61008e65	0.945686	0.472843	+	0.881147i	$0.343228\pi$
$488$	9.73798e65	1.32490
$489$	−1.90488e64	−0.0246490
$490$	−1.43724e64	−0.0176899
$491$	5.46658e65	0.640057	0.320029	−	0.947408i	$-0.396307\pi$
$491$	5.46658e65	0.640057	0.320029	+	0.947408i	$0.396307\pi$
$492$	2.62051e61	2.91905e−5 0
$493$	−5.45450e65	−0.578103
$494$	−8.31220e64	−0.0838312
$495$	−1.98293e64	−0.0190318
$496$	−1.33245e66	−1.21717
$497$	−5.13777e64	−0.0446728
$498$	−8.21874e64	−0.0680278
$499$	−1.68475e65	−0.132761	−0.0663806	−	0.997794i	$-0.521145\pi$
$499$	−1.68475e65	−0.132761	−0.0663806	+	0.997794i	$0.521145\pi$
$500$	−1.89913e62	−0.000142492 0
$501$	8.54692e64	0.0610641
$502$	−1.30212e66	−0.885954
$503$	1.02596e66	0.664839	0.332419	−	0.943132i	$-0.392135\pi$
$503$	1.02596e66	0.664839	0.332419	+	0.943132i	$0.392135\pi$
$504$	−7.16251e65	−0.442096
$505$	−2.11691e64	−0.0124470
$506$	2.03972e66	1.14257
$507$	1.63437e62	8.72279e−5 0
$508$	4.82606e63	0.00245432
$509$	−5.35584e65	−0.259562	−0.129781	−	0.991543i	$-0.541427\pi$
$509$	−5.35584e65	−0.259562	−0.129781	+	0.991543i	$0.541427\pi$
$510$	3.53948e63	0.00163482
$511$	1.21324e66	0.534115
$512$	−2.37126e66	−0.995095
$513$	1.72662e64	0.00690752
$514$	3.67565e66	1.40197
$515$	5.98125e64	0.0217528
$516$	4.19871e62	0.000145612 0
$517$	1.49078e66	0.493055
$518$	−1.80456e66	−0.569237
$519$	8.49047e64	0.0255465
$520$	7.63996e64	0.0219285
$521$	2.71103e64	0.00742354	0.00371177	−	0.999993i	$-0.498819\pi$
$521$	2.71103e64	0.00742354	0.00371177	+	0.999993i	$0.498819\pi$
$522$	−1.22971e66	−0.321274
$523$	−1.09355e66	−0.272614	−0.136307	−	0.990667i	$-0.543523\pi$
$523$	−1.09355e66	−0.272614	−0.136307	+	0.990667i	$0.543523\pi$
$524$	−1.85793e64	−0.00441991
$525$	−8.05668e64	−0.0182917
$526$	−1.78386e66	−0.386555
$527$	−1.05536e67	−2.18294
$528$	1.81751e65	0.0358876
$529$	3.87722e66	0.730897
$530$	7.89695e64	0.0142135
$531$	6.85347e66	1.17786
$532$	−7.33925e62	−0.000120453 0
$533$	1.39126e66	0.218069
$534$	−1.15143e65	−0.0172376
$535$	−1.79196e65	−0.0256248
$536$	1.02710e67	1.40305
$537$	−1.72379e65	−0.0224965
$538$	1.24323e67	1.55019
$539$	−5.84544e66	−0.696454
$540$	5.16026e61	5.87523e−6 0
$541$	−4.75971e66	−0.517902	−0.258951	−	0.965890i	$-0.583377\pi$
$541$	−4.75971e66	−0.517902	−0.258951	+	0.965890i	$0.583377\pi$
$542$	−1.29464e67	−1.34637
$543$	−4.00135e65	−0.0397751
$544$	1.22739e65	0.0116630
$545$	−2.76367e65	−0.0251057
$546$	−2.10827e65	−0.0183107
$547$	−2.22629e67	−1.84881	−0.924404	−	0.381415i	$-0.875437\pi$
$547$	−2.22629e67	−1.84881	−0.924404	+	0.381415i	$0.875437\pi$
$548$	−1.48276e64	−0.00117746
$549$	1.74451e67	1.32480
$550$	−1.19515e67	−0.868036
$551$	3.87516e65	0.0269201
$552$	8.15520e65	0.0541910
$553$	1.14578e67	0.728342
$554$	1.44602e67	0.879395
$555$	−1.99747e64	−0.00116225
$556$	3.64118e64	0.00202726
$557$	8.48625e66	0.452130	0.226065	−	0.974112i	$-0.427414\pi$
$557$	8.48625e66	0.452130	0.226065	+	0.974112i	$0.427414\pi$
$558$	−2.37931e67	−1.21314
$559$	2.22915e67	1.08780
$560$	2.09482e65	0.00978454
$561$	1.43955e66	0.0643630
$562$	−8.29123e66	−0.354878
$563$	8.21369e66	0.336576	0.168288	−	0.985738i	$-0.446176\pi$
$563$	8.21369e66	0.336576	0.168288	+	0.985738i	$0.446176\pi$
$564$	−1.93811e63	−7.60395e−5 0
$565$	2.44567e65	0.00918780
$566$	−7.49625e66	−0.269676
$567$	−1.28093e67	−0.441308
$568$	−3.04723e66	−0.100548
$569$	1.61987e67	0.511954	0.255977	−	0.966683i	$-0.417603\pi$
$569$	1.61987e67	0.511954	0.255977	+	0.966683i	$0.417603\pi$
$570$	−2.51463e63	−7.61273e−5 0
$571$	−9.59751e66	−0.278339	−0.139169	−	0.990269i	$-0.544443\pi$
$571$	−9.59751e66	−0.278339	−0.139169	+	0.990269i	$0.544443\pi$
$572$	−1.01036e65	−0.00280721
$573$	−2.80837e66	−0.0747595
$574$	3.80243e66	0.0969883
$575$	−5.38007e67	−1.31500
$576$	−4.24807e67	−0.995041
$577$	−1.47797e67	−0.331786	−0.165893	−	0.986144i	$-0.553051\pi$
$577$	−1.47797e67	−0.331786	−0.165893	+	0.986144i	$0.553051\pi$
$578$	1.04151e68	2.24094
$579$	9.56750e63	0.000197321 0
$580$	1.15815e63	2.28970e−5 0
$581$	−3.85269e67	−0.730211
$582$	−1.33521e66	−0.0242625
$583$	3.21179e67	0.559587
$584$	7.19579e67	1.20216
$585$	1.36866e66	0.0219269
$586$	3.20711e67	0.492746
$587$	3.28500e67	0.484063	0.242031	−	0.970268i	$-0.422186\pi$
$587$	3.28500e67	0.484063	0.242031	+	0.970268i	$0.422186\pi$
$588$	7.59942e63	0.000107408 0
$589$	7.49786e66	0.101651
$590$	−1.99796e66	−0.0259844
$591$	6.23169e65	0.00777522
$592$	−1.07377e68	−1.28537
$593$	−1.09237e68	−1.25467	−0.627335	−	0.778750i	$-0.715854\pi$
$593$	−1.09237e68	−1.25467	−0.627335	+	0.778750i	$0.715854\pi$
$594$	6.49643e66	0.0715990
$595$	1.65920e66	0.0175482
$596$	−2.10463e65	−0.00213620
$597$	3.61878e66	0.0352526
$598$	−1.40785e68	−1.31637
$599$	−7.08549e66	−0.0635935	−0.0317967	−	0.999494i	$-0.510123\pi$
$599$	−7.08549e66	−0.0635935	−0.0317967	+	0.999494i	$0.510123\pi$
$600$	−4.77845e66	−0.0411701
$601$	3.03561e67	0.251086	0.125543	−	0.992088i	$-0.459933\pi$
$601$	3.03561e67	0.251086	0.125543	+	0.992088i	$0.459933\pi$
$602$	6.09242e67	0.483811
$603$	1.83999e68	1.40295
$604$	3.53897e65	0.00259103
$605$	−7.76287e65	−0.00545777
$606$	3.46473e66	0.0233932
$607$	1.74970e68	1.13459	0.567297	−	0.823513i	$-0.307989\pi$
$607$	1.74970e68	1.13459	0.567297	+	0.823513i	$0.307989\pi$
$608$	−8.72004e64	−0.000543101 0
$609$	9.82878e65	0.00587998
$610$	−5.08569e66	−0.0292260
$611$	−1.02897e68	−0.568056
$612$	1.09762e66	0.00582160
$613$	−1.66573e67	−0.0848835	−0.0424418	−	0.999099i	$-0.513514\pi$
$613$	−1.66573e67	−0.0848835	−0.0424418	+	0.999099i	$0.513514\pi$
$614$	−4.83106e67	−0.236547
$615$	4.20889e64	0.000198028 0
$616$	8.49237e67	0.383974
$617$	−3.08243e68	−1.33939	−0.669694	−	0.742637i	$-0.733575\pi$
$617$	−3.08243e68	−1.33939	−0.669694	+	0.742637i	$0.733575\pi$
$618$	−9.78945e66	−0.0408828
$619$	1.30673e68	0.524524	0.262262	−	0.964997i	$-0.415532\pi$
$619$	1.30673e68	0.524524	0.262262	+	0.964997i	$0.415532\pi$
$620$	2.24084e64	8.64600e−5 0
$621$	2.92441e67	0.108466
$622$	−2.27217e68	−0.810169
$623$	−5.39753e67	−0.185028
$624$	−1.25448e67	−0.0413466
$625$	3.15087e68	0.998550
$626$	5.07881e67	0.154772
$627$	−1.02273e66	−0.00299714
$628$	−3.67724e65	−0.00103636
$629$	−8.50472e68	−2.30526
$630$	3.74064e66	0.00975220
$631$	5.14386e68	1.28994	0.644970	−	0.764208i	$-0.276870\pi$
$631$	5.14386e68	1.28994	0.644970	+	0.764208i	$0.276870\pi$
$632$	6.79567e68	1.63932
$633$	−2.00591e67	−0.0465502
$634$	−2.26878e68	−0.506532
$635$	7.75129e66	0.0166501
$636$	−4.17552e64	−8.63000e−5 0
$637$	4.03463e68	0.802394
$638$	1.45803e68	0.279036
$639$	−5.45896e67	−0.100540
$640$	1.24646e67	0.0220938
$641$	2.16647e68	0.369599	0.184800	−	0.982776i	$-0.440836\pi$
$641$	2.16647e68	0.369599	0.184800	+	0.982776i	$0.440836\pi$
$642$	2.93288e67	0.0481600
$643$	−7.92344e68	−1.25240	−0.626202	−	0.779661i	$-0.715392\pi$
$643$	−7.92344e68	−1.25240	−0.626202	+	0.779661i	$0.715392\pi$
$644$	−1.24306e66	−0.00189143
$645$	6.74368e65	0.000987834 0
$646$	−1.07067e68	−0.150993
$647$	−6.48775e68	−0.880926	−0.440463	−	0.897771i	$-0.645186\pi$
$647$	−6.48775e68	−0.880926	−0.440463	+	0.897771i	$0.645186\pi$
$648$	−7.59728e68	−0.993278
$649$	−8.12595e68	−1.02301
$650$	8.24917e68	1.00008
$651$	1.90172e67	0.0222031
$652$	1.72209e66	0.00193638
$653$	6.73230e68	0.729106	0.364553	−	0.931183i	$-0.381222\pi$
$653$	6.73230e68	0.729106	0.364553	+	0.931183i	$0.381222\pi$
$654$	4.52327e67	0.0471844
$655$	−2.98409e67	−0.0299847
$656$	2.26255e68	0.219005
$657$	1.28909e69	1.20207
$658$	−2.81224e68	−0.252649
$659$	1.04435e69	0.903971	0.451985	−	0.892025i	$-0.350716\pi$
$659$	1.04435e69	0.903971	0.451985	+	0.892025i	$0.350716\pi$
$660$	−3.05658e63	−2.54923e−6 0
$661$	2.33040e68	0.187281	0.0936406	−	0.995606i	$-0.470150\pi$
$661$	2.33040e68	0.187281	0.0936406	+	0.995606i	$0.470150\pi$
$662$	1.62718e69	1.26013
$663$	−9.93604e67	−0.0741535
$664$	−2.28505e69	−1.64353
$665$	−1.17878e66	−0.000817151 0
$666$	−1.91738e69	−1.28112
$667$	6.56344e68	0.422716
$668$	−7.72680e66	−0.00479707
$669$	−2.90640e67	−0.0173946
$670$	−5.36404e67	−0.0309499
$671$	−2.06841e69	−1.15063
$672$	−2.21171e65	−0.000118626 0
$673$	7.43695e68	0.384614	0.192307	−	0.981335i	$-0.438403\pi$
$673$	7.43695e68	0.384614	0.192307	+	0.981335i	$0.438403\pi$
$674$	−9.31466e68	−0.464515
$675$	−1.71353e68	−0.0824042
$676$	−1.47754e64	−6.85246e−6 0
$677$	2.93326e69	1.31198	0.655991	−	0.754768i	$-0.272251\pi$
$677$	2.93326e69	1.31198	0.655991	+	0.754768i	$0.272251\pi$
$678$	−4.00281e67	−0.0172678
$679$	−6.25905e68	−0.260435
$680$	9.84077e67	0.0394967
$681$	1.62405e68	0.0628775
$682$	2.82107e69	1.05365
$683$	−3.75946e69	−1.35462	−0.677312	−	0.735696i	$-0.736855\pi$
$683$	−3.75946e69	−1.35462	−0.677312	+	0.735696i	$0.736855\pi$
$684$	−7.79807e65	−0.000271089 0
$685$	−2.38151e67	−0.00798792
$686$	2.47549e69	0.801163
$687$	1.13931e68	0.0355796
$688$	3.62516e69	1.09247
$689$	−2.21684e69	−0.644708
$690$	−4.25908e66	−0.00119540
$691$	−2.65308e69	−0.718683	−0.359342	−	0.933206i	$-0.616999\pi$
$691$	−2.65308e69	−0.718683	−0.359342	+	0.933206i	$0.616999\pi$
$692$	−7.67576e66	−0.00200688
$693$	1.52136e69	0.383945
$694$	2.90224e69	0.707012
$695$	5.84822e67	0.0137529
$696$	5.82950e67	0.0132344
$697$	1.79204e69	0.392776
$698$	−8.92996e69	−1.88969
$699$	1.06226e68	0.0217040
$700$	7.28359e66	0.00143696
$701$	−7.31131e69	−1.39285	−0.696424	−	0.717630i	$-0.745227\pi$
$701$	−7.31131e69	−1.39285	−0.696424	+	0.717630i	$0.745227\pi$
$702$	−4.48396e68	−0.0824902
$703$	6.04220e68	0.107347
$704$	5.03682e69	0.864223
$705$	−3.11286e66	−0.000515853 0
$706$	−5.03949e69	−0.806624
$707$	1.62416e69	0.251103
$708$	1.05642e66	0.000157769 0
$709$	2.17234e69	0.313397	0.156699	−	0.987646i	$-0.449915\pi$
$709$	2.17234e69	0.313397	0.156699	+	0.987646i	$0.449915\pi$
$710$	1.59143e67	0.00221798
$711$	1.21741e70	1.63920
$712$	−3.20130e69	−0.416454
$713$	1.26993e70	1.59619
$714$	−2.71559e68	−0.0329806
$715$	−1.62278e68	−0.0190441
$716$	1.55839e67	0.00176728
$717$	4.06772e68	0.0445792
$718$	2.83208e69	0.299956
$719$	−1.06469e70	−1.08984	−0.544922	−	0.838487i	$-0.683441\pi$
$719$	−1.06469e70	−1.08984	−0.544922	+	0.838487i	$0.683441\pi$
$720$	2.22578e68	0.0220210
$721$	−4.58899e69	−0.438837
$722$	−1.07598e70	−0.994588
$723$	−6.65584e68	−0.0594723
$724$	3.61740e67	0.00312465
$725$	−3.84578e69	−0.321146
$726$	1.27054e68	0.0102575
$727$	−3.79077e69	−0.295893	−0.147946	−	0.988995i	$-0.547266\pi$
$727$	−3.79077e69	−0.295893	−0.147946	+	0.988995i	$0.547266\pi$
$728$	−5.86160e69	−0.442382
$729$	−1.35635e70	−0.989802
$730$	−3.75802e68	−0.0265185
$731$	2.87129e70	1.95930
$732$	2.68906e66	0.000177451 0
$733$	−5.09174e69	−0.324952	−0.162476	−	0.986713i	$-0.551948\pi$
$733$	−5.09174e69	−0.324952	−0.162476	+	0.986713i	$0.551948\pi$
$734$	2.84930e70	1.75867
$735$	1.22057e67	0.000728655 0
$736$	−1.47693e68	−0.00852812
$737$	−2.18162e70	−1.21850
$738$	4.04014e69	0.218281
$739$	1.98249e70	1.03615	0.518075	−	0.855335i	$-0.326649\pi$
$739$	1.98249e70	1.03615	0.518075	+	0.855335i	$0.326649\pi$
$740$	1.80580e66	9.13045e−5 0
$741$	7.05908e67	0.00345305
$742$	−6.05877e69	−0.286741
$743$	3.83707e69	0.175701	0.0878503	−	0.996134i	$-0.472000\pi$
$743$	3.83707e69	0.175701	0.0878503	+	0.996134i	$0.472000\pi$
$744$	1.12792e69	0.0499737
$745$	−3.38031e68	−0.0144920
$746$	7.94543e69	0.329622
$747$	−4.09354e70	−1.64341
$748$	−1.30142e68	−0.00505623
$749$	1.37484e70	0.516950
$750$	4.99233e67	0.00181678
$751$	2.09915e70	0.739376	0.369688	−	0.929156i	$-0.379464\pi$
$751$	2.09915e70	0.739376	0.369688	+	0.929156i	$0.379464\pi$
$752$	−1.67336e70	−0.570495
$753$	1.10582e69	0.0364928
$754$	−1.00636e70	−0.321482
$755$	5.68406e68	0.0175775
$756$	−3.95910e66	−0.000118526 0
$757$	−4.86595e70	−1.41032	−0.705161	−	0.709047i	$-0.749125\pi$
$757$	−4.86595e70	−1.41032	−0.705161	+	0.709047i	$0.749125\pi$
$758$	2.26428e70	0.635380
$759$	−1.73222e69	−0.0470630
$760$	−6.99140e67	−0.00183921
$761$	−1.65408e70	−0.421339	−0.210670	−	0.977557i	$-0.567564\pi$
$761$	−1.65408e70	−0.421339	−0.210670	+	0.977557i	$0.567564\pi$
$762$	−1.26865e69	−0.0312927
$763$	2.12037e70	0.506478
$764$	2.53889e68	0.00587296
$765$	1.76292e69	0.0394937
$766$	1.17437e70	0.254801
$767$	5.60869e70	1.17862
$768$	−1.97086e67	−0.000401149 0
$769$	2.08104e70	0.410285	0.205142	−	0.978732i	$-0.434234\pi$
$769$	2.08104e70	0.410285	0.205142	+	0.978732i	$0.434234\pi$
$770$	−4.43517e68	−0.00847007
$771$	−3.12153e69	−0.0577477
$772$	−8.64944e65	−1.55012e−5 0
$773$	5.14751e70	0.893715	0.446858	−	0.894605i	$-0.352543\pi$
$773$	5.14751e70	0.893715	0.446858	+	0.894605i	$0.352543\pi$
$774$	6.47330e70	1.08886
$775$	−7.44100e70	−1.21266
$776$	−3.71227e70	−0.586175
$777$	1.53251e69	0.0234471
$778$	−8.85207e70	−1.31234
$779$	−1.27316e69	−0.0182901
$780$	2.10971e65	2.93701e−6 0
$781$	6.47253e69	0.0873220
$782$	−1.81341e71	−2.37100
$783$	2.09043e69	0.0264894
$784$	6.56133e70	0.805839
$785$	−5.90613e68	−0.00703067
$786$	4.88402e69	0.0563541
$787$	4.94511e70	0.553089	0.276544	−	0.961001i	$-0.410811\pi$
$787$	4.94511e70	0.553089	0.276544	+	0.961001i	$0.410811\pi$
$788$	−5.63373e67	−0.000610806 0
$789$	1.51493e69	0.0159224
$790$	−3.54906e69	−0.0361618
$791$	−1.87639e70	−0.185353
$792$	9.02329e70	0.864167
$793$	1.42766e71	1.32566
$794$	8.17438e70	0.735957
$795$	−6.70644e67	−0.000585460 0
$796$	−3.27154e68	−0.00276938
$797$	−2.16656e70	−0.177845	−0.0889224	−	0.996039i	$-0.528342\pi$
$797$	−2.16656e70	−0.177845	−0.0889224	+	0.996039i	$0.528342\pi$
$798$	1.92930e68	0.00153578
$799$	−1.32538e71	−1.02316
$800$	8.65391e68	0.00647900
$801$	−5.73497e70	−0.416423
$802$	1.89799e71	1.33666
$803$	−1.52843e71	−1.04404
$804$	2.83624e67	0.000187919 0
$805$	−1.99652e69	−0.0128314
$806$	−1.94716e71	−1.21393
$807$	−1.05580e70	−0.0638529
$808$	9.63295e70	0.565172
$809$	2.44601e70	0.139226	0.0696128	−	0.997574i	$-0.477824\pi$
$809$	2.44601e70	0.139226	0.0696128	+	0.997574i	$0.477824\pi$
$810$	3.96770e69	0.0219107
$811$	−1.87289e71	−1.00346	−0.501732	−	0.865023i	$-0.667304\pi$
$811$	−1.87289e71	−1.00346	−0.501732	+	0.865023i	$0.667304\pi$
$812$	−8.88565e67	−0.000461920 0
$813$	1.09946e70	0.0554577
$814$	2.27338e71	1.11269
$815$	2.76591e69	0.0131364
$816$	−1.61585e70	−0.0744718
$817$	−2.03992e70	−0.0912373
$818$	−1.57584e71	−0.683999
$819$	−1.05007e71	−0.442348
$820$	−3.80502e66	−1.55567e−5 0
$821$	3.89124e71	1.54412	0.772060	−	0.635550i	$-0.219227\pi$
$821$	3.89124e71	1.54412	0.772060	+	0.635550i	$0.219227\pi$
$822$	3.89780e69	0.0150127
$823$	−2.90370e69	−0.0108557	−0.00542783	−	0.999985i	$-0.501728\pi$
$823$	−2.90370e69	−0.0108557	−0.00542783	+	0.999985i	$0.501728\pi$
$824$	−2.72175e71	−0.987716
$825$	1.01498e70	0.0357548
$826$	1.53289e71	0.524205
$827$	5.33545e71	1.77128	0.885638	−	0.464376i	$-0.153721\pi$
$827$	5.33545e71	1.77128	0.885638	+	0.464376i	$0.153721\pi$
$828$	−1.32077e69	−0.00425682
$829$	−1.86675e71	−0.584116	−0.292058	−	0.956401i	$-0.594340\pi$
$829$	−1.86675e71	−0.584116	−0.292058	+	0.956401i	$0.594340\pi$
$830$	1.19337e70	0.0362546
$831$	−1.22802e70	−0.0362226
$832$	−3.47651e71	−0.995684
$833$	5.19688e71	1.44524
$834$	−9.57172e69	−0.0258477
$835$	−1.24103e70	−0.0325434
$836$	9.24594e67	0.000235449 0
$837$	4.04467e70	0.100025
$838$	−7.09111e71	−1.70308
$839$	−5.99163e71	−1.39758	−0.698790	−	0.715327i	$-0.746278\pi$
$839$	−5.99163e71	−1.39758	−0.698790	+	0.715327i	$0.746278\pi$
$840$	−1.77327e68	−0.000401727 0
$841$	−4.07550e71	−0.896765
$842$	6.34492e71	1.35606
$843$	7.04127e69	0.0146176
$844$	1.81344e69	0.00365689
$845$	−2.37313e67	−4.64871e−5 0
$846$	−2.98805e71	−0.568609
$847$	5.95590e70	0.110104
$848$	−3.60514e71	−0.647475
$849$	6.36614e69	0.0111081
$850$	1.06255e72	1.80130
$851$	1.02338e72	1.68563
$852$	−8.41468e66	−1.34669e−5 0
$853$	−3.03012e71	−0.471204	−0.235602	−	0.971850i	$-0.575706\pi$
$853$	−3.03012e71	−0.471204	−0.235602	+	0.971850i	$0.575706\pi$
$854$	3.90189e71	0.589599
$855$	−1.25247e69	−0.00183907
$856$	8.15426e71	1.16353
$857$	−3.11091e71	−0.431377	−0.215689	−	0.976462i	$-0.569200\pi$
$857$	−3.11091e71	−0.431377	−0.215689	+	0.976462i	$0.569200\pi$
$858$	2.65598e70	0.0357921
$859$	−1.12603e72	−1.47475	−0.737376	−	0.675482i	$-0.763936\pi$
$859$	−1.12603e72	−1.47475	−0.737376	+	0.675482i	$0.763936\pi$
$860$	−6.09659e67	−7.76023e−5 0
$861$	−3.22919e69	−0.00399499
$862$	−4.99432e71	−0.600548
$863$	3.73861e71	0.436964	0.218482	−	0.975841i	$-0.429889\pi$
$863$	3.73861e71	0.436964	0.218482	+	0.975841i	$0.429889\pi$
$864$	−4.70396e68	−0.000534413 0
$865$	−1.23283e70	−0.0136147
$866$	−1.39598e72	−1.49862
$867$	−8.84492e70	−0.0923051
$868$	−1.71924e69	−0.00174423
$869$	−1.44345e72	−1.42369
$870$	−3.04447e68	−0.000291938 0
$871$	1.50580e72	1.40385
$872$	1.25760e72	1.13996
$873$	−6.65034e71	−0.586131
$874$	1.28834e71	0.110408
$875$	2.34025e70	0.0195014
$876$	1.98705e68	0.000161012 0
$877$	1.31087e72	1.03292	0.516462	−	0.856310i	$-0.327249\pi$
$877$	1.31087e72	1.03292	0.516462	+	0.856310i	$0.327249\pi$
$878$	−1.01452e72	−0.777402
$879$	−2.72362e70	−0.0202964
$880$	−2.63905e70	−0.0191259
$881$	−7.81602e71	−0.550904	−0.275452	−	0.961315i	$-0.588828\pi$
$881$	−7.81602e71	−0.550904	−0.275452	+	0.961315i	$0.588828\pi$
$882$	1.17163e72	0.803175
$883$	1.45341e72	0.969063	0.484531	−	0.874774i	$-0.338990\pi$
$883$	1.45341e72	0.969063	0.484531	+	0.874774i	$0.338990\pi$
$884$	8.98262e69	0.00582536
$885$	1.69676e69	0.00107031
$886$	−1.62966e71	−0.0999934
$887$	−1.10215e72	−0.657829	−0.328914	−	0.944360i	$-0.606683\pi$
$887$	−1.10215e72	−0.657829	−0.328914	+	0.944360i	$0.606683\pi$
$888$	9.08942e70	0.0527738
$889$	−5.94702e71	−0.335897
$890$	1.67189e70	0.00918655
$891$	1.61371e72	0.862626
$892$	2.62751e69	0.00136649
$893$	9.41617e70	0.0476446
$894$	5.53252e70	0.0272366
$895$	2.50297e70	0.0119893
$896$	−9.56323e71	−0.445716
$897$	1.19561e71	0.0542219
$898$	−2.11143e72	−0.931767
$899$	9.07769e71	0.389819
$900$	7.73894e69	0.00323400
$901$	−2.85543e72	−1.16122
$902$	−4.79028e71	−0.189583
$903$	−5.17395e70	−0.0199284
$904$	−1.11290e72	−0.417185
$905$	5.81002e70	0.0211976
$906$	−9.30304e70	−0.0330357
$907$	2.81958e72	0.974553	0.487276	−	0.873248i	$-0.337990\pi$
$907$	2.81958e72	0.974553	0.487276	+	0.873248i	$0.337990\pi$
$908$	−1.46821e70	−0.00493953
$909$	1.72569e72	0.565130
$910$	3.06124e70	0.00975849
$911$	−4.35139e72	−1.35029	−0.675146	−	0.737684i	$-0.735919\pi$
$911$	−4.35139e72	−1.35029	−0.675146	+	0.737684i	$0.735919\pi$
$912$	1.14798e70	0.00346787
$913$	4.85360e72	1.42735
$914$	6.25427e72	1.79058
$915$	4.31899e69	0.00120383
$916$	−1.02999e70	−0.00279507
$917$	2.28948e72	0.604906
$918$	−5.77564e71	−0.148578
$919$	−3.26406e71	−0.0817576	−0.0408788	−	0.999164i	$-0.513016\pi$
$919$	−3.26406e71	−0.0817576	−0.0408788	+	0.999164i	$0.513016\pi$
$920$	−1.18415e71	−0.0288805
$921$	4.10274e70	0.00974347
$922$	−5.53441e72	−1.27986
$923$	−4.46746e71	−0.100605
$924$	2.34510e68	5.14277e−5 0
$925$	−5.99638e72	−1.28061
$926$	6.06463e72	1.26135
$927$	−4.87588e72	−0.987641
$928$	−1.05574e70	−0.00208272
$929$	−8.04143e72	−1.54507	−0.772535	−	0.634972i	$-0.781012\pi$
$929$	−8.04143e72	−1.54507	−0.772535	+	0.634972i	$0.781012\pi$
$930$	−5.89060e69	−0.00110237
$931$	−3.69213e71	−0.0672993
$932$	−9.60331e69	−0.00170503
$933$	1.92962e71	0.0333712
$934$	7.05783e72	1.18897
$935$	−2.09025e71	−0.0343015
$936$	−6.22804e72	−0.995619
$937$	7.50384e72	1.16859	0.584297	−	0.811540i	$-0.301370\pi$
$937$	7.50384e72	1.16859	0.584297	+	0.811540i	$0.301370\pi$
$938$	4.11545e72	0.624379
$939$	−4.31315e70	−0.00637511
$940$	2.81416e68	4.05244e−5 0
$941$	7.35980e72	1.03257	0.516286	−	0.856416i	$-0.327314\pi$
$941$	7.35980e72	1.03257	0.516286	+	0.856416i	$0.327314\pi$
$942$	9.66651e70	0.0132136
$943$	−2.15638e72	−0.287203
$944$	9.12114e72	1.18368
$945$	−6.35884e69	−0.000804079 0
$946$	−7.67520e72	−0.945708
$947$	−9.69759e72	−1.16436	−0.582182	−	0.813058i	$-0.697801\pi$
$947$	−9.69759e72	−1.16436	−0.582182	+	0.813058i	$0.697801\pi$
$948$	1.87657e69	0.000219563 0
$949$	1.05495e73	1.20285
$950$	−7.54890e71	−0.0838794
$951$	1.92675e71	0.0208643
$952$	−7.55013e72	−0.796800
$953$	5.05982e72	0.520426	0.260213	−	0.965551i	$-0.416207\pi$
$953$	5.05982e72	0.520426	0.260213	+	0.965551i	$0.416207\pi$
$954$	−6.43755e72	−0.645335
$955$	4.07780e71	0.0398422
$956$	−3.67740e70	−0.00350205
$957$	−1.23822e71	−0.0114936
$958$	−6.40718e72	−0.579712
$959$	1.82716e72	0.161147
$960$	−1.05172e70	−0.000904182 0
$961$	5.63169e72	0.471971
$962$	−1.56913e73	−1.28195
$963$	1.46079e73	1.16344
$964$	6.01717e70	0.00467202
$965$	−1.38922e69	−0.000105160 0
$966$	3.26769e71	0.0241158
$967$	−2.42428e73	−1.74435	−0.872176	−	0.489192i	$-0.837292\pi$
$967$	−2.42428e73	−1.74435	−0.872176	+	0.489192i	$0.837292\pi$
$968$	3.53247e72	0.247818
$969$	9.09257e70	0.00621948
$970$	1.93874e71	0.0129304
$971$	1.32065e73	0.858846	0.429423	−	0.903104i	$-0.358717\pi$
$971$	1.32065e73	0.858846	0.429423	+	0.903104i	$0.358717\pi$
$972$	−6.31171e69	−0.000400243 0
$973$	−4.48692e72	−0.277450
$974$	1.57088e73	0.947217
$975$	−7.00555e71	−0.0411936
$976$	2.32173e73	1.33135
$977$	−1.73470e73	−0.970080	−0.485040	−	0.874492i	$-0.661195\pi$
$977$	−1.73470e73	−0.970080	−0.485040	+	0.874492i	$0.661195\pi$
$978$	−4.52694e71	−0.0246890
$979$	6.79978e72	0.361675
$980$	−1.10345e69	−5.72417e−5 0
$981$	2.25293e73	1.13987
$982$	1.29913e73	0.641094
$983$	−1.67956e73	−0.808413	−0.404207	−	0.914668i	$-0.632452\pi$
$983$	−1.67956e73	−0.808413	−0.404207	+	0.914668i	$0.632452\pi$
$984$	−1.91525e71	−0.00899176
$985$	−9.04851e70	−0.00414371
$986$	−1.29626e73	−0.579039
$987$	2.38827e71	0.0104067
$988$	−6.38172e69	−0.000271264 0
$989$	−3.45505e73	−1.43267
$990$	−4.71244e71	−0.0190627
$991$	−2.77137e73	−1.09368	−0.546839	−	0.837238i	$-0.684169\pi$
$991$	−2.77137e73	−1.09368	−0.546839	+	0.837238i	$0.684169\pi$
$992$	−2.04270e71	−0.00786444
$993$	−1.38187e72	−0.0519051
$994$	−1.22099e72	−0.0447451
$995$	−5.25453e71	−0.0187875
$996$	−6.30997e69	−0.000220127 0
$997$	−4.99544e72	−0.170036	−0.0850182	−	0.996379i	$-0.527095\pi$
$997$	−4.99544e72	−0.170036	−0.0850182	+	0.996379i	$0.527095\pi$
$998$	−4.00380e72	−0.132976
$999$	3.25942e72	0.105630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.50.a.a.1.3	✓	3
3.2	odd	2		9.50.a.a.1.1		3
4.3	odd	2		16.50.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.50.a.a.1.3	✓	3	1.1	even	1	trivial
9.50.a.a.1.1		3	3.2	odd	2
16.50.a.c.1.2		3	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:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.37650e7 q^{2} -2.01823e10 q^{3} +1.82457e12 q^{4} +2.93049e15 q^{5} -4.79631e17 q^{6} -2.24836e20 q^{7} -1.33351e22 q^{8} -2.38892e23 q^{9} +O(q^{10})\)	\(q+2.37650e7 q^{2} -2.01823e10 q^{3} +1.82457e12 q^{4} +2.93049e15 q^{5} -4.79631e17 q^{6} -2.24836e20 q^{7} -1.33351e22 q^{8} -2.38892e23 q^{9} +6.96431e22 q^{10} +2.83247e25 q^{11} -3.68238e22 q^{12} -1.95503e27 q^{13} -5.34323e27 q^{14} -5.91440e25 q^{15} -3.17936e29 q^{16} -2.51820e30 q^{17} -5.67726e30 q^{18} +1.78906e30 q^{19} +5.34688e27 q^{20} +4.53770e30 q^{21} +6.73137e32 q^{22} +3.03017e33 q^{23} +2.69133e32 q^{24} -1.77550e34 q^{25} -4.64612e34 q^{26} +9.65098e33 q^{27} -4.10228e32 q^{28} +2.16603e35 q^{29} -1.40556e33 q^{30} +4.19094e36 q^{31} -4.87408e34 q^{32} -5.71657e35 q^{33} -5.98451e37 q^{34} -6.58881e35 q^{35} -4.35874e35 q^{36} +3.37729e38 q^{37} +4.25171e37 q^{38} +3.94568e37 q^{39} -3.90785e37 q^{40} -7.11635e38 q^{41} +1.07838e38 q^{42} -1.14021e40 q^{43} +5.16803e37 q^{44} -7.00072e38 q^{45} +7.20120e40 q^{46} +5.26318e40 q^{47} +6.41668e39 q^{48} -2.06372e41 q^{49} -4.21947e41 q^{50} +5.08230e40 q^{51} -3.56707e39 q^{52} +1.13392e42 q^{53} +2.29355e41 q^{54} +8.30054e40 q^{55} +2.99822e42 q^{56} -3.61074e40 q^{57} +5.14756e42 q^{58} -2.86886e43 q^{59} -1.07912e38 q^{60} -7.30250e43 q^{61} +9.95976e43 q^{62} +5.37115e43 q^{63} +1.77824e44 q^{64} -5.72919e42 q^{65} -1.35854e43 q^{66} -7.70219e44 q^{67} -4.59463e42 q^{68} -6.11558e43 q^{69} -1.56583e43 q^{70} +2.28512e44 q^{71} +3.18566e45 q^{72} -5.39611e45 q^{73} +8.02614e45 q^{74} +3.58336e44 q^{75} +3.26427e42 q^{76} -6.36842e45 q^{77} +9.37691e44 q^{78} -5.09606e46 q^{79} -9.31711e44 q^{80} +5.69719e46 q^{81} -1.69120e46 q^{82} +1.71355e47 q^{83} +8.27933e42 q^{84} -7.37958e45 q^{85} -2.70972e47 q^{86} -4.37153e45 q^{87} -3.77714e47 q^{88} +2.40065e47 q^{89} -1.66372e46 q^{90} +4.39560e47 q^{91} +5.52875e45 q^{92} -8.45826e46 q^{93} +1.25079e48 q^{94} +5.24284e45 q^{95} +9.83699e44 q^{96} +2.78383e48 q^{97} -4.90444e48 q^{98} -6.76655e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 24225168 q^{2} - 326954692404 q^{3} + 31502767984896 q^{4} + 63\!\cdots\!50 q^{5}+ \cdots + 34\!\cdots\!19 q^{9}+O(q^{10}) \) 3 * q - 24225168 * q^2 - 326954692404 * q^3 + 31502767984896 * q^4 + 63884035717079250 * q^5 + 8906136249246768576 * q^6 + 509391477498711192 * q^7 + 12774393005516465664000 * q^8 + 341625690512280455369319 * q^9	\( 3 q - 24225168 q^{2} - 326954692404 q^{3} + 31502767984896 q^{4} + 63\!\cdots\!50 q^{5}+ \cdots - 11\!\cdots\!52 q^{99}+O(q^{100}) \) 3 * q - 24225168 * q^2 - 326954692404 * q^3 + 31502767984896 * q^4 + 63884035717079250 * q^5 + 8906136249246768576 * q^6 + 509391477498711192 * q^7 + 12774393005516465664000 * q^8 + 341625690512280455369319 * q^9 - 1782704508900495946524000 * q^10 - 20839986192711815613370524 * q^11 - 101756595014280089890126848 * q^12 - 187524857197340618282341014 * q^13 - 9454369415029168241295938688 * q^14 - 204230679539215002884128467000 * q^15 - 958699697068386571735634214912 * q^16 - 3305035636247475259184114894538 * q^17 - 20227965712272756371678796043344 * q^18 - 45882942802931464757155696518660 * q^19 + 19614616637279540996591887296000 * q^20 + 617794442803555252870956383262816 * q^21 + 1789915191438262082177360193562944 * q^22 + 4533392548023086653463590407813576 * q^23 - 2513947703938508593953436558049280 * q^24 - 13921151905580403838435182832171875 * q^25 - 85826222237480824536590109710199264 * q^26 - 316454625615073819697154158592097800 * q^27 - 59263339345763305527729286468663296 * q^28 + 1118089919316361970349176934175494810 * q^29 + 5019197819712535273166303836165776000 * q^30 + 934226816157578575389156342339525216 * q^31 + 731728685735702515419064521056059392 * q^32 - 24487068877327908023713382739550873968 * q^33 - 44386547077569962679458968510685418528 * q^34 - 118496887985378726635932152589238374000 * q^35 + 37986811000754375090144064848875953408 * q^36 + 242135148519373130928922851818564983602 * q^37 + 1156029602765443663092741329710471492800 * q^38 + 1291017145684876237790670030697385259048 * q^39 + 521466322563622592824981612412298240000 * q^40 - 6211739675976490815696297371880432723714 * q^41 - 14577965575239226149151901656398676210176 * q^42 - 7795173962887472637660666233812713782844 * q^43 + 2342252938597505040255206661879982328832 * q^44 + 76758284157261249391010855229819118430250 * q^45 + 26787138361451470082912377308943265940096 * q^46 + 72757717838871152990888073123214445891472 * q^47 + 156517630976899733143320027855300206002176 * q^48 - 280157966384090888246597869444400847657429 * q^49 - 537697283161263679965664107392030595750000 * q^50 - 1538734957331600122304206020917586572488104 * q^51 - 123529799747407597799198092229890019578368 * q^52 - 155850890670432045962015052011776669693854 * q^53 + 8252737541190722285688590807826219494394240 * q^54 + 4640026560861316230546160030865773419591000 * q^55 + 6722101775263505338291028050795018900439040 * q^56 - 7909742361043655643598112535376781525014800 * q^57 - 16549417550295130349814323361508282251506400 * q^58 - 62596927936822013761436024025606581543386380 * q^59 - 8860237536153508564855019737671281942784000 * q^60 - 24037263967789435219196348055077866809754374 * q^61 + 188825800588885099392385526941761279238024704 * q^62 - 79613772299337773967480392108297858821089864 * q^63 + 514652981263254699809134733483815976080244736 * q^64 - 244975900670806240216695171564505814930314500 * q^65 + 520146826433507127417478540282210913545819392 * q^66 - 1019040852324305100821779153549119164107459188 * q^67 + 147929481309005416179289053660840704965292544 * q^68 - 4867866269191569039747093560336346164459611872 * q^69 + 2807457123724968989995337407321309803024672000 * q^70 - 3208129335291950593367863544185773469328334504 * q^71 + 10389376832262916146131931928642229401854259200 * q^72 + 5668108076325412165814435883536677392865317726 * q^73 + 10012493148932275797653251806650724700277983392 * q^74 - 12104818074938487392123628092507024931595687500 * q^75 + 753841821393723585433963960120373529551508480 * q^76 - 32043339793247959180079389483660528277811891936 * q^77 - 27771485354519690073790188371684714833523265408 * q^78 - 7871365395380306420112251724245018715125364240 * q^79 - 30434832804539714147732706266001913558351872000 * q^80 + 67270927730095597004530465543730351634592280043 * q^81 + 118639125705754411670909153459409940471487282784 * q^82 + 94164681901361229355849854653903786480577085116 * q^83 + 7700494417700399139591084235352419616317120512 * q^84 + 297863286656785614551226799130947646752077538500 * q^85 - 347916436657924446515600473690440815675104929984 * q^86 - 175500245979701689466461020645367234129141215000 * q^87 - 1057522149818049090984983413770258669302102016000 * q^88 + 367807201561165354579457777200332871192114777230 * q^89 - 2007318616781959003323900738484966136471887212000 * q^90 + 1613372397893666548508325640004129525440352221776 * q^91 + 467187868629171186038576611613065932844001728512 * q^92 + 5954871901405488350696717407304686000200433533312 * q^93 + 904097685092930858948295844890436017323554129152 * q^94 + 1475636199748052355599968141572624301097796705000 * q^95 - 2698554985048479483842995984936051823306493394944 * q^96 - 10431108583780665799950508389192126734793760399578 * q^97 - 2841886978251444216347516645227034756825518204176 * q^98 - 11387023179914295087805432025124514927226421923052 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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