LMFDB - Embedded newform 1.50.a.a.1.1

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			1.1
Root			$-168486.$ 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)

$f(q)$	$=$	$q-2.54182e7 q^{2} -8.64745e11 q^{3} +8.31363e13 q^{4} +1.67413e17 q^{5} +2.19803e19 q^{6} -3.42668e20 q^{7} +1.21960e22 q^{8} +5.08484e23 q^{9} +O(q^{10})$	\(q-2.54182e7 q^{2} -8.64745e11 q^{3} +8.31363e13 q^{4} +1.67413e17 q^{5} +2.19803e19 q^{6} -3.42668e20 q^{7} +1.21960e22 q^{8} +5.08484e23 q^{9} -4.25535e24 q^{10} -2.47212e24 q^{11} -7.18917e25 q^{12} -1.86505e26 q^{13} +8.71003e27 q^{14} -1.44770e29 q^{15} -3.56803e29 q^{16} +8.08684e29 q^{17} -1.29248e31 q^{18} -1.31622e31 q^{19} +1.39181e31 q^{20} +2.96321e32 q^{21} +6.28370e31 q^{22} +3.96809e33 q^{23} -1.05464e34 q^{24} +1.02637e34 q^{25} +4.74062e33 q^{26} -2.32776e35 q^{27} -2.84882e34 q^{28} +4.73835e35 q^{29} +3.67979e36 q^{30} -5.52226e36 q^{31} +2.20354e36 q^{32} +2.13775e36 q^{33} -2.05553e37 q^{34} -5.73673e37 q^{35} +4.22735e37 q^{36} +6.02154e37 q^{37} +3.34559e38 q^{38} +1.61279e38 q^{39} +2.04178e39 q^{40} -4.00631e39 q^{41} -7.53195e39 q^{42} -1.57103e39 q^{43} -2.05523e38 q^{44} +8.51271e40 q^{45} -1.00862e41 q^{46} -3.77976e40 q^{47} +3.08543e41 q^{48} -1.39502e41 q^{49} -2.60885e41 q^{50} -6.99305e41 q^{51} -1.55053e40 q^{52} -7.38411e41 q^{53} +5.91675e42 q^{54} -4.13866e41 q^{55} -4.17919e42 q^{56} +1.13819e43 q^{57} -1.20441e43 q^{58} -3.19771e43 q^{59} -1.20356e43 q^{60} +2.48724e43 q^{61} +1.40366e44 q^{62} -1.74241e44 q^{63} +1.44852e44 q^{64} -3.12234e43 q^{65} -5.43379e43 q^{66} +5.76819e44 q^{67} +6.72310e43 q^{68} -3.43138e45 q^{69} +1.45818e45 q^{70} -1.66436e45 q^{71} +6.20148e45 q^{72} +4.80904e45 q^{73} -1.53057e45 q^{74} -8.87547e45 q^{75} -1.09425e45 q^{76} +8.47118e44 q^{77} -4.09943e45 q^{78} -4.21047e45 q^{79} -5.97335e46 q^{80} +7.96119e46 q^{81} +1.01833e47 q^{82} -1.20169e47 q^{83} +2.46350e46 q^{84} +1.35385e47 q^{85} +3.99327e46 q^{86} -4.09747e47 q^{87} -3.01500e46 q^{88} +8.70490e47 q^{89} -2.16378e48 q^{90} +6.39094e46 q^{91} +3.29892e47 q^{92} +4.77534e48 q^{93} +9.60748e47 q^{94} -2.20352e48 q^{95} -1.90550e48 q^{96} -7.30863e48 q^{97} +3.54589e48 q^{98} -1.25703e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54182e7	−1.07130	−0.535649	−	0.844441i	$-0.679933\pi$
$2$	−2.54182e7	−1.07130	−0.535649	+	0.844441i	$0.679933\pi$
$3$	−8.64745e11	−1.76773	−0.883867	−	0.467737i	$-0.845069\pi$
$3$	−8.64745e11	−1.76773	−0.883867	+	0.467737i	$0.845069\pi$
$4$	8.31363e13	0.147680
$5$	1.67413e17	1.25610	0.628051	−	0.778172i	$-0.283853\pi$
$5$	1.67413e17	1.25610	0.628051	+	0.778172i	$0.283853\pi$
$6$	2.19803e19	1.89377
$7$	−3.42668e20	−0.676040	−0.338020	−	0.941139i	$-0.609757\pi$
$7$	−3.42668e20	−0.676040	−0.338020	+	0.941139i	$0.609757\pi$
$8$	1.21960e22	0.913089
$9$	5.08484e23	2.12489
$10$	−4.25535e24	−1.34566
$11$	−2.47212e24	−0.0756744	−0.0378372	−	0.999284i	$-0.512047\pi$
$11$	−2.47212e24	−0.0756744	−0.0378372	+	0.999284i	$0.512047\pi$
$12$	−7.18917e25	−0.261059
$13$	−1.86505e26	−0.0952968	−0.0476484	−	0.998864i	$-0.515173\pi$
$13$	−1.86505e26	−0.0952968	−0.0476484	+	0.998864i	$0.515173\pi$
$14$	8.71003e27	0.724240
$15$	−1.44770e29	−2.22046
$16$	−3.56803e29	−1.12587
$17$	8.08684e29	0.577803	0.288902	−	0.957359i	$-0.406710\pi$
$17$	8.08684e29	0.577803	0.288902	+	0.957359i	$0.406710\pi$
$18$	−1.29248e31	−2.27639
$19$	−1.31622e31	−0.616402	−0.308201	−	0.951321i	$-0.599727\pi$
$19$	−1.31622e31	−0.616402	−0.308201	+	0.951321i	$0.599727\pi$
$20$	1.39181e31	0.185501
$21$	2.96321e32	1.19506
$22$	6.28370e31	0.0810699
$23$	3.96809e33	1.72286	0.861428	−	0.507879i	$-0.169570\pi$
$23$	3.96809e33	1.72286	0.861428	+	0.507879i	$0.169570\pi$
$24$	−1.05464e34	−1.61410
$25$	1.02637e34	0.577794
$26$	4.74062e33	0.102091
$27$	−2.32776e35	−1.98850
$28$	−2.84882e34	−0.0998373
$29$	4.73835e35	0.702872	0.351436	−	0.936212i	$-0.385693\pi$
$29$	4.73835e35	0.702872	0.351436	+	0.936212i	$0.385693\pi$
$30$	3.67979e36	2.37877
$31$	−5.52226e36	−1.59866	−0.799328	−	0.600895i	$-0.794811\pi$
$31$	−5.52226e36	−1.59866	−0.799328	+	0.600895i	$0.794811\pi$
$32$	2.20354e36	0.293054
$33$	2.13775e36	0.133772
$34$	−2.05553e37	−0.619000
$35$	−5.73673e37	−0.849175
$36$	4.22735e37	0.313803
$37$	6.02154e37	0.228436	0.114218	−	0.993456i	$-0.463564\pi$
$37$	6.02154e37	0.228436	0.114218	+	0.993456i	$0.463564\pi$
$38$	3.34559e38	0.660350
$39$	1.61279e38	0.168459
$40$	2.04178e39	1.14693
$41$	−4.00631e39	−1.22897	−0.614483	−	0.788930i	$-0.710635\pi$
$41$	−4.00631e39	−1.22897	−0.614483	+	0.788930i	$0.710635\pi$
$42$	−7.53195e39	−1.28026
$43$	−1.57103e39	−0.150040	−0.0750198	−	0.997182i	$-0.523902\pi$
$43$	−1.57103e39	−0.150040	−0.0750198	+	0.997182i	$0.523902\pi$
$44$	−2.05523e38	−0.0111756
$45$	8.51271e40	2.66908
$46$	−1.00862e41	−1.84569
$47$	−3.77976e40	−0.408382	−0.204191	−	0.978931i	$-0.565456\pi$
$47$	−3.77976e40	−0.408382	−0.204191	+	0.978931i	$0.565456\pi$
$48$	3.08543e41	1.99024
$49$	−1.39502e41	−0.542970
$50$	−2.60885e41	−0.618990
$51$	−6.99305e41	−1.02140
$52$	−1.55053e40	−0.0140734
$53$	−7.38411e41	−0.420281	−0.210140	−	0.977671i	$-0.567392\pi$
$53$	−7.38411e41	−0.420281	−0.210140	+	0.977671i	$0.567392\pi$
$54$	5.91675e42	2.13028
$55$	−4.13866e41	−0.0950549
$56$	−4.17919e42	−0.617284
$57$	1.13819e43	1.08963
$58$	−1.20441e43	−0.752986
$59$	−3.19771e43	−1.31512	−0.657560	−	0.753403i	$-0.728411\pi$
$59$	−3.19771e43	−1.31512	−0.657560	+	0.753403i	$0.728411\pi$
$60$	−1.20356e43	−0.327916
$61$	2.48724e43	0.451998	0.225999	−	0.974127i	$-0.427435\pi$
$61$	2.48724e43	0.451998	0.225999	+	0.974127i	$0.427435\pi$
$62$	1.40366e44	1.71264
$63$	−1.74241e44	−1.43651
$64$	1.44852e44	0.811923
$65$	−3.12234e43	−0.119703
$66$	−5.43379e43	−0.143310
$67$	5.76819e44	1.05246	0.526232	−	0.850341i	$-0.323604\pi$
$67$	5.76819e44	1.05246	0.526232	+	0.850341i	$0.323604\pi$
$68$	6.72310e43	0.0853298
$69$	−3.43138e45	−3.04555
$70$	1.45818e45	0.909720
$71$	−1.66436e45	−0.733530	−0.366765	−	0.930314i	$-0.619535\pi$
$71$	−1.66436e45	−0.733530	−0.366765	+	0.930314i	$0.619535\pi$
$72$	6.20148e45	1.94021
$73$	4.80904e45	1.07312	0.536561	−	0.843862i	$-0.319723\pi$
$73$	4.80904e45	1.07312	0.536561	+	0.843862i	$0.319723\pi$
$74$	−1.53057e45	−0.244723
$75$	−8.87547e45	−1.02139
$76$	−1.09425e45	−0.0910300
$77$	8.47118e44	0.0511589
$78$	−4.09943e45	−0.180470
$79$	−4.21047e45	−0.135665	−0.0678323	−	0.997697i	$-0.521608\pi$
$79$	−4.21047e45	−0.135665	−0.0678323	+	0.997697i	$0.521608\pi$
$80$	−5.97335e46	−1.41421
$81$	7.96119e46	1.39026
$82$	1.01833e47	1.31659
$83$	−1.20169e47	−1.15446	−0.577232	−	0.816581i	$-0.695867\pi$
$83$	−1.20169e47	−1.15446	−0.577232	+	0.816581i	$0.695867\pi$
$84$	2.46350e46	0.176486
$85$	1.35385e47	0.725781
$86$	3.99327e46	0.160737
$87$	−4.09747e47	−1.24249
$88$	−3.01500e46	−0.0690975
$89$	8.70490e47	1.51255	0.756273	−	0.654256i	$-0.227018\pi$
$89$	8.70490e47	1.51255	0.756273	+	0.654256i	$0.227018\pi$
$90$	−2.16378e48	−2.85938
$91$	6.39094e46	0.0644244
$92$	3.29892e47	0.254431
$93$	4.77534e48	2.82600
$94$	9.60748e47	0.437499
$95$	−2.20352e48	−0.774264
$96$	−1.90550e48	−0.518041
$97$	−7.30863e48	−1.54145	−0.770723	−	0.637171i	$-0.780105\pi$
$97$	−7.30863e48	−1.54145	−0.770723	+	0.637171i	$0.780105\pi$
$98$	3.54589e48	0.581683
$99$	−1.25703e48	−0.160800
$100$	8.53285e47	0.0853285
$101$	1.06900e48	0.0837733	0.0418867	−	0.999122i	$-0.486663\pi$
$101$	1.06900e48	0.0837733	0.0418867	+	0.999122i	$0.486663\pi$
$102$	1.77751e49	1.09423
$103$	−3.01827e49	−1.46301	−0.731503	−	0.681839i	$-0.761181\pi$
$103$	−3.01827e49	−1.46301	−0.731503	+	0.681839i	$0.761181\pi$
$104$	−2.27462e48	−0.0870145
$105$	4.96081e49	1.50112
$106$	1.87691e49	0.450246
$107$	−4.53746e48	−0.0864790	−0.0432395	−	0.999065i	$-0.513768\pi$
$107$	−4.53746e48	−0.0864790	−0.0432395	+	0.999065i	$0.513768\pi$
$108$	−1.93521e49	−0.293661
$109$	−1.12199e50	−1.35844	−0.679221	−	0.733933i	$-0.737682\pi$
$109$	−1.12199e50	−1.35844	−0.679221	+	0.733933i	$0.737682\pi$
$110$	1.05198e49	0.101832
$111$	−5.20709e49	−0.403815
$112$	1.22265e50	0.761133
$113$	−4.95437e49	−0.248066	−0.124033	−	0.992278i	$-0.539583\pi$
$113$	−4.95437e49	−0.248066	−0.124033	+	0.992278i	$0.539583\pi$
$114$	−2.89308e50	−1.16732
$115$	6.64311e50	2.16409
$116$	3.93929e49	0.103800
$117$	−9.48348e49	−0.202495
$118$	8.12802e50	1.40888
$119$	−2.77110e50	−0.390618
$120$	−1.76562e51	−2.02748
$121$	−1.06108e51	−0.994273
$122$	−6.32212e50	−0.484225
$123$	3.46444e51	2.17249
$124$	−4.59100e50	−0.236089
$125$	−1.25558e51	−0.530334
$126$	4.42891e51	1.53893
$127$	−5.79879e50	−0.166015	−0.0830073	−	0.996549i	$-0.526452\pi$
$127$	−5.79879e50	−0.166015	−0.0830073	+	0.996549i	$0.526452\pi$
$128$	−4.92236e51	−1.16286
$129$	1.35854e51	0.265230
$130$	7.93644e50	0.128237
$131$	5.77681e51	0.773645	0.386822	−	0.922154i	$-0.373573\pi$
$131$	5.77681e51	0.773645	0.386822	+	0.922154i	$0.373573\pi$
$132$	1.77725e50	0.0197555
$133$	4.51026e51	0.416712
$134$	−1.46617e52	−1.12750
$135$	−3.89698e52	−2.49776
$136$	9.86272e51	0.527586
$137$	9.99643e51	0.446880	0.223440	−	0.974718i	$-0.428271\pi$
$137$	9.99643e51	0.446880	0.223440	+	0.974718i	$0.428271\pi$
$138$	8.72197e52	3.26270
$139$	−5.47789e52	−1.71692	−0.858461	−	0.512878i	$-0.828579\pi$
$139$	−5.47789e52	−1.71692	−0.858461	+	0.512878i	$0.828579\pi$
$140$	−4.76930e51	−0.125406
$141$	3.26853e52	0.721911
$142$	4.23051e52	0.785829
$143$	4.61063e50	0.00721153
$144$	−1.81428e53	−2.39235
$145$	7.93264e52	0.882880
$146$	−1.22237e53	−1.14963
$147$	1.20634e53	0.959828
$148$	5.00608e51	0.0337354
$149$	−3.17720e53	−1.81543	−0.907717	−	0.419584i	$-0.862176\pi$
$149$	−3.17720e53	−1.81543	−0.907717	+	0.419584i	$0.862176\pi$
$150$	2.25599e53	1.09421
$151$	4.36140e53	1.79759	0.898796	−	0.438367i	$-0.144443\pi$
$151$	4.36140e53	1.79759	0.898796	+	0.438367i	$0.144443\pi$
$152$	−1.60526e53	−0.562830
$153$	4.11203e53	1.22777
$154$	−2.15322e52	−0.0548064
$155$	−9.24500e53	−2.00808
$156$	1.34081e52	0.0248780
$157$	6.03339e52	0.0957238	0.0478619	−	0.998854i	$-0.484759\pi$
$157$	6.03339e52	0.0957238	0.0478619	+	0.998854i	$0.484759\pi$
$158$	1.07023e53	0.145337
$159$	6.38537e53	0.742945
$160$	3.68903e53	0.368106
$161$	−1.35974e54	−1.16472
$162$	−2.02359e54	−1.48938
$163$	1.51529e54	0.959179	0.479590	−	0.877493i	$-0.340786\pi$
$163$	1.51529e54	0.959179	0.479590	+	0.877493i	$0.340786\pi$
$164$	−3.33070e53	−0.181493
$165$	3.57889e53	0.168032
$166$	3.05449e54	1.23677
$167$	2.55570e54	0.893217	0.446608	−	0.894730i	$-0.352632\pi$
$167$	2.55570e54	0.893217	0.446608	+	0.894730i	$0.352632\pi$
$168$	3.61393e54	1.09120
$169$	−3.79544e54	−0.990919
$170$	−3.44123e54	−0.777527
$171$	−6.69275e54	−1.30978
$172$	−1.30609e53	−0.0221578
$173$	−8.31345e54	−1.22363	−0.611817	−	0.790999i	$-0.709561\pi$
$173$	−8.31345e54	−1.22363	−0.611817	+	0.790999i	$0.709561\pi$
$174$	1.04150e55	1.33108
$175$	−3.51704e54	−0.390612
$176$	8.82060e53	0.0851996
$177$	2.76520e55	2.32478
$178$	−2.21263e55	−1.62039
$179$	5.23266e54	0.334059	0.167030	−	0.985952i	$-0.446582\pi$
$179$	5.23266e54	0.334059	0.167030	+	0.985952i	$0.446582\pi$
$180$	7.07715e54	0.394168
$181$	1.38390e54	0.0672946	0.0336473	−	0.999434i	$-0.489288\pi$
$181$	1.38390e54	0.0672946	0.0336473	+	0.999434i	$0.489288\pi$
$182$	−1.62446e54	−0.0690177
$183$	−2.15083e55	−0.799013
$184$	4.83948e55	1.57312
$185$	1.00809e55	0.286940
$186$	−1.21381e56	−3.02749
$187$	−1.99916e54	−0.0437249
$188$	−3.14235e54	−0.0603097
$189$	7.97650e55	1.34431
$190$	5.60096e55	0.829467
$191$	−4.46194e54	−0.0581040	−0.0290520	−	0.999578i	$-0.509249\pi$
$191$	−4.46194e54	−0.0581040	−0.0290520	+	0.999578i	$0.509249\pi$
$192$	−1.25260e56	−1.43526
$193$	−3.91405e55	−0.394886	−0.197443	−	0.980314i	$-0.563264\pi$
$193$	−3.91405e55	−0.394886	−0.197443	+	0.980314i	$0.563264\pi$
$194$	1.85772e56	1.65135
$195$	2.70003e55	0.211602
$196$	−1.15977e55	−0.0801857
$197$	8.64318e55	0.527535	0.263767	−	0.964586i	$-0.415035\pi$
$197$	8.64318e55	0.527535	0.263767	+	0.964586i	$0.415035\pi$
$198$	3.19516e55	0.172264
$199$	−1.38403e56	−0.659545	−0.329773	−	0.944060i	$-0.606972\pi$
$199$	−1.38403e56	−0.659545	−0.329773	+	0.944060i	$0.606972\pi$
$200$	1.25176e56	0.527578
$201$	−4.98802e56	−1.86048
$202$	−2.71722e55	−0.0897462
$203$	−1.62368e56	−0.475170
$204$	−5.81376e55	−0.150841
$205$	−6.70710e56	−1.54371
$206$	7.67190e56	1.56731
$207$	2.01771e57	3.66088
$208$	6.65454e55	0.107292
$209$	3.25385e55	0.0466458
$210$	−1.26095e57	−1.60814
$211$	−1.39140e57	−1.57954	−0.789770	−	0.613404i	$-0.789800\pi$
$211$	−1.39140e57	−1.57954	−0.789770	+	0.613404i	$0.789800\pi$
$212$	−6.13888e55	−0.0620669
$213$	1.43925e57	1.29669
$214$	1.15334e56	0.0926448
$215$	−2.63011e56	−0.188465
$216$	−2.83894e57	−1.81568
$217$	1.89230e57	1.08076
$218$	2.85191e57	1.45530
$219$	−4.15860e57	−1.89699
$220$	−3.44073e55	−0.0140377
$221$	−1.50824e56	−0.0550628
$222$	1.32355e57	0.432606
$223$	2.03036e57	0.594434	0.297217	−	0.954810i	$-0.403941\pi$
$223$	2.03036e57	0.594434	0.297217	+	0.954810i	$0.403941\pi$
$224$	−7.55085e56	−0.198116
$225$	5.21892e57	1.22775
$226$	1.25931e57	0.265752
$227$	−4.69172e57	−0.888585	−0.444292	−	0.895882i	$-0.646545\pi$
$227$	−4.69172e57	−0.888585	−0.444292	+	0.895882i	$0.646545\pi$
$228$	9.46249e56	0.160917
$229$	5.97819e57	0.913273	0.456636	−	0.889653i	$-0.349054\pi$
$229$	5.97819e57	0.913273	0.456636	+	0.889653i	$0.349054\pi$
$230$	−1.68856e58	−2.31838
$231$	−7.32541e56	−0.0904354
$232$	5.77890e57	0.641785
$233$	−4.46843e57	−0.446617	−0.223308	−	0.974748i	$-0.571686\pi$
$233$	−4.46843e57	−0.446617	−0.223308	+	0.974748i	$0.571686\pi$
$234$	2.41053e57	0.216932
$235$	−6.32782e57	−0.512970
$236$	−2.65846e57	−0.194216
$237$	3.64098e57	0.239819
$238$	7.04366e57	0.418468
$239$	−4.13711e57	−0.221793	−0.110897	−	0.993832i	$-0.535372\pi$
$239$	−4.13711e57	−0.221793	−0.110897	+	0.993832i	$0.535372\pi$
$240$	5.16543e58	2.49995
$241$	−2.18261e58	−0.954022	−0.477011	−	0.878897i	$-0.658280\pi$
$241$	−2.18261e58	−0.954022	−0.477011	+	0.878897i	$0.658280\pi$
$242$	2.69707e58	1.06516
$243$	−1.31409e58	−0.469105
$244$	2.06780e57	0.0667510
$245$	−2.33545e58	−0.682027
$246$	−8.80598e58	−2.32738
$247$	2.45481e57	0.0587411
$248$	−6.73495e58	−1.45972
$249$	1.03916e59	2.04078
$250$	3.19146e58	0.568146
$251$	5.93439e58	0.958009	0.479005	−	0.877812i	$-0.340998\pi$
$251$	5.93439e58	0.958009	0.479005	+	0.877812i	$0.340998\pi$
$252$	−1.44858e58	−0.212143
$253$	−9.80960e57	−0.130376
$254$	1.47395e58	0.177851
$255$	−1.17073e59	−1.28299
$256$	4.35734e58	0.433852
$257$	9.93030e58	0.898671	0.449336	−	0.893363i	$-0.351661\pi$
$257$	9.93030e58	0.898671	0.449336	+	0.893363i	$0.351661\pi$
$258$	−3.45316e58	−0.284141
$259$	−2.06339e58	−0.154432
$260$	−2.59580e57	−0.0176776
$261$	2.40938e59	1.49352
$262$	−1.46836e59	−0.828804
$263$	−6.39723e58	−0.328909	−0.164455	−	0.986385i	$-0.552586\pi$
$263$	−6.39723e58	−0.328909	−0.164455	+	0.986385i	$0.552586\pi$
$264$	2.60721e58	0.122146
$265$	−1.23620e59	−0.527916
$266$	−1.14643e59	−0.446423
$267$	−7.52752e59	−2.67378
$268$	4.79546e58	0.155428
$269$	3.93934e59	1.16545	0.582723	−	0.812671i	$-0.301987\pi$
$269$	3.93934e59	1.16545	0.582723	+	0.812671i	$0.301987\pi$
$270$	9.90544e59	2.67585
$271$	2.92581e59	0.721935	0.360968	−	0.932578i	$-0.382446\pi$
$271$	2.92581e59	0.721935	0.360968	+	0.932578i	$0.382446\pi$
$272$	−2.88540e59	−0.650532
$273$	−5.52653e58	−0.113885
$274$	−2.54092e59	−0.478742
$275$	−2.53731e58	−0.0437243
$276$	−2.85272e59	−0.449767
$277$	8.20576e59	1.18403	0.592017	−	0.805925i	$-0.298332\pi$
$277$	8.20576e59	1.18403	0.592017	+	0.805925i	$0.298332\pi$
$278$	1.39238e60	1.83934
$279$	−2.80798e60	−3.39696
$280$	−6.99652e59	−0.775373
$281$	1.23805e60	1.25729	0.628643	−	0.777694i	$-0.283611\pi$
$281$	1.23805e60	1.25729	0.628643	+	0.777694i	$0.283611\pi$
$282$	−8.30801e59	−0.773382
$283$	−1.21811e60	−1.03972	−0.519862	−	0.854250i	$-0.674017\pi$
$283$	−1.21811e60	−1.03972	−0.519862	+	0.854250i	$0.674017\pi$
$284$	−1.38369e59	−0.108327
$285$	1.90548e60	1.36869
$286$	−1.17194e58	−0.00772570
$287$	1.37284e60	0.830830
$288$	1.12047e60	0.622706
$289$	−1.30486e60	−0.666143
$290$	−2.01634e60	−0.945828
$291$	6.32009e60	2.72487
$292$	3.99806e59	0.158478
$293$	−2.58132e60	−0.940992	−0.470496	−	0.882402i	$-0.655925\pi$
$293$	−2.58132e60	−0.940992	−0.470496	+	0.882402i	$0.655925\pi$
$294$	−3.06629e60	−1.02826
$295$	−5.35340e60	−1.65192
$296$	7.34388e59	0.208583
$297$	5.75451e59	0.150479
$298$	8.07587e60	1.94487
$299$	−7.40068e59	−0.164183
$300$	−7.37874e59	−0.150838
$301$	5.38341e59	0.101433
$302$	−1.10859e61	−1.92576
$303$	−9.24416e59	−0.148089
$304$	4.69629e60	0.693988
$305$	4.16398e60	0.567756
$306$	−1.04520e61	−1.31530
$307$	2.63375e60	0.305974	0.152987	−	0.988228i	$-0.451111\pi$
$307$	2.63375e60	0.305974	0.152987	+	0.988228i	$0.451111\pi$
$308$	7.04263e58	0.00755513
$309$	2.61003e61	2.58621
$310$	2.34992e61	2.15125
$311$	−1.91232e61	−1.61783	−0.808913	−	0.587928i	$-0.799944\pi$
$311$	−1.91232e61	−1.61783	−0.808913	+	0.587928i	$0.799944\pi$
$312$	1.96696e60	0.153818
$313$	−1.92491e61	−1.39179	−0.695896	−	0.718143i	$-0.744992\pi$
$313$	−1.92491e61	−1.39179	−0.695896	+	0.718143i	$0.744992\pi$
$314$	−1.53358e60	−0.102549
$315$	−2.91704e61	−1.80440
$316$	−3.50043e59	−0.0200349
$317$	4.85204e60	0.257023	0.128512	−	0.991708i	$-0.458980\pi$
$317$	4.85204e60	0.257023	0.128512	+	0.991708i	$0.458980\pi$
$318$	−1.62305e61	−0.795916
$319$	−1.17138e60	−0.0531895
$320$	2.42501e61	1.01986
$321$	3.92375e60	0.152872
$322$	3.45621e61	1.24776
$323$	−1.06440e61	−0.356159
$324$	6.61864e60	0.205313
$325$	−1.91423e60	−0.0550619
$326$	−3.85160e61	−1.02757
$327$	9.70238e61	2.40137
$328$	−4.88610e61	−1.12216
$329$	1.29520e61	0.276082
$330$	−9.09690e60	−0.180012
$331$	−3.46456e61	−0.636594	−0.318297	−	0.947991i	$-0.603111\pi$
$331$	−3.46456e61	−0.636594	−0.318297	+	0.947991i	$0.603111\pi$
$332$	−9.99042e60	−0.170491
$333$	3.06186e61	0.485401
$334$	−6.49614e61	−0.956901
$335$	9.65673e61	1.32200
$336$	−1.05728e62	−1.34548
$337$	−1.47496e62	−1.74521	−0.872605	−	0.488427i	$-0.837571\pi$
$337$	−1.47496e62	−1.74521	−0.872605	+	0.488427i	$0.837571\pi$
$338$	9.64734e61	1.06157
$339$	4.28427e61	0.438515
$340$	1.12554e61	0.107183
$341$	1.36517e61	0.120977
$342$	1.70118e62	1.40317
$343$	1.35843e62	1.04311
$344$	−1.91602e61	−0.137000
$345$	−5.74459e62	−3.82553
$346$	2.11313e62	1.31088
$347$	1.49446e62	0.863799	0.431900	−	0.901922i	$-0.357843\pi$
$347$	1.49446e62	0.863799	0.431900	+	0.901922i	$0.357843\pi$
$348$	−3.40648e61	−0.183491
$349$	2.27300e62	1.14124	0.570620	−	0.821214i	$-0.306703\pi$
$349$	2.27300e62	1.14124	0.570620	+	0.821214i	$0.306703\pi$
$350$	8.93970e61	0.418462
$351$	4.34139e61	0.189498
$352$	−5.44743e60	−0.0221767
$353$	−2.58609e61	−0.0982119	−0.0491059	−	0.998794i	$-0.515637\pi$
$353$	−2.58609e61	−0.0982119	−0.0491059	+	0.998794i	$0.515637\pi$
$354$	−7.02866e62	−2.49053
$355$	−2.78636e62	−0.921389
$356$	7.23693e61	0.223372
$357$	2.39630e62	0.690509
$358$	−1.33005e62	−0.357877
$359$	−5.12401e62	−1.28765	−0.643823	−	0.765175i	$-0.722653\pi$
$359$	−5.12401e62	−1.28765	−0.643823	+	0.765175i	$0.722653\pi$
$360$	1.03821e63	2.43710
$361$	−2.82717e62	−0.620049
$362$	−3.51763e61	−0.0720926
$363$	9.17562e62	1.75761
$364$	5.31319e60	0.00951418
$365$	8.05099e62	1.34795
$366$	5.46702e62	0.855981
$367$	1.03293e61	0.0151270	0.00756348	−	0.999971i	$-0.497592\pi$
$367$	1.03293e61	0.0151270	0.00756348	+	0.999971i	$0.497592\pi$
$368$	−1.41582e63	−1.93971
$369$	−2.03714e63	−2.61141
$370$	−2.56238e62	−0.307398
$371$	2.53030e62	0.284127
$372$	3.97004e62	0.417343
$373$	6.36683e62	0.626696	0.313348	−	0.949638i	$-0.398549\pi$
$373$	6.36683e62	0.626696	0.313348	+	0.949638i	$0.398549\pi$
$374$	5.08152e61	0.0468425
$375$	1.08576e63	0.937490
$376$	−4.60980e62	−0.372889
$377$	−8.83726e61	−0.0669815
$378$	−2.02748e63	−1.44015
$379$	1.19758e63	0.797340	0.398670	−	0.917094i	$-0.369472\pi$
$379$	1.19758e63	0.797340	0.398670	+	0.917094i	$0.369472\pi$
$380$	−1.83193e62	−0.114343
$381$	5.01447e62	0.293470
$382$	1.13415e62	0.0622467
$383$	−1.72054e63	−0.885717	−0.442859	−	0.896591i	$-0.646036\pi$
$383$	−1.72054e63	−0.885717	−0.442859	+	0.896591i	$0.646036\pi$
$384$	4.25659e63	2.05564
$385$	1.41819e62	0.0642609
$386$	9.94881e62	0.423041
$387$	−7.98841e62	−0.318817
$388$	−6.07612e62	−0.227640
$389$	−1.24290e63	−0.437189	−0.218595	−	0.975816i	$-0.570147\pi$
$389$	−1.24290e63	−0.437189	−0.218595	+	0.975816i	$0.570147\pi$
$390$	−6.86300e62	−0.226689
$391$	3.20893e63	0.995473
$392$	−1.70137e63	−0.495780
$393$	−4.99547e63	−1.36760
$394$	−2.19694e63	−0.565147
$395$	−7.04889e62	−0.170409
$396$	−1.04505e62	−0.0237468
$397$	5.98417e63	1.27831	0.639155	−	0.769078i	$-0.279284\pi$
$397$	5.98417e63	1.27831	0.639155	+	0.769078i	$0.279284\pi$
$398$	3.51795e63	0.706570
$399$	−3.90022e63	−0.736636
$400$	−3.66211e63	−0.650522
$401$	−9.27508e63	−1.54982	−0.774909	−	0.632073i	$-0.782204\pi$
$401$	−9.27508e63	−1.54982	−0.774909	+	0.632073i	$0.782204\pi$
$402$	1.26786e64	1.99313
$403$	1.02993e63	0.152347
$404$	8.88730e61	0.0123716
$405$	1.33281e64	1.74631
$406$	4.12712e63	0.509048
$407$	−1.48860e62	−0.0172868
$408$	−8.52873e63	−0.932632
$409$	−9.43587e63	−0.971764	−0.485882	−	0.874024i	$-0.661502\pi$
$409$	−9.43587e63	−0.971764	−0.485882	+	0.874024i	$0.661502\pi$
$410$	1.70483e64	1.65377
$411$	−8.64436e63	−0.789966
$412$	−2.50928e63	−0.216056
$413$	1.09576e64	0.889073
$414$	−5.12866e64	−3.92189
$415$	−2.01179e64	−1.45012
$416$	−4.10972e62	−0.0279271
$417$	4.73698e64	3.03506
$418$	−8.27070e62	−0.0499716
$419$	7.04245e63	0.401310	0.200655	−	0.979662i	$-0.435693\pi$
$419$	7.04245e63	0.401310	0.200655	+	0.979662i	$0.435693\pi$
$420$	4.12423e63	0.221684
$421$	1.20251e64	0.609788	0.304894	−	0.952386i	$-0.401379\pi$
$421$	1.20251e64	0.609788	0.304894	+	0.952386i	$0.401379\pi$
$422$	3.53668e64	1.69216
$423$	−1.92195e64	−0.867765
$424$	−9.00567e63	−0.383754
$425$	8.30008e63	0.333852
$426$	−3.65831e64	−1.38914
$427$	−8.52299e63	−0.305569
$428$	−3.77228e62	−0.0127712
$429$	−3.98702e62	−0.0127481
$430$	6.68527e63	0.201902
$431$	4.44020e63	0.126680	0.0633402	−	0.997992i	$-0.479825\pi$
$431$	4.44020e63	0.126680	0.0633402	+	0.997992i	$0.479825\pi$
$432$	8.30551e64	2.23880
$433$	−1.83425e63	−0.0467201	−0.0233601	−	0.999727i	$-0.507436\pi$
$433$	−1.83425e63	−0.0467201	−0.0233601	+	0.999727i	$0.507436\pi$
$434$	−4.80990e64	−1.15781
$435$	−6.85971e64	−1.56070
$436$	−9.32784e63	−0.200614
$437$	−5.22286e64	−1.06197
$438$	1.05704e65	2.03225
$439$	−1.95740e64	−0.355876	−0.177938	−	0.984042i	$-0.556943\pi$
$439$	−1.95740e64	−0.355876	−0.177938	+	0.984042i	$0.556943\pi$
$440$	−5.04752e63	−0.0867936
$441$	−7.09345e64	−1.15375
$442$	3.83367e63	0.0589887
$443$	−3.98745e63	−0.0580502	−0.0290251	−	0.999579i	$-0.509240\pi$
$443$	−3.98745e63	−0.0580502	−0.0290251	+	0.999579i	$0.509240\pi$
$444$	−4.32898e63	−0.0596353
$445$	1.45732e65	1.89991
$446$	−5.16081e64	−0.636816
$447$	2.74746e65	3.20921
$448$	−4.96362e64	−0.548892
$449$	1.31465e64	0.137649	0.0688246	−	0.997629i	$-0.478075\pi$
$449$	1.31465e64	0.137649	0.0688246	+	0.997629i	$0.478075\pi$
$450$	−1.32656e65	−1.31528
$451$	9.90409e63	0.0930013
$452$	−4.11888e63	−0.0366343
$453$	−3.77150e65	−3.17767
$454$	1.19255e65	0.951939
$455$	1.06993e64	0.0809237
$456$	1.38814e65	0.994934
$457$	1.24818e65	0.847873	0.423937	−	0.905692i	$-0.360648\pi$
$457$	1.24818e65	0.847873	0.423937	+	0.905692i	$0.360648\pi$
$458$	−1.51955e65	−0.978388
$459$	−1.88242e65	−1.14896
$460$	5.52284e64	0.319591
$461$	−6.76961e64	−0.371442	−0.185721	−	0.982603i	$-0.559462\pi$
$461$	−6.76961e64	−0.371442	−0.185721	+	0.982603i	$0.559462\pi$
$462$	1.86199e64	0.0968833
$463$	−2.06723e65	−1.02013	−0.510063	−	0.860137i	$-0.670378\pi$
$463$	−2.06723e65	−1.02013	−0.510063	+	0.860137i	$0.670378\pi$
$464$	−1.69066e65	−0.791343
$465$	7.99456e65	3.54975
$466$	1.13580e65	0.478460
$467$	2.20986e65	0.883284	0.441642	−	0.897191i	$-0.354396\pi$
$467$	2.20986e65	0.883284	0.441642	+	0.897191i	$0.354396\pi$
$468$	−7.88421e63	−0.0299044
$469$	−1.97658e65	−0.711507
$470$	1.60842e65	0.549544
$471$	−5.21734e64	−0.169214
$472$	−3.89993e65	−1.20082
$473$	3.88377e63	0.0113542
$474$	−9.25472e64	−0.256918
$475$	−1.35092e65	−0.356153
$476$	−2.30379e64	−0.0576864
$477$	−3.75470e65	−0.893049
$478$	1.05158e65	0.237607
$479$	7.25016e64	0.155642	0.0778211	−	0.996967i	$-0.475204\pi$
$479$	7.25016e64	0.155642	0.0778211	+	0.996967i	$0.475204\pi$
$480$	−3.19007e65	−0.650713
$481$	−1.12305e64	−0.0217693
$482$	5.54781e65	1.02204
$483$	1.17583e66	2.05892
$484$	−8.82141e64	−0.146834
$485$	−1.22356e66	−1.93621
$486$	3.34017e65	0.502551
$487$	−5.28007e65	−0.755405	−0.377702	−	0.925927i	$-0.623286\pi$
$487$	−5.28007e65	−0.755405	−0.377702	+	0.925927i	$0.623286\pi$
$488$	3.03344e65	0.412715
$489$	−1.31034e66	−1.69557
$490$	5.93630e65	0.730654
$491$	1.31061e66	1.53454	0.767271	−	0.641324i	$-0.221614\pi$
$491$	1.31061e66	1.53454	0.767271	+	0.641324i	$0.221614\pi$
$492$	2.88020e65	0.320832
$493$	3.83183e65	0.406122
$494$	−6.23968e64	−0.0629292
$495$	−2.10444e65	−0.201981
$496$	1.97036e66	1.79988
$497$	5.70324e65	0.495895
$498$	−2.64135e66	−2.18629
$499$	−2.40608e65	−0.189603	−0.0948016	−	0.995496i	$-0.530222\pi$
$499$	−2.40608e65	−0.189603	−0.0948016	+	0.995496i	$0.530222\pi$
$500$	−1.04384e65	−0.0783195
$501$	−2.21003e66	−1.57897
$502$	−1.50842e66	−1.02631
$503$	1.13819e66	0.737560	0.368780	−	0.929517i	$-0.379776\pi$
$503$	1.13819e66	0.737560	0.368780	+	0.929517i	$0.379776\pi$
$504$	−2.12505e66	−1.31166
$505$	1.78966e65	0.105228
$506$	2.49343e65	0.139672
$507$	3.28209e66	1.75168
$508$	−4.82090e64	−0.0245170
$509$	1.25631e66	0.608849	0.304425	−	0.952536i	$-0.401536\pi$
$509$	1.25631e66	0.608849	0.304425	+	0.952536i	$0.401536\pi$
$510$	2.97579e66	1.37446
$511$	−1.64791e66	−0.725472
$512$	1.66349e66	0.698080
$513$	3.06383e66	1.22572
$514$	−2.52411e66	−0.962745
$515$	−5.05299e66	−1.83769
$516$	1.12944e65	0.0391691
$517$	9.34402e64	0.0309041
$518$	5.24478e65	0.165443
$519$	7.18901e66	2.16306
$520$	−3.80801e65	−0.109299
$521$	−5.06272e66	−1.38631	−0.693154	−	0.720789i	$-0.743780\pi$
$521$	−5.06272e66	−1.38631	−0.693154	+	0.720789i	$0.743780\pi$
$522$	−6.12421e66	−1.60001
$523$	−2.50752e66	−0.625105	−0.312552	−	0.949901i	$-0.601184\pi$
$523$	−2.50752e66	−0.625105	−0.312552	+	0.949901i	$0.601184\pi$
$524$	4.80263e65	0.114252
$525$	3.04134e66	0.690498
$526$	1.62606e66	0.352360
$527$	−4.46576e66	−0.923709
$528$	−7.62756e65	−0.150610
$529$	1.04410e67	1.96824
$530$	3.14220e66	0.565555
$531$	−1.62599e67	−2.79448
$532$	3.74966e65	0.0615399
$533$	7.47197e65	0.117117
$534$	1.91336e67	2.86442
$535$	−7.59632e65	−0.108627
$536$	7.03490e66	0.960993
$537$	−4.52492e66	−0.590528
$538$	−1.00131e67	−1.24854
$539$	3.44866e65	0.0410890
$540$	−3.23981e66	−0.368869
$541$	9.85403e66	1.07221	0.536106	−	0.844151i	$-0.319895\pi$
$541$	9.85403e66	1.07221	0.536106	+	0.844151i	$0.319895\pi$
$542$	−7.43689e66	−0.773408
$543$	−1.19672e66	−0.118959
$544$	1.78197e66	0.169327
$545$	−1.87837e67	−1.70634
$546$	1.40475e66	0.122005
$547$	2.04995e67	1.70237	0.851185	−	0.524866i	$-0.175885\pi$
$547$	2.04995e67	1.70237	0.851185	+	0.524866i	$0.175885\pi$
$548$	8.31066e65	0.0659951
$549$	1.26472e67	0.960445
$550$	6.44939e65	0.0468417
$551$	−6.23669e66	−0.433252
$552$	−4.18492e67	−2.78086
$553$	1.44279e66	0.0917147
$554$	−2.08576e67	−1.26845
$555$	−8.71737e66	−0.507233
$556$	−4.55411e66	−0.253555
$557$	2.90683e67	1.54870	0.774351	−	0.632757i	$-0.218077\pi$
$557$	2.90683e67	1.54870	0.774351	+	0.632757i	$0.218077\pi$
$558$	7.13739e67	3.63916
$559$	2.93004e65	0.0142983
$560$	2.04688e67	0.956061
$561$	1.72877e66	0.0772941
$562$	−3.14691e67	−1.34693
$563$	6.00209e65	0.0245950	0.0122975	−	0.999924i	$-0.496085\pi$
$563$	6.00209e65	0.0245950	0.0122975	+	0.999924i	$0.496085\pi$
$564$	2.71733e66	0.106612
$565$	−8.29429e66	−0.311596
$566$	3.09621e67	1.11385
$567$	−2.72805e67	−0.939869
$568$	−2.02986e67	−0.669778
$569$	−2.48462e67	−0.785252	−0.392626	−	0.919698i	$-0.628433\pi$
$569$	−2.48462e67	−0.785252	−0.392626	+	0.919698i	$0.628433\pi$
$570$	−4.84340e67	−1.46628
$571$	−8.26527e66	−0.239702	−0.119851	−	0.992792i	$-0.538242\pi$
$571$	−8.26527e66	−0.239702	−0.119851	+	0.992792i	$0.538242\pi$
$572$	3.83311e64	0.00106500
$573$	3.85844e66	0.102712
$574$	−3.48951e67	−0.890067
$575$	4.07272e67	0.995457
$576$	7.36548e67	1.72524
$577$	−1.45109e67	−0.325751	−0.162875	−	0.986647i	$-0.552077\pi$
$577$	−1.45109e67	−0.325751	−0.162875	+	0.986647i	$0.552077\pi$
$578$	3.31673e67	0.713638
$579$	3.38465e67	0.698054
$580$	6.59490e66	0.130383
$581$	4.11782e67	0.780463
$582$	−1.60646e68	−2.91915
$583$	1.82544e66	0.0318045
$584$	5.86512e67	0.979855
$585$	−1.58766e67	−0.254354
$586$	6.56127e67	1.00808
$587$	−8.02541e67	−1.18259	−0.591295	−	0.806456i	$-0.701383\pi$
$587$	−8.02541e67	−1.18259	−0.591295	+	0.806456i	$0.701383\pi$
$588$	1.00290e67	0.141747
$589$	7.26848e67	0.985414
$590$	1.36074e68	1.76970
$591$	−7.47415e67	−0.932542
$592$	−2.14850e67	−0.257190
$593$	−1.46805e68	−1.68617	−0.843086	−	0.537779i	$-0.819263\pi$
$593$	−1.46805e68	−1.68617	−0.843086	+	0.537779i	$0.819263\pi$
$594$	−1.46269e67	−0.161208
$595$	−4.63920e67	−0.490656
$596$	−2.64140e67	−0.268103
$597$	1.19683e68	1.16590
$598$	1.88112e67	0.175889
$599$	−9.17136e67	−0.823145	−0.411573	−	0.911377i	$-0.635020\pi$
$599$	−9.17136e67	−0.823145	−0.411573	+	0.911377i	$0.635020\pi$
$600$	−1.08245e68	−0.932618
$601$	−2.27601e67	−0.188257	−0.0941283	−	0.995560i	$-0.530006\pi$
$601$	−2.27601e67	−0.188257	−0.0941283	+	0.995560i	$0.530006\pi$
$602$	−1.36837e67	−0.108665
$603$	2.93303e68	2.23637
$604$	3.62591e67	0.265468
$605$	−1.77639e68	−1.24891
$606$	2.34970e67	0.158648
$607$	1.39704e68	0.905914	0.452957	−	0.891532i	$-0.350369\pi$
$607$	1.39704e68	0.905914	0.452957	+	0.891532i	$0.350369\pi$
$608$	−2.90034e67	−0.180639
$609$	1.40407e68	0.839974
$610$	−1.05841e68	−0.608236
$611$	7.04944e66	0.0389175
$612$	3.41859e67	0.181316
$613$	−1.66422e68	−0.848066	−0.424033	−	0.905647i	$-0.639386\pi$
$613$	−1.66422e68	−0.848066	−0.424033	+	0.905647i	$0.639386\pi$
$614$	−6.69452e67	−0.327789
$615$	5.79993e68	2.72887
$616$	1.03315e67	0.0467126
$617$	7.60071e67	0.330269	0.165134	−	0.986271i	$-0.447194\pi$
$617$	7.60071e67	0.330269	0.165134	+	0.986271i	$0.447194\pi$
$618$	−6.63424e68	−2.77060
$619$	3.95260e68	1.58658	0.793291	−	0.608843i	$-0.208366\pi$
$619$	3.95260e68	1.58658	0.793291	+	0.608843i	$0.208366\pi$
$620$	−7.68595e67	−0.296552
$621$	−9.23676e68	−3.42590
$622$	4.86079e68	1.73317
$623$	−2.98290e68	−1.02254
$624$	−5.75448e67	−0.189664
$625$	−3.92521e68	−1.24395
$626$	4.89278e68	1.49102
$627$	−2.81375e67	−0.0824575
$628$	5.01593e66	0.0141365
$629$	4.86952e67	0.131991
$630$	7.41459e68	1.93305
$631$	−2.28574e68	−0.573201	−0.286600	−	0.958050i	$-0.592525\pi$
$631$	−2.28574e68	−0.573201	−0.286600	+	0.958050i	$0.592525\pi$
$632$	−5.13509e67	−0.123874
$633$	1.20320e69	2.79221
$634$	−1.23330e68	−0.275348
$635$	−9.70796e67	−0.208531
$636$	5.30856e67	0.109718
$637$	2.60178e67	0.0517433
$638$	2.97744e67	0.0569818
$639$	−8.46300e68	−1.55867
$640$	−8.24069e68	−1.46068
$641$	−1.91449e68	−0.326611	−0.163305	−	0.986576i	$-0.552216\pi$
$641$	−1.91449e68	−0.326611	−0.163305	+	0.986576i	$0.552216\pi$
$642$	−9.97347e67	−0.163771
$643$	−2.09210e68	−0.330684	−0.165342	−	0.986236i	$-0.552873\pi$
$643$	−2.09210e68	−0.330684	−0.165342	+	0.986236i	$0.552873\pi$
$644$	−1.13044e68	−0.172005
$645$	2.27437e68	0.333157
$646$	2.70552e68	0.381552
$647$	9.01802e68	1.22449	0.612247	−	0.790667i	$-0.290266\pi$
$647$	9.01802e68	1.22449	0.612247	+	0.790667i	$0.290266\pi$
$648$	9.70948e68	1.26943
$649$	7.90514e67	0.0995209
$650$	4.86563e67	0.0589878
$651$	−1.63636e69	−1.91049
$652$	1.25976e68	0.141651
$653$	−8.06774e68	−0.873734	−0.436867	−	0.899526i	$-0.643912\pi$
$653$	−8.06774e68	−0.873734	−0.436867	+	0.899526i	$0.643912\pi$
$654$	−2.46617e69	−2.57258
$655$	9.67116e68	0.971777
$656$	1.42946e69	1.38366
$657$	2.44532e69	2.28026
$658$	−3.29218e68	−0.295767
$659$	−1.45122e69	−1.25615	−0.628075	−	0.778153i	$-0.716157\pi$
$659$	−1.45122e69	−1.25615	−0.628075	+	0.778153i	$0.716157\pi$
$660$	2.97535e67	0.0248149
$661$	1.72306e69	1.38473	0.692365	−	0.721548i	$-0.256569\pi$
$661$	1.72306e69	1.38473	0.692365	+	0.721548i	$0.256569\pi$
$662$	8.80631e68	0.681982
$663$	1.30424e68	0.0973364
$664$	−1.46559e69	−1.05413
$665$	7.55077e68	0.523433
$666$	−7.78270e68	−0.520010
$667$	1.88022e69	1.21095
$668$	2.12472e68	0.131910
$669$	−1.75574e69	−1.05080
$670$	−2.45457e69	−1.41626
$671$	−6.14876e67	−0.0342047
$672$	6.52956e68	0.350216
$673$	−3.25113e69	−1.68138	−0.840690	−	0.541517i	$-0.817850\pi$
$673$	−3.25113e69	−1.68138	−0.840690	+	0.541517i	$0.817850\pi$
$674$	3.74909e69	1.86964
$675$	−2.38914e69	−1.14895
$676$	−3.15539e68	−0.146339
$677$	−2.07144e69	−0.926512	−0.463256	−	0.886225i	$-0.653319\pi$
$677$	−2.07144e69	−0.926512	−0.463256	+	0.886225i	$0.653319\pi$
$678$	−1.08899e69	−0.469780
$679$	2.50444e69	1.04208
$680$	1.65115e69	0.662702
$681$	4.05714e69	1.57078
$682$	−3.47002e68	−0.129603
$683$	1.47023e69	0.529760	0.264880	−	0.964281i	$-0.414668\pi$
$683$	1.47023e69	0.529760	0.264880	+	0.964281i	$0.414668\pi$
$684$	−5.56410e68	−0.193428
$685$	1.67354e69	0.561327
$686$	−3.45288e69	−1.11748
$687$	−5.16961e69	−1.61442
$688$	5.60546e68	0.168925
$689$	1.37717e68	0.0400514
$690$	1.46017e70	4.09828
$691$	1.33225e69	0.360890	0.180445	−	0.983585i	$-0.442246\pi$
$691$	1.33225e69	0.360890	0.180445	+	0.983585i	$0.442246\pi$
$692$	−6.91149e68	−0.180706
$693$	4.30746e68	0.108707
$694$	−3.79866e69	−0.925386
$695$	−9.17073e69	−2.15663
$696$	−4.99727e69	−1.13451
$697$	−3.23984e69	−0.710101
$698$	−5.77757e69	−1.22261
$699$	3.86405e69	0.789500
$700$	−2.92394e68	−0.0576854
$701$	7.12825e69	1.35797	0.678987	−	0.734150i	$-0.262419\pi$
$701$	7.12825e69	1.35797	0.678987	+	0.734150i	$0.262419\pi$
$702$	−1.10350e69	−0.203009
$703$	−7.92564e68	−0.140809
$704$	−3.58091e68	−0.0614418
$705$	5.47195e69	0.906795
$706$	6.57339e68	0.105214
$707$	−3.66314e68	−0.0566341
$708$	2.29889e69	0.343323
$709$	4.28430e69	0.618083	0.309042	−	0.951049i	$-0.399992\pi$
$709$	4.28430e69	0.618083	0.309042	+	0.951049i	$0.399992\pi$
$710$	7.08244e69	0.987082
$711$	−2.14096e69	−0.288272
$712$	1.06165e70	1.38109
$713$	−2.19128e70	−2.75426
$714$	−6.09096e69	−0.739741
$715$	7.71881e67	0.00905842
$716$	4.35024e68	0.0493338
$717$	3.57754e69	0.392072
$718$	1.30243e70	1.37945
$719$	3.53639e69	0.361995	0.180997	−	0.983484i	$-0.442067\pi$
$719$	3.53639e69	0.361995	0.180997	+	0.983484i	$0.442067\pi$
$720$	−3.03736e70	−3.00503
$721$	1.03427e70	0.989050
$722$	7.18617e69	0.664257
$723$	1.88740e70	1.68646
$724$	1.15052e68	0.00993804
$725$	4.86330e69	0.406116
$726$	−2.33228e70	−1.88293
$727$	−3.98958e69	−0.311411	−0.155706	−	0.987804i	$-0.549765\pi$
$727$	−3.98958e69	−0.311411	−0.155706	+	0.987804i	$0.549765\pi$
$728$	7.79439e68	0.0588252
$729$	−7.68760e69	−0.561004
$730$	−2.04642e70	−1.44406
$731$	−1.27046e69	−0.0866934
$732$	−1.78812e69	−0.117998
$733$	−8.35656e69	−0.533310	−0.266655	−	0.963792i	$-0.585918\pi$
$733$	−8.35656e69	−0.533310	−0.266655	+	0.963792i	$0.585918\pi$
$734$	−2.62552e68	−0.0162055
$735$	2.01957e70	1.20564
$736$	8.74385e69	0.504890
$737$	−1.42597e69	−0.0796446
$738$	5.17806e70	2.79760
$739$	−1.56314e70	−0.816974	−0.408487	−	0.912764i	$-0.633944\pi$
$739$	−1.56314e70	−0.816974	−0.408487	+	0.912764i	$0.633944\pi$
$740$	8.38086e68	0.0423751
$741$	−2.12278e69	−0.103839
$742$	−6.43158e69	−0.304384
$743$	3.92359e70	1.79662	0.898312	−	0.439357i	$-0.144794\pi$
$743$	3.92359e70	1.79662	0.898312	+	0.439357i	$0.144794\pi$
$744$	5.82401e70	2.58039
$745$	−5.31905e70	−2.28037
$746$	−1.61833e70	−0.671378
$747$	−6.11041e70	−2.45310
$748$	−1.66203e68	−0.00645729
$749$	1.55485e69	0.0584632
$750$	−2.75980e70	−1.00433
$751$	1.76438e70	0.621462	0.310731	−	0.950498i	$-0.399426\pi$
$751$	1.76438e70	0.621462	0.310731	+	0.950498i	$0.399426\pi$
$752$	1.34863e70	0.459785
$753$	−5.13173e70	−1.69351
$754$	2.24628e69	0.0717571
$755$	7.30158e70	2.25796
$756$	6.63137e69	0.198527
$757$	−1.73845e70	−0.503864	−0.251932	−	0.967745i	$-0.581066\pi$
$757$	−1.73845e70	−0.503864	−0.251932	+	0.967745i	$0.581066\pi$
$758$	−3.04403e70	−0.854189
$759$	8.48280e69	0.230471
$760$	−2.68742e70	−0.706972
$761$	−1.36361e70	−0.347349	−0.173675	−	0.984803i	$-0.555564\pi$
$761$	−1.36361e70	−0.347349	−0.173675	+	0.984803i	$0.555564\pi$
$762$	−1.27459e70	−0.314394
$763$	3.84472e70	0.918361
$764$	−3.70949e68	−0.00858078
$765$	6.88409e70	1.54220
$766$	4.37331e70	0.948867
$767$	5.96389e69	0.125327
$768$	−3.76798e70	−0.766936
$769$	8.59382e70	1.69430	0.847152	−	0.531351i	$-0.178316\pi$
$769$	8.59382e70	1.69430	0.847152	+	0.531351i	$0.178316\pi$
$770$	−3.60479e69	−0.0688425
$771$	−8.58718e70	−1.58861
$772$	−3.25399e69	−0.0583167
$773$	4.66524e69	0.0809983	0.0404992	−	0.999180i	$-0.487105\pi$
$773$	4.66524e69	0.0809983	0.0404992	+	0.999180i	$0.487105\pi$
$774$	2.03051e70	0.341548
$775$	−5.66787e70	−0.923695
$776$	−8.91361e70	−1.40748
$777$	1.78431e70	0.272995
$778$	3.15922e70	0.468360
$779$	5.27317e70	0.757537
$780$	2.24470e69	0.0312494
$781$	4.11450e69	0.0555094
$782$	−8.15652e70	−1.06645
$783$	−1.10297e71	−1.39766
$784$	4.97746e70	0.611314
$785$	1.01007e70	0.120239
$786$	1.26976e71	1.46511
$787$	−6.73785e70	−0.753599	−0.376799	−	0.926295i	$-0.622975\pi$
$787$	−6.73785e70	−0.753599	−0.376799	+	0.926295i	$0.622975\pi$
$788$	7.18562e69	0.0779062
$789$	5.53197e70	0.581425
$790$	1.79170e70	0.182559
$791$	1.69771e70	0.167702
$792$	−1.53308e70	−0.146824
$793$	−4.63883e69	−0.0430740
$794$	−1.52107e71	−1.36945
$795$	1.06900e71	0.933215
$796$	−1.15063e70	−0.0974014
$797$	−1.67868e71	−1.37797	−0.688985	−	0.724775i	$-0.741944\pi$
$797$	−1.67868e71	−1.37797	−0.688985	+	0.724775i	$0.741944\pi$
$798$	9.91367e70	0.789157
$799$	−3.05663e70	−0.235964
$800$	2.26165e70	0.169325
$801$	4.42630e71	3.21399
$802$	2.35756e71	1.66032
$803$	−1.18885e70	−0.0812078
$804$	−4.14685e70	−0.274755
$805$	−2.27638e71	−1.46301
$806$	−2.61790e70	−0.163209
$807$	−3.40652e71	−2.06020
$808$	1.30376e70	0.0764925
$809$	7.08887e70	0.403495	0.201748	−	0.979438i	$-0.435338\pi$
$809$	7.08887e70	0.403495	0.201748	+	0.979438i	$0.435338\pi$
$810$	−3.38777e71	−1.87081
$811$	−1.30313e71	−0.698193	−0.349097	−	0.937087i	$-0.613512\pi$
$811$	−1.30313e71	−0.698193	−0.349097	+	0.937087i	$0.613512\pi$
$812$	−1.34987e70	−0.0701729
$813$	−2.53008e71	−1.27619
$814$	3.78375e69	0.0185193
$815$	2.53680e71	1.20483
$816$	2.49514e71	1.14997
$817$	2.06781e70	0.0924847
$818$	2.39843e71	1.04105
$819$	3.24969e70	0.136895
$820$	−5.57603e70	−0.227974
$821$	6.12434e70	0.243026	0.121513	−	0.992590i	$-0.461225\pi$
$821$	6.12434e70	0.243026	0.121513	+	0.992590i	$0.461225\pi$
$822$	2.19724e71	0.846289
$823$	4.66189e71	1.74288	0.871438	−	0.490506i	$-0.163188\pi$
$823$	4.66189e71	1.74288	0.871438	+	0.490506i	$0.163188\pi$
$824$	−3.68108e71	−1.33585
$825$	2.19412e70	0.0772929
$826$	−2.78522e71	−0.952462
$827$	1.89180e71	0.628043	0.314022	−	0.949416i	$-0.398324\pi$
$827$	1.89180e71	0.628043	0.314022	+	0.949416i	$0.398324\pi$
$828$	1.67745e71	0.540637
$829$	−1.94307e71	−0.607998	−0.303999	−	0.952672i	$-0.598322\pi$
$829$	−1.94307e71	−0.607998	−0.303999	+	0.952672i	$0.598322\pi$
$830$	5.11362e71	1.55352
$831$	−7.09589e71	−2.09306
$832$	−2.70156e70	−0.0773736
$833$	−1.12813e71	−0.313730
$834$	−1.20406e72	−3.25146
$835$	4.27859e71	1.12197
$836$	2.70513e69	0.00688864
$837$	1.28545e72	3.17893
$838$	−1.79007e71	−0.429923
$839$	−1.81889e71	−0.424266	−0.212133	−	0.977241i	$-0.568041\pi$
$839$	−1.81889e71	−0.424266	−0.212133	+	0.977241i	$0.568041\pi$
$840$	6.05021e71	1.37065
$841$	−2.29947e71	−0.505970
$842$	−3.05658e71	−0.653265
$843$	−1.07060e72	−2.22255
$844$	−1.15675e71	−0.233266
$845$	−6.35408e71	−1.24470
$846$	4.88525e71	0.929636
$847$	3.63598e71	0.672168
$848$	2.63467e71	0.473182
$849$	1.05335e72	1.83796
$850$	−2.10973e71	−0.357655
$851$	2.38940e71	0.393563
$852$	1.19654e71	0.191494
$853$	−8.16161e70	−0.126918	−0.0634592	−	0.997984i	$-0.520213\pi$
$853$	−8.16161e70	−0.126918	−0.0634592	+	0.997984i	$0.520213\pi$
$854$	2.16639e71	0.327355
$855$	−1.12046e72	−1.64522
$856$	−5.53390e70	−0.0789630
$857$	1.39103e72	1.92889	0.964445	−	0.264285i	$-0.0851358\pi$
$857$	1.39103e72	1.92889	0.964445	+	0.264285i	$0.0851358\pi$
$858$	1.01343e70	0.0136570
$859$	3.97272e71	0.520301	0.260151	−	0.965568i	$-0.416228\pi$
$859$	3.97272e71	0.520301	0.260151	+	0.965568i	$0.416228\pi$
$860$	−2.18657e70	−0.0278325
$861$	−1.18715e72	−1.46869
$862$	−1.12862e71	−0.135712
$863$	4.45935e71	0.521203	0.260601	−	0.965446i	$-0.416079\pi$
$863$	4.45935e71	0.521203	0.260601	+	0.965446i	$0.416079\pi$
$864$	−5.12932e71	−0.582738
$865$	−1.39178e72	−1.53701
$866$	4.66233e70	0.0500512
$867$	1.12837e72	1.17756
$868$	1.57319e71	0.159606
$869$	1.04088e70	0.0102663
$870$	1.74362e72	1.67197
$871$	−1.07580e71	−0.100296
$872$	−1.36839e72	−1.24038
$873$	−3.71632e72	−3.27540
$874$	1.32756e72	1.13769
$875$	4.30248e71	0.358527
$876$	−3.45730e71	−0.280147
$877$	−1.15171e72	−0.907512	−0.453756	−	0.891126i	$-0.649916\pi$
$877$	−1.15171e72	−0.907512	−0.453756	+	0.891126i	$0.649916\pi$
$878$	4.97536e71	0.381249
$879$	2.23219e72	1.66342
$880$	1.47669e71	0.107019
$881$	−2.42451e72	−1.70889	−0.854447	−	0.519539i	$-0.826104\pi$
$881$	−2.42451e72	−1.70889	−0.854447	+	0.519539i	$0.826104\pi$
$882$	1.80303e72	1.23601
$883$	1.55419e72	1.03626	0.518128	−	0.855303i	$-0.326629\pi$
$883$	1.55419e72	1.03626	0.518128	+	0.855303i	$0.326629\pi$
$884$	−1.25389e70	−0.00813166
$885$	4.62932e72	2.92017
$886$	1.01354e71	0.0621891
$887$	5.49889e71	0.328206	0.164103	−	0.986443i	$-0.447527\pi$
$887$	5.49889e71	0.328206	0.164103	+	0.986443i	$0.447527\pi$
$888$	−6.35058e71	−0.368719
$889$	1.98706e71	0.112232
$890$	−3.70424e72	−2.03537
$891$	−1.96810e71	−0.105207
$892$	1.68797e71	0.0877859
$893$	4.97498e71	0.251727
$894$	−6.98356e72	−3.43802
$895$	8.76018e71	0.419613
$896$	1.68674e72	0.786143
$897$	6.39970e71	0.290232
$898$	−3.34160e71	−0.147463
$899$	−2.61664e72	−1.12365
$900$	4.33882e71	0.181313
$901$	−5.97141e71	−0.242840
$902$	−2.51744e71	−0.0996322
$903$	−4.65527e71	−0.179306
$904$	−6.04236e71	−0.226506
$905$	2.31684e71	0.0845289
$906$	9.58649e72	3.40423
$907$	2.00638e72	0.693482	0.346741	−	0.937961i	$-0.387288\pi$
$907$	2.00638e72	0.693482	0.346741	+	0.937961i	$0.387288\pi$
$908$	−3.90052e71	−0.131226
$909$	5.43572e71	0.178009
$910$	−2.71957e71	−0.0866934
$911$	−6.79753e70	−0.0210936	−0.0105468	−	0.999944i	$-0.503357\pi$
$911$	−6.79753e70	−0.0210936	−0.0105468	+	0.999944i	$0.503357\pi$
$912$	−4.06109e72	−1.22679
$913$	2.97073e71	0.0873633
$914$	−3.17266e72	−0.908325
$915$	−3.60078e72	−1.00364
$916$	4.97005e71	0.134872
$917$	−1.97953e72	−0.523014
$918$	4.78478e72	1.23088
$919$	7.92073e71	0.198397	0.0991985	−	0.995068i	$-0.468372\pi$
$919$	7.92073e71	0.198397	0.0991985	+	0.995068i	$0.468372\pi$
$920$	8.10195e72	1.97600
$921$	−2.27752e72	−0.540881
$922$	1.72071e72	0.397925
$923$	3.10411e71	0.0699030
$924$	−6.09007e70	−0.0133555
$925$	6.18032e71	0.131989
$926$	5.25453e72	1.09286
$927$	−1.53474e73	−3.10872
$928$	1.04412e72	0.205979
$929$	4.36095e72	0.837908	0.418954	−	0.908008i	$-0.362397\pi$
$929$	4.36095e72	0.837908	0.418954	+	0.908008i	$0.362397\pi$
$930$	−2.03208e73	−3.80284
$931$	1.83615e72	0.334688
$932$	−3.71489e71	−0.0659562
$933$	1.65367e73	2.85989
$934$	−5.61706e72	−0.946260
$935$	−3.34687e71	−0.0549230
$936$	−1.15661e72	−0.184896
$937$	−8.38565e72	−1.30592	−0.652960	−	0.757392i	$-0.726473\pi$
$937$	−8.38565e72	−1.30592	−0.652960	+	0.757392i	$0.726473\pi$
$938$	5.02411e72	0.762236
$939$	1.66456e73	2.46032
$940$	−5.26072e71	−0.0757552
$941$	−5.95096e72	−0.834913	−0.417456	−	0.908697i	$-0.637078\pi$
$941$	−5.95096e72	−0.834913	−0.417456	+	0.908697i	$0.637078\pi$
$942$	1.32616e72	0.181279
$943$	−1.58974e73	−2.11733
$944$	1.14095e73	1.48065
$945$	1.33537e73	1.68859
$946$	−9.87184e70	−0.0121637
$947$	5.80008e72	0.696402	0.348201	−	0.937420i	$-0.386793\pi$
$947$	5.80008e72	0.696402	0.348201	+	0.937420i	$0.386793\pi$
$948$	3.02697e71	0.0354164
$949$	−8.96911e71	−0.102265
$950$	3.43381e72	0.381546
$951$	−4.19577e72	−0.454349
$952$	−3.37964e72	−0.356669
$953$	−1.78856e73	−1.83962	−0.919810	−	0.392365i	$-0.871657\pi$
$953$	−1.78856e73	−1.83962	−0.919810	+	0.392365i	$0.871657\pi$
$954$	9.54379e72	0.956722
$955$	−7.46988e71	−0.0729846
$956$	−3.43944e71	−0.0327544
$957$	1.01294e72	0.0940249
$958$	−1.84286e72	−0.166739
$959$	−3.42546e72	−0.302109
$960$	−2.09702e73	−1.80284
$961$	1.85631e73	1.55570
$962$	2.85459e71	0.0233214
$963$	−2.30723e72	−0.183758
$964$	−1.81454e72	−0.140890
$965$	−6.55264e72	−0.496018
$966$	−2.98874e73	−2.20571
$967$	8.21075e72	0.590792	0.295396	−	0.955375i	$-0.404548\pi$
$967$	8.21075e72	0.590792	0.295396	+	0.955375i	$0.404548\pi$
$968$	−1.29409e73	−0.907860
$969$	9.20436e72	0.629595
$970$	3.11008e73	2.07426
$971$	1.52584e73	0.992288	0.496144	−	0.868240i	$-0.334749\pi$
$971$	1.52584e73	0.992288	0.496144	+	0.868240i	$0.334749\pi$
$972$	−1.09248e72	−0.0692773
$973$	1.87710e73	1.16071
$974$	1.34210e73	0.809264
$975$	1.65532e72	0.0973349
$976$	−8.87454e72	−0.508892
$977$	5.10455e72	0.285457	0.142728	−	0.989762i	$-0.454412\pi$
$977$	5.10455e72	0.285457	0.142728	+	0.989762i	$0.454412\pi$
$978$	3.33065e73	1.81647
$979$	−2.15196e72	−0.114461
$980$	−1.94161e72	−0.100721
$981$	−5.70516e73	−2.88654
$982$	−3.33135e73	−1.64395
$983$	−3.35654e73	−1.61559	−0.807793	−	0.589466i	$-0.799338\pi$
$983$	−3.35654e73	−1.61559	−0.807793	+	0.589466i	$0.799338\pi$
$984$	4.22523e73	1.98367
$985$	1.44699e73	0.662638
$986$	−9.73983e72	−0.435078
$987$	−1.12002e73	−0.488041
$988$	2.04084e71	0.00867487
$989$	−6.23396e72	−0.258497
$990$	5.34913e72	0.216382
$991$	3.04908e73	1.20327	0.601637	−	0.798770i	$-0.294516\pi$
$991$	3.04908e73	1.20327	0.601637	+	0.798770i	$0.294516\pi$
$992$	−1.21685e73	−0.468492
$993$	2.99596e73	1.12533
$994$	−1.44966e73	−0.531251
$995$	−2.31705e73	−0.828457
$996$	8.63916e72	0.301382
$997$	−5.00437e70	−0.00170341	−0.000851703	−	1.00000i	$-0.500271\pi$
$997$	−5.00437e70	−0.00170341	−0.000851703		1.00000i	$0.500271\pi$
$998$	6.11582e72	0.203122
$999$	−1.40167e73	−0.454246

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.50.a.a.1.1	✓	3	1.1	even	1	trivial
9.50.a.a.1.3		3	3.2	odd	2
16.50.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q-2.54182e7 q^{2} -8.64745e11 q^{3} +8.31363e13 q^{4} +1.67413e17 q^{5} +2.19803e19 q^{6} -3.42668e20 q^{7} +1.21960e22 q^{8} +5.08484e23 q^{9} +O(q^{10})\)	\(q-2.54182e7 q^{2} -8.64745e11 q^{3} +8.31363e13 q^{4} +1.67413e17 q^{5} +2.19803e19 q^{6} -3.42668e20 q^{7} +1.21960e22 q^{8} +5.08484e23 q^{9} -4.25535e24 q^{10} -2.47212e24 q^{11} -7.18917e25 q^{12} -1.86505e26 q^{13} +8.71003e27 q^{14} -1.44770e29 q^{15} -3.56803e29 q^{16} +8.08684e29 q^{17} -1.29248e31 q^{18} -1.31622e31 q^{19} +1.39181e31 q^{20} +2.96321e32 q^{21} +6.28370e31 q^{22} +3.96809e33 q^{23} -1.05464e34 q^{24} +1.02637e34 q^{25} +4.74062e33 q^{26} -2.32776e35 q^{27} -2.84882e34 q^{28} +4.73835e35 q^{29} +3.67979e36 q^{30} -5.52226e36 q^{31} +2.20354e36 q^{32} +2.13775e36 q^{33} -2.05553e37 q^{34} -5.73673e37 q^{35} +4.22735e37 q^{36} +6.02154e37 q^{37} +3.34559e38 q^{38} +1.61279e38 q^{39} +2.04178e39 q^{40} -4.00631e39 q^{41} -7.53195e39 q^{42} -1.57103e39 q^{43} -2.05523e38 q^{44} +8.51271e40 q^{45} -1.00862e41 q^{46} -3.77976e40 q^{47} +3.08543e41 q^{48} -1.39502e41 q^{49} -2.60885e41 q^{50} -6.99305e41 q^{51} -1.55053e40 q^{52} -7.38411e41 q^{53} +5.91675e42 q^{54} -4.13866e41 q^{55} -4.17919e42 q^{56} +1.13819e43 q^{57} -1.20441e43 q^{58} -3.19771e43 q^{59} -1.20356e43 q^{60} +2.48724e43 q^{61} +1.40366e44 q^{62} -1.74241e44 q^{63} +1.44852e44 q^{64} -3.12234e43 q^{65} -5.43379e43 q^{66} +5.76819e44 q^{67} +6.72310e43 q^{68} -3.43138e45 q^{69} +1.45818e45 q^{70} -1.66436e45 q^{71} +6.20148e45 q^{72} +4.80904e45 q^{73} -1.53057e45 q^{74} -8.87547e45 q^{75} -1.09425e45 q^{76} +8.47118e44 q^{77} -4.09943e45 q^{78} -4.21047e45 q^{79} -5.97335e46 q^{80} +7.96119e46 q^{81} +1.01833e47 q^{82} -1.20169e47 q^{83} +2.46350e46 q^{84} +1.35385e47 q^{85} +3.99327e46 q^{86} -4.09747e47 q^{87} -3.01500e46 q^{88} +8.70490e47 q^{89} -2.16378e48 q^{90} +6.39094e46 q^{91} +3.29892e47 q^{92} +4.77534e48 q^{93} +9.60748e47 q^{94} -2.20352e48 q^{95} -1.90550e48 q^{96} -7.30863e48 q^{97} +3.54589e48 q^{98} -1.25703e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 24225168 q^{2} - 326954692404 q^{3} + 31502767984896 q^{4} + 63\!\cdots\!50 q^{5}+ \cdots + 34\!\cdots\!19 q^{9}+O(q^{10}) \) 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

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