LMFDB - Embedded newform 2.38.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,38,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	2.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:	$17.3428076249$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 756643680 $ x^2 - x - 756643680
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-27506.7$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-262144. q^{2} +1.16218e9 q^{3} +6.87195e10 q^{4} -1.00278e13 q^{5} -3.04659e14 q^{6} -3.32061e15 q^{7} -1.80144e16 q^{8} +9.00385e17 q^{9} +O(q^{10})$	\(q-262144. q^{2} +1.16218e9 q^{3} +6.87195e10 q^{4} -1.00278e13 q^{5} -3.04659e14 q^{6} -3.32061e15 q^{7} -1.80144e16 q^{8} +9.00385e17 q^{9} +2.62873e18 q^{10} -2.20179e19 q^{11} +7.98646e19 q^{12} -2.47054e20 q^{13} +8.70479e20 q^{14} -1.16541e22 q^{15} +4.72237e21 q^{16} +6.99239e22 q^{17} -2.36031e23 q^{18} -8.30820e23 q^{19} -6.89105e23 q^{20} -3.85916e24 q^{21} +5.77187e24 q^{22} -1.05566e25 q^{23} -2.09360e25 q^{24} +2.77971e25 q^{25} +6.47638e25 q^{26} +5.23100e26 q^{27} -2.28191e26 q^{28} -2.42517e26 q^{29} +3.05506e27 q^{30} -1.93516e27 q^{31} -1.23794e27 q^{32} -2.55889e28 q^{33} -1.83301e28 q^{34} +3.32984e28 q^{35} +6.18740e28 q^{36} -8.55331e28 q^{37} +2.17794e29 q^{38} -2.87122e29 q^{39} +1.80645e29 q^{40} +5.59412e29 q^{41} +1.01166e30 q^{42} -3.15675e29 q^{43} -1.51306e30 q^{44} -9.02888e30 q^{45} +2.76735e30 q^{46} +1.56788e30 q^{47} +5.48825e30 q^{48} -7.53564e30 q^{49} -7.28684e30 q^{50} +8.12643e31 q^{51} -1.69774e31 q^{52} +3.66286e31 q^{53} -1.37128e32 q^{54} +2.20791e32 q^{55} +5.98189e31 q^{56} -9.65565e32 q^{57} +6.35743e31 q^{58} +8.04503e32 q^{59} -8.00866e32 q^{60} +1.21434e33 q^{61} +5.07292e32 q^{62} -2.98983e33 q^{63} +3.24519e32 q^{64} +2.47741e33 q^{65} +6.70797e33 q^{66} +1.45851e33 q^{67} +4.80513e33 q^{68} -1.22687e34 q^{69} -8.72898e33 q^{70} -2.91230e34 q^{71} -1.62199e34 q^{72} +3.11895e34 q^{73} +2.24220e34 q^{74} +3.23053e34 q^{75} -5.70935e34 q^{76} +7.31130e34 q^{77} +7.52674e34 q^{78} -8.04771e34 q^{79} -4.73549e34 q^{80} +2.02509e35 q^{81} -1.46647e35 q^{82} +2.48909e35 q^{83} -2.65200e35 q^{84} -7.01182e35 q^{85} +8.27523e34 q^{86} -2.81849e35 q^{87} +3.96640e35 q^{88} -1.00339e36 q^{89} +2.36687e36 q^{90} +8.20372e35 q^{91} -7.25443e35 q^{92} -2.24901e36 q^{93} -4.11010e35 q^{94} +8.33129e36 q^{95} -1.43871e36 q^{96} +2.19237e36 q^{97} +1.97542e36 q^{98} -1.98246e37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 524288 q^{2} + 423071208 q^{3} + 137438953472 q^{4} - 13507530555540 q^{5} - 110905578749952 q^{6} + 31\!\cdots\!56 q^{7}+ \cdots + 99\!\cdots\!06 q^{9}+O(q^{10}) $ 2 * q - 524288 * q^2 + 423071208 * q^3 + 137438953472 * q^4 - 13507530555540 * q^5 - 110905578749952 * q^6 + 3106174162962256 * q^7 - 36028797018963968 * q^8 + 996387550079387706 * q^9	$ 2 q - 524288 q^{2} + 423071208 q^{3} + 137438953472 q^{4} - 13507530555540 q^{5} - 110905578749952 q^{6} + 31\!\cdots\!56 q^{7}+ \cdots - 17\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 524288 * q^2 + 423071208 * q^3 + 137438953472 * q^4 - 13507530555540 * q^5 - 110905578749952 * q^6 + 3106174162962256 * q^7 - 36028797018963968 * q^8 + 996387550079387706 * q^9 + 3540918089951477760 * q^10 + 4002878661541032504 * q^11 + 29073232035827417088 * q^12 - 417717305951174459972 * q^13 - 814264919775577636864 * q^14 - 9082218417464777049360 * q^15 + 9444732965739290427392 * q^16 + 924888511508274921636 * q^17 - 261197017928011010801664 * q^18 - 1502800666863954423438200 * q^19 - 928230431772240185917440 * q^20 - 8609275073860282063267776 * q^21 - 1049330623851012424728576 * q^22 + 4977294427767526272845808 * q^23 - 7621373338799942425116672 * q^24 - 32853923797109170328639650 * q^25 + 109502085451264677634899968 * q^26 + 784953884198822073793762320 * q^27 + 213454663129649024038076416 * q^28 + 1174284943679786618741874780 * q^29 + 2380849064827886514827427840 * q^30 - 5529622970549622212915224256 * q^31 - 2475880078570760549798248448 * q^32 - 44821137705190940628425921184 * q^33 - 242453973960825221057347584 * q^34 + 10934908922823267414476448480 * q^35 + 68471231067720518415591407616 * q^36 - 115976327866820065024925346644 * q^37 + 393950178014384468377783500800 * q^38 - 160983234676250224910988001488 * q^39 + 243330038306502131297141391360 * q^40 + 479903809827585250071775594644 * q^41 + 2256869804962029781193267871744 * q^42 - 3191808379897050809392290082952 * q^43 + 275075727058799801068047826944 * q^44 - 9362941394381803786652901761220 * q^45 - 1304767870472690407268891492352 * q^46 - 11214072446606967601132239964704 * q^47 + 1997897292526372107089784864768 * q^48 + 15205846893444101799554822389554 * q^49 + 8612458999869386346630912409600 * q^50 + 132262288085411921255362031678544 * q^51 - 28705314688536327653923217211392 * q^52 + 53695242990369729463598618231628 * q^53 - 205770951019416013712592029614080 * q^54 + 130245707009259764446614200122320 * q^55 - 55955859211458713757437503995904 * q^56 - 468896146209528218251899751202400 * q^57 - 307831752275993983383470022328320 * q^58 + 58132414930279452353014089908760 * q^59 - 624125297250241482542921243688960 * q^60 + 949379410209793628730917745257884 * q^61 + 1449557483991760165382448547364864 * q^62 - 2372845660625082937916074533710832 * q^63 + 649037107316853453566312041152512 * q^64 + 3071271884553430462753913899952040 * q^65 + 11749592322589573940098084682858496 * q^66 + 3280488273924335151706569871726696 * q^67 + 63557854549986566748857325060096 * q^68 - 23749969120311478380705506108559168 * q^69 - 2866520764664582613100514110341120 * q^70 - 36632636242259358919270327956284976 * q^71 - 17949322397016527579536793958088704 * q^72 - 10722559667485328549057125275606572 * q^73 + 30402498492319679125894030070644736 * q^74 + 77133181870178710270426539420629400 * q^75 - 103271675465402802078425678033715200 * q^76 + 240343208006950469127380344317189312 * q^77 + 42200789070970938959066038662070272 * q^78 + 41775981111170500771329248250783520 * q^79 - 63787509561819694706757832896675840 * q^80 - 34258358055565679771691854070856398 * q^81 - 125803904323442507794815541482356736 * q^82 + 173069025965519133350295483333594888 * q^83 - 591624878151966334961128012970459136 * q^84 - 461083992329885864995977782015209320 * q^85 + 836713415939732487377332491505369088 * q^86 - 1329023474711207186565010011774976080 * q^87 - 72109451394102015051182329546407936 * q^88 - 770863557920750582452392321302299020 * q^89 + 2454438908888823571848338279293255680 * q^90 - 276443184133973152010668401471277216 * q^91 + 342037068637192954123096291371122688 * q^92 + 407692825919874357767105668290130176 * q^93 + 2939701807443336914831209913307365376 * q^94 + 10669607994591022203853874284760756400 * q^95 - 523736787852033289640944563589742592 * q^96 - 6502221928957848822710145562502442044 * q^97 - 3986121528035010622142499360487243776 * q^98 - 17326559760258527834659445830047870888 * 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 $

$2$	−262144.	−0.707107
$2$	−262144.	−0.707107
$3$	1.16218e9	1.73193	0.865967	−	0.500101i	$-0.166704\pi$
$3$	1.16218e9	1.73193	0.865967	+	0.500101i	$0.166704\pi$
$4$	6.87195e10	0.500000
$5$	−1.00278e13	−1.17560	−0.587801	−	0.809006i	$-0.700006\pi$
$5$	−1.00278e13	−1.17560	−0.587801	+	0.809006i	$0.700006\pi$
$6$	−3.04659e14	−1.22466
$7$	−3.32061e15	−0.770734	−0.385367	−	0.922763i	$-0.625925\pi$
$7$	−3.32061e15	−0.770734	−0.385367	+	0.922763i	$0.625925\pi$
$8$	−1.80144e16	−0.353553
$9$	9.00385e17	1.99959
$10$	2.62873e18	0.831276
$11$	−2.20179e19	−1.19402	−0.597010	−	0.802234i	$-0.703645\pi$
$11$	−2.20179e19	−1.19402	−0.597010	+	0.802234i	$0.703645\pi$
$12$	7.98646e19	0.865967
$13$	−2.47054e20	−0.609313	−0.304656	−	0.952462i	$-0.598542\pi$
$13$	−2.47054e20	−0.609313	−0.304656	+	0.952462i	$0.598542\pi$
$14$	8.70479e20	0.544991
$15$	−1.16541e22	−2.03607
$16$	4.72237e21	0.250000
$17$	6.99239e22	1.20593	0.602963	−	0.797769i	$-0.293987\pi$
$17$	6.99239e22	1.20593	0.602963	+	0.797769i	$0.293987\pi$
$18$	−2.36031e23	−1.41393
$19$	−8.30820e23	−1.83048	−0.915241	−	0.402907i	$-0.868000\pi$
$19$	−8.30820e23	−1.83048	−0.915241	+	0.402907i	$0.868000\pi$
$20$	−6.89105e23	−0.587801
$21$	−3.85916e24	−1.33486
$22$	5.77187e24	0.844300
$23$	−1.05566e25	−0.678514	−0.339257	−	0.940694i	$-0.610176\pi$
$23$	−1.05566e25	−0.678514	−0.339257	+	0.940694i	$0.610176\pi$
$24$	−2.09360e25	−0.612331
$25$	2.77971e25	0.382040
$26$	6.47638e25	0.430849
$27$	5.23100e26	1.73123
$28$	−2.28191e26	−0.385367
$29$	−2.42517e26	−0.213983	−0.106991	−	0.994260i	$-0.534122\pi$
$29$	−2.42517e26	−0.213983	−0.106991	+	0.994260i	$0.534122\pi$
$30$	3.05506e27	1.43972
$31$	−1.93516e27	−0.497195	−0.248597	−	0.968607i	$-0.579970\pi$
$31$	−1.93516e27	−0.497195	−0.248597	+	0.968607i	$0.579970\pi$
$32$	−1.23794e27	−0.176777
$33$	−2.55889e28	−2.06796
$34$	−1.83301e28	−0.852718
$35$	3.32984e28	0.906077
$36$	6.18740e28	0.999797
$37$	−8.55331e28	−0.832535	−0.416268	−	0.909242i	$-0.636662\pi$
$37$	−8.55331e28	−0.832535	−0.416268	+	0.909242i	$0.636662\pi$
$38$	2.17794e29	1.29435
$39$	−2.87122e29	−1.05529
$40$	1.80645e29	0.415638
$41$	5.59412e29	0.815137	0.407569	−	0.913175i	$-0.366377\pi$
$41$	5.59412e29	0.815137	0.407569	+	0.913175i	$0.366377\pi$
$42$	1.01166e30	0.943889
$43$	−3.15675e29	−0.190579	−0.0952893	−	0.995450i	$-0.530378\pi$
$43$	−3.15675e29	−0.190579	−0.0952893	+	0.995450i	$0.530378\pi$
$44$	−1.51306e30	−0.597010
$45$	−9.02888e30	−2.35073
$46$	2.76735e30	0.479782
$47$	1.56788e30	0.182601	0.0913003	−	0.995823i	$-0.470898\pi$
$47$	1.56788e30	0.182601	0.0913003	+	0.995823i	$0.470898\pi$
$48$	5.48825e30	0.432983
$49$	−7.53564e30	−0.405969
$50$	−7.28684e30	−0.270143
$51$	8.12643e31	2.08858
$52$	−1.69774e31	−0.304656
$53$	3.66286e31	0.462080	0.231040	−	0.972944i	$-0.425787\pi$
$53$	3.66286e31	0.462080	0.231040	+	0.972944i	$0.425787\pi$
$54$	−1.37128e32	−1.22417
$55$	2.20791e32	1.40369
$56$	5.98189e31	0.272496
$57$	−9.65565e32	−3.17027
$58$	6.35743e31	0.151309
$59$	8.04503e32	1.39561	0.697807	−	0.716286i	$-0.254159\pi$
$59$	8.04503e32	1.39561	0.697807	+	0.716286i	$0.254159\pi$
$60$	−8.00866e32	−1.01803
$61$	1.21434e33	1.13694	0.568470	−	0.822704i	$-0.307536\pi$
$61$	1.21434e33	1.13694	0.568470	+	0.822704i	$0.307536\pi$
$62$	5.07292e32	0.351570
$63$	−2.98983e33	−1.54116
$64$	3.24519e32	0.125000
$65$	2.47741e33	0.716310
$66$	6.70797e33	1.46227
$67$	1.45851e33	0.240727	0.120364	−	0.992730i	$-0.461594\pi$
$67$	1.45851e33	0.240727	0.120364	+	0.992730i	$0.461594\pi$
$68$	4.80513e33	0.602963
$69$	−1.22687e34	−1.17514
$70$	−8.72898e33	−0.640693
$71$	−2.91230e34	−1.64421	−0.822105	−	0.569336i	$-0.807200\pi$
$71$	−2.91230e34	−1.64421	−0.822105	+	0.569336i	$0.807200\pi$
$72$	−1.62199e34	−0.706963
$73$	3.11895e34	1.05326	0.526629	−	0.850095i	$-0.323456\pi$
$73$	3.11895e34	1.05326	0.526629	+	0.850095i	$0.323456\pi$
$74$	2.24220e34	0.588691
$75$	3.23053e34	0.661669
$76$	−5.70935e34	−0.915241
$77$	7.31130e34	0.920272
$78$	7.52674e34	0.746202
$79$	−8.04771e34	−0.630334	−0.315167	−	0.949036i	$-0.602061\pi$
$79$	−8.04771e34	−0.630334	−0.315167	+	0.949036i	$0.602061\pi$
$80$	−4.73549e34	−0.293901
$81$	2.02509e35	0.998784
$82$	−1.46647e35	−0.576389
$83$	2.48909e35	0.781800	0.390900	−	0.920433i	$-0.372164\pi$
$83$	2.48909e35	0.781800	0.390900	+	0.920433i	$0.372164\pi$
$84$	−2.65200e35	−0.667430
$85$	−7.01182e35	−1.41769
$86$	8.27523e34	0.134759
$87$	−2.81849e35	−0.370604
$88$	3.96640e35	0.422150
$89$	−1.00339e36	−0.866470	−0.433235	−	0.901281i	$-0.642628\pi$
$89$	−1.00339e36	−0.866470	−0.433235	+	0.901281i	$0.642628\pi$
$90$	2.36687e36	1.66222
$91$	8.20372e35	0.469618
$92$	−7.25443e35	−0.339257
$93$	−2.24901e36	−0.861108
$94$	−4.11010e35	−0.129118
$95$	8.33129e36	2.15192
$96$	−1.43871e36	−0.306166
$97$	2.19237e36	0.385156	0.192578	−	0.981282i	$-0.438315\pi$
$97$	2.19237e36	0.385156	0.192578	+	0.981282i	$0.438315\pi$
$98$	1.97542e36	0.287063
$99$	−1.98246e37	−2.38756
$100$	1.91020e36	0.191020
$101$	7.59676e36	0.631950	0.315975	−	0.948767i	$-0.397668\pi$
$101$	7.59676e36	0.631950	0.315975	+	0.948767i	$0.397668\pi$
$102$	−2.13030e37	−1.47685
$103$	−1.64045e37	−0.949458	−0.474729	−	0.880132i	$-0.657454\pi$
$103$	−1.64045e37	−0.949458	−0.474729	+	0.880132i	$0.657454\pi$
$104$	4.45053e36	0.215425
$105$	3.86989e37	1.56926
$106$	−9.60197e36	−0.326740
$107$	4.91223e37	1.40501	0.702504	−	0.711680i	$-0.252065\pi$
$107$	4.91223e37	1.40501	0.702504	+	0.711680i	$0.252065\pi$
$108$	3.59472e37	0.865616
$109$	3.28303e37	0.666630	0.333315	−	0.942816i	$-0.391833\pi$
$109$	3.28303e37	0.666630	0.333315	+	0.942816i	$0.391833\pi$
$110$	−5.78791e37	−0.992561
$111$	−9.94052e37	−1.44190
$112$	−1.56812e37	−0.192684
$113$	−1.12641e38	−1.17421	−0.587104	−	0.809512i	$-0.699732\pi$
$113$	−1.12641e38	−1.17421	−0.587104	+	0.809512i	$0.699732\pi$
$114$	2.53117e38	2.24172
$115$	1.05859e38	0.797662
$116$	−1.66656e37	−0.106991
$117$	−2.22444e38	−1.21838
$118$	−2.10896e38	−0.986848
$119$	−2.32190e38	−0.929448
$120$	2.09942e38	0.719858
$121$	1.44750e38	0.425684
$122$	−3.18331e38	−0.803937
$123$	6.50139e38	1.41176
$124$	−1.32983e38	−0.248597
$125$	4.50875e38	0.726475
$126$	7.83766e38	1.08976
$127$	−2.82173e38	−0.338959	−0.169479	−	0.985534i	$-0.554209\pi$
$127$	−2.82173e38	−0.338959	−0.169479	+	0.985534i	$0.554209\pi$
$128$	−8.50706e37	−0.0883883
$129$	−3.66872e38	−0.330069
$130$	−6.49438e38	−0.506507
$131$	3.02759e38	0.204917	0.102459	−	0.994737i	$-0.467329\pi$
$131$	3.02759e38	0.204917	0.102459	+	0.994737i	$0.467329\pi$
$132$	−1.75845e39	−1.03398
$133$	2.75883e39	1.41081
$134$	−3.82339e38	−0.170220
$135$	−5.24554e39	−2.03524
$136$	−1.25964e39	−0.426359
$137$	2.26804e39	0.670377	0.335189	−	0.942151i	$-0.391200\pi$
$137$	2.26804e39	0.670377	0.335189	+	0.942151i	$0.391200\pi$
$138$	3.21616e39	0.830950
$139$	−4.94024e39	−1.11680	−0.558398	−	0.829573i	$-0.688584\pi$
$139$	−4.94024e39	−1.11680	−0.558398	+	0.829573i	$0.688584\pi$
$140$	2.28825e39	0.453038
$141$	1.82216e39	0.316252
$142$	7.63443e39	1.16263
$143$	5.43962e39	0.727532
$144$	4.25195e39	0.499899
$145$	2.43191e39	0.251559
$146$	−8.17613e39	−0.744767
$147$	−8.75779e39	−0.703111
$148$	−5.87779e39	−0.416268
$149$	−5.44741e38	−0.0340600	−0.0170300	−	0.999855i	$-0.505421\pi$
$149$	−5.44741e38	−0.0340600	−0.0170300	+	0.999855i	$0.505421\pi$
$150$	−8.46864e39	−0.467870
$151$	−3.86430e40	−1.88798	−0.943989	−	0.329976i	$-0.892959\pi$
$151$	−3.86430e40	−1.88798	−0.943989	+	0.329976i	$0.892959\pi$
$152$	1.49667e40	0.647173
$153$	6.29584e40	2.41136
$154$	−1.91661e40	−0.650731
$155$	1.94054e40	0.584503
$156$	−1.97309e40	−0.527645
$157$	−8.04588e40	−1.91175	−0.955873	−	0.293781i	$-0.905086\pi$
$157$	−8.04588e40	−1.91175	−0.955873	+	0.293781i	$0.905086\pi$
$158$	2.10966e40	0.445714
$159$	4.25691e40	0.800291
$160$	1.24138e40	0.207819
$161$	3.50544e40	0.522954
$162$	−5.30865e40	−0.706247
$163$	3.58379e40	0.425472	0.212736	−	0.977110i	$-0.431763\pi$
$163$	3.58379e40	0.425472	0.212736	+	0.977110i	$0.431763\pi$
$164$	3.84425e40	0.407569
$165$	2.56600e41	2.43110
$166$	−6.52500e40	−0.552816
$167$	−2.31369e41	−1.75409	−0.877043	−	0.480411i	$-0.840487\pi$
$167$	−2.31369e41	−1.75409	−0.877043	+	0.480411i	$0.840487\pi$
$168$	6.95205e40	0.471944
$169$	−1.03365e41	−0.628738
$170$	1.83811e41	1.00246
$171$	−7.48058e41	−3.66022
$172$	−2.16930e40	−0.0952893
$173$	2.42959e41	0.958693	0.479346	−	0.877626i	$-0.340874\pi$
$173$	2.42959e41	0.958693	0.479346	+	0.877626i	$0.340874\pi$
$174$	7.38850e40	0.262057
$175$	−9.23034e40	−0.294452
$176$	−1.03977e41	−0.298505
$177$	9.34980e41	2.41711
$178$	2.63032e41	0.612687
$179$	1.97163e41	0.414042	0.207021	−	0.978336i	$-0.433623\pi$
$179$	1.97163e41	0.414042	0.207021	+	0.978336i	$0.433623\pi$
$180$	−6.20460e41	−1.17536
$181$	−8.74626e41	−1.49544	−0.747719	−	0.664015i	$-0.768851\pi$
$181$	−8.74626e41	−1.49544	−0.747719	+	0.664015i	$0.768851\pi$
$182$	−2.15056e41	−0.332070
$183$	1.41128e42	1.96910
$184$	1.90171e41	0.239891
$185$	8.57709e41	0.978730
$186$	5.89566e41	0.608895
$187$	−1.53958e42	−1.43990
$188$	1.07744e41	0.0913003
$189$	−1.73701e42	−1.33432
$190$	−2.18400e42	−1.52164
$191$	6.05957e41	0.383111	0.191555	−	0.981482i	$-0.438647\pi$
$191$	6.05957e41	0.383111	0.191555	+	0.981482i	$0.438647\pi$
$192$	3.77150e41	0.216492
$193$	−1.72991e41	−0.0902016	−0.0451008	−	0.998982i	$-0.514361\pi$
$193$	−1.72991e41	−0.0902016	−0.0451008	+	0.998982i	$0.514361\pi$
$194$	−5.74716e41	−0.272346
$195$	2.87920e42	1.24060
$196$	−5.17845e41	−0.202984
$197$	−7.91100e41	−0.282232	−0.141116	−	0.989993i	$-0.545069\pi$
$197$	−7.91100e41	−0.282232	−0.141116	+	0.989993i	$0.545069\pi$
$198$	5.19690e42	1.68826
$199$	−2.54348e42	−0.752744	−0.376372	−	0.926469i	$-0.622828\pi$
$199$	−2.54348e42	−0.752744	−0.376372	+	0.926469i	$0.622828\pi$
$200$	−5.00748e41	−0.135072
$201$	1.69505e42	0.416923
$202$	−1.99145e42	−0.446856
$203$	8.05304e41	0.164924
$204$	5.58444e42	1.04429
$205$	−5.60967e42	−0.958277
$206$	4.30035e42	0.671368
$207$	−9.50500e42	−1.35675
$208$	−1.16668e42	−0.152328
$209$	1.82929e43	2.18563
$210$	−1.01447e43	−1.10964
$211$	1.20546e43	1.20761	0.603807	−	0.797131i	$-0.293650\pi$
$211$	1.20546e43	1.20761	0.603807	+	0.797131i	$0.293650\pi$
$212$	2.51710e42	0.231040
$213$	−3.38463e43	−2.84766
$214$	−1.28771e43	−0.993490
$215$	3.16553e42	0.224045
$216$	−9.42333e42	−0.612083
$217$	6.42593e42	0.383205
$218$	−8.60626e42	−0.471378
$219$	3.62479e43	1.82417
$220$	1.51727e43	0.701846
$221$	−1.72750e43	−0.734786
$222$	2.60585e43	1.01957
$223$	2.30674e43	0.830536	0.415268	−	0.909699i	$-0.363688\pi$
$223$	2.30674e43	0.830536	0.415268	+	0.909699i	$0.363688\pi$
$224$	4.11072e42	0.136248
$225$	2.50281e43	0.763926
$226$	2.95281e43	0.830290
$227$	−3.57525e43	−0.926463	−0.463231	−	0.886237i	$-0.653310\pi$
$227$	−3.57525e43	−0.926463	−0.463231	+	0.886237i	$0.653310\pi$
$228$	−6.63531e43	−1.58514
$229$	−6.86230e43	−1.51187	−0.755933	−	0.654649i	$-0.772817\pi$
$229$	−6.86230e43	−1.51187	−0.755933	+	0.654649i	$0.772817\pi$
$230$	−2.77504e43	−0.564033
$231$	8.49707e43	1.59385
$232$	4.36879e42	0.0756543
$233$	−7.73057e43	−1.23631	−0.618154	−	0.786057i	$-0.712119\pi$
$233$	−7.73057e43	−1.23631	−0.618154	+	0.786057i	$0.712119\pi$
$234$	5.83124e43	0.861524
$235$	−1.57224e43	−0.214666
$236$	5.52850e43	0.697807
$237$	−9.35291e43	−1.09170
$238$	6.08673e43	0.657219
$239$	−8.60047e43	−0.859332	−0.429666	−	0.902988i	$-0.641369\pi$
$239$	−8.60047e43	−0.859332	−0.429666	+	0.902988i	$0.641369\pi$
$240$	−5.50351e43	−0.509016
$241$	1.68453e44	1.44266	0.721328	−	0.692593i	$-0.243532\pi$
$241$	1.68453e44	1.44266	0.721328	+	0.692593i	$0.243532\pi$
$242$	−3.79452e43	−0.301004
$243$	−1.90988e41	−0.00140375
$244$	8.34486e43	0.568470
$245$	7.55659e43	0.477258
$246$	−1.70430e44	−0.998268
$247$	2.05258e44	1.11534
$248$	3.48608e43	0.175785
$249$	2.89278e44	1.35403
$250$	−1.18194e44	−0.513695
$251$	−1.93198e44	−0.779899	−0.389949	−	0.920836i	$-0.627508\pi$
$251$	−1.93198e44	−0.779899	−0.389949	+	0.920836i	$0.627508\pi$
$252$	−2.05460e44	−0.770578
$253$	2.32434e44	0.810159
$254$	7.39700e43	0.239680
$255$	−8.14902e44	−2.45534
$256$	2.23007e43	0.0625000
$257$	−6.84920e43	−0.178598	−0.0892991	−	0.996005i	$-0.528463\pi$
$257$	−6.84920e43	−0.178598	−0.0892991	+	0.996005i	$0.528463\pi$
$258$	9.61734e43	0.233394
$259$	2.84023e44	0.641663
$260$	1.70246e44	0.358155
$261$	−2.18358e44	−0.427879
$262$	−7.93665e43	−0.144898
$263$	3.42473e44	0.582700	0.291350	−	0.956617i	$-0.405896\pi$
$263$	3.42473e44	0.582700	0.291350	+	0.956617i	$0.405896\pi$
$264$	4.60968e44	0.731136
$265$	−3.67304e44	−0.543222
$266$	−7.23211e44	−0.997597
$267$	−1.16612e45	−1.50067
$268$	1.00228e44	0.120364
$269$	1.17310e45	1.31497	0.657486	−	0.753467i	$-0.271620\pi$
$269$	1.17310e45	1.31497	0.657486	+	0.753467i	$0.271620\pi$
$270$	1.37509e45	1.43913
$271$	1.48009e45	1.44662	0.723311	−	0.690522i	$-0.242619\pi$
$271$	1.48009e45	1.44662	0.723311	+	0.690522i	$0.242619\pi$
$272$	3.30206e44	0.301481
$273$	9.53422e44	0.813348
$274$	−5.94552e44	−0.474028
$275$	−6.12034e44	−0.456164
$276$	−8.43098e44	−0.587571
$277$	−2.54630e45	−1.65972	−0.829858	−	0.557975i	$-0.811578\pi$
$277$	−2.54630e45	−1.65972	−0.829858	+	0.557975i	$0.811578\pi$
$278$	1.29505e45	0.789694
$279$	−1.74239e45	−0.994188
$280$	−5.99851e44	−0.320347
$281$	−2.93334e45	−1.46655	−0.733273	−	0.679934i	$-0.762008\pi$
$281$	−2.93334e45	−1.46655	−0.733273	+	0.679934i	$0.762008\pi$
$282$	−4.77669e44	−0.223624
$283$	4.02101e44	0.176314	0.0881568	−	0.996107i	$-0.471902\pi$
$283$	4.02101e44	0.176314	0.0881568	+	0.996107i	$0.471902\pi$
$284$	−2.00132e45	−0.822105
$285$	9.68249e45	3.72698
$286$	−1.42596e45	−0.514443
$287$	−1.85759e45	−0.628254
$288$	−1.11462e45	−0.353482
$289$	1.52725e45	0.454256
$290$	−6.37510e44	−0.177879
$291$	2.54793e45	0.667064
$292$	2.14332e45	0.526629
$293$	5.50714e45	1.27021	0.635105	−	0.772426i	$-0.280957\pi$
$293$	5.50714e45	1.27021	0.635105	+	0.772426i	$0.280957\pi$
$294$	2.29580e45	0.497175
$295$	−8.06739e45	−1.64069
$296$	1.54083e45	0.294346
$297$	−1.15176e46	−2.06713
$298$	1.42801e44	0.0240840
$299$	2.60805e45	0.413427
$300$	2.22000e45	0.330834
$301$	1.04824e45	0.146885
$302$	1.01300e46	1.33500
$303$	8.82882e45	1.09450
$304$	−3.92344e45	−0.457620
$305$	−1.21771e46	−1.33659
$306$	−1.65042e46	−1.70509
$307$	6.23539e45	0.606462	0.303231	−	0.952917i	$-0.401935\pi$
$307$	6.23539e45	0.606462	0.303231	+	0.952917i	$0.401935\pi$
$308$	5.02429e45	0.460136
$309$	−1.90651e46	−1.64440
$310$	−5.08702e45	−0.413306
$311$	1.00705e46	0.770872	0.385436	−	0.922735i	$-0.374051\pi$
$311$	1.00705e46	0.770872	0.385436	+	0.922735i	$0.374051\pi$
$312$	5.17234e45	0.373101
$313$	−2.62521e46	−1.78482	−0.892408	−	0.451230i	$-0.850985\pi$
$313$	−2.62521e46	−1.78482	−0.892408	+	0.451230i	$0.850985\pi$
$314$	2.10918e46	1.35181
$315$	2.99814e46	1.81179
$316$	−5.53034e45	−0.315167
$317$	1.16596e46	0.626741	0.313371	−	0.949631i	$-0.398542\pi$
$317$	1.16596e46	0.626741	0.313371	+	0.949631i	$0.398542\pi$
$318$	−1.11592e46	−0.565891
$319$	5.33971e45	0.255500
$320$	−3.25421e45	−0.146950
$321$	5.70891e46	2.43338
$322$	−9.18929e45	−0.369784
$323$	−5.80942e46	−2.20742
$324$	1.39163e46	0.499392
$325$	−6.86739e45	−0.232782
$326$	−9.39468e45	−0.300854
$327$	3.81548e46	1.15456
$328$	−1.00775e46	−0.288194
$329$	−5.20632e45	−0.140736
$330$	−6.72661e46	−1.71905
$331$	2.95352e46	0.713712	0.356856	−	0.934159i	$-0.383849\pi$
$331$	2.95352e46	0.713712	0.356856	+	0.934159i	$0.383849\pi$
$332$	1.71049e46	0.390900
$333$	−7.70128e46	−1.66473
$334$	6.06521e46	1.24033
$335$	−1.46256e46	−0.282999
$336$	−1.82244e46	−0.333715
$337$	−1.12287e46	−0.194615	−0.0973074	−	0.995254i	$-0.531023\pi$
$337$	−1.12287e46	−0.194615	−0.0973074	+	0.995254i	$0.531023\pi$
$338$	2.70965e46	0.444585
$339$	−1.30909e47	−2.03365
$340$	−4.81849e46	−0.708844
$341$	4.26083e46	0.593660
$342$	1.96099e47	2.58817
$343$	8.66606e46	1.08363
$344$	5.68670e45	0.0673797
$345$	1.23028e47	1.38150
$346$	−6.36901e46	−0.677898
$347$	−3.38484e46	−0.341541	−0.170770	−	0.985311i	$-0.554626\pi$
$347$	−3.38484e46	−0.341541	−0.170770	+	0.985311i	$0.554626\pi$
$348$	−1.93685e46	−0.185302
$349$	8.62093e46	0.782138	0.391069	−	0.920361i	$-0.372105\pi$
$349$	8.62093e46	0.782138	0.391069	+	0.920361i	$0.372105\pi$
$350$	2.41968e46	0.208209
$351$	−1.29234e47	−1.05486
$352$	2.72569e46	0.211075
$353$	−1.39430e47	−1.02453	−0.512263	−	0.858828i	$-0.671193\pi$
$353$	−1.39430e47	−1.02453	−0.512263	+	0.858828i	$0.671193\pi$
$354$	−2.45099e47	−1.70916
$355$	2.92040e47	1.93294
$356$	−6.89523e46	−0.433235
$357$	−2.69847e47	−1.60974
$358$	−5.16852e46	−0.292772
$359$	−2.55899e47	−1.37664	−0.688321	−	0.725407i	$-0.741652\pi$
$359$	−2.55899e47	−1.37664	−0.688321	+	0.725407i	$0.741652\pi$
$360$	1.62650e47	0.831108
$361$	4.84254e47	2.35066
$362$	2.29278e47	1.05743
$363$	1.68225e47	0.737257
$364$	5.63755e46	0.234809
$365$	−3.12762e47	−1.23821
$366$	−3.69959e47	−1.39237
$367$	−3.41199e47	−1.22091	−0.610457	−	0.792049i	$-0.709014\pi$
$367$	−3.41199e47	−1.22091	−0.610457	+	0.792049i	$0.709014\pi$
$368$	−4.98521e46	−0.169628
$369$	5.03687e47	1.62994
$370$	−2.24843e47	−0.692067
$371$	−1.21629e47	−0.356141
$372$	−1.54551e47	−0.430554
$373$	4.46224e47	1.18288	0.591438	−	0.806351i	$-0.298560\pi$
$373$	4.46224e47	1.18288	0.591438	+	0.806351i	$0.298560\pi$
$374$	4.03591e47	1.01816
$375$	5.23999e47	1.25821
$376$	−2.82444e46	−0.0645590
$377$	5.99148e46	0.130382
$378$	4.55348e47	0.943506
$379$	−7.46655e47	−1.47331	−0.736655	−	0.676268i	$-0.763596\pi$
$379$	−7.46655e47	−1.47331	−0.736655	+	0.676268i	$0.763596\pi$
$380$	5.72522e47	1.07596
$381$	−3.27937e47	−0.587054
$382$	−1.58848e47	−0.270900
$383$	−6.01186e47	−0.976858	−0.488429	−	0.872604i	$-0.662430\pi$
$383$	−6.01186e47	−0.976858	−0.488429	+	0.872604i	$0.662430\pi$
$384$	−9.88676e46	−0.153083
$385$	−7.33162e47	−1.08187
$386$	4.53487e46	0.0637822
$387$	−2.84229e47	−0.381080
$388$	1.50658e47	0.192578
$389$	5.11575e47	0.623508	0.311754	−	0.950163i	$-0.399084\pi$
$389$	5.11575e47	0.623508	0.311754	+	0.950163i	$0.399084\pi$
$390$	−7.54766e47	−0.877237
$391$	−7.38158e47	−0.818237
$392$	1.35750e47	0.143532
$393$	3.51861e47	0.354903
$394$	2.07382e47	0.199568
$395$	8.07007e47	0.741022
$396$	−1.36234e48	−1.19378
$397$	1.07709e48	0.900795	0.450398	−	0.892828i	$-0.351282\pi$
$397$	1.07709e48	0.900795	0.450398	+	0.892828i	$0.351282\pi$
$398$	6.66759e47	0.532270
$399$	3.20627e48	2.44344
$400$	1.31268e47	0.0955101
$401$	−1.61629e48	−1.12292	−0.561458	−	0.827505i	$-0.689759\pi$
$401$	−1.61629e48	−1.12292	−0.561458	+	0.827505i	$0.689759\pi$
$402$	−4.44348e47	−0.294809
$403$	4.78090e47	0.302947
$404$	5.22045e47	0.315975
$405$	−2.03072e48	−1.17417
$406$	−2.11106e47	−0.116619
$407$	1.88326e48	0.994064
$408$	−1.46393e48	−0.738426
$409$	−7.70085e47	−0.371242	−0.185621	−	0.982621i	$-0.559430\pi$
$409$	−7.70085e47	−0.371242	−0.185621	+	0.982621i	$0.559430\pi$
$410$	1.47054e48	0.677604
$411$	2.63587e48	1.16105
$412$	−1.12731e48	−0.474729
$413$	−2.67144e48	−1.07565
$414$	2.49168e48	0.959369
$415$	−2.49601e48	−0.919086
$416$	3.05838e47	0.107712
$417$	−5.74146e48	−1.93422
$418$	−4.79538e48	−1.54548
$419$	−2.95178e47	−0.0910175	−0.0455087	−	0.998964i	$-0.514491\pi$
$419$	−2.95178e47	−0.0910175	−0.0455087	+	0.998964i	$0.514491\pi$
$420$	2.65937e48	0.784632
$421$	6.03774e48	1.70473	0.852365	−	0.522947i	$-0.175167\pi$
$421$	6.03774e48	1.70473	0.852365	+	0.522947i	$0.175167\pi$
$422$	−3.16005e48	−0.853912
$423$	1.41169e48	0.365127
$424$	−6.59842e47	−0.163370
$425$	1.94368e48	0.460712
$426$	8.87261e48	2.01360
$427$	−4.03234e48	−0.876278
$428$	3.37566e48	0.702504
$429$	6.32184e48	1.26004
$430$	−8.29823e47	−0.158423
$431$	−7.52239e48	−1.37571	−0.687854	−	0.725849i	$-0.741447\pi$
$431$	−7.52239e48	−1.37571	−0.687854	+	0.725849i	$0.741447\pi$
$432$	2.47027e48	0.432808
$433$	−9.12185e48	−1.53129	−0.765644	−	0.643265i	$-0.777579\pi$
$433$	−9.12185e48	−1.53129	−0.765644	+	0.643265i	$0.777579\pi$
$434$	−1.68452e48	−0.270967
$435$	2.82632e48	0.435683
$436$	2.25608e48	0.333315
$437$	8.77063e48	1.24201
$438$	−9.50216e48	−1.28989
$439$	9.21085e48	1.19869	0.599344	−	0.800492i	$-0.295428\pi$
$439$	9.21085e48	1.19869	0.599344	+	0.800492i	$0.295428\pi$
$440$	−3.97742e48	−0.496280
$441$	−6.78498e48	−0.811773
$442$	4.52854e48	0.519572
$443$	−1.02129e48	−0.112377	−0.0561887	−	0.998420i	$-0.517895\pi$
$443$	−1.02129e48	−0.112377	−0.0561887	+	0.998420i	$0.517895\pi$
$444$	−6.83107e48	−0.720948
$445$	1.00618e49	1.01862
$446$	−6.04698e48	−0.587278
$447$	−6.33089e47	−0.0589896
$448$	−1.07760e48	−0.0963418
$449$	1.62214e49	1.39165	0.695825	−	0.718211i	$-0.255039\pi$
$449$	1.62214e49	1.39165	0.695825	+	0.718211i	$0.255039\pi$
$450$	−6.56096e48	−0.540177
$451$	−1.23171e49	−0.973290
$452$	−7.74062e48	−0.587104
$453$	−4.49102e49	−3.26985
$454$	9.37230e48	0.655108
$455$	−8.22652e48	−0.552084
$456$	1.73941e49	1.12086
$457$	1.55439e49	0.961858	0.480929	−	0.876759i	$-0.340299\pi$
$457$	1.55439e49	0.961858	0.480929	+	0.876759i	$0.340299\pi$
$458$	1.79891e49	1.06905
$459$	3.65772e49	2.08774
$460$	7.27460e48	0.398831
$461$	5.47057e48	0.288115	0.144057	−	0.989569i	$-0.453985\pi$
$461$	5.47057e48	0.288115	0.144057	+	0.989569i	$0.453985\pi$
$462$	−2.22746e49	−1.12702
$463$	9.95251e48	0.483821	0.241910	−	0.970299i	$-0.422226\pi$
$463$	9.95251e48	0.483821	0.241910	+	0.970299i	$0.422226\pi$
$464$	−1.14525e48	−0.0534957
$465$	2.25527e49	1.01232
$466$	2.02652e49	0.874202
$467$	−8.97489e48	−0.372106	−0.186053	−	0.982540i	$-0.559570\pi$
$467$	−8.97489e48	−0.372106	−0.186053	+	0.982540i	$0.559570\pi$
$468$	−1.52862e49	−0.609189
$469$	−4.84314e48	−0.185537
$470$	4.12152e48	0.151791
$471$	−9.35079e49	−3.31102
$472$	−1.44926e49	−0.493424
$473$	6.95051e48	0.227555
$474$	2.45181e49	0.771946
$475$	−2.30944e49	−0.699318
$476$	−1.59560e49	−0.464724
$477$	3.29799e49	0.923972
$478$	2.25456e49	0.607640
$479$	−2.92109e49	−0.757421	−0.378711	−	0.925515i	$-0.623632\pi$
$479$	−2.92109e49	−0.757421	−0.378711	+	0.925515i	$0.623632\pi$
$480$	1.44271e49	0.359929
$481$	2.11313e49	0.507274
$482$	−4.41589e49	−1.02011
$483$	4.07396e49	0.905722
$484$	9.94711e48	0.212842
$485$	−2.19846e49	−0.452790
$486$	5.00665e46	0.000992604 0
$487$	7.31257e48	0.139568	0.0697838	−	0.997562i	$-0.477769\pi$
$487$	7.31257e48	0.139568	0.0697838	+	0.997562i	$0.477769\pi$
$488$	−2.18755e49	−0.401969
$489$	4.16501e49	0.736890
$490$	−1.98091e49	−0.337472
$491$	−1.60707e49	−0.263649	−0.131825	−	0.991273i	$-0.542084\pi$
$491$	−1.60707e49	−0.263649	−0.131825	+	0.991273i	$0.542084\pi$
$492$	4.46772e49	0.705882
$493$	−1.69577e49	−0.258047
$494$	−5.38071e49	−0.788662
$495$	1.98797e50	2.80682
$496$	−9.13855e48	−0.124299
$497$	9.67064e49	1.26725
$498$	−7.58324e49	−0.957441
$499$	2.11587e49	0.257412	0.128706	−	0.991683i	$-0.458918\pi$
$499$	2.11587e49	0.257412	0.128706	+	0.991683i	$0.458918\pi$
$500$	3.09839e49	0.363237
$501$	−2.68894e50	−3.03796
$502$	5.06456e49	0.551472
$503$	−3.29392e48	−0.0345705	−0.0172853	−	0.999851i	$-0.505502\pi$
$503$	−3.29392e48	−0.0345705	−0.0172853	+	0.999851i	$0.505502\pi$
$504$	5.38600e49	0.544881
$505$	−7.61787e49	−0.742922
$506$	−6.09312e49	−0.572869
$507$	−1.20129e50	−1.08893
$508$	−1.93908e49	−0.169479
$509$	2.11519e50	1.78267	0.891333	−	0.453349i	$-0.149771\pi$
$509$	2.11519e50	1.78267	0.891333	+	0.453349i	$0.149771\pi$
$510$	2.13622e50	1.73619
$511$	−1.03568e50	−0.811783
$512$	−5.84601e48	−0.0441942
$513$	−4.34602e50	−3.16899
$514$	1.79548e49	0.126288
$515$	1.64501e50	1.11618
$516$	−2.52113e49	−0.165035
$517$	−3.45214e49	−0.218029
$518$	−7.44548e49	−0.453724
$519$	2.82362e50	1.66039
$520$	−4.46290e49	−0.253254
$521$	2.89219e50	1.58391	0.791954	−	0.610581i	$-0.209064\pi$
$521$	2.89219e50	1.58391	0.791954	+	0.610581i	$0.209064\pi$
$522$	5.72414e49	0.302556
$523$	−4.61612e49	−0.235503	−0.117751	−	0.993043i	$-0.537569\pi$
$523$	−4.61612e49	−0.235503	−0.117751	+	0.993043i	$0.537569\pi$
$524$	2.08054e49	0.102459
$525$	−1.07273e50	−0.509971
$526$	−8.97773e49	−0.412031
$527$	−1.35314e50	−0.599580
$528$	−1.20840e50	−0.516991
$529$	−1.30622e50	−0.539619
$530$	9.62866e49	0.384116
$531$	7.24363e50	2.79066
$532$	1.89586e50	0.705407
$533$	−1.38205e50	−0.496674
$534$	3.05691e50	1.06113
$535$	−4.92588e50	−1.65173
$536$	−2.62741e49	−0.0851099
$537$	2.29140e50	0.717094
$538$	−3.07520e50	−0.929826
$539$	1.65919e50	0.484735
$540$	−3.60471e50	−1.01762
$541$	4.12287e50	1.12473	0.562367	−	0.826888i	$-0.309891\pi$
$541$	4.12287e50	1.12473	0.562367	+	0.826888i	$0.309891\pi$
$542$	−3.87996e50	−1.02292
$543$	−1.01648e51	−2.59000
$544$	−8.65616e49	−0.213179
$545$	−3.29215e50	−0.783691
$546$	−2.49934e50	−0.575124
$547$	−3.85047e50	−0.856540	−0.428270	−	0.903651i	$-0.640877\pi$
$547$	−3.85047e50	−0.856540	−0.428270	+	0.903651i	$0.640877\pi$
$548$	1.55858e50	0.335189
$549$	1.09337e51	2.27342
$550$	1.60441e50	0.322557
$551$	2.01488e50	0.391691
$552$	2.21013e50	0.415475
$553$	2.67233e50	0.485820
$554$	6.67497e50	1.17360
$555$	9.96815e50	1.69510
$556$	−3.39490e50	−0.558398
$557$	−5.73633e50	−0.912668	−0.456334	−	0.889809i	$-0.650838\pi$
$557$	−5.73633e50	−0.912668	−0.456334	+	0.889809i	$0.650838\pi$
$558$	4.56758e50	0.702997
$559$	7.79889e49	0.116122
$560$	1.57247e50	0.226519
$561$	−1.78927e51	−2.49381
$562$	7.68958e50	1.03700
$563$	−6.88670e50	−0.898682	−0.449341	−	0.893360i	$-0.648341\pi$
$563$	−6.88670e50	−0.898682	−0.449341	+	0.893360i	$0.648341\pi$
$564$	1.25218e50	0.158126
$565$	1.12954e51	1.38040
$566$	−1.05408e50	−0.124673
$567$	−6.72454e50	−0.769797
$568$	5.24634e50	0.581316
$569$	−4.67962e50	−0.501919	−0.250960	−	0.967998i	$-0.580746\pi$
$569$	−4.67962e50	−0.501919	−0.250960	+	0.967998i	$0.580746\pi$
$570$	−2.53821e51	−2.63537
$571$	8.40413e50	0.844743	0.422371	−	0.906423i	$-0.361198\pi$
$571$	8.40413e50	0.844743	0.422371	+	0.906423i	$0.361198\pi$
$572$	3.73808e50	0.363766
$573$	7.04233e50	0.663523
$574$	4.86957e50	0.444243
$575$	−2.93443e50	−0.259220
$576$	2.92192e50	0.249949
$577$	2.43834e50	0.201996	0.100998	−	0.994887i	$-0.467796\pi$
$577$	2.43834e50	0.201996	0.100998	+	0.994887i	$0.467796\pi$
$578$	−4.00360e50	−0.321207
$579$	−2.01048e50	−0.156223
$580$	1.67119e50	0.125779
$581$	−8.26531e50	−0.602560
$582$	−6.67925e50	−0.471685
$583$	−8.06486e50	−0.551732
$584$	−5.61860e50	−0.372383
$585$	2.23062e51	1.43233
$586$	−1.44366e51	−0.898174
$587$	−1.26888e51	−0.764921	−0.382460	−	0.923972i	$-0.624923\pi$
$587$	−1.26888e51	−0.764921	−0.382460	+	0.923972i	$0.624923\pi$
$588$	−6.01831e50	−0.351556
$589$	1.60777e51	0.910105
$590$	2.11482e51	1.16014
$591$	−9.19403e50	−0.488807
$592$	−4.03919e50	−0.208134
$593$	3.44917e51	1.72267	0.861335	−	0.508037i	$-0.169629\pi$
$593$	3.44917e51	1.72267	0.861335	+	0.508037i	$0.169629\pi$
$594$	3.01926e51	1.46168
$595$	2.32836e51	1.09266
$596$	−3.74343e49	−0.0170300
$597$	−2.95599e51	−1.30370
$598$	−6.83685e50	−0.292337
$599$	−1.03421e51	−0.428759	−0.214379	−	0.976750i	$-0.568773\pi$
$599$	−1.03421e51	−0.428759	−0.214379	+	0.976750i	$0.568773\pi$
$600$	−5.81961e50	−0.233935
$601$	3.31491e50	0.129209	0.0646046	−	0.997911i	$-0.479421\pi$
$601$	3.31491e50	0.129209	0.0646046	+	0.997911i	$0.479421\pi$
$602$	−2.74789e50	−0.103864
$603$	1.31322e51	0.481357
$604$	−2.65552e51	−0.943989
$605$	−1.45152e51	−0.500436
$606$	−2.31442e51	−0.773926
$607$	−1.31827e51	−0.427577	−0.213788	−	0.976880i	$-0.568580\pi$
$607$	−1.31827e51	−0.427577	−0.213788	+	0.976880i	$0.568580\pi$
$608$	1.02851e51	0.323586
$609$	9.35911e50	0.285637
$610$	3.19216e51	0.945110
$611$	−3.87351e50	−0.111261
$612$	4.32647e51	1.20568
$613$	−4.00784e51	−1.08366	−0.541829	−	0.840489i	$-0.682268\pi$
$613$	−4.00784e51	−1.08366	−0.541829	+	0.840489i	$0.682268\pi$
$614$	−1.63457e51	−0.428833
$615$	−6.51946e51	−1.65967
$616$	−1.31709e51	−0.325365
$617$	−3.89908e51	−0.934731	−0.467366	−	0.884064i	$-0.654797\pi$
$617$	−3.89908e51	−0.934731	−0.467366	+	0.884064i	$0.654797\pi$
$618$	4.99780e51	1.16276
$619$	6.80067e51	1.53559	0.767794	−	0.640697i	$-0.221354\pi$
$619$	6.80067e51	1.53559	0.767794	+	0.640697i	$0.221354\pi$
$620$	1.33353e51	0.292251
$621$	−5.52215e51	−1.17466
$622$	−2.63991e51	−0.545089
$623$	3.33186e51	0.667818
$624$	−1.35590e51	−0.263822
$625$	−6.54378e51	−1.23609
$626$	6.88182e51	1.26206
$627$	2.12597e52	3.78537
$628$	−5.52909e51	−0.955873
$629$	−5.98081e51	−1.00398
$630$	−7.85945e51	−1.28113
$631$	8.58407e51	1.35878	0.679392	−	0.733776i	$-0.262244\pi$
$631$	8.58407e51	1.35878	0.679392	+	0.733776i	$0.262244\pi$
$632$	1.44975e51	0.222857
$633$	1.40097e52	2.09151
$634$	−3.05650e51	−0.443173
$635$	2.82957e51	0.398480
$636$	2.92533e51	0.400146
$637$	1.86171e51	0.247362
$638$	−1.39977e51	−0.180666
$639$	−2.62220e52	−3.28775
$640$	8.53070e50	0.103910
$641$	4.76661e51	0.564074	0.282037	−	0.959404i	$-0.408990\pi$
$641$	4.76661e51	0.564074	0.282037	+	0.959404i	$0.408990\pi$
$642$	−1.49656e52	−1.72066
$643$	−1.36823e52	−1.52846	−0.764231	−	0.644942i	$-0.776881\pi$
$643$	−1.36823e52	−1.52846	−0.764231	+	0.644942i	$0.776881\pi$
$644$	2.40892e51	0.261477
$645$	3.67892e51	0.388030
$646$	1.52290e52	1.56088
$647$	2.16321e51	0.215461	0.107731	−	0.994180i	$-0.465642\pi$
$647$	2.16321e51	0.215461	0.107731	+	0.994180i	$0.465642\pi$
$648$	−3.64808e51	−0.353124
$649$	−1.77135e52	−1.66639
$650$	1.80025e51	0.164602
$651$	7.46811e51	0.663685
$652$	2.46276e51	0.212736
$653$	−8.05478e49	−0.00676332	−0.00338166	−	0.999994i	$-0.501076\pi$
$653$	−8.05478e49	−0.00676332	−0.00338166	+	0.999994i	$0.501076\pi$
$654$	−1.00021e52	−0.816396
$655$	−3.03601e51	−0.240901
$656$	2.64175e51	0.203784
$657$	2.80825e52	2.10609
$658$	1.36481e51	0.0995157
$659$	1.39232e52	0.987098	0.493549	−	0.869718i	$-0.335699\pi$
$659$	1.39232e52	0.987098	0.493549	+	0.869718i	$0.335699\pi$
$660$	1.76334e52	1.21555
$661$	−1.05998e51	−0.0710511	−0.0355255	−	0.999369i	$-0.511311\pi$
$661$	−1.05998e51	−0.0710511	−0.0355255	+	0.999369i	$0.511311\pi$
$662$	−7.74249e51	−0.504670
$663$	−2.00767e52	−1.27260
$664$	−4.48395e51	−0.276408
$665$	−2.76650e52	−1.65856
$666$	2.01884e52	1.17714
$667$	2.56015e51	0.145190
$668$	−1.58996e52	−0.877043
$669$	2.68085e52	1.43843
$670$	3.83402e51	0.200111
$671$	−2.67372e52	−1.35753
$672$	4.77741e51	0.235972
$673$	1.75123e51	0.0841522	0.0420761	−	0.999114i	$-0.486603\pi$
$673$	1.75123e51	0.0841522	0.0420761	+	0.999114i	$0.486603\pi$
$674$	2.94353e51	0.137613
$675$	1.45407e52	0.661400
$676$	−7.10319e51	−0.314369
$677$	3.00931e52	1.29592	0.647958	−	0.761676i	$-0.275623\pi$
$677$	3.00931e52	1.29592	0.647958	+	0.761676i	$0.275623\pi$
$678$	3.43171e52	1.43801
$679$	−7.28000e51	−0.296853
$680$	1.26314e52	0.501229
$681$	−4.15509e52	−1.60457
$682$	−1.11695e52	−0.419781
$683$	3.45300e52	1.26303	0.631515	−	0.775364i	$-0.282433\pi$
$683$	3.45300e52	1.26303	0.631515	+	0.775364i	$0.282433\pi$
$684$	−5.14062e52	−1.83011
$685$	−2.27434e52	−0.788097
$686$	−2.27175e52	−0.766241
$687$	−7.97525e52	−2.61845
$688$	−1.49073e51	−0.0476446
$689$	−9.04925e51	−0.281551
$690$	−3.22510e52	−0.976867
$691$	5.56197e52	1.64015	0.820077	−	0.572253i	$-0.193931\pi$
$691$	5.56197e52	1.64015	0.820077	+	0.572253i	$0.193931\pi$
$692$	1.66960e52	0.479346
$693$	6.58299e52	1.84017
$694$	8.87315e51	0.241506
$695$	4.95397e52	1.31291
$696$	5.07734e51	0.131028
$697$	3.91163e52	0.982994
$698$	−2.25992e52	−0.553055
$699$	−8.98433e52	−2.14120
$700$	−6.34304e51	−0.147226
$701$	2.61308e52	0.590704	0.295352	−	0.955389i	$-0.404563\pi$
$701$	2.61308e52	0.590704	0.295352	+	0.955389i	$0.404563\pi$
$702$	3.38780e52	0.745900
$703$	7.10627e52	1.52394
$704$	−7.14523e51	−0.149253
$705$	−1.82723e52	−0.371787
$706$	3.65507e52	0.724450
$707$	−2.52259e52	−0.487066
$708$	6.42513e52	1.20856
$709$	−1.30761e52	−0.239620	−0.119810	−	0.992797i	$-0.538229\pi$
$709$	−1.30761e52	−0.239620	−0.119810	+	0.992797i	$0.538229\pi$
$710$	−7.65565e52	−1.36679
$711$	−7.24604e52	−1.26041
$712$	1.80754e52	0.306344
$713$	2.04287e52	0.337353
$714$	7.07389e52	1.13826
$715$	−5.45474e52	−0.855288
$716$	1.35490e52	0.207021
$717$	−9.99532e52	−1.48831
$718$	6.70823e52	0.973432
$719$	−5.28485e52	−0.747391	−0.373695	−	0.927551i	$-0.621909\pi$
$719$	−5.28485e52	−0.747391	−0.373695	+	0.927551i	$0.621909\pi$
$720$	−4.26377e52	−0.587682
$721$	5.44732e52	0.731780
$722$	−1.26944e53	−1.66217
$723$	1.95773e53	2.49859
$724$	−6.01038e52	−0.747719
$725$	−6.74126e51	−0.0817500
$726$	−4.40993e52	−0.521320
$727$	−8.62636e52	−0.994125	−0.497062	−	0.867715i	$-0.665588\pi$
$727$	−8.62636e52	−0.994125	−0.497062	+	0.867715i	$0.665588\pi$
$728$	−1.47785e52	−0.166035
$729$	−9.14085e52	−1.00122
$730$	8.19886e52	0.875549
$731$	−2.20732e52	−0.229823
$732$	9.69825e52	0.984552
$733$	−4.61809e52	−0.457129	−0.228565	−	0.973529i	$-0.573403\pi$
$733$	−4.61809e52	−0.457129	−0.228565	+	0.973529i	$0.573403\pi$
$734$	8.94432e52	0.863317
$735$	8.78213e52	0.826579
$736$	1.30684e52	0.119945
$737$	−3.21133e52	−0.287433
$738$	−1.32038e53	−1.15254
$739$	9.79613e52	0.833935	0.416968	−	0.908921i	$-0.363093\pi$
$739$	9.79613e52	0.833935	0.416968	+	0.908921i	$0.363093\pi$
$740$	5.89413e52	0.489365
$741$	2.38547e53	1.93169
$742$	3.18844e52	0.251829
$743$	3.68344e52	0.283766	0.141883	−	0.989883i	$-0.454684\pi$
$743$	3.68344e52	0.283766	0.141883	+	0.989883i	$0.454684\pi$
$744$	4.05146e52	0.304448
$745$	5.46255e51	0.0400409
$746$	−1.16975e53	−0.836419
$747$	2.24114e53	1.56328
$748$	−1.05799e53	−0.719950
$749$	−1.63116e53	−1.08289
$750$	−1.37363e53	−0.889686
$751$	−2.91686e53	−1.84322	−0.921610	−	0.388116i	$-0.873126\pi$
$751$	−2.91686e53	−1.84322	−0.921610	+	0.388116i	$0.873126\pi$
$752$	7.40410e51	0.0456501
$753$	−2.24531e53	−1.35073
$754$	−1.57063e52	−0.0921943
$755$	3.87504e53	2.21951
$756$	−1.19367e53	−0.667160
$757$	−2.14424e53	−1.16950	−0.584749	−	0.811214i	$-0.698807\pi$
$757$	−2.14424e53	−1.16950	−0.584749	+	0.811214i	$0.698807\pi$
$758$	1.95731e53	1.04179
$759$	2.70131e53	1.40314
$760$	−1.50083e53	−0.760818
$761$	3.02873e53	1.49846	0.749228	−	0.662312i	$-0.230425\pi$
$761$	3.02873e53	1.49846	0.749228	+	0.662312i	$0.230425\pi$
$762$	8.59666e52	0.415110
$763$	−1.09017e53	−0.513794
$764$	4.16410e52	0.191555
$765$	−6.31334e53	−2.83480
$766$	1.57597e53	0.690743
$767$	−1.98756e53	−0.850366
$768$	2.59175e52	0.108246
$769$	2.09535e53	0.854318	0.427159	−	0.904176i	$-0.359514\pi$
$769$	2.09535e53	0.854318	0.427159	+	0.904176i	$0.359514\pi$
$770$	1.92194e53	0.765000
$771$	−7.96002e52	−0.309320
$772$	−1.18879e52	−0.0451008
$773$	−2.74843e53	−1.01804	−0.509018	−	0.860756i	$-0.669991\pi$
$773$	−2.74843e53	−1.01804	−0.509018	+	0.860756i	$0.669991\pi$
$774$	7.45090e52	0.269464
$775$	−5.37919e52	−0.189948
$776$	−3.94942e52	−0.136173
$777$	3.30086e53	1.11132
$778$	−1.34106e53	−0.440887
$779$	−4.64771e53	−1.49209
$780$	1.97857e53	0.620300
$781$	6.41229e53	1.96322
$782$	1.93504e53	0.578581
$783$	−1.26861e53	−0.370454
$784$	−3.55861e52	−0.101492
$785$	8.06824e53	2.24745
$786$	−9.22383e52	−0.250954
$787$	−4.09272e53	−1.08762	−0.543812	−	0.839207i	$-0.683020\pi$
$787$	−4.09272e53	−1.08762	−0.543812	+	0.839207i	$0.683020\pi$
$788$	−5.43640e52	−0.141116
$789$	3.98016e53	1.00920
$790$	−2.11552e53	−0.523982
$791$	3.74037e53	0.905002
$792$	3.57129e53	0.844129
$793$	−3.00007e53	−0.692752
$794$	−2.82352e53	−0.636958
$795$	−4.26875e53	−0.940824
$796$	−1.74787e53	−0.376372
$797$	3.09131e51	0.00650374	0.00325187	−	0.999995i	$-0.498965\pi$
$797$	3.09131e51	0.00650374	0.00325187	+	0.999995i	$0.498965\pi$
$798$	−8.40504e53	−1.72777
$799$	1.09632e53	0.220203
$800$	−3.44111e52	−0.0675358
$801$	−9.03436e53	−1.73259
$802$	4.23700e53	0.794022
$803$	−6.86728e53	−1.25761
$804$	1.16483e53	0.208462
$805$	−3.51518e53	−0.614786
$806$	−1.25329e53	−0.214216
$807$	1.36335e54	2.27744
$808$	−1.36851e53	−0.223428
$809$	−2.71214e53	−0.432778	−0.216389	−	0.976307i	$-0.569428\pi$
$809$	−2.71214e53	−0.432778	−0.216389	+	0.976307i	$0.569428\pi$
$810$	5.32341e53	0.830266
$811$	−9.27510e52	−0.141395	−0.0706973	−	0.997498i	$-0.522522\pi$
$811$	−9.27510e52	−0.141395	−0.0706973	+	0.997498i	$0.522522\pi$
$812$	5.53401e52	0.0824619
$813$	1.72013e54	2.50545
$814$	−4.93686e53	−0.702909
$815$	−3.59375e53	−0.500186
$816$	3.83760e53	0.522146
$817$	2.62269e53	0.348850
$818$	2.01873e53	0.262508
$819$	7.38651e53	0.939046
$820$	−3.85494e53	−0.479138
$821$	−9.54561e53	−1.15999	−0.579996	−	0.814619i	$-0.696946\pi$
$821$	−9.54561e53	−1.15999	−0.579996	+	0.814619i	$0.696946\pi$
$822$	−6.90978e53	−0.820986
$823$	1.19456e54	1.38775	0.693873	−	0.720097i	$-0.255903\pi$
$823$	1.19456e54	1.38775	0.693873	+	0.720097i	$0.255903\pi$
$824$	2.95518e53	0.335684
$825$	−7.11296e53	−0.790046
$826$	7.00303e53	0.760598
$827$	−1.05798e54	−1.12364	−0.561820	−	0.827260i	$-0.689898\pi$
$827$	−1.05798e54	−1.12364	−0.561820	+	0.827260i	$0.689898\pi$
$828$	−6.53179e53	−0.678376
$829$	1.68391e54	1.71025	0.855124	−	0.518424i	$-0.173481\pi$
$829$	1.68391e54	1.71025	0.855124	+	0.518424i	$0.173481\pi$
$830$	6.54314e53	0.649892
$831$	−2.95926e54	−2.87452
$832$	−8.01737e52	−0.0761641
$833$	−5.26921e53	−0.489568
$834$	1.50509e54	1.36770
$835$	2.32012e54	2.06211
$836$	1.25708e54	1.09282
$837$	−1.01228e54	−0.860759
$838$	7.73792e52	0.0643591
$839$	−3.78194e53	−0.307693	−0.153847	−	0.988095i	$-0.549166\pi$
$839$	−3.78194e53	−0.307693	−0.153847	+	0.988095i	$0.549166\pi$
$840$	−6.97137e53	−0.554819
$841$	−1.22566e54	−0.954211
$842$	−1.58276e54	−1.20543
$843$	−3.40908e54	−2.53996
$844$	8.28387e53	0.603807
$845$	1.03652e54	0.739145
$846$	−3.70067e53	−0.258184
$847$	−4.80657e53	−0.328090
$848$	1.72974e53	0.115520
$849$	4.67315e53	0.305364
$850$	−5.09524e53	−0.325773
$851$	9.02939e53	0.564887
$852$	−2.32590e54	−1.42383
$853$	2.34797e54	1.40649	0.703244	−	0.710948i	$-0.251734\pi$
$853$	2.34797e54	1.40649	0.703244	+	0.710948i	$0.251734\pi$
$854$	1.05705e54	0.619622
$855$	7.50137e54	4.30296
$856$	−8.84908e53	−0.496745
$857$	5.17381e53	0.284227	0.142114	−	0.989850i	$-0.454610\pi$
$857$	5.17381e53	0.284227	0.142114	+	0.989850i	$0.454610\pi$
$858$	−1.65723e54	−0.890981
$859$	−2.26122e54	−1.18979	−0.594893	−	0.803805i	$-0.702806\pi$
$859$	−2.26122e54	−1.18979	−0.594893	+	0.803805i	$0.702806\pi$
$860$	2.17533e53	0.112022
$861$	−2.15886e54	−1.08809
$862$	1.97195e54	0.972773
$863$	−1.13614e54	−0.548572	−0.274286	−	0.961648i	$-0.588442\pi$
$863$	−1.13614e54	−0.548572	−0.274286	+	0.961648i	$0.588442\pi$
$864$	−6.47567e53	−0.306041
$865$	−2.43634e54	−1.12704
$866$	2.39124e54	1.08278
$867$	1.77495e54	0.786741
$868$	4.41587e53	0.191602
$869$	1.77194e54	0.752632
$870$	−7.40903e53	−0.308074
$871$	−3.60331e53	−0.146678
$872$	−5.91418e53	−0.235689
$873$	1.97397e54	0.770155
$874$	−2.29917e54	−0.878232
$875$	−1.49718e54	−0.559919
$876$	2.49094e54	0.912087
$877$	−3.53444e54	−1.26715	−0.633575	−	0.773682i	$-0.718413\pi$
$877$	−3.53444e54	−1.26715	−0.633575	+	0.773682i	$0.718413\pi$
$878$	−2.41457e54	−0.847600
$879$	6.40031e54	2.19992
$880$	1.04266e54	0.350923
$881$	−2.74692e54	−0.905300	−0.452650	−	0.891688i	$-0.649521\pi$
$881$	−2.74692e54	−0.905300	−0.452650	+	0.891688i	$0.649521\pi$
$882$	1.77864e54	0.574010
$883$	9.56723e53	0.302352	0.151176	−	0.988507i	$-0.451694\pi$
$883$	9.56723e53	0.302352	0.151176	+	0.988507i	$0.451694\pi$
$884$	−1.18713e54	−0.367393
$885$	−9.37578e54	−2.84156
$886$	2.67724e53	0.0794629
$887$	2.37072e54	0.689118	0.344559	−	0.938765i	$-0.388028\pi$
$887$	2.37072e54	0.689118	0.344559	+	0.938765i	$0.388028\pi$
$888$	1.79072e54	0.509787
$889$	9.36988e53	0.261247
$890$	−2.63763e54	−0.720276
$891$	−4.45883e54	−1.19257
$892$	1.58518e54	0.415268
$893$	−1.30263e54	−0.334247
$894$	1.65960e53	0.0417119
$895$	−1.97711e54	−0.486749
$896$	2.82487e53	0.0681239
$897$	3.03103e54	0.716029
$898$	−4.25234e54	−0.984046
$899$	4.69309e53	0.106391
$900$	1.71992e54	0.381963
$901$	2.56121e54	0.557234
$902$	3.22885e54	0.688220
$903$	1.21824e54	0.254396
$904$	2.02916e54	0.415145
$905$	8.77057e54	1.75804
$906$	1.17729e55	2.31214
$907$	−3.89376e54	−0.749264	−0.374632	−	0.927174i	$-0.622231\pi$
$907$	−3.89376e54	−0.749264	−0.374632	+	0.927174i	$0.622231\pi$
$908$	−2.45689e54	−0.463231
$909$	6.84001e54	1.26364
$910$	2.15653e54	0.390383
$911$	4.15122e54	0.736353	0.368177	−	0.929756i	$-0.379982\pi$
$911$	4.15122e54	0.736353	0.368177	+	0.929756i	$0.379982\pi$
$912$	−4.55975e54	−0.792568
$913$	−5.48046e54	−0.933486
$914$	−4.07475e54	−0.680137
$915$	−1.41520e55	−2.31488
$916$	−4.71574e54	−0.755933
$917$	−1.00535e54	−0.157937
$918$	−9.58849e54	−1.47625
$919$	2.84350e54	0.429058	0.214529	−	0.976718i	$-0.431178\pi$
$919$	2.84350e54	0.429058	0.214529	+	0.976718i	$0.431178\pi$
$920$	−1.90699e54	−0.282016
$921$	7.24666e54	1.05035
$922$	−1.43408e54	−0.203728
$923$	7.19497e54	1.00184
$924$	5.83914e54	0.796925
$925$	−2.37757e54	−0.318062
$926$	−2.60899e54	−0.342113
$927$	−1.47704e55	−1.89853
$928$	3.00221e53	0.0378272
$929$	−3.00016e53	−0.0370555	−0.0185278	−	0.999828i	$-0.505898\pi$
$929$	−3.00016e53	−0.0370555	−0.0185278	+	0.999828i	$0.505898\pi$
$930$	−5.91204e54	−0.715819
$931$	6.26076e54	0.743118
$932$	−5.31241e54	−0.618154
$933$	1.17037e55	1.33510
$934$	2.35271e54	0.263119
$935$	1.54386e55	1.69275
$936$	4.00720e54	0.430762
$937$	5.72228e54	0.603096	0.301548	−	0.953451i	$-0.402497\pi$
$937$	5.72228e54	0.603096	0.301548	+	0.953451i	$0.402497\pi$
$938$	1.26960e54	0.131194
$939$	−3.05097e55	−3.09118
$940$	−1.08043e54	−0.107333
$941$	−1.79388e55	−1.74737	−0.873684	−	0.486494i	$-0.838275\pi$
$941$	−1.79388e55	−1.74737	−0.873684	+	0.486494i	$0.838275\pi$
$942$	2.45125e55	2.34124
$943$	−5.90549e54	−0.553082
$944$	3.79916e54	0.348904
$945$	1.74184e55	1.56863
$946$	−1.82203e54	−0.160905
$947$	−1.24204e53	−0.0107563	−0.00537813	−	0.999986i	$-0.501712\pi$
$947$	−1.24204e53	−0.0107563	−0.00537813	+	0.999986i	$0.501712\pi$
$948$	−6.42727e54	−0.545849
$949$	−7.70549e54	−0.641764
$950$	6.05405e54	0.494492
$951$	1.35506e55	1.08547
$952$	4.18277e54	0.328609
$953$	8.24909e54	0.635605	0.317803	−	0.948157i	$-0.397055\pi$
$953$	8.24909e54	0.635605	0.317803	+	0.948157i	$0.397055\pi$
$954$	−8.64547e54	−0.653347
$955$	−6.07641e54	−0.450386
$956$	−5.91020e54	−0.429666
$957$	6.20572e54	0.442509
$958$	7.65745e54	0.535578
$959$	−7.53127e54	−0.516683
$960$	−3.78198e54	−0.254508
$961$	−1.14041e55	−0.752798
$962$	−5.53945e54	−0.358697
$963$	4.42290e55	2.80945
$964$	1.15760e55	0.721328
$965$	1.73472e54	0.106041
$966$	−1.06796e55	−0.640442
$967$	−5.68031e54	−0.334182	−0.167091	−	0.985942i	$-0.553437\pi$
$967$	−5.68031e54	−0.334182	−0.167091	+	0.985942i	$0.553437\pi$
$968$	−2.60758e54	−0.150502
$969$	−6.75160e55	−3.82311
$970$	5.76313e54	0.320171
$971$	−2.27277e55	−1.23880	−0.619399	−	0.785077i	$-0.712623\pi$
$971$	−2.27277e55	−1.23880	−0.619399	+	0.785077i	$0.712623\pi$
$972$	−1.31246e52	−0.000701877 0
$973$	1.64046e55	0.860753
$974$	−1.91695e54	−0.0986892
$975$	−7.98116e54	−0.403163
$976$	5.73454e54	0.284235
$977$	−7.73374e54	−0.376132	−0.188066	−	0.982156i	$-0.560222\pi$
$977$	−7.73374e54	−0.376132	−0.188066	+	0.982156i	$0.560222\pi$
$978$	−1.09183e55	−0.521060
$979$	2.20925e55	1.03458
$980$	5.19285e54	0.238629
$981$	2.95599e55	1.33299
$982$	4.21283e54	0.186428
$983$	1.64593e55	0.714777	0.357389	−	0.933956i	$-0.383667\pi$
$983$	1.64593e55	0.714777	0.357389	+	0.933956i	$0.383667\pi$
$984$	−1.17119e55	−0.499134
$985$	7.93299e54	0.331793
$986$	4.44536e54	0.182467
$987$	−6.05070e54	−0.243746
$988$	1.41052e55	0.557668
$989$	3.33245e54	0.129310
$990$	−5.21135e55	−1.98472
$991$	3.05470e54	0.114184	0.0570921	−	0.998369i	$-0.481817\pi$
$991$	3.05470e54	0.114184	0.0570921	+	0.998369i	$0.481817\pi$
$992$	2.39562e54	0.0878924
$993$	3.43254e55	1.23610
$994$	−2.53510e55	−0.896080
$995$	2.55055e55	0.884927
$996$	1.98790e55	0.677013
$997$	1.64945e55	0.551416	0.275708	−	0.961241i	$-0.411088\pi$
$997$	1.64945e55	0.551416	0.275708	+	0.961241i	$0.411088\pi$
$998$	−5.54662e54	−0.182018
$999$	−4.47424e55	−1.44131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.38.a.a.1.2	✓	2
3.2	odd	2		18.38.a.f.1.2		2
4.3	odd	2		16.38.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.38.a.a.1.2	✓	2	1.1	even	1	trivial
16.38.a.a.1.1		2	4.3	odd	2
18.38.a.f.1.2		2	3.2	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-262144. q^{2} +1.16218e9 q^{3} +6.87195e10 q^{4} -1.00278e13 q^{5} -3.04659e14 q^{6} -3.32061e15 q^{7} -1.80144e16 q^{8} +9.00385e17 q^{9} +O(q^{10})\)	\(q-262144. q^{2} +1.16218e9 q^{3} +6.87195e10 q^{4} -1.00278e13 q^{5} -3.04659e14 q^{6} -3.32061e15 q^{7} -1.80144e16 q^{8} +9.00385e17 q^{9} +2.62873e18 q^{10} -2.20179e19 q^{11} +7.98646e19 q^{12} -2.47054e20 q^{13} +8.70479e20 q^{14} -1.16541e22 q^{15} +4.72237e21 q^{16} +6.99239e22 q^{17} -2.36031e23 q^{18} -8.30820e23 q^{19} -6.89105e23 q^{20} -3.85916e24 q^{21} +5.77187e24 q^{22} -1.05566e25 q^{23} -2.09360e25 q^{24} +2.77971e25 q^{25} +6.47638e25 q^{26} +5.23100e26 q^{27} -2.28191e26 q^{28} -2.42517e26 q^{29} +3.05506e27 q^{30} -1.93516e27 q^{31} -1.23794e27 q^{32} -2.55889e28 q^{33} -1.83301e28 q^{34} +3.32984e28 q^{35} +6.18740e28 q^{36} -8.55331e28 q^{37} +2.17794e29 q^{38} -2.87122e29 q^{39} +1.80645e29 q^{40} +5.59412e29 q^{41} +1.01166e30 q^{42} -3.15675e29 q^{43} -1.51306e30 q^{44} -9.02888e30 q^{45} +2.76735e30 q^{46} +1.56788e30 q^{47} +5.48825e30 q^{48} -7.53564e30 q^{49} -7.28684e30 q^{50} +8.12643e31 q^{51} -1.69774e31 q^{52} +3.66286e31 q^{53} -1.37128e32 q^{54} +2.20791e32 q^{55} +5.98189e31 q^{56} -9.65565e32 q^{57} +6.35743e31 q^{58} +8.04503e32 q^{59} -8.00866e32 q^{60} +1.21434e33 q^{61} +5.07292e32 q^{62} -2.98983e33 q^{63} +3.24519e32 q^{64} +2.47741e33 q^{65} +6.70797e33 q^{66} +1.45851e33 q^{67} +4.80513e33 q^{68} -1.22687e34 q^{69} -8.72898e33 q^{70} -2.91230e34 q^{71} -1.62199e34 q^{72} +3.11895e34 q^{73} +2.24220e34 q^{74} +3.23053e34 q^{75} -5.70935e34 q^{76} +7.31130e34 q^{77} +7.52674e34 q^{78} -8.04771e34 q^{79} -4.73549e34 q^{80} +2.02509e35 q^{81} -1.46647e35 q^{82} +2.48909e35 q^{83} -2.65200e35 q^{84} -7.01182e35 q^{85} +8.27523e34 q^{86} -2.81849e35 q^{87} +3.96640e35 q^{88} -1.00339e36 q^{89} +2.36687e36 q^{90} +8.20372e35 q^{91} -7.25443e35 q^{92} -2.24901e36 q^{93} -4.11010e35 q^{94} +8.33129e36 q^{95} -1.43871e36 q^{96} +2.19237e36 q^{97} +1.97542e36 q^{98} -1.98246e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 524288 q^{2} + 423071208 q^{3} + 137438953472 q^{4} - 13507530555540 q^{5} - 110905578749952 q^{6} + 31\!\cdots\!56 q^{7}+ \cdots + 99\!\cdots\!06 q^{9}+O(q^{10}) \) 2 * q - 524288 * q^2 + 423071208 * q^3 + 137438953472 * q^4 - 13507530555540 * q^5 - 110905578749952 * q^6 + 3106174162962256 * q^7 - 36028797018963968 * q^8 + 996387550079387706 * q^9	\( 2 q - 524288 q^{2} + 423071208 q^{3} + 137438953472 q^{4} - 13507530555540 q^{5} - 110905578749952 q^{6} + 31\!\cdots\!56 q^{7}+ \cdots - 17\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 524288 * q^2 + 423071208 * q^3 + 137438953472 * q^4 - 13507530555540 * q^5 - 110905578749952 * q^6 + 3106174162962256 * q^7 - 36028797018963968 * q^8 + 996387550079387706 * q^9 + 3540918089951477760 * q^10 + 4002878661541032504 * q^11 + 29073232035827417088 * q^12 - 417717305951174459972 * q^13 - 814264919775577636864 * q^14 - 9082218417464777049360 * q^15 + 9444732965739290427392 * q^16 + 924888511508274921636 * q^17 - 261197017928011010801664 * q^18 - 1502800666863954423438200 * q^19 - 928230431772240185917440 * q^20 - 8609275073860282063267776 * q^21 - 1049330623851012424728576 * q^22 + 4977294427767526272845808 * q^23 - 7621373338799942425116672 * q^24 - 32853923797109170328639650 * q^25 + 109502085451264677634899968 * q^26 + 784953884198822073793762320 * q^27 + 213454663129649024038076416 * q^28 + 1174284943679786618741874780 * q^29 + 2380849064827886514827427840 * q^30 - 5529622970549622212915224256 * q^31 - 2475880078570760549798248448 * q^32 - 44821137705190940628425921184 * q^33 - 242453973960825221057347584 * q^34 + 10934908922823267414476448480 * q^35 + 68471231067720518415591407616 * q^36 - 115976327866820065024925346644 * q^37 + 393950178014384468377783500800 * q^38 - 160983234676250224910988001488 * q^39 + 243330038306502131297141391360 * q^40 + 479903809827585250071775594644 * q^41 + 2256869804962029781193267871744 * q^42 - 3191808379897050809392290082952 * q^43 + 275075727058799801068047826944 * q^44 - 9362941394381803786652901761220 * q^45 - 1304767870472690407268891492352 * q^46 - 11214072446606967601132239964704 * q^47 + 1997897292526372107089784864768 * q^48 + 15205846893444101799554822389554 * q^49 + 8612458999869386346630912409600 * q^50 + 132262288085411921255362031678544 * q^51 - 28705314688536327653923217211392 * q^52 + 53695242990369729463598618231628 * q^53 - 205770951019416013712592029614080 * q^54 + 130245707009259764446614200122320 * q^55 - 55955859211458713757437503995904 * q^56 - 468896146209528218251899751202400 * q^57 - 307831752275993983383470022328320 * q^58 + 58132414930279452353014089908760 * q^59 - 624125297250241482542921243688960 * q^60 + 949379410209793628730917745257884 * q^61 + 1449557483991760165382448547364864 * q^62 - 2372845660625082937916074533710832 * q^63 + 649037107316853453566312041152512 * q^64 + 3071271884553430462753913899952040 * q^65 + 11749592322589573940098084682858496 * q^66 + 3280488273924335151706569871726696 * q^67 + 63557854549986566748857325060096 * q^68 - 23749969120311478380705506108559168 * q^69 - 2866520764664582613100514110341120 * q^70 - 36632636242259358919270327956284976 * q^71 - 17949322397016527579536793958088704 * q^72 - 10722559667485328549057125275606572 * q^73 + 30402498492319679125894030070644736 * q^74 + 77133181870178710270426539420629400 * q^75 - 103271675465402802078425678033715200 * q^76 + 240343208006950469127380344317189312 * q^77 + 42200789070970938959066038662070272 * q^78 + 41775981111170500771329248250783520 * q^79 - 63787509561819694706757832896675840 * q^80 - 34258358055565679771691854070856398 * q^81 - 125803904323442507794815541482356736 * q^82 + 173069025965519133350295483333594888 * q^83 - 591624878151966334961128012970459136 * q^84 - 461083992329885864995977782015209320 * q^85 + 836713415939732487377332491505369088 * q^86 - 1329023474711207186565010011774976080 * q^87 - 72109451394102015051182329546407936 * q^88 - 770863557920750582452392321302299020 * q^89 + 2454438908888823571848338279293255680 * q^90 - 276443184133973152010668401471277216 * q^91 + 342037068637192954123096291371122688 * q^92 + 407692825919874357767105668290130176 * q^93 + 2939701807443336914831209913307365376 * q^94 + 10669607994591022203853874284760756400 * q^95 - 523736787852033289640944563589742592 * q^96 - 6502221928957848822710145562502442044 * q^97 - 3986121528035010622142499360487243776 * q^98 - 17326559760258527834659445830047870888 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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