LMFDB - Embedded newform 2.40.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,40,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, 40, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 40 $
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:	$19.2679102779$
Analytic rank:	$0$
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 - 1050523661880 $ x^2 - x - 1050523661880
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.02495e6$ 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)

$f(q)$	$=$	$q-524288. q^{2} -1.82420e9 q^{3} +2.74878e11 q^{4} -1.63330e13 q^{5} +9.56404e14 q^{6} -4.83820e16 q^{7} -1.44115e17 q^{8} -7.24864e17 q^{9} +O(q^{10})$	\(q-524288. q^{2} -1.82420e9 q^{3} +2.74878e11 q^{4} -1.63330e13 q^{5} +9.56404e14 q^{6} -4.83820e16 q^{7} -1.44115e17 q^{8} -7.24864e17 q^{9} +8.56319e18 q^{10} -2.19692e20 q^{11} -5.01431e20 q^{12} -2.70174e21 q^{13} +2.53661e22 q^{14} +2.97946e22 q^{15} +7.55579e22 q^{16} -3.41577e23 q^{17} +3.80038e23 q^{18} +1.08294e25 q^{19} -4.48958e24 q^{20} +8.82583e25 q^{21} +1.15182e26 q^{22} +5.60481e26 q^{23} +2.62894e26 q^{24} -1.55222e27 q^{25} +1.41649e27 q^{26} +8.71495e27 q^{27} -1.32992e28 q^{28} -2.70870e28 q^{29} -1.56209e28 q^{30} -2.06375e29 q^{31} -3.96141e28 q^{32} +4.00761e29 q^{33} +1.79085e29 q^{34} +7.90223e29 q^{35} -1.99249e29 q^{36} +5.44740e30 q^{37} -5.67770e30 q^{38} +4.92850e30 q^{39} +2.35383e30 q^{40} -1.91644e31 q^{41} -4.62728e31 q^{42} +3.74314e31 q^{43} -6.03885e31 q^{44} +1.18392e31 q^{45} -2.93853e32 q^{46} +4.61267e32 q^{47} -1.37832e32 q^{48} +1.43128e33 q^{49} +8.13812e32 q^{50} +6.23104e32 q^{51} -7.42648e32 q^{52} -6.71634e33 q^{53} -4.56914e33 q^{54} +3.58823e33 q^{55} +6.97258e33 q^{56} -1.97549e34 q^{57} +1.42014e34 q^{58} -3.99113e33 q^{59} +8.18987e33 q^{60} -1.94732e34 q^{61} +1.08200e35 q^{62} +3.50704e34 q^{63} +2.07692e34 q^{64} +4.41274e34 q^{65} -2.10114e35 q^{66} +1.42194e35 q^{67} -9.38920e34 q^{68} -1.02243e36 q^{69} -4.14304e35 q^{70} +2.33433e35 q^{71} +1.04464e35 q^{72} +2.09176e36 q^{73} -2.85601e36 q^{74} +2.83156e36 q^{75} +2.97675e36 q^{76} +1.06291e37 q^{77} -2.58395e36 q^{78} -1.21764e37 q^{79} -1.23409e36 q^{80} -1.29602e37 q^{81} +1.00477e37 q^{82} -3.66144e37 q^{83} +2.42603e37 q^{84} +5.57897e36 q^{85} -1.96248e37 q^{86} +4.94120e37 q^{87} +3.16610e37 q^{88} -1.38898e38 q^{89} -6.20715e36 q^{90} +1.30716e38 q^{91} +1.54064e38 q^{92} +3.76469e38 q^{93} -2.41837e38 q^{94} -1.76876e38 q^{95} +7.22638e37 q^{96} -4.64378e38 q^{97} -7.50401e38 q^{98} +1.59247e38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots - 31\!\cdots\!86 q^{9}+O(q^{10}) $ 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9	$ 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots + 72\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9 - 28113758147900866560 * q^10 - 432928873549526253816 * q^11 + 79004930825798025216 * q^12 - 1110716884377980399156 * q^13 - 3931107033531816083456 * q^14 + 177514053087296176226640 * q^15 + 151115727451828646838272 * q^16 - 361727800957394760654108 * q^17 + 166988256371990061907968 * q^18 + 11531090014904148017962360 * q^19 + 14739706031846649527009280 * q^20 + 206255336094912268749797184 * q^21 + 226979413255534020560683008 * q^22 + 733399930716618125168143824 * q^23 - 41421337172795995044446208 * q^24 + 1522590281438531446348943150 * q^25 + 582335533876762587512700928 * q^26 + 1015590507281331347888066160 * q^27 + 2061032244396328790762979328 * q^28 - 66283478621079021435470040660 * q^29 - 93068487865032337641512632320 * q^30 - 186790705491150225840859566656 * q^31 - 79228162514264337593543950336 * q^32 - 49512382311136707894463876512 * q^33 + 189649545308350584273820975104 * q^34 + 4699349644576524589906668345120 * q^35 - 87549938956757925577604726784 * q^36 + 2975477658591913559588340321052 * q^37 - 6045612121734065956041449799680 * q^38 + 8288123926734148196202973745808 * q^39 - 7727850996024816187216641392640 * q^40 + 16770326730060018362152407596724 * q^41 - 108137197650529363558293666004992 * q^42 - 9812395004866851368387130850616 * q^43 - 119002582616917420571719372898304 * q^44 + 40266363304618629851608344270540 * q^45 - 384512782875554283608155789197312 * q^46 + 672278426349701905666521369769632 * q^47 + 21716710023650866649862613499904 * q^48 + 3644309465778284633118680596157586 * q^49 - 798275813474844774943394706227200 * q^50 + 580553528426174218705101873396144 * q^51 - 305311532385180103481858944139264 * q^52 - 8761864571633558324701150169407236 * q^53 - 532461915881514649721538430894080 * q^54 - 11328905370645770966149273576022160 * q^55 - 1080574473350062429051540905918464 * q^56 - 18273076268563776391813920538819680 * q^57 + 34751632439288277990359716677550080 * q^58 - 12819225750671101391169533921560920 * q^59 + 48794691365782074237393374973788160 * q^60 - 20956924322550570450554426592045716 * q^61 + 97932125400544169605652580482940928 * q^62 + 57777775631084010576555882975543984 * q^63 + 41538374868278621028243970633760768 * q^64 + 155428501009224030268997780328195240 * q^65 + 25958747897141242308572676888723456 * q^66 - 430210910797386482647696776154188008 * q^67 - 99430980810624511127753051395325952 * q^68 - 657289380718196443693542397362196032 * q^69 - 2463812626455736924192987333326274560 * q^70 - 505835127408773713626404787885403536 * q^71 + 45901382395760699285231226996129792 * q^72 + 5225008613368893844954971696153387124 * q^73 - 1560007230667837176329451770243710976 * q^74 + 9324378759630332095186368293653381800 * q^75 + 3169641888079709971961059632574627840 * q^76 - 1286526284405007303669629309781343296 * q^77 - 4345363917299593089490864699242184704 * q^78 + 5133106059230199144047658337509305440 * q^79 + 4051619543003858829163438482464440320 * q^80 - 30865091955632000468542250095184041518 * q^81 - 8792481060649706907056161474071232512 * q^82 - 64869811713330760861780892502955295496 * q^83 + 56695035081800738961250669562425245696 * q^84 + 4169326167850982553612360321923472120 * q^85 + 5144520952311631770228952059407761408 * q^86 - 33355767685492704090236226944356001520 * q^87 + 62391626035058400596705606578106007552 * q^88 - 35854914207967073080588387127246110380 * q^89 - 21111171084251892207640035600912875520 * q^90 + 219621888597383210927045163285292559264 * q^91 + 201595437908258604244352782406680313856 * q^92 + 417824530946031783400120882011006743808 * q^93 - 352467511594032512718089155913780822016 * q^94 - 127785377061536603773906538331287257200 * q^95 - 11385810464879865574123169906637668352 * q^96 - 145570707650873901517300801294356641468 * q^97 - 1910667721193965293728526812398268448768 * q^98 + 72596170648714013699688849065341538088 * 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 $

$2$	−524288.	−0.707107
$2$	−524288.	−0.707107
$3$	−1.82420e9	−0.906164	−0.453082	−	0.891469i	$-0.649676\pi$
$3$	−1.82420e9	−0.906164	−0.453082	+	0.891469i	$0.649676\pi$
$4$	2.74878e11	0.500000
$5$	−1.63330e13	−0.382957	−0.191479	−	0.981497i	$-0.561328\pi$
$5$	−1.63330e13	−0.382957	−0.191479	+	0.981497i	$0.561328\pi$
$6$	9.56404e14	0.640755
$7$	−4.83820e16	−1.60425	−0.802125	−	0.597156i	$-0.796297\pi$
$7$	−4.83820e16	−1.60425	−0.802125	+	0.597156i	$0.796297\pi$
$8$	−1.44115e17	−0.353553
$9$	−7.24864e17	−0.178866
$10$	8.56319e18	0.270792
$11$	−2.19692e20	−1.08307	−0.541536	−	0.840678i	$-0.682157\pi$
$11$	−2.19692e20	−1.08307	−0.541536	+	0.840678i	$0.682157\pi$
$12$	−5.01431e20	−0.453082
$13$	−2.70174e21	−0.512564	−0.256282	−	0.966602i	$-0.582498\pi$
$13$	−2.70174e21	−0.512564	−0.256282	+	0.966602i	$0.582498\pi$
$14$	2.53661e22	1.13438
$15$	2.97946e22	0.347022
$16$	7.55579e22	0.250000
$17$	−3.41577e23	−0.346525	−0.173263	−	0.984876i	$-0.555431\pi$
$17$	−3.41577e23	−0.346525	−0.173263	+	0.984876i	$0.555431\pi$
$18$	3.80038e23	0.126477
$19$	1.08294e25	1.25576	0.627881	−	0.778309i	$-0.283922\pi$
$19$	1.08294e25	1.25576	0.627881	+	0.778309i	$0.283922\pi$
$20$	−4.48958e24	−0.191479
$21$	8.82583e25	1.45372
$22$	1.15182e26	0.765847
$23$	5.60481e26	1.56628	0.783138	−	0.621848i	$-0.213618\pi$
$23$	5.60481e26	1.56628	0.783138	+	0.621848i	$0.213618\pi$
$24$	2.62894e26	0.320378
$25$	−1.55222e27	−0.853344
$26$	1.41649e27	0.362437
$27$	8.71495e27	1.06825
$28$	−1.32992e28	−0.802125
$29$	−2.70870e28	−0.824139	−0.412069	−	0.911153i	$-0.635194\pi$
$29$	−2.70870e28	−0.824139	−0.412069	+	0.911153i	$0.635194\pi$
$30$	−1.56209e28	−0.245382
$31$	−2.06375e29	−1.71043	−0.855214	−	0.518275i	$-0.826575\pi$
$31$	−2.06375e29	−1.71043	−0.855214	+	0.518275i	$0.826575\pi$
$32$	−3.96141e28	−0.176777
$33$	4.00761e29	0.981441
$34$	1.79085e29	0.245030
$35$	7.90223e29	0.614360
$36$	−1.99249e29	−0.0894330
$37$	5.44740e30	1.43303	0.716516	−	0.697571i	$-0.245736\pi$
$37$	5.44740e30	1.43303	0.716516	+	0.697571i	$0.245736\pi$
$38$	−5.67770e30	−0.887958
$39$	4.92850e30	0.464467
$40$	2.35383e30	0.135396
$41$	−1.91644e31	−0.681098	−0.340549	−	0.940227i	$-0.610613\pi$
$41$	−1.91644e31	−0.681098	−0.340549	+	0.940227i	$0.610613\pi$
$42$	−4.62728e31	−1.02793
$43$	3.74314e31	0.525535	0.262767	−	0.964859i	$-0.415365\pi$
$43$	3.74314e31	0.525535	0.262767	+	0.964859i	$0.415365\pi$
$44$	−6.03885e31	−0.541536
$45$	1.18392e31	0.0684980
$46$	−2.93853e32	−1.10752
$47$	4.61267e32	1.14299	0.571497	−	0.820604i	$-0.306363\pi$
$47$	4.61267e32	1.14299	0.571497	+	0.820604i	$0.306363\pi$
$48$	−1.37832e32	−0.226541
$49$	1.43128e33	1.57362
$50$	8.13812e32	0.603405
$51$	6.23104e32	0.314009
$52$	−7.42648e32	−0.256282
$53$	−6.71634e33	−1.59865	−0.799325	−	0.600899i	$-0.794810\pi$
$53$	−6.71634e33	−1.59865	−0.799325	+	0.600899i	$0.794810\pi$
$54$	−4.56914e33	−0.755364
$55$	3.58823e33	0.414770
$56$	6.97258e33	0.567188
$57$	−1.97549e34	−1.13793
$58$	1.42014e34	0.582754
$59$	−3.99113e33	−0.117350	−0.0586749	−	0.998277i	$-0.518688\pi$
$59$	−3.99113e33	−0.117350	−0.0586749	+	0.998277i	$0.518688\pi$
$60$	8.18987e33	0.173511
$61$	−1.94732e34	−0.298886	−0.149443	−	0.988770i	$-0.547748\pi$
$61$	−1.94732e34	−0.298886	−0.149443	+	0.988770i	$0.547748\pi$
$62$	1.08200e35	1.20946
$63$	3.50704e34	0.286946
$64$	2.07692e34	0.125000
$65$	4.41274e34	0.196290
$66$	−2.10114e35	−0.693983
$67$	1.42194e35	0.350286	0.175143	−	0.984543i	$-0.443961\pi$
$67$	1.42194e35	0.350286	0.175143	+	0.984543i	$0.443961\pi$
$68$	−9.38920e34	−0.173263
$69$	−1.02243e36	−1.41930
$70$	−4.14304e35	−0.434418
$71$	2.33433e35	0.185620	0.0928101	−	0.995684i	$-0.470415\pi$
$71$	2.33433e35	0.185620	0.0928101	+	0.995684i	$0.470415\pi$
$72$	1.04464e35	0.0632387
$73$	2.09176e36	0.967646	0.483823	−	0.875166i	$-0.339248\pi$
$73$	2.09176e36	0.967646	0.483823	+	0.875166i	$0.339248\pi$
$74$	−2.85601e36	−1.01331
$75$	2.83156e36	0.773270
$76$	2.97675e36	0.627881
$77$	1.06291e37	1.73752
$78$	−2.58395e36	−0.328428
$79$	−1.21764e37	−1.20723	−0.603617	−	0.797275i	$-0.706274\pi$
$79$	−1.21764e37	−1.20723	−0.603617	+	0.797275i	$0.706274\pi$
$80$	−1.23409e36	−0.0957393
$81$	−1.29602e37	−0.789141
$82$	1.00477e37	0.481609
$83$	−3.66144e37	−1.38557	−0.692786	−	0.721143i	$-0.743617\pi$
$83$	−3.66144e37	−1.38557	−0.692786	+	0.721143i	$0.743617\pi$
$84$	2.42603e37	0.726858
$85$	5.57897e36	0.132704
$86$	−1.96248e37	−0.371609
$87$	4.94120e37	0.746805
$88$	3.16610e37	0.382924
$89$	−1.38898e38	−1.34769	−0.673845	−	0.738872i	$-0.735359\pi$
$89$	−1.38898e38	−1.34769	−0.673845	+	0.738872i	$0.735359\pi$
$90$	−6.20715e36	−0.0484354
$91$	1.30716e38	0.822281
$92$	1.54064e38	0.783138
$93$	3.76469e38	1.54993
$94$	−2.41837e38	−0.808219
$95$	−1.76876e38	−0.480903
$96$	7.22638e37	0.160189
$97$	−4.64378e38	−0.841052	−0.420526	−	0.907280i	$-0.638155\pi$
$97$	−4.64378e38	−0.841052	−0.420526	+	0.907280i	$0.638155\pi$
$98$	−7.50401e38	−1.11272
$99$	1.59247e38	0.193725
$100$	−4.26672e38	−0.426672
$101$	2.69559e37	0.0222017	0.0111009	−	0.999938i	$-0.496466\pi$
$101$	2.69559e37	0.0222017	0.0111009	+	0.999938i	$0.496466\pi$
$102$	−3.26686e38	−0.222038
$103$	2.28170e39	1.28213	0.641066	−	0.767486i	$-0.278492\pi$
$103$	2.28170e39	1.28213	0.641066	+	0.767486i	$0.278492\pi$
$104$	3.89362e38	0.181219
$105$	−1.44152e39	−0.556711
$106$	3.52130e39	1.13042
$107$	−1.19012e39	−0.318133	−0.159067	−	0.987268i	$-0.550848\pi$
$107$	−1.19012e39	−0.318133	−0.159067	+	0.987268i	$0.550848\pi$
$108$	2.39555e39	0.534123
$109$	5.17710e39	0.964427	0.482214	−	0.876054i	$-0.339833\pi$
$109$	5.17710e39	0.964427	0.482214	+	0.876054i	$0.339833\pi$
$110$	−1.88126e39	−0.293287
$111$	−9.93713e39	−1.29856
$112$	−3.65564e39	−0.401063
$113$	−6.35561e39	−0.586311	−0.293155	−	0.956065i	$-0.594705\pi$
$113$	−6.35561e39	−0.586311	−0.293155	+	0.956065i	$0.594705\pi$
$114$	1.03572e40	0.804636
$115$	−9.15433e39	−0.599817
$116$	−7.44562e39	−0.412069
$117$	1.95839e39	0.0916802
$118$	2.09250e39	0.0829788
$119$	1.65262e40	0.555913
$120$	−4.29385e39	−0.122691
$121$	7.11984e39	0.173044
$122$	1.02096e40	0.211344
$123$	3.49596e40	0.617187
$124$	−5.67280e40	−0.855214
$125$	5.50620e40	0.709752
$126$	−1.83870e40	−0.202901
$127$	1.12201e41	1.06126	0.530631	−	0.847603i	$-0.321955\pi$
$127$	1.12201e41	1.06126	0.530631	+	0.847603i	$0.321955\pi$
$128$	−1.08890e40	−0.0883883
$129$	−6.82823e40	−0.476221
$130$	−2.31355e40	−0.138798
$131$	−1.21172e41	−0.626054	−0.313027	−	0.949744i	$-0.601343\pi$
$131$	−1.21172e41	−0.626054	−0.313027	+	0.949744i	$0.601343\pi$
$132$	1.10160e41	0.490720
$133$	−5.23946e41	−2.01456
$134$	−7.45506e40	−0.247689
$135$	−1.42341e41	−0.409093
$136$	4.92265e40	0.122515
$137$	5.10278e41	1.10092	0.550460	−	0.834862i	$-0.314452\pi$
$137$	5.10278e41	1.10092	0.550460	+	0.834862i	$0.314452\pi$
$138$	5.36046e41	1.00360
$139$	7.29160e41	1.18586	0.592931	−	0.805253i	$-0.297971\pi$
$139$	7.29160e41	1.18586	0.592931	+	0.805253i	$0.297971\pi$
$140$	2.17215e41	0.307180
$141$	−8.41442e41	−1.03574
$142$	−1.22386e41	−0.131253
$143$	5.93551e41	0.555143
$144$	−5.47692e40	−0.0447165
$145$	4.42412e41	0.315610
$146$	−1.09669e42	−0.684229
$147$	−2.61093e42	−1.42596
$148$	1.49737e42	0.716516
$149$	1.82198e41	0.0764559	0.0382280	−	0.999269i	$-0.487829\pi$
$149$	1.82198e41	0.0764559	0.0382280	+	0.999269i	$0.487829\pi$
$150$	−1.48455e42	−0.546784
$151$	1.72698e42	0.558775	0.279387	−	0.960178i	$-0.409869\pi$
$151$	1.72698e42	0.558775	0.279387	+	0.960178i	$0.409869\pi$
$152$	−1.56067e42	−0.443979
$153$	2.47597e41	0.0619816
$154$	−5.57274e42	−1.22861
$155$	3.37073e42	0.655021
$156$	1.35474e42	0.232234
$157$	1.72536e42	0.261118	0.130559	−	0.991441i	$-0.458323\pi$
$157$	1.72536e42	0.261118	0.130559	+	0.991441i	$0.458323\pi$
$158$	6.38395e42	0.853643
$159$	1.22519e43	1.44864
$160$	6.47016e41	0.0676979
$161$	−2.71172e43	−2.51270
$162$	6.79489e42	0.558007
$163$	1.60401e43	1.16828	0.584142	−	0.811652i	$-0.301431\pi$
$163$	1.60401e43	1.16828	0.584142	+	0.811652i	$0.301431\pi$
$164$	−5.26786e42	−0.340549
$165$	−6.54563e42	−0.375850
$166$	1.91965e43	0.979748
$167$	−1.43788e43	−0.652755	−0.326377	−	0.945240i	$-0.605828\pi$
$167$	−1.43788e43	−0.652755	−0.326377	+	0.945240i	$0.605828\pi$
$168$	−1.27194e43	−0.513966
$169$	−2.04844e43	−0.737278
$170$	−2.92499e42	−0.0938362
$171$	−7.84981e42	−0.224613
$172$	1.02891e43	0.262767
$173$	−3.61218e43	−0.823892	−0.411946	−	0.911208i	$-0.635151\pi$
$173$	−3.61218e43	−0.823892	−0.411946	+	0.911208i	$0.635151\pi$
$174$	−2.59061e43	−0.528071
$175$	7.50997e43	1.36898
$176$	−1.65995e43	−0.270768
$177$	7.28061e42	0.106338
$178$	7.28224e43	0.952961
$179$	1.30727e44	1.53367	0.766833	−	0.641847i	$-0.221832\pi$
$179$	1.30727e44	1.53367	0.766833	+	0.641847i	$0.221832\pi$
$180$	3.25433e42	0.0342490
$181$	4.97304e42	0.0469775	0.0234887	−	0.999724i	$-0.492523\pi$
$181$	4.97304e42	0.0469775	0.0234887	+	0.999724i	$0.492523\pi$
$182$	−6.85326e43	−0.581440
$183$	3.55229e43	0.270840
$184$	−8.07738e43	−0.553762
$185$	−8.89724e43	−0.548790
$186$	−1.97378e44	−1.09597
$187$	7.50418e43	0.375312
$188$	1.26792e44	0.571497
$189$	−4.21647e44	−1.71374
$190$	9.27338e43	0.340050
$191$	−7.56519e43	−0.250420	−0.125210	−	0.992130i	$-0.539960\pi$
$191$	−7.56519e43	−0.250420	−0.125210	+	0.992130i	$0.539960\pi$
$192$	−3.78871e43	−0.113271
$193$	4.98511e44	1.34681	0.673406	−	0.739273i	$-0.264831\pi$
$193$	4.98511e44	1.34681	0.673406	+	0.739273i	$0.264831\pi$
$194$	2.43468e44	0.594714
$195$	−8.04971e43	−0.177871
$196$	3.93426e44	0.786810
$197$	−1.02377e45	−1.85400	−0.927002	−	0.375057i	$-0.877623\pi$
$197$	−1.02377e45	−1.85400	−0.927002	+	0.375057i	$0.877623\pi$
$198$	−8.34913e43	−0.136984
$199$	6.96706e44	1.03613	0.518065	−	0.855341i	$-0.326652\pi$
$199$	6.96706e44	1.03613	0.518065	+	0.855341i	$0.326652\pi$
$200$	2.23699e44	0.301703
$201$	−2.59390e44	−0.317417
$202$	−1.41327e43	−0.0156990
$203$	1.31052e45	1.32213
$204$	1.71277e44	0.157004
$205$	3.13011e44	0.260831
$206$	−1.19627e45	−0.906604
$207$	−4.06273e44	−0.280153
$208$	−2.04138e44	−0.128141
$209$	−2.37912e45	−1.36008
$210$	7.55772e44	0.393654
$211$	1.87344e44	0.0889470	0.0444735	−	0.999011i	$-0.485839\pi$
$211$	1.87344e44	0.0889470	0.0444735	+	0.999011i	$0.485839\pi$
$212$	−1.84617e45	−0.799325
$213$	−4.25828e44	−0.168202
$214$	6.23968e44	0.224954
$215$	−6.11367e44	−0.201257
$216$	−1.25596e45	−0.377682
$217$	9.98486e45	2.74396
$218$	−2.71429e45	−0.681953
$219$	−3.81578e45	−0.876846
$220$	9.86324e44	0.207385
$221$	9.22852e44	0.177616
$222$	5.20992e45	0.918223
$223$	2.17369e45	0.350956	0.175478	−	0.984483i	$-0.443853\pi$
$223$	2.17369e45	0.350956	0.175478	+	0.984483i	$0.443853\pi$
$224$	1.91661e45	0.283594
$225$	1.12515e45	0.152634
$226$	3.33217e45	0.414584
$227$	−6.39333e45	−0.729832	−0.364916	−	0.931040i	$-0.618902\pi$
$227$	−6.39333e45	−0.729832	−0.364916	+	0.931040i	$0.618902\pi$
$228$	−5.43018e45	−0.568964
$229$	−5.88996e45	−0.566657	−0.283329	−	0.959023i	$-0.591439\pi$
$229$	−5.88996e45	−0.566657	−0.283329	+	0.959023i	$0.591439\pi$
$230$	4.79950e45	0.424134
$231$	−1.93897e46	−1.57448
$232$	3.90365e45	0.291377
$233$	−7.39929e45	−0.507866	−0.253933	−	0.967222i	$-0.581724\pi$
$233$	−7.39929e45	−0.507866	−0.253933	+	0.967222i	$0.581724\pi$
$234$	−1.02676e45	−0.0648277
$235$	−7.53387e45	−0.437718
$236$	−1.09707e45	−0.0586749
$237$	2.22122e46	1.09395
$238$	−8.66449e45	−0.393090
$239$	2.23772e46	0.935505	0.467753	−	0.883859i	$-0.345064\pi$
$239$	2.23772e46	0.935505	0.467753	+	0.883859i	$0.345064\pi$
$240$	2.25121e45	0.0867556
$241$	4.76330e46	1.69268	0.846342	−	0.532640i	$-0.178800\pi$
$241$	4.76330e46	1.69268	0.846342	+	0.532640i	$0.178800\pi$
$242$	−3.73285e45	−0.122360
$243$	−1.16758e46	−0.353155
$244$	−5.35275e45	−0.149443
$245$	−2.33770e46	−0.602630
$246$	−1.83289e46	−0.436417
$247$	−2.92581e46	−0.643658
$248$	2.97418e46	0.604728
$249$	6.67919e46	1.25556
$250$	−2.88683e46	−0.501870
$251$	5.17200e46	0.831804	0.415902	−	0.909409i	$-0.363466\pi$
$251$	5.17200e46	0.831804	0.415902	+	0.909409i	$0.363466\pi$
$252$	9.64008e45	0.143473
$253$	−1.23133e47	−1.69639
$254$	−5.88254e46	−0.750426
$255$	−1.01771e46	−0.120252
$256$	5.70899e45	0.0625000
$257$	1.31420e47	1.33342	0.666709	−	0.745318i	$-0.267702\pi$
$257$	1.31420e47	1.33342	0.666709	+	0.745318i	$0.267702\pi$
$258$	3.57996e46	0.336739
$259$	−2.63556e47	−2.29894
$260$	1.21297e46	0.0981450
$261$	1.96344e46	0.147410
$262$	6.35290e46	0.442687
$263$	−8.91240e46	−0.576577	−0.288289	−	0.957544i	$-0.593086\pi$
$263$	−8.91240e46	−0.576577	−0.288289	+	0.957544i	$0.593086\pi$
$264$	−5.77558e46	−0.346992
$265$	1.09698e47	0.612215
$266$	2.74699e47	1.42451
$267$	2.53377e47	1.22123
$268$	3.90860e46	0.175143
$269$	−6.25084e46	−0.260477	−0.130238	−	0.991483i	$-0.541574\pi$
$269$	−6.25084e46	−0.260477	−0.130238	+	0.991483i	$0.541574\pi$
$270$	7.46277e46	0.289272
$271$	4.00744e45	0.0144533	0.00722663	−	0.999974i	$-0.497700\pi$
$271$	4.00744e45	0.0144533	0.00722663	+	0.999974i	$0.497700\pi$
$272$	−2.58088e46	−0.0866313
$273$	−2.38451e47	−0.745122
$274$	−2.67533e47	−0.778468
$275$	3.41011e47	0.924232
$276$	−2.81043e47	−0.709652
$277$	−2.15083e47	−0.506118	−0.253059	−	0.967451i	$-0.581437\pi$
$277$	−2.15083e47	−0.506118	−0.253059	+	0.967451i	$0.581437\pi$
$278$	−3.82290e47	−0.838531
$279$	1.49594e47	0.305937
$280$	−1.13883e47	−0.217209
$281$	−5.84722e47	−1.04034	−0.520171	−	0.854062i	$-0.674132\pi$
$281$	−5.84722e47	−1.04034	−0.520171	+	0.854062i	$0.674132\pi$
$282$	4.41158e47	0.732380
$283$	1.70464e47	0.264118	0.132059	−	0.991242i	$-0.457841\pi$
$283$	1.70464e47	0.264118	0.132059	+	0.991242i	$0.457841\pi$
$284$	6.41657e46	0.0928101
$285$	3.22656e47	0.435778
$286$	−3.11191e47	−0.392545
$287$	9.27211e47	1.09265
$288$	2.87148e46	0.0316193
$289$	−8.54971e47	−0.879920
$290$	−2.31951e47	−0.223170
$291$	8.47117e47	0.762132
$292$	5.74979e47	0.483823
$293$	1.12292e48	0.883955	0.441978	−	0.897026i	$-0.354277\pi$
$293$	1.12292e48	0.883955	0.441978	+	0.897026i	$0.354277\pi$
$294$	1.36888e48	1.00831
$295$	6.51871e46	0.0449399
$296$	−7.85054e47	−0.506653
$297$	−1.91461e48	−1.15699
$298$	−9.55242e46	−0.0540625
$299$	−1.51427e48	−0.802816
$300$	7.78333e47	0.386635
$301$	−1.81101e48	−0.843090
$302$	−9.05435e47	−0.395114
$303$	−4.91728e46	−0.0201184
$304$	8.18243e47	0.313941
$305$	3.18055e47	0.114460
$306$	−1.29812e47	−0.0438276
$307$	1.47725e48	0.468011	0.234006	−	0.972235i	$-0.424817\pi$
$307$	1.47725e48	0.468011	0.234006	+	0.972235i	$0.424817\pi$
$308$	2.92172e48	0.868759
$309$	−4.16227e48	−1.16182
$310$	−1.76723e48	−0.463170
$311$	−1.07656e47	−0.0264979	−0.0132489	−	0.999912i	$-0.504217\pi$
$311$	−1.07656e47	−0.0264979	−0.0132489	+	0.999912i	$0.504217\pi$
$312$	−7.10272e47	−0.164214
$313$	5.00199e48	1.08650	0.543249	−	0.839572i	$-0.317194\pi$
$313$	5.00199e48	1.08650	0.543249	+	0.839572i	$0.317194\pi$
$314$	−9.04587e47	−0.184638
$315$	−5.72804e47	−0.109888
$316$	−3.34703e48	−0.603617
$317$	8.99911e48	1.52596	0.762982	−	0.646420i	$-0.223735\pi$
$317$	8.99911e48	1.52596	0.762982	+	0.646420i	$0.223735\pi$
$318$	−6.42354e48	−1.02434
$319$	5.95080e48	0.892601
$320$	−3.39223e47	−0.0478697
$321$	2.17102e48	0.288281
$322$	1.42172e49	1.77675
$323$	−3.69906e48	−0.435153
$324$	−3.56248e48	−0.394570
$325$	4.19370e48	0.437393
$326$	−8.40962e48	−0.826101
$327$	−9.44404e48	−0.873930
$328$	2.76188e48	0.240804
$329$	−2.23170e49	−1.83365
$330$	3.43179e48	0.265766
$331$	−1.96107e48	−0.143168	−0.0715841	−	0.997435i	$-0.522805\pi$
$331$	−1.96107e48	−0.143168	−0.0715841	+	0.997435i	$0.522805\pi$
$332$	−1.00645e49	−0.692786
$333$	−3.94863e48	−0.256321
$334$	7.53861e48	0.461567
$335$	−2.32245e48	−0.134145
$336$	6.66861e48	0.363429
$337$	−1.07617e48	−0.0553473	−0.0276736	−	0.999617i	$-0.508810\pi$
$337$	−1.07617e48	−0.0553473	−0.0276736	+	0.999617i	$0.508810\pi$
$338$	1.07397e49	0.521335
$339$	1.15939e49	0.531294
$340$	1.53354e48	0.0663522
$341$	4.53390e49	1.85252
$342$	4.11556e48	0.158825
$343$	−2.52425e49	−0.920231
$344$	−5.39444e48	−0.185805
$345$	1.66993e49	0.543533
$346$	1.89382e49	0.582579
$347$	−5.52963e49	−1.60795	−0.803973	−	0.594666i	$-0.797284\pi$
$347$	−5.52963e49	−1.60795	−0.803973	+	0.594666i	$0.797284\pi$
$348$	1.35823e49	0.373403
$349$	4.48430e49	1.16573	0.582866	−	0.812568i	$-0.301931\pi$
$349$	4.48430e49	1.16573	0.582866	+	0.812568i	$0.301931\pi$
$350$	−3.93739e49	−0.968013
$351$	−2.35455e49	−0.547544
$352$	8.70290e48	0.191462
$353$	1.18535e48	0.0246740	0.0123370	−	0.999924i	$-0.496073\pi$
$353$	1.18535e48	0.0246740	0.0123370	+	0.999924i	$0.496073\pi$
$354$	−3.81714e48	−0.0751924
$355$	−3.81266e48	−0.0710846
$356$	−3.81799e49	−0.673845
$357$	−3.01470e49	−0.503749
$358$	−6.85385e49	−1.08447
$359$	7.51423e49	1.12601	0.563006	−	0.826453i	$-0.309645\pi$
$359$	7.51423e49	1.12601	0.563006	+	0.826453i	$0.309645\pi$
$360$	−1.70621e48	−0.0242177
$361$	4.29062e49	0.576939
$362$	−2.60730e48	−0.0332181
$363$	−1.29880e49	−0.156806
$364$	3.59308e49	0.411140
$365$	−3.41647e49	−0.370567
$366$	−1.86242e49	−0.191513
$367$	−8.22686e49	−0.802132	−0.401066	−	0.916049i	$-0.631360\pi$
$367$	−8.22686e49	−0.802132	−0.401066	+	0.916049i	$0.631360\pi$
$368$	4.23488e49	0.391569
$369$	1.38916e49	0.121825
$370$	4.66471e49	0.388053
$371$	3.24950e50	2.56464
$372$	1.03483e50	0.774965
$373$	−1.76822e50	−1.25665	−0.628323	−	0.777952i	$-0.716258\pi$
$373$	−1.76822e50	−1.25665	−0.628323	+	0.777952i	$0.716258\pi$
$374$	−3.93435e49	−0.265385
$375$	−1.00444e50	−0.643152
$376$	−6.64756e49	−0.404110
$377$	7.31820e49	0.422424
$378$	2.21064e50	1.21179
$379$	−2.84337e50	−1.48037	−0.740183	−	0.672405i	$-0.765261\pi$
$379$	−2.84337e50	−1.48037	−0.740183	+	0.672405i	$0.765261\pi$
$380$	−4.86192e49	−0.240452
$381$	−2.04676e50	−0.961678
$382$	3.96634e49	0.177074
$383$	4.63099e50	1.96471	0.982353	−	0.187035i	$-0.0598879\pi$
$383$	4.63099e50	1.96471	0.982353	+	0.187035i	$0.0598879\pi$
$384$	1.98637e49	0.0800944
$385$	−1.73606e50	−0.665395
$386$	−2.61363e50	−0.952340
$387$	−2.71327e49	−0.0940003
$388$	−1.27647e50	−0.420526
$389$	−2.51757e50	−0.788796	−0.394398	−	0.918940i	$-0.629047\pi$
$389$	−2.51757e50	−0.788796	−0.394398	+	0.918940i	$0.629047\pi$
$390$	4.22037e49	0.125774
$391$	−1.91448e50	−0.542754
$392$	−2.06269e50	−0.556359
$393$	2.21041e50	0.567308
$394$	5.36750e50	1.31098
$395$	1.98877e50	0.462319
$396$	4.37735e49	0.0968623
$397$	−2.13004e50	−0.448718	−0.224359	−	0.974507i	$-0.572029\pi$
$397$	−2.13004e50	−0.448718	−0.224359	+	0.974507i	$0.572029\pi$
$398$	−3.65274e50	−0.732655
$399$	9.55781e50	1.82552
$400$	−1.17283e50	−0.213336
$401$	8.38099e50	1.45205	0.726023	−	0.687671i	$-0.241367\pi$
$401$	8.38099e50	1.45205	0.726023	+	0.687671i	$0.241367\pi$
$402$	1.35995e50	0.224447
$403$	5.57572e50	0.876704
$404$	7.40958e48	0.0111009
$405$	2.11679e50	0.302207
$406$	−6.87092e50	−0.934884
$407$	−1.19675e51	−1.55208
$408$	−8.97987e49	−0.111019
$409$	−1.19965e51	−1.41400	−0.707000	−	0.707213i	$-0.749952\pi$
$409$	−1.19965e51	−1.41400	−0.707000	+	0.707213i	$0.749952\pi$
$410$	−1.64108e50	−0.184436
$411$	−9.30847e50	−0.997614
$412$	6.27189e50	0.641066
$413$	1.93099e50	0.188258
$414$	2.13004e50	0.198098
$415$	5.98023e50	0.530615
$416$	1.07027e50	0.0906093
$417$	−1.33013e51	−1.07459
$418$	1.24735e51	0.961722
$419$	7.52445e49	0.0553734	0.0276867	−	0.999617i	$-0.491186\pi$
$419$	7.52445e49	0.0553734	0.0276867	+	0.999617i	$0.491186\pi$
$420$	−3.96242e50	−0.278355
$421$	2.01587e50	0.135195	0.0675976	−	0.997713i	$-0.478467\pi$
$421$	2.01587e50	0.135195	0.0675976	+	0.997713i	$0.478467\pi$
$422$	−9.82221e49	−0.0628950
$423$	−3.34356e50	−0.204443
$424$	9.67927e50	0.565208
$425$	5.30204e50	0.295705
$426$	2.23257e50	0.118937
$427$	9.42152e50	0.479488
$428$	−3.27139e50	−0.159067
$429$	−1.08275e51	−0.503051
$430$	3.20532e50	0.142310
$431$	1.38759e51	0.588780	0.294390	−	0.955685i	$-0.404883\pi$
$431$	1.38759e51	0.588780	0.294390	+	0.955685i	$0.404883\pi$
$432$	6.58483e50	0.267062
$433$	2.08220e51	0.807249	0.403624	−	0.914925i	$-0.367750\pi$
$433$	2.08220e51	0.807249	0.403624	+	0.914925i	$0.367750\pi$
$434$	−5.23494e51	−1.94027
$435$	−8.07046e50	−0.285995
$436$	1.42307e51	0.482214
$437$	6.06965e51	1.96687
$438$	2.00057e51	0.620024
$439$	−5.34984e51	−1.58592	−0.792962	−	0.609271i	$-0.791462\pi$
$439$	−5.34984e51	−1.58592	−0.792962	+	0.609271i	$0.791462\pi$
$440$	−5.17118e50	−0.146643
$441$	−1.03748e51	−0.281467
$442$	−4.83840e50	−0.125594
$443$	−4.80718e51	−1.19404	−0.597019	−	0.802227i	$-0.703648\pi$
$443$	−4.80718e51	−1.19404	−0.597019	+	0.802227i	$0.703648\pi$
$444$	−2.73150e51	−0.649281
$445$	2.26862e51	0.516108
$446$	−1.13964e51	−0.248163
$447$	−3.32365e50	−0.0692816
$448$	−1.00486e51	−0.200531
$449$	1.04947e51	0.200524	0.100262	−	0.994961i	$-0.468032\pi$
$449$	1.04947e51	0.200524	0.100262	+	0.994961i	$0.468032\pi$
$450$	−5.89903e50	−0.107929
$451$	4.21026e51	0.737677
$452$	−1.74702e51	−0.293155
$453$	−3.15035e51	−0.506342
$454$	3.35195e51	0.516069
$455$	−2.13498e51	−0.314899
$456$	2.84698e51	0.402318
$457$	7.53292e51	1.01999	0.509997	−	0.860176i	$-0.329646\pi$
$457$	7.53292e51	1.01999	0.509997	+	0.860176i	$0.329646\pi$
$458$	3.08804e51	0.400687
$459$	−2.97683e51	−0.370174
$460$	−2.51632e51	−0.299908
$461$	4.54750e51	0.519523	0.259761	−	0.965673i	$-0.416356\pi$
$461$	4.54750e51	0.519523	0.259761	+	0.965673i	$0.416356\pi$
$462$	1.01658e52	1.11332
$463$	2.69935e51	0.283419	0.141710	−	0.989908i	$-0.454740\pi$
$463$	2.69935e51	0.283419	0.141710	+	0.989908i	$0.454740\pi$
$464$	−2.04664e51	−0.206035
$465$	−6.14886e51	−0.593557
$466$	3.87936e51	0.359116
$467$	−3.74523e51	−0.332506	−0.166253	−	0.986083i	$-0.553167\pi$
$467$	−3.74523e51	−0.332506	−0.166253	+	0.986083i	$0.553167\pi$
$468$	5.38319e50	0.0458401
$469$	−6.87963e51	−0.561946
$470$	3.94992e51	0.309514
$471$	−3.14740e51	−0.236616
$472$	5.75183e50	0.0414894
$473$	−8.22339e51	−0.569192
$474$	−1.16456e52	−0.773541
$475$	−1.68096e52	−1.07160
$476$	4.54269e51	0.277957
$477$	4.86844e51	0.285944
$478$	−1.17321e52	−0.661502
$479$	9.21392e51	0.498772	0.249386	−	0.968404i	$-0.419771\pi$
$479$	9.21392e51	0.498772	0.249386	+	0.968404i	$0.419771\pi$
$480$	−1.18028e51	−0.0613455
$481$	−1.47175e52	−0.734520
$482$	−2.49734e52	−1.19691
$483$	4.94671e52	2.27692
$484$	1.95709e51	0.0865218
$485$	7.58468e51	0.322087
$486$	6.12150e51	0.249718
$487$	3.89447e52	1.52628	0.763138	−	0.646235i	$-0.223658\pi$
$487$	3.89447e52	1.52628	0.763138	+	0.646235i	$0.223658\pi$
$488$	2.80638e51	0.105672
$489$	−2.92603e52	−1.05866
$490$	1.22563e52	0.426123
$491$	1.10918e52	0.370607	0.185304	−	0.982681i	$-0.440673\pi$
$491$	1.10918e52	0.370607	0.185304	+	0.982681i	$0.440673\pi$
$492$	9.60961e51	0.308593
$493$	9.25231e51	0.285585
$494$	1.53397e52	0.455135
$495$	−2.60098e51	−0.0741883
$496$	−1.55933e52	−0.427607
$497$	−1.12940e52	−0.297781
$498$	−3.50182e52	−0.887813
$499$	−7.57687e52	−1.84727	−0.923633	−	0.383279i	$-0.874795\pi$
$499$	−7.57687e52	−1.84727	−0.923633	+	0.383279i	$0.874795\pi$
$500$	1.51353e52	0.354876
$501$	2.62297e52	0.591503
$502$	−2.71162e52	−0.588175
$503$	3.33794e52	0.696472	0.348236	−	0.937407i	$-0.386781\pi$
$503$	3.33794e52	0.696472	0.348236	+	0.937407i	$0.386781\pi$
$504$	−5.05418e51	−0.101451
$505$	−4.40270e50	−0.00850232
$506$	6.45573e52	1.19953
$507$	3.73675e52	0.668095
$508$	3.08415e52	0.530631
$509$	−1.15021e53	−1.90450	−0.952251	−	0.305318i	$-0.901237\pi$
$509$	−1.15021e53	−1.90450	−0.952251	+	0.305318i	$0.901237\pi$
$510$	5.33575e51	0.0850310
$511$	−1.01204e53	−1.55235
$512$	−2.99316e51	−0.0441942
$513$	9.43773e52	1.34146
$514$	−6.89021e52	−0.942869
$515$	−3.72670e52	−0.491002
$516$	−1.87693e52	−0.238110
$517$	−1.01337e53	−1.23795
$518$	1.38179e53	1.62560
$519$	6.58932e52	0.746581
$520$	−6.35944e51	−0.0693990
$521$	9.40376e52	0.988476	0.494238	−	0.869327i	$-0.335447\pi$
$521$	9.40376e52	0.988476	0.494238	+	0.869327i	$0.335447\pi$
$522$	−1.02941e52	−0.104235
$523$	1.45735e53	1.42161	0.710804	−	0.703390i	$-0.248331\pi$
$523$	1.45735e53	1.42161	0.710804	+	0.703390i	$0.248331\pi$
$524$	−3.33075e52	−0.313027
$525$	−1.36997e53	−1.24052
$526$	4.67266e52	0.407702
$527$	7.04931e52	0.592707
$528$	3.02807e52	0.245360
$529$	1.86087e53	1.45322
$530$	−5.75133e52	−0.432901
$531$	2.89303e51	0.0209899
$532$	−1.44021e53	−1.00728
$533$	5.17771e52	0.349106
$534$	−1.32842e53	−0.863540
$535$	1.94383e52	0.121831
$536$	−2.04923e52	−0.123845
$537$	−2.38471e53	−1.38975
$538$	3.27724e52	0.184185
$539$	−3.14440e53	−1.70434
$540$	−3.91264e52	−0.204546
$541$	3.06716e53	1.54664	0.773321	−	0.634014i	$-0.218594\pi$
$541$	3.06716e53	1.54664	0.773321	+	0.634014i	$0.218594\pi$
$542$	−2.10105e51	−0.0102200
$543$	−9.07180e51	−0.0425693
$544$	1.35313e52	0.0612576
$545$	−8.45574e52	−0.369335
$546$	1.25017e53	0.526881
$547$	−1.78310e53	−0.725142	−0.362571	−	0.931956i	$-0.618101\pi$
$547$	−1.78310e53	−0.725142	−0.362571	+	0.931956i	$0.618101\pi$
$548$	1.40264e53	0.550460
$549$	1.41154e52	0.0534605
$550$	−1.78788e53	−0.653531
$551$	−2.93335e53	−1.03492
$552$	1.47347e53	0.501799
$553$	5.89120e53	1.93671
$554$	1.12766e53	0.357879
$555$	1.62303e53	0.497294
$556$	2.00430e53	0.592931
$557$	1.84275e53	0.526369	0.263185	−	0.964745i	$-0.415227\pi$
$557$	1.84275e53	0.526369	0.263185	+	0.964745i	$0.415227\pi$
$558$	−7.84304e52	−0.216330
$559$	−1.01130e53	−0.269370
$560$	5.97075e52	0.153590
$561$	−1.36891e53	−0.340094
$562$	3.06563e53	0.735633
$563$	−5.23191e53	−1.21268	−0.606341	−	0.795205i	$-0.707363\pi$
$563$	−5.23191e53	−1.21268	−0.606341	+	0.795205i	$0.707363\pi$
$564$	−2.31294e53	−0.517871
$565$	1.03806e53	0.224532
$566$	−8.93723e52	−0.186759
$567$	6.27042e53	1.26598
$568$	−3.36413e52	−0.0656266
$569$	−9.35194e53	−1.76284	−0.881419	−	0.472335i	$-0.843411\pi$
$569$	−9.35194e53	−1.76284	−0.881419	+	0.472335i	$0.843411\pi$
$570$	−1.69165e53	−0.308141
$571$	1.20988e53	0.212979	0.106490	−	0.994314i	$-0.466039\pi$
$571$	1.20988e53	0.212979	0.106490	+	0.994314i	$0.466039\pi$
$572$	1.63154e53	0.277572
$573$	1.38004e53	0.226922
$574$	−4.86126e53	−0.772621
$575$	−8.69992e53	−1.33657
$576$	−1.50548e52	−0.0223582
$577$	8.12328e52	0.116628	0.0583140	−	0.998298i	$-0.481428\pi$
$577$	8.12328e52	0.116628	0.0583140	+	0.998298i	$0.481428\pi$
$578$	4.48251e53	0.622198
$579$	−9.09381e53	−1.22043
$580$	1.21609e53	0.157805
$581$	1.77148e54	2.22281
$582$	−4.44133e53	−0.538909
$583$	1.47553e54	1.73145
$584$	−3.01455e53	−0.342114
$585$	−3.19864e52	−0.0351096
$586$	−5.88734e53	−0.625051
$587$	8.92327e53	0.916391	0.458196	−	0.888851i	$-0.348496\pi$
$587$	8.92327e53	0.916391	0.458196	+	0.888851i	$0.348496\pi$
$588$	−7.17687e53	−0.712980
$589$	−2.23491e54	−2.14789
$590$	−3.41768e52	−0.0317773
$591$	1.86756e54	1.68003
$592$	4.11594e53	0.358258
$593$	4.40300e53	0.370836	0.185418	−	0.982660i	$-0.440636\pi$
$593$	4.40300e53	0.370836	0.185418	+	0.982660i	$0.440636\pi$
$594$	1.00380e54	0.818113
$595$	−2.69922e53	−0.212891
$596$	5.00822e52	0.0382280
$597$	−1.27093e54	−0.938904
$598$	7.93915e53	0.567677
$599$	4.21241e53	0.291546	0.145773	−	0.989318i	$-0.453433\pi$
$599$	4.21241e53	0.291546	0.145773	+	0.989318i	$0.453433\pi$
$600$	−4.08071e53	−0.273392
$601$	−6.19377e53	−0.401701	−0.200850	−	0.979622i	$-0.564371\pi$
$601$	−6.19377e53	−0.401701	−0.200850	+	0.979622i	$0.564371\pi$
$602$	9.49490e53	0.596154
$603$	−1.03071e53	−0.0626542
$604$	4.74709e53	0.279387
$605$	−1.16288e53	−0.0662683
$606$	2.57807e52	0.0142259
$607$	−4.65300e53	−0.248630	−0.124315	−	0.992243i	$-0.539673\pi$
$607$	−4.65300e53	−0.248630	−0.124315	+	0.992243i	$0.539673\pi$
$608$	−4.28995e53	−0.221989
$609$	−2.39065e54	−1.19806
$610$	−1.66753e53	−0.0809358
$611$	−1.24622e54	−0.585858
$612$	6.80590e52	0.0309908
$613$	−3.85750e53	−0.170148	−0.0850739	−	0.996375i	$-0.527113\pi$
$613$	−3.85750e53	−0.170148	−0.0850739	+	0.996375i	$0.527113\pi$
$614$	−7.74505e53	−0.330934
$615$	−5.70994e53	−0.236356
$616$	−1.53182e54	−0.614305
$617$	−8.01633e53	−0.311469	−0.155735	−	0.987799i	$-0.549774\pi$
$617$	−8.01633e53	−0.311469	−0.155735	+	0.987799i	$0.549774\pi$
$618$	2.18223e54	0.821533
$619$	−3.25450e54	−1.18718	−0.593590	−	0.804767i	$-0.702290\pi$
$619$	−3.25450e54	−1.18718	−0.593590	+	0.804767i	$0.702290\pi$
$620$	9.26538e53	0.327511
$621$	4.88456e54	1.67317
$622$	5.64428e52	0.0187368
$623$	6.72016e54	2.16203
$624$	3.72387e53	0.116117
$625$	1.92415e54	0.581539
$626$	−2.62249e54	−0.768270
$627$	4.33999e54	1.23246
$628$	4.74264e53	0.130559
$629$	−1.86071e54	−0.496582
$630$	3.00314e53	0.0777026
$631$	−1.61425e54	−0.404948	−0.202474	−	0.979288i	$-0.564898\pi$
$631$	−1.61425e54	−0.404948	−0.202474	+	0.979288i	$0.564898\pi$
$632$	1.75481e54	0.426821
$633$	−3.41752e53	−0.0806006
$634$	−4.71813e54	−1.07902
$635$	−1.83257e54	−0.406418
$636$	3.36778e54	0.724320
$637$	−3.86694e54	−0.806581
$638$	−3.11994e54	−0.631164
$639$	−1.69207e53	−0.0332011
$640$	1.77850e53	0.0338490
$641$	2.00214e54	0.369626	0.184813	−	0.982774i	$-0.440832\pi$
$641$	2.00214e54	0.369626	0.184813	+	0.982774i	$0.440832\pi$
$642$	−1.13824e54	−0.203845
$643$	−9.72790e53	−0.169007	−0.0845036	−	0.996423i	$-0.526930\pi$
$643$	−9.72790e53	−0.169007	−0.0845036	+	0.996423i	$0.526930\pi$
$644$	−7.45392e54	−1.25635
$645$	1.11525e54	0.182372
$646$	1.93937e54	0.307700
$647$	6.72069e54	1.03462	0.517309	−	0.855799i	$-0.326934\pi$
$647$	6.72069e54	1.03462	0.517309	+	0.855799i	$0.326934\pi$
$648$	1.86776e54	0.279003
$649$	8.76820e53	0.127098
$650$	−2.19871e54	−0.309284
$651$	−1.82143e55	−2.48648
$652$	4.40907e54	0.584142
$653$	−8.56438e53	−0.110126	−0.0550629	−	0.998483i	$-0.517536\pi$
$653$	−8.56438e53	−0.110126	−0.0550629	+	0.998483i	$0.517536\pi$
$654$	4.95140e54	0.617962
$655$	1.97910e54	0.239752
$656$	−1.44802e54	−0.170274
$657$	−1.51624e54	−0.173079
$658$	1.17006e55	1.29659
$659$	4.42081e54	0.475594	0.237797	−	0.971315i	$-0.423575\pi$
$659$	4.42081e54	0.475594	0.237797	+	0.971315i	$0.423575\pi$
$660$	−1.79925e54	−0.187925
$661$	7.16606e54	0.726695	0.363347	−	0.931654i	$-0.381634\pi$
$661$	7.16606e54	0.726695	0.363347	+	0.931654i	$0.381634\pi$
$662$	1.02816e54	0.101235
$663$	−1.68346e54	−0.160950
$664$	5.27669e54	0.489874
$665$	8.55760e54	0.771490
$666$	2.07022e54	0.181246
$667$	−1.51818e55	−1.29083
$668$	−3.95240e54	−0.326377
$669$	−3.96524e54	−0.318024
$670$	1.21763e54	0.0948545
$671$	4.27811e54	0.323715
$672$	−3.49627e54	−0.256983
$673$	9.69573e54	0.692288	0.346144	−	0.938181i	$-0.387491\pi$
$673$	9.69573e54	0.692288	0.346144	+	0.938181i	$0.387491\pi$
$674$	5.64221e53	0.0391364
$675$	−1.35275e55	−0.911581
$676$	−5.63070e54	−0.368639
$677$	−1.27595e54	−0.0811620	−0.0405810	−	0.999176i	$-0.512921\pi$
$677$	−1.27595e54	−0.0811620	−0.0405810	+	0.999176i	$0.512921\pi$
$678$	−6.07853e54	−0.375681
$679$	2.24676e55	1.34926
$680$	−8.04015e53	−0.0469181
$681$	1.16627e55	0.661348
$682$	−2.37707e55	−1.30993
$683$	−3.02887e55	−1.62210	−0.811050	−	0.584978i	$-0.801103\pi$
$683$	−3.02887e55	−1.62210	−0.811050	+	0.584978i	$0.801103\pi$
$684$	−2.15774e54	−0.112307
$685$	−8.33436e54	−0.421605
$686$	1.32343e55	0.650702
$687$	1.07444e55	0.513485
$688$	2.82824e54	0.131384
$689$	1.81458e55	0.819410
$690$	−8.75524e54	−0.384336
$691$	−1.23833e55	−0.528464	−0.264232	−	0.964459i	$-0.585118\pi$
$691$	−1.23833e55	−0.528464	−0.264232	+	0.964459i	$0.585118\pi$
$692$	−9.92908e54	−0.411946
$693$	−7.70469e54	−0.310783
$694$	2.89912e55	1.13699
$695$	−1.19094e55	−0.454134
$696$	−7.12102e54	−0.264035
$697$	6.54611e54	0.236018
$698$	−2.35106e55	−0.824297
$699$	1.34977e55	0.460210
$700$	2.06432e55	0.684489
$701$	1.68667e55	0.543911	0.271956	−	0.962310i	$-0.412330\pi$
$701$	1.68667e55	0.543911	0.271956	+	0.962310i	$0.412330\pi$
$702$	1.23446e55	0.387172
$703$	5.89919e55	1.79955
$704$	−4.56283e54	−0.135384
$705$	1.37433e55	0.396645
$706$	−6.21465e53	−0.0174472
$707$	−1.30418e54	−0.0356172
$708$	2.00128e54	0.0531691
$709$	−2.74582e55	−0.709693	−0.354846	−	0.934925i	$-0.615467\pi$
$709$	−2.74582e55	−0.709693	−0.354846	+	0.934925i	$0.615467\pi$
$710$	1.99893e54	0.0502644
$711$	8.82625e54	0.215933
$712$	2.00173e55	0.476481
$713$	−1.15670e56	−2.67900
$714$	1.58057e55	0.356204
$715$	−9.69445e54	−0.212596
$716$	3.59339e55	0.766833
$717$	−4.08204e55	−0.847722
$718$	−3.93962e55	−0.796211
$719$	7.38193e55	1.45197	0.725983	−	0.687713i	$-0.241385\pi$
$719$	7.38193e55	1.45197	0.725983	+	0.687713i	$0.241385\pi$
$720$	8.94544e53	0.0171245
$721$	−1.10393e56	−2.05686
$722$	−2.24952e55	−0.407957
$723$	−8.68920e55	−1.53385
$724$	1.36698e54	0.0234887
$725$	4.20451e55	0.703273
$726$	6.80944e54	0.110879
$727$	6.36181e55	1.00846	0.504231	−	0.863569i	$-0.331776\pi$
$727$	6.36181e55	1.00846	0.504231	+	0.863569i	$0.331776\pi$
$728$	−1.88381e55	−0.290720
$729$	7.38210e55	1.10916
$730$	1.79121e55	0.262030
$731$	−1.27857e55	−0.182111
$732$	9.76446e54	0.135420
$733$	1.13206e56	1.52877	0.764387	−	0.644757i	$-0.223042\pi$
$733$	1.13206e56	1.52877	0.764387	+	0.644757i	$0.223042\pi$
$734$	4.31325e55	0.567193
$735$	4.26443e55	0.546082
$736$	−2.22029e55	−0.276881
$737$	−3.12389e55	−0.379384
$738$	−7.28318e54	−0.0861434
$739$	−1.60231e55	−0.184578	−0.0922892	−	0.995732i	$-0.529418\pi$
$739$	−1.60231e55	−0.184578	−0.0922892	+	0.995732i	$0.529418\pi$
$740$	−2.44565e55	−0.274395
$741$	5.33725e55	0.583260
$742$	−1.70368e56	−1.81347
$743$	6.06694e55	0.629054	0.314527	−	0.949249i	$-0.398154\pi$
$743$	6.06694e55	0.629054	0.314527	+	0.949249i	$0.398154\pi$
$744$	−5.42549e55	−0.547983
$745$	−2.97584e54	−0.0292794
$746$	9.27055e55	0.888583
$747$	2.65405e55	0.247832
$748$	2.06273e55	0.187656
$749$	5.75807e55	0.510365
$750$	5.26615e55	0.454777
$751$	−1.16446e56	−0.979815	−0.489908	−	0.871774i	$-0.662970\pi$
$751$	−1.16446e56	−0.979815	−0.489908	+	0.871774i	$0.662970\pi$
$752$	3.48524e55	0.285749
$753$	−9.43475e55	−0.753752
$754$	−3.83685e55	−0.298699
$755$	−2.82067e55	−0.213987
$756$	−1.15901e56	−0.856868
$757$	−1.70573e56	−1.22897	−0.614485	−	0.788929i	$-0.710636\pi$
$757$	−1.70573e56	−1.22897	−0.614485	+	0.788929i	$0.710636\pi$
$758$	1.49075e56	1.04678
$759$	2.24619e56	1.53721
$760$	2.54905e55	0.170025
$761$	−6.74390e55	−0.438440	−0.219220	−	0.975675i	$-0.570351\pi$
$761$	−6.74390e55	−0.438440	−0.219220	+	0.975675i	$0.570351\pi$
$762$	1.07309e56	0.680009
$763$	−2.50478e56	−1.54718
$764$	−2.07950e55	−0.125210
$765$	−4.04400e54	−0.0237363
$766$	−2.42797e56	−1.38926
$767$	1.07830e55	0.0601492
$768$	−1.04143e55	−0.0566353
$769$	1.95634e56	1.03725	0.518623	−	0.855003i	$-0.326445\pi$
$769$	1.95634e56	1.03725	0.518623	+	0.855003i	$0.326445\pi$
$770$	9.10194e55	0.470506
$771$	−2.39736e56	−1.20830
$772$	1.37030e56	0.673406
$773$	−1.50394e56	−0.720661	−0.360330	−	0.932825i	$-0.617336\pi$
$773$	−1.50394e56	−0.720661	−0.360330	+	0.932825i	$0.617336\pi$
$774$	1.42254e55	0.0664682
$775$	3.20341e56	1.45958
$776$	6.69240e55	0.297357
$777$	4.80779e56	2.08322
$778$	1.31993e56	0.557763
$779$	−2.07538e56	−0.855297
$780$	−2.21269e55	−0.0889355
$781$	−5.12835e55	−0.201040
$782$	1.00374e56	0.383785
$783$	−2.36062e56	−0.880383
$784$	1.08144e56	0.393405
$785$	−2.81803e55	−0.0999971
$786$	−1.15889e56	−0.401147
$787$	1.68844e55	0.0570135	0.0285067	−	0.999594i	$-0.490925\pi$
$787$	1.68844e55	0.0570135	0.0285067	+	0.999594i	$0.490925\pi$
$788$	−2.81411e56	−0.927002
$789$	1.62580e56	0.522474
$790$	−1.04269e56	−0.326909
$791$	3.07497e56	0.940589
$792$	−2.29499e55	−0.0684920
$793$	5.26115e55	0.153198
$794$	1.11676e56	0.317292
$795$	−2.00111e56	−0.554767
$796$	1.91509e56	0.518065
$797$	−1.50671e56	−0.397733	−0.198867	−	0.980027i	$-0.563726\pi$
$797$	−1.50671e56	−0.397733	−0.198867	+	0.980027i	$0.563726\pi$
$798$	−5.01104e56	−1.29084
$799$	−1.57558e56	−0.396077
$800$	6.14899e55	0.150851
$801$	1.00682e56	0.241056
$802$	−4.39405e56	−1.02675
$803$	−4.59544e56	−1.04803
$804$	−7.13005e55	−0.158708
$805$	4.42905e56	0.962256
$806$	−2.92329e56	−0.619923
$807$	1.14027e56	0.236035
$808$	−3.88475e54	−0.00784950
$809$	−1.39565e56	−0.275284	−0.137642	−	0.990482i	$-0.543952\pi$
$809$	−1.39565e56	−0.275284	−0.137642	+	0.990482i	$0.543952\pi$
$810$	−1.10981e56	−0.213693
$811$	4.56956e56	0.858950	0.429475	−	0.903079i	$-0.358699\pi$
$811$	4.56956e56	0.858950	0.429475	+	0.903079i	$0.358699\pi$
$812$	3.60234e56	0.661063
$813$	−7.31036e54	−0.0130970
$814$	6.27443e56	1.09748
$815$	−2.61982e56	−0.447403
$816$	4.70804e55	0.0785022
$817$	4.05358e56	0.659947
$818$	6.28962e56	0.999850
$819$	−9.47511e55	−0.147078
$820$	8.60399e55	0.130416
$821$	4.42835e56	0.655466	0.327733	−	0.944770i	$-0.393715\pi$
$821$	4.42835e56	0.655466	0.327733	+	0.944770i	$0.393715\pi$
$822$	4.88032e56	0.705420
$823$	5.42145e56	0.765277	0.382639	−	0.923898i	$-0.375015\pi$
$823$	5.42145e56	0.765277	0.382639	+	0.923898i	$0.375015\pi$
$824$	−3.28828e56	−0.453302
$825$	−6.22071e56	−0.837506
$826$	−1.01240e56	−0.133119
$827$	−1.23224e57	−1.58248	−0.791242	−	0.611504i	$-0.790565\pi$
$827$	−1.23224e57	−1.58248	−0.791242	+	0.611504i	$0.790565\pi$
$828$	−1.11675e56	−0.140077
$829$	−1.09397e56	−0.134027	−0.0670136	−	0.997752i	$-0.521347\pi$
$829$	−1.09397e56	−0.134027	−0.0670136	+	0.997752i	$0.521347\pi$
$830$	−3.13536e56	−0.375202
$831$	3.92354e56	0.458626
$832$	−5.61129e55	−0.0640705
$833$	−4.88892e56	−0.545299
$834$	6.97371e56	0.759847
$835$	2.34848e56	0.249977
$836$	−6.53969e56	−0.680040
$837$	−1.79855e57	−1.82716
$838$	−3.94498e55	−0.0391549
$839$	3.36063e56	0.325884	0.162942	−	0.986636i	$-0.447902\pi$
$839$	3.36063e56	0.325884	0.162942	+	0.986636i	$0.447902\pi$
$840$	2.07745e56	0.196827
$841$	−3.46537e56	−0.320796
$842$	−1.05690e56	−0.0955974
$843$	1.06665e57	0.942721
$844$	5.14967e55	0.0444735
$845$	3.34571e56	0.282346
$846$	1.75299e56	0.144563
$847$	−3.44472e56	−0.277605
$848$	−5.07473e56	−0.399663
$849$	−3.10960e56	−0.239334
$850$	−2.77980e56	−0.209095
$851$	3.05317e57	2.24452
$852$	−1.17051e56	−0.0841012
$853$	−1.66626e57	−1.17014	−0.585070	−	0.810983i	$-0.698933\pi$
$853$	−1.66626e57	−1.17014	−0.585070	+	0.810983i	$0.698933\pi$
$854$	−4.93959e56	−0.339049
$855$	1.28211e56	0.0860173
$856$	1.71515e56	0.112477
$857$	1.98611e57	1.27315	0.636573	−	0.771217i	$-0.280351\pi$
$857$	1.98611e57	1.27315	0.636573	+	0.771217i	$0.280351\pi$
$858$	5.67674e56	0.355711
$859$	−1.03574e57	−0.634429	−0.317215	−	0.948354i	$-0.602748\pi$
$859$	−1.03574e57	−0.634429	−0.317215	+	0.948354i	$0.602748\pi$
$860$	−1.68051e56	−0.100629
$861$	−1.69141e57	−0.990122
$862$	−7.27495e56	−0.416331
$863$	1.56174e57	0.873773	0.436887	−	0.899517i	$-0.356081\pi$
$863$	1.56174e57	0.873773	0.436887	+	0.899517i	$0.356081\pi$
$864$	−3.45235e56	−0.188841
$865$	5.89976e56	0.315515
$866$	−1.09167e57	−0.570811
$867$	1.55963e57	0.797352
$868$	2.74462e57	1.37198
$869$	2.67506e57	1.30752
$870$	4.23124e56	0.202229
$871$	−3.84171e56	−0.179544
$872$	−7.46098e56	−0.340977
$873$	3.36611e56	0.150436
$874$	−3.18224e57	−1.39079
$875$	−2.66401e57	−1.13862
$876$	−1.04887e57	−0.438423
$877$	1.06650e57	0.435981	0.217991	−	0.975951i	$-0.430050\pi$
$877$	1.06650e57	0.435981	0.217991	+	0.975951i	$0.430050\pi$
$878$	2.80486e57	1.12142
$879$	−2.04843e57	−0.801009
$880$	2.71119e56	0.103693
$881$	−4.14145e57	−1.54925	−0.774627	−	0.632419i	$-0.782062\pi$
$881$	−4.14145e57	−1.54925	−0.774627	+	0.632419i	$0.782062\pi$
$882$	5.43939e56	0.199027
$883$	−1.60432e57	−0.574193	−0.287096	−	0.957902i	$-0.592690\pi$
$883$	−1.60432e57	−0.574193	−0.287096	+	0.957902i	$0.592690\pi$
$884$	2.53672e56	0.0888082
$885$	−1.18914e56	−0.0407230
$886$	2.52035e57	0.844312
$887$	−3.80178e57	−1.24588	−0.622940	−	0.782269i	$-0.714062\pi$
$887$	−3.80178e57	−1.24588	−0.622940	+	0.782269i	$0.714062\pi$
$888$	1.43209e57	0.459111
$889$	−5.42849e57	−1.70253
$890$	−1.18941e57	−0.364943
$891$	2.84726e57	0.854696
$892$	5.97499e56	0.175478
$893$	4.99523e57	1.43533
$894$	1.74255e56	0.0489895
$895$	−2.13516e57	−0.587329
$896$	5.26834e56	0.141797
$897$	2.76233e57	0.727483
$898$	−5.50226e56	−0.141792
$899$	5.59009e57	1.40963
$900$	3.09279e56	0.0763171
$901$	2.29415e57	0.553973
$902$	−2.20739e57	−0.521617
$903$	3.30363e57	0.763978
$904$	9.15940e56	0.207292
$905$	−8.12246e55	−0.0179904
$906$	1.65169e57	0.358038
$907$	−4.93697e57	−1.04741	−0.523707	−	0.851899i	$-0.675451\pi$
$907$	−4.93697e57	−1.04741	−0.523707	+	0.851899i	$0.675451\pi$
$908$	−1.75739e57	−0.364916
$909$	−1.95394e55	−0.00397114
$910$	1.11934e57	0.222667
$911$	−1.90511e57	−0.370948	−0.185474	−	0.982649i	$-0.559382\pi$
$911$	−1.90511e57	−0.370948	−0.185474	+	0.982649i	$0.559382\pi$
$912$	−1.49264e57	−0.284482
$913$	8.04390e57	1.50067
$914$	−3.94942e57	−0.721245
$915$	−5.80195e56	−0.103720
$916$	−1.61902e57	−0.283329
$917$	5.86255e57	1.00435
$918$	1.56072e57	0.261753
$919$	−6.96417e57	−1.14345	−0.571724	−	0.820446i	$-0.693725\pi$
$919$	−6.96417e57	−1.14345	−0.571724	+	0.820446i	$0.693725\pi$
$920$	1.31928e57	0.212067
$921$	−2.69480e57	−0.424095
$922$	−2.38420e57	−0.367358
$923$	−6.30676e56	−0.0951422
$924$	−5.32979e57	−0.787239
$925$	−8.45559e57	−1.22287
$926$	−1.41524e57	−0.200408
$927$	−1.65392e57	−0.229330
$928$	1.07303e57	0.145689
$929$	−1.09571e58	−1.45676	−0.728381	−	0.685172i	$-0.759727\pi$
$929$	−1.09571e58	−1.45676	−0.728381	+	0.685172i	$0.759727\pi$
$930$	3.22378e57	0.419708
$931$	1.54998e58	1.97609
$932$	−2.03390e57	−0.253933
$933$	1.96386e56	0.0240114
$934$	1.96358e57	0.235117
$935$	−1.22566e57	−0.143728
$936$	−2.82234e56	−0.0324139
$937$	1.45396e58	1.63543	0.817714	−	0.575625i	$-0.195241\pi$
$937$	1.45396e58	1.63543	0.817714	+	0.575625i	$0.195241\pi$
$938$	3.60691e57	0.397356
$939$	−9.12462e57	−0.984545
$940$	−2.07089e57	−0.218859
$941$	9.69075e57	1.00314	0.501568	−	0.865118i	$-0.332757\pi$
$941$	9.69075e57	1.00314	0.501568	+	0.865118i	$0.332757\pi$
$942$	1.65014e57	0.167313
$943$	−1.07413e58	−1.06679
$944$	−3.01562e56	−0.0293374
$945$	6.88675e57	0.656287
$946$	4.31142e57	0.402479
$947$	1.86673e58	1.70709	0.853546	−	0.521018i	$-0.174447\pi$
$947$	1.86673e58	1.70709	0.853546	+	0.521018i	$0.174447\pi$
$948$	6.10563e57	0.546976
$949$	−5.65139e57	−0.495980
$950$	8.81306e57	0.757733
$951$	−1.64161e58	−1.38277
$952$	−2.38168e57	−0.196545
$953$	−1.29859e58	−1.04993	−0.524964	−	0.851124i	$-0.675921\pi$
$953$	−1.29859e58	−1.04993	−0.524964	+	0.851124i	$0.675921\pi$
$954$	−2.55246e57	−0.202193
$955$	1.23562e57	0.0959003
$956$	6.15099e57	0.467753
$957$	−1.08554e58	−0.808843
$958$	−4.83075e57	−0.352685
$959$	−2.46883e58	−1.76615
$960$	6.18809e56	0.0433778
$961$	2.80327e58	1.92557
$962$	7.71619e57	0.519384
$963$	8.62679e56	0.0569032
$964$	1.30933e58	0.846342
$965$	−8.14216e57	−0.515771
$966$	−2.59350e58	−1.61002
$967$	2.82879e58	1.72101	0.860506	−	0.509440i	$-0.170148\pi$
$967$	2.82879e58	1.72101	0.860506	+	0.509440i	$0.170148\pi$
$968$	−1.02608e57	−0.0611801
$969$	6.74781e57	0.394321
$970$	−3.97656e57	−0.227750
$971$	1.13038e58	0.634525	0.317263	−	0.948338i	$-0.397236\pi$
$971$	1.13038e58	0.634525	0.317263	+	0.948338i	$0.397236\pi$
$972$	−3.20943e57	−0.176577
$973$	−3.52782e58	−1.90242
$974$	−2.04182e58	−1.07924
$975$	−7.65013e57	−0.396350
$976$	−1.47135e57	−0.0747214
$977$	−3.30653e58	−1.64600	−0.822998	−	0.568045i	$-0.807700\pi$
$977$	−3.30653e58	−1.64600	−0.822998	+	0.568045i	$0.807700\pi$
$978$	1.53408e58	0.748584
$979$	3.05147e58	1.45965
$980$	−6.42583e57	−0.301315
$981$	−3.75269e57	−0.172503
$982$	−5.81531e57	−0.262059
$983$	1.60625e58	0.709611	0.354805	−	0.934940i	$-0.384547\pi$
$983$	1.60625e58	0.709611	0.354805	+	0.934940i	$0.384547\pi$
$984$	−5.03821e57	−0.218208
$985$	1.67212e58	0.710004
$986$	−4.85087e57	−0.201939
$987$	4.07107e58	1.66159
$988$	−8.04240e57	−0.321829
$989$	2.09796e58	0.823132
$990$	1.36366e57	0.0524590
$991$	−1.89051e58	−0.713086	−0.356543	−	0.934279i	$-0.616045\pi$
$991$	−1.89051e58	−0.713086	−0.356543	+	0.934279i	$0.616045\pi$
$992$	8.17537e57	0.302364
$993$	3.57737e57	0.129734
$994$	5.92130e57	0.210563
$995$	−1.13793e58	−0.396794
$996$	1.83596e58	0.627778
$997$	−1.61839e58	−0.542658	−0.271329	−	0.962487i	$-0.587463\pi$
$997$	−1.61839e58	−0.542658	−0.271329	+	0.962487i	$0.587463\pi$
$998$	3.97246e58	1.30621
$999$	4.74739e58	1.53083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.40.a.b.1.1	✓	2
3.2	odd	2		18.40.a.e.1.2		2
4.3	odd	2		16.40.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.40.a.b.1.1	✓	2	1.1	even	1	trivial
16.40.a.b.1.2		2	4.3	odd	2
18.40.a.e.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:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-524288. q^{2} -1.82420e9 q^{3} +2.74878e11 q^{4} -1.63330e13 q^{5} +9.56404e14 q^{6} -4.83820e16 q^{7} -1.44115e17 q^{8} -7.24864e17 q^{9} +O(q^{10})\)	\(q-524288. q^{2} -1.82420e9 q^{3} +2.74878e11 q^{4} -1.63330e13 q^{5} +9.56404e14 q^{6} -4.83820e16 q^{7} -1.44115e17 q^{8} -7.24864e17 q^{9} +8.56319e18 q^{10} -2.19692e20 q^{11} -5.01431e20 q^{12} -2.70174e21 q^{13} +2.53661e22 q^{14} +2.97946e22 q^{15} +7.55579e22 q^{16} -3.41577e23 q^{17} +3.80038e23 q^{18} +1.08294e25 q^{19} -4.48958e24 q^{20} +8.82583e25 q^{21} +1.15182e26 q^{22} +5.60481e26 q^{23} +2.62894e26 q^{24} -1.55222e27 q^{25} +1.41649e27 q^{26} +8.71495e27 q^{27} -1.32992e28 q^{28} -2.70870e28 q^{29} -1.56209e28 q^{30} -2.06375e29 q^{31} -3.96141e28 q^{32} +4.00761e29 q^{33} +1.79085e29 q^{34} +7.90223e29 q^{35} -1.99249e29 q^{36} +5.44740e30 q^{37} -5.67770e30 q^{38} +4.92850e30 q^{39} +2.35383e30 q^{40} -1.91644e31 q^{41} -4.62728e31 q^{42} +3.74314e31 q^{43} -6.03885e31 q^{44} +1.18392e31 q^{45} -2.93853e32 q^{46} +4.61267e32 q^{47} -1.37832e32 q^{48} +1.43128e33 q^{49} +8.13812e32 q^{50} +6.23104e32 q^{51} -7.42648e32 q^{52} -6.71634e33 q^{53} -4.56914e33 q^{54} +3.58823e33 q^{55} +6.97258e33 q^{56} -1.97549e34 q^{57} +1.42014e34 q^{58} -3.99113e33 q^{59} +8.18987e33 q^{60} -1.94732e34 q^{61} +1.08200e35 q^{62} +3.50704e34 q^{63} +2.07692e34 q^{64} +4.41274e34 q^{65} -2.10114e35 q^{66} +1.42194e35 q^{67} -9.38920e34 q^{68} -1.02243e36 q^{69} -4.14304e35 q^{70} +2.33433e35 q^{71} +1.04464e35 q^{72} +2.09176e36 q^{73} -2.85601e36 q^{74} +2.83156e36 q^{75} +2.97675e36 q^{76} +1.06291e37 q^{77} -2.58395e36 q^{78} -1.21764e37 q^{79} -1.23409e36 q^{80} -1.29602e37 q^{81} +1.00477e37 q^{82} -3.66144e37 q^{83} +2.42603e37 q^{84} +5.57897e36 q^{85} -1.96248e37 q^{86} +4.94120e37 q^{87} +3.16610e37 q^{88} -1.38898e38 q^{89} -6.20715e36 q^{90} +1.30716e38 q^{91} +1.54064e38 q^{92} +3.76469e38 q^{93} -2.41837e38 q^{94} -1.76876e38 q^{95} +7.22638e37 q^{96} -4.64378e38 q^{97} -7.50401e38 q^{98} +1.59247e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots - 31\!\cdots\!86 q^{9}+O(q^{10}) \) 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9	\( 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots + 72\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9 - 28113758147900866560 * q^10 - 432928873549526253816 * q^11 + 79004930825798025216 * q^12 - 1110716884377980399156 * q^13 - 3931107033531816083456 * q^14 + 177514053087296176226640 * q^15 + 151115727451828646838272 * q^16 - 361727800957394760654108 * q^17 + 166988256371990061907968 * q^18 + 11531090014904148017962360 * q^19 + 14739706031846649527009280 * q^20 + 206255336094912268749797184 * q^21 + 226979413255534020560683008 * q^22 + 733399930716618125168143824 * q^23 - 41421337172795995044446208 * q^24 + 1522590281438531446348943150 * q^25 + 582335533876762587512700928 * q^26 + 1015590507281331347888066160 * q^27 + 2061032244396328790762979328 * q^28 - 66283478621079021435470040660 * q^29 - 93068487865032337641512632320 * q^30 - 186790705491150225840859566656 * q^31 - 79228162514264337593543950336 * q^32 - 49512382311136707894463876512 * q^33 + 189649545308350584273820975104 * q^34 + 4699349644576524589906668345120 * q^35 - 87549938956757925577604726784 * q^36 + 2975477658591913559588340321052 * q^37 - 6045612121734065956041449799680 * q^38 + 8288123926734148196202973745808 * q^39 - 7727850996024816187216641392640 * q^40 + 16770326730060018362152407596724 * q^41 - 108137197650529363558293666004992 * q^42 - 9812395004866851368387130850616 * q^43 - 119002582616917420571719372898304 * q^44 + 40266363304618629851608344270540 * q^45 - 384512782875554283608155789197312 * q^46 + 672278426349701905666521369769632 * q^47 + 21716710023650866649862613499904 * q^48 + 3644309465778284633118680596157586 * q^49 - 798275813474844774943394706227200 * q^50 + 580553528426174218705101873396144 * q^51 - 305311532385180103481858944139264 * q^52 - 8761864571633558324701150169407236 * q^53 - 532461915881514649721538430894080 * q^54 - 11328905370645770966149273576022160 * q^55 - 1080574473350062429051540905918464 * q^56 - 18273076268563776391813920538819680 * q^57 + 34751632439288277990359716677550080 * q^58 - 12819225750671101391169533921560920 * q^59 + 48794691365782074237393374973788160 * q^60 - 20956924322550570450554426592045716 * q^61 + 97932125400544169605652580482940928 * q^62 + 57777775631084010576555882975543984 * q^63 + 41538374868278621028243970633760768 * q^64 + 155428501009224030268997780328195240 * q^65 + 25958747897141242308572676888723456 * q^66 - 430210910797386482647696776154188008 * q^67 - 99430980810624511127753051395325952 * q^68 - 657289380718196443693542397362196032 * q^69 - 2463812626455736924192987333326274560 * q^70 - 505835127408773713626404787885403536 * q^71 + 45901382395760699285231226996129792 * q^72 + 5225008613368893844954971696153387124 * q^73 - 1560007230667837176329451770243710976 * q^74 + 9324378759630332095186368293653381800 * q^75 + 3169641888079709971961059632574627840 * q^76 - 1286526284405007303669629309781343296 * q^77 - 4345363917299593089490864699242184704 * q^78 + 5133106059230199144047658337509305440 * q^79 + 4051619543003858829163438482464440320 * q^80 - 30865091955632000468542250095184041518 * q^81 - 8792481060649706907056161474071232512 * q^82 - 64869811713330760861780892502955295496 * q^83 + 56695035081800738961250669562425245696 * q^84 + 4169326167850982553612360321923472120 * q^85 + 5144520952311631770228952059407761408 * q^86 - 33355767685492704090236226944356001520 * q^87 + 62391626035058400596705606578106007552 * q^88 - 35854914207967073080588387127246110380 * q^89 - 21111171084251892207640035600912875520 * q^90 + 219621888597383210927045163285292559264 * q^91 + 201595437908258604244352782406680313856 * q^92 + 417824530946031783400120882011006743808 * q^93 - 352467511594032512718089155913780822016 * q^94 - 127785377061536603773906538331287257200 * q^95 - 11385810464879865574123169906637668352 * q^96 - 145570707650873901517300801294356641468 * q^97 - 1910667721193965293728526812398268448768 * q^98 + 72596170648714013699688849065341538088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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