LMFDB - Embedded newform 10.24.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,24,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	10.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:	$33.5204037345$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{219241}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 54810 $ x^2 - x - 54810
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-233.616$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2048.00 q^{2} +229540. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} -4.70098e8 q^{6} +1.11945e9 q^{7} -8.58993e9 q^{8} -4.14545e10 q^{9} -1.00000e11 q^{10} -9.54047e11 q^{11} +9.62761e11 q^{12} -2.42139e12 q^{13} -2.29263e12 q^{14} +1.12080e13 q^{15} +1.75922e13 q^{16} -1.35256e14 q^{17} +8.48988e13 q^{18} +8.28157e14 q^{19} +2.04800e14 q^{20} +2.56958e14 q^{21} +1.95389e15 q^{22} -7.88972e13 q^{23} -1.97174e15 q^{24} +2.38419e15 q^{25} +4.95901e15 q^{26} -3.11251e16 q^{27} +4.69531e15 q^{28} -3.21917e16 q^{29} -2.29540e16 q^{30} -1.85689e17 q^{31} -3.60288e16 q^{32} -2.18992e17 q^{33} +2.77004e17 q^{34} +5.46606e16 q^{35} -1.73873e17 q^{36} -3.74188e17 q^{37} -1.69607e18 q^{38} -5.55806e17 q^{39} -4.19430e17 q^{40} -3.22679e18 q^{41} -5.26251e17 q^{42} -2.74344e18 q^{43} -4.00156e18 q^{44} -2.02414e18 q^{45} +1.61582e17 q^{46} +5.25271e17 q^{47} +4.03811e18 q^{48} -2.61156e19 q^{49} -4.88281e18 q^{50} -3.10466e19 q^{51} -1.01560e19 q^{52} -4.40675e19 q^{53} +6.37442e19 q^{54} -4.65843e19 q^{55} -9.61599e18 q^{56} +1.90095e20 q^{57} +6.59286e19 q^{58} +1.56115e20 q^{59} +4.70098e19 q^{60} +5.13552e20 q^{61} +3.80291e20 q^{62} -4.64061e19 q^{63} +7.37870e19 q^{64} -1.18232e20 q^{65} +4.48496e20 q^{66} -7.59236e19 q^{67} -5.67304e20 q^{68} -1.81101e19 q^{69} -1.11945e20 q^{70} -4.54949e20 q^{71} +3.56091e20 q^{72} -4.50124e21 q^{73} +7.66337e20 q^{74} +5.47267e20 q^{75} +3.47354e21 q^{76} -1.06801e21 q^{77} +1.13829e21 q^{78} -1.03553e22 q^{79} +8.58993e20 q^{80} -3.24181e21 q^{81} +6.60847e21 q^{82} -5.91206e21 q^{83} +1.07776e21 q^{84} -6.60428e21 q^{85} +5.61857e21 q^{86} -7.38929e21 q^{87} +8.19520e21 q^{88} -2.39717e22 q^{89} +4.14545e21 q^{90} -2.71062e21 q^{91} -3.30919e20 q^{92} -4.26231e22 q^{93} -1.07575e21 q^{94} +4.04373e22 q^{95} -8.27006e21 q^{96} +1.24537e23 q^{97} +5.34847e22 q^{98} +3.95495e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4096 q^{2} - 18516 q^{3} + 8388608 q^{4} + 97656250 q^{5} + 37920768 q^{6} - 4415735108 q^{7} - 17179869184 q^{8} - 74065768326 q^{9} - 200000000000 q^{10} + 195017239824 q^{11} - 77661732864 q^{12}+ \cdots + 20\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 4096 * q^2 - 18516 * q^3 + 8388608 * q^4 + 97656250 * q^5 + 37920768 * q^6 - 4415735108 * q^7 - 17179869184 * q^8 - 74065768326 * q^9 - 200000000000 * q^10 + 195017239824 * q^11 - 77661732864 * q^12 + 2583183058684 * q^13 + 9043425501184 * q^14 - 904101562500 * q^15 + 35184372088832 * q^16 + 131668862600532 * q^17 + 151686693531648 * q^18 - 1760888418200 * q^19 + 409600000000000 * q^20 + 1629995023906464 * q^21 - 399395307159552 * q^22 + 4012836105342564 * q^23 + 159051228905472 * q^24 + 4768371582031250 * q^25 - 5290358904184832 * q^26 + 317121583931640 * q^27 - 18520935426424832 * q^28 - 108385465473787380 * q^29 + 1851600000000000 * q^30 - 282534241930647896 * q^31 - 72057594037927936 * q^32 - 504024591095725392 * q^33 - 269657830605889536 * q^34 - 215612065820312500 * q^35 - 310654348352815104 * q^36 - 326855967548366468 * q^37 + 3606299480473600 * q^38 - 1797221588702622072 * q^39 - 838860800000000000 * q^40 - 5378411403014673276 * q^41 - 3338229808960438272 * q^42 - 9824206470496391636 * q^43 + 817961589062762496 * q^44 - 3616492594042968750 * q^45 - 8218288343741571072 * q^46 - 18459008132084260308 * q^47 - 325736916798406656 * q^48 - 22846074207183681054 * q^49 - 9765625000000000000 * q^50 - 97258917604973930856 * q^51 + 10834655035770535936 * q^52 - 6735586459267392756 * q^53 - 649465003891998720 * q^54 + 9522326163281250000 * q^55 + 37930875753318055936 * q^56 + 395961513009676856400 * q^57 + 221973433290316554240 * q^58 + 404431460611319194440 * q^59 - 3792076800000000000 * q^60 + 267288639406230095404 * q^61 + 578630127473966891008 * q^62 + 134103369179566769004 * q^63 + 147573952589676412928 * q^64 + 126131985287304687500 * q^65 + 1032242362564045602816 * q^66 - 878259028011046311548 * q^67 + 552259237080861769728 * q^68 - 1033089938007493665312 * q^69 + 441573510800000000000 * q^70 - 1422290577065242851336 * q^71 + 636220105426565332992 * q^72 - 2737850090767514630876 * q^73 + 669401021539054526464 * q^74 - 44145584106445312500 * q^75 - 7385701336009932800 * q^76 - 7428286679002982182896 * q^77 + 3680709813662970003456 * q^78 - 16358236398140542679120 * q^79 + 1717986918400000000000 * q^80 - 7971119473850267877918 * q^81 + 11014986553374050869248 * q^82 - 24918314799609836009556 * q^83 + 6836694648750977581056 * q^84 + 6429143681666601562500 * q^85 + 20119974851576610070528 * q^86 + 11511051890670005309640 * q^87 - 1675185334400537591808 * q^88 - 69086711107654759066380 * q^89 + 7406576832600000000000 * q^90 - 30411848367847894491736 * q^91 + 16831054527982737555456 * q^92 - 18600007517643336450432 * q^93 + 37804048654508565110784 * q^94 - 85980879794921875000 * q^95 + 667109205603136831488 * q^96 + 142113717247845486800212 * q^97 + 46788759976312178798592 * q^98 + 2077038401308192249488 * q^99

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 $

$2$	−2048.00	−0.707107
$2$	−2048.00	−0.707107
$3$	229540.	0.748108	0.374054	−	0.927407i	$-0.377967\pi$
$3$	229540.	0.748108	0.374054	+	0.927407i	$0.377967\pi$
$4$	4.19430e6	0.500000
$5$	4.88281e7	0.447214
$5$	4.88281e7	0.447214
$6$	−4.70098e8	−0.528992
$7$	1.11945e9	0.213982	0.106991	−	0.994260i	$-0.465878\pi$
$7$	1.11945e9	0.213982	0.106991	+	0.994260i	$0.465878\pi$
$8$	−8.58993e9	−0.353553
$9$	−4.14545e10	−0.440334
$10$	−1.00000e11	−0.316228
$11$	−9.54047e11	−1.00822	−0.504108	−	0.863640i	$-0.668179\pi$
$11$	−9.54047e11	−1.00822	−0.504108	+	0.863640i	$0.668179\pi$
$12$	9.62761e11	0.374054
$13$	−2.42139e12	−0.374728	−0.187364	−	0.982291i	$-0.559994\pi$
$13$	−2.42139e12	−0.374728	−0.187364	+	0.982291i	$0.559994\pi$
$14$	−2.29263e12	−0.151308
$15$	1.12080e13	0.334564
$16$	1.75922e13	0.250000
$17$	−1.35256e14	−0.957179	−0.478589	−	0.878039i	$-0.658852\pi$
$17$	−1.35256e14	−0.957179	−0.478589	+	0.878039i	$0.658852\pi$
$18$	8.48988e13	0.311363
$19$	8.28157e14	1.63097	0.815485	−	0.578778i	$-0.196470\pi$
$19$	8.28157e14	1.63097	0.815485	+	0.578778i	$0.196470\pi$
$20$	2.04800e14	0.223607
$21$	2.56958e14	0.160081
$22$	1.95389e15	0.712917
$23$	−7.88972e13	−0.0172660	−0.00863300	−	0.999963i	$-0.502748\pi$
$23$	−7.88972e13	−0.0172660	−0.00863300	+	0.999963i	$0.502748\pi$
$24$	−1.97174e15	−0.264496
$25$	2.38419e15	0.200000
$26$	4.95901e15	0.264973
$27$	−3.11251e16	−1.07753
$28$	4.69531e15	0.106991
$29$	−3.21917e16	−0.489967	−0.244983	−	0.969527i	$-0.578783\pi$
$29$	−3.21917e16	−0.489967	−0.244983	+	0.969527i	$0.578783\pi$
$30$	−2.29540e16	−0.236573
$31$	−1.85689e17	−1.31258	−0.656291	−	0.754508i	$-0.727876\pi$
$31$	−1.85689e17	−1.31258	−0.656291	+	0.754508i	$0.727876\pi$
$32$	−3.60288e16	−0.176777
$33$	−2.18992e17	−0.754255
$34$	2.77004e17	0.676827
$35$	5.46606e16	0.0956955
$36$	−1.73873e17	−0.220167
$37$	−3.74188e17	−0.345756	−0.172878	−	0.984943i	$-0.555307\pi$
$37$	−3.74188e17	−0.345756	−0.172878	+	0.984943i	$0.555307\pi$
$38$	−1.69607e18	−1.15327
$39$	−5.55806e17	−0.280337
$40$	−4.19430e17	−0.158114
$41$	−3.22679e18	−0.915707	−0.457853	−	0.889028i	$-0.651382\pi$
$41$	−3.22679e18	−0.915707	−0.457853	+	0.889028i	$0.651382\pi$
$42$	−5.26251e17	−0.113195
$43$	−2.74344e18	−0.450203	−0.225102	−	0.974335i	$-0.572271\pi$
$43$	−2.74344e18	−0.450203	−0.225102	+	0.974335i	$0.572271\pi$
$44$	−4.00156e18	−0.504108
$45$	−2.02414e18	−0.196923
$46$	1.61582e17	0.0122089
$47$	5.25271e17	0.0309926	0.0154963	−	0.999880i	$-0.495067\pi$
$47$	5.25271e17	0.0309926	0.0154963	+	0.999880i	$0.495067\pi$
$48$	4.03811e18	0.187027
$49$	−2.61156e19	−0.954212
$50$	−4.88281e18	−0.141421
$51$	−3.10466e19	−0.716073
$52$	−1.01560e19	−0.187364
$53$	−4.40675e19	−0.653050	−0.326525	−	0.945189i	$-0.605878\pi$
$53$	−4.40675e19	−0.653050	−0.326525	+	0.945189i	$0.605878\pi$
$54$	6.37442e19	0.761926
$55$	−4.65843e19	−0.450888
$56$	−9.61599e18	−0.0756539
$57$	1.90095e20	1.22014
$58$	6.59286e19	0.346459
$59$	1.56115e20	0.673979	0.336989	−	0.941508i	$-0.390591\pi$
$59$	1.56115e20	0.673979	0.336989	+	0.941508i	$0.390591\pi$
$60$	4.70098e19	0.167282
$61$	5.13552e20	1.51109	0.755546	−	0.655095i	$-0.227372\pi$
$61$	5.13552e20	1.51109	0.755546	+	0.655095i	$0.227372\pi$
$62$	3.80291e20	0.928136
$63$	−4.64061e19	−0.0942235
$64$	7.37870e19	0.125000
$65$	−1.18232e20	−0.167583
$66$	4.48496e20	0.533339
$67$	−7.59236e19	−0.0759480	−0.0379740	−	0.999279i	$-0.512090\pi$
$67$	−7.59236e19	−0.0759480	−0.0379740	+	0.999279i	$0.512090\pi$
$68$	−5.67304e20	−0.478589
$69$	−1.81101e19	−0.0129168
$70$	−1.11945e20	−0.0676669
$71$	−4.54949e20	−0.233610	−0.116805	−	0.993155i	$-0.537265\pi$
$71$	−4.54949e20	−0.233610	−0.116805	+	0.993155i	$0.537265\pi$
$72$	3.56091e20	0.155682
$73$	−4.50124e21	−1.67927	−0.839633	−	0.543154i	$-0.817230\pi$
$73$	−4.50124e21	−1.67927	−0.839633	+	0.543154i	$0.817230\pi$
$74$	7.66337e20	0.244487
$75$	5.47267e20	0.149622
$76$	3.47354e21	0.815485
$77$	−1.06801e21	−0.215740
$78$	1.13829e21	0.198228
$79$	−1.03553e22	−1.55759	−0.778794	−	0.627280i	$-0.784168\pi$
$79$	−1.03553e22	−1.55759	−0.778794	+	0.627280i	$0.784168\pi$
$80$	8.58993e20	0.111803
$81$	−3.24181e21	−0.365771
$82$	6.60847e21	0.647503
$83$	−5.91206e21	−0.503895	−0.251948	−	0.967741i	$-0.581071\pi$
$83$	−5.91206e21	−0.503895	−0.251948	+	0.967741i	$0.581071\pi$
$84$	1.07776e21	0.0800407
$85$	−6.60428e21	−0.428063
$86$	5.61857e21	0.318342
$87$	−7.38929e21	−0.366548
$88$	8.19520e21	0.356458
$89$	−2.39717e22	−0.915617	−0.457808	−	0.889051i	$-0.651365\pi$
$89$	−2.39717e22	−0.915617	−0.457808	+	0.889051i	$0.651365\pi$
$90$	4.14545e21	0.139246
$91$	−2.71062e21	−0.0801849
$92$	−3.30919e20	−0.00863300
$93$	−4.26231e22	−0.981954
$94$	−1.07575e21	−0.0219151
$95$	4.04373e22	0.729392
$96$	−8.27006e21	−0.132248
$97$	1.24537e23	1.76776	0.883878	−	0.467717i	$-0.154923\pi$
$97$	1.24537e23	1.76776	0.883878	+	0.467717i	$0.154923\pi$
$98$	5.34847e22	0.674730
$99$	3.95495e22	0.443952
$100$	1.00000e22	0.100000
$101$	−1.49773e23	−1.33579	−0.667893	−	0.744257i	$-0.732804\pi$
$101$	−1.49773e23	−1.33579	−0.667893	+	0.744257i	$0.732804\pi$
$102$	6.35835e22	0.506340
$103$	2.00999e23	1.43076	0.715380	−	0.698736i	$-0.246254\pi$
$103$	2.00999e23	1.43076	0.715380	+	0.698736i	$0.246254\pi$
$104$	2.07996e22	0.132486
$105$	1.25468e22	0.0715906
$106$	9.02503e22	0.461776
$107$	1.12988e23	0.518943	0.259471	−	0.965751i	$-0.416452\pi$
$107$	1.12988e23	0.518943	0.259471	+	0.965751i	$0.416452\pi$
$108$	−1.30548e23	−0.538763
$109$	−2.77607e23	−1.03045	−0.515224	−	0.857056i	$-0.672291\pi$
$109$	−2.77607e23	−1.03045	−0.515224	+	0.857056i	$0.672291\pi$
$110$	9.54047e22	0.318826
$111$	−8.58912e22	−0.258663
$112$	1.96935e22	0.0534954
$113$	5.91159e22	0.144978	0.0724890	−	0.997369i	$-0.476906\pi$
$113$	5.91159e22	0.144978	0.0724890	+	0.997369i	$0.476906\pi$
$114$	−3.89315e23	−0.862771
$115$	−3.85240e21	−0.00772159
$116$	−1.35022e23	−0.244983
$117$	1.00377e23	0.165006
$118$	−3.19723e23	−0.476575
$119$	−1.51412e23	−0.204819
$120$	−9.62761e22	−0.118286
$121$	1.47751e22	0.0165006
$122$	−1.05175e24	−1.06850
$123$	−7.40678e23	−0.685048
$124$	−7.78836e23	−0.656291
$125$	1.16415e23	0.0894427
$126$	9.50398e22	0.0666261
$127$	1.52582e24	0.976696	0.488348	−	0.872649i	$-0.337600\pi$
$127$	1.52582e24	0.976696	0.488348	+	0.872649i	$0.337600\pi$
$128$	−1.51116e23	−0.0883883
$129$	−6.29730e23	−0.336801
$130$	2.42139e23	0.118499
$131$	1.92350e24	0.861930	0.430965	−	0.902369i	$-0.358173\pi$
$131$	1.92350e24	0.861930	0.430965	+	0.902369i	$0.358173\pi$
$132$	−9.18519e23	−0.377127
$133$	9.27079e23	0.348998
$134$	1.55492e23	0.0537034
$135$	−1.51978e24	−0.481884
$136$	1.16184e24	0.338414
$137$	3.29993e24	0.883525	0.441762	−	0.897132i	$-0.354353\pi$
$137$	3.29993e24	0.883525	0.441762	+	0.897132i	$0.354353\pi$
$138$	3.70895e22	0.00913358
$139$	6.17390e24	1.39923	0.699616	−	0.714519i	$-0.253355\pi$
$139$	6.17390e24	1.39923	0.699616	+	0.714519i	$0.253355\pi$
$140$	2.29263e23	0.0478478
$141$	1.20571e23	0.0231858
$142$	9.31735e23	0.165187
$143$	2.31012e24	0.377807
$144$	−7.29275e23	−0.110084
$145$	−1.57186e24	−0.219120
$146$	9.21854e24	1.18742
$147$	−5.99458e24	−0.713854
$148$	−1.56946e24	−0.172878
$149$	−4.79152e24	−0.488462	−0.244231	−	0.969717i	$-0.578536\pi$
$149$	−4.79152e24	−0.488462	−0.244231	+	0.969717i	$0.578536\pi$
$150$	−1.12080e24	−0.105798
$151$	−1.17176e25	−1.02472	−0.512358	−	0.858772i	$-0.671228\pi$
$151$	−1.17176e25	−1.02472	−0.512358	+	0.858772i	$0.671228\pi$
$152$	−7.11381e24	−0.576635
$153$	5.60695e24	0.421479
$154$	2.18728e24	0.152551
$155$	−9.06684e24	−0.587005
$156$	−2.33122e24	−0.140169
$157$	1.45572e24	0.0813263	0.0406631	−	0.999173i	$-0.487053\pi$
$157$	1.45572e24	0.0813263	0.0406631	+	0.999173i	$0.487053\pi$
$158$	2.12077e25	1.10138
$159$	−1.01153e25	−0.488552
$160$	−1.75922e24	−0.0790569
$161$	−8.83214e22	−0.00369461
$162$	6.63923e24	0.258639
$163$	3.81476e25	1.38455	0.692277	−	0.721632i	$-0.256608\pi$
$163$	3.81476e25	1.38455	0.692277	+	0.721632i	$0.256608\pi$
$164$	−1.35341e25	−0.457853
$165$	−1.06930e25	−0.337313
$166$	1.21079e25	0.356308
$167$	−6.46554e25	−1.77568	−0.887842	−	0.460149i	$-0.847796\pi$
$167$	−6.46554e25	−1.77568	−0.887842	+	0.460149i	$0.847796\pi$
$168$	−2.20726e24	−0.0565973
$169$	−3.58908e25	−0.859579
$170$	1.35256e25	0.302686
$171$	−3.43308e25	−0.718172
$172$	−1.15068e25	−0.225102
$173$	−2.31249e25	−0.423203	−0.211602	−	0.977356i	$-0.567868\pi$
$173$	−2.31249e25	−0.423203	−0.211602	+	0.977356i	$0.567868\pi$
$174$	1.51333e25	0.259189
$175$	2.66897e24	0.0427963
$176$	−1.67838e25	−0.252054
$177$	3.58347e25	0.504209
$178$	4.90941e25	0.647439
$179$	−9.97940e25	−1.23394	−0.616971	−	0.786986i	$-0.711640\pi$
$179$	−9.97940e25	−1.23394	−0.616971	+	0.786986i	$0.711640\pi$
$180$	−8.48988e24	−0.0984617
$181$	1.18405e26	1.28845	0.644224	−	0.764837i	$-0.277180\pi$
$181$	1.18405e26	1.28845	0.644224	+	0.764837i	$0.277180\pi$
$182$	5.55135e24	0.0566993
$183$	1.17881e26	1.13046
$184$	6.77722e23	0.00610445
$185$	−1.82709e25	−0.154627
$186$	8.72921e25	0.694346
$187$	1.29040e26	0.965043
$188$	2.20315e24	0.0154963
$189$	−3.48430e25	−0.230571
$190$	−8.28157e25	−0.515758
$191$	2.47442e26	1.45074	0.725369	−	0.688360i	$-0.241669\pi$
$191$	2.47442e26	1.45074	0.725369	+	0.688360i	$0.241669\pi$
$192$	1.69371e25	0.0935135
$193$	2.80515e26	1.45897	0.729486	−	0.683996i	$-0.239760\pi$
$193$	2.80515e26	1.45897	0.729486	+	0.683996i	$0.239760\pi$
$194$	−2.55051e26	−1.24999
$195$	−2.71390e25	−0.125371
$196$	−1.09537e26	−0.477106
$197$	2.28927e26	0.940451	0.470226	−	0.882546i	$-0.344173\pi$
$197$	2.28927e26	0.940451	0.470226	+	0.882546i	$0.344173\pi$
$198$	−8.09974e25	−0.313922
$199$	−3.84077e26	−1.40478	−0.702390	−	0.711792i	$-0.747884\pi$
$199$	−3.84077e26	−1.40478	−0.702390	+	0.711792i	$0.747884\pi$
$200$	−2.04800e25	−0.0707107
$201$	−1.74275e25	−0.0568173
$202$	3.06735e26	0.944543
$203$	−3.60369e25	−0.104844
$204$	−1.30219e26	−0.358037
$205$	−1.57558e26	−0.409517
$206$	−4.11647e26	−1.01170
$207$	3.27064e24	0.00760281
$208$	−4.25975e25	−0.0936820
$209$	−7.90100e26	−1.64437
$210$	−2.56958e25	−0.0506222
$211$	5.46973e26	1.02028	0.510138	−	0.860092i	$-0.329594\pi$
$211$	5.46973e26	1.02028	0.510138	+	0.860092i	$0.329594\pi$
$212$	−1.84833e26	−0.326525
$213$	−1.04429e26	−0.174766
$214$	−2.31400e26	−0.366948
$215$	−1.33957e26	−0.201337
$216$	2.67363e26	0.380963
$217$	−2.07869e26	−0.280869
$218$	5.68539e26	0.728636
$219$	−1.03322e27	−1.25627
$220$	−1.95389e26	−0.225444
$221$	3.27507e26	0.358682
$222$	1.75905e26	0.182902
$223$	8.07759e26	0.797583	0.398792	−	0.917042i	$-0.369430\pi$
$223$	8.07759e26	0.797583	0.398792	+	0.917042i	$0.369430\pi$
$224$	−4.03324e25	−0.0378270
$225$	−9.88352e25	−0.0880669
$226$	−1.21069e26	−0.102515
$227$	7.29025e26	0.586739	0.293370	−	0.955999i	$-0.405223\pi$
$227$	7.29025e26	0.586739	0.293370	+	0.955999i	$0.405223\pi$
$228$	7.97317e26	0.610071
$229$	−1.53114e26	−0.111406	−0.0557028	−	0.998447i	$-0.517740\pi$
$229$	−1.53114e26	−0.111406	−0.0557028	+	0.998447i	$0.517740\pi$
$230$	7.88972e24	0.00545999
$231$	−2.45150e26	−0.161397
$232$	2.76525e26	0.173229
$233$	2.78414e27	1.65996	0.829981	−	0.557791i	$-0.188351\pi$
$233$	2.78414e27	1.65996	0.829981	+	0.557791i	$0.188351\pi$
$234$	−2.05573e26	−0.116677
$235$	2.56480e25	0.0138603
$236$	6.54794e26	0.336989
$237$	−2.37696e27	−1.16524
$238$	3.10091e26	0.144829
$239$	−1.57931e27	−0.702896	−0.351448	−	0.936207i	$-0.614311\pi$
$239$	−1.57931e27	−0.702896	−0.351448	+	0.936207i	$0.614311\pi$
$240$	1.97174e26	0.0836410
$241$	1.98820e27	0.804013	0.402006	−	0.915637i	$-0.368313\pi$
$241$	1.98820e27	0.804013	0.402006	+	0.915637i	$0.368313\pi$
$242$	−3.02595e25	−0.0116677
$243$	2.18609e27	0.803889
$244$	2.15399e27	0.755546
$245$	−1.27517e27	−0.426737
$246$	1.51691e27	0.484402
$247$	−2.00529e27	−0.611170
$248$	1.59506e27	0.464068
$249$	−1.35705e27	−0.376968
$250$	−2.38419e26	−0.0632456
$251$	−3.79632e27	−0.961866	−0.480933	−	0.876757i	$-0.659702\pi$
$251$	−3.79632e27	−0.961866	−0.480933	+	0.876757i	$0.659702\pi$
$252$	−1.94641e26	−0.0471117
$253$	7.52716e25	0.0174079
$254$	−3.12487e27	−0.690628
$255$	−1.51595e27	−0.320238
$256$	3.09485e26	0.0625000
$257$	3.87160e27	0.747583	0.373791	−	0.927513i	$-0.378058\pi$
$257$	3.87160e27	0.747583	0.373791	+	0.927513i	$0.378058\pi$
$258$	1.28969e27	0.238154
$259$	−4.18884e26	−0.0739855
$260$	−4.95901e26	−0.0837917
$261$	1.33449e27	0.215749
$262$	−3.93933e27	−0.609477
$263$	−1.11317e28	−1.64842	−0.824212	−	0.566281i	$-0.808382\pi$
$263$	−1.11317e28	−1.64842	−0.824212	+	0.566281i	$0.808382\pi$
$264$	1.88113e27	0.266669
$265$	−2.15173e27	−0.292053
$266$	−1.89866e27	−0.246779
$267$	−5.50247e27	−0.684980
$268$	−3.18447e26	−0.0379740
$269$	1.52514e28	1.74244	0.871220	−	0.490893i	$-0.163329\pi$
$269$	1.52514e28	1.74244	0.871220	+	0.490893i	$0.163329\pi$
$270$	3.11251e27	0.340744
$271$	−1.10913e27	−0.116369	−0.0581843	−	0.998306i	$-0.518531\pi$
$271$	−1.10913e27	−0.116369	−0.0581843	+	0.998306i	$0.518531\pi$
$272$	−2.37944e27	−0.239295
$273$	−6.22196e26	−0.0599870
$274$	−6.75826e27	−0.624746
$275$	−2.27462e27	−0.201643
$276$	−7.59592e25	−0.00645841
$277$	1.90865e28	1.55671	0.778356	−	0.627824i	$-0.216054\pi$
$277$	1.90865e28	1.55671	0.778356	+	0.627824i	$0.216054\pi$
$278$	−1.26442e28	−0.989406
$279$	7.69764e27	0.577975
$280$	−4.69531e26	−0.0338335
$281$	−5.75634e27	−0.398129	−0.199064	−	0.979986i	$-0.563790\pi$
$281$	−5.75634e27	−0.398129	−0.199064	+	0.979986i	$0.563790\pi$
$282$	−2.46929e26	−0.0163948
$283$	−9.14645e27	−0.583054	−0.291527	−	0.956563i	$-0.594163\pi$
$283$	−9.14645e27	−0.583054	−0.291527	+	0.956563i	$0.594163\pi$
$284$	−1.90819e27	−0.116805
$285$	9.28200e27	0.545664
$286$	−4.73112e27	−0.267150
$287$	−3.61223e27	−0.195945
$288$	1.49355e27	0.0778408
$289$	−1.67346e27	−0.0838091
$290$	3.21917e27	0.154941
$291$	2.85862e28	1.32247
$292$	−1.88796e28	−0.839633
$293$	1.07789e28	0.460889	0.230445	−	0.973085i	$-0.425982\pi$
$293$	1.07789e28	0.460889	0.230445	+	0.973085i	$0.425982\pi$
$294$	1.22769e28	0.504771
$295$	7.62280e27	0.301413
$296$	3.21425e27	0.122243
$297$	2.96948e28	1.08638
$298$	9.81303e27	0.345395
$299$	1.91041e26	0.00647005
$300$	2.29540e27	0.0748108
$301$	−3.07114e27	−0.0963353
$302$	2.39977e28	0.724584
$303$	−3.43789e28	−0.999312
$304$	1.45691e28	0.407743
$305$	2.50758e28	0.675781
$306$	−1.14830e28	−0.298030
$307$	1.06872e28	0.267161	0.133581	−	0.991038i	$-0.457352\pi$
$307$	1.06872e28	0.267161	0.133581	+	0.991038i	$0.457352\pi$
$308$	−4.47954e27	−0.107870
$309$	4.61375e28	1.07036
$310$	1.85689e28	0.415075
$311$	−8.23745e28	−1.77439	−0.887194	−	0.461397i	$-0.847348\pi$
$311$	−8.23745e28	−1.77439	−0.887194	+	0.461397i	$0.847348\pi$
$312$	4.77434e27	0.0991141
$313$	−7.21679e28	−1.44406	−0.722028	−	0.691863i	$-0.756790\pi$
$313$	−7.21679e28	−1.44406	−0.722028	+	0.691863i	$0.756790\pi$
$314$	−2.98131e27	−0.0575064
$315$	−2.26592e27	−0.0421380
$316$	−4.34334e28	−0.778794
$317$	−8.73563e28	−1.51047	−0.755236	−	0.655453i	$-0.772478\pi$
$317$	−8.73563e28	−1.51047	−0.755236	+	0.655453i	$0.772478\pi$
$318$	2.07161e28	0.345458
$319$	3.07124e28	0.493993
$320$	3.60288e27	0.0559017
$321$	2.59353e28	0.388225
$322$	1.80882e26	0.00261248
$323$	−1.12013e29	−1.56113
$324$	−1.35971e28	−0.182886
$325$	−5.77304e27	−0.0749456
$326$	−7.81263e28	−0.979027
$327$	−6.37220e28	−0.770886
$328$	2.77179e28	0.323751
$329$	5.88014e26	0.00663185
$330$	2.18992e28	0.238516
$331$	−4.91673e28	−0.517195	−0.258597	−	0.965985i	$-0.583260\pi$
$331$	−4.91673e28	−0.517195	−0.258597	+	0.965985i	$0.583260\pi$
$332$	−2.47970e28	−0.251948
$333$	1.55118e28	0.152248
$334$	1.32414e29	1.25560
$335$	−3.70721e27	−0.0339650
$336$	4.52046e27	0.0400204
$337$	1.56219e29	1.33656	0.668280	−	0.743910i	$-0.267031\pi$
$337$	1.56219e29	1.33656	0.668280	+	0.743910i	$0.267031\pi$
$338$	7.35043e28	0.607814
$339$	1.35695e28	0.108459
$340$	−2.77004e28	−0.214032
$341$	1.77156e29	1.32337
$342$	7.03095e28	0.507825
$343$	−5.98729e28	−0.418166
$344$	2.35660e28	0.159171
$345$	−8.84281e26	−0.00577658
$346$	4.73597e28	0.299250
$347$	−1.50078e29	−0.917335	−0.458668	−	0.888608i	$-0.651673\pi$
$347$	−1.50078e29	−0.917335	−0.458668	+	0.888608i	$0.651673\pi$
$348$	−3.09929e28	−0.183274
$349$	2.61518e29	1.49627	0.748134	−	0.663548i	$-0.230950\pi$
$349$	2.61518e29	1.49627	0.748134	+	0.663548i	$0.230950\pi$
$350$	−5.46606e27	−0.0302616
$351$	7.53660e28	0.403779
$352$	3.43732e28	0.178229
$353$	−2.25089e29	−1.12965	−0.564827	−	0.825209i	$-0.691057\pi$
$353$	−2.25089e29	−1.12965	−0.564827	+	0.825209i	$0.691057\pi$
$354$	−7.33894e28	−0.356530
$355$	−2.22143e28	−0.104474
$356$	−1.00545e29	−0.457808
$357$	−3.47551e28	−0.153227
$358$	2.04378e29	0.872528
$359$	−4.75724e28	−0.196684	−0.0983420	−	0.995153i	$-0.531354\pi$
$359$	−4.75724e28	−0.196684	−0.0983420	+	0.995153i	$0.531354\pi$
$360$	1.73873e28	0.0696230
$361$	4.28014e29	1.66007
$362$	−2.42494e29	−0.911070
$363$	3.39149e27	0.0123442
$364$	−1.13692e28	−0.0400925
$365$	−2.19787e29	−0.750991
$366$	−2.41420e29	−0.799356
$367$	1.94572e29	0.624339	0.312170	−	0.950026i	$-0.398944\pi$
$367$	1.94572e29	0.624339	0.312170	+	0.950026i	$0.398944\pi$
$368$	−1.38797e27	−0.00431650
$369$	1.33765e29	0.403217
$370$	3.74188e28	0.109338
$371$	−4.93313e28	−0.139741
$372$	−1.78774e29	−0.490977
$373$	5.99622e29	1.59671	0.798355	−	0.602187i	$-0.205704\pi$
$373$	5.99622e29	1.59671	0.798355	+	0.602187i	$0.205704\pi$
$374$	−2.64274e29	−0.682389
$375$	2.67220e28	0.0669128
$376$	−4.51204e27	−0.0109575
$377$	7.79486e28	0.183604
$378$	7.13584e28	0.163038
$379$	−6.46441e29	−1.43277	−0.716387	−	0.697703i	$-0.754206\pi$
$379$	−6.46441e29	−1.43277	−0.716387	+	0.697703i	$0.754206\pi$
$380$	1.69607e29	0.364696
$381$	3.50236e29	0.730674
$382$	−5.06761e29	−1.02583
$383$	−8.91098e29	−1.75041	−0.875205	−	0.483752i	$-0.839274\pi$
$383$	−8.91098e29	−1.75041	−0.875205	+	0.483752i	$0.839274\pi$
$384$	−3.46871e28	−0.0661240
$385$	−5.21487e28	−0.0964818
$386$	−5.74494e29	−1.03165
$387$	1.13728e29	0.198240
$388$	5.22345e29	0.883878
$389$	−3.75725e29	−0.617233	−0.308617	−	0.951187i	$-0.599866\pi$
$389$	−3.75725e29	−0.617233	−0.308617	+	0.951187i	$0.599866\pi$
$390$	5.55806e28	0.0886504
$391$	1.06713e28	0.0165266
$392$	2.24331e29	0.337365
$393$	4.41520e29	0.644817
$394$	−4.68843e29	−0.664999
$395$	−5.05631e29	−0.696574
$396$	1.65883e29	0.221976
$397$	7.49782e29	0.974640	0.487320	−	0.873223i	$-0.337975\pi$
$397$	7.49782e29	0.974640	0.487320	+	0.873223i	$0.337975\pi$
$398$	7.86590e29	0.993329
$399$	2.12802e29	0.261088
$400$	4.19430e28	0.0500000
$401$	−8.25665e29	−0.956409	−0.478205	−	0.878248i	$-0.658712\pi$
$401$	−8.25665e29	−0.956409	−0.478205	+	0.878248i	$0.658712\pi$
$402$	3.56916e28	0.0401759
$403$	4.49625e29	0.491861
$404$	−6.28192e29	−0.667893
$405$	−1.58291e29	−0.163578
$406$	7.38036e28	0.0741359
$407$	3.56993e29	0.348597
$408$	2.66688e29	0.253170
$409$	−2.03509e30	−1.87830	−0.939149	−	0.343509i	$-0.888384\pi$
$409$	−2.03509e30	−1.87830	−0.939149	+	0.343509i	$0.888384\pi$
$410$	3.22679e29	0.289572
$411$	7.57467e29	0.660972
$412$	8.43053e29	0.715380
$413$	1.74763e29	0.144219
$414$	−6.69828e27	−0.00537600
$415$	−2.88675e29	−0.225349
$416$	8.72398e28	0.0662432
$417$	1.41716e30	1.04678
$418$	1.61813e30	1.16275
$419$	−1.17686e30	−0.822742	−0.411371	−	0.911468i	$-0.634950\pi$
$419$	−1.17686e30	−0.822742	−0.411371	+	0.911468i	$0.634950\pi$
$420$	5.26251e28	0.0357953
$421$	1.99473e30	1.32020	0.660100	−	0.751178i	$-0.270514\pi$
$421$	1.99473e30	1.32020	0.660100	+	0.751178i	$0.270514\pi$
$422$	−1.12020e30	−0.721444
$423$	−2.17748e28	−0.0136471
$424$	3.78537e29	0.230888
$425$	−3.22475e29	−0.191436
$426$	2.13871e29	0.123578
$427$	5.74894e29	0.323346
$428$	4.73907e29	0.259471
$429$	5.30265e29	0.282640
$430$	2.74344e29	0.142367
$431$	9.01027e29	0.455249	0.227625	−	0.973749i	$-0.426904\pi$
$431$	9.01027e29	0.455249	0.227625	+	0.973749i	$0.426904\pi$
$432$	−5.47559e29	−0.269381
$433$	−3.28011e30	−1.57137	−0.785685	−	0.618627i	$-0.787689\pi$
$433$	−3.28011e30	−1.57137	−0.785685	+	0.618627i	$0.787689\pi$
$434$	4.25716e29	0.198604
$435$	−3.60805e29	−0.163925
$436$	−1.16437e30	−0.515224
$437$	−6.53393e28	−0.0281603
$438$	2.11603e30	0.888319
$439$	1.34681e30	0.550763	0.275382	−	0.961335i	$-0.411196\pi$
$439$	1.34681e30	0.550763	0.275382	+	0.961335i	$0.411196\pi$
$440$	4.00156e29	0.159413
$441$	1.08261e30	0.420172
$442$	−6.70734e29	−0.253626
$443$	−2.42126e30	−0.892068	−0.446034	−	0.895016i	$-0.647164\pi$
$443$	−2.42126e30	−0.892068	−0.446034	+	0.895016i	$0.647164\pi$
$444$	−3.60254e29	−0.129331
$445$	−1.17049e30	−0.409476
$446$	−1.65429e30	−0.563977
$447$	−1.09985e30	−0.365423
$448$	8.26007e28	0.0267477
$449$	−3.10296e30	−0.979361	−0.489681	−	0.871902i	$-0.662887\pi$
$449$	−3.10296e30	−0.979361	−0.489681	+	0.871902i	$0.662887\pi$
$450$	2.02414e29	0.0622727
$451$	3.07851e30	0.923231
$452$	2.47950e29	0.0724890
$453$	−2.68966e30	−0.766599
$454$	−1.49304e30	−0.414887
$455$	−1.32355e29	−0.0358598
$456$	−1.63291e30	−0.431385
$457$	−5.07608e30	−1.30765	−0.653826	−	0.756645i	$-0.726837\pi$
$457$	−5.07608e30	−1.30765	−0.653826	+	0.756645i	$0.726837\pi$
$458$	3.13578e29	0.0787757
$459$	4.20985e30	1.03138
$460$	−1.61582e28	−0.00386079
$461$	4.69993e29	0.109530	0.0547648	−	0.998499i	$-0.482559\pi$
$461$	4.69993e29	0.109530	0.0547648	+	0.998499i	$0.482559\pi$
$462$	5.02068e29	0.114125
$463$	−3.39682e29	−0.0753166	−0.0376583	−	0.999291i	$-0.511990\pi$
$463$	−3.39682e29	−0.0753166	−0.0376583	+	0.999291i	$0.511990\pi$
$464$	−5.66322e29	−0.122492
$465$	−2.08121e30	−0.439143
$466$	−5.70192e30	−1.17377
$467$	1.07622e30	0.216150	0.108075	−	0.994143i	$-0.465531\pi$
$467$	1.07622e30	0.216150	0.108075	+	0.994143i	$0.465531\pi$
$468$	4.21013e29	0.0825028
$469$	−8.49926e28	−0.0162515
$470$	−5.25271e28	−0.00980072
$471$	3.34145e29	0.0608408
$472$	−1.34102e30	−0.238288
$473$	2.61737e30	0.453902
$474$	4.86802e30	0.823952
$475$	1.97448e30	0.326194
$476$	−6.35067e29	−0.102409
$477$	1.82680e30	0.287560
$478$	3.23442e30	0.497022
$479$	1.27284e31	1.90949	0.954744	−	0.297429i	$-0.0961293\pi$
$479$	1.27284e31	1.90949	0.954744	+	0.297429i	$0.0961293\pi$
$480$	−4.03811e29	−0.0591431
$481$	9.06055e29	0.129565
$482$	−4.07182e30	−0.568523
$483$	−2.02733e28	−0.00276397
$484$	6.19714e28	0.00825030
$485$	6.08089e30	0.790565
$486$	−4.47712e30	−0.568436
$487$	4.08137e30	0.506084	0.253042	−	0.967455i	$-0.418569\pi$
$487$	4.08137e30	0.506084	0.253042	+	0.967455i	$0.418569\pi$
$488$	−4.41137e30	−0.534252
$489$	8.75641e30	1.03580
$490$	2.61156e30	0.301748
$491$	6.22475e30	0.702562	0.351281	−	0.936270i	$-0.385746\pi$
$491$	6.22475e30	0.702562	0.351281	+	0.936270i	$0.385746\pi$
$492$	−3.10663e30	−0.342524
$493$	4.35411e30	0.468986
$494$	4.10683e30	0.432163
$495$	1.93113e30	0.198542
$496$	−3.26667e30	−0.328146
$497$	−5.09292e29	−0.0499883
$498$	2.77925e30	0.266557
$499$	6.71277e30	0.629137	0.314569	−	0.949235i	$-0.398140\pi$
$499$	6.71277e30	0.629137	0.314569	+	0.949235i	$0.398140\pi$
$500$	4.88281e29	0.0447214
$501$	−1.48410e31	−1.32840
$502$	7.77485e30	0.680142
$503$	−2.13145e31	−1.82240	−0.911200	−	0.411965i	$-0.864843\pi$
$503$	−2.13145e31	−1.82240	−0.911200	+	0.411965i	$0.864843\pi$
$504$	3.98626e29	0.0333130
$505$	−7.31312e30	−0.597382
$506$	−1.54156e29	−0.0123092
$507$	−8.23838e30	−0.643058
$508$	6.39974e30	0.488348
$509$	−3.48709e30	−0.260141	−0.130070	−	0.991505i	$-0.541520\pi$
$509$	−3.48709e30	−0.260141	−0.130070	+	0.991505i	$0.541520\pi$
$510$	3.10466e30	0.226442
$511$	−5.03891e30	−0.359332
$512$	−6.33825e29	−0.0441942
$513$	−2.57765e31	−1.75741
$514$	−7.92903e30	−0.528621
$515$	9.81443e30	0.639855
$516$	−2.64128e30	−0.168400
$517$	−5.01133e29	−0.0312472
$518$	8.57875e29	0.0523156
$519$	−5.30809e30	−0.316602
$520$	1.01560e30	0.0592497
$521$	6.35728e30	0.362775	0.181388	−	0.983412i	$-0.441941\pi$
$521$	6.35728e30	0.362775	0.181388	+	0.983412i	$0.441941\pi$
$522$	−2.73303e30	−0.152558
$523$	−2.07982e31	−1.13568	−0.567842	−	0.823138i	$-0.692221\pi$
$523$	−2.07982e31	−1.13568	−0.567842	+	0.823138i	$0.692221\pi$
$524$	8.06774e30	0.430965
$525$	6.12637e29	0.0320163
$526$	2.27977e31	1.16561
$527$	2.51155e31	1.25638
$528$	−3.85255e30	−0.188564
$529$	−2.08742e31	−0.999702
$530$	4.40675e30	0.206512
$531$	−6.47166e30	−0.296776
$532$	3.88845e30	0.174499
$533$	7.81332e30	0.343141
$534$	1.12691e31	0.484354
$535$	5.51700e30	0.232078
$536$	6.52179e29	0.0268517
$537$	−2.29067e31	−0.923122
$538$	−3.12348e31	−1.23209
$539$	2.49155e31	0.962052
$540$	−6.37442e30	−0.240942
$541$	−5.19131e30	−0.192092	−0.0960458	−	0.995377i	$-0.530620\pi$
$541$	−5.19131e30	−0.192092	−0.0960458	+	0.995377i	$0.530620\pi$
$542$	2.27150e30	0.0822850
$543$	2.71787e31	0.963899
$544$	4.87310e30	0.169207
$545$	−1.35550e31	−0.460830
$546$	1.27426e30	0.0424172
$547$	1.22758e31	0.400125	0.200063	−	0.979783i	$-0.435885\pi$
$547$	1.22758e31	0.400125	0.200063	+	0.979783i	$0.435885\pi$
$548$	1.38409e31	0.441762
$549$	−2.12890e31	−0.665386
$550$	4.65843e30	0.142583
$551$	−2.66598e31	−0.799122
$552$	1.55564e29	0.00456679
$553$	−1.15923e31	−0.333295
$554$	−3.90891e31	−1.10076
$555$	−4.19390e30	−0.115678
$556$	2.58952e31	0.699616
$557$	3.14791e31	0.833081	0.416540	−	0.909117i	$-0.363242\pi$
$557$	3.14791e31	0.833081	0.416540	+	0.909117i	$0.363242\pi$
$558$	−1.57648e31	−0.408690
$559$	6.64294e30	0.168704
$560$	9.61599e29	0.0239239
$561$	2.96199e31	0.721957
$562$	1.17890e31	0.281520
$563$	4.85033e31	1.13481	0.567407	−	0.823437i	$-0.307947\pi$
$563$	4.85033e31	1.13481	0.567407	+	0.823437i	$0.307947\pi$
$564$	5.05711e29	0.0115929
$565$	2.88652e30	0.0648362
$566$	1.87319e31	0.412281
$567$	−3.62904e30	−0.0782684
$568$	3.90798e30	0.0825936
$569$	1.58999e31	0.329309	0.164654	−	0.986351i	$-0.447349\pi$
$569$	1.58999e31	0.329309	0.164654	+	0.986351i	$0.447349\pi$
$570$	−1.90095e31	−0.385843
$571$	−3.92722e31	−0.781214	−0.390607	−	0.920557i	$-0.627735\pi$
$571$	−3.92722e31	−0.781214	−0.390607	+	0.920557i	$0.627735\pi$
$572$	9.68934e30	0.188903
$573$	5.67978e31	1.08531
$574$	7.39784e30	0.138554
$575$	−1.88106e29	−0.00345320
$576$	−3.05880e30	−0.0550418
$577$	5.05036e30	0.0890841	0.0445420	−	0.999008i	$-0.485817\pi$
$577$	5.05036e30	0.0890841	0.0445420	+	0.999008i	$0.485817\pi$
$578$	3.42725e30	0.0592620
$579$	6.43894e31	1.09147
$580$	−6.59286e30	−0.109560
$581$	−6.61824e30	−0.107824
$582$	−5.85445e31	−0.935130
$583$	4.20425e31	0.658415
$584$	3.86654e31	0.593710
$585$	4.90124e30	0.0737927
$586$	−2.20752e31	−0.325898
$587$	−3.04905e31	−0.441394	−0.220697	−	0.975342i	$-0.570833\pi$
$587$	−3.04905e31	−0.441394	−0.220697	+	0.975342i	$0.570833\pi$
$588$	−2.51431e31	−0.356927
$589$	−1.53780e32	−2.14078
$590$	−1.56115e31	−0.213131
$591$	5.25481e31	0.703559
$592$	−6.58278e30	−0.0864390
$593$	1.36625e32	1.75955	0.879777	−	0.475387i	$-0.157692\pi$
$593$	1.36625e32	1.75955	0.879777	+	0.475387i	$0.157692\pi$
$594$	−6.08150e31	−0.768186
$595$	−7.39315e30	−0.0915977
$596$	−2.00971e31	−0.244231
$597$	−8.81612e31	−1.05093
$598$	−3.91252e29	−0.00457502
$599$	−9.92624e31	−1.13861	−0.569307	−	0.822125i	$-0.692788\pi$
$599$	−9.92624e31	−1.13861	−0.569307	+	0.822125i	$0.692788\pi$
$600$	−4.70098e30	−0.0528992
$601$	−1.76086e31	−0.194387	−0.0971937	−	0.995265i	$-0.530987\pi$
$601$	−1.76086e31	−0.194387	−0.0971937	+	0.995265i	$0.530987\pi$
$602$	6.28970e30	0.0681193
$603$	3.14737e30	0.0334425
$604$	−4.91472e31	−0.512358
$605$	7.21442e29	0.00737929
$606$	7.04079e31	0.706621
$607$	−1.39464e32	−1.37338	−0.686691	−	0.726949i	$-0.740937\pi$
$607$	−1.39464e32	−1.37338	−0.686691	+	0.726949i	$0.740937\pi$
$608$	−2.98375e31	−0.288318
$609$	−8.27193e30	−0.0784346
$610$	−5.13552e31	−0.477849
$611$	−1.27189e30	−0.0116138
$612$	2.35173e31	0.210739
$613$	1.82366e32	1.60380	0.801898	−	0.597461i	$-0.203824\pi$
$613$	1.82366e32	1.60380	0.801898	+	0.597461i	$0.203824\pi$
$614$	−2.18874e31	−0.188912
$615$	−3.61659e31	−0.306363
$616$	9.17410e30	0.0762756
$617$	1.13184e32	0.923650	0.461825	−	0.886971i	$-0.347195\pi$
$617$	1.13184e32	0.923650	0.461825	+	0.886971i	$0.347195\pi$
$618$	−9.44895e31	−0.756861
$619$	−8.35127e31	−0.656614	−0.328307	−	0.944571i	$-0.606478\pi$
$619$	−8.35127e31	−0.656614	−0.328307	+	0.944571i	$0.606478\pi$
$620$	−3.80291e31	−0.293502
$621$	2.45568e30	0.0186046
$622$	1.68703e32	1.25468
$623$	−2.68351e31	−0.195925
$624$	−9.77785e30	−0.0700843
$625$	5.68434e30	0.0400000
$626$	1.47800e32	1.02110
$627$	−1.81360e32	−1.23017
$628$	6.10572e30	0.0406631
$629$	5.06110e31	0.330950
$630$	4.64061e30	0.0297961
$631$	−7.94078e31	−0.500640	−0.250320	−	0.968163i	$-0.580536\pi$
$631$	−7.94078e31	−0.500640	−0.250320	+	0.968163i	$0.580536\pi$
$632$	8.89516e31	0.550690
$633$	1.25552e32	0.763277
$634$	1.78906e32	1.06807
$635$	7.45027e31	0.436792
$636$	−4.24265e31	−0.244276
$637$	6.32360e31	0.357570
$638$	−6.28990e31	−0.349306
$639$	1.88597e31	0.102867
$640$	−7.37870e30	−0.0395285
$641$	1.60774e32	0.845955	0.422978	−	0.906140i	$-0.360985\pi$
$641$	1.60774e32	0.845955	0.422978	+	0.906140i	$0.360985\pi$
$642$	−5.31155e31	−0.274517
$643$	−3.25183e32	−1.65083	−0.825413	−	0.564529i	$-0.809058\pi$
$643$	−3.25183e32	−1.65083	−0.825413	+	0.564529i	$0.809058\pi$
$644$	−3.70447e29	−0.00184730
$645$	−3.07486e31	−0.150622
$646$	2.29402e32	1.10389
$647$	2.35559e32	1.11353	0.556763	−	0.830672i	$-0.312043\pi$
$647$	2.35559e32	1.11353	0.556763	+	0.830672i	$0.312043\pi$
$648$	2.78469e31	0.129320
$649$	−1.48941e32	−0.679517
$650$	1.18232e31	0.0529945
$651$	−4.77143e31	−0.210120
$652$	1.60003e32	0.692277
$653$	1.72242e32	0.732215	0.366108	−	0.930573i	$-0.380690\pi$
$653$	1.72242e32	0.732215	0.366108	+	0.930573i	$0.380690\pi$
$654$	1.30503e32	0.545099
$655$	9.39208e31	0.385467
$656$	−5.67663e31	−0.228927
$657$	1.86597e32	0.739438
$658$	−1.20425e30	−0.00468942
$659$	−2.10755e32	−0.806483	−0.403242	−	0.915094i	$-0.632117\pi$
$659$	−2.10755e32	−0.806483	−0.403242	+	0.915094i	$0.632117\pi$
$660$	−4.48496e31	−0.168657
$661$	−1.56345e32	−0.577786	−0.288893	−	0.957361i	$-0.593287\pi$
$661$	−1.56345e32	−0.577786	−0.288893	+	0.957361i	$0.593287\pi$
$662$	1.00695e32	0.365712
$663$	7.51760e31	0.268333
$664$	5.07842e31	0.178154
$665$	4.52675e31	0.156077
$666$	−3.17681e31	−0.107656
$667$	2.53983e30	0.00845977
$668$	−2.71184e32	−0.887842
$669$	1.85413e32	0.596678
$670$	7.59236e30	0.0240169
$671$	−4.89952e32	−1.52351
$672$	−9.25790e30	−0.0282987
$673$	−3.51032e32	−1.05481	−0.527405	−	0.849614i	$-0.676835\pi$
$673$	−3.51032e32	−1.05481	−0.527405	+	0.849614i	$0.676835\pi$
$674$	−3.19936e32	−0.945091
$675$	−7.42081e31	−0.215505
$676$	−1.50537e32	−0.429789
$677$	−5.04787e32	−1.41690	−0.708448	−	0.705763i	$-0.750604\pi$
$677$	−5.04787e32	−1.41690	−0.708448	+	0.705763i	$0.750604\pi$
$678$	−2.77903e31	−0.0766923
$679$	1.39412e32	0.378268
$680$	5.67304e31	0.151343
$681$	1.67341e32	0.438944
$682$	−3.62815e32	−0.935762
$683$	2.13585e32	0.541668	0.270834	−	0.962626i	$-0.412701\pi$
$683$	2.13585e32	0.541668	0.270834	+	0.962626i	$0.412701\pi$
$684$	−1.43994e32	−0.359086
$685$	1.61130e32	0.395124
$686$	1.22620e32	0.295688
$687$	−3.51458e31	−0.0833435
$688$	−4.82632e31	−0.112551
$689$	1.06705e32	0.244716
$690$	1.81101e30	0.00408466
$691$	−4.74070e32	−1.05159	−0.525793	−	0.850613i	$-0.676231\pi$
$691$	−4.74070e32	−1.05159	−0.525793	+	0.850613i	$0.676231\pi$
$692$	−9.69927e31	−0.211602
$693$	4.42736e31	0.0949977
$694$	3.07360e32	0.648654
$695$	3.01460e32	0.625755
$696$	6.34735e31	0.129594
$697$	4.36442e32	0.876495
$698$	−5.35589e32	−1.05802
$699$	6.39073e32	1.24183
$700$	1.11945e31	0.0213982
$701$	−4.92407e32	−0.925906	−0.462953	−	0.886383i	$-0.653210\pi$
$701$	−4.92407e32	−0.925906	−0.462953	+	0.886383i	$0.653210\pi$
$702$	−1.54350e32	−0.285515
$703$	−3.09886e32	−0.563918
$704$	−7.03962e31	−0.126027
$705$	5.88725e30	0.0103690
$706$	4.60983e32	0.798786
$707$	−1.67663e32	−0.285834
$708$	1.50301e32	0.252105
$709$	8.64776e32	1.42716	0.713578	−	0.700575i	$-0.247073\pi$
$709$	8.64776e32	1.42716	0.713578	+	0.700575i	$0.247073\pi$
$710$	4.54949e31	0.0738740
$711$	4.29275e32	0.685859
$712$	2.05915e32	0.323719
$713$	1.46503e31	0.0226630
$714$	7.11784e31	0.108348
$715$	1.12799e32	0.168960
$716$	−4.18566e32	−0.616971
$717$	−3.62515e32	−0.525842
$718$	9.74283e31	0.139077
$719$	−6.11269e31	−0.0858717	−0.0429359	−	0.999078i	$-0.513671\pi$
$719$	−6.11269e31	−0.0858717	−0.0429359	+	0.999078i	$0.513671\pi$
$720$	−3.56091e31	−0.0492309
$721$	2.25009e32	0.306156
$722$	−8.76573e32	−1.17384
$723$	4.56371e32	0.601489
$724$	4.96627e32	0.644224
$725$	−7.67510e31	−0.0979934
$726$	−6.94577e30	−0.00872869
$727$	3.03244e30	0.00375099	0.00187550	−	0.999998i	$-0.499403\pi$
$727$	3.03244e30	0.00375099	0.00187550	+	0.999998i	$0.499403\pi$
$728$	2.32841e31	0.0283497
$729$	8.06990e32	0.967167
$730$	4.50124e32	0.531031
$731$	3.71066e32	0.430925
$732$	4.94428e32	0.565230
$733$	−5.01686e32	−0.564595	−0.282297	−	0.959327i	$-0.591096\pi$
$733$	−5.01686e32	−0.564595	−0.282297	+	0.959327i	$0.591096\pi$
$734$	−3.98484e32	−0.441475
$735$	−2.92704e32	−0.319245
$736$	2.84257e30	0.00305223
$737$	7.24347e31	0.0765721
$738$	−2.73951e32	−0.285118
$739$	7.88978e32	0.808451	0.404226	−	0.914659i	$-0.367541\pi$
$739$	7.88978e32	0.808451	0.404226	+	0.914659i	$0.367541\pi$
$740$	−7.66337e31	−0.0773134
$741$	−4.60295e32	−0.457221
$742$	1.01031e32	0.0988116
$743$	−1.01205e33	−0.974609	−0.487304	−	0.873232i	$-0.662020\pi$
$743$	−1.01205e33	−0.974609	−0.487304	+	0.873232i	$0.662020\pi$
$744$	3.66129e32	0.347173
$745$	−2.33961e32	−0.218447
$746$	−1.22803e33	−1.12904
$747$	2.45081e32	0.221882
$748$	5.41234e32	0.482522
$749$	1.26484e32	0.111044
$750$	−5.47267e31	−0.0473145
$751$	9.01052e32	0.767169	0.383584	−	0.923506i	$-0.374690\pi$
$751$	9.01052e32	0.767169	0.383584	+	0.923506i	$0.374690\pi$
$752$	9.24066e30	0.00774815
$753$	−8.71407e32	−0.719580
$754$	−1.59639e32	−0.129828
$755$	−5.72149e32	−0.458267
$756$	−1.46142e32	−0.115285
$757$	3.32781e32	0.258557	0.129279	−	0.991608i	$-0.458734\pi$
$757$	3.32781e32	0.258557	0.129279	+	0.991608i	$0.458734\pi$
$758$	1.32391e33	1.01312
$759$	1.72779e31	0.0130230
$760$	−3.47354e32	−0.257879
$761$	−3.01945e32	−0.220803	−0.110401	−	0.993887i	$-0.535214\pi$
$761$	−3.01945e32	−0.220803	−0.110401	+	0.993887i	$0.535214\pi$
$762$	−7.17284e32	−0.516665
$763$	−3.10767e32	−0.220497
$764$	1.03785e33	0.725369
$765$	2.73777e32	0.188491
$766$	1.82497e33	1.23773
$767$	−3.78015e32	−0.252559
$768$	7.10393e31	0.0467568
$769$	−2.38000e33	−1.54320	−0.771602	−	0.636106i	$-0.780544\pi$
$769$	−2.38000e33	−1.54320	−0.771602	+	0.636106i	$0.780544\pi$
$770$	1.06801e32	0.0682229
$771$	8.88687e32	0.559273
$772$	1.17656e33	0.729486
$773$	−1.65561e33	−1.01133	−0.505666	−	0.862729i	$-0.668753\pi$
$773$	−1.65561e33	−1.01133	−0.505666	+	0.862729i	$0.668753\pi$
$774$	−2.32915e32	−0.140177
$775$	−4.42717e32	−0.262516
$776$	−1.06976e33	−0.624996
$777$	−9.61507e31	−0.0553491
$778$	7.69484e32	0.436450
$779$	−2.67229e33	−1.49349
$780$	−1.13829e32	−0.0626853
$781$	4.34043e32	0.235530
$782$	−2.18548e31	−0.0116861
$783$	1.00197e33	0.527952
$784$	−4.59430e32	−0.238553
$785$	7.10799e31	0.0363702
$786$	−9.04234e32	−0.455954
$787$	−1.04035e33	−0.516974	−0.258487	−	0.966015i	$-0.583224\pi$
$787$	−1.04035e33	−0.516974	−0.258487	+	0.966015i	$0.583224\pi$
$788$	9.60191e32	0.470226
$789$	−2.55517e33	−1.23320
$790$	1.03553e33	0.492552
$791$	6.61772e31	0.0310227
$792$	−3.39728e32	−0.156961
$793$	−1.24351e33	−0.566249
$794$	−1.53555e33	−0.689175
$795$	−4.93910e32	−0.218487
$796$	−1.61094e33	−0.702390
$797$	2.16453e32	0.0930238	0.0465119	−	0.998918i	$-0.485189\pi$
$797$	2.16453e32	0.0930238	0.0465119	+	0.998918i	$0.485189\pi$
$798$	−4.35818e32	−0.184617
$799$	−7.10459e31	−0.0296655
$800$	−8.58993e31	−0.0353553
$801$	9.93734e32	0.403178
$802$	1.69096e33	0.676283
$803$	4.29440e33	1.69306
$804$	−7.30963e31	−0.0284087
$805$	−4.31257e30	−0.00165228
$806$	−9.20833e32	−0.347799
$807$	3.50080e33	1.30353
$808$	1.28654e33	0.472272
$809$	2.79297e33	1.01078	0.505392	−	0.862890i	$-0.331348\pi$
$809$	2.79297e33	1.01078	0.505392	+	0.862890i	$0.331348\pi$
$810$	3.24181e32	0.115667
$811$	2.01537e33	0.708948	0.354474	−	0.935066i	$-0.384660\pi$
$811$	2.01537e33	0.708948	0.354474	+	0.935066i	$0.384660\pi$
$812$	−1.51150e32	−0.0524220
$813$	−2.54590e32	−0.0870562
$814$	−7.31121e32	−0.246495
$815$	1.86268e33	0.619191
$816$	−5.46178e32	−0.179018
$817$	−2.27200e33	−0.734268
$818$	4.16786e33	1.32816
$819$	1.12367e32	0.0353082
$820$	−6.60847e32	−0.204758
$821$	4.42385e33	1.35162	0.675808	−	0.737077i	$-0.263795\pi$
$821$	4.42385e33	1.35162	0.675808	+	0.737077i	$0.263795\pi$
$822$	−1.55129e33	−0.467378
$823$	−6.10731e31	−0.0181448	−0.00907239	−	0.999959i	$-0.502888\pi$
$823$	−6.10731e31	−0.0181448	−0.00907239	+	0.999959i	$0.502888\pi$
$824$	−1.72657e33	−0.505850
$825$	−5.22118e32	−0.150851
$826$	−3.57914e32	−0.101978
$827$	4.78632e33	1.34489	0.672447	−	0.740145i	$-0.265243\pi$
$827$	4.78632e33	1.34489	0.672447	+	0.740145i	$0.265243\pi$
$828$	1.37181e31	0.00380140
$829$	−3.13389e33	−0.856459	−0.428230	−	0.903670i	$-0.640863\pi$
$829$	−3.13389e33	−0.856459	−0.428230	+	0.903670i	$0.640863\pi$
$830$	5.91206e32	0.159346
$831$	4.38111e33	1.16459
$832$	−1.78667e32	−0.0468410
$833$	3.53228e33	0.913351
$834$	−2.90234e33	−0.740183
$835$	−3.15700e33	−0.794110
$836$	−3.31392e33	−0.822186
$837$	5.77959e33	1.41434
$838$	2.41021e33	0.581767
$839$	−4.05251e33	−0.964855	−0.482427	−	0.875936i	$-0.660245\pi$
$839$	−4.05251e33	−0.964855	−0.482427	+	0.875936i	$0.660245\pi$
$840$	−1.07776e32	−0.0253111
$841$	−3.28042e33	−0.759932
$842$	−4.08520e33	−0.933522
$843$	−1.32131e33	−0.297843
$844$	2.29417e33	0.510138
$845$	−1.75248e33	−0.384415
$846$	4.45948e31	0.00964996
$847$	1.65400e31	0.00353083
$848$	−7.75244e32	−0.163262
$849$	−2.09948e33	−0.436187
$850$	6.60428e32	0.135365
$851$	2.95224e31	0.00596982
$852$	−4.38007e32	−0.0873828
$853$	−4.75268e33	−0.935459	−0.467729	−	0.883872i	$-0.654928\pi$
$853$	−4.75268e33	−0.935459	−0.467729	+	0.883872i	$0.654928\pi$
$854$	−1.17738e33	−0.228640
$855$	−1.67631e33	−0.321176
$856$	−9.70561e32	−0.183474
$857$	−9.71517e33	−1.81205	−0.906027	−	0.423221i	$-0.860900\pi$
$857$	−9.71517e33	−1.81205	−0.906027	+	0.423221i	$0.860900\pi$
$858$	−1.08598e33	−0.199857
$859$	−8.89769e32	−0.161568	−0.0807841	−	0.996732i	$-0.525742\pi$
$859$	−8.89769e32	−0.161568	−0.0807841	+	0.996732i	$0.525742\pi$
$860$	−5.61857e32	−0.100669
$861$	−8.29151e32	−0.146588
$862$	−1.84530e33	−0.321910
$863$	4.93774e33	0.849972	0.424986	−	0.905200i	$-0.360279\pi$
$863$	4.93774e33	0.849972	0.424986	+	0.905200i	$0.360279\pi$
$864$	1.12140e33	0.190481
$865$	−1.12914e33	−0.189262
$866$	6.71768e33	1.11113
$867$	−3.84127e32	−0.0626983
$868$	−8.71867e32	−0.140434
$869$	9.87947e33	1.57039
$870$	7.38929e32	0.115913
$871$	1.83841e32	0.0284599
$872$	2.38463e33	0.364318
$873$	−5.16260e33	−0.778404
$874$	1.33815e32	0.0199124
$875$	1.30321e32	0.0191391
$876$	−4.33362e33	−0.628136
$877$	8.97071e32	0.128331	0.0641655	−	0.997939i	$-0.479561\pi$
$877$	8.97071e32	0.128331	0.0641655	+	0.997939i	$0.479561\pi$
$878$	−2.75827e33	−0.389448
$879$	2.47419e33	0.344795
$880$	−8.19520e32	−0.112722
$881$	−1.00868e34	−1.36940	−0.684699	−	0.728826i	$-0.740066\pi$
$881$	−1.00868e34	−1.36940	−0.684699	+	0.728826i	$0.740066\pi$
$882$	−2.21718e33	−0.297107
$883$	−9.65735e33	−1.27735	−0.638675	−	0.769476i	$-0.720517\pi$
$883$	−9.65735e33	−1.27735	−0.638675	+	0.769476i	$0.720517\pi$
$884$	1.37366e33	0.179341
$885$	1.74974e33	0.225489
$886$	4.95873e33	0.630787
$887$	5.68517e33	0.713874	0.356937	−	0.934128i	$-0.383821\pi$
$887$	5.68517e33	0.713874	0.356937	+	0.934128i	$0.383821\pi$
$888$	7.37800e32	0.0914512
$889$	1.70807e33	0.208995
$890$	2.39717e33	0.289544
$891$	3.09284e33	0.368777
$892$	3.38799e33	0.398792
$893$	4.35007e32	0.0505480
$894$	2.25249e33	0.258393
$895$	−4.87275e33	−0.551835
$896$	−1.69166e32	−0.0189135
$897$	4.38516e31	0.00484030
$898$	6.35486e33	0.692513
$899$	5.97764e33	0.643122
$900$	−4.14545e32	−0.0440334
$901$	5.96038e33	0.625085
$902$	−6.30479e33	−0.652823
$903$	−7.04951e32	−0.0720692
$904$	−5.07802e32	−0.0512575
$905$	5.78150e33	0.576212
$906$	5.50843e33	0.542067
$907$	−1.49169e34	−1.44942	−0.724712	−	0.689052i	$-0.758027\pi$
$907$	−1.49169e34	−1.44942	−0.724712	+	0.689052i	$0.758027\pi$
$908$	3.05775e33	0.293370
$909$	6.20875e33	0.588192
$910$	2.71062e32	0.0253567
$911$	1.98559e33	0.183412	0.0917062	−	0.995786i	$-0.470768\pi$
$911$	1.98559e33	0.183412	0.0917062	+	0.995786i	$0.470768\pi$
$912$	3.34419e33	0.305036
$913$	5.64038e33	0.508036
$914$	1.03958e34	0.924650
$915$	5.75590e33	0.505557
$916$	−6.42207e32	−0.0557028
$917$	2.15326e33	0.184437
$918$	−8.62177e33	−0.729299
$919$	−2.72785e32	−0.0227873	−0.0113936	−	0.999935i	$-0.503627\pi$
$919$	−2.72785e32	−0.0227873	−0.0113936	+	0.999935i	$0.503627\pi$
$920$	3.30919e31	0.00272999
$921$	2.45315e33	0.199866
$922$	−9.62547e32	−0.0774491
$923$	1.10161e33	0.0875402
$924$	−1.02824e33	−0.0806984
$925$	−8.92133e32	−0.0691512
$926$	6.95668e32	0.0532569
$927$	−8.33233e33	−0.630013
$928$	1.15983e33	0.0866147
$929$	1.45553e34	1.07360	0.536798	−	0.843711i	$-0.319634\pi$
$929$	1.45553e34	1.07360	0.536798	+	0.843711i	$0.319634\pi$
$930$	4.26231e33	0.310521
$931$	−2.16278e34	−1.55629
$932$	1.16775e34	0.829981
$933$	−1.89083e34	−1.32743
$934$	−2.20409e33	−0.152841
$935$	6.30079e33	0.431580
$936$	−8.62236e32	−0.0583383
$937$	1.67847e34	1.12178	0.560889	−	0.827891i	$-0.310459\pi$
$937$	1.67847e34	1.12178	0.560889	+	0.827891i	$0.310459\pi$
$938$	1.74065e32	0.0114915
$939$	−1.65654e34	−1.08031
$940$	1.07575e32	0.00693016
$941$	−1.26349e34	−0.804064	−0.402032	−	0.915626i	$-0.631696\pi$
$941$	−1.26349e34	−0.804064	−0.402032	+	0.915626i	$0.631696\pi$
$942$	−6.84330e32	−0.0430210
$943$	2.54585e32	0.0158106
$944$	2.74640e33	0.168495
$945$	−1.70132e33	−0.103114
$946$	−5.36038e33	−0.320957
$947$	−1.44322e34	−0.853703	−0.426851	−	0.904322i	$-0.640377\pi$
$947$	−1.44322e34	−0.853703	−0.426851	+	0.904322i	$0.640377\pi$
$948$	−9.96971e33	−0.582622
$949$	1.08993e34	0.629268
$950$	−4.04373e33	−0.230654
$951$	−2.00518e34	−1.13000
$952$	1.30062e33	0.0724143
$953$	1.65674e34	0.911350	0.455675	−	0.890146i	$-0.349398\pi$
$953$	1.65674e34	0.911350	0.455675	+	0.890146i	$0.349398\pi$
$954$	−3.74128e33	−0.203336
$955$	1.20821e34	0.648790
$956$	−6.62409e33	−0.351448
$957$	7.04973e33	0.369560
$958$	−2.60678e34	−1.35021
$959$	3.69411e33	0.189058
$960$	8.27006e32	0.0418205
$961$	1.44671e34	0.722873
$962$	−1.85560e33	−0.0916159
$963$	−4.68386e33	−0.228508
$964$	8.33909e33	0.402006
$965$	1.36970e34	0.652472
$966$	4.15197e31	0.00195442
$967$	1.67020e33	0.0776896	0.0388448	−	0.999245i	$-0.487632\pi$
$967$	1.67020e33	0.0776896	0.0388448	+	0.999245i	$0.487632\pi$
$968$	−1.26917e32	−0.00583384
$969$	−2.57115e34	−1.16789
$970$	−1.24537e34	−0.559014
$971$	−1.89959e34	−0.842633	−0.421317	−	0.906914i	$-0.638432\pi$
$971$	−1.89959e34	−0.842633	−0.421317	+	0.906914i	$0.638432\pi$
$972$	9.16913e33	0.401945
$973$	6.91137e33	0.299410
$974$	−8.35865e33	−0.357856
$975$	−1.32515e33	−0.0560674
$976$	9.03450e33	0.377773
$977$	1.78605e34	0.738086	0.369043	−	0.929412i	$-0.379686\pi$
$977$	1.78605e34	0.738086	0.369043	+	0.929412i	$0.379686\pi$
$978$	−1.79331e34	−0.732418
$979$	2.28701e34	0.923140
$980$	−5.34847e33	−0.213368
$981$	1.15081e34	0.453741
$982$	−1.27483e34	−0.496786
$983$	9.74109e33	0.375182	0.187591	−	0.982247i	$-0.439932\pi$
$983$	9.74109e33	0.375182	0.187591	+	0.982247i	$0.439932\pi$
$984$	6.36238e33	0.242201
$985$	1.11781e34	0.420583
$986$	−8.91722e33	−0.331623
$987$	1.34973e32	0.00496134
$988$	−8.41080e33	−0.305585
$989$	2.16450e32	0.00777321
$990$	−3.95495e33	−0.140390
$991$	1.52559e34	0.535292	0.267646	−	0.963517i	$-0.413754\pi$
$991$	1.52559e34	0.535292	0.267646	+	0.963517i	$0.413754\pi$
$992$	6.69015e33	0.232034
$993$	−1.12859e34	−0.386918
$994$	1.04303e33	0.0353471
$995$	−1.87538e34	−0.628237
$996$	−5.69190e33	−0.188484
$997$	−9.21743e33	−0.301728	−0.150864	−	0.988555i	$-0.548206\pi$
$997$	−9.21743e33	−0.301728	−0.150864	+	0.988555i	$0.548206\pi$
$998$	−1.37477e34	−0.444867
$999$	1.16466e34	0.372561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.24.a.a.1.2	✓	2
5.2	odd	4		50.24.b.d.49.1		4
5.3	odd	4		50.24.b.d.49.4		4
5.4	even	2		50.24.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.a.a.1.2	✓	2	1.1	even	1	trivial
50.24.a.d.1.1		2	5.4	even	2
50.24.b.d.49.1		4	5.2	odd	4
50.24.b.d.49.4		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-2048.00 q^{2} +229540. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} -4.70098e8 q^{6} +1.11945e9 q^{7} -8.58993e9 q^{8} -4.14545e10 q^{9} -1.00000e11 q^{10} -9.54047e11 q^{11} +9.62761e11 q^{12} -2.42139e12 q^{13} -2.29263e12 q^{14} +1.12080e13 q^{15} +1.75922e13 q^{16} -1.35256e14 q^{17} +8.48988e13 q^{18} +8.28157e14 q^{19} +2.04800e14 q^{20} +2.56958e14 q^{21} +1.95389e15 q^{22} -7.88972e13 q^{23} -1.97174e15 q^{24} +2.38419e15 q^{25} +4.95901e15 q^{26} -3.11251e16 q^{27} +4.69531e15 q^{28} -3.21917e16 q^{29} -2.29540e16 q^{30} -1.85689e17 q^{31} -3.60288e16 q^{32} -2.18992e17 q^{33} +2.77004e17 q^{34} +5.46606e16 q^{35} -1.73873e17 q^{36} -3.74188e17 q^{37} -1.69607e18 q^{38} -5.55806e17 q^{39} -4.19430e17 q^{40} -3.22679e18 q^{41} -5.26251e17 q^{42} -2.74344e18 q^{43} -4.00156e18 q^{44} -2.02414e18 q^{45} +1.61582e17 q^{46} +5.25271e17 q^{47} +4.03811e18 q^{48} -2.61156e19 q^{49} -4.88281e18 q^{50} -3.10466e19 q^{51} -1.01560e19 q^{52} -4.40675e19 q^{53} +6.37442e19 q^{54} -4.65843e19 q^{55} -9.61599e18 q^{56} +1.90095e20 q^{57} +6.59286e19 q^{58} +1.56115e20 q^{59} +4.70098e19 q^{60} +5.13552e20 q^{61} +3.80291e20 q^{62} -4.64061e19 q^{63} +7.37870e19 q^{64} -1.18232e20 q^{65} +4.48496e20 q^{66} -7.59236e19 q^{67} -5.67304e20 q^{68} -1.81101e19 q^{69} -1.11945e20 q^{70} -4.54949e20 q^{71} +3.56091e20 q^{72} -4.50124e21 q^{73} +7.66337e20 q^{74} +5.47267e20 q^{75} +3.47354e21 q^{76} -1.06801e21 q^{77} +1.13829e21 q^{78} -1.03553e22 q^{79} +8.58993e20 q^{80} -3.24181e21 q^{81} +6.60847e21 q^{82} -5.91206e21 q^{83} +1.07776e21 q^{84} -6.60428e21 q^{85} +5.61857e21 q^{86} -7.38929e21 q^{87} +8.19520e21 q^{88} -2.39717e22 q^{89} +4.14545e21 q^{90} -2.71062e21 q^{91} -3.30919e20 q^{92} -4.26231e22 q^{93} -1.07575e21 q^{94} +4.04373e22 q^{95} -8.27006e21 q^{96} +1.24537e23 q^{97} +5.34847e22 q^{98} +3.95495e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4096 q^{2} - 18516 q^{3} + 8388608 q^{4} + 97656250 q^{5} + 37920768 q^{6} - 4415735108 q^{7} - 17179869184 q^{8} - 74065768326 q^{9} - 200000000000 q^{10} + 195017239824 q^{11} - 77661732864 q^{12}+ \cdots + 20\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 4096 * q^2 - 18516 * q^3 + 8388608 * q^4 + 97656250 * q^5 + 37920768 * q^6 - 4415735108 * q^7 - 17179869184 * q^8 - 74065768326 * q^9 - 200000000000 * q^10 + 195017239824 * q^11 - 77661732864 * q^12 + 2583183058684 * q^13 + 9043425501184 * q^14 - 904101562500 * q^15 + 35184372088832 * q^16 + 131668862600532 * q^17 + 151686693531648 * q^18 - 1760888418200 * q^19 + 409600000000000 * q^20 + 1629995023906464 * q^21 - 399395307159552 * q^22 + 4012836105342564 * q^23 + 159051228905472 * q^24 + 4768371582031250 * q^25 - 5290358904184832 * q^26 + 317121583931640 * q^27 - 18520935426424832 * q^28 - 108385465473787380 * q^29 + 1851600000000000 * q^30 - 282534241930647896 * q^31 - 72057594037927936 * q^32 - 504024591095725392 * q^33 - 269657830605889536 * q^34 - 215612065820312500 * q^35 - 310654348352815104 * q^36 - 326855967548366468 * q^37 + 3606299480473600 * q^38 - 1797221588702622072 * q^39 - 838860800000000000 * q^40 - 5378411403014673276 * q^41 - 3338229808960438272 * q^42 - 9824206470496391636 * q^43 + 817961589062762496 * q^44 - 3616492594042968750 * q^45 - 8218288343741571072 * q^46 - 18459008132084260308 * q^47 - 325736916798406656 * q^48 - 22846074207183681054 * q^49 - 9765625000000000000 * q^50 - 97258917604973930856 * q^51 + 10834655035770535936 * q^52 - 6735586459267392756 * q^53 - 649465003891998720 * q^54 + 9522326163281250000 * q^55 + 37930875753318055936 * q^56 + 395961513009676856400 * q^57 + 221973433290316554240 * q^58 + 404431460611319194440 * q^59 - 3792076800000000000 * q^60 + 267288639406230095404 * q^61 + 578630127473966891008 * q^62 + 134103369179566769004 * q^63 + 147573952589676412928 * q^64 + 126131985287304687500 * q^65 + 1032242362564045602816 * q^66 - 878259028011046311548 * q^67 + 552259237080861769728 * q^68 - 1033089938007493665312 * q^69 + 441573510800000000000 * q^70 - 1422290577065242851336 * q^71 + 636220105426565332992 * q^72 - 2737850090767514630876 * q^73 + 669401021539054526464 * q^74 - 44145584106445312500 * q^75 - 7385701336009932800 * q^76 - 7428286679002982182896 * q^77 + 3680709813662970003456 * q^78 - 16358236398140542679120 * q^79 + 1717986918400000000000 * q^80 - 7971119473850267877918 * q^81 + 11014986553374050869248 * q^82 - 24918314799609836009556 * q^83 + 6836694648750977581056 * q^84 + 6429143681666601562500 * q^85 + 20119974851576610070528 * q^86 + 11511051890670005309640 * q^87 - 1675185334400537591808 * q^88 - 69086711107654759066380 * q^89 + 7406576832600000000000 * q^90 - 30411848367847894491736 * q^91 + 16831054527982737555456 * q^92 - 18600007517643336450432 * q^93 + 37804048654508565110784 * q^94 - 85980879794921875000 * q^95 + 667109205603136831488 * q^96 + 142113717247845486800212 * q^97 + 46788759976312178798592 * q^98 + 2077038401308192249488 * q^99

Introduction

L-functions

Modular forms

Varieties

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