LMFDB - Embedded newform 105.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,10,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	105.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:	$54.0787627972$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 988x^{2} - 844x + 192256 $ x^4 - x^3 - 988x^2 - 844x + 192256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-17.8249$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-38.2301 q^{2} -81.0000 q^{3} +949.541 q^{4} +625.000 q^{5} +3096.64 q^{6} +2401.00 q^{7} -16727.3 q^{8} +6561.00 q^{9} -23893.8 q^{10} +40565.3 q^{11} -76912.9 q^{12} -32722.1 q^{13} -91790.5 q^{14} -50625.0 q^{15} +153320. q^{16} -520250. q^{17} -250828. q^{18} -519011. q^{19} +593463. q^{20} -194481. q^{21} -1.55081e6 q^{22} +745417. q^{23} +1.35491e6 q^{24} +390625. q^{25} +1.25097e6 q^{26} -531441. q^{27} +2.27985e6 q^{28} +1.80612e6 q^{29} +1.93540e6 q^{30} +3.91154e6 q^{31} +2.70293e6 q^{32} -3.28579e6 q^{33} +1.98892e7 q^{34} +1.50062e6 q^{35} +6.22994e6 q^{36} -4.95683e6 q^{37} +1.98418e7 q^{38} +2.65049e6 q^{39} -1.04545e7 q^{40} +1.54834e7 q^{41} +7.43503e6 q^{42} -3.17606e7 q^{43} +3.85184e7 q^{44} +4.10062e6 q^{45} -2.84974e7 q^{46} +2.61252e7 q^{47} -1.24189e7 q^{48} +5.76480e6 q^{49} -1.49336e7 q^{50} +4.21403e7 q^{51} -3.10710e7 q^{52} -2.11451e7 q^{53} +2.03170e7 q^{54} +2.53533e7 q^{55} -4.01621e7 q^{56} +4.20399e7 q^{57} -6.90481e7 q^{58} +9.89155e7 q^{59} -4.80705e7 q^{60} -4.80918e7 q^{61} -1.49539e8 q^{62} +1.57530e7 q^{63} -1.81833e8 q^{64} -2.04513e7 q^{65} +1.25616e8 q^{66} -6.60758e7 q^{67} -4.93999e8 q^{68} -6.03788e7 q^{69} -5.73691e7 q^{70} -2.44963e8 q^{71} -1.09748e8 q^{72} -2.04226e8 q^{73} +1.89500e8 q^{74} -3.16406e7 q^{75} -4.92822e8 q^{76} +9.73972e7 q^{77} -1.01329e8 q^{78} +2.39876e8 q^{79} +9.58248e7 q^{80} +4.30467e7 q^{81} -5.91932e8 q^{82} +2.98577e8 q^{83} -1.84668e8 q^{84} -3.25157e8 q^{85} +1.21421e9 q^{86} -1.46296e8 q^{87} -6.78545e8 q^{88} -3.94988e8 q^{89} -1.56767e8 q^{90} -7.85659e7 q^{91} +7.07804e8 q^{92} -3.16835e8 q^{93} -9.98771e8 q^{94} -3.24382e8 q^{95} -2.18937e8 q^{96} -1.22147e8 q^{97} -2.20389e8 q^{98} +2.66149e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) $ 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * 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 $

$2$	−38.2301	−1.68955	−0.844774	−	0.535123i	$-0.820265\pi$
$2$	−38.2301	−1.68955	−0.844774	+	0.535123i	$0.820265\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	949.541	1.85457
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	3096.64	0.975461
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−16727.3	−1.44384
$9$	6561.00	0.333333
$10$	−23893.8	−0.755589
$11$	40565.3	0.835386	0.417693	−	0.908588i	$-0.362839\pi$
$11$	40565.3	0.835386	0.417693	+	0.908588i	$0.362839\pi$
$12$	−76912.9	−1.07074
$13$	−32722.1	−0.317758	−0.158879	−	0.987298i	$-0.550788\pi$
$13$	−32722.1	−0.317758	−0.158879	+	0.987298i	$0.550788\pi$
$14$	−91790.5	−0.638589
$15$	−50625.0	−0.258199
$16$	153320.	0.584868
$17$	−520250.	−1.51075	−0.755375	−	0.655293i	$-0.772545\pi$
$17$	−520250.	−1.51075	−0.755375	+	0.655293i	$0.772545\pi$
$18$	−250828.	−0.563183
$19$	−519011.	−0.913661	−0.456830	−	0.889554i	$-0.651015\pi$
$19$	−519011.	−0.913661	−0.456830	+	0.889554i	$0.651015\pi$
$20$	593463.	0.829390
$21$	−194481.	−0.218218
$22$	−1.55081e6	−1.41142
$23$	745417.	0.555423	0.277712	−	0.960665i	$-0.410424\pi$
$23$	745417.	0.555423	0.277712	+	0.960665i	$0.410424\pi$
$24$	1.35491e6	0.833603
$25$	390625.	0.200000
$26$	1.25097e6	0.536868
$27$	−531441.	−0.192450
$28$	2.27985e6	0.700963
$29$	1.80612e6	0.474193	0.237096	−	0.971486i	$-0.423804\pi$
$29$	1.80612e6	0.474193	0.237096	+	0.971486i	$0.423804\pi$
$30$	1.93540e6	0.436239
$31$	3.91154e6	0.760712	0.380356	−	0.924840i	$-0.375801\pi$
$31$	3.91154e6	0.760712	0.380356	+	0.924840i	$0.375801\pi$
$32$	2.70293e6	0.455680
$33$	−3.28579e6	−0.482310
$34$	1.98892e7	2.55248
$35$	1.50062e6	0.169031
$36$	6.22994e6	0.618191
$37$	−4.95683e6	−0.434806	−0.217403	−	0.976082i	$-0.569759\pi$
$37$	−4.95683e6	−0.434806	−0.217403	+	0.976082i	$0.569759\pi$
$38$	1.98418e7	1.54367
$39$	2.65049e6	0.183458
$40$	−1.04545e7	−0.645706
$41$	1.54834e7	0.855735	0.427867	−	0.903841i	$-0.359265\pi$
$41$	1.54834e7	0.855735	0.427867	+	0.903841i	$0.359265\pi$
$42$	7.43503e6	0.368690
$43$	−3.17606e7	−1.41671	−0.708353	−	0.705858i	$-0.750562\pi$
$43$	−3.17606e7	−1.41671	−0.708353	+	0.705858i	$0.750562\pi$
$44$	3.85184e7	1.54928
$45$	4.10062e6	0.149071
$46$	−2.84974e7	−0.938414
$47$	2.61252e7	0.780944	0.390472	−	0.920615i	$-0.372312\pi$
$47$	2.61252e7	0.780944	0.390472	+	0.920615i	$0.372312\pi$
$48$	−1.24189e7	−0.337674
$49$	5.76480e6	0.142857
$50$	−1.49336e7	−0.337910
$51$	4.21403e7	0.872231
$52$	−3.10710e7	−0.589306
$53$	−2.11451e7	−0.368102	−0.184051	−	0.982917i	$-0.558921\pi$
$53$	−2.11451e7	−0.368102	−0.184051	+	0.982917i	$0.558921\pi$
$54$	2.03170e7	0.325154
$55$	2.53533e7	0.373596
$56$	−4.01621e7	−0.545721
$57$	4.20399e7	0.527502
$58$	−6.90481e7	−0.801172
$59$	9.89155e7	1.06275	0.531374	−	0.847137i	$-0.321676\pi$
$59$	9.89155e7	1.06275	0.531374	+	0.847137i	$0.321676\pi$
$60$	−4.80705e7	−0.478849
$61$	−4.80918e7	−0.444720	−0.222360	−	0.974965i	$-0.571376\pi$
$61$	−4.80918e7	−0.444720	−0.222360	+	0.974965i	$0.571376\pi$
$62$	−1.49539e8	−1.28526
$63$	1.57530e7	0.125988
$64$	−1.81833e8	−1.35476
$65$	−2.04513e7	−0.142106
$66$	1.25616e8	0.814886
$67$	−6.60758e7	−0.400595	−0.200298	−	0.979735i	$-0.564191\pi$
$67$	−6.60758e7	−0.400595	−0.200298	+	0.979735i	$0.564191\pi$
$68$	−4.93999e8	−2.80179
$69$	−6.03788e7	−0.320674
$70$	−5.73691e7	−0.285586
$71$	−2.44963e8	−1.14403	−0.572016	−	0.820243i	$-0.693838\pi$
$71$	−2.44963e8	−1.14403	−0.572016	+	0.820243i	$0.693838\pi$
$72$	−1.09748e8	−0.481281
$73$	−2.04226e8	−0.841704	−0.420852	−	0.907129i	$-0.638269\pi$
$73$	−2.04226e8	−0.841704	−0.420852	+	0.907129i	$0.638269\pi$
$74$	1.89500e8	0.734626
$75$	−3.16406e7	−0.115470
$76$	−4.92822e8	−1.69445
$77$	9.73972e7	0.315746
$78$	−1.01329e8	−0.309961
$79$	2.39876e8	0.692891	0.346446	−	0.938070i	$-0.387389\pi$
$79$	2.39876e8	0.692891	0.346446	+	0.938070i	$0.387389\pi$
$80$	9.58248e7	0.261561
$81$	4.30467e7	0.111111
$82$	−5.91932e8	−1.44581
$83$	2.98577e8	0.690565	0.345282	−	0.938499i	$-0.387783\pi$
$83$	2.98577e8	0.690565	0.345282	+	0.938499i	$0.387783\pi$
$84$	−1.84668e8	−0.404701
$85$	−3.25157e8	−0.675628
$86$	1.21421e9	2.39359
$87$	−1.46296e8	−0.273775
$88$	−6.78545e8	−1.20617
$89$	−3.94988e8	−0.667312	−0.333656	−	0.942695i	$-0.608282\pi$
$89$	−3.94988e8	−0.667312	−0.333656	+	0.942695i	$0.608282\pi$
$90$	−1.56767e8	−0.251863
$91$	−7.85659e7	−0.120101
$92$	7.07804e8	1.03007
$93$	−3.16835e8	−0.439197
$94$	−9.98771e8	−1.31944
$95$	−3.24382e8	−0.408602
$96$	−2.18937e8	−0.263087
$97$	−1.22147e8	−0.140091	−0.0700456	−	0.997544i	$-0.522314\pi$
$97$	−1.22147e8	−0.140091	−0.0700456	+	0.997544i	$0.522314\pi$
$98$	−2.20389e8	−0.241364
$99$	2.66149e8	0.278462
$100$	3.70915e8	0.370915
$101$	1.83040e9	1.75025	0.875126	−	0.483895i	$-0.160778\pi$
$101$	1.83040e9	1.75025	0.875126	+	0.483895i	$0.160778\pi$
$102$	−1.61103e9	−1.47368
$103$	−6.66440e8	−0.583436	−0.291718	−	0.956504i	$-0.594227\pi$
$103$	−6.66440e8	−0.583436	−0.291718	+	0.956504i	$0.594227\pi$
$104$	5.47352e8	0.458793
$105$	−1.21551e8	−0.0975900
$106$	8.08379e8	0.621926
$107$	−3.53233e8	−0.260516	−0.130258	−	0.991480i	$-0.541581\pi$
$107$	−3.53233e8	−0.260516	−0.130258	+	0.991480i	$0.541581\pi$
$108$	−5.04625e8	−0.356913
$109$	−9.29576e8	−0.630762	−0.315381	−	0.948965i	$-0.602132\pi$
$109$	−9.29576e8	−0.630762	−0.315381	+	0.948965i	$0.602132\pi$
$110$	−9.69259e8	−0.631208
$111$	4.01503e8	0.251036
$112$	3.68120e8	0.221059
$113$	−2.47756e9	−1.42946	−0.714729	−	0.699402i	$-0.753450\pi$
$113$	−2.47756e9	−1.42946	−0.714729	+	0.699402i	$0.753450\pi$
$114$	−1.60719e9	−0.891241
$115$	4.65886e8	0.248393
$116$	1.71498e9	0.879426
$117$	−2.14690e8	−0.105919
$118$	−3.78155e9	−1.79556
$119$	−1.24912e9	−0.571010
$120$	8.46817e8	0.372798
$121$	−7.12408e8	−0.302130
$122$	1.83856e9	0.751376
$123$	−1.25416e9	−0.494059
$124$	3.71417e9	1.41080
$125$	2.44141e8	0.0894427
$126$	−6.02237e8	−0.212863
$127$	2.33656e9	0.797004	0.398502	−	0.917168i	$-0.369530\pi$
$127$	2.33656e9	0.797004	0.398502	+	0.917168i	$0.369530\pi$
$128$	5.56759e9	1.83325
$129$	2.57260e9	0.817936
$130$	7.81857e8	0.240094
$131$	5.92791e9	1.75865	0.879327	−	0.476218i	$-0.157993\pi$
$131$	5.92791e9	1.75865	0.879327	+	0.476218i	$0.157993\pi$
$132$	−3.11999e9	−0.894480
$133$	−1.24614e9	−0.345331
$134$	2.52609e9	0.676825
$135$	−3.32151e8	−0.0860663
$136$	8.70236e9	2.18128
$137$	−6.29615e9	−1.52698	−0.763488	−	0.645822i	$-0.776515\pi$
$137$	−6.29615e9	−1.52698	−0.763488	+	0.645822i	$0.776515\pi$
$138$	2.30829e9	0.541794
$139$	−2.24534e9	−0.510172	−0.255086	−	0.966918i	$-0.582104\pi$
$139$	−2.24534e9	−0.510172	−0.255086	+	0.966918i	$0.582104\pi$
$140$	1.42491e9	0.313480
$141$	−2.11615e9	−0.450878
$142$	9.36496e9	1.93290
$143$	−1.32738e9	−0.265451
$144$	1.00593e9	0.194956
$145$	1.12882e9	0.212066
$146$	7.80760e9	1.42210
$147$	−4.66949e8	−0.0824786
$148$	−4.70671e9	−0.806380
$149$	7.37067e9	1.22509	0.612546	−	0.790435i	$-0.290145\pi$
$149$	7.37067e9	1.22509	0.612546	+	0.790435i	$0.290145\pi$
$150$	1.20962e9	0.195092
$151$	2.45041e8	0.0383569	0.0191784	−	0.999816i	$-0.493895\pi$
$151$	2.45041e8	0.0383569	0.0191784	+	0.999816i	$0.493895\pi$
$152$	8.68162e9	1.31918
$153$	−3.41336e9	−0.503583
$154$	−3.72350e9	−0.533468
$155$	2.44471e9	0.340201
$156$	2.51675e9	0.340236
$157$	5.01037e9	0.658144	0.329072	−	0.944305i	$-0.393264\pi$
$157$	5.01037e9	0.658144	0.329072	+	0.944305i	$0.393264\pi$
$158$	−9.17049e9	−1.17067
$159$	1.71275e9	0.212524
$160$	1.68933e9	0.203786
$161$	1.78975e9	0.209930
$162$	−1.64568e9	−0.187728
$163$	−1.33476e10	−1.48102	−0.740508	−	0.672048i	$-0.765415\pi$
$163$	−1.33476e10	−1.48102	−0.740508	+	0.672048i	$0.765415\pi$
$164$	1.47021e10	1.58702
$165$	−2.05362e9	−0.215696
$166$	−1.14146e10	−1.16674
$167$	−1.48390e10	−1.47632	−0.738162	−	0.674624i	$-0.764306\pi$
$167$	−1.48390e10	−1.47632	−0.738162	+	0.674624i	$0.764306\pi$
$168$	3.25313e9	0.315072
$169$	−9.53376e9	−0.899030
$170$	1.24308e10	1.14151
$171$	−3.40523e9	−0.304554
$172$	−3.01580e10	−2.62739
$173$	2.13061e10	1.80841	0.904203	−	0.427103i	$-0.140466\pi$
$173$	2.13061e10	1.80841	0.904203	+	0.427103i	$0.140466\pi$
$174$	5.59290e9	0.462557
$175$	9.37891e8	0.0755929
$176$	6.21945e9	0.488591
$177$	−8.01215e9	−0.613578
$178$	1.51004e10	1.12746
$179$	−2.40065e10	−1.74780	−0.873898	−	0.486108i	$-0.838416\pi$
$179$	−2.40065e10	−1.74780	−0.873898	+	0.486108i	$0.838416\pi$
$180$	3.89371e9	0.276463
$181$	−1.97843e10	−1.37015	−0.685073	−	0.728475i	$-0.740230\pi$
$181$	−1.97843e10	−1.37015	−0.685073	+	0.728475i	$0.740230\pi$
$182$	3.00358e9	0.202917
$183$	3.89544e9	0.256759
$184$	−1.24688e10	−0.801943
$185$	−3.09802e9	−0.194451
$186$	1.21126e10	0.742045
$187$	−2.11041e10	−1.26206
$188$	2.48070e10	1.44832
$189$	−1.27599e9	−0.0727393
$190$	1.24011e10	0.690352
$191$	2.75446e9	0.149757	0.0748783	−	0.997193i	$-0.476143\pi$
$191$	2.75446e9	0.149757	0.0748783	+	0.997193i	$0.476143\pi$
$192$	1.47285e10	0.782171
$193$	−1.34655e10	−0.698577	−0.349288	−	0.937015i	$-0.613577\pi$
$193$	−1.34655e10	−0.698577	−0.349288	+	0.937015i	$0.613577\pi$
$194$	4.66971e9	0.236691
$195$	1.65656e9	0.0820448
$196$	5.47392e9	0.264939
$197$	−3.46991e10	−1.64142	−0.820711	−	0.571343i	$-0.806423\pi$
$197$	−3.46991e10	−1.64142	−0.820711	+	0.571343i	$0.806423\pi$
$198$	−1.01749e10	−0.470475
$199$	−1.30842e10	−0.591436	−0.295718	−	0.955275i	$-0.595559\pi$
$199$	−1.30842e10	−0.591436	−0.295718	+	0.955275i	$0.595559\pi$
$200$	−6.53408e9	−0.288768
$201$	5.35214e9	0.231284
$202$	−6.99765e10	−2.95713
$203$	4.33649e9	0.179228
$204$	4.00139e10	1.61762
$205$	9.67713e9	0.382696
$206$	2.54781e10	0.985744
$207$	4.89068e9	0.185141
$208$	−5.01695e9	−0.185847
$209$	−2.10538e10	−0.763259
$210$	4.64689e9	0.164883
$211$	2.25770e10	0.784141	0.392071	−	0.919935i	$-0.371759\pi$
$211$	2.25770e10	0.784141	0.392071	+	0.919935i	$0.371759\pi$
$212$	−2.00781e10	−0.682672
$213$	1.98420e10	0.660507
$214$	1.35041e10	0.440154
$215$	−1.98503e10	−0.633571
$216$	8.88955e9	0.277868
$217$	9.39161e9	0.287522
$218$	3.55378e10	1.06570
$219$	1.65423e10	0.485958
$220$	2.40740e10	0.692861
$221$	1.70237e10	0.480053
$222$	−1.53495e10	−0.424137
$223$	5.60624e10	1.51810	0.759049	−	0.651033i	$-0.225664\pi$
$223$	5.60624e10	1.51810	0.759049	+	0.651033i	$0.225664\pi$
$224$	6.48973e9	0.172231
$225$	2.56289e9	0.0666667
$226$	9.47174e10	2.41514
$227$	−6.58614e10	−1.64632	−0.823160	−	0.567809i	$-0.807791\pi$
$227$	−6.58614e10	−1.64632	−0.823160	+	0.567809i	$0.807791\pi$
$228$	3.99186e10	0.978291
$229$	−2.80263e10	−0.673451	−0.336725	−	0.941603i	$-0.609319\pi$
$229$	−2.80263e10	−0.673451	−0.336725	+	0.941603i	$0.609319\pi$
$230$	−1.78109e10	−0.419672
$231$	−7.88917e9	−0.182296
$232$	−3.02114e10	−0.684660
$233$	5.33778e10	1.18648	0.593238	−	0.805027i	$-0.297849\pi$
$233$	5.33778e10	1.18648	0.593238	+	0.805027i	$0.297849\pi$
$234$	8.20762e9	0.178956
$235$	1.63283e10	0.349249
$236$	9.39243e10	1.97094
$237$	−1.94300e10	−0.400041
$238$	4.77541e10	0.964748
$239$	−5.25189e10	−1.04118	−0.520589	−	0.853807i	$-0.674288\pi$
$239$	−5.25189e10	−1.04118	−0.520589	+	0.853807i	$0.674288\pi$
$240$	−7.76181e9	−0.151012
$241$	−5.77458e10	−1.10267	−0.551333	−	0.834285i	$-0.685881\pi$
$241$	−5.77458e10	−1.10267	−0.551333	+	0.834285i	$0.685881\pi$
$242$	2.72354e10	0.510464
$243$	−3.48678e9	−0.0641500
$244$	−4.56652e10	−0.824766
$245$	3.60300e9	0.0638877
$246$	4.79465e10	0.834736
$247$	1.69831e10	0.290323
$248$	−6.54293e10	−1.09835
$249$	−2.41847e10	−0.398698
$250$	−9.33352e9	−0.151118
$251$	−9.13469e10	−1.45265	−0.726327	−	0.687350i	$-0.758774\pi$
$251$	−9.13469e10	−1.45265	−0.726327	+	0.687350i	$0.758774\pi$
$252$	1.49581e10	0.233654
$253$	3.02380e10	0.463993
$254$	−8.93270e10	−1.34658
$255$	2.63377e10	0.390074
$256$	−1.19751e11	−1.74261
$257$	3.84547e9	0.0549858	0.0274929	−	0.999622i	$-0.491248\pi$
$257$	3.84547e9	0.0549858	0.0274929	+	0.999622i	$0.491248\pi$
$258$	−9.83510e10	−1.38194
$259$	−1.19013e10	−0.164341
$260$	−1.94194e10	−0.263545
$261$	1.18499e10	0.158064
$262$	−2.26625e11	−2.97133
$263$	−1.50995e11	−1.94609	−0.973045	−	0.230617i	$-0.925926\pi$
$263$	−1.50995e11	−1.94609	−0.973045	+	0.230617i	$0.925926\pi$
$264$	5.49622e10	0.696380
$265$	−1.32157e10	−0.164620
$266$	4.76402e10	0.583454
$267$	3.19940e10	0.385273
$268$	−6.27417e10	−0.742933
$269$	−9.07553e10	−1.05679	−0.528393	−	0.849000i	$-0.677205\pi$
$269$	−9.07553e10	−1.05679	−0.528393	+	0.849000i	$0.677205\pi$
$270$	1.26982e10	0.145413
$271$	8.25031e10	0.929198	0.464599	−	0.885521i	$-0.346198\pi$
$271$	8.25031e10	0.929198	0.464599	+	0.885521i	$0.346198\pi$
$272$	−7.97646e10	−0.883589
$273$	6.36383e9	0.0693405
$274$	2.40702e11	2.57990
$275$	1.58458e10	0.167077
$276$	−5.73321e10	−0.594713
$277$	6.69132e10	0.682893	0.341446	−	0.939901i	$-0.389083\pi$
$277$	6.69132e10	0.682893	0.341446	+	0.939901i	$0.389083\pi$
$278$	8.58398e10	0.861960
$279$	2.56636e10	0.253571
$280$	−2.51013e10	−0.244054
$281$	3.07859e10	0.294560	0.147280	−	0.989095i	$-0.452948\pi$
$281$	3.07859e10	0.294560	0.147280	+	0.989095i	$0.452948\pi$
$282$	8.09005e10	0.761781
$283$	−1.80035e11	−1.66847	−0.834236	−	0.551407i	$-0.814091\pi$
$283$	−1.80035e11	−1.66847	−0.834236	+	0.551407i	$0.814091\pi$
$284$	−2.32602e11	−2.12169
$285$	2.62749e10	0.235906
$286$	5.07460e10	0.448492
$287$	3.71757e10	0.323437
$288$	1.77339e10	0.151893
$289$	1.52073e11	1.28236
$290$	−4.31551e10	−0.358295
$291$	9.89393e9	0.0808817
$292$	−1.93922e11	−1.56100
$293$	9.27235e10	0.734997	0.367498	−	0.930024i	$-0.380214\pi$
$293$	9.27235e10	0.734997	0.367498	+	0.930024i	$0.380214\pi$
$294$	1.78515e10	0.139352
$295$	6.18222e10	0.475275
$296$	8.29141e10	0.627792
$297$	−2.15580e10	−0.160770
$298$	−2.81782e11	−2.06985
$299$	−2.43916e10	−0.176490
$300$	−3.00441e10	−0.214148
$301$	−7.62571e10	−0.535465
$302$	−9.36796e9	−0.0648058
$303$	−1.48263e11	−1.01051
$304$	−7.95745e10	−0.534371
$305$	−3.00574e10	−0.198885
$306$	1.30493e11	0.850828
$307$	−6.52650e10	−0.419332	−0.209666	−	0.977773i	$-0.567238\pi$
$307$	−6.52650e10	−0.419332	−0.209666	+	0.977773i	$0.567238\pi$
$308$	9.24826e10	0.585574
$309$	5.39816e10	0.336847
$310$	−9.34616e10	−0.574785
$311$	4.00711e10	0.242890	0.121445	−	0.992598i	$-0.461247\pi$
$311$	4.00711e10	0.242890	0.121445	+	0.992598i	$0.461247\pi$
$312$	−4.43355e10	−0.264884
$313$	2.97753e10	0.175350	0.0876752	−	0.996149i	$-0.472056\pi$
$313$	2.97753e10	0.175350	0.0876752	+	0.996149i	$0.472056\pi$
$314$	−1.91547e11	−1.11197
$315$	9.84560e9	0.0563436
$316$	2.27772e11	1.28502
$317$	−9.46291e10	−0.526330	−0.263165	−	0.964751i	$-0.584766\pi$
$317$	−9.46291e10	−0.526330	−0.263165	+	0.964751i	$0.584766\pi$
$318$	−6.54787e10	−0.359069
$319$	7.32656e10	0.396134
$320$	−1.13646e11	−0.605867
$321$	2.86119e10	0.150409
$322$	−6.84222e10	−0.354687
$323$	2.70015e11	1.38031
$324$	4.08746e10	0.206064
$325$	−1.27821e10	−0.0635516
$326$	5.10281e11	2.50225
$327$	7.52956e10	0.364171
$328$	−2.58995e11	−1.23555
$329$	6.27267e10	0.295169
$330$	7.85100e10	0.364428
$331$	4.88930e10	0.223883	0.111941	−	0.993715i	$-0.464293\pi$
$331$	4.88930e10	0.223883	0.111941	+	0.993715i	$0.464293\pi$
$332$	2.83511e11	1.28070
$333$	−3.25217e10	−0.144935
$334$	5.67298e11	2.49432
$335$	−4.12974e10	−0.179152
$336$	−2.98178e10	−0.127629
$337$	−8.32812e10	−0.351732	−0.175866	−	0.984414i	$-0.556273\pi$
$337$	−8.32812e10	−0.351732	−0.175866	+	0.984414i	$0.556273\pi$
$338$	3.64477e11	1.51895
$339$	2.00682e11	0.825298
$340$	−3.08750e11	−1.25300
$341$	1.58673e11	0.635488
$342$	1.30182e11	0.514558
$343$	1.38413e10	0.0539949
$344$	5.31267e11	2.04550
$345$	−3.77367e10	−0.143410
$346$	−8.14534e11	−3.05539
$347$	4.23123e10	0.156670	0.0783348	−	0.996927i	$-0.475040\pi$
$347$	4.23123e10	0.156670	0.0783348	+	0.996927i	$0.475040\pi$
$348$	−1.38914e11	−0.507737
$349$	−6.55677e10	−0.236579	−0.118289	−	0.992979i	$-0.537741\pi$
$349$	−6.55677e10	−0.236579	−0.118289	+	0.992979i	$0.537741\pi$
$350$	−3.58557e10	−0.127718
$351$	1.73899e10	0.0611526
$352$	1.09645e11	0.380668
$353$	2.12530e11	0.728509	0.364254	−	0.931299i	$-0.381324\pi$
$353$	2.12530e11	0.728509	0.364254	+	0.931299i	$0.381324\pi$
$354$	3.06305e11	1.03667
$355$	−1.53102e11	−0.511626
$356$	−3.75058e11	−1.23758
$357$	1.01179e11	0.329672
$358$	9.17773e11	2.95299
$359$	−2.56017e10	−0.0813475	−0.0406737	−	0.999172i	$-0.512950\pi$
$359$	−2.56017e10	−0.0813475	−0.0406737	+	0.999172i	$0.512950\pi$
$360$	−6.85922e10	−0.215235
$361$	−5.33158e10	−0.165224
$362$	7.56355e11	2.31493
$363$	5.77050e10	0.174435
$364$	−7.46015e10	−0.222737
$365$	−1.27642e11	−0.376421
$366$	−1.48923e11	−0.433807
$367$	−1.97966e11	−0.569629	−0.284815	−	0.958583i	$-0.591932\pi$
$367$	−1.97966e11	−0.569629	−0.284815	+	0.958583i	$0.591932\pi$
$368$	1.14287e11	0.324849
$369$	1.01587e11	0.285245
$370$	1.18438e11	0.328535
$371$	−5.07693e10	−0.139129
$372$	−3.00848e11	−0.814523
$373$	5.96647e11	1.59598	0.797990	−	0.602670i	$-0.205897\pi$
$373$	5.96647e11	1.59598	0.797990	+	0.602670i	$0.205897\pi$
$374$	8.06812e11	2.13231
$375$	−1.97754e10	−0.0516398
$376$	−4.37004e11	−1.12756
$377$	−5.91000e10	−0.150679
$378$	4.87812e10	0.122897
$379$	−6.04738e11	−1.50553	−0.752767	−	0.658287i	$-0.771282\pi$
$379$	−6.04738e11	−1.50553	−0.752767	+	0.658287i	$0.771282\pi$
$380$	−3.08014e11	−0.757781
$381$	−1.89261e11	−0.460150
$382$	−1.05303e11	−0.253021
$383$	−1.08351e11	−0.257300	−0.128650	−	0.991690i	$-0.541064\pi$
$383$	−1.08351e11	−0.257300	−0.128650	+	0.991690i	$0.541064\pi$
$384$	−4.50975e11	−1.05843
$385$	6.08732e10	0.141206
$386$	5.14787e11	1.18028
$387$	−2.08381e11	−0.472236
$388$	−1.15984e11	−0.259810
$389$	−1.19530e11	−0.264669	−0.132335	−	0.991205i	$-0.542247\pi$
$389$	−1.19530e11	−0.264669	−0.132335	+	0.991205i	$0.542247\pi$
$390$	−6.33304e10	−0.138619
$391$	−3.87803e11	−0.839105
$392$	−9.64293e10	−0.206263
$393$	−4.80161e11	−1.01536
$394$	1.32655e12	2.77326
$395$	1.49923e11	0.309870
$396$	2.52719e11	0.516428
$397$	3.05536e11	0.617312	0.308656	−	0.951174i	$-0.400121\pi$
$397$	3.05536e11	0.617312	0.308656	+	0.951174i	$0.400121\pi$
$398$	5.00210e11	0.999260
$399$	1.00938e11	0.199377
$400$	5.98905e10	0.116974
$401$	−1.50964e11	−0.291556	−0.145778	−	0.989317i	$-0.546569\pi$
$401$	−1.50964e11	−0.291556	−0.145778	+	0.989317i	$0.546569\pi$
$402$	−2.04613e11	−0.390765
$403$	−1.27994e11	−0.241722
$404$	1.73804e12	3.24597
$405$	2.69042e10	0.0496904
$406$	−1.65784e11	−0.302815
$407$	−2.01075e11	−0.363231
$408$	−7.04891e11	−1.25936
$409$	2.43266e11	0.429860	0.214930	−	0.976629i	$-0.431048\pi$
$409$	2.43266e11	0.429860	0.214930	+	0.976629i	$0.431048\pi$
$410$	−3.69958e11	−0.646584
$411$	5.09988e11	0.881600
$412$	−6.32812e11	−1.08203
$413$	2.37496e11	0.401681
$414$	−1.86971e11	−0.312805
$415$	1.86610e11	0.308830
$416$	−8.84456e10	−0.144796
$417$	1.81873e11	0.294548
$418$	8.04889e11	1.28956
$419$	−1.23486e12	−1.95728	−0.978642	−	0.205571i	$-0.934095\pi$
$419$	−1.23486e12	−1.95728	−0.978642	+	0.205571i	$0.934095\pi$
$420$	−1.15417e11	−0.180988
$421$	−1.00586e12	−1.56051	−0.780257	−	0.625459i	$-0.784912\pi$
$421$	−1.00586e12	−1.56051	−0.780257	+	0.625459i	$0.784912\pi$
$422$	−8.63119e11	−1.32484
$423$	1.71408e11	0.260315
$424$	3.53699e11	0.531481
$425$	−2.03223e11	−0.302150
$426$	−7.58562e11	−1.11596
$427$	−1.15468e11	−0.168089
$428$	−3.35409e11	−0.483145
$429$	1.07518e11	0.153258
$430$	7.58881e11	1.07045
$431$	1.63130e11	0.227712	0.113856	−	0.993497i	$-0.463680\pi$
$431$	1.63130e11	0.227712	0.113856	+	0.993497i	$0.463680\pi$
$432$	−8.14803e10	−0.112558
$433$	1.14929e12	1.57121	0.785607	−	0.618726i	$-0.212351\pi$
$433$	1.14929e12	1.57121	0.785607	+	0.618726i	$0.212351\pi$
$434$	−3.59042e11	−0.485782
$435$	−9.14347e10	−0.122436
$436$	−8.82671e11	−1.16979
$437$	−3.86879e11	−0.507468
$438$	−6.32416e11	−0.821049
$439$	−6.34274e11	−0.815054	−0.407527	−	0.913193i	$-0.633609\pi$
$439$	−6.34274e11	−0.815054	−0.407527	+	0.913193i	$0.633609\pi$
$440$	−4.24091e11	−0.539414
$441$	3.78229e10	0.0476190
$442$	−6.50818e11	−0.811072
$443$	−1.42336e12	−1.75589	−0.877947	−	0.478757i	$-0.841087\pi$
$443$	−1.42336e12	−1.75589	−0.877947	+	0.478757i	$0.841087\pi$
$444$	3.81244e11	0.465564
$445$	−2.46868e11	−0.298431
$446$	−2.14327e12	−2.56490
$447$	−5.97024e11	−0.707307
$448$	−4.36581e11	−0.512051
$449$	−4.63355e11	−0.538029	−0.269014	−	0.963136i	$-0.586698\pi$
$449$	−4.63355e11	−0.538029	−0.269014	+	0.963136i	$0.586698\pi$
$450$	−9.79796e10	−0.112637
$451$	6.28088e11	0.714869
$452$	−2.35255e12	−2.65103
$453$	−1.98483e10	−0.0221453
$454$	2.51789e12	2.78154
$455$	−4.91037e10	−0.0537109
$456$	−7.03211e11	−0.761630
$457$	7.75098e11	0.831254	0.415627	−	0.909535i	$-0.363562\pi$
$457$	7.75098e11	0.831254	0.415627	+	0.909535i	$0.363562\pi$
$458$	1.07145e12	1.13783
$459$	2.76482e11	0.290744
$460$	4.42378e11	0.460663
$461$	−1.65390e12	−1.70551	−0.852755	−	0.522311i	$-0.825070\pi$
$461$	−1.65390e12	−1.70551	−0.852755	+	0.522311i	$0.825070\pi$
$462$	3.01604e11	0.307998
$463$	4.51887e11	0.456999	0.228499	−	0.973544i	$-0.426618\pi$
$463$	4.51887e11	0.456999	0.228499	+	0.973544i	$0.426618\pi$
$464$	2.76913e11	0.277340
$465$	−1.98022e11	−0.196415
$466$	−2.04064e12	−2.00461
$467$	5.45457e11	0.530683	0.265341	−	0.964155i	$-0.414515\pi$
$467$	5.45457e11	0.530683	0.265341	+	0.964155i	$0.414515\pi$
$468$	−2.03857e11	−0.196435
$469$	−1.58648e11	−0.151411
$470$	−6.24232e11	−0.590073
$471$	−4.05840e11	−0.379980
$472$	−1.65458e12	−1.53444
$473$	−1.28837e12	−1.18350
$474$	7.42809e11	0.675888
$475$	−2.02738e11	−0.182732
$476$	−1.18609e12	−1.05898
$477$	−1.38733e11	−0.122701
$478$	2.00780e12	1.75912
$479$	1.55694e11	0.135134	0.0675668	−	0.997715i	$-0.478476\pi$
$479$	1.55694e11	0.135134	0.0675668	+	0.997715i	$0.478476\pi$
$480$	−1.36836e11	−0.117656
$481$	1.62198e11	0.138163
$482$	2.20763e12	1.86301
$483$	−1.44969e11	−0.121203
$484$	−6.76461e11	−0.560323
$485$	−7.63421e10	−0.0626507
$486$	1.33300e11	0.108385
$487$	7.65869e10	0.0616984	0.0308492	−	0.999524i	$-0.490179\pi$
$487$	7.65869e10	0.0616984	0.0308492	+	0.999524i	$0.490179\pi$
$488$	8.04444e11	0.642106
$489$	1.08116e12	0.855065
$490$	−1.37743e11	−0.107941
$491$	7.48651e11	0.581316	0.290658	−	0.956827i	$-0.406126\pi$
$491$	7.48651e11	0.581316	0.290658	+	0.956827i	$0.406126\pi$
$492$	−1.19087e12	−0.916268
$493$	−9.39634e11	−0.716387
$494$	−6.49267e11	−0.490515
$495$	1.66343e11	0.124532
$496$	5.99716e11	0.444916
$497$	−5.88156e11	−0.432403
$498$	9.24584e11	0.673619
$499$	2.05979e11	0.148720	0.0743601	−	0.997231i	$-0.476309\pi$
$499$	2.05979e11	0.148720	0.0743601	+	0.997231i	$0.476309\pi$
$500$	2.31822e11	0.165878
$501$	1.20196e12	0.852356
$502$	3.49220e12	2.45433
$503$	−1.70065e11	−0.118456	−0.0592281	−	0.998244i	$-0.518864\pi$
$503$	−1.70065e11	−0.118456	−0.0592281	+	0.998244i	$0.518864\pi$
$504$	−2.63504e11	−0.181907
$505$	1.14400e12	0.782736
$506$	−1.15600e12	−0.783938
$507$	7.72235e11	0.519055
$508$	2.21866e12	1.47810
$509$	3.03892e11	0.200673	0.100337	−	0.994954i	$-0.468008\pi$
$509$	3.03892e11	0.200673	0.100337	+	0.994954i	$0.468008\pi$
$510$	−1.00689e12	−0.659048
$511$	−4.90348e11	−0.318134
$512$	1.72750e12	1.11097
$513$	2.75823e11	0.175834
$514$	−1.47013e11	−0.0929011
$515$	−4.16525e11	−0.260921
$516$	2.44279e12	1.51692
$517$	1.05978e12	0.652390
$518$	4.54990e11	0.277663
$519$	−1.72579e12	−1.04408
$520$	3.42095e11	0.205178
$521$	2.14013e12	1.27254	0.636269	−	0.771467i	$-0.280477\pi$
$521$	2.14013e12	1.27254	0.636269	+	0.771467i	$0.280477\pi$
$522$	−4.53025e11	−0.267057
$523$	−8.40211e10	−0.0491055	−0.0245528	−	0.999699i	$-0.507816\pi$
$523$	−8.40211e10	−0.0491055	−0.0245528	+	0.999699i	$0.507816\pi$
$524$	5.62879e12	3.26155
$525$	−7.59691e10	−0.0436436
$526$	5.77257e12	3.28801
$527$	−2.03498e12	−1.14924
$528$	−5.03776e11	−0.282088
$529$	−1.24551e12	−0.691505
$530$	5.05237e11	0.278134
$531$	6.48984e11	0.354249
$532$	−1.18327e12	−0.640442
$533$	−5.06650e11	−0.271917
$534$	−1.22314e12	−0.650937
$535$	−2.20770e11	−0.116506
$536$	1.10527e12	0.578397
$537$	1.94453e12	1.00909
$538$	3.46959e12	1.78549
$539$	2.33851e11	0.119341
$540$	−3.15391e11	−0.159616
$541$	−1.14445e12	−0.574394	−0.287197	−	0.957872i	$-0.592723\pi$
$541$	−1.14445e12	−0.574394	−0.287197	+	0.957872i	$0.592723\pi$
$542$	−3.15410e12	−1.56993
$543$	1.60253e12	0.791054
$544$	−1.40620e12	−0.688417
$545$	−5.80985e11	−0.282085
$546$	−2.43290e11	−0.117154
$547$	−3.37118e12	−1.61005	−0.805024	−	0.593242i	$-0.797848\pi$
$547$	−3.37118e12	−1.61005	−0.805024	+	0.593242i	$0.797848\pi$
$548$	−5.97845e12	−2.83189
$549$	−3.15530e11	−0.148240
$550$	−6.05787e11	−0.282285
$551$	−9.37394e11	−0.433252
$552$	1.00997e12	0.463002
$553$	5.75942e11	0.261888
$554$	−2.55810e12	−1.15378
$555$	2.50939e11	0.112267
$556$	−2.13205e12	−0.946151
$557$	−2.73596e11	−0.120437	−0.0602186	−	0.998185i	$-0.519180\pi$
$557$	−2.73596e11	−0.120437	−0.0602186	+	0.998185i	$0.519180\pi$
$558$	−9.81123e11	−0.428420
$559$	1.03927e12	0.450170
$560$	2.30075e11	0.0988607
$561$	1.70943e12	0.728650
$562$	−1.17695e12	−0.497673
$563$	−2.98549e12	−1.25236	−0.626178	−	0.779680i	$-0.715382\pi$
$563$	−2.98549e12	−1.25236	−0.626178	+	0.779680i	$0.715382\pi$
$564$	−2.00937e12	−0.836187
$565$	−1.54848e12	−0.639273
$566$	6.88277e12	2.81896
$567$	1.03355e11	0.0419961
$568$	4.09756e12	1.65180
$569$	3.24777e11	0.129891	0.0649457	−	0.997889i	$-0.479313\pi$
$569$	3.24777e11	0.129891	0.0649457	+	0.997889i	$0.479313\pi$
$570$	−1.00449e12	−0.398575
$571$	3.47643e12	1.36858	0.684292	−	0.729209i	$-0.260112\pi$
$571$	3.47643e12	1.36858	0.684292	+	0.729209i	$0.260112\pi$
$572$	−1.26040e12	−0.492298
$573$	−2.23111e11	−0.0864620
$574$	−1.42123e12	−0.546463
$575$	2.91178e11	0.111085
$576$	−1.19301e12	−0.451587
$577$	−2.05156e12	−0.770537	−0.385269	−	0.922804i	$-0.625891\pi$
$577$	−2.05156e12	−0.770537	−0.385269	+	0.922804i	$0.625891\pi$
$578$	−5.81376e12	−2.16661
$579$	1.09070e12	0.403323
$580$	1.07186e12	0.393291
$581$	7.16883e11	0.261009
$582$	−3.78246e11	−0.136654
$583$	−8.57756e11	−0.307507
$584$	3.41615e12	1.21529
$585$	−1.34181e11	−0.0473686
$586$	−3.54483e12	−1.24181
$587$	3.09869e12	1.07723	0.538613	−	0.842553i	$-0.318949\pi$
$587$	3.09869e12	1.07723	0.538613	+	0.842553i	$0.318949\pi$
$588$	−4.43387e11	−0.152963
$589$	−2.03013e12	−0.695033
$590$	−2.36347e12	−0.803000
$591$	2.81063e12	0.947676
$592$	−7.59979e11	−0.254304
$593$	−1.36692e12	−0.453938	−0.226969	−	0.973902i	$-0.572882\pi$
$593$	−1.36692e12	−0.453938	−0.226969	+	0.973902i	$0.572882\pi$
$594$	8.24166e11	0.271629
$595$	−7.80701e11	−0.255363
$596$	6.99876e12	2.27202
$597$	1.05982e12	0.341466
$598$	9.32495e11	0.298189
$599$	−3.88429e12	−1.23279	−0.616397	−	0.787435i	$-0.711408\pi$
$599$	−3.88429e12	−1.23279	−0.616397	+	0.787435i	$0.711408\pi$
$600$	5.29261e11	0.166721
$601$	3.91783e12	1.22493	0.612465	−	0.790498i	$-0.290178\pi$
$601$	3.91783e12	1.22493	0.612465	+	0.790498i	$0.290178\pi$
$602$	2.91532e12	0.904694
$603$	−4.33524e11	−0.133532
$604$	2.32677e11	0.0711356
$605$	−4.45255e11	−0.135117
$606$	5.66810e12	1.70730
$607$	−1.05489e12	−0.315397	−0.157698	−	0.987487i	$-0.550407\pi$
$607$	−1.05489e12	−0.315397	−0.157698	+	0.987487i	$0.550407\pi$
$608$	−1.40285e12	−0.416336
$609$	−3.51256e11	−0.103477
$610$	1.14910e12	0.336026
$611$	−8.54874e11	−0.248151
$612$	−3.24113e12	−0.933932
$613$	6.11902e12	1.75029	0.875145	−	0.483861i	$-0.160766\pi$
$613$	6.11902e12	1.75029	0.875145	+	0.483861i	$0.160766\pi$
$614$	2.49509e12	0.708481
$615$	−7.83848e11	−0.220950
$616$	−1.62919e12	−0.455888
$617$	−6.12963e12	−1.70275	−0.851375	−	0.524558i	$-0.824231\pi$
$617$	−6.12963e12	−1.70275	−0.851375	+	0.524558i	$0.824231\pi$
$618$	−2.06372e12	−0.569120
$619$	−4.02744e12	−1.10261	−0.551304	−	0.834304i	$-0.685870\pi$
$619$	−4.02744e12	−1.10261	−0.551304	+	0.834304i	$0.685870\pi$
$620$	2.32136e12	0.630927
$621$	−3.96145e11	−0.106891
$622$	−1.53192e12	−0.410374
$623$	−9.48366e11	−0.252220
$624$	4.06373e11	0.107299
$625$	1.52588e11	0.0400000
$626$	−1.13831e12	−0.296263
$627$	1.70536e12	0.440668
$628$	4.75755e12	1.22058
$629$	2.57879e12	0.656883
$630$	−3.76398e11	−0.0951953
$631$	4.89021e12	1.22799	0.613995	−	0.789310i	$-0.289561\pi$
$631$	4.89021e12	1.22799	0.613995	+	0.789310i	$0.289561\pi$
$632$	−4.01247e12	−1.00043
$633$	−1.82873e12	−0.452724
$634$	3.61768e12	0.889260
$635$	1.46035e12	0.356431
$636$	1.62633e12	0.394141
$637$	−1.88637e11	−0.0453940
$638$	−2.80095e12	−0.669288
$639$	−1.60720e12	−0.381344
$640$	3.47975e12	0.819856
$641$	9.61649e11	0.224986	0.112493	−	0.993653i	$-0.464116\pi$
$641$	9.61649e11	0.224986	0.112493	+	0.993653i	$0.464116\pi$
$642$	−1.09383e12	−0.254123
$643$	7.51237e12	1.73312	0.866558	−	0.499076i	$-0.166327\pi$
$643$	7.51237e12	1.73312	0.866558	+	0.499076i	$0.166327\pi$
$644$	1.69944e12	0.389331
$645$	1.60788e12	0.365792
$646$	−1.03227e13	−2.33210
$647$	6.85945e12	1.53893	0.769467	−	0.638687i	$-0.220522\pi$
$647$	6.85945e12	1.53893	0.769467	+	0.638687i	$0.220522\pi$
$648$	−7.20054e11	−0.160427
$649$	4.01253e12	0.887804
$650$	4.88661e11	0.107374
$651$	−7.60720e11	−0.166001
$652$	−1.26741e13	−2.74665
$653$	3.46648e12	0.746070	0.373035	−	0.927817i	$-0.378317\pi$
$653$	3.46648e12	0.746070	0.373035	+	0.927817i	$0.378317\pi$
$654$	−2.87856e12	−0.615284
$655$	3.70494e12	0.786494
$656$	2.37391e12	0.500492
$657$	−1.33993e12	−0.280568
$658$	−2.39805e12	−0.498703
$659$	3.94649e12	0.815130	0.407565	−	0.913176i	$-0.366378\pi$
$659$	3.94649e12	0.815130	0.407565	+	0.913176i	$0.366378\pi$
$660$	−1.94999e12	−0.400023
$661$	7.04248e12	1.43489	0.717446	−	0.696614i	$-0.245311\pi$
$661$	7.04248e12	1.43489	0.717446	+	0.696614i	$0.245311\pi$
$662$	−1.86918e12	−0.378261
$663$	−1.37892e12	−0.277159
$664$	−4.99437e12	−0.997067
$665$	−7.78840e11	−0.154437
$666$	1.24331e12	0.244875
$667$	1.34631e12	0.263378
$668$	−1.40903e13	−2.73795
$669$	−4.54106e12	−0.876475
$670$	1.57880e12	0.302685
$671$	−1.95086e12	−0.371513
$672$	−5.25668e11	−0.0994374
$673$	5.67306e12	1.06598	0.532991	−	0.846121i	$-0.321068\pi$
$673$	5.67306e12	1.06598	0.532991	+	0.846121i	$0.321068\pi$
$674$	3.18385e12	0.594269
$675$	−2.07594e11	−0.0384900
$676$	−9.05270e12	−1.66732
$677$	9.36432e11	0.171328	0.0856638	−	0.996324i	$-0.472699\pi$
$677$	9.36432e11	0.171328	0.0856638	+	0.996324i	$0.472699\pi$
$678$	−7.67211e12	−1.39438
$679$	−2.93276e11	−0.0529495
$680$	5.43898e12	0.975500
$681$	5.33477e12	0.950503
$682$	−6.06607e12	−1.07369
$683$	5.73316e12	1.00809	0.504047	−	0.863676i	$-0.331844\pi$
$683$	5.73316e12	1.00809	0.504047	+	0.863676i	$0.331844\pi$
$684$	−3.23340e12	−0.564817
$685$	−3.93509e12	−0.682885
$686$	−5.29154e11	−0.0912270
$687$	2.27013e12	0.388817
$688$	−4.86952e12	−0.828587
$689$	6.91912e11	0.116967
$690$	1.44268e12	0.242297
$691$	−2.53360e12	−0.422752	−0.211376	−	0.977405i	$-0.567795\pi$
$691$	−2.53360e12	−0.422752	−0.211376	+	0.977405i	$0.567795\pi$
$692$	2.02310e13	3.35382
$693$	6.39023e11	0.105249
$694$	−1.61761e12	−0.264701
$695$	−1.40334e12	−0.228156
$696$	2.44712e12	0.395289
$697$	−8.05525e12	−1.29280
$698$	2.50666e12	0.399711
$699$	−4.32360e12	−0.685012
$700$	8.90566e11	0.140193
$701$	8.38501e12	1.31151	0.655756	−	0.754973i	$-0.272350\pi$
$701$	8.38501e12	1.31151	0.655756	+	0.754973i	$0.272350\pi$
$702$	−6.64817e11	−0.103320
$703$	2.57265e12	0.397266
$704$	−7.37610e12	−1.13175
$705$	−1.32259e12	−0.201639
$706$	−8.12506e12	−1.23085
$707$	4.39480e12	0.661533
$708$	−7.60787e12	−1.13792
$709$	−5.77903e12	−0.858909	−0.429454	−	0.903089i	$-0.641294\pi$
$709$	−5.77903e12	−0.858909	−0.429454	+	0.903089i	$0.641294\pi$
$710$	5.85310e12	0.864417
$711$	1.57383e12	0.230964
$712$	6.60707e12	0.963493
$713$	2.91573e12	0.422517
$714$	−3.86808e12	−0.556998
$715$	−8.29614e11	−0.118713
$716$	−2.27952e13	−3.24142
$717$	4.25403e12	0.601124
$718$	9.78756e11	0.137440
$719$	3.57599e12	0.499019	0.249509	−	0.968372i	$-0.419731\pi$
$719$	3.57599e12	0.499019	0.249509	+	0.968372i	$0.419731\pi$
$720$	6.28706e11	0.0871870
$721$	−1.60012e12	−0.220518
$722$	2.03827e12	0.279154
$723$	4.67741e12	0.636624
$724$	−1.87860e13	−2.54103
$725$	7.05515e11	0.0948386
$726$	−2.20607e12	−0.294717
$727$	−3.33031e12	−0.442161	−0.221080	−	0.975256i	$-0.570958\pi$
$727$	−3.33031e12	−0.442161	−0.221080	+	0.975256i	$0.570958\pi$
$728$	1.31419e12	0.173407
$729$	2.82430e11	0.0370370
$730$	4.87975e12	0.635982
$731$	1.65234e13	2.14029
$732$	3.69888e12	0.476179
$733$	1.20640e13	1.54356	0.771779	−	0.635891i	$-0.219367\pi$
$733$	1.20640e13	1.54356	0.771779	+	0.635891i	$0.219367\pi$
$734$	7.56824e12	0.962416
$735$	−2.91843e11	−0.0368856
$736$	2.01481e12	0.253095
$737$	−2.68038e12	−0.334652
$738$	−3.88367e12	−0.481935
$739$	−4.54937e12	−0.561114	−0.280557	−	0.959837i	$-0.590519\pi$
$739$	−4.54937e12	−0.561114	−0.280557	+	0.959837i	$0.590519\pi$
$740$	−2.94170e12	−0.360624
$741$	−1.37563e12	−0.167618
$742$	1.94092e12	0.235066
$743$	4.15549e12	0.500233	0.250117	−	0.968216i	$-0.419531\pi$
$743$	4.15549e12	0.500233	0.250117	+	0.968216i	$0.419531\pi$
$744$	5.29978e12	0.634131
$745$	4.60667e12	0.547878
$746$	−2.28099e13	−2.69649
$747$	1.95896e12	0.230188
$748$	−2.00392e13	−2.34058
$749$	−8.48112e11	−0.0984657
$750$	7.56015e11	0.0872479
$751$	−1.10338e13	−1.26575	−0.632873	−	0.774256i	$-0.718124\pi$
$751$	−1.10338e13	−1.26575	−0.632873	+	0.774256i	$0.718124\pi$
$752$	4.00551e12	0.456749
$753$	7.39910e12	0.838690
$754$	2.25940e12	0.254579
$755$	1.53151e11	0.0171537
$756$	−1.21161e12	−0.134900
$757$	−2.12370e12	−0.235051	−0.117526	−	0.993070i	$-0.537496\pi$
$757$	−2.12370e12	−0.235051	−0.117526	+	0.993070i	$0.537496\pi$
$758$	2.31192e13	2.54367
$759$	−2.44928e12	−0.267886
$760$	5.42601e12	0.589956
$761$	5.96068e11	0.0644266	0.0322133	−	0.999481i	$-0.489744\pi$
$761$	5.96068e11	0.0644266	0.0322133	+	0.999481i	$0.489744\pi$
$762$	7.23548e12	0.777446
$763$	−2.23191e12	−0.238406
$764$	2.61547e12	0.277735
$765$	−2.13335e12	−0.225209
$766$	4.14228e12	0.434720
$767$	−3.23673e12	−0.337697
$768$	9.69985e12	1.00610
$769$	−1.80083e13	−1.85697	−0.928486	−	0.371369i	$-0.878889\pi$
$769$	−1.80083e13	−1.85697	−0.928486	+	0.371369i	$0.878889\pi$
$770$	−2.32719e12	−0.238574
$771$	−3.11483e11	−0.0317461
$772$	−1.27860e13	−1.29556
$773$	7.42350e12	0.747827	0.373914	−	0.927464i	$-0.378016\pi$
$773$	7.42350e12	0.747827	0.373914	+	0.927464i	$0.378016\pi$
$774$	7.96643e12	0.797865
$775$	1.52795e12	0.152142
$776$	2.04319e12	0.202270
$777$	9.64009e11	0.0948825
$778$	4.56965e12	0.447172
$779$	−8.03605e12	−0.781851
$780$	1.57297e12	0.152158
$781$	−9.93699e12	−0.955708
$782$	1.48258e13	1.41771
$783$	−9.59845e11	−0.0912585
$784$	8.83857e11	0.0835526
$785$	3.13148e12	0.294331
$786$	1.83566e13	1.71550
$787$	1.11276e13	1.03399	0.516996	−	0.855988i	$-0.327050\pi$
$787$	1.11276e13	1.03399	0.516996	+	0.855988i	$0.327050\pi$
$788$	−3.29483e13	−3.04414
$789$	1.22306e13	1.12358
$790$	−5.73155e12	−0.523541
$791$	−5.94862e12	−0.540284
$792$	−4.45194e12	−0.402055
$793$	1.57367e12	0.141313
$794$	−1.16807e13	−1.04298
$795$	1.07047e12	0.0950435
$796$	−1.24240e13	−1.09686
$797$	1.07702e13	0.945501	0.472751	−	0.881196i	$-0.343261\pi$
$797$	1.07702e13	0.945501	0.472751	+	0.881196i	$0.343261\pi$
$798$	−3.85886e12	−0.336857
$799$	−1.35917e13	−1.17981
$800$	1.05583e12	0.0911359
$801$	−2.59152e12	−0.222437
$802$	5.77136e12	0.492599
$803$	−8.28450e12	−0.703147
$804$	5.08208e12	0.428933
$805$	1.11859e12	0.0938836
$806$	4.89322e12	0.408402
$807$	7.35118e12	0.610135
$808$	−3.06176e13	−2.52709
$809$	−1.87031e13	−1.53513	−0.767563	−	0.640973i	$-0.778531\pi$
$809$	−1.87031e13	−1.53513	−0.767563	+	0.640973i	$0.778531\pi$
$810$	−1.02855e12	−0.0839543
$811$	−1.60043e13	−1.29910	−0.649552	−	0.760317i	$-0.725044\pi$
$811$	−1.60043e13	−1.29910	−0.649552	+	0.760317i	$0.725044\pi$
$812$	4.11768e12	0.332392
$813$	−6.68275e12	−0.536473
$814$	7.68712e12	0.613697
$815$	−8.34226e12	−0.662330
$816$	6.46093e12	0.510140
$817$	1.64841e13	1.29439
$818$	−9.30010e12	−0.726270
$819$	−5.15471e11	−0.0400338
$820$	9.18884e12	0.709738
$821$	1.76863e13	1.35860	0.679302	−	0.733859i	$-0.262283\pi$
$821$	1.76863e13	1.35860	0.679302	+	0.733859i	$0.262283\pi$
$822$	−1.94969e13	−1.48951
$823$	−1.01226e13	−0.769116	−0.384558	−	0.923101i	$-0.625646\pi$
$823$	−1.01226e13	−0.769116	−0.384558	+	0.923101i	$0.625646\pi$
$824$	1.11477e13	0.842390
$825$	−1.28351e12	−0.0964621
$826$	−9.07950e12	−0.678659
$827$	−2.37896e13	−1.76853	−0.884264	−	0.466987i	$-0.845339\pi$
$827$	−2.37896e13	−1.76853	−0.884264	+	0.466987i	$0.845339\pi$
$828$	4.64390e12	0.343358
$829$	1.21693e13	0.894892	0.447446	−	0.894311i	$-0.352334\pi$
$829$	1.21693e13	0.894892	0.447446	+	0.894311i	$0.352334\pi$
$830$	−7.13414e12	−0.521783
$831$	−5.41997e12	−0.394268
$832$	5.94996e12	0.430486
$833$	−2.99914e12	−0.215821
$834$	−6.95302e12	−0.497653
$835$	−9.27440e12	−0.660232
$836$	−1.99914e13	−1.41552
$837$	−2.07875e12	−0.146399
$838$	4.72088e13	3.30693
$839$	1.66708e12	0.116152	0.0580762	−	0.998312i	$-0.481503\pi$
$839$	1.66708e12	0.116152	0.0580762	+	0.998312i	$0.481503\pi$
$840$	2.03321e12	0.140905
$841$	−1.12451e13	−0.775141
$842$	3.84541e13	2.63656
$843$	−2.49366e12	−0.170064
$844$	2.14378e13	1.45425
$845$	−5.95860e12	−0.402058
$846$	−6.55294e12	−0.439814
$847$	−1.71049e12	−0.114195
$848$	−3.24196e12	−0.215291
$849$	1.45829e13	0.963293
$850$	7.76923e12	0.510497
$851$	−3.69490e12	−0.241502
$852$	1.88408e13	1.22496
$853$	−2.05771e13	−1.33080	−0.665400	−	0.746487i	$-0.731739\pi$
$853$	−2.05771e13	−1.33080	−0.665400	+	0.746487i	$0.731739\pi$
$854$	4.41437e12	0.283994
$855$	−2.12827e12	−0.136201
$856$	5.90861e12	0.376144
$857$	1.50467e13	0.952856	0.476428	−	0.879214i	$-0.341931\pi$
$857$	1.50467e13	0.952856	0.476428	+	0.879214i	$0.341931\pi$
$858$	−4.11042e12	−0.258937
$859$	−2.57827e13	−1.61570	−0.807848	−	0.589391i	$-0.799368\pi$
$859$	−2.57827e13	−1.61570	−0.807848	+	0.589391i	$0.799368\pi$
$860$	−1.88487e13	−1.17500
$861$	−3.01123e12	−0.186737
$862$	−6.23646e12	−0.384730
$863$	2.18283e13	1.33959	0.669794	−	0.742547i	$-0.266382\pi$
$863$	2.18283e13	1.33959	0.669794	+	0.742547i	$0.266382\pi$
$864$	−1.43645e12	−0.0876956
$865$	1.33163e13	0.808744
$866$	−4.39376e13	−2.65464
$867$	−1.23179e13	−0.740373
$868$	8.91772e12	0.533231
$869$	9.73063e12	0.578831
$870$	3.49556e12	0.206862
$871$	2.16214e12	0.127292
$872$	1.55492e13	0.910721
$873$	−8.01409e11	−0.0466971
$874$	1.47904e13	0.857392
$875$	5.86182e11	0.0338062
$876$	1.57076e13	0.901244
$877$	−8.76867e11	−0.0500536	−0.0250268	−	0.999687i	$-0.507967\pi$
$877$	−8.76867e11	−0.0500536	−0.0250268	+	0.999687i	$0.507967\pi$
$878$	2.42484e13	1.37707
$879$	−7.51060e12	−0.424351
$880$	3.88716e12	0.218504
$881$	−1.60376e13	−0.896907	−0.448453	−	0.893806i	$-0.648025\pi$
$881$	−1.60376e13	−0.896907	−0.448453	+	0.893806i	$0.648025\pi$
$882$	−1.44597e12	−0.0804547
$883$	−2.77919e13	−1.53849	−0.769245	−	0.638954i	$-0.779367\pi$
$883$	−2.77919e13	−1.53849	−0.769245	+	0.638954i	$0.779367\pi$
$884$	1.61647e13	0.890293
$885$	−5.00760e12	−0.274400
$886$	5.44153e13	2.96667
$887$	1.11765e13	0.606245	0.303123	−	0.952952i	$-0.401971\pi$
$887$	1.11765e13	0.606245	0.303123	+	0.952952i	$0.401971\pi$
$888$	−6.71604e12	−0.362456
$889$	5.61008e12	0.301239
$890$	9.43777e12	0.504214
$891$	1.74620e12	0.0928207
$892$	5.32336e13	2.81542
$893$	−1.35593e13	−0.713518
$894$	2.28243e13	1.19503
$895$	−1.50041e13	−0.781639
$896$	1.33678e13	0.692905
$897$	1.97572e12	0.101897
$898$	1.77141e13	0.909025
$899$	7.06470e12	0.360724
$900$	2.43357e12	0.123638
$901$	1.10007e13	0.556110
$902$	−2.40119e13	−1.20781
$903$	6.17682e12	0.309151
$904$	4.14428e13	2.06391
$905$	−1.23652e13	−0.612747
$906$	7.58804e11	0.0374156
$907$	7.07364e12	0.347064	0.173532	−	0.984828i	$-0.444482\pi$
$907$	7.07364e12	0.347064	0.173532	+	0.984828i	$0.444482\pi$
$908$	−6.25381e13	−3.05322
$909$	1.20093e13	0.583417
$910$	1.87724e12	0.0907472
$911$	3.11381e13	1.49782	0.748909	−	0.662673i	$-0.230578\pi$
$911$	3.11381e13	1.49782	0.748909	+	0.662673i	$0.230578\pi$
$912$	6.44554e12	0.308519
$913$	1.21118e13	0.576888
$914$	−2.96321e13	−1.40444
$915$	2.43465e12	0.114826
$916$	−2.66121e13	−1.24896
$917$	1.42329e13	0.664709
$918$	−1.05700e13	−0.491226
$919$	2.71434e13	1.25529	0.627645	−	0.778499i	$-0.284019\pi$
$919$	2.71434e13	1.25529	0.627645	+	0.778499i	$0.284019\pi$
$920$	−7.79299e12	−0.358640
$921$	5.28647e12	0.242101
$922$	6.32287e13	2.88154
$923$	8.01571e12	0.363525
$924$	−7.49109e12	−0.338082
$925$	−1.93626e12	−0.0869613
$926$	−1.72757e13	−0.772121
$927$	−4.37251e12	−0.194479
$928$	4.88181e12	0.216080
$929$	−4.44090e13	−1.95614	−0.978070	−	0.208276i	$-0.933215\pi$
$929$	−4.44090e13	−1.95614	−0.978070	+	0.208276i	$0.933215\pi$
$930$	7.57039e12	0.331853
$931$	−2.99199e12	−0.130523
$932$	5.06844e13	2.20041
$933$	−3.24576e12	−0.140233
$934$	−2.08529e13	−0.896614
$935$	−1.31901e13	−0.564410
$936$	3.59117e12	0.152931
$937$	−6.59610e12	−0.279550	−0.139775	−	0.990183i	$-0.544638\pi$
$937$	−6.59610e12	−0.279550	−0.139775	+	0.990183i	$0.544638\pi$
$938$	6.06513e12	0.255816
$939$	−2.41180e12	−0.101239
$940$	1.55044e13	0.647708
$941$	2.21969e13	0.922866	0.461433	−	0.887175i	$-0.347335\pi$
$941$	2.21969e13	0.922866	0.461433	+	0.887175i	$0.347335\pi$
$942$	1.55153e13	0.641994
$943$	1.15416e13	0.475295
$944$	1.51657e13	0.621567
$945$	−7.97494e11	−0.0325300
$946$	4.92547e13	1.99958
$947$	1.48169e13	0.598662	0.299331	−	0.954149i	$-0.403237\pi$
$947$	1.48169e13	0.598662	0.299331	+	0.954149i	$0.403237\pi$
$948$	−1.84495e13	−0.741905
$949$	6.68273e12	0.267458
$950$	7.75071e12	0.308735
$951$	7.66496e12	0.303877
$952$	2.08944e13	0.824448
$953$	2.22316e13	0.873077	0.436538	−	0.899686i	$-0.356204\pi$
$953$	2.22316e13	0.873077	0.436538	+	0.899686i	$0.356204\pi$
$954$	5.30377e12	0.207309
$955$	1.72154e12	0.0669732
$956$	−4.98689e13	−1.93094
$957$	−5.93452e12	−0.228708
$958$	−5.95221e12	−0.228315
$959$	−1.51170e13	−0.577143
$960$	9.20529e12	0.349798
$961$	−1.11395e13	−0.421318
$962$	−6.20085e12	−0.233433
$963$	−2.31756e12	−0.0868386
$964$	−5.48321e13	−2.04497
$965$	−8.41593e12	−0.312413
$966$	5.54220e12	0.204779
$967$	−1.82881e13	−0.672588	−0.336294	−	0.941757i	$-0.609174\pi$
$967$	−1.82881e13	−0.672588	−0.336294	+	0.941757i	$0.609174\pi$
$968$	1.19166e13	0.436229
$969$	−2.18713e13	−0.796924
$970$	2.91857e12	0.105851
$971$	−3.48920e13	−1.25962	−0.629810	−	0.776750i	$-0.716867\pi$
$971$	−3.48920e13	−1.25962	−0.629810	+	0.776750i	$0.716867\pi$
$972$	−3.31085e12	−0.118971
$973$	−5.39107e12	−0.192827
$974$	−2.92793e12	−0.104242
$975$	1.03535e12	0.0366915
$976$	−7.37342e12	−0.260103
$977$	−9.21421e12	−0.323543	−0.161772	−	0.986828i	$-0.551721\pi$
$977$	−9.21421e12	−0.323543	−0.161772	+	0.986828i	$0.551721\pi$
$978$	−4.13328e13	−1.44467
$979$	−1.60228e13	−0.557463
$980$	3.42120e12	0.118484
$981$	−6.09895e12	−0.210254
$982$	−2.86210e13	−0.982162
$983$	4.22250e13	1.44238	0.721189	−	0.692738i	$-0.243596\pi$
$983$	4.22250e13	1.44238	0.721189	+	0.692738i	$0.243596\pi$
$984$	2.09786e13	0.713343
$985$	−2.16870e13	−0.734067
$986$	3.59223e13	1.21037
$987$	−5.08086e12	−0.170416
$988$	1.61262e13	0.538425
$989$	−2.36749e13	−0.786872
$990$	−6.35931e12	−0.210403
$991$	2.72210e13	0.896544	0.448272	−	0.893897i	$-0.352040\pi$
$991$	2.72210e13	0.896544	0.448272	+	0.893897i	$0.352040\pi$
$992$	1.05726e13	0.346641
$993$	−3.96033e12	−0.129259
$994$	2.24853e13	0.730566
$995$	−8.17762e12	−0.264498
$996$	−2.29644e13	−0.739414
$997$	−2.07222e13	−0.664214	−0.332107	−	0.943242i	$-0.607760\pi$
$997$	−2.07222e13	−0.664214	−0.332107	+	0.943242i	$0.607760\pi$
$998$	−7.87459e12	−0.251270
$999$	2.63426e12	0.0836785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.a.1.1	✓	4
3.2	odd	2		315.10.a.i.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.a.1.1	✓	4	1.1	even	1	trivial
315.10.a.i.1.4		4	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q-38.2301 q^{2} -81.0000 q^{3} +949.541 q^{4} +625.000 q^{5} +3096.64 q^{6} +2401.00 q^{7} -16727.3 q^{8} +6561.00 q^{9} -23893.8 q^{10} +40565.3 q^{11} -76912.9 q^{12} -32722.1 q^{13} -91790.5 q^{14} -50625.0 q^{15} +153320. q^{16} -520250. q^{17} -250828. q^{18} -519011. q^{19} +593463. q^{20} -194481. q^{21} -1.55081e6 q^{22} +745417. q^{23} +1.35491e6 q^{24} +390625. q^{25} +1.25097e6 q^{26} -531441. q^{27} +2.27985e6 q^{28} +1.80612e6 q^{29} +1.93540e6 q^{30} +3.91154e6 q^{31} +2.70293e6 q^{32} -3.28579e6 q^{33} +1.98892e7 q^{34} +1.50062e6 q^{35} +6.22994e6 q^{36} -4.95683e6 q^{37} +1.98418e7 q^{38} +2.65049e6 q^{39} -1.04545e7 q^{40} +1.54834e7 q^{41} +7.43503e6 q^{42} -3.17606e7 q^{43} +3.85184e7 q^{44} +4.10062e6 q^{45} -2.84974e7 q^{46} +2.61252e7 q^{47} -1.24189e7 q^{48} +5.76480e6 q^{49} -1.49336e7 q^{50} +4.21403e7 q^{51} -3.10710e7 q^{52} -2.11451e7 q^{53} +2.03170e7 q^{54} +2.53533e7 q^{55} -4.01621e7 q^{56} +4.20399e7 q^{57} -6.90481e7 q^{58} +9.89155e7 q^{59} -4.80705e7 q^{60} -4.80918e7 q^{61} -1.49539e8 q^{62} +1.57530e7 q^{63} -1.81833e8 q^{64} -2.04513e7 q^{65} +1.25616e8 q^{66} -6.60758e7 q^{67} -4.93999e8 q^{68} -6.03788e7 q^{69} -5.73691e7 q^{70} -2.44963e8 q^{71} -1.09748e8 q^{72} -2.04226e8 q^{73} +1.89500e8 q^{74} -3.16406e7 q^{75} -4.92822e8 q^{76} +9.73972e7 q^{77} -1.01329e8 q^{78} +2.39876e8 q^{79} +9.58248e7 q^{80} +4.30467e7 q^{81} -5.91932e8 q^{82} +2.98577e8 q^{83} -1.84668e8 q^{84} -3.25157e8 q^{85} +1.21421e9 q^{86} -1.46296e8 q^{87} -6.78545e8 q^{88} -3.94988e8 q^{89} -1.56767e8 q^{90} -7.85659e7 q^{91} +7.07804e8 q^{92} -3.16835e8 q^{93} -9.98771e8 q^{94} -3.24382e8 q^{95} -2.18937e8 q^{96} -1.22147e8 q^{97} -2.20389e8 q^{98} +2.66149e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) \) 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * q^99

Introduction

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