LMFDB - Embedded newform 130.8.a.j.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,8,Mod(1,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	130.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,32,60,256,500,480,616] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$40.6100533129$
Analytic rank:	$0$
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} - 7066x^{2} - 15288x + 8343477 $ x^4 - 7066x^2 - 15288x + 8343477
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-40.7169$ of defining polynomial
Character	$\chi$	$=$	130.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000 q^{2} -25.7169 q^{3} +64.0000 q^{4} +125.000 q^{5} -205.735 q^{6} -1385.39 q^{7} +512.000 q^{8} -1525.64 q^{9} +1000.00 q^{10} +5984.24 q^{11} -1645.88 q^{12} -2197.00 q^{13} -11083.1 q^{14} -3214.61 q^{15} +4096.00 q^{16} +19887.1 q^{17} -12205.1 q^{18} +14264.7 q^{19} +8000.00 q^{20} +35627.9 q^{21} +47873.9 q^{22} +25147.6 q^{23} -13167.0 q^{24} +15625.0 q^{25} -17576.0 q^{26} +95477.6 q^{27} -88665.0 q^{28} -28976.9 q^{29} -25716.9 q^{30} -113213. q^{31} +32768.0 q^{32} -153896. q^{33} +159097. q^{34} -173174. q^{35} -97641.1 q^{36} +272600. q^{37} +114118. q^{38} +56500.0 q^{39} +64000.0 q^{40} +107960. q^{41} +285023. q^{42} +786402. q^{43} +382992. q^{44} -190705. q^{45} +201181. q^{46} +882239. q^{47} -105336. q^{48} +1.09576e6 q^{49} +125000. q^{50} -511434. q^{51} -140608. q^{52} +562825. q^{53} +763821. q^{54} +748030. q^{55} -709320. q^{56} -366845. q^{57} -231815. q^{58} -247924. q^{59} -205735. q^{60} +1.51269e6 q^{61} -905706. q^{62} +2.11361e6 q^{63} +262144. q^{64} -274625. q^{65} -1.23117e6 q^{66} +1.65807e6 q^{67} +1.27277e6 q^{68} -646717. q^{69} -1.38539e6 q^{70} -1.05278e6 q^{71} -781129. q^{72} +5.61859e6 q^{73} +2.18080e6 q^{74} -401826. q^{75} +912943. q^{76} -8.29051e6 q^{77} +452000. q^{78} -6.77442e6 q^{79} +512000. q^{80} +881193. q^{81} +863676. q^{82} -6.82922e6 q^{83} +2.28019e6 q^{84} +2.48588e6 q^{85} +6.29122e6 q^{86} +745195. q^{87} +3.06393e6 q^{88} -5.36760e6 q^{89} -1.52564e6 q^{90} +3.04370e6 q^{91} +1.60945e6 q^{92} +2.91149e6 q^{93} +7.05791e6 q^{94} +1.78309e6 q^{95} -842691. q^{96} +1.67079e7 q^{97} +8.76611e6 q^{98} -9.12981e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 60 q^{3} + 256 q^{4} + 500 q^{5} + 480 q^{6} + 616 q^{7} + 2048 q^{8} + 6284 q^{9} + 4000 q^{10} + 10116 q^{11} + 3840 q^{12} - 8788 q^{13} + 4928 q^{14} + 7500 q^{15} + 16384 q^{16} - 21136 q^{17}+ \cdots - 3168468 q^{99}+O(q^{100}) $ 4 * q + 32 * q^2 + 60 * q^3 + 256 * q^4 + 500 * q^5 + 480 * q^6 + 616 * q^7 + 2048 * q^8 + 6284 * q^9 + 4000 * q^10 + 10116 * q^11 + 3840 * q^12 - 8788 * q^13 + 4928 * q^14 + 7500 * q^15 + 16384 * q^16 - 21136 * q^17 + 50272 * q^18 + 41644 * q^19 + 32000 * q^20 - 31784 * q^21 + 80928 * q^22 + 163252 * q^23 + 30720 * q^24 + 62500 * q^25 - 70304 * q^26 + 432864 * q^27 + 39424 * q^28 - 35024 * q^29 + 60000 * q^30 - 45084 * q^31 + 131072 * q^32 + 132768 * q^33 - 169088 * q^34 + 77000 * q^35 + 402176 * q^36 - 22552 * q^37 + 333152 * q^38 - 131820 * q^39 + 256000 * q^40 + 480864 * q^41 - 254272 * q^42 + 1524508 * q^43 + 647424 * q^44 + 785500 * q^45 + 1306016 * q^46 + 263320 * q^47 + 245760 * q^48 + 1819444 * q^49 + 500000 * q^50 - 1248248 * q^51 - 562432 * q^52 + 916656 * q^53 + 3462912 * q^54 + 1264500 * q^55 + 315392 * q^56 + 2353648 * q^57 - 280192 * q^58 + 46660 * q^59 + 480000 * q^60 - 138016 * q^61 - 360672 * q^62 + 1628248 * q^63 + 1048576 * q^64 - 1098500 * q^65 + 1062144 * q^66 + 2802528 * q^67 - 1352704 * q^68 + 4683288 * q^69 + 616000 * q^70 - 2655204 * q^71 + 3217408 * q^72 + 7883656 * q^73 - 180416 * q^74 + 937500 * q^75 + 2665216 * q^76 - 5311096 * q^77 - 1054560 * q^78 - 4424056 * q^79 + 2048000 * q^80 + 9022268 * q^81 + 3846912 * q^82 + 4442376 * q^83 - 2034176 * q^84 - 2642000 * q^85 + 12196064 * q^86 - 6151920 * q^87 + 5179392 * q^88 + 25080 * q^89 + 6284000 * q^90 - 1353352 * q^91 + 10448128 * q^92 - 15987872 * q^93 + 2106560 * q^94 + 5205500 * q^95 + 1966080 * q^96 + 4112168 * q^97 + 14555552 * q^98 - 3168468 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	−25.7169	−0.549913	−0.274956	−	0.961457i	$-0.588663\pi$
$3$	−25.7169	−0.549913	−0.274956	+	0.961457i	$0.588663\pi$
$4$	64.0000	0.500000
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	−205.735	−0.388847
$7$	−1385.39	−1.52661	−0.763307	−	0.646036i	$-0.776425\pi$
$7$	−1385.39	−1.52661	−0.763307	+	0.646036i	$0.776425\pi$
$8$	512.000	0.353553
$9$	−1525.64	−0.697596
$10$	1000.00	0.316228
$11$	5984.24	1.35561	0.677805	−	0.735242i	$-0.262931\pi$
$11$	5984.24	1.35561	0.677805	+	0.735242i	$0.262931\pi$
$12$	−1645.88	−0.274956
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−11083.1	−1.07948
$15$	−3214.61	−0.245929
$16$	4096.00	0.250000
$17$	19887.1	0.981747	0.490874	−	0.871231i	$-0.336678\pi$
$17$	19887.1	0.981747	0.490874	+	0.871231i	$0.336678\pi$
$18$	−12205.1	−0.493275
$19$	14264.7	0.477118	0.238559	−	0.971128i	$-0.423325\pi$
$19$	14264.7	0.477118	0.238559	+	0.971128i	$0.423325\pi$
$20$	8000.00	0.223607
$21$	35627.9	0.839504
$22$	47873.9	0.958561
$23$	25147.6	0.430972	0.215486	−	0.976507i	$-0.430866\pi$
$23$	25147.6	0.430972	0.215486	+	0.976507i	$0.430866\pi$
$24$	−13167.0	−0.194424
$25$	15625.0	0.200000
$26$	−17576.0	−0.196116
$27$	95477.6	0.933530
$28$	−88665.0	−0.763307
$29$	−28976.9	−0.220627	−0.110314	−	0.993897i	$-0.535185\pi$
$29$	−28976.9	−0.220627	−0.110314	+	0.993897i	$0.535185\pi$
$30$	−25716.9	−0.173898
$31$	−113213.	−0.682545	−0.341273	−	0.939964i	$-0.610858\pi$
$31$	−113213.	−0.682545	−0.341273	+	0.939964i	$0.610858\pi$
$32$	32768.0	0.176777
$33$	−153896.	−0.745468
$34$	159097.	0.694200
$35$	−173174.	−0.682722
$36$	−97641.1	−0.348798
$37$	272600.	0.884748	0.442374	−	0.896831i	$-0.354136\pi$
$37$	272600.	0.884748	0.442374	+	0.896831i	$0.354136\pi$
$38$	114118.	0.337374
$39$	56500.0	0.152518
$40$	64000.0	0.158114
$41$	107960.	0.244634	0.122317	−	0.992491i	$-0.460967\pi$
$41$	107960.	0.244634	0.122317	+	0.992491i	$0.460967\pi$
$42$	285023.	0.593619
$43$	786402.	1.50836	0.754180	−	0.656668i	$-0.228035\pi$
$43$	786402.	1.50836	0.754180	+	0.656668i	$0.228035\pi$
$44$	382992.	0.677805
$45$	−190705.	−0.311974
$46$	201181.	0.304743
$47$	882239.	1.23949	0.619746	−	0.784802i	$-0.287236\pi$
$47$	882239.	1.23949	0.619746	+	0.784802i	$0.287236\pi$
$48$	−105336.	−0.137478
$49$	1.09576e6	1.33055
$50$	125000.	0.141421
$51$	−511434.	−0.539876
$52$	−140608.	−0.138675
$53$	562825.	0.519287	0.259644	−	0.965705i	$-0.416395\pi$
$53$	562825.	0.519287	0.259644	+	0.965705i	$0.416395\pi$
$54$	763821.	0.660105
$55$	748030.	0.606247
$56$	−709320.	−0.539739
$57$	−366845.	−0.262374
$58$	−231815.	−0.156007
$59$	−247924.	−0.157158	−0.0785789	−	0.996908i	$-0.525038\pi$
$59$	−247924.	−0.157158	−0.0785789	+	0.996908i	$0.525038\pi$
$60$	−205735.	−0.122964
$61$	1.51269e6	0.853287	0.426644	−	0.904420i	$-0.359696\pi$
$61$	1.51269e6	0.853287	0.426644	+	0.904420i	$0.359696\pi$
$62$	−905706.	−0.482632
$63$	2.11361e6	1.06496
$64$	262144.	0.125000
$65$	−274625.	−0.124035
$66$	−1.23117e6	−0.527125
$67$	1.65807e6	0.673504	0.336752	−	0.941593i	$-0.390672\pi$
$67$	1.65807e6	0.673504	0.336752	+	0.941593i	$0.390672\pi$
$68$	1.27277e6	0.490874
$69$	−646717.	−0.236997
$70$	−1.38539e6	−0.482757
$71$	−1.05278e6	−0.349087	−0.174544	−	0.984649i	$-0.555845\pi$
$71$	−1.05278e6	−0.349087	−0.174544	+	0.984649i	$0.555845\pi$
$72$	−781129.	−0.246637
$73$	5.61859e6	1.69043	0.845215	−	0.534426i	$-0.179472\pi$
$73$	5.61859e6	1.69043	0.845215	+	0.534426i	$0.179472\pi$
$74$	2.18080e6	0.625612
$75$	−401826.	−0.109983
$76$	912943.	0.238559
$77$	−8.29051e6	−2.06949
$78$	452000.	0.107847
$79$	−6.77442e6	−1.54588	−0.772942	−	0.634476i	$-0.781216\pi$
$79$	−6.77442e6	−1.54588	−0.772942	+	0.634476i	$0.781216\pi$
$80$	512000.	0.111803
$81$	881193.	0.184235
$82$	863676.	0.172983
$83$	−6.82922e6	−1.31098	−0.655492	−	0.755202i	$-0.727539\pi$
$83$	−6.82922e6	−1.31098	−0.655492	+	0.755202i	$0.727539\pi$
$84$	2.28019e6	0.419752
$85$	2.48588e6	0.439051
$86$	6.29122e6	1.06657
$87$	745195.	0.121326
$88$	3.06393e6	0.479281
$89$	−5.36760e6	−0.807077	−0.403539	−	0.914963i	$-0.632220\pi$
$89$	−5.36760e6	−0.807077	−0.403539	+	0.914963i	$0.632220\pi$
$90$	−1.52564e6	−0.220599
$91$	3.04370e6	0.423406
$92$	1.60945e6	0.215486
$93$	2.91149e6	0.375340
$94$	7.05791e6	0.876454
$95$	1.78309e6	0.213374
$96$	−842691.	−0.0972118
$97$	1.67079e7	1.85875	0.929375	−	0.369137i	$-0.120347\pi$
$97$	1.67079e7	1.85875	0.929375	+	0.369137i	$0.120347\pi$
$98$	8.76611e6	0.940839
$99$	−9.12981e6	−0.945668
$100$	1.00000e6	0.100000
$101$	9.24298e6	0.892662	0.446331	−	0.894868i	$-0.352730\pi$
$101$	9.24298e6	0.892662	0.446331	+	0.894868i	$0.352730\pi$
$102$	−4.09147e6	−0.381750
$103$	−1.23098e7	−1.10999	−0.554995	−	0.831854i	$-0.687280\pi$
$103$	−1.23098e7	−1.10999	−0.554995	+	0.831854i	$0.687280\pi$
$104$	−1.12486e6	−0.0980581
$105$	4.45349e6	0.375438
$106$	4.50260e6	0.367191
$107$	−1.37221e7	−1.08288	−0.541438	−	0.840741i	$-0.682120\pi$
$107$	−1.37221e7	−1.08288	−0.541438	+	0.840741i	$0.682120\pi$
$108$	6.11057e6	0.466765
$109$	−1.13000e7	−0.835766	−0.417883	−	0.908501i	$-0.637228\pi$
$109$	−1.13000e7	−0.835766	−0.417883	+	0.908501i	$0.637228\pi$
$110$	5.98424e6	0.428682
$111$	−7.01042e6	−0.486535
$112$	−5.67456e6	−0.381653
$113$	1.78396e7	1.16308	0.581542	−	0.813517i	$-0.302450\pi$
$113$	1.78396e7	1.16308	0.581542	+	0.813517i	$0.302450\pi$
$114$	−2.93476e6	−0.185526
$115$	3.14345e6	0.192736
$116$	−1.85452e6	−0.110314
$117$	3.35184e6	0.193478
$118$	−1.98339e6	−0.111127
$119$	−2.75514e7	−1.49875
$120$	−1.64588e6	−0.0869489
$121$	1.63240e7	0.837679
$122$	1.21015e7	0.603365
$123$	−2.77638e6	−0.134528
$124$	−7.24565e6	−0.341273
$125$	1.95312e6	0.0894427
$126$	1.69089e7	0.753040
$127$	5.06683e6	0.219494	0.109747	−	0.993960i	$-0.464996\pi$
$127$	5.06683e6	0.219494	0.109747	+	0.993960i	$0.464996\pi$
$128$	2.09715e6	0.0883883
$129$	−2.02238e7	−0.829467
$130$	−2.19700e6	−0.0877058
$131$	−4.03617e6	−0.156863	−0.0784313	−	0.996920i	$-0.524991\pi$
$131$	−4.03617e6	−0.156863	−0.0784313	+	0.996920i	$0.524991\pi$
$132$	−9.84935e6	−0.372734
$133$	−1.97622e7	−0.728375
$134$	1.32645e7	0.476239
$135$	1.19347e7	0.417487
$136$	1.01822e7	0.347100
$137$	−2.08510e7	−0.692794	−0.346397	−	0.938088i	$-0.612595\pi$
$137$	−2.08510e7	−0.692794	−0.346397	+	0.938088i	$0.612595\pi$
$138$	−5.17374e6	−0.167582
$139$	2.71927e7	0.858816	0.429408	−	0.903111i	$-0.358722\pi$
$139$	2.71927e7	0.858816	0.429408	+	0.903111i	$0.358722\pi$
$140$	−1.10831e7	−0.341361
$141$	−2.26884e7	−0.681613
$142$	−8.42226e6	−0.246842
$143$	−1.31474e7	−0.375979
$144$	−6.24903e6	−0.174399
$145$	−3.62211e6	−0.0986674
$146$	4.49487e7	1.19531
$147$	−2.81796e7	−0.731685
$148$	1.74464e7	0.442374
$149$	−8.50536e6	−0.210640	−0.105320	−	0.994438i	$-0.533587\pi$
$149$	−8.50536e6	−0.210640	−0.105320	+	0.994438i	$0.533587\pi$
$150$	−3.21461e6	−0.0777694
$151$	−6.31447e6	−0.149251	−0.0746256	−	0.997212i	$-0.523776\pi$
$151$	−6.31447e6	−0.149251	−0.0746256	+	0.997212i	$0.523776\pi$
$152$	7.30354e6	0.168687
$153$	−3.03406e7	−0.684863
$154$	−6.63241e7	−1.46335
$155$	−1.41517e7	−0.305244
$156$	3.61600e6	0.0762592
$157$	−3.55725e7	−0.733611	−0.366806	−	0.930298i	$-0.619549\pi$
$157$	−3.55725e7	−0.733611	−0.366806	+	0.930298i	$0.619549\pi$
$158$	−5.41953e7	−1.09311
$159$	−1.44741e7	−0.285563
$160$	4.09600e6	0.0790569
$161$	−3.48392e7	−0.657927
$162$	7.04954e6	0.130274
$163$	−6.46035e7	−1.16842	−0.584211	−	0.811602i	$-0.698596\pi$
$163$	−6.46035e7	−1.16842	−0.584211	+	0.811602i	$0.698596\pi$
$164$	6.90941e6	0.122317
$165$	−1.92370e7	−0.333383
$166$	−5.46337e7	−0.927006
$167$	−3.37958e7	−0.561507	−0.280753	−	0.959780i	$-0.590584\pi$
$167$	−3.37958e7	−0.561507	−0.280753	+	0.959780i	$0.590584\pi$
$168$	1.82415e7	0.296810
$169$	4.82681e6	0.0769231
$170$	1.98871e7	0.310456
$171$	−2.17629e7	−0.332836
$172$	5.03297e7	0.754180
$173$	−8.03428e6	−0.117974	−0.0589869	−	0.998259i	$-0.518787\pi$
$173$	−8.03428e6	−0.117974	−0.0589869	+	0.998259i	$0.518787\pi$
$174$	5.96156e6	0.0857902
$175$	−2.16467e7	−0.305323
$176$	2.45115e7	0.338903
$177$	6.37583e6	0.0864232
$178$	−4.29408e7	−0.570690
$179$	3.09151e7	0.402889	0.201445	−	0.979500i	$-0.435436\pi$
$179$	3.09151e7	0.402889	0.201445	+	0.979500i	$0.435436\pi$
$180$	−1.22051e7	−0.155987
$181$	−9.55699e7	−1.19797	−0.598985	−	0.800760i	$-0.704429\pi$
$181$	−9.55699e7	−1.19797	−0.598985	+	0.800760i	$0.704429\pi$
$182$	2.43496e7	0.299393
$183$	−3.89017e7	−0.469234
$184$	1.28756e7	0.152372
$185$	3.40750e7	0.395672
$186$	2.32919e7	0.265406
$187$	1.19009e8	1.33087
$188$	5.64633e7	0.619746
$189$	−1.32274e8	−1.42514
$190$	1.42647e7	0.150878
$191$	1.74551e8	1.81262	0.906310	−	0.422614i	$-0.138887\pi$
$191$	1.74551e8	1.81262	0.906310	+	0.422614i	$0.138887\pi$
$192$	−6.74153e6	−0.0687391
$193$	1.82983e8	1.83215	0.916074	−	0.401010i	$-0.131341\pi$
$193$	1.82983e8	1.83215	0.916074	+	0.401010i	$0.131341\pi$
$194$	1.33663e8	1.31433
$195$	7.06250e6	0.0682083
$196$	7.01288e7	0.665274
$197$	−3.86648e7	−0.360316	−0.180158	−	0.983638i	$-0.557661\pi$
$197$	−3.86648e7	−0.360316	−0.180158	+	0.983638i	$0.557661\pi$
$198$	−7.30385e7	−0.668688
$199$	−1.14685e8	−1.03162	−0.515811	−	0.856703i	$-0.672509\pi$
$199$	−1.14685e8	−1.03162	−0.515811	+	0.856703i	$0.672509\pi$
$200$	8.00000e6	0.0707107
$201$	−4.26403e7	−0.370368
$202$	7.39438e7	0.631208
$203$	4.01443e7	0.336812
$204$	−3.27318e7	−0.269938
$205$	1.34949e7	0.109404
$206$	−9.84780e7	−0.784881
$207$	−3.83662e7	−0.300644
$208$	−8.99891e6	−0.0693375
$209$	8.53636e7	0.646786
$210$	3.56279e7	0.265475
$211$	9.52133e7	0.697765	0.348882	−	0.937167i	$-0.386561\pi$
$211$	9.52133e7	0.697765	0.348882	+	0.937167i	$0.386561\pi$
$212$	3.60208e7	0.259644
$213$	2.70743e7	0.191968
$214$	−1.09777e8	−0.765709
$215$	9.83002e7	0.674559
$216$	4.88845e7	0.330053
$217$	1.56845e8	1.04198
$218$	−9.03998e7	−0.590976
$219$	−1.44493e8	−0.929590
$220$	4.78739e7	0.303124
$221$	−4.36919e7	−0.272288
$222$	−5.60834e7	−0.344032
$223$	4.19120e7	0.253088	0.126544	−	0.991961i	$-0.459611\pi$
$223$	4.19120e7	0.253088	0.126544	+	0.991961i	$0.459611\pi$
$224$	−4.53965e7	−0.269870
$225$	−2.38382e7	−0.139519
$226$	1.42717e8	0.822424
$227$	−1.78109e8	−1.01064	−0.505318	−	0.862933i	$-0.668625\pi$
$227$	−1.78109e8	−1.01064	−0.505318	+	0.862933i	$0.668625\pi$
$228$	−2.34781e7	−0.131187
$229$	2.41493e7	0.132886	0.0664431	−	0.997790i	$-0.478835\pi$
$229$	2.41493e7	0.132886	0.0664431	+	0.997790i	$0.478835\pi$
$230$	2.51476e7	0.136285
$231$	2.13206e8	1.13804
$232$	−1.48362e7	−0.0780034
$233$	1.66011e8	0.859787	0.429894	−	0.902879i	$-0.358551\pi$
$233$	1.66011e8	0.859787	0.429894	+	0.902879i	$0.358551\pi$
$234$	2.68147e7	0.136810
$235$	1.10280e8	0.554318
$236$	−1.58671e7	−0.0785789
$237$	1.74217e8	0.850102
$238$	−2.20411e8	−1.05978
$239$	2.11511e8	1.00217	0.501083	−	0.865399i	$-0.332935\pi$
$239$	2.11511e8	1.00217	0.501083	+	0.865399i	$0.332935\pi$
$240$	−1.31670e7	−0.0614821
$241$	3.43807e8	1.58218	0.791088	−	0.611703i	$-0.209515\pi$
$241$	3.43807e8	1.58218	0.791088	+	0.611703i	$0.209515\pi$
$242$	1.30592e8	0.592328
$243$	−2.31471e8	−1.03484
$244$	9.68121e7	0.426644
$245$	1.36970e8	0.595039
$246$	−2.22111e7	−0.0951254
$247$	−3.13396e7	−0.132329
$248$	−5.79652e7	−0.241316
$249$	1.75626e8	0.720927
$250$	1.56250e7	0.0632456
$251$	−1.16659e8	−0.465651	−0.232825	−	0.972519i	$-0.574797\pi$
$251$	−1.16659e8	−0.465651	−0.232825	+	0.972519i	$0.574797\pi$
$252$	1.35271e8	0.532479
$253$	1.50489e8	0.584230
$254$	4.05346e7	0.155206
$255$	−6.39292e7	−0.241440
$256$	1.67772e7	0.0625000
$257$	2.01467e8	0.740350	0.370175	−	0.928962i	$-0.379298\pi$
$257$	2.01467e8	0.740350	0.370175	+	0.928962i	$0.379298\pi$
$258$	−1.61790e8	−0.586522
$259$	−3.77657e8	−1.35067
$260$	−1.75760e7	−0.0620174
$261$	4.42083e7	0.153908
$262$	−3.22893e7	−0.110919
$263$	−3.35455e8	−1.13708	−0.568538	−	0.822657i	$-0.692491\pi$
$263$	−3.35455e8	−1.13708	−0.568538	+	0.822657i	$0.692491\pi$
$264$	−7.87948e7	−0.263563
$265$	7.03531e7	0.232232
$266$	−1.58098e8	−0.515039
$267$	1.38038e8	0.443822
$268$	1.06116e8	0.336752
$269$	−1.84300e8	−0.577289	−0.288644	−	0.957436i	$-0.593205\pi$
$269$	−1.84300e8	−0.577289	−0.288644	+	0.957436i	$0.593205\pi$
$270$	9.54776e7	0.295208
$271$	5.91915e8	1.80662	0.903309	−	0.428990i	$-0.141130\pi$
$271$	5.91915e8	1.80662	0.903309	+	0.428990i	$0.141130\pi$
$272$	8.14575e7	0.245437
$273$	−7.82745e7	−0.232837
$274$	−1.66808e8	−0.489879
$275$	9.35038e7	0.271122
$276$	−4.13899e7	−0.118498
$277$	−1.45729e8	−0.411970	−0.205985	−	0.978555i	$-0.566040\pi$
$277$	−1.45729e8	−0.411970	−0.205985	+	0.978555i	$0.566040\pi$
$278$	2.17541e8	0.607274
$279$	1.72723e8	0.476141
$280$	−8.86650e7	−0.241379
$281$	−3.11664e8	−0.837944	−0.418972	−	0.907999i	$-0.637609\pi$
$281$	−3.11664e8	−0.837944	−0.418972	+	0.907999i	$0.637609\pi$
$282$	−1.81508e8	−0.481973
$283$	−3.94385e8	−1.03435	−0.517175	−	0.855879i	$-0.673016\pi$
$283$	−3.94385e8	−1.03435	−0.517175	+	0.855879i	$0.673016\pi$
$284$	−6.73780e7	−0.174544
$285$	−4.58556e7	−0.117337
$286$	−1.05179e8	−0.265857
$287$	−1.49566e8	−0.373462
$288$	−4.99922e7	−0.123319
$289$	−1.48429e7	−0.0361722
$290$	−2.89769e7	−0.0697684
$291$	−4.29675e8	−1.02215
$292$	3.59590e8	0.845215
$293$	6.61653e8	1.53672	0.768358	−	0.640020i	$-0.221074\pi$
$293$	6.61653e8	1.53672	0.768358	+	0.640020i	$0.221074\pi$
$294$	−2.25437e8	−0.517380
$295$	−3.09905e7	−0.0702831
$296$	1.39571e8	0.312806
$297$	5.71361e8	1.26550
$298$	−6.80429e7	−0.148945
$299$	−5.52492e7	−0.119530
$300$	−2.57169e7	−0.0549913
$301$	−1.08947e9	−2.30268
$302$	−5.05158e7	−0.105537
$303$	−2.37701e8	−0.490887
$304$	5.84284e7	0.119280
$305$	1.89086e8	0.381602
$306$	−2.42724e8	−0.484271
$307$	8.19225e8	1.61592	0.807958	−	0.589240i	$-0.200573\pi$
$307$	8.19225e8	1.61592	0.807958	+	0.589240i	$0.200573\pi$
$308$	−5.30593e8	−1.03475
$309$	3.16569e8	0.610398
$310$	−1.13213e8	−0.215840
$311$	−5.41501e8	−1.02079	−0.510397	−	0.859939i	$-0.670501\pi$
$311$	−5.41501e8	−1.02079	−0.510397	+	0.859939i	$0.670501\pi$
$312$	2.89280e7	0.0539234
$313$	7.38093e8	1.36052	0.680261	−	0.732970i	$-0.261866\pi$
$313$	7.38093e8	1.36052	0.680261	+	0.732970i	$0.261866\pi$
$314$	−2.84580e8	−0.518741
$315$	2.64201e8	0.476264
$316$	−4.33563e8	−0.772942
$317$	4.00476e8	0.706106	0.353053	−	0.935603i	$-0.385144\pi$
$317$	4.00476e8	0.706106	0.353053	+	0.935603i	$0.385144\pi$
$318$	−1.15793e8	−0.201923
$319$	−1.73405e8	−0.299084
$320$	3.27680e7	0.0559017
$321$	3.52891e8	0.595488
$322$	−2.78714e8	−0.465225
$323$	2.83684e8	0.468410
$324$	5.63963e7	0.0921177
$325$	−3.43281e7	−0.0554700
$326$	−5.16828e8	−0.826199
$327$	2.90600e8	0.459599
$328$	5.52753e7	0.0864913
$329$	−1.22225e9	−1.89223
$330$	−1.53896e8	−0.235738
$331$	−1.06548e8	−0.161490	−0.0807450	−	0.996735i	$-0.525730\pi$
$331$	−1.06548e8	−0.161490	−0.0807450	+	0.996735i	$0.525730\pi$
$332$	−4.37070e8	−0.655492
$333$	−4.15890e8	−0.617197
$334$	−2.70366e8	−0.397045
$335$	2.07258e8	0.301200
$336$	1.45932e8	0.209876
$337$	1.37689e9	1.95972	0.979859	−	0.199690i	$-0.0639934\pi$
$337$	1.37689e9	1.95972	0.979859	+	0.199690i	$0.0639934\pi$
$338$	3.86145e7	0.0543928
$339$	−4.58779e8	−0.639595
$340$	1.59097e8	0.219525
$341$	−6.77496e8	−0.925265
$342$	−1.74103e8	−0.235350
$343$	−3.77131e8	−0.504618
$344$	4.02638e8	0.533286
$345$	−8.08397e7	−0.105988
$346$	−6.42742e7	−0.0834201
$347$	4.65761e8	0.598425	0.299212	−	0.954187i	$-0.403276\pi$
$347$	4.65761e8	0.598425	0.299212	+	0.954187i	$0.403276\pi$
$348$	4.76925e7	0.0606628
$349$	−9.79780e8	−1.23378	−0.616892	−	0.787048i	$-0.711609\pi$
$349$	−9.79780e8	−1.23378	−0.616892	+	0.787048i	$0.711609\pi$
$350$	−1.73174e8	−0.215896
$351$	−2.09764e8	−0.258915
$352$	1.96092e8	0.239640
$353$	−1.01470e9	−1.22779	−0.613896	−	0.789387i	$-0.710399\pi$
$353$	−1.01470e9	−1.22779	−0.613896	+	0.789387i	$0.710399\pi$
$354$	5.10066e7	0.0611104
$355$	−1.31598e8	−0.156117
$356$	−3.43526e8	−0.403539
$357$	7.08535e8	0.824181
$358$	2.47321e8	0.284886
$359$	−1.08685e9	−1.23976	−0.619879	−	0.784697i	$-0.712819\pi$
$359$	−1.08685e9	−1.23976	−0.619879	+	0.784697i	$0.712819\pi$
$360$	−9.76411e7	−0.110300
$361$	−6.90389e8	−0.772358
$362$	−7.64559e8	−0.847093
$363$	−4.19802e8	−0.460650
$364$	1.94797e8	0.211703
$365$	7.02324e8	0.755983
$366$	−3.11213e8	−0.331798
$367$	1.34094e9	1.41604	0.708022	−	0.706190i	$-0.249588\pi$
$367$	1.34094e9	1.41604	0.708022	+	0.706190i	$0.249588\pi$
$368$	1.03004e8	0.107743
$369$	−1.64708e8	−0.170656
$370$	2.72600e8	0.279782
$371$	−7.79732e8	−0.792750
$372$	1.86336e8	0.187670
$373$	−4.81624e8	−0.480538	−0.240269	−	0.970706i	$-0.577236\pi$
$373$	−4.81624e8	−0.480538	−0.240269	+	0.970706i	$0.577236\pi$
$374$	9.52073e8	0.941065
$375$	−5.02283e7	−0.0491857
$376$	4.51707e8	0.438227
$377$	6.36622e7	0.0611909
$378$	−1.05819e9	−1.00773
$379$	−1.27201e9	−1.20020	−0.600098	−	0.799926i	$-0.704872\pi$
$379$	−1.27201e9	−1.20020	−0.600098	+	0.799926i	$0.704872\pi$
$380$	1.14118e8	0.106687
$381$	−1.30303e8	−0.120703
$382$	1.39641e9	1.28172
$383$	2.01846e9	1.83580	0.917899	−	0.396814i	$-0.129884\pi$
$383$	2.01846e9	1.83580	0.917899	+	0.396814i	$0.129884\pi$
$384$	−5.39322e7	−0.0486059
$385$	−1.03631e9	−0.925505
$386$	1.46386e9	1.29552
$387$	−1.19977e9	−1.05223
$388$	1.06931e9	0.929375
$389$	−7.76726e8	−0.669028	−0.334514	−	0.942391i	$-0.608572\pi$
$389$	−7.76726e8	−0.669028	−0.334514	+	0.942391i	$0.608572\pi$
$390$	5.65000e7	0.0482306
$391$	5.00112e8	0.423105
$392$	5.61031e8	0.470420
$393$	1.03798e8	0.0862608
$394$	−3.09318e8	−0.254782
$395$	−8.46802e8	−0.691341
$396$	−5.84308e8	−0.472834
$397$	1.60439e9	1.28689	0.643446	−	0.765491i	$-0.277504\pi$
$397$	1.60439e9	1.28689	0.643446	+	0.765491i	$0.277504\pi$
$398$	−9.17479e8	−0.729467
$399$	5.08223e8	0.400543
$400$	6.40000e7	0.0500000
$401$	1.63363e9	1.26517	0.632584	−	0.774491i	$-0.281994\pi$
$401$	1.63363e9	1.26517	0.632584	+	0.774491i	$0.281994\pi$
$402$	−3.41122e8	−0.261890
$403$	2.48730e8	0.189304
$404$	5.91551e8	0.446331
$405$	1.10149e8	0.0823926
$406$	3.21154e8	0.238162
$407$	1.63130e9	1.19937
$408$	−2.61854e8	−0.190875
$409$	3.02999e8	0.218983	0.109491	−	0.993988i	$-0.465078\pi$
$409$	3.02999e8	0.218983	0.109491	+	0.993988i	$0.465078\pi$
$410$	1.07960e8	0.0773602
$411$	5.36222e8	0.380976
$412$	−7.87824e8	−0.554995
$413$	3.43471e8	0.239919
$414$	−3.06930e8	−0.212587
$415$	−8.53652e8	−0.586290
$416$	−7.19913e7	−0.0490290
$417$	−6.99311e8	−0.472274
$418$	6.82909e8	0.457347
$419$	1.50517e9	0.999623	0.499812	−	0.866134i	$-0.333403\pi$
$419$	1.50517e9	0.999623	0.499812	+	0.866134i	$0.333403\pi$
$420$	2.85023e8	0.187719
$421$	2.34240e9	1.52994	0.764968	−	0.644069i	$-0.222755\pi$
$421$	2.34240e9	1.52994	0.764968	+	0.644069i	$0.222755\pi$
$422$	7.61706e8	0.493394
$423$	−1.34598e9	−0.864665
$424$	2.88166e8	0.183596
$425$	3.10736e8	0.196349
$426$	2.16594e8	0.135742
$427$	−2.09567e9	−1.30264
$428$	−8.78217e8	−0.541438
$429$	3.38110e8	0.206756
$430$	7.86402e8	0.476985
$431$	7.56002e8	0.454834	0.227417	−	0.973797i	$-0.426972\pi$
$431$	7.56002e8	0.454834	0.227417	+	0.973797i	$0.426972\pi$
$432$	3.91076e8	0.233382
$433$	2.45123e9	1.45103	0.725515	−	0.688207i	$-0.241602\pi$
$433$	2.45123e9	1.45103	0.725515	+	0.688207i	$0.241602\pi$
$434$	1.25476e9	0.736793
$435$	9.31494e7	0.0542585
$436$	−7.23198e8	−0.417883
$437$	3.58724e8	0.205625
$438$	−1.15594e9	−0.657319
$439$	−2.62694e9	−1.48192	−0.740959	−	0.671550i	$-0.765629\pi$
$439$	−2.62694e9	−1.48192	−0.740959	+	0.671550i	$0.765629\pi$
$440$	3.82992e8	0.214341
$441$	−1.67174e9	−0.928184
$442$	−3.49535e8	−0.192536
$443$	−2.14963e9	−1.17476	−0.587381	−	0.809310i	$-0.699841\pi$
$443$	−2.14963e9	−1.17476	−0.587381	+	0.809310i	$0.699841\pi$
$444$	−4.48667e8	−0.243267
$445$	−6.70950e8	−0.360936
$446$	3.35296e8	0.178960
$447$	2.18731e8	0.115834
$448$	−3.63172e8	−0.190827
$449$	−2.77752e9	−1.44809	−0.724045	−	0.689753i	$-0.757719\pi$
$449$	−2.77752e9	−1.44809	−0.724045	+	0.689753i	$0.757719\pi$
$450$	−1.90705e8	−0.0986549
$451$	6.46056e8	0.331629
$452$	1.14173e9	0.581542
$453$	1.62389e8	0.0820752
$454$	−1.42487e9	−0.714627
$455$	3.80463e8	0.189353
$456$	−1.87824e8	−0.0927631
$457$	−3.87434e9	−1.89885	−0.949426	−	0.313990i	$-0.898334\pi$
$457$	−3.87434e9	−1.89885	−0.949426	+	0.313990i	$0.898334\pi$
$458$	1.93194e8	0.0939647
$459$	1.89877e9	0.916490
$460$	2.01181e8	0.0963682
$461$	1.46095e9	0.694514	0.347257	−	0.937770i	$-0.387113\pi$
$461$	1.46095e9	0.694514	0.347257	+	0.937770i	$0.387113\pi$
$462$	1.70565e9	0.804716
$463$	−4.21691e9	−1.97452	−0.987259	−	0.159124i	$-0.949133\pi$
$463$	−4.21691e9	−1.97452	−0.987259	+	0.159124i	$0.949133\pi$
$464$	−1.18689e8	−0.0551568
$465$	3.63937e8	0.167857
$466$	1.32809e9	0.607962
$467$	2.74327e9	1.24640	0.623202	−	0.782061i	$-0.285831\pi$
$467$	2.74327e9	1.24640	0.623202	+	0.782061i	$0.285831\pi$
$468$	2.14517e8	0.0967391
$469$	−2.29707e9	−1.02818
$470$	8.82239e8	0.391962
$471$	9.14814e8	0.403422
$472$	−1.26937e8	−0.0555637
$473$	4.70602e9	2.04475
$474$	1.39374e9	0.601113
$475$	2.22886e8	0.0954237
$476$	−1.76329e9	−0.749374
$477$	−8.58669e8	−0.362252
$478$	1.69209e9	0.708639
$479$	−2.34714e9	−0.975810	−0.487905	−	0.872897i	$-0.662239\pi$
$479$	−2.34714e9	−0.975810	−0.487905	+	0.872897i	$0.662239\pi$
$480$	−1.05336e8	−0.0434744
$481$	−5.98902e8	−0.245385
$482$	2.75045e9	1.11877
$483$	8.95956e8	0.361803
$484$	1.04474e9	0.418839
$485$	2.08849e9	0.831258
$486$	−1.85177e9	−0.731745
$487$	3.36131e9	1.31873	0.659367	−	0.751821i	$-0.270824\pi$
$487$	3.36131e9	1.31873	0.659367	+	0.751821i	$0.270824\pi$
$488$	7.74497e8	0.301683
$489$	1.66140e9	0.642530
$490$	1.09576e9	0.420756
$491$	2.56010e9	0.976051	0.488026	−	0.872829i	$-0.337717\pi$
$491$	2.56010e9	0.976051	0.488026	+	0.872829i	$0.337717\pi$
$492$	−1.77689e8	−0.0672638
$493$	−5.76266e8	−0.216600
$494$	−2.50717e8	−0.0935706
$495$	−1.14123e9	−0.422915
$496$	−4.63722e8	−0.170636
$497$	1.45851e9	0.532921
$498$	1.40501e9	0.509773
$499$	−2.46043e9	−0.886459	−0.443230	−	0.896408i	$-0.646167\pi$
$499$	−2.46043e9	−0.886459	−0.443230	+	0.896408i	$0.646167\pi$
$500$	1.25000e8	0.0447214
$501$	8.69123e8	0.308780
$502$	−9.33272e8	−0.329265
$503$	−2.00729e9	−0.703272	−0.351636	−	0.936137i	$-0.614374\pi$
$503$	−2.00729e9	−0.703272	−0.351636	+	0.936137i	$0.614374\pi$
$504$	1.08217e9	0.376520
$505$	1.15537e9	0.399211
$506$	1.20391e9	0.413113
$507$	−1.24130e8	−0.0423010
$508$	3.24277e8	0.109747
$509$	3.74795e9	1.25974	0.629871	−	0.776700i	$-0.283108\pi$
$509$	3.74795e9	1.25974	0.629871	+	0.776700i	$0.283108\pi$
$510$	−5.11434e8	−0.170724
$511$	−7.78394e9	−2.58063
$512$	1.34218e8	0.0441942
$513$	1.36196e9	0.445404
$514$	1.61173e9	0.523506
$515$	−1.53872e9	−0.496403
$516$	−1.29432e9	−0.414733
$517$	5.27953e9	1.68027
$518$	−3.02126e9	−0.955067
$519$	2.06617e8	0.0648753
$520$	−1.40608e8	−0.0438529
$521$	−4.62413e8	−0.143251	−0.0716256	−	0.997432i	$-0.522819\pi$
$521$	−4.62413e8	−0.143251	−0.0716256	+	0.997432i	$0.522819\pi$
$522$	3.53667e8	0.108830
$523$	−5.16321e9	−1.57821	−0.789104	−	0.614260i	$-0.789455\pi$
$523$	−5.16321e9	−1.57821	−0.789104	+	0.614260i	$0.789455\pi$
$524$	−2.58315e8	−0.0784313
$525$	5.56686e8	0.167901
$526$	−2.68364e9	−0.804034
$527$	−2.25148e9	−0.670087
$528$	−6.30358e8	−0.186367
$529$	−2.77242e9	−0.814263
$530$	5.62825e8	0.164213
$531$	3.78243e8	0.109633
$532$	−1.26478e9	−0.364188
$533$	−2.37187e8	−0.0678494
$534$	1.10430e9	0.313830
$535$	−1.71527e9	−0.484277
$536$	8.48930e8	0.238120
$537$	−7.95041e8	−0.221554
$538$	−1.47440e9	−0.408205
$539$	6.55731e9	1.80370
$540$	7.63821e8	0.208744
$541$	1.14669e9	0.311354	0.155677	−	0.987808i	$-0.450244\pi$
$541$	1.14669e9	0.311354	0.155677	+	0.987808i	$0.450244\pi$
$542$	4.73532e9	1.27747
$543$	2.45776e9	0.658779
$544$	6.51660e8	0.173550
$545$	−1.41250e9	−0.373766
$546$	−6.26196e8	−0.164640
$547$	−6.17772e9	−1.61388	−0.806942	−	0.590630i	$-0.798879\pi$
$547$	−6.17772e9	−1.61388	−0.806942	+	0.590630i	$0.798879\pi$
$548$	−1.33446e9	−0.346397
$549$	−2.30782e9	−0.595250
$550$	7.48030e8	0.191712
$551$	−4.13348e8	−0.105265
$552$	−3.31119e8	−0.0837911
$553$	9.38521e9	2.35997
$554$	−1.16583e9	−0.291307
$555$	−8.76303e8	−0.217585
$556$	1.74033e9	0.429408
$557$	−4.19462e9	−1.02849	−0.514245	−	0.857643i	$-0.671928\pi$
$557$	−4.19462e9	−1.02849	−0.514245	+	0.857643i	$0.671928\pi$
$558$	1.38178e9	0.336682
$559$	−1.72773e9	−0.418344
$560$	−7.09320e8	−0.170681
$561$	−3.06054e9	−0.731861
$562$	−2.49331e9	−0.592516
$563$	1.54720e9	0.365398	0.182699	−	0.983169i	$-0.441517\pi$
$563$	1.54720e9	0.365398	0.182699	+	0.983169i	$0.441517\pi$
$564$	−1.45206e9	−0.340807
$565$	2.22995e9	0.520147
$566$	−3.15508e9	−0.731396
$567$	−1.22080e9	−0.281256
$568$	−5.39024e8	−0.123421
$569$	3.35925e9	0.764451	0.382225	−	0.924069i	$-0.375158\pi$
$569$	3.35925e9	0.764451	0.382225	+	0.924069i	$0.375158\pi$
$570$	−3.66845e8	−0.0829698
$571$	3.67087e9	0.825168	0.412584	−	0.910920i	$-0.364626\pi$
$571$	3.67087e9	0.825168	0.412584	+	0.910920i	$0.364626\pi$
$572$	−8.41432e8	−0.187989
$573$	−4.48892e9	−0.996783
$574$	−1.19653e9	−0.264078
$575$	3.92931e8	0.0861943
$576$	−3.99938e8	−0.0871995
$577$	6.59453e7	0.0142912	0.00714559	−	0.999974i	$-0.497725\pi$
$577$	6.59453e7	0.0142912	0.00714559	+	0.999974i	$0.497725\pi$
$578$	−1.18743e8	−0.0255776
$579$	−4.70576e9	−1.00752
$580$	−2.31815e8	−0.0493337
$581$	9.46113e9	2.00137
$582$	−3.43740e9	−0.722770
$583$	3.36808e9	0.703951
$584$	2.87672e9	0.597657
$585$	4.18979e8	0.0865261
$586$	5.29323e9	1.08662
$587$	−2.53103e9	−0.516492	−0.258246	−	0.966079i	$-0.583145\pi$
$587$	−2.53103e9	−0.516492	−0.258246	+	0.966079i	$0.583145\pi$
$588$	−1.80350e9	−0.365843
$589$	−1.61496e9	−0.325655
$590$	−2.47924e8	−0.0496977
$591$	9.94337e8	0.198142
$592$	1.11657e9	0.221187
$593$	−6.42139e9	−1.26456	−0.632278	−	0.774742i	$-0.717880\pi$
$593$	−6.42139e9	−1.26456	−0.632278	+	0.774742i	$0.717880\pi$
$594$	4.57089e9	0.894845
$595$	−3.44392e9	−0.670261
$596$	−5.44343e8	−0.105320
$597$	2.94934e9	0.567302
$598$	−4.41994e8	−0.0845205
$599$	−2.91569e9	−0.554304	−0.277152	−	0.960826i	$-0.589391\pi$
$599$	−2.91569e9	−0.554304	−0.277152	+	0.960826i	$0.589391\pi$
$600$	−2.05735e8	−0.0388847
$601$	1.81872e9	0.341747	0.170873	−	0.985293i	$-0.445341\pi$
$601$	1.81872e9	0.341747	0.170873	+	0.985293i	$0.445341\pi$
$602$	−8.71579e9	−1.62824
$603$	−2.52962e9	−0.469833
$604$	−4.04126e8	−0.0746256
$605$	2.04050e9	0.374621
$606$	−1.90161e9	−0.347109
$607$	−6.76925e9	−1.22851	−0.614257	−	0.789106i	$-0.710544\pi$
$607$	−6.76925e9	−1.22851	−0.614257	+	0.789106i	$0.710544\pi$
$608$	4.67427e8	0.0843434
$609$	−1.03239e9	−0.185217
$610$	1.51269e9	0.269833
$611$	−1.93828e9	−0.343773
$612$	−1.94180e9	−0.342431
$613$	4.63092e9	0.811999	0.405999	−	0.913873i	$-0.366923\pi$
$613$	4.63092e9	0.811999	0.405999	+	0.913873i	$0.366923\pi$
$614$	6.55380e9	1.14262
$615$	−3.47048e8	−0.0601626
$616$	−4.24474e9	−0.731676
$617$	−4.85871e9	−0.832766	−0.416383	−	0.909189i	$-0.636702\pi$
$617$	−4.85871e9	−0.832766	−0.416383	+	0.909189i	$0.636702\pi$
$618$	2.53255e9	0.431617
$619$	−1.01047e9	−0.171241	−0.0856203	−	0.996328i	$-0.527287\pi$
$619$	−1.01047e9	−0.171241	−0.0856203	+	0.996328i	$0.527287\pi$
$620$	−9.05706e8	−0.152622
$621$	2.40103e9	0.402325
$622$	−4.33201e9	−0.721810
$623$	7.43622e9	1.23209
$624$	2.31424e8	0.0381296
$625$	2.44141e8	0.0400000
$626$	5.90474e9	0.962035
$627$	−2.19529e9	−0.355676
$628$	−2.27664e9	−0.366806
$629$	5.42122e9	0.868599
$630$	2.11361e9	0.336770
$631$	−3.64738e9	−0.577934	−0.288967	−	0.957339i	$-0.593312\pi$
$631$	−3.64738e9	−0.577934	−0.288967	+	0.957339i	$0.593312\pi$
$632$	−3.46850e9	−0.546553
$633$	−2.44859e9	−0.383710
$634$	3.20381e9	0.499292
$635$	6.33353e8	0.0981608
$636$	−9.26342e8	−0.142781
$637$	−2.40739e9	−0.369028
$638$	−1.38724e9	−0.211484
$639$	1.60617e9	0.243522
$640$	2.62144e8	0.0395285
$641$	−2.27639e9	−0.341384	−0.170692	−	0.985324i	$-0.554600\pi$
$641$	−2.27639e9	−0.341384	−0.170692	+	0.985324i	$0.554600\pi$
$642$	2.82313e9	0.421073
$643$	−1.94818e9	−0.288995	−0.144498	−	0.989505i	$-0.546157\pi$
$643$	−1.94818e9	−0.288995	−0.144498	+	0.989505i	$0.546157\pi$
$644$	−2.22971e9	−0.328964
$645$	−2.52798e9	−0.370949
$646$	2.26947e9	0.331216
$647$	−2.36358e9	−0.343088	−0.171544	−	0.985176i	$-0.554876\pi$
$647$	−2.36358e9	−0.343088	−0.171544	+	0.985176i	$0.554876\pi$
$648$	4.51171e8	0.0651371
$649$	−1.48364e9	−0.213045
$650$	−2.74625e8	−0.0392232
$651$	−4.03355e9	−0.573000
$652$	−4.13462e9	−0.584211
$653$	−4.09914e9	−0.576098	−0.288049	−	0.957616i	$-0.593007\pi$
$653$	−4.09914e9	−0.576098	−0.288049	+	0.957616i	$0.593007\pi$
$654$	2.32480e9	0.324985
$655$	−5.04521e8	−0.0701511
$656$	4.42202e8	0.0611586
$657$	−8.57196e9	−1.17924
$658$	−9.77797e9	−1.33801
$659$	4.89248e9	0.665932	0.332966	−	0.942939i	$-0.391951\pi$
$659$	4.89248e9	0.665932	0.332966	+	0.942939i	$0.391951\pi$
$660$	−1.23117e9	−0.166692
$661$	−2.62013e9	−0.352873	−0.176436	−	0.984312i	$-0.556457\pi$
$661$	−2.62013e9	−0.352873	−0.176436	+	0.984312i	$0.556457\pi$
$662$	−8.52381e8	−0.114191
$663$	1.12362e9	0.149735
$664$	−3.49656e9	−0.463503
$665$	−2.47028e9	−0.325739
$666$	−3.32712e9	−0.436424
$667$	−7.28699e8	−0.0950840
$668$	−2.16293e9	−0.280753
$669$	−1.07785e9	−0.139176
$670$	1.65807e9	0.212981
$671$	9.05230e9	1.15673
$672$	1.16746e9	0.148405
$673$	7.23036e8	0.0914339	0.0457170	−	0.998954i	$-0.485443\pi$
$673$	7.23036e8	0.0914339	0.0457170	+	0.998954i	$0.485443\pi$
$674$	1.10151e10	1.38573
$675$	1.49184e9	0.186706
$676$	3.08916e8	0.0384615
$677$	1.37778e10	1.70656	0.853279	−	0.521455i	$-0.174610\pi$
$677$	1.37778e10	1.70656	0.853279	+	0.521455i	$0.174610\pi$
$678$	−3.67023e9	−0.452262
$679$	−2.31470e10	−2.83759
$680$	1.27277e9	0.155228
$681$	4.58040e9	0.555761
$682$	−5.41997e9	−0.654261
$683$	1.51093e10	1.81457	0.907283	−	0.420521i	$-0.138153\pi$
$683$	1.51093e10	1.81457	0.907283	+	0.420521i	$0.138153\pi$
$684$	−1.39282e9	−0.166418
$685$	−2.60637e9	−0.309827
$686$	−3.01705e9	−0.356819
$687$	−6.21044e8	−0.0730758
$688$	3.22110e9	0.377090
$689$	−1.23653e9	−0.144024
$690$	−6.46717e8	−0.0749450
$691$	−9.03723e9	−1.04199	−0.520993	−	0.853561i	$-0.674438\pi$
$691$	−9.03723e9	−1.04199	−0.520993	+	0.853561i	$0.674438\pi$
$692$	−5.14194e8	−0.0589869
$693$	1.26484e10	1.44367
$694$	3.72609e9	0.423150
$695$	3.39908e9	0.384074
$696$	3.81540e8	0.0428951
$697$	2.14700e9	0.240169
$698$	−7.83824e9	−0.872417
$699$	−4.26929e9	−0.472808
$700$	−1.38539e9	−0.152661
$701$	1.39276e10	1.52709	0.763543	−	0.645757i	$-0.223458\pi$
$701$	1.39276e10	1.52709	0.763543	+	0.645757i	$0.223458\pi$
$702$	−1.67811e9	−0.183080
$703$	3.88857e9	0.422130
$704$	1.56873e9	0.169451
$705$	−2.83606e9	−0.304827
$706$	−8.11758e9	−0.868180
$707$	−1.28051e10	−1.36275
$708$	4.08053e8	0.0432116
$709$	4.70055e9	0.495321	0.247661	−	0.968847i	$-0.420338\pi$
$709$	4.70055e9	0.495321	0.247661	+	0.968847i	$0.420338\pi$
$710$	−1.05278e9	−0.110391
$711$	1.03353e10	1.07840
$712$	−2.74821e9	−0.285345
$713$	−2.84704e9	−0.294158
$714$	5.66828e9	0.582784
$715$	−1.64342e9	−0.168143
$716$	1.97857e9	0.201445
$717$	−5.43940e9	−0.551104
$718$	−8.69476e9	−0.876642
$719$	9.95369e9	0.998695	0.499347	−	0.866402i	$-0.333573\pi$
$719$	9.95369e9	0.998695	0.499347	+	0.866402i	$0.333573\pi$
$720$	−7.81129e8	−0.0779936
$721$	1.70538e10	1.69453
$722$	−5.52311e9	−0.546140
$723$	−8.84164e9	−0.870059
$724$	−6.11647e9	−0.598985
$725$	−4.52764e8	−0.0441254
$726$	−3.35842e9	−0.325729
$727$	8.37125e9	0.808016	0.404008	−	0.914755i	$-0.367617\pi$
$727$	8.37125e9	0.808016	0.404008	+	0.914755i	$0.367617\pi$
$728$	1.55838e9	0.149697
$729$	4.02554e9	0.384838
$730$	5.61859e9	0.534561
$731$	1.56392e10	1.48083
$732$	−2.48971e9	−0.234617
$733$	6.45894e9	0.605756	0.302878	−	0.953029i	$-0.402053\pi$
$733$	6.45894e9	0.605756	0.302878	+	0.953029i	$0.402053\pi$
$734$	1.07275e10	1.00129
$735$	−3.52245e9	−0.327220
$736$	8.24036e8	0.0761858
$737$	9.92227e9	0.913009
$738$	−1.31766e9	−0.120672
$739$	4.58379e9	0.417801	0.208901	−	0.977937i	$-0.433012\pi$
$739$	4.58379e9	0.417801	0.208901	+	0.977937i	$0.433012\pi$
$740$	2.18080e9	0.197836
$741$	8.05957e8	0.0727693
$742$	−6.23785e9	−0.560559
$743$	2.14306e10	1.91678	0.958392	−	0.285457i	$-0.0921454\pi$
$743$	2.14306e10	1.91678	0.958392	+	0.285457i	$0.0921454\pi$
$744$	1.49068e9	0.132703
$745$	−1.06317e9	−0.0942011
$746$	−3.85299e9	−0.339791
$747$	1.04189e10	0.914537
$748$	7.61658e9	0.665433
$749$	1.90105e10	1.65313
$750$	−4.01826e8	−0.0347796
$751$	−1.64491e9	−0.141711	−0.0708555	−	0.997487i	$-0.522573\pi$
$751$	−1.64491e9	−0.141711	−0.0708555	+	0.997487i	$0.522573\pi$
$752$	3.61365e9	0.309873
$753$	3.00011e9	0.256067
$754$	5.09298e8	0.0432685
$755$	−7.89309e8	−0.0667472
$756$	−8.46552e9	−0.712570
$757$	6.21258e9	0.520519	0.260260	−	0.965539i	$-0.416192\pi$
$757$	6.21258e9	0.520519	0.260260	+	0.965539i	$0.416192\pi$
$758$	−1.01761e10	−0.848667
$759$	−3.87011e9	−0.321275
$760$	9.12943e8	0.0754390
$761$	−3.66858e9	−0.301753	−0.150877	−	0.988553i	$-0.548210\pi$
$761$	−3.66858e9	−0.301753	−0.150877	+	0.988553i	$0.548210\pi$
$762$	−1.04242e9	−0.0853497
$763$	1.56549e10	1.27589
$764$	1.11713e10	0.906310
$765$	−3.79257e9	−0.306280
$766$	1.61477e10	1.29811
$767$	5.44689e8	0.0435878
$768$	−4.31458e8	−0.0343696
$769$	−2.22396e10	−1.76354	−0.881770	−	0.471680i	$-0.843648\pi$
$769$	−2.22396e10	−1.76354	−0.881770	+	0.471680i	$0.843648\pi$
$770$	−8.29051e9	−0.654431
$771$	−5.18109e9	−0.407128
$772$	1.17109e10	0.916074
$773$	1.23669e10	0.963010	0.481505	−	0.876443i	$-0.340090\pi$
$773$	1.23669e10	0.963010	0.481505	+	0.876443i	$0.340090\pi$
$774$	−9.59814e9	−0.744036
$775$	−1.76896e9	−0.136509
$776$	8.55445e9	0.657167
$777$	9.71217e9	0.742750
$778$	−6.21381e9	−0.473074
$779$	1.54001e9	0.116720
$780$	4.52000e8	0.0341042
$781$	−6.30010e9	−0.473226
$782$	4.00089e9	0.299181
$783$	−2.76664e9	−0.205962
$784$	4.48825e9	0.332637
$785$	−4.44656e9	−0.328081
$786$	8.30381e8	0.0609956
$787$	−2.43423e10	−1.78012	−0.890060	−	0.455843i	$-0.849338\pi$
$787$	−2.43423e10	−1.78012	−0.890060	+	0.455843i	$0.849338\pi$
$788$	−2.47454e9	−0.180158
$789$	8.62686e9	0.625293
$790$	−6.77442e9	−0.488852
$791$	−2.47148e10	−1.77558
$792$	−4.67446e9	−0.334344
$793$	−3.32338e9	−0.236659
$794$	1.28351e10	0.909970
$795$	−1.80926e9	−0.127708
$796$	−7.33983e9	−0.515811
$797$	8.56180e9	0.599047	0.299524	−	0.954089i	$-0.403172\pi$
$797$	8.56180e9	0.599047	0.299524	+	0.954089i	$0.403172\pi$
$798$	4.06578e9	0.283227
$799$	1.75452e10	1.21687
$800$	5.12000e8	0.0353553
$801$	8.18903e9	0.563013
$802$	1.30690e10	0.894609
$803$	3.36230e10	2.29156
$804$	−2.72898e9	−0.185184
$805$	−4.35490e9	−0.294234
$806$	1.98984e9	0.133858
$807$	4.73963e9	0.317459
$808$	4.73241e9	0.315604
$809$	3.77273e9	0.250516	0.125258	−	0.992124i	$-0.460024\pi$
$809$	3.77273e9	0.250516	0.125258	+	0.992124i	$0.460024\pi$
$810$	8.81193e8	0.0582604
$811$	−9.76912e9	−0.643106	−0.321553	−	0.946892i	$-0.604205\pi$
$811$	−9.76912e9	−0.643106	−0.321553	+	0.946892i	$0.604205\pi$
$812$	2.56923e9	0.168406
$813$	−1.52222e10	−0.993483
$814$	1.30504e10	0.848085
$815$	−8.07544e9	−0.522534
$816$	−2.09483e9	−0.134969
$817$	1.12178e10	0.719666
$818$	2.42399e9	0.154844
$819$	−4.64360e9	−0.295366
$820$	8.63676e8	0.0547019
$821$	−2.91885e10	−1.84082	−0.920410	−	0.390955i	$-0.872145\pi$
$821$	−2.91885e10	−1.84082	−0.920410	+	0.390955i	$0.872145\pi$
$822$	4.28977e9	0.269391
$823$	−3.16808e7	−0.00198106	−0.000990528	−	1.00000i	$-0.500315\pi$
$823$	−3.16808e7	−0.00198106	−0.000990528		1.00000i	$0.500315\pi$
$824$	−6.30259e9	−0.392441
$825$	−2.40463e9	−0.149094
$826$	2.74777e9	0.169649
$827$	−2.03440e10	−1.25074	−0.625369	−	0.780329i	$-0.715052\pi$
$827$	−2.03440e10	−1.25074	−0.625369	+	0.780329i	$0.715052\pi$
$828$	−2.45544e9	−0.150322
$829$	2.23613e10	1.36319	0.681594	−	0.731731i	$-0.261287\pi$
$829$	2.23613e10	1.36319	0.681594	+	0.731731i	$0.261287\pi$
$830$	−6.82922e9	−0.414570
$831$	3.74769e9	0.226548
$832$	−5.75930e8	−0.0346688
$833$	2.17915e10	1.30626
$834$	−5.59449e9	−0.333948
$835$	−4.22447e9	−0.251113
$836$	5.46327e9	0.323393
$837$	−1.08093e10	−0.637176
$838$	1.20414e10	0.706840
$839$	−1.11761e10	−0.653319	−0.326659	−	0.945142i	$-0.605923\pi$
$839$	−1.11761e10	−0.653319	−0.326659	+	0.945142i	$0.605923\pi$
$840$	2.28019e9	0.132737
$841$	−1.64102e10	−0.951324
$842$	1.87392e10	1.08183
$843$	8.01503e9	0.460796
$844$	6.09365e9	0.348882
$845$	6.03351e8	0.0344010
$846$	−1.07679e10	−0.611410
$847$	−2.26151e10	−1.27881
$848$	2.30533e9	0.129822
$849$	1.01424e10	0.568803
$850$	2.48588e9	0.138840
$851$	6.85523e9	0.381302
$852$	1.73275e9	0.0959839
$853$	−1.57039e10	−0.866336	−0.433168	−	0.901313i	$-0.642604\pi$
$853$	−1.57039e10	−0.866336	−0.433168	+	0.901313i	$0.642604\pi$
$854$	−1.67653e10	−0.921106
$855$	−2.72036e9	−0.148849
$856$	−7.02574e9	−0.382855
$857$	−1.01560e10	−0.551174	−0.275587	−	0.961276i	$-0.588872\pi$
$857$	−1.01560e10	−0.551174	−0.275587	+	0.961276i	$0.588872\pi$
$858$	2.70488e9	0.146198
$859$	2.43067e10	1.30843	0.654214	−	0.756309i	$-0.272999\pi$
$859$	2.43067e10	1.30843	0.654214	+	0.756309i	$0.272999\pi$
$860$	6.29122e9	0.337280
$861$	3.84637e9	0.205372
$862$	6.04802e9	0.321616
$863$	−2.95200e10	−1.56343	−0.781716	−	0.623634i	$-0.785656\pi$
$863$	−2.95200e10	−1.56343	−0.781716	+	0.623634i	$0.785656\pi$
$864$	3.12861e9	0.165026
$865$	−1.00428e9	−0.0527595
$866$	1.96098e10	1.02603
$867$	3.81712e8	0.0198916
$868$	1.00381e10	0.520991
$869$	−4.05398e10	−2.09562
$870$	7.45195e8	0.0383665
$871$	−3.64277e9	−0.186796
$872$	−5.78559e9	−0.295488
$873$	−2.54903e10	−1.29666
$874$	2.86979e9	0.145398
$875$	−2.70584e9	−0.136544
$876$	−9.24753e9	−0.464795
$877$	−3.08282e10	−1.54330	−0.771649	−	0.636048i	$-0.780568\pi$
$877$	−3.08282e10	−1.54330	−0.771649	+	0.636048i	$0.780568\pi$
$878$	−2.10155e10	−1.04787
$879$	−1.70157e10	−0.845060
$880$	3.06393e9	0.151562
$881$	2.07134e10	1.02055	0.510276	−	0.860011i	$-0.329543\pi$
$881$	2.07134e10	1.02055	0.510276	+	0.860011i	$0.329543\pi$
$882$	−1.33739e10	−0.656325
$883$	−2.02076e10	−0.987762	−0.493881	−	0.869529i	$-0.664422\pi$
$883$	−2.02076e10	−0.987762	−0.493881	+	0.869529i	$0.664422\pi$
$884$	−2.79628e9	−0.136144
$885$	7.96978e8	0.0386496
$886$	−1.71970e10	−0.830683
$887$	−2.94541e10	−1.41714	−0.708569	−	0.705641i	$-0.750659\pi$
$887$	−2.94541e10	−1.41714	−0.708569	+	0.705641i	$0.750659\pi$
$888$	−3.58934e9	−0.172016
$889$	−7.01953e9	−0.335083
$890$	−5.36760e9	−0.255220
$891$	5.27327e9	0.249751
$892$	2.68237e9	0.126544
$893$	1.25849e10	0.591385
$894$	1.74985e9	0.0819068
$895$	3.86439e9	0.180178
$896$	−2.90537e9	−0.134935
$897$	1.42084e9	0.0657311
$898$	−2.22202e10	−1.02395
$899$	3.28057e9	0.150588
$900$	−1.52564e9	−0.0697596
$901$	1.11929e10	0.509809
$902$	5.16845e9	0.234497
$903$	2.80179e10	1.26627
$904$	9.13388e9	0.411212
$905$	−1.19462e10	−0.535749
$906$	1.29911e9	0.0580359
$907$	5.11479e9	0.227616	0.113808	−	0.993503i	$-0.463695\pi$
$907$	5.11479e9	0.227616	0.113808	+	0.993503i	$0.463695\pi$
$908$	−1.13990e10	−0.505318
$909$	−1.41015e10	−0.622717
$910$	3.04370e9	0.133893
$911$	−3.47003e10	−1.52061	−0.760307	−	0.649564i	$-0.774951\pi$
$911$	−3.47003e10	−1.52061	−0.760307	+	0.649564i	$0.774951\pi$
$912$	−1.50260e9	−0.0655934
$913$	−4.08677e10	−1.77718
$914$	−3.09947e10	−1.34269
$915$	−4.86271e9	−0.209848
$916$	1.54555e9	0.0664431
$917$	5.59167e9	0.239469
$918$	1.51902e10	0.648057
$919$	1.25541e10	0.533557	0.266779	−	0.963758i	$-0.414041\pi$
$919$	1.25541e10	0.533557	0.266779	+	0.963758i	$0.414041\pi$
$920$	1.60945e9	0.0681426
$921$	−2.10679e10	−0.888613
$922$	1.16876e10	0.491096
$923$	2.31296e9	0.0968194
$924$	1.36452e10	0.569020
$925$	4.25937e9	0.176950
$926$	−3.37353e10	−1.39619
$927$	1.87803e10	0.774324
$928$	−9.49515e8	−0.0390017
$929$	−1.78911e10	−0.732119	−0.366060	−	0.930591i	$-0.619293\pi$
$929$	−1.78911e10	−0.732119	−0.366060	+	0.930591i	$0.619293\pi$
$930$	2.91149e9	0.118693
$931$	1.56308e10	0.634829
$932$	1.06247e10	0.429894
$933$	1.39257e10	0.561347
$934$	2.19461e10	0.881341
$935$	1.48761e10	0.595182
$936$	1.71614e9	0.0684049
$937$	2.25955e10	0.897292	0.448646	−	0.893710i	$-0.351906\pi$
$937$	2.25955e10	0.897292	0.448646	+	0.893710i	$0.351906\pi$
$938$	−1.83766e10	−0.727033
$939$	−1.89814e10	−0.748169
$940$	7.05791e9	0.277159
$941$	5.23130e9	0.204666	0.102333	−	0.994750i	$-0.467369\pi$
$941$	5.23130e9	0.204666	0.102333	+	0.994750i	$0.467369\pi$
$942$	7.31852e9	0.285263
$943$	2.71492e9	0.105431
$944$	−1.01550e9	−0.0392895
$945$	−1.65342e10	−0.637342
$946$	3.76482e10	1.44586
$947$	−2.22249e10	−0.850382	−0.425191	−	0.905104i	$-0.639793\pi$
$947$	−2.22249e10	−0.850382	−0.425191	+	0.905104i	$0.639793\pi$
$948$	1.11499e10	0.425051
$949$	−1.23440e10	−0.468841
$950$	1.78309e9	0.0674747
$951$	−1.02990e10	−0.388297
$952$	−1.41063e10	−0.529888
$953$	4.07918e10	1.52668	0.763340	−	0.645997i	$-0.223558\pi$
$953$	4.07918e10	1.52668	0.763340	+	0.645997i	$0.223558\pi$
$954$	−6.86935e9	−0.256151
$955$	2.18189e10	0.810628
$956$	1.35367e10	0.501083
$957$	4.45943e9	0.164470
$958$	−1.87771e10	−0.690002
$959$	2.88867e10	1.05763
$960$	−8.42691e8	−0.0307411
$961$	−1.46954e10	−0.534132
$962$	−4.79122e9	−0.173513
$963$	2.09351e10	0.755410
$964$	2.20036e10	0.791088
$965$	2.28729e10	0.819361
$966$	7.16765e9	0.255833
$967$	−1.39014e10	−0.494384	−0.247192	−	0.968967i	$-0.579508\pi$
$967$	−1.39014e10	−0.494384	−0.247192	+	0.968967i	$0.579508\pi$
$968$	8.35788e9	0.296164
$969$	−7.29547e9	−0.257585
$970$	1.67079e10	0.587788
$971$	3.68316e10	1.29108	0.645540	−	0.763726i	$-0.276632\pi$
$971$	3.68316e10	1.29108	0.645540	+	0.763726i	$0.276632\pi$
$972$	−1.48141e10	−0.517422
$973$	−3.76725e10	−1.31108
$974$	2.68905e10	0.932486
$975$	8.82812e8	0.0305037
$976$	6.19598e9	0.213322
$977$	−5.04435e10	−1.73051	−0.865255	−	0.501331i	$-0.832844\pi$
$977$	−5.04435e10	−1.73051	−0.865255	+	0.501331i	$0.832844\pi$
$978$	1.32912e10	0.454337
$979$	−3.21210e10	−1.09408
$980$	8.76611e9	0.297520
$981$	1.72397e10	0.583027
$982$	2.04808e10	0.690172
$983$	3.92636e9	0.131842	0.0659209	−	0.997825i	$-0.479001\pi$
$983$	3.92636e9	0.131842	0.0659209	+	0.997825i	$0.479001\pi$
$984$	−1.42151e9	−0.0475627
$985$	−4.83310e9	−0.161138
$986$	−4.61012e9	−0.153159
$987$	3.14324e10	1.04056
$988$	−2.00574e9	−0.0661644
$989$	1.97761e10	0.650061
$990$	−9.12981e9	−0.299046
$991$	−3.43878e10	−1.12240	−0.561199	−	0.827681i	$-0.689660\pi$
$991$	−3.43878e10	−1.12240	−0.561199	+	0.827681i	$0.689660\pi$
$992$	−3.70977e9	−0.120658
$993$	2.74007e9	0.0888054
$994$	1.16681e10	0.376832
$995$	−1.43356e10	−0.461355
$996$	1.12401e10	0.360464
$997$	1.18053e10	0.377264	0.188632	−	0.982048i	$-0.439595\pi$
$997$	1.18053e10	0.377264	0.188632	+	0.982048i	$0.439595\pi$
$998$	−1.96834e10	−0.626821
$999$	2.60272e10	0.825939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.8.a.j.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.8.a.j.1.2	✓	4	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -25.7169 q^{3} +64.0000 q^{4} +125.000 q^{5} -205.735 q^{6} -1385.39 q^{7} +512.000 q^{8} -1525.64 q^{9} +1000.00 q^{10} +5984.24 q^{11} -1645.88 q^{12} -2197.00 q^{13} -11083.1 q^{14} -3214.61 q^{15} +4096.00 q^{16} +19887.1 q^{17} -12205.1 q^{18} +14264.7 q^{19} +8000.00 q^{20} +35627.9 q^{21} +47873.9 q^{22} +25147.6 q^{23} -13167.0 q^{24} +15625.0 q^{25} -17576.0 q^{26} +95477.6 q^{27} -88665.0 q^{28} -28976.9 q^{29} -25716.9 q^{30} -113213. q^{31} +32768.0 q^{32} -153896. q^{33} +159097. q^{34} -173174. q^{35} -97641.1 q^{36} +272600. q^{37} +114118. q^{38} +56500.0 q^{39} +64000.0 q^{40} +107960. q^{41} +285023. q^{42} +786402. q^{43} +382992. q^{44} -190705. q^{45} +201181. q^{46} +882239. q^{47} -105336. q^{48} +1.09576e6 q^{49} +125000. q^{50} -511434. q^{51} -140608. q^{52} +562825. q^{53} +763821. q^{54} +748030. q^{55} -709320. q^{56} -366845. q^{57} -231815. q^{58} -247924. q^{59} -205735. q^{60} +1.51269e6 q^{61} -905706. q^{62} +2.11361e6 q^{63} +262144. q^{64} -274625. q^{65} -1.23117e6 q^{66} +1.65807e6 q^{67} +1.27277e6 q^{68} -646717. q^{69} -1.38539e6 q^{70} -1.05278e6 q^{71} -781129. q^{72} +5.61859e6 q^{73} +2.18080e6 q^{74} -401826. q^{75} +912943. q^{76} -8.29051e6 q^{77} +452000. q^{78} -6.77442e6 q^{79} +512000. q^{80} +881193. q^{81} +863676. q^{82} -6.82922e6 q^{83} +2.28019e6 q^{84} +2.48588e6 q^{85} +6.29122e6 q^{86} +745195. q^{87} +3.06393e6 q^{88} -5.36760e6 q^{89} -1.52564e6 q^{90} +3.04370e6 q^{91} +1.60945e6 q^{92} +2.91149e6 q^{93} +7.05791e6 q^{94} +1.78309e6 q^{95} -842691. q^{96} +1.67079e7 q^{97} +8.76611e6 q^{98} -9.12981e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 60 q^{3} + 256 q^{4} + 500 q^{5} + 480 q^{6} + 616 q^{7} + 2048 q^{8} + 6284 q^{9} + 4000 q^{10} + 10116 q^{11} + 3840 q^{12} - 8788 q^{13} + 4928 q^{14} + 7500 q^{15} + 16384 q^{16} - 21136 q^{17}+ \cdots - 3168468 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 60 * q^3 + 256 * q^4 + 500 * q^5 + 480 * q^6 + 616 * q^7 + 2048 * q^8 + 6284 * q^9 + 4000 * q^10 + 10116 * q^11 + 3840 * q^12 - 8788 * q^13 + 4928 * q^14 + 7500 * q^15 + 16384 * q^16 - 21136 * q^17 + 50272 * q^18 + 41644 * q^19 + 32000 * q^20 - 31784 * q^21 + 80928 * q^22 + 163252 * q^23 + 30720 * q^24 + 62500 * q^25 - 70304 * q^26 + 432864 * q^27 + 39424 * q^28 - 35024 * q^29 + 60000 * q^30 - 45084 * q^31 + 131072 * q^32 + 132768 * q^33 - 169088 * q^34 + 77000 * q^35 + 402176 * q^36 - 22552 * q^37 + 333152 * q^38 - 131820 * q^39 + 256000 * q^40 + 480864 * q^41 - 254272 * q^42 + 1524508 * q^43 + 647424 * q^44 + 785500 * q^45 + 1306016 * q^46 + 263320 * q^47 + 245760 * q^48 + 1819444 * q^49 + 500000 * q^50 - 1248248 * q^51 - 562432 * q^52 + 916656 * q^53 + 3462912 * q^54 + 1264500 * q^55 + 315392 * q^56 + 2353648 * q^57 - 280192 * q^58 + 46660 * q^59 + 480000 * q^60 - 138016 * q^61 - 360672 * q^62 + 1628248 * q^63 + 1048576 * q^64 - 1098500 * q^65 + 1062144 * q^66 + 2802528 * q^67 - 1352704 * q^68 + 4683288 * q^69 + 616000 * q^70 - 2655204 * q^71 + 3217408 * q^72 + 7883656 * q^73 - 180416 * q^74 + 937500 * q^75 + 2665216 * q^76 - 5311096 * q^77 - 1054560 * q^78 - 4424056 * q^79 + 2048000 * q^80 + 9022268 * q^81 + 3846912 * q^82 + 4442376 * q^83 - 2034176 * q^84 - 2642000 * q^85 + 12196064 * q^86 - 6151920 * q^87 + 5179392 * q^88 + 25080 * q^89 + 6284000 * q^90 - 1353352 * q^91 + 10448128 * q^92 - 15987872 * q^93 + 2106560 * q^94 + 5205500 * q^95 + 1966080 * q^96 + 4112168 * q^97 + 14555552 * q^98 - 3168468 * q^99

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