LMFDB - Embedded newform 361.10.a.f.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,10,Mod(1,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	361.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$185.927936855$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 5069 x^{12} + 6049 x^{11} + 9806858 x^{10} - 13799702 x^{9} - 9054174058 x^{8} + \cdots - 17\!\cdots\!44 $ x^14 - x^13 - 5069x^12 + 6049x^11 + 9806858x^10 - 13799702x^9 - 9054174058x^8 + 14987065714x^7 + 4091858205557x^6 - 7191639085837x^5 - 853231603258457x^4 + 901465319435261x^3 + 73615201302121104x^2 + 11736003542411028x - 1795361907615663744
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 19 $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$39.3897$ of defining polynomial
Character	$\chi$	$=$	361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+40.3897 q^{2} -130.181 q^{3} +1119.32 q^{4} -1773.63 q^{5} -5257.96 q^{6} -9612.95 q^{7} +24529.6 q^{8} -2735.95 q^{9} -71636.1 q^{10} -50797.0 q^{11} -145715. q^{12} +21423.0 q^{13} -388264. q^{14} +230892. q^{15} +417648. q^{16} -464495. q^{17} -110504. q^{18} -1.98526e6 q^{20} +1.25142e6 q^{21} -2.05167e6 q^{22} +107093. q^{23} -3.19329e6 q^{24} +1.19262e6 q^{25} +865267. q^{26} +2.91852e6 q^{27} -1.07600e7 q^{28} -4.47852e6 q^{29} +9.32565e6 q^{30} -8.18175e6 q^{31} +4.30952e6 q^{32} +6.61279e6 q^{33} -1.87608e7 q^{34} +1.70498e7 q^{35} -3.06241e6 q^{36} -1.82843e7 q^{37} -2.78886e6 q^{39} -4.35063e7 q^{40} -2.60375e6 q^{41} +5.05445e7 q^{42} +1.06336e7 q^{43} -5.68583e7 q^{44} +4.85254e6 q^{45} +4.32545e6 q^{46} +5.45915e7 q^{47} -5.43698e7 q^{48} +5.20552e7 q^{49} +4.81696e7 q^{50} +6.04683e7 q^{51} +2.39793e7 q^{52} +1.89840e7 q^{53} +1.17878e8 q^{54} +9.00948e7 q^{55} -2.35802e8 q^{56} -1.80886e8 q^{58} -4.37047e7 q^{59} +2.58443e8 q^{60} -1.99367e7 q^{61} -3.30458e8 q^{62} +2.63005e7 q^{63} -3.97761e7 q^{64} -3.79963e7 q^{65} +2.67088e8 q^{66} +8.97698e7 q^{67} -5.19920e8 q^{68} -1.39415e7 q^{69} +6.88634e8 q^{70} +2.75493e7 q^{71} -6.71117e7 q^{72} +2.82917e8 q^{73} -7.38496e8 q^{74} -1.55257e8 q^{75} +4.88309e8 q^{77} -1.12641e8 q^{78} +9.54984e6 q^{79} -7.40752e8 q^{80} -3.26083e8 q^{81} -1.05165e8 q^{82} -6.70013e8 q^{83} +1.40075e9 q^{84} +8.23840e8 q^{85} +4.29486e8 q^{86} +5.83017e8 q^{87} -1.24603e9 q^{88} +5.44309e8 q^{89} +1.95993e8 q^{90} -2.05938e8 q^{91} +1.19872e8 q^{92} +1.06511e9 q^{93} +2.20493e9 q^{94} -5.61017e8 q^{96} +1.03589e9 q^{97} +2.10249e9 q^{98} +1.38978e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 15 q^{2} - 74 q^{3} + 2987 q^{4} + 285 q^{5} + 535 q^{6} - 1338 q^{7} + 12135 q^{8} + 57928 q^{9} + 41180 q^{10} - 57405 q^{11} - 117729 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} + 279203 q^{16}+ \cdots + 736622698 q^{99}+O(q^{100}) $ 14 * q + 15 * q^2 - 74 * q^3 + 2987 * q^4 + 285 * q^5 + 535 * q^6 - 1338 * q^7 + 12135 * q^8 + 57928 * q^9 + 41180 * q^10 - 57405 * q^11 - 117729 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 + 279203 * q^16 - 466251 * q^17 - 367482 * q^18 - 1671810 * q^20 + 689090 * q^21 - 1689395 * q^22 + 3087747 * q^23 + 234183 * q^24 + 3260823 * q^25 + 4516572 * q^26 - 2108270 * q^27 + 703814 * q^28 + 7831383 * q^29 - 5929612 * q^30 + 4632816 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 + 13222428 * q^35 - 7355018 * q^36 - 13602510 * q^37 - 10387851 * q^39 - 16500258 * q^40 + 20419440 * q^41 + 10220798 * q^42 - 27415427 * q^43 - 41775405 * q^44 - 42991294 * q^45 + 68617354 * q^46 + 90906681 * q^47 + 33057375 * q^48 + 114912446 * q^49 - 22203357 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 + 130507669 * q^54 + 157712310 * q^55 - 191229558 * q^56 - 172013024 * q^58 + 255540 * q^59 + 287916794 * q^60 - 304035459 * q^61 - 693626280 * q^62 + 122148024 * q^63 - 454245757 * q^64 + 712480095 * q^65 + 611099417 * q^66 + 165758480 * q^67 + 178759254 * q^68 - 135618639 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 + 602867050 * q^73 + 82104492 * q^74 - 950137387 * q^75 - 245997378 * q^77 - 911449840 * q^78 + 78162339 * q^79 - 227607150 * q^80 - 1230916118 * q^81 - 360208019 * q^82 + 206919963 * q^83 + 233652462 * q^84 + 1440537237 * q^85 + 936824310 * q^86 - 339438159 * q^87 + 823388847 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 + 677003592 * q^92 + 492493440 * q^93 + 424187592 * q^94 - 3020794465 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 + 736622698 * 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 $

$2$	40.3897	1.78499	0.892494	−	0.451060i	$-0.148954\pi$
$2$	40.3897	1.78499	0.892494	+	0.451060i	$0.148954\pi$
$3$	−130.181	−0.927901	−0.463950	−	0.885861i	$-0.653568\pi$
$3$	−130.181	−0.927901	−0.463950	+	0.885861i	$0.653568\pi$
$4$	1119.32	2.18618
$5$	−1773.63	−1.26910	−0.634552	−	0.772881i	$-0.718815\pi$
$5$	−1773.63	−1.26910	−0.634552	+	0.772881i	$0.718815\pi$
$6$	−5257.96	−1.65629
$7$	−9612.95	−1.51327	−0.756633	−	0.653839i	$-0.773157\pi$
$7$	−9612.95	−1.51327	−0.756633	+	0.653839i	$0.773157\pi$
$8$	24529.6	2.11732
$9$	−2735.95	−0.139000
$10$	−71636.1	−2.26533
$11$	−50797.0	−1.04609	−0.523047	−	0.852304i	$-0.675205\pi$
$11$	−50797.0	−1.04609	−0.523047	+	0.852304i	$0.675205\pi$
$12$	−145715.	−2.02856
$13$	21423.0	0.208034	0.104017	−	0.994576i	$-0.466830\pi$
$13$	21423.0	0.208034	0.104017	+	0.994576i	$0.466830\pi$
$14$	−388264.	−2.70116
$15$	230892.	1.17760
$16$	417648.	1.59320
$17$	−464495.	−1.34884	−0.674421	−	0.738347i	$-0.735606\pi$
$17$	−464495.	−1.34884	−0.674421	+	0.738347i	$0.735606\pi$
$18$	−110504.	−0.248114
$19$	0	0
$19$	0	0
$20$	−1.98526e6	−2.77449
$21$	1.25142e6	1.40416
$22$	−2.05167e6	−1.86726
$23$	107093.	0.0797969	0.0398984	−	0.999204i	$-0.487297\pi$
$23$	107093.	0.0797969	0.0398984	+	0.999204i	$0.487297\pi$
$24$	−3.19329e6	−1.96466
$25$	1.19262e6	0.610622
$26$	865267.	0.371338
$27$	2.91852e6	1.05688
$28$	−1.07600e7	−3.30827
$29$	−4.47852e6	−1.17583	−0.587913	−	0.808924i	$-0.700050\pi$
$29$	−4.47852e6	−1.17583	−0.587913	+	0.808924i	$0.700050\pi$
$30$	9.32565e6	2.10200
$31$	−8.18175e6	−1.59118	−0.795588	−	0.605838i	$-0.792838\pi$
$31$	−8.18175e6	−1.59118	−0.795588	+	0.605838i	$0.792838\pi$
$32$	4.30952e6	0.726530
$33$	6.61279e6	0.970671
$34$	−1.87608e7	−2.40766
$35$	1.70498e7	1.92049
$36$	−3.06241e6	−0.303880
$37$	−1.82843e7	−1.60388	−0.801938	−	0.597408i	$-0.796197\pi$
$37$	−1.82843e7	−1.60388	−0.801938	+	0.597408i	$0.796197\pi$
$38$	0	0
$39$	−2.78886e6	−0.193035
$40$	−4.35063e7	−2.68709
$41$	−2.60375e6	−0.143904	−0.0719519	−	0.997408i	$-0.522923\pi$
$41$	−2.60375e6	−0.143904	−0.0719519	+	0.997408i	$0.522923\pi$
$42$	5.05445e7	2.50641
$43$	1.06336e7	0.474320	0.237160	−	0.971471i	$-0.423784\pi$
$43$	1.06336e7	0.474320	0.237160	+	0.971471i	$0.423784\pi$
$44$	−5.68583e7	−2.28695
$45$	4.85254e6	0.176406
$46$	4.32545e6	0.142436
$47$	5.45915e7	1.63187	0.815934	−	0.578145i	$-0.196223\pi$
$47$	5.45915e7	1.63187	0.815934	+	0.578145i	$0.196223\pi$
$48$	−5.43698e7	−1.47833
$49$	5.20552e7	1.28998
$50$	4.81696e7	1.08995
$51$	6.04683e7	1.25159
$52$	2.39793e7	0.454800
$53$	1.89840e7	0.330481	0.165241	−	0.986253i	$-0.447160\pi$
$53$	1.89840e7	0.330481	0.165241	+	0.986253i	$0.447160\pi$
$54$	1.17878e8	1.88652
$55$	9.00948e7	1.32760
$56$	−2.35802e8	−3.20406
$57$	0	0
$58$	−1.80886e8	−2.09884
$59$	−4.37047e7	−0.469564	−0.234782	−	0.972048i	$-0.575438\pi$
$59$	−4.37047e7	−0.469564	−0.234782	+	0.972048i	$0.575438\pi$
$60$	2.58443e8	2.57445
$61$	−1.99367e7	−0.184361	−0.0921806	−	0.995742i	$-0.529384\pi$
$61$	−1.99367e7	−0.184361	−0.0921806	+	0.995742i	$0.529384\pi$
$62$	−3.30458e8	−2.84023
$63$	2.63005e7	0.210345
$64$	−3.97761e7	−0.296355
$65$	−3.79963e7	−0.264017
$66$	2.67088e8	1.73264
$67$	8.97698e7	0.544244	0.272122	−	0.962263i	$-0.412275\pi$
$67$	8.97698e7	0.544244	0.272122	+	0.962263i	$0.412275\pi$
$68$	−5.19920e8	−2.94881
$69$	−1.39415e7	−0.0740436
$70$	6.88634e8	3.42805
$71$	2.75493e7	0.128661	0.0643306	−	0.997929i	$-0.479509\pi$
$71$	2.75493e7	0.128661	0.0643306	+	0.997929i	$0.479509\pi$
$72$	−6.71117e7	−0.294308
$73$	2.82917e8	1.16602	0.583009	−	0.812465i	$-0.301875\pi$
$73$	2.82917e8	1.16602	0.583009	+	0.812465i	$0.301875\pi$
$74$	−7.38496e8	−2.86290
$75$	−1.55257e8	−0.566597
$76$	0	0
$77$	4.88309e8	1.58302
$78$	−1.12641e8	−0.344565
$79$	9.54984e6	0.0275851	0.0137925	−	0.999905i	$-0.495610\pi$
$79$	9.54984e6	0.0275851	0.0137925	+	0.999905i	$0.495610\pi$
$80$	−7.40752e8	−2.02194
$81$	−3.26083e8	−0.841678
$82$	−1.05165e8	−0.256866
$83$	−6.70013e8	−1.54964	−0.774821	−	0.632180i	$-0.782160\pi$
$83$	−6.70013e8	−1.54964	−0.774821	+	0.632180i	$0.782160\pi$
$84$	1.40075e9	3.06975
$85$	8.23840e8	1.71182
$86$	4.29486e8	0.846654
$87$	5.83017e8	1.09105
$88$	−1.24603e9	−2.21491
$89$	5.44309e8	0.919582	0.459791	−	0.888027i	$-0.347924\pi$
$89$	5.44309e8	0.919582	0.459791	+	0.888027i	$0.347924\pi$
$90$	1.95993e8	0.314882
$91$	−2.05938e8	−0.314811
$92$	1.19872e8	0.174450
$93$	1.06511e9	1.47645
$94$	2.20493e9	2.91286
$95$	0	0
$96$	−5.61017e8	−0.674148
$97$	1.03589e9	1.18807	0.594033	−	0.804441i	$-0.297535\pi$
$97$	1.03589e9	1.18807	0.594033	+	0.804441i	$0.297535\pi$
$98$	2.10249e9	2.30259
$99$	1.38978e8	0.145408
$100$	1.33493e9	1.33493
$101$	−2.37416e8	−0.227020	−0.113510	−	0.993537i	$-0.536209\pi$
$101$	−2.37416e8	−0.227020	−0.113510	+	0.993537i	$0.536209\pi$
$102$	2.44230e9	2.23407
$103$	−1.52038e9	−1.33102	−0.665509	−	0.746389i	$-0.731786\pi$
$103$	−1.52038e9	−1.33102	−0.665509	+	0.746389i	$0.731786\pi$
$104$	5.25497e8	0.440474
$105$	−2.21955e9	−1.78203
$106$	7.66758e8	0.589905
$107$	−8.05083e8	−0.593764	−0.296882	−	0.954914i	$-0.595947\pi$
$107$	−8.05083e8	−0.593764	−0.296882	+	0.954914i	$0.595947\pi$
$108$	3.26677e9	2.31053
$109$	1.54756e9	1.05009	0.525046	−	0.851074i	$-0.324048\pi$
$109$	1.54756e9	1.05009	0.525046	+	0.851074i	$0.324048\pi$
$110$	3.63890e9	2.36975
$111$	2.38027e9	1.48824
$112$	−4.01483e9	−2.41094
$113$	2.08633e9	1.20373	0.601865	−	0.798598i	$-0.294424\pi$
$113$	2.08633e9	1.20373	0.601865	+	0.798598i	$0.294424\pi$
$114$	0	0
$115$	−1.89943e8	−0.101270
$116$	−5.01291e9	−2.57057
$117$	−5.86121e7	−0.0289168
$118$	−1.76522e9	−0.838165
$119$	4.46517e9	2.04116
$120$	5.66369e9	2.49335
$121$	2.22385e8	0.0943131
$122$	−8.05237e8	−0.329082
$123$	3.38959e8	0.133528
$124$	−9.15803e9	−3.47860
$125$	1.34885e9	0.494160
$126$	1.06227e9	0.375463
$127$	−4.37782e9	−1.49328	−0.746640	−	0.665229i	$-0.768334\pi$
$127$	−4.37782e9	−1.49328	−0.746640	+	0.665229i	$0.768334\pi$
$128$	−3.81302e9	−1.25552
$129$	−1.38429e9	−0.440121
$130$	−1.53466e9	−0.471267
$131$	−5.64424e9	−1.67450	−0.837249	−	0.546822i	$-0.815837\pi$
$131$	−5.64424e9	−1.67450	−0.837249	+	0.546822i	$0.815837\pi$
$132$	7.40186e9	2.12206
$133$	0	0
$134$	3.62577e9	0.971468
$135$	−5.17636e9	−1.34129
$136$	−1.13939e10	−2.85592
$137$	2.33386e7	0.00566020	0.00283010	−	0.999996i	$-0.499099\pi$
$137$	2.33386e7	0.00566020	0.00283010	+	0.999996i	$0.499099\pi$
$138$	−5.63091e8	−0.132167
$139$	−3.81015e9	−0.865717	−0.432858	−	0.901462i	$-0.642495\pi$
$139$	−3.81015e9	−0.865717	−0.432858	+	0.901462i	$0.642495\pi$
$140$	1.90842e10	4.19854
$141$	−7.10677e9	−1.51421
$142$	1.11271e9	0.229659
$143$	−1.08822e9	−0.217623
$144$	−1.14266e9	−0.221456
$145$	7.94321e9	1.49225
$146$	1.14269e10	2.08133
$147$	−6.77659e9	−1.19697
$148$	−2.04661e10	−3.50636
$149$	−2.52303e9	−0.419357	−0.209678	−	0.977770i	$-0.567242\pi$
$149$	−2.52303e9	−0.419357	−0.209678	+	0.977770i	$0.567242\pi$
$150$	−6.27076e9	−1.01137
$151$	1.86229e9	0.291508	0.145754	−	0.989321i	$-0.453439\pi$
$151$	1.86229e9	0.291508	0.145754	+	0.989321i	$0.453439\pi$
$152$	0	0
$153$	1.27083e9	0.187489
$154$	1.97226e10	2.82567
$155$	1.45114e10	2.01937
$156$	−3.12164e9	−0.422009
$157$	3.15882e9	0.414932	0.207466	−	0.978242i	$-0.433478\pi$
$157$	3.15882e9	0.414932	0.207466	+	0.978242i	$0.433478\pi$
$158$	3.85715e8	0.0492390
$159$	−2.47136e9	−0.306654
$160$	−7.64347e9	−0.922042
$161$	−1.02948e9	−0.120754
$162$	−1.31704e10	−1.50239
$163$	1.36849e10	1.51844	0.759218	−	0.650837i	$-0.225582\pi$
$163$	1.36849e10	1.51844	0.759218	+	0.650837i	$0.225582\pi$
$164$	−2.91444e9	−0.314600
$165$	−1.17286e10	−1.23188
$166$	−2.70616e10	−2.76609
$167$	2.63102e9	0.261758	0.130879	−	0.991398i	$-0.458220\pi$
$167$	2.63102e9	0.261758	0.130879	+	0.991398i	$0.458220\pi$
$168$	3.06969e10	2.97305
$169$	−1.01456e10	−0.956722
$170$	3.32746e10	3.05557
$171$	0	0
$172$	1.19024e10	1.03695
$173$	−9.66556e9	−0.820388	−0.410194	−	0.911998i	$-0.634539\pi$
$173$	−9.66556e9	−0.820388	−0.410194	+	0.911998i	$0.634539\pi$
$174$	2.35479e10	1.94751
$175$	−1.14646e10	−0.924035
$176$	−2.12153e10	−1.66664
$177$	5.68952e9	0.435708
$178$	2.19845e10	1.64144
$179$	2.66812e9	0.194252	0.0971261	−	0.995272i	$-0.469035\pi$
$179$	2.66812e9	0.194252	0.0971261	+	0.995272i	$0.469035\pi$
$180$	5.43157e9	0.385655
$181$	−1.09480e10	−0.758195	−0.379097	−	0.925357i	$-0.623765\pi$
$181$	−1.09480e10	−0.758195	−0.379097	+	0.925357i	$0.623765\pi$
$182$	−8.31776e9	−0.561934
$183$	2.59538e9	0.171069
$184$	2.62695e9	0.168955
$185$	3.24295e10	2.03548
$186$	4.30193e10	2.63545
$187$	2.35949e10	1.41101
$188$	6.11056e10	3.56756
$189$	−2.80556e10	−1.59934
$190$	0	0
$191$	6.71373e8	0.0365018	0.0182509	−	0.999833i	$-0.494190\pi$
$191$	6.71373e8	0.0365018	0.0182509	+	0.999833i	$0.494190\pi$
$192$	5.17809e9	0.274988
$193$	−5.24308e9	−0.272006	−0.136003	−	0.990708i	$-0.543426\pi$
$193$	−5.24308e9	−0.272006	−0.136003	+	0.990708i	$0.543426\pi$
$194$	4.18392e10	2.12068
$195$	4.94640e9	0.244981
$196$	5.82666e10	2.82012
$197$	−5.28793e9	−0.250143	−0.125071	−	0.992148i	$-0.539916\pi$
$197$	−5.28793e9	−0.250143	−0.125071	+	0.992148i	$0.539916\pi$
$198$	5.61326e9	0.259551
$199$	−2.61806e10	−1.18342	−0.591712	−	0.806149i	$-0.701548\pi$
$199$	−2.61806e10	−1.18342	−0.591712	+	0.806149i	$0.701548\pi$
$200$	2.92545e10	1.29288
$201$	−1.16863e10	−0.505004
$202$	−9.58915e9	−0.405228
$203$	4.30518e10	1.77934
$204$	6.76837e10	2.73620
$205$	4.61808e9	0.182629
$206$	−6.14076e10	−2.37585
$207$	−2.93001e8	−0.0110918
$208$	8.94727e9	0.331441
$209$	0	0
$210$	−8.96470e10	−3.18089
$211$	−1.06696e10	−0.370576	−0.185288	−	0.982684i	$-0.559322\pi$
$211$	−1.06696e10	−0.370576	−0.185288	+	0.982684i	$0.559322\pi$
$212$	2.12493e10	0.722491
$213$	−3.58639e9	−0.119385
$214$	−3.25170e10	−1.05986
$215$	−1.88600e10	−0.601960
$216$	7.15901e10	2.23775
$217$	7.86507e10	2.40787
$218$	6.25053e10	1.87440
$219$	−3.68303e10	−1.08195
$220$	1.00845e11	2.90238
$221$	−9.95086e9	−0.280605
$222$	9.61381e10	2.65648
$223$	1.46530e10	0.396785	0.198392	−	0.980123i	$-0.436428\pi$
$223$	1.46530e10	0.396785	0.198392	+	0.980123i	$0.436428\pi$
$224$	−4.14272e10	−1.09943
$225$	−3.26295e9	−0.0848768
$226$	8.42660e10	2.14864
$227$	−1.69607e10	−0.423961	−0.211981	−	0.977274i	$-0.567991\pi$
$227$	−1.69607e10	−0.423961	−0.211981	+	0.977274i	$0.567991\pi$
$228$	0	0
$229$	4.78651e10	1.15016	0.575081	−	0.818096i	$-0.304970\pi$
$229$	4.78651e10	1.15016	0.575081	+	0.818096i	$0.304970\pi$
$230$	−7.67173e9	−0.180766
$231$	−6.35685e10	−1.46888
$232$	−1.09856e11	−2.48960
$233$	−5.41380e10	−1.20337	−0.601687	−	0.798732i	$-0.705505\pi$
$233$	−5.41380e10	−1.20337	−0.601687	+	0.798732i	$0.705505\pi$
$234$	−2.36732e9	−0.0516162
$235$	−9.68249e10	−2.07101
$236$	−4.89198e10	−1.02655
$237$	−1.24321e9	−0.0255962
$238$	1.80346e11	3.64344
$239$	2.11901e10	0.420090	0.210045	−	0.977692i	$-0.432639\pi$
$239$	2.11901e10	0.420090	0.210045	+	0.977692i	$0.432639\pi$
$240$	9.64317e10	1.87616
$241$	−4.79693e10	−0.915982	−0.457991	−	0.888957i	$-0.651431\pi$
$241$	−4.79693e10	−0.915982	−0.457991	+	0.888957i	$0.651431\pi$
$242$	8.98206e9	0.168348
$243$	−1.49954e10	−0.275885
$244$	−2.23156e10	−0.403047
$245$	−9.23264e10	−1.63711
$246$	1.36904e10	0.238346
$247$	0	0
$248$	−2.00695e11	−3.36902
$249$	8.72228e10	1.43791
$250$	5.44795e10	0.882070
$251$	4.36437e10	0.694048	0.347024	−	0.937856i	$-0.387192\pi$
$251$	4.36437e10	0.694048	0.347024	+	0.937856i	$0.387192\pi$
$252$	2.94388e10	0.459851
$253$	−5.44000e9	−0.0834750
$254$	−1.76819e11	−2.66549
$255$	−1.07248e11	−1.58840
$256$	−1.33641e11	−1.94473
$257$	−2.66936e10	−0.381688	−0.190844	−	0.981620i	$-0.561122\pi$
$257$	−2.66936e10	−0.381688	−0.190844	+	0.981620i	$0.561122\pi$
$258$	−5.59109e10	−0.785611
$259$	1.75766e11	2.42709
$260$	−4.25302e10	−0.577188
$261$	1.22530e10	0.163440
$262$	−2.27969e11	−2.98896
$263$	5.72495e10	0.737854	0.368927	−	0.929458i	$-0.379725\pi$
$263$	5.72495e10	0.737854	0.368927	+	0.929458i	$0.379725\pi$
$264$	1.62209e11	2.05522
$265$	−3.36705e10	−0.419415
$266$	0	0
$267$	−7.08586e10	−0.853281
$268$	1.00481e11	1.18981
$269$	−1.91009e10	−0.222418	−0.111209	−	0.993797i	$-0.535472\pi$
$269$	−1.91009e10	−0.222418	−0.111209	+	0.993797i	$0.535472\pi$
$270$	−2.09071e11	−2.39418
$271$	−2.06615e10	−0.232702	−0.116351	−	0.993208i	$-0.537120\pi$
$271$	−2.06615e10	−0.232702	−0.116351	+	0.993208i	$0.537120\pi$
$272$	−1.93996e11	−2.14898
$273$	2.68092e10	0.292114
$274$	9.42637e8	0.0101034
$275$	−6.05816e10	−0.638769
$276$	−1.56050e10	−0.161873
$277$	−2.89600e10	−0.295556	−0.147778	−	0.989021i	$-0.547212\pi$
$277$	−2.89600e10	−0.295556	−0.147778	+	0.989021i	$0.547212\pi$
$278$	−1.53891e11	−1.54529
$279$	2.23848e10	0.221174
$280$	4.18224e11	4.06629
$281$	−1.23174e11	−1.17853	−0.589266	−	0.807939i	$-0.700583\pi$
$281$	−1.23174e11	−1.17853	−0.589266	+	0.807939i	$0.700583\pi$
$282$	−2.87040e11	−2.70285
$283$	1.18222e11	1.09562	0.547811	−	0.836602i	$-0.315461\pi$
$283$	1.18222e11	1.09562	0.547811	+	0.836602i	$0.315461\pi$
$284$	3.08366e10	0.281277
$285$	0	0
$286$	−4.39529e10	−0.388455
$287$	2.50297e10	0.217765
$288$	−1.17906e10	−0.100988
$289$	9.71676e10	0.819372
$290$	3.20824e11	2.66364
$291$	−1.34853e11	−1.10241
$292$	3.16675e11	2.54913
$293$	1.53730e11	1.21858	0.609290	−	0.792948i	$-0.291455\pi$
$293$	1.53730e11	1.21858	0.609290	+	0.792948i	$0.291455\pi$
$294$	−2.73704e11	−2.13658
$295$	7.75158e10	0.595925
$296$	−4.48507e11	−3.39591
$297$	−1.48252e11	−1.10560
$298$	−1.01904e11	−0.748546
$299$	2.29425e9	0.0166005
$300$	−1.73782e11	−1.23868
$301$	−1.02220e11	−0.717772
$302$	7.52172e10	0.520339
$303$	3.09070e10	0.210652
$304$	0	0
$305$	3.53603e10	0.233973
$306$	5.13285e10	0.334666
$307$	−1.67271e11	−1.07473	−0.537365	−	0.843350i	$-0.680580\pi$
$307$	−1.67271e11	−1.07473	−0.537365	+	0.843350i	$0.680580\pi$
$308$	5.46576e11	3.46077
$309$	1.97924e11	1.23505
$310$	5.86109e11	3.60454
$311$	2.16624e11	1.31306	0.656531	−	0.754299i	$-0.272023\pi$
$311$	2.16624e11	1.31306	0.656531	+	0.754299i	$0.272023\pi$
$312$	−6.84097e10	−0.408716
$313$	−3.34946e10	−0.197254	−0.0986270	−	0.995124i	$-0.531445\pi$
$313$	−3.34946e10	−0.197254	−0.0986270	+	0.995124i	$0.531445\pi$
$314$	1.27584e11	0.740648
$315$	−4.66472e10	−0.266949
$316$	1.06894e10	0.0603059
$317$	−2.04437e11	−1.13709	−0.568543	−	0.822653i	$-0.692493\pi$
$317$	−2.04437e11	−1.13709	−0.568543	+	0.822653i	$0.692493\pi$
$318$	−9.98172e10	−0.547373
$319$	2.27495e11	1.23003
$320$	7.05480e10	0.376105
$321$	1.04806e11	0.550954
$322$	−4.15803e10	−0.215544
$323$	0	0
$324$	−3.64993e11	−1.84006
$325$	2.55495e10	0.127030
$326$	5.52727e11	2.71039
$327$	−2.01462e11	−0.974382
$328$	−6.38690e10	−0.304690
$329$	−5.24786e11	−2.46945
$330$	−4.73715e11	−2.19889
$331$	−2.97146e11	−1.36064	−0.680320	−	0.732915i	$-0.738159\pi$
$331$	−2.97146e11	−1.36064	−0.680320	+	0.732915i	$0.738159\pi$
$332$	−7.49961e11	−3.38780
$333$	5.00248e10	0.222939
$334$	1.06266e11	0.467235
$335$	−1.59218e11	−0.690701
$336$	5.22654e11	2.23711
$337$	−2.53746e11	−1.07168	−0.535838	−	0.844321i	$-0.680004\pi$
$337$	−2.53746e11	−1.07168	−0.535838	+	0.844321i	$0.680004\pi$
$338$	−4.09775e11	−1.70774
$339$	−2.71600e11	−1.11694
$340$	9.22144e11	3.74234
$341$	4.15608e11	1.66452
$342$	0	0
$343$	−1.12487e11	−0.438811
$344$	2.60837e11	1.00428
$345$	2.47269e10	0.0939689
$346$	−3.90389e11	−1.46438
$347$	−4.41660e11	−1.63533	−0.817666	−	0.575693i	$-0.804732\pi$
$347$	−4.41660e11	−1.63533	−0.817666	+	0.575693i	$0.804732\pi$
$348$	6.52585e11	2.38523
$349$	−5.67673e10	−0.204825	−0.102413	−	0.994742i	$-0.532656\pi$
$349$	−5.67673e10	−0.204825	−0.102413	+	0.994742i	$0.532656\pi$
$350$	−4.63052e11	−1.64939
$351$	6.25233e10	0.219867
$352$	−2.18910e11	−0.760019
$353$	1.62704e11	0.557713	0.278857	−	0.960333i	$-0.410045\pi$
$353$	1.62704e11	0.557713	0.278857	+	0.960333i	$0.410045\pi$
$354$	2.29798e11	0.777734
$355$	−4.88621e10	−0.163284
$356$	6.09258e11	2.01037
$357$	−5.81279e11	−1.89399
$358$	1.07764e11	0.346738
$359$	−3.17431e11	−1.00861	−0.504306	−	0.863525i	$-0.668252\pi$
$359$	−3.17431e11	−1.00861	−0.504306	+	0.863525i	$0.668252\pi$
$360$	1.19031e11	0.373507
$361$	0	0
$362$	−4.42186e11	−1.35337
$363$	−2.89503e10	−0.0875132
$364$	−2.30511e11	−0.688234
$365$	−5.01788e11	−1.47980
$366$	1.04826e11	0.305356
$367$	−1.70962e11	−0.491928	−0.245964	−	0.969279i	$-0.579105\pi$
$367$	−1.70962e11	−0.491928	−0.245964	+	0.969279i	$0.579105\pi$
$368$	4.47272e10	0.127133
$369$	7.12372e9	0.0200027
$370$	1.30982e12	3.63331
$371$	−1.82492e11	−0.500106
$372$	1.19220e12	3.22779
$373$	2.39356e11	0.640257	0.320129	−	0.947374i	$-0.396274\pi$
$373$	2.39356e11	0.640257	0.320129	+	0.947374i	$0.396274\pi$
$374$	9.52991e11	2.51864
$375$	−1.75594e11	−0.458532
$376$	1.33911e12	3.45518
$377$	−9.59432e10	−0.244612
$378$	−1.13315e12	−2.85480
$379$	1.72464e10	0.0429361	0.0214680	−	0.999770i	$-0.493166\pi$
$379$	1.72464e10	0.0429361	0.0214680	+	0.999770i	$0.493166\pi$
$380$	0	0
$381$	5.69908e11	1.38562
$382$	2.71165e10	0.0651552
$383$	2.91742e11	0.692796	0.346398	−	0.938088i	$-0.387405\pi$
$383$	2.91742e11	0.692796	0.346398	+	0.938088i	$0.387405\pi$
$384$	4.96382e11	1.16500
$385$	−8.66077e11	−2.00901
$386$	−2.11766e11	−0.485528
$387$	−2.90929e10	−0.0659306
$388$	1.15950e12	2.59732
$389$	−1.93578e11	−0.428630	−0.214315	−	0.976765i	$-0.568752\pi$
$389$	−1.93578e11	−0.428630	−0.214315	+	0.976765i	$0.568752\pi$
$390$	1.99783e11	0.437289
$391$	−4.97441e10	−0.107633
$392$	1.27689e12	2.73129
$393$	7.34772e11	1.55377
$394$	−2.13578e11	−0.446502
$395$	−1.69378e10	−0.0350083
$396$	1.55561e11	0.317887
$397$	5.93498e11	1.19912	0.599559	−	0.800331i	$-0.295343\pi$
$397$	5.93498e11	1.19912	0.599559	+	0.800331i	$0.295343\pi$
$398$	−1.05743e12	−2.11240
$399$	0	0
$400$	4.98097e11	0.972845
$401$	1.07171e11	0.206980	0.103490	−	0.994630i	$-0.466999\pi$
$401$	1.07171e11	0.206980	0.103490	+	0.994630i	$0.466999\pi$
$402$	−4.72006e11	−0.901426
$403$	−1.75277e11	−0.331019
$404$	−2.65745e11	−0.496306
$405$	5.78350e11	1.06818
$406$	1.73885e12	3.17610
$407$	9.28787e11	1.67780
$408$	1.48326e12	2.65001
$409$	3.80962e10	0.0673174	0.0336587	−	0.999433i	$-0.489284\pi$
$409$	3.80962e10	0.0673174	0.0336587	+	0.999433i	$0.489284\pi$
$410$	1.86523e11	0.325990
$411$	−3.03824e9	−0.00525211
$412$	−1.70180e12	−2.90985
$413$	4.20131e11	0.710575
$414$	−1.18342e10	−0.0197987
$415$	1.18835e12	1.96666
$416$	9.23227e10	0.151143
$417$	4.96009e11	0.803299
$418$	0	0
$419$	2.80944e10	0.0445305	0.0222652	−	0.999752i	$-0.492912\pi$
$419$	2.80944e10	0.0445305	0.0222652	+	0.999752i	$0.492912\pi$
$420$	−2.48440e12	−3.89583
$421$	−5.96519e11	−0.925453	−0.462727	−	0.886501i	$-0.653129\pi$
$421$	−5.96519e11	−0.925453	−0.462727	+	0.886501i	$0.653129\pi$
$422$	−4.30942e11	−0.661474
$423$	−1.49359e11	−0.226830
$424$	4.65671e11	0.699733
$425$	−5.53967e11	−0.823633
$426$	−1.44853e11	−0.213100
$427$	1.91651e11	0.278988
$428$	−9.01149e11	−1.29807
$429$	1.41666e11	0.201933
$430$	−7.61748e11	−1.07449
$431$	7.77897e11	1.08586	0.542931	−	0.839778i	$-0.317315\pi$
$431$	7.77897e11	1.08586	0.542931	+	0.839778i	$0.317315\pi$
$432$	1.21891e12	1.68382
$433$	−1.91800e11	−0.262213	−0.131106	−	0.991368i	$-0.541853\pi$
$433$	−1.91800e11	−0.262213	−0.131106	+	0.991368i	$0.541853\pi$
$434$	3.17668e12	4.29803
$435$	−1.03405e12	−1.38466
$436$	1.73222e12	2.29569
$437$	0	0
$438$	−1.48756e12	−1.93127
$439$	9.14173e11	1.17473	0.587365	−	0.809322i	$-0.300165\pi$
$439$	9.14173e11	1.17473	0.587365	+	0.809322i	$0.300165\pi$
$440$	2.20999e12	2.81095
$441$	−1.42420e11	−0.179307
$442$	−4.01912e11	−0.500876
$443$	1.13845e12	1.40442	0.702211	−	0.711969i	$-0.252196\pi$
$443$	1.13845e12	1.40442	0.702211	+	0.711969i	$0.252196\pi$
$444$	2.66429e12	3.25355
$445$	−9.65401e11	−1.16704
$446$	5.91830e11	0.708256
$447$	3.28450e11	0.389121
$448$	3.82366e11	0.448465
$449$	−8.78278e11	−1.01982	−0.509910	−	0.860228i	$-0.670321\pi$
$449$	−8.78278e11	−1.01982	−0.509910	+	0.860228i	$0.670321\pi$
$450$	−1.31789e11	−0.151504
$451$	1.32263e11	0.150537
$452$	2.33528e12	2.63157
$453$	−2.42434e11	−0.270491
$454$	−6.85035e11	−0.756766
$455$	3.65257e11	0.399528
$456$	0	0
$457$	7.14022e11	0.765753	0.382877	−	0.923800i	$-0.374933\pi$
$457$	7.14022e11	0.765753	0.382877	+	0.923800i	$0.374933\pi$
$458$	1.93325e12	2.05302
$459$	−1.35564e12	−1.42556
$460$	−2.12608e11	−0.221395
$461$	1.51036e12	1.55750	0.778748	−	0.627337i	$-0.215855\pi$
$461$	1.51036e12	1.55750	0.778748	+	0.627337i	$0.215855\pi$
$462$	−2.56751e12	−2.62194
$463$	−6.77202e11	−0.684863	−0.342432	−	0.939543i	$-0.611251\pi$
$463$	−6.77202e11	−0.684863	−0.342432	+	0.939543i	$0.611251\pi$
$464$	−1.87045e12	−1.87333
$465$	−1.88910e12	−1.87377
$466$	−2.18662e12	−2.14801
$467$	−2.81510e11	−0.273884	−0.136942	−	0.990579i	$-0.543727\pi$
$467$	−2.81510e11	−0.273884	−0.136942	+	0.990579i	$0.543727\pi$
$468$	−6.56059e10	−0.0632174
$469$	−8.62952e11	−0.823586
$470$	−3.91072e12	−3.69672
$471$	−4.11218e11	−0.385016
$472$	−1.07206e12	−0.994214
$473$	−5.40153e11	−0.496183
$474$	−5.02127e10	−0.0456889
$475$	0	0
$476$	4.99797e12	4.46233
$477$	−5.19392e10	−0.0459370
$478$	8.55860e11	0.749855
$479$	9.08984e11	0.788945	0.394472	−	0.918908i	$-0.370927\pi$
$479$	9.08984e11	0.788945	0.394472	+	0.918908i	$0.370927\pi$
$480$	9.95033e11	0.855563
$481$	−3.91704e11	−0.333661
$482$	−1.93746e12	−1.63502
$483$	1.34019e11	0.112048
$484$	2.48921e11	0.206185
$485$	−1.83728e12	−1.50778
$486$	−6.05657e11	−0.492452
$487$	−1.95171e12	−1.57230	−0.786148	−	0.618038i	$-0.787928\pi$
$487$	−1.95171e12	−1.57230	−0.786148	+	0.618038i	$0.787928\pi$
$488$	−4.89040e11	−0.390351
$489$	−1.78151e12	−1.40896
$490$	−3.72903e12	−2.92222
$491$	−1.47294e12	−1.14372	−0.571860	−	0.820351i	$-0.693778\pi$
$491$	−1.47294e12	−1.14372	−0.571860	+	0.820351i	$0.693778\pi$
$492$	3.79405e11	0.291917
$493$	2.08025e12	1.58600
$494$	0	0
$495$	−2.46494e11	−0.184537
$496$	−3.41709e12	−2.53507
$497$	−2.64830e11	−0.194699
$498$	3.52290e12	2.56666
$499$	−1.57148e12	−1.13464	−0.567319	−	0.823498i	$-0.692019\pi$
$499$	−1.57148e12	−1.13464	−0.567319	+	0.823498i	$0.692019\pi$
$500$	1.50980e12	1.08032
$501$	−3.42508e11	−0.242885
$502$	1.76275e12	1.23887
$503$	−1.78836e12	−1.24566	−0.622831	−	0.782357i	$-0.714017\pi$
$503$	−1.78836e12	−1.24566	−0.622831	+	0.782357i	$0.714017\pi$
$504$	6.45141e11	0.445366
$505$	4.21087e11	0.288112
$506$	−2.19720e11	−0.149002
$507$	1.32076e12	0.887743
$508$	−4.90020e12	−3.26458
$509$	1.58538e12	1.04690	0.523448	−	0.852057i	$-0.324645\pi$
$509$	1.58538e12	1.04690	0.523448	+	0.852057i	$0.324645\pi$
$510$	−4.33172e12	−2.83527
$511$	−2.71966e12	−1.76450
$512$	−3.44545e12	−2.21580
$513$	0	0
$514$	−1.07815e12	−0.681308
$515$	2.69658e12	1.68920
$516$	−1.54947e12	−0.962184
$517$	−2.77308e12	−1.70709
$518$	7.09913e12	4.33233
$519$	1.25827e12	0.761239
$520$	−9.32035e11	−0.559007
$521$	4.70053e11	0.279497	0.139748	−	0.990187i	$-0.455371\pi$
$521$	4.70053e11	0.279497	0.139748	+	0.990187i	$0.455371\pi$
$522$	4.94894e11	0.291739
$523$	2.84074e12	1.66025	0.830125	−	0.557577i	$-0.188269\pi$
$523$	2.84074e12	1.66025	0.830125	+	0.557577i	$0.188269\pi$
$524$	−6.31773e12	−3.66075
$525$	1.49247e12	0.857412
$526$	2.31229e12	1.31706
$527$	3.80038e12	2.14624
$528$	2.76182e12	1.54648
$529$	−1.78968e12	−0.993632
$530$	−1.35994e12	−0.748650
$531$	1.19574e11	0.0652695
$532$	0	0
$533$	−5.57801e10	−0.0299369
$534$	−2.86196e12	−1.52310
$535$	1.42792e12	0.753548
$536$	2.20202e12	1.15234
$537$	−3.47338e11	−0.180247
$538$	−7.71480e11	−0.397013
$539$	−2.64425e12	−1.34944
$540$	−5.79402e12	−2.93230
$541$	−2.55519e12	−1.28243	−0.641217	−	0.767359i	$-0.721570\pi$
$541$	−2.55519e12	−1.28243	−0.641217	+	0.767359i	$0.721570\pi$
$542$	−8.34511e11	−0.415370
$543$	1.42522e12	0.703529
$544$	−2.00175e12	−0.979974
$545$	−2.74479e12	−1.33268
$546$	1.08281e12	0.521419
$547$	−2.95756e12	−1.41251	−0.706254	−	0.707958i	$-0.749616\pi$
$547$	−2.95756e12	−1.41251	−0.706254	+	0.707958i	$0.749616\pi$
$548$	2.61234e10	0.0123742
$549$	5.45458e10	0.0256263
$550$	−2.44687e12	−1.14019
$551$	0	0
$552$	−3.41978e11	−0.156774
$553$	−9.18021e10	−0.0417436
$554$	−1.16969e12	−0.527564
$555$	−4.22170e12	−1.88873
$556$	−4.26480e12	−1.89261
$557$	−3.17079e12	−1.39579	−0.697894	−	0.716201i	$-0.745880\pi$
$557$	−3.17079e12	−1.39579	−0.697894	+	0.716201i	$0.745880\pi$
$558$	9.04115e11	0.394793
$559$	2.27803e11	0.0986747
$560$	7.12081e12	3.05973
$561$	−3.07161e12	−1.30928
$562$	−4.97496e12	−2.10366
$563$	2.44299e12	1.02479	0.512393	−	0.858751i	$-0.328759\pi$
$563$	2.44299e12	1.02479	0.512393	+	0.858751i	$0.328759\pi$
$564$	−7.95478e12	−3.31034
$565$	−3.70036e12	−1.52766
$566$	4.77496e12	1.95567
$567$	3.13462e12	1.27368
$568$	6.75773e11	0.272416
$569$	−1.82279e12	−0.729007	−0.364503	−	0.931202i	$-0.618761\pi$
$569$	−1.82279e12	−0.729007	−0.364503	+	0.931202i	$0.618761\pi$
$570$	0	0
$571$	1.27674e12	0.502621	0.251310	−	0.967907i	$-0.419139\pi$
$571$	1.27674e12	0.502621	0.251310	+	0.967907i	$0.419139\pi$
$572$	−1.21807e12	−0.475764
$573$	−8.73999e10	−0.0338700
$574$	1.01094e12	0.388707
$575$	1.27721e11	0.0487258
$576$	1.08825e11	0.0411935
$577$	−3.78237e12	−1.42060	−0.710301	−	0.703898i	$-0.751441\pi$
$577$	−3.78237e12	−1.42060	−0.710301	+	0.703898i	$0.751441\pi$
$578$	3.92457e12	1.46257
$579$	6.82549e11	0.252395
$580$	8.89103e12	3.26232
$581$	6.44080e12	2.34502
$582$	−5.44666e12	−1.96778
$583$	−9.64331e11	−0.345714
$584$	6.93983e12	2.46883
$585$	1.03956e11	0.0366985
$586$	6.20909e12	2.17515
$587$	3.85151e12	1.33894	0.669468	−	0.742841i	$-0.266522\pi$
$587$	3.85151e12	1.33894	0.669468	+	0.742841i	$0.266522\pi$
$588$	−7.58520e12	−2.61679
$589$	0	0
$590$	3.13084e12	1.06372
$591$	6.88388e11	0.232108
$592$	−7.63641e12	−2.55530
$593$	3.95614e12	1.31379	0.656894	−	0.753983i	$-0.271870\pi$
$593$	3.95614e12	1.31379	0.656894	+	0.753983i	$0.271870\pi$
$594$	−5.98784e12	−1.97347
$595$	−7.91953e12	−2.59044
$596$	−2.82408e12	−0.916789
$597$	3.40821e12	1.09810
$598$	9.26640e10	0.0296316
$599$	2.16141e12	0.685988	0.342994	−	0.939338i	$-0.388559\pi$
$599$	2.16141e12	0.685988	0.342994	+	0.939338i	$0.388559\pi$
$600$	−3.80838e12	−1.19966
$601$	−3.76890e12	−1.17836	−0.589181	−	0.808001i	$-0.700550\pi$
$601$	−3.76890e12	−1.17836	−0.589181	+	0.808001i	$0.700550\pi$
$602$	−4.12863e12	−1.28121
$603$	−2.45605e11	−0.0756501
$604$	2.08451e12	0.637290
$605$	−3.94428e11	−0.119693
$606$	1.24832e12	0.376011
$607$	4.08291e11	0.122073	0.0610366	−	0.998136i	$-0.480559\pi$
$607$	4.08291e11	0.122073	0.0610366	+	0.998136i	$0.480559\pi$
$608$	0	0
$609$	−5.60452e12	−1.65105
$610$	1.42819e12	0.417639
$611$	1.16951e12	0.339484
$612$	1.42247e12	0.409886
$613$	6.27548e12	1.79504	0.897522	−	0.440970i	$-0.145365\pi$
$613$	6.27548e12	1.79504	0.897522	+	0.440970i	$0.145365\pi$
$614$	−6.75604e12	−1.91838
$615$	−6.01186e11	−0.169461
$616$	1.19780e13	3.35175
$617$	−3.92160e12	−1.08938	−0.544691	−	0.838637i	$-0.683353\pi$
$617$	−3.92160e12	−1.08938	−0.544691	+	0.838637i	$0.683353\pi$
$618$	7.99409e12	2.20455
$619$	4.37972e12	1.19905	0.599527	−	0.800354i	$-0.295355\pi$
$619$	4.37972e12	1.19905	0.599527	+	0.800354i	$0.295355\pi$
$620$	1.62429e13	4.41470
$621$	3.12553e11	0.0843356
$622$	8.74938e12	2.34380
$623$	−5.23242e12	−1.39157
$624$	−1.16476e12	−0.307544
$625$	−4.72169e12	−1.23776
$626$	−1.35284e12	−0.352096
$627$	0	0
$628$	3.53575e12	0.907116
$629$	8.49296e12	2.16337
$630$	−1.88407e12	−0.476501
$631$	−1.91970e12	−0.482059	−0.241030	−	0.970518i	$-0.577485\pi$
$631$	−1.91970e12	−0.482059	−0.241030	+	0.970518i	$0.577485\pi$
$632$	2.34254e11	0.0584063
$633$	1.38898e12	0.343858
$634$	−8.25715e12	−2.02968
$635$	7.76461e12	1.89513
$636$	−2.76625e12	−0.670400
$637$	1.11518e12	0.268359
$638$	9.18845e12	2.19558
$639$	−7.53733e10	−0.0178840
$640$	6.76286e12	1.59338
$641$	3.17631e12	0.743126	0.371563	−	0.928408i	$-0.378822\pi$
$641$	3.17631e12	0.743126	0.371563	+	0.928408i	$0.378822\pi$
$642$	4.23310e12	0.983446
$643$	1.40839e12	0.324919	0.162459	−	0.986715i	$-0.448057\pi$
$643$	1.40839e12	0.324919	0.162459	+	0.986715i	$0.448057\pi$
$644$	−1.15232e12	−0.263990
$645$	2.45521e12	0.558559
$646$	0	0
$647$	−2.75462e12	−0.618005	−0.309003	−	0.951061i	$-0.599995\pi$
$647$	−2.75462e12	−0.618005	−0.309003	+	0.951061i	$0.599995\pi$
$648$	−7.99870e12	−1.78210
$649$	2.22007e12	0.491208
$650$	1.03194e12	0.226748
$651$	−1.02388e13	−2.23427
$652$	1.53178e13	3.31957
$653$	−6.16480e12	−1.32681	−0.663406	−	0.748260i	$-0.730890\pi$
$653$	−6.16480e12	−1.32681	−0.663406	+	0.748260i	$0.730890\pi$
$654$	−8.13700e12	−1.73926
$655$	1.00108e13	2.12511
$656$	−1.08745e12	−0.229268
$657$	−7.74045e11	−0.162077
$658$	−2.11959e13	−4.40794
$659$	1.17650e12	0.243000	0.121500	−	0.992591i	$-0.461229\pi$
$659$	1.17650e12	0.243000	0.121500	+	0.992591i	$0.461229\pi$
$660$	−1.31281e13	−2.69312
$661$	−4.98495e12	−1.01567	−0.507837	−	0.861453i	$-0.669555\pi$
$661$	−4.98495e12	−1.01567	−0.507837	+	0.861453i	$0.669555\pi$
$662$	−1.20016e13	−2.42873
$663$	1.29541e12	0.260374
$664$	−1.64351e13	−3.28108
$665$	0	0
$666$	2.02049e12	0.397944
$667$	−4.79618e11	−0.0938273
$668$	2.94496e12	0.572250
$669$	−1.90754e12	−0.368177
$670$	−6.43076e12	−1.23289
$671$	1.01272e12	0.192859
$672$	5.39302e12	1.02017
$673$	−8.79480e12	−1.65256	−0.826282	−	0.563257i	$-0.809548\pi$
$673$	−8.79480e12	−1.65256	−0.826282	+	0.563257i	$0.809548\pi$
$674$	−1.02487e13	−1.91293
$675$	3.48069e12	0.645354
$676$	−1.13562e13	−2.09157
$677$	9.07801e12	1.66089	0.830446	−	0.557099i	$-0.188086\pi$
$677$	9.07801e12	1.66089	0.830446	+	0.557099i	$0.188086\pi$
$678$	−1.09698e13	−1.99373
$679$	−9.95795e12	−1.79786
$680$	2.02085e13	3.62446
$681$	2.20795e12	0.393394
$682$	1.67863e13	2.97115
$683$	−3.54139e12	−0.622702	−0.311351	−	0.950295i	$-0.600782\pi$
$683$	−3.54139e12	−0.622702	−0.311351	+	0.950295i	$0.600782\pi$
$684$	0	0
$685$	−4.13939e10	−0.00718338
$686$	−4.54330e12	−0.783272
$687$	−6.23112e12	−1.06724
$688$	4.44109e12	0.755687
$689$	4.06694e11	0.0687514
$690$	9.98712e11	0.167733
$691$	3.84132e12	0.640957	0.320479	−	0.947256i	$-0.396156\pi$
$691$	3.84132e12	0.640957	0.320479	+	0.947256i	$0.396156\pi$
$692$	−1.08189e13	−1.79352
$693$	−1.33599e12	−0.220040
$694$	−1.78385e13	−2.91905
$695$	6.75778e12	1.09868
$696$	1.43012e13	2.31010
$697$	1.20943e12	0.194103
$698$	−2.29281e12	−0.365611
$699$	7.04774e12	1.11661
$700$	−1.28326e13	−2.02011
$701$	−9.72170e12	−1.52059	−0.760293	−	0.649580i	$-0.774945\pi$
$701$	−9.72170e12	−1.52059	−0.760293	+	0.649580i	$0.774945\pi$
$702$	2.52530e12	0.392460
$703$	0	0
$704$	2.02051e12	0.310016
$705$	1.26048e13	1.92169
$706$	6.57154e12	0.995511
$707$	2.28227e12	0.343542
$708$	6.36842e12	0.952537
$709$	2.09029e12	0.310669	0.155335	−	0.987862i	$-0.450354\pi$
$709$	2.09029e12	0.310669	0.155335	+	0.987862i	$0.450354\pi$
$710$	−1.97352e12	−0.291460
$711$	−2.61278e10	−0.00383434
$712$	1.33517e13	1.94705
$713$	−8.76208e11	−0.126971
$714$	−2.34777e13	−3.38075
$715$	1.93010e12	0.276186
$716$	2.98649e12	0.424670
$717$	−2.75854e12	−0.389802
$718$	−1.28209e13	−1.80036
$719$	4.28698e12	0.598235	0.299117	−	0.954216i	$-0.403308\pi$
$719$	4.28698e12	0.598235	0.299117	+	0.954216i	$0.403308\pi$
$720$	2.02666e12	0.281050
$721$	1.46153e13	2.01419
$722$	0	0
$723$	6.24469e12	0.849940
$724$	−1.22543e13	−1.65755
$725$	−5.34118e12	−0.717986
$726$	−1.16929e12	−0.156210
$727$	8.65994e12	1.14977	0.574884	−	0.818235i	$-0.305047\pi$
$727$	8.65994e12	1.14977	0.574884	+	0.818235i	$0.305047\pi$
$728$	−5.05158e12	−0.666555
$729$	8.37041e12	1.09767
$730$	−2.02670e13	−2.64142
$731$	−4.93924e12	−0.639782
$732$	2.90507e12	0.373987
$733$	3.40841e12	0.436098	0.218049	−	0.975938i	$-0.430031\pi$
$733$	3.40841e12	0.436098	0.218049	+	0.975938i	$0.430031\pi$
$734$	−6.90509e12	−0.878085
$735$	1.20191e13	1.51908
$736$	4.61519e11	0.0579748
$737$	−4.56003e12	−0.569330
$738$	2.87725e11	0.0357045
$739$	8.47639e12	1.04547	0.522734	−	0.852496i	$-0.324912\pi$
$739$	8.47639e12	1.04547	0.522734	+	0.852496i	$0.324912\pi$
$740$	3.62991e13	4.44993
$741$	0	0
$742$	−7.37080e12	−0.892683
$743$	−1.09797e13	−1.32172	−0.660860	−	0.750510i	$-0.729808\pi$
$743$	−1.09797e13	−1.32172	−0.660860	+	0.750510i	$0.729808\pi$
$744$	2.61267e13	3.12612
$745$	4.47490e12	0.532207
$746$	9.66751e12	1.14285
$747$	1.83312e12	0.215401
$748$	2.64104e13	3.08473
$749$	7.73922e12	0.898523
$750$	−7.09219e12	−0.818473
$751$	7.89916e12	0.906152	0.453076	−	0.891472i	$-0.350327\pi$
$751$	7.89916e12	0.906152	0.453076	+	0.891472i	$0.350327\pi$
$752$	2.28001e13	2.59990
$753$	−5.68157e12	−0.644008
$754$	−3.87511e12	−0.436630
$755$	−3.30300e12	−0.369954
$756$	−3.14033e13	−3.49644
$757$	4.24235e12	0.469543	0.234771	−	0.972051i	$-0.424566\pi$
$757$	4.24235e12	0.469543	0.234771	+	0.972051i	$0.424566\pi$
$758$	6.96576e11	0.0766403
$759$	7.08184e11	0.0774565
$760$	0	0
$761$	1.64007e13	1.77268	0.886342	−	0.463031i	$-0.153238\pi$
$761$	1.64007e13	1.77268	0.886342	+	0.463031i	$0.153238\pi$
$762$	2.30184e13	2.47331
$763$	−1.48766e13	−1.58907
$764$	7.51484e11	0.0797994
$765$	−2.25398e12	−0.237943
$766$	1.17834e13	1.23663
$767$	−9.36285e11	−0.0976853
$768$	1.73975e13	1.80452
$769$	−1.34378e13	−1.38567	−0.692835	−	0.721096i	$-0.743638\pi$
$769$	−1.34378e13	−1.38567	−0.692835	+	0.721096i	$0.743638\pi$
$770$	−3.49805e13	−3.58607
$771$	3.47500e12	0.354169
$772$	−5.86871e12	−0.594655
$773$	−6.63378e12	−0.668272	−0.334136	−	0.942525i	$-0.608444\pi$
$773$	−6.63378e12	−0.668272	−0.334136	+	0.942525i	$0.608444\pi$
$774$	−1.17505e12	−0.117685
$775$	−9.75773e12	−0.971608
$776$	2.54099e13	2.51551
$777$	−2.28814e13	−2.25210
$778$	−7.81854e12	−0.765099
$779$	0	0
$780$	5.53662e12	0.535573
$781$	−1.39942e12	−0.134592
$782$	−2.00915e12	−0.192124
$783$	−1.30706e13	−1.24271
$784$	2.17408e13	2.05519
$785$	−5.60257e12	−0.526591
$786$	2.96772e13	2.77345
$787$	3.85149e12	0.357884	0.178942	−	0.983860i	$-0.442733\pi$
$787$	3.85149e12	0.357884	0.178942	+	0.983860i	$0.442733\pi$
$788$	−5.91891e12	−0.546857
$789$	−7.45279e12	−0.684656
$790$	−6.84113e11	−0.0624894
$791$	−2.00558e13	−1.82157
$792$	3.40907e12	0.307874
$793$	−4.27104e11	−0.0383534
$794$	2.39712e13	2.14041
$795$	4.38326e12	0.389175
$796$	−2.93046e13	−2.58718
$797$	8.96871e12	0.787349	0.393675	−	0.919250i	$-0.371204\pi$
$797$	8.96871e12	0.787349	0.393675	+	0.919250i	$0.371204\pi$
$798$	0	0
$799$	−2.53575e13	−2.20113
$800$	5.13962e12	0.443636
$801$	−1.48920e12	−0.127822
$802$	4.32861e12	0.369457
$803$	−1.43713e13	−1.21977
$804$	−1.30808e13	−1.10403
$805$	1.82591e12	0.153249
$806$	−7.07939e12	−0.590865
$807$	2.48658e12	0.206381
$808$	−5.82372e12	−0.480673
$809$	7.19472e12	0.590535	0.295268	−	0.955415i	$-0.404591\pi$
$809$	7.19472e12	0.590535	0.295268	+	0.955415i	$0.404591\pi$
$810$	2.33594e13	1.90668
$811$	−1.32351e13	−1.07432	−0.537160	−	0.843480i	$-0.680503\pi$
$811$	−1.32351e13	−1.07432	−0.537160	+	0.843480i	$0.680503\pi$
$812$	4.81889e13	3.88996
$813$	2.68973e12	0.215924
$814$	3.75134e13	2.99486
$815$	−2.42718e13	−1.92705
$816$	2.52545e13	1.99404
$817$	0	0
$818$	1.53869e12	0.120161
$819$	5.63435e11	0.0437589
$820$	5.16913e12	0.399259
$821$	−5.68620e12	−0.436796	−0.218398	−	0.975860i	$-0.570083\pi$
$821$	−5.68620e12	−0.436796	−0.218398	+	0.975860i	$0.570083\pi$
$822$	−1.22713e11	−0.00937494
$823$	2.35782e13	1.79148	0.895739	−	0.444579i	$-0.146647\pi$
$823$	2.35782e13	1.79148	0.895739	+	0.444579i	$0.146647\pi$
$824$	−3.72943e13	−2.81819
$825$	7.88656e12	0.592714
$826$	1.69690e13	1.26837
$827$	−9.82813e11	−0.0730628	−0.0365314	−	0.999333i	$-0.511631\pi$
$827$	−9.82813e11	−0.0730628	−0.0365314	+	0.999333i	$0.511631\pi$
$828$	−3.27963e11	−0.0242487
$829$	8.04163e12	0.591356	0.295678	−	0.955288i	$-0.404454\pi$
$829$	8.04163e12	0.591356	0.295678	+	0.955288i	$0.404454\pi$
$830$	4.79971e13	3.51046
$831$	3.77004e12	0.274247
$832$	−8.52123e11	−0.0616520
$833$	−2.41794e13	−1.73997
$834$	2.00336e13	1.43388
$835$	−4.66644e12	−0.332198
$836$	0	0
$837$	−2.38786e13	−1.68168
$838$	1.13472e12	0.0794863
$839$	−5.28475e12	−0.368210	−0.184105	−	0.982907i	$-0.558939\pi$
$839$	−5.28475e12	−0.368210	−0.184105	+	0.982907i	$0.558939\pi$
$840$	−5.44448e13	−3.77311
$841$	5.54998e12	0.382569
$842$	−2.40932e13	−1.65192
$843$	1.60349e13	1.09356
$844$	−1.19427e13	−0.810146
$845$	1.79944e13	1.21418
$846$	−6.03258e12	−0.404889
$847$	−2.13778e12	−0.142721
$848$	7.92865e12	0.526523
$849$	−1.53903e13	−1.01663
$850$	−2.23745e13	−1.47017
$851$	−1.95812e12	−0.127984
$852$	−4.01433e12	−0.260997
$853$	1.61791e13	1.04636	0.523182	−	0.852221i	$-0.324745\pi$
$853$	1.61791e13	1.04636	0.523182	+	0.852221i	$0.324745\pi$
$854$	7.74070e12	0.497989
$855$	0	0
$856$	−1.97484e13	−1.25719
$857$	−7.87950e12	−0.498982	−0.249491	−	0.968377i	$-0.580263\pi$
$857$	−7.87950e12	−0.498982	−0.249491	+	0.968377i	$0.580263\pi$
$858$	5.72183e12	0.360448
$859$	−1.99033e13	−1.24726	−0.623629	−	0.781720i	$-0.714343\pi$
$859$	−1.99033e13	−1.24726	−0.623629	+	0.781720i	$0.714343\pi$
$860$	−2.11104e13	−1.31599
$861$	−3.25839e12	−0.202064
$862$	3.14190e13	1.93825
$863$	6.88670e12	0.422632	0.211316	−	0.977418i	$-0.432225\pi$
$863$	6.88670e12	0.422632	0.211316	+	0.977418i	$0.432225\pi$
$864$	1.25774e13	0.767855
$865$	1.71431e13	1.04116
$866$	−7.74675e12	−0.468047
$867$	−1.26494e13	−0.760296
$868$	8.80356e13	5.26405
$869$	−4.85103e11	−0.0288566
$870$	−4.17651e13	−2.47159
$871$	1.92314e12	0.113221
$872$	3.79610e13	2.22338
$873$	−2.83414e12	−0.165142
$874$	0	0
$875$	−1.29664e13	−0.747796
$876$	−4.12251e13	−2.36534
$877$	2.71377e13	1.54908	0.774542	−	0.632522i	$-0.217980\pi$
$877$	2.71377e13	1.54908	0.774542	+	0.632522i	$0.217980\pi$
$878$	3.69231e13	2.09688
$879$	−2.00127e13	−1.13072
$880$	3.76280e13	2.11514
$881$	−5.73268e12	−0.320602	−0.160301	−	0.987068i	$-0.551246\pi$
$881$	−5.73268e12	−0.320602	−0.160301	+	0.987068i	$0.551246\pi$
$882$	−5.75230e12	−0.320061
$883$	3.14591e13	1.74150	0.870750	−	0.491726i	$-0.163634\pi$
$883$	3.14591e13	1.74150	0.870750	+	0.491726i	$0.163634\pi$
$884$	−1.11382e13	−0.613453
$885$	−1.00911e13	−0.552959
$886$	4.59816e13	2.50688
$887$	2.79211e13	1.51453	0.757263	−	0.653110i	$-0.226536\pi$
$887$	2.79211e13	1.51453	0.757263	+	0.653110i	$0.226536\pi$
$888$	5.83870e13	3.15107
$889$	4.20838e13	2.25973
$890$	−3.89922e13	−2.08316
$891$	1.65641e13	0.880475
$892$	1.64015e13	0.867443
$893$	0	0
$894$	1.32660e13	0.694577
$895$	−4.73224e12	−0.246526
$896$	3.66543e13	1.89994
$897$	−2.98668e11	−0.0154036
$898$	−3.54733e13	−1.82037
$899$	3.66421e13	1.87095
$900$	−3.65230e12	−0.185556
$901$	−8.81798e12	−0.445767
$902$	5.34204e12	0.268706
$903$	1.33071e13	0.666021
$904$	5.11768e13	2.54868
$905$	1.94176e13	0.962227
$906$	−9.79185e12	−0.482823
$907$	−9.54271e12	−0.468208	−0.234104	−	0.972212i	$-0.575216\pi$
$907$	−9.54271e12	−0.468208	−0.234104	+	0.972212i	$0.575216\pi$
$908$	−1.89845e13	−0.926856
$909$	6.49557e11	0.0315559
$910$	1.47526e13	0.713152
$911$	−2.01303e13	−0.968315	−0.484158	−	0.874981i	$-0.660874\pi$
$911$	−2.01303e13	−0.968315	−0.484158	+	0.874981i	$0.660874\pi$
$912$	0	0
$913$	3.40346e13	1.62107
$914$	2.88391e13	1.36686
$915$	−4.60323e12	−0.217104
$916$	5.35765e13	2.51446
$917$	5.42578e13	2.53396
$918$	−5.47537e13	−2.54461
$919$	−2.20807e13	−1.02116	−0.510580	−	0.859830i	$-0.670569\pi$
$919$	−2.20807e13	−1.02116	−0.510580	+	0.859830i	$0.670569\pi$
$920$	−4.65922e12	−0.214421
$921$	2.17755e13	0.997242
$922$	6.10030e13	2.78011
$923$	5.90188e11	0.0267659
$924$	−7.11537e13	−3.21125
$925$	−2.18063e13	−0.979362
$926$	−2.73520e13	−1.22247
$927$	4.15967e12	0.185012
$928$	−1.93002e13	−0.854274
$929$	1.59561e12	0.0702840	0.0351420	−	0.999382i	$-0.488812\pi$
$929$	1.59561e12	0.0702840	0.0351420	+	0.999382i	$0.488812\pi$
$930$	−7.63001e13	−3.34466
$931$	0	0
$932$	−6.05980e13	−2.63079
$933$	−2.82003e13	−1.21839
$934$	−1.13701e13	−0.488880
$935$	−4.18486e13	−1.79072
$936$	−1.43773e12	−0.0612261
$937$	1.11135e13	0.471003	0.235502	−	0.971874i	$-0.424327\pi$
$937$	1.11135e13	0.471003	0.235502	+	0.971874i	$0.424327\pi$
$938$	−3.48543e13	−1.47009
$939$	4.36036e12	0.183032
$940$	−1.08378e14	−4.52760
$941$	2.43184e13	1.01107	0.505535	−	0.862806i	$-0.331295\pi$
$941$	2.43184e13	1.01107	0.505535	+	0.862806i	$0.331295\pi$
$942$	−1.66090e13	−0.687248
$943$	−2.78844e11	−0.0114831
$944$	−1.82532e13	−0.748110
$945$	4.97601e13	2.02973
$946$	−2.18166e13	−0.885680
$947$	−3.00100e12	−0.121252	−0.0606262	−	0.998161i	$-0.519310\pi$
$947$	−3.00100e12	−0.121252	−0.0606262	+	0.998161i	$0.519310\pi$
$948$	−1.39155e12	−0.0559579
$949$	6.06092e12	0.242572
$950$	0	0
$951$	2.66138e13	1.05510
$952$	1.09529e14	4.32177
$953$	−2.15171e13	−0.845017	−0.422509	−	0.906359i	$-0.638850\pi$
$953$	−2.15171e13	−0.845017	−0.422509	+	0.906359i	$0.638850\pi$
$954$	−2.09781e12	−0.0819970
$955$	−1.19076e12	−0.0463245
$956$	2.37186e13	0.918392
$957$	−2.96155e13	−1.14134
$958$	3.67136e13	1.40826
$959$	−2.24353e11	−0.00856540
$960$	−9.18399e12	−0.348988
$961$	4.05014e13	1.53184
$962$	−1.58208e13	−0.595580
$963$	2.20266e12	0.0825334
$964$	−5.36932e13	−2.00250
$965$	9.29927e12	0.345204
$966$	5.41296e12	0.200004
$967$	1.71091e13	0.629228	0.314614	−	0.949220i	$-0.398125\pi$
$967$	1.71091e13	0.629228	0.314614	+	0.949220i	$0.398125\pi$
$968$	5.45502e12	0.199691
$969$	0	0
$970$	−7.42070e13	−2.69136
$971$	1.22718e13	0.443020	0.221510	−	0.975158i	$-0.428902\pi$
$971$	1.22718e13	0.443020	0.221510	+	0.975158i	$0.428902\pi$
$972$	−1.67847e13	−0.603135
$973$	3.66268e13	1.31006
$974$	−7.88288e13	−2.80653
$975$	−3.32606e12	−0.117872
$976$	−8.32654e12	−0.293725
$977$	−1.53208e13	−0.537969	−0.268984	−	0.963145i	$-0.586688\pi$
$977$	−1.53208e13	−0.537969	−0.268984	+	0.963145i	$0.586688\pi$
$978$	−7.19545e13	−2.51497
$979$	−2.76493e13	−0.961970
$980$	−1.03343e14	−3.57902
$981$	−4.23403e12	−0.145963
$982$	−5.94917e13	−2.04153
$983$	5.63651e13	1.92539	0.962696	−	0.270584i	$-0.0872167\pi$
$983$	5.63651e13	1.92539	0.962696	+	0.270584i	$0.0872167\pi$
$984$	8.31452e12	0.282722
$985$	9.37881e12	0.317457
$986$	8.40205e13	2.83100
$987$	6.83170e13	2.29140
$988$	0	0
$989$	1.13878e12	0.0378492
$990$	−9.95583e12	−0.329396
$991$	4.55615e12	0.150061	0.0750304	−	0.997181i	$-0.476095\pi$
$991$	4.55615e12	0.150061	0.0750304	+	0.997181i	$0.476095\pi$
$992$	−3.52594e13	−1.15604
$993$	3.86827e13	1.26254
$994$	−1.06964e13	−0.347535
$995$	4.64346e13	1.50189
$996$	9.76306e13	3.14354
$997$	−3.02485e13	−0.969561	−0.484781	−	0.874636i	$-0.661101\pi$
$997$	−3.02485e13	−0.969561	−0.484781	+	0.874636i	$0.661101\pi$
$998$	−6.34717e13	−2.02531
$999$	−5.33630e13	−1.69510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.10.a.f.1.14		14
19.8	odd	6		19.10.c.a.7.14	✓	28
19.12	odd	6		19.10.c.a.11.14	yes	28
19.18	odd	2		361.10.a.e.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.14	✓	28	19.8	odd	6
19.10.c.a.11.14	yes	28	19.12	odd	6
361.10.a.e.1.1		14	19.18	odd	2
361.10.a.f.1.14		14	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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	361.a (trivial)

\(f(q)\)	\(=\)	\(q+40.3897 q^{2} -130.181 q^{3} +1119.32 q^{4} -1773.63 q^{5} -5257.96 q^{6} -9612.95 q^{7} +24529.6 q^{8} -2735.95 q^{9} -71636.1 q^{10} -50797.0 q^{11} -145715. q^{12} +21423.0 q^{13} -388264. q^{14} +230892. q^{15} +417648. q^{16} -464495. q^{17} -110504. q^{18} -1.98526e6 q^{20} +1.25142e6 q^{21} -2.05167e6 q^{22} +107093. q^{23} -3.19329e6 q^{24} +1.19262e6 q^{25} +865267. q^{26} +2.91852e6 q^{27} -1.07600e7 q^{28} -4.47852e6 q^{29} +9.32565e6 q^{30} -8.18175e6 q^{31} +4.30952e6 q^{32} +6.61279e6 q^{33} -1.87608e7 q^{34} +1.70498e7 q^{35} -3.06241e6 q^{36} -1.82843e7 q^{37} -2.78886e6 q^{39} -4.35063e7 q^{40} -2.60375e6 q^{41} +5.05445e7 q^{42} +1.06336e7 q^{43} -5.68583e7 q^{44} +4.85254e6 q^{45} +4.32545e6 q^{46} +5.45915e7 q^{47} -5.43698e7 q^{48} +5.20552e7 q^{49} +4.81696e7 q^{50} +6.04683e7 q^{51} +2.39793e7 q^{52} +1.89840e7 q^{53} +1.17878e8 q^{54} +9.00948e7 q^{55} -2.35802e8 q^{56} -1.80886e8 q^{58} -4.37047e7 q^{59} +2.58443e8 q^{60} -1.99367e7 q^{61} -3.30458e8 q^{62} +2.63005e7 q^{63} -3.97761e7 q^{64} -3.79963e7 q^{65} +2.67088e8 q^{66} +8.97698e7 q^{67} -5.19920e8 q^{68} -1.39415e7 q^{69} +6.88634e8 q^{70} +2.75493e7 q^{71} -6.71117e7 q^{72} +2.82917e8 q^{73} -7.38496e8 q^{74} -1.55257e8 q^{75} +4.88309e8 q^{77} -1.12641e8 q^{78} +9.54984e6 q^{79} -7.40752e8 q^{80} -3.26083e8 q^{81} -1.05165e8 q^{82} -6.70013e8 q^{83} +1.40075e9 q^{84} +8.23840e8 q^{85} +4.29486e8 q^{86} +5.83017e8 q^{87} -1.24603e9 q^{88} +5.44309e8 q^{89} +1.95993e8 q^{90} -2.05938e8 q^{91} +1.19872e8 q^{92} +1.06511e9 q^{93} +2.20493e9 q^{94} -5.61017e8 q^{96} +1.03589e9 q^{97} +2.10249e9 q^{98} +1.38978e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 15 q^{2} - 74 q^{3} + 2987 q^{4} + 285 q^{5} + 535 q^{6} - 1338 q^{7} + 12135 q^{8} + 57928 q^{9} + 41180 q^{10} - 57405 q^{11} - 117729 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} + 279203 q^{16}+ \cdots + 736622698 q^{99}+O(q^{100}) \) 14 * q + 15 * q^2 - 74 * q^3 + 2987 * q^4 + 285 * q^5 + 535 * q^6 - 1338 * q^7 + 12135 * q^8 + 57928 * q^9 + 41180 * q^10 - 57405 * q^11 - 117729 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 + 279203 * q^16 - 466251 * q^17 - 367482 * q^18 - 1671810 * q^20 + 689090 * q^21 - 1689395 * q^22 + 3087747 * q^23 + 234183 * q^24 + 3260823 * q^25 + 4516572 * q^26 - 2108270 * q^27 + 703814 * q^28 + 7831383 * q^29 - 5929612 * q^30 + 4632816 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 + 13222428 * q^35 - 7355018 * q^36 - 13602510 * q^37 - 10387851 * q^39 - 16500258 * q^40 + 20419440 * q^41 + 10220798 * q^42 - 27415427 * q^43 - 41775405 * q^44 - 42991294 * q^45 + 68617354 * q^46 + 90906681 * q^47 + 33057375 * q^48 + 114912446 * q^49 - 22203357 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 + 130507669 * q^54 + 157712310 * q^55 - 191229558 * q^56 - 172013024 * q^58 + 255540 * q^59 + 287916794 * q^60 - 304035459 * q^61 - 693626280 * q^62 + 122148024 * q^63 - 454245757 * q^64 + 712480095 * q^65 + 611099417 * q^66 + 165758480 * q^67 + 178759254 * q^68 - 135618639 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 + 602867050 * q^73 + 82104492 * q^74 - 950137387 * q^75 - 245997378 * q^77 - 911449840 * q^78 + 78162339 * q^79 - 227607150 * q^80 - 1230916118 * q^81 - 360208019 * q^82 + 206919963 * q^83 + 233652462 * q^84 + 1440537237 * q^85 + 936824310 * q^86 - 339438159 * q^87 + 823388847 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 + 677003592 * q^92 + 492493440 * q^93 + 424187592 * q^94 - 3020794465 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 + 736622698 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more