LMFDB - Embedded newform 11.8.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [11,8,Mod(1,11)] 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("11.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	11.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.43623528033$
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} - x^{3} - 341x^{2} + 1417x - 1412 $ x^4 - x^3 - 341x^2 + 1417x - 1412
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.64802$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+11.0598 q^{2} +59.6211 q^{3} -5.68000 q^{4} -60.1766 q^{5} +659.400 q^{6} +698.069 q^{7} -1478.48 q^{8} +1367.68 q^{9} -665.544 q^{10} -1331.00 q^{11} -338.648 q^{12} -10970.2 q^{13} +7720.53 q^{14} -3587.80 q^{15} -15624.7 q^{16} -1820.14 q^{17} +15126.3 q^{18} +49614.4 q^{19} +341.803 q^{20} +41619.7 q^{21} -14720.6 q^{22} +80659.2 q^{23} -88148.6 q^{24} -74503.8 q^{25} -121329. q^{26} -48848.8 q^{27} -3965.03 q^{28} +88686.8 q^{29} -39680.5 q^{30} +176260. q^{31} +16438.7 q^{32} -79355.7 q^{33} -20130.5 q^{34} -42007.4 q^{35} -7768.43 q^{36} +106270. q^{37} +548728. q^{38} -654056. q^{39} +88969.9 q^{40} -464715. q^{41} +460307. q^{42} +837231. q^{43} +7560.08 q^{44} -82302.4 q^{45} +892077. q^{46} -679973. q^{47} -931562. q^{48} -336243. q^{49} -824000. q^{50} -108519. q^{51} +62310.8 q^{52} -177071. q^{53} -540259. q^{54} +80095.1 q^{55} -1.03208e6 q^{56} +2.95807e6 q^{57} +980861. q^{58} -2.54327e6 q^{59} +20378.7 q^{60} -23420.1 q^{61} +1.94941e6 q^{62} +954735. q^{63} +2.18177e6 q^{64} +660150. q^{65} -877662. q^{66} -1.88677e6 q^{67} +10338.4 q^{68} +4.80899e6 q^{69} -464595. q^{70} -4.49270e6 q^{71} -2.02209e6 q^{72} +3.15445e6 q^{73} +1.17533e6 q^{74} -4.44200e6 q^{75} -281810. q^{76} -929130. q^{77} -7.23375e6 q^{78} +4.45391e6 q^{79} +940241. q^{80} -5.90354e6 q^{81} -5.13968e6 q^{82} +2.74298e6 q^{83} -236400. q^{84} +109530. q^{85} +9.25964e6 q^{86} +5.28761e6 q^{87} +1.96786e6 q^{88} +1.10880e7 q^{89} -910251. q^{90} -7.65796e6 q^{91} -458144. q^{92} +1.05088e7 q^{93} -7.52039e6 q^{94} -2.98563e6 q^{95} +980095. q^{96} -3.95601e6 q^{97} -3.71879e6 q^{98} -1.82038e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 35 q^{3} + 604 q^{4} + 537 q^{5} + 1558 q^{6} + 170 q^{7} - 420 q^{8} + 1823 q^{9} + 1470 q^{10} - 5324 q^{11} - 34360 q^{12} + 4250 q^{13} - 29988 q^{14} + 6841 q^{15} + 52744 q^{16} + 54300 q^{17}+ \cdots - 2426413 q^{99}+O(q^{100}) $ 4 * q - 35 * q^3 + 604 * q^4 + 537 * q^5 + 1558 * q^6 + 170 * q^7 - 420 * q^8 + 1823 * q^9 + 1470 * q^10 - 5324 * q^11 - 34360 * q^12 + 4250 * q^13 - 29988 * q^14 + 6841 * q^15 + 52744 * q^16 + 54300 * q^17 - 71350 * q^18 + 67844 * q^19 + 15888 * q^20 + 102262 * q^21 - 9015 * q^23 + 140844 * q^24 + 22531 * q^25 - 311700 * q^26 - 123005 * q^27 - 475840 * q^28 + 234078 * q^29 - 470786 * q^30 + 189857 * q^31 - 175560 * q^32 + 46585 * q^33 + 406536 * q^34 + 154098 * q^35 + 847780 * q^36 + 127895 * q^37 - 584760 * q^38 - 1010660 * q^39 + 2249268 * q^40 + 289842 * q^41 + 1046980 * q^42 + 704930 * q^43 - 803924 * q^44 - 1946752 * q^45 + 3519102 * q^46 - 1729080 * q^47 - 5738680 * q^48 + 139920 * q^49 - 2115918 * q^50 - 2047658 * q^51 + 2030120 * q^52 + 1098660 * q^53 + 4819690 * q^54 - 714747 * q^55 - 4311720 * q^56 + 1566240 * q^57 + 1046100 * q^58 - 4665777 * q^59 + 1373432 * q^60 + 310610 * q^61 + 4286670 * q^62 + 482900 * q^63 + 9539488 * q^64 + 4526160 * q^65 - 2073698 * q^66 - 3368245 * q^67 + 14958120 * q^68 + 7154939 * q^69 - 12580596 * q^70 - 3416541 * q^71 - 25536720 * q^72 + 11466230 * q^73 - 16581438 * q^74 + 3217760 * q^75 + 2169824 * q^76 - 226270 * q^77 + 242200 * q^78 + 566282 * q^79 - 4469544 * q^80 - 862228 * q^81 - 11151780 * q^82 - 4220790 * q^83 + 14471168 * q^84 + 10312902 * q^85 - 5991972 * q^86 - 16784760 * q^87 + 559020 * q^88 + 18265191 * q^89 + 15233552 * q^90 - 1133480 * q^91 - 6399240 * q^92 + 13247755 * q^93 + 8464656 * q^94 - 5662968 * q^95 + 26225096 * q^96 + 11425325 * q^97 + 36460200 * q^98 - 2426413 * 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 $

$2$	11.0598	0.977561	0.488780	−	0.872407i	$-0.337442\pi$
$2$	11.0598	0.977561	0.488780	+	0.872407i	$0.337442\pi$
$3$	59.6211	1.27490	0.637450	−	0.770492i	$-0.279989\pi$
$3$	59.6211	1.27490	0.637450	+	0.770492i	$0.279989\pi$
$4$	−5.68000	−0.0443750
$5$	−60.1766	−0.215294	−0.107647	−	0.994189i	$-0.534332\pi$
$5$	−60.1766	−0.215294	−0.107647	+	0.994189i	$0.534332\pi$
$6$	659.400	1.24629
$7$	698.069	0.769228	0.384614	−	0.923077i	$-0.374335\pi$
$7$	698.069	0.769228	0.384614	+	0.923077i	$0.374335\pi$
$8$	−1478.48	−1.02094
$9$	1367.68	0.625368
$10$	−665.544	−0.210463
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	−338.648	−0.0565737
$13$	−10970.2	−1.38488	−0.692441	−	0.721474i	$-0.743465\pi$
$13$	−10970.2	−1.38488	−0.692441	+	0.721474i	$0.743465\pi$
$14$	7720.53	0.751967
$15$	−3587.80	−0.274479
$16$	−15624.7	−0.953656
$17$	−1820.14	−0.0898533	−0.0449266	−	0.998990i	$-0.514305\pi$
$17$	−1820.14	−0.0898533	−0.0449266	+	0.998990i	$0.514305\pi$
$18$	15126.3	0.611335
$19$	49614.4	1.65947	0.829737	−	0.558154i	$-0.188490\pi$
$19$	49614.4	1.65947	0.829737	+	0.558154i	$0.188490\pi$
$20$	341.803	0.00955369
$21$	41619.7	0.980688
$22$	−14720.6	−0.294746
$23$	80659.2	1.38231	0.691157	−	0.722705i	$-0.257102\pi$
$23$	80659.2	1.38231	0.691157	+	0.722705i	$0.257102\pi$
$24$	−88148.6	−1.30160
$25$	−74503.8	−0.953648
$26$	−121329.	−1.35381
$27$	−48848.8	−0.477618
$28$	−3965.03	−0.0341345
$29$	88686.8	0.675252	0.337626	−	0.941280i	$-0.390376\pi$
$29$	88686.8	0.675252	0.337626	+	0.941280i	$0.390376\pi$
$30$	−39680.5	−0.268320
$31$	176260.	1.06265	0.531323	−	0.847170i	$-0.321695\pi$
$31$	176260.	1.06265	0.531323	+	0.847170i	$0.321695\pi$
$32$	16438.7	0.0886835
$33$	−79355.7	−0.384397
$34$	−20130.5	−0.0878370
$35$	−42007.4	−0.165611
$36$	−7768.43	−0.0277507
$37$	106270.	0.344909	0.172454	−	0.985017i	$-0.444830\pi$
$37$	106270.	0.344909	0.172454	+	0.985017i	$0.444830\pi$
$38$	548728.	1.62224
$39$	−654056.	−1.76559
$40$	88969.9	0.219803
$41$	−464715.	−1.05304	−0.526519	−	0.850164i	$-0.676503\pi$
$41$	−464715.	−1.05304	−0.526519	+	0.850164i	$0.676503\pi$
$42$	460307.	0.958683
$43$	837231.	1.60585	0.802927	−	0.596078i	$-0.203275\pi$
$43$	837231.	1.60585	0.802927	+	0.596078i	$0.203275\pi$
$44$	7560.08	0.0133796
$45$	−82302.4	−0.134638
$46$	892077.	1.35129
$47$	−679973.	−0.955321	−0.477661	−	0.878544i	$-0.658515\pi$
$47$	−679973.	−0.955321	−0.477661	+	0.878544i	$0.658515\pi$
$48$	−931562.	−1.21582
$49$	−336243.	−0.408288
$50$	−824000.	−0.932249
$51$	−108519.	−0.114554
$52$	62310.8	0.0614542
$53$	−177071.	−0.163374	−0.0816868	−	0.996658i	$-0.526031\pi$
$53$	−177071.	−0.163374	−0.0816868	+	0.996658i	$0.526031\pi$
$54$	−540259.	−0.466900
$55$	80095.1	0.0649137
$56$	−1.03208e6	−0.785336
$57$	2.95807e6	2.11566
$58$	980861.	0.660100
$59$	−2.54327e6	−1.61217	−0.806083	−	0.591803i	$-0.798417\pi$
$59$	−2.54327e6	−1.61217	−0.806083	+	0.591803i	$0.798417\pi$
$60$	20378.7	0.0121800
$61$	−23420.1	−0.0132110	−0.00660548	−	0.999978i	$-0.502103\pi$
$61$	−23420.1	−0.0132110	−0.00660548	+	0.999978i	$0.502103\pi$
$62$	1.94941e6	1.03880
$63$	954735.	0.481051
$64$	2.18177e6	1.04035
$65$	660150.	0.298158
$66$	−877662.	−0.375771
$67$	−1.88677e6	−0.766404	−0.383202	−	0.923665i	$-0.625179\pi$
$67$	−1.88677e6	−0.766404	−0.383202	+	0.923665i	$0.625179\pi$
$68$	10338.4	0.00398724
$69$	4.80899e6	1.76231
$70$	−464595.	−0.161894
$71$	−4.49270e6	−1.48971	−0.744857	−	0.667224i	$-0.767483\pi$
$71$	−4.49270e6	−1.48971	−0.744857	+	0.667224i	$0.767483\pi$
$72$	−2.02209e6	−0.638463
$73$	3.15445e6	0.949058	0.474529	−	0.880240i	$-0.342618\pi$
$73$	3.15445e6	0.949058	0.474529	+	0.880240i	$0.342618\pi$
$74$	1.17533e6	0.337169
$75$	−4.44200e6	−1.21581
$76$	−281810.	−0.0736392
$77$	−929130.	−0.231931
$78$	−7.23375e6	−1.72597
$79$	4.45391e6	1.01636	0.508178	−	0.861252i	$-0.330319\pi$
$79$	4.45391e6	1.01636	0.508178	+	0.861252i	$0.330319\pi$
$80$	940241.	0.205317
$81$	−5.90354e6	−1.23428
$82$	−5.13968e6	−1.02941
$83$	2.74298e6	0.526562	0.263281	−	0.964719i	$-0.415195\pi$
$83$	2.74298e6	0.526562	0.263281	+	0.964719i	$0.415195\pi$
$84$	−236400.	−0.0435181
$85$	109530.	0.0193449
$86$	9.25964e6	1.56982
$87$	5.28761e6	0.860878
$88$	1.96786e6	0.307825
$89$	1.10880e7	1.66721	0.833603	−	0.552365i	$-0.186274\pi$
$89$	1.10880e7	1.66721	0.833603	+	0.552365i	$0.186274\pi$
$90$	−910251.	−0.131617
$91$	−7.65796e6	−1.06529
$92$	−458144.	−0.0613402
$93$	1.05088e7	1.35477
$94$	−7.52039e6	−0.933884
$95$	−2.98563e6	−0.357276
$96$	980095.	0.113063
$97$	−3.95601e6	−0.440105	−0.220053	−	0.975488i	$-0.570623\pi$
$97$	−3.95601e6	−0.440105	−0.220053	+	0.975488i	$0.570623\pi$
$98$	−3.71879e6	−0.399126
$99$	−1.82038e6	−0.188556
$100$	423182.	0.0423182
$101$	−818011.	−0.0790013	−0.0395007	−	0.999220i	$-0.512577\pi$
$101$	−818011.	−0.0790013	−0.0395007	+	0.999220i	$0.512577\pi$
$102$	−1.20020e6	−0.111983
$103$	750708.	0.0676925	0.0338463	−	0.999427i	$-0.489224\pi$
$103$	750708.	0.0676925	0.0338463	+	0.999427i	$0.489224\pi$
$104$	1.62192e7	1.41388
$105$	−2.50453e6	−0.211137
$106$	−1.95838e6	−0.159708
$107$	−9.70597e6	−0.765942	−0.382971	−	0.923760i	$-0.625099\pi$
$107$	−9.70597e6	−0.765942	−0.382971	+	0.923760i	$0.625099\pi$
$108$	277461.	0.0211943
$109$	65223.6	0.00482406	0.00241203	−	0.999997i	$-0.499232\pi$
$109$	65223.6	0.00482406	0.00241203	+	0.999997i	$0.499232\pi$
$110$	885839.	0.0634571
$111$	6.33594e6	0.439724
$112$	−1.09071e7	−0.733579
$113$	−1.58160e7	−1.03115	−0.515574	−	0.856845i	$-0.672421\pi$
$113$	−1.58160e7	−1.03115	−0.515574	+	0.856845i	$0.672421\pi$
$114$	3.27158e7	2.06819
$115$	−4.85380e6	−0.297604
$116$	−503741.	−0.0299643
$117$	−1.50037e7	−0.866062
$118$	−2.81281e7	−1.57599
$119$	−1.27058e6	−0.0691177
$120$	5.30449e6	0.280226
$121$	1.77156e6	0.0909091
$122$	−259023.	−0.0129145
$123$	−2.77069e7	−1.34252
$124$	−1.00116e6	−0.0471549
$125$	9.18468e6	0.420610
$126$	1.05592e7	0.470256
$127$	2.14149e7	0.927690	0.463845	−	0.885916i	$-0.346469\pi$
$127$	2.14149e7	0.927690	0.463845	+	0.885916i	$0.346469\pi$
$128$	2.20259e7	0.928321
$129$	4.99167e7	2.04730
$130$	7.30115e6	0.291467
$131$	−5.41196e6	−0.210332	−0.105166	−	0.994455i	$-0.533537\pi$
$131$	−5.41196e6	−0.210332	−0.105166	+	0.994455i	$0.533537\pi$
$132$	450741.	0.0170576
$133$	3.46343e7	1.27651
$134$	−2.08674e7	−0.749206
$135$	2.93955e6	0.102828
$136$	2.69104e6	0.0917348
$137$	−4.18596e7	−1.39083	−0.695413	−	0.718610i	$-0.744779\pi$
$137$	−4.18596e7	−1.39083	−0.695413	+	0.718610i	$0.744779\pi$
$138$	5.31867e7	1.72276
$139$	−2.86132e7	−0.903681	−0.451840	−	0.892099i	$-0.649232\pi$
$139$	−2.86132e7	−0.903681	−0.451840	+	0.892099i	$0.649232\pi$
$140$	238602.	0.00734897
$141$	−4.05408e7	−1.21794
$142$	−4.96885e7	−1.45629
$143$	1.46013e7	0.417558
$144$	−2.13696e7	−0.596386
$145$	−5.33687e6	−0.145378
$146$	3.48877e7	0.927762
$147$	−2.00472e7	−0.520526
$148$	−603614.	−0.0153053
$149$	4.55561e6	0.112822	0.0564111	−	0.998408i	$-0.482034\pi$
$149$	4.55561e6	0.112822	0.0564111	+	0.998408i	$0.482034\pi$
$150$	−4.91278e7	−1.18852
$151$	5.18767e7	1.22618	0.613089	−	0.790014i	$-0.289927\pi$
$151$	5.18767e7	1.22618	0.613089	+	0.790014i	$0.289927\pi$
$152$	−7.33539e7	−1.69422
$153$	−2.48937e6	−0.0561914
$154$	−1.02760e7	−0.226727
$155$	−1.06067e7	−0.228782
$156$	3.71504e6	0.0783479
$157$	5.01985e7	1.03524	0.517621	−	0.855610i	$-0.326818\pi$
$157$	5.01985e7	1.03524	0.517621	+	0.855610i	$0.326818\pi$
$158$	4.92595e7	0.993551
$159$	−1.05572e7	−0.208285
$160$	−989226.	−0.0190931
$161$	5.63057e7	1.06331
$162$	−6.52922e7	−1.20659
$163$	3.13082e7	0.566242	0.283121	−	0.959084i	$-0.408630\pi$
$163$	3.13082e7	0.566242	0.283121	+	0.959084i	$0.408630\pi$
$164$	2.63958e6	0.0467285
$165$	4.77536e6	0.0827584
$166$	3.03369e7	0.514747
$167$	3.30269e6	0.0548731	0.0274366	−	0.999624i	$-0.491266\pi$
$167$	3.30269e6	0.0548731	0.0274366	+	0.999624i	$0.491266\pi$
$168$	−6.15338e7	−1.00122
$169$	5.75969e7	0.917901
$170$	1.21138e6	0.0189108
$171$	6.78567e7	1.03778
$172$	−4.75547e6	−0.0712598
$173$	1.76609e7	0.259329	0.129664	−	0.991558i	$-0.458610\pi$
$173$	1.76609e7	0.259329	0.129664	+	0.991558i	$0.458610\pi$
$174$	5.84801e7	0.841561
$175$	−5.20088e7	−0.733573
$176$	2.07965e7	0.287538
$177$	−1.51632e8	−2.05535
$178$	1.22632e8	1.62979
$179$	2.48730e7	0.324148	0.162074	−	0.986779i	$-0.448182\pi$
$179$	2.48730e7	0.324148	0.162074	+	0.986779i	$0.448182\pi$
$180$	467478.	0.00597458
$181$	−1.60151e6	−0.0200749	−0.0100374	−	0.999950i	$-0.503195\pi$
$181$	−1.60151e6	−0.0200749	−0.0100374	+	0.999950i	$0.503195\pi$
$182$	−8.46958e7	−1.04139
$183$	−1.39633e6	−0.0168427
$184$	−1.19253e8	−1.41126
$185$	−6.39497e6	−0.0742570
$186$	1.16226e8	1.32437
$187$	2.42261e6	0.0270918
$188$	3.86225e6	0.0423924
$189$	−3.40998e7	−0.367397
$190$	−3.30206e7	−0.349259
$191$	−1.34327e8	−1.39491	−0.697454	−	0.716630i	$-0.745684\pi$
$191$	−1.34327e8	−1.39491	−0.697454	+	0.716630i	$0.745684\pi$
$192$	1.30080e8	1.32634
$193$	−1.67372e8	−1.67584	−0.837919	−	0.545795i	$-0.816228\pi$
$193$	−1.67372e8	−1.67584	−0.837919	+	0.545795i	$0.816228\pi$
$194$	−4.37529e7	−0.430230
$195$	3.93589e7	0.380121
$196$	1.90986e6	0.0181178
$197$	−8.17612e7	−0.761930	−0.380965	−	0.924589i	$-0.624408\pi$
$197$	−8.17612e7	−0.761930	−0.380965	+	0.924589i	$0.624408\pi$
$198$	−2.01331e7	−0.184325
$199$	2.04375e8	1.83841	0.919206	−	0.393778i	$-0.128832\pi$
$199$	2.04375e8	1.83841	0.919206	+	0.393778i	$0.128832\pi$
$200$	1.10152e8	0.973618
$201$	−1.12492e8	−0.977088
$202$	−9.04707e6	−0.0772286
$203$	6.19095e7	0.519423
$204$	616387.	0.00508333
$205$	2.79650e7	0.226713
$206$	8.30271e6	0.0661735
$207$	1.10316e8	0.864455
$208$	1.71406e8	1.32070
$209$	−6.60368e7	−0.500350
$210$	−2.76997e7	−0.206399
$211$	−1.14120e8	−0.836319	−0.418159	−	0.908374i	$-0.637325\pi$
$211$	−1.14120e8	−0.836319	−0.418159	+	0.908374i	$0.637325\pi$
$212$	1.00576e6	0.00724970
$213$	−2.67860e8	−1.89924
$214$	−1.07346e8	−0.748754
$215$	−5.03817e7	−0.345731
$216$	7.22219e7	0.487619
$217$	1.23042e8	0.817417
$218$	721363.	0.00471581
$219$	1.88072e8	1.20995
$220$	−454940.	−0.00288055
$221$	1.99673e7	0.124436
$222$	7.00744e7	0.429857
$223$	2.10742e8	1.27258	0.636288	−	0.771452i	$-0.280469\pi$
$223$	2.10742e8	1.27258	0.636288	+	0.771452i	$0.280469\pi$
$224$	1.14754e7	0.0682178
$225$	−1.01897e8	−0.596381
$226$	−1.74922e8	−1.00801
$227$	2.75513e8	1.56334	0.781668	−	0.623695i	$-0.214369\pi$
$227$	2.75513e8	1.56334	0.781668	+	0.623695i	$0.214369\pi$
$228$	−1.68018e7	−0.0938826
$229$	2.46934e8	1.35880	0.679402	−	0.733767i	$-0.262239\pi$
$229$	2.46934e8	1.35880	0.679402	+	0.733767i	$0.262239\pi$
$230$	−5.36822e7	−0.290926
$231$	−5.53958e7	−0.295689
$232$	−1.31122e8	−0.689392
$233$	−1.43817e8	−0.744841	−0.372421	−	0.928064i	$-0.621472\pi$
$233$	−1.43817e8	−0.744841	−0.372421	+	0.928064i	$0.621472\pi$
$234$	−1.65939e8	−0.846628
$235$	4.09185e7	0.205675
$236$	1.44458e7	0.0715399
$237$	2.65547e8	1.29575
$238$	−1.40525e7	−0.0675667
$239$	−1.04920e8	−0.497123	−0.248561	−	0.968616i	$-0.579958\pi$
$239$	−1.04920e8	−0.497123	−0.248561	+	0.968616i	$0.579958\pi$
$240$	5.60583e7	0.261758
$241$	−7.87388e7	−0.362351	−0.181175	−	0.983451i	$-0.557990\pi$
$241$	−7.87388e7	−0.362351	−0.181175	+	0.983451i	$0.557990\pi$
$242$	1.95932e7	0.0888692
$243$	−2.45143e8	−1.09597
$244$	133026.	0.000586237 0
$245$	2.02339e7	0.0879021
$246$	−3.06433e8	−1.31239
$247$	−5.44281e8	−2.29818
$248$	−2.60597e8	−1.08490
$249$	1.63540e8	0.671314
$250$	1.01581e8	0.411171
$251$	−1.47720e8	−0.589634	−0.294817	−	0.955554i	$-0.595259\pi$
$251$	−1.47720e8	−0.589634	−0.294817	+	0.955554i	$0.595259\pi$
$252$	−5.42290e6	−0.0213466
$253$	−1.07357e8	−0.416783
$254$	2.36845e8	0.906873
$255$	6.53030e6	0.0246628
$256$	−3.56641e7	−0.132859
$257$	1.68032e8	0.617484	0.308742	−	0.951146i	$-0.400092\pi$
$257$	1.68032e8	0.617484	0.308742	+	0.951146i	$0.400092\pi$
$258$	5.52070e8	2.00136
$259$	7.41838e7	0.265314
$260$	−3.74965e6	−0.0132307
$261$	1.21295e8	0.422281
$262$	−5.98554e7	−0.205612
$263$	2.11675e8	0.717503	0.358751	−	0.933433i	$-0.383203\pi$
$263$	2.11675e8	0.717503	0.358751	+	0.933433i	$0.383203\pi$
$264$	1.17326e8	0.392446
$265$	1.06555e7	0.0351734
$266$	3.83050e8	1.24787
$267$	6.61081e8	2.12552
$268$	1.07169e7	0.0340092
$269$	9.94546e7	0.311524	0.155762	−	0.987795i	$-0.450217\pi$
$269$	9.94546e7	0.311524	0.155762	+	0.987795i	$0.450217\pi$
$270$	3.25110e7	0.100521
$271$	−5.89823e8	−1.80023	−0.900117	−	0.435648i	$-0.856519\pi$
$271$	−5.89823e8	−1.80023	−0.900117	+	0.435648i	$0.856519\pi$
$272$	2.84392e7	0.0856891
$273$	−4.56576e8	−1.35814
$274$	−4.62960e8	−1.35962
$275$	9.91645e7	0.287536
$276$	−2.73151e7	−0.0782025
$277$	5.73183e8	1.62037	0.810185	−	0.586174i	$-0.199367\pi$
$277$	5.73183e8	1.62037	0.810185	+	0.586174i	$0.199367\pi$
$278$	−3.16458e8	−0.883403
$279$	2.41068e8	0.664545
$280$	6.21071e7	0.169078
$281$	2.95626e8	0.794824	0.397412	−	0.917640i	$-0.369908\pi$
$281$	2.95626e8	0.794824	0.397412	+	0.917640i	$0.369908\pi$
$282$	−4.48375e8	−1.19061
$283$	−3.02985e8	−0.794636	−0.397318	−	0.917681i	$-0.630059\pi$
$283$	−3.02985e8	−0.794636	−0.397318	+	0.917681i	$0.630059\pi$
$284$	2.55185e7	0.0661061
$285$	−1.78007e8	−0.455490
$286$	1.61488e8	0.408188
$287$	−3.24403e8	−0.810026
$288$	2.24829e7	0.0554598
$289$	−4.07026e8	−0.991926
$290$	−5.90249e7	−0.142116
$291$	−2.35862e8	−0.561090
$292$	−1.79173e7	−0.0421145
$293$	7.64795e8	1.77627	0.888133	−	0.459586i	$-0.152002\pi$
$293$	7.64795e8	1.77627	0.888133	+	0.459586i	$0.152002\pi$
$294$	−2.21718e8	−0.508846
$295$	1.53045e8	0.347090
$296$	−1.57118e8	−0.352131
$297$	6.50177e7	0.144007
$298$	5.03843e7	0.110291
$299$	−8.84848e8	−1.91434
$300$	2.52306e7	0.0539514
$301$	5.84445e8	1.23527
$302$	5.73748e8	1.19866
$303$	−4.87708e7	−0.100719
$304$	−7.75211e8	−1.58257
$305$	1.40934e6	0.00284425
$306$	−2.75320e7	−0.0549305
$307$	2.50216e8	0.493550	0.246775	−	0.969073i	$-0.420629\pi$
$307$	2.50216e8	0.493550	0.246775	+	0.969073i	$0.420629\pi$
$308$	5.27746e6	0.0102919
$309$	4.47581e7	0.0863011
$310$	−1.17309e8	−0.223648
$311$	−1.10731e8	−0.208741	−0.104370	−	0.994538i	$-0.533283\pi$
$311$	−1.10731e8	−0.208741	−0.104370	+	0.994538i	$0.533283\pi$
$312$	9.67008e8	1.80256
$313$	−5.21969e8	−0.962143	−0.481071	−	0.876681i	$-0.659752\pi$
$313$	−5.21969e8	−0.962143	−0.481071	+	0.876681i	$0.659752\pi$
$314$	5.55187e8	1.01201
$315$	−5.74527e7	−0.103568
$316$	−2.52982e7	−0.0451008
$317$	−6.18490e8	−1.09050	−0.545250	−	0.838274i	$-0.683565\pi$
$317$	−6.18490e8	−1.09050	−0.545250	+	0.838274i	$0.683565\pi$
$318$	−1.16761e8	−0.203611
$319$	−1.18042e8	−0.203596
$320$	−1.31292e8	−0.223981
$321$	−5.78681e8	−0.976498
$322$	6.22732e8	1.03945
$323$	−9.03053e7	−0.149109
$324$	3.35321e7	0.0547713
$325$	8.17322e8	1.32069
$326$	3.46264e8	0.553535
$327$	3.88871e6	0.00615019
$328$	6.87072e8	1.07509
$329$	−4.74668e8	−0.734860
$330$	5.28147e7	0.0809014
$331$	9.84142e8	1.49163	0.745813	−	0.666156i	$-0.232061\pi$
$331$	9.84142e8	1.49163	0.745813	+	0.666156i	$0.232061\pi$
$332$	−1.55801e7	−0.0233662
$333$	1.45343e8	0.215695
$334$	3.65272e7	0.0536418
$335$	1.13540e8	0.165002
$336$	−6.50295e8	−0.935239
$337$	8.42573e6	0.0119923	0.00599616	−	0.999982i	$-0.498091\pi$
$337$	8.42573e6	0.0119923	0.00599616	+	0.999982i	$0.498091\pi$
$338$	6.37012e8	0.897303
$339$	−9.42966e8	−1.31461
$340$	−622130.	−0.000858430 0
$341$	−2.34602e8	−0.320400
$342$	7.50484e8	1.01450
$343$	−8.09610e8	−1.08329
$344$	−1.23783e9	−1.63948
$345$	−2.89389e8	−0.379415
$346$	1.95326e8	0.253509
$347$	3.48322e8	0.447536	0.223768	−	0.974642i	$-0.428164\pi$
$347$	3.48322e8	0.447536	0.223768	+	0.974642i	$0.428164\pi$
$348$	−3.00336e7	−0.0382015
$349$	7.40547e8	0.932532	0.466266	−	0.884645i	$-0.345599\pi$
$349$	7.40547e8	0.932532	0.466266	+	0.884645i	$0.345599\pi$
$350$	−5.75209e8	−0.717112
$351$	5.35881e8	0.661445
$352$	−2.18799e7	−0.0267391
$353$	2.96936e8	0.359295	0.179647	−	0.983731i	$-0.442504\pi$
$353$	2.96936e8	0.359295	0.179647	+	0.983731i	$0.442504\pi$
$354$	−1.67703e9	−2.00923
$355$	2.70355e8	0.320727
$356$	−6.29800e7	−0.0739823
$357$	−7.57537e7	−0.0881181
$358$	2.75092e8	0.316874
$359$	−4.98228e8	−0.568326	−0.284163	−	0.958776i	$-0.591716\pi$
$359$	−4.98228e8	−0.568326	−0.284163	+	0.958776i	$0.591716\pi$
$360$	1.21682e8	0.137458
$361$	1.56772e9	1.75386
$362$	−1.77124e7	−0.0196244
$363$	1.05622e8	0.115900
$364$	4.34972e7	0.0472723
$365$	−1.89824e8	−0.204327
$366$	−1.54432e7	−0.0164647
$367$	−1.05029e9	−1.10911	−0.554557	−	0.832146i	$-0.687112\pi$
$367$	−1.05029e9	−1.10911	−0.554557	+	0.832146i	$0.687112\pi$
$368$	−1.26028e9	−1.31825
$369$	−6.35582e8	−0.658536
$370$	−7.07273e7	−0.0725907
$371$	−1.23608e8	−0.125672
$372$	−5.96902e7	−0.0601177
$373$	−2.53790e8	−0.253217	−0.126609	−	0.991953i	$-0.540409\pi$
$373$	−2.53790e8	−0.253217	−0.126609	+	0.991953i	$0.540409\pi$
$374$	2.67936e7	0.0264839
$375$	5.47601e8	0.536235
$376$	1.00533e9	0.975326
$377$	−9.72912e8	−0.935145
$378$	−3.77138e8	−0.359153
$379$	9.42700e8	0.889480	0.444740	−	0.895660i	$-0.353296\pi$
$379$	9.42700e8	0.889480	0.444740	+	0.895660i	$0.353296\pi$
$380$	1.69584e7	0.0158541
$381$	1.27678e9	1.18271
$382$	−1.48563e9	−1.36361
$383$	9.93096e8	0.903224	0.451612	−	0.892214i	$-0.350849\pi$
$383$	9.93096e8	0.903224	0.451612	+	0.892214i	$0.350849\pi$
$384$	1.31321e9	1.18352
$385$	5.59119e7	0.0499335
$386$	−1.85111e9	−1.63823
$387$	1.14506e9	1.00425
$388$	2.24702e7	0.0195297
$389$	1.85245e9	1.59559	0.797797	−	0.602926i	$-0.205998\pi$
$389$	1.85245e9	1.59559	0.797797	+	0.602926i	$0.205998\pi$
$390$	4.35303e8	0.371591
$391$	−1.46811e8	−0.124205
$392$	4.97128e8	0.416838
$393$	−3.22667e8	−0.268152
$394$	−9.04265e8	−0.744833
$395$	−2.68021e8	−0.218816
$396$	1.03398e7	0.00836716
$397$	−9.21943e8	−0.739499	−0.369749	−	0.929132i	$-0.620556\pi$
$397$	−9.21943e8	−0.739499	−0.369749	+	0.929132i	$0.620556\pi$
$398$	2.26036e9	1.79716
$399$	2.06494e9	1.62743
$400$	1.16410e9	0.909452
$401$	8.72543e8	0.675743	0.337872	−	0.941192i	$-0.390293\pi$
$401$	8.72543e8	0.675743	0.337872	+	0.941192i	$0.390293\pi$
$402$	−1.24414e9	−0.955163
$403$	−1.93361e9	−1.47164
$404$	4.64631e6	0.00350569
$405$	3.55255e8	0.265734
$406$	6.84709e8	0.507767
$407$	−1.41445e8	−0.103994
$408$	1.60443e8	0.116953
$409$	3.83123e8	0.276890	0.138445	−	0.990370i	$-0.455790\pi$
$409$	3.83123e8	0.276890	0.138445	+	0.990370i	$0.455790\pi$
$410$	3.09288e8	0.221626
$411$	−2.49572e9	−1.77316
$412$	−4.26402e6	−0.00300386
$413$	−1.77538e9	−1.24012
$414$	1.22008e9	0.845057
$415$	−1.65063e8	−0.113366
$416$	−1.80336e8	−0.122816
$417$	−1.70595e9	−1.15210
$418$	−7.30357e8	−0.489123
$419$	−1.25662e9	−0.834552	−0.417276	−	0.908780i	$-0.637015\pi$
$419$	−1.25662e9	−0.834552	−0.417276	+	0.908780i	$0.637015\pi$
$420$	1.42257e7	0.00936920
$421$	−1.19966e9	−0.783560	−0.391780	−	0.920059i	$-0.628141\pi$
$421$	−1.19966e9	−0.783560	−0.391780	+	0.920059i	$0.628141\pi$
$422$	−1.26214e9	−0.817552
$423$	−9.29986e8	−0.597427
$424$	2.61796e8	0.166795
$425$	1.35607e8	0.0856884
$426$	−2.96249e9	−1.85662
$427$	−1.63489e7	−0.0101622
$428$	5.51299e7	0.0339887
$429$	8.70549e8	0.532344
$430$	−5.57214e8	−0.337973
$431$	3.22074e9	1.93770	0.968848	−	0.247655i	$-0.0796600\pi$
$431$	3.22074e9	1.93770	0.968848	+	0.247655i	$0.0796600\pi$
$432$	7.63247e8	0.455483
$433$	−2.53616e9	−1.50130	−0.750652	−	0.660697i	$-0.770261\pi$
$433$	−2.53616e9	−1.50130	−0.750652	+	0.660697i	$0.770261\pi$
$434$	1.36082e9	0.799074
$435$	−3.18190e8	−0.185342
$436$	−370470.	−0.000214068 0
$437$	4.00186e9	2.29391
$438$	2.08004e9	1.18280
$439$	1.18782e9	0.670079	0.335039	−	0.942204i	$-0.391250\pi$
$439$	1.18782e9	0.670079	0.335039	+	0.942204i	$0.391250\pi$
$440$	−1.18419e8	−0.0662730
$441$	−4.59873e8	−0.255330
$442$	2.20835e8	0.121644
$443$	−9.76489e8	−0.533647	−0.266824	−	0.963745i	$-0.585974\pi$
$443$	−9.76489e8	−0.533647	−0.266824	+	0.963745i	$0.585974\pi$
$444$	−3.59881e7	−0.0195128
$445$	−6.67240e8	−0.358940
$446$	2.33077e9	1.24402
$447$	2.71611e8	0.143837
$448$	1.52303e9	0.800266
$449$	−2.52186e9	−1.31480	−0.657398	−	0.753543i	$-0.728343\pi$
$449$	−2.52186e9	−1.31480	−0.657398	+	0.753543i	$0.728343\pi$
$450$	−1.12697e9	−0.582999
$451$	6.18536e8	0.317503
$452$	8.98347e7	0.0457572
$453$	3.09295e9	1.56325
$454$	3.04713e9	1.52826
$455$	4.60830e8	0.229351
$456$	−4.37344e9	−2.15996
$457$	−2.36676e9	−1.15997	−0.579987	−	0.814626i	$-0.696942\pi$
$457$	−2.36676e9	−1.15997	−0.579987	+	0.814626i	$0.696942\pi$
$458$	2.73105e9	1.32831
$459$	8.89117e7	0.0429155
$460$	2.75696e7	0.0132062
$461$	−4.52148e8	−0.214945	−0.107472	−	0.994208i	$-0.534276\pi$
$461$	−4.52148e8	−0.214945	−0.107472	+	0.994208i	$0.534276\pi$
$462$	−6.12668e8	−0.289054
$463$	−1.36961e9	−0.641302	−0.320651	−	0.947197i	$-0.603902\pi$
$463$	−1.36961e9	−0.641302	−0.320651	+	0.947197i	$0.603902\pi$
$464$	−1.38570e9	−0.643958
$465$	−6.32386e8	−0.291673
$466$	−1.59059e9	−0.728128
$467$	−1.76054e7	−0.00799902	−0.00399951	−	0.999992i	$-0.501273\pi$
$467$	−1.76054e7	−0.00799902	−0.00399951	+	0.999992i	$0.501273\pi$
$468$	8.52212e7	0.0384315
$469$	−1.31710e9	−0.589539
$470$	4.52552e8	0.201060
$471$	2.99289e9	1.31983
$472$	3.76017e9	1.64592
$473$	−1.11435e9	−0.484183
$474$	2.93691e9	1.26668
$475$	−3.69646e9	−1.58255
$476$	7.21692e6	0.00306710
$477$	−2.42176e8	−0.102169
$478$	−1.16039e9	−0.485968
$479$	1.20785e9	0.502154	0.251077	−	0.967967i	$-0.419215\pi$
$479$	1.20785e9	0.502154	0.251077	+	0.967967i	$0.419215\pi$
$480$	−5.89788e7	−0.0243417
$481$	−1.16580e9	−0.477659
$482$	−8.70838e8	−0.354220
$483$	3.35701e9	1.35562
$484$	−1.00625e7	−0.00403409
$485$	2.38059e8	0.0947522
$486$	−2.71124e9	−1.07138
$487$	1.01854e7	0.00399600	0.00199800	−	0.999998i	$-0.499364\pi$
$487$	1.01854e7	0.00399600	0.00199800	+	0.999998i	$0.499364\pi$
$488$	3.46262e7	0.0134876
$489$	1.86663e9	0.721901
$490$	2.23784e8	0.0859297
$491$	2.93964e9	1.12075	0.560375	−	0.828239i	$-0.310657\pi$
$491$	2.93964e9	1.12075	0.560375	+	0.828239i	$0.310657\pi$
$492$	1.57375e8	0.0595742
$493$	−1.61422e8	−0.0606736
$494$	−6.01966e9	−2.24661
$495$	1.09544e8	0.0405950
$496$	−2.75401e9	−1.01340
$497$	−3.13621e9	−1.14593
$498$	1.80872e9	0.656250
$499$	3.42779e9	1.23499	0.617493	−	0.786576i	$-0.288148\pi$
$499$	3.42779e9	1.23499	0.617493	+	0.786576i	$0.288148\pi$
$500$	−5.21690e7	−0.0186646
$501$	1.96910e8	0.0699577
$502$	−1.63376e9	−0.576403
$503$	−1.81978e9	−0.637573	−0.318786	−	0.947827i	$-0.603275\pi$
$503$	−1.81978e9	−0.637573	−0.318786	+	0.947827i	$0.603275\pi$
$504$	−1.41156e9	−0.491124
$505$	4.92252e7	0.0170085
$506$	−1.18736e9	−0.407431
$507$	3.43399e9	1.17023
$508$	−1.21637e8	−0.0411663
$509$	−2.42087e9	−0.813691	−0.406846	−	0.913497i	$-0.633371\pi$
$509$	−2.42087e9	−0.813691	−0.406846	+	0.913497i	$0.633371\pi$
$510$	7.22241e7	0.0241094
$511$	2.20202e9	0.730043
$512$	−3.21375e9	−1.05820
$513$	−2.42361e9	−0.792595
$514$	1.85841e9	0.603628
$515$	−4.51751e7	−0.0145738
$516$	−2.83527e8	−0.0908490
$517$	9.05045e8	0.288040
$518$	8.20460e8	0.259360
$519$	1.05296e9	0.330618
$520$	−9.76018e8	−0.304401
$521$	2.08008e9	0.644390	0.322195	−	0.946673i	$-0.395579\pi$
$521$	2.08008e9	0.644390	0.322195	+	0.946673i	$0.395579\pi$
$522$	1.34150e9	0.412806
$523$	3.00947e8	0.0919887	0.0459944	−	0.998942i	$-0.485354\pi$
$523$	3.00947e8	0.0919887	0.0459944	+	0.998942i	$0.485354\pi$
$524$	3.07399e7	0.00933347
$525$	−3.10082e9	−0.935232
$526$	2.34109e9	0.701403
$527$	−3.20818e8	−0.0954821
$528$	1.23991e9	0.366582
$529$	3.10108e9	0.910789
$530$	1.17848e8	0.0343841
$531$	−3.47837e9	−1.00820
$532$	−1.96723e8	−0.0566453
$533$	5.09802e9	1.45833
$534$	7.31144e9	2.07782
$535$	5.84072e8	0.164903
$536$	2.78955e9	0.782452
$537$	1.48296e9	0.413256
$538$	1.09995e9	0.304534
$539$	4.47539e8	0.123103
$540$	−1.66967e7	−0.00456301
$541$	−5.12243e8	−0.139087	−0.0695433	−	0.997579i	$-0.522154\pi$
$541$	−5.12243e8	−0.139087	−0.0695433	+	0.997579i	$0.522154\pi$
$542$	−6.52334e9	−1.75984
$543$	−9.54836e7	−0.0255935
$544$	−2.99208e7	−0.00796850
$545$	−3.92494e6	−0.00103859
$546$	−5.04966e9	−1.32766
$547$	−4.24814e9	−1.10979	−0.554897	−	0.831919i	$-0.687243\pi$
$547$	−4.24814e9	−1.10979	−0.554897	+	0.831919i	$0.687243\pi$
$548$	2.37762e8	0.0617179
$549$	−3.20312e7	−0.00826172
$550$	1.09674e9	0.281084
$551$	4.40015e9	1.12056
$552$	−7.10999e9	−1.79921
$553$	3.10913e9	0.781810
$554$	6.33931e9	1.58401
$555$	−3.81275e8	−0.0946702
$556$	1.62523e8	0.0401009
$557$	−4.61753e9	−1.13218	−0.566091	−	0.824343i	$-0.691545\pi$
$557$	−4.61753e9	−1.13218	−0.566091	+	0.824343i	$0.691545\pi$
$558$	2.66617e9	0.649633
$559$	−9.18460e9	−2.22392
$560$	6.56353e8	0.157935
$561$	1.44439e8	0.0345393
$562$	3.26958e9	0.776988
$563$	7.29234e9	1.72222	0.861108	−	0.508422i	$-0.169771\pi$
$563$	7.29234e9	1.72222	0.861108	+	0.508422i	$0.169771\pi$
$564$	2.30272e8	0.0540460
$565$	9.51751e8	0.222000
$566$	−3.35096e9	−0.776805
$567$	−4.12108e9	−0.949445
$568$	6.64236e9	1.52091
$569$	−8.21738e8	−0.186999	−0.0934997	−	0.995619i	$-0.529805\pi$
$569$	−8.21738e8	−0.186999	−0.0934997	+	0.995619i	$0.529805\pi$
$570$	−1.96872e9	−0.445270
$571$	−1.38125e9	−0.310490	−0.155245	−	0.987876i	$-0.549617\pi$
$571$	−1.38125e9	−0.310490	−0.155245	+	0.987876i	$0.549617\pi$
$572$	−8.29357e7	−0.0185291
$573$	−8.00871e9	−1.77837
$574$	−3.58785e9	−0.791849
$575$	−6.00941e9	−1.31824
$576$	2.98396e9	0.650601
$577$	4.15413e9	0.900254	0.450127	−	0.892965i	$-0.351379\pi$
$577$	4.15413e9	0.900254	0.450127	+	0.892965i	$0.351379\pi$
$578$	−4.50164e9	−0.969668
$579$	−9.97890e9	−2.13652
$580$	3.03134e7	0.00645115
$581$	1.91479e9	0.405046
$582$	−2.60860e9	−0.548500
$583$	2.35681e8	0.0492590
$584$	−4.66378e9	−0.968932
$585$	9.02874e8	0.186458
$586$	8.45850e9	1.73641
$587$	7.46108e9	1.52254	0.761269	−	0.648436i	$-0.224577\pi$
$587$	7.46108e9	1.52254	0.761269	+	0.648436i	$0.224577\pi$
$588$	1.13868e8	0.0230983
$589$	8.74505e9	1.76343
$590$	1.69265e9	0.339302
$591$	−4.87469e9	−0.971385
$592$	−1.66044e9	−0.328924
$593$	−5.81111e9	−1.14437	−0.572187	−	0.820123i	$-0.693905\pi$
$593$	−5.81111e9	−1.14437	−0.572187	+	0.820123i	$0.693905\pi$
$594$	7.19085e8	0.140776
$595$	7.64595e7	0.0148806
$596$	−2.58759e7	−0.00500649
$597$	1.21851e10	2.34379
$598$	−9.78627e9	−1.87139
$599$	−6.11327e9	−1.16220	−0.581099	−	0.813833i	$-0.697377\pi$
$599$	−6.11327e9	−1.16220	−0.581099	+	0.813833i	$0.697377\pi$
$600$	6.56740e9	1.24126
$601$	5.94867e9	1.11779	0.558893	−	0.829240i	$-0.311226\pi$
$601$	5.94867e9	1.11779	0.558893	+	0.829240i	$0.311226\pi$
$602$	6.46387e9	1.20755
$603$	−2.58050e9	−0.479285
$604$	−2.94660e8	−0.0544116
$605$	−1.06607e8	−0.0195722
$606$	−5.39397e8	−0.0984587
$607$	−1.95313e9	−0.354463	−0.177232	−	0.984169i	$-0.556714\pi$
$607$	−1.95313e9	−0.354463	−0.177232	+	0.984169i	$0.556714\pi$
$608$	8.15597e8	0.147168
$609$	3.69111e9	0.662212
$610$	1.55871e7	0.00278042
$611$	7.45945e9	1.32301
$612$	1.41396e7	0.00249349
$613$	−3.31869e9	−0.581908	−0.290954	−	0.956737i	$-0.593973\pi$
$613$	−3.31869e9	−0.581908	−0.290954	+	0.956737i	$0.593973\pi$
$614$	2.76735e9	0.482475
$615$	1.66731e9	0.289036
$616$	1.37370e9	0.236788
$617$	2.71103e9	0.464661	0.232330	−	0.972637i	$-0.425365\pi$
$617$	2.71103e9	0.464661	0.232330	+	0.972637i	$0.425365\pi$
$618$	4.95017e8	0.0843646
$619$	1.20094e9	0.203519	0.101759	−	0.994809i	$-0.467553\pi$
$619$	1.20094e9	0.203519	0.101759	+	0.994809i	$0.467553\pi$
$620$	6.02463e7	0.0101522
$621$	−3.94010e9	−0.660217
$622$	−1.22467e9	−0.204057
$623$	7.74020e9	1.28246
$624$	1.02194e10	1.68376
$625$	5.26790e9	0.863093
$626$	−5.77289e9	−0.940553
$627$	−3.93719e9	−0.637896
$628$	−2.85127e8	−0.0459388
$629$	−1.93426e8	−0.0309912
$630$	−6.35418e8	−0.101244
$631$	−6.09708e9	−0.966093	−0.483047	−	0.875595i	$-0.660470\pi$
$631$	−6.09708e9	−0.966093	−0.483047	+	0.875595i	$0.660470\pi$
$632$	−6.58501e9	−1.03764
$633$	−6.80394e9	−1.06622
$634$	−6.84040e9	−1.06603
$635$	−1.28868e9	−0.199726
$636$	5.99647e7	0.00924264
$637$	3.68865e9	0.565431
$638$	−1.30553e9	−0.199028
$639$	−6.14458e9	−0.931620
$640$	−1.32544e9	−0.199862
$641$	−7.99109e9	−1.19840	−0.599201	−	0.800598i	$-0.704515\pi$
$641$	−7.99109e9	−1.19840	−0.599201	+	0.800598i	$0.704515\pi$
$642$	−6.40012e9	−0.954587
$643$	−7.57666e7	−0.0112393	−0.00561966	−	0.999984i	$-0.501789\pi$
$643$	−7.57666e7	−0.0112393	−0.00561966	+	0.999984i	$0.501789\pi$
$644$	−3.19816e8	−0.0471846
$645$	−3.00382e9	−0.440773
$646$	−9.98762e8	−0.145763
$647$	−1.01975e10	−1.48023	−0.740116	−	0.672479i	$-0.765229\pi$
$647$	−1.01975e10	−1.48023	−0.740116	+	0.672479i	$0.765229\pi$
$648$	8.72825e9	1.26013
$649$	3.38509e9	0.486086
$650$	9.03945e9	1.29106
$651$	7.33589e9	1.04212
$652$	−1.77831e8	−0.0251270
$653$	−1.53376e9	−0.215556	−0.107778	−	0.994175i	$-0.534374\pi$
$653$	−1.53376e9	−0.215556	−0.107778	+	0.994175i	$0.534374\pi$
$654$	4.30085e7	0.00601218
$655$	3.25673e8	0.0452832
$656$	7.26104e9	1.00423
$657$	4.31427e9	0.593511
$658$	−5.24975e9	−0.718370
$659$	−7.32323e9	−0.996790	−0.498395	−	0.866950i	$-0.666077\pi$
$659$	−7.32323e9	−0.996790	−0.498395	+	0.866950i	$0.666077\pi$
$660$	−2.71241e7	−0.00367241
$661$	−7.01205e9	−0.944365	−0.472183	−	0.881501i	$-0.656534\pi$
$661$	−7.01205e9	−0.944365	−0.472183	+	0.881501i	$0.656534\pi$
$662$	1.08844e10	1.45815
$663$	1.19047e9	0.158644
$664$	−4.05544e9	−0.537588
$665$	−2.08418e9	−0.274826
$666$	1.60747e9	0.210855
$667$	7.15340e9	0.933410
$668$	−1.87593e7	−0.00243500
$669$	1.25647e10	1.62241
$670$	1.25573e9	0.161300
$671$	3.11722e7	0.00398326
$672$	6.84174e8	0.0869709
$673$	−4.37758e9	−0.553582	−0.276791	−	0.960930i	$-0.589271\pi$
$673$	−4.37758e9	−0.553582	−0.276791	+	0.960930i	$0.589271\pi$
$674$	9.31872e7	0.0117232
$675$	3.63942e9	0.455479
$676$	−3.27150e8	−0.0407318
$677$	−1.42594e10	−1.76620	−0.883099	−	0.469186i	$-0.844547\pi$
$677$	−1.42594e10	−1.76620	−0.883099	+	0.469186i	$0.844547\pi$
$678$	−1.04290e10	−1.28511
$679$	−2.76157e9	−0.338541
$680$	−1.61938e8	−0.0197500
$681$	1.64264e10	1.99309
$682$	−2.59466e9	−0.313210
$683$	−4.51198e9	−0.541870	−0.270935	−	0.962598i	$-0.587333\pi$
$683$	−4.51198e9	−0.541870	−0.270935	+	0.962598i	$0.587333\pi$
$684$	−3.85426e8	−0.0460516
$685$	2.51897e9	0.299437
$686$	−8.95416e9	−1.05899
$687$	1.47225e10	1.73234
$688$	−1.30815e10	−1.53143
$689$	1.94250e9	0.226253
$690$	−3.20059e9	−0.370902
$691$	9.24446e9	1.06588	0.532940	−	0.846153i	$-0.321087\pi$
$691$	9.24446e9	1.06588	0.532940	+	0.846153i	$0.321087\pi$
$692$	−1.00314e8	−0.0115077
$693$	−1.27075e9	−0.145042
$694$	3.85238e9	0.437493
$695$	1.72185e9	0.194557
$696$	−7.81762e9	−0.878905
$697$	8.45848e8	0.0946188
$698$	8.19033e9	0.911606
$699$	−8.57452e9	−0.949598
$700$	2.95410e8	0.0325523
$701$	1.80992e9	0.198448	0.0992238	−	0.995065i	$-0.468364\pi$
$701$	1.80992e9	0.198448	0.0992238	+	0.995065i	$0.468364\pi$
$702$	5.92676e9	0.646602
$703$	5.27253e9	0.572368
$704$	−2.90394e9	−0.313677
$705$	2.43961e9	0.262215
$706$	3.28406e9	0.351233
$707$	−5.71028e8	−0.0607701
$708$	8.61272e8	0.0912061
$709$	5.14612e9	0.542273	0.271137	−	0.962541i	$-0.412600\pi$
$709$	5.14612e9	0.542273	0.271137	+	0.962541i	$0.412600\pi$
$710$	2.99009e9	0.313530
$711$	6.09152e9	0.635597
$712$	−1.63934e10	−1.70212
$713$	1.42170e10	1.46891
$714$	−8.37823e8	−0.0861408
$715$	−8.78660e8	−0.0898979
$716$	−1.41279e8	−0.0143841
$717$	−6.25542e9	−0.633782
$718$	−5.51032e9	−0.555573
$719$	6.56632e9	0.658827	0.329413	−	0.944186i	$-0.393149\pi$
$719$	6.56632e9	0.658827	0.329413	+	0.944186i	$0.393149\pi$
$720$	1.28595e9	0.128399
$721$	5.24046e8	0.0520710
$722$	1.73387e10	1.71450
$723$	−4.69450e9	−0.461961
$724$	9.09655e6	0.000890824 0
$725$	−6.60750e9	−0.643953
$726$	1.16817e9	0.113299
$727$	4.82284e9	0.465514	0.232757	−	0.972535i	$-0.425225\pi$
$727$	4.82284e9	0.465514	0.232757	+	0.972535i	$0.425225\pi$
$728$	1.13221e10	1.08760
$729$	−1.70469e9	−0.162967
$730$	−2.09942e9	−0.199742
$731$	−1.52388e9	−0.144291
$732$	7.93118e6	0.000747393 0
$733$	−6.22780e9	−0.584078	−0.292039	−	0.956406i	$-0.594334\pi$
$733$	−6.22780e9	−0.584078	−0.292039	+	0.956406i	$0.594334\pi$
$734$	−1.16160e10	−1.08423
$735$	1.20637e9	0.112066
$736$	1.32593e9	0.122588
$737$	2.51129e9	0.231079
$738$	−7.02944e9	−0.643759
$739$	−2.50070e9	−0.227932	−0.113966	−	0.993485i	$-0.536355\pi$
$739$	−2.50070e9	−0.227932	−0.113966	+	0.993485i	$0.536355\pi$
$740$	3.63234e7	0.00329515
$741$	−3.24506e10	−2.92995
$742$	−1.36708e9	−0.122852
$743$	3.39408e9	0.303571	0.151786	−	0.988413i	$-0.451498\pi$
$743$	3.39408e9	0.303571	0.151786	+	0.988413i	$0.451498\pi$
$744$	−1.55371e10	−1.38313
$745$	−2.74141e8	−0.0242900
$746$	−2.80687e9	−0.247535
$747$	3.75152e9	0.329295
$748$	−1.37604e7	−0.00120220
$749$	−6.77544e9	−0.589184
$750$	6.05638e9	0.524202
$751$	−1.15314e10	−0.993438	−0.496719	−	0.867911i	$-0.665462\pi$
$751$	−1.15314e10	−0.993438	−0.496719	+	0.867911i	$0.665462\pi$
$752$	1.06244e10	0.911048
$753$	−8.80726e9	−0.751724
$754$	−1.07603e10	−0.914161
$755$	−3.12177e9	−0.263989
$756$	1.93687e8	0.0163032
$757$	−3.22313e9	−0.270049	−0.135024	−	0.990842i	$-0.543111\pi$
$757$	−3.22313e9	−0.270049	−0.135024	+	0.990842i	$0.543111\pi$
$758$	1.04261e10	0.869521
$759$	−6.40077e9	−0.531356
$760$	4.41419e9	0.364757
$761$	−6.00476e9	−0.493911	−0.246956	−	0.969027i	$-0.579430\pi$
$761$	−6.00476e9	−0.493911	−0.246956	+	0.969027i	$0.579430\pi$
$762$	1.41210e10	1.15617
$763$	4.55306e7	0.00371080
$764$	7.62975e8	0.0618990
$765$	1.49802e8	0.0120977
$766$	1.09835e10	0.882956
$767$	2.79002e10	2.23266
$768$	−2.12633e9	−0.169382
$769$	−2.67592e9	−0.212193	−0.106097	−	0.994356i	$-0.533835\pi$
$769$	−2.67592e9	−0.212193	−0.106097	+	0.994356i	$0.533835\pi$
$770$	6.18376e8	0.0488130
$771$	1.00183e10	0.787230
$772$	9.50672e8	0.0743653
$773$	8.00647e9	0.623466	0.311733	−	0.950170i	$-0.399091\pi$
$773$	8.00647e9	0.623466	0.311733	+	0.950170i	$0.399091\pi$
$774$	1.26642e10	0.981715
$775$	−1.31320e10	−1.01339
$776$	5.84888e9	0.449321
$777$	4.42292e9	0.338248
$778$	2.04878e10	1.55979
$779$	−2.30566e10	−1.74749
$780$	−2.23559e8	−0.0168679
$781$	5.97978e9	0.449166
$782$	−1.62371e9	−0.121418
$783$	−4.33224e9	−0.322512
$784$	5.25369e9	0.389366
$785$	−3.02077e9	−0.222882
$786$	−3.56864e9	−0.262135
$787$	1.09870e9	0.0803465	0.0401733	−	0.999193i	$-0.487209\pi$
$787$	1.09870e9	0.0803465	0.0401733	+	0.999193i	$0.487209\pi$
$788$	4.64404e8	0.0338107
$789$	1.26203e10	0.914744
$790$	−2.96427e9	−0.213906
$791$	−1.10406e10	−0.793188
$792$	2.69140e9	0.192504
$793$	2.56923e8	0.0182956
$794$	−1.01965e10	−0.722905
$795$	6.35295e8	0.0448425
$796$	−1.16085e9	−0.0815795
$797$	4.45517e8	0.0311717	0.0155858	−	0.999879i	$-0.495039\pi$
$797$	4.45517e8	0.0311717	0.0155858	+	0.999879i	$0.495039\pi$
$798$	2.28379e10	1.59091
$799$	1.23765e9	0.0858387
$800$	−1.22475e9	−0.0845729
$801$	1.51649e10	1.04262
$802$	9.65019e9	0.660580
$803$	−4.19857e9	−0.286152
$804$	6.38952e8	0.0433583
$805$	−3.38829e9	−0.228926
$806$	−2.13854e10	−1.43862
$807$	5.92960e9	0.397162
$808$	1.20941e9	0.0806556
$809$	1.72932e8	0.0114830	0.00574150	−	0.999984i	$-0.498172\pi$
$809$	1.72932e8	0.0114830	0.00574150	+	0.999984i	$0.498172\pi$
$810$	3.92906e9	0.259771
$811$	−1.88310e9	−0.123965	−0.0619826	−	0.998077i	$-0.519742\pi$
$811$	−1.88310e9	−0.123965	−0.0619826	+	0.998077i	$0.519742\pi$
$812$	−3.51646e8	−0.0230494
$813$	−3.51659e10	−2.29512
$814$	−1.56436e9	−0.101660
$815$	−1.88402e9	−0.121909
$816$	1.69557e9	0.109245
$817$	4.15388e10	2.66487
$818$	4.23728e9	0.270677
$819$	−1.04736e10	−0.666199
$820$	−1.58841e8	−0.0100604
$821$	−1.81880e10	−1.14706	−0.573529	−	0.819186i	$-0.694426\pi$
$821$	−1.81880e10	−1.14706	−0.573529	+	0.819186i	$0.694426\pi$
$822$	−2.76022e10	−1.73338
$823$	−1.31757e10	−0.823899	−0.411949	−	0.911207i	$-0.635152\pi$
$823$	−1.31757e10	−0.823899	−0.411949	+	0.911207i	$0.635152\pi$
$824$	−1.10991e9	−0.0691100
$825$	5.91230e9	0.366579
$826$	−1.96354e10	−1.21230
$827$	1.60104e10	0.984313	0.492157	−	0.870507i	$-0.336209\pi$
$827$	1.60104e10	0.984313	0.492157	+	0.870507i	$0.336209\pi$
$828$	−6.26595e8	−0.0383602
$829$	8.99595e9	0.548411	0.274206	−	0.961671i	$-0.411585\pi$
$829$	8.99595e9	0.548411	0.274206	+	0.961671i	$0.411585\pi$
$830$	−1.82557e9	−0.110822
$831$	3.41738e10	2.06581
$832$	−2.39345e10	−1.44076
$833$	6.12009e8	0.0366860
$834$	−1.88676e10	−1.12625
$835$	−1.98744e8	−0.0118139
$836$	3.75089e8	0.0222031
$837$	−8.61009e9	−0.507538
$838$	−1.38980e10	−0.815825
$839$	7.43957e9	0.434892	0.217446	−	0.976072i	$-0.430227\pi$
$839$	7.43957e9	0.434892	0.217446	+	0.976072i	$0.430227\pi$
$840$	3.70290e9	0.215558
$841$	−9.38453e9	−0.544035
$842$	−1.32681e10	−0.765977
$843$	1.76256e10	1.01332
$844$	6.48200e8	0.0371117
$845$	−3.46599e9	−0.197619
$846$	−1.02855e10	−0.584022
$847$	1.23667e9	0.0699298
$848$	2.76668e9	0.155802
$849$	−1.80643e10	−1.01308
$850$	1.49980e9	0.0837656
$851$	8.57165e9	0.476772
$852$	1.52144e9	0.0842786
$853$	2.81819e10	1.55471	0.777353	−	0.629064i	$-0.216562\pi$
$853$	2.81819e10	1.55471	0.777353	+	0.629064i	$0.216562\pi$
$854$	−1.80816e8	−0.00993422
$855$	−4.08339e9	−0.223429
$856$	1.43501e10	0.781980
$857$	−1.63183e10	−0.885608	−0.442804	−	0.896618i	$-0.646016\pi$
$857$	−1.63183e10	−0.885608	−0.442804	+	0.896618i	$0.646016\pi$
$858$	9.62813e9	0.520399
$859$	1.52511e10	0.820964	0.410482	−	0.911869i	$-0.365360\pi$
$859$	1.52511e10	0.820964	0.410482	+	0.911869i	$0.365360\pi$
$860$	2.86168e8	0.0153418
$861$	−1.93413e10	−1.03270
$862$	3.56209e10	1.89422
$863$	3.50608e9	0.185688	0.0928440	−	0.995681i	$-0.470404\pi$
$863$	3.50608e9	0.185688	0.0928440	+	0.995681i	$0.470404\pi$
$864$	−8.03011e8	−0.0423568
$865$	−1.06277e9	−0.0558320
$866$	−2.80495e10	−1.46762
$867$	−2.42673e10	−1.26461
$868$	−6.98877e8	−0.0362729
$869$	−5.92815e9	−0.306443
$870$	−3.51913e9	−0.181183
$871$	2.06983e10	1.06138
$872$	−9.64318e7	−0.00492507
$873$	−5.41056e9	−0.275228
$874$	4.42599e10	2.24244
$875$	6.41154e9	0.323545
$876$	−1.06825e9	−0.0536917
$877$	1.83413e10	0.918190	0.459095	−	0.888387i	$-0.348174\pi$
$877$	1.83413e10	0.918190	0.459095	+	0.888387i	$0.348174\pi$
$878$	1.31371e10	0.655043
$879$	4.55979e10	2.26456
$880$	−1.25146e9	−0.0619053
$881$	2.35342e10	1.15953	0.579766	−	0.814783i	$-0.303144\pi$
$881$	2.35342e10	1.15953	0.579766	+	0.814783i	$0.303144\pi$
$882$	−5.08612e9	−0.249601
$883$	−3.39126e10	−1.65767	−0.828837	−	0.559490i	$-0.810997\pi$
$883$	−3.39126e10	−1.65767	−0.828837	+	0.559490i	$0.810997\pi$
$884$	−1.13414e8	−0.00552186
$885$	9.12473e9	0.442505
$886$	−1.07998e10	−0.521673
$887$	−1.88887e10	−0.908800	−0.454400	−	0.890798i	$-0.650146\pi$
$887$	−1.88887e10	−0.908800	−0.454400	+	0.890798i	$0.650146\pi$
$888$	−9.36755e9	−0.448932
$889$	1.49491e10	0.713605
$890$	−7.37956e9	−0.350886
$891$	7.85761e9	0.372150
$892$	−1.19701e9	−0.0564706
$893$	−3.37365e10	−1.58533
$894$	3.00397e9	0.140609
$895$	−1.49677e9	−0.0697872
$896$	1.53756e10	0.714091
$897$	−5.27556e10	−2.44059
$898$	−2.78913e10	−1.28529
$899$	1.56319e10	0.717553
$900$	5.78777e8	0.0264644
$901$	3.22294e8	0.0146796
$902$	6.84091e9	0.310378
$903$	3.48453e10	1.57484
$904$	2.33836e10	1.05274
$905$	9.63732e7	0.00432201
$906$	3.42075e10	1.52817
$907$	−2.28453e10	−1.01665	−0.508324	−	0.861166i	$-0.669735\pi$
$907$	−2.28453e10	−1.01665	−0.508324	+	0.861166i	$0.669735\pi$
$908$	−1.56492e9	−0.0693730
$909$	−1.11878e9	−0.0494049
$910$	5.09671e9	0.224205
$911$	−2.64329e10	−1.15832	−0.579162	−	0.815212i	$-0.696620\pi$
$911$	−2.64329e10	−1.15832	−0.579162	+	0.815212i	$0.696620\pi$
$912$	−4.62189e10	−2.01761
$913$	−3.65091e9	−0.158764
$914$	−2.61760e10	−1.13394
$915$	8.40267e7	0.00362613
$916$	−1.40259e9	−0.0602969
$917$	−3.77792e9	−0.161793
$918$	9.83349e8	0.0419525
$919$	1.26026e10	0.535620	0.267810	−	0.963472i	$-0.413700\pi$
$919$	1.26026e10	0.535620	0.267810	+	0.963472i	$0.413700\pi$
$920$	7.17624e9	0.303836
$921$	1.49182e10	0.629227
$922$	−5.00068e9	−0.210122
$923$	4.92858e10	2.06308
$924$	3.14648e8	0.0131212
$925$	−7.91751e9	−0.328922
$926$	−1.51476e10	−0.626912
$927$	1.02673e9	0.0423327
$928$	1.45790e9	0.0598837
$929$	3.04525e10	1.24614	0.623072	−	0.782164i	$-0.285884\pi$
$929$	3.04525e10	1.24614	0.623072	+	0.782164i	$0.285884\pi$
$930$	−6.99409e9	−0.285129
$931$	−1.66825e10	−0.677543
$932$	8.16879e8	0.0330523
$933$	−6.60190e9	−0.266124
$934$	−1.94713e8	−0.00781952
$935$	−1.45784e8	−0.00583271
$936$	2.21827e10	0.884197
$937$	−9.24061e9	−0.366954	−0.183477	−	0.983024i	$-0.558735\pi$
$937$	−9.24061e9	−0.366954	−0.183477	+	0.983024i	$0.558735\pi$
$938$	−1.45669e10	−0.576311
$939$	−3.11204e10	−1.22664
$940$	−2.32417e8	−0.00912684
$941$	3.02061e10	1.18177	0.590883	−	0.806757i	$-0.298780\pi$
$941$	3.02061e10	1.18177	0.590883	+	0.806757i	$0.298780\pi$
$942$	3.31009e10	1.29021
$943$	−3.74836e10	−1.45563
$944$	3.97378e10	1.53745
$945$	2.05201e9	0.0790985
$946$	−1.23246e10	−0.473318
$947$	1.81462e9	0.0694322	0.0347161	−	0.999397i	$-0.488947\pi$
$947$	1.81462e9	0.0694322	0.0347161	+	0.999397i	$0.488947\pi$
$948$	−1.50831e9	−0.0574990
$949$	−3.46049e10	−1.31433
$950$	−4.08823e10	−1.54704
$951$	−3.68751e10	−1.39028
$952$	1.87853e9	0.0705650
$953$	2.33932e10	0.875517	0.437758	−	0.899093i	$-0.355773\pi$
$953$	2.33932e10	0.875517	0.437758	+	0.899093i	$0.355773\pi$
$954$	−2.67843e9	−0.0998760
$955$	8.08332e9	0.300316
$956$	5.95943e8	0.0220598
$957$	−7.03781e9	−0.259565
$958$	1.33586e10	0.490886
$959$	−2.92209e10	−1.06986
$960$	−7.82775e9	−0.285554
$961$	3.55504e9	0.129215
$962$	−1.28936e10	−0.466940
$963$	−1.32747e10	−0.478996
$964$	4.47236e8	0.0160793
$965$	1.00719e10	0.360798
$966$	3.71280e10	1.32520
$967$	−3.73590e10	−1.32863	−0.664314	−	0.747454i	$-0.731276\pi$
$967$	−3.73590e10	−1.32863	−0.664314	+	0.747454i	$0.731276\pi$
$968$	−2.61922e9	−0.0928127
$969$	−5.38410e9	−0.190099
$970$	2.63290e9	0.0926261
$971$	2.54149e10	0.890883	0.445442	−	0.895311i	$-0.353047\pi$
$971$	2.54149e10	0.890883	0.445442	+	0.895311i	$0.353047\pi$
$972$	1.39241e9	0.0486336
$973$	−1.99740e10	−0.695137
$974$	1.12649e8	0.00390633
$975$	4.87297e10	1.68375
$976$	3.65932e8	0.0125987
$977$	−1.70188e10	−0.583844	−0.291922	−	0.956442i	$-0.594295\pi$
$977$	−1.70188e10	−0.583844	−0.291922	+	0.956442i	$0.594295\pi$
$978$	2.06446e10	0.705702
$979$	−1.47582e10	−0.502681
$980$	−1.14929e8	−0.00390066
$981$	8.92051e7	0.00301681
$982$	3.25119e10	1.09560
$983$	2.17173e10	0.729237	0.364619	−	0.931157i	$-0.381199\pi$
$983$	2.17173e10	0.729237	0.364619	+	0.931157i	$0.381199\pi$
$984$	4.09640e10	1.37063
$985$	4.92011e9	0.164039
$986$	−1.78531e9	−0.0593121
$987$	−2.83003e10	−0.936872
$988$	3.09152e9	0.101982
$989$	6.75304e10	2.21979
$990$	1.21154e9	0.0396840
$991$	−4.06405e9	−0.132648	−0.0663240	−	0.997798i	$-0.521127\pi$
$991$	−4.06405e9	−0.132648	−0.0663240	+	0.997798i	$0.521127\pi$
$992$	2.89749e9	0.0942391
$993$	5.86757e10	1.90167
$994$	−3.46860e10	−1.12022
$995$	−1.22986e10	−0.395800
$996$	−9.28906e8	−0.0297896
$997$	−4.73391e9	−0.151282	−0.0756410	−	0.997135i	$-0.524100\pi$
$997$	−4.73391e9	−0.151282	−0.0756410	+	0.997135i	$0.524100\pi$
$998$	3.79108e10	1.20727
$999$	−5.19116e9	−0.164735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.8.a.b.1.3	✓	4
3.2	odd	2		99.8.a.g.1.2		4
4.3	odd	2		176.8.a.j.1.1		4
5.4	even	2		275.8.a.b.1.2		4
7.6	odd	2		539.8.a.b.1.3		4
11.10	odd	2		121.8.a.c.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.8.a.b.1.3	✓	4	1.1	even	1	trivial
99.8.a.g.1.2		4	3.2	odd	2
121.8.a.c.1.2		4	11.10	odd	2
176.8.a.j.1.1		4	4.3	odd	2
275.8.a.b.1.2		4	5.4	even	2
539.8.a.b.1.3		4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+11.0598 q^{2} +59.6211 q^{3} -5.68000 q^{4} -60.1766 q^{5} +659.400 q^{6} +698.069 q^{7} -1478.48 q^{8} +1367.68 q^{9} -665.544 q^{10} -1331.00 q^{11} -338.648 q^{12} -10970.2 q^{13} +7720.53 q^{14} -3587.80 q^{15} -15624.7 q^{16} -1820.14 q^{17} +15126.3 q^{18} +49614.4 q^{19} +341.803 q^{20} +41619.7 q^{21} -14720.6 q^{22} +80659.2 q^{23} -88148.6 q^{24} -74503.8 q^{25} -121329. q^{26} -48848.8 q^{27} -3965.03 q^{28} +88686.8 q^{29} -39680.5 q^{30} +176260. q^{31} +16438.7 q^{32} -79355.7 q^{33} -20130.5 q^{34} -42007.4 q^{35} -7768.43 q^{36} +106270. q^{37} +548728. q^{38} -654056. q^{39} +88969.9 q^{40} -464715. q^{41} +460307. q^{42} +837231. q^{43} +7560.08 q^{44} -82302.4 q^{45} +892077. q^{46} -679973. q^{47} -931562. q^{48} -336243. q^{49} -824000. q^{50} -108519. q^{51} +62310.8 q^{52} -177071. q^{53} -540259. q^{54} +80095.1 q^{55} -1.03208e6 q^{56} +2.95807e6 q^{57} +980861. q^{58} -2.54327e6 q^{59} +20378.7 q^{60} -23420.1 q^{61} +1.94941e6 q^{62} +954735. q^{63} +2.18177e6 q^{64} +660150. q^{65} -877662. q^{66} -1.88677e6 q^{67} +10338.4 q^{68} +4.80899e6 q^{69} -464595. q^{70} -4.49270e6 q^{71} -2.02209e6 q^{72} +3.15445e6 q^{73} +1.17533e6 q^{74} -4.44200e6 q^{75} -281810. q^{76} -929130. q^{77} -7.23375e6 q^{78} +4.45391e6 q^{79} +940241. q^{80} -5.90354e6 q^{81} -5.13968e6 q^{82} +2.74298e6 q^{83} -236400. q^{84} +109530. q^{85} +9.25964e6 q^{86} +5.28761e6 q^{87} +1.96786e6 q^{88} +1.10880e7 q^{89} -910251. q^{90} -7.65796e6 q^{91} -458144. q^{92} +1.05088e7 q^{93} -7.52039e6 q^{94} -2.98563e6 q^{95} +980095. q^{96} -3.95601e6 q^{97} -3.71879e6 q^{98} -1.82038e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 35 q^{3} + 604 q^{4} + 537 q^{5} + 1558 q^{6} + 170 q^{7} - 420 q^{8} + 1823 q^{9} + 1470 q^{10} - 5324 q^{11} - 34360 q^{12} + 4250 q^{13} - 29988 q^{14} + 6841 q^{15} + 52744 q^{16} + 54300 q^{17}+ \cdots - 2426413 q^{99}+O(q^{100}) \) 4 * q - 35 * q^3 + 604 * q^4 + 537 * q^5 + 1558 * q^6 + 170 * q^7 - 420 * q^8 + 1823 * q^9 + 1470 * q^10 - 5324 * q^11 - 34360 * q^12 + 4250 * q^13 - 29988 * q^14 + 6841 * q^15 + 52744 * q^16 + 54300 * q^17 - 71350 * q^18 + 67844 * q^19 + 15888 * q^20 + 102262 * q^21 - 9015 * q^23 + 140844 * q^24 + 22531 * q^25 - 311700 * q^26 - 123005 * q^27 - 475840 * q^28 + 234078 * q^29 - 470786 * q^30 + 189857 * q^31 - 175560 * q^32 + 46585 * q^33 + 406536 * q^34 + 154098 * q^35 + 847780 * q^36 + 127895 * q^37 - 584760 * q^38 - 1010660 * q^39 + 2249268 * q^40 + 289842 * q^41 + 1046980 * q^42 + 704930 * q^43 - 803924 * q^44 - 1946752 * q^45 + 3519102 * q^46 - 1729080 * q^47 - 5738680 * q^48 + 139920 * q^49 - 2115918 * q^50 - 2047658 * q^51 + 2030120 * q^52 + 1098660 * q^53 + 4819690 * q^54 - 714747 * q^55 - 4311720 * q^56 + 1566240 * q^57 + 1046100 * q^58 - 4665777 * q^59 + 1373432 * q^60 + 310610 * q^61 + 4286670 * q^62 + 482900 * q^63 + 9539488 * q^64 + 4526160 * q^65 - 2073698 * q^66 - 3368245 * q^67 + 14958120 * q^68 + 7154939 * q^69 - 12580596 * q^70 - 3416541 * q^71 - 25536720 * q^72 + 11466230 * q^73 - 16581438 * q^74 + 3217760 * q^75 + 2169824 * q^76 - 226270 * q^77 + 242200 * q^78 + 566282 * q^79 - 4469544 * q^80 - 862228 * q^81 - 11151780 * q^82 - 4220790 * q^83 + 14471168 * q^84 + 10312902 * q^85 - 5991972 * q^86 - 16784760 * q^87 + 559020 * q^88 + 18265191 * q^89 + 15233552 * q^90 - 1133480 * q^91 - 6399240 * q^92 + 13247755 * q^93 + 8464656 * q^94 - 5662968 * q^95 + 26225096 * q^96 + 11425325 * q^97 + 36460200 * q^98 - 2426413 * q^99

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