LMFDB - Embedded newform 11.10.a.b.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [11,10,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, 10); 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, 10, names="a")

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	11.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5] 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:	$5.66539419780$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 1608x^{3} - 7720x^{2} + 616135x + 6122025 $ x^5 - x^4 - 1608x^3 - 7720x^2 + 616135*x + 6122025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$34.7870$ 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)

$f(q)$	$=$	\(q+37.7870 q^{2} +186.277 q^{3} +915.861 q^{4} -1746.78 q^{5} +7038.85 q^{6} -6901.51 q^{7} +15260.7 q^{8} +15016.0 q^{9} -66005.6 q^{10} +14641.0 q^{11} +170604. q^{12} +176975. q^{13} -260788. q^{14} -325384. q^{15} +107736. q^{16} -478011. q^{17} +567412. q^{18} +193539. q^{19} -1.59981e6 q^{20} -1.28559e6 q^{21} +553240. q^{22} +1.49623e6 q^{23} +2.84271e6 q^{24} +1.09811e6 q^{25} +6.68735e6 q^{26} -869347. q^{27} -6.32082e6 q^{28} +921233. q^{29} -1.22953e7 q^{30} +7.62795e6 q^{31} -3.74245e6 q^{32} +2.72728e6 q^{33} -1.80626e7 q^{34} +1.20554e7 q^{35} +1.37526e7 q^{36} -1.10914e7 q^{37} +7.31326e6 q^{38} +3.29663e7 q^{39} -2.66571e7 q^{40} -190166. q^{41} -4.85787e7 q^{42} -8.56236e6 q^{43} +1.34091e7 q^{44} -2.62297e7 q^{45} +5.65380e7 q^{46} +1.40637e7 q^{47} +2.00687e7 q^{48} +7.27725e6 q^{49} +4.14944e7 q^{50} -8.90423e7 q^{51} +1.62084e8 q^{52} -1.78790e7 q^{53} -3.28501e7 q^{54} -2.55746e7 q^{55} -1.05322e8 q^{56} +3.60518e7 q^{57} +3.48107e7 q^{58} +2.12006e7 q^{59} -2.98007e8 q^{60} +1.17020e8 q^{61} +2.88238e8 q^{62} -1.03633e8 q^{63} -1.96577e8 q^{64} -3.09136e8 q^{65} +1.03056e8 q^{66} +1.97388e6 q^{67} -4.37791e8 q^{68} +2.78712e8 q^{69} +4.55539e8 q^{70} +1.92889e8 q^{71} +2.29155e8 q^{72} +3.43655e6 q^{73} -4.19110e8 q^{74} +2.04553e8 q^{75} +1.77254e8 q^{76} -1.01045e8 q^{77} +1.24570e9 q^{78} -1.83553e8 q^{79} -1.88191e8 q^{80} -4.57500e8 q^{81} -7.18583e6 q^{82} -5.96839e8 q^{83} -1.17742e9 q^{84} +8.34980e8 q^{85} -3.23546e8 q^{86} +1.71604e8 q^{87} +2.23432e8 q^{88} -2.88850e8 q^{89} -9.91143e8 q^{90} -1.22139e9 q^{91} +1.37034e9 q^{92} +1.42091e9 q^{93} +5.31426e8 q^{94} -3.38069e8 q^{95} -6.97132e8 q^{96} +3.19612e8 q^{97} +2.74986e8 q^{98} +2.19850e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16}+ \cdots + 1094985749 q^{99}+O(q^{100}) $ 5 * q + 16 * q^2 + 112 * q^3 + 708 * q^4 + 1594 * q^5 + 10378 * q^6 + 8400 * q^7 + 40716 * q^8 + 74789 * q^9 + 2986 * q^10 + 73205 * q^11 + 110288 * q^12 + 47214 * q^13 - 299852 * q^14 - 559436 * q^15 - 454776 * q^16 - 547238 * q^17 - 822418 * q^18 - 162940 * q^19 - 1913320 * q^20 + 825496 * q^21 + 234256 * q^22 + 3415892 * q^23 + 1435932 * q^24 + 6164943 * q^25 + 5356756 * q^26 + 5240140 * q^27 - 2477216 * q^28 + 5868414 * q^29 - 9766670 * q^30 + 11730396 * q^31 - 18454552 * q^32 + 1639792 * q^33 - 25579352 * q^34 - 6567848 * q^35 - 26683532 * q^36 + 7021250 * q^37 - 22257720 * q^38 + 29114872 * q^39 - 22406796 * q^40 + 5595418 * q^41 - 65554916 * q^42 + 29161940 * q^43 + 10365828 * q^44 + 68008838 * q^45 + 47468978 * q^46 + 33703664 * q^47 + 96997832 * q^48 + 106606605 * q^49 + 84598070 * q^50 - 135853760 * q^51 + 185107192 * q^52 - 88905666 * q^53 - 95103866 * q^54 + 23337754 * q^55 - 78057672 * q^56 - 362541120 * q^57 + 63640668 * q^58 + 13747712 * q^59 - 208875616 * q^60 + 274324430 * q^61 - 161612942 * q^62 - 436710568 * q^63 - 46082368 * q^64 - 658499468 * q^65 + 151944298 * q^66 + 323117752 * q^67 - 679289848 * q^68 - 60345676 * q^69 + 1608436228 * q^70 + 9655356 * q^71 + 1168471200 * q^72 + 159287274 * q^73 + 76718502 * q^74 - 963596116 * q^75 + 483002000 * q^76 + 122984400 * q^77 + 1270322200 * q^78 - 668342072 * q^79 - 424312360 * q^80 + 1578463805 * q^81 + 666585700 * q^82 + 378353820 * q^83 - 2381947456 * q^84 + 1459757140 * q^85 - 2133621276 * q^86 - 2822691048 * q^87 + 596122956 * q^88 + 851774166 * q^89 - 4463334016 * q^90 - 991736368 * q^91 + 1919755168 * q^92 + 1149973204 * q^93 + 2620937360 * q^94 - 2812243800 * q^95 - 1157568712 * q^96 - 240502490 * q^97 - 2298624888 * q^98 + 1094985749 * 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 $

$2$	37.7870	1.66997	0.834984	−	0.550275i	$-0.185477\pi$
$2$	37.7870	1.66997	0.834984	+	0.550275i	$0.185477\pi$
$3$	186.277	1.32774	0.663870	−	0.747848i	$-0.268913\pi$
$3$	186.277	1.32774	0.663870	+	0.747848i	$0.268913\pi$
$4$	915.861	1.78879
$5$	−1746.78	−1.24989	−0.624947	−	0.780667i	$-0.714879\pi$
$5$	−1746.78	−1.24989	−0.624947	+	0.780667i	$0.714879\pi$
$6$	7038.85	2.21728
$7$	−6901.51	−1.08643	−0.543217	−	0.839593i	$-0.682794\pi$
$7$	−6901.51	−1.08643	−0.543217	+	0.839593i	$0.682794\pi$
$8$	15260.7	1.31725
$9$	15016.0	0.762894
$10$	−66005.6	−2.08728
$11$	14641.0	0.301511
$11$	14641.0	0.301511
$12$	170604.	2.37505
$13$	176975.	1.71856	0.859282	−	0.511502i	$-0.170911\pi$
$13$	176975.	1.71856	0.859282	+	0.511502i	$0.170911\pi$
$14$	−260788.	−1.81431
$15$	−325384.	−1.65953
$16$	107736.	0.410980
$17$	−478011.	−1.38809	−0.694045	−	0.719932i	$-0.744173\pi$
$17$	−478011.	−1.38809	−0.694045	+	0.719932i	$0.744173\pi$
$18$	567412.	1.27401
$19$	193539.	0.340704	0.170352	−	0.985383i	$-0.445510\pi$
$19$	193539.	0.340704	0.170352	+	0.985383i	$0.445510\pi$
$20$	−1.59981e6	−2.23580
$21$	−1.28559e6	−1.44250
$22$	553240.	0.503514
$23$	1.49623e6	1.11487	0.557433	−	0.830222i	$-0.311786\pi$
$23$	1.49623e6	1.11487	0.557433	+	0.830222i	$0.311786\pi$
$24$	2.84271e6	1.74897
$25$	1.09811e6	0.562234
$26$	6.68735e6	2.86995
$27$	−869347.	−0.314816
$28$	−6.32082e6	−1.94340
$29$	921233.	0.241868	0.120934	−	0.992661i	$-0.461411\pi$
$29$	921233.	0.241868	0.120934	+	0.992661i	$0.461411\pi$
$30$	−1.22953e7	−2.77137
$31$	7.62795e6	1.48348	0.741738	−	0.670690i	$-0.234002\pi$
$31$	7.62795e6	1.48348	0.741738	+	0.670690i	$0.234002\pi$
$32$	−3.74245e6	−0.630931
$33$	2.72728e6	0.400329
$34$	−1.80626e7	−2.31806
$35$	1.20554e7	1.35793
$36$	1.37526e7	1.36466
$37$	−1.10914e7	−0.972921	−0.486460	−	0.873703i	$-0.661712\pi$
$37$	−1.10914e7	−0.972921	−0.486460	+	0.873703i	$0.661712\pi$
$38$	7.31326e6	0.568964
$39$	3.29663e7	2.28181
$40$	−2.66571e7	−1.64643
$41$	−190166.	−0.0105101	−0.00525505	−	0.999986i	$-0.501673\pi$
$41$	−190166.	−0.0105101	−0.00525505	+	0.999986i	$0.501673\pi$
$42$	−4.85787e7	−2.40893
$43$	−8.56236e6	−0.381931	−0.190966	−	0.981597i	$-0.561162\pi$
$43$	−8.56236e6	−0.381931	−0.190966	+	0.981597i	$0.561162\pi$
$44$	1.34091e7	0.539341
$45$	−2.62297e7	−0.953536
$46$	5.65380e7	1.86179
$47$	1.40637e7	0.420397	0.210199	−	0.977659i	$-0.432589\pi$
$47$	1.40637e7	0.420397	0.210199	+	0.977659i	$0.432589\pi$
$48$	2.00687e7	0.545675
$49$	7.27725e6	0.180337
$50$	4.14944e7	0.938912
$51$	−8.90423e7	−1.84302
$52$	1.62084e8	3.07415
$53$	−1.78790e7	−0.311244	−0.155622	−	0.987817i	$-0.549738\pi$
$53$	−1.78790e7	−0.311244	−0.155622	+	0.987817i	$0.549738\pi$
$54$	−3.28501e7	−0.525732
$55$	−2.55746e7	−0.376857
$56$	−1.05322e8	−1.43111
$57$	3.60518e7	0.452366
$58$	3.48107e7	0.403912
$59$	2.12006e7	0.227779	0.113890	−	0.993493i	$-0.463669\pi$
$59$	2.12006e7	0.227779	0.113890	+	0.993493i	$0.463669\pi$
$60$	−2.98007e8	−2.96856
$61$	1.17020e8	1.08212	0.541059	−	0.840985i	$-0.318024\pi$
$61$	1.17020e8	1.08212	0.541059	+	0.840985i	$0.318024\pi$
$62$	2.88238e8	2.47736
$63$	−1.03633e8	−0.828833
$64$	−1.96577e8	−1.46461
$65$	−3.09136e8	−2.14802
$66$	1.03056e8	0.668536
$67$	1.97388e6	0.0119670	0.00598348	−	0.999982i	$-0.498095\pi$
$67$	1.97388e6	0.0119670	0.00598348	+	0.999982i	$0.498095\pi$
$68$	−4.37791e8	−2.48300
$69$	2.78712e8	1.48025
$70$	4.55539e8	2.26769
$71$	1.92889e8	0.900836	0.450418	−	0.892818i	$-0.351275\pi$
$71$	1.92889e8	0.900836	0.450418	+	0.892818i	$0.351275\pi$
$72$	2.29155e8	1.00492
$73$	3.43655e6	0.0141635	0.00708173	−	0.999975i	$-0.497746\pi$
$73$	3.43655e6	0.0141635	0.00708173	+	0.999975i	$0.497746\pi$
$74$	−4.19110e8	−1.62475
$75$	2.04553e8	0.746500
$76$	1.77254e8	0.609447
$77$	−1.01045e8	−0.327572
$78$	1.24570e9	3.81054
$79$	−1.83553e8	−0.530200	−0.265100	−	0.964221i	$-0.585405\pi$
$79$	−1.83553e8	−0.530200	−0.265100	+	0.964221i	$0.585405\pi$
$80$	−1.88191e8	−0.513681
$81$	−4.57500e8	−1.18089
$82$	−7.18583e6	−0.0175515
$83$	−5.96839e8	−1.38040	−0.690202	−	0.723617i	$-0.742478\pi$
$83$	−5.96839e8	−1.38040	−0.690202	+	0.723617i	$0.742478\pi$
$84$	−1.17742e9	−2.58033
$85$	8.34980e8	1.73496
$86$	−3.23546e8	−0.637813
$87$	1.71604e8	0.321138
$88$	2.23432e8	0.397167
$89$	−2.88850e8	−0.487997	−0.243999	−	0.969776i	$-0.578459\pi$
$89$	−2.88850e8	−0.487997	−0.243999	+	0.969776i	$0.578459\pi$
$90$	−9.91143e8	−1.59237
$91$	−1.22139e9	−1.86711
$92$	1.37034e9	1.99426
$93$	1.42091e9	1.96967
$94$	5.31426e8	0.702049
$95$	−3.38069e8	−0.425843
$96$	−6.97132e8	−0.837712
$97$	3.19612e8	0.366565	0.183282	−	0.983060i	$-0.441328\pi$
$97$	3.19612e8	0.366565	0.183282	+	0.983060i	$0.441328\pi$
$98$	2.74986e8	0.301157
$99$	2.19850e8	0.230021
$100$	1.00572e9	1.00572
$101$	−1.66615e9	−1.59320	−0.796598	−	0.604510i	$-0.793369\pi$
$101$	−1.66615e9	−1.59320	−0.796598	+	0.604510i	$0.793369\pi$
$102$	−3.36465e9	−3.07779
$103$	1.69407e9	1.48308	0.741538	−	0.670911i	$-0.234097\pi$
$103$	1.69407e9	1.48308	0.741538	+	0.670911i	$0.234097\pi$
$104$	2.70076e9	2.26379
$105$	2.24564e9	1.80297
$106$	−6.75593e8	−0.519767
$107$	−9.49695e8	−0.700418	−0.350209	−	0.936672i	$-0.613889\pi$
$107$	−9.49695e8	−0.700418	−0.350209	+	0.936672i	$0.613889\pi$
$108$	−7.96201e8	−0.563139
$109$	8.16040e8	0.553723	0.276861	−	0.960910i	$-0.410706\pi$
$109$	8.16040e8	0.553723	0.276861	+	0.960910i	$0.410706\pi$
$110$	−9.66388e8	−0.629339
$111$	−2.06606e9	−1.29179
$112$	−7.43541e8	−0.446502
$113$	1.38716e9	0.800340	0.400170	−	0.916441i	$-0.368951\pi$
$113$	1.38716e9	0.800340	0.400170	+	0.916441i	$0.368951\pi$
$114$	1.36229e9	0.755436
$115$	−2.61358e9	−1.39346
$116$	8.43721e8	0.432651
$117$	2.65746e9	1.31108
$118$	8.01109e8	0.380384
$119$	3.29900e9	1.50807
$120$	−4.96559e9	−2.18603
$121$	2.14359e8	0.0909091
$122$	4.42182e9	1.80710
$123$	−3.54236e7	−0.0139547
$124$	6.98614e9	2.65363
$125$	1.49352e9	0.547161
$126$	−3.91600e9	−1.38412
$127$	−4.62969e9	−1.57919	−0.789596	−	0.613628i	$-0.789710\pi$
$127$	−4.62969e9	−1.57919	−0.789596	+	0.613628i	$0.789710\pi$
$128$	−5.51193e9	−1.81493
$129$	−1.59497e9	−0.507106
$130$	−1.16813e10	−3.58713
$131$	−2.60178e9	−0.771879	−0.385940	−	0.922524i	$-0.626123\pi$
$131$	−2.60178e9	−0.771879	−0.385940	+	0.922524i	$0.626123\pi$
$132$	2.49781e9	0.716104
$133$	−1.33571e9	−0.370152
$134$	7.45870e7	0.0199844
$135$	1.51856e9	0.393486
$136$	−7.29478e9	−1.82847
$137$	−1.07365e9	−0.260389	−0.130194	−	0.991488i	$-0.541560\pi$
$137$	−1.07365e9	−0.260389	−0.130194	+	0.991488i	$0.541560\pi$
$138$	1.05317e10	2.47197
$139$	4.08617e9	0.928432	0.464216	−	0.885722i	$-0.346336\pi$
$139$	4.08617e9	0.928432	0.464216	+	0.885722i	$0.346336\pi$
$140$	1.10411e10	2.42904
$141$	2.61974e9	0.558178
$142$	7.28872e9	1.50437
$143$	2.59109e9	0.518167
$144$	1.61777e9	0.313534
$145$	−1.60919e9	−0.302309
$146$	1.29857e8	0.0236525
$147$	1.35558e9	0.239441
$148$	−1.01581e10	−1.74035
$149$	−7.66479e9	−1.27398	−0.636989	−	0.770873i	$-0.719820\pi$
$149$	−7.66479e9	−1.27398	−0.636989	+	0.770873i	$0.719820\pi$
$150$	7.72945e9	1.24663
$151$	−6.92089e8	−0.108334	−0.0541671	−	0.998532i	$-0.517250\pi$
$151$	−6.92089e8	−0.108334	−0.0541671	+	0.998532i	$0.517250\pi$
$152$	2.95354e9	0.448793
$153$	−7.17783e9	−1.05896
$154$	−3.81819e9	−0.547034
$155$	−1.33244e10	−1.85419
$156$	3.01925e10	4.08167
$157$	1.07386e10	1.41059	0.705295	−	0.708914i	$-0.250815\pi$
$157$	1.07386e10	1.41059	0.705295	+	0.708914i	$0.250815\pi$
$158$	−6.93593e9	−0.885416
$159$	−3.33043e9	−0.413251
$160$	6.53724e9	0.788596
$161$	−1.03262e10	−1.21123
$162$	−1.72876e10	−1.97204
$163$	−3.95770e8	−0.0439136	−0.0219568	−	0.999759i	$-0.506990\pi$
$163$	−3.95770e8	−0.0439136	−0.0219568	+	0.999759i	$0.506990\pi$
$164$	−1.74166e8	−0.0188003
$165$	−4.76395e9	−0.500368
$166$	−2.25528e10	−2.30523
$167$	−2.64762e9	−0.263409	−0.131705	−	0.991289i	$-0.542045\pi$
$167$	−2.64762e9	−0.263409	−0.131705	+	0.991289i	$0.542045\pi$
$168$	−1.96190e10	−1.90014
$169$	2.07155e10	1.95346
$170$	3.15514e10	2.89733
$171$	2.90618e9	0.259921
$172$	−7.84193e9	−0.683195
$173$	7.34562e8	0.0623478	0.0311739	−	0.999514i	$-0.490075\pi$
$173$	7.34562e8	0.0623478	0.0311739	+	0.999514i	$0.490075\pi$
$174$	6.48442e9	0.536289
$175$	−7.57864e9	−0.610830
$176$	1.57736e9	0.123915
$177$	3.94918e9	0.302432
$178$	−1.09148e10	−0.814939
$179$	−9.31362e8	−0.0678078	−0.0339039	−	0.999425i	$-0.510794\pi$
$179$	−9.31362e8	−0.0678078	−0.0339039	+	0.999425i	$0.510794\pi$
$180$	−2.40227e10	−1.70568
$181$	2.76071e10	1.91191	0.955955	−	0.293512i	$-0.0948240\pi$
$181$	2.76071e10	1.91191	0.955955	+	0.293512i	$0.0948240\pi$
$182$	−4.61528e10	−3.11801
$183$	2.17980e10	1.43677
$184$	2.28335e10	1.46856
$185$	1.93742e10	1.21605
$186$	5.36920e10	3.28928
$187$	−6.99856e9	−0.418525
$188$	1.28804e10	0.752002
$189$	5.99981e9	0.342026
$190$	−1.27746e10	−0.711144
$191$	−1.73007e10	−0.940620	−0.470310	−	0.882501i	$-0.655858\pi$
$191$	−1.73007e10	−0.940620	−0.470310	+	0.882501i	$0.655858\pi$
$192$	−3.66177e10	−1.94463
$193$	1.84839e10	0.958930	0.479465	−	0.877561i	$-0.340831\pi$
$193$	1.84839e10	0.958930	0.479465	+	0.877561i	$0.340831\pi$
$194$	1.20772e10	0.612151
$195$	−5.75848e10	−2.85202
$196$	6.66495e9	0.322585
$197$	−2.69918e8	−0.0127683	−0.00638417	−	0.999980i	$-0.502032\pi$
$197$	−2.69918e8	−0.0127683	−0.00638417	+	0.999980i	$0.502032\pi$
$198$	8.30747e9	0.384128
$199$	3.30838e10	1.49546	0.747732	−	0.664000i	$-0.231143\pi$
$199$	3.30838e10	1.49546	0.747732	+	0.664000i	$0.231143\pi$
$200$	1.67580e10	0.740605
$201$	3.67688e8	0.0158890
$202$	−6.29591e10	−2.66058
$203$	−6.35790e9	−0.262773
$204$	−8.15503e10	−3.29678
$205$	3.32179e8	0.0131365
$206$	6.40138e10	2.47669
$207$	2.24674e10	0.850524
$208$	1.90665e10	0.706296
$209$	2.83360e9	0.102726
$210$	8.48563e10	3.01090
$211$	−1.65131e10	−0.573532	−0.286766	−	0.958001i	$-0.592580\pi$
$211$	−1.65131e10	−0.573532	−0.286766	+	0.958001i	$0.592580\pi$
$212$	−1.63746e10	−0.556750
$213$	3.59308e10	1.19608
$214$	−3.58862e10	−1.16967
$215$	1.49566e10	0.477374
$216$	−1.32668e10	−0.414692
$217$	−5.26444e10	−1.61170
$218$	3.08357e10	0.924698
$219$	6.40149e8	0.0188054
$220$	−2.34228e10	−0.674118
$221$	−8.45958e10	−2.38552
$222$	−7.80705e10	−2.15724
$223$	6.66167e9	0.180389	0.0901947	−	0.995924i	$-0.471251\pi$
$223$	6.66167e9	0.180389	0.0901947	+	0.995924i	$0.471251\pi$
$224$	2.58286e10	0.685464
$225$	1.64893e10	0.428925
$226$	5.24168e10	1.33654
$227$	5.36225e10	1.34039	0.670194	−	0.742186i	$-0.266211\pi$
$227$	5.36225e10	1.34039	0.670194	+	0.742186i	$0.266211\pi$
$228$	3.30184e10	0.809187
$229$	−5.82017e10	−1.39854	−0.699272	−	0.714856i	$-0.746492\pi$
$229$	−5.82017e10	−1.39854	−0.699272	+	0.714856i	$0.746492\pi$
$230$	−9.87594e10	−2.32704
$231$	−1.88223e10	−0.434930
$232$	1.40586e10	0.318601
$233$	−3.76554e10	−0.837000	−0.418500	−	0.908217i	$-0.637444\pi$
$233$	−3.76554e10	−0.837000	−0.418500	+	0.908217i	$0.637444\pi$
$234$	1.00417e11	2.18946
$235$	−2.45662e10	−0.525452
$236$	1.94168e10	0.407450
$237$	−3.41917e10	−0.703968
$238$	1.24659e11	2.51842
$239$	8.85989e9	0.175646	0.0878229	−	0.996136i	$-0.472009\pi$
$239$	8.85989e9	0.175646	0.0878229	+	0.996136i	$0.472009\pi$
$240$	−3.50556e10	−0.682035
$241$	9.59085e10	1.83139	0.915694	−	0.401877i	$-0.131642\pi$
$241$	9.59085e10	1.83139	0.915694	+	0.401877i	$0.131642\pi$
$242$	8.09999e9	0.151815
$243$	−6.81102e10	−1.25310
$244$	1.07174e11	1.93568
$245$	−1.27118e10	−0.225402
$246$	−1.33855e9	−0.0233038
$247$	3.42514e10	0.585521
$248$	1.16408e11	1.95411
$249$	−1.11177e11	−1.83282
$250$	5.64356e10	0.913741
$251$	7.20438e10	1.14568	0.572842	−	0.819666i	$-0.305841\pi$
$251$	7.20438e10	1.14568	0.572842	+	0.819666i	$0.305841\pi$
$252$	−9.49137e10	−1.48261
$253$	2.19063e10	0.336145
$254$	−1.74942e11	−2.63720
$255$	1.55537e11	2.30358
$256$	−1.07632e11	−1.56625
$257$	9.49867e10	1.35820	0.679100	−	0.734046i	$-0.262370\pi$
$257$	9.49867e10	1.35820	0.679100	+	0.734046i	$0.262370\pi$
$258$	−6.02691e10	−0.846850
$259$	7.65472e10	1.05701
$260$	−2.83125e11	−3.84236
$261$	1.38333e10	0.184520
$262$	−9.83135e10	−1.28901
$263$	3.34976e10	0.431731	0.215865	−	0.976423i	$-0.430743\pi$
$263$	3.34976e10	0.431731	0.215865	+	0.976423i	$0.430743\pi$
$264$	4.16202e10	0.527334
$265$	3.12306e10	0.389022
$266$	−5.04725e10	−0.618141
$267$	−5.38060e10	−0.647933
$268$	1.80780e9	0.0214064
$269$	−1.13277e11	−1.31903	−0.659516	−	0.751690i	$-0.729239\pi$
$269$	−1.13277e11	−1.31903	−0.659516	+	0.751690i	$0.729239\pi$
$270$	5.73818e10	0.657109
$271$	−5.85641e10	−0.659583	−0.329792	−	0.944054i	$-0.606979\pi$
$271$	−5.85641e10	−0.659583	−0.329792	+	0.944054i	$0.606979\pi$
$272$	−5.14989e10	−0.570477
$273$	−2.27517e11	−2.47903
$274$	−4.05702e10	−0.434840
$275$	1.60775e10	0.169520
$276$	2.55262e11	2.64786
$277$	−5.61058e10	−0.572596	−0.286298	−	0.958141i	$-0.592425\pi$
$277$	−5.61058e10	−0.572596	−0.286298	+	0.958141i	$0.592425\pi$
$278$	1.54404e11	1.55045
$279$	1.14542e11	1.13173
$280$	1.83974e11	1.78873
$281$	−5.82633e10	−0.557464	−0.278732	−	0.960369i	$-0.589914\pi$
$281$	−5.82633e10	−0.557464	−0.278732	+	0.960369i	$0.589914\pi$
$282$	9.89924e10	0.932139
$283$	−8.51619e10	−0.789235	−0.394617	−	0.918846i	$-0.629123\pi$
$283$	−8.51619e10	−0.789235	−0.394617	+	0.918846i	$0.629123\pi$
$284$	1.76660e11	1.61141
$285$	−6.29745e10	−0.565409
$286$	9.79094e10	0.865321
$287$	1.31244e9	0.0114185
$288$	−5.61968e10	−0.481333
$289$	1.09907e11	0.926794
$290$	−6.08065e10	−0.504846
$291$	5.95363e10	0.486702
$292$	3.14740e9	0.0253355
$293$	4.86121e10	0.385337	0.192668	−	0.981264i	$-0.438286\pi$
$293$	4.86121e10	0.385337	0.192668	+	0.981264i	$0.438286\pi$
$294$	5.12235e10	0.399858
$295$	−3.70328e10	−0.284700
$296$	−1.69262e11	−1.28158
$297$	−1.27281e10	−0.0949205
$298$	−2.89630e11	−2.12750
$299$	2.64794e11	1.91597
$300$	1.87342e11	1.33533
$301$	5.90932e10	0.414943
$302$	−2.61520e10	−0.180915
$303$	−3.10366e11	−2.11535
$304$	2.08511e10	0.140022
$305$	−2.04407e11	−1.35253
$306$	−2.71229e11	−1.76844
$307$	5.54371e10	0.356187	0.178093	−	0.984014i	$-0.443007\pi$
$307$	5.54371e10	0.356187	0.178093	+	0.984014i	$0.443007\pi$
$308$	−9.25432e10	−0.585957
$309$	3.15565e11	1.96914
$310$	−5.03488e11	−3.09643
$311$	−1.91969e11	−1.16362	−0.581809	−	0.813326i	$-0.697655\pi$
$311$	−1.91969e11	−1.16362	−0.581809	+	0.813326i	$0.697655\pi$
$312$	5.03088e11	3.00572
$313$	1.21549e11	0.715819	0.357909	−	0.933756i	$-0.383490\pi$
$313$	1.21549e11	0.715819	0.357909	+	0.933756i	$0.383490\pi$
$314$	4.05781e11	2.35564
$315$	1.81025e11	1.03595
$316$	−1.68109e11	−0.948416
$317$	3.42125e11	1.90291	0.951456	−	0.307786i	$-0.0995880\pi$
$317$	3.42125e11	1.90291	0.951456	+	0.307786i	$0.0995880\pi$
$318$	−1.25847e11	−0.690115
$319$	1.34878e10	0.0729259
$320$	3.43377e11	1.83061
$321$	−1.76906e11	−0.929973
$322$	−3.90198e11	−2.02271
$323$	−9.25136e10	−0.472927
$324$	−4.19006e11	−2.11236
$325$	1.94338e11	0.966235
$326$	−1.49550e10	−0.0733343
$327$	1.52009e11	0.735200
$328$	−2.90207e9	−0.0138445
$329$	−9.70609e10	−0.456733
$330$	−1.80016e11	−0.835599
$331$	−1.16598e11	−0.533907	−0.266953	−	0.963709i	$-0.586017\pi$
$331$	−1.16598e11	−0.533907	−0.266953	+	0.963709i	$0.586017\pi$
$332$	−5.46622e11	−2.46925
$333$	−1.66548e11	−0.742235
$334$	−1.00046e11	−0.439885
$335$	−3.44793e9	−0.0149574
$336$	−1.38504e11	−0.592839
$337$	−1.93953e11	−0.819147	−0.409574	−	0.912277i	$-0.634322\pi$
$337$	−1.93953e11	−0.819147	−0.409574	+	0.912277i	$0.634322\pi$
$338$	7.82778e11	3.26222
$339$	2.58396e11	1.06264
$340$	7.64725e11	3.10349
$341$	1.11681e11	0.447285
$342$	1.09816e11	0.434059
$343$	2.28277e11	0.890509
$344$	−1.30668e11	−0.503100
$345$	−4.86849e11	−1.85016
$346$	2.77569e10	0.104119
$347$	−8.60648e10	−0.318671	−0.159336	−	0.987224i	$-0.550935\pi$
$347$	−8.60648e10	−0.318671	−0.159336	+	0.987224i	$0.550935\pi$
$348$	1.57166e11	0.574448
$349$	1.92176e11	0.693402	0.346701	−	0.937976i	$-0.387302\pi$
$349$	1.92176e11	0.693402	0.346701	+	0.937976i	$0.387302\pi$
$350$	−2.86374e11	−1.02007
$351$	−1.53852e11	−0.541031
$352$	−5.47933e10	−0.190233
$353$	2.92048e11	1.00108	0.500538	−	0.865714i	$-0.333135\pi$
$353$	2.92048e11	1.00108	0.500538	+	0.865714i	$0.333135\pi$
$354$	1.49228e11	0.505051
$355$	−3.36935e11	−1.12595
$356$	−2.64546e11	−0.872925
$357$	6.14527e11	2.00232
$358$	−3.51934e10	−0.113237
$359$	−4.95274e11	−1.57369	−0.786847	−	0.617148i	$-0.788288\pi$
$359$	−4.95274e11	−1.57369	−0.786847	+	0.617148i	$0.788288\pi$
$360$	−4.00283e11	−1.25605
$361$	−2.85230e11	−0.883921
$362$	1.04319e12	3.19283
$363$	3.99301e10	0.120704
$364$	−1.11863e12	−3.33986
$365$	−6.00289e9	−0.0177028
$366$	8.23683e11	2.39936
$367$	−3.88365e11	−1.11749	−0.558744	−	0.829340i	$-0.688717\pi$
$367$	−3.88365e11	−1.11749	−0.558744	+	0.829340i	$0.688717\pi$
$368$	1.61197e11	0.458187
$369$	−2.85555e9	−0.00801808
$370$	7.32093e11	2.03076
$371$	1.23392e11	0.338146
$372$	1.30136e12	3.52333
$373$	−5.39272e11	−1.44251	−0.721254	−	0.692671i	$-0.756434\pi$
$373$	−5.39272e11	−1.44251	−0.721254	+	0.692671i	$0.756434\pi$
$374$	−2.64455e11	−0.698923
$375$	2.78208e11	0.726488
$376$	2.14622e11	0.553770
$377$	1.63035e11	0.415666
$378$	2.26715e11	0.571172
$379$	7.49252e11	1.86531	0.932656	−	0.360766i	$-0.117485\pi$
$379$	7.49252e11	1.86531	0.932656	+	0.360766i	$0.117485\pi$
$380$	−3.09624e11	−0.761744
$381$	−8.62403e11	−2.09676
$382$	−6.53744e11	−1.57081
$383$	−6.85788e11	−1.62853	−0.814264	−	0.580495i	$-0.802859\pi$
$383$	−6.85788e11	−1.62853	−0.814264	+	0.580495i	$0.802859\pi$
$384$	−1.02674e12	−2.40975
$385$	1.76503e11	0.409430
$386$	6.98454e11	1.60138
$387$	−1.28573e11	−0.291373
$388$	2.92720e11	0.655707
$389$	3.64740e11	0.807627	0.403813	−	0.914841i	$-0.367685\pi$
$389$	3.64740e11	0.807627	0.403813	+	0.914841i	$0.367685\pi$
$390$	−2.17596e12	−4.76277
$391$	−7.15213e11	−1.54753
$392$	1.11056e11	0.237550
$393$	−4.84651e11	−1.02486
$394$	−1.01994e10	−0.0213227
$395$	3.20627e11	0.662693
$396$	2.01352e11	0.411459
$397$	−1.71931e11	−0.347375	−0.173687	−	0.984801i	$-0.555568\pi$
$397$	−1.71931e11	−0.347375	−0.173687	+	0.984801i	$0.555568\pi$
$398$	1.25014e12	2.49738
$399$	−2.48812e11	−0.491465
$400$	1.18306e11	0.231067
$401$	−3.46992e11	−0.670146	−0.335073	−	0.942192i	$-0.608761\pi$
$401$	−3.46992e11	−0.670146	−0.335073	+	0.942192i	$0.608761\pi$
$402$	1.38938e10	0.0265341
$403$	1.34995e12	2.54945
$404$	−1.52597e12	−2.84989
$405$	7.99151e11	1.47598
$406$	−2.40246e11	−0.438823
$407$	−1.62389e11	−0.293347
$408$	−1.35885e12	−2.42773
$409$	1.06588e12	1.88344	0.941719	−	0.336399i	$-0.109209\pi$
$409$	1.06588e12	1.88344	0.941719	+	0.336399i	$0.109209\pi$
$410$	1.25521e10	0.0219375
$411$	−1.99997e11	−0.345728
$412$	1.55153e12	2.65291
$413$	−1.46316e11	−0.247467
$414$	8.48977e11	1.42035
$415$	1.04255e12	1.72536
$416$	−6.62319e11	−1.08429
$417$	7.61159e11	1.23272
$418$	1.07073e11	0.171549
$419$	−1.21217e12	−1.92133	−0.960665	−	0.277709i	$-0.910425\pi$
$419$	−1.21217e12	−1.92133	−0.960665	+	0.277709i	$0.910425\pi$
$420$	2.05670e12	3.22514
$421$	7.44489e11	1.15502	0.577509	−	0.816384i	$-0.304025\pi$
$421$	7.44489e11	1.15502	0.577509	+	0.816384i	$0.304025\pi$
$422$	−6.23981e11	−0.957779
$423$	2.11181e11	0.320718
$424$	−2.72845e11	−0.409987
$425$	−5.24910e11	−0.780431
$426$	1.35772e12	1.99741
$427$	−8.07612e11	−1.17565
$428$	−8.69788e11	−1.25290
$429$	4.82659e11	0.687991
$430$	5.65164e11	0.797198
$431$	6.48927e11	0.905833	0.452917	−	0.891553i	$-0.350384\pi$
$431$	6.48927e11	0.905833	0.452917	+	0.891553i	$0.350384\pi$
$432$	−9.36599e10	−0.129383
$433$	−2.13599e11	−0.292013	−0.146007	−	0.989284i	$-0.546642\pi$
$433$	−2.13599e11	−0.292013	−0.146007	+	0.989284i	$0.546642\pi$
$434$	−1.98928e12	−2.69148
$435$	−2.99755e11	−0.401388
$436$	7.47379e11	0.990493
$437$	2.89578e11	0.379839
$438$	2.41893e10	0.0314044
$439$	−5.97567e11	−0.767885	−0.383943	−	0.923357i	$-0.625434\pi$
$439$	−5.97567e11	−0.767885	−0.383943	+	0.923357i	$0.625434\pi$
$440$	−3.90286e11	−0.496416
$441$	1.09275e11	0.137578
$442$	−3.19662e12	−3.98374
$443$	−9.46336e11	−1.16742	−0.583712	−	0.811961i	$-0.698400\pi$
$443$	−9.46336e11	−1.16742	−0.583712	+	0.811961i	$0.698400\pi$
$444$	−1.89223e12	−2.31073
$445$	5.04557e11	0.609945
$446$	2.51725e11	0.301244
$447$	−1.42777e12	−1.69151
$448$	1.35668e12	1.59120
$449$	6.30900e11	0.732575	0.366288	−	0.930502i	$-0.380629\pi$
$449$	6.30900e11	0.732575	0.366288	+	0.930502i	$0.380629\pi$
$450$	6.23082e11	0.716290
$451$	−2.78423e9	−0.00316891
$452$	1.27045e12	1.43164
$453$	−1.28920e11	−0.143840
$454$	2.02624e12	2.23840
$455$	2.13350e12	2.33368
$456$	5.50175e11	0.595880
$457$	7.97795e11	0.855596	0.427798	−	0.903874i	$-0.359289\pi$
$457$	7.97795e11	0.855596	0.427798	+	0.903874i	$0.359289\pi$
$458$	−2.19927e12	−2.33552
$459$	4.15557e11	0.436992
$460$	−2.39367e12	−2.49261
$461$	1.61323e12	1.66358	0.831789	−	0.555091i	$-0.187317\pi$
$461$	1.61323e12	1.66358	0.831789	+	0.555091i	$0.187317\pi$
$462$	−7.11241e11	−0.726319
$463$	−3.08097e11	−0.311583	−0.155791	−	0.987790i	$-0.549793\pi$
$463$	−3.08097e11	−0.311583	−0.155791	+	0.987790i	$0.549793\pi$
$464$	9.92498e10	0.0994029
$465$	−2.48202e12	−2.46188
$466$	−1.42289e12	−1.39776
$467$	−6.29999e11	−0.612934	−0.306467	−	0.951881i	$-0.599147\pi$
$467$	−6.29999e11	−0.612934	−0.306467	+	0.951881i	$0.599147\pi$
$468$	2.43386e12	2.34525
$469$	−1.36227e10	−0.0130013
$470$	−9.28284e11	−0.877487
$471$	2.00036e12	1.87290
$472$	3.23536e11	0.300043
$473$	−1.25361e11	−0.115157
$474$	−1.29200e12	−1.17560
$475$	2.12527e11	0.191555
$476$	3.02142e12	2.69762
$477$	−2.68471e11	−0.237446
$478$	3.34789e11	0.293323
$479$	−5.78348e10	−0.0501972	−0.0250986	−	0.999685i	$-0.507990\pi$
$479$	−5.78348e10	−0.0501972	−0.0250986	+	0.999685i	$0.507990\pi$
$480$	1.21774e12	1.04705
$481$	−1.96289e12	−1.67203
$482$	3.62410e12	3.05836
$483$	−1.92354e12	−1.60819
$484$	1.96323e11	0.162617
$485$	−5.58292e11	−0.458167
$486$	−2.57368e12	−2.09263
$487$	−4.44052e11	−0.357729	−0.178864	−	0.983874i	$-0.557242\pi$
$487$	−4.44052e11	−0.357729	−0.178864	+	0.983874i	$0.557242\pi$
$488$	1.78580e12	1.42542
$489$	−7.37228e10	−0.0583058
$490$	−4.80340e11	−0.376414
$491$	5.36565e11	0.416635	0.208317	−	0.978061i	$-0.433201\pi$
$491$	5.36565e11	0.416635	0.208317	+	0.978061i	$0.433201\pi$
$492$	−3.24431e10	−0.0249620
$493$	−4.40359e11	−0.335734
$494$	1.29426e12	0.977801
$495$	−3.84029e11	−0.287502
$496$	8.21805e11	0.609679
$497$	−1.33123e12	−0.978698
$498$	−4.20106e12	−3.06074
$499$	−1.27663e12	−0.921751	−0.460875	−	0.887465i	$-0.652464\pi$
$499$	−1.27663e12	−0.921751	−0.460875	+	0.887465i	$0.652464\pi$
$500$	1.36785e12	0.978756
$501$	−4.93189e11	−0.349739
$502$	2.72232e12	1.91325
$503$	−1.81225e12	−1.26230	−0.631148	−	0.775662i	$-0.717416\pi$
$503$	−1.81225e12	−1.26230	−0.631148	+	0.775662i	$0.717416\pi$
$504$	−1.58152e12	−1.09178
$505$	2.91040e12	1.99132
$506$	8.27773e11	0.561350
$507$	3.85882e12	2.59369
$508$	−4.24015e12	−2.82484
$509$	2.77734e12	1.83400	0.917000	−	0.398887i	$-0.130603\pi$
$509$	2.77734e12	1.83400	0.917000	+	0.398887i	$0.130603\pi$
$510$	5.87729e12	3.84691
$511$	−2.37174e10	−0.0153877
$512$	−1.24499e12	−0.800665
$513$	−1.68252e11	−0.107259
$514$	3.58927e12	2.26815
$515$	−2.95916e12	−1.85369
$516$	−1.46077e12	−0.907106
$517$	2.05907e11	0.126755
$518$	2.89249e12	1.76518
$519$	1.36832e11	0.0827816
$520$	−4.71762e12	−2.82949
$521$	−2.46844e11	−0.146775	−0.0733875	−	0.997304i	$-0.523381\pi$
$521$	−2.46844e11	−0.146775	−0.0733875	+	0.997304i	$0.523381\pi$
$522$	5.22718e11	0.308142
$523$	−4.70491e11	−0.274975	−0.137488	−	0.990503i	$-0.543903\pi$
$523$	−4.70491e11	−0.274975	−0.137488	+	0.990503i	$0.543903\pi$
$524$	−2.38287e12	−1.38073
$525$	−1.41172e12	−0.811023
$526$	1.26578e12	0.720977
$527$	−3.64625e12	−2.05920
$528$	2.93826e11	0.164527
$529$	4.37545e11	0.242925
$530$	1.18011e12	0.649653
$531$	3.18349e11	0.173772
$532$	−1.22332e12	−0.662124
$533$	−3.36546e10	−0.0180623
$534$	−2.03317e12	−1.08203
$535$	1.65891e12	0.875447
$536$	3.01228e10	0.0157635
$537$	−1.73491e11	−0.0900311
$538$	−4.28039e12	−2.20274
$539$	1.06546e11	0.0543737
$540$	1.39079e12	0.703864
$541$	7.44378e11	0.373599	0.186800	−	0.982398i	$-0.440189\pi$
$541$	7.44378e11	0.373599	0.186800	+	0.982398i	$0.440189\pi$
$542$	−2.21296e12	−1.10148
$543$	5.14257e12	2.53852
$544$	1.78893e12	0.875788
$545$	−1.42544e12	−0.692094
$546$	−8.59720e12	−4.13990
$547$	−2.66193e12	−1.27131	−0.635657	−	0.771972i	$-0.719271\pi$
$547$	−2.66193e12	−1.27131	−0.635657	+	0.771972i	$0.719271\pi$
$548$	−9.83318e11	−0.465781
$549$	1.75717e12	0.825540
$550$	6.07520e11	0.283093
$551$	1.78294e11	0.0824053
$552$	4.25335e12	1.94987
$553$	1.26679e12	0.576027
$554$	−2.12007e12	−0.956217
$555$	3.60896e12	1.61459
$556$	3.74236e12	1.66077
$557$	6.59469e11	0.290299	0.145150	−	0.989410i	$-0.453634\pi$
$557$	6.59469e11	0.290299	0.145150	+	0.989410i	$0.453634\pi$
$558$	4.32819e12	1.88996
$559$	−1.51532e12	−0.656374
$560$	1.29880e12	0.558080
$561$	−1.30367e12	−0.555692
$562$	−2.20160e12	−0.930946
$563$	2.33871e12	0.981044	0.490522	−	0.871429i	$-0.336806\pi$
$563$	2.33871e12	0.981044	0.490522	+	0.871429i	$0.336806\pi$
$564$	2.39932e12	0.998464
$565$	−2.42307e12	−1.00034
$566$	−3.21802e12	−1.31800
$567$	3.15744e12	1.28295
$568$	2.94363e12	1.18663
$569$	−2.41826e12	−0.967160	−0.483580	−	0.875300i	$-0.660664\pi$
$569$	−2.41826e12	−0.967160	−0.483580	+	0.875300i	$0.660664\pi$
$570$	−2.37962e12	−0.944215
$571$	2.10936e12	0.830403	0.415201	−	0.909730i	$-0.363711\pi$
$571$	2.10936e12	0.830403	0.415201	+	0.909730i	$0.363711\pi$
$572$	2.37307e12	0.926892
$573$	−3.22272e12	−1.24890
$574$	4.95931e10	0.0190685
$575$	1.64303e12	0.626815
$576$	−2.95181e12	−1.11734
$577$	−3.57287e12	−1.34192	−0.670960	−	0.741494i	$-0.734118\pi$
$577$	−3.57287e12	−1.34192	−0.670960	+	0.741494i	$0.734118\pi$
$578$	4.15304e12	1.54772
$579$	3.44313e12	1.27321
$580$	−1.47379e12	−0.540768
$581$	4.11909e12	1.49972
$582$	2.24970e12	0.812777
$583$	−2.61766e11	−0.0938435
$584$	5.24441e10	0.0186569
$585$	−4.64199e12	−1.63871
$586$	1.83691e12	0.643500
$587$	8.17852e11	0.284317	0.142159	−	0.989844i	$-0.454596\pi$
$587$	8.17852e11	0.284317	0.142159	+	0.989844i	$0.454596\pi$
$588$	1.24153e12	0.428309
$589$	1.47630e12	0.505425
$590$	−1.39936e12	−0.475440
$591$	−5.02795e10	−0.0169530
$592$	−1.19494e12	−0.399851
$593$	−5.72237e12	−1.90033	−0.950166	−	0.311744i	$-0.899087\pi$
$593$	−5.72237e12	−1.90033	−0.950166	+	0.311744i	$0.899087\pi$
$594$	−4.80958e11	−0.158514
$595$	−5.76262e12	−1.88492
$596$	−7.01988e12	−2.27888
$597$	6.16274e12	1.98559
$598$	1.00058e13	3.19960
$599$	2.47346e12	0.785026	0.392513	−	0.919747i	$-0.371606\pi$
$599$	2.47346e12	0.785026	0.392513	+	0.919747i	$0.371606\pi$
$600$	3.12162e12	0.983330
$601$	−3.56879e12	−1.11580	−0.557899	−	0.829909i	$-0.688392\pi$
$601$	−3.56879e12	−1.11580	−0.557899	+	0.829909i	$0.688392\pi$
$602$	2.23296e12	0.692941
$603$	2.96398e10	0.00912951
$604$	−6.33857e11	−0.193787
$605$	−3.74438e11	−0.113627
$606$	−1.17278e13	−3.53256
$607$	2.18785e11	0.0654136	0.0327068	−	0.999465i	$-0.489587\pi$
$607$	2.18785e11	0.0654136	0.0327068	+	0.999465i	$0.489587\pi$
$608$	−7.24310e11	−0.214960
$609$	−1.18433e12	−0.348895
$610$	−7.72395e12	−2.25868
$611$	2.48892e12	0.722480
$612$	−6.57389e12	−1.89427
$613$	7.35293e10	0.0210324	0.0105162	−	0.999945i	$-0.496653\pi$
$613$	7.35293e10	0.0210324	0.0105162	+	0.999945i	$0.496653\pi$
$614$	2.09480e12	0.594820
$615$	6.18772e10	0.0174418
$616$	−1.54202e12	−0.431495
$617$	−2.07966e12	−0.577708	−0.288854	−	0.957373i	$-0.593274\pi$
$617$	−2.07966e12	−0.577708	−0.288854	+	0.957373i	$0.593274\pi$
$618$	1.19243e13	3.28840
$619$	−4.74329e12	−1.29859	−0.649294	−	0.760537i	$-0.724936\pi$
$619$	−4.74329e12	−1.29859	−0.649294	+	0.760537i	$0.724936\pi$
$620$	−1.22032e13	−3.31675
$621$	−1.30074e12	−0.350977
$622$	−7.25396e12	−1.94320
$623$	1.99350e12	0.530176
$624$	3.55165e12	0.937777
$625$	−4.75360e12	−1.24613
$626$	4.59299e12	1.19539
$627$	5.27834e11	0.136393
$628$	9.83509e12	2.52325
$629$	5.30180e12	1.35050
$630$	6.84038e12	1.73001
$631$	6.48301e12	1.62796	0.813981	−	0.580891i	$-0.197296\pi$
$631$	6.48301e12	1.62796	0.813981	+	0.580891i	$0.197296\pi$
$632$	−2.80115e12	−0.698408
$633$	−3.07601e12	−0.761501
$634$	1.29279e13	3.17780
$635$	8.08704e12	1.97382
$636$	−3.05021e12	−0.739219
$637$	1.28789e12	0.309921
$638$	5.09663e11	0.121784
$639$	2.89643e12	0.687242
$640$	9.62812e12	2.26846
$641$	4.07928e12	0.954383	0.477191	−	0.878799i	$-0.341655\pi$
$641$	4.07928e12	0.954383	0.477191	+	0.878799i	$0.341655\pi$
$642$	−6.68476e12	−1.55302
$643$	−6.68210e12	−1.54157	−0.770786	−	0.637095i	$-0.780136\pi$
$643$	−6.68210e12	−1.54157	−0.770786	+	0.637095i	$0.780136\pi$
$644$	−9.45739e12	−2.16663
$645$	2.78606e12	0.633828
$646$	−3.49582e12	−0.789773
$647$	5.99370e12	1.34470	0.672351	−	0.740233i	$-0.265285\pi$
$647$	5.99370e12	1.34470	0.672351	+	0.740233i	$0.265285\pi$
$648$	−6.98176e12	−1.55553
$649$	3.10398e11	0.0686781
$650$	7.34346e12	1.61358
$651$	−9.80643e12	−2.13992
$652$	−3.62470e11	−0.0785522
$653$	−3.72436e12	−0.801571	−0.400785	−	0.916172i	$-0.631263\pi$
$653$	−3.72436e12	−0.801571	−0.400785	+	0.916172i	$0.631263\pi$
$654$	5.74398e12	1.22776
$655$	4.54473e12	0.964767
$656$	−2.04878e10	−0.00431944
$657$	5.16033e10	0.0108052
$658$	−3.66764e12	−0.762730
$659$	−4.31652e11	−0.0891557	−0.0445779	−	0.999006i	$-0.514194\pi$
$659$	−4.31652e11	−0.0891557	−0.0445779	+	0.999006i	$0.514194\pi$
$660$	−4.36312e12	−0.895054
$661$	6.45586e12	1.31537	0.657685	−	0.753293i	$-0.271536\pi$
$661$	6.45586e12	1.31537	0.657685	+	0.753293i	$0.271536\pi$
$662$	−4.40589e12	−0.891606
$663$	−1.57582e13	−3.16735
$664$	−9.10818e12	−1.81834
$665$	2.33319e12	0.462650
$666$	−6.29337e12	−1.23951
$667$	1.37837e12	0.269650
$668$	−2.42485e12	−0.471184
$669$	1.24091e12	0.239510
$670$	−1.30287e11	−0.0249784
$671$	1.71328e12	0.326271
$672$	4.81127e12	0.910118
$673$	2.96787e11	0.0557670	0.0278835	−	0.999611i	$-0.491123\pi$
$673$	2.96787e11	0.0557670	0.0278835	+	0.999611i	$0.491123\pi$
$674$	−7.32891e12	−1.36795
$675$	−9.54642e11	−0.177000
$676$	1.89725e13	3.49434
$677$	7.10476e11	0.129987	0.0649936	−	0.997886i	$-0.479297\pi$
$677$	7.10476e11	0.129987	0.0649936	+	0.997886i	$0.479297\pi$
$678$	9.76403e12	1.77458
$679$	−2.20581e12	−0.398248
$680$	1.27424e13	2.28539
$681$	9.98863e12	1.77969
$682$	4.22009e12	0.746951
$683$	−7.65172e12	−1.34544	−0.672722	−	0.739895i	$-0.734875\pi$
$683$	−7.65172e12	−1.34544	−0.672722	+	0.739895i	$0.734875\pi$
$684$	2.66166e12	0.464943
$685$	1.87544e12	0.325458
$686$	8.62591e12	1.48712
$687$	−1.08416e13	−1.85690
$688$	−9.22474e11	−0.156966
$689$	−3.16412e12	−0.534893
$690$	−1.83966e13	−3.08970
$691$	2.61735e12	0.436728	0.218364	−	0.975867i	$-0.429928\pi$
$691$	2.61735e12	0.436728	0.218364	+	0.975867i	$0.429928\pi$
$692$	6.72756e11	0.111527
$693$	−1.51730e12	−0.249903
$694$	−3.25214e12	−0.532171
$695$	−7.13764e12	−1.16044
$696$	2.61880e12	0.423020
$697$	9.09016e10	0.0145890
$698$	7.26177e12	1.15796
$699$	−7.01433e12	−1.11132
$700$	−6.94098e12	−1.09265
$701$	−1.25535e12	−0.196351	−0.0981757	−	0.995169i	$-0.531301\pi$
$701$	−1.25535e12	−0.196351	−0.0981757	+	0.995169i	$0.531301\pi$
$702$	−5.81363e12	−0.903504
$703$	−2.14661e12	−0.331478
$704$	−2.87808e12	−0.441597
$705$	−4.57611e12	−0.697663
$706$	1.10356e13	1.67177
$707$	1.14990e13	1.73090
$708$	3.61690e12	0.540987
$709$	−1.99447e12	−0.296428	−0.148214	−	0.988955i	$-0.547352\pi$
$709$	−1.99447e12	−0.296428	−0.148214	+	0.988955i	$0.547352\pi$
$710$	−1.27318e13	−1.88030
$711$	−2.75624e12	−0.404486
$712$	−4.40805e12	−0.642816
$713$	1.14132e13	1.65388
$714$	2.32211e13	3.34381
$715$	−4.52605e12	−0.647653
$716$	−8.52997e11	−0.121294
$717$	1.65039e12	0.233212
$718$	−1.87149e13	−2.62802
$719$	−7.70921e12	−1.07580	−0.537898	−	0.843010i	$-0.680782\pi$
$719$	−7.70921e12	−1.07580	−0.537898	+	0.843010i	$0.680782\pi$
$720$	−2.82588e12	−0.391884
$721$	−1.16916e13	−1.61126
$722$	−1.07780e13	−1.47612
$723$	1.78655e13	2.43161
$724$	2.52843e13	3.42001
$725$	1.01162e12	0.135986
$726$	1.50884e12	0.201571
$727$	−4.68468e12	−0.621979	−0.310989	−	0.950413i	$-0.600660\pi$
$727$	−4.68468e12	−0.621979	−0.310989	+	0.950413i	$0.600660\pi$
$728$	−1.86393e13	−2.45945
$729$	−3.68238e12	−0.482898
$730$	−2.26831e11	−0.0295631
$731$	4.09290e12	0.530155
$732$	1.99640e13	2.57008
$733$	−5.45837e12	−0.698386	−0.349193	−	0.937051i	$-0.613544\pi$
$733$	−5.45837e12	−0.698386	−0.349193	+	0.937051i	$0.613544\pi$
$734$	−1.46752e13	−1.86617
$735$	−2.36790e12	−0.299276
$736$	−5.59956e12	−0.703403
$737$	2.88995e10	0.00360817
$738$	−1.07903e11	−0.0133899
$739$	2.64808e11	0.0326611	0.0163306	−	0.999867i	$-0.494802\pi$
$739$	2.64808e11	0.0326611	0.0163306	+	0.999867i	$0.494802\pi$
$740$	1.77440e13	2.17525
$741$	6.38025e12	0.777420
$742$	4.66261e12	0.564692
$743$	7.14179e12	0.859721	0.429860	−	0.902895i	$-0.358563\pi$
$743$	7.14179e12	0.859721	0.429860	+	0.902895i	$0.358563\pi$
$744$	2.16841e13	2.59456
$745$	1.33887e13	1.59234
$746$	−2.03775e13	−2.40894
$747$	−8.96216e12	−1.05310
$748$	−6.40970e12	−0.748653
$749$	6.55433e12	0.760957
$750$	1.05126e13	1.21321
$751$	1.16806e13	1.33994	0.669969	−	0.742389i	$-0.266307\pi$
$751$	1.16806e13	1.33994	0.669969	+	0.742389i	$0.266307\pi$
$752$	1.51517e12	0.172775
$753$	1.34201e13	1.52117
$754$	6.16060e12	0.694148
$755$	1.20893e12	0.135406
$756$	5.49499e12	0.611813
$757$	−1.58048e13	−1.74927	−0.874634	−	0.484784i	$-0.838898\pi$
$757$	−1.58048e13	−1.74927	−0.874634	+	0.484784i	$0.838898\pi$
$758$	2.83120e13	3.11501
$759$	4.08063e12	0.446313
$760$	−5.15917e12	−0.560943
$761$	−1.44129e13	−1.55784	−0.778918	−	0.627126i	$-0.784231\pi$
$761$	−1.44129e13	−1.55784	−0.778918	+	0.627126i	$0.784231\pi$
$762$	−3.25877e13	−3.50151
$763$	−5.63191e12	−0.601583
$764$	−1.58451e13	−1.68257
$765$	1.25381e13	1.32359
$766$	−2.59139e13	−2.71959
$767$	3.75197e12	0.391454
$768$	−2.00493e13	−2.07958
$769$	−5.16582e12	−0.532686	−0.266343	−	0.963878i	$-0.585815\pi$
$769$	−5.16582e12	−0.532686	−0.266343	+	0.963878i	$0.585815\pi$
$770$	6.66954e12	0.683735
$771$	1.76938e13	1.80334
$772$	1.69287e13	1.71532
$773$	−1.55878e12	−0.157028	−0.0785142	−	0.996913i	$-0.525018\pi$
$773$	−1.55878e12	−0.157028	−0.0785142	+	0.996913i	$0.525018\pi$
$774$	−4.85838e12	−0.486583
$775$	8.37636e12	0.834060
$776$	4.87750e12	0.482858
$777$	1.42590e13	1.40344
$778$	1.37825e13	1.34871
$779$	−3.68046e10	−0.00358083
$780$	−5.27396e13	−5.10166
$781$	2.82409e12	0.271612
$782$	−2.70258e13	−2.58433
$783$	−8.00871e11	−0.0761438
$784$	7.84022e11	0.0741149
$785$	−1.87580e13	−1.76309
$786$	−1.83135e13	−1.71147
$787$	7.02163e12	0.652457	0.326228	−	0.945291i	$-0.394222\pi$
$787$	7.02163e12	0.652457	0.326228	+	0.945291i	$0.394222\pi$
$788$	−2.47208e11	−0.0228399
$789$	6.23983e12	0.573226
$790$	1.21155e13	1.10668
$791$	−9.57352e12	−0.869516
$792$	3.35506e12	0.302996
$793$	2.07095e13	1.85969
$794$	−6.49678e12	−0.580104
$795$	5.81753e12	0.516520
$796$	3.03001e13	2.67507
$797$	−1.97524e13	−1.73403	−0.867015	−	0.498282i	$-0.833964\pi$
$797$	−1.97524e13	−1.73403	−0.867015	+	0.498282i	$0.833964\pi$
$798$	−9.40186e12	−0.820731
$799$	−6.72261e12	−0.583549
$800$	−4.10964e12	−0.354731
$801$	−4.33738e12	−0.372290
$802$	−1.31118e13	−1.11912
$803$	5.03145e10	0.00427045
$804$	3.36751e11	0.0284221
$805$	1.80377e13	1.51390
$806$	5.10108e13	4.25750
$807$	−2.11008e13	−1.75133
$808$	−2.54267e13	−2.09864
$809$	1.32781e12	0.108985	0.0544927	−	0.998514i	$-0.482646\pi$
$809$	1.32781e12	0.108985	0.0544927	+	0.998514i	$0.482646\pi$
$810$	3.01976e13	2.46484
$811$	−4.86137e12	−0.394607	−0.197303	−	0.980342i	$-0.563218\pi$
$811$	−4.86137e12	−0.394607	−0.197303	+	0.980342i	$0.563218\pi$
$812$	−5.82295e12	−0.470046
$813$	−1.09091e13	−0.875755
$814$	−6.13619e12	−0.489879
$815$	6.91324e11	0.0548873
$816$	−9.59306e12	−0.757445
$817$	−1.65715e12	−0.130125
$818$	4.02763e13	3.14528
$819$	−1.83405e13	−1.42440
$820$	3.04229e11	0.0234984
$821$	1.78619e13	1.37209	0.686046	−	0.727558i	$-0.259345\pi$
$821$	1.78619e13	1.37209	0.686046	+	0.727558i	$0.259345\pi$
$822$	−7.55729e12	−0.577355
$823$	−1.21898e13	−0.926184	−0.463092	−	0.886310i	$-0.653260\pi$
$823$	−1.21898e13	−0.926184	−0.463092	+	0.886310i	$0.653260\pi$
$824$	2.58526e13	1.95359
$825$	2.99486e12	0.225078
$826$	−5.52886e12	−0.413262
$827$	2.23842e13	1.66405	0.832027	−	0.554735i	$-0.187180\pi$
$827$	2.23842e13	1.66405	0.832027	+	0.554735i	$0.187180\pi$
$828$	2.05770e13	1.52141
$829$	1.35823e13	0.998800	0.499400	−	0.866372i	$-0.333554\pi$
$829$	1.35823e13	0.998800	0.499400	+	0.866372i	$0.333554\pi$
$830$	3.93947e13	2.88129
$831$	−1.04512e13	−0.760259
$832$	−3.47891e13	−2.51703
$833$	−3.47861e12	−0.250324
$834$	2.87619e13	2.05860
$835$	4.62480e12	0.329233
$836$	2.59518e12	0.183755
$837$	−6.63134e12	−0.467021
$838$	−4.58045e13	−3.20856
$839$	−1.61585e13	−1.12583	−0.562915	−	0.826515i	$-0.690320\pi$
$839$	−1.61585e13	−1.12583	−0.562915	+	0.826515i	$0.690320\pi$
$840$	3.42701e13	2.37497
$841$	−1.36585e13	−0.941500
$842$	2.81320e13	1.92884
$843$	−1.08531e13	−0.740167
$844$	−1.51237e13	−1.02593
$845$	−3.61854e13	−2.44162
$846$	7.97992e12	0.535589
$847$	−1.47940e12	−0.0987667
$848$	−1.92621e12	−0.127915
$849$	−1.58637e13	−1.04790
$850$	−1.98348e13	−1.30329
$851$	−1.65952e13	−1.08468
$852$	3.29076e13	2.13953
$853$	9.90861e12	0.640829	0.320414	−	0.947277i	$-0.396178\pi$
$853$	9.90861e12	0.640829	0.320414	+	0.947277i	$0.396178\pi$
$854$	−3.05173e13	−1.96329
$855$	−5.07646e12	−0.324873
$856$	−1.44930e13	−0.922628
$857$	1.84954e13	1.17125	0.585624	−	0.810582i	$-0.300849\pi$
$857$	1.84954e13	1.17125	0.585624	+	0.810582i	$0.300849\pi$
$858$	1.82383e13	1.14892
$859$	−2.83772e12	−0.177828	−0.0889141	−	0.996039i	$-0.528340\pi$
$859$	−2.83772e12	−0.177828	−0.0889141	+	0.996039i	$0.528340\pi$
$860$	1.36981e13	0.853921
$861$	2.44476e11	0.0151608
$862$	2.45210e13	1.51271
$863$	1.23192e13	0.756019	0.378010	−	0.925802i	$-0.376609\pi$
$863$	1.23192e13	0.756019	0.378010	+	0.925802i	$0.376609\pi$
$864$	3.25349e12	0.198627
$865$	−1.28312e12	−0.0779281
$866$	−8.07126e12	−0.487653
$867$	2.04730e13	1.23054
$868$	−4.82149e13	−2.88299
$869$	−2.68740e12	−0.159861
$870$	−1.13268e13	−0.670305
$871$	3.49326e11	0.0205660
$872$	1.24533e13	0.729393
$873$	4.79931e12	0.279650
$874$	1.09423e13	0.634318
$875$	−1.03075e13	−0.594454
$876$	5.86287e11	0.0336389
$877$	1.02172e13	0.583223	0.291611	−	0.956537i	$-0.405809\pi$
$877$	1.02172e13	0.583223	0.291611	+	0.956537i	$0.405809\pi$
$878$	−2.25803e13	−1.28234
$879$	9.05531e12	0.511627
$880$	−2.75530e12	−0.154881
$881$	9.94286e12	0.556058	0.278029	−	0.960573i	$-0.410319\pi$
$881$	9.94286e12	0.556058	0.278029	+	0.960573i	$0.410319\pi$
$882$	4.12920e12	0.229751
$883$	1.22195e13	0.676440	0.338220	−	0.941067i	$-0.390175\pi$
$883$	1.22195e13	0.676440	0.338220	+	0.941067i	$0.390175\pi$
$884$	−7.74779e13	−4.26720
$885$	−6.89835e12	−0.378008
$886$	−3.57592e13	−1.94956
$887$	−6.23629e12	−0.338275	−0.169137	−	0.985592i	$-0.554098\pi$
$887$	−6.23629e12	−0.338275	−0.169137	+	0.985592i	$0.554098\pi$
$888$	−3.15296e13	−1.70161
$889$	3.19518e13	1.71569
$890$	1.90657e13	1.01859
$891$	−6.69825e12	−0.356051
$892$	6.10116e12	0.322679
$893$	2.72187e12	0.143231
$894$	−5.39513e13	−2.82477
$895$	1.62688e12	0.0847525
$896$	3.80406e13	1.97180
$897$	4.93250e13	2.54391
$898$	2.38399e13	1.22338
$899$	7.02712e12	0.358805
$900$	1.51019e13	0.767256
$901$	8.54633e12	0.432034
$902$	−1.05208e11	−0.00529198
$903$	1.10077e13	0.550936
$904$	2.11691e13	1.05425
$905$	−4.82236e13	−2.38969
$906$	−4.87151e12	−0.240207
$907$	−7.49095e12	−0.367540	−0.183770	−	0.982969i	$-0.558830\pi$
$907$	−7.49095e12	−0.367540	−0.183770	+	0.982969i	$0.558830\pi$
$908$	4.91107e13	2.39767
$909$	−2.50190e13	−1.21544
$910$	8.06188e13	3.89717
$911$	−6.38388e12	−0.307080	−0.153540	−	0.988142i	$-0.549067\pi$
$911$	−6.38388e12	−0.307080	−0.153540	+	0.988142i	$0.549067\pi$
$912$	3.88407e12	0.185913
$913$	−8.73832e12	−0.416207
$914$	3.01463e13	1.42882
$915$	−3.80763e13	−1.79581
$916$	−5.33046e13	−2.50170
$917$	1.79562e13	0.838595
$918$	1.57027e13	0.729763
$919$	−4.13467e13	−1.91215	−0.956074	−	0.293125i	$-0.905305\pi$
$919$	−4.13467e13	−1.91215	−0.956074	+	0.293125i	$0.905305\pi$
$920$	−3.98850e13	−1.83554
$921$	1.03266e13	0.472924
$922$	6.09594e13	2.77812
$923$	3.41365e13	1.54815
$924$	−1.72386e13	−0.777999
$925$	−1.21796e13	−0.547009
$926$	−1.16421e13	−0.520333
$927$	2.54382e13	1.13143
$928$	−3.44767e12	−0.152602
$929$	−9.00173e12	−0.396511	−0.198255	−	0.980150i	$-0.563528\pi$
$929$	−9.00173e12	−0.396511	−0.198255	+	0.980150i	$0.563528\pi$
$930$	−9.37881e13	−4.11126
$931$	1.40843e12	0.0614415
$932$	−3.44871e13	−1.49722
$933$	−3.57594e13	−1.54498
$934$	−2.38058e13	−1.02358
$935$	1.22249e13	0.523112
$936$	4.05546e13	1.72703
$937$	1.35851e13	0.575752	0.287876	−	0.957668i	$-0.407051\pi$
$937$	1.35851e13	0.575752	0.287876	+	0.957668i	$0.407051\pi$
$938$	−5.14763e11	−0.0217117
$939$	2.26418e13	0.950421
$940$	−2.24992e13	−0.939923
$941$	−5.55297e12	−0.230872	−0.115436	−	0.993315i	$-0.536827\pi$
$941$	−5.55297e12	−0.230872	−0.115436	+	0.993315i	$0.536827\pi$
$942$	7.55876e13	3.12767
$943$	−2.84532e11	−0.0117173
$944$	2.28407e12	0.0936128
$945$	−1.04803e13	−0.427496
$946$	−4.73704e12	−0.192308
$947$	−5.91071e12	−0.238817	−0.119408	−	0.992845i	$-0.538100\pi$
$947$	−5.91071e12	−0.238817	−0.119408	+	0.992845i	$0.538100\pi$
$948$	−3.13148e13	−1.25925
$949$	6.08182e11	0.0243408
$950$	8.03078e12	0.319891
$951$	6.37300e13	2.52657
$952$	5.03450e13	1.98651
$953$	−1.11396e13	−0.437474	−0.218737	−	0.975784i	$-0.570194\pi$
$953$	−1.11396e13	−0.437474	−0.218737	+	0.975784i	$0.570194\pi$
$954$	−1.01447e13	−0.396527
$955$	3.02206e13	1.17568
$956$	8.11442e12	0.314193
$957$	2.51246e12	0.0968267
$958$	−2.18540e12	−0.0838276
$959$	7.40984e12	0.282895
$960$	6.39631e13	2.43057
$961$	3.17461e13	1.20070
$962$	−7.41719e13	−2.79223
$963$	−1.42607e13	−0.534344
$964$	8.78388e13	3.27597
$965$	−3.22874e13	−1.19856
$966$	−7.26848e13	−2.68563
$967$	3.61835e13	1.33074	0.665368	−	0.746516i	$-0.268275\pi$
$967$	3.61835e13	1.33074	0.665368	+	0.746516i	$0.268275\pi$
$968$	3.27127e12	0.119750
$969$	−1.72331e13	−0.627924
$970$	−2.10962e13	−0.765123
$971$	3.39332e13	1.22500	0.612502	−	0.790469i	$-0.290163\pi$
$971$	3.39332e13	1.22500	0.612502	+	0.790469i	$0.290163\pi$
$972$	−6.23795e13	−2.24152
$973$	−2.82008e13	−1.00868
$974$	−1.67794e13	−0.597395
$975$	3.62007e13	1.28291
$976$	1.26072e13	0.444728
$977$	−5.50249e12	−0.193212	−0.0966059	−	0.995323i	$-0.530799\pi$
$977$	−5.50249e12	−0.193212	−0.0966059	+	0.995323i	$0.530799\pi$
$978$	−2.78577e12	−0.0973688
$979$	−4.22905e12	−0.147137
$980$	−1.16422e13	−0.403197
$981$	1.22537e13	0.422431
$982$	2.02752e13	0.695766
$983$	−1.04553e13	−0.357145	−0.178572	−	0.983927i	$-0.557148\pi$
$983$	−1.04553e13	−0.357145	−0.178572	+	0.983927i	$0.557148\pi$
$984$	−5.40589e11	−0.0183818
$985$	4.71488e11	0.0159591
$986$	−1.66399e13	−0.560666
$987$	−1.80802e13	−0.606423
$988$	3.13695e13	1.04737
$989$	−1.28112e13	−0.425802
$990$	−1.45113e13	−0.480119
$991$	−1.90183e13	−0.626383	−0.313191	−	0.949690i	$-0.601398\pi$
$991$	−1.90183e13	−0.626383	−0.313191	+	0.949690i	$0.601398\pi$
$992$	−2.85473e13	−0.935970
$993$	−2.17195e13	−0.708889
$994$	−5.03032e13	−1.63439
$995$	−5.77900e13	−1.86917
$996$	−1.01823e14	−3.27852
$997$	1.67341e13	0.536382	0.268191	−	0.963366i	$-0.413574\pi$
$997$	1.67341e13	0.536382	0.268191	+	0.963366i	$0.413574\pi$
$998$	−4.82402e13	−1.53929
$999$	9.64225e12	0.306291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.a.b.1.5	✓	5
3.2	odd	2		99.10.a.f.1.1		5
4.3	odd	2		176.10.a.j.1.2		5
5.4	even	2		275.10.a.b.1.1		5
11.10	odd	2		121.10.a.c.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.a.b.1.5	✓	5	1.1	even	1	trivial
99.10.a.f.1.1		5	3.2	odd	2
121.10.a.c.1.1		5	11.10	odd	2
176.10.a.j.1.2		5	4.3	odd	2
275.10.a.b.1.1		5	5.4	even	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+37.7870 q^{2} +186.277 q^{3} +915.861 q^{4} -1746.78 q^{5} +7038.85 q^{6} -6901.51 q^{7} +15260.7 q^{8} +15016.0 q^{9} -66005.6 q^{10} +14641.0 q^{11} +170604. q^{12} +176975. q^{13} -260788. q^{14} -325384. q^{15} +107736. q^{16} -478011. q^{17} +567412. q^{18} +193539. q^{19} -1.59981e6 q^{20} -1.28559e6 q^{21} +553240. q^{22} +1.49623e6 q^{23} +2.84271e6 q^{24} +1.09811e6 q^{25} +6.68735e6 q^{26} -869347. q^{27} -6.32082e6 q^{28} +921233. q^{29} -1.22953e7 q^{30} +7.62795e6 q^{31} -3.74245e6 q^{32} +2.72728e6 q^{33} -1.80626e7 q^{34} +1.20554e7 q^{35} +1.37526e7 q^{36} -1.10914e7 q^{37} +7.31326e6 q^{38} +3.29663e7 q^{39} -2.66571e7 q^{40} -190166. q^{41} -4.85787e7 q^{42} -8.56236e6 q^{43} +1.34091e7 q^{44} -2.62297e7 q^{45} +5.65380e7 q^{46} +1.40637e7 q^{47} +2.00687e7 q^{48} +7.27725e6 q^{49} +4.14944e7 q^{50} -8.90423e7 q^{51} +1.62084e8 q^{52} -1.78790e7 q^{53} -3.28501e7 q^{54} -2.55746e7 q^{55} -1.05322e8 q^{56} +3.60518e7 q^{57} +3.48107e7 q^{58} +2.12006e7 q^{59} -2.98007e8 q^{60} +1.17020e8 q^{61} +2.88238e8 q^{62} -1.03633e8 q^{63} -1.96577e8 q^{64} -3.09136e8 q^{65} +1.03056e8 q^{66} +1.97388e6 q^{67} -4.37791e8 q^{68} +2.78712e8 q^{69} +4.55539e8 q^{70} +1.92889e8 q^{71} +2.29155e8 q^{72} +3.43655e6 q^{73} -4.19110e8 q^{74} +2.04553e8 q^{75} +1.77254e8 q^{76} -1.01045e8 q^{77} +1.24570e9 q^{78} -1.83553e8 q^{79} -1.88191e8 q^{80} -4.57500e8 q^{81} -7.18583e6 q^{82} -5.96839e8 q^{83} -1.17742e9 q^{84} +8.34980e8 q^{85} -3.23546e8 q^{86} +1.71604e8 q^{87} +2.23432e8 q^{88} -2.88850e8 q^{89} -9.91143e8 q^{90} -1.22139e9 q^{91} +1.37034e9 q^{92} +1.42091e9 q^{93} +5.31426e8 q^{94} -3.38069e8 q^{95} -6.97132e8 q^{96} +3.19612e8 q^{97} +2.74986e8 q^{98} +2.19850e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16}+ \cdots + 1094985749 q^{99}+O(q^{100}) \) 5 * q + 16 * q^2 + 112 * q^3 + 708 * q^4 + 1594 * q^5 + 10378 * q^6 + 8400 * q^7 + 40716 * q^8 + 74789 * q^9 + 2986 * q^10 + 73205 * q^11 + 110288 * q^12 + 47214 * q^13 - 299852 * q^14 - 559436 * q^15 - 454776 * q^16 - 547238 * q^17 - 822418 * q^18 - 162940 * q^19 - 1913320 * q^20 + 825496 * q^21 + 234256 * q^22 + 3415892 * q^23 + 1435932 * q^24 + 6164943 * q^25 + 5356756 * q^26 + 5240140 * q^27 - 2477216 * q^28 + 5868414 * q^29 - 9766670 * q^30 + 11730396 * q^31 - 18454552 * q^32 + 1639792 * q^33 - 25579352 * q^34 - 6567848 * q^35 - 26683532 * q^36 + 7021250 * q^37 - 22257720 * q^38 + 29114872 * q^39 - 22406796 * q^40 + 5595418 * q^41 - 65554916 * q^42 + 29161940 * q^43 + 10365828 * q^44 + 68008838 * q^45 + 47468978 * q^46 + 33703664 * q^47 + 96997832 * q^48 + 106606605 * q^49 + 84598070 * q^50 - 135853760 * q^51 + 185107192 * q^52 - 88905666 * q^53 - 95103866 * q^54 + 23337754 * q^55 - 78057672 * q^56 - 362541120 * q^57 + 63640668 * q^58 + 13747712 * q^59 - 208875616 * q^60 + 274324430 * q^61 - 161612942 * q^62 - 436710568 * q^63 - 46082368 * q^64 - 658499468 * q^65 + 151944298 * q^66 + 323117752 * q^67 - 679289848 * q^68 - 60345676 * q^69 + 1608436228 * q^70 + 9655356 * q^71 + 1168471200 * q^72 + 159287274 * q^73 + 76718502 * q^74 - 963596116 * q^75 + 483002000 * q^76 + 122984400 * q^77 + 1270322200 * q^78 - 668342072 * q^79 - 424312360 * q^80 + 1578463805 * q^81 + 666585700 * q^82 + 378353820 * q^83 - 2381947456 * q^84 + 1459757140 * q^85 - 2133621276 * q^86 - 2822691048 * q^87 + 596122956 * q^88 + 851774166 * q^89 - 4463334016 * q^90 - 991736368 * q^91 + 1919755168 * q^92 + 1149973204 * q^93 + 2620937360 * q^94 - 2812243800 * q^95 - 1157568712 * q^96 - 240502490 * q^97 - 2298624888 * q^98 + 1094985749 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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