LMFDB - Embedded newform 11.10.a.b.1.2

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			1.2
Root			$-18.6530$ 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)

$f(q)$	$=$	\(q-15.6530 q^{2} -245.723 q^{3} -266.983 q^{4} +2148.33 q^{5} +3846.30 q^{6} -7680.33 q^{7} +12193.4 q^{8} +40696.7 q^{9} -33627.8 q^{10} +14641.0 q^{11} +65603.9 q^{12} -54948.1 q^{13} +120220. q^{14} -527892. q^{15} -54168.5 q^{16} +353899. q^{17} -637025. q^{18} +268903. q^{19} -573567. q^{20} +1.88723e6 q^{21} -229176. q^{22} +388124. q^{23} -2.99620e6 q^{24} +2.66218e6 q^{25} +860104. q^{26} -5.16354e6 q^{27} +2.05052e6 q^{28} +4.13797e6 q^{29} +8.26311e6 q^{30} +6.38666e6 q^{31} -5.39514e6 q^{32} -3.59763e6 q^{33} -5.53958e6 q^{34} -1.64998e7 q^{35} -1.08653e7 q^{36} -5.32172e6 q^{37} -4.20914e6 q^{38} +1.35020e7 q^{39} +2.61955e7 q^{40} -551287. q^{41} -2.95409e7 q^{42} -6.73430e6 q^{43} -3.90890e6 q^{44} +8.74297e7 q^{45} -6.07532e6 q^{46} -275206. q^{47} +1.33104e7 q^{48} +1.86338e7 q^{49} -4.16711e7 q^{50} -8.69609e7 q^{51} +1.46702e7 q^{52} +5.30922e7 q^{53} +8.08249e7 q^{54} +3.14536e7 q^{55} -9.36496e7 q^{56} -6.60756e7 q^{57} -6.47718e7 q^{58} +9.37783e7 q^{59} +1.40938e8 q^{60} -7.41160e7 q^{61} -9.99705e7 q^{62} -3.12564e8 q^{63} +1.12184e8 q^{64} -1.18046e8 q^{65} +5.63137e7 q^{66} +1.55620e8 q^{67} -9.44850e7 q^{68} -9.53710e7 q^{69} +2.58272e8 q^{70} +1.76306e8 q^{71} +4.96232e8 q^{72} +2.44413e7 q^{73} +8.33010e7 q^{74} -6.54157e8 q^{75} -7.17926e7 q^{76} -1.12448e8 q^{77} -2.11347e8 q^{78} +3.64150e8 q^{79} -1.16372e8 q^{80} +4.67766e8 q^{81} +8.62930e6 q^{82} +2.62327e8 q^{83} -5.03859e8 q^{84} +7.60289e8 q^{85} +1.05412e8 q^{86} -1.01679e9 q^{87} +1.78524e8 q^{88} +7.49967e8 q^{89} -1.36854e9 q^{90} +4.22020e8 q^{91} -1.03623e8 q^{92} -1.56935e9 q^{93} +4.30781e6 q^{94} +5.77691e8 q^{95} +1.32571e9 q^{96} -1.65962e9 q^{97} -2.91675e8 q^{98} +5.95840e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.6530	−0.691772	−0.345886	−	0.938277i	$-0.612422\pi$
$2$	−15.6530	−0.691772	−0.345886	+	0.938277i	$0.612422\pi$
$3$	−245.723	−1.75146	−0.875729	−	0.482803i	$-0.839619\pi$
$3$	−245.723	−1.75146	−0.875729	+	0.482803i	$0.839619\pi$
$4$	−266.983	−0.521452
$5$	2148.33	1.53722	0.768608	−	0.639720i	$-0.220950\pi$
$5$	2148.33	1.53722	0.768608	+	0.639720i	$0.220950\pi$
$6$	3846.30	1.21161
$7$	−7680.33	−1.20903	−0.604517	−	0.796592i	$-0.706634\pi$
$7$	−7680.33	−1.20903	−0.604517	+	0.796592i	$0.706634\pi$
$8$	12193.4	1.05250
$9$	40696.7	2.06761
$10$	−33627.8	−1.06340
$11$	14641.0	0.301511
$11$	14641.0	0.301511
$12$	65603.9	0.913301
$13$	−54948.1	−0.533590	−0.266795	−	0.963753i	$-0.585965\pi$
$13$	−54948.1	−0.533590	−0.266795	+	0.963753i	$0.585965\pi$
$14$	120220.	0.836376
$15$	−527892.	−2.69237
$16$	−54168.5	−0.206637
$17$	353899.	1.02768	0.513841	−	0.857885i	$-0.328222\pi$
$17$	353899.	1.02768	0.513841	+	0.857885i	$0.328222\pi$
$18$	−637025.	−1.43031
$19$	268903.	0.473374	0.236687	−	0.971586i	$-0.423938\pi$
$19$	268903.	0.473374	0.236687	+	0.971586i	$0.423938\pi$
$20$	−573567.	−0.801584
$21$	1.88723e6	2.11757
$22$	−229176.	−0.208577
$23$	388124.	0.289198	0.144599	−	0.989490i	$-0.453811\pi$
$23$	388124.	0.289198	0.144599	+	0.989490i	$0.453811\pi$
$24$	−2.99620e6	−1.84341
$25$	2.66218e6	1.36303
$26$	860104.	0.369123
$27$	−5.16354e6	−1.86987
$28$	2.05052e6	0.630453
$29$	4.13797e6	1.08642	0.543209	−	0.839598i	$-0.317209\pi$
$29$	4.13797e6	1.08642	0.543209	+	0.839598i	$0.317209\pi$
$30$	8.26311e6	1.86251
$31$	6.38666e6	1.24207	0.621035	−	0.783783i	$-0.286712\pi$
$31$	6.38666e6	1.24207	0.621035	+	0.783783i	$0.286712\pi$
$32$	−5.39514e6	−0.909552
$33$	−3.59763e6	−0.528084
$34$	−5.53958e6	−0.710921
$35$	−1.64998e7	−1.85855
$36$	−1.08653e7	−1.07816
$37$	−5.32172e6	−0.466814	−0.233407	−	0.972379i	$-0.574988\pi$
$37$	−5.32172e6	−0.466814	−0.233407	+	0.972379i	$0.574988\pi$
$38$	−4.20914e6	−0.327467
$39$	1.35020e7	0.934561
$40$	2.61955e7	1.61792
$41$	−551287.	−0.0304684	−0.0152342	−	0.999884i	$-0.504849\pi$
$41$	−551287.	−0.0304684	−0.0152342	+	0.999884i	$0.504849\pi$
$42$	−2.95409e7	−1.46488
$43$	−6.73430e6	−0.300389	−0.150195	−	0.988656i	$-0.547990\pi$
$43$	−6.73430e6	−0.300389	−0.150195	+	0.988656i	$0.547990\pi$
$44$	−3.90890e6	−0.157224
$45$	8.74297e7	3.17836
$46$	−6.07532e6	−0.200059
$47$	−275206.	−0.00822655	−0.00411328	−	0.999992i	$-0.501309\pi$
$47$	−275206.	−0.00822655	−0.00411328	+	0.999992i	$0.501309\pi$
$48$	1.33104e7	0.361915
$49$	1.86338e7	0.461764
$50$	−4.16711e7	−0.942909
$51$	−8.69609e7	−1.79994
$52$	1.46702e7	0.278242
$53$	5.30922e7	0.924250	0.462125	−	0.886815i	$-0.347087\pi$
$53$	5.30922e7	0.924250	0.462125	+	0.886815i	$0.347087\pi$
$54$	8.08249e7	1.29352
$55$	3.14536e7	0.463488
$56$	−9.36496e7	−1.27251
$57$	−6.60756e7	−0.829095
$58$	−6.47718e7	−0.751553
$59$	9.37783e7	1.00755	0.503777	−	0.863834i	$-0.331943\pi$
$59$	9.37783e7	1.00755	0.503777	+	0.863834i	$0.331943\pi$
$60$	1.40938e8	1.40394
$61$	−7.41160e7	−0.685374	−0.342687	−	0.939450i	$-0.611337\pi$
$61$	−7.41160e7	−0.685374	−0.342687	+	0.939450i	$0.611337\pi$
$62$	−9.99705e7	−0.859230
$63$	−3.12564e8	−2.49981
$64$	1.12184e8	0.835839
$65$	−1.18046e8	−0.820244
$66$	5.63137e7	0.365314
$67$	1.55620e8	0.943470	0.471735	−	0.881740i	$-0.343628\pi$
$67$	1.55620e8	0.943470	0.471735	+	0.881740i	$0.343628\pi$
$68$	−9.44850e7	−0.535886
$69$	−9.53710e7	−0.506519
$70$	2.58272e8	1.28569
$71$	1.76306e8	0.823386	0.411693	−	0.911323i	$-0.364938\pi$
$71$	1.76306e8	0.823386	0.411693	+	0.911323i	$0.364938\pi$
$72$	4.96232e8	2.17615
$73$	2.44413e7	0.100733	0.0503665	−	0.998731i	$-0.483961\pi$
$73$	2.44413e7	0.100733	0.0503665	+	0.998731i	$0.483961\pi$
$74$	8.33010e7	0.322929
$75$	−6.54157e8	−2.38730
$76$	−7.17926e7	−0.246842
$77$	−1.12448e8	−0.364538
$78$	−2.11347e8	−0.646503
$79$	3.64150e8	1.05186	0.525931	−	0.850527i	$-0.323717\pi$
$79$	3.64150e8	1.05186	0.525931	+	0.850527i	$0.323717\pi$
$80$	−1.16372e8	−0.317645
$81$	4.67766e8	1.20739
$82$	8.62930e6	0.0210772
$83$	2.62327e8	0.606725	0.303362	−	0.952875i	$-0.401891\pi$
$83$	2.62327e8	0.606725	0.303362	+	0.952875i	$0.401891\pi$
$84$	−5.03859e8	−1.10421
$85$	7.60289e8	1.57977
$86$	1.05412e8	0.207801
$87$	−1.01679e9	−1.90282
$88$	1.78524e8	0.317340
$89$	7.49967e8	1.26703	0.633515	−	0.773730i	$-0.281611\pi$
$89$	7.49967e8	1.26703	0.633515	+	0.773730i	$0.281611\pi$
$90$	−1.36854e9	−2.19870
$91$	4.22020e8	0.645129
$92$	−1.03623e8	−0.150803
$93$	−1.56935e9	−2.17543
$94$	4.30781e6	0.00569090
$95$	5.77691e8	0.727678
$96$	1.32571e9	1.59304
$97$	−1.65962e9	−1.90343	−0.951715	−	0.306984i	$-0.900680\pi$
$97$	−1.65962e9	−1.90343	−0.951715	+	0.306984i	$0.900680\pi$
$98$	−2.91675e8	−0.319435
$99$	5.95840e8	0.623406
$100$	−7.10756e8	−0.710756
$101$	−1.61386e9	−1.54319	−0.771596	−	0.636112i	$-0.780541\pi$
$101$	−1.61386e9	−1.54319	−0.771596	+	0.636112i	$0.780541\pi$
$102$	1.36120e9	1.24515
$103$	1.25691e9	1.10036	0.550181	−	0.835045i	$-0.314559\pi$
$103$	1.25691e9	1.10036	0.550181	+	0.835045i	$0.314559\pi$
$104$	−6.70007e8	−0.561603
$105$	4.05439e9	3.25517
$106$	−8.31053e8	−0.639370
$107$	−2.39591e9	−1.76703	−0.883513	−	0.468408i	$-0.844828\pi$
$107$	−2.39591e9	−1.76703	−0.883513	+	0.468408i	$0.844828\pi$
$108$	1.37858e9	0.975044
$109$	2.32742e9	1.57927	0.789634	−	0.613578i	$-0.210270\pi$
$109$	2.32742e9	1.57927	0.789634	+	0.613578i	$0.210270\pi$
$110$	−4.92344e8	−0.320628
$111$	1.30767e9	0.817606
$112$	4.16032e8	0.249831
$113$	9.18555e8	0.529971	0.264986	−	0.964252i	$-0.414633\pi$
$113$	9.18555e8	0.529971	0.264986	+	0.964252i	$0.414633\pi$
$114$	1.03428e9	0.573544
$115$	8.33817e8	0.444560
$116$	−1.10477e9	−0.566514
$117$	−2.23621e9	−1.10325
$118$	−1.46791e9	−0.696998
$119$	−2.71806e9	−1.24250
$120$	−6.43682e9	−2.83371
$121$	2.14359e8	0.0909091
$122$	1.16014e9	0.474123
$123$	1.35464e8	0.0533642
$124$	−1.70513e9	−0.647680
$125$	1.52327e9	0.558062
$126$	4.89256e9	1.72929
$127$	−3.61865e9	−1.23432	−0.617162	−	0.786836i	$-0.711718\pi$
$127$	−3.61865e9	−1.23432	−0.617162	+	0.786836i	$0.711718\pi$
$128$	1.00629e9	0.331342
$129$	1.65477e9	0.526119
$130$	1.84778e9	0.567422
$131$	4.28677e9	1.27177	0.635886	−	0.771783i	$-0.280635\pi$
$131$	4.28677e9	1.27177	0.635886	+	0.771783i	$0.280635\pi$
$132$	9.60506e8	0.275371
$133$	−2.06526e9	−0.572325
$134$	−2.43592e9	−0.652666
$135$	−1.10930e10	−2.87439
$136$	4.31524e9	1.08163
$137$	4.54711e9	1.10279	0.551396	−	0.834244i	$-0.314095\pi$
$137$	4.54711e9	1.10279	0.551396	+	0.834244i	$0.314095\pi$
$138$	1.49284e9	0.350395
$139$	−5.22593e9	−1.18740	−0.593700	−	0.804687i	$-0.702333\pi$
$139$	−5.22593e9	−1.18740	−0.593700	+	0.804687i	$0.702333\pi$
$140$	4.40518e9	0.969142
$141$	6.76244e7	0.0144085
$142$	−2.75971e9	−0.569595
$143$	−8.04496e8	−0.160884
$144$	−2.20448e9	−0.427243
$145$	8.88972e9	1.67006
$146$	−3.82580e8	−0.0696842
$147$	−4.57875e9	−0.808760
$148$	1.42081e9	0.243421
$149$	−8.78579e8	−0.146030	−0.0730151	−	0.997331i	$-0.523262\pi$
$149$	−8.78579e8	−0.146030	−0.0730151	+	0.997331i	$0.523262\pi$
$150$	1.02395e10	1.65147
$151$	−1.04463e10	−1.63518	−0.817592	−	0.575798i	$-0.804691\pi$
$151$	−1.04463e10	−1.63518	−0.817592	+	0.575798i	$0.804691\pi$
$152$	3.27885e9	0.498225
$153$	1.44025e10	2.12484
$154$	1.76014e9	0.252177
$155$	1.37206e10	1.90933
$156$	−3.60481e9	−0.487328
$157$	2.78178e9	0.365404	0.182702	−	0.983168i	$-0.441516\pi$
$157$	2.78178e9	0.365404	0.182702	+	0.983168i	$0.441516\pi$
$158$	−5.70005e9	−0.727649
$159$	−1.30460e10	−1.61878
$160$	−1.15905e10	−1.39818
$161$	−2.98092e9	−0.349651
$162$	−7.32195e9	−0.835235
$163$	1.64346e9	0.182354	0.0911768	−	0.995835i	$-0.470937\pi$
$163$	1.64346e9	0.182354	0.0911768	+	0.995835i	$0.470937\pi$
$164$	1.47184e8	0.0158878
$165$	−7.72887e9	−0.811780
$166$	−4.10621e9	−0.419715
$167$	−8.19245e9	−0.815060	−0.407530	−	0.913192i	$-0.633610\pi$
$167$	−8.19245e9	−0.815060	−0.407530	+	0.913192i	$0.633610\pi$
$168$	2.30118e10	2.22874
$169$	−7.58520e9	−0.715281
$170$	−1.19008e10	−1.09284
$171$	1.09435e10	0.978750
$172$	1.79795e9	0.156639
$173$	1.92877e10	1.63709	0.818547	−	0.574439i	$-0.194780\pi$
$173$	1.92877e10	1.63709	0.818547	+	0.574439i	$0.194780\pi$
$174$	1.59159e10	1.31631
$175$	−2.04464e10	−1.64795
$176$	−7.93081e8	−0.0623033
$177$	−2.30435e10	−1.76469
$178$	−1.17392e10	−0.876496
$179$	1.58961e10	1.15731	0.578657	−	0.815571i	$-0.303577\pi$
$179$	1.58961e10	1.15731	0.578657	+	0.815571i	$0.303577\pi$
$180$	−2.33423e10	−1.65736
$181$	1.69974e10	1.17714	0.588571	−	0.808445i	$-0.299691\pi$
$181$	1.69974e10	1.17714	0.588571	+	0.808445i	$0.299691\pi$
$182$	−6.60588e9	−0.446282
$183$	1.82120e10	1.20040
$184$	4.73257e9	0.304380
$185$	−1.14328e10	−0.717595
$186$	2.45650e10	1.50490
$187$	5.18143e9	0.309858
$188$	7.34755e7	0.00428975
$189$	3.96577e10	2.26073
$190$	−9.04260e9	−0.503387
$191$	−1.53939e10	−0.836951	−0.418475	−	0.908228i	$-0.637435\pi$
$191$	−1.53939e10	−0.836951	−0.418475	+	0.908228i	$0.637435\pi$
$192$	−2.75663e10	−1.46394
$193$	−2.53192e10	−1.31354	−0.656768	−	0.754093i	$-0.728077\pi$
$193$	−2.53192e10	−1.31354	−0.656768	+	0.754093i	$0.728077\pi$
$194$	2.59781e10	1.31674
$195$	2.90067e10	1.43662
$196$	−4.97492e9	−0.240787
$197$	2.02470e9	0.0957775	0.0478887	−	0.998853i	$-0.484751\pi$
$197$	2.02470e9	0.0957775	0.0478887	+	0.998853i	$0.484751\pi$
$198$	−9.32669e9	−0.431255
$199$	2.03347e10	0.919178	0.459589	−	0.888132i	$-0.347997\pi$
$199$	2.03347e10	0.919178	0.459589	+	0.888132i	$0.347997\pi$
$200$	3.24611e10	1.43459
$201$	−3.82393e10	−1.65245
$202$	2.52618e10	1.06754
$203$	−3.17810e10	−1.31352
$204$	2.32171e10	0.938583
$205$	−1.18434e9	−0.0468366
$206$	−1.96744e10	−0.761200
$207$	1.57954e10	0.597948
$208$	2.97646e9	0.110259
$209$	3.93701e9	0.142728
$210$	−6.34634e10	−2.25183
$211$	4.86974e10	1.69135	0.845677	−	0.533696i	$-0.179197\pi$
$211$	4.86974e10	1.69135	0.845677	+	0.533696i	$0.179197\pi$
$212$	−1.41747e10	−0.481952
$213$	−4.33223e10	−1.44213
$214$	3.75031e10	1.22238
$215$	−1.44675e10	−0.461764
$216$	−6.29612e10	−1.96803
$217$	−4.90517e10	−1.50171
$218$	−3.64312e10	−1.09249
$219$	−6.00578e9	−0.176430
$220$	−8.39759e9	−0.241687
$221$	−1.94461e10	−0.548361
$222$	−2.04689e10	−0.565597
$223$	3.67789e10	0.995926	0.497963	−	0.867198i	$-0.334081\pi$
$223$	3.67789e10	0.995926	0.497963	+	0.867198i	$0.334081\pi$
$224$	4.14364e10	1.09968
$225$	1.08342e11	2.81822
$226$	−1.43782e10	−0.366619
$227$	5.59603e9	0.139883	0.0699413	−	0.997551i	$-0.477719\pi$
$227$	5.59603e9	0.139883	0.0699413	+	0.997551i	$0.477719\pi$
$228$	1.76411e10	0.432333
$229$	6.52333e10	1.56751	0.783754	−	0.621071i	$-0.213302\pi$
$229$	6.52333e10	1.56751	0.783754	+	0.621071i	$0.213302\pi$
$230$	−1.30518e10	−0.307534
$231$	2.76310e10	0.638472
$232$	5.04561e10	1.14345
$233$	−8.93197e9	−0.198539	−0.0992694	−	0.995061i	$-0.531651\pi$
$233$	−8.93197e9	−0.198539	−0.0992694	+	0.995061i	$0.531651\pi$
$234$	3.50034e10	0.763200
$235$	−5.91233e8	−0.0126460
$236$	−2.50372e10	−0.525391
$237$	−8.94800e10	−1.84229
$238$	4.25458e10	0.859528
$239$	−8.67116e10	−1.71904	−0.859521	−	0.511100i	$-0.829238\pi$
$239$	−8.67116e10	−1.71904	−0.859521	+	0.511100i	$0.829238\pi$
$240$	2.85952e10	0.556342
$241$	−1.29986e10	−0.248210	−0.124105	−	0.992269i	$-0.539606\pi$
$241$	−1.29986e10	−0.248210	−0.124105	+	0.992269i	$0.539606\pi$
$242$	−3.35536e9	−0.0628884
$243$	−1.33068e10	−0.244820
$244$	1.97877e10	0.357389
$245$	4.00315e10	0.709831
$246$	−2.12041e9	−0.0369158
$247$	−1.47757e10	−0.252588
$248$	7.78753e10	1.30728
$249$	−6.44597e10	−1.06265
$250$	−2.38438e10	−0.386052
$251$	−2.00599e10	−0.319005	−0.159503	−	0.987197i	$-0.550989\pi$
$251$	−2.00599e10	−0.319005	−0.159503	+	0.987197i	$0.550989\pi$
$252$	8.34493e10	1.30353
$253$	5.68253e9	0.0871966
$254$	5.66427e10	0.853871
$255$	−1.86820e11	−2.76690
$256$	−7.31898e10	−1.06505
$257$	3.78901e10	0.541784	0.270892	−	0.962610i	$-0.412681\pi$
$257$	3.78901e10	0.541784	0.270892	+	0.962610i	$0.412681\pi$
$258$	−2.59022e10	−0.363955
$259$	4.08726e10	0.564395
$260$	3.15164e10	0.427718
$261$	1.68402e11	2.24628
$262$	−6.71008e10	−0.879776
$263$	−2.13394e8	−0.00275031	−0.00137516	−	0.999999i	$-0.500438\pi$
$263$	−2.13394e8	−0.00275031	−0.00137516	+	0.999999i	$0.500438\pi$
$264$	−4.38674e10	−0.555808
$265$	1.14059e11	1.42077
$266$	3.23276e10	0.395919
$267$	−1.84284e11	−2.21915
$268$	−4.15478e10	−0.491974
$269$	−1.19091e11	−1.38673	−0.693366	−	0.720585i	$-0.743873\pi$
$269$	−1.19091e11	−1.38673	−0.693366	+	0.720585i	$0.743873\pi$
$270$	1.73638e11	1.98842
$271$	−2.63842e10	−0.297154	−0.148577	−	0.988901i	$-0.547469\pi$
$271$	−2.63842e10	−0.297154	−0.148577	+	0.988901i	$0.547469\pi$
$272$	−1.91702e10	−0.212357
$273$	−1.03700e11	−1.12992
$274$	−7.11760e10	−0.762880
$275$	3.89769e10	0.410970
$276$	2.54625e10	0.264125
$277$	−7.60197e10	−0.775831	−0.387916	−	0.921695i	$-0.626805\pi$
$277$	−7.60197e10	−0.775831	−0.387916	+	0.921695i	$0.626805\pi$
$278$	8.18015e10	0.821410
$279$	2.59916e11	2.56811
$280$	−2.01190e11	−1.95612
$281$	−1.09769e11	−1.05027	−0.525136	−	0.851018i	$-0.675985\pi$
$281$	−1.09769e11	−1.05027	−0.525136	+	0.851018i	$0.675985\pi$
$282$	−1.05853e9	−0.00996737
$283$	1.85495e11	1.71907	0.859536	−	0.511075i	$-0.170752\pi$
$283$	1.85495e11	1.71907	0.859536	+	0.511075i	$0.170752\pi$
$284$	−4.70706e10	−0.429356
$285$	−1.41952e11	−1.27450
$286$	1.25928e10	0.111295
$287$	4.23406e9	0.0368374
$288$	−2.19564e11	−1.88059
$289$	6.65635e9	0.0561301
$290$	−1.39151e11	−1.15530
$291$	4.07807e11	3.33378
$292$	−6.52542e9	−0.0525274
$293$	1.89754e11	1.50414	0.752069	−	0.659084i	$-0.229056\pi$
$293$	1.89754e11	1.50414	0.752069	+	0.659084i	$0.229056\pi$
$294$	7.16713e10	0.559477
$295$	2.01466e11	1.54883
$296$	−6.48900e10	−0.491321
$297$	−7.55993e10	−0.563786
$298$	1.37524e10	0.101020
$299$	−2.13267e10	−0.154313
$300$	1.74649e11	1.24486
$301$	5.17217e10	0.363181
$302$	1.63516e11	1.13117
$303$	3.96563e11	2.70284
$304$	−1.45661e10	−0.0978164
$305$	−1.59225e11	−1.05357
$306$	−2.25442e11	−1.46990
$307$	−2.52119e9	−0.0161988	−0.00809941	−	0.999967i	$-0.502578\pi$
$307$	−2.52119e9	−0.0161988	−0.00809941	+	0.999967i	$0.502578\pi$
$308$	3.00216e10	0.190089
$309$	−3.08851e11	−1.92724
$310$	−2.14769e11	−1.32082
$311$	−2.21193e10	−0.134076	−0.0670379	−	0.997750i	$-0.521355\pi$
$311$	−2.21193e10	−0.134076	−0.0670379	+	0.997750i	$0.521355\pi$
$312$	1.64636e11	0.983623
$313$	−2.93908e11	−1.73086	−0.865429	−	0.501032i	$-0.832954\pi$
$313$	−2.93908e11	−1.73086	−0.865429	+	0.501032i	$0.832954\pi$
$314$	−4.35432e10	−0.252776
$315$	−6.71489e11	−3.84274
$316$	−9.72220e10	−0.548495
$317$	6.46979e10	0.359852	0.179926	−	0.983680i	$-0.442414\pi$
$317$	6.46979e10	0.359852	0.179926	+	0.983680i	$0.442414\pi$
$318$	2.04209e11	1.11983
$319$	6.05841e10	0.327567
$320$	2.41009e11	1.28487
$321$	5.88729e11	3.09487
$322$	4.66604e10	0.241878
$323$	9.51644e10	0.486478
$324$	−1.24886e11	−0.629593
$325$	−1.46282e11	−0.727302
$326$	−2.57251e10	−0.126147
$327$	−5.71900e11	−2.76602
$328$	−6.72208e9	−0.0320680
$329$	2.11367e9	0.00994618
$330$	1.20980e11	0.561567
$331$	7.03322e10	0.322054	0.161027	−	0.986950i	$-0.448519\pi$
$331$	7.03322e10	0.322054	0.161027	+	0.986950i	$0.448519\pi$
$332$	−7.00369e10	−0.316378
$333$	−2.16576e11	−0.965188
$334$	1.28236e11	0.563835
$335$	3.34322e11	1.45032
$336$	−1.02229e11	−0.437568
$337$	2.26055e11	0.954729	0.477364	−	0.878705i	$-0.341592\pi$
$337$	2.26055e11	0.954729	0.477364	+	0.878705i	$0.341592\pi$
$338$	1.18731e11	0.494812
$339$	−2.25710e11	−0.928222
$340$	−2.02985e11	−0.823773
$341$	9.35071e10	0.374498
$342$	−1.71298e11	−0.677072
$343$	1.66815e11	0.650746
$344$	−8.21143e10	−0.316159
$345$	−2.04888e11	−0.778629
$346$	−3.01911e11	−1.13250
$347$	−9.43951e10	−0.349516	−0.174758	−	0.984611i	$-0.555914\pi$
$347$	−9.43951e10	−0.349516	−0.174758	+	0.984611i	$0.555914\pi$
$348$	2.71467e11	0.992226
$349$	−2.92610e10	−0.105578	−0.0527892	−	0.998606i	$-0.516811\pi$
$349$	−2.92610e10	−0.105578	−0.0527892	+	0.998606i	$0.516811\pi$
$350$	3.20048e11	1.14001
$351$	2.83727e11	0.997742
$352$	−7.89902e10	−0.274240
$353$	−1.37893e10	−0.0472669	−0.0236335	−	0.999721i	$-0.507523\pi$
$353$	−1.37893e10	−0.0472669	−0.0236335	+	0.999721i	$0.507523\pi$
$354$	3.60700e11	1.22076
$355$	3.78762e11	1.26572
$356$	−2.00229e11	−0.660695
$357$	6.67889e11	2.17619
$358$	−2.48821e11	−0.800598
$359$	−3.12880e11	−0.994153	−0.497077	−	0.867707i	$-0.665593\pi$
$359$	−3.12880e11	−0.994153	−0.497077	+	0.867707i	$0.665593\pi$
$360$	1.06607e12	3.34521
$361$	−2.50379e11	−0.775917
$362$	−2.66061e11	−0.814314
$363$	−5.26729e10	−0.159223
$364$	−1.12672e11	−0.336404
$365$	5.25079e10	0.154848
$366$	−2.85072e11	−0.830406
$367$	1.08747e11	0.312911	0.156455	−	0.987685i	$-0.449993\pi$
$367$	1.08747e11	0.312911	0.156455	+	0.987685i	$0.449993\pi$
$368$	−2.10241e10	−0.0597589
$369$	−2.24355e10	−0.0629967
$370$	1.78958e11	0.496412
$371$	−4.07766e11	−1.11745
$372$	4.18990e11	1.13438
$373$	−2.90313e11	−0.776562	−0.388281	−	0.921541i	$-0.626931\pi$
$373$	−2.90313e11	−0.776562	−0.388281	+	0.921541i	$0.626931\pi$
$374$	−8.11050e10	−0.214351
$375$	−3.74303e11	−0.977423
$376$	−3.35571e9	−0.00865843
$377$	−2.27374e11	−0.579702
$378$	−6.20762e11	−1.56391
$379$	−5.65217e11	−1.40715	−0.703573	−	0.710623i	$-0.748413\pi$
$379$	−5.65217e11	−1.40715	−0.703573	+	0.710623i	$0.748413\pi$
$380$	−1.54234e11	−0.379449
$381$	8.89184e11	2.16187
$382$	2.40962e11	0.578979
$383$	−3.54899e11	−0.842772	−0.421386	−	0.906881i	$-0.638456\pi$
$383$	−3.54899e11	−0.842772	−0.421386	+	0.906881i	$0.638456\pi$
$384$	−2.47267e11	−0.580332
$385$	−2.41574e11	−0.560373
$386$	3.96322e11	0.908667
$387$	−2.74064e11	−0.621087
$388$	4.43092e11	0.992546
$389$	1.54025e11	0.341051	0.170525	−	0.985353i	$-0.445453\pi$
$389$	1.54025e11	0.341051	0.170525	+	0.985353i	$0.445453\pi$
$390$	−4.54042e11	−0.993815
$391$	1.37357e11	0.297204
$392$	2.27210e11	0.486005
$393$	−1.05336e12	−2.22745
$394$	−3.16927e10	−0.0662562
$395$	7.82313e11	1.61694
$396$	−1.59079e11	−0.325076
$397$	5.26364e11	1.06348	0.531740	−	0.846908i	$-0.321539\pi$
$397$	5.26364e11	1.06348	0.531740	+	0.846908i	$0.321539\pi$
$398$	−3.18300e11	−0.635862
$399$	5.07482e11	1.00240
$400$	−1.44206e11	−0.281653
$401$	−2.95496e11	−0.570692	−0.285346	−	0.958425i	$-0.592108\pi$
$401$	−2.95496e11	−0.570692	−0.285346	+	0.958425i	$0.592108\pi$
$402$	5.98560e11	1.14312
$403$	−3.50935e11	−0.662757
$404$	4.30874e11	0.804700
$405$	1.00491e12	1.85601
$406$	4.97468e11	0.908654
$407$	−7.79153e10	−0.140750
$408$	−1.06035e12	−1.89443
$409$	7.45480e11	1.31729	0.658645	−	0.752454i	$-0.271130\pi$
$409$	7.45480e11	1.31729	0.658645	+	0.752454i	$0.271130\pi$
$410$	1.85385e10	0.0324002
$411$	−1.11733e12	−1.93149
$412$	−3.35573e11	−0.573786
$413$	−7.20248e11	−1.21817
$414$	−2.47245e11	−0.413643
$415$	5.63564e11	0.932667
$416$	2.96453e11	0.485328
$417$	1.28413e12	2.07968
$418$	−6.16260e10	−0.0987350
$419$	−1.04045e11	−0.164915	−0.0824574	−	0.996595i	$-0.526277\pi$
$419$	−1.04045e11	−0.164915	−0.0824574	+	0.996595i	$0.526277\pi$
$420$	−1.08245e12	−1.69741
$421$	−9.39130e11	−1.45699	−0.728495	−	0.685052i	$-0.759780\pi$
$421$	−9.39130e11	−1.45699	−0.728495	+	0.685052i	$0.759780\pi$
$422$	−7.62260e11	−1.17003
$423$	−1.12000e10	−0.0170093
$424$	6.47376e11	0.972771
$425$	9.42141e11	1.40077
$426$	6.78124e11	0.997622
$427$	5.69235e11	0.828641
$428$	6.39667e11	0.921418
$429$	1.97683e11	0.281781
$430$	2.26460e11	0.319435
$431$	−3.61080e11	−0.504029	−0.252015	−	0.967723i	$-0.581093\pi$
$431$	−3.61080e11	−0.504029	−0.252015	+	0.967723i	$0.581093\pi$
$432$	2.79701e11	0.386383
$433$	4.69247e11	0.641514	0.320757	−	0.947162i	$-0.396063\pi$
$433$	4.69247e11	0.641514	0.320757	+	0.947162i	$0.396063\pi$
$434$	7.67806e11	1.03884
$435$	−2.18441e12	−2.92504
$436$	−6.21383e11	−0.823512
$437$	1.04368e11	0.136899
$438$	9.40086e10	0.122049
$439$	−7.12546e11	−0.915636	−0.457818	−	0.889046i	$-0.651369\pi$
$439$	−7.12546e11	−0.915636	−0.457818	+	0.889046i	$0.651369\pi$
$440$	3.83528e11	0.487820
$441$	7.58335e11	0.954745
$442$	3.04390e11	0.379341
$443$	1.02429e12	1.26359	0.631795	−	0.775135i	$-0.282318\pi$
$443$	1.02429e12	1.26359	0.631795	+	0.775135i	$0.282318\pi$
$444$	−3.49125e11	−0.426342
$445$	1.61117e12	1.94770
$446$	−5.75701e11	−0.688954
$447$	2.15887e11	0.255766
$448$	−8.61613e11	−1.01056
$449$	−1.05516e12	−1.22521	−0.612605	−	0.790389i	$-0.709878\pi$
$449$	−1.05516e12	−1.22521	−0.612605	+	0.790389i	$0.709878\pi$
$450$	−1.69587e12	−1.94956
$451$	−8.07139e9	−0.00918658
$452$	−2.45239e11	−0.276354
$453$	2.56690e12	2.86396
$454$	−8.75948e10	−0.0967669
$455$	9.06636e11	0.991703
$456$	−8.05688e11	−0.872620
$457$	5.58535e10	0.0599001	0.0299501	−	0.999551i	$-0.490465\pi$
$457$	5.58535e10	0.0599001	0.0299501	+	0.999551i	$0.490465\pi$
$458$	−1.02110e12	−1.08436
$459$	−1.82737e12	−1.92163
$460$	−2.22615e11	−0.231817
$461$	−1.26794e12	−1.30751	−0.653754	−	0.756707i	$-0.726807\pi$
$461$	−1.26794e12	−1.30751	−0.653754	+	0.756707i	$0.726807\pi$
$462$	−4.32508e11	−0.441677
$463$	4.38622e11	0.443584	0.221792	−	0.975094i	$-0.428809\pi$
$463$	4.38622e11	0.443584	0.221792	+	0.975094i	$0.428809\pi$
$464$	−2.24148e11	−0.224494
$465$	−3.37147e12	−3.34411
$466$	1.39812e11	0.137344
$467$	1.14940e10	0.0111826	0.00559131	−	0.999984i	$-0.498220\pi$
$467$	1.14940e10	0.0111826	0.00559131	+	0.999984i	$0.498220\pi$
$468$	5.97030e11	0.575294
$469$	−1.19521e12	−1.14069
$470$	9.25457e9	0.00874814
$471$	−6.83546e11	−0.639990
$472$	1.14348e12	1.06045
$473$	−9.85969e10	−0.0905708
$474$	1.40063e12	1.27445
$475$	7.15867e11	0.645225
$476$	7.25676e11	0.647905
$477$	2.16068e12	1.91098
$478$	1.35730e12	1.18919
$479$	1.54682e12	1.34255	0.671273	−	0.741210i	$-0.265748\pi$
$479$	1.54682e12	1.34255	0.671273	+	0.741210i	$0.265748\pi$
$480$	2.84805e12	2.44885
$481$	2.92419e11	0.249088
$482$	2.03467e11	0.171705
$483$	7.32480e11	0.612398
$484$	−5.72302e10	−0.0474047
$485$	−3.56541e12	−2.92598
$486$	2.08292e11	0.169359
$487$	1.92206e11	0.154841	0.0774207	−	0.996999i	$-0.475332\pi$
$487$	1.92206e11	0.154841	0.0774207	+	0.996999i	$0.475332\pi$
$488$	−9.03728e11	−0.721355
$489$	−4.03835e11	−0.319385
$490$	−6.26614e11	−0.491041
$491$	−5.09058e11	−0.395276	−0.197638	−	0.980275i	$-0.563327\pi$
$491$	−5.09058e11	−0.395276	−0.197638	+	0.980275i	$0.563327\pi$
$492$	−3.61665e10	−0.0278268
$493$	1.46442e12	1.11649
$494$	2.31285e11	0.174733
$495$	1.28006e12	0.958311
$496$	−3.45956e11	−0.256657
$497$	−1.35408e12	−0.995502
$498$	1.00899e12	0.735113
$499$	7.55851e11	0.545738	0.272869	−	0.962051i	$-0.412027\pi$
$499$	7.55851e11	0.545738	0.272869	+	0.962051i	$0.412027\pi$
$500$	−4.06688e11	−0.291002
$501$	2.01307e12	1.42754
$502$	3.13999e11	0.220679
$503$	−6.11582e11	−0.425989	−0.212995	−	0.977053i	$-0.568322\pi$
$503$	−6.11582e11	−0.425989	−0.212995	+	0.977053i	$0.568322\pi$
$504$	−3.81123e12	−2.63104
$505$	−3.46710e12	−2.37222
$506$	−8.89487e10	−0.0603201
$507$	1.86386e12	1.25279
$508$	9.66118e11	0.643641
$509$	1.75245e12	1.15722	0.578610	−	0.815604i	$-0.303595\pi$
$509$	1.75245e12	1.15722	0.578610	+	0.815604i	$0.303595\pi$
$510$	2.92430e12	1.91406
$511$	−1.87717e11	−0.121790
$512$	6.30423e11	0.405431
$513$	−1.38849e12	−0.885146
$514$	−5.93094e11	−0.374791
$515$	2.70025e12	1.69149
$516$	−4.41796e11	−0.274346
$517$	−4.02929e9	−0.00248040
$518$	−6.39779e11	−0.390432
$519$	−4.73944e12	−2.86730
$520$	−1.43939e12	−0.863305
$521$	−1.39631e12	−0.830256	−0.415128	−	0.909763i	$-0.636263\pi$
$521$	−1.39631e12	−0.830256	−0.415128	+	0.909763i	$0.636263\pi$
$522$	−2.63600e12	−1.55392
$523$	−2.28933e12	−1.33799	−0.668993	−	0.743269i	$-0.733274\pi$
$523$	−2.28933e12	−1.33799	−0.668993	+	0.743269i	$0.733274\pi$
$524$	−1.14449e12	−0.663167
$525$	5.02414e12	2.88632
$526$	3.34027e9	0.00190259
$527$	2.26023e12	1.27645
$528$	1.94878e11	0.109122
$529$	−1.65051e12	−0.916364
$530$	−1.78537e12	−0.982850
$531$	3.81647e12	2.08322
$532$	5.51391e11	0.298440
$533$	3.02922e10	0.0162577
$534$	2.88460e12	1.53515
$535$	−5.14718e12	−2.71630
$536$	1.89754e12	0.992999
$537$	−3.90603e12	−2.02699
$538$	1.86413e12	0.959303
$539$	2.72818e11	0.139227
$540$	2.96163e12	1.49885
$541$	−9.52669e11	−0.478139	−0.239070	−	0.971002i	$-0.576842\pi$
$541$	−9.52669e11	−0.478139	−0.239070	+	0.971002i	$0.576842\pi$
$542$	4.12992e11	0.205563
$543$	−4.17665e12	−2.06172
$544$	−1.90933e12	−0.934730
$545$	5.00006e12	2.42768
$546$	1.62322e12	0.781644
$547$	9.62712e11	0.459783	0.229892	−	0.973216i	$-0.426163\pi$
$547$	9.62712e11	0.459783	0.229892	+	0.973216i	$0.426163\pi$
$548$	−1.21400e12	−0.575052
$549$	−3.01627e12	−1.41708
$550$	−6.10106e11	−0.284298
$551$	1.11271e12	0.514282
$552$	−1.16290e12	−0.533110
$553$	−2.79679e12	−1.27174
$554$	1.18994e12	0.536698
$555$	2.80930e12	1.25684
$556$	1.39524e12	0.619171
$557$	6.11109e11	0.269011	0.134506	−	0.990913i	$-0.457055\pi$
$557$	6.11109e11	0.269011	0.134506	+	0.990913i	$0.457055\pi$
$558$	−4.06847e12	−1.77655
$559$	3.70038e11	0.160285
$560$	8.93772e11	0.384044
$561$	−1.27320e12	−0.542703
$562$	1.71822e12	0.726548
$563$	3.64977e12	1.53101	0.765505	−	0.643429i	$-0.222489\pi$
$563$	3.64977e12	1.53101	0.765505	+	0.643429i	$0.222489\pi$
$564$	−1.80546e10	−0.00751332
$565$	1.97336e12	0.814680
$566$	−2.90356e12	−1.18921
$567$	−3.59260e12	−1.45977
$568$	2.14977e12	0.866612
$569$	4.84961e11	0.193955	0.0969776	−	0.995287i	$-0.469082\pi$
$569$	4.84961e11	0.193955	0.0969776	+	0.995287i	$0.469082\pi$
$570$	2.22197e12	0.881662
$571$	5.45393e11	0.214708	0.107354	−	0.994221i	$-0.465762\pi$
$571$	5.45393e11	0.214708	0.107354	+	0.994221i	$0.465762\pi$
$572$	2.14787e11	0.0838930
$573$	3.78264e12	1.46588
$574$	−6.62758e10	−0.0254831
$575$	1.03326e12	0.394187
$576$	4.56553e12	1.72819
$577$	2.63251e12	0.988733	0.494367	−	0.869253i	$-0.335400\pi$
$577$	2.63251e12	0.988733	0.494367	+	0.869253i	$0.335400\pi$
$578$	−1.04192e11	−0.0388293
$579$	6.22150e12	2.30060
$580$	−2.37341e12	−0.870855
$581$	−2.01476e12	−0.733551
$582$	−6.38341e12	−2.30621
$583$	7.77323e11	0.278672
$584$	2.98023e11	0.106021
$585$	−4.80410e12	−1.69594
$586$	−2.97023e12	−1.04052
$587$	−2.59718e12	−0.902880	−0.451440	−	0.892302i	$-0.649089\pi$
$587$	−2.59718e12	−0.902880	−0.451440	+	0.892302i	$0.649089\pi$
$588$	1.22245e12	0.421729
$589$	1.71739e12	0.587964
$590$	−3.15355e12	−1.07144
$591$	−4.97516e11	−0.167750
$592$	2.88270e11	0.0964609
$593$	1.31351e12	0.436200	0.218100	−	0.975926i	$-0.430014\pi$
$593$	1.31351e12	0.436200	0.218100	+	0.975926i	$0.430014\pi$
$594$	1.18336e12	0.390011
$595$	−5.83927e12	−1.91000
$596$	2.34566e11	0.0761476
$597$	−4.99671e12	−1.60990
$598$	3.33827e11	0.106750
$599$	3.07199e12	0.974988	0.487494	−	0.873126i	$-0.337911\pi$
$599$	3.07199e12	0.974988	0.487494	+	0.873126i	$0.337911\pi$
$600$	−7.97642e12	−2.51262
$601$	3.06955e12	0.959709	0.479855	−	0.877348i	$-0.340689\pi$
$601$	3.06955e12	0.959709	0.479855	+	0.877348i	$0.340689\pi$
$602$	−8.09600e11	−0.251238
$603$	6.33320e12	1.95072
$604$	2.78899e12	0.852669
$605$	4.60513e11	0.139747
$606$	−6.20740e12	−1.86975
$607$	1.83982e12	0.550082	0.275041	−	0.961433i	$-0.411309\pi$
$607$	1.83982e12	0.550082	0.275041	+	0.961433i	$0.411309\pi$
$608$	−1.45077e12	−0.430558
$609$	7.80932e12	2.30057
$610$	2.49235e12	0.728829
$611$	1.51221e10	0.00438961
$612$	−3.84522e12	−1.10800
$613$	2.60106e12	0.744010	0.372005	−	0.928231i	$-0.378670\pi$
$613$	2.60106e12	0.744010	0.372005	+	0.928231i	$0.378670\pi$
$614$	3.94642e10	0.0112059
$615$	2.91020e11	0.0820323
$616$	−1.37112e12	−0.383675
$617$	4.22433e12	1.17348	0.586738	−	0.809777i	$-0.300412\pi$
$617$	4.22433e12	1.17348	0.586738	+	0.809777i	$0.300412\pi$
$618$	4.83444e12	1.33321
$619$	−4.28266e12	−1.17248	−0.586240	−	0.810137i	$-0.699393\pi$
$619$	−4.28266e12	−1.17248	−0.586240	+	0.810137i	$0.699393\pi$
$620$	−3.66318e12	−0.995624
$621$	−2.00409e12	−0.540762
$622$	3.46234e11	0.0927499
$623$	−5.75999e12	−1.53188
$624$	−7.31384e11	−0.193114
$625$	−1.92708e12	−0.505172
$626$	4.60054e12	1.19736
$627$	−9.67413e11	−0.249981
$628$	−7.42688e11	−0.190541
$629$	−1.88335e12	−0.479737
$630$	1.05108e13	2.65830
$631$	−2.27266e12	−0.570692	−0.285346	−	0.958425i	$-0.592109\pi$
$631$	−2.27266e12	−0.570692	−0.285346	+	0.958425i	$0.592109\pi$
$632$	4.44024e12	1.10708
$633$	−1.19660e13	−2.96233
$634$	−1.01272e12	−0.248935
$635$	−7.77403e12	−1.89742
$636$	3.48305e12	0.844118
$637$	−1.02389e12	−0.246393
$638$	−9.48323e11	−0.226602
$639$	7.17505e12	1.70244
$640$	2.16183e12	0.509345
$641$	−2.28220e11	−0.0533940	−0.0266970	−	0.999644i	$-0.508499\pi$
$641$	−2.28220e11	−0.0533940	−0.0266970	+	0.999644i	$0.508499\pi$
$642$	−9.21537e12	−2.14094
$643$	−7.48389e12	−1.72654	−0.863272	−	0.504739i	$-0.831589\pi$
$643$	−7.48389e12	−1.72654	−0.863272	+	0.504739i	$0.831589\pi$
$644$	7.95856e11	0.182326
$645$	3.55499e12	0.808760
$646$	−1.48961e12	−0.336532
$647$	−2.80052e11	−0.0628303	−0.0314152	−	0.999506i	$-0.510001\pi$
$647$	−2.80052e11	−0.0628303	−0.0314152	+	0.999506i	$0.510001\pi$
$648$	5.70367e12	1.27077
$649$	1.37301e12	0.303789
$650$	2.28975e12	0.503127
$651$	1.20531e13	2.63017
$652$	−4.38776e11	−0.0950886
$653$	−4.25977e12	−0.916804	−0.458402	−	0.888745i	$-0.651578\pi$
$653$	−4.25977e12	−0.916804	−0.458402	+	0.888745i	$0.651578\pi$
$654$	8.95196e12	1.91346
$655$	9.20937e12	1.95499
$656$	2.98624e10	0.00629589
$657$	9.94680e11	0.208276
$658$	−3.30854e10	−0.00688049
$659$	6.25498e12	1.29194	0.645969	−	0.763364i	$-0.276454\pi$
$659$	6.25498e12	1.29194	0.645969	+	0.763364i	$0.276454\pi$
$660$	2.06348e12	0.423304
$661$	−2.38132e12	−0.485189	−0.242594	−	0.970128i	$-0.577998\pi$
$661$	−2.38132e12	−0.485189	−0.242594	+	0.970128i	$0.577998\pi$
$662$	−1.10091e12	−0.222788
$663$	4.77834e12	0.960432
$664$	3.19867e12	0.638576
$665$	−4.43686e12	−0.879788
$666$	3.39007e12	0.667690
$667$	1.60605e12	0.314190
$668$	2.18725e12	0.425014
$669$	−9.03742e12	−1.74432
$670$	−5.23314e12	−1.00329
$671$	−1.08513e12	−0.206648
$672$	−1.01819e13	−1.92604
$673$	2.81014e11	0.0528032	0.0264016	−	0.999651i	$-0.491595\pi$
$673$	2.81014e11	0.0528032	0.0264016	+	0.999651i	$0.491595\pi$
$674$	−3.53844e12	−0.660454
$675$	−1.37462e13	−2.54869
$676$	2.02512e12	0.372985
$677$	−1.45117e12	−0.265503	−0.132751	−	0.991149i	$-0.542381\pi$
$677$	−1.45117e12	−0.265503	−0.132751	+	0.991149i	$0.542381\pi$
$678$	3.53304e12	0.642118
$679$	1.27464e13	2.30131
$680$	9.27054e12	1.66270
$681$	−1.37507e12	−0.244999
$682$	−1.46367e12	−0.259067
$683$	−7.93030e12	−1.39443	−0.697215	−	0.716863i	$-0.745578\pi$
$683$	−7.93030e12	−1.39443	−0.697215	+	0.716863i	$0.745578\pi$
$684$	−2.92172e12	−0.510371
$685$	9.76868e12	1.69523
$686$	−2.61116e12	−0.450168
$687$	−1.60293e13	−2.74543
$688$	3.64787e11	0.0620714
$689$	−2.91732e12	−0.493171
$690$	3.20711e12	0.538633
$691$	8.55555e12	1.42757	0.713784	−	0.700366i	$-0.246980\pi$
$691$	8.55555e12	1.42757	0.713784	+	0.700366i	$0.246980\pi$
$692$	−5.14950e12	−0.853666
$693$	−4.57625e12	−0.753720
$694$	1.47757e12	0.241785
$695$	−1.12270e13	−1.82529
$696$	−1.23982e13	−2.00271
$697$	−1.95100e11	−0.0313119
$698$	4.58023e11	0.0730362
$699$	2.19479e12	0.347733
$700$	5.45884e12	0.859329
$701$	−9.03988e12	−1.41394	−0.706971	−	0.707243i	$-0.749939\pi$
$701$	−9.03988e12	−1.41394	−0.706971	+	0.707243i	$0.749939\pi$
$702$	−4.44118e12	−0.690210
$703$	−1.43103e12	−0.220978
$704$	1.64249e12	0.252015
$705$	1.45279e11	0.0221489
$706$	2.15845e11	0.0326979
$707$	1.23950e13	1.86577
$708$	6.15222e12	0.920200
$709$	−6.71158e12	−0.997509	−0.498754	−	0.866743i	$-0.666209\pi$
$709$	−6.71158e12	−0.997509	−0.498754	+	0.866743i	$0.666209\pi$
$710$	−5.92876e12	−0.875591
$711$	1.48197e13	2.17484
$712$	9.14467e12	1.33355
$713$	2.47882e12	0.359205
$714$	−1.04545e13	−1.50543
$715$	−1.72832e12	−0.247313
$716$	−4.24399e12	−0.603483
$717$	2.13070e13	3.01083
$718$	4.89752e12	0.687727
$719$	8.62374e12	1.20342	0.601708	−	0.798716i	$-0.294487\pi$
$719$	8.62374e12	1.20342	0.601708	+	0.798716i	$0.294487\pi$
$720$	−4.73594e12	−0.656765
$721$	−9.65346e12	−1.33038
$722$	3.91918e12	0.536758
$723$	3.19405e12	0.434730
$724$	−4.53802e12	−0.613823
$725$	1.10160e13	1.48082
$726$	8.24489e11	0.110146
$727$	−2.25456e12	−0.299335	−0.149667	−	0.988736i	$-0.547820\pi$
$727$	−2.25456e12	−0.299335	−0.149667	+	0.988736i	$0.547820\pi$
$728$	5.14587e12	0.678997
$729$	−5.93724e12	−0.778594
$730$	−8.21906e11	−0.107120
$731$	−2.38326e12	−0.308705
$732$	−4.86230e12	−0.625953
$733$	1.36664e13	1.74858	0.874289	−	0.485406i	$-0.161328\pi$
$733$	1.36664e13	1.74858	0.874289	+	0.485406i	$0.161328\pi$
$734$	−1.70222e12	−0.216463
$735$	−9.83665e12	−1.24324
$736$	−2.09398e12	−0.263041
$737$	2.27843e12	0.284467
$738$	3.51184e11	0.0435793
$739$	−1.41824e13	−1.74924	−0.874622	−	0.484806i	$-0.838890\pi$
$739$	−1.41824e13	−1.74924	−0.874622	+	0.484806i	$0.838890\pi$
$740$	3.05236e12	0.374191
$741$	3.63073e12	0.442397
$742$	6.38276e12	0.773020
$743$	5.11027e12	0.615168	0.307584	−	0.951521i	$-0.400479\pi$
$743$	5.11027e12	0.615168	0.307584	+	0.951521i	$0.400479\pi$
$744$	−1.91357e13	−2.28964
$745$	−1.88747e12	−0.224480
$746$	4.54427e12	0.537204
$747$	1.06758e13	1.25447
$748$	−1.38335e12	−0.161576
$749$	1.84013e13	2.13639
$750$	5.85897e12	0.676153
$751$	−2.93643e12	−0.336853	−0.168426	−	0.985714i	$-0.553869\pi$
$751$	−2.93643e12	−0.336853	−0.168426	+	0.985714i	$0.553869\pi$
$752$	1.49075e10	0.00169991
$753$	4.92918e12	0.558724
$754$	3.55909e12	0.401022
$755$	−2.24421e13	−2.51363
$756$	−1.05879e13	−1.17886
$757$	−1.56994e13	−1.73760	−0.868801	−	0.495162i	$-0.835109\pi$
$757$	−1.56994e13	−1.73760	−0.868801	+	0.495162i	$0.835109\pi$
$758$	8.84735e12	0.973424
$759$	−1.39633e12	−0.152721
$760$	7.04404e12	0.765880
$761$	1.11983e11	0.0121038	0.00605190	−	0.999982i	$-0.498074\pi$
$761$	1.11983e11	0.0121038	0.00605190	+	0.999982i	$0.498074\pi$
$762$	−1.39184e13	−1.49552
$763$	−1.78754e13	−1.90939
$764$	4.10993e12	0.436429
$765$	3.09412e13	3.26634
$766$	5.55523e12	0.583006
$767$	−5.15294e12	−0.537621
$768$	1.79844e13	1.86539
$769$	−1.24501e13	−1.28382	−0.641908	−	0.766781i	$-0.721857\pi$
$769$	−1.24501e13	−1.28382	−0.641908	+	0.766781i	$0.721857\pi$
$770$	3.78136e12	0.387650
$771$	−9.31045e12	−0.948912
$772$	6.75980e12	0.684945
$773$	1.52002e13	1.53123	0.765616	−	0.643298i	$-0.222434\pi$
$773$	1.52002e13	1.53123	0.765616	+	0.643298i	$0.222434\pi$
$774$	4.28992e12	0.429650
$775$	1.70024e13	1.69298
$776$	−2.02365e13	−2.00335
$777$	−1.00433e13	−0.988514
$778$	−2.41096e12	−0.235929
$779$	−1.48243e11	−0.0144230
$780$	−7.74431e12	−0.749129
$781$	2.58129e12	0.248260
$782$	−2.15005e12	−0.205597
$783$	−2.13666e13	−2.03146
$784$	−1.00937e12	−0.0954172
$785$	5.97616e12	0.561706
$786$	1.64882e13	1.54089
$787$	−7.52186e12	−0.698938	−0.349469	−	0.936948i	$-0.613638\pi$
$787$	−7.52186e12	−0.698938	−0.349469	+	0.936948i	$0.613638\pi$
$788$	−5.40562e11	−0.0499433
$789$	5.24359e10	0.00481706
$790$	−1.22456e13	−1.11855
$791$	−7.05480e12	−0.640753
$792$	7.26533e12	0.656134
$793$	4.07254e12	0.365709
$794$	−8.23918e12	−0.735685
$795$	−2.80270e13	−2.48842
$796$	−5.42903e12	−0.479307
$797$	2.24661e12	0.197226	0.0986131	−	0.995126i	$-0.468559\pi$
$797$	2.24661e12	0.197226	0.0986131	+	0.995126i	$0.468559\pi$
$798$	−7.94362e12	−0.693435
$799$	−9.73951e10	−0.00845428
$800$	−1.43628e13	−1.23975
$801$	3.05212e13	2.61972
$802$	4.62540e12	0.394788
$803$	3.57845e11	0.0303721
$804$	1.02093e13	0.861671
$805$	−6.40399e12	−0.537489
$806$	5.49319e12	0.458477
$807$	2.92633e13	2.42880
$808$	−1.96785e13	−1.62421
$809$	4.86941e11	0.0399676	0.0199838	−	0.999800i	$-0.493639\pi$
$809$	4.86941e11	0.0399676	0.0199838	+	0.999800i	$0.493639\pi$
$810$	−1.57299e13	−1.28394
$811$	−2.42320e12	−0.196696	−0.0983481	−	0.995152i	$-0.531356\pi$
$811$	−2.42320e12	−0.196696	−0.0983481	+	0.995152i	$0.531356\pi$
$812$	8.48500e12	0.684935
$813$	6.48319e12	0.520453
$814$	1.21961e12	0.0973668
$815$	3.53068e12	0.280317
$816$	4.71055e12	0.371934
$817$	−1.81087e12	−0.142197
$818$	−1.16690e13	−0.911264
$819$	1.71748e13	1.33387
$820$	3.16200e11	0.0244230
$821$	−6.21539e12	−0.477446	−0.238723	−	0.971088i	$-0.576729\pi$
$821$	−6.21539e12	−0.477446	−0.238723	+	0.971088i	$0.576729\pi$
$822$	1.74896e13	1.33615
$823$	−8.91410e12	−0.677295	−0.338648	−	0.940913i	$-0.609969\pi$
$823$	−8.91410e12	−0.677295	−0.338648	+	0.940913i	$0.609969\pi$
$824$	1.53260e13	1.15813
$825$	−9.57752e12	−0.719797
$826$	1.12741e13	0.842694
$827$	7.37630e12	0.548358	0.274179	−	0.961679i	$-0.411594\pi$
$827$	7.37630e12	0.548358	0.274179	+	0.961679i	$0.411594\pi$
$828$	−4.21710e12	−0.311801
$829$	2.13119e13	1.56721	0.783603	−	0.621261i	$-0.213379\pi$
$829$	2.13119e13	1.56721	0.783603	+	0.621261i	$0.213379\pi$
$830$	−8.82147e12	−0.645193
$831$	1.86798e13	1.35884
$832$	−6.16433e12	−0.445996
$833$	6.59449e12	0.474546
$834$	−2.01005e13	−1.43866
$835$	−1.76000e13	−1.25292
$836$	−1.05112e12	−0.0744256
$837$	−3.29778e13	−2.32250
$838$	1.62862e12	0.114083
$839$	9.15096e12	0.637585	0.318792	−	0.947825i	$-0.396723\pi$
$839$	9.15096e12	0.637585	0.318792	+	0.947825i	$0.396723\pi$
$840$	4.94369e13	3.42606
$841$	2.61569e12	0.180304
$842$	1.47002e13	1.00790
$843$	2.69728e13	1.83951
$844$	−1.30014e13	−0.881959
$845$	−1.62955e13	−1.09954
$846$	1.75313e11	0.0117665
$847$	−1.64635e12	−0.109912
$848$	−2.87593e12	−0.190984
$849$	−4.55804e13	−3.01088
$850$	−1.47473e13	−0.969010
$851$	−2.06549e12	−0.135002
$852$	1.15663e13	0.751999
$853$	5.05835e12	0.327143	0.163572	−	0.986531i	$-0.447698\pi$
$853$	5.05835e12	0.327143	0.163572	+	0.986531i	$0.447698\pi$
$854$	−8.91024e12	−0.573230
$855$	2.35101e13	1.50455
$856$	−2.92143e13	−1.85979
$857$	−1.35574e12	−0.0858544	−0.0429272	−	0.999078i	$-0.513668\pi$
$857$	−1.35574e12	−0.0858544	−0.0429272	+	0.999078i	$0.513668\pi$
$858$	−3.09433e12	−0.194928
$859$	4.25759e12	0.266805	0.133403	−	0.991062i	$-0.457410\pi$
$859$	4.25759e12	0.266805	0.133403	+	0.991062i	$0.457410\pi$
$860$	3.86257e12	0.240787
$861$	−1.04041e12	−0.0645191
$862$	5.65199e12	0.348673
$863$	−2.58603e13	−1.58703	−0.793514	−	0.608552i	$-0.791751\pi$
$863$	−2.58603e13	−1.58703	−0.793514	+	0.608552i	$0.791751\pi$
$864$	2.78580e13	1.70074
$865$	4.14363e13	2.51657
$866$	−7.34513e12	−0.443781
$867$	−1.63562e12	−0.0983096
$868$	1.30960e13	0.783067
$869$	5.33152e12	0.317148
$870$	3.41925e13	2.02346
$871$	−8.55101e12	−0.503426
$872$	2.83793e13	1.66218
$873$	−6.75411e13	−3.93554
$874$	−1.63367e12	−0.0947028
$875$	−1.16992e13	−0.674716
$876$	1.60344e12	0.0919995
$877$	5.89456e11	0.0336475	0.0168238	−	0.999858i	$-0.494645\pi$
$877$	5.89456e11	0.0336475	0.0168238	+	0.999858i	$0.494645\pi$
$878$	1.11535e13	0.633411
$879$	−4.66270e13	−2.63443
$880$	−1.70380e12	−0.0957736
$881$	2.09056e13	1.16915	0.584575	−	0.811340i	$-0.301261\pi$
$881$	2.09056e13	1.16915	0.584575	+	0.811340i	$0.301261\pi$
$882$	−1.18702e13	−0.660466
$883$	−1.58306e13	−0.876344	−0.438172	−	0.898891i	$-0.644374\pi$
$883$	−1.58306e13	−0.876344	−0.438172	+	0.898891i	$0.644374\pi$
$884$	5.19178e12	0.285944
$885$	−4.95049e13	−2.71271
$886$	−1.60332e13	−0.874117
$887$	−1.59297e13	−0.864075	−0.432037	−	0.901856i	$-0.642205\pi$
$887$	−1.59297e13	−0.864075	−0.432037	+	0.901856i	$0.642205\pi$
$888$	1.59450e13	0.860528
$889$	2.77924e13	1.49234
$890$	−2.52197e13	−1.34736
$891$	6.84856e12	0.364040
$892$	−9.81936e12	−0.519327
$893$	−7.40038e10	−0.00389424
$894$	−3.37928e12	−0.176931
$895$	3.41499e13	1.77904
$896$	−7.72861e12	−0.400604
$897$	5.24046e12	0.270273
$898$	1.65165e13	0.847566
$899$	2.64278e13	1.34941
$900$	−2.89254e13	−1.46956
$901$	1.87893e13	0.949835
$902$	1.26342e11	0.00635502
$903$	−1.27092e13	−0.636096
$904$	1.12003e13	0.557793
$905$	3.65160e13	1.80952
$906$	−4.01797e13	−1.98120
$907$	2.53311e13	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$907$	2.53311e13	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$908$	−1.49405e12	−0.0729420
$909$	−6.56788e13	−3.19071
$910$	−1.41916e13	−0.686032
$911$	1.93496e13	0.930765	0.465382	−	0.885110i	$-0.345917\pi$
$911$	1.93496e13	0.930765	0.465382	+	0.885110i	$0.345917\pi$
$912$	3.57922e12	0.171321
$913$	3.84073e12	0.182934
$914$	−8.74276e11	−0.0414372
$915$	3.91253e13	1.84528
$916$	−1.74162e13	−0.817380
$917$	−3.29238e13	−1.53761
$918$	2.86038e13	1.32933
$919$	−2.91803e12	−0.134949	−0.0674746	−	0.997721i	$-0.521494\pi$
$919$	−2.91803e12	−0.134949	−0.0674746	+	0.997721i	$0.521494\pi$
$920$	1.01671e13	0.467899
$921$	6.19514e11	0.0283715
$922$	1.98471e13	0.904498
$923$	−9.68766e12	−0.439351
$924$	−7.37700e12	−0.332932
$925$	−1.41674e13	−0.636284
$926$	−6.86576e12	−0.306859
$927$	5.11519e13	2.27511
$928$	−2.23249e13	−0.988154
$929$	−1.62530e13	−0.715915	−0.357958	−	0.933738i	$-0.616527\pi$
$929$	−1.62530e13	−0.715915	−0.357958	+	0.933738i	$0.616527\pi$
$930$	5.27737e13	2.31336
$931$	5.01069e12	0.218587
$932$	2.38469e12	0.103528
$933$	5.43523e12	0.234828
$934$	−1.79915e11	−0.00773582
$935$	1.11314e13	0.476318
$936$	−2.72670e13	−1.16117
$937$	−2.33363e12	−0.0989015	−0.0494508	−	0.998777i	$-0.515747\pi$
$937$	−2.33363e12	−0.0989015	−0.0494508	+	0.998777i	$0.515747\pi$
$938$	1.87086e13	0.789095
$939$	7.22198e13	3.03152
$940$	1.57849e11	0.00659427
$941$	−4.28151e12	−0.178010	−0.0890049	−	0.996031i	$-0.528369\pi$
$941$	−4.28151e12	−0.178010	−0.0890049	+	0.996031i	$0.528369\pi$
$942$	1.06995e13	0.442727
$943$	−2.13968e11	−0.00881142
$944$	−5.07983e12	−0.208197
$945$	8.51975e13	3.47523
$946$	1.54334e12	0.0626544
$947$	2.80221e13	1.13221	0.566104	−	0.824334i	$-0.308450\pi$
$947$	2.80221e13	1.13221	0.566104	+	0.824334i	$0.308450\pi$
$948$	2.38897e13	0.960666
$949$	−1.34300e12	−0.0537501
$950$	−1.12055e13	−0.446349
$951$	−1.58977e13	−0.630265
$952$	−3.31425e13	−1.30773
$953$	−1.20996e13	−0.475176	−0.237588	−	0.971366i	$-0.576357\pi$
$953$	−1.20996e13	−0.475176	−0.237588	+	0.971366i	$0.576357\pi$
$954$	−3.38211e13	−1.32196
$955$	−3.30712e13	−1.28657
$956$	2.31505e13	0.896398
$957$	−1.48869e13	−0.573720
$958$	−2.42124e13	−0.928736
$959$	−3.49233e13	−1.33331
$960$	−5.92213e13	−2.25039
$961$	1.43498e13	0.542739
$962$	−4.57723e12	−0.172312
$963$	−9.75054e13	−3.65351
$964$	3.47041e12	0.129430
$965$	−5.43939e13	−2.01919
$966$	−1.14655e13	−0.423640
$967$	−4.40787e13	−1.62110	−0.810549	−	0.585671i	$-0.800831\pi$
$967$	−4.40787e13	−1.62110	−0.810549	+	0.585671i	$0.800831\pi$
$968$	2.61377e12	0.0956816
$969$	−2.33841e13	−0.852046
$970$	5.58094e13	2.02411
$971$	−1.79676e13	−0.648641	−0.324320	−	0.945947i	$-0.605136\pi$
$971$	−1.79676e13	−0.648641	−0.324320	+	0.945947i	$0.605136\pi$
$972$	3.55270e12	0.127662
$973$	4.01368e13	1.43561
$974$	−3.00861e12	−0.107115
$975$	3.59447e13	1.27384
$976$	4.01475e12	0.141623
$977$	1.45335e13	0.510322	0.255161	−	0.966899i	$-0.417872\pi$
$977$	1.45335e13	0.510322	0.255161	+	0.966899i	$0.417872\pi$
$978$	6.32123e12	0.220941
$979$	1.09803e13	0.382024
$980$	−1.06877e13	−0.370142
$981$	9.47183e13	3.26530
$982$	7.96828e12	0.273441
$983$	−1.21016e13	−0.413382	−0.206691	−	0.978406i	$-0.566269\pi$
$983$	−1.21016e13	−0.413382	−0.206691	+	0.978406i	$0.566269\pi$
$984$	1.65177e12	0.0561657
$985$	4.34972e12	0.147231
$986$	−2.29226e13	−0.772358
$987$	−5.19378e11	−0.0174203
$988$	3.94487e12	0.131712
$989$	−2.61375e12	−0.0868721
$990$	−2.00368e13	−0.662932
$991$	3.67306e12	0.120975	0.0604877	−	0.998169i	$-0.480734\pi$
$991$	3.67306e12	0.120975	0.0604877	+	0.998169i	$0.480734\pi$
$992$	−3.44569e13	−1.12973
$993$	−1.72822e13	−0.564064
$994$	2.11955e13	0.688660
$995$	4.36856e13	1.41298
$996$	1.72097e13	0.554122
$997$	1.95902e13	0.627930	0.313965	−	0.949435i	$-0.398343\pi$
$997$	1.95902e13	0.627930	0.313965	+	0.949435i	$0.398343\pi$
$998$	−1.18313e13	−0.377526
$999$	2.74789e13	0.872880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.a.b.1.2	✓	5
3.2	odd	2		99.10.a.f.1.4		5
4.3	odd	2		176.10.a.j.1.5		5
5.4	even	2		275.10.a.b.1.4		5
11.10	odd	2		121.10.a.c.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.a.b.1.2	✓	5	1.1	even	1	trivial
99.10.a.f.1.4		5	3.2	odd	2
121.10.a.c.1.4		5	11.10	odd	2
176.10.a.j.1.5		5	4.3	odd	2
275.10.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q-15.6530 q^{2} -245.723 q^{3} -266.983 q^{4} +2148.33 q^{5} +3846.30 q^{6} -7680.33 q^{7} +12193.4 q^{8} +40696.7 q^{9} -33627.8 q^{10} +14641.0 q^{11} +65603.9 q^{12} -54948.1 q^{13} +120220. q^{14} -527892. q^{15} -54168.5 q^{16} +353899. q^{17} -637025. q^{18} +268903. q^{19} -573567. q^{20} +1.88723e6 q^{21} -229176. q^{22} +388124. q^{23} -2.99620e6 q^{24} +2.66218e6 q^{25} +860104. q^{26} -5.16354e6 q^{27} +2.05052e6 q^{28} +4.13797e6 q^{29} +8.26311e6 q^{30} +6.38666e6 q^{31} -5.39514e6 q^{32} -3.59763e6 q^{33} -5.53958e6 q^{34} -1.64998e7 q^{35} -1.08653e7 q^{36} -5.32172e6 q^{37} -4.20914e6 q^{38} +1.35020e7 q^{39} +2.61955e7 q^{40} -551287. q^{41} -2.95409e7 q^{42} -6.73430e6 q^{43} -3.90890e6 q^{44} +8.74297e7 q^{45} -6.07532e6 q^{46} -275206. q^{47} +1.33104e7 q^{48} +1.86338e7 q^{49} -4.16711e7 q^{50} -8.69609e7 q^{51} +1.46702e7 q^{52} +5.30922e7 q^{53} +8.08249e7 q^{54} +3.14536e7 q^{55} -9.36496e7 q^{56} -6.60756e7 q^{57} -6.47718e7 q^{58} +9.37783e7 q^{59} +1.40938e8 q^{60} -7.41160e7 q^{61} -9.99705e7 q^{62} -3.12564e8 q^{63} +1.12184e8 q^{64} -1.18046e8 q^{65} +5.63137e7 q^{66} +1.55620e8 q^{67} -9.44850e7 q^{68} -9.53710e7 q^{69} +2.58272e8 q^{70} +1.76306e8 q^{71} +4.96232e8 q^{72} +2.44413e7 q^{73} +8.33010e7 q^{74} -6.54157e8 q^{75} -7.17926e7 q^{76} -1.12448e8 q^{77} -2.11347e8 q^{78} +3.64150e8 q^{79} -1.16372e8 q^{80} +4.67766e8 q^{81} +8.62930e6 q^{82} +2.62327e8 q^{83} -5.03859e8 q^{84} +7.60289e8 q^{85} +1.05412e8 q^{86} -1.01679e9 q^{87} +1.78524e8 q^{88} +7.49967e8 q^{89} -1.36854e9 q^{90} +4.22020e8 q^{91} -1.03623e8 q^{92} -1.56935e9 q^{93} +4.30781e6 q^{94} +5.77691e8 q^{95} +1.32571e9 q^{96} -1.65962e9 q^{97} -2.91675e8 q^{98} +5.95840e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16}+ \cdots + 1094985749 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more