LMFDB - Embedded newform 11.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,10,Mod(1,11)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			1.3
Root			$-12.6389$ 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)

$f(q)$	$=$	$q-9.63895 q^{2} +265.389 q^{3} -419.091 q^{4} +610.442 q^{5} -2558.07 q^{6} +4856.42 q^{7} +8974.73 q^{8} +50748.6 q^{9} +O(q^{10})$	\(q-9.63895 q^{2} +265.389 q^{3} -419.091 q^{4} +610.442 q^{5} -2558.07 q^{6} +4856.42 q^{7} +8974.73 q^{8} +50748.6 q^{9} -5884.02 q^{10} +14641.0 q^{11} -111222. q^{12} -54118.2 q^{13} -46810.8 q^{14} +162005. q^{15} +128067. q^{16} +67139.6 q^{17} -489163. q^{18} -990055. q^{19} -255830. q^{20} +1.28884e6 q^{21} -141124. q^{22} -496126. q^{23} +2.38180e6 q^{24} -1.58049e6 q^{25} +521643. q^{26} +8.24447e6 q^{27} -2.03528e6 q^{28} -6.30563e6 q^{29} -1.56156e6 q^{30} +5.17367e6 q^{31} -5.82950e6 q^{32} +3.88557e6 q^{33} -647156. q^{34} +2.96456e6 q^{35} -2.12682e7 q^{36} +9.19207e6 q^{37} +9.54309e6 q^{38} -1.43624e7 q^{39} +5.47855e6 q^{40} -2.82965e7 q^{41} -1.24231e7 q^{42} +2.72268e7 q^{43} -6.13591e6 q^{44} +3.09790e7 q^{45} +4.78213e6 q^{46} +2.32412e7 q^{47} +3.39877e7 q^{48} -1.67688e7 q^{49} +1.52342e7 q^{50} +1.78182e7 q^{51} +2.26804e7 q^{52} +1.16245e7 q^{53} -7.94680e7 q^{54} +8.93748e6 q^{55} +4.35851e7 q^{56} -2.62750e8 q^{57} +6.07796e7 q^{58} -5.47787e7 q^{59} -6.78947e7 q^{60} +1.11925e8 q^{61} -4.98688e7 q^{62} +2.46456e8 q^{63} -9.38028e6 q^{64} -3.30360e7 q^{65} -3.74528e7 q^{66} +1.73109e7 q^{67} -2.81376e7 q^{68} -1.31667e8 q^{69} -2.85753e7 q^{70} -1.84426e8 q^{71} +4.55455e8 q^{72} -2.35067e7 q^{73} -8.86019e7 q^{74} -4.19444e8 q^{75} +4.14923e8 q^{76} +7.11028e7 q^{77} +1.38438e8 q^{78} -1.48610e8 q^{79} +7.81777e7 q^{80} +1.18911e9 q^{81} +2.72749e8 q^{82} +1.48409e7 q^{83} -5.40142e8 q^{84} +4.09848e7 q^{85} -2.62437e8 q^{86} -1.67345e9 q^{87} +1.31399e8 q^{88} -4.26751e8 q^{89} -2.98605e8 q^{90} -2.62821e8 q^{91} +2.07922e8 q^{92} +1.37304e9 q^{93} -2.24020e8 q^{94} -6.04371e8 q^{95} -1.54709e9 q^{96} +9.28863e8 q^{97} +1.61634e8 q^{98} +7.43010e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+O(q^{10}) $ 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	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16} - 547238 q^{17} - 822418 q^{18} - 162940 q^{19} - 1913320 q^{20} + 825496 q^{21} + 234256 q^{22} + 3415892 q^{23} + 1435932 q^{24} + 6164943 q^{25} + 5356756 q^{26} + 5240140 q^{27} - 2477216 q^{28} + 5868414 q^{29} - 9766670 q^{30} + 11730396 q^{31} - 18454552 q^{32} + 1639792 q^{33} - 25579352 q^{34} - 6567848 q^{35} - 26683532 q^{36} + 7021250 q^{37} - 22257720 q^{38} + 29114872 q^{39} - 22406796 q^{40} + 5595418 q^{41} - 65554916 q^{42} + 29161940 q^{43} + 10365828 q^{44} + 68008838 q^{45} + 47468978 q^{46} + 33703664 q^{47} + 96997832 q^{48} + 106606605 q^{49} + 84598070 q^{50} - 135853760 q^{51} + 185107192 q^{52} - 88905666 q^{53} - 95103866 q^{54} + 23337754 q^{55} - 78057672 q^{56} - 362541120 q^{57} + 63640668 q^{58} + 13747712 q^{59} - 208875616 q^{60} + 274324430 q^{61} - 161612942 q^{62} - 436710568 q^{63} - 46082368 q^{64} - 658499468 q^{65} + 151944298 q^{66} + 323117752 q^{67} - 679289848 q^{68} - 60345676 q^{69} + 1608436228 q^{70} + 9655356 q^{71} + 1168471200 q^{72} + 159287274 q^{73} + 76718502 q^{74} - 963596116 q^{75} + 483002000 q^{76} + 122984400 q^{77} + 1270322200 q^{78} - 668342072 q^{79} - 424312360 q^{80} + 1578463805 q^{81} + 666585700 q^{82} + 378353820 q^{83} - 2381947456 q^{84} + 1459757140 q^{85} - 2133621276 q^{86} - 2822691048 q^{87} + 596122956 q^{88} + 851774166 q^{89} - 4463334016 q^{90} - 991736368 q^{91} + 1919755168 q^{92} + 1149973204 q^{93} + 2620937360 q^{94} - 2812243800 q^{95} - 1157568712 q^{96} - 240502490 q^{97} - 2298624888 q^{98} + 1094985749 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

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 $

$2$	−9.63895	−0.425985	−0.212993	−	0.977054i	$-0.568321\pi$
$2$	−9.63895	−0.425985	−0.212993	+	0.977054i	$0.568321\pi$
$3$	265.389	1.89164	0.945819	−	0.324695i	$-0.105262\pi$
$3$	265.389	1.89164	0.945819	+	0.324695i	$0.105262\pi$
$4$	−419.091	−0.818536
$5$	610.442	0.436797	0.218398	−	0.975860i	$-0.429917\pi$
$5$	610.442	0.436797	0.218398	+	0.975860i	$0.429917\pi$
$6$	−2558.07	−0.805810
$7$	4856.42	0.764496	0.382248	−	0.924060i	$-0.375150\pi$
$7$	4856.42	0.764496	0.382248	+	0.924060i	$0.375150\pi$
$8$	8974.73	0.774670
$9$	50748.6	2.57829
$10$	−5884.02	−0.186069
$11$	14641.0	0.301511
$11$	14641.0	0.301511
$12$	−111222.	−1.54837
$13$	−54118.2	−0.525531	−0.262765	−	0.964860i	$-0.584635\pi$
$13$	−54118.2	−0.525531	−0.262765	+	0.964860i	$0.584635\pi$
$14$	−46810.8	−0.325664
$15$	162005.	0.826261
$16$	128067.	0.488538
$17$	67139.6	0.194966	0.0974830	−	0.995237i	$-0.468921\pi$
$17$	67139.6	0.194966	0.0974830	+	0.995237i	$0.468921\pi$
$18$	−489163.	−1.09832
$19$	−990055.	−1.74288	−0.871442	−	0.490499i	$-0.836814\pi$
$19$	−990055.	−1.74288	−0.871442	+	0.490499i	$0.836814\pi$
$20$	−255830.	−0.357534
$21$	1.28884e6	1.44615
$22$	−141124.	−0.128439
$23$	−496126.	−0.369672	−0.184836	−	0.982769i	$-0.559175\pi$
$23$	−496126.	−0.369672	−0.184836	+	0.982769i	$0.559175\pi$
$24$	2.38180e6	1.46539
$25$	−1.58049e6	−0.809209
$26$	521643.	0.223869
$27$	8.24447e6	2.98556
$28$	−2.03528e6	−0.625768
$29$	−6.30563e6	−1.65553	−0.827765	−	0.561074i	$-0.810388\pi$
$29$	−6.30563e6	−1.65553	−0.827765	+	0.561074i	$0.810388\pi$
$30$	−1.56156e6	−0.351975
$31$	5.17367e6	1.00617	0.503085	−	0.864237i	$-0.332198\pi$
$31$	5.17367e6	1.00617	0.503085	+	0.864237i	$0.332198\pi$
$32$	−5.82950e6	−0.982780
$33$	3.88557e6	0.570350
$34$	−647156.	−0.0830527
$35$	2.96456e6	0.333929
$36$	−2.12682e7	−2.11043
$37$	9.19207e6	0.806317	0.403158	−	0.915130i	$-0.367912\pi$
$37$	9.19207e6	0.806317	0.403158	+	0.915130i	$0.367912\pi$
$38$	9.54309e6	0.742443
$39$	−1.43624e7	−0.994114
$40$	5.47855e6	0.338373
$41$	−2.82965e7	−1.56389	−0.781944	−	0.623349i	$-0.785772\pi$
$41$	−2.82965e7	−1.56389	−0.781944	+	0.623349i	$0.785772\pi$
$42$	−1.24231e7	−0.616038
$43$	2.72268e7	1.21447	0.607236	−	0.794521i	$-0.292278\pi$
$43$	2.72268e7	1.21447	0.607236	+	0.794521i	$0.292278\pi$
$44$	−6.13591e6	−0.246798
$45$	3.09790e7	1.12619
$46$	4.78213e6	0.157475
$47$	2.32412e7	0.694732	0.347366	−	0.937730i	$-0.387076\pi$
$47$	2.32412e7	0.694732	0.347366	+	0.937730i	$0.387076\pi$
$48$	3.39877e7	0.924138
$49$	−1.67688e7	−0.415546
$50$	1.52342e7	0.344711
$51$	1.78182e7	0.368805
$52$	2.26804e7	0.430166
$53$	1.16245e7	0.202363	0.101182	−	0.994868i	$-0.467738\pi$
$53$	1.16245e7	0.202363	0.101182	+	0.994868i	$0.467738\pi$
$54$	−7.94680e7	−1.27180
$55$	8.93748e6	0.131699
$56$	4.35851e7	0.592232
$57$	−2.62750e8	−3.29690
$58$	6.07796e7	0.705232
$59$	−5.47787e7	−0.588542	−0.294271	−	0.955722i	$-0.595077\pi$
$59$	−5.47787e7	−0.588542	−0.294271	+	0.955722i	$0.595077\pi$
$60$	−6.78947e7	−0.676325
$61$	1.11925e8	1.03501	0.517505	−	0.855680i	$-0.326861\pi$
$61$	1.11925e8	1.03501	0.517505	+	0.855680i	$0.326861\pi$
$62$	−4.98688e7	−0.428614
$63$	2.46456e8	1.97109
$64$	−9.38028e6	−0.0698886
$65$	−3.30360e7	−0.229550
$66$	−3.74528e7	−0.242961
$67$	1.73109e7	0.104950	0.0524751	−	0.998622i	$-0.483289\pi$
$67$	1.73109e7	0.104950	0.0524751	+	0.998622i	$0.483289\pi$
$68$	−2.81376e7	−0.159587
$69$	−1.31667e8	−0.699285
$70$	−2.85753e7	−0.142249
$71$	−1.84426e8	−0.861311	−0.430655	−	0.902516i	$-0.641718\pi$
$71$	−1.84426e8	−0.861311	−0.430655	+	0.902516i	$0.641718\pi$
$72$	4.55455e8	1.99733
$73$	−2.35067e7	−0.0968809	−0.0484405	−	0.998826i	$-0.515425\pi$
$73$	−2.35067e7	−0.0968809	−0.0484405	+	0.998826i	$0.515425\pi$
$74$	−8.86019e7	−0.343479
$75$	−4.19444e8	−1.53073
$76$	4.14923e8	1.42661
$77$	7.11028e7	0.230504
$78$	1.38438e8	0.423478
$79$	−1.48610e8	−0.429264	−0.214632	−	0.976695i	$-0.568855\pi$
$79$	−1.48610e8	−0.429264	−0.214632	+	0.976695i	$0.568855\pi$
$80$	7.81777e7	0.213392
$81$	1.18911e9	3.06930
$82$	2.72749e8	0.666193
$83$	1.48409e7	0.0343248	0.0171624	−	0.999853i	$-0.494537\pi$
$83$	1.48409e7	0.0343248	0.0171624	+	0.999853i	$0.494537\pi$
$84$	−5.40142e8	−1.18373
$85$	4.09848e7	0.0851605
$86$	−2.62437e8	−0.517348
$87$	−1.67345e9	−3.13166
$88$	1.31399e8	0.233572
$89$	−4.26751e8	−0.720974	−0.360487	−	0.932764i	$-0.617389\pi$
$89$	−4.26751e8	−0.720974	−0.360487	+	0.932764i	$0.617389\pi$
$90$	−2.98605e8	−0.479740
$91$	−2.62821e8	−0.401766
$92$	2.07922e8	0.302590
$93$	1.37304e9	1.90331
$94$	−2.24020e8	−0.295946
$95$	−6.04371e8	−0.761285
$96$	−1.54709e9	−1.85906
$97$	9.28863e8	1.06532	0.532659	−	0.846330i	$-0.321193\pi$
$97$	9.28863e8	1.06532	0.532659	+	0.846330i	$0.321193\pi$
$98$	1.61634e8	0.177017
$99$	7.43010e8	0.777385
$100$	6.62367e8	0.662367
$101$	5.50059e8	0.525973	0.262986	−	0.964800i	$-0.415293\pi$
$101$	5.50059e8	0.525973	0.262986	+	0.964800i	$0.415293\pi$
$102$	−1.71748e8	−0.157106
$103$	1.08134e9	0.946661	0.473331	−	0.880885i	$-0.343052\pi$
$103$	1.08134e9	0.946661	0.473331	+	0.880885i	$0.343052\pi$
$104$	−4.85697e8	−0.407113
$105$	7.86763e8	0.631673
$106$	−1.12048e8	−0.0862037
$107$	−6.30932e7	−0.0465324	−0.0232662	−	0.999729i	$-0.507407\pi$
$107$	−6.30932e7	−0.0465324	−0.0232662	+	0.999729i	$0.507407\pi$
$108$	−3.45518e9	−2.44379
$109$	−3.63239e8	−0.246475	−0.123238	−	0.992377i	$-0.539328\pi$
$109$	−3.63239e8	−0.246475	−0.123238	+	0.992377i	$0.539328\pi$
$110$	−8.61479e7	−0.0561019
$111$	2.43948e9	1.52526
$112$	6.21949e8	0.373486
$113$	4.55141e8	0.262599	0.131299	−	0.991343i	$-0.458085\pi$
$113$	4.55141e8	0.262599	0.131299	+	0.991343i	$0.458085\pi$
$114$	2.53264e9	1.40443
$115$	−3.02856e8	−0.161471
$116$	2.64263e9	1.35511
$117$	−2.74642e9	−1.35497
$118$	5.28009e8	0.250710
$119$	3.26058e8	0.149051
$120$	1.45395e9	0.640080
$121$	2.14359e8	0.0909091
$122$	−1.07884e9	−0.440899
$123$	−7.50960e9	−2.95831
$124$	−2.16824e9	−0.823587
$125$	−2.15706e9	−0.790256
$126$	−2.37558e9	−0.839657
$127$	−3.76335e8	−0.128368	−0.0641842	−	0.997938i	$-0.520445\pi$
$127$	−3.76335e8	−0.128368	−0.0641842	+	0.997938i	$0.520445\pi$
$128$	3.07512e9	1.01255
$129$	7.22569e9	2.29734
$130$	3.18432e8	0.0977850
$131$	−4.11350e9	−1.22037	−0.610184	−	0.792260i	$-0.708904\pi$
$131$	−4.11350e9	−1.22037	−0.610184	+	0.792260i	$0.708904\pi$
$132$	−1.62840e9	−0.466852
$133$	−4.80812e9	−1.33243
$134$	−1.66859e8	−0.0447073
$135$	5.03277e9	1.30408
$136$	6.02560e8	0.151034
$137$	9.42749e8	0.228641	0.114320	−	0.993444i	$-0.463531\pi$
$137$	9.42749e8	0.228641	0.114320	+	0.993444i	$0.463531\pi$
$138$	1.26913e9	0.297885
$139$	1.31700e9	0.299239	0.149620	−	0.988744i	$-0.452195\pi$
$139$	1.31700e9	0.299239	0.149620	+	0.988744i	$0.452195\pi$
$140$	−1.24242e9	−0.273333
$141$	6.16796e9	1.31418
$142$	1.77767e9	0.366906
$143$	−7.92345e8	−0.158454
$144$	6.49924e9	1.25960
$145$	−3.84922e9	−0.723130
$146$	2.26580e8	0.0412698
$147$	−4.45026e9	−0.786063
$148$	−3.85231e9	−0.660000
$149$	6.66331e9	1.10752	0.553760	−	0.832676i	$-0.313192\pi$
$149$	6.66331e9	1.10752	0.553760	+	0.832676i	$0.313192\pi$
$150$	4.04300e9	0.652068
$151$	−2.17194e9	−0.339979	−0.169990	−	0.985446i	$-0.554373\pi$
$151$	−2.17194e9	−0.339979	−0.169990	+	0.985446i	$0.554373\pi$
$152$	−8.88548e9	−1.35016
$153$	3.40724e9	0.502680
$154$	−6.85357e8	−0.0981914
$155$	3.15823e9	0.439492
$156$	6.01915e9	0.813719
$157$	−1.15137e10	−1.51240	−0.756198	−	0.654343i	$-0.772945\pi$
$157$	−1.15137e10	−1.51240	−0.756198	+	0.654343i	$0.772945\pi$
$158$	1.43244e9	0.182860
$159$	3.08501e9	0.382798
$160$	−3.55857e9	−0.429275
$161$	−2.40939e9	−0.282613
$162$	−1.14618e10	−1.30748
$163$	3.93534e9	0.436654	0.218327	−	0.975876i	$-0.429940\pi$
$163$	3.93534e9	0.436654	0.218327	+	0.975876i	$0.429940\pi$
$164$	1.18588e10	1.28010
$165$	2.37191e9	0.249127
$166$	−1.43051e8	−0.0146219
$167$	1.70414e10	1.69544	0.847719	−	0.530446i	$-0.177975\pi$
$167$	1.70414e10	1.69544	0.847719	+	0.530446i	$0.177975\pi$
$168$	1.15670e10	1.12029
$169$	−7.67572e9	−0.723817
$170$	−3.95051e8	−0.0362771
$171$	−5.02439e10	−4.49366
$172$	−1.14105e10	−0.994090
$173$	3.47261e9	0.294746	0.147373	−	0.989081i	$-0.452918\pi$
$173$	3.47261e9	0.294746	0.147373	+	0.989081i	$0.452918\pi$
$174$	1.61303e10	1.33404
$175$	−7.67550e9	−0.618637
$176$	1.87504e9	0.147300
$177$	−1.45377e10	−1.11331
$178$	4.11343e9	0.307124
$179$	−9.97902e9	−0.726523	−0.363261	−	0.931687i	$-0.618337\pi$
$179$	−9.97902e9	−0.726523	−0.363261	+	0.931687i	$0.618337\pi$
$180$	−1.29830e10	−0.921828
$181$	2.65420e10	1.83815	0.919074	−	0.394084i	$-0.128938\pi$
$181$	2.65420e10	1.83815	0.919074	+	0.394084i	$0.128938\pi$
$182$	2.53332e9	0.171147
$183$	2.97038e10	1.95786
$184$	−4.45260e9	−0.286374
$185$	5.61123e9	0.352196
$186$	−1.32346e10	−0.810782
$187$	9.82992e8	0.0587845
$188$	−9.74015e9	−0.568664
$189$	4.00386e10	2.28245
$190$	5.82550e9	0.324296
$191$	5.61931e9	0.305515	0.152758	−	0.988264i	$-0.451185\pi$
$191$	5.61931e9	0.305515	0.152758	+	0.988264i	$0.451185\pi$
$192$	−2.48943e9	−0.132204
$193$	2.48054e10	1.28688	0.643439	−	0.765497i	$-0.277507\pi$
$193$	2.48054e10	1.28688	0.643439	+	0.765497i	$0.277507\pi$
$194$	−8.95327e9	−0.453810
$195$	−8.76741e9	−0.434226
$196$	7.02764e9	0.340140
$197$	3.76953e10	1.78315	0.891577	−	0.452869i	$-0.149599\pi$
$197$	3.76953e10	1.78315	0.891577	+	0.452869i	$0.149599\pi$
$198$	−7.16183e9	−0.331154
$199$	−8.55588e9	−0.386746	−0.193373	−	0.981125i	$-0.561943\pi$
$199$	−8.55588e9	−0.386746	−0.193373	+	0.981125i	$0.561943\pi$
$200$	−1.41844e10	−0.626870
$201$	4.59414e9	0.198528
$202$	−5.30199e9	−0.224057
$203$	−3.06228e10	−1.26565
$204$	−7.46742e9	−0.301880
$205$	−1.72734e10	−0.683101
$206$	−1.04230e10	−0.403264
$207$	−2.51777e10	−0.953123
$208$	−6.93078e9	−0.256742
$209$	−1.44954e10	−0.525499
$210$	−7.58357e9	−0.269083
$211$	2.46919e10	0.857599	0.428799	−	0.903400i	$-0.358937\pi$
$211$	2.46919e10	0.857599	0.428799	+	0.903400i	$0.358937\pi$
$212$	−4.87170e9	−0.165642
$213$	−4.89447e10	−1.62929
$214$	6.08153e8	0.0198221
$215$	1.66203e10	0.530478
$216$	7.39919e10	2.31282
$217$	2.51255e10	0.769212
$218$	3.50124e9	0.104995
$219$	−6.23842e9	−0.183264
$220$	−3.74561e9	−0.107801
$221$	−3.63348e9	−0.102461
$222$	−2.35140e10	−0.649738
$223$	3.74783e10	1.01486	0.507432	−	0.861692i	$-0.330595\pi$
$223$	3.74783e10	1.01486	0.507432	+	0.861692i	$0.330595\pi$
$224$	−2.83105e10	−0.751331
$225$	−8.02074e10	−2.08638
$226$	−4.38708e9	−0.111863
$227$	−3.60149e10	−0.900255	−0.450127	−	0.892964i	$-0.648621\pi$
$227$	−3.60149e10	−0.900255	−0.450127	+	0.892964i	$0.648621\pi$
$228$	1.10116e11	2.69864
$229$	2.95011e10	0.708890	0.354445	−	0.935077i	$-0.384670\pi$
$229$	2.95011e10	0.708890	0.354445	+	0.935077i	$0.384670\pi$
$230$	2.91921e9	0.0687845
$231$	1.88699e10	0.436030
$232$	−5.65913e10	−1.28249
$233$	−5.35146e10	−1.18952	−0.594758	−	0.803904i	$-0.702752\pi$
$233$	−5.35146e10	−1.18952	−0.594758	+	0.803904i	$0.702752\pi$
$234$	2.64726e10	0.577199
$235$	1.41874e10	0.303457
$236$	2.29572e10	0.481743
$237$	−3.94394e10	−0.812012
$238$	−3.14286e9	−0.0634934
$239$	−1.31459e10	−0.260615	−0.130308	−	0.991474i	$-0.541596\pi$
$239$	−1.31459e10	−0.260615	−0.130308	+	0.991474i	$0.541596\pi$
$240$	2.07475e10	0.403660
$241$	3.31185e10	0.632403	0.316202	−	0.948692i	$-0.397592\pi$
$241$	3.31185e10	0.632403	0.316202	+	0.948692i	$0.397592\pi$
$242$	−2.06619e9	−0.0387259
$243$	1.53302e11	2.82045
$244$	−4.69069e10	−0.847193
$245$	−1.02364e10	−0.181509
$246$	7.23846e10	1.26020
$247$	5.35800e10	0.915939
$248$	4.64323e10	0.779449
$249$	3.93861e9	0.0649302
$250$	2.07918e10	0.336638
$251$	−9.65650e10	−1.53563	−0.767817	−	0.640669i	$-0.778657\pi$
$251$	−9.65650e10	−1.53563	−0.767817	+	0.640669i	$0.778657\pi$
$252$	−1.03288e11	−1.61341
$253$	−7.26378e9	−0.111460
$254$	3.62747e9	0.0546830
$255$	1.08769e10	0.161093
$256$	−2.48382e10	−0.361444
$257$	7.27526e9	0.104028	0.0520139	−	0.998646i	$-0.483436\pi$
$257$	7.27526e9	0.104028	0.0520139	+	0.998646i	$0.483436\pi$
$258$	−6.96481e10	−0.978634
$259$	4.46406e10	0.616426
$260$	1.38451e10	0.187895
$261$	−3.20001e11	−4.26844
$262$	3.96498e10	0.519859
$263$	6.69755e10	0.863207	0.431604	−	0.902063i	$-0.357948\pi$
$263$	6.69755e10	0.863207	0.431604	+	0.902063i	$0.357948\pi$
$264$	3.48719e10	0.441833
$265$	7.09605e9	0.0883915
$266$	4.63453e10	0.567594
$267$	−1.13255e11	−1.36382
$268$	−7.25485e9	−0.0859056
$269$	1.54292e11	1.79663	0.898314	−	0.439353i	$-0.144792\pi$
$269$	1.54292e11	1.79663	0.898314	+	0.439353i	$0.144792\pi$
$270$	−4.85106e10	−0.555520
$271$	−8.65258e10	−0.974505	−0.487252	−	0.873261i	$-0.662001\pi$
$271$	−8.65258e10	−0.974505	−0.487252	+	0.873261i	$0.662001\pi$
$272$	8.59840e9	0.0952484
$273$	−6.97498e10	−0.759996
$274$	−9.08710e9	−0.0973975
$275$	−2.31399e10	−0.243986
$276$	5.51802e10	0.572391
$277$	8.57257e10	0.874887	0.437444	−	0.899246i	$-0.355884\pi$
$277$	8.57257e10	0.874887	0.437444	+	0.899246i	$0.355884\pi$
$278$	−1.26945e10	−0.127472
$279$	2.62556e11	2.59420
$280$	2.66062e10	0.258685
$281$	1.10747e10	0.105963	0.0529815	−	0.998595i	$-0.483128\pi$
$281$	1.10747e10	0.105963	0.0529815	+	0.998595i	$0.483128\pi$
$282$	−5.94526e10	−0.559822
$283$	1.36293e11	1.26309	0.631545	−	0.775339i	$-0.282421\pi$
$283$	1.36293e11	1.26309	0.631545	+	0.775339i	$0.282421\pi$
$284$	7.72913e10	0.705014
$285$	−1.60394e11	−1.44008
$286$	7.63737e9	0.0674989
$287$	−1.37420e11	−1.19559
$288$	−2.95839e11	−2.53390
$289$	−1.14080e11	−0.961988
$290$	3.71024e10	0.308043
$291$	2.46511e11	2.01519
$292$	9.85142e9	0.0793006
$293$	−1.11670e11	−0.885180	−0.442590	−	0.896724i	$-0.645940\pi$
$293$	−1.11670e11	−0.885180	−0.442590	+	0.896724i	$0.645940\pi$
$294$	4.28958e10	0.334851
$295$	−3.34392e10	−0.257073
$296$	8.24964e10	0.624629
$297$	1.20707e11	0.900180
$298$	−6.42273e10	−0.471787
$299$	2.68494e10	0.194274
$300$	1.75785e11	1.25296
$301$	1.32225e11	0.928459
$302$	2.09352e10	0.144826
$303$	1.45980e11	0.994950
$304$	−1.26794e11	−0.851465
$305$	6.83239e10	0.452089
$306$	−3.28422e10	−0.214134
$307$	−1.75780e10	−0.112940	−0.0564698	−	0.998404i	$-0.517984\pi$
$307$	−1.75780e10	−0.112940	−0.0564698	+	0.998404i	$0.517984\pi$
$308$	−2.97985e10	−0.188676
$309$	2.86976e11	1.79074
$310$	−3.04420e10	−0.187217
$311$	−1.80737e11	−1.09554	−0.547768	−	0.836630i	$-0.684522\pi$
$311$	−1.80737e11	−1.09554	−0.547768	+	0.836630i	$0.684522\pi$
$312$	−1.28899e11	−0.770110
$313$	−2.24443e11	−1.32177	−0.660887	−	0.750486i	$-0.729820\pi$
$313$	−2.24443e11	−1.32177	−0.660887	+	0.750486i	$0.729820\pi$
$314$	1.10980e11	0.644258
$315$	1.50447e11	0.860967
$316$	6.22809e10	0.351368
$317$	−1.39983e11	−0.778590	−0.389295	−	0.921113i	$-0.627281\pi$
$317$	−1.39983e11	−0.778590	−0.389295	+	0.921113i	$0.627281\pi$
$318$	−2.97362e10	−0.163066
$319$	−9.23207e10	−0.499161
$320$	−5.72612e9	−0.0305271
$321$	−1.67443e10	−0.0880225
$322$	2.32240e10	0.120389
$323$	−6.64720e10	−0.339803
$324$	−4.98345e11	−2.51234
$325$	8.55331e10	0.425264
$326$	−3.79325e10	−0.186008
$327$	−9.63999e10	−0.466242
$328$	−2.53954e11	−1.21150
$329$	1.12869e11	0.531120
$330$	−2.28627e10	−0.106124
$331$	−3.23341e11	−1.48059	−0.740294	−	0.672283i	$-0.765314\pi$
$331$	−3.23341e11	−1.48059	−0.740294	+	0.672283i	$0.765314\pi$
$332$	−6.21968e9	−0.0280961
$333$	4.66484e11	2.07892
$334$	−1.64261e11	−0.722232
$335$	1.05673e10	0.0458419
$336$	1.65059e11	0.706499
$337$	−6.30715e10	−0.266378	−0.133189	−	0.991091i	$-0.542522\pi$
$337$	−6.30715e10	−0.266378	−0.133189	+	0.991091i	$0.542522\pi$
$338$	7.39859e10	0.308336
$339$	1.20790e11	0.496742
$340$	−1.71764e10	−0.0697070
$341$	7.57477e10	0.303372
$342$	4.84298e11	1.91424
$343$	−2.77410e11	−1.08218
$344$	2.44353e11	0.940815
$345$	−8.03747e10	−0.305445
$346$	−3.34723e10	−0.125558
$347$	6.00375e10	0.222300	0.111150	−	0.993804i	$-0.464547\pi$
$347$	6.00375e10	0.222300	0.111150	+	0.993804i	$0.464547\pi$
$348$	7.01326e11	2.56338
$349$	7.67921e9	0.0277078	0.0138539	−	0.999904i	$-0.495590\pi$
$349$	7.67921e9	0.0277078	0.0138539	+	0.999904i	$0.495590\pi$
$350$	7.39838e10	0.263530
$351$	−4.46176e11	−1.56900
$352$	−8.53497e10	−0.296319
$353$	−2.69340e11	−0.923239	−0.461620	−	0.887078i	$-0.652731\pi$
$353$	−2.69340e11	−0.923239	−0.461620	+	0.887078i	$0.652731\pi$
$354$	1.40128e11	0.474253
$355$	−1.12581e11	−0.376218
$356$	1.78847e11	0.590143
$357$	8.65324e10	0.281950
$358$	9.61873e10	0.309488
$359$	−8.38663e10	−0.266479	−0.133239	−	0.991084i	$-0.542538\pi$
$359$	−8.38663e10	−0.266479	−0.133239	+	0.991084i	$0.542538\pi$
$360$	2.78029e11	0.872425
$361$	6.57522e11	2.03764
$362$	−2.55837e11	−0.783024
$363$	5.68886e10	0.171967
$364$	1.10146e11	0.328860
$365$	−1.43495e10	−0.0423173
$366$	−2.86313e11	−0.834021
$367$	2.37828e11	0.684329	0.342164	−	0.939640i	$-0.388840\pi$
$367$	2.37828e11	0.684329	0.342164	+	0.939640i	$0.388840\pi$
$368$	−6.35375e10	−0.180599
$369$	−1.43601e12	−4.03216
$370$	−5.40863e10	−0.150031
$371$	5.64532e10	0.154706
$372$	−5.75427e11	−1.55793
$373$	5.05007e11	1.35085	0.675425	−	0.737429i	$-0.263960\pi$
$373$	5.05007e11	1.35085	0.675425	+	0.737429i	$0.263960\pi$
$374$	−9.47500e9	−0.0250413
$375$	−5.72462e11	−1.49488
$376$	2.08583e11	0.538188
$377$	3.41249e11	0.870033
$378$	−3.85930e11	−0.972289
$379$	2.67081e11	0.664917	0.332458	−	0.943118i	$-0.392122\pi$
$379$	2.67081e11	0.664917	0.332458	+	0.943118i	$0.392122\pi$
$380$	2.53286e11	0.623140
$381$	−9.98754e10	−0.242826
$382$	−5.41643e10	−0.130145
$383$	3.37420e11	0.801264	0.400632	−	0.916239i	$-0.368791\pi$
$383$	3.37420e11	0.801264	0.400632	+	0.916239i	$0.368791\pi$
$384$	8.16104e11	1.91538
$385$	4.34042e10	0.100683
$386$	−2.39098e11	−0.548192
$387$	1.38172e12	3.13127
$388$	−3.89278e11	−0.872001
$389$	−7.35819e11	−1.62929	−0.814644	−	0.579961i	$-0.803068\pi$
$389$	−7.35819e11	−1.62929	−0.814644	+	0.579961i	$0.803068\pi$
$390$	8.45086e10	0.184974
$391$	−3.33097e10	−0.0720735
$392$	−1.50495e11	−0.321911
$393$	−1.09168e12	−2.30849
$394$	−3.63343e11	−0.759598
$395$	−9.07175e10	−0.187501
$396$	−3.11388e11	−0.636318
$397$	3.69510e11	0.746567	0.373284	−	0.927717i	$-0.378232\pi$
$397$	3.69510e11	0.746567	0.373284	+	0.927717i	$0.378232\pi$
$398$	8.24697e10	0.164748
$399$	−1.27603e12	−2.52047
$400$	−2.02409e11	−0.395330
$401$	7.91274e11	1.52819	0.764095	−	0.645104i	$-0.223186\pi$
$401$	7.91274e11	1.52819	0.764095	+	0.645104i	$0.223186\pi$
$402$	−4.42826e10	−0.0845700
$403$	−2.79990e11	−0.528773
$404$	−2.30525e11	−0.430528
$405$	7.25883e11	1.34066
$406$	2.95171e11	0.539147
$407$	1.34581e11	0.243114
$408$	1.59913e11	0.285702
$409$	3.78307e11	0.668482	0.334241	−	0.942488i	$-0.391520\pi$
$409$	3.78307e11	0.668482	0.334241	+	0.942488i	$0.391520\pi$
$410$	1.66497e11	0.290991
$411$	2.50196e11	0.432505
$412$	−4.53179e11	−0.774877
$413$	−2.66028e11	−0.449938
$414$	2.42686e11	0.406016
$415$	9.05950e9	0.0149930
$416$	3.15482e11	0.516481
$417$	3.49518e11	0.566053
$418$	1.39720e11	0.223855
$419$	−1.52626e11	−0.241917	−0.120958	−	0.992658i	$-0.538597\pi$
$419$	−1.52626e11	−0.241917	−0.120958	+	0.992658i	$0.538597\pi$
$420$	−3.29725e11	−0.517047
$421$	5.47323e11	0.849131	0.424565	−	0.905397i	$-0.360427\pi$
$421$	5.47323e11	0.849131	0.424565	+	0.905397i	$0.360427\pi$
$422$	−2.38004e11	−0.365324
$423$	1.17946e12	1.79122
$424$	1.04326e11	0.156765
$425$	−1.06113e11	−0.157768
$426$	4.71776e11	0.694053
$427$	5.43557e11	0.791260
$428$	2.64418e10	0.0380885
$429$	−2.10280e11	−0.299737
$430$	−1.60203e11	−0.225976
$431$	−5.65892e11	−0.789925	−0.394963	−	0.918697i	$-0.629242\pi$
$431$	−5.65892e11	−0.789925	−0.394963	+	0.918697i	$0.629242\pi$
$432$	1.05585e12	1.45856
$433$	9.82005e10	0.134251	0.0671256	−	0.997745i	$-0.478617\pi$
$433$	9.82005e10	0.134251	0.0671256	+	0.997745i	$0.478617\pi$
$434$	−2.42184e11	−0.327673
$435$	−1.02154e12	−1.36790
$436$	1.52230e11	0.201749
$437$	4.91192e11	0.644295
$438$	6.01318e10	0.0780676
$439$	−1.51858e12	−1.95140	−0.975702	−	0.219104i	$-0.929687\pi$
$439$	−1.51858e12	−1.95140	−0.975702	+	0.219104i	$0.929687\pi$
$440$	8.02115e10	0.102023
$441$	−8.50992e11	−1.07140
$442$	3.50229e10	0.0436467
$443$	−5.58767e11	−0.689309	−0.344655	−	0.938730i	$-0.612004\pi$
$443$	−5.58767e11	−0.689309	−0.344655	+	0.938730i	$0.612004\pi$
$444$	−1.02236e12	−1.24848
$445$	−2.60507e11	−0.314919
$446$	−3.61251e11	−0.432317
$447$	1.76837e12	2.09503
$448$	−4.55546e10	−0.0534295
$449$	2.43635e11	0.282899	0.141449	−	0.989946i	$-0.454824\pi$
$449$	2.43635e11	0.282899	0.141449	+	0.989946i	$0.454824\pi$
$450$	7.73115e11	0.888766
$451$	−4.14289e11	−0.471530
$452$	−1.90745e11	−0.214947
$453$	−5.76411e11	−0.643117
$454$	3.47145e11	0.383495
$455$	−1.60437e11	−0.175490
$456$	−2.35811e12	−2.55401
$457$	7.23705e11	0.776138	0.388069	−	0.921630i	$-0.373142\pi$
$457$	7.23705e11	0.776138	0.388069	+	0.921630i	$0.373142\pi$
$458$	−2.84360e11	−0.301977
$459$	5.53531e11	0.582083
$460$	1.26924e11	0.132170
$461$	8.90557e11	0.918349	0.459174	−	0.888346i	$-0.348145\pi$
$461$	8.90557e11	0.918349	0.459174	+	0.888346i	$0.348145\pi$
$462$	−1.81886e11	−0.185743
$463$	1.75816e12	1.77805	0.889025	−	0.457858i	$-0.151383\pi$
$463$	1.75816e12	1.77805	0.889025	+	0.457858i	$0.151383\pi$
$464$	−8.07545e11	−0.808791
$465$	8.38160e11	0.831359
$466$	5.15824e11	0.506717
$467$	−1.76507e12	−1.71726	−0.858631	−	0.512594i	$-0.828685\pi$
$467$	−1.76507e12	−1.71726	−0.858631	+	0.512594i	$0.828685\pi$
$468$	1.15100e12	1.10909
$469$	8.40691e10	0.0802340
$470$	−1.36751e11	−0.129268
$471$	−3.05561e12	−2.86090
$472$	−4.91624e11	−0.455926
$473$	3.98627e11	0.366177
$474$	3.80154e11	0.345905
$475$	1.56477e12	1.41036
$476$	−1.36648e11	−0.122003
$477$	5.89924e11	0.521751
$478$	1.26713e11	0.111018
$479$	−1.26263e11	−0.109589	−0.0547945	−	0.998498i	$-0.517450\pi$
$479$	−1.26263e11	−0.109589	−0.0547945	+	0.998498i	$0.517450\pi$
$480$	−9.44407e11	−0.812033
$481$	−4.97459e11	−0.423744
$482$	−3.19227e11	−0.269394
$483$	−6.39428e11	−0.534601
$484$	−8.98358e10	−0.0744124
$485$	5.67017e11	0.465327
$486$	−1.47767e12	−1.20147
$487$	−1.22304e12	−0.985282	−0.492641	−	0.870233i	$-0.663968\pi$
$487$	−1.22304e12	−0.985282	−0.492641	+	0.870233i	$0.663968\pi$
$488$	1.00450e12	0.801791
$489$	1.04440e12	0.825992
$490$	9.86679e10	0.0773203
$491$	1.80182e12	1.39909	0.699543	−	0.714591i	$-0.253387\pi$
$491$	1.80182e12	1.39909	0.699543	+	0.714591i	$0.253387\pi$
$492$	3.14720e12	2.42148
$493$	−4.23358e11	−0.322772
$494$	−5.16455e11	−0.390177
$495$	4.53564e11	0.339559
$496$	6.62579e11	0.491553
$497$	−8.95651e11	−0.658468
$498$	−3.79641e10	−0.0276593
$499$	−1.49397e11	−0.107868	−0.0539338	−	0.998545i	$-0.517176\pi$
$499$	−1.49397e11	−0.107868	−0.0539338	+	0.998545i	$0.517176\pi$
$500$	9.04005e11	0.646854
$501$	4.52262e12	3.20715
$502$	9.30785e11	0.654158
$503$	−1.50839e12	−1.05065	−0.525323	−	0.850903i	$-0.676055\pi$
$503$	−1.50839e12	−1.05065	−0.525323	+	0.850903i	$0.676055\pi$
$504$	2.21188e12	1.52695
$505$	3.35779e11	0.229743
$506$	7.00152e10	0.0474804
$507$	−2.03705e12	−1.36920
$508$	1.57719e11	0.105074
$509$	2.02975e12	1.34033	0.670165	−	0.742212i	$-0.266223\pi$
$509$	2.02975e12	1.34033	0.670165	+	0.742212i	$0.266223\pi$
$510$	−1.04842e11	−0.0686232
$511$	−1.14158e11	−0.0740650
$512$	−1.33505e12	−0.858582
$513$	−8.16248e12	−5.20348
$514$	−7.01258e10	−0.0443143
$515$	6.60095e11	0.413498
$516$	−3.02822e12	−1.88046
$517$	3.40274e11	0.209470
$518$	−4.30288e11	−0.262588
$519$	9.21594e11	0.557553
$520$	−2.96490e11	−0.177826
$521$	−5.21192e11	−0.309905	−0.154952	−	0.987922i	$-0.549522\pi$
$521$	−5.21192e11	−0.309905	−0.154952	+	0.987922i	$0.549522\pi$
$522$	3.08448e12	1.81829
$523$	−2.73866e12	−1.60059	−0.800297	−	0.599604i	$-0.795325\pi$
$523$	−2.73866e12	−1.60059	−0.800297	+	0.599604i	$0.795325\pi$
$524$	1.72393e12	0.998916
$525$	−2.03700e12	−1.17024
$526$	−6.45573e11	−0.367714
$527$	3.47358e11	0.196169
$528$	4.97615e11	0.278638
$529$	−1.55501e12	−0.863343
$530$	−6.83985e10	−0.0376535
$531$	−2.77994e12	−1.51744
$532$	2.01504e12	1.09064
$533$	1.53136e12	0.821871
$534$	1.09166e12	0.580968
$535$	−3.85148e10	−0.0203252
$536$	1.55361e11	0.0813018
$537$	−2.64833e12	−1.37432
$538$	−1.48721e12	−0.765337
$539$	−2.45512e11	−0.125292
$540$	−2.10919e12	−1.06744
$541$	−3.82842e11	−0.192146	−0.0960732	−	0.995374i	$-0.530628\pi$
$541$	−3.82842e11	−0.192146	−0.0960732	+	0.995374i	$0.530628\pi$
$542$	8.34018e11	0.415125
$543$	7.04397e12	3.47711
$544$	−3.91391e11	−0.191609
$545$	−2.21736e11	−0.107660
$546$	6.72315e11	0.323747
$547$	−1.69658e12	−0.810275	−0.405137	−	0.914256i	$-0.632776\pi$
$547$	−1.69658e12	−0.810275	−0.405137	+	0.914256i	$0.632776\pi$
$548$	−3.95097e11	−0.187151
$549$	5.68005e12	2.66856
$550$	2.23044e11	0.103934
$551$	6.24292e12	2.88540
$552$	−1.18167e12	−0.541715
$553$	−7.21710e11	−0.328171
$554$	−8.26305e11	−0.372689
$555$	1.48916e12	0.666228
$556$	−5.51942e11	−0.244938
$557$	−3.76097e12	−1.65558	−0.827792	−	0.561035i	$-0.810403\pi$
$557$	−3.76097e12	−1.65558	−0.827792	+	0.561035i	$0.810403\pi$
$558$	−2.53077e12	−1.10509
$559$	−1.47346e12	−0.638243
$560$	3.79664e11	0.163137
$561$	2.60876e11	0.111199
$562$	−1.06749e11	−0.0451387
$563$	5.06081e11	0.212291	0.106146	−	0.994351i	$-0.466149\pi$
$563$	5.06081e11	0.212291	0.106146	+	0.994351i	$0.466149\pi$
$564$	−2.58493e12	−1.07571
$565$	2.77837e11	0.114702
$566$	−1.31372e12	−0.538058
$567$	5.77482e12	2.34647
$568$	−1.65518e12	−0.667232
$569$	−1.93060e12	−0.772122	−0.386061	−	0.922473i	$-0.626165\pi$
$569$	−1.93060e12	−0.772122	−0.386061	+	0.922473i	$0.626165\pi$
$570$	1.54603e12	0.613451
$571$	−2.96813e12	−1.16848	−0.584239	−	0.811581i	$-0.698607\pi$
$571$	−2.96813e12	−1.16848	−0.584239	+	0.811581i	$0.698607\pi$
$572$	3.32064e11	0.129700
$573$	1.49131e12	0.577925
$574$	1.32458e12	0.509302
$575$	7.84120e11	0.299142
$576$	−4.76036e11	−0.180193
$577$	−2.75976e12	−1.03652	−0.518262	−	0.855222i	$-0.673421\pi$
$577$	−2.75976e12	−1.03652	−0.518262	+	0.855222i	$0.673421\pi$
$578$	1.09961e12	0.409793
$579$	6.58308e12	2.43431
$580$	1.61317e12	0.591909
$581$	7.20736e10	0.0262412
$582$	−2.37610e12	−0.858443
$583$	1.70194e11	0.0610148
$584$	−2.10966e11	−0.0750507
$585$	−1.67653e12	−0.591848
$586$	1.07638e12	0.377074
$587$	−2.07452e12	−0.721185	−0.360592	−	0.932724i	$-0.617425\pi$
$587$	−2.07452e12	−0.721185	−0.360592	+	0.932724i	$0.617425\pi$
$588$	1.86506e12	0.643421
$589$	−5.12222e12	−1.75364
$590$	3.22319e11	0.109509
$591$	1.00039e13	3.37308
$592$	1.17721e12	0.393917
$593$	3.46977e11	0.115227	0.0576135	−	0.998339i	$-0.481651\pi$
$593$	3.46977e11	0.115227	0.0576135	+	0.998339i	$0.481651\pi$
$594$	−1.16349e12	−0.383464
$595$	1.99040e11	0.0651048
$596$	−2.79253e12	−0.906546
$597$	−2.27064e12	−0.731583
$598$	−2.58800e11	−0.0827579
$599$	−2.24201e12	−0.711569	−0.355784	−	0.934568i	$-0.615786\pi$
$599$	−2.24201e12	−0.711569	−0.355784	+	0.934568i	$0.615786\pi$
$600$	−3.76440e12	−1.18581
$601$	4.18791e12	1.30937	0.654685	−	0.755902i	$-0.272801\pi$
$601$	4.18791e12	1.30937	0.654685	+	0.755902i	$0.272801\pi$
$602$	−1.27451e12	−0.395510
$603$	8.78504e11	0.270593
$604$	9.10241e11	0.278285
$605$	1.30854e11	0.0397088
$606$	−1.40709e12	−0.423834
$607$	−2.35584e12	−0.704364	−0.352182	−	0.935931i	$-0.614560\pi$
$607$	−2.35584e12	−0.704364	−0.352182	+	0.935931i	$0.614560\pi$
$608$	5.77153e12	1.71287
$609$	−8.12696e12	−2.39414
$610$	−6.58571e11	−0.192583
$611$	−1.25777e12	−0.365103
$612$	−1.42794e12	−0.411462
$613$	1.80436e12	0.516120	0.258060	−	0.966129i	$-0.416917\pi$
$613$	1.80436e12	0.516120	0.258060	+	0.966129i	$0.416917\pi$
$614$	1.69433e11	0.0481106
$615$	−4.58417e12	−1.29218
$616$	6.38129e11	0.178565
$617$	2.91040e12	0.808480	0.404240	−	0.914653i	$-0.367536\pi$
$617$	2.91040e12	0.808480	0.404240	+	0.914653i	$0.367536\pi$
$618$	−2.76615e12	−0.762829
$619$	2.92959e11	0.0802044	0.0401022	−	0.999196i	$-0.487232\pi$
$619$	2.92959e11	0.0802044	0.0401022	+	0.999196i	$0.487232\pi$
$620$	−1.32358e12	−0.359740
$621$	−4.09029e12	−1.10368
$622$	1.74212e12	0.466682
$623$	−2.07248e12	−0.551181
$624$	−1.83936e12	−0.485663
$625$	1.77012e12	0.464027
$626$	2.16340e12	0.563056
$627$	−3.84693e12	−0.994054
$628$	4.82527e12	1.23795
$629$	6.17152e11	0.157204
$630$	−1.45015e12	−0.366759
$631$	3.05053e12	0.766026	0.383013	−	0.923743i	$-0.374887\pi$
$631$	3.05053e12	0.766026	0.383013	+	0.923743i	$0.374887\pi$
$632$	−1.33373e12	−0.332538
$633$	6.55298e12	1.62227
$634$	1.34929e12	0.331668
$635$	−2.29731e11	−0.0560709
$636$	−1.29290e12	−0.313334
$637$	9.07497e11	0.218382
$638$	8.89874e11	0.212635
$639$	−9.35936e12	−2.22071
$640$	1.87718e12	0.442279
$641$	5.05415e12	1.18246	0.591230	−	0.806503i	$-0.298642\pi$
$641$	5.05415e12	1.18246	0.591230	+	0.806503i	$0.298642\pi$
$642$	1.61397e11	0.0374963
$643$	8.68906e11	0.200458	0.100229	−	0.994964i	$-0.468042\pi$
$643$	8.68906e11	0.200458	0.100229	+	0.994964i	$0.468042\pi$
$644$	1.00975e12	0.231329
$645$	4.41086e12	1.00347
$646$	6.40720e11	0.144751
$647$	−2.82545e12	−0.633898	−0.316949	−	0.948443i	$-0.602658\pi$
$647$	−2.82545e12	−0.633898	−0.316949	+	0.948443i	$0.602658\pi$
$648$	1.06720e13	2.37770
$649$	−8.02015e11	−0.177452
$650$	−8.24449e11	−0.181156
$651$	6.66805e12	1.45507
$652$	−1.64926e12	−0.357418
$653$	−1.84568e11	−0.0397235	−0.0198617	−	0.999803i	$-0.506323\pi$
$653$	−1.84568e11	−0.0397235	−0.0198617	+	0.999803i	$0.506323\pi$
$654$	9.29193e11	0.198612
$655$	−2.51105e12	−0.533053
$656$	−3.62386e12	−0.764019
$657$	−1.19293e12	−0.249787
$658$	−1.08794e12	−0.226249
$659$	7.99917e12	1.65219	0.826097	−	0.563529i	$-0.190557\pi$
$659$	7.99917e12	1.65219	0.826097	+	0.563529i	$0.190557\pi$
$660$	−9.94046e11	−0.203920
$661$	5.29290e11	0.107842	0.0539209	−	0.998545i	$-0.482828\pi$
$661$	5.29290e11	0.107842	0.0539209	+	0.998545i	$0.482828\pi$
$662$	3.11666e12	0.630709
$663$	−9.64286e11	−0.193818
$664$	1.33193e11	0.0265904
$665$	−2.93508e12	−0.581999
$666$	−4.49642e12	−0.885590
$667$	3.12838e12	0.612003
$668$	−7.14190e12	−1.38778
$669$	9.94634e12	1.91975
$670$	−1.01858e11	−0.0195280
$671$	1.63870e12	0.312067
$672$	−7.51331e12	−1.42125
$673$	−4.50015e12	−0.845588	−0.422794	−	0.906226i	$-0.638951\pi$
$673$	−4.50015e12	−0.845588	−0.422794	+	0.906226i	$0.638951\pi$
$674$	6.07943e11	0.113473
$675$	−1.30303e13	−2.41594
$676$	3.21682e12	0.592471
$677$	−7.93113e12	−1.45106	−0.725531	−	0.688189i	$-0.758406\pi$
$677$	−7.93113e12	−1.45106	−0.725531	+	0.688189i	$0.758406\pi$
$678$	−1.16428e12	−0.211605
$679$	4.51095e12	0.814431
$680$	3.67828e11	0.0659713
$681$	−9.55796e12	−1.70296
$682$	−7.30128e11	−0.129232
$683$	−6.95559e12	−1.22304	−0.611520	−	0.791229i	$-0.709442\pi$
$683$	−6.95559e12	−1.22304	−0.611520	+	0.791229i	$0.709442\pi$
$684$	2.10567e13	3.67823
$685$	5.75493e11	0.0998694
$686$	2.67394e12	0.460992
$687$	7.82928e12	1.34096
$688$	3.48686e12	0.593317
$689$	−6.29095e11	−0.106348
$690$	7.74728e11	0.130115
$691$	5.27032e12	0.879398	0.439699	−	0.898145i	$-0.355085\pi$
$691$	5.27032e12	0.879398	0.439699	+	0.898145i	$0.355085\pi$
$692$	−1.45534e12	−0.241261
$693$	3.60837e12	0.594307
$694$	−5.78698e11	−0.0946966
$695$	8.03951e11	0.130707
$696$	−1.50187e13	−2.42601
$697$	−1.89982e12	−0.304905
$698$	−7.40195e10	−0.0118031
$699$	−1.42022e13	−2.25014
$700$	3.21673e12	0.506377
$701$	−7.90290e12	−1.23610	−0.618052	−	0.786137i	$-0.712078\pi$
$701$	−7.90290e12	−1.23610	−0.618052	+	0.786137i	$0.712078\pi$
$702$	4.30067e12	0.668373
$703$	−9.10066e12	−1.40532
$704$	−1.37337e11	−0.0210722
$705$	3.76518e12	0.574030
$706$	2.59615e12	0.393286
$707$	2.67132e12	0.402104
$708$	6.09261e12	0.911284
$709$	5.12718e12	0.762027	0.381013	−	0.924570i	$-0.375575\pi$
$709$	5.12718e12	0.762027	0.381013	+	0.924570i	$0.375575\pi$
$710$	1.08517e12	0.160263
$711$	−7.54172e12	−1.10677
$712$	−3.82998e12	−0.558517
$713$	−2.56679e12	−0.371953
$714$	−8.34082e11	−0.120107
$715$	−4.83680e11	−0.0692120
$716$	4.18211e12	0.594686
$717$	−3.48878e12	−0.492989
$718$	8.08383e11	0.113516
$719$	−9.19254e12	−1.28279	−0.641395	−	0.767211i	$-0.721644\pi$
$719$	−9.19254e12	−1.28279	−0.641395	+	0.767211i	$0.721644\pi$
$720$	3.96741e12	0.550187
$721$	5.25144e12	0.723718
$722$	−6.33782e12	−0.868005
$723$	8.78930e12	1.19628
$724$	−1.11235e13	−1.50459
$725$	9.96595e12	1.33967
$726$	−5.48346e11	−0.0732555
$727$	−3.28087e12	−0.435596	−0.217798	−	0.975994i	$-0.569887\pi$
$727$	−3.28087e12	−0.435596	−0.217798	+	0.975994i	$0.569887\pi$
$728$	−2.35875e12	−0.311236
$729$	1.72794e13	2.26597
$730$	1.38314e11	0.0180265
$731$	1.82799e12	0.236781
$732$	−1.24486e13	−1.60258
$733$	8.01417e12	1.02539	0.512697	−	0.858570i	$-0.328646\pi$
$733$	8.01417e12	1.02539	0.512697	+	0.858570i	$0.328646\pi$
$734$	−2.29241e12	−0.291514
$735$	−2.71663e12	−0.343350
$736$	2.89216e12	0.363306
$737$	2.53449e11	0.0316437
$738$	1.38416e13	1.71764
$739$	1.04082e13	1.28374	0.641870	−	0.766813i	$-0.278159\pi$
$739$	1.04082e13	1.28374	0.641870	+	0.766813i	$0.278159\pi$
$740$	−2.35161e12	−0.288286
$741$	1.42196e13	1.73263
$742$	−5.44150e11	−0.0659024
$743$	1.51857e13	1.82804	0.914021	−	0.405666i	$-0.132961\pi$
$743$	1.51857e13	1.82804	0.914021	+	0.405666i	$0.132961\pi$
$744$	1.23226e13	1.47444
$745$	4.06756e12	0.483761
$746$	−4.86773e12	−0.575442
$747$	7.53154e11	0.0884995
$748$	−4.11963e11	−0.0481172
$749$	−3.06407e11	−0.0355739
$750$	5.51793e12	0.636796
$751$	−1.01987e13	−1.16995	−0.584973	−	0.811053i	$-0.698895\pi$
$751$	−1.01987e13	−1.16995	−0.584973	+	0.811053i	$0.698895\pi$
$752$	2.97644e12	0.339403
$753$	−2.56273e13	−2.90486
$754$	−3.28928e12	−0.370621
$755$	−1.32585e12	−0.148502
$756$	−1.67798e13	−1.86827
$757$	2.07940e12	0.230147	0.115074	−	0.993357i	$-0.463290\pi$
$757$	2.07940e12	0.230147	0.115074	+	0.993357i	$0.463290\pi$
$758$	−2.57438e12	−0.283245
$759$	−1.92773e12	−0.210842
$760$	−5.42407e12	−0.589745
$761$	−3.07566e12	−0.332435	−0.166218	−	0.986089i	$-0.553155\pi$
$761$	−3.07566e12	−0.332435	−0.166218	+	0.986089i	$0.553155\pi$
$762$	9.62693e11	0.103441
$763$	−1.76404e12	−0.188429
$764$	−2.35500e12	−0.250076
$765$	2.07992e12	0.219569
$766$	−3.25237e12	−0.341327
$767$	2.96453e12	0.309297
$768$	−6.59180e12	−0.683720
$769$	−1.95807e12	−0.201911	−0.100956	−	0.994891i	$-0.532190\pi$
$769$	−1.95807e12	−0.201911	−0.100956	+	0.994891i	$0.532190\pi$
$770$	−4.18370e11	−0.0428897
$771$	1.93078e12	0.196783
$772$	−1.03957e13	−1.05336
$773$	1.24595e13	1.25515	0.627573	−	0.778558i	$-0.284049\pi$
$773$	1.24595e13	1.25515	0.627573	+	0.778558i	$0.284049\pi$
$774$	−1.33183e13	−1.33387
$775$	−8.17691e12	−0.814201
$776$	8.33630e12	0.825269
$777$	1.18471e13	1.16605
$778$	7.09252e12	0.694053
$779$	2.80151e13	2.72567
$780$	3.67434e12	0.355430
$781$	−2.70018e12	−0.259695
$782$	3.21070e11	0.0307022
$783$	−5.19865e13	−4.94269
$784$	−2.14754e12	−0.203010
$785$	−7.02843e12	−0.660609
$786$	1.05226e13	0.983384
$787$	6.36414e12	0.591362	0.295681	−	0.955287i	$-0.404453\pi$
$787$	6.36414e12	0.591362	0.295681	+	0.955287i	$0.404453\pi$
$788$	−1.57977e13	−1.45958
$789$	1.77746e13	1.63288
$790$	8.74421e11	0.0798727
$791$	2.21036e12	0.200756
$792$	6.66831e12	0.602217
$793$	−6.05720e12	−0.543929
$794$	−3.56169e12	−0.318027
$795$	1.88322e12	0.167205
$796$	3.58569e12	0.316566
$797$	9.01928e11	0.0791789	0.0395894	−	0.999216i	$-0.487395\pi$
$797$	9.01928e11	0.0791789	0.0395894	+	0.999216i	$0.487395\pi$
$798$	1.22995e13	1.07368
$799$	1.56040e12	0.135449
$800$	9.21344e12	0.795274
$801$	−2.16570e13	−1.85888
$802$	−7.62705e12	−0.650987
$803$	−3.44161e11	−0.0292107
$804$	−1.92536e12	−0.162502
$805$	−1.47080e12	−0.123444
$806$	2.69881e12	0.225250
$807$	4.09475e13	3.39857
$808$	4.93663e12	0.407455
$809$	−3.78449e12	−0.310627	−0.155313	−	0.987865i	$-0.549639\pi$
$809$	−3.78449e12	−0.310627	−0.155313	+	0.987865i	$0.549639\pi$
$810$	−6.99675e12	−0.571102
$811$	1.07196e13	0.870129	0.435064	−	0.900399i	$-0.356726\pi$
$811$	1.07196e13	0.870129	0.435064	+	0.900399i	$0.356726\pi$
$812$	1.28337e13	1.03598
$813$	−2.29630e13	−1.84341
$814$	−1.29722e12	−0.103563
$815$	2.40229e12	0.190729
$816$	2.28192e12	0.180175
$817$	−2.69560e13	−2.11668
$818$	−3.64649e12	−0.284764
$819$	−1.33378e13	−1.03587
$820$	7.23911e12	0.559143
$821$	−1.45588e13	−1.11836	−0.559181	−	0.829045i	$-0.688884\pi$
$821$	−1.45588e13	−1.11836	−0.559181	+	0.829045i	$0.688884\pi$
$822$	−2.41162e12	−0.184241
$823$	−2.00361e13	−1.52234	−0.761172	−	0.648550i	$-0.775376\pi$
$823$	−2.00361e13	−1.52234	−0.761172	+	0.648550i	$0.775376\pi$
$824$	9.70473e12	0.733350
$825$	−6.14108e12	−0.461532
$826$	2.56423e12	0.191667
$827$	−8.36659e12	−0.621976	−0.310988	−	0.950414i	$-0.600660\pi$
$827$	−8.36659e12	−0.621976	−0.310988	+	0.950414i	$0.600660\pi$
$828$	1.05517e13	0.780166
$829$	−1.29153e13	−0.949752	−0.474876	−	0.880053i	$-0.657507\pi$
$829$	−1.29153e13	−0.949752	−0.474876	+	0.880053i	$0.657507\pi$
$830$	−8.73240e10	−0.00638679
$831$	2.27507e13	1.65497
$832$	5.07644e11	0.0367286
$833$	−1.12585e12	−0.0810174
$834$	−3.36898e12	−0.241130
$835$	1.04028e13	0.740562
$836$	6.07489e12	0.430140
$837$	4.26542e13	3.00398
$838$	1.47116e12	0.103053
$839$	1.10546e13	0.770217	0.385108	−	0.922871i	$-0.374164\pi$
$839$	1.10546e13	0.770217	0.385108	+	0.922871i	$0.374164\pi$
$840$	7.06099e12	0.489338
$841$	2.52538e13	1.74078
$842$	−5.27562e12	−0.361717
$843$	2.93911e12	0.200444
$844$	−1.03482e13	−0.701976
$845$	−4.68558e12	−0.316161
$846$	−1.13687e13	−0.763035
$847$	1.04102e12	0.0694996
$848$	1.48871e12	0.0988621
$849$	3.61707e13	2.38931
$850$	1.02282e12	0.0672069
$851$	−4.56042e12	−0.298073
$852$	2.05123e13	1.33363
$853$	1.70767e13	1.10442	0.552209	−	0.833706i	$-0.313785\pi$
$853$	1.70767e13	1.10442	0.552209	+	0.833706i	$0.313785\pi$
$854$	−5.23931e12	−0.337065
$855$	−3.06710e13	−1.96282
$856$	−5.66245e11	−0.0360473
$857$	2.78246e13	1.76204	0.881019	−	0.473080i	$-0.156858\pi$
$857$	2.78246e13	1.76204	0.881019	+	0.473080i	$0.156858\pi$
$858$	2.02688e12	0.127683
$859$	−1.78384e13	−1.11786	−0.558928	−	0.829216i	$-0.688787\pi$
$859$	−1.78384e13	−1.11786	−0.558928	+	0.829216i	$0.688787\pi$
$860$	−6.96543e12	−0.434215
$861$	−3.64697e13	−2.26161
$862$	5.45461e12	0.336497
$863$	−5.65481e11	−0.0347032	−0.0173516	−	0.999849i	$-0.505523\pi$
$863$	−5.65481e11	−0.0347032	−0.0173516	+	0.999849i	$0.505523\pi$
$864$	−4.80611e13	−2.93415
$865$	2.11983e12	0.128744
$866$	−9.46549e11	−0.0571890
$867$	−3.02757e13	−1.81973
$868$	−1.05299e13	−0.629628
$869$	−2.17579e12	−0.129428
$870$	9.84659e12	0.582706
$871$	−9.36836e11	−0.0551546
$872$	−3.25998e12	−0.190937
$873$	4.71385e13	2.74670
$874$	−4.73457e12	−0.274460
$875$	−1.04756e13	−0.604148
$876$	2.61446e12	0.150008
$877$	−1.17075e13	−0.668293	−0.334146	−	0.942521i	$-0.608448\pi$
$877$	−1.17075e13	−0.668293	−0.334146	+	0.942521i	$0.608448\pi$
$878$	1.46375e13	0.831269
$879$	−2.96360e13	−1.67444
$880$	1.14460e12	0.0643401
$881$	−2.93685e13	−1.64244	−0.821221	−	0.570610i	$-0.806707\pi$
$881$	−2.93685e13	−1.64244	−0.821221	+	0.570610i	$0.806707\pi$
$882$	8.20267e12	0.456401
$883$	1.09588e13	0.606652	0.303326	−	0.952887i	$-0.401903\pi$
$883$	1.09588e13	0.606652	0.303326	+	0.952887i	$0.401903\pi$
$884$	1.52276e12	0.0838678
$885$	−8.87442e12	−0.486290
$886$	5.38593e12	0.293636
$887$	−3.21722e13	−1.74511	−0.872557	−	0.488512i	$-0.837540\pi$
$887$	−3.21722e13	−1.74511	−0.872557	+	0.488512i	$0.837540\pi$
$888$	2.18937e13	1.18157
$889$	−1.82764e12	−0.0981371
$890$	2.51101e12	0.134151
$891$	1.74098e13	0.925430
$892$	−1.57068e13	−0.830703
$893$	−2.30100e13	−1.21084
$894$	−1.70452e13	−0.892451
$895$	−6.09161e12	−0.317343
$896$	1.49341e13	0.774091
$897$	7.12556e12	0.367496
$898$	−2.34838e12	−0.120511
$899$	−3.26232e13	−1.66575
$900$	3.36142e13	1.70778
$901$	7.80462e11	0.0394539
$902$	3.99331e12	0.200865
$903$	3.50910e13	1.75631
$904$	4.08477e12	0.203427
$905$	1.62024e13	0.802897
$906$	5.55599e12	0.273959
$907$	5.85043e11	0.0287048	0.0143524	−	0.999897i	$-0.495431\pi$
$907$	5.85043e11	0.0287048	0.0143524	+	0.999897i	$0.495431\pi$
$908$	1.50935e13	0.736891
$909$	2.79147e13	1.35611
$910$	1.54644e12	0.0747562
$911$	3.98824e13	1.91844	0.959220	−	0.282660i	$-0.0912169\pi$
$911$	3.98824e13	1.91844	0.959220	+	0.282660i	$0.0912169\pi$
$912$	−3.36497e13	−1.61066
$913$	2.17285e11	0.0103493
$914$	−6.97576e12	−0.330623
$915$	1.81324e13	0.855188
$916$	−1.23636e13	−0.580252
$917$	−1.99769e13	−0.932966
$918$	−5.33545e12	−0.247959
$919$	−2.24277e13	−1.03721	−0.518604	−	0.855015i	$-0.673548\pi$
$919$	−2.24277e13	−1.03721	−0.518604	+	0.855015i	$0.673548\pi$
$920$	−2.71805e12	−0.125087
$921$	−4.66501e12	−0.213641
$922$	−8.58403e12	−0.391203
$923$	9.98081e12	0.452646
$924$	−7.90822e12	−0.356907
$925$	−1.45279e13	−0.652479
$926$	−1.69468e13	−0.757424
$927$	5.48764e13	2.44077
$928$	3.67587e13	1.62702
$929$	5.20466e12	0.229256	0.114628	−	0.993408i	$-0.463432\pi$
$929$	5.20466e12	0.229256	0.114628	+	0.993408i	$0.463432\pi$
$930$	−8.07898e12	−0.354147
$931$	1.66020e13	0.724249
$932$	2.24275e13	0.973663
$933$	−4.79658e13	−2.07236
$934$	1.70134e13	0.731528
$935$	6.00059e11	0.0256769
$936$	−2.46484e13	−1.04966
$937$	3.66907e13	1.55499	0.777496	−	0.628887i	$-0.216489\pi$
$937$	3.66907e13	1.55499	0.777496	+	0.628887i	$0.216489\pi$
$938$	−8.10338e11	−0.0341785
$939$	−5.95649e13	−2.50032
$940$	−5.94580e12	−0.248390
$941$	1.21062e13	0.503331	0.251666	−	0.967814i	$-0.419022\pi$
$941$	1.21062e13	0.503331	0.251666	+	0.967814i	$0.419022\pi$
$942$	2.94528e13	1.21870
$943$	1.40386e13	0.578125
$944$	−7.01537e12	−0.287526
$945$	2.44412e13	0.996965
$946$	−3.84234e12	−0.155986
$947$	2.79414e13	1.12894	0.564472	−	0.825452i	$-0.309080\pi$
$947$	2.79414e13	1.12894	0.564472	+	0.825452i	$0.309080\pi$
$948$	1.65287e13	0.664662
$949$	1.27214e12	0.0509139
$950$	−1.50827e13	−0.600791
$951$	−3.71500e13	−1.47281
$952$	2.92629e12	0.115465
$953$	−4.12362e13	−1.61942	−0.809712	−	0.586828i	$-0.800376\pi$
$953$	−4.12362e13	−1.61942	−0.809712	+	0.586828i	$0.800376\pi$
$954$	−5.68625e12	−0.222258
$955$	3.43026e12	0.133448
$956$	5.50932e12	0.213323
$957$	−2.45009e13	−0.944233
$958$	1.21704e12	0.0466833
$959$	4.57838e12	0.174795
$960$	−1.51965e12	−0.0577462
$961$	3.27256e11	0.0123775
$962$	4.79498e12	0.180509
$963$	−3.20189e12	−0.119974
$964$	−1.38797e13	−0.517645
$965$	1.51422e13	0.562104
$966$	6.16341e12	0.227732
$967$	4.86248e13	1.78829	0.894146	−	0.447775i	$-0.147783\pi$
$967$	4.86248e13	1.78829	0.894146	+	0.447775i	$0.147783\pi$
$968$	1.92381e12	0.0704245
$969$	−1.76410e13	−0.642784
$970$	−5.46545e12	−0.198223
$971$	4.27912e13	1.54478	0.772392	−	0.635147i	$-0.219060\pi$
$971$	4.27912e13	1.54478	0.772392	+	0.635147i	$0.219060\pi$
$972$	−6.42473e13	−2.30864
$973$	6.39590e12	0.228767
$974$	1.17888e13	0.419716
$975$	2.26996e13	0.804446
$976$	1.43340e13	0.505642
$977$	−1.65580e13	−0.581410	−0.290705	−	0.956813i	$-0.593890\pi$
$977$	−1.65580e13	−0.581410	−0.290705	+	0.956813i	$0.593890\pi$
$978$	−1.00669e13	−0.351860
$979$	−6.24806e12	−0.217382
$980$	4.28997e12	0.148572
$981$	−1.84339e13	−0.635486
$982$	−1.73676e13	−0.595990
$983$	−2.64542e13	−0.903657	−0.451829	−	0.892105i	$-0.649228\pi$
$983$	−2.64542e13	−0.903657	−0.451829	+	0.892105i	$0.649228\pi$
$984$	−6.73966e13	−2.29171
$985$	2.30108e13	0.778876
$986$	4.08072e12	0.137496
$987$	2.99542e13	1.00469
$988$	−2.24549e13	−0.749730
$989$	−1.35079e13	−0.448956
$990$	−4.37188e12	−0.144647
$991$	2.05592e13	0.677135	0.338568	−	0.940942i	$-0.390058\pi$
$991$	2.05592e13	0.677135	0.338568	+	0.940942i	$0.390058\pi$
$992$	−3.01599e13	−0.988844
$993$	−8.58112e13	−2.80074
$994$	8.63313e12	0.280498
$995$	−5.22287e12	−0.168929
$996$	−1.65064e12	−0.0531477
$997$	3.97335e13	1.27359	0.636793	−	0.771035i	$-0.280261\pi$
$997$	3.97335e13	1.27359	0.636793	+	0.771035i	$0.280261\pi$
$998$	1.44003e12	0.0459500
$999$	7.57838e13	2.40731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.a.b.1.3	✓	5
3.2	odd	2		99.10.a.f.1.3		5
4.3	odd	2		176.10.a.j.1.1		5
5.4	even	2		275.10.a.b.1.3		5
11.10	odd	2		121.10.a.c.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.a.b.1.3	✓	5	1.1	even	1	trivial
99.10.a.f.1.3		5	3.2	odd	2
121.10.a.c.1.3		5	11.10	odd	2
176.10.a.j.1.1		5	4.3	odd	2
275.10.a.b.1.3		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-9.63895 q^{2} +265.389 q^{3} -419.091 q^{4} +610.442 q^{5} -2558.07 q^{6} +4856.42 q^{7} +8974.73 q^{8} +50748.6 q^{9} +O(q^{10})\)	\(q-9.63895 q^{2} +265.389 q^{3} -419.091 q^{4} +610.442 q^{5} -2558.07 q^{6} +4856.42 q^{7} +8974.73 q^{8} +50748.6 q^{9} -5884.02 q^{10} +14641.0 q^{11} -111222. q^{12} -54118.2 q^{13} -46810.8 q^{14} +162005. q^{15} +128067. q^{16} +67139.6 q^{17} -489163. q^{18} -990055. q^{19} -255830. q^{20} +1.28884e6 q^{21} -141124. q^{22} -496126. q^{23} +2.38180e6 q^{24} -1.58049e6 q^{25} +521643. q^{26} +8.24447e6 q^{27} -2.03528e6 q^{28} -6.30563e6 q^{29} -1.56156e6 q^{30} +5.17367e6 q^{31} -5.82950e6 q^{32} +3.88557e6 q^{33} -647156. q^{34} +2.96456e6 q^{35} -2.12682e7 q^{36} +9.19207e6 q^{37} +9.54309e6 q^{38} -1.43624e7 q^{39} +5.47855e6 q^{40} -2.82965e7 q^{41} -1.24231e7 q^{42} +2.72268e7 q^{43} -6.13591e6 q^{44} +3.09790e7 q^{45} +4.78213e6 q^{46} +2.32412e7 q^{47} +3.39877e7 q^{48} -1.67688e7 q^{49} +1.52342e7 q^{50} +1.78182e7 q^{51} +2.26804e7 q^{52} +1.16245e7 q^{53} -7.94680e7 q^{54} +8.93748e6 q^{55} +4.35851e7 q^{56} -2.62750e8 q^{57} +6.07796e7 q^{58} -5.47787e7 q^{59} -6.78947e7 q^{60} +1.11925e8 q^{61} -4.98688e7 q^{62} +2.46456e8 q^{63} -9.38028e6 q^{64} -3.30360e7 q^{65} -3.74528e7 q^{66} +1.73109e7 q^{67} -2.81376e7 q^{68} -1.31667e8 q^{69} -2.85753e7 q^{70} -1.84426e8 q^{71} +4.55455e8 q^{72} -2.35067e7 q^{73} -8.86019e7 q^{74} -4.19444e8 q^{75} +4.14923e8 q^{76} +7.11028e7 q^{77} +1.38438e8 q^{78} -1.48610e8 q^{79} +7.81777e7 q^{80} +1.18911e9 q^{81} +2.72749e8 q^{82} +1.48409e7 q^{83} -5.40142e8 q^{84} +4.09848e7 q^{85} -2.62437e8 q^{86} -1.67345e9 q^{87} +1.31399e8 q^{88} -4.26751e8 q^{89} -2.98605e8 q^{90} -2.62821e8 q^{91} +2.07922e8 q^{92} +1.37304e9 q^{93} -2.24020e8 q^{94} -6.04371e8 q^{95} -1.54709e9 q^{96} +9.28863e8 q^{97} +1.61634e8 q^{98} +7.43010e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9}+O(q^{10}) \) 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	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16} - 547238 q^{17} - 822418 q^{18} - 162940 q^{19} - 1913320 q^{20} + 825496 q^{21} + 234256 q^{22} + 3415892 q^{23} + 1435932 q^{24} + 6164943 q^{25} + 5356756 q^{26} + 5240140 q^{27} - 2477216 q^{28} + 5868414 q^{29} - 9766670 q^{30} + 11730396 q^{31} - 18454552 q^{32} + 1639792 q^{33} - 25579352 q^{34} - 6567848 q^{35} - 26683532 q^{36} + 7021250 q^{37} - 22257720 q^{38} + 29114872 q^{39} - 22406796 q^{40} + 5595418 q^{41} - 65554916 q^{42} + 29161940 q^{43} + 10365828 q^{44} + 68008838 q^{45} + 47468978 q^{46} + 33703664 q^{47} + 96997832 q^{48} + 106606605 q^{49} + 84598070 q^{50} - 135853760 q^{51} + 185107192 q^{52} - 88905666 q^{53} - 95103866 q^{54} + 23337754 q^{55} - 78057672 q^{56} - 362541120 q^{57} + 63640668 q^{58} + 13747712 q^{59} - 208875616 q^{60} + 274324430 q^{61} - 161612942 q^{62} - 436710568 q^{63} - 46082368 q^{64} - 658499468 q^{65} + 151944298 q^{66} + 323117752 q^{67} - 679289848 q^{68} - 60345676 q^{69} + 1608436228 q^{70} + 9655356 q^{71} + 1168471200 q^{72} + 159287274 q^{73} + 76718502 q^{74} - 963596116 q^{75} + 483002000 q^{76} + 122984400 q^{77} + 1270322200 q^{78} - 668342072 q^{79} - 424312360 q^{80} + 1578463805 q^{81} + 666585700 q^{82} + 378353820 q^{83} - 2381947456 q^{84} + 1459757140 q^{85} - 2133621276 q^{86} - 2822691048 q^{87} + 596122956 q^{88} + 851774166 q^{89} - 4463334016 q^{90} - 991736368 q^{91} + 1919755168 q^{92} + 1149973204 q^{93} + 2620937360 q^{94} - 2812243800 q^{95} - 1157568712 q^{96} - 240502490 q^{97} - 2298624888 q^{98} + 1094985749 q^{99}+O(q^{100}) \) 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

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