LMFDB - Embedded newform 17.12.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.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:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 13381 x^{6} - 182353 x^{5} + 49101741 x^{4} + 1188560917 x^{3} - 22633823135 x^{2} + \cdots + 2663203205942 $ x^8 - x^7 - 13381x^6 - 182353x^5 + 49101741x^4 + 1188560917x^3 - 22633823135x^2 - 272713840835x + 2663203205942
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$15.6721$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.67209 q^{2} -94.4314 q^{3} -1972.79 q^{4} -10913.0 q^{5} +818.918 q^{6} +68029.8 q^{7} +34868.7 q^{8} -168230. q^{9} +O(q^{10})$	\(q-8.67209 q^{2} -94.4314 q^{3} -1972.79 q^{4} -10913.0 q^{5} +818.918 q^{6} +68029.8 q^{7} +34868.7 q^{8} -168230. q^{9} +94638.1 q^{10} -320482. q^{11} +186294. q^{12} +2.24443e6 q^{13} -589961. q^{14} +1.03053e6 q^{15} +3.73790e6 q^{16} -1.41986e6 q^{17} +1.45890e6 q^{18} +1.00845e7 q^{19} +2.15290e7 q^{20} -6.42416e6 q^{21} +2.77925e6 q^{22} -1.23086e7 q^{23} -3.29270e6 q^{24} +7.02645e7 q^{25} -1.94639e7 q^{26} +3.26144e7 q^{27} -1.34209e8 q^{28} -4.88857e7 q^{29} -8.93681e6 q^{30} +1.10368e8 q^{31} -1.03826e8 q^{32} +3.02635e7 q^{33} +1.23131e7 q^{34} -7.42407e8 q^{35} +3.31883e8 q^{36} -9.07466e7 q^{37} -8.74540e7 q^{38} -2.11944e8 q^{39} -3.80521e8 q^{40} +1.03759e9 q^{41} +5.57108e7 q^{42} -1.38019e9 q^{43} +6.32245e8 q^{44} +1.83588e9 q^{45} +1.06742e8 q^{46} -1.21312e9 q^{47} -3.52975e8 q^{48} +2.65073e9 q^{49} -6.09340e8 q^{50} +1.34079e8 q^{51} -4.42779e9 q^{52} +5.71084e9 q^{53} -2.82835e8 q^{54} +3.49740e9 q^{55} +2.37211e9 q^{56} -9.52297e8 q^{57} +4.23941e8 q^{58} +8.22976e9 q^{59} -2.03302e9 q^{60} +1.59397e9 q^{61} -9.57118e8 q^{62} -1.14446e10 q^{63} -6.75483e9 q^{64} -2.44933e10 q^{65} -2.62448e8 q^{66} -1.12895e9 q^{67} +2.80109e9 q^{68} +1.16232e9 q^{69} +6.43822e9 q^{70} +4.27119e9 q^{71} -5.86595e9 q^{72} +3.45110e10 q^{73} +7.86963e8 q^{74} -6.63518e9 q^{75} -1.98947e10 q^{76} -2.18023e10 q^{77} +1.83800e9 q^{78} -3.48726e9 q^{79} -4.07915e10 q^{80} +2.67216e10 q^{81} -8.99810e9 q^{82} +4.29833e10 q^{83} +1.26735e10 q^{84} +1.54948e10 q^{85} +1.19691e10 q^{86} +4.61635e9 q^{87} -1.11748e10 q^{88} +1.16178e10 q^{89} -1.59209e10 q^{90} +1.52688e11 q^{91} +2.42824e10 q^{92} -1.04222e10 q^{93} +1.05203e10 q^{94} -1.10052e11 q^{95} +9.80448e9 q^{96} +5.65060e10 q^{97} -2.29874e10 q^{98} +5.39145e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9}+O(q^{10}) $ 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9} + 2824 q^{10} + 435256 q^{11} + 4295182 q^{12} + 4193784 q^{13} + 4377132 q^{14} + 10362648 q^{15} + 20722897 q^{16} - 11358856 q^{17} + 28881887 q^{18} + 15158192 q^{19} + 91612472 q^{20} + 98415768 q^{21} + 81767186 q^{22} + 22374432 q^{23} - 41056218 q^{24} + 133926472 q^{25} - 70553178 q^{26} + 68932744 q^{27} + 108010892 q^{28} - 424656432 q^{29} - 561465200 q^{30} - 172323152 q^{31} - 540258159 q^{32} - 764794592 q^{33} - 78092135 q^{34} - 117251352 q^{35} - 1812061939 q^{36} - 262792640 q^{37} - 674758596 q^{38} - 302706728 q^{39} - 3575120264 q^{40} - 1283308512 q^{41} - 1036128840 q^{42} + 2219398472 q^{43} + 4256110614 q^{44} + 3982117536 q^{45} + 6081288184 q^{46} + 260684408 q^{47} + 6860204310 q^{48} + 12060045320 q^{49} - 1911832923 q^{50} - 704249072 q^{51} + 3548505010 q^{52} + 9402026896 q^{53} - 848951924 q^{54} + 4430702936 q^{55} - 11881582644 q^{56} + 1366983408 q^{57} + 814919720 q^{58} + 14325543480 q^{59} + 4281784208 q^{60} - 9811064576 q^{61} - 41469249572 q^{62} + 14666072688 q^{63} - 27038375199 q^{64} + 29701570288 q^{65} - 43330462276 q^{66} + 52928023248 q^{67} - 15273401749 q^{68} - 13481294472 q^{69} - 128492187744 q^{70} - 34868356504 q^{71} - 52662987279 q^{72} + 1248764080 q^{73} - 135359144436 q^{74} + 59235735072 q^{75} - 49428813052 q^{76} + 112631449800 q^{77} - 87670698684 q^{78} + 18209008736 q^{79} + 96412241400 q^{80} + 67350111224 q^{81} + 41461375370 q^{82} + 169643760088 q^{83} + 117131104968 q^{84} - 12199411344 q^{85} + 88510231200 q^{86} + 35491052136 q^{87} - 51404280146 q^{88} + 201694397904 q^{89} - 4670596888 q^{90} + 36284010568 q^{91} - 3754023808 q^{92} + 106318637912 q^{93} + 253870878768 q^{94} - 383491632 q^{95} - 102115750890 q^{96} + 163430440672 q^{97} - 110963034673 q^{98} - 716459488 q^{99}+O(q^{100}) \) 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9 + 2824 * q^10 + 435256 * q^11 + 4295182 * q^12 + 4193784 * q^13 + 4377132 * q^14 + 10362648 * q^15 + 20722897 * q^16 - 11358856 * q^17 + 28881887 * q^18 + 15158192 * q^19 + 91612472 * q^20 + 98415768 * q^21 + 81767186 * q^22 + 22374432 * q^23 - 41056218 * q^24 + 133926472 * q^25 - 70553178 * q^26 + 68932744 * q^27 + 108010892 * q^28 - 424656432 * q^29 - 561465200 * q^30 - 172323152 * q^31 - 540258159 * q^32 - 764794592 * q^33 - 78092135 * q^34 - 117251352 * q^35 - 1812061939 * q^36 - 262792640 * q^37 - 674758596 * q^38 - 302706728 * q^39 - 3575120264 * q^40 - 1283308512 * q^41 - 1036128840 * q^42 + 2219398472 * q^43 + 4256110614 * q^44 + 3982117536 * q^45 + 6081288184 * q^46 + 260684408 * q^47 + 6860204310 * q^48 + 12060045320 * q^49 - 1911832923 * q^50 - 704249072 * q^51 + 3548505010 * q^52 + 9402026896 * q^53 - 848951924 * q^54 + 4430702936 * q^55 - 11881582644 * q^56 + 1366983408 * q^57 + 814919720 * q^58 + 14325543480 * q^59 + 4281784208 * q^60 - 9811064576 * q^61 - 41469249572 * q^62 + 14666072688 * q^63 - 27038375199 * q^64 + 29701570288 * q^65 - 43330462276 * q^66 + 52928023248 * q^67 - 15273401749 * q^68 - 13481294472 * q^69 - 128492187744 * q^70 - 34868356504 * q^71 - 52662987279 * q^72 + 1248764080 * q^73 - 135359144436 * q^74 + 59235735072 * q^75 - 49428813052 * q^76 + 112631449800 * q^77 - 87670698684 * q^78 + 18209008736 * q^79 + 96412241400 * q^80 + 67350111224 * q^81 + 41461375370 * q^82 + 169643760088 * q^83 + 117131104968 * q^84 - 12199411344 * q^85 + 88510231200 * q^86 + 35491052136 * q^87 - 51404280146 * q^88 + 201694397904 * q^89 - 4670596888 * q^90 + 36284010568 * q^91 - 3754023808 * q^92 + 106318637912 * q^93 + 253870878768 * q^94 - 383491632 * q^95 - 102115750890 * q^96 + 163430440672 * q^97 - 110963034673 * q^98 - 716459488 * 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 $

$2$	−8.67209	−0.191628	−0.0958140	−	0.995399i	$-0.530545\pi$
$2$	−8.67209	−0.191628	−0.0958140	+	0.995399i	$0.530545\pi$
$3$	−94.4314	−0.224362	−0.112181	−	0.993688i	$-0.535784\pi$
$3$	−94.4314	−0.224362	−0.112181	+	0.993688i	$0.535784\pi$
$4$	−1972.79	−0.963279
$5$	−10913.0	−1.56174	−0.780868	−	0.624697i	$-0.785223\pi$
$5$	−10913.0	−1.56174	−0.780868	+	0.624697i	$0.785223\pi$
$6$	818.918	0.0429941
$7$	68029.8	1.52989	0.764945	−	0.644096i	$-0.222766\pi$
$7$	68029.8	1.52989	0.764945	+	0.644096i	$0.222766\pi$
$8$	34868.7	0.376219
$9$	−168230.	−0.949662
$10$	94638.1	0.299272
$11$	−320482.	−0.599989	−0.299995	−	0.953941i	$-0.596985\pi$
$11$	−320482.	−0.599989	−0.299995	+	0.953941i	$0.596985\pi$
$12$	186294.	0.216123
$13$	2.24443e6	1.67655	0.838275	−	0.545247i	$-0.183564\pi$
$13$	2.24443e6	1.67655	0.838275	+	0.545247i	$0.183564\pi$
$14$	−589961.	−0.293170
$15$	1.03053e6	0.350394
$16$	3.73790e6	0.891185
$17$	−1.41986e6	−0.242536
$17$	−1.41986e6	−0.242536
$18$	1.45890e6	0.181982
$19$	1.00845e7	0.934354	0.467177	−	0.884164i	$-0.345271\pi$
$19$	1.00845e7	0.934354	0.467177	+	0.884164i	$0.345271\pi$
$20$	2.15290e7	1.50439
$21$	−6.42416e6	−0.343249
$22$	2.77925e6	0.114975
$23$	−1.23086e7	−0.398756	−0.199378	−	0.979923i	$-0.563892\pi$
$23$	−1.23086e7	−0.398756	−0.199378	+	0.979923i	$0.563892\pi$
$24$	−3.29270e6	−0.0844093
$25$	7.02645e7	1.43902
$26$	−1.94639e7	−0.321274
$27$	3.26144e7	0.437430
$28$	−1.34209e8	−1.47371
$29$	−4.88857e7	−0.442581	−0.221291	−	0.975208i	$-0.571027\pi$
$29$	−4.88857e7	−0.442581	−0.221291	+	0.975208i	$0.571027\pi$
$30$	−8.93681e6	−0.0671453
$31$	1.10368e8	0.692392	0.346196	−	0.938162i	$-0.387473\pi$
$31$	1.10368e8	0.692392	0.346196	+	0.938162i	$0.387473\pi$
$32$	−1.03826e8	−0.546995
$33$	3.02635e7	0.134615
$34$	1.23131e7	0.0464766
$35$	−7.42407e8	−2.38928
$36$	3.31883e8	0.914789
$37$	−9.07466e7	−0.215140	−0.107570	−	0.994198i	$-0.534307\pi$
$37$	−9.07466e7	−0.215140	−0.107570	+	0.994198i	$0.534307\pi$
$38$	−8.74540e7	−0.179048
$39$	−2.11944e8	−0.376155
$40$	−3.80521e8	−0.587554
$41$	1.03759e9	1.39867	0.699336	−	0.714793i	$-0.253479\pi$
$41$	1.03759e9	1.39867	0.699336	+	0.714793i	$0.253479\pi$
$42$	5.57108e7	0.0657762
$43$	−1.38019e9	−1.43174	−0.715868	−	0.698236i	$-0.753969\pi$
$43$	−1.38019e9	−1.43174	−0.715868	+	0.698236i	$0.753969\pi$
$44$	6.32245e8	0.577957
$45$	1.83588e9	1.48312
$46$	1.06742e8	0.0764127
$47$	−1.21312e9	−0.771554	−0.385777	−	0.922592i	$-0.626067\pi$
$47$	−1.21312e9	−0.771554	−0.385777	+	0.922592i	$0.626067\pi$
$48$	−3.52975e8	−0.199948
$49$	2.65073e9	1.34056
$50$	−6.09340e8	−0.275756
$51$	1.34079e8	0.0544158
$52$	−4.42779e9	−1.61499
$53$	5.71084e9	1.87578	0.937891	−	0.346929i	$-0.112775\pi$
$53$	5.71084e9	1.87578	0.937891	+	0.346929i	$0.112775\pi$
$54$	−2.82835e8	−0.0838239
$55$	3.49740e9	0.937024
$56$	2.37211e9	0.575574
$57$	−9.52297e8	−0.209634
$58$	4.23941e8	0.0848110
$59$	8.22976e9	1.49865	0.749326	−	0.662201i	$-0.230377\pi$
$59$	8.22976e9	1.49865	0.749326	+	0.662201i	$0.230377\pi$
$60$	−2.03302e9	−0.337527
$61$	1.59397e9	0.241639	0.120819	−	0.992675i	$-0.461448\pi$
$61$	1.59397e9	0.241639	0.120819	+	0.992675i	$0.461448\pi$
$62$	−9.57118e8	−0.132682
$63$	−1.14446e10	−1.45288
$64$	−6.75483e9	−0.786365
$65$	−2.44933e10	−2.61833
$66$	−2.62448e8	−0.0257960
$67$	−1.12895e9	−0.102156	−0.0510781	−	0.998695i	$-0.516266\pi$
$67$	−1.12895e9	−0.102156	−0.0510781	+	0.998695i	$0.516266\pi$
$68$	2.80109e9	0.233629
$69$	1.16232e9	0.0894657
$70$	6.43822e9	0.457853
$71$	4.27119e9	0.280949	0.140475	−	0.990084i	$-0.455137\pi$
$71$	4.27119e9	0.280949	0.140475	+	0.990084i	$0.455137\pi$
$72$	−5.86595e9	−0.357281
$73$	3.45110e10	1.94842	0.974209	−	0.225647i	$-0.0724496\pi$
$73$	3.45110e10	1.94842	0.974209	+	0.225647i	$0.0724496\pi$
$74$	7.86963e8	0.0412268
$75$	−6.63518e9	−0.322861
$76$	−1.98947e10	−0.900043
$77$	−2.18023e10	−0.917918
$78$	1.83800e9	0.0720817
$79$	−3.48726e9	−0.127507	−0.0637537	−	0.997966i	$-0.520307\pi$
$79$	−3.48726e9	−0.127507	−0.0637537	+	0.997966i	$0.520307\pi$
$80$	−4.07915e10	−1.39179
$81$	2.67216e10	0.851519
$82$	−8.99810e9	−0.268025
$83$	4.29833e10	1.19776	0.598881	−	0.800838i	$-0.295612\pi$
$83$	4.29833e10	1.19776	0.598881	+	0.800838i	$0.295612\pi$
$84$	1.26735e10	0.330645
$85$	1.54948e10	0.378776
$86$	1.19691e10	0.274361
$87$	4.61635e9	0.0992985
$88$	−1.11748e10	−0.225727
$89$	1.16178e10	0.220536	0.110268	−	0.993902i	$-0.464829\pi$
$89$	1.16178e10	0.220536	0.110268	+	0.993902i	$0.464829\pi$
$90$	−1.59209e10	−0.284207
$91$	1.52688e11	2.56494
$92$	2.42824e10	0.384113
$93$	−1.04222e10	−0.155347
$94$	1.05203e10	0.147851
$95$	−1.10052e11	−1.45921
$96$	9.80448e9	0.122725
$97$	5.65060e10	0.668113	0.334057	−	0.942553i	$-0.391582\pi$
$97$	5.65060e10	0.668113	0.334057	+	0.942553i	$0.391582\pi$
$98$	−2.29874e10	−0.256889
$99$	5.39145e10	0.569787
$100$	−1.38617e11	−1.38617
$101$	−7.07654e10	−0.669967	−0.334983	−	0.942224i	$-0.608731\pi$
$101$	−7.07654e10	−0.669967	−0.334983	+	0.942224i	$0.608731\pi$
$102$	−1.16275e9	−0.0104276
$103$	−1.58464e10	−0.134687	−0.0673435	−	0.997730i	$-0.521452\pi$
$103$	−1.58464e10	−0.134687	−0.0673435	+	0.997730i	$0.521452\pi$
$104$	7.82602e10	0.630750
$105$	7.01065e10	0.536065
$106$	−4.95249e10	−0.359452
$107$	−9.20318e10	−0.634347	−0.317174	−	0.948368i	$-0.602734\pi$
$107$	−9.20318e10	−0.634347	−0.317174	+	0.948368i	$0.602734\pi$
$108$	−6.43416e10	−0.421367
$109$	−1.94108e11	−1.20837	−0.604183	−	0.796845i	$-0.706500\pi$
$109$	−1.94108e11	−1.20837	−0.604183	+	0.796845i	$0.706500\pi$
$110$	−3.03298e10	−0.179560
$111$	8.56933e9	0.0482693
$112$	2.54289e11	1.36341
$113$	5.61855e9	0.0286875	0.0143437	−	0.999897i	$-0.495434\pi$
$113$	5.61855e9	0.0286875	0.0143437	+	0.999897i	$0.495434\pi$
$114$	8.25841e9	0.0401716
$115$	1.34324e11	0.622751
$116$	9.64415e10	0.426329
$117$	−3.77579e11	−1.59216
$118$	−7.13692e10	−0.287184
$119$	−9.65926e10	−0.371053
$120$	3.59331e10	0.131825
$121$	−1.82603e11	−0.640013
$122$	−1.38231e10	−0.0463047
$123$	−9.79814e10	−0.313809
$124$	−2.17733e11	−0.666967
$125$	−2.33934e11	−0.685628
$126$	9.92489e10	0.278412
$127$	4.79008e11	1.28654	0.643268	−	0.765641i	$-0.277578\pi$
$127$	4.79008e11	1.28654	0.643268	+	0.765641i	$0.277578\pi$
$128$	2.71215e11	0.697684
$129$	1.30333e11	0.321227
$130$	2.12408e11	0.501745
$131$	3.46164e11	0.783952	0.391976	−	0.919976i	$-0.371792\pi$
$131$	3.46164e11	0.783952	0.391976	+	0.919976i	$0.371792\pi$
$132$	−5.97038e10	−0.129672
$133$	6.86050e11	1.42946
$134$	9.79039e9	0.0195760
$135$	−3.55920e11	−0.683150
$136$	−4.95086e10	−0.0912465
$137$	−1.83236e11	−0.324376	−0.162188	−	0.986760i	$-0.551855\pi$
$137$	−1.83236e11	−0.324376	−0.162188	+	0.986760i	$0.551855\pi$
$138$	−1.00798e10	−0.0171441
$139$	−3.87607e11	−0.633593	−0.316797	−	0.948494i	$-0.602607\pi$
$139$	−3.87607e11	−0.633593	−0.316797	+	0.948494i	$0.602607\pi$
$140$	1.46462e12	2.30155
$141$	1.14557e11	0.173107
$142$	−3.70401e10	−0.0538377
$143$	−7.19297e11	−1.00591
$144$	−6.28826e11	−0.846324
$145$	5.33488e11	0.691195
$146$	−2.99283e11	−0.373371
$147$	−2.50312e11	−0.300772
$148$	1.79025e11	0.207240
$149$	−6.89560e11	−0.769215	−0.384608	−	0.923080i	$-0.625663\pi$
$149$	−6.89560e11	−0.769215	−0.384608	+	0.923080i	$0.625663\pi$
$150$	5.75408e10	0.0618692
$151$	1.86605e12	1.93441	0.967207	−	0.253991i	$-0.0817433\pi$
$151$	1.86605e12	1.93441	0.967207	+	0.253991i	$0.0817433\pi$
$152$	3.51635e11	0.351522
$153$	2.38862e11	0.230327
$154$	1.89072e11	0.175899
$155$	−1.20444e12	−1.08133
$156$	4.18123e11	0.362342
$157$	−1.83291e12	−1.53353	−0.766765	−	0.641928i	$-0.778135\pi$
$157$	−1.83291e12	−1.53353	−0.766765	+	0.641928i	$0.778135\pi$
$158$	3.02418e10	0.0244340
$159$	−5.39283e11	−0.420855
$160$	1.13305e12	0.854261
$161$	−8.37355e11	−0.610053
$162$	−2.31732e11	−0.163175
$163$	−1.09803e12	−0.747448	−0.373724	−	0.927540i	$-0.621919\pi$
$163$	−1.09803e12	−0.747448	−0.373724	+	0.927540i	$0.621919\pi$
$164$	−2.04696e12	−1.34731
$165$	−3.30265e11	−0.210233
$166$	−3.72755e11	−0.229525
$167$	−2.00683e12	−1.19556	−0.597778	−	0.801661i	$-0.703950\pi$
$167$	−2.00683e12	−1.19556	−0.597778	+	0.801661i	$0.703950\pi$
$168$	−2.24002e11	−0.129137
$169$	3.24528e12	1.81082
$170$	−1.34373e11	−0.0725841
$171$	−1.69652e12	−0.887320
$172$	2.72284e12	1.37916
$173$	−1.34937e12	−0.662031	−0.331016	−	0.943625i	$-0.607391\pi$
$173$	−1.34937e12	−0.662031	−0.331016	+	0.943625i	$0.607391\pi$
$174$	−4.00334e10	−0.0190284
$175$	4.78008e12	2.20154
$176$	−1.19793e12	−0.534701
$177$	−7.77148e11	−0.336241
$178$	−1.00751e11	−0.0422608
$179$	3.26569e12	1.32826	0.664131	−	0.747617i	$-0.268802\pi$
$179$	3.26569e12	1.32826	0.664131	+	0.747617i	$0.268802\pi$
$180$	−3.62182e12	−1.42866
$181$	4.95978e11	0.189771	0.0948856	−	0.995488i	$-0.469751\pi$
$181$	4.95978e11	0.189771	0.0948856	+	0.995488i	$0.469751\pi$
$182$	−1.32412e12	−0.491514
$183$	−1.50521e11	−0.0542145
$184$	−4.29186e11	−0.150020
$185$	9.90314e11	0.335992
$186$	9.03820e10	0.0297688
$187$	4.55038e11	0.145519
$188$	2.39324e12	0.743221
$189$	2.21875e12	0.669220
$190$	9.54382e11	0.279626
$191$	1.42972e12	0.406973	0.203487	−	0.979078i	$-0.434773\pi$
$191$	1.42972e12	0.406973	0.203487	+	0.979078i	$0.434773\pi$
$192$	6.37868e11	0.176431
$193$	1.88826e12	0.507572	0.253786	−	0.967260i	$-0.418324\pi$
$193$	1.88826e12	0.507572	0.253786	+	0.967260i	$0.418324\pi$
$194$	−4.90025e11	−0.128029
$195$	2.31294e12	0.587454
$196$	−5.22935e12	−1.29134
$197$	5.71675e12	1.37273	0.686364	−	0.727258i	$-0.259206\pi$
$197$	5.71675e12	1.37273	0.686364	+	0.727258i	$0.259206\pi$
$198$	−4.67552e11	−0.109187
$199$	2.07239e11	0.0470739	0.0235369	−	0.999723i	$-0.492507\pi$
$199$	2.07239e11	0.0470739	0.0235369	+	0.999723i	$0.492507\pi$
$200$	2.45003e12	0.541386
$201$	1.06609e11	0.0229200
$202$	6.13684e11	0.128384
$203$	−3.32569e12	−0.677101
$204$	−2.64511e11	−0.0524176
$205$	−1.13232e13	−2.18436
$206$	1.37421e11	0.0258098
$207$	2.07068e12	0.378683
$208$	8.38944e12	1.49412
$209$	−3.23191e12	−0.560602
$210$	−6.07970e11	−0.102725
$211$	−1.03509e13	−1.70383	−0.851913	−	0.523684i	$-0.824557\pi$
$211$	−1.03509e13	−1.70383	−0.851913	+	0.523684i	$0.824557\pi$
$212$	−1.12663e13	−1.80690
$213$	−4.03334e11	−0.0630344
$214$	7.98108e11	0.121559
$215$	1.50620e13	2.23599
$216$	1.13722e12	0.164570
$217$	7.50829e12	1.05928
$218$	1.68333e12	0.231557
$219$	−3.25893e12	−0.437151
$220$	−6.89966e12	−0.902616
$221$	−3.18676e12	−0.406623
$222$	−7.43140e10	−0.00924974
$223$	7.92202e12	0.961965	0.480983	−	0.876730i	$-0.340280\pi$
$223$	7.92202e12	0.961965	0.480983	+	0.876730i	$0.340280\pi$
$224$	−7.06330e12	−0.836842
$225$	−1.18206e13	−1.36658
$226$	−4.87246e10	−0.00549733
$227$	2.30256e12	0.253553	0.126777	−	0.991931i	$-0.459537\pi$
$227$	2.30256e12	0.253553	0.126777	+	0.991931i	$0.459537\pi$
$228$	1.87869e12	0.201936
$229$	−3.64581e12	−0.382559	−0.191280	−	0.981536i	$-0.561264\pi$
$229$	−3.64581e12	−0.382559	−0.191280	+	0.981536i	$0.561264\pi$
$230$	−1.16487e12	−0.119336
$231$	2.05882e12	0.205946
$232$	−1.70458e12	−0.166508
$233$	−9.12258e12	−0.870283	−0.435141	−	0.900362i	$-0.643302\pi$
$233$	−9.12258e12	−0.870283	−0.435141	+	0.900362i	$0.643302\pi$
$234$	3.27440e12	0.305101
$235$	1.32387e13	1.20496
$236$	−1.62356e13	−1.44362
$237$	3.29307e11	0.0286078
$238$	8.37660e11	0.0711041
$239$	3.18410e12	0.264118	0.132059	−	0.991242i	$-0.457841\pi$
$239$	3.18410e12	0.264118	0.132059	+	0.991242i	$0.457841\pi$
$240$	3.85200e12	0.312266
$241$	1.64656e13	1.30462	0.652311	−	0.757952i	$-0.273800\pi$
$241$	1.64656e13	1.30462	0.652311	+	0.757952i	$0.273800\pi$
$242$	1.58355e12	0.122644
$243$	−8.30090e12	−0.628479
$244$	−3.14458e12	−0.232765
$245$	−2.89273e13	−2.09361
$246$	8.49704e11	0.0601346
$247$	2.26340e13	1.56649
$248$	3.84837e12	0.260491
$249$	−4.05898e12	−0.268733
$250$	2.02870e12	0.131386
$251$	1.04379e13	0.661315	0.330657	−	0.943751i	$-0.392730\pi$
$251$	1.04379e13	0.661315	0.330657	+	0.943751i	$0.392730\pi$
$252$	2.25779e13	1.39953
$253$	3.94469e12	0.239249
$254$	−4.15400e12	−0.246536
$255$	−1.46320e12	−0.0849831
$256$	1.14819e13	0.652669
$257$	1.80712e13	1.00544	0.502719	−	0.864450i	$-0.332333\pi$
$257$	1.80712e13	1.00544	0.502719	+	0.864450i	$0.332333\pi$
$258$	−1.13026e12	−0.0615561
$259$	−6.17348e12	−0.329140
$260$	4.83203e13	2.52218
$261$	8.22403e12	0.420303
$262$	−3.00196e12	−0.150227
$263$	−1.97135e13	−0.966067	−0.483033	−	0.875602i	$-0.660465\pi$
$263$	−1.97135e13	−0.966067	−0.483033	+	0.875602i	$0.660465\pi$
$264$	1.05525e12	0.0506447
$265$	−6.23221e13	−2.92948
$266$	−5.94948e12	−0.273924
$267$	−1.09709e12	−0.0494799
$268$	2.22720e12	0.0984049
$269$	−5.55306e12	−0.240378	−0.120189	−	0.992751i	$-0.538350\pi$
$269$	−5.55306e12	−0.240378	−0.120189	+	0.992751i	$0.538350\pi$
$270$	3.08657e12	0.130911
$271$	4.21000e13	1.74965	0.874825	−	0.484440i	$-0.160977\pi$
$271$	4.21000e13	1.74965	0.874825	+	0.484440i	$0.160977\pi$
$272$	−5.30728e12	−0.216144
$273$	−1.44185e13	−0.575475
$274$	1.58904e12	0.0621595
$275$	−2.25185e13	−0.863395
$276$	−2.29302e12	−0.0861804
$277$	−1.77295e13	−0.653217	−0.326609	−	0.945160i	$-0.605906\pi$
$277$	−1.77295e13	−0.653217	−0.326609	+	0.945160i	$0.605906\pi$
$278$	3.36136e12	0.121414
$279$	−1.85671e13	−0.657538
$280$	−2.58868e13	−0.898894
$281$	1.79421e13	0.610927	0.305464	−	0.952204i	$-0.401189\pi$
$281$	1.79421e13	0.610927	0.305464	+	0.952204i	$0.401189\pi$
$282$	−9.93447e11	−0.0331722
$283$	4.98727e12	0.163319	0.0816597	−	0.996660i	$-0.473978\pi$
$283$	4.98727e12	0.163319	0.0816597	+	0.996660i	$0.473978\pi$
$284$	−8.42618e12	−0.270632
$285$	1.03924e13	0.327392
$286$	6.23781e12	0.192761
$287$	7.05873e13	2.13982
$288$	1.74667e13	0.519460
$289$	2.01599e12	0.0588235
$290$	−4.62646e12	−0.132452
$291$	−5.33594e12	−0.149899
$292$	−6.80832e13	−1.87687
$293$	5.11277e13	1.38320	0.691599	−	0.722282i	$-0.256907\pi$
$293$	5.11277e13	1.38320	0.691599	+	0.722282i	$0.256907\pi$
$294$	2.17073e12	0.0576363
$295$	−8.98110e13	−2.34050
$296$	−3.16422e12	−0.0809397
$297$	−1.04523e13	−0.262453
$298$	5.97993e12	0.147403
$299$	−2.76258e13	−0.668534
$300$	1.30898e13	0.311005
$301$	−9.38942e13	−2.19040
$302$	−1.61825e13	−0.370688
$303$	6.68247e12	0.150315
$304$	3.76950e13	0.832682
$305$	−1.73949e13	−0.377375
$306$	−2.07143e12	−0.0441370
$307$	−5.81284e13	−1.21654	−0.608272	−	0.793729i	$-0.708137\pi$
$307$	−5.81284e13	−1.21654	−0.608272	+	0.793729i	$0.708137\pi$
$308$	4.30115e13	0.884210
$309$	1.49640e12	0.0302186
$310$	1.04450e13	0.207214
$311$	9.08038e13	1.76979	0.884896	−	0.465789i	$-0.154229\pi$
$311$	9.08038e13	1.76979	0.884896	+	0.465789i	$0.154229\pi$
$312$	−7.39022e12	−0.141516
$313$	−6.83124e13	−1.28530	−0.642652	−	0.766158i	$-0.722166\pi$
$313$	−6.83124e13	−1.28530	−0.642652	+	0.766158i	$0.722166\pi$
$314$	1.58951e13	0.293867
$315$	1.24895e14	2.26901
$316$	6.87965e12	0.122825
$317$	6.22327e12	0.109192	0.0545962	−	0.998509i	$-0.482613\pi$
$317$	6.22327e12	0.109192	0.0545962	+	0.998509i	$0.482613\pi$
$318$	4.67671e12	0.0806475
$319$	1.56670e13	0.265544
$320$	7.37151e13	1.22809
$321$	8.69069e12	0.142323
$322$	7.26162e12	0.116903
$323$	−1.43186e13	−0.226614
$324$	−5.27162e13	−0.820250
$325$	1.57703e14	2.41258
$326$	9.52218e12	0.143232
$327$	1.83299e13	0.271112
$328$	3.61795e13	0.526207
$329$	−8.25285e13	−1.18039
$330$	2.86409e12	0.0402865
$331$	5.33968e12	0.0738689	0.0369345	−	0.999318i	$-0.488241\pi$
$331$	5.33968e12	0.0738689	0.0369345	+	0.999318i	$0.488241\pi$
$332$	−8.47973e13	−1.15378
$333$	1.52663e13	0.204310
$334$	1.74034e13	0.229102
$335$	1.23202e13	0.159541
$336$	−2.40128e13	−0.305899
$337$	−2.12376e13	−0.266159	−0.133079	−	0.991105i	$-0.542487\pi$
$337$	−2.12376e13	−0.266159	−0.133079	+	0.991105i	$0.542487\pi$
$338$	−2.81434e13	−0.347004
$339$	−5.30568e11	−0.00643639
$340$	−3.05681e13	−0.364867
$341$	−3.53708e13	−0.415428
$342$	1.47124e13	0.170035
$343$	4.58117e13	0.521025
$344$	−4.81255e13	−0.538646
$345$	−1.26844e13	−0.139722
$346$	1.17019e13	0.126864
$347$	−3.78459e13	−0.403838	−0.201919	−	0.979402i	$-0.564718\pi$
$347$	−3.78459e13	−0.403838	−0.201919	+	0.979402i	$0.564718\pi$
$348$	−9.10711e12	−0.0956522
$349$	9.72162e12	0.100508	0.0502538	−	0.998736i	$-0.483997\pi$
$349$	9.72162e12	0.100508	0.0502538	+	0.998736i	$0.483997\pi$
$350$	−4.14533e13	−0.421876
$351$	7.32006e13	0.733374
$352$	3.32745e13	0.328191
$353$	1.51547e14	1.47159	0.735796	−	0.677203i	$-0.236808\pi$
$353$	1.51547e14	1.47159	0.735796	+	0.677203i	$0.236808\pi$
$354$	6.73950e12	0.0644332
$355$	−4.66113e13	−0.438768
$356$	−2.29196e13	−0.212437
$357$	9.12138e12	0.0832502
$358$	−2.83204e13	−0.254532
$359$	1.02154e14	0.904143	0.452071	−	0.891982i	$-0.350685\pi$
$359$	1.02154e14	0.904143	0.452071	+	0.891982i	$0.350685\pi$
$360$	6.40149e13	0.557978
$361$	−1.47923e13	−0.126983
$362$	−4.30116e12	−0.0363654
$363$	1.72435e13	0.143595
$364$	−3.01222e14	−2.47075
$365$	−3.76617e14	−3.04291
$366$	1.30533e12	0.0103890
$367$	−1.15413e14	−0.904878	−0.452439	−	0.891795i	$-0.649446\pi$
$367$	−1.15413e14	−0.904878	−0.452439	+	0.891795i	$0.649446\pi$
$368$	−4.60085e13	−0.355365
$369$	−1.74554e14	−1.32827
$370$	−8.58809e12	−0.0643854
$371$	3.88507e14	2.86974
$372$	2.05608e13	0.149642
$373$	3.12680e13	0.224234	0.112117	−	0.993695i	$-0.464237\pi$
$373$	3.12680e13	0.224234	0.112117	+	0.993695i	$0.464237\pi$
$374$	−3.94613e12	−0.0278855
$375$	2.20907e13	0.153829
$376$	−4.23000e13	−0.290273
$377$	−1.09720e14	−0.742010
$378$	−1.92412e13	−0.128241
$379$	2.60442e13	0.171078	0.0855392	−	0.996335i	$-0.472739\pi$
$379$	2.60442e13	0.171078	0.0855392	+	0.996335i	$0.472739\pi$
$380$	2.17110e14	1.40563
$381$	−4.52334e13	−0.288650
$382$	−1.23986e13	−0.0779875
$383$	−1.06307e13	−0.0659127	−0.0329564	−	0.999457i	$-0.510492\pi$
$383$	−1.06307e13	−0.0659127	−0.0329564	+	0.999457i	$0.510492\pi$
$384$	−2.56112e13	−0.156534
$385$	2.37928e14	1.43354
$386$	−1.63752e13	−0.0972649
$387$	2.32189e14	1.35966
$388$	−1.11475e14	−0.643579
$389$	−2.58532e14	−1.47160	−0.735802	−	0.677197i	$-0.763194\pi$
$389$	−2.58532e14	−1.47160	−0.735802	+	0.677197i	$0.763194\pi$
$390$	−2.00580e13	−0.112573
$391$	1.74765e13	0.0967125
$392$	9.24276e13	0.504346
$393$	−3.26887e13	−0.175889
$394$	−4.95761e13	−0.263053
$395$	3.80563e13	0.199133
$396$	−1.06362e14	−0.548863
$397$	2.22439e14	1.13205	0.566023	−	0.824390i	$-0.308481\pi$
$397$	2.22439e14	1.13205	0.566023	+	0.824390i	$0.308481\pi$
$398$	−1.79720e12	−0.00902067
$399$	−6.47846e13	−0.320716
$400$	2.62642e14	1.28243
$401$	1.94835e13	0.0938370	0.0469185	−	0.998899i	$-0.485060\pi$
$401$	1.94835e13	0.0938370	0.0469185	+	0.998899i	$0.485060\pi$
$402$	−9.24521e11	−0.00439211
$403$	2.47712e14	1.16083
$404$	1.39606e14	0.645365
$405$	−2.91611e14	−1.32985
$406$	2.88407e13	0.129751
$407$	2.90826e13	0.129082
$408$	4.67516e12	0.0204723
$409$	−6.19333e13	−0.267575	−0.133788	−	0.991010i	$-0.542714\pi$
$409$	−6.19333e13	−0.267575	−0.133788	+	0.991010i	$0.542714\pi$
$410$	9.81959e13	0.418584
$411$	1.73033e13	0.0727777
$412$	3.12617e13	0.129741
$413$	5.59869e14	2.29277
$414$	−1.79571e13	−0.0725663
$415$	−4.69075e14	−1.87059
$416$	−2.33031e14	−0.917065
$417$	3.66023e13	0.142154
$418$	2.80274e13	0.107427
$419$	−4.72697e14	−1.78816	−0.894079	−	0.447909i	$-0.852169\pi$
$419$	−4.72697e14	−1.78816	−0.894079	+	0.447909i	$0.852169\pi$
$420$	−1.38306e14	−0.516380
$421$	2.08288e14	0.767562	0.383781	−	0.923424i	$-0.374622\pi$
$421$	2.08288e14	0.767562	0.383781	+	0.923424i	$0.374622\pi$
$422$	8.97640e13	0.326500
$423$	2.04083e14	0.732715
$424$	1.99129e14	0.705705
$425$	−9.97655e13	−0.349013
$426$	3.49775e12	0.0120791
$427$	1.08438e14	0.369680
$428$	1.81560e14	0.611053
$429$	6.79243e13	0.225689
$430$	−1.30619e14	−0.428479
$431$	−4.49358e14	−1.45535	−0.727674	−	0.685923i	$-0.759399\pi$
$431$	−4.49358e14	−1.45535	−0.727674	+	0.685923i	$0.759399\pi$
$432$	1.21909e14	0.389831
$433$	3.75868e14	1.18673	0.593365	−	0.804934i	$-0.297799\pi$
$433$	3.75868e14	1.18673	0.593365	+	0.804934i	$0.297799\pi$
$434$	−6.51126e13	−0.202988
$435$	−5.03780e13	−0.155078
$436$	3.82936e14	1.16399
$437$	−1.24127e14	−0.372579
$438$	2.82617e13	0.0837704
$439$	−1.49875e14	−0.438706	−0.219353	−	0.975646i	$-0.570395\pi$
$439$	−1.49875e14	−0.438706	−0.219353	+	0.975646i	$0.570395\pi$
$440$	1.21950e14	0.352526
$441$	−4.45932e14	−1.27308
$442$	2.76359e13	0.0779204
$443$	−1.25445e14	−0.349328	−0.174664	−	0.984628i	$-0.555884\pi$
$443$	−1.25445e14	−0.349328	−0.174664	+	0.984628i	$0.555884\pi$
$444$	−1.69055e13	−0.0464968
$445$	−1.26785e14	−0.344419
$446$	−6.87005e13	−0.184339
$447$	6.51162e13	0.172583
$448$	−4.59530e14	−1.20305
$449$	6.11241e14	1.58073	0.790364	−	0.612637i	$-0.209891\pi$
$449$	6.11241e14	1.58073	0.790364	+	0.612637i	$0.209891\pi$
$450$	1.02509e14	0.261875
$451$	−3.32530e14	−0.839188
$452$	−1.10842e13	−0.0276341
$453$	−1.76213e14	−0.434009
$454$	−1.99680e13	−0.0485879
$455$	−1.66628e15	−4.00575
$456$	−3.32054e13	−0.0788681
$457$	1.60312e14	0.376207	0.188103	−	0.982149i	$-0.439766\pi$
$457$	1.60312e14	0.376207	0.188103	+	0.982149i	$0.439766\pi$
$458$	3.16168e13	0.0733091
$459$	−4.63078e13	−0.106092
$460$	−2.64993e14	−0.599883
$461$	2.88574e14	0.645509	0.322755	−	0.946483i	$-0.395391\pi$
$461$	2.88574e14	0.645509	0.322755	+	0.946483i	$0.395391\pi$
$462$	−1.78543e13	−0.0394650
$463$	3.89135e14	0.849972	0.424986	−	0.905200i	$-0.360279\pi$
$463$	3.89135e14	0.849972	0.424986	+	0.905200i	$0.360279\pi$
$464$	−1.82730e14	−0.394422
$465$	1.13737e14	0.242610
$466$	7.91119e13	0.166770
$467$	2.32200e13	0.0483748	0.0241874	−	0.999707i	$-0.492300\pi$
$467$	2.32200e13	0.0483748	0.0241874	+	0.999707i	$0.492300\pi$
$468$	7.44886e14	1.53369
$469$	−7.68026e13	−0.156288
$470$	−1.14808e14	−0.230904
$471$	1.73084e14	0.344066
$472$	2.86961e14	0.563822
$473$	4.42326e14	0.859026
$474$	−2.85578e12	−0.00548206
$475$	7.08585e14	1.34455
$476$	1.90557e14	0.357427
$477$	−9.60733e14	−1.78136
$478$	−2.76128e13	−0.0506124
$479$	−5.39756e14	−0.978029	−0.489015	−	0.872276i	$-0.662644\pi$
$479$	−5.39756e14	−0.978029	−0.489015	+	0.872276i	$0.662644\pi$
$480$	−1.06996e14	−0.191664
$481$	−2.03674e14	−0.360693
$482$	−1.42791e14	−0.250002
$483$	7.90726e13	0.136873
$484$	3.60239e14	0.616511
$485$	−6.16648e14	−1.04342
$486$	7.19862e13	0.120434
$487$	4.01906e14	0.664836	0.332418	−	0.943132i	$-0.392135\pi$
$487$	4.01906e14	0.664836	0.332418	+	0.943132i	$0.392135\pi$
$488$	5.55797e13	0.0909090
$489$	1.03688e14	0.167699
$490$	2.50860e14	0.401193
$491$	1.13071e15	1.78815	0.894075	−	0.447917i	$-0.147834\pi$
$491$	1.13071e15	1.78815	0.894075	+	0.447917i	$0.147834\pi$
$492$	1.93297e14	0.302286
$493$	6.94108e13	0.107342
$494$	−1.96284e14	−0.300183
$495$	−5.88367e14	−0.889856
$496$	4.12543e14	0.617049
$497$	2.90568e14	0.429821
$498$	3.51998e13	0.0514967
$499$	−3.11990e14	−0.451428	−0.225714	−	0.974194i	$-0.572471\pi$
$499$	−3.11990e14	−0.451428	−0.225714	+	0.974194i	$0.572471\pi$
$500$	4.61504e14	0.660451
$501$	1.89508e14	0.268238
$502$	−9.05185e13	−0.126726
$503$	9.38067e14	1.29900	0.649501	−	0.760361i	$-0.274978\pi$
$503$	9.38067e14	1.29900	0.649501	+	0.760361i	$0.274978\pi$
$504$	−3.99060e14	−0.546600
$505$	7.72259e14	1.04631
$506$	−3.42087e13	−0.0458468
$507$	−3.06457e14	−0.406280
$508$	−9.44984e14	−1.23929
$509$	−6.89691e14	−0.894761	−0.447381	−	0.894344i	$-0.647643\pi$
$509$	−6.89691e14	−0.894761	−0.447381	+	0.894344i	$0.647643\pi$
$510$	1.26890e13	0.0162851
$511$	2.34778e15	2.98087
$512$	−6.55020e14	−0.822754
$513$	3.28901e14	0.408715
$514$	−1.56715e14	−0.192670
$515$	1.72931e14	0.210345
$516$	−2.57121e14	−0.309432
$517$	3.88783e14	0.462924
$518$	5.35370e13	0.0630725
$519$	1.27423e14	0.148535
$520$	−8.54050e14	−0.985065
$521$	−1.14146e15	−1.30273	−0.651366	−	0.758764i	$-0.725804\pi$
$521$	−1.14146e15	−1.30273	−0.651366	+	0.758764i	$0.725804\pi$
$522$	−7.13195e13	−0.0805417
$523$	−1.82253e14	−0.203665	−0.101832	−	0.994802i	$-0.532471\pi$
$523$	−1.82253e14	−0.203665	−0.101832	+	0.994802i	$0.532471\pi$
$524$	−6.82910e14	−0.755164
$525$	−4.51390e14	−0.493942
$526$	1.70957e14	0.185125
$527$	−1.56706e14	−0.167930
$528$	1.13122e14	0.119967
$529$	−8.01307e14	−0.840994
$530$	5.40463e14	0.561369
$531$	−1.38449e15	−1.42321
$532$	−1.35344e15	−1.37697
$533$	2.32880e15	2.34495
$534$	9.51403e12	0.00948173
$535$	1.00434e15	0.990682
$536$	−3.93652e13	−0.0384331
$537$	−3.08384e14	−0.298012
$538$	4.81567e13	0.0460632
$539$	−8.49511e14	−0.804324
$540$	7.02157e14	0.658064
$541$	−7.64800e14	−0.709517	−0.354759	−	0.934958i	$-0.615437\pi$
$541$	−7.64800e14	−0.709517	−0.354759	+	0.934958i	$0.615437\pi$
$542$	−3.65095e14	−0.335282
$543$	−4.68359e13	−0.0425775
$544$	1.47419e14	0.132666
$545$	2.11830e15	1.88715
$546$	1.25039e14	0.110277
$547$	−1.46359e15	−1.27788	−0.638938	−	0.769258i	$-0.720626\pi$
$547$	−1.46359e15	−1.27788	−0.638938	+	0.769258i	$0.720626\pi$
$548$	3.61488e14	0.312464
$549$	−2.68153e14	−0.229475
$550$	1.95282e14	0.165451
$551$	−4.92990e14	−0.413528
$552$	4.05287e13	0.0336587
$553$	−2.37238e14	−0.195072
$554$	1.53752e14	0.125175
$555$	−9.35168e13	−0.0753838
$556$	7.64669e14	0.610327
$557$	6.86887e14	0.542852	0.271426	−	0.962459i	$-0.412505\pi$
$557$	6.86887e14	0.542852	0.271426	+	0.962459i	$0.412505\pi$
$558$	1.61016e14	0.126003
$559$	−3.09774e15	−2.40038
$560$	−2.77504e15	−2.12929
$561$	−4.29699e13	−0.0326489
$562$	−1.55596e14	−0.117071
$563$	−1.58767e15	−1.18294	−0.591470	−	0.806327i	$-0.701452\pi$
$563$	−1.58767e15	−1.18294	−0.591470	+	0.806327i	$0.701452\pi$
$564$	−2.25997e14	−0.166751
$565$	−6.13150e13	−0.0448023
$566$	−4.32501e13	−0.0312966
$567$	1.81786e15	1.30273
$568$	1.48931e14	0.105698
$569$	−1.30719e14	−0.0918804	−0.0459402	−	0.998944i	$-0.514628\pi$
$569$	−1.30719e14	−0.0918804	−0.0459402	+	0.998944i	$0.514628\pi$
$570$	−9.01236e13	−0.0627375
$571$	2.26420e15	1.56105	0.780525	−	0.625125i	$-0.214952\pi$
$571$	2.26420e15	1.56105	0.780525	+	0.625125i	$0.214952\pi$
$572$	1.41903e15	0.968974
$573$	−1.35010e14	−0.0913095
$574$	−6.12140e14	−0.410048
$575$	−8.64861e14	−0.573816
$576$	1.13636e15	0.746781
$577$	1.67031e15	1.08725	0.543626	−	0.839328i	$-0.317051\pi$
$577$	1.67031e15	1.08725	0.543626	+	0.839328i	$0.317051\pi$
$578$	−1.74829e13	−0.0112722
$579$	−1.78311e14	−0.113880
$580$	−1.05246e15	−0.665813
$581$	2.92415e15	1.83244
$582$	4.62738e13	0.0287249
$583$	−1.83022e15	−1.12545
$584$	1.20335e15	0.733032
$585$	4.12050e15	2.48653
$586$	−4.43384e14	−0.265059
$587$	−1.54986e15	−0.917875	−0.458937	−	0.888469i	$-0.651770\pi$
$587$	−1.54986e15	−0.917875	−0.458937	+	0.888469i	$0.651770\pi$
$588$	4.93815e14	0.289727
$589$	1.11301e15	0.646939
$590$	7.78849e14	0.448505
$591$	−5.39840e14	−0.307988
$592$	−3.39202e14	−0.191729
$593$	3.86552e14	0.216475	0.108237	−	0.994125i	$-0.465479\pi$
$593$	3.86552e14	0.216475	0.108237	+	0.994125i	$0.465479\pi$
$594$	9.06435e13	0.0502934
$595$	1.05411e15	0.579486
$596$	1.36036e15	0.740969
$597$	−1.95699e13	−0.0105616
$598$	2.39574e14	0.128110
$599$	−1.13540e15	−0.601591	−0.300795	−	0.953689i	$-0.597252\pi$
$599$	−1.13540e15	−0.601591	−0.300795	+	0.953689i	$0.597252\pi$
$600$	−2.31360e14	−0.121466
$601$	−1.46592e15	−0.762607	−0.381304	−	0.924450i	$-0.624525\pi$
$601$	−1.46592e15	−0.762607	−0.381304	+	0.924450i	$0.624525\pi$
$602$	8.14259e14	0.419742
$603$	1.89924e14	0.0970139
$604$	−3.68133e15	−1.86338
$605$	1.99274e15	0.999531
$606$	−5.79510e13	−0.0288046
$607$	2.06717e15	1.01821	0.509106	−	0.860704i	$-0.329976\pi$
$607$	2.06717e15	1.01821	0.509106	+	0.860704i	$0.329976\pi$
$608$	−1.04704e15	−0.511087
$609$	3.14050e14	0.151916
$610$	1.50850e14	0.0723157
$611$	−2.72276e15	−1.29355
$612$	−4.71226e14	−0.221869
$613$	−2.80126e15	−1.30714	−0.653568	−	0.756867i	$-0.726729\pi$
$613$	−2.80126e15	−1.30714	−0.653568	+	0.756867i	$0.726729\pi$
$614$	5.04095e14	0.233124
$615$	1.06927e15	0.490087
$616$	−7.60218e14	−0.345338
$617$	−1.47620e15	−0.664623	−0.332312	−	0.943170i	$-0.607829\pi$
$617$	−1.47620e15	−0.664623	−0.332312	+	0.943170i	$0.607829\pi$
$618$	−1.29769e13	−0.00579074
$619$	1.48450e14	0.0656571	0.0328286	−	0.999461i	$-0.489548\pi$
$619$	1.48450e14	0.0656571	0.0328286	+	0.999461i	$0.489548\pi$
$620$	2.37611e15	1.04163
$621$	−4.01439e14	−0.174428
$622$	−7.87459e14	−0.339141
$623$	7.90358e14	0.337396
$624$	−7.92226e14	−0.335223
$625$	−8.77969e14	−0.368247
$626$	5.92412e14	0.246300
$627$	3.05194e14	0.125778
$628$	3.61595e15	1.47722
$629$	1.28847e14	0.0521791
$630$	−1.08310e15	−0.434806
$631$	1.86133e15	0.740732	0.370366	−	0.928886i	$-0.379232\pi$
$631$	1.86133e15	0.740732	0.370366	+	0.928886i	$0.379232\pi$
$632$	−1.21596e14	−0.0479707
$633$	9.77451e14	0.382274
$634$	−5.39687e13	−0.0209243
$635$	−5.22739e15	−2.00923
$636$	1.06389e15	0.405400
$637$	5.94937e15	2.24752
$638$	−1.35865e14	−0.0508857
$639$	−7.18541e14	−0.266807
$640$	−2.95976e15	−1.08960
$641$	−2.97364e15	−1.08535	−0.542675	−	0.839943i	$-0.682588\pi$
$641$	−2.97364e15	−1.08535	−0.542675	+	0.839943i	$0.682588\pi$
$642$	−7.53664e13	−0.0272732
$643$	−5.19616e15	−1.86433	−0.932164	−	0.362035i	$-0.882082\pi$
$643$	−5.19616e15	−1.86433	−0.932164	+	0.362035i	$0.882082\pi$
$644$	1.65193e15	0.587651
$645$	−1.42232e15	−0.501672
$646$	1.24172e14	0.0434256
$647$	1.61082e15	0.558564	0.279282	−	0.960209i	$-0.409904\pi$
$647$	1.61082e15	0.558564	0.279282	+	0.960209i	$0.409904\pi$
$648$	9.31746e14	0.320358
$649$	−2.63749e15	−0.899176
$650$	−1.36762e15	−0.462319
$651$	−7.09019e14	−0.237663
$652$	2.16618e15	0.720001
$653$	4.17423e15	1.37579	0.687897	−	0.725808i	$-0.258534\pi$
$653$	4.17423e15	1.37579	0.687897	+	0.725808i	$0.258534\pi$
$654$	−1.58959e14	−0.0519526
$655$	−3.77767e15	−1.22432
$656$	3.87842e15	1.24648
$657$	−5.80578e15	−1.85034
$658$	7.15694e14	0.226196
$659$	−1.32973e15	−0.416769	−0.208384	−	0.978047i	$-0.566821\pi$
$659$	−1.32973e15	−0.416769	−0.208384	+	0.978047i	$0.566821\pi$
$660$	6.51545e14	0.202513
$661$	6.08983e14	0.187714	0.0938571	−	0.995586i	$-0.470080\pi$
$661$	6.08983e14	0.187714	0.0938571	+	0.995586i	$0.470080\pi$
$662$	−4.63062e13	−0.0141553
$663$	3.00931e14	0.0912309
$664$	1.49877e15	0.450621
$665$	−7.48683e15	−2.23244
$666$	−1.32391e14	−0.0391515
$667$	6.01717e14	0.176482
$668$	3.95907e15	1.15165
$669$	−7.48088e14	−0.215829
$670$	−1.06842e14	−0.0305725
$671$	−5.10838e14	−0.144981
$672$	6.66997e14	0.187756
$673$	−1.91567e15	−0.534857	−0.267429	−	0.963578i	$-0.586174\pi$
$673$	−1.91567e15	−0.534857	−0.267429	+	0.963578i	$0.586174\pi$
$674$	1.84174e14	0.0510035
$675$	2.29164e15	0.629470
$676$	−6.40228e15	−1.74433
$677$	−4.65062e15	−1.25682	−0.628410	−	0.777882i	$-0.716294\pi$
$677$	−4.65062e15	−1.25682	−0.628410	+	0.777882i	$0.716294\pi$
$678$	4.60113e12	0.00123339
$679$	3.84409e15	1.02214
$680$	5.40285e14	0.142503
$681$	−2.17434e14	−0.0568878
$682$	3.06739e14	0.0796076
$683$	5.68644e15	1.46395	0.731976	−	0.681331i	$-0.238598\pi$
$683$	5.68644e15	1.46395	0.731976	+	0.681331i	$0.238598\pi$
$684$	3.34688e15	0.854736
$685$	1.99965e15	0.506589
$686$	−3.97283e14	−0.0998430
$687$	3.44279e14	0.0858319
$688$	−5.15902e15	−1.27594
$689$	1.28175e16	3.14485
$690$	1.10000e14	0.0267746
$691$	5.64769e15	1.36377	0.681886	−	0.731459i	$-0.261160\pi$
$691$	5.64769e15	1.36377	0.681886	+	0.731459i	$0.261160\pi$
$692$	2.66204e15	0.637721
$693$	3.66780e15	0.871711
$694$	3.28203e14	0.0773866
$695$	4.22994e15	0.989505
$696$	1.60966e14	0.0373580
$697$	−1.47323e15	−0.339228
$698$	−8.43067e13	−0.0192600
$699$	8.61459e14	0.195258
$700$	−9.43012e15	−2.12069
$701$	−1.33898e15	−0.298763	−0.149381	−	0.988780i	$-0.547728\pi$
$701$	−1.33898e15	−0.298763	−0.149381	+	0.988780i	$0.547728\pi$
$702$	−6.34802e14	−0.140535
$703$	−9.15138e14	−0.201017
$704$	2.16480e15	0.471811
$705$	−1.25015e15	−0.270348
$706$	−1.31423e15	−0.281998
$707$	−4.81416e15	−1.02498
$708$	1.53315e15	0.323894
$709$	3.26019e14	0.0683422	0.0341711	−	0.999416i	$-0.489121\pi$
$709$	3.26019e14	0.0683422	0.0341711	+	0.999416i	$0.489121\pi$
$710$	4.04217e14	0.0840802
$711$	5.86661e14	0.121089
$712$	4.05098e14	0.0829698
$713$	−1.35848e15	−0.276096
$714$	−7.91014e13	−0.0159531
$715$	7.84966e15	1.57097
$716$	−6.44254e15	−1.27949
$717$	−3.00679e14	−0.0592582
$718$	−8.85891e14	−0.173259
$719$	−7.19294e15	−1.39604	−0.698020	−	0.716078i	$-0.745935\pi$
$719$	−7.19294e15	−1.39604	−0.698020	+	0.716078i	$0.745935\pi$
$720$	6.86235e15	1.32173
$721$	−1.07803e15	−0.206056
$722$	1.28280e14	0.0243336
$723$	−1.55487e15	−0.292708
$724$	−9.78463e14	−0.182803
$725$	−3.43493e15	−0.636882
$726$	−1.49537e14	−0.0275168
$727$	6.37766e15	1.16472	0.582361	−	0.812930i	$-0.302129\pi$
$727$	6.37766e15	1.16472	0.582361	+	0.812930i	$0.302129\pi$
$728$	5.32403e15	0.964978
$729$	−3.94978e15	−0.710512
$730$	3.26606e15	0.583107
$731$	1.95967e15	0.347247
$732$	2.96947e14	0.0522237
$733$	−5.23628e15	−0.914010	−0.457005	−	0.889464i	$-0.651078\pi$
$733$	−5.23628e15	−0.914010	−0.457005	+	0.889464i	$0.651078\pi$
$734$	1.00087e15	0.173400
$735$	2.73165e15	0.469726
$736$	1.27796e15	0.218117
$737$	3.61809e14	0.0612926
$738$	1.51375e15	0.254533
$739$	7.01803e15	1.17131	0.585654	−	0.810561i	$-0.300838\pi$
$739$	7.01803e15	1.17131	0.585654	+	0.810561i	$0.300838\pi$
$740$	−1.95369e15	−0.323654
$741$	−2.13736e15	−0.351461
$742$	−3.36917e15	−0.549923
$743$	2.81709e15	0.456418	0.228209	−	0.973612i	$-0.426713\pi$
$743$	2.81709e15	0.456418	0.228209	+	0.973612i	$0.426713\pi$
$744$	−3.63407e14	−0.0584444
$745$	7.52514e15	1.20131
$746$	−2.71159e14	−0.0429695
$747$	−7.23107e15	−1.13747
$748$	−8.97697e14	−0.140175
$749$	−6.26091e15	−0.970481
$750$	−1.91573e14	−0.0294779
$751$	1.16280e15	0.177617	0.0888087	−	0.996049i	$-0.471694\pi$
$751$	1.16280e15	0.177617	0.0888087	+	0.996049i	$0.471694\pi$
$752$	−4.53453e15	−0.687597
$753$	−9.85667e14	−0.148374
$754$	9.51505e14	0.142190
$755$	−2.03641e16	−3.02104
$756$	−4.37715e15	−0.644646
$757$	3.51009e15	0.513204	0.256602	−	0.966517i	$-0.417397\pi$
$757$	3.51009e15	0.513204	0.256602	+	0.966517i	$0.417397\pi$
$758$	−2.25858e14	−0.0327834
$759$	−3.72503e14	−0.0536785
$760$	−3.83737e15	−0.548984
$761$	−4.54596e15	−0.645669	−0.322835	−	0.946455i	$-0.604636\pi$
$761$	−4.54596e15	−0.645669	−0.322835	+	0.946455i	$0.604636\pi$
$762$	3.92268e14	0.0553134
$763$	−1.32052e16	−1.84867
$764$	−2.82054e15	−0.392029
$765$	−2.60669e15	−0.359709
$766$	9.21905e13	0.0126307
$767$	1.84711e16	2.51257
$768$	−1.08425e15	−0.146434
$769$	2.02708e15	0.271816	0.135908	−	0.990721i	$-0.456605\pi$
$769$	2.02708e15	0.271816	0.135908	+	0.990721i	$0.456605\pi$
$770$	−2.06333e15	−0.274707
$771$	−1.70649e15	−0.225582
$772$	−3.72516e15	−0.488933
$773$	−7.05136e15	−0.918936	−0.459468	−	0.888194i	$-0.651960\pi$
$773$	−7.05136e15	−0.918936	−0.459468	+	0.888194i	$0.651960\pi$
$774$	−2.01357e15	−0.260550
$775$	7.75492e15	0.996364
$776$	1.97029e15	0.251357
$777$	5.82970e14	0.0738467
$778$	2.24201e15	0.282000
$779$	1.04637e16	1.30685
$780$	−4.56295e15	−0.565882
$781$	−1.36884e15	−0.168566
$782$	−1.51558e14	−0.0185328
$783$	−1.59438e15	−0.193599
$784$	9.90817e15	1.19469
$785$	2.00024e16	2.39497
$786$	2.83480e14	0.0337053
$787$	6.94375e15	0.819847	0.409924	−	0.912120i	$-0.365555\pi$
$787$	6.94375e15	0.819847	0.409924	+	0.912120i	$0.365555\pi$
$788$	−1.12780e16	−1.32232
$789$	1.86157e15	0.216749
$790$	−3.30028e14	−0.0381594
$791$	3.82229e14	0.0438887
$792$	1.87993e15	0.214365
$793$	3.57755e15	0.405119
$794$	−1.92901e15	−0.216932
$795$	5.88517e15	0.657264
$796$	−4.08840e14	−0.0453453
$797$	3.30147e15	0.363652	0.181826	−	0.983331i	$-0.441799\pi$
$797$	3.30147e15	0.363652	0.181826	+	0.983331i	$0.441799\pi$
$798$	5.61818e14	0.0614582
$799$	1.72246e15	0.187129
$800$	−7.29532e15	−0.787135
$801$	−1.95446e15	−0.209434
$802$	−1.68963e14	−0.0179818
$803$	−1.10602e16	−1.16903
$804$	−2.10317e14	−0.0220783
$805$	9.13802e15	0.952741
$806$	−2.14818e15	−0.222448
$807$	5.24384e14	0.0539318
$808$	−2.46750e15	−0.252054
$809$	5.35601e15	0.543406	0.271703	−	0.962381i	$-0.412413\pi$
$809$	5.35601e15	0.543406	0.271703	+	0.962381i	$0.412413\pi$
$810$	2.52888e15	0.254836
$811$	4.16969e15	0.417339	0.208669	−	0.977986i	$-0.433087\pi$
$811$	4.16969e15	0.417339	0.208669	+	0.977986i	$0.433087\pi$
$812$	6.56090e15	0.652237
$813$	−3.97556e15	−0.392555
$814$	−2.52207e14	−0.0247356
$815$	1.19827e16	1.16732
$816$	5.01174e14	0.0484945
$817$	−1.39186e16	−1.33775
$818$	5.37091e14	0.0512749
$819$	−2.56866e16	−2.43582
$820$	2.23384e16	2.10414
$821$	5.91170e15	0.553128	0.276564	−	0.960996i	$-0.410804\pi$
$821$	5.91170e15	0.553128	0.276564	+	0.960996i	$0.410804\pi$
$822$	−1.50055e14	−0.0139462
$823$	−1.34575e15	−0.124241	−0.0621206	−	0.998069i	$-0.519786\pi$
$823$	−1.34575e15	−0.124241	−0.0621206	+	0.998069i	$0.519786\pi$
$824$	−5.52543e14	−0.0506718
$825$	2.12645e15	0.193713
$826$	−4.85524e15	−0.439360
$827$	6.94361e15	0.624173	0.312087	−	0.950054i	$-0.398972\pi$
$827$	6.94361e15	0.624173	0.312087	+	0.950054i	$0.398972\pi$
$828$	−4.08503e15	−0.364777
$829$	−9.98331e14	−0.0885573	−0.0442787	−	0.999019i	$-0.514099\pi$
$829$	−9.98331e14	−0.0885573	−0.0442787	+	0.999019i	$0.514099\pi$
$830$	4.06786e15	0.358457
$831$	1.67422e15	0.146557
$832$	−1.51607e16	−1.31838
$833$	−3.76366e15	−0.325134
$834$	−3.17418e14	−0.0272407
$835$	2.19005e16	1.86714
$836$	6.37590e15	0.540016
$837$	3.59957e15	0.302873
$838$	4.09927e15	0.342661
$839$	7.65231e15	0.635480	0.317740	−	0.948178i	$-0.397076\pi$
$839$	7.65231e15	0.635480	0.317740	+	0.948178i	$0.397076\pi$
$840$	2.44452e15	0.201678
$841$	−9.81069e15	−0.804122
$842$	−1.80630e15	−0.147086
$843$	−1.69430e15	−0.137069
$844$	2.04202e16	1.64126
$845$	−3.54156e16	−2.82802
$846$	−1.76983e15	−0.140409
$847$	−1.24225e16	−0.979149
$848$	2.13465e16	1.67167
$849$	−4.70955e14	−0.0366427
$850$	8.65176e14	0.0668806
$851$	1.11697e15	0.0857883
$852$	7.95696e14	0.0607197
$853$	−4.98132e15	−0.377681	−0.188840	−	0.982008i	$-0.560473\pi$
$853$	−4.98132e15	−0.377681	−0.188840	+	0.982008i	$0.560473\pi$
$854$	−9.40380e14	−0.0708411
$855$	1.85140e16	1.38576
$856$	−3.20903e15	−0.238653
$857$	−2.20500e16	−1.62935	−0.814674	−	0.579920i	$-0.803084\pi$
$857$	−2.20500e16	−1.62935	−0.814674	+	0.579920i	$0.803084\pi$
$858$	−5.89045e14	−0.0432482
$859$	1.54976e16	1.13058	0.565290	−	0.824892i	$-0.308764\pi$
$859$	1.54976e16	1.13058	0.565290	+	0.824892i	$0.308764\pi$
$860$	−2.97142e16	−2.15388
$861$	−6.66566e15	−0.480094
$862$	3.89687e15	0.278885
$863$	−5.56635e15	−0.395832	−0.197916	−	0.980219i	$-0.563417\pi$
$863$	−5.56635e15	−0.395832	−0.197916	+	0.980219i	$0.563417\pi$
$864$	−3.38624e15	−0.239272
$865$	1.47256e16	1.03392
$866$	−3.25956e15	−0.227410
$867$	−1.90373e14	−0.0131978
$868$	−1.48123e16	−1.02039
$869$	1.11760e15	0.0765031
$870$	4.36883e14	0.0297173
$871$	−2.53385e15	−0.171270
$872$	−6.76831e15	−0.454610
$873$	−9.50599e15	−0.634481
$874$	1.07644e15	0.0713965
$875$	−1.59145e16	−1.04894
$876$	6.42919e15	0.421099
$877$	−1.81367e16	−1.18049	−0.590243	−	0.807226i	$-0.700968\pi$
$877$	−1.81367e16	−1.18049	−0.590243	+	0.807226i	$0.700968\pi$
$878$	1.29973e15	0.0840683
$879$	−4.82806e15	−0.310337
$880$	1.30729e16	0.835062
$881$	−4.27606e15	−0.271441	−0.135721	−	0.990747i	$-0.543335\pi$
$881$	−4.27606e15	−0.271441	−0.135721	+	0.990747i	$0.543335\pi$
$882$	3.86716e15	0.243958
$883$	1.42386e16	0.892656	0.446328	−	0.894869i	$-0.352731\pi$
$883$	1.42386e16	0.892656	0.446328	+	0.894869i	$0.352731\pi$
$884$	6.28683e15	0.391692
$885$	8.48098e15	0.525119
$886$	1.08787e15	0.0669410
$887$	−1.20759e16	−0.738480	−0.369240	−	0.929334i	$-0.620382\pi$
$887$	−1.20759e16	−0.738480	−0.369240	+	0.929334i	$0.620382\pi$
$888$	2.98801e14	0.0181598
$889$	3.25868e16	1.96826
$890$	1.09949e15	0.0660002
$891$	−8.56377e15	−0.510902
$892$	−1.56285e16	−0.926641
$893$	−1.22338e16	−0.720904
$894$	−5.64693e14	−0.0330717
$895$	−3.56383e16	−2.07439
$896$	1.84507e16	1.06738
$897$	2.60875e15	0.149994
$898$	−5.30073e15	−0.302912
$899$	−5.39540e15	−0.306440
$900$	2.33196e16	1.31640
$901$	−8.10857e15	−0.454944
$902$	2.88373e15	0.160812
$903$	8.86657e15	0.491443
$904$	1.95911e14	0.0107928
$905$	−5.41259e15	−0.296372
$906$	1.52814e15	0.0831683
$907$	−2.25444e16	−1.21955	−0.609774	−	0.792576i	$-0.708740\pi$
$907$	−2.25444e16	−1.21955	−0.609774	+	0.792576i	$0.708740\pi$
$908$	−4.54248e15	−0.244243
$909$	1.19048e16	0.636242
$910$	1.44501e16	0.767614
$911$	2.07851e16	1.09749	0.548745	−	0.835990i	$-0.315106\pi$
$911$	2.07851e16	1.09749	0.548745	+	0.835990i	$0.315106\pi$
$912$	−3.55959e15	−0.186822
$913$	−1.37754e16	−0.718644
$914$	−1.39024e15	−0.0720917
$915$	1.64263e15	0.0846688
$916$	7.19244e15	0.368511
$917$	2.35495e16	1.19936
$918$	4.01585e14	0.0203303
$919$	7.50380e15	0.377612	0.188806	−	0.982014i	$-0.439538\pi$
$919$	7.50380e15	0.377612	0.188806	+	0.982014i	$0.439538\pi$
$920$	4.68369e15	0.234291
$921$	5.48915e15	0.272946
$922$	−2.50254e15	−0.123698
$923$	9.58636e15	0.471025
$924$	−4.06164e15	−0.198383
$925$	−6.37627e15	−0.309590
$926$	−3.37461e15	−0.162878
$927$	2.66583e15	0.127907
$928$	5.07563e15	0.242090
$929$	4.79045e15	0.227138	0.113569	−	0.993530i	$-0.463772\pi$
$929$	4.79045e15	0.227138	0.113569	+	0.993530i	$0.463772\pi$
$930$	−9.86335e14	−0.0464909
$931$	2.67314e16	1.25256
$932$	1.79970e16	0.838325
$933$	−8.57474e15	−0.397074
$934$	−2.01366e14	−0.00926997
$935$	−4.96581e15	−0.227262
$936$	−1.31657e16	−0.598999
$937$	−9.82331e15	−0.444314	−0.222157	−	0.975011i	$-0.571310\pi$
$937$	−9.82331e15	−0.444314	−0.222157	+	0.975011i	$0.571310\pi$
$938$	6.66039e14	0.0299491
$939$	6.45084e15	0.288374
$940$	−2.61173e16	−1.16071
$941$	−9.13679e15	−0.403693	−0.201846	−	0.979417i	$-0.564694\pi$
$941$	−9.13679e15	−0.403693	−0.201846	+	0.979417i	$0.564694\pi$
$942$	−1.50100e15	−0.0659326
$943$	−1.27714e16	−0.557729
$944$	3.07620e16	1.33558
$945$	−2.42132e16	−1.04515
$946$	−3.83589e15	−0.164613
$947$	2.38178e16	1.01620	0.508098	−	0.861299i	$-0.330349\pi$
$947$	2.38178e16	1.01620	0.508098	+	0.861299i	$0.330349\pi$
$948$	−6.49655e14	−0.0275573
$949$	7.74574e16	3.26662
$950$	−6.14491e15	−0.257653
$951$	−5.87672e14	−0.0244987
$952$	−3.36806e15	−0.139597
$953$	6.63692e15	0.273499	0.136749	−	0.990606i	$-0.456334\pi$
$953$	6.63692e15	0.273499	0.136749	+	0.990606i	$0.456334\pi$
$954$	8.33156e15	0.341358
$955$	−1.56024e16	−0.635585
$956$	−6.28158e15	−0.254420
$957$	−1.47946e15	−0.0595780
$958$	4.68081e15	0.187418
$959$	−1.24655e16	−0.496259
$960$	−6.96102e15	−0.275538
$961$	−1.32275e16	−0.520593
$962$	1.76628e15	0.0691188
$963$	1.54825e16	0.602415
$964$	−3.24833e16	−1.25671
$965$	−2.06065e16	−0.792692
$966$	−6.85725e14	−0.0262286
$967$	1.80800e16	0.687625	0.343813	−	0.939038i	$-0.388282\pi$
$967$	1.80800e16	0.687625	0.343813	+	0.939038i	$0.388282\pi$
$968$	−6.36713e15	−0.240785
$969$	1.35213e15	0.0508436
$970$	5.34762e15	0.199948
$971$	2.09753e16	0.779836	0.389918	−	0.920850i	$-0.372503\pi$
$971$	2.09753e16	0.779836	0.389918	+	0.920850i	$0.372503\pi$
$972$	1.63760e16	0.605400
$973$	−2.63689e16	−0.969328
$974$	−3.48536e15	−0.127401
$975$	−1.48922e16	−0.541293
$976$	5.95810e15	0.215345
$977$	1.25390e16	0.450652	0.225326	−	0.974283i	$-0.427655\pi$
$977$	1.25390e16	0.450652	0.225326	+	0.974283i	$0.427655\pi$
$978$	−8.99193e14	−0.0321358
$979$	−3.72329e15	−0.132319
$980$	5.70677e16	2.01673
$981$	3.26548e16	1.14754
$982$	−9.80564e15	−0.342660
$983$	6.18279e15	0.214852	0.107426	−	0.994213i	$-0.465739\pi$
$983$	6.18279e15	0.214852	0.107426	+	0.994213i	$0.465739\pi$
$984$	−3.41648e15	−0.118061
$985$	−6.23866e16	−2.14384
$986$	−6.01936e14	−0.0205697
$987$	7.79328e15	0.264835
$988$	−4.46522e16	−1.50897
$989$	1.69883e16	0.570913
$990$	5.10237e15	0.170521
$991$	−5.43000e16	−1.80466	−0.902329	−	0.431048i	$-0.858144\pi$
$991$	−5.43000e16	−1.80466	−0.902329	+	0.431048i	$0.858144\pi$
$992$	−1.14591e16	−0.378735
$993$	−5.04234e14	−0.0165734
$994$	−2.51983e15	−0.0823658
$995$	−2.26159e15	−0.0735169
$996$	8.00753e15	0.258864
$997$	1.36970e15	0.0440355	0.0220178	−	0.999758i	$-0.492991\pi$
$997$	1.36970e15	0.0440355	0.0220178	+	0.999758i	$0.492991\pi$
$998$	2.70561e15	0.0865062
$999$	−2.95965e15	−0.0941087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.a.b.1.3	✓	8
3.2	odd	2		153.12.a.d.1.6		8
4.3	odd	2		272.12.a.h.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.a.b.1.3	✓	8	1.1	even	1	trivial
153.12.a.d.1.6		8	3.2	odd	2
272.12.a.h.1.5		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-8.67209 q^{2} -94.4314 q^{3} -1972.79 q^{4} -10913.0 q^{5} +818.918 q^{6} +68029.8 q^{7} +34868.7 q^{8} -168230. q^{9} +O(q^{10})\)	\(q-8.67209 q^{2} -94.4314 q^{3} -1972.79 q^{4} -10913.0 q^{5} +818.918 q^{6} +68029.8 q^{7} +34868.7 q^{8} -168230. q^{9} +94638.1 q^{10} -320482. q^{11} +186294. q^{12} +2.24443e6 q^{13} -589961. q^{14} +1.03053e6 q^{15} +3.73790e6 q^{16} -1.41986e6 q^{17} +1.45890e6 q^{18} +1.00845e7 q^{19} +2.15290e7 q^{20} -6.42416e6 q^{21} +2.77925e6 q^{22} -1.23086e7 q^{23} -3.29270e6 q^{24} +7.02645e7 q^{25} -1.94639e7 q^{26} +3.26144e7 q^{27} -1.34209e8 q^{28} -4.88857e7 q^{29} -8.93681e6 q^{30} +1.10368e8 q^{31} -1.03826e8 q^{32} +3.02635e7 q^{33} +1.23131e7 q^{34} -7.42407e8 q^{35} +3.31883e8 q^{36} -9.07466e7 q^{37} -8.74540e7 q^{38} -2.11944e8 q^{39} -3.80521e8 q^{40} +1.03759e9 q^{41} +5.57108e7 q^{42} -1.38019e9 q^{43} +6.32245e8 q^{44} +1.83588e9 q^{45} +1.06742e8 q^{46} -1.21312e9 q^{47} -3.52975e8 q^{48} +2.65073e9 q^{49} -6.09340e8 q^{50} +1.34079e8 q^{51} -4.42779e9 q^{52} +5.71084e9 q^{53} -2.82835e8 q^{54} +3.49740e9 q^{55} +2.37211e9 q^{56} -9.52297e8 q^{57} +4.23941e8 q^{58} +8.22976e9 q^{59} -2.03302e9 q^{60} +1.59397e9 q^{61} -9.57118e8 q^{62} -1.14446e10 q^{63} -6.75483e9 q^{64} -2.44933e10 q^{65} -2.62448e8 q^{66} -1.12895e9 q^{67} +2.80109e9 q^{68} +1.16232e9 q^{69} +6.43822e9 q^{70} +4.27119e9 q^{71} -5.86595e9 q^{72} +3.45110e10 q^{73} +7.86963e8 q^{74} -6.63518e9 q^{75} -1.98947e10 q^{76} -2.18023e10 q^{77} +1.83800e9 q^{78} -3.48726e9 q^{79} -4.07915e10 q^{80} +2.67216e10 q^{81} -8.99810e9 q^{82} +4.29833e10 q^{83} +1.26735e10 q^{84} +1.54948e10 q^{85} +1.19691e10 q^{86} +4.61635e9 q^{87} -1.11748e10 q^{88} +1.16178e10 q^{89} -1.59209e10 q^{90} +1.52688e11 q^{91} +2.42824e10 q^{92} -1.04222e10 q^{93} +1.05203e10 q^{94} -1.10052e11 q^{95} +9.80448e9 q^{96} +5.65060e10 q^{97} -2.29874e10 q^{98} +5.39145e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9}+O(q^{10}) \) 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9} + 2824 q^{10} + 435256 q^{11} + 4295182 q^{12} + 4193784 q^{13} + 4377132 q^{14} + 10362648 q^{15} + 20722897 q^{16} - 11358856 q^{17} + 28881887 q^{18} + 15158192 q^{19} + 91612472 q^{20} + 98415768 q^{21} + 81767186 q^{22} + 22374432 q^{23} - 41056218 q^{24} + 133926472 q^{25} - 70553178 q^{26} + 68932744 q^{27} + 108010892 q^{28} - 424656432 q^{29} - 561465200 q^{30} - 172323152 q^{31} - 540258159 q^{32} - 764794592 q^{33} - 78092135 q^{34} - 117251352 q^{35} - 1812061939 q^{36} - 262792640 q^{37} - 674758596 q^{38} - 302706728 q^{39} - 3575120264 q^{40} - 1283308512 q^{41} - 1036128840 q^{42} + 2219398472 q^{43} + 4256110614 q^{44} + 3982117536 q^{45} + 6081288184 q^{46} + 260684408 q^{47} + 6860204310 q^{48} + 12060045320 q^{49} - 1911832923 q^{50} - 704249072 q^{51} + 3548505010 q^{52} + 9402026896 q^{53} - 848951924 q^{54} + 4430702936 q^{55} - 11881582644 q^{56} + 1366983408 q^{57} + 814919720 q^{58} + 14325543480 q^{59} + 4281784208 q^{60} - 9811064576 q^{61} - 41469249572 q^{62} + 14666072688 q^{63} - 27038375199 q^{64} + 29701570288 q^{65} - 43330462276 q^{66} + 52928023248 q^{67} - 15273401749 q^{68} - 13481294472 q^{69} - 128492187744 q^{70} - 34868356504 q^{71} - 52662987279 q^{72} + 1248764080 q^{73} - 135359144436 q^{74} + 59235735072 q^{75} - 49428813052 q^{76} + 112631449800 q^{77} - 87670698684 q^{78} + 18209008736 q^{79} + 96412241400 q^{80} + 67350111224 q^{81} + 41461375370 q^{82} + 169643760088 q^{83} + 117131104968 q^{84} - 12199411344 q^{85} + 88510231200 q^{86} + 35491052136 q^{87} - 51404280146 q^{88} + 201694397904 q^{89} - 4670596888 q^{90} + 36284010568 q^{91} - 3754023808 q^{92} + 106318637912 q^{93} + 253870878768 q^{94} - 383491632 q^{95} - 102115750890 q^{96} + 163430440672 q^{97} - 110963034673 q^{98} - 716459488 q^{99}+O(q^{100}) \) 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9 + 2824 * q^10 + 435256 * q^11 + 4295182 * q^12 + 4193784 * q^13 + 4377132 * q^14 + 10362648 * q^15 + 20722897 * q^16 - 11358856 * q^17 + 28881887 * q^18 + 15158192 * q^19 + 91612472 * q^20 + 98415768 * q^21 + 81767186 * q^22 + 22374432 * q^23 - 41056218 * q^24 + 133926472 * q^25 - 70553178 * q^26 + 68932744 * q^27 + 108010892 * q^28 - 424656432 * q^29 - 561465200 * q^30 - 172323152 * q^31 - 540258159 * q^32 - 764794592 * q^33 - 78092135 * q^34 - 117251352 * q^35 - 1812061939 * q^36 - 262792640 * q^37 - 674758596 * q^38 - 302706728 * q^39 - 3575120264 * q^40 - 1283308512 * q^41 - 1036128840 * q^42 + 2219398472 * q^43 + 4256110614 * q^44 + 3982117536 * q^45 + 6081288184 * q^46 + 260684408 * q^47 + 6860204310 * q^48 + 12060045320 * q^49 - 1911832923 * q^50 - 704249072 * q^51 + 3548505010 * q^52 + 9402026896 * q^53 - 848951924 * q^54 + 4430702936 * q^55 - 11881582644 * q^56 + 1366983408 * q^57 + 814919720 * q^58 + 14325543480 * q^59 + 4281784208 * q^60 - 9811064576 * q^61 - 41469249572 * q^62 + 14666072688 * q^63 - 27038375199 * q^64 + 29701570288 * q^65 - 43330462276 * q^66 + 52928023248 * q^67 - 15273401749 * q^68 - 13481294472 * q^69 - 128492187744 * q^70 - 34868356504 * q^71 - 52662987279 * q^72 + 1248764080 * q^73 - 135359144436 * q^74 + 59235735072 * q^75 - 49428813052 * q^76 + 112631449800 * q^77 - 87670698684 * q^78 + 18209008736 * q^79 + 96412241400 * q^80 + 67350111224 * q^81 + 41461375370 * q^82 + 169643760088 * q^83 + 117131104968 * q^84 - 12199411344 * q^85 + 88510231200 * q^86 + 35491052136 * q^87 - 51404280146 * q^88 + 201694397904 * q^89 - 4670596888 * q^90 + 36284010568 * q^91 - 3754023808 * q^92 + 106318637912 * q^93 + 253870878768 * q^94 - 383491632 * q^95 - 102115750890 * q^96 + 163430440672 * q^97 - 110963034673 * q^98 - 716459488 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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