LMFDB - Embedded newform 17.12.a.a.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:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 8440x^{4} - 21100x^{3} + 19034528x^{2} + 24205632x - 12354600960 $ x^6 - 3x^5 - 8440x^4 - 21100x^3 + 19034528x^2 + 24205632*x - 12354600960
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			$-33.8139$ 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)

$f(q)$	$=$	$q-35.8139 q^{2} -519.883 q^{3} -765.364 q^{4} +12105.2 q^{5} +18619.1 q^{6} +7435.72 q^{7} +100758. q^{8} +93131.8 q^{9} +O(q^{10})$	\(q-35.8139 q^{2} -519.883 q^{3} -765.364 q^{4} +12105.2 q^{5} +18619.1 q^{6} +7435.72 q^{7} +100758. q^{8} +93131.8 q^{9} -433535. q^{10} -781301. q^{11} +397900. q^{12} +1.71791e6 q^{13} -266302. q^{14} -6.29330e6 q^{15} -2.04106e6 q^{16} +1.41986e6 q^{17} -3.33541e6 q^{18} -1.35548e7 q^{19} -9.26490e6 q^{20} -3.86571e6 q^{21} +2.79814e7 q^{22} -4.17860e7 q^{23} -5.23822e7 q^{24} +9.77083e7 q^{25} -6.15251e7 q^{26} +4.36781e7 q^{27} -5.69103e6 q^{28} -2.26029e6 q^{29} +2.25388e8 q^{30} -1.62502e7 q^{31} -1.33253e8 q^{32} +4.06185e8 q^{33} -5.08506e7 q^{34} +9.00111e7 q^{35} -7.12797e7 q^{36} -5.95893e8 q^{37} +4.85452e8 q^{38} -8.93113e8 q^{39} +1.21969e9 q^{40} -8.14451e8 q^{41} +1.38446e8 q^{42} +2.54294e8 q^{43} +5.97979e8 q^{44} +1.12738e9 q^{45} +1.49652e9 q^{46} -7.46370e8 q^{47} +1.06111e9 q^{48} -1.92204e9 q^{49} -3.49932e9 q^{50} -7.38160e8 q^{51} -1.31483e9 q^{52} -2.08577e9 q^{53} -1.56428e9 q^{54} -9.45782e9 q^{55} +7.49205e8 q^{56} +7.04694e9 q^{57} +8.09497e7 q^{58} +8.05831e8 q^{59} +4.81667e9 q^{60} -1.63884e9 q^{61} +5.81982e8 q^{62} +6.92502e8 q^{63} +8.95241e9 q^{64} +2.07957e10 q^{65} -1.45471e10 q^{66} -1.24685e10 q^{67} -1.08671e9 q^{68} +2.17239e10 q^{69} -3.22365e9 q^{70} +2.71187e10 q^{71} +9.38373e9 q^{72} -1.65791e10 q^{73} +2.13413e10 q^{74} -5.07969e10 q^{75} +1.03744e10 q^{76} -5.80954e9 q^{77} +3.19859e10 q^{78} -1.56714e10 q^{79} -2.47075e10 q^{80} -3.92055e10 q^{81} +2.91687e10 q^{82} -2.55794e10 q^{83} +2.95867e9 q^{84} +1.71877e10 q^{85} -9.10728e9 q^{86} +1.17509e9 q^{87} -7.87220e10 q^{88} +7.98375e10 q^{89} -4.03759e10 q^{90} +1.27739e10 q^{91} +3.19815e10 q^{92} +8.44819e9 q^{93} +2.67304e10 q^{94} -1.64084e11 q^{95} +6.92762e10 q^{96} -2.04506e10 q^{97} +6.88357e10 q^{98} -7.27639e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9}+O(q^{10}) $ 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9} - 676038 q^{10} - 962060 q^{11} - 2352344 q^{12} - 435268 q^{13} - 7990948 q^{14} - 9450288 q^{15} - 12496671 q^{16} + 8519142 q^{17} - 20195421 q^{18} - 26398480 q^{19} - 47202914 q^{20} - 56428792 q^{21} - 51774200 q^{22} - 99172772 q^{23} - 110557128 q^{24} + 66085866 q^{25} + 74451914 q^{26} + 105183712 q^{27} + 102848900 q^{28} + 165683964 q^{29} + 401475744 q^{30} - 199133468 q^{31} + 465766501 q^{32} + 518429376 q^{33} - 12778713 q^{34} + 804442912 q^{35} + 627274777 q^{36} - 785778644 q^{37} + 2174484940 q^{38} + 627357728 q^{39} + 657666206 q^{40} + 166444428 q^{41} + 652753248 q^{42} - 1110947880 q^{43} - 997577064 q^{44} - 1706447988 q^{45} - 1891667412 q^{46} - 5828211928 q^{47} - 2359114472 q^{48} - 1968801674 q^{49} - 126509183 q^{50} - 675851932 q^{51} - 6633403554 q^{52} - 9889898636 q^{53} - 1961072736 q^{54} - 10730153984 q^{55} + 5703448884 q^{56} - 13522850128 q^{57} + 14316796258 q^{58} + 204095112 q^{59} + 22313648592 q^{60} - 15864546948 q^{61} - 1838602020 q^{62} + 504344540 q^{63} + 6177095465 q^{64} + 12794774792 q^{65} + 56255165136 q^{66} + 17196640232 q^{67} + 6549800341 q^{68} + 2949266904 q^{69} + 52391765944 q^{70} + 8751653884 q^{71} + 38682669705 q^{72} - 13704156916 q^{73} - 9383651494 q^{74} - 15917467268 q^{75} + 59548672452 q^{76} - 12012382872 q^{77} + 35038956192 q^{78} - 89923384436 q^{79} + 25877503334 q^{80} - 152313828506 q^{81} + 57834669670 q^{82} - 26042106648 q^{83} + 3397466240 q^{84} - 18293437588 q^{85} + 29108045060 q^{86} - 195382431072 q^{87} - 228837945880 q^{88} + 53269579420 q^{89} - 10044062046 q^{90} - 226028668544 q^{91} - 9212077436 q^{92} - 62709484936 q^{93} + 83948222448 q^{94} - 170219637424 q^{95} + 116885663928 q^{96} - 106272517044 q^{97} + 132039821039 q^{98} - 10550584980 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9 - 676038 * q^10 - 962060 * q^11 - 2352344 * q^12 - 435268 * q^13 - 7990948 * q^14 - 9450288 * q^15 - 12496671 * q^16 + 8519142 * q^17 - 20195421 * q^18 - 26398480 * q^19 - 47202914 * q^20 - 56428792 * q^21 - 51774200 * q^22 - 99172772 * q^23 - 110557128 * q^24 + 66085866 * q^25 + 74451914 * q^26 + 105183712 * q^27 + 102848900 * q^28 + 165683964 * q^29 + 401475744 * q^30 - 199133468 * q^31 + 465766501 * q^32 + 518429376 * q^33 - 12778713 * q^34 + 804442912 * q^35 + 627274777 * q^36 - 785778644 * q^37 + 2174484940 * q^38 + 627357728 * q^39 + 657666206 * q^40 + 166444428 * q^41 + 652753248 * q^42 - 1110947880 * q^43 - 997577064 * q^44 - 1706447988 * q^45 - 1891667412 * q^46 - 5828211928 * q^47 - 2359114472 * q^48 - 1968801674 * q^49 - 126509183 * q^50 - 675851932 * q^51 - 6633403554 * q^52 - 9889898636 * q^53 - 1961072736 * q^54 - 10730153984 * q^55 + 5703448884 * q^56 - 13522850128 * q^57 + 14316796258 * q^58 + 204095112 * q^59 + 22313648592 * q^60 - 15864546948 * q^61 - 1838602020 * q^62 + 504344540 * q^63 + 6177095465 * q^64 + 12794774792 * q^65 + 56255165136 * q^66 + 17196640232 * q^67 + 6549800341 * q^68 + 2949266904 * q^69 + 52391765944 * q^70 + 8751653884 * q^71 + 38682669705 * q^72 - 13704156916 * q^73 - 9383651494 * q^74 - 15917467268 * q^75 + 59548672452 * q^76 - 12012382872 * q^77 + 35038956192 * q^78 - 89923384436 * q^79 + 25877503334 * q^80 - 152313828506 * q^81 + 57834669670 * q^82 - 26042106648 * q^83 + 3397466240 * q^84 - 18293437588 * q^85 + 29108045060 * q^86 - 195382431072 * q^87 - 228837945880 * q^88 + 53269579420 * q^89 - 10044062046 * q^90 - 226028668544 * q^91 - 9212077436 * q^92 - 62709484936 * q^93 + 83948222448 * q^94 - 170219637424 * q^95 + 116885663928 * q^96 - 106272517044 * q^97 + 132039821039 * q^98 - 10550584980 * 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 $

$2$	−35.8139	−0.791383	−0.395692	−	0.918383i	$-0.629495\pi$
$2$	−35.8139	−0.791383	−0.395692	+	0.918383i	$0.629495\pi$
$3$	−519.883	−1.23521	−0.617603	−	0.786490i	$-0.711896\pi$
$3$	−519.883	−1.23521	−0.617603	+	0.786490i	$0.711896\pi$
$4$	−765.364	−0.373713
$5$	12105.2	1.73236	0.866179	−	0.499733i	$-0.166569\pi$
$5$	12105.2	1.73236	0.866179	+	0.499733i	$0.166569\pi$
$6$	18619.1	0.977521
$7$	7435.72	0.167218	0.0836092	−	0.996499i	$-0.473355\pi$
$7$	7435.72	0.167218	0.0836092	+	0.996499i	$0.473355\pi$
$8$	100758.	1.08713
$9$	93131.8	0.525732
$10$	−433535.	−1.37096
$11$	−781301.	−1.46271	−0.731355	−	0.681997i	$-0.761112\pi$
$11$	−781301.	−1.46271	−0.731355	+	0.681997i	$0.761112\pi$
$12$	397900.	0.461612
$13$	1.71791e6	1.28325	0.641626	−	0.767018i	$-0.278260\pi$
$13$	1.71791e6	1.28325	0.641626	+	0.767018i	$0.278260\pi$
$14$	−266302.	−0.132334
$15$	−6.29330e6	−2.13982
$16$	−2.04106e6	−0.486626
$17$	1.41986e6	0.242536
$17$	1.41986e6	0.242536
$18$	−3.33541e6	−0.416055
$19$	−1.35548e7	−1.25588	−0.627942	−	0.778260i	$-0.716102\pi$
$19$	−1.35548e7	−1.25588	−0.627942	+	0.778260i	$0.716102\pi$
$20$	−9.26490e6	−0.647404
$21$	−3.86571e6	−0.206549
$22$	2.79814e7	1.15756
$23$	−4.17860e7	−1.35372	−0.676858	−	0.736113i	$-0.736659\pi$
$23$	−4.17860e7	−1.35372	−0.676858	+	0.736113i	$0.736659\pi$
$24$	−5.23822e7	−1.34283
$25$	9.77083e7	2.00107
$26$	−6.15251e7	−1.01554
$27$	4.36781e7	0.585819
$28$	−5.69103e6	−0.0624916
$29$	−2.26029e6	−0.0204633	−0.0102316	−	0.999948i	$-0.503257\pi$
$29$	−2.26029e6	−0.0204633	−0.0102316	+	0.999948i	$0.503257\pi$
$30$	2.25388e8	1.69342
$31$	−1.62502e7	−0.101946	−0.0509728	−	0.998700i	$-0.516232\pi$
$31$	−1.62502e7	−0.101946	−0.0509728	+	0.998700i	$0.516232\pi$
$32$	−1.33253e8	−0.702025
$33$	4.06185e8	1.80675
$34$	−5.08506e7	−0.191939
$35$	9.00111e7	0.289682
$36$	−7.12797e7	−0.196473
$37$	−5.95893e8	−1.41273	−0.706364	−	0.707848i	$-0.749666\pi$
$37$	−5.95893e8	−1.41273	−0.706364	+	0.707848i	$0.749666\pi$
$38$	4.85452e8	0.993885
$39$	−8.93113e8	−1.58508
$40$	1.21969e9	1.88330
$41$	−8.14451e8	−1.09788	−0.548938	−	0.835863i	$-0.684968\pi$
$41$	−8.14451e8	−1.09788	−0.548938	+	0.835863i	$0.684968\pi$
$42$	1.38446e8	0.163459
$43$	2.54294e8	0.263791	0.131896	−	0.991264i	$-0.457894\pi$
$43$	2.54294e8	0.263791	0.131896	+	0.991264i	$0.457894\pi$
$44$	5.97979e8	0.546634
$45$	1.12738e9	0.910756
$46$	1.49652e9	1.07131
$47$	−7.46370e8	−0.474696	−0.237348	−	0.971425i	$-0.576278\pi$
$47$	−7.46370e8	−0.474696	−0.237348	+	0.971425i	$0.576278\pi$
$48$	1.06111e9	0.601083
$49$	−1.92204e9	−0.972038
$50$	−3.49932e9	−1.58361
$51$	−7.38160e8	−0.299581
$52$	−1.31483e9	−0.479568
$53$	−2.08577e9	−0.685091	−0.342546	−	0.939501i	$-0.611289\pi$
$53$	−2.08577e9	−0.685091	−0.342546	+	0.939501i	$0.611289\pi$
$54$	−1.56428e9	−0.463607
$55$	−9.45782e9	−2.53394
$56$	7.49205e8	0.181789
$57$	7.04694e9	1.55127
$58$	8.09497e7	0.0161943
$59$	8.05831e8	0.146743	0.0733716	−	0.997305i	$-0.476624\pi$
$59$	8.05831e8	0.146743	0.0733716	+	0.997305i	$0.476624\pi$
$60$	4.81667e9	0.799677
$61$	−1.63884e9	−0.248441	−0.124220	−	0.992255i	$-0.539643\pi$
$61$	−1.63884e9	−0.248441	−0.124220	+	0.992255i	$0.539643\pi$
$62$	5.81982e8	0.0806780
$63$	6.92502e8	0.0879120
$64$	8.95241e9	1.04220
$65$	2.07957e10	2.22305
$66$	−1.45471e10	−1.42983
$67$	−1.24685e10	−1.12825	−0.564123	−	0.825690i	$-0.690786\pi$
$67$	−1.24685e10	−1.12825	−0.564123	+	0.825690i	$0.690786\pi$
$68$	−1.08671e9	−0.0906387
$69$	2.17239e10	1.67212
$70$	−3.22365e9	−0.229250
$71$	2.71187e10	1.78381	0.891905	−	0.452224i	$-0.149369\pi$
$71$	2.71187e10	1.78381	0.891905	+	0.452224i	$0.149369\pi$
$72$	9.38373e9	0.571540
$73$	−1.65791e10	−0.936022	−0.468011	−	0.883723i	$-0.655029\pi$
$73$	−1.65791e10	−0.936022	−0.468011	+	0.883723i	$0.655029\pi$
$74$	2.13413e10	1.11801
$75$	−5.07969e10	−2.47173
$76$	1.03744e10	0.469340
$77$	−5.80954e9	−0.244592
$78$	3.19859e10	1.25440
$79$	−1.56714e10	−0.573005	−0.286503	−	0.958079i	$-0.592493\pi$
$79$	−1.56714e10	−0.573005	−0.286503	+	0.958079i	$0.592493\pi$
$80$	−2.47075e10	−0.843011
$81$	−3.92055e10	−1.24934
$82$	2.91687e10	0.868841
$83$	−2.55794e10	−0.712790	−0.356395	−	0.934335i	$-0.615994\pi$
$83$	−2.55794e10	−0.712790	−0.356395	+	0.934335i	$0.615994\pi$
$84$	2.95867e9	0.0771900
$85$	1.71877e10	0.420159
$86$	−9.10728e9	−0.208760
$87$	1.17509e9	0.0252763
$88$	−7.87220e10	−1.59016
$89$	7.98375e10	1.51552	0.757760	−	0.652533i	$-0.226294\pi$
$89$	7.98375e10	1.51552	0.757760	+	0.652533i	$0.226294\pi$
$90$	−4.03759e10	−0.720757
$91$	1.27739e10	0.214583
$92$	3.19815e10	0.505901
$93$	8.44819e9	0.125924
$94$	2.67304e10	0.375667
$95$	−1.64084e11	−2.17564
$96$	6.92762e10	0.867145
$97$	−2.04506e10	−0.241802	−0.120901	−	0.992665i	$-0.538578\pi$
$97$	−2.04506e10	−0.241802	−0.120901	+	0.992665i	$0.538578\pi$
$98$	6.88357e10	0.769254
$99$	−7.27639e10	−0.768994
$100$	−7.47824e10	−0.747824
$101$	−1.60110e11	−1.51583	−0.757917	−	0.652350i	$-0.773783\pi$
$101$	−1.60110e11	−1.51583	−0.757917	+	0.652350i	$0.773783\pi$
$102$	2.64364e10	0.237084
$103$	2.39387e10	0.203468	0.101734	−	0.994812i	$-0.467561\pi$
$103$	2.39387e10	0.203468	0.101734	+	0.994812i	$0.467561\pi$
$104$	1.73092e11	1.39507
$105$	−4.67953e10	−0.357817
$106$	7.46995e10	0.542170
$107$	2.27527e11	1.56828	0.784138	−	0.620587i	$-0.213105\pi$
$107$	2.27527e11	1.56828	0.784138	+	0.620587i	$0.213105\pi$
$108$	−3.34296e10	−0.218928
$109$	1.30410e11	0.811831	0.405916	−	0.913911i	$-0.366953\pi$
$109$	1.30410e11	0.811831	0.405916	+	0.913911i	$0.366953\pi$
$110$	3.38721e11	2.00532
$111$	3.09795e11	1.74501
$112$	−1.51767e10	−0.0813728
$113$	−2.59233e11	−1.32361	−0.661804	−	0.749677i	$-0.730209\pi$
$113$	−2.59233e11	−1.32361	−0.661804	+	0.749677i	$0.730209\pi$
$114$	−2.52378e11	−1.22765
$115$	−5.05829e11	−2.34512
$116$	1.72994e9	0.00764738
$117$	1.59992e11	0.674646
$118$	−2.88600e10	−0.116130
$119$	1.05577e10	0.0405564
$120$	−6.34098e11	−2.32627
$121$	3.25119e11	1.13952
$122$	5.86933e10	0.196612
$123$	4.23419e11	1.35610
$124$	1.24373e10	0.0380984
$125$	5.91705e11	1.73420
$126$	−2.48012e10	−0.0695721
$127$	1.64128e11	0.440821	0.220410	−	0.975407i	$-0.429260\pi$
$127$	1.64128e11	0.440821	0.220410	+	0.975407i	$0.429260\pi$
$128$	−4.77180e10	−0.122752
$129$	−1.32203e11	−0.325836
$130$	−7.44775e11	−1.75929
$131$	−5.28986e10	−0.119799	−0.0598994	−	0.998204i	$-0.519078\pi$
$131$	−5.28986e10	−0.119799	−0.0598994	+	0.998204i	$0.519078\pi$
$132$	−3.10880e11	−0.675205
$133$	−1.00790e11	−0.210007
$134$	4.46547e11	0.892876
$135$	5.28733e11	1.01485
$136$	1.43061e11	0.263669
$137$	−3.20295e10	−0.0567004	−0.0283502	−	0.999598i	$-0.509025\pi$
$137$	−3.20295e10	−0.0567004	−0.0283502	+	0.999598i	$0.509025\pi$
$138$	−7.78016e11	−1.32329
$139$	−5.37493e11	−0.878600	−0.439300	−	0.898340i	$-0.644773\pi$
$139$	−5.37493e11	−0.878600	−0.439300	+	0.898340i	$0.644773\pi$
$140$	−6.88912e10	−0.108258
$141$	3.88025e11	0.586348
$142$	−9.71228e11	−1.41168
$143$	−1.34220e12	−1.87703
$144$	−1.90087e11	−0.255835
$145$	−2.73613e10	−0.0354497
$146$	5.93764e11	0.740752
$147$	9.99235e11	1.20067
$148$	4.56075e11	0.527955
$149$	−5.45864e11	−0.608920	−0.304460	−	0.952525i	$-0.598476\pi$
$149$	−5.45864e11	−0.608920	−0.304460	+	0.952525i	$0.598476\pi$
$150$	1.81924e12	1.95608
$151$	−8.46659e11	−0.877679	−0.438839	−	0.898566i	$-0.644610\pi$
$151$	−8.46659e11	−0.877679	−0.438839	+	0.898566i	$0.644610\pi$
$152$	−1.36575e12	−1.36531
$153$	1.32234e11	0.127509
$154$	2.08062e11	0.193566
$155$	−1.96712e11	−0.176606
$156$	6.83556e11	0.592364
$157$	1.58659e11	0.132744	0.0663721	−	0.997795i	$-0.478858\pi$
$157$	1.58659e11	0.132744	0.0663721	+	0.997795i	$0.478858\pi$
$158$	5.61254e11	0.453467
$159$	1.08436e12	0.846228
$160$	−1.61306e12	−1.21616
$161$	−3.10709e11	−0.226366
$162$	1.40410e12	0.988705
$163$	3.21350e10	0.0218749	0.0109375	−	0.999940i	$-0.496518\pi$
$163$	3.21350e10	0.0218749	0.0109375	+	0.999940i	$0.496518\pi$
$164$	6.23351e11	0.410291
$165$	4.91696e12	3.12993
$166$	9.16099e11	0.564090
$167$	−1.09934e12	−0.654927	−0.327464	−	0.944864i	$-0.606194\pi$
$167$	−1.09934e12	−0.654927	−0.327464	+	0.944864i	$0.606194\pi$
$168$	−3.89499e11	−0.224546
$169$	1.15905e12	0.646735
$170$	−6.15558e11	−0.332506
$171$	−1.26239e12	−0.660258
$172$	−1.94628e11	−0.0985822
$173$	3.14066e11	0.154087	0.0770436	−	0.997028i	$-0.475452\pi$
$173$	3.14066e11	0.154087	0.0770436	+	0.997028i	$0.475452\pi$
$174$	−4.20844e10	−0.0200033
$175$	7.26532e11	0.334615
$176$	1.59468e12	0.711793
$177$	−4.18938e11	−0.181258
$178$	−2.85929e12	−1.19936
$179$	2.32686e12	0.946407	0.473203	−	0.880953i	$-0.343098\pi$
$179$	2.32686e12	0.946407	0.473203	+	0.880953i	$0.343098\pi$
$180$	−8.62857e11	−0.340361
$181$	−4.60860e12	−1.76334	−0.881672	−	0.471862i	$-0.843582\pi$
$181$	−4.60860e12	−1.76334	−0.881672	+	0.471862i	$0.843582\pi$
$182$	−4.57483e11	−0.169818
$183$	8.52006e11	0.306875
$184$	−4.21026e12	−1.47167
$185$	−7.21342e12	−2.44735
$186$	−3.02563e11	−0.0996539
$187$	−1.10934e12	−0.354759
$188$	5.71245e11	0.177400
$189$	3.24778e11	0.0979596
$190$	5.87650e12	1.72177
$191$	3.75532e12	1.06897	0.534483	−	0.845179i	$-0.320507\pi$
$191$	3.75532e12	1.06897	0.534483	+	0.845179i	$0.320507\pi$
$192$	−4.65421e12	−1.28733
$193$	−3.52854e12	−0.948485	−0.474242	−	0.880394i	$-0.657278\pi$
$193$	−3.52854e12	−0.948485	−0.474242	+	0.880394i	$0.657278\pi$
$194$	7.32415e11	0.191358
$195$	−1.08113e13	−2.74593
$196$	1.47106e12	0.363263
$197$	4.87788e12	1.17130	0.585648	−	0.810565i	$-0.300840\pi$
$197$	4.87788e12	1.17130	0.585648	+	0.810565i	$0.300840\pi$
$198$	2.60596e12	0.608568
$199$	1.32339e12	0.300605	0.150302	−	0.988640i	$-0.451975\pi$
$199$	1.32339e12	0.300605	0.150302	+	0.988640i	$0.451975\pi$
$200$	9.84485e12	2.17542
$201$	6.48219e12	1.39362
$202$	5.73418e12	1.19961
$203$	−1.68069e10	−0.00342183
$204$	5.64961e11	0.111957
$205$	−9.85911e12	−1.90192
$206$	−8.57337e11	−0.161021
$207$	−3.89161e12	−0.711692
$208$	−3.50635e12	−0.624464
$209$	1.05904e13	1.83699
$210$	1.67592e12	0.283170
$211$	−2.39375e12	−0.394027	−0.197013	−	0.980401i	$-0.563124\pi$
$211$	−2.39375e12	−0.394027	−0.197013	+	0.980401i	$0.563124\pi$
$212$	1.59637e12	0.256027
$213$	−1.40986e13	−2.20337
$214$	−8.14864e12	−1.24111
$215$	3.07829e12	0.456981
$216$	4.40090e12	0.636863
$217$	−1.20832e11	−0.0170472
$218$	−4.67050e12	−0.642470
$219$	8.61922e12	1.15618
$220$	7.23867e12	0.946965
$221$	2.43919e12	0.311234
$222$	−1.10950e13	−1.38097
$223$	1.13233e13	1.37498	0.687491	−	0.726192i	$-0.258712\pi$
$223$	1.13233e13	1.37498	0.687491	+	0.726192i	$0.258712\pi$
$224$	−9.90834e11	−0.117392
$225$	9.09975e12	1.05202
$226$	9.28416e12	1.04748
$227$	−1.53438e13	−1.68963	−0.844814	−	0.535061i	$-0.820289\pi$
$227$	−1.53438e13	−1.68963	−0.844814	+	0.535061i	$0.820289\pi$
$228$	−5.39347e12	−0.579731
$229$	4.34859e11	0.0456303	0.0228151	−	0.999740i	$-0.492737\pi$
$229$	4.34859e11	0.0456303	0.0228151	+	0.999740i	$0.492737\pi$
$230$	1.81157e13	1.85589
$231$	3.02028e12	0.302121
$232$	−2.27741e11	−0.0222463
$233$	−6.62012e12	−0.631550	−0.315775	−	0.948834i	$-0.602265\pi$
$233$	−6.62012e12	−0.631550	−0.315775	+	0.948834i	$0.602265\pi$
$234$	−5.72994e12	−0.533904
$235$	−9.03498e12	−0.822344
$236$	−6.16754e11	−0.0548398
$237$	8.14730e12	0.707779
$238$	−3.78111e11	−0.0320957
$239$	2.10010e13	1.74202	0.871008	−	0.491270i	$-0.163467\pi$
$239$	2.10010e13	1.74202	0.871008	+	0.491270i	$0.163467\pi$
$240$	1.28450e13	1.04129
$241$	1.98775e12	0.157495	0.0787476	−	0.996895i	$-0.474908\pi$
$241$	1.98775e12	0.157495	0.0787476	+	0.996895i	$0.474908\pi$
$242$	−1.16438e13	−0.901799
$243$	1.26449e13	0.957370
$244$	1.25431e12	0.0928454
$245$	−2.32667e13	−1.68392
$246$	−1.51643e13	−1.07320
$247$	−2.32860e13	−1.61162
$248$	−1.63733e12	−0.110828
$249$	1.32983e13	0.880441
$250$	−2.11913e13	−1.37242
$251$	−2.39444e13	−1.51705	−0.758524	−	0.651645i	$-0.774079\pi$
$251$	−2.39444e13	−1.51705	−0.758524	+	0.651645i	$0.774079\pi$
$252$	−5.30016e11	−0.0328538
$253$	3.26474e13	1.98010
$254$	−5.87807e12	−0.348858
$255$	−8.93559e12	−0.518982
$256$	−1.66256e13	−0.945053
$257$	1.98303e13	1.10331	0.551653	−	0.834074i	$-0.313997\pi$
$257$	1.98303e13	1.10331	0.551653	+	0.834074i	$0.313997\pi$
$258$	4.73472e12	0.257861
$259$	−4.43090e12	−0.236234
$260$	−1.59163e13	−0.830783
$261$	−2.10505e11	−0.0107582
$262$	1.89451e12	0.0948067
$263$	1.81170e13	0.887832	0.443916	−	0.896068i	$-0.353589\pi$
$263$	1.81170e13	0.887832	0.443916	+	0.896068i	$0.353589\pi$
$264$	4.09262e13	1.96418
$265$	−2.52487e13	−1.18682
$266$	3.60968e12	0.166196
$267$	−4.15062e13	−1.87198
$268$	9.54297e12	0.421640
$269$	4.58392e13	1.98426	0.992131	−	0.125203i	$-0.0399582\pi$
$269$	4.58392e13	1.98426	0.992131	+	0.125203i	$0.0399582\pi$
$270$	−1.89360e13	−0.803133
$271$	−2.77669e12	−0.115397	−0.0576987	−	0.998334i	$-0.518376\pi$
$271$	−2.77669e12	−0.115397	−0.0576987	+	0.998334i	$0.518376\pi$
$272$	−2.89801e12	−0.118024
$273$	−6.64094e12	−0.265054
$274$	1.14710e12	0.0448718
$275$	−7.63396e13	−2.92698
$276$	−1.66267e13	−0.624892
$277$	4.30641e13	1.58663	0.793316	−	0.608810i	$-0.208353\pi$
$277$	4.30641e13	1.58663	0.793316	+	0.608810i	$0.208353\pi$
$278$	1.92497e13	0.695309
$279$	−1.51341e12	−0.0535960
$280$	9.06930e12	0.314923
$281$	2.49363e13	0.849077	0.424538	−	0.905410i	$-0.360436\pi$
$281$	2.49363e13	0.849077	0.424538	+	0.905410i	$0.360436\pi$
$282$	−1.38967e13	−0.464026
$283$	−9.60330e12	−0.314481	−0.157241	−	0.987560i	$-0.550260\pi$
$283$	−9.60330e12	−0.314481	−0.157241	+	0.987560i	$0.550260\pi$
$284$	−2.07557e13	−0.666632
$285$	8.53047e13	2.68736
$286$	4.80696e13	1.48545
$287$	−6.05603e12	−0.183585
$288$	−1.24101e13	−0.369077
$289$	2.01599e12	0.0588235
$290$	9.79915e11	0.0280543
$291$	1.06319e13	0.298676
$292$	1.26891e13	0.349803
$293$	5.81782e13	1.57394	0.786971	−	0.616990i	$-0.211648\pi$
$293$	5.81782e13	1.57394	0.786971	+	0.616990i	$0.211648\pi$
$294$	−3.57865e13	−0.950187
$295$	9.75476e12	0.254212
$296$	−6.00407e13	−1.53582
$297$	−3.41257e13	−0.856883
$298$	1.95495e13	0.481889
$299$	−7.17846e13	−1.73716
$300$	3.88781e13	0.923716
$301$	1.89086e12	0.0441107
$302$	3.03222e13	0.694580
$303$	8.32387e13	1.87237
$304$	2.76662e13	0.611146
$305$	−1.98385e13	−0.430388
$306$	−4.73581e12	−0.100908
$307$	3.96262e13	0.829318	0.414659	−	0.909977i	$-0.363901\pi$
$307$	3.96262e13	0.829318	0.414659	+	0.909977i	$0.363901\pi$
$308$	4.44641e12	0.0914072
$309$	−1.24453e13	−0.251324
$310$	7.04502e12	0.139763
$311$	−6.24402e13	−1.21698	−0.608489	−	0.793563i	$-0.708224\pi$
$311$	−6.24402e13	−1.21698	−0.608489	+	0.793563i	$0.708224\pi$
$312$	−8.99879e13	−1.72319
$313$	5.24710e12	0.0987246	0.0493623	−	0.998781i	$-0.484281\pi$
$313$	5.24710e12	0.0987246	0.0493623	+	0.998781i	$0.484281\pi$
$314$	−5.68219e12	−0.105052
$315$	8.38289e12	0.152295
$316$	1.19943e13	0.214139
$317$	−5.34517e12	−0.0937854	−0.0468927	−	0.998900i	$-0.514932\pi$
$317$	−5.34517e12	−0.0937854	−0.0468927	+	0.998900i	$0.514932\pi$
$318$	−3.88350e13	−0.669691
$319$	1.76596e12	0.0299318
$320$	1.08371e14	1.80546
$321$	−1.18288e14	−1.93714
$322$	1.11277e13	0.179142
$323$	−1.92459e13	−0.304597
$324$	3.00065e13	0.466894
$325$	1.67854e14	2.56787
$326$	−1.15088e12	−0.0173115
$327$	−6.77981e13	−1.00278
$328$	−8.20621e13	−1.19354
$329$	−5.54980e12	−0.0793780
$330$	−1.76096e14	−2.47698
$331$	−7.85574e13	−1.08676	−0.543379	−	0.839487i	$-0.682855\pi$
$331$	−7.85574e13	−1.08676	−0.543379	+	0.839487i	$0.682855\pi$
$332$	1.95776e13	0.266379
$333$	−5.54966e13	−0.742716
$334$	3.93718e13	0.518298
$335$	−1.50934e14	−1.95453
$336$	7.89013e12	0.100512
$337$	−1.21049e14	−1.51704	−0.758520	−	0.651650i	$-0.774077\pi$
$337$	−1.21049e14	−1.51704	−0.758520	+	0.651650i	$0.774077\pi$
$338$	−4.15102e13	−0.511815
$339$	1.34771e14	1.63493
$340$	−1.31548e13	−0.157019
$341$	1.26963e13	0.149117
$342$	4.52110e13	0.522517
$343$	−2.89946e13	−0.329761
$344$	2.56221e13	0.286776
$345$	2.62972e14	2.89671
$346$	−1.12479e13	−0.121942
$347$	2.27051e13	0.242277	0.121138	−	0.992636i	$-0.461346\pi$
$347$	2.27051e13	0.242277	0.121138	+	0.992636i	$0.461346\pi$
$348$	−8.99368e11	−0.00944608
$349$	8.01407e13	0.828539	0.414270	−	0.910154i	$-0.364037\pi$
$349$	8.01407e13	0.828539	0.414270	+	0.910154i	$0.364037\pi$
$350$	−2.60199e13	−0.264809
$351$	7.50350e13	0.751753
$352$	1.04111e14	1.02686
$353$	−1.20566e14	−1.17075	−0.585377	−	0.810761i	$-0.699053\pi$
$353$	−1.20566e14	−1.17075	−0.585377	+	0.810761i	$0.699053\pi$
$354$	1.50038e13	0.143444
$355$	3.28278e14	3.09020
$356$	−6.11047e13	−0.566369
$357$	−5.48875e12	−0.0500955
$358$	−8.33338e13	−0.748971
$359$	4.55686e13	0.403317	0.201658	−	0.979456i	$-0.435367\pi$
$359$	4.55686e13	0.403317	0.201658	+	0.979456i	$0.435367\pi$
$360$	1.13592e14	0.990113
$361$	6.72433e13	0.577244
$362$	1.65052e14	1.39548
$363$	−1.69024e14	−1.40754
$364$	−9.77668e12	−0.0801925
$365$	−2.00694e14	−1.62153
$366$	−3.05137e13	−0.242856
$367$	−1.00154e13	−0.0785241	−0.0392621	−	0.999229i	$-0.512501\pi$
$367$	−1.00154e13	−0.0785241	−0.0392621	+	0.999229i	$0.512501\pi$
$368$	8.52877e13	0.658754
$369$	−7.58513e13	−0.577189
$370$	2.58341e14	1.93679
$371$	−1.55092e13	−0.114560
$372$	−6.46594e12	−0.0470593
$373$	−2.42490e14	−1.73898	−0.869491	−	0.493948i	$-0.835553\pi$
$373$	−2.42490e14	−1.73898	−0.869491	+	0.493948i	$0.835553\pi$
$374$	3.97296e13	0.280751
$375$	−3.07618e14	−2.14210
$376$	−7.52024e13	−0.516058
$377$	−3.88297e12	−0.0262595
$378$	−1.16316e13	−0.0775236
$379$	1.51028e14	0.992070	0.496035	−	0.868302i	$-0.334789\pi$
$379$	1.51028e14	0.992070	0.496035	+	0.868302i	$0.334789\pi$
$380$	1.25584e14	0.813065
$381$	−8.53274e13	−0.544504
$382$	−1.34493e14	−0.845961
$383$	−5.83513e13	−0.361790	−0.180895	−	0.983502i	$-0.557899\pi$
$383$	−5.83513e13	−0.361790	−0.180895	+	0.983502i	$0.557899\pi$
$384$	2.48078e13	0.151624
$385$	−7.03257e13	−0.423721
$386$	1.26371e14	0.750615
$387$	2.36829e13	0.138683
$388$	1.56521e13	0.0903647
$389$	2.57550e14	1.46602	0.733008	−	0.680220i	$-0.238116\pi$
$389$	2.57550e14	1.46602	0.733008	+	0.680220i	$0.238116\pi$
$390$	3.87196e14	2.17308
$391$	−5.93302e13	−0.328325
$392$	−1.93660e14	−1.05673
$393$	2.75011e13	0.147976
$394$	−1.74696e14	−0.926945
$395$	−1.89706e14	−0.992651
$396$	5.56909e13	0.287383
$397$	1.59455e13	0.0811505	0.0405752	−	0.999176i	$-0.487081\pi$
$397$	1.59455e13	0.0811505	0.0405752	+	0.999176i	$0.487081\pi$
$398$	−4.73958e13	−0.237894
$399$	5.23991e13	0.259402
$400$	−1.99428e14	−0.973771
$401$	2.94459e14	1.41818	0.709089	−	0.705119i	$-0.249106\pi$
$401$	2.94459e14	1.41818	0.709089	+	0.705119i	$0.249106\pi$
$402$	−2.32152e14	−1.10288
$403$	−2.79163e13	−0.130822
$404$	1.22543e14	0.566487
$405$	−4.74592e14	−2.16430
$406$	6.01920e11	0.00270798
$407$	4.65572e14	2.06641
$408$	−7.43752e13	−0.325685
$409$	−3.71421e14	−1.60468	−0.802339	−	0.596869i	$-0.796411\pi$
$409$	−3.71421e14	−1.60468	−0.802339	+	0.596869i	$0.796411\pi$
$410$	3.53093e14	1.50514
$411$	1.66516e13	0.0700367
$412$	−1.83218e13	−0.0760384
$413$	5.99194e12	0.0245382
$414$	1.39374e14	0.563221
$415$	−3.09645e14	−1.23481
$416$	−2.28917e14	−0.900875
$417$	2.79434e14	1.08525
$418$	−3.79284e14	−1.45377
$419$	6.50604e12	0.0246116	0.0123058	−	0.999924i	$-0.496083\pi$
$419$	6.50604e12	0.0246116	0.0123058	+	0.999924i	$0.496083\pi$
$420$	3.58154e13	0.133721
$421$	−4.37364e13	−0.161173	−0.0805863	−	0.996748i	$-0.525679\pi$
$421$	−4.37364e13	−0.161173	−0.0805863	+	0.996748i	$0.525679\pi$
$422$	8.57296e13	0.311826
$423$	−6.95108e13	−0.249563
$424$	−2.10157e14	−0.744785
$425$	1.38732e14	0.485330
$426$	5.04925e14	1.74371
$427$	−1.21860e13	−0.0415438
$428$	−1.74141e14	−0.586085
$429$	6.97790e14	2.31851
$430$	−1.10246e14	−0.361647
$431$	−3.52265e14	−1.14089	−0.570446	−	0.821335i	$-0.693230\pi$
$431$	−3.52265e14	−1.14089	−0.570446	+	0.821335i	$0.693230\pi$
$432$	−8.91495e13	−0.285075
$433$	−1.14948e14	−0.362927	−0.181464	−	0.983398i	$-0.558083\pi$
$433$	−1.14948e14	−0.362927	−0.181464	+	0.983398i	$0.558083\pi$
$434$	4.32746e12	0.0134908
$435$	1.42247e13	0.0437876
$436$	−9.98112e13	−0.303392
$437$	5.66403e14	1.70011
$438$	−3.08688e14	−0.914981
$439$	1.65947e14	0.485753	0.242877	−	0.970057i	$-0.421909\pi$
$439$	1.65947e14	0.485753	0.242877	+	0.970057i	$0.421909\pi$
$440$	−9.52947e14	−2.75473
$441$	−1.79003e14	−0.511031
$442$	−8.73568e13	−0.246306
$443$	−2.33677e14	−0.650722	−0.325361	−	0.945590i	$-0.605486\pi$
$443$	−2.33677e14	−0.650722	−0.325361	+	0.945590i	$0.605486\pi$
$444$	−2.37106e14	−0.652133
$445$	9.66450e14	2.62542
$446$	−4.05533e14	−1.08814
$447$	2.83786e14	0.752141
$448$	6.65676e13	0.174274
$449$	−1.54601e14	−0.399813	−0.199906	−	0.979815i	$-0.564064\pi$
$449$	−1.54601e14	−0.399813	−0.199906	+	0.979815i	$0.564064\pi$
$450$	−3.25898e14	−0.832554
$451$	6.36331e14	1.60588
$452$	1.98408e14	0.494649
$453$	4.40164e14	1.08411
$454$	5.49522e14	1.33714
$455$	1.54631e14	0.371735
$456$	7.10032e14	1.68644
$457$	−1.84834e14	−0.433753	−0.216876	−	0.976199i	$-0.569587\pi$
$457$	−1.84834e14	−0.433753	−0.216876	+	0.976199i	$0.569587\pi$
$458$	−1.55740e13	−0.0361110
$459$	6.20167e13	0.142082
$460$	3.87143e14	0.876402
$461$	8.69287e13	0.194450	0.0972251	−	0.995262i	$-0.469003\pi$
$461$	8.69287e13	0.194450	0.0972251	+	0.995262i	$0.469003\pi$
$462$	−1.08168e14	−0.239094
$463$	−4.75077e12	−0.0103769	−0.00518846	−	0.999987i	$-0.501652\pi$
$463$	−4.75077e12	−0.0103769	−0.00518846	+	0.999987i	$0.501652\pi$
$464$	4.61338e12	0.00995795
$465$	1.02267e14	0.218145
$466$	2.37092e14	0.499798
$467$	6.99247e14	1.45676	0.728379	−	0.685174i	$-0.240274\pi$
$467$	6.99247e14	1.45676	0.728379	+	0.685174i	$0.240274\pi$
$468$	−1.22452e14	−0.252124
$469$	−9.27126e13	−0.188664
$470$	3.23578e14	0.650789
$471$	−8.24840e13	−0.163966
$472$	8.11936e13	0.159529
$473$	−1.98680e14	−0.385850
$474$	−2.91787e14	−0.560125
$475$	−1.32442e15	−2.51311
$476$	−8.08045e12	−0.0151564
$477$	−1.94251e14	−0.360174
$478$	−7.52129e14	−1.37860
$479$	−4.15365e14	−0.752635	−0.376318	−	0.926491i	$-0.622810\pi$
$479$	−4.15365e14	−0.752635	−0.376318	+	0.926491i	$0.622810\pi$
$480$	8.38603e14	1.50221
$481$	−1.02369e15	−1.81289
$482$	−7.11890e13	−0.124639
$483$	1.61533e14	0.279609
$484$	−2.48834e14	−0.425854
$485$	−2.47559e14	−0.418889
$486$	−4.52862e14	−0.757646
$487$	−1.15329e15	−1.90779	−0.953896	−	0.300138i	$-0.902967\pi$
$487$	−1.15329e15	−1.90779	−0.953896	+	0.300138i	$0.902967\pi$
$488$	−1.65126e14	−0.270088
$489$	−1.67065e13	−0.0270200
$490$	8.33271e14	1.33262
$491$	1.00128e15	1.58347	0.791734	−	0.610866i	$-0.209179\pi$
$491$	1.00128e15	1.58347	0.791734	+	0.610866i	$0.209179\pi$
$492$	−3.24070e14	−0.506793
$493$	−3.20929e12	−0.00496307
$494$	8.33962e14	1.27540
$495$	−8.80824e14	−1.33217
$496$	3.31675e13	0.0496094
$497$	2.01647e14	0.298286
$498$	−4.76265e14	−0.696766
$499$	1.17145e15	1.69500	0.847500	−	0.530796i	$-0.178107\pi$
$499$	1.17145e15	1.69500	0.847500	+	0.530796i	$0.178107\pi$
$500$	−4.52870e14	−0.648094
$501$	5.71531e14	0.808970
$502$	8.57544e14	1.20057
$503$	1.79347e14	0.248354	0.124177	−	0.992260i	$-0.460371\pi$
$503$	1.79347e14	0.248354	0.124177	+	0.992260i	$0.460371\pi$
$504$	6.97748e13	0.0955721
$505$	−1.93817e15	−2.62597
$506$	−1.16923e15	−1.56701
$507$	−6.02572e14	−0.798850
$508$	−1.25618e14	−0.164740
$509$	8.11791e14	1.05316	0.526582	−	0.850124i	$-0.323473\pi$
$509$	8.11791e14	1.05316	0.526582	+	0.850124i	$0.323473\pi$
$510$	3.20019e14	0.410714
$511$	−1.23278e14	−0.156520
$512$	6.93153e14	0.870651
$513$	−5.92050e14	−0.735720
$514$	−7.10199e14	−0.873138
$515$	2.89783e14	0.352479
$516$	1.01184e14	0.121769
$517$	5.83139e14	0.694344
$518$	1.58688e14	0.186952
$519$	−1.63277e14	−0.190329
$520$	2.09532e15	2.41675
$521$	−8.89959e14	−1.01569	−0.507846	−	0.861448i	$-0.669558\pi$
$521$	−8.89959e14	−1.01569	−0.507846	+	0.861448i	$0.669558\pi$
$522$	7.53900e12	0.00851384
$523$	−1.66040e14	−0.185547	−0.0927733	−	0.995687i	$-0.529573\pi$
$523$	−1.66040e14	−0.185547	−0.0927733	+	0.995687i	$0.529573\pi$
$524$	4.04867e13	0.0447703
$525$	−3.77712e14	−0.413318
$526$	−6.48842e14	−0.702615
$527$	−2.30729e13	−0.0247254
$528$	−8.29048e14	−0.879211
$529$	7.93261e14	0.832549
$530$	9.04253e14	0.939232
$531$	7.50485e13	0.0771475
$532$	7.71410e13	0.0784822
$533$	−1.39915e15	−1.40885
$534$	1.48650e15	1.48145
$535$	2.75427e15	2.71682
$536$	−1.25630e15	−1.22655
$537$	−1.20969e15	−1.16901
$538$	−1.64168e15	−1.57031
$539$	1.50169e15	1.42181
$540$	−4.04673e14	−0.379262
$541$	−1.20938e15	−1.12196	−0.560981	−	0.827829i	$-0.689576\pi$
$541$	−1.20938e15	−1.12196	−0.560981	+	0.827829i	$0.689576\pi$
$542$	9.94441e13	0.0913236
$543$	2.39594e15	2.17809
$544$	−1.89201e14	−0.170266
$545$	1.57864e15	1.40638
$546$	2.37838e14	0.209760
$547$	−2.20591e15	−1.92601	−0.963004	−	0.269487i	$-0.913146\pi$
$547$	−2.20591e15	−1.92601	−0.963004	+	0.269487i	$0.913146\pi$
$548$	2.45142e13	0.0211897
$549$	−1.52628e14	−0.130613
$550$	2.73402e15	2.31636
$551$	3.06378e13	0.0256995
$552$	2.18884e15	1.81781
$553$	−1.16528e14	−0.0958170
$554$	−1.54229e15	−1.25563
$555$	3.75014e15	3.02298
$556$	4.11377e14	0.328344
$557$	−3.83727e14	−0.303263	−0.151631	−	0.988437i	$-0.548453\pi$
$557$	−3.83727e14	−0.303263	−0.151631	+	0.988437i	$0.548453\pi$
$558$	5.42010e13	0.0424150
$559$	4.36855e14	0.338511
$560$	−1.83718e14	−0.140967
$561$	5.76725e14	0.438201
$562$	−8.93066e14	−0.671945
$563$	−2.06251e15	−1.53674	−0.768368	−	0.640008i	$-0.778931\pi$
$563$	−2.06251e15	−1.53674	−0.768368	+	0.640008i	$0.778931\pi$
$564$	−2.96981e14	−0.219126
$565$	−3.13808e15	−2.29296
$566$	3.43932e14	0.248875
$567$	−2.91522e14	−0.208912
$568$	2.73242e15	1.93924
$569$	2.22490e14	0.156384	0.0781920	−	0.996938i	$-0.475085\pi$
$569$	2.22490e14	0.156384	0.0781920	+	0.996938i	$0.475085\pi$
$570$	−3.05510e15	−2.12673
$571$	7.00937e14	0.483259	0.241630	−	0.970369i	$-0.422318\pi$
$571$	7.00937e14	0.483259	0.241630	+	0.970369i	$0.422318\pi$
$572$	1.02727e15	0.701469
$573$	−1.95233e15	−1.32039
$574$	2.16890e14	0.145286
$575$	−4.08284e15	−2.70888
$576$	8.33754e14	0.547916
$577$	−1.82953e15	−1.19089	−0.595447	−	0.803395i	$-0.703025\pi$
$577$	−1.82953e15	−1.19089	−0.595447	+	0.803395i	$0.703025\pi$
$578$	−7.22006e13	−0.0465519
$579$	1.83443e15	1.17157
$580$	2.09413e13	0.0132480
$581$	−1.90202e14	−0.119192
$582$	−3.80770e14	−0.236367
$583$	1.62961e15	1.00209
$584$	−1.67047e15	−1.01758
$585$	1.93674e15	1.16873
$586$	−2.08359e15	−1.24559
$587$	−9.96306e14	−0.590042	−0.295021	−	0.955491i	$-0.595327\pi$
$587$	−9.96306e14	−0.590042	−0.295021	+	0.955491i	$0.595327\pi$
$588$	−7.64778e14	−0.448704
$589$	2.20268e14	0.128032
$590$	−3.49356e14	−0.201179
$591$	−2.53593e15	−1.44679
$592$	1.21625e15	0.687471
$593$	1.58454e15	0.887366	0.443683	−	0.896184i	$-0.353672\pi$
$593$	1.58454e15	0.887366	0.443683	+	0.896184i	$0.353672\pi$
$594$	1.22218e15	0.678123
$595$	1.27803e14	0.0702582
$596$	4.17785e14	0.227561
$597$	−6.88008e14	−0.371309
$598$	2.57089e15	1.37476
$599$	1.87253e15	0.992161	0.496080	−	0.868277i	$-0.334772\pi$
$599$	1.87253e15	0.992161	0.496080	+	0.868277i	$0.334772\pi$
$600$	−5.11817e15	−2.68710
$601$	−1.51995e15	−0.790716	−0.395358	−	0.918527i	$-0.629379\pi$
$601$	−1.51995e15	−0.790716	−0.395358	+	0.918527i	$0.629379\pi$
$602$	−6.77192e13	−0.0349085
$603$	−1.16122e15	−0.593155
$604$	6.48002e14	0.328000
$605$	3.93564e15	1.97406
$606$	−2.98110e15	−1.48176
$607$	−8.11739e14	−0.399833	−0.199916	−	0.979813i	$-0.564067\pi$
$607$	−8.11739e14	−0.399833	−0.199916	+	0.979813i	$0.564067\pi$
$608$	1.80623e15	0.881662
$609$	8.73761e12	0.00422666
$610$	7.10495e14	0.340602
$611$	−1.28220e15	−0.609155
$612$	−1.01207e14	−0.0476516
$613$	2.58698e15	1.20715	0.603575	−	0.797306i	$-0.293742\pi$
$613$	2.58698e15	1.20715	0.603575	+	0.797306i	$0.293742\pi$
$614$	−1.41917e15	−0.656308
$615$	5.12559e15	2.34926
$616$	−5.85355e14	−0.265904
$617$	−3.41131e15	−1.53586	−0.767931	−	0.640532i	$-0.778714\pi$
$617$	−3.41131e15	−1.53586	−0.767931	+	0.640532i	$0.778714\pi$
$618$	4.45715e14	0.198894
$619$	2.69490e15	1.19191	0.595956	−	0.803017i	$-0.296773\pi$
$619$	2.69490e15	1.19191	0.595956	+	0.803017i	$0.296773\pi$
$620$	1.50556e14	0.0660000
$621$	−1.82513e15	−0.793032
$622$	2.23623e15	0.963095
$623$	5.93649e14	0.253423
$624$	1.82289e15	0.771341
$625$	2.39181e15	1.00320
$626$	−1.87919e14	−0.0781290
$627$	−5.50578e15	−2.26907
$628$	−1.21432e14	−0.0496082
$629$	−8.46083e14	−0.342637
$630$	−3.00224e14	−0.120524
$631$	−1.53346e15	−0.610254	−0.305127	−	0.952312i	$-0.598699\pi$
$631$	−1.53346e15	−0.610254	−0.305127	+	0.952312i	$0.598699\pi$
$632$	−1.57901e15	−0.622933
$633$	1.24447e15	0.486704
$634$	1.91431e14	0.0742202
$635$	1.98681e15	0.763660
$636$	−8.29926e14	−0.316246
$637$	−3.30189e15	−1.24737
$638$	−6.32461e13	−0.0236875
$639$	2.52562e15	0.937805
$640$	−5.77637e14	−0.212650
$641$	4.42124e15	1.61371	0.806854	−	0.590751i	$-0.201169\pi$
$641$	4.42124e15	1.61371	0.806854	+	0.590751i	$0.201169\pi$
$642$	4.23634e15	1.53302
$643$	5.45855e14	0.195847	0.0979235	−	0.995194i	$-0.468780\pi$
$643$	5.45855e14	0.195847	0.0979235	+	0.995194i	$0.468780\pi$
$644$	2.37806e14	0.0845960
$645$	−1.60035e15	−0.564465
$646$	6.89272e14	0.241053
$647$	3.92942e15	1.36256	0.681279	−	0.732024i	$-0.261424\pi$
$647$	3.92942e15	1.36256	0.681279	+	0.732024i	$0.261424\pi$
$648$	−3.95026e15	−1.35820
$649$	−6.29596e14	−0.214643
$650$	−6.01151e15	−2.03217
$651$	6.28184e13	0.0210568
$652$	−2.45950e13	−0.00817495
$653$	1.56087e14	0.0514450	0.0257225	−	0.999669i	$-0.491811\pi$
$653$	1.56087e14	0.0514450	0.0257225	+	0.999669i	$0.491811\pi$
$654$	2.42812e15	0.793582
$655$	−6.40350e14	−0.207534
$656$	1.66234e15	0.534255
$657$	−1.54404e15	−0.492096
$658$	1.98760e14	0.0628184
$659$	6.07395e14	0.190371	0.0951856	−	0.995460i	$-0.469656\pi$
$659$	6.07395e14	0.190371	0.0951856	+	0.995460i	$0.469656\pi$
$660$	−3.76327e15	−1.16970
$661$	2.39985e15	0.739735	0.369867	−	0.929085i	$-0.379403\pi$
$661$	2.39985e15	0.739735	0.369867	+	0.929085i	$0.379403\pi$
$662$	2.81345e15	0.860042
$663$	−1.26809e15	−0.384438
$664$	−2.57732e15	−0.774897
$665$	−1.22009e15	−0.363807
$666$	1.98755e15	0.587773
$667$	9.44484e13	0.0277015
$668$	8.41398e14	0.244755
$669$	−5.88681e15	−1.69839
$670$	5.40555e15	1.54678
$671$	1.28043e15	0.363397
$672$	5.15118e14	0.145003
$673$	−1.48452e15	−0.414478	−0.207239	−	0.978290i	$-0.566448\pi$
$673$	−1.48452e15	−0.414478	−0.207239	+	0.978290i	$0.566448\pi$
$674$	4.33524e15	1.20056
$675$	4.26771e15	1.17226
$676$	−8.87097e14	−0.241693
$677$	3.59423e15	0.971333	0.485666	−	0.874144i	$-0.338577\pi$
$677$	3.59423e15	0.971333	0.485666	+	0.874144i	$0.338577\pi$
$678$	−4.82668e15	−1.29385
$679$	−1.52065e14	−0.0404338
$680$	1.73179e15	0.456768
$681$	7.97699e15	2.08704
$682$	−4.54703e14	−0.118009
$683$	1.07980e14	0.0277990	0.0138995	−	0.999903i	$-0.495576\pi$
$683$	1.07980e14	0.0277990	0.0138995	+	0.999903i	$0.495576\pi$
$684$	9.66185e14	0.246747
$685$	−3.87724e14	−0.0982255
$686$	1.03841e15	0.260967
$687$	−2.26076e14	−0.0563628
$688$	−5.19030e14	−0.128368
$689$	−3.58316e15	−0.879144
$690$	−9.41806e15	−2.29241
$691$	−1.07336e15	−0.259189	−0.129595	−	0.991567i	$-0.541368\pi$
$691$	−1.07336e15	−0.259189	−0.129595	+	0.991567i	$0.541368\pi$
$692$	−2.40374e14	−0.0575844
$693$	−5.41053e14	−0.128590
$694$	−8.13159e14	−0.191734
$695$	−6.50647e15	−1.52205
$696$	1.18399e14	0.0274787
$697$	−1.15640e15	−0.266274
$698$	−2.87015e15	−0.655692
$699$	3.44169e15	0.780094
$700$	−5.56061e14	−0.125050
$701$	−2.00183e14	−0.0446660	−0.0223330	−	0.999751i	$-0.507109\pi$
$701$	−2.00183e14	−0.0446660	−0.0223330	+	0.999751i	$0.507109\pi$
$702$	−2.68730e15	−0.594924
$703$	8.07723e15	1.77422
$704$	−6.99452e15	−1.52443
$705$	4.69713e15	1.01576
$706$	4.31796e15	0.926515
$707$	−1.19054e15	−0.253475
$708$	3.20640e14	0.0677384
$709$	1.97788e15	0.414615	0.207307	−	0.978276i	$-0.433530\pi$
$709$	1.97788e15	0.414615	0.207307	+	0.978276i	$0.433530\pi$
$710$	−1.17569e16	−2.44553
$711$	−1.45951e15	−0.301247
$712$	8.04423e15	1.64757
$713$	6.79030e14	0.138005
$714$	1.96574e14	0.0396447
$715$	−1.62477e16	−3.25168
$716$	−1.78089e15	−0.353684
$717$	−1.09181e16	−2.15175
$718$	−1.63199e15	−0.319178
$719$	−1.60931e15	−0.312342	−0.156171	−	0.987730i	$-0.549915\pi$
$719$	−1.60931e15	−0.312342	−0.156171	+	0.987730i	$0.549915\pi$
$720$	−2.30105e15	−0.443197
$721$	1.78001e14	0.0340235
$722$	−2.40825e15	−0.456821
$723$	−1.03340e15	−0.194539
$724$	3.52726e15	0.658984
$725$	−2.20849e14	−0.0409483
$726$	6.05341e15	1.11391
$727$	−2.25356e15	−0.411557	−0.205779	−	0.978599i	$-0.565973\pi$
$727$	−2.25356e15	−0.411557	−0.205779	+	0.978599i	$0.565973\pi$
$728$	1.28707e15	0.233281
$729$	3.71287e14	0.0667895
$730$	7.18764e15	1.28325
$731$	3.61062e14	0.0639788
$732$	−6.52095e14	−0.114683
$733$	−4.05489e15	−0.707794	−0.353897	−	0.935284i	$-0.615144\pi$
$733$	−4.05489e15	−0.707794	−0.353897	+	0.935284i	$0.615144\pi$
$734$	3.58689e14	0.0621427
$735$	1.20960e16	2.07998
$736$	5.56812e15	0.950344
$737$	9.74168e15	1.65030
$738$	2.71653e15	0.456777
$739$	4.90967e14	0.0819423	0.0409711	−	0.999160i	$-0.486955\pi$
$739$	4.90967e14	0.0819423	0.0409711	+	0.999160i	$0.486955\pi$
$740$	5.52089e15	0.914607
$741$	1.21060e16	1.99068
$742$	5.55444e14	0.0906607
$743$	−9.73550e15	−1.57732	−0.788660	−	0.614829i	$-0.789225\pi$
$743$	−9.73550e15	−1.57732	−0.788660	+	0.614829i	$0.789225\pi$
$744$	8.51219e14	0.136896
$745$	−6.60781e15	−1.05487
$746$	8.68452e15	1.37620
$747$	−2.38226e15	−0.374736
$748$	8.49045e14	0.132578
$749$	1.69183e15	0.262245
$750$	1.10170e16	1.69522
$751$	1.68916e15	0.258019	0.129010	−	0.991643i	$-0.458820\pi$
$751$	1.68916e15	0.258019	0.129010	+	0.991643i	$0.458820\pi$
$752$	1.52338e15	0.231000
$753$	1.24483e16	1.87386
$754$	1.39064e14	0.0207813
$755$	−1.02490e16	−1.52045
$756$	−2.48574e14	−0.0366088
$757$	9.39397e15	1.37348	0.686739	−	0.726904i	$-0.259042\pi$
$757$	9.39397e15	1.37348	0.686739	+	0.726904i	$0.259042\pi$
$758$	−5.40891e15	−0.785108
$759$	−1.69729e16	−2.44583
$760$	−1.65327e16	−2.36521
$761$	−1.65898e15	−0.235627	−0.117814	−	0.993036i	$-0.537589\pi$
$761$	−1.65898e15	−0.235627	−0.117814	+	0.993036i	$0.537589\pi$
$762$	3.05591e15	0.430912
$763$	9.69694e14	0.135753
$764$	−2.87419e15	−0.399486
$765$	1.60072e15	0.220891
$766$	2.08979e15	0.286315
$767$	1.38434e15	0.188308
$768$	8.64335e15	1.16733
$769$	−1.15486e15	−0.154858	−0.0774292	−	0.996998i	$-0.524671\pi$
$769$	−1.15486e15	−0.154858	−0.0774292	+	0.996998i	$0.524671\pi$
$770$	2.51864e15	0.335326
$771$	−1.03094e16	−1.36281
$772$	2.70062e15	0.354461
$773$	1.23632e16	1.61117	0.805587	−	0.592478i	$-0.201850\pi$
$773$	1.23632e16	1.61117	0.805587	+	0.592478i	$0.201850\pi$
$774$	−8.48177e14	−0.109752
$775$	−1.58778e15	−0.204000
$776$	−2.06055e15	−0.262871
$777$	2.30355e15	0.291798
$778$	−9.22387e15	−1.16018
$779$	1.10397e16	1.37881
$780$	8.27460e15	1.02619
$781$	−2.11879e16	−2.60920
$782$	2.12485e15	0.259831
$783$	−9.87251e13	−0.0119878
$784$	3.92299e15	0.473019
$785$	1.92060e15	0.229961
$786$	−9.84923e14	−0.117106
$787$	1.17147e16	1.38315	0.691575	−	0.722304i	$-0.256917\pi$
$787$	1.17147e16	1.38315	0.691575	+	0.722304i	$0.256917\pi$
$788$	−3.73335e15	−0.437729
$789$	−9.41875e15	−1.09665
$790$	6.79411e15	0.785567
$791$	−1.92759e15	−0.221332
$792$	−7.33152e15	−0.835998
$793$	−2.81538e15	−0.318812
$794$	−5.71072e14	−0.0642211
$795$	1.31264e16	1.46597
$796$	−1.01287e15	−0.112340
$797$	−3.50295e15	−0.385845	−0.192922	−	0.981214i	$-0.561797\pi$
$797$	−3.50295e15	−0.385845	−0.192922	+	0.981214i	$0.561797\pi$
$798$	−1.87662e15	−0.205286
$799$	−1.05974e15	−0.115131
$800$	−1.30199e16	−1.40480
$801$	7.43541e15	0.796757
$802$	−1.05457e16	−1.12232
$803$	1.29533e16	1.36913
$804$	−4.96123e15	−0.520812
$805$	−3.76120e15	−0.392148
$806$	9.99792e14	0.103530
$807$	−2.38310e16	−2.45097
$808$	−1.61323e16	−1.64791
$809$	−1.02187e16	−1.03676	−0.518380	−	0.855150i	$-0.673465\pi$
$809$	−1.02187e16	−1.03676	−0.518380	+	0.855150i	$0.673465\pi$
$810$	1.69970e16	1.71279
$811$	−4.05578e15	−0.405938	−0.202969	−	0.979185i	$-0.565059\pi$
$811$	−4.05578e15	−0.405938	−0.202969	+	0.979185i	$0.565059\pi$
$812$	1.28634e13	0.00127878
$813$	1.44356e15	0.142540
$814$	−1.66739e16	−1.63532
$815$	3.89002e14	0.0378952
$816$	1.50663e15	0.145784
$817$	−3.44692e15	−0.331291
$818$	1.33020e16	1.26991
$819$	1.18966e15	0.112813
$820$	7.54580e15	0.710770
$821$	−6.19237e15	−0.579388	−0.289694	−	0.957119i	$-0.593554\pi$
$821$	−6.19237e15	−0.579388	−0.289694	+	0.957119i	$0.593554\pi$
$822$	−5.96358e14	−0.0554259
$823$	−1.22066e16	−1.12693	−0.563464	−	0.826141i	$-0.690532\pi$
$823$	−1.22066e16	−1.12693	−0.563464	+	0.826141i	$0.690532\pi$
$824$	2.41200e15	0.221196
$825$	3.96877e16	3.61542
$826$	−2.14595e14	−0.0194191
$827$	8.88851e15	0.799004	0.399502	−	0.916732i	$-0.369183\pi$
$827$	8.88851e15	0.799004	0.399502	+	0.916732i	$0.369183\pi$
$828$	2.97849e15	0.265968
$829$	9.77057e14	0.0866702	0.0433351	−	0.999061i	$-0.486202\pi$
$829$	9.77057e14	0.0866702	0.0433351	+	0.999061i	$0.486202\pi$
$830$	1.10896e16	0.977205
$831$	−2.23883e16	−1.95982
$832$	1.53794e16	1.33740
$833$	−2.72902e15	−0.235754
$834$	−1.00076e16	−0.858849
$835$	−1.33078e16	−1.13457
$836$	−8.10551e15	−0.686508
$837$	−7.09777e14	−0.0597216
$838$	−2.33007e14	−0.0194772
$839$	1.03132e16	0.856450	0.428225	−	0.903672i	$-0.359139\pi$
$839$	1.03132e16	0.856450	0.428225	+	0.903672i	$0.359139\pi$
$840$	−4.71498e15	−0.388995
$841$	−1.21954e16	−0.999581
$842$	1.56637e15	0.127549
$843$	−1.29640e16	−1.04878
$844$	1.83209e15	0.147253
$845$	1.40306e16	1.12038
$846$	2.48945e15	0.197500
$847$	2.41750e15	0.190549
$848$	4.25717e15	0.333383
$849$	4.99260e15	0.388449
$850$	−4.96853e15	−0.384082
$851$	2.49000e16	1.91243
$852$	1.07905e16	0.823428
$853$	9.03394e15	0.684948	0.342474	−	0.939527i	$-0.388735\pi$
$853$	9.03394e15	0.684948	0.342474	+	0.939527i	$0.388735\pi$
$854$	4.36427e14	0.0328771
$855$	−1.52815e16	−1.14380
$856$	2.29251e16	1.70492
$857$	−1.57318e16	−1.16248	−0.581240	−	0.813732i	$-0.697432\pi$
$857$	−1.57318e16	−1.16248	−0.581240	+	0.813732i	$0.697432\pi$
$858$	−2.49906e16	−1.83483
$859$	−9.57293e15	−0.698365	−0.349183	−	0.937055i	$-0.613541\pi$
$859$	−9.57293e15	−0.698365	−0.349183	+	0.937055i	$0.613541\pi$
$860$	−2.35601e15	−0.170780
$861$	3.14843e15	0.226765
$862$	1.26160e16	0.902883
$863$	2.12751e15	0.151291	0.0756454	−	0.997135i	$-0.475898\pi$
$863$	2.12751e15	0.151291	0.0756454	+	0.997135i	$0.475898\pi$
$864$	−5.82025e15	−0.411260
$865$	3.80183e15	0.266934
$866$	4.11675e15	0.287215
$867$	−1.04808e15	−0.0726591
$868$	9.24802e13	0.00637075
$869$	1.22441e16	0.838141
$870$	−5.09441e14	−0.0346528
$871$	−2.14198e16	−1.44782
$872$	1.31398e16	0.882569
$873$	−1.90460e15	−0.127123
$874$	−2.02851e16	−1.34544
$875$	4.39976e15	0.289991
$876$	−6.59684e15	−0.432079
$877$	1.79099e16	1.16572	0.582862	−	0.812571i	$-0.301933\pi$
$877$	1.79099e16	1.16572	0.582862	+	0.812571i	$0.301933\pi$
$878$	−5.94323e15	−0.384417
$879$	−3.02459e16	−1.94414
$880$	1.93040e16	1.23308
$881$	1.81728e16	1.15360	0.576799	−	0.816886i	$-0.304301\pi$
$881$	1.81728e16	1.15360	0.576799	+	0.816886i	$0.304301\pi$
$882$	6.41079e15	0.404422
$883$	1.86477e16	1.16907	0.584536	−	0.811368i	$-0.301276\pi$
$883$	1.86477e16	1.16907	0.584536	+	0.811368i	$0.301276\pi$
$884$	−1.86686e15	−0.116312
$885$	−5.07134e15	−0.314004
$886$	8.36889e15	0.514970
$887$	1.76039e16	1.07653	0.538267	−	0.842774i	$-0.319079\pi$
$887$	1.76039e16	1.07653	0.538267	+	0.842774i	$0.319079\pi$
$888$	3.12142e16	1.89706
$889$	1.22041e15	0.0737134
$890$	−3.46124e16	−2.07772
$891$	3.06313e16	1.82742
$892$	−8.66646e15	−0.513849
$893$	1.01169e16	0.596164
$894$	−1.01635e16	−0.595232
$895$	2.81671e16	1.63952
$896$	−3.54818e14	−0.0205263
$897$	3.73196e16	2.14575
$898$	5.53686e15	0.316405
$899$	3.67300e13	0.00208614
$900$	−6.96462e15	−0.393155
$901$	−2.96149e15	−0.166159
$902$	−2.27895e16	−1.27086
$903$	−9.83028e14	−0.0544858
$904$	−2.61197e16	−1.43894
$905$	−5.57882e16	−3.05474
$906$	−1.57640e16	−0.857949
$907$	−1.80438e16	−0.976088	−0.488044	−	0.872819i	$-0.662290\pi$
$907$	−1.80438e16	−0.976088	−0.488044	+	0.872819i	$0.662290\pi$
$908$	1.17436e16	0.631435
$909$	−1.49114e16	−0.796923
$910$	−5.53794e15	−0.294185
$911$	4.70302e15	0.248328	0.124164	−	0.992262i	$-0.460375\pi$
$911$	4.70302e15	0.248328	0.124164	+	0.992262i	$0.460375\pi$
$912$	−1.43832e16	−0.754890
$913$	1.99852e16	1.04260
$914$	6.61962e15	0.343265
$915$	1.03137e16	0.531618
$916$	−3.32825e14	−0.0170526
$917$	−3.93340e14	−0.0200326
$918$	−2.22106e15	−0.112441
$919$	1.38933e16	0.699149	0.349574	−	0.936909i	$-0.386326\pi$
$919$	1.38933e16	0.699149	0.349574	+	0.936909i	$0.386326\pi$
$920$	−5.09661e16	−2.54946
$921$	−2.06010e16	−1.02438
$922$	−3.11326e15	−0.153885
$923$	4.65875e16	2.28908
$924$	−2.31161e15	−0.112907
$925$	−5.82237e16	−2.82696
$926$	1.70144e14	0.00821212
$927$	2.22945e15	0.106969
$928$	3.01191e14	0.0143657
$929$	−2.30305e16	−1.09199	−0.545994	−	0.837789i	$-0.683848\pi$
$929$	−2.30305e16	−1.09199	−0.545994	+	0.837789i	$0.683848\pi$
$930$	−3.66259e15	−0.172636
$931$	2.60529e16	1.22077
$932$	5.06680e15	0.236018
$933$	3.24616e16	1.50322
$934$	−2.50428e16	−1.15285
$935$	−1.34288e16	−0.614571
$936$	1.61204e16	0.733430
$937$	3.88634e16	1.75781	0.878906	−	0.476994i	$-0.158274\pi$
$937$	3.88634e16	1.75781	0.878906	+	0.476994i	$0.158274\pi$
$938$	3.32040e15	0.149305
$939$	−2.72788e15	−0.121945
$940$	6.91504e15	0.307321
$941$	5.33588e15	0.235756	0.117878	−	0.993028i	$-0.462391\pi$
$941$	5.33588e15	0.235756	0.117878	+	0.993028i	$0.462391\pi$
$942$	2.95408e15	0.129760
$943$	3.40326e16	1.48621
$944$	−1.64475e15	−0.0714090
$945$	3.93151e15	0.169701
$946$	7.11552e15	0.305355
$947$	−3.67488e16	−1.56790	−0.783951	−	0.620823i	$-0.786798\pi$
$947$	−3.67488e16	−1.56790	−0.783951	+	0.620823i	$0.786798\pi$
$948$	−6.23565e15	−0.264506
$949$	−2.84814e16	−1.20115
$950$	4.74327e16	1.98883
$951$	2.77886e15	0.115844
$952$	1.06376e15	0.0440902
$953$	−3.65900e16	−1.50783	−0.753914	−	0.656973i	$-0.771837\pi$
$953$	−3.65900e16	−1.50783	−0.753914	+	0.656973i	$0.771837\pi$
$954$	6.95689e15	0.285036
$955$	4.54590e16	1.85183
$956$	−1.60734e16	−0.651013
$957$	−9.18096e14	−0.0369719
$958$	1.48758e16	0.595623
$959$	−2.38162e14	−0.00948136
$960$	−5.63402e16	−2.23011
$961$	−2.51444e16	−0.989607
$962$	3.66624e16	1.43469
$963$	2.11900e16	0.824492
$964$	−1.52135e15	−0.0588579
$965$	−4.27138e16	−1.64312
$966$	−5.78511e15	−0.221278
$967$	−3.30766e14	−0.0125798	−0.00628992	−	0.999980i	$-0.502002\pi$
$967$	−3.30766e14	−0.0125798	−0.00628992	+	0.999980i	$0.502002\pi$
$968$	3.27582e16	1.23881
$969$	1.00056e16	0.376239
$970$	8.86604e15	0.331501
$971$	−1.98566e16	−0.738243	−0.369121	−	0.929381i	$-0.620341\pi$
$971$	−1.98566e16	−0.738243	−0.369121	+	0.929381i	$0.620341\pi$
$972$	−9.67792e15	−0.357781
$973$	−3.99665e15	−0.146918
$974$	4.13040e16	1.50979
$975$	−8.72645e16	−3.17185
$976$	3.34497e15	0.120898
$977$	−2.83782e16	−1.01992	−0.509958	−	0.860199i	$-0.670339\pi$
$977$	−2.83782e16	−1.01992	−0.509958	+	0.860199i	$0.670339\pi$
$978$	5.98324e14	0.0213832
$979$	−6.23771e16	−2.21677
$980$	1.78075e16	0.629302
$981$	1.21453e16	0.426806
$982$	−3.58599e16	−1.25313
$983$	−4.15936e16	−1.44538	−0.722690	−	0.691172i	$-0.757095\pi$
$983$	−4.15936e16	−1.44538	−0.722690	+	0.691172i	$0.757095\pi$
$984$	4.26627e16	1.47426
$985$	5.90478e16	2.02911
$986$	1.14937e14	0.00392769
$987$	2.88525e15	0.0980481
$988$	1.78222e16	0.602281
$989$	−1.06260e16	−0.357099
$990$	3.15457e16	1.05426
$991$	−4.20736e16	−1.39831	−0.699157	−	0.714969i	$-0.746441\pi$
$991$	−4.20736e16	−1.39831	−0.699157	+	0.714969i	$0.746441\pi$
$992$	2.16539e15	0.0715684
$993$	4.08407e16	1.34237
$994$	−7.22178e15	−0.236058
$995$	1.60199e16	0.520755
$996$	−1.01781e16	−0.329032
$997$	3.14906e16	1.01241	0.506207	−	0.862412i	$-0.331047\pi$
$997$	3.14906e16	1.01241	0.506207	+	0.862412i	$0.331047\pi$
$998$	−4.19541e16	−1.34139
$999$	−2.60275e16	−0.827603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.a.a.1.3	✓	6
3.2	odd	2		153.12.a.a.1.4		6
4.3	odd	2		272.12.a.f.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.a.a.1.3	✓	6	1.1	even	1	trivial
153.12.a.a.1.4		6	3.2	odd	2
272.12.a.f.1.5		6	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)

\(f(q)\)	\(=\)	\(q-35.8139 q^{2} -519.883 q^{3} -765.364 q^{4} +12105.2 q^{5} +18619.1 q^{6} +7435.72 q^{7} +100758. q^{8} +93131.8 q^{9} +O(q^{10})\)	\(q-35.8139 q^{2} -519.883 q^{3} -765.364 q^{4} +12105.2 q^{5} +18619.1 q^{6} +7435.72 q^{7} +100758. q^{8} +93131.8 q^{9} -433535. q^{10} -781301. q^{11} +397900. q^{12} +1.71791e6 q^{13} -266302. q^{14} -6.29330e6 q^{15} -2.04106e6 q^{16} +1.41986e6 q^{17} -3.33541e6 q^{18} -1.35548e7 q^{19} -9.26490e6 q^{20} -3.86571e6 q^{21} +2.79814e7 q^{22} -4.17860e7 q^{23} -5.23822e7 q^{24} +9.77083e7 q^{25} -6.15251e7 q^{26} +4.36781e7 q^{27} -5.69103e6 q^{28} -2.26029e6 q^{29} +2.25388e8 q^{30} -1.62502e7 q^{31} -1.33253e8 q^{32} +4.06185e8 q^{33} -5.08506e7 q^{34} +9.00111e7 q^{35} -7.12797e7 q^{36} -5.95893e8 q^{37} +4.85452e8 q^{38} -8.93113e8 q^{39} +1.21969e9 q^{40} -8.14451e8 q^{41} +1.38446e8 q^{42} +2.54294e8 q^{43} +5.97979e8 q^{44} +1.12738e9 q^{45} +1.49652e9 q^{46} -7.46370e8 q^{47} +1.06111e9 q^{48} -1.92204e9 q^{49} -3.49932e9 q^{50} -7.38160e8 q^{51} -1.31483e9 q^{52} -2.08577e9 q^{53} -1.56428e9 q^{54} -9.45782e9 q^{55} +7.49205e8 q^{56} +7.04694e9 q^{57} +8.09497e7 q^{58} +8.05831e8 q^{59} +4.81667e9 q^{60} -1.63884e9 q^{61} +5.81982e8 q^{62} +6.92502e8 q^{63} +8.95241e9 q^{64} +2.07957e10 q^{65} -1.45471e10 q^{66} -1.24685e10 q^{67} -1.08671e9 q^{68} +2.17239e10 q^{69} -3.22365e9 q^{70} +2.71187e10 q^{71} +9.38373e9 q^{72} -1.65791e10 q^{73} +2.13413e10 q^{74} -5.07969e10 q^{75} +1.03744e10 q^{76} -5.80954e9 q^{77} +3.19859e10 q^{78} -1.56714e10 q^{79} -2.47075e10 q^{80} -3.92055e10 q^{81} +2.91687e10 q^{82} -2.55794e10 q^{83} +2.95867e9 q^{84} +1.71877e10 q^{85} -9.10728e9 q^{86} +1.17509e9 q^{87} -7.87220e10 q^{88} +7.98375e10 q^{89} -4.03759e10 q^{90} +1.27739e10 q^{91} +3.19815e10 q^{92} +8.44819e9 q^{93} +2.67304e10 q^{94} -1.64084e11 q^{95} +6.92762e10 q^{96} -2.04506e10 q^{97} +6.88357e10 q^{98} -7.27639e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9}+O(q^{10}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9} - 676038 q^{10} - 962060 q^{11} - 2352344 q^{12} - 435268 q^{13} - 7990948 q^{14} - 9450288 q^{15} - 12496671 q^{16} + 8519142 q^{17} - 20195421 q^{18} - 26398480 q^{19} - 47202914 q^{20} - 56428792 q^{21} - 51774200 q^{22} - 99172772 q^{23} - 110557128 q^{24} + 66085866 q^{25} + 74451914 q^{26} + 105183712 q^{27} + 102848900 q^{28} + 165683964 q^{29} + 401475744 q^{30} - 199133468 q^{31} + 465766501 q^{32} + 518429376 q^{33} - 12778713 q^{34} + 804442912 q^{35} + 627274777 q^{36} - 785778644 q^{37} + 2174484940 q^{38} + 627357728 q^{39} + 657666206 q^{40} + 166444428 q^{41} + 652753248 q^{42} - 1110947880 q^{43} - 997577064 q^{44} - 1706447988 q^{45} - 1891667412 q^{46} - 5828211928 q^{47} - 2359114472 q^{48} - 1968801674 q^{49} - 126509183 q^{50} - 675851932 q^{51} - 6633403554 q^{52} - 9889898636 q^{53} - 1961072736 q^{54} - 10730153984 q^{55} + 5703448884 q^{56} - 13522850128 q^{57} + 14316796258 q^{58} + 204095112 q^{59} + 22313648592 q^{60} - 15864546948 q^{61} - 1838602020 q^{62} + 504344540 q^{63} + 6177095465 q^{64} + 12794774792 q^{65} + 56255165136 q^{66} + 17196640232 q^{67} + 6549800341 q^{68} + 2949266904 q^{69} + 52391765944 q^{70} + 8751653884 q^{71} + 38682669705 q^{72} - 13704156916 q^{73} - 9383651494 q^{74} - 15917467268 q^{75} + 59548672452 q^{76} - 12012382872 q^{77} + 35038956192 q^{78} - 89923384436 q^{79} + 25877503334 q^{80} - 152313828506 q^{81} + 57834669670 q^{82} - 26042106648 q^{83} + 3397466240 q^{84} - 18293437588 q^{85} + 29108045060 q^{86} - 195382431072 q^{87} - 228837945880 q^{88} + 53269579420 q^{89} - 10044062046 q^{90} - 226028668544 q^{91} - 9212077436 q^{92} - 62709484936 q^{93} + 83948222448 q^{94} - 170219637424 q^{95} + 116885663928 q^{96} - 106272517044 q^{97} + 132039821039 q^{98} - 10550584980 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9 - 676038 * q^10 - 962060 * q^11 - 2352344 * q^12 - 435268 * q^13 - 7990948 * q^14 - 9450288 * q^15 - 12496671 * q^16 + 8519142 * q^17 - 20195421 * q^18 - 26398480 * q^19 - 47202914 * q^20 - 56428792 * q^21 - 51774200 * q^22 - 99172772 * q^23 - 110557128 * q^24 + 66085866 * q^25 + 74451914 * q^26 + 105183712 * q^27 + 102848900 * q^28 + 165683964 * q^29 + 401475744 * q^30 - 199133468 * q^31 + 465766501 * q^32 + 518429376 * q^33 - 12778713 * q^34 + 804442912 * q^35 + 627274777 * q^36 - 785778644 * q^37 + 2174484940 * q^38 + 627357728 * q^39 + 657666206 * q^40 + 166444428 * q^41 + 652753248 * q^42 - 1110947880 * q^43 - 997577064 * q^44 - 1706447988 * q^45 - 1891667412 * q^46 - 5828211928 * q^47 - 2359114472 * q^48 - 1968801674 * q^49 - 126509183 * q^50 - 675851932 * q^51 - 6633403554 * q^52 - 9889898636 * q^53 - 1961072736 * q^54 - 10730153984 * q^55 + 5703448884 * q^56 - 13522850128 * q^57 + 14316796258 * q^58 + 204095112 * q^59 + 22313648592 * q^60 - 15864546948 * q^61 - 1838602020 * q^62 + 504344540 * q^63 + 6177095465 * q^64 + 12794774792 * q^65 + 56255165136 * q^66 + 17196640232 * q^67 + 6549800341 * q^68 + 2949266904 * q^69 + 52391765944 * q^70 + 8751653884 * q^71 + 38682669705 * q^72 - 13704156916 * q^73 - 9383651494 * q^74 - 15917467268 * q^75 + 59548672452 * q^76 - 12012382872 * q^77 + 35038956192 * q^78 - 89923384436 * q^79 + 25877503334 * q^80 - 152313828506 * q^81 + 57834669670 * q^82 - 26042106648 * q^83 + 3397466240 * q^84 - 18293437588 * q^85 + 29108045060 * q^86 - 195382431072 * q^87 - 228837945880 * q^88 + 53269579420 * q^89 - 10044062046 * q^90 - 226028668544 * q^91 - 9212077436 * q^92 - 62709484936 * q^93 + 83948222448 * q^94 - 170219637424 * q^95 + 116885663928 * q^96 - 106272517044 * q^97 + 132039821039 * q^98 - 10550584980 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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