LMFDB - Embedded newform 6713.2.a.l.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6713,2,Mod(1,6713)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6713, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6713.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6713 = 7^{2} \cdot 137 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6713.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:	$53.6035748769$
Analytic rank:	$0$
Dimension:	$45$
Twist minimal:	no (minimal twist has level 959)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	6713.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.92886 q^{2} -2.29737 q^{3} +1.72049 q^{4} +1.09188 q^{5} -4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} +O(q^{10})$	\(q+1.92886 q^{2} -2.29737 q^{3} +1.72049 q^{4} +1.09188 q^{5} -4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} +2.10607 q^{10} -0.0928769 q^{11} -3.95261 q^{12} +5.52150 q^{13} -2.50845 q^{15} -4.48089 q^{16} -1.48098 q^{17} +4.39378 q^{18} -0.762544 q^{19} +1.87856 q^{20} -0.179146 q^{22} -5.36773 q^{23} +1.23859 q^{24} -3.80781 q^{25} +10.6502 q^{26} +1.65889 q^{27} -1.44696 q^{29} -4.83843 q^{30} +7.19415 q^{31} -7.56474 q^{32} +0.213373 q^{33} -2.85660 q^{34} +3.91913 q^{36} +3.36621 q^{37} -1.47084 q^{38} -12.6849 q^{39} -0.588668 q^{40} +5.80988 q^{41} +10.7384 q^{43} -0.159794 q^{44} +2.48720 q^{45} -10.3536 q^{46} -9.80224 q^{47} +10.2943 q^{48} -7.34472 q^{50} +3.40236 q^{51} +9.49968 q^{52} -0.405891 q^{53} +3.19977 q^{54} -0.101410 q^{55} +1.75185 q^{57} -2.79098 q^{58} +10.3079 q^{59} -4.31576 q^{60} +8.76468 q^{61} +13.8765 q^{62} -5.62951 q^{64} +6.02879 q^{65} +0.411566 q^{66} +1.52684 q^{67} -2.54801 q^{68} +12.3317 q^{69} -4.98542 q^{71} -1.22810 q^{72} -10.3229 q^{73} +6.49294 q^{74} +8.74795 q^{75} -1.31195 q^{76} -24.4674 q^{78} +9.66300 q^{79} -4.89258 q^{80} -10.6448 q^{81} +11.2064 q^{82} +11.7043 q^{83} -1.61705 q^{85} +20.7129 q^{86} +3.32420 q^{87} +0.0500732 q^{88} -10.5625 q^{89} +4.79746 q^{90} -9.23512 q^{92} -16.5276 q^{93} -18.9071 q^{94} -0.832603 q^{95} +17.3790 q^{96} +12.5772 q^{97} -0.211566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q + 11 q^{3} + 44 q^{4} + 4 q^{5} + 10 q^{6} - 3 q^{8} + 44 q^{9}+O(q^{10}) $ 45 * q + 11 * q^3 + 44 * q^4 + 4 * q^5 + 10 * q^6 - 3 * q^8 + 44 * q^9	$ 45 q + 11 q^{3} + 44 q^{4} + 4 q^{5} + 10 q^{6} - 3 q^{8} + 44 q^{9} + 25 q^{10} + 33 q^{12} + 36 q^{13} + 38 q^{16} + 18 q^{17} - 5 q^{18} + 43 q^{19} + 10 q^{20} - q^{23} + 20 q^{24} + 43 q^{25} + 2 q^{26} + 53 q^{27} - 4 q^{29} - 12 q^{30} + 59 q^{31} - 11 q^{32} + 37 q^{33} + 48 q^{34} + 14 q^{36} + 39 q^{38} + 16 q^{39} + 56 q^{40} + 15 q^{41} - q^{43} - 2 q^{44} + 28 q^{45} + 31 q^{46} + 58 q^{47} + 12 q^{48} - 74 q^{50} - 5 q^{51} + 115 q^{52} + 10 q^{53} + 39 q^{54} + 81 q^{55} - 18 q^{57} - 11 q^{58} + 41 q^{59} + 90 q^{60} + 40 q^{61} - 29 q^{62} + 15 q^{64} - 9 q^{65} + 42 q^{66} + 56 q^{68} + 5 q^{69} - 42 q^{71} - 11 q^{72} + 67 q^{73} + 39 q^{74} + 40 q^{75} + 68 q^{76} - 78 q^{78} - 9 q^{79} + 14 q^{80} + 73 q^{81} + 34 q^{82} + 48 q^{83} + 6 q^{85} - 13 q^{86} + 135 q^{87} + 47 q^{88} + 17 q^{89} - 44 q^{90} - 61 q^{92} - q^{93} + 28 q^{94} + 47 q^{95} + 50 q^{96} + 81 q^{97} - 35 q^{99}+O(q^{100}) $ 45 * q + 11 * q^3 + 44 * q^4 + 4 * q^5 + 10 * q^6 - 3 * q^8 + 44 * q^9 + 25 * q^10 + 33 * q^12 + 36 * q^13 + 38 * q^16 + 18 * q^17 - 5 * q^18 + 43 * q^19 + 10 * q^20 - q^23 + 20 * q^24 + 43 * q^25 + 2 * q^26 + 53 * q^27 - 4 * q^29 - 12 * q^30 + 59 * q^31 - 11 * q^32 + 37 * q^33 + 48 * q^34 + 14 * q^36 + 39 * q^38 + 16 * q^39 + 56 * q^40 + 15 * q^41 - q^43 - 2 * q^44 + 28 * q^45 + 31 * q^46 + 58 * q^47 + 12 * q^48 - 74 * q^50 - 5 * q^51 + 115 * q^52 + 10 * q^53 + 39 * q^54 + 81 * q^55 - 18 * q^57 - 11 * q^58 + 41 * q^59 + 90 * q^60 + 40 * q^61 - 29 * q^62 + 15 * q^64 - 9 * q^65 + 42 * q^66 + 56 * q^68 + 5 * q^69 - 42 * q^71 - 11 * q^72 + 67 * q^73 + 39 * q^74 + 40 * q^75 + 68 * q^76 - 78 * q^78 - 9 * q^79 + 14 * q^80 + 73 * q^81 + 34 * q^82 + 48 * q^83 + 6 * q^85 - 13 * q^86 + 135 * q^87 + 47 * q^88 + 17 * q^89 - 44 * q^90 - 61 * q^92 - q^93 + 28 * q^94 + 47 * q^95 + 50 * q^96 + 81 * q^97 - 35 * 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 $

$2$	1.92886	1.36391	0.681954	−	0.731395i	$-0.261130\pi$
$2$	1.92886	1.36391	0.681954	+	0.731395i	$0.261130\pi$
$3$	−2.29737	−1.32639	−0.663194	−	0.748447i	$-0.730800\pi$
$3$	−2.29737	−1.32639	−0.663194	+	0.748447i	$0.730800\pi$
$4$	1.72049	0.860245
$5$	1.09188	0.488302	0.244151	−	0.969737i	$-0.421491\pi$
$5$	1.09188	0.488302	0.244151	+	0.969737i	$0.421491\pi$
$6$	−4.43130	−1.80907
$7$	0	0
$7$	0	0
$8$	−0.539134	−0.190613
$9$	2.27792	0.759306
$10$	2.10607	0.665999
$11$	−0.0928769	−0.0280034	−0.0140017	−	0.999902i	$-0.504457\pi$
$11$	−0.0928769	−0.0280034	−0.0140017	+	0.999902i	$0.504457\pi$
$12$	−3.95261	−1.14102
$13$	5.52150	1.53139	0.765694	−	0.643205i	$-0.222396\pi$
$13$	5.52150	1.53139	0.765694	+	0.643205i	$0.222396\pi$
$14$	0	0
$15$	−2.50845	−0.647678
$16$	−4.48089	−1.12022
$17$	−1.48098	−0.359190	−0.179595	−	0.983741i	$-0.557479\pi$
$17$	−1.48098	−0.359190	−0.179595	+	0.983741i	$0.557479\pi$
$18$	4.39378	1.03562
$19$	−0.762544	−0.174939	−0.0874697	−	0.996167i	$-0.527878\pi$
$19$	−0.762544	−0.174939	−0.0874697	+	0.996167i	$0.527878\pi$
$20$	1.87856	0.420059
$21$	0	0
$22$	−0.179146	−0.0381941
$23$	−5.36773	−1.11925	−0.559624	−	0.828746i	$-0.689055\pi$
$23$	−5.36773	−1.11925	−0.559624	+	0.828746i	$0.689055\pi$
$24$	1.23859	0.252827
$25$	−3.80781	−0.761561
$26$	10.6502	2.08867
$27$	1.65889	0.319254
$28$	0	0
$29$	−1.44696	−0.268693	−0.134347	−	0.990934i	$-0.542894\pi$
$29$	−1.44696	−0.268693	−0.134347	+	0.990934i	$0.542894\pi$
$30$	−4.83843	−0.883373
$31$	7.19415	1.29211	0.646054	−	0.763292i	$-0.276418\pi$
$31$	7.19415	1.29211	0.646054	+	0.763292i	$0.276418\pi$
$32$	−7.56474	−1.33727
$33$	0.213373	0.0371434
$34$	−2.85660	−0.489903
$35$	0	0
$36$	3.91913	0.653189
$37$	3.36621	0.553401	0.276701	−	0.960956i	$-0.410759\pi$
$37$	3.36621	0.553401	0.276701	+	0.960956i	$0.410759\pi$
$38$	−1.47084	−0.238601
$39$	−12.6849	−2.03121
$40$	−0.588668	−0.0930766
$41$	5.80988	0.907351	0.453676	−	0.891167i	$-0.350112\pi$
$41$	5.80988	0.907351	0.453676	+	0.891167i	$0.350112\pi$
$42$	0	0
$43$	10.7384	1.63759	0.818797	−	0.574084i	$-0.194642\pi$
$43$	10.7384	1.63759	0.818797	+	0.574084i	$0.194642\pi$
$44$	−0.159794	−0.0240898
$45$	2.48720	0.370770
$46$	−10.3536	−1.52655
$47$	−9.80224	−1.42980	−0.714902	−	0.699225i	$-0.753529\pi$
$47$	−9.80224	−1.42980	−0.714902	+	0.699225i	$0.753529\pi$
$48$	10.2943	1.48585
$49$	0	0
$50$	−7.34472	−1.03870
$51$	3.40236	0.476426
$52$	9.49968	1.31737
$53$	−0.405891	−0.0557534	−0.0278767	−	0.999611i	$-0.508875\pi$
$53$	−0.405891	−0.0557534	−0.0278767	+	0.999611i	$0.508875\pi$
$54$	3.19977	0.435433
$55$	−0.101410	−0.0136741
$56$	0	0
$57$	1.75185	0.232038
$58$	−2.79098	−0.366473
$59$	10.3079	1.34197	0.670984	−	0.741472i	$-0.265872\pi$
$59$	10.3079	1.34197	0.670984	+	0.741472i	$0.265872\pi$
$60$	−4.31576	−0.557162
$61$	8.76468	1.12220	0.561101	−	0.827747i	$-0.310378\pi$
$61$	8.76468	1.12220	0.561101	+	0.827747i	$0.310378\pi$
$62$	13.8765	1.76232
$63$	0	0
$64$	−5.62951	−0.703688
$65$	6.02879	0.747779
$66$	0.411566	0.0506602
$67$	1.52684	0.186533	0.0932666	−	0.995641i	$-0.470269\pi$
$67$	1.52684	0.186533	0.0932666	+	0.995641i	$0.470269\pi$
$68$	−2.54801	−0.308992
$69$	12.3317	1.48456
$70$	0	0
$71$	−4.98542	−0.591660	−0.295830	−	0.955241i	$-0.595596\pi$
$71$	−4.98542	−0.591660	−0.295830	+	0.955241i	$0.595596\pi$
$72$	−1.22810	−0.144733
$73$	−10.3229	−1.20820	−0.604102	−	0.796907i	$-0.706468\pi$
$73$	−10.3229	−1.20820	−0.604102	+	0.796907i	$0.706468\pi$
$74$	6.49294	0.754789
$75$	8.74795	1.01013
$76$	−1.31195	−0.150491
$77$	0	0
$78$	−24.4674	−2.77039
$79$	9.66300	1.08717	0.543586	−	0.839353i	$-0.317066\pi$
$79$	9.66300	1.08717	0.543586	+	0.839353i	$0.317066\pi$
$80$	−4.89258	−0.547007
$81$	−10.6448	−1.18276
$82$	11.2064	1.23754
$83$	11.7043	1.28471	0.642356	−	0.766406i	$-0.277957\pi$
$83$	11.7043	1.28471	0.642356	+	0.766406i	$0.277957\pi$
$84$	0	0
$85$	−1.61705	−0.175393
$86$	20.7129	2.23353
$87$	3.32420	0.356392
$88$	0.0500732	0.00533782
$89$	−10.5625	−1.11963	−0.559814	−	0.828619i	$-0.689127\pi$
$89$	−10.5625	−1.11963	−0.559814	+	0.828619i	$0.689127\pi$
$90$	4.79746	0.505697
$91$	0	0
$92$	−9.23512	−0.962828
$93$	−16.5276	−1.71384
$94$	−18.9071	−1.95012
$95$	−0.832603	−0.0854233
$96$	17.3790	1.77374
$97$	12.5772	1.27703	0.638513	−	0.769611i	$-0.279550\pi$
$97$	12.5772	1.27703	0.638513	+	0.769611i	$0.279550\pi$
$98$	0	0
$99$	−0.211566	−0.0212632
$100$	−6.55129	−0.655129
$101$	−12.9792	−1.29148	−0.645739	−	0.763558i	$-0.723451\pi$
$101$	−12.9792	−1.29148	−0.645739	+	0.763558i	$0.723451\pi$
$102$	6.56267	0.649801
$103$	2.12573	0.209454	0.104727	−	0.994501i	$-0.466603\pi$
$103$	2.12573	0.209454	0.104727	+	0.994501i	$0.466603\pi$
$104$	−2.97683	−0.291902
$105$	0	0
$106$	−0.782905	−0.0760424
$107$	2.27186	0.219629	0.109815	−	0.993952i	$-0.464974\pi$
$107$	2.27186	0.219629	0.109815	+	0.993952i	$0.464974\pi$
$108$	2.85411	0.274637
$109$	−12.6892	−1.21541	−0.607704	−	0.794164i	$-0.707909\pi$
$109$	−12.6892	−1.21541	−0.607704	+	0.794164i	$0.707909\pi$
$110$	−0.195606	−0.0186503
$111$	−7.73343	−0.734025
$112$	0	0
$113$	−6.75715	−0.635659	−0.317830	−	0.948148i	$-0.602954\pi$
$113$	−6.75715	−0.635659	−0.317830	+	0.948148i	$0.602954\pi$
$114$	3.37906	0.316478
$115$	−5.86089	−0.546531
$116$	−2.48948	−0.231142
$117$	12.5775	1.16279
$118$	19.8824	1.83032
$119$	0	0
$120$	1.35239	0.123456
$121$	−10.9914	−0.999216
$122$	16.9058	1.53058
$123$	−13.3475	−1.20350
$124$	12.3775	1.11153
$125$	−9.61703	−0.860174
$126$	0	0
$127$	16.9966	1.50821	0.754103	−	0.656757i	$-0.228072\pi$
$127$	16.9966	1.50821	0.754103	+	0.656757i	$0.228072\pi$
$128$	4.27096	0.377503
$129$	−24.6701	−2.17208
$130$	11.6287	1.01990
$131$	1.70546	0.149007	0.0745033	−	0.997221i	$-0.476263\pi$
$131$	1.70546	0.149007	0.0745033	+	0.997221i	$0.476263\pi$
$132$	0.367106	0.0319525
$133$	0	0
$134$	2.94506	0.254414
$135$	1.81131	0.155892
$136$	0.798447	0.0684663
$137$	−1.00000	−0.0854358
$137$	−1.00000	−0.0854358
$138$	23.7860	2.02480
$139$	12.3348	1.04622	0.523112	−	0.852264i	$-0.324771\pi$
$139$	12.3348	1.04622	0.523112	+	0.852264i	$0.324771\pi$
$140$	0	0
$141$	22.5194	1.89647
$142$	−9.61616	−0.806970
$143$	−0.512820	−0.0428841
$144$	−10.2071	−0.850592
$145$	−1.57990	−0.131204
$146$	−19.9114	−1.64788
$147$	0	0
$148$	5.79153	0.476061
$149$	13.4660	1.10318	0.551589	−	0.834116i	$-0.314022\pi$
$149$	13.4660	1.10318	0.551589	+	0.834116i	$0.314022\pi$
$150$	16.8735	1.37772
$151$	1.73078	0.140849	0.0704246	−	0.997517i	$-0.477565\pi$
$151$	1.73078	0.140849	0.0704246	+	0.997517i	$0.477565\pi$
$152$	0.411114	0.0333457
$153$	−3.37355	−0.272735
$154$	0	0
$155$	7.85512	0.630938
$156$	−21.8243	−1.74734
$157$	2.88497	0.230246	0.115123	−	0.993351i	$-0.463274\pi$
$157$	2.88497	0.230246	0.115123	+	0.993351i	$0.463274\pi$
$158$	18.6385	1.48280
$159$	0.932482	0.0739506
$160$	−8.25975	−0.652991
$161$	0	0
$162$	−20.5324	−1.61318
$163$	14.7113	1.15227	0.576137	−	0.817353i	$-0.304559\pi$
$163$	14.7113	1.15227	0.576137	+	0.817353i	$0.304559\pi$
$164$	9.99585	0.780545
$165$	0.232977	0.0181372
$166$	22.5759	1.75223
$167$	−1.01831	−0.0787989	−0.0393994	−	0.999224i	$-0.512544\pi$
$167$	−1.01831	−0.0787989	−0.0393994	+	0.999224i	$0.512544\pi$
$168$	0	0
$169$	17.4869	1.34515
$170$	−3.11905	−0.239220
$171$	−1.73701	−0.132833
$172$	18.4753	1.40873
$173$	8.49169	0.645612	0.322806	−	0.946465i	$-0.395374\pi$
$173$	8.49169	0.645612	0.322806	+	0.946465i	$0.395374\pi$
$174$	6.41191	0.486086
$175$	0	0
$176$	0.416172	0.0313701
$177$	−23.6810	−1.77997
$178$	−20.3736	−1.52707
$179$	21.8147	1.63051	0.815254	−	0.579104i	$-0.196597\pi$
$179$	21.8147	1.63051	0.815254	+	0.579104i	$0.196597\pi$
$180$	4.27921	0.318953
$181$	5.56506	0.413648	0.206824	−	0.978378i	$-0.433687\pi$
$181$	5.56506	0.413648	0.206824	+	0.978378i	$0.433687\pi$
$182$	0	0
$183$	−20.1357	−1.48848
$184$	2.89393	0.213343
$185$	3.67548	0.270227
$186$	−31.8794	−2.33751
$187$	0.137549	0.0100586
$188$	−16.8647	−1.22998
$189$	0	0
$190$	−1.60597	−0.116509
$191$	5.06463	0.366464	0.183232	−	0.983070i	$-0.441344\pi$
$191$	5.06463	0.366464	0.183232	+	0.983070i	$0.441344\pi$
$192$	12.9331	0.933364
$193$	19.1208	1.37634	0.688171	−	0.725548i	$-0.258414\pi$
$193$	19.1208	1.37634	0.688171	+	0.725548i	$0.258414\pi$
$194$	24.2597	1.74175
$195$	−13.8504	−0.991846
$196$	0	0
$197$	1.14288	0.0814265	0.0407133	−	0.999171i	$-0.487037\pi$
$197$	1.14288	0.0814265	0.0407133	+	0.999171i	$0.487037\pi$
$198$	−0.408081	−0.0290010
$199$	26.1023	1.85034	0.925171	−	0.379551i	$-0.123922\pi$
$199$	26.1023	1.85034	0.925171	+	0.379551i	$0.123922\pi$
$200$	2.05292	0.145163
$201$	−3.50772	−0.247415
$202$	−25.0350	−1.76146
$203$	0	0
$204$	5.85373	0.409843
$205$	6.34367	0.443061
$206$	4.10023	0.285676
$207$	−12.2272	−0.849852
$208$	−24.7412	−1.71550
$209$	0.0708227	0.00489891
$210$	0	0
$211$	13.6521	0.939851	0.469926	−	0.882706i	$-0.344281\pi$
$211$	13.6521	0.939851	0.469926	+	0.882706i	$0.344281\pi$
$212$	−0.698331	−0.0479616
$213$	11.4534	0.784771
$214$	4.38210	0.299554
$215$	11.7250	0.799640
$216$	−0.894366	−0.0608539
$217$	0	0
$218$	−24.4757	−1.65770
$219$	23.7155	1.60255
$220$	−0.174475	−0.0117631
$221$	−8.17722	−0.550060
$222$	−14.9167	−1.00114
$223$	11.6557	0.780521	0.390261	−	0.920704i	$-0.372385\pi$
$223$	11.6557	0.780521	0.390261	+	0.920704i	$0.372385\pi$
$224$	0	0
$225$	−8.67387	−0.578258
$226$	−13.0336	−0.866981
$227$	25.3759	1.68426	0.842129	−	0.539276i	$-0.181302\pi$
$227$	25.3759	1.68426	0.842129	+	0.539276i	$0.181302\pi$
$228$	3.01403	0.199609
$229$	28.0348	1.85259	0.926294	−	0.376801i	$-0.122976\pi$
$229$	28.0348	1.85259	0.926294	+	0.376801i	$0.122976\pi$
$230$	−11.3048	−0.745418
$231$	0	0
$232$	0.780105	0.0512164
$233$	11.2332	0.735913	0.367956	−	0.929843i	$-0.380058\pi$
$233$	11.2332	0.735913	0.367956	+	0.929843i	$0.380058\pi$
$234$	24.2602	1.58594
$235$	−10.7028	−0.698175
$236$	17.7346	1.15442
$237$	−22.1995	−1.44201
$238$	0	0
$239$	−11.1649	−0.722197	−0.361099	−	0.932528i	$-0.617598\pi$
$239$	−11.1649	−0.722197	−0.361099	+	0.932528i	$0.617598\pi$
$240$	11.2401	0.725544
$241$	12.0903	0.778802	0.389401	−	0.921068i	$-0.372682\pi$
$241$	12.0903	0.778802	0.389401	+	0.921068i	$0.372682\pi$
$242$	−21.2008	−1.36284
$243$	19.4785	1.24955
$244$	15.0795	0.965369
$245$	0	0
$246$	−25.7454	−1.64146
$247$	−4.21038	−0.267900
$248$	−3.87861	−0.246292
$249$	−26.8891	−1.70403
$250$	−18.5499	−1.17320
$251$	9.17226	0.578948	0.289474	−	0.957186i	$-0.406520\pi$
$251$	9.17226	0.578948	0.289474	+	0.957186i	$0.406520\pi$
$252$	0	0
$253$	0.498538	0.0313428
$254$	32.7840	2.05705
$255$	3.71496	0.232640
$256$	19.4971	1.21857
$257$	−17.6073	−1.09831	−0.549156	−	0.835720i	$-0.685051\pi$
$257$	−17.6073	−1.09831	−0.549156	+	0.835720i	$0.685051\pi$
$258$	−47.5852	−2.96252
$259$	0	0
$260$	10.3725	0.643273
$261$	−3.29605	−0.204020
$262$	3.28958	0.203231
$263$	−4.79339	−0.295573	−0.147787	−	0.989019i	$-0.547215\pi$
$263$	−4.79339	−0.295573	−0.147787	+	0.989019i	$0.547215\pi$
$264$	−0.115037	−0.00708002
$265$	−0.443182	−0.0272245
$266$	0	0
$267$	24.2661	1.48506
$268$	2.62691	0.160464
$269$	−10.7542	−0.655696	−0.327848	−	0.944731i	$-0.606323\pi$
$269$	−10.7542	−0.655696	−0.327848	+	0.944731i	$0.606323\pi$
$270$	3.49375	0.212623
$271$	16.0132	0.972735	0.486367	−	0.873754i	$-0.338322\pi$
$271$	16.0132	0.972735	0.486367	+	0.873754i	$0.338322\pi$
$272$	6.63611	0.402373
$273$	0	0
$274$	−1.92886	−0.116527
$275$	0.353657	0.0213263
$276$	21.2165	1.27708
$277$	11.3295	0.680723	0.340361	−	0.940295i	$-0.389451\pi$
$277$	11.3295	0.680723	0.340361	+	0.940295i	$0.389451\pi$
$278$	23.7920	1.42695
$279$	16.3877	0.981104
$280$	0	0
$281$	−28.0552	−1.67363	−0.836815	−	0.547486i	$-0.815585\pi$
$281$	−28.0552	−1.67363	−0.836815	+	0.547486i	$0.815585\pi$
$282$	43.4367	2.58662
$283$	−6.16696	−0.366588	−0.183294	−	0.983058i	$-0.558676\pi$
$283$	−6.16696	−0.366588	−0.183294	+	0.983058i	$0.558676\pi$
$284$	−8.57736	−0.508973
$285$	1.91280	0.113304
$286$	−0.989156	−0.0584900
$287$	0	0
$288$	−17.2318	−1.01540
$289$	−14.8067	−0.870982
$290$	−3.04740	−0.178950
$291$	−28.8946	−1.69383
$292$	−17.7605	−1.03935
$293$	11.9097	0.695772	0.347886	−	0.937537i	$-0.386900\pi$
$293$	11.9097	0.695772	0.347886	+	0.937537i	$0.386900\pi$
$294$	0	0
$295$	11.2549	0.655286
$296$	−1.81484	−0.105485
$297$	−0.154073	−0.00894021
$298$	25.9740	1.50463
$299$	−29.6379	−1.71400
$300$	15.0508	0.868956
$301$	0	0
$302$	3.33843	0.192105
$303$	29.8180	1.71300
$304$	3.41688	0.195971
$305$	9.56994	0.547973
$306$	−6.50709	−0.371986
$307$	−21.9454	−1.25249	−0.626246	−	0.779626i	$-0.715409\pi$
$307$	−21.9454	−1.25249	−0.626246	+	0.779626i	$0.715409\pi$
$308$	0	0
$309$	−4.88359	−0.277818
$310$	15.1514	0.860542
$311$	17.6949	1.00339	0.501693	−	0.865046i	$-0.332711\pi$
$311$	17.6949	1.00339	0.501693	+	0.865046i	$0.332711\pi$
$312$	6.83888	0.387175
$313$	−22.3103	−1.26105	−0.630526	−	0.776168i	$-0.717161\pi$
$313$	−22.3103	−1.26105	−0.630526	+	0.776168i	$0.717161\pi$
$314$	5.56470	0.314034
$315$	0	0
$316$	16.6251	0.935235
$317$	−13.7637	−0.773049	−0.386524	−	0.922279i	$-0.626324\pi$
$317$	−13.7637	−0.773049	−0.386524	+	0.922279i	$0.626324\pi$
$318$	1.79862	0.100862
$319$	0.134389	0.00752434
$320$	−6.14672	−0.343612
$321$	−5.21931	−0.291314
$322$	0	0
$323$	1.12931	0.0628366
$324$	−18.3144	−1.01746
$325$	−21.0248	−1.16625
$326$	28.3759	1.57160
$327$	29.1519	1.61210
$328$	−3.13231	−0.172953
$329$	0	0
$330$	0.449379	0.0247375
$331$	−4.45220	−0.244715	−0.122357	−	0.992486i	$-0.539045\pi$
$331$	−4.45220	−0.244715	−0.122357	+	0.992486i	$0.539045\pi$
$332$	20.1371	1.10517
$333$	7.66795	0.420201
$334$	−1.96417	−0.107474
$335$	1.66712	0.0910845
$336$	0	0
$337$	9.43535	0.513976	0.256988	−	0.966415i	$-0.417270\pi$
$337$	9.43535	0.513976	0.256988	+	0.966415i	$0.417270\pi$
$338$	33.7298	1.83466
$339$	15.5237	0.843131
$340$	−2.78211	−0.150881
$341$	−0.668170	−0.0361835
$342$	−3.35045	−0.181171
$343$	0	0
$344$	−5.78945	−0.312146
$345$	13.4647	0.724912
$346$	16.3793	0.880555
$347$	29.1989	1.56748	0.783739	−	0.621090i	$-0.213310\pi$
$347$	29.1989	1.56748	0.783739	+	0.621090i	$0.213310\pi$
$348$	5.71926	0.306584
$349$	1.51188	0.0809293	0.0404647	−	0.999181i	$-0.487116\pi$
$349$	1.51188	0.0809293	0.0404647	+	0.999181i	$0.487116\pi$
$350$	0	0
$351$	9.15957	0.488902
$352$	0.702589	0.0374481
$353$	−13.4177	−0.714149	−0.357075	−	0.934076i	$-0.616226\pi$
$353$	−13.4177	−0.714149	−0.357075	+	0.934076i	$0.616226\pi$
$354$	−45.6772	−2.42772
$355$	−5.44346	−0.288909
$356$	−18.1728	−0.963154
$357$	0	0
$358$	42.0775	2.22386
$359$	−12.6190	−0.666006	−0.333003	−	0.942926i	$-0.608062\pi$
$359$	−12.6190	−0.666006	−0.333003	+	0.942926i	$0.608062\pi$
$360$	−1.34094	−0.0706736
$361$	−18.4185	−0.969396
$362$	10.7342	0.564177
$363$	25.2513	1.32535
$364$	0	0
$365$	−11.2713	−0.589968
$366$	−38.8389	−2.03014
$367$	−24.3425	−1.27067	−0.635334	−	0.772237i	$-0.719138\pi$
$367$	−24.3425	−1.27067	−0.635334	+	0.772237i	$0.719138\pi$
$368$	24.0522	1.25381
$369$	13.2344	0.688957
$370$	7.08948	0.368565
$371$	0	0
$372$	−28.4356	−1.47432
$373$	5.16273	0.267316	0.133658	−	0.991028i	$-0.457328\pi$
$373$	5.16273	0.267316	0.133658	+	0.991028i	$0.457328\pi$
$374$	0.265312	0.0137190
$375$	22.0939	1.14092
$376$	5.28472	0.272539
$377$	−7.98938	−0.411474
$378$	0	0
$379$	−17.4509	−0.896391	−0.448195	−	0.893936i	$-0.647933\pi$
$379$	−17.4509	−0.896391	−0.448195	+	0.893936i	$0.647933\pi$
$380$	−1.43249	−0.0734850
$381$	−39.0475	−2.00047
$382$	9.76894	0.499823
$383$	2.87438	0.146874	0.0734370	−	0.997300i	$-0.476603\pi$
$383$	2.87438	0.146874	0.0734370	+	0.997300i	$0.476603\pi$
$384$	−9.81197	−0.500715
$385$	0	0
$386$	36.8812	1.87720
$387$	24.4612	1.24343
$388$	21.6390	1.09856
$389$	28.3223	1.43600	0.717998	−	0.696045i	$-0.245059\pi$
$389$	28.3223	1.43600	0.717998	+	0.696045i	$0.245059\pi$
$390$	−26.7154	−1.35279
$391$	7.94950	0.402023
$392$	0	0
$393$	−3.91807	−0.197640
$394$	2.20444	0.111058
$395$	10.5508	0.530868
$396$	−0.363997	−0.0182915
$397$	18.0673	0.906774	0.453387	−	0.891314i	$-0.350216\pi$
$397$	18.0673	0.906774	0.453387	+	0.891314i	$0.350216\pi$
$398$	50.3476	2.52370
$399$	0	0
$400$	17.0624	0.853119
$401$	−0.245407	−0.0122550	−0.00612751	−	0.999981i	$-0.501950\pi$
$401$	−0.245407	−0.0122550	−0.00612751	+	0.999981i	$0.501950\pi$
$402$	−6.76589	−0.337452
$403$	39.7225	1.97872
$404$	−22.3306	−1.11099
$405$	−11.6229	−0.577544
$406$	0	0
$407$	−0.312643	−0.0154971
$408$	−1.83433	−0.0908129
$409$	−29.0796	−1.43790	−0.718948	−	0.695064i	$-0.755376\pi$
$409$	−29.0796	−1.43790	−0.718948	+	0.695064i	$0.755376\pi$
$410$	12.2360	0.604295
$411$	2.29737	0.113321
$412$	3.65730	0.180182
$413$	0	0
$414$	−23.5846	−1.15912
$415$	12.7796	0.627327
$416$	−41.7687	−2.04788
$417$	−28.3376	−1.38770
$418$	0.136607	0.00668166
$419$	−14.6653	−0.716448	−0.358224	−	0.933636i	$-0.616618\pi$
$419$	−14.6653	−0.716448	−0.358224	+	0.933636i	$0.616618\pi$
$420$	0	0
$421$	−9.45353	−0.460737	−0.230368	−	0.973103i	$-0.573993\pi$
$421$	−9.45353	−0.460737	−0.230368	+	0.973103i	$0.573993\pi$
$422$	26.3330	1.28187
$423$	−22.3287	−1.08566
$424$	0.218830	0.0106273
$425$	5.63928	0.273545
$426$	22.0919	1.07036
$427$	0	0
$428$	3.90872	0.188935
$429$	1.17814	0.0568810
$430$	22.6159	1.09063
$431$	−24.0203	−1.15702	−0.578508	−	0.815676i	$-0.696365\pi$
$431$	−24.0203	−1.15702	−0.578508	+	0.815676i	$0.696365\pi$
$432$	−7.43332	−0.357636
$433$	30.3434	1.45821	0.729104	−	0.684402i	$-0.239937\pi$
$433$	30.3434	1.45821	0.729104	+	0.684402i	$0.239937\pi$
$434$	0	0
$435$	3.62962	0.174027
$436$	−21.8317	−1.04555
$437$	4.09313	0.195801
$438$	45.7439	2.18573
$439$	−22.9494	−1.09532	−0.547658	−	0.836702i	$-0.684480\pi$
$439$	−22.9494	−1.09532	−0.547658	+	0.836702i	$0.684480\pi$
$440$	0.0546737	0.00260647
$441$	0	0
$442$	−15.7727	−0.750231
$443$	−14.0744	−0.668693	−0.334347	−	0.942450i	$-0.608516\pi$
$443$	−14.0744	−0.668693	−0.334347	+	0.942450i	$0.608516\pi$
$444$	−13.3053	−0.631441
$445$	−11.5330	−0.546716
$446$	22.4821	1.06456
$447$	−30.9364	−1.46324
$448$	0	0
$449$	−30.2652	−1.42830	−0.714151	−	0.699992i	$-0.753187\pi$
$449$	−30.2652	−1.42830	−0.714151	+	0.699992i	$0.753187\pi$
$450$	−16.7307	−0.788691
$451$	−0.539604	−0.0254090
$452$	−11.6256	−0.546823
$453$	−3.97625	−0.186821
$454$	48.9465	2.29717
$455$	0	0
$456$	−0.944481	−0.0442294
$457$	25.6042	1.19771	0.598857	−	0.800856i	$-0.295622\pi$
$457$	25.6042	1.19771	0.598857	+	0.800856i	$0.295622\pi$
$458$	54.0750	2.52676
$459$	−2.45679	−0.114673
$460$	−10.0836	−0.470151
$461$	37.3845	1.74117	0.870586	−	0.492016i	$-0.163740\pi$
$461$	37.3845	1.74117	0.870586	+	0.492016i	$0.163740\pi$
$462$	0	0
$463$	−14.4887	−0.673346	−0.336673	−	0.941622i	$-0.609302\pi$
$463$	−14.4887	−0.673346	−0.336673	+	0.941622i	$0.609302\pi$
$464$	6.48367	0.300997
$465$	−18.0461	−0.836869
$466$	21.6673	1.00372
$467$	−15.2102	−0.703843	−0.351922	−	0.936030i	$-0.614472\pi$
$467$	−15.2102	−0.703843	−0.351922	+	0.936030i	$0.614472\pi$
$468$	21.6395	1.00029
$469$	0	0
$470$	−20.6442	−0.952247
$471$	−6.62785	−0.305395
$472$	−5.55732	−0.255796
$473$	−0.997351	−0.0458583
$474$	−42.8197	−1.96677
$475$	2.90362	0.133227
$476$	0	0
$477$	−0.924585	−0.0423338
$478$	−21.5355	−0.985010
$479$	−24.1582	−1.10382	−0.551908	−	0.833905i	$-0.686100\pi$
$479$	−24.1582	−1.10382	−0.551908	+	0.833905i	$0.686100\pi$
$480$	18.9757	0.866119
$481$	18.5865	0.847472
$482$	23.3204	1.06221
$483$	0	0
$484$	−18.9106	−0.859571
$485$	13.7328	0.623574
$486$	37.5712	1.70427
$487$	−21.2094	−0.961089	−0.480545	−	0.876970i	$-0.659561\pi$
$487$	−21.2094	−0.961089	−0.480545	+	0.876970i	$0.659561\pi$
$488$	−4.72534	−0.213906
$489$	−33.7972	−1.52836
$490$	0	0
$491$	−15.0104	−0.677410	−0.338705	−	0.940893i	$-0.609989\pi$
$491$	−15.0104	−0.677410	−0.338705	+	0.940893i	$0.609989\pi$
$492$	−22.9642	−1.03531
$493$	2.14292	0.0965121
$494$	−8.12122	−0.365391
$495$	−0.231004	−0.0103828
$496$	−32.2362	−1.44745
$497$	0	0
$498$	−51.8652	−2.32414
$499$	16.5400	0.740431	0.370216	−	0.928946i	$-0.379284\pi$
$499$	16.5400	0.740431	0.370216	+	0.928946i	$0.379284\pi$
$500$	−16.5460	−0.739960
$501$	2.33943	0.104518
$502$	17.6920	0.789632
$503$	11.0462	0.492527	0.246264	−	0.969203i	$-0.420797\pi$
$503$	11.0462	0.492527	0.246264	+	0.969203i	$0.420797\pi$
$504$	0	0
$505$	−14.1717	−0.630631
$506$	0.961609	0.0427487
$507$	−40.1739	−1.78419
$508$	29.2425	1.29743
$509$	41.4806	1.83859	0.919297	−	0.393565i	$-0.128758\pi$
$509$	41.4806	1.83859	0.919297	+	0.393565i	$0.128758\pi$
$510$	7.16562	0.317299
$511$	0	0
$512$	29.0652	1.28451
$513$	−1.26498	−0.0558501
$514$	−33.9619	−1.49800
$515$	2.32103	0.102277
$516$	−42.4447	−1.86852
$517$	0.910402	0.0400394
$518$	0	0
$519$	−19.5086	−0.856332
$520$	−3.25033	−0.142536
$521$	12.3926	0.542931	0.271466	−	0.962448i	$-0.412492\pi$
$521$	12.3926	0.542931	0.271466	+	0.962448i	$0.412492\pi$
$522$	−6.35761	−0.278265
$523$	24.9733	1.09201	0.546004	−	0.837783i	$-0.316148\pi$
$523$	24.9733	1.09201	0.546004	+	0.837783i	$0.316148\pi$
$524$	2.93422	0.128182
$525$	0	0
$526$	−9.24577	−0.403135
$527$	−10.6544	−0.464112
$528$	−0.956101	−0.0416090
$529$	5.81250	0.252717
$530$	−0.854835	−0.0371317
$531$	23.4804	1.01896
$532$	0	0
$533$	32.0793	1.38951
$534$	46.8058	2.02549
$535$	2.48059	0.107245
$536$	−0.823172	−0.0355556
$537$	−50.1165	−2.16269
$538$	−20.7433	−0.894309
$539$	0	0
$540$	3.11633	0.134106
$541$	2.47732	0.106508	0.0532542	−	0.998581i	$-0.483041\pi$
$541$	2.47732	0.106508	0.0532542	+	0.998581i	$0.483041\pi$
$542$	30.8872	1.32672
$543$	−12.7850	−0.548657
$544$	11.2032	0.480334
$545$	−13.8551	−0.593486
$546$	0	0
$547$	−1.67277	−0.0715225	−0.0357612	−	0.999360i	$-0.511386\pi$
$547$	−1.67277	−0.0715225	−0.0357612	+	0.999360i	$0.511386\pi$
$548$	−1.72049	−0.0734957
$549$	19.9652	0.852094
$550$	0.682155	0.0290872
$551$	1.10337	0.0470051
$552$	−6.64843	−0.282976
$553$	0	0
$554$	21.8530	0.928443
$555$	−8.44395	−0.358426
$556$	21.2219	0.900008
$557$	0.916098	0.0388163	0.0194082	−	0.999812i	$-0.493822\pi$
$557$	0.916098	0.0388163	0.0194082	+	0.999812i	$0.493822\pi$
$558$	31.6095	1.33814
$559$	59.2921	2.50779
$560$	0	0
$561$	−0.316001	−0.0133416
$562$	−54.1144	−2.28268
$563$	−1.88965	−0.0796394	−0.0398197	−	0.999207i	$-0.512678\pi$
$563$	−1.88965	−0.0796394	−0.0398197	+	0.999207i	$0.512678\pi$
$564$	38.7444	1.63143
$565$	−7.37797	−0.310394
$566$	−11.8952	−0.499992
$567$	0	0
$568$	2.68781	0.112778
$569$	−4.29192	−0.179927	−0.0899633	−	0.995945i	$-0.528675\pi$
$569$	−4.29192	−0.179927	−0.0899633	+	0.995945i	$0.528675\pi$
$570$	3.68952	0.154537
$571$	15.8294	0.662439	0.331219	−	0.943554i	$-0.392540\pi$
$571$	15.8294	0.662439	0.331219	+	0.943554i	$0.392540\pi$
$572$	−0.882301	−0.0368909
$573$	−11.6353	−0.486073
$574$	0	0
$575$	20.4393	0.852376
$576$	−12.8236	−0.534315
$577$	26.6285	1.10856	0.554279	−	0.832331i	$-0.312994\pi$
$577$	26.6285	1.10856	0.554279	+	0.832331i	$0.312994\pi$
$578$	−28.5600	−1.18794
$579$	−43.9275	−1.82556
$580$	−2.71820	−0.112867
$581$	0	0
$582$	−55.7336	−2.31023
$583$	0.0376979	0.00156129
$584$	5.56543	0.230299
$585$	13.7331	0.567793
$586$	22.9721	0.948970
$587$	18.1406	0.748742	0.374371	−	0.927279i	$-0.377859\pi$
$587$	18.1406	0.748742	0.374371	+	0.927279i	$0.377859\pi$
$588$	0	0
$589$	−5.48585	−0.226041
$590$	21.7091	0.893749
$591$	−2.62561	−0.108003
$592$	−15.0836	−0.619933
$593$	−26.5153	−1.08885	−0.544426	−	0.838809i	$-0.683252\pi$
$593$	−26.5153	−1.08885	−0.544426	+	0.838809i	$0.683252\pi$
$594$	−0.297185	−0.0121936
$595$	0	0
$596$	23.1681	0.949004
$597$	−59.9666	−2.45427
$598$	−57.1672	−2.33774
$599$	−22.7847	−0.930956	−0.465478	−	0.885059i	$-0.654118\pi$
$599$	−22.7847	−0.930956	−0.465478	+	0.885059i	$0.654118\pi$
$600$	−4.71632	−0.192543
$601$	−1.27019	−0.0518123	−0.0259061	−	0.999664i	$-0.508247\pi$
$601$	−1.27019	−0.0518123	−0.0259061	+	0.999664i	$0.508247\pi$
$602$	0	0
$603$	3.47802	0.141636
$604$	2.97780	0.121165
$605$	−12.0012	−0.487919
$606$	57.5147	2.33638
$607$	−37.8796	−1.53749	−0.768743	−	0.639558i	$-0.779118\pi$
$607$	−37.8796	−1.53749	−0.768743	+	0.639558i	$0.779118\pi$
$608$	5.76844	0.233941
$609$	0	0
$610$	18.4590	0.747385
$611$	−54.1230	−2.18958
$612$	−5.80416	−0.234619
$613$	−28.3610	−1.14549	−0.572746	−	0.819733i	$-0.694122\pi$
$613$	−28.3610	−1.14549	−0.572746	+	0.819733i	$0.694122\pi$
$614$	−42.3296	−1.70828
$615$	−14.5738	−0.587671
$616$	0	0
$617$	−6.44088	−0.259300	−0.129650	−	0.991560i	$-0.541385\pi$
$617$	−6.44088	−0.259300	−0.129650	+	0.991560i	$0.541385\pi$
$618$	−9.41975	−0.378918
$619$	−4.58503	−0.184288	−0.0921441	−	0.995746i	$-0.529372\pi$
$619$	−4.58503	−0.184288	−0.0921441	+	0.995746i	$0.529372\pi$
$620$	13.5147	0.542762
$621$	−8.90448	−0.357325
$622$	34.1309	1.36853
$623$	0	0
$624$	56.8398	2.27541
$625$	8.53842	0.341537
$626$	−43.0334	−1.71996
$627$	−0.162706	−0.00649786
$628$	4.96357	0.198068
$629$	−4.98529	−0.198776
$630$	0	0
$631$	47.0342	1.87240	0.936201	−	0.351464i	$-0.114316\pi$
$631$	47.0342	1.87240	0.936201	+	0.351464i	$0.114316\pi$
$632$	−5.20966	−0.207229
$633$	−31.3640	−1.24661
$634$	−26.5483	−1.05437
$635$	18.5582	0.736459
$636$	1.60433	0.0636156
$637$	0	0
$638$	0.259217	0.0102625
$639$	−11.3564	−0.449251
$640$	4.66335	0.184335
$641$	2.25607	0.0891092	0.0445546	−	0.999007i	$-0.485813\pi$
$641$	2.25607	0.0891092	0.0445546	+	0.999007i	$0.485813\pi$
$642$	−10.0673	−0.397325
$643$	−34.8323	−1.37365	−0.686826	−	0.726822i	$-0.740997\pi$
$643$	−34.8323	−1.37365	−0.686826	+	0.726822i	$0.740997\pi$
$644$	0	0
$645$	−26.9367	−1.06063
$646$	2.17828	0.0857033
$647$	14.8599	0.584201	0.292101	−	0.956388i	$-0.405646\pi$
$647$	14.8599	0.584201	0.292101	+	0.956388i	$0.405646\pi$
$648$	5.73900	0.225449
$649$	−0.957362	−0.0375797
$650$	−40.5538	−1.59065
$651$	0	0
$652$	25.3106	0.991238
$653$	29.3773	1.14962	0.574812	−	0.818285i	$-0.305075\pi$
$653$	29.3773	1.14962	0.574812	+	0.818285i	$0.305075\pi$
$654$	56.2298	2.19876
$655$	1.86215	0.0727602
$656$	−26.0335	−1.01644
$657$	−23.5147	−0.917396
$658$	0	0
$659$	−17.1556	−0.668288	−0.334144	−	0.942522i	$-0.608447\pi$
$659$	−17.1556	−0.668288	−0.334144	+	0.942522i	$0.608447\pi$
$660$	0.400834	0.0156024
$661$	26.6730	1.03746	0.518729	−	0.854939i	$-0.326405\pi$
$661$	26.6730	1.03746	0.518729	+	0.854939i	$0.326405\pi$
$662$	−8.58765	−0.333769
$663$	18.7861	0.729593
$664$	−6.31018	−0.244883
$665$	0	0
$666$	14.7904	0.573115
$667$	7.76688	0.300735
$668$	−1.75199	−0.0677864
$669$	−26.7774	−1.03527
$670$	3.21564	0.124231
$671$	−0.814036	−0.0314255
$672$	0	0
$673$	32.0325	1.23476	0.617382	−	0.786664i	$-0.288193\pi$
$673$	32.0325	1.23476	0.617382	+	0.786664i	$0.288193\pi$
$674$	18.1994	0.701016
$675$	−6.31674	−0.243132
$676$	30.0861	1.15716
$677$	−23.7374	−0.912303	−0.456151	−	0.889902i	$-0.650772\pi$
$677$	−23.7374	−0.912303	−0.456151	+	0.889902i	$0.650772\pi$
$678$	29.9430	1.14995
$679$	0	0
$680$	0.871805	0.0334322
$681$	−58.2979	−2.23398
$682$	−1.28881	−0.0493509
$683$	2.76441	0.105777	0.0528886	−	0.998600i	$-0.483157\pi$
$683$	2.76441	0.105777	0.0528886	+	0.998600i	$0.483157\pi$
$684$	−2.98851	−0.114269
$685$	−1.09188	−0.0417184
$686$	0	0
$687$	−64.4063	−2.45725
$688$	−48.1177	−1.83447
$689$	−2.24112	−0.0853800
$690$	25.9714	0.988714
$691$	−47.2507	−1.79750	−0.898752	−	0.438458i	$-0.855525\pi$
$691$	−47.2507	−1.79750	−0.898752	+	0.438458i	$0.855525\pi$
$692$	14.6099	0.555384
$693$	0	0
$694$	56.3205	2.13790
$695$	13.4681	0.510873
$696$	−1.79219	−0.0679328
$697$	−8.60432	−0.325912
$698$	2.91621	0.110380
$699$	−25.8069	−0.976106
$700$	0	0
$701$	−40.7327	−1.53845	−0.769227	−	0.638976i	$-0.779358\pi$
$701$	−40.7327	−1.53845	−0.769227	+	0.638976i	$0.779358\pi$
$702$	17.6675	0.666817
$703$	−2.56688	−0.0968118
$704$	0.522851	0.0197057
$705$	24.5884	0.926052
$706$	−25.8807	−0.974034
$707$	0	0
$708$	−40.7429	−1.53121
$709$	4.62971	0.173872	0.0869362	−	0.996214i	$-0.472292\pi$
$709$	4.62971	0.173872	0.0869362	+	0.996214i	$0.472292\pi$
$710$	−10.4997	−0.394045
$711$	22.0115	0.825496
$712$	5.69463	0.213415
$713$	−38.6162	−1.44619
$714$	0	0
$715$	−0.559935	−0.0209404
$716$	37.5320	1.40264
$717$	25.6499	0.957914
$718$	−24.3403	−0.908371
$719$	−20.4501	−0.762661	−0.381331	−	0.924439i	$-0.624534\pi$
$719$	−20.4501	−0.762661	−0.381331	+	0.924439i	$0.624534\pi$
$720$	−11.1449	−0.415346
$721$	0	0
$722$	−35.5267	−1.32217
$723$	−27.7758	−1.03299
$724$	9.57463	0.355838
$725$	5.50974	0.204627
$726$	48.7061	1.80765
$727$	−5.98752	−0.222065	−0.111032	−	0.993817i	$-0.535416\pi$
$727$	−5.98752	−0.222065	−0.111032	+	0.993817i	$0.535416\pi$
$728$	0	0
$729$	−12.8148	−0.474622
$730$	−21.7408	−0.804663
$731$	−15.9034	−0.588208
$732$	−34.6433	−1.28045
$733$	0.722356	0.0266808	0.0133404	−	0.999911i	$-0.495753\pi$
$733$	0.722356	0.0266808	0.0133404	+	0.999911i	$0.495753\pi$
$734$	−46.9532	−1.73307
$735$	0	0
$736$	40.6054	1.49674
$737$	−0.141808	−0.00522357
$738$	25.5273	0.939674
$739$	39.2349	1.44328	0.721640	−	0.692268i	$-0.243388\pi$
$739$	39.2349	1.44328	0.721640	+	0.692268i	$0.243388\pi$
$740$	6.32363	0.232461
$741$	9.67281	0.355340
$742$	0	0
$743$	−15.7573	−0.578081	−0.289041	−	0.957317i	$-0.593336\pi$
$743$	−15.7573	−0.578081	−0.289041	+	0.957317i	$0.593336\pi$
$744$	8.91062	0.326679
$745$	14.7032	0.538684
$746$	9.95816	0.364594
$747$	26.6614	0.975489
$748$	0.236651	0.00865283
$749$	0	0
$750$	42.6160	1.55612
$751$	31.5460	1.15113	0.575565	−	0.817756i	$-0.304782\pi$
$751$	31.5460	1.15113	0.575565	+	0.817756i	$0.304782\pi$
$752$	43.9228	1.60170
$753$	−21.0721	−0.767910
$754$	−15.4104	−0.561212
$755$	1.88980	0.0687769
$756$	0	0
$757$	−49.4085	−1.79578	−0.897891	−	0.440218i	$-0.854901\pi$
$757$	−49.4085	−1.79578	−0.897891	+	0.440218i	$0.854901\pi$
$758$	−33.6602	−1.22259
$759$	−1.14533	−0.0415727
$760$	0.448885	0.0162828
$761$	1.39665	0.0506284	0.0253142	−	0.999680i	$-0.491941\pi$
$761$	1.39665	0.0506284	0.0253142	+	0.999680i	$0.491941\pi$
$762$	−75.3171	−2.72845
$763$	0	0
$764$	8.71364	0.315248
$765$	−3.68350	−0.133177
$766$	5.54427	0.200323
$767$	56.9148	2.05507
$768$	−44.7920	−1.61629
$769$	−4.95291	−0.178607	−0.0893033	−	0.996004i	$-0.528464\pi$
$769$	−4.95291	−0.178607	−0.0893033	+	0.996004i	$0.528464\pi$
$770$	0	0
$771$	40.4504	1.45679
$772$	32.8971	1.18399
$773$	−48.8648	−1.75754	−0.878772	−	0.477243i	$-0.841636\pi$
$773$	−48.8648	−1.75754	−0.878772	+	0.477243i	$0.841636\pi$
$774$	47.1822	1.69593
$775$	−27.3939	−0.984019
$776$	−6.78083	−0.243418
$777$	0	0
$778$	54.6296	1.95857
$779$	−4.43029	−0.158732
$780$	−23.8294	−0.853230
$781$	0.463030	0.0165685
$782$	15.3334	0.548323
$783$	−2.40035	−0.0857815
$784$	0	0
$785$	3.15003	0.112429
$786$	−7.55740	−0.269563
$787$	−17.4733	−0.622856	−0.311428	−	0.950270i	$-0.600807\pi$
$787$	−17.4733	−0.622856	−0.311428	+	0.950270i	$0.600807\pi$
$788$	1.96631	0.0700468
$789$	11.0122	0.392045
$790$	20.3510	0.724055
$791$	0	0
$792$	0.114062	0.00405303
$793$	48.3941	1.71853
$794$	34.8493	1.23676
$795$	1.01815	0.0361102
$796$	44.9087	1.59175
$797$	6.38717	0.226245	0.113123	−	0.993581i	$-0.463915\pi$
$797$	6.38717	0.226245	0.113123	+	0.993581i	$0.463915\pi$
$798$	0	0
$799$	14.5169	0.513571
$800$	28.8051	1.01841
$801$	−24.0606	−0.850139
$802$	−0.473354	−0.0167147
$803$	0.958759	0.0338339
$804$	−6.03500	−0.212838
$805$	0	0
$806$	76.6190	2.69879
$807$	24.7064	0.869707
$808$	6.99753	0.246172
$809$	−54.0959	−1.90191	−0.950956	−	0.309328i	$-0.899896\pi$
$809$	−54.0959	−1.90191	−0.950956	+	0.309328i	$0.899896\pi$
$810$	−22.4188	−0.787717
$811$	3.57360	0.125486	0.0627430	−	0.998030i	$-0.480015\pi$
$811$	3.57360	0.125486	0.0627430	+	0.998030i	$0.480015\pi$
$812$	0	0
$813$	−36.7883	−1.29022
$814$	−0.603044	−0.0211367
$815$	16.0629	0.562658
$816$	−15.2456	−0.533703
$817$	−8.18851	−0.286480
$818$	−56.0905	−1.96116
$819$	0	0
$820$	10.9142	0.381141
$821$	21.3809	0.746200	0.373100	−	0.927791i	$-0.378295\pi$
$821$	21.3809	0.746200	0.373100	+	0.927791i	$0.378295\pi$
$822$	4.43130	0.154559
$823$	−42.6542	−1.48683	−0.743416	−	0.668829i	$-0.766796\pi$
$823$	−42.6542	−1.48683	−0.743416	+	0.668829i	$0.766796\pi$
$824$	−1.14605	−0.0399247
$825$	−0.812483	−0.0282870
$826$	0	0
$827$	−24.2213	−0.842257	−0.421129	−	0.907001i	$-0.638366\pi$
$827$	−24.2213	−0.842257	−0.421129	+	0.907001i	$0.638366\pi$
$828$	−21.0368	−0.731081
$829$	14.6958	0.510406	0.255203	−	0.966887i	$-0.417858\pi$
$829$	14.6958	0.510406	0.255203	+	0.966887i	$0.417858\pi$
$830$	24.6501	0.855617
$831$	−26.0280	−0.902903
$832$	−31.0833	−1.07762
$833$	0	0
$834$	−54.6592	−1.89269
$835$	−1.11186	−0.0384776
$836$	0.121850	0.00421426
$837$	11.9343	0.412510
$838$	−28.2873	−0.977170
$839$	0.165133	0.00570103	0.00285052	−	0.999996i	$-0.499093\pi$
$839$	0.165133	0.00570103	0.00285052	+	0.999996i	$0.499093\pi$
$840$	0	0
$841$	−26.9063	−0.927804
$842$	−18.2345	−0.628403
$843$	64.4531	2.21988
$844$	23.4883	0.808502
$845$	19.0935	0.656838
$846$	−43.0688	−1.48074
$847$	0	0
$848$	1.81875	0.0624562
$849$	14.1678	0.486238
$850$	10.8774	0.373091
$851$	−18.0689	−0.619394
$852$	19.7054	0.675096
$853$	20.7532	0.710575	0.355288	−	0.934757i	$-0.384383\pi$
$853$	20.7532	0.710575	0.355288	+	0.934757i	$0.384383\pi$
$854$	0	0
$855$	−1.89660	−0.0648624
$856$	−1.22484	−0.0418641
$857$	−33.9252	−1.15886	−0.579431	−	0.815022i	$-0.696725\pi$
$857$	−33.9252	−1.15886	−0.579431	+	0.815022i	$0.696725\pi$
$858$	2.27246	0.0775805
$859$	3.75554	0.128137	0.0640687	−	0.997945i	$-0.479592\pi$
$859$	3.75554	0.128137	0.0640687	+	0.997945i	$0.479592\pi$
$860$	20.1728	0.687886
$861$	0	0
$862$	−46.3317	−1.57806
$863$	33.6984	1.14711	0.573554	−	0.819168i	$-0.305564\pi$
$863$	33.6984	1.14711	0.573554	+	0.819168i	$0.305564\pi$
$864$	−12.5491	−0.426929
$865$	9.27188	0.315253
$866$	58.5280	1.98886
$867$	34.0165	1.15526
$868$	0	0
$869$	−0.897470	−0.0304446
$870$	7.00101	0.237357
$871$	8.43044	0.285655
$872$	6.84120	0.231672
$873$	28.6499	0.969653
$874$	7.89506	0.267054
$875$	0	0
$876$	40.8024	1.37858
$877$	−8.18652	−0.276439	−0.138220	−	0.990402i	$-0.544138\pi$
$877$	−8.18652	−0.276439	−0.138220	+	0.990402i	$0.544138\pi$
$878$	−44.2661	−1.49391
$879$	−27.3610	−0.922864
$880$	0.454408	0.0153181
$881$	−10.9583	−0.369195	−0.184597	−	0.982814i	$-0.559098\pi$
$881$	−10.9583	−0.369195	−0.184597	+	0.982814i	$0.559098\pi$
$882$	0	0
$883$	−5.13051	−0.172655	−0.0863276	−	0.996267i	$-0.527513\pi$
$883$	−5.13051	−0.172655	−0.0863276	+	0.996267i	$0.527513\pi$
$884$	−14.0688	−0.473186
$885$	−25.8567	−0.869163
$886$	−27.1474	−0.912036
$887$	51.7535	1.73771	0.868857	−	0.495063i	$-0.164855\pi$
$887$	51.7535	1.73771	0.868857	+	0.495063i	$0.164855\pi$
$888$	4.16936	0.139915
$889$	0	0
$890$	−22.2455	−0.745670
$891$	0.988661	0.0331214
$892$	20.0535	0.671439
$893$	7.47463	0.250129
$894$	−59.6719	−1.99573
$895$	23.8190	0.796180
$896$	0	0
$897$	68.0892	2.27343
$898$	−58.3772	−1.94807
$899$	−10.4096	−0.347181
$900$	−14.9233	−0.497444
$901$	0.601116	0.0200261
$902$	−1.04082	−0.0346555
$903$	0	0
$904$	3.64301	0.121165
$905$	6.07636	0.201985
$906$	−7.66962	−0.254806
$907$	5.24883	0.174285	0.0871423	−	0.996196i	$-0.472227\pi$
$907$	5.24883	0.174285	0.0871423	+	0.996196i	$0.472227\pi$
$908$	43.6590	1.44887
$909$	−29.5655	−0.980627
$910$	0	0
$911$	34.8795	1.15561	0.577805	−	0.816175i	$-0.303910\pi$
$911$	34.8795	1.15561	0.577805	+	0.816175i	$0.303910\pi$
$912$	−7.84984	−0.259934
$913$	−1.08706	−0.0359764
$914$	49.3868	1.63357
$915$	−21.9857	−0.726825
$916$	48.2335	1.59368
$917$	0	0
$918$	−4.73879	−0.156403
$919$	−43.1979	−1.42497	−0.712484	−	0.701689i	$-0.752430\pi$
$919$	−43.1979	−1.42497	−0.712484	+	0.701689i	$0.752430\pi$
$920$	3.15981	0.104176
$921$	50.4168	1.66129
$922$	72.1095	2.37480
$923$	−27.5270	−0.906061
$924$	0	0
$925$	−12.8179	−0.421449
$926$	−27.9466	−0.918382
$927$	4.84223	0.159040
$928$	10.9459	0.359315
$929$	−57.4511	−1.88491	−0.942454	−	0.334335i	$-0.891488\pi$
$929$	−57.4511	−1.88491	−0.942454	+	0.334335i	$0.891488\pi$
$930$	−34.8084	−1.14141
$931$	0	0
$932$	19.3266	0.633065
$933$	−40.6518	−1.33088
$934$	−29.3383	−0.959977
$935$	0.150186	0.00491162
$936$	−6.78097	−0.221643
$937$	45.4822	1.48584	0.742920	−	0.669380i	$-0.233440\pi$
$937$	45.4822	1.48584	0.742920	+	0.669380i	$0.233440\pi$
$938$	0	0
$939$	51.2550	1.67264
$940$	−18.4141	−0.600602
$941$	−0.888552	−0.0289660	−0.0144830	−	0.999895i	$-0.504610\pi$
$941$	−0.888552	−0.0289660	−0.0144830	+	0.999895i	$0.504610\pi$
$942$	−12.7842	−0.416531
$943$	−31.1859	−1.01555
$944$	−46.1884	−1.50330
$945$	0	0
$946$	−1.92375	−0.0625464
$947$	2.30399	0.0748697	0.0374349	−	0.999299i	$-0.488081\pi$
$947$	2.30399	0.0748697	0.0374349	+	0.999299i	$0.488081\pi$
$948$	−38.1940	−1.24048
$949$	−56.9979	−1.85023
$950$	5.60067	0.181710
$951$	31.6204	1.02536
$952$	0	0
$953$	−18.3900	−0.595712	−0.297856	−	0.954611i	$-0.596271\pi$
$953$	−18.3900	−0.595712	−0.297856	+	0.954611i	$0.596271\pi$
$954$	−1.78339	−0.0577395
$955$	5.52994	0.178945
$956$	−19.2091	−0.621267
$957$	−0.308742	−0.00998020
$958$	−46.5977	−1.50550
$959$	0	0
$960$	14.1213	0.455763
$961$	20.7558	0.669541
$962$	35.8507	1.15587
$963$	5.17511	0.166766
$964$	20.8012	0.669960
$965$	20.8775	0.672071
$966$	0	0
$967$	−42.2737	−1.35943	−0.679716	−	0.733476i	$-0.737897\pi$
$967$	−42.2737	−1.35943	−0.679716	+	0.733476i	$0.737897\pi$
$968$	5.92583	0.190463
$969$	−2.59445	−0.0833457
$970$	26.4886	0.850498
$971$	50.0697	1.60681	0.803406	−	0.595432i	$-0.203019\pi$
$971$	50.0697	1.60681	0.803406	+	0.595432i	$0.203019\pi$
$972$	33.5125	1.07492
$973$	0	0
$974$	−40.9099	−1.31084
$975$	48.3018	1.54689
$976$	−39.2736	−1.25712
$977$	54.1319	1.73183	0.865916	−	0.500190i	$-0.166736\pi$
$977$	54.1319	1.73183	0.865916	+	0.500190i	$0.166736\pi$
$978$	−65.1900	−2.08455
$979$	0.981017	0.0313534
$980$	0	0
$981$	−28.9050	−0.922866
$982$	−28.9529	−0.923925
$983$	8.44047	0.269209	0.134605	−	0.990899i	$-0.457024\pi$
$983$	8.44047	0.269209	0.134605	+	0.990899i	$0.457024\pi$
$984$	7.19608	0.229403
$985$	1.24788	0.0397607
$986$	4.13338	0.131634
$987$	0	0
$988$	−7.24392	−0.230460
$989$	−57.6409	−1.83287
$990$	−0.445573	−0.0141613
$991$	−50.2828	−1.59729	−0.798643	−	0.601805i	$-0.794448\pi$
$991$	−50.2828	−1.59729	−0.798643	+	0.601805i	$0.794448\pi$
$992$	−54.4218	−1.72789
$993$	10.2284	0.324587
$994$	0	0
$995$	28.5005	0.903525
$996$	−46.2624	−1.46588
$997$	38.8807	1.23136	0.615682	−	0.787995i	$-0.288881\pi$
$997$	38.8807	1.23136	0.615682	+	0.787995i	$0.288881\pi$
$998$	31.9033	1.00988
$999$	5.58418	0.176676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6713.2.a.l.1.38		45
7.3	odd	6		959.2.e.b.275.8	✓	90
7.5	odd	6		959.2.e.b.823.8	yes	90
7.6	odd	2		6713.2.a.k.1.38		45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.2.e.b.275.8	✓	90	7.3	odd	6
959.2.e.b.823.8	yes	90	7.5	odd	6
6713.2.a.k.1.38		45	7.6	odd	2
6713.2.a.l.1.38		45	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6713 = 7^{2} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6713.a (trivial)

\(f(q)\)	\(=\)	\(q+1.92886 q^{2} -2.29737 q^{3} +1.72049 q^{4} +1.09188 q^{5} -4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} +O(q^{10})\)	\(q+1.92886 q^{2} -2.29737 q^{3} +1.72049 q^{4} +1.09188 q^{5} -4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} +2.10607 q^{10} -0.0928769 q^{11} -3.95261 q^{12} +5.52150 q^{13} -2.50845 q^{15} -4.48089 q^{16} -1.48098 q^{17} +4.39378 q^{18} -0.762544 q^{19} +1.87856 q^{20} -0.179146 q^{22} -5.36773 q^{23} +1.23859 q^{24} -3.80781 q^{25} +10.6502 q^{26} +1.65889 q^{27} -1.44696 q^{29} -4.83843 q^{30} +7.19415 q^{31} -7.56474 q^{32} +0.213373 q^{33} -2.85660 q^{34} +3.91913 q^{36} +3.36621 q^{37} -1.47084 q^{38} -12.6849 q^{39} -0.588668 q^{40} +5.80988 q^{41} +10.7384 q^{43} -0.159794 q^{44} +2.48720 q^{45} -10.3536 q^{46} -9.80224 q^{47} +10.2943 q^{48} -7.34472 q^{50} +3.40236 q^{51} +9.49968 q^{52} -0.405891 q^{53} +3.19977 q^{54} -0.101410 q^{55} +1.75185 q^{57} -2.79098 q^{58} +10.3079 q^{59} -4.31576 q^{60} +8.76468 q^{61} +13.8765 q^{62} -5.62951 q^{64} +6.02879 q^{65} +0.411566 q^{66} +1.52684 q^{67} -2.54801 q^{68} +12.3317 q^{69} -4.98542 q^{71} -1.22810 q^{72} -10.3229 q^{73} +6.49294 q^{74} +8.74795 q^{75} -1.31195 q^{76} -24.4674 q^{78} +9.66300 q^{79} -4.89258 q^{80} -10.6448 q^{81} +11.2064 q^{82} +11.7043 q^{83} -1.61705 q^{85} +20.7129 q^{86} +3.32420 q^{87} +0.0500732 q^{88} -10.5625 q^{89} +4.79746 q^{90} -9.23512 q^{92} -16.5276 q^{93} -18.9071 q^{94} -0.832603 q^{95} +17.3790 q^{96} +12.5772 q^{97} -0.211566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q + 11 q^{3} + 44 q^{4} + 4 q^{5} + 10 q^{6} - 3 q^{8} + 44 q^{9}+O(q^{10}) \) 45 * q + 11 * q^3 + 44 * q^4 + 4 * q^5 + 10 * q^6 - 3 * q^8 + 44 * q^9	\( 45 q + 11 q^{3} + 44 q^{4} + 4 q^{5} + 10 q^{6} - 3 q^{8} + 44 q^{9} + 25 q^{10} + 33 q^{12} + 36 q^{13} + 38 q^{16} + 18 q^{17} - 5 q^{18} + 43 q^{19} + 10 q^{20} - q^{23} + 20 q^{24} + 43 q^{25} + 2 q^{26} + 53 q^{27} - 4 q^{29} - 12 q^{30} + 59 q^{31} - 11 q^{32} + 37 q^{33} + 48 q^{34} + 14 q^{36} + 39 q^{38} + 16 q^{39} + 56 q^{40} + 15 q^{41} - q^{43} - 2 q^{44} + 28 q^{45} + 31 q^{46} + 58 q^{47} + 12 q^{48} - 74 q^{50} - 5 q^{51} + 115 q^{52} + 10 q^{53} + 39 q^{54} + 81 q^{55} - 18 q^{57} - 11 q^{58} + 41 q^{59} + 90 q^{60} + 40 q^{61} - 29 q^{62} + 15 q^{64} - 9 q^{65} + 42 q^{66} + 56 q^{68} + 5 q^{69} - 42 q^{71} - 11 q^{72} + 67 q^{73} + 39 q^{74} + 40 q^{75} + 68 q^{76} - 78 q^{78} - 9 q^{79} + 14 q^{80} + 73 q^{81} + 34 q^{82} + 48 q^{83} + 6 q^{85} - 13 q^{86} + 135 q^{87} + 47 q^{88} + 17 q^{89} - 44 q^{90} - 61 q^{92} - q^{93} + 28 q^{94} + 47 q^{95} + 50 q^{96} + 81 q^{97} - 35 q^{99}+O(q^{100}) \) 45 * q + 11 * q^3 + 44 * q^4 + 4 * q^5 + 10 * q^6 - 3 * q^8 + 44 * q^9 + 25 * q^10 + 33 * q^12 + 36 * q^13 + 38 * q^16 + 18 * q^17 - 5 * q^18 + 43 * q^19 + 10 * q^20 - q^23 + 20 * q^24 + 43 * q^25 + 2 * q^26 + 53 * q^27 - 4 * q^29 - 12 * q^30 + 59 * q^31 - 11 * q^32 + 37 * q^33 + 48 * q^34 + 14 * q^36 + 39 * q^38 + 16 * q^39 + 56 * q^40 + 15 * q^41 - q^43 - 2 * q^44 + 28 * q^45 + 31 * q^46 + 58 * q^47 + 12 * q^48 - 74 * q^50 - 5 * q^51 + 115 * q^52 + 10 * q^53 + 39 * q^54 + 81 * q^55 - 18 * q^57 - 11 * q^58 + 41 * q^59 + 90 * q^60 + 40 * q^61 - 29 * q^62 + 15 * q^64 - 9 * q^65 + 42 * q^66 + 56 * q^68 + 5 * q^69 - 42 * q^71 - 11 * q^72 + 67 * q^73 + 39 * q^74 + 40 * q^75 + 68 * q^76 - 78 * q^78 - 9 * q^79 + 14 * q^80 + 73 * q^81 + 34 * q^82 + 48 * q^83 + 6 * q^85 - 13 * q^86 + 135 * q^87 + 47 * q^88 + 17 * q^89 - 44 * q^90 - 61 * q^92 - q^93 + 28 * q^94 + 47 * q^95 + 50 * q^96 + 81 * q^97 - 35 * q^99

Introduction

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