LMFDB - Embedded newform 8470.2.a.cn.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.24914 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.24914 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +1.00000 q^{10} -2.24914 q^{12} +1.00000 q^{14} -2.24914 q^{15} +1.00000 q^{16} +1.05863 q^{17} +2.05863 q^{18} +5.19051 q^{19} +1.00000 q^{20} -2.24914 q^{21} +5.30777 q^{23} -2.24914 q^{24} +1.00000 q^{25} +2.11727 q^{27} +1.00000 q^{28} -3.30777 q^{29} -2.24914 q^{30} -4.61555 q^{31} +1.00000 q^{32} +1.05863 q^{34} +1.00000 q^{35} +2.05863 q^{36} +5.30777 q^{37} +5.19051 q^{38} +1.00000 q^{40} +8.74742 q^{41} -2.24914 q^{42} -5.55691 q^{43} +2.05863 q^{45} +5.30777 q^{46} -3.43965 q^{47} -2.24914 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.38101 q^{51} -7.92332 q^{53} +2.11727 q^{54} +1.00000 q^{56} -11.6742 q^{57} -3.30777 q^{58} -3.05863 q^{59} -2.24914 q^{60} +5.43965 q^{61} -4.61555 q^{62} +2.05863 q^{63} +1.00000 q^{64} -4.11727 q^{67} +1.05863 q^{68} -11.9379 q^{69} +1.00000 q^{70} +12.9966 q^{71} +2.05863 q^{72} +1.55691 q^{73} +5.30777 q^{74} -2.24914 q^{75} +5.19051 q^{76} +1.42504 q^{79} +1.00000 q^{80} -10.9379 q^{81} +8.74742 q^{82} +1.88273 q^{83} -2.24914 q^{84} +1.05863 q^{85} -5.55691 q^{86} +7.43965 q^{87} -6.99656 q^{89} +2.05863 q^{90} +5.30777 q^{92} +10.3810 q^{93} -3.43965 q^{94} +5.19051 q^{95} -2.24914 q^{96} +17.3078 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 2 q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} + 7 q^{18} + 6 q^{19} + 3 q^{20} + 2 q^{21} + 8 q^{23} + 2 q^{24} + 3 q^{25} + 8 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 3 q^{32} + 4 q^{34} + 3 q^{35} + 7 q^{36} + 8 q^{37} + 6 q^{38} + 3 q^{40} + 2 q^{42} + 7 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 8 q^{54} + 3 q^{56} - 20 q^{57} - 2 q^{58} - 10 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 7 q^{63} + 3 q^{64} - 14 q^{67} + 4 q^{68} + 3 q^{70} + 4 q^{71} + 7 q^{72} - 12 q^{73} + 8 q^{74} + 2 q^{75} + 6 q^{76} - 2 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{83} + 2 q^{84} + 4 q^{85} + 4 q^{87} + 14 q^{89} + 7 q^{90} + 8 q^{92} + 12 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{96} + 44 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 2 * q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 + 7 * q^18 + 6 * q^19 + 3 * q^20 + 2 * q^21 + 8 * q^23 + 2 * q^24 + 3 * q^25 + 8 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 3 * q^32 + 4 * q^34 + 3 * q^35 + 7 * q^36 + 8 * q^37 + 6 * q^38 + 3 * q^40 + 2 * q^42 + 7 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 8 * q^54 + 3 * q^56 - 20 * q^57 - 2 * q^58 - 10 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 7 * q^63 + 3 * q^64 - 14 * q^67 + 4 * q^68 + 3 * q^70 + 4 * q^71 + 7 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 + 6 * q^76 - 2 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^83 + 2 * q^84 + 4 * q^85 + 4 * q^87 + 14 * q^89 + 7 * q^90 + 8 * q^92 + 12 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^96 + 44 * q^97 + 3 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.24914	−1.29854	−0.649271	−	0.760557i	$-0.724926\pi$
$3$	−2.24914	−1.29854	−0.649271	+	0.760557i	$0.724926\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.24914	−0.918208
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	2.05863	0.686211
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−2.24914	−0.649271
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	−2.24914	−0.580726
$16$	1.00000	0.250000
$17$	1.05863	0.256756	0.128378	−	0.991725i	$-0.459023\pi$
$17$	1.05863	0.256756	0.128378	+	0.991725i	$0.459023\pi$
$18$	2.05863	0.485224
$19$	5.19051	1.19078	0.595392	−	0.803435i	$-0.296997\pi$
$19$	5.19051	1.19078	0.595392	+	0.803435i	$0.296997\pi$
$20$	1.00000	0.223607
$21$	−2.24914	−0.490803
$22$	0	0
$23$	5.30777	1.10675	0.553374	−	0.832933i	$-0.313340\pi$
$23$	5.30777	1.10675	0.553374	+	0.832933i	$0.313340\pi$
$24$	−2.24914	−0.459104
$25$	1.00000	0.200000
$26$	0	0
$27$	2.11727	0.407468
$28$	1.00000	0.188982
$29$	−3.30777	−0.614238	−0.307119	−	0.951671i	$-0.599365\pi$
$29$	−3.30777	−0.614238	−0.307119	+	0.951671i	$0.599365\pi$
$30$	−2.24914	−0.410635
$31$	−4.61555	−0.828977	−0.414488	−	0.910055i	$-0.636039\pi$
$31$	−4.61555	−0.828977	−0.414488	+	0.910055i	$0.636039\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.05863	0.181554
$35$	1.00000	0.169031
$36$	2.05863	0.343106
$37$	5.30777	0.872593	0.436296	−	0.899803i	$-0.356290\pi$
$37$	5.30777	0.872593	0.436296	+	0.899803i	$0.356290\pi$
$38$	5.19051	0.842011
$39$	0	0
$40$	1.00000	0.158114
$41$	8.74742	1.36612	0.683059	−	0.730363i	$-0.260649\pi$
$41$	8.74742	1.36612	0.683059	+	0.730363i	$0.260649\pi$
$42$	−2.24914	−0.347050
$43$	−5.55691	−0.847421	−0.423711	−	0.905798i	$-0.639273\pi$
$43$	−5.55691	−0.847421	−0.423711	+	0.905798i	$0.639273\pi$
$44$	0	0
$45$	2.05863	0.306883
$46$	5.30777	0.782589
$47$	−3.43965	−0.501724	−0.250862	−	0.968023i	$-0.580714\pi$
$47$	−3.43965	−0.501724	−0.250862	+	0.968023i	$0.580714\pi$
$48$	−2.24914	−0.324635
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−2.38101	−0.333409
$52$	0	0
$53$	−7.92332	−1.08835	−0.544176	−	0.838971i	$-0.683158\pi$
$53$	−7.92332	−1.08835	−0.544176	+	0.838971i	$0.683158\pi$
$54$	2.11727	0.288123
$55$	0	0
$56$	1.00000	0.133631
$57$	−11.6742	−1.54628
$58$	−3.30777	−0.434332
$59$	−3.05863	−0.398200	−0.199100	−	0.979979i	$-0.563802\pi$
$59$	−3.05863	−0.398200	−0.199100	+	0.979979i	$0.563802\pi$
$60$	−2.24914	−0.290363
$61$	5.43965	0.696476	0.348238	−	0.937406i	$-0.386780\pi$
$61$	5.43965	0.696476	0.348238	+	0.937406i	$0.386780\pi$
$62$	−4.61555	−0.586175
$63$	2.05863	0.259363
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−4.11727	−0.503004	−0.251502	−	0.967857i	$-0.580925\pi$
$67$	−4.11727	−0.503004	−0.251502	+	0.967857i	$0.580925\pi$
$68$	1.05863	0.128378
$69$	−11.9379	−1.43716
$70$	1.00000	0.119523
$71$	12.9966	1.54241	0.771204	−	0.636588i	$-0.219655\pi$
$71$	12.9966	1.54241	0.771204	+	0.636588i	$0.219655\pi$
$72$	2.05863	0.242612
$73$	1.55691	0.182223	0.0911115	−	0.995841i	$-0.470958\pi$
$73$	1.55691	0.182223	0.0911115	+	0.995841i	$0.470958\pi$
$74$	5.30777	0.617016
$75$	−2.24914	−0.259708
$76$	5.19051	0.595392
$77$	0	0
$78$	0	0
$79$	1.42504	0.160330	0.0801648	−	0.996782i	$-0.474455\pi$
$79$	1.42504	0.160330	0.0801648	+	0.996782i	$0.474455\pi$
$80$	1.00000	0.111803
$81$	−10.9379	−1.21533
$82$	8.74742	0.965991
$83$	1.88273	0.206657	0.103328	−	0.994647i	$-0.467051\pi$
$83$	1.88273	0.206657	0.103328	+	0.994647i	$0.467051\pi$
$84$	−2.24914	−0.245401
$85$	1.05863	0.114825
$86$	−5.55691	−0.599217
$87$	7.43965	0.797614
$88$	0	0
$89$	−6.99656	−0.741634	−0.370817	−	0.928706i	$-0.620922\pi$
$89$	−6.99656	−0.741634	−0.370817	+	0.928706i	$0.620922\pi$
$90$	2.05863	0.216999
$91$	0	0
$92$	5.30777	0.553374
$93$	10.3810	1.07646
$94$	−3.43965	−0.354773
$95$	5.19051	0.532535
$96$	−2.24914	−0.229552
$97$	17.3078	1.75734	0.878669	−	0.477431i	$-0.158432\pi$
$97$	17.3078	1.75734	0.878669	+	0.477431i	$0.158432\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−11.5569	−1.14996	−0.574978	−	0.818169i	$-0.694989\pi$
$101$	−11.5569	−1.14996	−0.574978	+	0.818169i	$0.694989\pi$
$102$	−2.38101	−0.235756
$103$	−1.05863	−0.104310	−0.0521551	−	0.998639i	$-0.516609\pi$
$103$	−1.05863	−0.104310	−0.0521551	+	0.998639i	$0.516609\pi$
$104$	0	0
$105$	−2.24914	−0.219494
$106$	−7.92332	−0.769581
$107$	3.43965	0.332523	0.166262	−	0.986082i	$-0.446830\pi$
$107$	3.43965	0.332523	0.166262	+	0.986082i	$0.446830\pi$
$108$	2.11727	0.203734
$109$	−16.3043	−1.56167	−0.780836	−	0.624736i	$-0.785207\pi$
$109$	−16.3043	−1.56167	−0.780836	+	0.624736i	$0.785207\pi$
$110$	0	0
$111$	−11.9379	−1.13310
$112$	1.00000	0.0944911
$113$	3.88273	0.365257	0.182628	−	0.983182i	$-0.441539\pi$
$113$	3.88273	0.365257	0.182628	+	0.983182i	$0.441539\pi$
$114$	−11.6742	−1.09339
$115$	5.30777	0.494952
$116$	−3.30777	−0.307119
$117$	0	0
$118$	−3.05863	−0.281570
$119$	1.05863	0.0970447
$120$	−2.24914	−0.205318
$121$	0	0
$122$	5.43965	0.492483
$123$	−19.6742	−1.77396
$124$	−4.61555	−0.414488
$125$	1.00000	0.0894427
$126$	2.05863	0.183398
$127$	8.26375	0.733289	0.366645	−	0.930361i	$-0.380507\pi$
$127$	8.26375	0.733289	0.366645	+	0.930361i	$0.380507\pi$
$128$	1.00000	0.0883883
$129$	12.4983	1.10041
$130$	0	0
$131$	9.42504	0.823470	0.411735	−	0.911304i	$-0.364923\pi$
$131$	9.42504	0.823470	0.411735	+	0.911304i	$0.364923\pi$
$132$	0	0
$133$	5.19051	0.450074
$134$	−4.11727	−0.355678
$135$	2.11727	0.182225
$136$	1.05863	0.0907770
$137$	14.9966	1.28124	0.640621	−	0.767857i	$-0.278677\pi$
$137$	14.9966	1.28124	0.640621	+	0.767857i	$0.278677\pi$
$138$	−11.9379	−1.01622
$139$	1.42504	0.120870	0.0604352	−	0.998172i	$-0.480751\pi$
$139$	1.42504	0.120870	0.0604352	+	0.998172i	$0.480751\pi$
$140$	1.00000	0.0845154
$141$	7.73625	0.651510
$142$	12.9966	1.09065
$143$	0	0
$144$	2.05863	0.171553
$145$	−3.30777	−0.274696
$146$	1.55691	0.128851
$147$	−2.24914	−0.185506
$148$	5.30777	0.436296
$149$	20.3043	1.66340	0.831698	−	0.555228i	$-0.187369\pi$
$149$	20.3043	1.66340	0.831698	+	0.555228i	$0.187369\pi$
$150$	−2.24914	−0.183642
$151$	0.926759	0.0754186	0.0377093	−	0.999289i	$-0.487994\pi$
$151$	0.926759	0.0754186	0.0377093	+	0.999289i	$0.487994\pi$
$152$	5.19051	0.421006
$153$	2.17934	0.176189
$154$	0	0
$155$	−4.61555	−0.370730
$156$	0	0
$157$	−13.6121	−1.08636	−0.543182	−	0.839615i	$-0.682781\pi$
$157$	−13.6121	−1.08636	−0.543182	+	0.839615i	$0.682781\pi$
$158$	1.42504	0.113370
$159$	17.8207	1.41327
$160$	1.00000	0.0790569
$161$	5.30777	0.418311
$162$	−10.9379	−0.859365
$163$	8.11727	0.635793	0.317897	−	0.948125i	$-0.397023\pi$
$163$	8.11727	0.635793	0.317897	+	0.948125i	$0.397023\pi$
$164$	8.74742	0.683059
$165$	0	0
$166$	1.88273	0.146128
$167$	16.1104	1.24666	0.623330	−	0.781959i	$-0.285779\pi$
$167$	16.1104	1.24666	0.623330	+	0.781959i	$0.285779\pi$
$168$	−2.24914	−0.173525
$169$	−13.0000	−1.00000
$170$	1.05863	0.0811935
$171$	10.6854	0.817129
$172$	−5.55691	−0.423711
$173$	−7.67418	−0.583457	−0.291729	−	0.956501i	$-0.594230\pi$
$173$	−7.67418	−0.583457	−0.291729	+	0.956501i	$0.594230\pi$
$174$	7.43965	0.563998
$175$	1.00000	0.0755929
$176$	0	0
$177$	6.87930	0.517080
$178$	−6.99656	−0.524415
$179$	−12.1725	−0.909812	−0.454906	−	0.890539i	$-0.650327\pi$
$179$	−12.1725	−0.909812	−0.454906	+	0.890539i	$0.650327\pi$
$180$	2.05863	0.153441
$181$	10.9966	0.817368	0.408684	−	0.912676i	$-0.365988\pi$
$181$	10.9966	0.817368	0.408684	+	0.912676i	$0.365988\pi$
$182$	0	0
$183$	−12.2345	−0.904403
$184$	5.30777	0.391294
$185$	5.30777	0.390235
$186$	10.3810	0.761173
$187$	0	0
$188$	−3.43965	−0.250862
$189$	2.11727	0.154008
$190$	5.19051	0.376559
$191$	−17.4948	−1.26588	−0.632941	−	0.774200i	$-0.718153\pi$
$191$	−17.4948	−1.26588	−0.632941	+	0.774200i	$0.718153\pi$
$192$	−2.24914	−0.162318
$193$	−20.3189	−1.46259	−0.731295	−	0.682062i	$-0.761084\pi$
$193$	−20.3189	−1.46259	−0.731295	+	0.682062i	$0.761084\pi$
$194$	17.3078	1.24263
$195$	0	0
$196$	1.00000	0.0714286
$197$	−19.7294	−1.40566	−0.702830	−	0.711358i	$-0.748081\pi$
$197$	−19.7294	−1.40566	−0.702830	+	0.711358i	$0.748081\pi$
$198$	0	0
$199$	3.79145	0.268769	0.134384	−	0.990929i	$-0.457094\pi$
$199$	3.79145	0.268769	0.134384	+	0.990929i	$0.457094\pi$
$200$	1.00000	0.0707107
$201$	9.26031	0.653172
$202$	−11.5569	−0.813142
$203$	−3.30777	−0.232160
$204$	−2.38101	−0.166704
$205$	8.74742	0.610946
$206$	−1.05863	−0.0737585
$207$	10.9268	0.759462
$208$	0	0
$209$	0	0
$210$	−2.24914	−0.155205
$211$	16.1104	1.10909	0.554543	−	0.832155i	$-0.312893\pi$
$211$	16.1104	1.10909	0.554543	+	0.832155i	$0.312893\pi$
$212$	−7.92332	−0.544176
$213$	−29.2311	−2.00288
$214$	3.43965	0.235129
$215$	−5.55691	−0.378978
$216$	2.11727	0.144062
$217$	−4.61555	−0.313324
$218$	−16.3043	−1.10427
$219$	−3.50172	−0.236624
$220$	0	0
$221$	0	0
$222$	−11.9379	−0.801221
$223$	5.05863	0.338751	0.169376	−	0.985552i	$-0.445825\pi$
$223$	5.05863	0.338751	0.169376	+	0.985552i	$0.445825\pi$
$224$	1.00000	0.0668153
$225$	2.05863	0.137242
$226$	3.88273	0.258276
$227$	13.4948	0.895684	0.447842	−	0.894113i	$-0.352193\pi$
$227$	13.4948	0.895684	0.447842	+	0.894113i	$0.352193\pi$
$228$	−11.6742	−0.773141
$229$	2.82410	0.186622	0.0933109	−	0.995637i	$-0.470255\pi$
$229$	2.82410	0.186622	0.0933109	+	0.995637i	$0.470255\pi$
$230$	5.30777	0.349984
$231$	0	0
$232$	−3.30777	−0.217166
$233$	−25.1138	−1.64526	−0.822631	−	0.568576i	$-0.807495\pi$
$233$	−25.1138	−1.64526	−0.822631	+	0.568576i	$0.807495\pi$
$234$	0	0
$235$	−3.43965	−0.224378
$236$	−3.05863	−0.199100
$237$	−3.20512	−0.208195
$238$	1.05863	0.0686210
$239$	3.69566	0.239053	0.119526	−	0.992831i	$-0.461862\pi$
$239$	3.69566	0.239053	0.119526	+	0.992831i	$0.461862\pi$
$240$	−2.24914	−0.145181
$241$	13.2457	0.853231	0.426615	−	0.904433i	$-0.359706\pi$
$241$	13.2457	0.853231	0.426615	+	0.904433i	$0.359706\pi$
$242$	0	0
$243$	18.2491	1.17068
$244$	5.43965	0.348238
$245$	1.00000	0.0638877
$246$	−19.6742	−1.25438
$247$	0	0
$248$	−4.61555	−0.293088
$249$	−4.23453	−0.268353
$250$	1.00000	0.0632456
$251$	−0.553476	−0.0349351	−0.0174676	−	0.999847i	$-0.505560\pi$
$251$	−0.553476	−0.0349351	−0.0174676	+	0.999847i	$0.505560\pi$
$252$	2.05863	0.129682
$253$	0	0
$254$	8.26375	0.518514
$255$	−2.38101	−0.149105
$256$	1.00000	0.0625000
$257$	20.9199	1.30495	0.652473	−	0.757812i	$-0.273731\pi$
$257$	20.9199	1.30495	0.652473	+	0.757812i	$0.273731\pi$
$258$	12.4983	0.778109
$259$	5.30777	0.329809
$260$	0	0
$261$	−6.80949	−0.421497
$262$	9.42504	0.582281
$263$	1.38445	0.0853690	0.0426845	−	0.999089i	$-0.486409\pi$
$263$	1.38445	0.0853690	0.0426845	+	0.999089i	$0.486409\pi$
$264$	0	0
$265$	−7.92332	−0.486726
$266$	5.19051	0.318250
$267$	15.7363	0.963043
$268$	−4.11727	−0.251502
$269$	10.8241	0.659957	0.329979	−	0.943988i	$-0.392958\pi$
$269$	10.8241	0.659957	0.329979	+	0.943988i	$0.392958\pi$
$270$	2.11727	0.128853
$271$	8.73281	0.530481	0.265240	−	0.964182i	$-0.414549\pi$
$271$	8.73281	0.530481	0.265240	+	0.964182i	$0.414549\pi$
$272$	1.05863	0.0641891
$273$	0	0
$274$	14.9966	0.905975
$275$	0	0
$276$	−11.9379	−0.718579
$277$	9.61211	0.577536	0.288768	−	0.957399i	$-0.406754\pi$
$277$	9.61211	0.577536	0.288768	+	0.957399i	$0.406754\pi$
$278$	1.42504	0.0854682
$279$	−9.50172	−0.568853
$280$	1.00000	0.0597614
$281$	10.8501	0.647262	0.323631	−	0.946183i	$-0.395096\pi$
$281$	10.8501	0.647262	0.323631	+	0.946183i	$0.395096\pi$
$282$	7.73625	0.460687
$283$	25.7294	1.52945	0.764726	−	0.644355i	$-0.222874\pi$
$283$	25.7294	1.52945	0.764726	+	0.644355i	$0.222874\pi$
$284$	12.9966	0.771204
$285$	−11.6742	−0.691519
$286$	0	0
$287$	8.74742	0.516344
$288$	2.05863	0.121306
$289$	−15.8793	−0.934076
$290$	−3.30777	−0.194239
$291$	−38.9276	−2.28198
$292$	1.55691	0.0911115
$293$	10.2277	0.597506	0.298753	−	0.954330i	$-0.403429\pi$
$293$	10.2277	0.597506	0.298753	+	0.954330i	$0.403429\pi$
$294$	−2.24914	−0.131173
$295$	−3.05863	−0.178081
$296$	5.30777	0.308508
$297$	0	0
$298$	20.3043	1.17620
$299$	0	0
$300$	−2.24914	−0.129854
$301$	−5.55691	−0.320295
$302$	0.926759	0.0533290
$303$	25.9931	1.49327
$304$	5.19051	0.297696
$305$	5.43965	0.311473
$306$	2.17934	0.124584
$307$	12.7328	0.726700	0.363350	−	0.931653i	$-0.381633\pi$
$307$	12.7328	0.726700	0.363350	+	0.931653i	$0.381633\pi$
$308$	0	0
$309$	2.38101	0.135451
$310$	−4.61555	−0.262145
$311$	0.615547	0.0349045	0.0174522	−	0.999848i	$-0.494444\pi$
$311$	0.615547	0.0349045	0.0174522	+	0.999848i	$0.494444\pi$
$312$	0	0
$313$	22.8026	1.28888	0.644440	−	0.764655i	$-0.277091\pi$
$313$	22.8026	1.28888	0.644440	+	0.764655i	$0.277091\pi$
$314$	−13.6121	−0.768176
$315$	2.05863	0.115991
$316$	1.42504	0.0801648
$317$	13.0732	0.734266	0.367133	−	0.930168i	$-0.380339\pi$
$317$	13.0732	0.734266	0.367133	+	0.930168i	$0.380339\pi$
$318$	17.8207	0.999333
$319$	0	0
$320$	1.00000	0.0559017
$321$	−7.73625	−0.431795
$322$	5.30777	0.295791
$323$	5.49484	0.305741
$324$	−10.9379	−0.607663
$325$	0	0
$326$	8.11727	0.449574
$327$	36.6707	2.02790
$328$	8.74742	0.482996
$329$	−3.43965	−0.189634
$330$	0	0
$331$	−17.8207	−0.979512	−0.489756	−	0.871859i	$-0.662914\pi$
$331$	−17.8207	−0.979512	−0.489756	+	0.871859i	$0.662914\pi$
$332$	1.88273	0.103328
$333$	10.9268	0.598783
$334$	16.1104	0.881521
$335$	−4.11727	−0.224950
$336$	−2.24914	−0.122701
$337$	−14.8862	−0.810901	−0.405451	−	0.914117i	$-0.632885\pi$
$337$	−14.8862	−0.810901	−0.405451	+	0.914117i	$0.632885\pi$
$338$	−13.0000	−0.707107
$339$	−8.73281	−0.474301
$340$	1.05863	0.0574124
$341$	0	0
$342$	10.6854	0.577798
$343$	1.00000	0.0539949
$344$	−5.55691	−0.299609
$345$	−11.9379	−0.642716
$346$	−7.67418	−0.412567
$347$	−6.67762	−0.358473	−0.179237	−	0.983806i	$-0.557363\pi$
$347$	−6.67762	−0.358473	−0.179237	+	0.983806i	$0.557363\pi$
$348$	7.43965	0.398807
$349$	−20.2897	−1.08608	−0.543042	−	0.839705i	$-0.682728\pi$
$349$	−20.2897	−1.08608	−0.543042	+	0.839705i	$0.682728\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	0	0
$353$	16.5750	0.882196	0.441098	−	0.897459i	$-0.354589\pi$
$353$	16.5750	0.882196	0.441098	+	0.897459i	$0.354589\pi$
$354$	6.87930	0.365630
$355$	12.9966	0.689786
$356$	−6.99656	−0.370817
$357$	−2.38101	−0.126017
$358$	−12.1725	−0.643335
$359$	−8.04059	−0.424366	−0.212183	−	0.977230i	$-0.568057\pi$
$359$	−8.04059	−0.424366	−0.212183	+	0.977230i	$0.568057\pi$
$360$	2.05863	0.108499
$361$	7.94137	0.417967
$362$	10.9966	0.577966
$363$	0	0
$364$	0	0
$365$	1.55691	0.0814926
$366$	−12.2345	−0.639509
$367$	5.16902	0.269821	0.134910	−	0.990858i	$-0.456925\pi$
$367$	5.16902	0.269821	0.134910	+	0.990858i	$0.456925\pi$
$368$	5.30777	0.276687
$369$	18.0077	0.937445
$370$	5.30777	0.275938
$371$	−7.92332	−0.411358
$372$	10.3810	0.538231
$373$	4.61555	0.238984	0.119492	−	0.992835i	$-0.461873\pi$
$373$	4.61555	0.238984	0.119492	+	0.992835i	$0.461873\pi$
$374$	0	0
$375$	−2.24914	−0.116145
$376$	−3.43965	−0.177386
$377$	0	0
$378$	2.11727	0.108900
$379$	2.87930	0.147899	0.0739497	−	0.997262i	$-0.476440\pi$
$379$	2.87930	0.147899	0.0739497	+	0.997262i	$0.476440\pi$
$380$	5.19051	0.266267
$381$	−18.5863	−0.952207
$382$	−17.4948	−0.895114
$383$	0.172462	0.00881238	0.00440619	−	0.999990i	$-0.498597\pi$
$383$	0.172462	0.00881238	0.00440619	+	0.999990i	$0.498597\pi$
$384$	−2.24914	−0.114776
$385$	0	0
$386$	−20.3189	−1.03421
$387$	−11.4396	−0.581510
$388$	17.3078	0.878669
$389$	−7.61899	−0.386298	−0.193149	−	0.981169i	$-0.561870\pi$
$389$	−7.61899	−0.386298	−0.193149	+	0.981169i	$0.561870\pi$
$390$	0	0
$391$	5.61899	0.284164
$392$	1.00000	0.0505076
$393$	−21.1982	−1.06931
$394$	−19.7294	−0.993952
$395$	1.42504	0.0717015
$396$	0	0
$397$	7.61899	0.382386	0.191193	−	0.981552i	$-0.438764\pi$
$397$	7.61899	0.382386	0.191193	+	0.981552i	$0.438764\pi$
$398$	3.79145	0.190048
$399$	−11.6742	−0.584440
$400$	1.00000	0.0500000
$401$	−6.17246	−0.308238	−0.154119	−	0.988052i	$-0.549254\pi$
$401$	−6.17246	−0.308238	−0.154119	+	0.988052i	$0.549254\pi$
$402$	9.26031	0.461862
$403$	0	0
$404$	−11.5569	−0.574978
$405$	−10.9379	−0.543510
$406$	−3.30777	−0.164162
$407$	0	0
$408$	−2.38101	−0.117878
$409$	−4.35953	−0.215565	−0.107782	−	0.994175i	$-0.534375\pi$
$409$	−4.35953	−0.215565	−0.107782	+	0.994175i	$0.534375\pi$
$410$	8.74742	0.432004
$411$	−33.7294	−1.66375
$412$	−1.05863	−0.0521551
$413$	−3.05863	−0.150505
$414$	10.9268	0.537021
$415$	1.88273	0.0924198
$416$	0	0
$417$	−3.20512	−0.156955
$418$	0	0
$419$	31.5569	1.54166	0.770828	−	0.637043i	$-0.219843\pi$
$419$	31.5569	1.54166	0.770828	+	0.637043i	$0.219843\pi$
$420$	−2.24914	−0.109747
$421$	30.6087	1.49178	0.745888	−	0.666072i	$-0.232026\pi$
$421$	30.6087	1.49178	0.745888	+	0.666072i	$0.232026\pi$
$422$	16.1104	0.784242
$423$	−7.08097	−0.344289
$424$	−7.92332	−0.384790
$425$	1.05863	0.0513513
$426$	−29.2311	−1.41625
$427$	5.43965	0.263243
$428$	3.43965	0.166262
$429$	0	0
$430$	−5.55691	−0.267978
$431$	15.9164	0.766668	0.383334	−	0.923610i	$-0.374776\pi$
$431$	15.9164	0.766668	0.383334	+	0.923610i	$0.374776\pi$
$432$	2.11727	0.101867
$433$	25.4182	1.22152	0.610760	−	0.791816i	$-0.290864\pi$
$433$	25.4182	1.22152	0.610760	+	0.791816i	$0.290864\pi$
$434$	−4.61555	−0.221553
$435$	7.43965	0.356704
$436$	−16.3043	−0.780836
$437$	27.5500	1.31790
$438$	−3.50172	−0.167319
$439$	−7.73625	−0.369231	−0.184616	−	0.982811i	$-0.559104\pi$
$439$	−7.73625	−0.369231	−0.184616	+	0.982811i	$0.559104\pi$
$440$	0	0
$441$	2.05863	0.0980302
$442$	0	0
$443$	16.8793	0.801960	0.400980	−	0.916087i	$-0.368670\pi$
$443$	16.8793	0.801960	0.400980	+	0.916087i	$0.368670\pi$
$444$	−11.9379	−0.566549
$445$	−6.99656	−0.331669
$446$	5.05863	0.239533
$447$	−45.6673	−2.15999
$448$	1.00000	0.0472456
$449$	32.1656	1.51799	0.758994	−	0.651098i	$-0.225691\pi$
$449$	32.1656	1.51799	0.758994	+	0.651098i	$0.225691\pi$
$450$	2.05863	0.0970449
$451$	0	0
$452$	3.88273	0.182628
$453$	−2.08441	−0.0979342
$454$	13.4948	0.633344
$455$	0	0
$456$	−11.6742	−0.546694
$457$	2.88617	0.135009	0.0675047	−	0.997719i	$-0.478496\pi$
$457$	2.88617	0.135009	0.0675047	+	0.997719i	$0.478496\pi$
$458$	2.82410	0.131962
$459$	2.24141	0.104620
$460$	5.30777	0.247476
$461$	1.82754	0.0851169	0.0425585	−	0.999094i	$-0.486449\pi$
$461$	1.82754	0.0851169	0.0425585	+	0.999094i	$0.486449\pi$
$462$	0	0
$463$	−3.68879	−0.171433	−0.0857163	−	0.996320i	$-0.527318\pi$
$463$	−3.68879	−0.171433	−0.0857163	+	0.996320i	$0.527318\pi$
$464$	−3.30777	−0.153560
$465$	10.3810	0.481408
$466$	−25.1138	−1.16338
$467$	26.0958	1.20757	0.603784	−	0.797148i	$-0.293659\pi$
$467$	26.0958	1.20757	0.603784	+	0.797148i	$0.293659\pi$
$468$	0	0
$469$	−4.11727	−0.190118
$470$	−3.43965	−0.158659
$471$	30.6155	1.41069
$472$	−3.05863	−0.140785
$473$	0	0
$474$	−3.20512	−0.147216
$475$	5.19051	0.238157
$476$	1.05863	0.0485224
$477$	−16.3112	−0.746839
$478$	3.69566	0.169036
$479$	8.99656	0.411063	0.205532	−	0.978650i	$-0.434108\pi$
$479$	8.99656	0.411063	0.205532	+	0.978650i	$0.434108\pi$
$480$	−2.24914	−0.102659
$481$	0	0
$482$	13.2457	0.603325
$483$	−11.9379	−0.543195
$484$	0	0
$485$	17.3078	0.785906
$486$	18.2491	0.827798
$487$	−2.53887	−0.115047	−0.0575236	−	0.998344i	$-0.518320\pi$
$487$	−2.53887	−0.115047	−0.0575236	+	0.998344i	$0.518320\pi$
$488$	5.43965	0.246241
$489$	−18.2569	−0.825604
$490$	1.00000	0.0451754
$491$	−18.2277	−0.822603	−0.411301	−	0.911499i	$-0.634926\pi$
$491$	−18.2277	−0.822603	−0.411301	+	0.911499i	$0.634926\pi$
$492$	−19.6742	−0.886981
$493$	−3.50172	−0.157709
$494$	0	0
$495$	0	0
$496$	−4.61555	−0.207244
$497$	12.9966	0.582975
$498$	−4.23453	−0.189754
$499$	0.406994	0.0182196	0.00910978	−	0.999959i	$-0.497100\pi$
$499$	0.406994	0.0182196	0.00910978	+	0.999959i	$0.497100\pi$
$500$	1.00000	0.0447214
$501$	−36.2345	−1.61884
$502$	−0.553476	−0.0247029
$503$	−14.6448	−0.652978	−0.326489	−	0.945201i	$-0.605866\pi$
$503$	−14.6448	−0.652978	−0.326489	+	0.945201i	$0.605866\pi$
$504$	2.05863	0.0916988
$505$	−11.5569	−0.514276
$506$	0	0
$507$	29.2388	1.29854
$508$	8.26375	0.366645
$509$	14.1104	0.625432	0.312716	−	0.949847i	$-0.398761\pi$
$509$	14.1104	0.625432	0.312716	+	0.949847i	$0.398761\pi$
$510$	−2.38101	−0.105433
$511$	1.55691	0.0688738
$512$	1.00000	0.0441942
$513$	10.9897	0.485207
$514$	20.9199	0.922736
$515$	−1.05863	−0.0466490
$516$	12.4983	0.550206
$517$	0	0
$518$	5.30777	0.233210
$519$	17.2603	0.757644
$520$	0	0
$521$	−40.4914	−1.77396	−0.886980	−	0.461807i	$-0.847201\pi$
$521$	−40.4914	−1.77396	−0.886980	+	0.461807i	$0.847201\pi$
$522$	−6.80949	−0.298043
$523$	20.0812	0.878088	0.439044	−	0.898465i	$-0.355317\pi$
$523$	20.0812	0.878088	0.439044	+	0.898465i	$0.355317\pi$
$524$	9.42504	0.411735
$525$	−2.24914	−0.0981605
$526$	1.38445	0.0603650
$527$	−4.88617	−0.212845
$528$	0	0
$529$	5.17246	0.224890
$530$	−7.92332	−0.344167
$531$	−6.29660	−0.273249
$532$	5.19051	0.225037
$533$	0	0
$534$	15.7363	0.680974
$535$	3.43965	0.148709
$536$	−4.11727	−0.177839
$537$	27.3776	1.18143
$538$	10.8241	0.466660
$539$	0	0
$540$	2.11727	0.0911126
$541$	−37.3009	−1.60369	−0.801845	−	0.597532i	$-0.796148\pi$
$541$	−37.3009	−1.60369	−0.801845	+	0.597532i	$0.796148\pi$
$542$	8.73281	0.375106
$543$	−24.7328	−1.06139
$544$	1.05863	0.0453885
$545$	−16.3043	−0.698401
$546$	0	0
$547$	42.2277	1.80552	0.902762	−	0.430140i	$-0.141536\pi$
$547$	42.2277	1.80552	0.902762	+	0.430140i	$0.141536\pi$
$548$	14.9966	0.640621
$549$	11.1982	0.477929
$550$	0	0
$551$	−17.1690	−0.731425
$552$	−11.9379	−0.508112
$553$	1.42504	0.0605989
$554$	9.61211	0.408379
$555$	−11.9379	−0.506737
$556$	1.42504	0.0604352
$557$	22.3449	0.946785	0.473392	−	0.880852i	$-0.343029\pi$
$557$	22.3449	0.946785	0.473392	+	0.880852i	$0.343029\pi$
$558$	−9.50172	−0.402240
$559$	0	0
$560$	1.00000	0.0422577
$561$	0	0
$562$	10.8501	0.457683
$563$	−40.2208	−1.69510	−0.847552	−	0.530712i	$-0.821924\pi$
$563$	−40.2208	−1.69510	−0.847552	+	0.530712i	$0.821924\pi$
$564$	7.73625	0.325755
$565$	3.88273	0.163348
$566$	25.7294	1.08149
$567$	−10.9379	−0.459350
$568$	12.9966	0.545324
$569$	18.2277	0.764143	0.382072	−	0.924133i	$-0.375211\pi$
$569$	18.2277	0.764143	0.382072	+	0.924133i	$0.375211\pi$
$570$	−11.6742	−0.488978
$571$	−34.2569	−1.43361	−0.716803	−	0.697276i	$-0.754395\pi$
$571$	−34.2569	−1.43361	−0.716803	+	0.697276i	$0.754395\pi$
$572$	0	0
$573$	39.3484	1.64380
$574$	8.74742	0.365110
$575$	5.30777	0.221349
$576$	2.05863	0.0857764
$577$	−30.3043	−1.26159	−0.630793	−	0.775951i	$-0.717270\pi$
$577$	−30.3043	−1.26159	−0.630793	+	0.775951i	$0.717270\pi$
$578$	−15.8793	−0.660492
$579$	45.7002	1.89923
$580$	−3.30777	−0.137348
$581$	1.88273	0.0781090
$582$	−38.9276	−1.61360
$583$	0	0
$584$	1.55691	0.0644256
$585$	0	0
$586$	10.2277	0.422501
$587$	43.6198	1.80038	0.900192	−	0.435494i	$-0.143426\pi$
$587$	43.6198	1.80038	0.900192	+	0.435494i	$0.143426\pi$
$588$	−2.24914	−0.0927530
$589$	−23.9570	−0.987132
$590$	−3.05863	−0.125922
$591$	44.3741	1.82531
$592$	5.30777	0.218148
$593$	12.7949	0.525423	0.262711	−	0.964874i	$-0.415383\pi$
$593$	12.7949	0.525423	0.262711	+	0.964874i	$0.415383\pi$
$594$	0	0
$595$	1.05863	0.0433997
$596$	20.3043	0.831698
$597$	−8.52750	−0.349007
$598$	0	0
$599$	36.9966	1.51164	0.755819	−	0.654780i	$-0.227239\pi$
$599$	36.9966	1.51164	0.755819	+	0.654780i	$0.227239\pi$
$600$	−2.24914	−0.0918208
$601$	−30.8647	−1.25900	−0.629498	−	0.777002i	$-0.716740\pi$
$601$	−30.8647	−1.25900	−0.629498	+	0.777002i	$0.716740\pi$
$602$	−5.55691	−0.226483
$603$	−8.47594	−0.345167
$604$	0.926759	0.0377093
$605$	0	0
$606$	25.9931	1.05590
$607$	28.4362	1.15419	0.577095	−	0.816677i	$-0.304186\pi$
$607$	28.4362	1.15419	0.577095	+	0.816677i	$0.304186\pi$
$608$	5.19051	0.210503
$609$	7.43965	0.301470
$610$	5.43965	0.220245
$611$	0	0
$612$	2.17934	0.0880945
$613$	9.53093	0.384951	0.192475	−	0.981302i	$-0.438348\pi$
$613$	9.53093	0.384951	0.192475	+	0.981302i	$0.438348\pi$
$614$	12.7328	0.513855
$615$	−19.6742	−0.793340
$616$	0	0
$617$	11.9639	0.481649	0.240824	−	0.970569i	$-0.422582\pi$
$617$	11.9639	0.481649	0.240824	+	0.970569i	$0.422582\pi$
$618$	2.38101	0.0957785
$619$	39.6673	1.59436	0.797182	−	0.603739i	$-0.206323\pi$
$619$	39.6673	1.59436	0.797182	+	0.603739i	$0.206323\pi$
$620$	−4.61555	−0.185365
$621$	11.2380	0.450964
$622$	0.615547	0.0246812
$623$	−6.99656	−0.280311
$624$	0	0
$625$	1.00000	0.0400000
$626$	22.8026	0.911376
$627$	0	0
$628$	−13.6121	−0.543182
$629$	5.61899	0.224044
$630$	2.05863	0.0820179
$631$	−22.4102	−0.892137	−0.446069	−	0.894999i	$-0.647176\pi$
$631$	−22.4102	−0.892137	−0.446069	+	0.894999i	$0.647176\pi$
$632$	1.42504	0.0566850
$633$	−36.2345	−1.44019
$634$	13.0732	0.519205
$635$	8.26375	0.327937
$636$	17.8207	0.706635
$637$	0	0
$638$	0	0
$639$	26.7552	1.05842
$640$	1.00000	0.0395285
$641$	30.2208	1.19365	0.596825	−	0.802372i	$-0.296429\pi$
$641$	30.2208	1.19365	0.596825	+	0.802372i	$0.296429\pi$
$642$	−7.73625	−0.305325
$643$	13.7801	0.543433	0.271717	−	0.962377i	$-0.412409\pi$
$643$	13.7801	0.543433	0.271717	+	0.962377i	$0.412409\pi$
$644$	5.30777	0.209156
$645$	12.4983	0.492119
$646$	5.49484	0.216192
$647$	16.9345	0.665764	0.332882	−	0.942969i	$-0.391979\pi$
$647$	16.9345	0.665764	0.332882	+	0.942969i	$0.391979\pi$
$648$	−10.9379	−0.429682
$649$	0	0
$650$	0	0
$651$	10.3810	0.406864
$652$	8.11727	0.317897
$653$	12.3112	0.481775	0.240887	−	0.970553i	$-0.422562\pi$
$653$	12.3112	0.481775	0.240887	+	0.970553i	$0.422562\pi$
$654$	36.6707	1.43394
$655$	9.42504	0.368267
$656$	8.74742	0.341529
$657$	3.20512	0.125043
$658$	−3.43965	−0.134091
$659$	−41.7294	−1.62555	−0.812773	−	0.582581i	$-0.802043\pi$
$659$	−41.7294	−1.62555	−0.812773	+	0.582581i	$0.802043\pi$
$660$	0	0
$661$	−47.5760	−1.85049	−0.925246	−	0.379367i	$-0.876142\pi$
$661$	−47.5760	−1.85049	−0.925246	+	0.379367i	$0.876142\pi$
$662$	−17.8207	−0.692620
$663$	0	0
$664$	1.88273	0.0730642
$665$	5.19051	0.201279
$666$	10.9268	0.423403
$667$	−17.5569	−0.679806
$668$	16.1104	0.623330
$669$	−11.3776	−0.439883
$670$	−4.11727	−0.159064
$671$	0	0
$672$	−2.24914	−0.0867625
$673$	36.2277	1.39647	0.698237	−	0.715867i	$-0.253968\pi$
$673$	36.2277	1.39647	0.698237	+	0.715867i	$0.253968\pi$
$674$	−14.8862	−0.573394
$675$	2.11727	0.0814936
$676$	−13.0000	−0.500000
$677$	−45.1982	−1.73711	−0.868555	−	0.495593i	$-0.834951\pi$
$677$	−45.1982	−1.73711	−0.868555	+	0.495593i	$0.834951\pi$
$678$	−8.73281	−0.335382
$679$	17.3078	0.664211
$680$	1.05863	0.0405967
$681$	−30.3518	−1.16308
$682$	0	0
$683$	32.3810	1.23903	0.619513	−	0.784987i	$-0.287330\pi$
$683$	32.3810	1.23903	0.619513	+	0.784987i	$0.287330\pi$
$684$	10.6854	0.408565
$685$	14.9966	0.572989
$686$	1.00000	0.0381802
$687$	−6.35180	−0.242336
$688$	−5.55691	−0.211855
$689$	0	0
$690$	−11.9379	−0.454469
$691$	51.1982	1.94767	0.973836	−	0.227250i	$-0.0729735\pi$
$691$	51.1982	1.94767	0.973836	+	0.227250i	$0.0729735\pi$
$692$	−7.67418	−0.291729
$693$	0	0
$694$	−6.67762	−0.253479
$695$	1.42504	0.0540548
$696$	7.43965	0.281999
$697$	9.26031	0.350759
$698$	−20.2897	−0.767978
$699$	56.4845	2.13644
$700$	1.00000	0.0377964
$701$	−18.1871	−0.686916	−0.343458	−	0.939168i	$-0.611598\pi$
$701$	−18.1871	−0.686916	−0.343458	+	0.939168i	$0.611598\pi$
$702$	0	0
$703$	27.5500	1.03907
$704$	0	0
$705$	7.73625	0.291364
$706$	16.5750	0.623807
$707$	−11.5569	−0.434642
$708$	6.87930	0.258540
$709$	−35.7586	−1.34294	−0.671471	−	0.741031i	$-0.734337\pi$
$709$	−35.7586	−1.34294	−0.671471	+	0.741031i	$0.734337\pi$
$710$	12.9966	0.487752
$711$	2.93363	0.110020
$712$	−6.99656	−0.262207
$713$	−24.4983	−0.917468
$714$	−2.38101	−0.0891072
$715$	0	0
$716$	−12.1725	−0.454906
$717$	−8.31207	−0.310420
$718$	−8.04059	−0.300072
$719$	29.9671	1.11759	0.558793	−	0.829307i	$-0.311265\pi$
$719$	29.9671	1.11759	0.558793	+	0.829307i	$0.311265\pi$
$720$	2.05863	0.0767207
$721$	−1.05863	−0.0394256
$722$	7.94137	0.295547
$723$	−29.7914	−1.10796
$724$	10.9966	0.408684
$725$	−3.30777	−0.122848
$726$	0	0
$727$	−8.14325	−0.302016	−0.151008	−	0.988533i	$-0.548252\pi$
$727$	−8.14325	−0.302016	−0.151008	+	0.988533i	$0.548252\pi$
$728$	0	0
$729$	−8.23109	−0.304855
$730$	1.55691	0.0576240
$731$	−5.88273	−0.217581
$732$	−12.2345	−0.452201
$733$	−32.9053	−1.21538	−0.607692	−	0.794173i	$-0.707904\pi$
$733$	−32.9053	−1.21538	−0.607692	+	0.794173i	$0.707904\pi$
$734$	5.16902	0.190792
$735$	−2.24914	−0.0829608
$736$	5.30777	0.195647
$737$	0	0
$738$	18.0077	0.662874
$739$	16.2345	0.597197	0.298598	−	0.954379i	$-0.403481\pi$
$739$	16.2345	0.597197	0.298598	+	0.954379i	$0.403481\pi$
$740$	5.30777	0.195118
$741$	0	0
$742$	−7.92332	−0.290874
$743$	−28.3741	−1.04095	−0.520473	−	0.853878i	$-0.674244\pi$
$743$	−28.3741	−1.04095	−0.520473	+	0.853878i	$0.674244\pi$
$744$	10.3810	0.380586
$745$	20.3043	0.743893
$746$	4.61555	0.168987
$747$	3.87586	0.141810
$748$	0	0
$749$	3.43965	0.125682
$750$	−2.24914	−0.0821270
$751$	28.2208	1.02979	0.514895	−	0.857253i	$-0.327831\pi$
$751$	28.2208	1.02979	0.514895	+	0.857253i	$0.327831\pi$
$752$	−3.43965	−0.125431
$753$	1.24485	0.0453647
$754$	0	0
$755$	0.926759	0.0337282
$756$	2.11727	0.0770042
$757$	37.6819	1.36957	0.684786	−	0.728744i	$-0.259896\pi$
$757$	37.6819	1.36957	0.684786	+	0.728744i	$0.259896\pi$
$758$	2.87930	0.104581
$759$	0	0
$760$	5.19051	0.188279
$761$	−19.3630	−0.701907	−0.350954	−	0.936393i	$-0.614142\pi$
$761$	−19.3630	−0.701907	−0.350954	+	0.936393i	$0.614142\pi$
$762$	−18.5863	−0.673312
$763$	−16.3043	−0.590257
$764$	−17.4948	−0.632941
$765$	2.17934	0.0787941
$766$	0.172462	0.00623129
$767$	0	0
$768$	−2.24914	−0.0811589
$769$	−51.0043	−1.83926	−0.919631	−	0.392784i	$-0.871512\pi$
$769$	−51.0043	−1.83926	−0.919631	+	0.392784i	$0.871512\pi$
$770$	0	0
$771$	−47.0518	−1.69453
$772$	−20.3189	−0.731295
$773$	−30.5795	−1.09987	−0.549933	−	0.835209i	$-0.685347\pi$
$773$	−30.5795	−1.09987	−0.549933	+	0.835209i	$0.685347\pi$
$774$	−11.4396	−0.411190
$775$	−4.61555	−0.165795
$776$	17.3078	0.621313
$777$	−11.9379	−0.428271
$778$	−7.61899	−0.273154
$779$	45.4036	1.62675
$780$	0	0
$781$	0	0
$782$	5.61899	0.200935
$783$	−7.00344	−0.250282
$784$	1.00000	0.0357143
$785$	−13.6121	−0.485837
$786$	−21.1982	−0.756116
$787$	39.2242	1.39819	0.699096	−	0.715028i	$-0.253586\pi$
$787$	39.2242	1.39819	0.699096	+	0.715028i	$0.253586\pi$
$788$	−19.7294	−0.702830
$789$	−3.11383	−0.110855
$790$	1.42504	0.0507006
$791$	3.88273	0.138054
$792$	0	0
$793$	0	0
$794$	7.61899	0.270388
$795$	17.8207	0.632034
$796$	3.79145	0.134384
$797$	−39.0777	−1.38420	−0.692102	−	0.721799i	$-0.743315\pi$
$797$	−39.0777	−1.38420	−0.692102	+	0.721799i	$0.743315\pi$
$798$	−11.6742	−0.413262
$799$	−3.64133	−0.128821
$800$	1.00000	0.0353553
$801$	−14.4034	−0.508918
$802$	−6.17246	−0.217957
$803$	0	0
$804$	9.26031	0.326586
$805$	5.30777	0.187074
$806$	0	0
$807$	−24.3449	−0.856982
$808$	−11.5569	−0.406571
$809$	−36.1396	−1.27060	−0.635300	−	0.772265i	$-0.719124\pi$
$809$	−36.1396	−1.27060	−0.635300	+	0.772265i	$0.719124\pi$
$810$	−10.9379	−0.384320
$811$	−26.6854	−0.937049	−0.468525	−	0.883450i	$-0.655214\pi$
$811$	−26.6854	−0.937049	−0.468525	+	0.883450i	$0.655214\pi$
$812$	−3.30777	−0.116080
$813$	−19.6413	−0.688851
$814$	0	0
$815$	8.11727	0.284335
$816$	−2.38101	−0.0833522
$817$	−28.8432	−1.00910
$818$	−4.35953	−0.152427
$819$	0	0
$820$	8.74742	0.305473
$821$	−5.84215	−0.203892	−0.101946	−	0.994790i	$-0.532507\pi$
$821$	−5.84215	−0.203892	−0.101946	+	0.994790i	$0.532507\pi$
$822$	−33.7294	−1.17645
$823$	−10.9560	−0.381901	−0.190951	−	0.981600i	$-0.561157\pi$
$823$	−10.9560	−0.381901	−0.190951	+	0.981600i	$0.561157\pi$
$824$	−1.05863	−0.0368792
$825$	0	0
$826$	−3.05863	−0.106423
$827$	26.7552	0.930368	0.465184	−	0.885214i	$-0.345988\pi$
$827$	26.7552	0.930368	0.465184	+	0.885214i	$0.345988\pi$
$828$	10.9268	0.379731
$829$	35.9311	1.24794	0.623969	−	0.781449i	$-0.285519\pi$
$829$	35.9311	1.24794	0.623969	+	0.781449i	$0.285519\pi$
$830$	1.88273	0.0653506
$831$	−21.6190	−0.749954
$832$	0	0
$833$	1.05863	0.0366795
$834$	−3.20512	−0.110984
$835$	16.1104	0.557523
$836$	0	0
$837$	−9.77234	−0.337782
$838$	31.5569	1.09012
$839$	−22.2637	−0.768630	−0.384315	−	0.923202i	$-0.625562\pi$
$839$	−22.2637	−0.768630	−0.384315	+	0.923202i	$0.625562\pi$
$840$	−2.24914	−0.0776027
$841$	−18.0586	−0.622711
$842$	30.6087	1.05484
$843$	−24.4034	−0.840496
$844$	16.1104	0.554543
$845$	−13.0000	−0.447214
$846$	−7.08097	−0.243449
$847$	0	0
$848$	−7.92332	−0.272088
$849$	−57.8690	−1.98606
$850$	1.05863	0.0363108
$851$	28.1725	0.965740
$852$	−29.2311	−1.00144
$853$	−30.5535	−1.04613	−0.523066	−	0.852292i	$-0.675212\pi$
$853$	−30.5535	−1.04613	−0.523066	+	0.852292i	$0.675212\pi$
$854$	5.43965	0.186141
$855$	10.6854	0.365431
$856$	3.43965	0.117565
$857$	52.5466	1.79496	0.897479	−	0.441058i	$-0.145397\pi$
$857$	52.5466	1.79496	0.897479	+	0.441058i	$0.145397\pi$
$858$	0	0
$859$	−10.7949	−0.368317	−0.184158	−	0.982897i	$-0.558956\pi$
$859$	−10.7949	−0.368317	−0.184158	+	0.982897i	$0.558956\pi$
$860$	−5.55691	−0.189489
$861$	−19.6742	−0.670494
$862$	15.9164	0.542116
$863$	42.3336	1.44105	0.720525	−	0.693429i	$-0.243901\pi$
$863$	42.3336	1.44105	0.720525	+	0.693429i	$0.243901\pi$
$864$	2.11727	0.0720309
$865$	−7.67418	−0.260930
$866$	25.4182	0.863744
$867$	35.7148	1.21294
$868$	−4.61555	−0.156662
$869$	0	0
$870$	7.43965	0.252228
$871$	0	0
$872$	−16.3043	−0.552134
$873$	35.6304	1.20590
$874$	27.5500	0.931894
$875$	1.00000	0.0338062
$876$	−3.50172	−0.118312
$877$	−39.3845	−1.32992	−0.664959	−	0.746880i	$-0.731551\pi$
$877$	−39.3845	−1.32992	−0.664959	+	0.746880i	$0.731551\pi$
$878$	−7.73625	−0.261086
$879$	−23.0034	−0.775887
$880$	0	0
$881$	−7.75859	−0.261394	−0.130697	−	0.991422i	$-0.541721\pi$
$881$	−7.75859	−0.261394	−0.130697	+	0.991422i	$0.541721\pi$
$882$	2.05863	0.0693178
$883$	38.4983	1.29557	0.647785	−	0.761823i	$-0.275695\pi$
$883$	38.4983	1.29557	0.647785	+	0.761823i	$0.275695\pi$
$884$	0	0
$885$	6.87930	0.231245
$886$	16.8793	0.567071
$887$	−39.6933	−1.33277	−0.666385	−	0.745608i	$-0.732159\pi$
$887$	−39.6933	−1.33277	−0.666385	+	0.745608i	$0.732159\pi$
$888$	−11.9379	−0.400611
$889$	8.26375	0.277157
$890$	−6.99656	−0.234525
$891$	0	0
$892$	5.05863	0.169376
$893$	−17.8535	−0.597445
$894$	−45.6673	−1.52734
$895$	−12.1725	−0.406881
$896$	1.00000	0.0334077
$897$	0	0
$898$	32.1656	1.07338
$899$	15.2672	0.509189
$900$	2.05863	0.0686211
$901$	−8.38789	−0.279441
$902$	0	0
$903$	12.4983	0.415917
$904$	3.88273	0.129138
$905$	10.9966	0.365538
$906$	−2.08441	−0.0692499
$907$	1.37758	0.0457417	0.0228708	−	0.999738i	$-0.492719\pi$
$907$	1.37758	0.0457417	0.0228708	+	0.999738i	$0.492719\pi$
$908$	13.4948	0.447842
$909$	−23.7914	−0.789112
$910$	0	0
$911$	−24.6087	−0.815322	−0.407661	−	0.913133i	$-0.633655\pi$
$911$	−24.6087	−0.815322	−0.407661	+	0.913133i	$0.633655\pi$
$912$	−11.6742	−0.386571
$913$	0	0
$914$	2.88617	0.0954661
$915$	−12.2345	−0.404461
$916$	2.82410	0.0933109
$917$	9.42504	0.311242
$918$	2.24141	0.0739775
$919$	47.5715	1.56924	0.784620	−	0.619977i	$-0.212858\pi$
$919$	47.5715	1.56924	0.784620	+	0.619977i	$0.212858\pi$
$920$	5.30777	0.174992
$921$	−28.6379	−0.943650
$922$	1.82754	0.0601868
$923$	0	0
$924$	0	0
$925$	5.30777	0.174519
$926$	−3.68879	−0.121221
$927$	−2.17934	−0.0715788
$928$	−3.30777	−0.108583
$929$	50.8432	1.66811	0.834056	−	0.551680i	$-0.186013\pi$
$929$	50.8432	1.66811	0.834056	+	0.551680i	$0.186013\pi$
$930$	10.3810	0.340407
$931$	5.19051	0.170112
$932$	−25.1138	−0.822631
$933$	−1.38445	−0.0453249
$934$	26.0958	0.853880
$935$	0	0
$936$	0	0
$937$	−4.17246	−0.136308	−0.0681542	−	0.997675i	$-0.521711\pi$
$937$	−4.17246	−0.136308	−0.0681542	+	0.997675i	$0.521711\pi$
$938$	−4.11727	−0.134434
$939$	−51.2863	−1.67366
$940$	−3.43965	−0.112189
$941$	−55.5569	−1.81110	−0.905552	−	0.424236i	$-0.860543\pi$
$941$	−55.5569	−1.81110	−0.905552	+	0.424236i	$0.860543\pi$
$942$	30.6155	0.997508
$943$	46.4293	1.51195
$944$	−3.05863	−0.0995500
$945$	2.11727	0.0688747
$946$	0	0
$947$	1.73625	0.0564206	0.0282103	−	0.999602i	$-0.491019\pi$
$947$	1.73625	0.0564206	0.0282103	+	0.999602i	$0.491019\pi$
$948$	−3.20512	−0.104097
$949$	0	0
$950$	5.19051	0.168402
$951$	−29.4036	−0.953476
$952$	1.05863	0.0343105
$953$	−30.2017	−0.978328	−0.489164	−	0.872192i	$-0.662698\pi$
$953$	−30.2017	−0.978328	−0.489164	+	0.872192i	$0.662698\pi$
$954$	−16.3112	−0.528095
$955$	−17.4948	−0.566120
$956$	3.69566	0.119526
$957$	0	0
$958$	8.99656	0.290666
$959$	14.9966	0.484264
$960$	−2.24914	−0.0725907
$961$	−9.69672	−0.312797
$962$	0	0
$963$	7.08097	0.228181
$964$	13.2457	0.426615
$965$	−20.3189	−0.654090
$966$	−11.9379	−0.384097
$967$	−28.3741	−0.912451	−0.456225	−	0.889864i	$-0.650799\pi$
$967$	−28.3741	−0.912451	−0.456225	+	0.889864i	$0.650799\pi$
$968$	0	0
$969$	−12.3587	−0.397018
$970$	17.3078	0.555719
$971$	−22.0621	−0.708006	−0.354003	−	0.935244i	$-0.615180\pi$
$971$	−22.0621	−0.708006	−0.354003	+	0.935244i	$0.615180\pi$
$972$	18.2491	0.585341
$973$	1.42504	0.0456847
$974$	−2.53887	−0.0813506
$975$	0	0
$976$	5.43965	0.174119
$977$	−6.11039	−0.195489	−0.0977444	−	0.995212i	$-0.531163\pi$
$977$	−6.11039	−0.195489	−0.0977444	+	0.995212i	$0.531163\pi$
$978$	−18.2569	−0.583790
$979$	0	0
$980$	1.00000	0.0319438
$981$	−33.5646	−1.07164
$982$	−18.2277	−0.581668
$983$	39.7554	1.26800	0.633999	−	0.773333i	$-0.281412\pi$
$983$	39.7554	1.26800	0.633999	+	0.773333i	$0.281412\pi$
$984$	−19.6742	−0.627190
$985$	−19.7294	−0.628630
$986$	−3.50172	−0.111517
$987$	7.73625	0.246248
$988$	0	0
$989$	−29.4948	−0.937881
$990$	0	0
$991$	−55.1430	−1.75168	−0.875838	−	0.482605i	$-0.839691\pi$
$991$	−55.1430	−1.75168	−0.875838	+	0.482605i	$0.839691\pi$
$992$	−4.61555	−0.146544
$993$	40.0812	1.27194
$994$	12.9966	0.412226
$995$	3.79145	0.120197
$996$	−4.23453	−0.134176
$997$	45.7777	1.44979	0.724897	−	0.688857i	$-0.241887\pi$
$997$	45.7777	1.44979	0.724897	+	0.688857i	$0.241887\pi$
$998$	0.406994	0.0128832
$999$	11.2380	0.355554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cn.1.1	yes	3
11.10	odd	2		8470.2.a.ch.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.ch.1.1	✓	3	11.10	odd	2
8470.2.a.cn.1.1	yes	3	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.24914 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.24914 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +1.00000 q^{10} -2.24914 q^{12} +1.00000 q^{14} -2.24914 q^{15} +1.00000 q^{16} +1.05863 q^{17} +2.05863 q^{18} +5.19051 q^{19} +1.00000 q^{20} -2.24914 q^{21} +5.30777 q^{23} -2.24914 q^{24} +1.00000 q^{25} +2.11727 q^{27} +1.00000 q^{28} -3.30777 q^{29} -2.24914 q^{30} -4.61555 q^{31} +1.00000 q^{32} +1.05863 q^{34} +1.00000 q^{35} +2.05863 q^{36} +5.30777 q^{37} +5.19051 q^{38} +1.00000 q^{40} +8.74742 q^{41} -2.24914 q^{42} -5.55691 q^{43} +2.05863 q^{45} +5.30777 q^{46} -3.43965 q^{47} -2.24914 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.38101 q^{51} -7.92332 q^{53} +2.11727 q^{54} +1.00000 q^{56} -11.6742 q^{57} -3.30777 q^{58} -3.05863 q^{59} -2.24914 q^{60} +5.43965 q^{61} -4.61555 q^{62} +2.05863 q^{63} +1.00000 q^{64} -4.11727 q^{67} +1.05863 q^{68} -11.9379 q^{69} +1.00000 q^{70} +12.9966 q^{71} +2.05863 q^{72} +1.55691 q^{73} +5.30777 q^{74} -2.24914 q^{75} +5.19051 q^{76} +1.42504 q^{79} +1.00000 q^{80} -10.9379 q^{81} +8.74742 q^{82} +1.88273 q^{83} -2.24914 q^{84} +1.05863 q^{85} -5.55691 q^{86} +7.43965 q^{87} -6.99656 q^{89} +2.05863 q^{90} +5.30777 q^{92} +10.3810 q^{93} -3.43965 q^{94} +5.19051 q^{95} -2.24914 q^{96} +17.3078 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 2 q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} + 7 q^{18} + 6 q^{19} + 3 q^{20} + 2 q^{21} + 8 q^{23} + 2 q^{24} + 3 q^{25} + 8 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 3 q^{32} + 4 q^{34} + 3 q^{35} + 7 q^{36} + 8 q^{37} + 6 q^{38} + 3 q^{40} + 2 q^{42} + 7 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 8 q^{54} + 3 q^{56} - 20 q^{57} - 2 q^{58} - 10 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 7 q^{63} + 3 q^{64} - 14 q^{67} + 4 q^{68} + 3 q^{70} + 4 q^{71} + 7 q^{72} - 12 q^{73} + 8 q^{74} + 2 q^{75} + 6 q^{76} - 2 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{83} + 2 q^{84} + 4 q^{85} + 4 q^{87} + 14 q^{89} + 7 q^{90} + 8 q^{92} + 12 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{96} + 44 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 2 * q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 + 7 * q^18 + 6 * q^19 + 3 * q^20 + 2 * q^21 + 8 * q^23 + 2 * q^24 + 3 * q^25 + 8 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 3 * q^32 + 4 * q^34 + 3 * q^35 + 7 * q^36 + 8 * q^37 + 6 * q^38 + 3 * q^40 + 2 * q^42 + 7 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 8 * q^54 + 3 * q^56 - 20 * q^57 - 2 * q^58 - 10 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 7 * q^63 + 3 * q^64 - 14 * q^67 + 4 * q^68 + 3 * q^70 + 4 * q^71 + 7 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 + 6 * q^76 - 2 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^83 + 2 * q^84 + 4 * q^85 + 4 * q^87 + 14 * q^89 + 7 * q^90 + 8 * q^92 + 12 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^96 + 44 * q^97 + 3 * q^98

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