LMFDB - Embedded newform 4998.2.a.co.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4998,2,Mod(1,4998)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4998, 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("4998.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4998.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:	$39.9092309302$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.16448.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 14 $ x^4 - 2x^3 - 7x^2 + 8*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.18398$ of defining polynomial
Character	$\chi$	$=$	4998.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.59819 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.59819 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.59819 q^{10} +5.85838 q^{11} -1.00000 q^{12} -1.23023 q^{13} +3.59819 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.08861 q^{19} -3.59819 q^{20} +5.85838 q^{22} -1.67440 q^{23} -1.00000 q^{24} +7.94699 q^{25} -1.23023 q^{26} -1.00000 q^{27} -3.91704 q^{29} +3.59819 q^{30} +5.08861 q^{31} +1.00000 q^{32} -5.85838 q^{33} -1.00000 q^{34} +1.00000 q^{36} -0.444165 q^{37} -3.08861 q^{38} +1.23023 q^{39} -3.59819 q^{40} +0.720655 q^{41} -11.4227 q^{43} +5.85838 q^{44} -3.59819 q^{45} -1.67440 q^{46} +11.2658 q^{47} -1.00000 q^{48} +7.94699 q^{50} +1.00000 q^{51} -1.23023 q^{52} -5.31495 q^{53} -1.00000 q^{54} -21.0796 q^{55} +3.08861 q^{57} -3.91704 q^{58} -4.84597 q^{59} +3.59819 q^{60} +10.5452 q^{61} +5.08861 q^{62} +1.00000 q^{64} +4.42662 q^{65} -5.85838 q^{66} +0.661993 q^{67} -1.00000 q^{68} +1.67440 q^{69} +4.95375 q^{71} +1.00000 q^{72} +13.2550 q^{73} -0.444165 q^{74} -7.94699 q^{75} -3.08861 q^{76} +1.23023 q^{78} -13.2320 q^{79} -3.59819 q^{80} +1.00000 q^{81} +0.720655 q^{82} +2.89508 q^{83} +3.59819 q^{85} -11.4227 q^{86} +3.91704 q^{87} +5.85838 q^{88} +8.24939 q^{89} -3.59819 q^{90} -1.67440 q^{92} -5.08861 q^{93} +11.2658 q^{94} +11.1134 q^{95} -1.00000 q^{96} +4.61735 q^{97} +5.85838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 10 q^{11} - 4 q^{12} - 6 q^{13} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 2 q^{20} + 10 q^{22} - 4 q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} + 8 q^{29} + 2 q^{30} + 8 q^{31} + 4 q^{32} - 10 q^{33} - 4 q^{34} + 4 q^{36} + 6 q^{37} + 6 q^{39} - 2 q^{40} + 4 q^{41} + 6 q^{43} + 10 q^{44} - 2 q^{45} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 4 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} - 10 q^{55} + 8 q^{58} - 24 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} - 10 q^{66} + 14 q^{67} - 4 q^{68} + 12 q^{71} + 4 q^{72} + 18 q^{73} + 6 q^{74} - 6 q^{75} + 6 q^{78} + 10 q^{79} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 14 q^{83} + 2 q^{85} + 6 q^{86} - 8 q^{87} + 10 q^{88} + 34 q^{89} - 2 q^{90} - 8 q^{93} + 8 q^{94} - 4 q^{95} - 4 q^{96} + 6 q^{97} + 10 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 10 * q^11 - 4 * q^12 - 6 * q^13 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 2 * q^20 + 10 * q^22 - 4 * q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 + 8 * q^29 + 2 * q^30 + 8 * q^31 + 4 * q^32 - 10 * q^33 - 4 * q^34 + 4 * q^36 + 6 * q^37 + 6 * q^39 - 2 * q^40 + 4 * q^41 + 6 * q^43 + 10 * q^44 - 2 * q^45 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 4 * q^51 - 6 * q^52 + 18 * q^53 - 4 * q^54 - 10 * q^55 + 8 * q^58 - 24 * q^59 + 2 * q^60 + 4 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 - 10 * q^66 + 14 * q^67 - 4 * q^68 + 12 * q^71 + 4 * q^72 + 18 * q^73 + 6 * q^74 - 6 * q^75 + 6 * q^78 + 10 * q^79 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 14 * q^83 + 2 * q^85 + 6 * q^86 - 8 * q^87 + 10 * q^88 + 34 * q^89 - 2 * q^90 - 8 * q^93 + 8 * q^94 - 4 * q^95 - 4 * q^96 + 6 * q^97 + 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.59819	−1.60916	−0.804580	−	0.593844i	$-0.797610\pi$
$5$	−3.59819	−1.60916	−0.804580	+	0.593844i	$0.797610\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.59819	−1.13785
$11$	5.85838	1.76637	0.883184	−	0.469027i	$-0.155395\pi$
$11$	5.85838	1.76637	0.883184	+	0.469027i	$0.155395\pi$
$12$	−1.00000	−0.288675
$13$	−1.23023	−0.341206	−0.170603	−	0.985340i	$-0.554571\pi$
$13$	−1.23023	−0.341206	−0.170603	+	0.985340i	$0.554571\pi$
$14$	0	0
$15$	3.59819	0.929049
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−3.08861	−0.708576	−0.354288	−	0.935136i	$-0.615277\pi$
$19$	−3.08861	−0.708576	−0.354288	+	0.935136i	$0.615277\pi$
$20$	−3.59819	−0.804580
$21$	0	0
$22$	5.85838	1.24901
$23$	−1.67440	−0.349136	−0.174568	−	0.984645i	$-0.555853\pi$
$23$	−1.67440	−0.349136	−0.174568	+	0.984645i	$0.555853\pi$
$24$	−1.00000	−0.204124
$25$	7.94699	1.58940
$26$	−1.23023	−0.241269
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.91704	−0.727376	−0.363688	−	0.931521i	$-0.618483\pi$
$29$	−3.91704	−0.727376	−0.363688	+	0.931521i	$0.618483\pi$
$30$	3.59819	0.656937
$31$	5.08861	0.913942	0.456971	−	0.889482i	$-0.348934\pi$
$31$	5.08861	0.913942	0.456971	+	0.889482i	$0.348934\pi$
$32$	1.00000	0.176777
$33$	−5.85838	−1.01981
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−0.444165	−0.0730203	−0.0365102	−	0.999333i	$-0.511624\pi$
$37$	−0.444165	−0.0730203	−0.0365102	+	0.999333i	$0.511624\pi$
$38$	−3.08861	−0.501039
$39$	1.23023	0.196995
$40$	−3.59819	−0.568924
$41$	0.720655	0.112547	0.0562737	−	0.998415i	$-0.482078\pi$
$41$	0.720655	0.112547	0.0562737	+	0.998415i	$0.482078\pi$
$42$	0	0
$43$	−11.4227	−1.74195	−0.870975	−	0.491328i	$-0.836512\pi$
$43$	−11.4227	−1.74195	−0.870975	+	0.491328i	$0.836512\pi$
$44$	5.85838	0.883184
$45$	−3.59819	−0.536387
$46$	−1.67440	−0.246877
$47$	11.2658	1.64329	0.821646	−	0.569998i	$-0.193056\pi$
$47$	11.2658	1.64329	0.821646	+	0.569998i	$0.193056\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	7.94699	1.12387
$51$	1.00000	0.140028
$52$	−1.23023	−0.170603
$53$	−5.31495	−0.730065	−0.365032	−	0.930995i	$-0.618942\pi$
$53$	−5.31495	−0.730065	−0.365032	+	0.930995i	$0.618942\pi$
$54$	−1.00000	−0.136083
$55$	−21.0796	−2.84237
$56$	0	0
$57$	3.08861	0.409097
$58$	−3.91704	−0.514333
$59$	−4.84597	−0.630892	−0.315446	−	0.948944i	$-0.602154\pi$
$59$	−4.84597	−0.630892	−0.315446	+	0.948944i	$0.602154\pi$
$60$	3.59819	0.464525
$61$	10.5452	1.35017	0.675086	−	0.737739i	$-0.264106\pi$
$61$	10.5452	1.35017	0.675086	+	0.737739i	$0.264106\pi$
$62$	5.08861	0.646255
$63$	0	0
$64$	1.00000	0.125000
$65$	4.42662	0.549055
$66$	−5.85838	−0.721117
$67$	0.661993	0.0808753	0.0404377	−	0.999182i	$-0.487125\pi$
$67$	0.661993	0.0808753	0.0404377	+	0.999182i	$0.487125\pi$
$68$	−1.00000	−0.121268
$69$	1.67440	0.201574
$70$	0	0
$71$	4.95375	0.587901	0.293951	−	0.955821i	$-0.405030\pi$
$71$	4.95375	0.587901	0.293951	+	0.955821i	$0.405030\pi$
$72$	1.00000	0.117851
$73$	13.2550	1.55139	0.775693	−	0.631110i	$-0.217401\pi$
$73$	13.2550	1.55139	0.775693	+	0.631110i	$0.217401\pi$
$74$	−0.444165	−0.0516332
$75$	−7.94699	−0.917640
$76$	−3.08861	−0.354288
$77$	0	0
$78$	1.23023	0.139297
$79$	−13.2320	−1.48872	−0.744358	−	0.667781i	$-0.767244\pi$
$79$	−13.2320	−1.48872	−0.744358	+	0.667781i	$0.767244\pi$
$80$	−3.59819	−0.402290
$81$	1.00000	0.111111
$82$	0.720655	0.0795830
$83$	2.89508	0.317777	0.158888	−	0.987297i	$-0.449209\pi$
$83$	2.89508	0.317777	0.158888	+	0.987297i	$0.449209\pi$
$84$	0	0
$85$	3.59819	0.390279
$86$	−11.4227	−1.23174
$87$	3.91704	0.419951
$88$	5.85838	0.624505
$89$	8.24939	0.874434	0.437217	−	0.899356i	$-0.355964\pi$
$89$	8.24939	0.874434	0.437217	+	0.899356i	$0.355964\pi$
$90$	−3.59819	−0.379283
$91$	0	0
$92$	−1.67440	−0.174568
$93$	−5.08861	−0.527665
$94$	11.2658	1.16198
$95$	11.1134	1.14021
$96$	−1.00000	−0.102062
$97$	4.61735	0.468821	0.234411	−	0.972138i	$-0.424684\pi$
$97$	4.61735	0.468821	0.234411	+	0.972138i	$0.424684\pi$
$98$	0	0
$99$	5.85838	0.588789
$100$	7.94699	0.794699
$101$	−1.10616	−0.110067	−0.0550334	−	0.998485i	$-0.517527\pi$
$101$	−1.10616	−0.110067	−0.0550334	+	0.998485i	$0.517527\pi$
$102$	1.00000	0.0990148
$103$	2.18398	0.215194	0.107597	−	0.994195i	$-0.465684\pi$
$103$	2.18398	0.215194	0.107597	+	0.994195i	$0.465684\pi$
$104$	−1.23023	−0.120634
$105$	0	0
$106$	−5.31495	−0.516234
$107$	14.7359	1.42457	0.712287	−	0.701888i	$-0.247659\pi$
$107$	14.7359	1.42457	0.712287	+	0.701888i	$0.247659\pi$
$108$	−1.00000	−0.0962250
$109$	−12.2196	−1.17042	−0.585212	−	0.810880i	$-0.698989\pi$
$109$	−12.2196	−1.17042	−0.585212	+	0.810880i	$0.698989\pi$
$110$	−21.0796	−2.00986
$111$	0.444165	0.0421583
$112$	0	0
$113$	−3.21269	−0.302224	−0.151112	−	0.988517i	$-0.548285\pi$
$113$	−3.21269	−0.302224	−0.151112	+	0.988517i	$0.548285\pi$
$114$	3.08861	0.289275
$115$	6.02481	0.561817
$116$	−3.91704	−0.363688
$117$	−1.23023	−0.113735
$118$	−4.84597	−0.446108
$119$	0	0
$120$	3.59819	0.328469
$121$	23.3206	2.12005
$122$	10.5452	0.954716
$123$	−0.720655	−0.0649792
$124$	5.08861	0.456971
$125$	−10.6038	−0.948437
$126$	0	0
$127$	20.2619	1.79796	0.898978	−	0.437993i	$-0.144311\pi$
$127$	20.2619	1.79796	0.898978	+	0.437993i	$0.144311\pi$
$128$	1.00000	0.0883883
$129$	11.4227	1.00571
$130$	4.42662	0.388240
$131$	−2.98084	−0.260437	−0.130219	−	0.991485i	$-0.541568\pi$
$131$	−2.98084	−0.260437	−0.130219	+	0.991485i	$0.541568\pi$
$132$	−5.85838	−0.509906
$133$	0	0
$134$	0.661993	0.0571875
$135$	3.59819	0.309683
$136$	−1.00000	−0.0857493
$137$	17.4814	1.49354	0.746768	−	0.665085i	$-0.231605\pi$
$137$	17.4814	1.49354	0.746768	+	0.665085i	$0.231605\pi$
$138$	1.67440	0.142534
$139$	−9.82329	−0.833200	−0.416600	−	0.909090i	$-0.636779\pi$
$139$	−9.82329	−0.833200	−0.416600	+	0.909090i	$0.636779\pi$
$140$	0	0
$141$	−11.2658	−0.948755
$142$	4.95375	0.415709
$143$	−7.20718	−0.602695
$144$	1.00000	0.0833333
$145$	14.0943	1.17047
$146$	13.2550	1.09700
$147$	0	0
$148$	−0.444165	−0.0365102
$149$	11.8679	0.972259	0.486129	−	0.873887i	$-0.338408\pi$
$149$	11.8679	0.972259	0.486129	+	0.873887i	$0.338408\pi$
$150$	−7.94699	−0.648869
$151$	−21.3889	−1.74060	−0.870301	−	0.492520i	$-0.836076\pi$
$151$	−21.3889	−1.74060	−0.870301	+	0.492520i	$0.836076\pi$
$152$	−3.08861	−0.250520
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−18.3098	−1.47068
$156$	1.23023	0.0984976
$157$	17.5260	1.39873	0.699365	−	0.714765i	$-0.253466\pi$
$157$	17.5260	1.39873	0.699365	+	0.714765i	$0.253466\pi$
$158$	−13.2320	−1.05268
$159$	5.31495	0.421503
$160$	−3.59819	−0.284462
$161$	0	0
$162$	1.00000	0.0785674
$163$	13.0463	1.02186	0.510931	−	0.859622i	$-0.329301\pi$
$163$	13.0463	1.02186	0.510931	+	0.859622i	$0.329301\pi$
$164$	0.720655	0.0562737
$165$	21.0796	1.64104
$166$	2.89508	0.224702
$167$	−0.534393	−0.0413525	−0.0206763	−	0.999786i	$-0.506582\pi$
$167$	−0.534393	−0.0413525	−0.0206763	+	0.999786i	$0.506582\pi$
$168$	0	0
$169$	−11.4865	−0.883579
$170$	3.59819	0.275969
$171$	−3.08861	−0.236192
$172$	−11.4227	−0.870975
$173$	−6.23713	−0.474200	−0.237100	−	0.971485i	$-0.576197\pi$
$173$	−6.23713	−0.474200	−0.237100	+	0.971485i	$0.576197\pi$
$174$	3.91704	0.296950
$175$	0	0
$176$	5.85838	0.441592
$177$	4.84597	0.364246
$178$	8.24939	0.618318
$179$	8.09427	0.604994	0.302497	−	0.953150i	$-0.402180\pi$
$179$	8.09427	0.604994	0.302497	+	0.953150i	$0.402180\pi$
$180$	−3.59819	−0.268193
$181$	13.7320	1.02069	0.510347	−	0.859969i	$-0.329517\pi$
$181$	13.7320	1.02069	0.510347	+	0.859969i	$0.329517\pi$
$182$	0	0
$183$	−10.5452	−0.779523
$184$	−1.67440	−0.123438
$185$	1.59819	0.117501
$186$	−5.08861	−0.373115
$187$	−5.85838	−0.428407
$188$	11.2658	0.821646
$189$	0	0
$190$	11.1134	0.806253
$191$	2.44968	0.177252	0.0886262	−	0.996065i	$-0.471752\pi$
$191$	2.44968	0.177252	0.0886262	+	0.996065i	$0.471752\pi$
$192$	−1.00000	−0.0721688
$193$	21.0808	1.51743	0.758715	−	0.651422i	$-0.225827\pi$
$193$	21.0808	1.51743	0.758715	+	0.651422i	$0.225827\pi$
$194$	4.61735	0.331507
$195$	−4.42662	−0.316997
$196$	0	0
$197$	11.3641	0.809656	0.404828	−	0.914393i	$-0.367331\pi$
$197$	11.3641	0.809656	0.404828	+	0.914393i	$0.367331\pi$
$198$	5.85838	0.416337
$199$	20.4023	1.44628	0.723141	−	0.690700i	$-0.242698\pi$
$199$	20.4023	1.44628	0.723141	+	0.690700i	$0.242698\pi$
$200$	7.94699	0.561937
$201$	−0.661993	−0.0466934
$202$	−1.10616	−0.0778290
$203$	0	0
$204$	1.00000	0.0700140
$205$	−2.59305	−0.181107
$206$	2.18398	0.152165
$207$	−1.67440	−0.116379
$208$	−1.23023	−0.0853014
$209$	−18.0943	−1.25161
$210$	0	0
$211$	11.1884	0.770241	0.385120	−	0.922866i	$-0.374160\pi$
$211$	11.1884	0.770241	0.385120	+	0.922866i	$0.374160\pi$
$212$	−5.31495	−0.365032
$213$	−4.95375	−0.339425
$214$	14.7359	1.00733
$215$	41.1012	2.80308
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−12.2196	−0.827615
$219$	−13.2550	−0.895693
$220$	−21.0796	−1.42118
$221$	1.23023	0.0827545
$222$	0.444165	0.0298104
$223$	−23.1653	−1.55127	−0.775633	−	0.631184i	$-0.782569\pi$
$223$	−23.1653	−1.55127	−0.775633	+	0.631184i	$0.782569\pi$
$224$	0	0
$225$	7.94699	0.529799
$226$	−3.21269	−0.213705
$227$	20.9706	1.39187	0.695933	−	0.718107i	$-0.254991\pi$
$227$	20.9706	1.39187	0.695933	+	0.718107i	$0.254991\pi$
$228$	3.08861	0.204548
$229$	−0.494317	−0.0326654	−0.0163327	−	0.999867i	$-0.505199\pi$
$229$	−0.494317	−0.0326654	−0.0163327	+	0.999867i	$0.505199\pi$
$230$	6.02481	0.397264
$231$	0	0
$232$	−3.91704	−0.257166
$233$	28.9543	1.89686	0.948428	−	0.316992i	$-0.102673\pi$
$233$	28.9543	1.89686	0.948428	+	0.316992i	$0.102673\pi$
$234$	−1.23023	−0.0804229
$235$	−40.5367	−2.64432
$236$	−4.84597	−0.315446
$237$	13.2320	0.859510
$238$	0	0
$239$	0.792822	0.0512834	0.0256417	−	0.999671i	$-0.491837\pi$
$239$	0.792822	0.0512834	0.0256417	+	0.999671i	$0.491837\pi$
$240$	3.59819	0.232262
$241$	−8.79582	−0.566589	−0.283294	−	0.959033i	$-0.591427\pi$
$241$	−8.79582	−0.566589	−0.283294	+	0.959033i	$0.591427\pi$
$242$	23.3206	1.49911
$243$	−1.00000	−0.0641500
$244$	10.5452	0.675086
$245$	0	0
$246$	−0.720655	−0.0459473
$247$	3.79972	0.241770
$248$	5.08861	0.323127
$249$	−2.89508	−0.183468
$250$	−10.6038	−0.670646
$251$	6.89508	0.435214	0.217607	−	0.976036i	$-0.430175\pi$
$251$	6.89508	0.435214	0.217607	+	0.976036i	$0.430175\pi$
$252$	0	0
$253$	−9.80927	−0.616703
$254$	20.2619	1.27135
$255$	−3.59819	−0.225328
$256$	1.00000	0.0625000
$257$	15.2302	0.950036	0.475018	−	0.879976i	$-0.342442\pi$
$257$	15.2302	0.950036	0.475018	+	0.879976i	$0.342442\pi$
$258$	11.4227	0.711148
$259$	0	0
$260$	4.42662	0.274527
$261$	−3.91704	−0.242459
$262$	−2.98084	−0.184157
$263$	21.4475	1.32251	0.661256	−	0.750160i	$-0.270024\pi$
$263$	21.4475	1.32251	0.661256	+	0.750160i	$0.270024\pi$
$264$	−5.85838	−0.360558
$265$	19.1242	1.17479
$266$	0	0
$267$	−8.24939	−0.504855
$268$	0.661993	0.0404377
$269$	3.80927	0.232255	0.116128	−	0.993234i	$-0.462952\pi$
$269$	3.80927	0.232255	0.116128	+	0.993234i	$0.462952\pi$
$270$	3.59819	0.218979
$271$	−24.7292	−1.50219	−0.751095	−	0.660194i	$-0.770474\pi$
$271$	−24.7292	−1.50219	−0.751095	+	0.660194i	$0.770474\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	17.4814	1.05609
$275$	46.5565	2.80746
$276$	1.67440	0.100787
$277$	−6.44292	−0.387118	−0.193559	−	0.981089i	$-0.562003\pi$
$277$	−6.44292	−0.387118	−0.193559	+	0.981089i	$0.562003\pi$
$278$	−9.82329	−0.589162
$279$	5.08861	0.304647
$280$	0	0
$281$	−9.96491	−0.594457	−0.297228	−	0.954806i	$-0.596062\pi$
$281$	−9.96491	−0.594457	−0.297228	+	0.954806i	$0.596062\pi$
$282$	−11.2658	−0.670871
$283$	20.5592	1.22212	0.611059	−	0.791585i	$-0.290744\pi$
$283$	20.5592	1.22212	0.611059	+	0.791585i	$0.290744\pi$
$284$	4.95375	0.293951
$285$	−11.1134	−0.658303
$286$	−7.20718	−0.426169
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	14.0943	0.827644
$291$	−4.61735	−0.270674
$292$	13.2550	0.775693
$293$	25.2061	1.47256	0.736279	−	0.676678i	$-0.236581\pi$
$293$	25.2061	1.47256	0.736279	+	0.676678i	$0.236581\pi$
$294$	0	0
$295$	17.4367	1.01521
$296$	−0.444165	−0.0258166
$297$	−5.85838	−0.339938
$298$	11.8679	0.687491
$299$	2.05990	0.119127
$300$	−7.94699	−0.458820
$301$	0	0
$302$	−21.3889	−1.23079
$303$	1.10616	0.0635472
$304$	−3.08861	−0.177144
$305$	−37.9436	−2.17264
$306$	−1.00000	−0.0571662
$307$	−25.2460	−1.44087	−0.720433	−	0.693525i	$-0.756057\pi$
$307$	−25.2460	−1.44087	−0.720433	+	0.693525i	$0.756057\pi$
$308$	0	0
$309$	−2.18398	−0.124242
$310$	−18.3098	−1.03993
$311$	18.6868	1.05963	0.529816	−	0.848113i	$-0.322261\pi$
$311$	18.6868	1.05963	0.529816	+	0.848113i	$0.322261\pi$
$312$	1.23023	0.0696483
$313$	−27.4583	−1.55204	−0.776018	−	0.630710i	$-0.782764\pi$
$313$	−27.4583	−1.55204	−0.776018	+	0.630710i	$0.782764\pi$
$314$	17.5260	0.989051
$315$	0	0
$316$	−13.2320	−0.744358
$317$	30.8996	1.73550	0.867748	−	0.497004i	$-0.165567\pi$
$317$	30.8996	1.73550	0.867748	+	0.497004i	$0.165567\pi$
$318$	5.31495	0.298048
$319$	−22.9475	−1.28481
$320$	−3.59819	−0.201145
$321$	−14.7359	−0.822479
$322$	0	0
$323$	3.08861	0.171855
$324$	1.00000	0.0555556
$325$	−9.77666	−0.542312
$326$	13.0463	0.722565
$327$	12.2196	0.675745
$328$	0.720655	0.0397915
$329$	0	0
$330$	21.0796	1.16039
$331$	−5.95089	−0.327090	−0.163545	−	0.986536i	$-0.552293\pi$
$331$	−5.95089	−0.327090	−0.163545	+	0.986536i	$0.552293\pi$
$332$	2.89508	0.158888
$333$	−0.444165	−0.0243401
$334$	−0.534393	−0.0292407
$335$	−2.38198	−0.130141
$336$	0	0
$337$	5.61854	0.306061	0.153031	−	0.988221i	$-0.451097\pi$
$337$	5.61854	0.306061	0.153031	+	0.988221i	$0.451097\pi$
$338$	−11.4865	−0.624785
$339$	3.21269	0.174489
$340$	3.59819	0.195139
$341$	29.8110	1.61436
$342$	−3.08861	−0.167013
$343$	0	0
$344$	−11.4227	−0.615872
$345$	−6.02481	−0.324365
$346$	−6.23713	−0.335310
$347$	25.7907	1.38452	0.692258	−	0.721650i	$-0.256616\pi$
$347$	25.7907	1.38452	0.692258	+	0.721650i	$0.256616\pi$
$348$	3.91704	0.209975
$349$	−28.1299	−1.50576	−0.752879	−	0.658159i	$-0.771335\pi$
$349$	−28.1299	−1.50576	−0.752879	+	0.658159i	$0.771335\pi$
$350$	0	0
$351$	1.23023	0.0656650
$352$	5.85838	0.312253
$353$	8.35321	0.444597	0.222298	−	0.974979i	$-0.428644\pi$
$353$	8.35321	0.444597	0.222298	+	0.974979i	$0.428644\pi$
$354$	4.84597	0.257561
$355$	−17.8245	−0.946028
$356$	8.24939	0.437217
$357$	0	0
$358$	8.09427	0.427795
$359$	−15.9539	−0.842014	−0.421007	−	0.907057i	$-0.638323\pi$
$359$	−15.9539	−0.842014	−0.421007	+	0.907057i	$0.638323\pi$
$360$	−3.59819	−0.189641
$361$	−9.46047	−0.497919
$362$	13.7320	0.721739
$363$	−23.3206	−1.22401
$364$	0	0
$365$	−47.6942	−2.49643
$366$	−10.5452	−0.551206
$367$	28.9706	1.51225	0.756126	−	0.654427i	$-0.227090\pi$
$367$	28.9706	1.51225	0.756126	+	0.654427i	$0.227090\pi$
$368$	−1.67440	−0.0872841
$369$	0.720655	0.0375158
$370$	1.59819	0.0830861
$371$	0	0
$372$	−5.08861	−0.263832
$373$	−12.8763	−0.666709	−0.333355	−	0.942801i	$-0.608181\pi$
$373$	−12.8763	−0.666709	−0.333355	+	0.942801i	$0.608181\pi$
$374$	−5.85838	−0.302930
$375$	10.6038	0.547580
$376$	11.2658	0.580991
$377$	4.81888	0.248185
$378$	0	0
$379$	19.6737	1.01057	0.505284	−	0.862953i	$-0.331388\pi$
$379$	19.6737	1.01057	0.505284	+	0.862953i	$0.331388\pi$
$380$	11.1134	0.570107
$381$	−20.2619	−1.03805
$382$	2.44968	0.125336
$383$	−12.4870	−0.638058	−0.319029	−	0.947745i	$-0.603357\pi$
$383$	−12.4870	−0.638058	−0.319029	+	0.947745i	$0.603357\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	21.0808	1.07299
$387$	−11.4227	−0.580650
$388$	4.61735	0.234411
$389$	−10.6129	−0.538094	−0.269047	−	0.963127i	$-0.586709\pi$
$389$	−10.6129	−0.538094	−0.269047	+	0.963127i	$0.586709\pi$
$390$	−4.42662	−0.224151
$391$	1.67440	0.0846780
$392$	0	0
$393$	2.98084	0.150364
$394$	11.3641	0.572513
$395$	47.6113	2.39558
$396$	5.85838	0.294395
$397$	−31.3984	−1.57584	−0.787921	−	0.615776i	$-0.788842\pi$
$397$	−31.3984	−1.57584	−0.787921	+	0.615776i	$0.788842\pi$
$398$	20.4023	1.02268
$399$	0	0
$400$	7.94699	0.397350
$401$	9.29616	0.464228	0.232114	−	0.972689i	$-0.425436\pi$
$401$	9.29616	0.464228	0.232114	+	0.972689i	$0.425436\pi$
$402$	−0.661993	−0.0330172
$403$	−6.26019	−0.311842
$404$	−1.10616	−0.0550334
$405$	−3.59819	−0.178796
$406$	0	0
$407$	−2.60209	−0.128981
$408$	1.00000	0.0495074
$409$	−20.5124	−1.01427	−0.507136	−	0.861866i	$-0.669296\pi$
$409$	−20.5124	−1.01427	−0.507136	+	0.861866i	$0.669296\pi$
$410$	−2.59305	−0.128062
$411$	−17.4814	−0.862293
$412$	2.18398	0.107597
$413$	0	0
$414$	−1.67440	−0.0822923
$415$	−10.4171	−0.511354
$416$	−1.23023	−0.0603172
$417$	9.82329	0.481048
$418$	−18.0943	−0.885020
$419$	−25.5909	−1.25020	−0.625099	−	0.780545i	$-0.714941\pi$
$419$	−25.5909	−1.25020	−0.625099	+	0.780545i	$0.714941\pi$
$420$	0	0
$421$	−10.6665	−0.519852	−0.259926	−	0.965629i	$-0.583698\pi$
$421$	−10.6665	−0.519852	−0.259926	+	0.965629i	$0.583698\pi$
$422$	11.1884	0.544642
$423$	11.2658	0.547764
$424$	−5.31495	−0.258117
$425$	−7.94699	−0.385486
$426$	−4.95375	−0.240010
$427$	0	0
$428$	14.7359	0.712287
$429$	7.20718	0.347966
$430$	41.1012	1.98207
$431$	−37.0115	−1.78278	−0.891389	−	0.453238i	$-0.850269\pi$
$431$	−37.0115	−1.78278	−0.891389	+	0.453238i	$0.850269\pi$
$432$	−1.00000	−0.0481125
$433$	2.48756	0.119545	0.0597723	−	0.998212i	$-0.480963\pi$
$433$	2.48756	0.119545	0.0597723	+	0.998212i	$0.480963\pi$
$434$	0	0
$435$	−14.0943	−0.675768
$436$	−12.2196	−0.585212
$437$	5.17157	0.247390
$438$	−13.2550	−0.633351
$439$	−6.26019	−0.298782	−0.149391	−	0.988778i	$-0.547731\pi$
$439$	−6.26019	−0.298782	−0.149391	+	0.988778i	$0.547731\pi$
$440$	−21.0796	−1.00493
$441$	0	0
$442$	1.23023	0.0585163
$443$	−34.4487	−1.63671	−0.818354	−	0.574714i	$-0.805113\pi$
$443$	−34.4487	−1.63671	−0.818354	+	0.574714i	$0.805113\pi$
$444$	0.444165	0.0210792
$445$	−29.6829	−1.40710
$446$	−23.1653	−1.09691
$447$	−11.8679	−0.561334
$448$	0	0
$449$	23.3821	1.10347	0.551735	−	0.834019i	$-0.313966\pi$
$449$	23.3821	1.10347	0.551735	+	0.834019i	$0.313966\pi$
$450$	7.94699	0.374625
$451$	4.22187	0.198800
$452$	−3.21269	−0.151112
$453$	21.3889	1.00494
$454$	20.9706	0.984197
$455$	0	0
$456$	3.08861	0.144638
$457$	−30.6152	−1.43212	−0.716058	−	0.698041i	$-0.754056\pi$
$457$	−30.6152	−1.43212	−0.716058	+	0.698041i	$0.754056\pi$
$458$	−0.494317	−0.0230979
$459$	1.00000	0.0466760
$460$	6.02481	0.280908
$461$	−32.0211	−1.49137	−0.745685	−	0.666299i	$-0.767877\pi$
$461$	−32.0211	−1.49137	−0.745685	+	0.666299i	$0.767877\pi$
$462$	0	0
$463$	25.3959	1.18025	0.590125	−	0.807312i	$-0.299079\pi$
$463$	25.3959	1.18025	0.590125	+	0.807312i	$0.299079\pi$
$464$	−3.91704	−0.181844
$465$	18.3098	0.849097
$466$	28.9543	1.34128
$467$	−29.8336	−1.38053	−0.690266	−	0.723556i	$-0.742507\pi$
$467$	−29.8336	−1.38053	−0.690266	+	0.723556i	$0.742507\pi$
$468$	−1.23023	−0.0568676
$469$	0	0
$470$	−40.5367	−1.86982
$471$	−17.5260	−0.807557
$472$	−4.84597	−0.223054
$473$	−66.9186	−3.07692
$474$	13.2320	0.607765
$475$	−24.5452	−1.12621
$476$	0	0
$477$	−5.31495	−0.243355
$478$	0.792822	0.0362628
$479$	−3.18237	−0.145406	−0.0727030	−	0.997354i	$-0.523163\pi$
$479$	−3.18237	−0.145406	−0.0727030	+	0.997354i	$0.523163\pi$
$480$	3.59819	0.164234
$481$	0.546428	0.0249149
$482$	−8.79582	−0.400639
$483$	0	0
$484$	23.3206	1.06003
$485$	−16.6141	−0.754409
$486$	−1.00000	−0.0453609
$487$	34.8888	1.58096	0.790482	−	0.612485i	$-0.209830\pi$
$487$	34.8888	1.58096	0.790482	+	0.612485i	$0.209830\pi$
$488$	10.5452	0.477358
$489$	−13.0463	−0.589972
$490$	0	0
$491$	12.6146	0.569291	0.284645	−	0.958633i	$-0.408124\pi$
$491$	12.6146	0.569291	0.284645	+	0.958633i	$0.408124\pi$
$492$	−0.720655	−0.0324896
$493$	3.91704	0.176415
$494$	3.79972	0.170957
$495$	−21.0796	−0.947457
$496$	5.08861	0.228485
$497$	0	0
$498$	−2.89508	−0.129732
$499$	−3.74137	−0.167487	−0.0837433	−	0.996487i	$-0.526688\pi$
$499$	−3.74137	−0.167487	−0.0837433	+	0.996487i	$0.526688\pi$
$500$	−10.6038	−0.474218
$501$	0.534393	0.0238749
$502$	6.89508	0.307743
$503$	−10.7720	−0.480301	−0.240151	−	0.970736i	$-0.577197\pi$
$503$	−10.7720	−0.480301	−0.240151	+	0.970736i	$0.577197\pi$
$504$	0	0
$505$	3.98017	0.177115
$506$	−9.80927	−0.436075
$507$	11.4865	0.510134
$508$	20.2619	0.898978
$509$	−0.216071	−0.00957717	−0.00478858	−	0.999989i	$-0.501524\pi$
$509$	−0.216071	−0.00957717	−0.00478858	+	0.999989i	$0.501524\pi$
$510$	−3.59819	−0.159331
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.08861	0.136366
$514$	15.2302	0.671777
$515$	−7.85838	−0.346282
$516$	11.4227	0.502857
$517$	65.9996	2.90266
$518$	0	0
$519$	6.23713	0.273780
$520$	4.42662	0.194120
$521$	11.2793	0.494157	0.247079	−	0.968995i	$-0.420529\pi$
$521$	11.2793	0.494157	0.247079	+	0.968995i	$0.420529\pi$
$522$	−3.91704	−0.171444
$523$	−23.7742	−1.03957	−0.519786	−	0.854296i	$-0.673988\pi$
$523$	−23.7742	−1.03957	−0.519786	+	0.854296i	$0.673988\pi$
$524$	−2.98084	−0.130219
$525$	0	0
$526$	21.4475	0.935157
$527$	−5.08861	−0.221663
$528$	−5.85838	−0.254953
$529$	−20.1964	−0.878104
$530$	19.1242	0.830703
$531$	−4.84597	−0.210297
$532$	0	0
$533$	−0.886574	−0.0384018
$534$	−8.24939	−0.356986
$535$	−53.0227	−2.29237
$536$	0.661993	0.0285938
$537$	−8.09427	−0.349293
$538$	3.80927	0.164229
$539$	0	0
$540$	3.59819	0.154842
$541$	−13.6157	−0.585386	−0.292693	−	0.956206i	$-0.594551\pi$
$541$	−13.6157	−0.585386	−0.292693	+	0.956206i	$0.594551\pi$
$542$	−24.7292	−1.06221
$543$	−13.7320	−0.589297
$544$	−1.00000	−0.0428746
$545$	43.9684	1.88340
$546$	0	0
$547$	10.1349	0.433336	0.216668	−	0.976245i	$-0.430481\pi$
$547$	10.1349	0.433336	0.216668	+	0.976245i	$0.430481\pi$
$548$	17.4814	0.746768
$549$	10.5452	0.450058
$550$	46.5565	1.98518
$551$	12.0982	0.515402
$552$	1.67440	0.0712672
$553$	0	0
$554$	−6.44292	−0.273734
$555$	−1.59819	−0.0678395
$556$	−9.82329	−0.416600
$557$	9.11975	0.386416	0.193208	−	0.981158i	$-0.438111\pi$
$557$	9.11975	0.386416	0.193208	+	0.981158i	$0.438111\pi$
$558$	5.08861	0.215418
$559$	14.0526	0.594363
$560$	0	0
$561$	5.85838	0.247341
$562$	−9.96491	−0.420344
$563$	39.6015	1.66900	0.834502	−	0.551005i	$-0.185755\pi$
$563$	39.6015	1.66900	0.834502	+	0.551005i	$0.185755\pi$
$564$	−11.2658	−0.474377
$565$	11.5599	0.486328
$566$	20.5592	0.864168
$567$	0	0
$568$	4.95375	0.207855
$569$	16.7121	0.700609	0.350305	−	0.936636i	$-0.386078\pi$
$569$	16.7121	0.700609	0.350305	+	0.936636i	$0.386078\pi$
$570$	−11.1134	−0.465490
$571$	33.3986	1.39769	0.698845	−	0.715274i	$-0.253698\pi$
$571$	33.3986	1.39769	0.698845	+	0.715274i	$0.253698\pi$
$572$	−7.20718	−0.301347
$573$	−2.44968	−0.102337
$574$	0	0
$575$	−13.3064	−0.554917
$576$	1.00000	0.0416667
$577$	18.5198	0.770991	0.385496	−	0.922710i	$-0.374030\pi$
$577$	18.5198	0.770991	0.385496	+	0.922710i	$0.374030\pi$
$578$	1.00000	0.0415945
$579$	−21.0808	−0.876089
$580$	14.0943	0.585233
$581$	0	0
$582$	−4.61735	−0.191395
$583$	−31.1370	−1.28956
$584$	13.2550	0.548498
$585$	4.42662	0.183018
$586$	25.2061	1.04126
$587$	−24.7044	−1.01966	−0.509829	−	0.860276i	$-0.670291\pi$
$587$	−24.7044	−1.01966	−0.509829	+	0.860276i	$0.670291\pi$
$588$	0	0
$589$	−15.7168	−0.647598
$590$	17.4367	0.717859
$591$	−11.3641	−0.467455
$592$	−0.444165	−0.0182551
$593$	38.2948	1.57258	0.786290	−	0.617857i	$-0.211999\pi$
$593$	38.2948	1.57258	0.786290	+	0.617857i	$0.211999\pi$
$594$	−5.85838	−0.240372
$595$	0	0
$596$	11.8679	0.486129
$597$	−20.4023	−0.835011
$598$	2.05990	0.0842357
$599$	5.92908	0.242255	0.121128	−	0.992637i	$-0.461349\pi$
$599$	5.92908	0.242255	0.121128	+	0.992637i	$0.461349\pi$
$600$	−7.94699	−0.324435
$601$	26.7089	1.08948	0.544739	−	0.838605i	$-0.316629\pi$
$601$	26.7089	1.08948	0.544739	+	0.838605i	$0.316629\pi$
$602$	0	0
$603$	0.661993	0.0269584
$604$	−21.3889	−0.870301
$605$	−83.9120	−3.41151
$606$	1.10616	0.0449346
$607$	−26.6994	−1.08369	−0.541847	−	0.840477i	$-0.682275\pi$
$607$	−26.6994	−1.08369	−0.541847	+	0.840477i	$0.682275\pi$
$608$	−3.08861	−0.125260
$609$	0	0
$610$	−37.9436	−1.53629
$611$	−13.8596	−0.560700
$612$	−1.00000	−0.0404226
$613$	16.2747	0.657330	0.328665	−	0.944447i	$-0.393401\pi$
$613$	16.2747	0.657330	0.328665	+	0.944447i	$0.393401\pi$
$614$	−25.2460	−1.01885
$615$	2.59305	0.104562
$616$	0	0
$617$	−9.05248	−0.364439	−0.182220	−	0.983258i	$-0.558328\pi$
$617$	−9.05248	−0.364439	−0.182220	+	0.983258i	$0.558328\pi$
$618$	−2.18398	−0.0878525
$619$	−15.2646	−0.613536	−0.306768	−	0.951784i	$-0.599248\pi$
$619$	−15.2646	−0.613536	−0.306768	+	0.951784i	$0.599248\pi$
$620$	−18.3098	−0.735340
$621$	1.67440	0.0671913
$622$	18.6868	0.749273
$623$	0	0
$624$	1.23023	0.0492488
$625$	−1.58028	−0.0632110
$626$	−27.4583	−1.09746
$627$	18.0943	0.722615
$628$	17.5260	0.699365
$629$	0.444165	0.0177100
$630$	0	0
$631$	−42.5502	−1.69390	−0.846948	−	0.531676i	$-0.821562\pi$
$631$	−42.5502	−1.69390	−0.846948	+	0.531676i	$0.821562\pi$
$632$	−13.2320	−0.526340
$633$	−11.1884	−0.444699
$634$	30.8996	1.22718
$635$	−72.9064	−2.89320
$636$	5.31495	0.210752
$637$	0	0
$638$	−22.9475	−0.908500
$639$	4.95375	0.195967
$640$	−3.59819	−0.142231
$641$	−12.5041	−0.493881	−0.246941	−	0.969031i	$-0.579425\pi$
$641$	−12.5041	−0.493881	−0.246941	+	0.969031i	$0.579425\pi$
$642$	−14.7359	−0.581580
$643$	−9.32450	−0.367722	−0.183861	−	0.982952i	$-0.558860\pi$
$643$	−9.32450	−0.367722	−0.183861	+	0.982952i	$0.558860\pi$
$644$	0	0
$645$	−41.1012	−1.61836
$646$	3.08861	0.121520
$647$	−25.1463	−0.988604	−0.494302	−	0.869290i	$-0.664576\pi$
$647$	−25.1463	−0.988604	−0.494302	+	0.869290i	$0.664576\pi$
$648$	1.00000	0.0392837
$649$	−28.3895	−1.11439
$650$	−9.77666	−0.383472
$651$	0	0
$652$	13.0463	0.510931
$653$	−11.1117	−0.434833	−0.217417	−	0.976079i	$-0.569763\pi$
$653$	−11.1117	−0.434833	−0.217417	+	0.976079i	$0.569763\pi$
$654$	12.2196	0.477824
$655$	10.7256	0.419085
$656$	0.720655	0.0281368
$657$	13.2550	0.517129
$658$	0	0
$659$	36.4449	1.41969	0.709846	−	0.704357i	$-0.248765\pi$
$659$	36.4449	1.41969	0.709846	+	0.704357i	$0.248765\pi$
$660$	21.0796	0.820521
$661$	−7.49873	−0.291667	−0.145833	−	0.989309i	$-0.546586\pi$
$661$	−7.49873	−0.291667	−0.145833	+	0.989309i	$0.546586\pi$
$662$	−5.95089	−0.231288
$663$	−1.23023	−0.0477783
$664$	2.89508	0.112351
$665$	0	0
$666$	−0.444165	−0.0172111
$667$	6.55869	0.253954
$668$	−0.534393	−0.0206763
$669$	23.1653	0.895624
$670$	−2.38198	−0.0920239
$671$	61.7777	2.38490
$672$	0	0
$673$	43.2230	1.66612	0.833061	−	0.553181i	$-0.186586\pi$
$673$	43.2230	1.66612	0.833061	+	0.553181i	$0.186586\pi$
$674$	5.61854	0.216418
$675$	−7.94699	−0.305880
$676$	−11.4865	−0.441789
$677$	−44.2068	−1.69901	−0.849503	−	0.527584i	$-0.823098\pi$
$677$	−44.2068	−1.69901	−0.849503	+	0.527584i	$0.823098\pi$
$678$	3.21269	0.123383
$679$	0	0
$680$	3.59819	0.137984
$681$	−20.9706	−0.803594
$682$	29.8110	1.14152
$683$	28.7958	1.10184	0.550921	−	0.834558i	$-0.314277\pi$
$683$	28.7958	1.10184	0.550921	+	0.834558i	$0.314277\pi$
$684$	−3.08861	−0.118096
$685$	−62.9014	−2.40334
$686$	0	0
$687$	0.494317	0.0188594
$688$	−11.4227	−0.435487
$689$	6.53863	0.249102
$690$	−6.02481	−0.229361
$691$	−31.5897	−1.20173	−0.600864	−	0.799351i	$-0.705177\pi$
$691$	−31.5897	−1.20173	−0.600864	+	0.799351i	$0.705177\pi$
$692$	−6.23713	−0.237100
$693$	0	0
$694$	25.7907	0.979001
$695$	35.3461	1.34075
$696$	3.91704	0.148475
$697$	−0.720655	−0.0272967
$698$	−28.1299	−1.06473
$699$	−28.9543	−1.09515
$700$	0	0
$701$	−15.7258	−0.593955	−0.296978	−	0.954884i	$-0.595979\pi$
$701$	−15.7258	−0.593955	−0.296978	+	0.954884i	$0.595979\pi$
$702$	1.23023	0.0464322
$703$	1.37186	0.0517405
$704$	5.85838	0.220796
$705$	40.5367	1.52670
$706$	8.35321	0.314377
$707$	0	0
$708$	4.84597	0.182123
$709$	−0.656197	−0.0246440	−0.0123220	−	0.999924i	$-0.503922\pi$
$709$	−0.656197	−0.0246440	−0.0123220	+	0.999924i	$0.503922\pi$
$710$	−17.8245	−0.668943
$711$	−13.2320	−0.496238
$712$	8.24939	0.309159
$713$	−8.52037	−0.319090
$714$	0	0
$715$	25.9328	0.969832
$716$	8.09427	0.302497
$717$	−0.792822	−0.0296085
$718$	−15.9539	−0.595394
$719$	12.0191	0.448237	0.224118	−	0.974562i	$-0.428050\pi$
$719$	12.0191	0.448237	0.224118	+	0.974562i	$0.428050\pi$
$720$	−3.59819	−0.134097
$721$	0	0
$722$	−9.46047	−0.352082
$723$	8.79582	0.327120
$724$	13.7320	0.510347
$725$	−31.1287	−1.15609
$726$	−23.3206	−0.865509
$727$	−14.1017	−0.523005	−0.261502	−	0.965203i	$-0.584218\pi$
$727$	−14.1017	−0.523005	−0.261502	+	0.965203i	$0.584218\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−47.6942	−1.76524
$731$	11.4227	0.422485
$732$	−10.5452	−0.389761
$733$	30.9763	1.14413	0.572067	−	0.820207i	$-0.306142\pi$
$733$	30.9763	1.14413	0.572067	+	0.820207i	$0.306142\pi$
$734$	28.9706	1.06932
$735$	0	0
$736$	−1.67440	−0.0617192
$737$	3.87821	0.142856
$738$	0.720655	0.0265277
$739$	44.3715	1.63223	0.816116	−	0.577889i	$-0.196123\pi$
$739$	44.3715	1.63223	0.816116	+	0.577889i	$0.196123\pi$
$740$	1.59819	0.0587507
$741$	−3.79972	−0.139586
$742$	0	0
$743$	−11.5929	−0.425303	−0.212651	−	0.977128i	$-0.568210\pi$
$743$	−11.5929	−0.425303	−0.212651	+	0.977128i	$0.568210\pi$
$744$	−5.08861	−0.186558
$745$	−42.7031	−1.56452
$746$	−12.8763	−0.471435
$747$	2.89508	0.105926
$748$	−5.85838	−0.214204
$749$	0	0
$750$	10.6038	0.387198
$751$	8.18045	0.298509	0.149255	−	0.988799i	$-0.452313\pi$
$751$	8.18045	0.298509	0.149255	+	0.988799i	$0.452313\pi$
$752$	11.2658	0.410823
$753$	−6.89508	−0.251271
$754$	4.81888	0.175493
$755$	76.9613	2.80091
$756$	0	0
$757$	−37.8549	−1.37586	−0.687931	−	0.725777i	$-0.741481\pi$
$757$	−37.8549	−1.37586	−0.687931	+	0.725777i	$0.741481\pi$
$758$	19.6737	0.714580
$759$	9.80927	0.356054
$760$	11.1134	0.403126
$761$	30.3454	1.10002	0.550010	−	0.835158i	$-0.314624\pi$
$761$	30.3454	1.10002	0.550010	+	0.835158i	$0.314624\pi$
$762$	−20.2619	−0.734013
$763$	0	0
$764$	2.44968	0.0886262
$765$	3.59819	0.130093
$766$	−12.4870	−0.451175
$767$	5.96168	0.215264
$768$	−1.00000	−0.0360844
$769$	−18.5893	−0.670347	−0.335174	−	0.942156i	$-0.608795\pi$
$769$	−18.5893	−0.670347	−0.335174	+	0.942156i	$0.608795\pi$
$770$	0	0
$771$	−15.2302	−0.548503
$772$	21.0808	0.758715
$773$	10.2118	0.367293	0.183646	−	0.982992i	$-0.441210\pi$
$773$	10.2118	0.367293	0.183646	+	0.982992i	$0.441210\pi$
$774$	−11.4227	−0.410581
$775$	40.4392	1.45262
$776$	4.61735	0.165753
$777$	0	0
$778$	−10.6129	−0.380490
$779$	−2.22582	−0.0797484
$780$	−4.42662	−0.158498
$781$	29.0209	1.03845
$782$	1.67440	0.0598764
$783$	3.91704	0.139984
$784$	0	0
$785$	−63.0620	−2.25078
$786$	2.98084	0.106323
$787$	−28.8371	−1.02793	−0.513967	−	0.857810i	$-0.671824\pi$
$787$	−28.8371	−1.02793	−0.513967	+	0.857810i	$0.671824\pi$
$788$	11.3641	0.404828
$789$	−21.4475	−0.763553
$790$	47.6113	1.69393
$791$	0	0
$792$	5.85838	0.208168
$793$	−12.9730	−0.460686
$794$	−31.3984	−1.11429
$795$	−19.1242	−0.678266
$796$	20.4023	0.723141
$797$	−42.0594	−1.48982	−0.744910	−	0.667165i	$-0.767508\pi$
$797$	−42.0594	−1.48982	−0.744910	+	0.667165i	$0.767508\pi$
$798$	0	0
$799$	−11.2658	−0.398557
$800$	7.94699	0.280969
$801$	8.24939	0.291478
$802$	9.29616	0.328259
$803$	77.6531	2.74032
$804$	−0.661993	−0.0233467
$805$	0	0
$806$	−6.26019	−0.220506
$807$	−3.80927	−0.134093
$808$	−1.10616	−0.0389145
$809$	−30.6914	−1.07905	−0.539525	−	0.841969i	$-0.681396\pi$
$809$	−30.6914	−1.07905	−0.539525	+	0.841969i	$0.681396\pi$
$810$	−3.59819	−0.126428
$811$	52.7094	1.85088	0.925439	−	0.378897i	$-0.123696\pi$
$811$	52.7094	1.85088	0.925439	+	0.378897i	$0.123696\pi$
$812$	0	0
$813$	24.7292	0.867290
$814$	−2.60209	−0.0912032
$815$	−46.9429	−1.64434
$816$	1.00000	0.0350070
$817$	35.2804	1.23430
$818$	−20.5124	−0.717198
$819$	0	0
$820$	−2.59305	−0.0905534
$821$	−39.5310	−1.37964	−0.689821	−	0.723980i	$-0.742311\pi$
$821$	−39.5310	−1.37964	−0.689821	+	0.723980i	$0.742311\pi$
$822$	−17.4814	−0.609733
$823$	−0.716184	−0.0249646	−0.0124823	−	0.999922i	$-0.503973\pi$
$823$	−0.716184	−0.0249646	−0.0124823	+	0.999922i	$0.503973\pi$
$824$	2.18398	0.0760825
$825$	−46.5565	−1.62089
$826$	0	0
$827$	18.1937	0.632658	0.316329	−	0.948650i	$-0.397550\pi$
$827$	18.1937	0.632658	0.316329	+	0.948650i	$0.397550\pi$
$828$	−1.67440	−0.0581894
$829$	−22.6365	−0.786196	−0.393098	−	0.919496i	$-0.628597\pi$
$829$	−22.6365	−0.786196	−0.393098	+	0.919496i	$0.628597\pi$
$830$	−10.4171	−0.361582
$831$	6.44292	0.223503
$832$	−1.23023	−0.0426507
$833$	0	0
$834$	9.82329	0.340153
$835$	1.92285	0.0665429
$836$	−18.0943	−0.625803
$837$	−5.08861	−0.175888
$838$	−25.5909	−0.884023
$839$	39.8293	1.37506	0.687530	−	0.726156i	$-0.258695\pi$
$839$	39.8293	1.37506	0.687530	+	0.726156i	$0.258695\pi$
$840$	0	0
$841$	−13.6568	−0.470924
$842$	−10.6665	−0.367591
$843$	9.96491	0.343210
$844$	11.1884	0.385120
$845$	41.3307	1.42182
$846$	11.2658	0.387328
$847$	0	0
$848$	−5.31495	−0.182516
$849$	−20.5592	−0.705590
$850$	−7.94699	−0.272580
$851$	0.743710	0.0254941
$852$	−4.95375	−0.169713
$853$	−38.0897	−1.30417	−0.652083	−	0.758147i	$-0.726105\pi$
$853$	−38.0897	−1.30417	−0.652083	+	0.758147i	$0.726105\pi$
$854$	0	0
$855$	11.1134	0.380071
$856$	14.7359	0.503663
$857$	14.6186	0.499362	0.249681	−	0.968328i	$-0.419674\pi$
$857$	14.6186	0.499362	0.249681	+	0.968328i	$0.419674\pi$
$858$	7.20718	0.246049
$859$	43.9797	1.50057	0.750285	−	0.661115i	$-0.229917\pi$
$859$	43.9797	1.50057	0.750285	+	0.661115i	$0.229917\pi$
$860$	41.1012	1.40154
$861$	0	0
$862$	−37.0115	−1.26061
$863$	30.0852	1.02411	0.512057	−	0.858952i	$-0.328884\pi$
$863$	30.0852	1.02411	0.512057	+	0.858952i	$0.328884\pi$
$864$	−1.00000	−0.0340207
$865$	22.4424	0.763064
$866$	2.48756	0.0845309
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−77.5180	−2.62962
$870$	−14.0943	−0.477840
$871$	−0.814407	−0.0275951
$872$	−12.2196	−0.413807
$873$	4.61735	0.156274
$874$	5.17157	0.174931
$875$	0	0
$876$	−13.2550	−0.447847
$877$	40.1269	1.35499	0.677494	−	0.735528i	$-0.263066\pi$
$877$	40.1269	1.35499	0.677494	+	0.735528i	$0.263066\pi$
$878$	−6.26019	−0.211271
$879$	−25.2061	−0.850182
$880$	−21.0796	−0.710592
$881$	44.2436	1.49060	0.745302	−	0.666727i	$-0.232305\pi$
$881$	44.2436	1.49060	0.745302	+	0.666727i	$0.232305\pi$
$882$	0	0
$883$	44.9786	1.51365	0.756826	−	0.653617i	$-0.226749\pi$
$883$	44.9786	1.51365	0.756826	+	0.653617i	$0.226749\pi$
$884$	1.23023	0.0413773
$885$	−17.4367	−0.586130
$886$	−34.4487	−1.15733
$887$	34.2682	1.15061	0.575306	−	0.817938i	$-0.304883\pi$
$887$	34.2682	1.15061	0.575306	+	0.817938i	$0.304883\pi$
$888$	0.444165	0.0149052
$889$	0	0
$890$	−29.6829	−0.994973
$891$	5.85838	0.196263
$892$	−23.1653	−0.775633
$893$	−34.7958	−1.16440
$894$	−11.8679	−0.396923
$895$	−29.1247	−0.973532
$896$	0	0
$897$	−2.05990	−0.0687782
$898$	23.3821	0.780272
$899$	−19.9323	−0.664780
$900$	7.94699	0.264900
$901$	5.31495	0.177067
$902$	4.22187	0.140573
$903$	0	0
$904$	−3.21269	−0.106852
$905$	−49.4105	−1.64246
$906$	21.3889	0.710598
$907$	−5.86305	−0.194679	−0.0973397	−	0.995251i	$-0.531033\pi$
$907$	−5.86305	−0.194679	−0.0973397	+	0.995251i	$0.531033\pi$
$908$	20.9706	0.695933
$909$	−1.10616	−0.0366890
$910$	0	0
$911$	−9.17105	−0.303850	−0.151925	−	0.988392i	$-0.548547\pi$
$911$	−9.17105	−0.303850	−0.151925	+	0.988392i	$0.548547\pi$
$912$	3.08861	0.102274
$913$	16.9605	0.561311
$914$	−30.6152	−1.01266
$915$	37.9436	1.25438
$916$	−0.494317	−0.0163327
$917$	0	0
$918$	1.00000	0.0330049
$919$	11.0081	0.363125	0.181562	−	0.983379i	$-0.441885\pi$
$919$	11.0081	0.363125	0.181562	+	0.983379i	$0.441885\pi$
$920$	6.02481	0.198632
$921$	25.2460	0.831884
$922$	−32.0211	−1.05456
$923$	−6.09427	−0.200595
$924$	0	0
$925$	−3.52978	−0.116058
$926$	25.3959	0.834562
$927$	2.18398	0.0717313
$928$	−3.91704	−0.128583
$929$	34.7831	1.14120	0.570598	−	0.821230i	$-0.306712\pi$
$929$	34.7831	1.14120	0.570598	+	0.821230i	$0.306712\pi$
$930$	18.3098	0.600402
$931$	0	0
$932$	28.9543	0.948428
$933$	−18.6868	−0.611779
$934$	−29.8336	−0.976184
$935$	21.0796	0.689376
$936$	−1.23023	−0.0402115
$937$	19.3154	0.631006	0.315503	−	0.948925i	$-0.397827\pi$
$937$	19.3154	0.631006	0.315503	+	0.948925i	$0.397827\pi$
$938$	0	0
$939$	27.4583	0.896069
$940$	−40.5367	−1.32216
$941$	0.658037	0.0214514	0.0107257	−	0.999942i	$-0.496586\pi$
$941$	0.658037	0.0214514	0.0107257	+	0.999942i	$0.496586\pi$
$942$	−17.5260	−0.571029
$943$	−1.20666	−0.0392944
$944$	−4.84597	−0.157723
$945$	0	0
$946$	−66.9186	−2.17571
$947$	9.06556	0.294591	0.147296	−	0.989093i	$-0.452943\pi$
$947$	9.06556	0.294591	0.147296	+	0.989093i	$0.452943\pi$
$948$	13.2320	0.429755
$949$	−16.3068	−0.529342
$950$	−24.5452	−0.796351
$951$	−30.8996	−1.00199
$952$	0	0
$953$	39.4711	1.27859	0.639297	−	0.768960i	$-0.279225\pi$
$953$	39.4711	1.27859	0.639297	+	0.768960i	$0.279225\pi$
$954$	−5.31495	−0.172078
$955$	−8.81441	−0.285228
$956$	0.792822	0.0256417
$957$	22.9475	0.741788
$958$	−3.18237	−0.102818
$959$	0	0
$960$	3.59819	0.116131
$961$	−5.10602	−0.164710
$962$	0.546428	0.0176175
$963$	14.7359	0.474858
$964$	−8.79582	−0.283294
$965$	−75.8529	−2.44179
$966$	0	0
$967$	33.4080	1.07433	0.537164	−	0.843478i	$-0.319496\pi$
$967$	33.4080	1.07433	0.537164	+	0.843478i	$0.319496\pi$
$968$	23.3206	0.749553
$969$	−3.08861	−0.0992206
$970$	−16.6141	−0.533447
$971$	22.5271	0.722930	0.361465	−	0.932386i	$-0.382277\pi$
$971$	22.5271	0.722930	0.361465	+	0.932386i	$0.382277\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	34.8888	1.11791
$975$	9.77666	0.313104
$976$	10.5452	0.337543
$977$	−55.1463	−1.76429	−0.882144	−	0.470981i	$-0.843900\pi$
$977$	−55.1463	−1.76429	−0.882144	+	0.470981i	$0.843900\pi$
$978$	−13.0463	−0.417173
$979$	48.3281	1.54457
$980$	0	0
$981$	−12.2196	−0.390141
$982$	12.6146	0.402549
$983$	23.3162	0.743671	0.371836	−	0.928299i	$-0.378729\pi$
$983$	23.3162	0.743671	0.371836	+	0.928299i	$0.378729\pi$
$984$	−0.720655	−0.0229736
$985$	−40.8901	−1.30287
$986$	3.91704	0.124744
$987$	0	0
$988$	3.79972	0.120885
$989$	19.1262	0.608178
$990$	−21.0796	−0.669953
$991$	19.3110	0.613434	0.306717	−	0.951801i	$-0.400769\pi$
$991$	19.3110	0.613434	0.306717	+	0.951801i	$0.400769\pi$
$992$	5.08861	0.161564
$993$	5.95089	0.188846
$994$	0	0
$995$	−73.4115	−2.32730
$996$	−2.89508	−0.0917342
$997$	15.1272	0.479084	0.239542	−	0.970886i	$-0.423003\pi$
$997$	15.1272	0.479084	0.239542	+	0.970886i	$0.423003\pi$
$998$	−3.74137	−0.118431
$999$	0.444165	0.0140528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.co.1.1	✓	4
7.6	odd	2		4998.2.a.cp.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4998.2.a.co.1.1	✓	4	1.1	even	1	trivial
4998.2.a.cp.1.4	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4998.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.59819 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.59819 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.59819 q^{10} +5.85838 q^{11} -1.00000 q^{12} -1.23023 q^{13} +3.59819 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.08861 q^{19} -3.59819 q^{20} +5.85838 q^{22} -1.67440 q^{23} -1.00000 q^{24} +7.94699 q^{25} -1.23023 q^{26} -1.00000 q^{27} -3.91704 q^{29} +3.59819 q^{30} +5.08861 q^{31} +1.00000 q^{32} -5.85838 q^{33} -1.00000 q^{34} +1.00000 q^{36} -0.444165 q^{37} -3.08861 q^{38} +1.23023 q^{39} -3.59819 q^{40} +0.720655 q^{41} -11.4227 q^{43} +5.85838 q^{44} -3.59819 q^{45} -1.67440 q^{46} +11.2658 q^{47} -1.00000 q^{48} +7.94699 q^{50} +1.00000 q^{51} -1.23023 q^{52} -5.31495 q^{53} -1.00000 q^{54} -21.0796 q^{55} +3.08861 q^{57} -3.91704 q^{58} -4.84597 q^{59} +3.59819 q^{60} +10.5452 q^{61} +5.08861 q^{62} +1.00000 q^{64} +4.42662 q^{65} -5.85838 q^{66} +0.661993 q^{67} -1.00000 q^{68} +1.67440 q^{69} +4.95375 q^{71} +1.00000 q^{72} +13.2550 q^{73} -0.444165 q^{74} -7.94699 q^{75} -3.08861 q^{76} +1.23023 q^{78} -13.2320 q^{79} -3.59819 q^{80} +1.00000 q^{81} +0.720655 q^{82} +2.89508 q^{83} +3.59819 q^{85} -11.4227 q^{86} +3.91704 q^{87} +5.85838 q^{88} +8.24939 q^{89} -3.59819 q^{90} -1.67440 q^{92} -5.08861 q^{93} +11.2658 q^{94} +11.1134 q^{95} -1.00000 q^{96} +4.61735 q^{97} +5.85838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 10 q^{11} - 4 q^{12} - 6 q^{13} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 2 q^{20} + 10 q^{22} - 4 q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} + 8 q^{29} + 2 q^{30} + 8 q^{31} + 4 q^{32} - 10 q^{33} - 4 q^{34} + 4 q^{36} + 6 q^{37} + 6 q^{39} - 2 q^{40} + 4 q^{41} + 6 q^{43} + 10 q^{44} - 2 q^{45} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 4 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} - 10 q^{55} + 8 q^{58} - 24 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} - 10 q^{66} + 14 q^{67} - 4 q^{68} + 12 q^{71} + 4 q^{72} + 18 q^{73} + 6 q^{74} - 6 q^{75} + 6 q^{78} + 10 q^{79} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 14 q^{83} + 2 q^{85} + 6 q^{86} - 8 q^{87} + 10 q^{88} + 34 q^{89} - 2 q^{90} - 8 q^{93} + 8 q^{94} - 4 q^{95} - 4 q^{96} + 6 q^{97} + 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 10 * q^11 - 4 * q^12 - 6 * q^13 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 2 * q^20 + 10 * q^22 - 4 * q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 + 8 * q^29 + 2 * q^30 + 8 * q^31 + 4 * q^32 - 10 * q^33 - 4 * q^34 + 4 * q^36 + 6 * q^37 + 6 * q^39 - 2 * q^40 + 4 * q^41 + 6 * q^43 + 10 * q^44 - 2 * q^45 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 4 * q^51 - 6 * q^52 + 18 * q^53 - 4 * q^54 - 10 * q^55 + 8 * q^58 - 24 * q^59 + 2 * q^60 + 4 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 - 10 * q^66 + 14 * q^67 - 4 * q^68 + 12 * q^71 + 4 * q^72 + 18 * q^73 + 6 * q^74 - 6 * q^75 + 6 * q^78 + 10 * q^79 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 14 * q^83 + 2 * q^85 + 6 * q^86 - 8 * q^87 + 10 * q^88 + 34 * q^89 - 2 * q^90 - 8 * q^93 + 8 * q^94 - 4 * q^95 - 4 * q^96 + 6 * q^97 + 10 * q^99

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