LMFDB - Embedded newform 4998.2.a.co.1.4

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			1.4
Root			$-1.87996$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.29417 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.29417 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.29417 q^{10} +4.19292 q^{11} -1.00000 q^{12} -2.46575 q^{13} -3.29417 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.65867 q^{19} +3.29417 q^{20} +4.19292 q^{22} -4.07288 q^{23} -1.00000 q^{24} +5.85158 q^{25} -2.46575 q^{26} -1.00000 q^{27} +2.16976 q^{29} -3.29417 q^{30} +4.65867 q^{31} +1.00000 q^{32} -4.19292 q^{33} -1.00000 q^{34} +1.00000 q^{36} -1.60713 q^{37} -2.65867 q^{38} +2.46575 q^{39} +3.29417 q^{40} +8.41859 q^{41} +12.1554 q^{43} +4.19292 q^{44} +3.29417 q^{45} -4.07288 q^{46} +9.97600 q^{47} -1.00000 q^{48} +5.85158 q^{50} +1.00000 q^{51} -2.46575 q^{52} +4.90834 q^{53} -1.00000 q^{54} +13.8122 q^{55} +2.65867 q^{57} +2.16976 q^{58} -12.9013 q^{59} -3.29417 q^{60} +1.55741 q^{61} +4.65867 q^{62} +1.00000 q^{64} -8.12260 q^{65} -4.19292 q^{66} +12.7813 q^{67} -1.00000 q^{68} +4.07288 q^{69} -0.345708 q^{71} +1.00000 q^{72} -4.95103 q^{73} -1.60713 q^{74} -5.85158 q^{75} -2.65867 q^{76} +2.46575 q^{78} +3.07810 q^{79} +3.29417 q^{80} +1.00000 q^{81} +8.41859 q^{82} +2.01697 q^{83} -3.29417 q^{85} +12.1554 q^{86} -2.16976 q^{87} +4.19292 q^{88} -3.43993 q^{89} +3.29417 q^{90} -4.07288 q^{92} -4.65867 q^{93} +9.97600 q^{94} -8.75811 q^{95} -1.00000 q^{96} -15.1999 q^{97} +4.19292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.29417	1.47320	0.736600	−	0.676329i	$-0.236430\pi$
$5$	3.29417	1.47320	0.736600	+	0.676329i	$0.236430\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.29417	1.04171
$11$	4.19292	1.26421	0.632106	−	0.774882i	$-0.282191\pi$
$11$	4.19292	1.26421	0.632106	+	0.774882i	$0.282191\pi$
$12$	−1.00000	−0.288675
$13$	−2.46575	−0.683875	−0.341938	−	0.939723i	$-0.611083\pi$
$13$	−2.46575	−0.683875	−0.341938	+	0.939723i	$0.611083\pi$
$14$	0	0
$15$	−3.29417	−0.850552
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−2.65867	−0.609940	−0.304970	−	0.952362i	$-0.598646\pi$
$19$	−2.65867	−0.609940	−0.304970	+	0.952362i	$0.598646\pi$
$20$	3.29417	0.736600
$21$	0	0
$22$	4.19292	0.893933
$23$	−4.07288	−0.849254	−0.424627	−	0.905368i	$-0.639595\pi$
$23$	−4.07288	−0.849254	−0.424627	+	0.905368i	$0.639595\pi$
$24$	−1.00000	−0.204124
$25$	5.85158	1.17032
$26$	−2.46575	−0.483573
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.16976	0.402915	0.201457	−	0.979497i	$-0.435432\pi$
$29$	2.16976	0.402915	0.201457	+	0.979497i	$0.435432\pi$
$30$	−3.29417	−0.601431
$31$	4.65867	0.836721	0.418361	−	0.908281i	$-0.362605\pi$
$31$	4.65867	0.836721	0.418361	+	0.908281i	$0.362605\pi$
$32$	1.00000	0.176777
$33$	−4.19292	−0.729893
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.60713	−0.264211	−0.132105	−	0.991236i	$-0.542174\pi$
$37$	−1.60713	−0.264211	−0.132105	+	0.991236i	$0.542174\pi$
$38$	−2.65867	−0.431293
$39$	2.46575	0.394836
$40$	3.29417	0.520855
$41$	8.41859	1.31476	0.657381	−	0.753558i	$-0.271664\pi$
$41$	8.41859	1.31476	0.657381	+	0.753558i	$0.271664\pi$
$42$	0	0
$43$	12.1554	1.85367	0.926837	−	0.375464i	$-0.122517\pi$
$43$	12.1554	1.85367	0.926837	+	0.375464i	$0.122517\pi$
$44$	4.19292	0.632106
$45$	3.29417	0.491067
$46$	−4.07288	−0.600513
$47$	9.97600	1.45515	0.727574	−	0.686029i	$-0.240648\pi$
$47$	9.97600	1.45515	0.727574	+	0.686029i	$0.240648\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	5.85158	0.827539
$51$	1.00000	0.140028
$52$	−2.46575	−0.341938
$53$	4.90834	0.674212	0.337106	−	0.941467i	$-0.390552\pi$
$53$	4.90834	0.674212	0.337106	+	0.941467i	$0.390552\pi$
$54$	−1.00000	−0.136083
$55$	13.8122	1.86244
$56$	0	0
$57$	2.65867	0.352149
$58$	2.16976	0.284904
$59$	−12.9013	−1.67961	−0.839804	−	0.542890i	$-0.817330\pi$
$59$	−12.9013	−1.67961	−0.839804	+	0.542890i	$0.817330\pi$
$60$	−3.29417	−0.425276
$61$	1.55741	0.199406	0.0997030	−	0.995017i	$-0.468211\pi$
$61$	1.55741	0.199406	0.0997030	+	0.995017i	$0.468211\pi$
$62$	4.65867	0.591651
$63$	0	0
$64$	1.00000	0.125000
$65$	−8.12260	−1.00748
$66$	−4.19292	−0.516113
$67$	12.7813	1.56148	0.780740	−	0.624856i	$-0.214842\pi$
$67$	12.7813	1.56148	0.780740	+	0.624856i	$0.214842\pi$
$68$	−1.00000	−0.121268
$69$	4.07288	0.490317
$70$	0	0
$71$	−0.345708	−0.0410280	−0.0205140	−	0.999790i	$-0.506530\pi$
$71$	−0.345708	−0.0410280	−0.0205140	+	0.999790i	$0.506530\pi$
$72$	1.00000	0.117851
$73$	−4.95103	−0.579474	−0.289737	−	0.957106i	$-0.593568\pi$
$73$	−4.95103	−0.579474	−0.289737	+	0.957106i	$0.593568\pi$
$74$	−1.60713	−0.186825
$75$	−5.85158	−0.675683
$76$	−2.65867	−0.304970
$77$	0	0
$78$	2.46575	0.279191
$79$	3.07810	0.346313	0.173157	−	0.984894i	$-0.444603\pi$
$79$	3.07810	0.346313	0.173157	+	0.984894i	$0.444603\pi$
$80$	3.29417	0.368300
$81$	1.00000	0.111111
$82$	8.41859	0.929677
$83$	2.01697	0.221391	0.110696	−	0.993854i	$-0.464692\pi$
$83$	2.01697	0.221391	0.110696	+	0.993854i	$0.464692\pi$
$84$	0	0
$85$	−3.29417	−0.357303
$86$	12.1554	1.31075
$87$	−2.16976	−0.232623
$88$	4.19292	0.446967
$89$	−3.43993	−0.364632	−0.182316	−	0.983240i	$-0.558359\pi$
$89$	−3.43993	−0.364632	−0.182316	+	0.983240i	$0.558359\pi$
$90$	3.29417	0.347236
$91$	0	0
$92$	−4.07288	−0.424627
$93$	−4.65867	−0.483081
$94$	9.97600	1.02895
$95$	−8.75811	−0.898563
$96$	−1.00000	−0.102062
$97$	−15.1999	−1.54331	−0.771656	−	0.636040i	$-0.780571\pi$
$97$	−15.1999	−1.54331	−0.771656	+	0.636040i	$0.780571\pi$
$98$	0	0
$99$	4.19292	0.421404
$100$	5.85158	0.585158
$101$	−14.3884	−1.43170	−0.715850	−	0.698254i	$-0.753960\pi$
$101$	−14.3884	−1.43170	−0.715850	+	0.698254i	$0.753960\pi$
$102$	1.00000	0.0990148
$103$	−1.87996	−0.185238	−0.0926190	−	0.995702i	$-0.529524\pi$
$103$	−1.87996	−0.185238	−0.0926190	+	0.995702i	$0.529524\pi$
$104$	−2.46575	−0.241786
$105$	0	0
$106$	4.90834	0.476740
$107$	−1.51984	−0.146929	−0.0734644	−	0.997298i	$-0.523406\pi$
$107$	−1.51984	−0.146929	−0.0734644	+	0.997298i	$0.523406\pi$
$108$	−1.00000	−0.0962250
$109$	−5.63029	−0.539284	−0.269642	−	0.962961i	$-0.586905\pi$
$109$	−5.63029	−0.539284	−0.269642	+	0.962961i	$0.586905\pi$
$110$	13.8122	1.31694
$111$	1.60713	0.152542
$112$	0	0
$113$	9.26399	0.871483	0.435741	−	0.900072i	$-0.356486\pi$
$113$	9.26399	0.871483	0.435741	+	0.900072i	$0.356486\pi$
$114$	2.65867	0.249007
$115$	−13.4168	−1.25112
$116$	2.16976	0.201457
$117$	−2.46575	−0.227958
$118$	−12.9013	−1.18766
$119$	0	0
$120$	−3.29417	−0.300716
$121$	6.58057	0.598233
$122$	1.55741	0.141001
$123$	−8.41859	−0.759078
$124$	4.65867	0.418361
$125$	2.80527	0.250911
$126$	0	0
$127$	7.94325	0.704849	0.352425	−	0.935840i	$-0.385357\pi$
$127$	7.94325	0.704849	0.352425	+	0.935840i	$0.385357\pi$
$128$	1.00000	0.0883883
$129$	−12.1554	−1.07022
$130$	−8.12260	−0.712399
$131$	−15.9057	−1.38969	−0.694843	−	0.719162i	$-0.744526\pi$
$131$	−15.9057	−1.38969	−0.694843	+	0.719162i	$0.744526\pi$
$132$	−4.19292	−0.364947
$133$	0	0
$134$	12.7813	1.10413
$135$	−3.29417	−0.283517
$136$	−1.00000	−0.0857493
$137$	−10.5180	−0.898616	−0.449308	−	0.893377i	$-0.648329\pi$
$137$	−10.5180	−0.898616	−0.449308	+	0.893377i	$0.648329\pi$
$138$	4.07288	0.346707
$139$	19.2665	1.63417	0.817084	−	0.576519i	$-0.195589\pi$
$139$	19.2665	1.63417	0.817084	+	0.576519i	$0.195589\pi$
$140$	0	0
$141$	−9.97600	−0.840131
$142$	−0.345708	−0.0290112
$143$	−10.3387	−0.864564
$144$	1.00000	0.0833333
$145$	7.14757	0.593573
$146$	−4.95103	−0.409750
$147$	0	0
$148$	−1.60713	−0.132105
$149$	14.7146	1.20546	0.602732	−	0.797943i	$-0.294079\pi$
$149$	14.7146	1.20546	0.602732	+	0.797943i	$0.294079\pi$
$150$	−5.85158	−0.477780
$151$	17.2094	1.40048	0.700242	−	0.713905i	$-0.253075\pi$
$151$	17.2094	1.40048	0.700242	+	0.713905i	$0.253075\pi$
$152$	−2.65867	−0.215646
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	15.3465	1.23266
$156$	2.46575	0.197418
$157$	21.4631	1.71294	0.856471	−	0.516196i	$-0.172652\pi$
$157$	21.4631	1.71294	0.856471	+	0.516196i	$0.172652\pi$
$158$	3.07810	0.244880
$159$	−4.90834	−0.389256
$160$	3.29417	0.260427
$161$	0	0
$162$	1.00000	0.0785674
$163$	18.3457	1.43695	0.718473	−	0.695554i	$-0.244841\pi$
$163$	18.3457	1.43695	0.718473	+	0.695554i	$0.244841\pi$
$164$	8.41859	0.657381
$165$	−13.8122	−1.07528
$166$	2.01697	0.156547
$167$	25.3696	1.96316	0.981580	−	0.191052i	$-0.0611899\pi$
$167$	25.3696	1.96316	0.981580	+	0.191052i	$0.0611899\pi$
$168$	0	0
$169$	−6.92009	−0.532315
$170$	−3.29417	−0.252652
$171$	−2.65867	−0.203313
$172$	12.1554	0.926837
$173$	−13.3600	−1.01574	−0.507872	−	0.861433i	$-0.669568\pi$
$173$	−13.3600	−1.01574	−0.507872	+	0.861433i	$0.669568\pi$
$174$	−2.16976	−0.164489
$175$	0	0
$176$	4.19292	0.316053
$177$	12.9013	0.969722
$178$	−3.43993	−0.257834
$179$	1.14757	0.0857735	0.0428867	−	0.999080i	$-0.486345\pi$
$179$	1.14757	0.0857735	0.0428867	+	0.999080i	$0.486345\pi$
$180$	3.29417	0.245533
$181$	−13.5526	−1.00736	−0.503678	−	0.863891i	$-0.668020\pi$
$181$	−13.5526	−1.00736	−0.503678	+	0.863891i	$0.668020\pi$
$182$	0	0
$183$	−1.55741	−0.115127
$184$	−4.07288	−0.300257
$185$	−5.29417	−0.389235
$186$	−4.65867	−0.341590
$187$	−4.19292	−0.306617
$188$	9.97600	0.727574
$189$	0	0
$190$	−8.75811	−0.635380
$191$	−11.9955	−0.867966	−0.433983	−	0.900921i	$-0.642892\pi$
$191$	−11.9955	−0.867966	−0.433983	+	0.900921i	$0.642892\pi$
$192$	−1.00000	−0.0721688
$193$	−1.40683	−0.101266	−0.0506331	−	0.998717i	$-0.516124\pi$
$193$	−1.40683	−0.101266	−0.0506331	+	0.998717i	$0.516124\pi$
$194$	−15.1999	−1.09129
$195$	8.12260	0.581672
$196$	0	0
$197$	−7.79267	−0.555205	−0.277602	−	0.960696i	$-0.589540\pi$
$197$	−7.79267	−0.555205	−0.277602	+	0.960696i	$0.589540\pi$
$198$	4.19292	0.297978
$199$	−2.65504	−0.188211	−0.0941055	−	0.995562i	$-0.529999\pi$
$199$	−2.65504	−0.188211	−0.0941055	+	0.995562i	$0.529999\pi$
$200$	5.85158	0.413770
$201$	−12.7813	−0.901521
$202$	−14.3884	−1.01236
$203$	0	0
$204$	1.00000	0.0700140
$205$	27.7323	1.93691
$206$	−1.87996	−0.130983
$207$	−4.07288	−0.283085
$208$	−2.46575	−0.170969
$209$	−11.1476	−0.771094
$210$	0	0
$211$	−11.7964	−0.812100	−0.406050	−	0.913851i	$-0.633094\pi$
$211$	−11.7964	−0.812100	−0.406050	+	0.913851i	$0.633094\pi$
$212$	4.90834	0.337106
$213$	0.345708	0.0236875
$214$	−1.51984	−0.103894
$215$	40.0418	2.73083
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−5.63029	−0.381331
$219$	4.95103	0.334560
$220$	13.8122	0.931219
$221$	2.46575	0.165864
$222$	1.60713	0.107864
$223$	−2.07650	−0.139053	−0.0695265	−	0.997580i	$-0.522149\pi$
$223$	−2.07650	−0.139053	−0.0695265	+	0.997580i	$0.522149\pi$
$224$	0	0
$225$	5.85158	0.390106
$226$	9.26399	0.616231
$227$	−12.9706	−0.860886	−0.430443	−	0.902618i	$-0.641643\pi$
$227$	−12.9706	−0.860886	−0.430443	+	0.902618i	$0.641643\pi$
$228$	2.65867	0.176074
$229$	−17.9856	−1.18852	−0.594261	−	0.804273i	$-0.702555\pi$
$229$	−17.9856	−1.18852	−0.594261	+	0.804273i	$0.702555\pi$
$230$	−13.4168	−0.884676
$231$	0	0
$232$	2.16976	0.142452
$233$	−6.29492	−0.412394	−0.206197	−	0.978510i	$-0.566109\pi$
$233$	−6.29492	−0.412394	−0.206197	+	0.978510i	$0.566109\pi$
$234$	−2.46575	−0.161191
$235$	32.8627	2.14372
$236$	−12.9013	−0.839804
$237$	−3.07810	−0.199944
$238$	0	0
$239$	−2.33868	−0.151277	−0.0756383	−	0.997135i	$-0.524099\pi$
$239$	−2.33868	−0.151277	−0.0756383	+	0.997135i	$0.524099\pi$
$240$	−3.29417	−0.212638
$241$	−0.522849	−0.0336796	−0.0168398	−	0.999858i	$-0.505361\pi$
$241$	−0.522849	−0.0336796	−0.0168398	+	0.999858i	$0.505361\pi$
$242$	6.58057	0.423015
$243$	−1.00000	−0.0641500
$244$	1.55741	0.0997030
$245$	0	0
$246$	−8.41859	−0.536750
$247$	6.55560	0.417123
$248$	4.65867	0.295826
$249$	−2.01697	−0.127820
$250$	2.80527	0.177421
$251$	6.01697	0.379788	0.189894	−	0.981805i	$-0.439186\pi$
$251$	6.01697	0.379788	0.189894	+	0.981805i	$0.439186\pi$
$252$	0	0
$253$	−17.0773	−1.07364
$254$	7.94325	0.498404
$255$	3.29417	0.206289
$256$	1.00000	0.0625000
$257$	16.4657	1.02711	0.513553	−	0.858058i	$-0.328329\pi$
$257$	16.4657	1.02711	0.513553	+	0.858058i	$0.328329\pi$
$258$	−12.1554	−0.756759
$259$	0	0
$260$	−8.12260	−0.503742
$261$	2.16976	0.134305
$262$	−15.9057	−0.982656
$263$	−21.5721	−1.33019	−0.665097	−	0.746757i	$-0.731610\pi$
$263$	−21.5721	−1.33019	−0.665097	+	0.746757i	$0.731610\pi$
$264$	−4.19292	−0.258056
$265$	16.1689	0.993249
$266$	0	0
$267$	3.43993	0.210521
$268$	12.7813	0.780740
$269$	11.0773	0.675392	0.337696	−	0.941255i	$-0.390352\pi$
$269$	11.0773	0.675392	0.337696	+	0.941255i	$0.390352\pi$
$270$	−3.29417	−0.200477
$271$	−11.6774	−0.709355	−0.354677	−	0.934989i	$-0.615409\pi$
$271$	−11.6774	−0.709355	−0.354677	+	0.934989i	$0.615409\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−10.5180	−0.635418
$275$	24.5352	1.47953
$276$	4.07288	0.245159
$277$	4.79824	0.288298	0.144149	−	0.989556i	$-0.453955\pi$
$277$	4.79824	0.288298	0.144149	+	0.989556i	$0.453955\pi$
$278$	19.2665	1.15553
$279$	4.65867	0.278907
$280$	0	0
$281$	17.4595	1.04154	0.520772	−	0.853696i	$-0.325644\pi$
$281$	17.4595	1.04154	0.520772	+	0.853696i	$0.325644\pi$
$282$	−9.97600	−0.594062
$283$	−24.7864	−1.47340	−0.736699	−	0.676221i	$-0.763617\pi$
$283$	−24.7864	−1.47340	−0.736699	+	0.676221i	$0.763617\pi$
$284$	−0.345708	−0.0205140
$285$	8.75811	0.518786
$286$	−10.3387	−0.611339
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	7.14757	0.419720
$291$	15.1999	0.891031
$292$	−4.95103	−0.289737
$293$	3.07588	0.179695	0.0898476	−	0.995956i	$-0.471362\pi$
$293$	3.07588	0.179695	0.0898476	+	0.995956i	$0.471362\pi$
$294$	0	0
$295$	−42.4992	−2.47440
$296$	−1.60713	−0.0934127
$297$	−4.19292	−0.243298
$298$	14.7146	0.852392
$299$	10.0427	0.580784
$300$	−5.85158	−0.337841
$301$	0	0
$302$	17.2094	0.990292
$303$	14.3884	0.826592
$304$	−2.65867	−0.152485
$305$	5.13038	0.293765
$306$	−1.00000	−0.0571662
$307$	27.4219	1.56505	0.782525	−	0.622619i	$-0.213931\pi$
$307$	27.4219	1.56505	0.782525	+	0.622619i	$0.213931\pi$
$308$	0	0
$309$	1.87996	0.106947
$310$	15.3465	0.871620
$311$	11.3645	0.644421	0.322211	−	0.946668i	$-0.395574\pi$
$311$	11.3645	0.644421	0.322211	+	0.946668i	$0.395574\pi$
$312$	2.46575	0.139595
$313$	−1.35490	−0.0765834	−0.0382917	−	0.999267i	$-0.512192\pi$
$313$	−1.35490	−0.0765834	−0.0382917	+	0.999267i	$0.512192\pi$
$314$	21.4631	1.21123
$315$	0	0
$316$	3.07810	0.173157
$317$	20.1921	1.13410	0.567050	−	0.823683i	$-0.308085\pi$
$317$	20.1921	1.13410	0.567050	+	0.823683i	$0.308085\pi$
$318$	−4.90834	−0.275246
$319$	9.09763	0.509370
$320$	3.29417	0.184150
$321$	1.51984	0.0848294
$322$	0	0
$323$	2.65867	0.147932
$324$	1.00000	0.0555556
$325$	−14.4285	−0.800351
$326$	18.3457	1.01607
$327$	5.63029	0.311356
$328$	8.41859	0.464839
$329$	0	0
$330$	−13.8122	−0.760337
$331$	−14.8843	−0.818117	−0.409059	−	0.912508i	$-0.634143\pi$
$331$	−14.8843	−0.818117	−0.409059	+	0.912508i	$0.634143\pi$
$332$	2.01697	0.110696
$333$	−1.60713	−0.0880703
$334$	25.3696	1.38816
$335$	42.1037	2.30037
$336$	0	0
$337$	20.1545	1.09789	0.548943	−	0.835860i	$-0.315030\pi$
$337$	20.1545	1.09789	0.548943	+	0.835860i	$0.315030\pi$
$338$	−6.92009	−0.376403
$339$	−9.26399	−0.503151
$340$	−3.29417	−0.178652
$341$	19.5334	1.05779
$342$	−2.65867	−0.143764
$343$	0	0
$344$	12.1554	0.655373
$345$	13.4168	0.722335
$346$	−13.3600	−0.718239
$347$	−5.91527	−0.317549	−0.158774	−	0.987315i	$-0.550754\pi$
$347$	−5.91527	−0.317549	−0.158774	+	0.987315i	$0.550754\pi$
$348$	−2.16976	−0.116311
$349$	−18.6578	−0.998730	−0.499365	−	0.866392i	$-0.666433\pi$
$349$	−18.6578	−0.998730	−0.499365	+	0.866392i	$0.666433\pi$
$350$	0	0
$351$	2.46575	0.131612
$352$	4.19292	0.223483
$353$	−5.77071	−0.307144	−0.153572	−	0.988137i	$-0.549078\pi$
$353$	−5.77071	−0.307144	−0.153572	+	0.988137i	$0.549078\pi$
$354$	12.9013	0.685697
$355$	−1.13882	−0.0604424
$356$	−3.43993	−0.182316
$357$	0	0
$358$	1.14757	0.0606510
$359$	−19.7459	−1.04215	−0.521073	−	0.853512i	$-0.674468\pi$
$359$	−19.7459	−1.04215	−0.521073	+	0.853512i	$0.674468\pi$
$360$	3.29417	0.173618
$361$	−11.9315	−0.627973
$362$	−13.5526	−0.712308
$363$	−6.58057	−0.345390
$364$	0	0
$365$	−16.3096	−0.853681
$366$	−1.55741	−0.0814072
$367$	−4.97056	−0.259461	−0.129731	−	0.991549i	$-0.541411\pi$
$367$	−4.97056	−0.259461	−0.129731	+	0.991549i	$0.541411\pi$
$368$	−4.07288	−0.212314
$369$	8.41859	0.438254
$370$	−5.29417	−0.275231
$371$	0	0
$372$	−4.65867	−0.241541
$373$	14.1181	0.731009	0.365505	−	0.930810i	$-0.380896\pi$
$373$	14.1181	0.731009	0.365505	+	0.930810i	$0.380896\pi$
$374$	−4.19292	−0.216811
$375$	−2.80527	−0.144863
$376$	9.97600	0.514473
$377$	−5.35008	−0.275543
$378$	0	0
$379$	−20.2817	−1.04180	−0.520901	−	0.853617i	$-0.674404\pi$
$379$	−20.2817	−1.04180	−0.520901	+	0.853617i	$0.674404\pi$
$380$	−8.75811	−0.449282
$381$	−7.94325	−0.406945
$382$	−11.9955	−0.613745
$383$	22.0291	1.12564	0.562818	−	0.826581i	$-0.309717\pi$
$383$	22.0291	1.12564	0.562818	+	0.826581i	$0.309717\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−1.40683	−0.0716060
$387$	12.1554	0.617891
$388$	−15.1999	−0.771656
$389$	−31.6656	−1.60551	−0.802755	−	0.596309i	$-0.796633\pi$
$389$	−31.6656	−1.60551	−0.802755	+	0.596309i	$0.796633\pi$
$390$	8.12260	0.411304
$391$	4.07288	0.205974
$392$	0	0
$393$	15.9057	0.802335
$394$	−7.79267	−0.392589
$395$	10.1398	0.510188
$396$	4.19292	0.210702
$397$	2.68779	0.134896	0.0674482	−	0.997723i	$-0.478514\pi$
$397$	2.68779	0.134896	0.0674482	+	0.997723i	$0.478514\pi$
$398$	−2.65504	−0.133085
$399$	0	0
$400$	5.85158	0.292579
$401$	−27.0434	−1.35049	−0.675243	−	0.737596i	$-0.735961\pi$
$401$	−27.0434	−1.35049	−0.675243	+	0.737596i	$0.735961\pi$
$402$	−12.7813	−0.637472
$403$	−11.4871	−0.572213
$404$	−14.3884	−0.715850
$405$	3.29417	0.163689
$406$	0	0
$407$	−6.73858	−0.334019
$408$	1.00000	0.0495074
$409$	−21.7661	−1.07626	−0.538132	−	0.842860i	$-0.680870\pi$
$409$	−21.7661	−1.07626	−0.538132	+	0.842860i	$0.680870\pi$
$410$	27.7323	1.36960
$411$	10.5180	0.518816
$412$	−1.87996	−0.0926190
$413$	0	0
$414$	−4.07288	−0.200171
$415$	6.64426	0.326154
$416$	−2.46575	−0.120893
$417$	−19.2665	−0.943487
$418$	−11.1476	−0.545246
$419$	33.3089	1.62725	0.813623	−	0.581393i	$-0.197492\pi$
$419$	33.3089	1.62725	0.813623	+	0.581393i	$0.197492\pi$
$420$	0	0
$421$	18.0842	0.881370	0.440685	−	0.897662i	$-0.354736\pi$
$421$	18.0842	0.881370	0.440685	+	0.897662i	$0.354736\pi$
$422$	−11.7964	−0.574241
$423$	9.97600	0.485050
$424$	4.90834	0.238370
$425$	−5.85158	−0.283844
$426$	0.345708	0.0167496
$427$	0	0
$428$	−1.51984	−0.0734644
$429$	10.3387	0.499156
$430$	40.0418	1.93099
$431$	−33.0694	−1.59290	−0.796448	−	0.604707i	$-0.793290\pi$
$431$	−33.0694	−1.59290	−0.796448	+	0.604707i	$0.793290\pi$
$432$	−1.00000	−0.0481125
$433$	23.1829	1.11410	0.557049	−	0.830480i	$-0.311933\pi$
$433$	23.1829	1.11410	0.557049	+	0.830480i	$0.311933\pi$
$434$	0	0
$435$	−7.14757	−0.342700
$436$	−5.63029	−0.269642
$437$	10.8284	0.517994
$438$	4.95103	0.236569
$439$	−11.4871	−0.548249	−0.274125	−	0.961694i	$-0.588388\pi$
$439$	−11.4871	−0.548249	−0.274125	+	0.961694i	$0.588388\pi$
$440$	13.8122	0.658471
$441$	0	0
$442$	2.46575	0.117284
$443$	−25.7822	−1.22495	−0.612475	−	0.790490i	$-0.709826\pi$
$443$	−25.7822	−1.22495	−0.612475	+	0.790490i	$0.709826\pi$
$444$	1.60713	0.0762711
$445$	−11.3317	−0.537176
$446$	−2.07650	−0.0983253
$447$	−14.7146	−0.695975
$448$	0	0
$449$	−12.0122	−0.566889	−0.283444	−	0.958989i	$-0.591477\pi$
$449$	−12.0122	−0.566889	−0.283444	+	0.958989i	$0.591477\pi$
$450$	5.85158	0.275846
$451$	35.2985	1.66214
$452$	9.26399	0.435741
$453$	−17.2094	−0.808570
$454$	−12.9706	−0.608739
$455$	0	0
$456$	2.65867	0.124503
$457$	−4.17254	−0.195183	−0.0975916	−	0.995227i	$-0.531114\pi$
$457$	−4.17254	−0.195183	−0.0975916	+	0.995227i	$0.531114\pi$
$458$	−17.9856	−0.840411
$459$	1.00000	0.0466760
$460$	−13.4168	−0.625560
$461$	−10.6420	−0.495649	−0.247825	−	0.968805i	$-0.579716\pi$
$461$	−10.6420	−0.495649	−0.247825	+	0.968805i	$0.579716\pi$
$462$	0	0
$463$	−33.4985	−1.55681	−0.778404	−	0.627763i	$-0.783971\pi$
$463$	−33.4985	−1.55681	−0.778404	+	0.627763i	$0.783971\pi$
$464$	2.16976	0.100729
$465$	−15.3465	−0.711675
$466$	−6.29492	−0.291607
$467$	37.5515	1.73768	0.868839	−	0.495095i	$-0.164867\pi$
$467$	37.5515	1.73768	0.868839	+	0.495095i	$0.164867\pi$
$468$	−2.46575	−0.113979
$469$	0	0
$470$	32.8627	1.51584
$471$	−21.4631	−0.988967
$472$	−12.9013	−0.593831
$473$	50.9664	2.34344
$474$	−3.07810	−0.141382
$475$	−15.5574	−0.713823
$476$	0	0
$477$	4.90834	0.224737
$478$	−2.33868	−0.106969
$479$	−25.7555	−1.17680	−0.588398	−	0.808571i	$-0.700241\pi$
$479$	−25.7555	−1.17680	−0.588398	+	0.808571i	$0.700241\pi$
$480$	−3.29417	−0.150358
$481$	3.96278	0.180687
$482$	−0.522849	−0.0238151
$483$	0	0
$484$	6.58057	0.299117
$485$	−50.0710	−2.27361
$486$	−1.00000	−0.0453609
$487$	7.26505	0.329211	0.164605	−	0.986360i	$-0.447365\pi$
$487$	7.26505	0.329211	0.164605	+	0.986360i	$0.447365\pi$
$488$	1.55741	0.0705007
$489$	−18.3457	−0.829622
$490$	0	0
$491$	16.1218	0.727565	0.363782	−	0.931484i	$-0.381485\pi$
$491$	16.1218	0.727565	0.363782	+	0.931484i	$0.381485\pi$
$492$	−8.41859	−0.379539
$493$	−2.16976	−0.0977211
$494$	6.55560	0.294950
$495$	13.8122	0.620812
$496$	4.65867	0.209180
$497$	0	0
$498$	−2.01697	−0.0903827
$499$	6.17352	0.276365	0.138182	−	0.990407i	$-0.455874\pi$
$499$	6.17352	0.276365	0.138182	+	0.990407i	$0.455874\pi$
$500$	2.80527	0.125455
$501$	−25.3696	−1.13343
$502$	6.01697	0.268551
$503$	37.9588	1.69250	0.846250	−	0.532786i	$-0.178855\pi$
$503$	37.9588	1.69250	0.846250	+	0.532786i	$0.178855\pi$
$504$	0	0
$505$	−47.3979	−2.10918
$506$	−17.0773	−0.759177
$507$	6.92009	0.307332
$508$	7.94325	0.352425
$509$	−28.7180	−1.27290	−0.636451	−	0.771317i	$-0.719598\pi$
$509$	−28.7180	−1.27290	−0.636451	+	0.771317i	$0.719598\pi$
$510$	3.29417	0.145868
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.65867	0.117383
$514$	16.4657	0.726273
$515$	−6.19292	−0.272893
$516$	−12.1554	−0.535110
$517$	41.8286	1.83962
$518$	0	0
$519$	13.3600	0.586440
$520$	−8.12260	−0.356200
$521$	3.58141	0.156905	0.0784523	−	0.996918i	$-0.475002\pi$
$521$	3.58141	0.156905	0.0784523	+	0.996918i	$0.475002\pi$
$522$	2.16976	0.0949679
$523$	−3.61779	−0.158195	−0.0790974	−	0.996867i	$-0.525204\pi$
$523$	−3.61779	−0.158195	−0.0790974	+	0.996867i	$0.525204\pi$
$524$	−15.9057	−0.694843
$525$	0	0
$526$	−21.5721	−0.940589
$527$	−4.65867	−0.202935
$528$	−4.19292	−0.182473
$529$	−6.41165	−0.278767
$530$	16.1689	0.702333
$531$	−12.9013	−0.559869
$532$	0	0
$533$	−20.7581	−0.899134
$534$	3.43993	0.148860
$535$	−5.00663	−0.216455
$536$	12.7813	0.552067
$537$	−1.14757	−0.0495214
$538$	11.0773	0.477574
$539$	0	0
$540$	−3.29417	−0.141759
$541$	−20.4356	−0.878593	−0.439297	−	0.898342i	$-0.644772\pi$
$541$	−20.4356	−0.878593	−0.439297	+	0.898342i	$0.644772\pi$
$542$	−11.6774	−0.501589
$543$	13.5526	0.581597
$544$	−1.00000	−0.0428746
$545$	−18.5472	−0.794473
$546$	0	0
$547$	15.0044	0.641541	0.320770	−	0.947157i	$-0.396058\pi$
$547$	15.0044	0.641541	0.320770	+	0.947157i	$0.396058\pi$
$548$	−10.5180	−0.449308
$549$	1.55741	0.0664687
$550$	24.5352	1.04619
$551$	−5.76867	−0.245754
$552$	4.07288	0.173353
$553$	0	0
$554$	4.79824	0.203858
$555$	5.29417	0.224725
$556$	19.2665	0.817084
$557$	47.0344	1.99291	0.996455	−	0.0841249i	$-0.0268095\pi$
$557$	47.0344	1.99291	0.996455	+	0.0841249i	$0.0268095\pi$
$558$	4.65867	0.197217
$559$	−29.9720	−1.26768
$560$	0	0
$561$	4.19292	0.177025
$562$	17.4595	0.736483
$563$	10.4756	0.441492	0.220746	−	0.975331i	$-0.429151\pi$
$563$	10.4756	0.441492	0.220746	+	0.975331i	$0.429151\pi$
$564$	−9.97600	−0.420065
$565$	30.5172	1.28387
$566$	−24.7864	−1.04185
$567$	0	0
$568$	−0.345708	−0.0145056
$569$	−40.0015	−1.67695	−0.838475	−	0.544940i	$-0.816552\pi$
$569$	−40.0015	−1.67695	−0.838475	+	0.544940i	$0.816552\pi$
$570$	8.75811	0.366837
$571$	−13.5452	−0.566850	−0.283425	−	0.958994i	$-0.591471\pi$
$571$	−13.5452	−0.566850	−0.283425	+	0.958994i	$0.591471\pi$
$572$	−10.3387	−0.432282
$573$	11.9955	0.501121
$574$	0	0
$575$	−23.8328	−0.993897
$576$	1.00000	0.0416667
$577$	−26.2378	−1.09229	−0.546147	−	0.837689i	$-0.683906\pi$
$577$	−26.2378	−1.09229	−0.546147	+	0.837689i	$0.683906\pi$
$578$	1.00000	0.0415945
$579$	1.40683	0.0584660
$580$	7.14757	0.296787
$581$	0	0
$582$	15.1999	0.630054
$583$	20.5803	0.852347
$584$	−4.95103	−0.204875
$585$	−8.12260	−0.335828
$586$	3.07588	0.127064
$587$	−31.0942	−1.28340	−0.641698	−	0.766957i	$-0.721770\pi$
$587$	−31.0942	−1.28340	−0.641698	+	0.766957i	$0.721770\pi$
$588$	0	0
$589$	−12.3858	−0.510350
$590$	−42.4992	−1.74966
$591$	7.79267	0.320548
$592$	−1.60713	−0.0660527
$593$	46.7751	1.92082	0.960412	−	0.278584i	$-0.0898651\pi$
$593$	46.7751	1.92082	0.960412	+	0.278584i	$0.0898651\pi$
$594$	−4.19292	−0.172038
$595$	0	0
$596$	14.7146	0.602732
$597$	2.65504	0.108664
$598$	10.0427	0.410676
$599$	29.1626	1.19155	0.595777	−	0.803150i	$-0.296844\pi$
$599$	29.1626	1.19155	0.595777	+	0.803150i	$0.296844\pi$
$600$	−5.85158	−0.238890
$601$	23.2693	0.949176	0.474588	−	0.880208i	$-0.342597\pi$
$601$	23.2693	0.949176	0.474588	+	0.880208i	$0.342597\pi$
$602$	0	0
$603$	12.7813	0.520493
$604$	17.2094	0.700242
$605$	21.6775	0.881317
$606$	14.3884	0.584489
$607$	−18.7477	−0.760945	−0.380472	−	0.924792i	$-0.624239\pi$
$607$	−18.7477	−0.760945	−0.380472	+	0.924792i	$0.624239\pi$
$608$	−2.65867	−0.107823
$609$	0	0
$610$	5.13038	0.207723
$611$	−24.5983	−0.995140
$612$	−1.00000	−0.0404226
$613$	−44.8059	−1.80969	−0.904847	−	0.425737i	$-0.860015\pi$
$613$	−44.8059	−1.80969	−0.904847	+	0.425737i	$0.860015\pi$
$614$	27.4219	1.10666
$615$	−27.7323	−1.11827
$616$	0	0
$617$	44.0636	1.77393	0.886967	−	0.461833i	$-0.152808\pi$
$617$	44.0636	1.77393	0.886967	+	0.461833i	$0.152808\pi$
$618$	1.87996	0.0756231
$619$	−1.57063	−0.0631288	−0.0315644	−	0.999502i	$-0.510049\pi$
$619$	−1.57063	−0.0631288	−0.0315644	+	0.999502i	$0.510049\pi$
$620$	15.3465	0.616329
$621$	4.07288	0.163439
$622$	11.3645	0.455675
$623$	0	0
$624$	2.46575	0.0987089
$625$	−20.0169	−0.800675
$626$	−1.35490	−0.0541527
$627$	11.1476	0.445191
$628$	21.4631	0.856471
$629$	1.60713	0.0640806
$630$	0	0
$631$	37.2573	1.48319	0.741594	−	0.670849i	$-0.234070\pi$
$631$	37.2573	1.48319	0.741594	+	0.670849i	$0.234070\pi$
$632$	3.07810	0.122440
$633$	11.7964	0.468866
$634$	20.1921	0.801930
$635$	26.1664	1.03838
$636$	−4.90834	−0.194628
$637$	0	0
$638$	9.09763	0.360179
$639$	−0.345708	−0.0136760
$640$	3.29417	0.130214
$641$	−21.6498	−0.855117	−0.427558	−	0.903988i	$-0.640626\pi$
$641$	−21.6498	−0.855117	−0.427558	+	0.903988i	$0.640626\pi$
$642$	1.51984	0.0599834
$643$	−3.61332	−0.142495	−0.0712477	−	0.997459i	$-0.522698\pi$
$643$	−3.61332	−0.142495	−0.0712477	+	0.997459i	$0.522698\pi$
$644$	0	0
$645$	−40.0418	−1.57665
$646$	2.65867	0.104604
$647$	−26.0738	−1.02507	−0.512533	−	0.858668i	$-0.671293\pi$
$647$	−26.0738	−1.02507	−0.512533	+	0.858668i	$0.671293\pi$
$648$	1.00000	0.0392837
$649$	−54.0941	−2.12338
$650$	−14.4285	−0.565933
$651$	0	0
$652$	18.3457	0.718473
$653$	−8.78574	−0.343812	−0.171906	−	0.985113i	$-0.554993\pi$
$653$	−8.78574	−0.343812	−0.171906	+	0.985113i	$0.554993\pi$
$654$	5.63029	0.220162
$655$	−52.3961	−2.04728
$656$	8.41859	0.328691
$657$	−4.95103	−0.193158
$658$	0	0
$659$	−5.19951	−0.202544	−0.101272	−	0.994859i	$-0.532291\pi$
$659$	−5.19951	−0.202544	−0.101272	+	0.994859i	$0.532291\pi$
$660$	−13.8122	−0.537639
$661$	−6.06912	−0.236062	−0.118031	−	0.993010i	$-0.537658\pi$
$661$	−6.06912	−0.236062	−0.118031	+	0.993010i	$0.537658\pi$
$662$	−14.8843	−0.578496
$663$	−2.46575	−0.0957617
$664$	2.01697	0.0782737
$665$	0	0
$666$	−1.60713	−0.0622751
$667$	−8.83718	−0.342177
$668$	25.3696	0.981580
$669$	2.07650	0.0802823
$670$	42.1037	1.62661
$671$	6.53010	0.252092
$672$	0	0
$673$	−7.54897	−0.290991	−0.145496	−	0.989359i	$-0.546478\pi$
$673$	−7.54897	−0.290991	−0.145496	+	0.989359i	$0.546478\pi$
$674$	20.1545	0.776323
$675$	−5.85158	−0.225228
$676$	−6.92009	−0.266157
$677$	−1.21824	−0.0468207	−0.0234103	−	0.999726i	$-0.507452\pi$
$677$	−1.21824	−0.0468207	−0.0234103	+	0.999726i	$0.507452\pi$
$678$	−9.26399	−0.355781
$679$	0	0
$680$	−3.29417	−0.126326
$681$	12.9706	0.497033
$682$	19.5334	0.747973
$683$	20.5228	0.785285	0.392642	−	0.919691i	$-0.371561\pi$
$683$	20.5228	0.785285	0.392642	+	0.919691i	$0.371561\pi$
$684$	−2.65867	−0.101657
$685$	−34.6482	−1.32384
$686$	0	0
$687$	17.9856	0.686193
$688$	12.1554	0.463418
$689$	−12.1027	−0.461077
$690$	13.4168	0.510768
$691$	39.7143	1.51080	0.755401	−	0.655263i	$-0.227442\pi$
$691$	39.7143	1.51080	0.755401	+	0.655263i	$0.227442\pi$
$692$	−13.3600	−0.507872
$693$	0	0
$694$	−5.91527	−0.224541
$695$	63.4674	2.40745
$696$	−2.16976	−0.0822446
$697$	−8.41859	−0.318877
$698$	−18.6578	−0.706209
$699$	6.29492	0.238096
$700$	0	0
$701$	−46.8567	−1.76975	−0.884877	−	0.465825i	$-0.845758\pi$
$701$	−46.8567	−1.76975	−0.884877	+	0.465825i	$0.845758\pi$
$702$	2.46575	0.0930636
$703$	4.27283	0.161153
$704$	4.19292	0.158027
$705$	−32.8627	−1.23768
$706$	−5.77071	−0.217183
$707$	0	0
$708$	12.9013	0.484861
$709$	−10.2008	−0.383099	−0.191549	−	0.981483i	$-0.561351\pi$
$709$	−10.2008	−0.383099	−0.191549	+	0.981483i	$0.561351\pi$
$710$	−1.13882	−0.0427393
$711$	3.07810	0.115438
$712$	−3.43993	−0.128917
$713$	−18.9742	−0.710589
$714$	0	0
$715$	−34.0574	−1.27367
$716$	1.14757	0.0428867
$717$	2.33868	0.0873395
$718$	−19.7459	−0.736909
$719$	21.0433	0.784783	0.392392	−	0.919798i	$-0.371648\pi$
$719$	21.0433	0.784783	0.392392	+	0.919798i	$0.371648\pi$
$720$	3.29417	0.122767
$721$	0	0
$722$	−11.9315	−0.444044
$723$	0.522849	0.0194449
$724$	−13.5526	−0.503678
$725$	12.6965	0.471538
$726$	−6.58057	−0.244228
$727$	−46.3049	−1.71735	−0.858676	−	0.512518i	$-0.828713\pi$
$727$	−46.3049	−1.71735	−0.858676	+	0.512518i	$0.828713\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−16.3096	−0.603644
$731$	−12.1554	−0.449582
$732$	−1.55741	−0.0575636
$733$	−31.4306	−1.16092	−0.580459	−	0.814290i	$-0.697127\pi$
$733$	−31.4306	−1.16092	−0.580459	+	0.814290i	$0.697127\pi$
$734$	−4.97056	−0.183467
$735$	0	0
$736$	−4.07288	−0.150128
$737$	53.5908	1.97404
$738$	8.41859	0.309892
$739$	1.15239	0.0423913	0.0211956	−	0.999775i	$-0.493253\pi$
$739$	1.15239	0.0423913	0.0211956	+	0.999775i	$0.493253\pi$
$740$	−5.29417	−0.194618
$741$	−6.55560	−0.240826
$742$	0	0
$743$	27.8239	1.02076	0.510379	−	0.859949i	$-0.329505\pi$
$743$	27.8239	1.02076	0.510379	+	0.859949i	$0.329505\pi$
$744$	−4.65867	−0.170795
$745$	48.4724	1.77589
$746$	14.1181	0.516902
$747$	2.01697	0.0737971
$748$	−4.19292	−0.153308
$749$	0	0
$750$	−2.80527	−0.102434
$751$	−45.9535	−1.67687	−0.838433	−	0.545004i	$-0.816528\pi$
$751$	−45.9535	−1.67687	−0.838433	+	0.545004i	$0.816528\pi$
$752$	9.97600	0.363787
$753$	−6.01697	−0.219271
$754$	−5.35008	−0.194839
$755$	56.6909	2.06319
$756$	0	0
$757$	−17.1599	−0.623689	−0.311844	−	0.950133i	$-0.600947\pi$
$757$	−17.1599	−0.623689	−0.311844	+	0.950133i	$0.600947\pi$
$758$	−20.2817	−0.736665
$759$	17.0773	0.619865
$760$	−8.75811	−0.317690
$761$	−5.83621	−0.211562	−0.105781	−	0.994389i	$-0.533734\pi$
$761$	−5.83621	−0.211562	−0.105781	+	0.994389i	$0.533734\pi$
$762$	−7.94325	−0.287754
$763$	0	0
$764$	−11.9955	−0.433983
$765$	−3.29417	−0.119101
$766$	22.0291	0.795945
$767$	31.8114	1.14864
$768$	−1.00000	−0.0360844
$769$	13.6735	0.493078	0.246539	−	0.969133i	$-0.420707\pi$
$769$	13.6735	0.493078	0.246539	+	0.969133i	$0.420707\pi$
$770$	0	0
$771$	−16.4657	−0.592999
$772$	−1.40683	−0.0506331
$773$	−18.4352	−0.663068	−0.331534	−	0.943443i	$-0.607566\pi$
$773$	−18.4352	−0.663068	−0.331534	+	0.943443i	$0.607566\pi$
$774$	12.1554	0.436915
$775$	27.2606	0.979229
$776$	−15.1999	−0.545643
$777$	0	0
$778$	−31.6656	−1.13527
$779$	−22.3822	−0.801926
$780$	8.12260	0.290836
$781$	−1.44953	−0.0518681
$782$	4.07288	0.145646
$783$	−2.16976	−0.0775409
$784$	0	0
$785$	70.7032	2.52350
$786$	15.9057	0.567337
$787$	10.4270	0.371682	0.185841	−	0.982580i	$-0.440499\pi$
$787$	10.4270	0.371682	0.185841	+	0.982580i	$0.440499\pi$
$788$	−7.79267	−0.277602
$789$	21.5721	0.767988
$790$	10.1398	0.360758
$791$	0	0
$792$	4.19292	0.148989
$793$	−3.84018	−0.136369
$794$	2.68779	0.0953862
$795$	−16.1689	−0.573452
$796$	−2.65504	−0.0941055
$797$	5.16932	0.183107	0.0915533	−	0.995800i	$-0.470817\pi$
$797$	5.16932	0.183107	0.0915533	+	0.995800i	$0.470817\pi$
$798$	0	0
$799$	−9.97600	−0.352925
$800$	5.85158	0.206885
$801$	−3.43993	−0.121544
$802$	−27.0434	−0.954937
$803$	−20.7593	−0.732578
$804$	−12.7813	−0.450761
$805$	0	0
$806$	−11.4871	−0.404616
$807$	−11.0773	−0.389938
$808$	−14.3884	−0.506182
$809$	−13.5396	−0.476027	−0.238013	−	0.971262i	$-0.576496\pi$
$809$	−13.5396	−0.476027	−0.238013	+	0.971262i	$0.576496\pi$
$810$	3.29417	0.115745
$811$	19.3201	0.678421	0.339210	−	0.940711i	$-0.389840\pi$
$811$	19.3201	0.678421	0.339210	+	0.940711i	$0.389840\pi$
$812$	0	0
$813$	11.6774	0.409546
$814$	−6.73858	−0.236187
$815$	60.4340	2.11691
$816$	1.00000	0.0350070
$817$	−32.3170	−1.13063
$818$	−21.7661	−0.761034
$819$	0	0
$820$	27.7323	0.968454
$821$	27.3516	0.954577	0.477288	−	0.878747i	$-0.341620\pi$
$821$	27.3516	0.954577	0.477288	+	0.878747i	$0.341620\pi$
$822$	10.5180	0.366858
$823$	−49.2840	−1.71793	−0.858967	−	0.512031i	$-0.828893\pi$
$823$	−49.2840	−1.71793	−0.858967	+	0.512031i	$0.828893\pi$
$824$	−1.87996	−0.0654915
$825$	−24.5352	−0.854207
$826$	0	0
$827$	5.78427	0.201139	0.100569	−	0.994930i	$-0.467934\pi$
$827$	5.78427	0.201139	0.100569	+	0.994930i	$0.467934\pi$
$828$	−4.07288	−0.141542
$829$	−11.8435	−0.411340	−0.205670	−	0.978621i	$-0.565937\pi$
$829$	−11.8435	−0.411340	−0.205670	+	0.978621i	$0.565937\pi$
$830$	6.64426	0.230626
$831$	−4.79824	−0.166449
$832$	−2.46575	−0.0854844
$833$	0	0
$834$	−19.2665	−0.667146
$835$	83.5719	2.89213
$836$	−11.1476	−0.385547
$837$	−4.65867	−0.161027
$838$	33.3089	1.15064
$839$	0.456505	0.0157603	0.00788014	−	0.999969i	$-0.497492\pi$
$839$	0.456505	0.0157603	0.00788014	+	0.999969i	$0.497492\pi$
$840$	0	0
$841$	−24.2921	−0.837660
$842$	18.0842	0.623222
$843$	−17.4595	−0.601336
$844$	−11.7964	−0.406050
$845$	−22.7960	−0.784206
$846$	9.97600	0.342982
$847$	0	0
$848$	4.90834	0.168553
$849$	24.7864	0.850667
$850$	−5.85158	−0.200708
$851$	6.54566	0.224382
$852$	0.345708	0.0118438
$853$	44.1888	1.51299	0.756497	−	0.653997i	$-0.226909\pi$
$853$	44.1888	1.51299	0.756497	+	0.653997i	$0.226909\pi$
$854$	0	0
$855$	−8.75811	−0.299521
$856$	−1.51984	−0.0519472
$857$	7.20552	0.246136	0.123068	−	0.992398i	$-0.460727\pi$
$857$	7.20552	0.246136	0.123068	+	0.992398i	$0.460727\pi$
$858$	10.3387	0.352957
$859$	−31.5693	−1.07713	−0.538566	−	0.842583i	$-0.681034\pi$
$859$	−31.5693	−1.07713	−0.538566	+	0.842583i	$0.681034\pi$
$860$	40.0418	1.36542
$861$	0	0
$862$	−33.0694	−1.12635
$863$	−11.3233	−0.385450	−0.192725	−	0.981253i	$-0.561732\pi$
$863$	−11.3233	−0.385450	−0.192725	+	0.981253i	$0.561732\pi$
$864$	−1.00000	−0.0340207
$865$	−44.0102	−1.49639
$866$	23.1829	0.787786
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	12.9062	0.437813
$870$	−7.14757	−0.242325
$871$	−31.5154	−1.06786
$872$	−5.63029	−0.190666
$873$	−15.1999	−0.514437
$874$	10.8284	0.366277
$875$	0	0
$876$	4.95103	0.167280
$877$	−49.3649	−1.66694	−0.833468	−	0.552568i	$-0.813648\pi$
$877$	−49.3649	−1.66694	−0.833468	+	0.552568i	$0.813648\pi$
$878$	−11.4871	−0.387671
$879$	−3.07588	−0.103747
$880$	13.8122	0.465609
$881$	−55.1816	−1.85912	−0.929558	−	0.368675i	$-0.879811\pi$
$881$	−55.1816	−1.85912	−0.929558	+	0.368675i	$0.879811\pi$
$882$	0	0
$883$	51.2781	1.72564	0.862822	−	0.505507i	$-0.168695\pi$
$883$	51.2781	1.72564	0.862822	+	0.505507i	$0.168695\pi$
$884$	2.46575	0.0829321
$885$	42.4992	1.42859
$886$	−25.7822	−0.866171
$887$	−36.4661	−1.22441	−0.612205	−	0.790699i	$-0.709717\pi$
$887$	−36.4661	−1.22441	−0.612205	+	0.790699i	$0.709717\pi$
$888$	1.60713	0.0539318
$889$	0	0
$890$	−11.3317	−0.379841
$891$	4.19292	0.140468
$892$	−2.07650	−0.0695265
$893$	−26.5228	−0.887553
$894$	−14.7146	−0.492129
$895$	3.78030	0.126361
$896$	0	0
$897$	−10.0427	−0.335316
$898$	−12.0122	−0.400851
$899$	10.1082	0.337127
$900$	5.85158	0.195053
$901$	−4.90834	−0.163520
$902$	35.2985	1.17531
$903$	0	0
$904$	9.26399	0.308116
$905$	−44.6446	−1.48404
$906$	−17.2094	−0.571746
$907$	49.5300	1.64462	0.822308	−	0.569043i	$-0.192686\pi$
$907$	49.5300	1.64462	0.822308	+	0.569043i	$0.192686\pi$
$908$	−12.9706	−0.430443
$909$	−14.3884	−0.477233
$910$	0	0
$911$	40.3836	1.33797	0.668984	−	0.743277i	$-0.266730\pi$
$911$	40.3836	1.33797	0.668984	+	0.743277i	$0.266730\pi$
$912$	2.65867	0.0880372
$913$	8.45700	0.279886
$914$	−4.17254	−0.138015
$915$	−5.13038	−0.169605
$916$	−17.9856	−0.594261
$917$	0	0
$918$	1.00000	0.0330049
$919$	29.2996	0.966506	0.483253	−	0.875481i	$-0.339455\pi$
$919$	29.2996	0.966506	0.483253	+	0.875481i	$0.339455\pi$
$920$	−13.4168	−0.442338
$921$	−27.4219	−0.903582
$922$	−10.6420	−0.350477
$923$	0.852429	0.0280580
$924$	0	0
$925$	−9.40427	−0.309211
$926$	−33.4985	−1.10083
$927$	−1.87996	−0.0617460
$928$	2.16976	0.0712259
$929$	−45.1641	−1.48179	−0.740894	−	0.671622i	$-0.765598\pi$
$929$	−45.1641	−1.48179	−0.740894	+	0.671622i	$0.765598\pi$
$930$	−15.3465	−0.503230
$931$	0	0
$932$	−6.29492	−0.206197
$933$	−11.3645	−0.372057
$934$	37.5515	1.22872
$935$	−13.8122	−0.451707
$936$	−2.46575	−0.0805955
$937$	−51.8981	−1.69544	−0.847719	−	0.530446i	$-0.822024\pi$
$937$	−51.8981	−1.69544	−0.847719	+	0.530446i	$0.822024\pi$
$938$	0	0
$939$	1.35490	0.0442155
$940$	32.8627	1.07186
$941$	23.6975	0.772517	0.386258	−	0.922391i	$-0.373767\pi$
$941$	23.6975	0.772517	0.386258	+	0.922391i	$0.373767\pi$
$942$	−21.4631	−0.699305
$943$	−34.2879	−1.11657
$944$	−12.9013	−0.419902
$945$	0	0
$946$	50.9664	1.65706
$947$	10.5316	0.342231	0.171115	−	0.985251i	$-0.445263\pi$
$947$	10.5316	0.342231	0.171115	+	0.985251i	$0.445263\pi$
$948$	−3.07810	−0.0999720
$949$	12.2080	0.396288
$950$	−15.5574	−0.504749
$951$	−20.1921	−0.654773
$952$	0	0
$953$	−35.3943	−1.14653	−0.573267	−	0.819369i	$-0.694324\pi$
$953$	−35.3943	−1.14653	−0.573267	+	0.819369i	$0.694324\pi$
$954$	4.90834	0.158913
$955$	−39.5154	−1.27869
$956$	−2.33868	−0.0756383
$957$	−9.09763	−0.294085
$958$	−25.7555	−0.832121
$959$	0	0
$960$	−3.29417	−0.106319
$961$	−9.29683	−0.299898
$962$	3.96278	0.127765
$963$	−1.51984	−0.0489763
$964$	−0.522849	−0.0168398
$965$	−4.63436	−0.149185
$966$	0	0
$967$	3.83386	0.123289	0.0616444	−	0.998098i	$-0.480366\pi$
$967$	3.83386	0.123289	0.0616444	+	0.998098i	$0.480366\pi$
$968$	6.58057	0.211507
$969$	−2.65867	−0.0854087
$970$	−50.0710	−1.60768
$971$	29.7769	0.955586	0.477793	−	0.878472i	$-0.341437\pi$
$971$	29.7769	0.955586	0.477793	+	0.878472i	$0.341437\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	7.26505	0.232787
$975$	14.4285	0.462083
$976$	1.55741	0.0498515
$977$	−56.0738	−1.79396	−0.896979	−	0.442073i	$-0.854243\pi$
$977$	−56.0738	−1.79396	−0.896979	+	0.442073i	$0.854243\pi$
$978$	−18.3457	−0.586631
$979$	−14.4234	−0.460973
$980$	0	0
$981$	−5.63029	−0.179761
$982$	16.1218	0.514466
$983$	25.4970	0.813229	0.406615	−	0.913600i	$-0.366709\pi$
$983$	25.4970	0.813229	0.406615	+	0.913600i	$0.366709\pi$
$984$	−8.41859	−0.268375
$985$	−25.6704	−0.817928
$986$	−2.16976	−0.0690993
$987$	0	0
$988$	6.55560	0.208561
$989$	−49.5073	−1.57424
$990$	13.8122	0.438981
$991$	20.0079	0.635572	0.317786	−	0.948162i	$-0.397061\pi$
$991$	20.0079	0.635572	0.317786	+	0.948162i	$0.397061\pi$
$992$	4.65867	0.147913
$993$	14.8843	0.472340
$994$	0	0
$995$	−8.74617	−0.277272
$996$	−2.01697	−0.0639102
$997$	7.03044	0.222656	0.111328	−	0.993784i	$-0.464490\pi$
$997$	7.03044	0.222656	0.111328	+	0.993784i	$0.464490\pi$
$998$	6.17352	0.195419
$999$	1.60713	0.0508474

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.29417 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.29417 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.29417 q^{10} +4.19292 q^{11} -1.00000 q^{12} -2.46575 q^{13} -3.29417 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.65867 q^{19} +3.29417 q^{20} +4.19292 q^{22} -4.07288 q^{23} -1.00000 q^{24} +5.85158 q^{25} -2.46575 q^{26} -1.00000 q^{27} +2.16976 q^{29} -3.29417 q^{30} +4.65867 q^{31} +1.00000 q^{32} -4.19292 q^{33} -1.00000 q^{34} +1.00000 q^{36} -1.60713 q^{37} -2.65867 q^{38} +2.46575 q^{39} +3.29417 q^{40} +8.41859 q^{41} +12.1554 q^{43} +4.19292 q^{44} +3.29417 q^{45} -4.07288 q^{46} +9.97600 q^{47} -1.00000 q^{48} +5.85158 q^{50} +1.00000 q^{51} -2.46575 q^{52} +4.90834 q^{53} -1.00000 q^{54} +13.8122 q^{55} +2.65867 q^{57} +2.16976 q^{58} -12.9013 q^{59} -3.29417 q^{60} +1.55741 q^{61} +4.65867 q^{62} +1.00000 q^{64} -8.12260 q^{65} -4.19292 q^{66} +12.7813 q^{67} -1.00000 q^{68} +4.07288 q^{69} -0.345708 q^{71} +1.00000 q^{72} -4.95103 q^{73} -1.60713 q^{74} -5.85158 q^{75} -2.65867 q^{76} +2.46575 q^{78} +3.07810 q^{79} +3.29417 q^{80} +1.00000 q^{81} +8.41859 q^{82} +2.01697 q^{83} -3.29417 q^{85} +12.1554 q^{86} -2.16976 q^{87} +4.19292 q^{88} -3.43993 q^{89} +3.29417 q^{90} -4.07288 q^{92} -4.65867 q^{93} +9.97600 q^{94} -8.75811 q^{95} -1.00000 q^{96} -15.1999 q^{97} +4.19292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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

Introduction

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