LMFDB - Embedded newform 4598.2.a.cb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 $ x^8 - 16x^6 - 4x^5 + 75x^4 + 32x^3 - 90x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.24609$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.79123 q^{3} +1.00000 q^{4} +4.02325 q^{5} +2.79123 q^{6} +0.274917 q^{7} +1.00000 q^{8} +4.79095 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.79123 q^{3} +1.00000 q^{4} +4.02325 q^{5} +2.79123 q^{6} +0.274917 q^{7} +1.00000 q^{8} +4.79095 q^{9} +4.02325 q^{10} +2.79123 q^{12} +0.597016 q^{13} +0.274917 q^{14} +11.2298 q^{15} +1.00000 q^{16} -2.62721 q^{17} +4.79095 q^{18} -1.00000 q^{19} +4.02325 q^{20} +0.767355 q^{21} +4.04740 q^{23} +2.79123 q^{24} +11.1866 q^{25} +0.597016 q^{26} +4.99894 q^{27} +0.274917 q^{28} -7.29532 q^{29} +11.2298 q^{30} -1.48056 q^{31} +1.00000 q^{32} -2.62721 q^{34} +1.10606 q^{35} +4.79095 q^{36} -8.31155 q^{37} -1.00000 q^{38} +1.66641 q^{39} +4.02325 q^{40} -12.3427 q^{41} +0.767355 q^{42} +5.58432 q^{43} +19.2752 q^{45} +4.04740 q^{46} -9.10733 q^{47} +2.79123 q^{48} -6.92442 q^{49} +11.1866 q^{50} -7.33314 q^{51} +0.597016 q^{52} +7.30127 q^{53} +4.99894 q^{54} +0.274917 q^{56} -2.79123 q^{57} -7.29532 q^{58} -7.53037 q^{59} +11.2298 q^{60} +4.83533 q^{61} -1.48056 q^{62} +1.31711 q^{63} +1.00000 q^{64} +2.40195 q^{65} -14.0217 q^{67} -2.62721 q^{68} +11.2972 q^{69} +1.10606 q^{70} -9.61823 q^{71} +4.79095 q^{72} -3.15625 q^{73} -8.31155 q^{74} +31.2242 q^{75} -1.00000 q^{76} +1.66641 q^{78} -2.42106 q^{79} +4.02325 q^{80} -0.419665 q^{81} -12.3427 q^{82} +15.7948 q^{83} +0.767355 q^{84} -10.5699 q^{85} +5.58432 q^{86} -20.3629 q^{87} +1.49871 q^{89} +19.2752 q^{90} +0.164130 q^{91} +4.04740 q^{92} -4.13259 q^{93} -9.10733 q^{94} -4.02325 q^{95} +2.79123 q^{96} +9.00939 q^{97} -6.92442 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9 + 8 * q^12 - 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 + 22 * q^18 - 8 * q^19 - 20 * q^21 + 14 * q^23 + 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 + 4 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^32 - 4 * q^34 + 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 + 16 * q^39 + 8 * q^41 - 20 * q^42 + 8 * q^43 + 16 * q^45 + 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 + 36 * q^50 + 18 * q^51 - 12 * q^52 + 36 * q^53 + 32 * q^54 + 4 * q^56 - 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 + 12 * q^61 + 24 * q^63 + 8 * q^64 + 16 * q^65 + 16 * q^67 - 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 + 22 * q^72 - 20 * q^73 + 24 * q^74 + 40 * q^75 - 8 * q^76 + 16 * q^78 - 12 * q^79 + 40 * q^81 + 8 * q^82 + 20 * q^83 - 20 * q^84 + 12 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 - 16 * q^94 + 8 * q^96 + 4 * q^97 + 34 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.79123	1.61152	0.805758	−	0.592245i	$-0.201758\pi$
$3$	2.79123	1.61152	0.805758	+	0.592245i	$0.201758\pi$
$4$	1.00000	0.500000
$5$	4.02325	1.79925	0.899627	−	0.436660i	$-0.143839\pi$
$5$	4.02325	1.79925	0.899627	+	0.436660i	$0.143839\pi$
$6$	2.79123	1.13951
$7$	0.274917	0.103909	0.0519544	−	0.998649i	$-0.483455\pi$
$7$	0.274917	0.103909	0.0519544	+	0.998649i	$0.483455\pi$
$8$	1.00000	0.353553
$9$	4.79095	1.59698
$10$	4.02325	1.27226
$11$	0	0
$11$	0	0
$12$	2.79123	0.805758
$13$	0.597016	0.165583	0.0827913	−	0.996567i	$-0.473617\pi$
$13$	0.597016	0.165583	0.0827913	+	0.996567i	$0.473617\pi$
$14$	0.274917	0.0734746
$15$	11.2298	2.89952
$16$	1.00000	0.250000
$17$	−2.62721	−0.637192	−0.318596	−	0.947891i	$-0.603211\pi$
$17$	−2.62721	−0.637192	−0.318596	+	0.947891i	$0.603211\pi$
$18$	4.79095	1.12924
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.02325	0.899627
$21$	0.767355	0.167451
$22$	0	0
$23$	4.04740	0.843942	0.421971	−	0.906609i	$-0.361338\pi$
$23$	4.04740	0.843942	0.421971	+	0.906609i	$0.361338\pi$
$24$	2.79123	0.569757
$25$	11.1866	2.23731
$26$	0.597016	0.117085
$27$	4.99894	0.962047
$28$	0.274917	0.0519544
$29$	−7.29532	−1.35471	−0.677354	−	0.735657i	$-0.736873\pi$
$29$	−7.29532	−1.35471	−0.677354	+	0.735657i	$0.736873\pi$
$30$	11.2298	2.05027
$31$	−1.48056	−0.265917	−0.132959	−	0.991122i	$-0.542448\pi$
$31$	−1.48056	−0.265917	−0.132959	+	0.991122i	$0.542448\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.62721	−0.450563
$35$	1.10606	0.186958
$36$	4.79095	0.798491
$37$	−8.31155	−1.36641	−0.683205	−	0.730227i	$-0.739414\pi$
$37$	−8.31155	−1.36641	−0.683205	+	0.730227i	$0.739414\pi$
$38$	−1.00000	−0.162221
$39$	1.66641	0.266839
$40$	4.02325	0.636132
$41$	−12.3427	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$41$	−12.3427	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$42$	0.767355	0.118405
$43$	5.58432	0.851601	0.425800	−	0.904817i	$-0.359993\pi$
$43$	5.58432	0.851601	0.425800	+	0.904817i	$0.359993\pi$
$44$	0	0
$45$	19.2752	2.87338
$46$	4.04740	0.596757
$47$	−9.10733	−1.32844	−0.664221	−	0.747537i	$-0.731236\pi$
$47$	−9.10733	−1.32844	−0.664221	+	0.747537i	$0.731236\pi$
$48$	2.79123	0.402879
$49$	−6.92442	−0.989203
$50$	11.1866	1.58202
$51$	−7.33314	−1.02684
$52$	0.597016	0.0827913
$53$	7.30127	1.00291	0.501454	−	0.865185i	$-0.332799\pi$
$53$	7.30127	1.00291	0.501454	+	0.865185i	$0.332799\pi$
$54$	4.99894	0.680270
$55$	0	0
$56$	0.274917	0.0367373
$57$	−2.79123	−0.369707
$58$	−7.29532	−0.957923
$59$	−7.53037	−0.980370	−0.490185	−	0.871618i	$-0.663071\pi$
$59$	−7.53037	−0.980370	−0.490185	+	0.871618i	$0.663071\pi$
$60$	11.2298	1.44976
$61$	4.83533	0.619100	0.309550	−	0.950883i	$-0.399822\pi$
$61$	4.83533	0.619100	0.309550	+	0.950883i	$0.399822\pi$
$62$	−1.48056	−0.188032
$63$	1.31711	0.165940
$64$	1.00000	0.125000
$65$	2.40195	0.297925
$66$	0	0
$67$	−14.0217	−1.71303	−0.856514	−	0.516124i	$-0.827374\pi$
$67$	−14.0217	−1.71303	−0.856514	+	0.516124i	$0.827374\pi$
$68$	−2.62721	−0.318596
$69$	11.2972	1.36003
$70$	1.10606	0.132199
$71$	−9.61823	−1.14147	−0.570737	−	0.821133i	$-0.693342\pi$
$71$	−9.61823	−1.14147	−0.570737	+	0.821133i	$0.693342\pi$
$72$	4.79095	0.564619
$73$	−3.15625	−0.369411	−0.184705	−	0.982794i	$-0.559133\pi$
$73$	−3.15625	−0.369411	−0.184705	+	0.982794i	$0.559133\pi$
$74$	−8.31155	−0.966198
$75$	31.2242	3.60546
$76$	−1.00000	−0.114708
$77$	0	0
$78$	1.66641	0.188684
$79$	−2.42106	−0.272391	−0.136195	−	0.990682i	$-0.543487\pi$
$79$	−2.42106	−0.272391	−0.136195	+	0.990682i	$0.543487\pi$
$80$	4.02325	0.449813
$81$	−0.419665	−0.0466294
$82$	−12.3427	−1.36302
$83$	15.7948	1.73370	0.866852	−	0.498566i	$-0.166140\pi$
$83$	15.7948	1.73370	0.866852	+	0.498566i	$0.166140\pi$
$84$	0.767355	0.0837253
$85$	−10.5699	−1.14647
$86$	5.58432	0.602173
$87$	−20.3629	−2.18313
$88$	0	0
$89$	1.49871	0.158863	0.0794315	−	0.996840i	$-0.474689\pi$
$89$	1.49871	0.158863	0.0794315	+	0.996840i	$0.474689\pi$
$90$	19.2752	2.03178
$91$	0.164130	0.0172055
$92$	4.04740	0.421971
$93$	−4.13259	−0.428530
$94$	−9.10733	−0.939350
$95$	−4.02325	−0.412777
$96$	2.79123	0.284878
$97$	9.00939	0.914765	0.457382	−	0.889270i	$-0.348787\pi$
$97$	9.00939	0.914765	0.457382	+	0.889270i	$0.348787\pi$
$98$	−6.92442	−0.699472
$99$	0	0
$100$	11.1866	1.11866
$101$	2.30943	0.229797	0.114898	−	0.993377i	$-0.463346\pi$
$101$	2.30943	0.229797	0.114898	+	0.993377i	$0.463346\pi$
$102$	−7.33314	−0.726089
$103$	10.3403	1.01886	0.509428	−	0.860513i	$-0.329857\pi$
$103$	10.3403	1.01886	0.509428	+	0.860513i	$0.329857\pi$
$104$	0.597016	0.0585423
$105$	3.08726	0.301286
$106$	7.30127	0.709162
$107$	−9.00544	−0.870589	−0.435294	−	0.900288i	$-0.643356\pi$
$107$	−9.00544	−0.870589	−0.435294	+	0.900288i	$0.643356\pi$
$108$	4.99894	0.481023
$109$	16.8995	1.61867	0.809337	−	0.587344i	$-0.199827\pi$
$109$	16.8995	1.61867	0.809337	+	0.587344i	$0.199827\pi$
$110$	0	0
$111$	−23.1994	−2.20199
$112$	0.274917	0.0259772
$113$	2.84546	0.267678	0.133839	−	0.991003i	$-0.457269\pi$
$113$	2.84546	0.267678	0.133839	+	0.991003i	$0.457269\pi$
$114$	−2.79123	−0.261422
$115$	16.2837	1.51847
$116$	−7.29532	−0.677354
$117$	2.86027	0.264432
$118$	−7.53037	−0.693227
$119$	−0.722264	−0.0662098
$120$	11.2298	1.02514
$121$	0	0
$122$	4.83533	0.437770
$123$	−34.4512	−3.10636
$124$	−1.48056	−0.132959
$125$	24.8901	2.22624
$126$	1.31711	0.117338
$127$	5.59695	0.496649	0.248324	−	0.968677i	$-0.420120\pi$
$127$	5.59695	0.496649	0.248324	+	0.968677i	$0.420120\pi$
$128$	1.00000	0.0883883
$129$	15.5871	1.37237
$130$	2.40195	0.210665
$131$	−7.73690	−0.675976	−0.337988	−	0.941150i	$-0.609746\pi$
$131$	−7.73690	−0.675976	−0.337988	+	0.941150i	$0.609746\pi$
$132$	0	0
$133$	−0.274917	−0.0238383
$134$	−14.0217	−1.21129
$135$	20.1120	1.73097
$136$	−2.62721	−0.225281
$137$	−1.10706	−0.0945829	−0.0472914	−	0.998881i	$-0.515059\pi$
$137$	−1.10706	−0.0945829	−0.0472914	+	0.998881i	$0.515059\pi$
$138$	11.2972	0.961683
$139$	14.8792	1.26204	0.631020	−	0.775767i	$-0.282637\pi$
$139$	14.8792	1.26204	0.631020	+	0.775767i	$0.282637\pi$
$140$	1.10606	0.0934791
$141$	−25.4206	−2.14080
$142$	−9.61823	−0.807144
$143$	0	0
$144$	4.79095	0.399246
$145$	−29.3509	−2.43746
$146$	−3.15625	−0.261213
$147$	−19.3276	−1.59412
$148$	−8.31155	−0.683205
$149$	20.9576	1.71691	0.858457	−	0.512885i	$-0.171423\pi$
$149$	20.9576	1.71691	0.858457	+	0.512885i	$0.171423\pi$
$150$	31.2242	2.54945
$151$	−4.07961	−0.331994	−0.165997	−	0.986126i	$-0.553084\pi$
$151$	−4.07961	−0.331994	−0.165997	+	0.986126i	$0.553084\pi$
$152$	−1.00000	−0.0811107
$153$	−12.5868	−1.01758
$154$	0	0
$155$	−5.95669	−0.478453
$156$	1.66641	0.133419
$157$	19.7161	1.57352	0.786758	−	0.617262i	$-0.211758\pi$
$157$	19.7161	1.57352	0.786758	+	0.617262i	$0.211758\pi$
$158$	−2.42106	−0.192609
$159$	20.3795	1.61620
$160$	4.02325	0.318066
$161$	1.11270	0.0876929
$162$	−0.419665	−0.0329720
$163$	16.9154	1.32492	0.662460	−	0.749098i	$-0.269513\pi$
$163$	16.9154	1.32492	0.662460	+	0.749098i	$0.269513\pi$
$164$	−12.3427	−0.963800
$165$	0	0
$166$	15.7948	1.22591
$167$	−23.1451	−1.79102	−0.895512	−	0.445038i	$-0.853190\pi$
$167$	−23.1451	−1.79102	−0.895512	+	0.445038i	$0.853190\pi$
$168$	0.767355	0.0592027
$169$	−12.6436	−0.972582
$170$	−10.5699	−0.810676
$171$	−4.79095	−0.366373
$172$	5.58432	0.425800
$173$	−23.5008	−1.78673	−0.893366	−	0.449330i	$-0.851663\pi$
$173$	−23.5008	−1.78673	−0.893366	+	0.449330i	$0.851663\pi$
$174$	−20.3629	−1.54371
$175$	3.07537	0.232476
$176$	0	0
$177$	−21.0190	−1.57988
$178$	1.49871	0.112333
$179$	7.52415	0.562381	0.281191	−	0.959652i	$-0.409271\pi$
$179$	7.52415	0.562381	0.281191	+	0.959652i	$0.409271\pi$
$180$	19.2752	1.43669
$181$	19.6253	1.45874	0.729370	−	0.684120i	$-0.239813\pi$
$181$	19.6253	1.45874	0.729370	+	0.684120i	$0.239813\pi$
$182$	0.164130	0.0121661
$183$	13.4965	0.997690
$184$	4.04740	0.298379
$185$	−33.4395	−2.45852
$186$	−4.13259	−0.303016
$187$	0	0
$188$	−9.10733	−0.664221
$189$	1.37429	0.0999650
$190$	−4.02325	−0.291877
$191$	20.9322	1.51460	0.757300	−	0.653067i	$-0.226518\pi$
$191$	20.9322	1.51460	0.757300	+	0.653067i	$0.226518\pi$
$192$	2.79123	0.201439
$193$	1.89921	0.136708	0.0683542	−	0.997661i	$-0.478225\pi$
$193$	1.89921	0.136708	0.0683542	+	0.997661i	$0.478225\pi$
$194$	9.00939	0.646836
$195$	6.70438	0.480111
$196$	−6.92442	−0.494601
$197$	−1.40362	−0.100004	−0.0500020	−	0.998749i	$-0.515923\pi$
$197$	−1.40362	−0.100004	−0.0500020	+	0.998749i	$0.515923\pi$
$198$	0	0
$199$	−3.60404	−0.255483	−0.127742	−	0.991807i	$-0.540773\pi$
$199$	−3.60404	−0.255483	−0.127742	+	0.991807i	$0.540773\pi$
$200$	11.1866	0.791009
$201$	−39.1379	−2.76057
$202$	2.30943	0.162491
$203$	−2.00561	−0.140766
$204$	−7.33314	−0.513422
$205$	−49.6576	−3.46824
$206$	10.3403	0.720441
$207$	19.3909	1.34776
$208$	0.597016	0.0413956
$209$	0	0
$210$	3.08726	0.213041
$211$	18.7715	1.29228	0.646141	−	0.763218i	$-0.276382\pi$
$211$	18.7715	1.29228	0.646141	+	0.763218i	$0.276382\pi$
$212$	7.30127	0.501454
$213$	−26.8467	−1.83950
$214$	−9.00544	−0.615599
$215$	22.4671	1.53225
$216$	4.99894	0.340135
$217$	−0.407032	−0.0276311
$218$	16.8995	1.14458
$219$	−8.80980	−0.595311
$220$	0	0
$221$	−1.56849	−0.105508
$222$	−23.1994	−1.55704
$223$	−14.6688	−0.982298	−0.491149	−	0.871075i	$-0.663423\pi$
$223$	−14.6688	−0.982298	−0.491149	+	0.871075i	$0.663423\pi$
$224$	0.274917	0.0183686
$225$	53.5942	3.57295
$226$	2.84546	0.189277
$227$	3.54422	0.235238	0.117619	−	0.993059i	$-0.462474\pi$
$227$	3.54422	0.235238	0.117619	+	0.993059i	$0.462474\pi$
$228$	−2.79123	−0.184854
$229$	−16.7749	−1.10852	−0.554259	−	0.832344i	$-0.686998\pi$
$229$	−16.7749	−1.10852	−0.554259	+	0.832344i	$0.686998\pi$
$230$	16.2837	1.07372
$231$	0	0
$232$	−7.29532	−0.478961
$233$	25.7392	1.68623	0.843115	−	0.537734i	$-0.180719\pi$
$233$	25.7392	1.68623	0.843115	+	0.537734i	$0.180719\pi$
$234$	2.86027	0.186982
$235$	−36.6411	−2.39020
$236$	−7.53037	−0.490185
$237$	−6.75773	−0.438962
$238$	−0.722264	−0.0468174
$239$	3.83627	0.248148	0.124074	−	0.992273i	$-0.460404\pi$
$239$	3.83627	0.248148	0.124074	+	0.992273i	$0.460404\pi$
$240$	11.2298	0.724881
$241$	−10.9064	−0.702540	−0.351270	−	0.936274i	$-0.614250\pi$
$241$	−10.9064	−0.702540	−0.351270	+	0.936274i	$0.614250\pi$
$242$	0	0
$243$	−16.1682	−1.03719
$244$	4.83533	0.309550
$245$	−27.8587	−1.77983
$246$	−34.4512	−2.19653
$247$	−0.597016	−0.0379872
$248$	−1.48056	−0.0940160
$249$	44.0868	2.79389
$250$	24.8901	1.57419
$251$	13.9463	0.880283	0.440141	−	0.897928i	$-0.354928\pi$
$251$	13.9463	0.880283	0.440141	+	0.897928i	$0.354928\pi$
$252$	1.31711	0.0829702
$253$	0	0
$254$	5.59695	0.351184
$255$	−29.5031	−1.84755
$256$	1.00000	0.0625000
$257$	16.8311	1.04989	0.524947	−	0.851135i	$-0.324085\pi$
$257$	16.8311	1.04989	0.524947	+	0.851135i	$0.324085\pi$
$258$	15.5871	0.970410
$259$	−2.28498	−0.141982
$260$	2.40195	0.148962
$261$	−34.9515	−2.16344
$262$	−7.73690	−0.477987
$263$	−1.71132	−0.105525	−0.0527623	−	0.998607i	$-0.516803\pi$
$263$	−1.71132	−0.105525	−0.0527623	+	0.998607i	$0.516803\pi$
$264$	0	0
$265$	29.3749	1.80448
$266$	−0.274917	−0.0168562
$267$	4.18324	0.256010
$268$	−14.0217	−0.856514
$269$	22.3017	1.35976	0.679880	−	0.733323i	$-0.262032\pi$
$269$	22.3017	1.35976	0.679880	+	0.733323i	$0.262032\pi$
$270$	20.1120	1.22398
$271$	−2.26292	−0.137463	−0.0687314	−	0.997635i	$-0.521895\pi$
$271$	−2.26292	−0.137463	−0.0687314	+	0.997635i	$0.521895\pi$
$272$	−2.62721	−0.159298
$273$	0.458123	0.0277269
$274$	−1.10706	−0.0668802
$275$	0	0
$276$	11.2972	0.680013
$277$	9.83937	0.591190	0.295595	−	0.955313i	$-0.404482\pi$
$277$	9.83937	0.591190	0.295595	+	0.955313i	$0.404482\pi$
$278$	14.8792	0.892397
$279$	−7.09331	−0.424665
$280$	1.10606	0.0660997
$281$	17.9598	1.07139	0.535697	−	0.844410i	$-0.320049\pi$
$281$	17.9598	1.07139	0.535697	+	0.844410i	$0.320049\pi$
$282$	−25.4206	−1.51378
$283$	26.5193	1.57641	0.788206	−	0.615412i	$-0.211010\pi$
$283$	26.5193	1.57641	0.788206	+	0.615412i	$0.211010\pi$
$284$	−9.61823	−0.570737
$285$	−11.2298	−0.665197
$286$	0	0
$287$	−3.39320	−0.200294
$288$	4.79095	0.282309
$289$	−10.0978	−0.593986
$290$	−29.3509	−1.72355
$291$	25.1472	1.47416
$292$	−3.15625	−0.184705
$293$	−12.3885	−0.723745	−0.361872	−	0.932228i	$-0.617862\pi$
$293$	−12.3885	−0.723745	−0.361872	+	0.932228i	$0.617862\pi$
$294$	−19.3276	−1.12721
$295$	−30.2966	−1.76393
$296$	−8.31155	−0.483099
$297$	0	0
$298$	20.9576	1.21404
$299$	2.41637	0.139742
$300$	31.2242	1.80273
$301$	1.53522	0.0884887
$302$	−4.07961	−0.234755
$303$	6.44614	0.370321
$304$	−1.00000	−0.0573539
$305$	19.4537	1.11392
$306$	−12.5868	−0.719541
$307$	−29.2289	−1.66818	−0.834090	−	0.551628i	$-0.814007\pi$
$307$	−29.2289	−1.66818	−0.834090	+	0.551628i	$0.814007\pi$
$308$	0	0
$309$	28.8620	1.64190
$310$	−5.95669	−0.338317
$311$	10.9986	0.623675	0.311837	−	0.950136i	$-0.399056\pi$
$311$	10.9986	0.623675	0.311837	+	0.950136i	$0.399056\pi$
$312$	1.66641	0.0943418
$313$	15.5213	0.877314	0.438657	−	0.898654i	$-0.355454\pi$
$313$	15.5213	0.877314	0.438657	+	0.898654i	$0.355454\pi$
$314$	19.7161	1.11264
$315$	5.29907	0.298569
$316$	−2.42106	−0.136195
$317$	−23.9485	−1.34508	−0.672541	−	0.740060i	$-0.734797\pi$
$317$	−23.9485	−1.34508	−0.672541	+	0.740060i	$0.734797\pi$
$318$	20.3795	1.14283
$319$	0	0
$320$	4.02325	0.224907
$321$	−25.1362	−1.40297
$322$	1.11270	0.0620083
$323$	2.62721	0.146182
$324$	−0.419665	−0.0233147
$325$	6.67856	0.370460
$326$	16.9154	0.936859
$327$	47.1702	2.60852
$328$	−12.3427	−0.681509
$329$	−2.50376	−0.138037
$330$	0	0
$331$	25.6584	1.41031	0.705156	−	0.709052i	$-0.250877\pi$
$331$	25.6584	1.41031	0.705156	+	0.709052i	$0.250877\pi$
$332$	15.7948	0.866852
$333$	−39.8202	−2.18213
$334$	−23.1451	−1.26644
$335$	−56.4130	−3.08217
$336$	0.767355	0.0418626
$337$	−2.94204	−0.160263	−0.0801314	−	0.996784i	$-0.525534\pi$
$337$	−2.94204	−0.160263	−0.0801314	+	0.996784i	$0.525534\pi$
$338$	−12.6436	−0.687720
$339$	7.94233	0.431368
$340$	−10.5699	−0.573235
$341$	0	0
$342$	−4.79095	−0.259065
$343$	−3.82806	−0.206696
$344$	5.58432	0.301086
$345$	45.4516	2.44703
$346$	−23.5008	−1.26341
$347$	−6.33884	−0.340287	−0.170144	−	0.985419i	$-0.554423\pi$
$347$	−6.33884	−0.340287	−0.170144	+	0.985419i	$0.554423\pi$
$348$	−20.3629	−1.09157
$349$	−10.5789	−0.566276	−0.283138	−	0.959079i	$-0.591375\pi$
$349$	−10.5789	−0.566276	−0.283138	+	0.959079i	$0.591375\pi$
$350$	3.07537	0.164386
$351$	2.98445	0.159298
$352$	0	0
$353$	−35.1642	−1.87160	−0.935800	−	0.352532i	$-0.885321\pi$
$353$	−35.1642	−1.87160	−0.935800	+	0.352532i	$0.885321\pi$
$354$	−21.0190	−1.11715
$355$	−38.6966	−2.05380
$356$	1.49871	0.0794315
$357$	−2.01600	−0.106698
$358$	7.52415	0.397664
$359$	24.1939	1.27691	0.638453	−	0.769661i	$-0.279575\pi$
$359$	24.1939	1.27691	0.638453	+	0.769661i	$0.279575\pi$
$360$	19.2752	1.01589
$361$	1.00000	0.0526316
$362$	19.6253	1.03148
$363$	0	0
$364$	0.164130	0.00860273
$365$	−12.6984	−0.664664
$366$	13.4965	0.705473
$367$	−23.2519	−1.21374	−0.606869	−	0.794802i	$-0.707575\pi$
$367$	−23.2519	−1.21374	−0.606869	+	0.794802i	$0.707575\pi$
$368$	4.04740	0.210986
$369$	−59.1330	−3.07834
$370$	−33.4395	−1.73843
$371$	2.00724	0.104211
$372$	−4.13259	−0.214265
$373$	8.15845	0.422429	0.211214	−	0.977440i	$-0.432258\pi$
$373$	8.15845	0.422429	0.211214	+	0.977440i	$0.432258\pi$
$374$	0	0
$375$	69.4739	3.58762
$376$	−9.10733	−0.469675
$377$	−4.35543	−0.224316
$378$	1.37429	0.0706860
$379$	−18.9997	−0.975951	−0.487976	−	0.872857i	$-0.662265\pi$
$379$	−18.9997	−0.975951	−0.487976	+	0.872857i	$0.662265\pi$
$380$	−4.02325	−0.206388
$381$	15.6224	0.800357
$382$	20.9322	1.07098
$383$	12.1817	0.622456	0.311228	−	0.950335i	$-0.399260\pi$
$383$	12.1817	0.622456	0.311228	+	0.950335i	$0.399260\pi$
$384$	2.79123	0.142439
$385$	0	0
$386$	1.89921	0.0966674
$387$	26.7542	1.35999
$388$	9.00939	0.457382
$389$	−24.1433	−1.22411	−0.612057	−	0.790814i	$-0.709658\pi$
$389$	−24.1433	−1.22411	−0.612057	+	0.790814i	$0.709658\pi$
$390$	6.70438	0.339489
$391$	−10.6334	−0.537753
$392$	−6.92442	−0.349736
$393$	−21.5954	−1.08935
$394$	−1.40362	−0.0707135
$395$	−9.74054	−0.490100
$396$	0	0
$397$	−10.1918	−0.511510	−0.255755	−	0.966742i	$-0.582324\pi$
$397$	−10.1918	−0.511510	−0.255755	+	0.966742i	$0.582324\pi$
$398$	−3.60404	−0.180654
$399$	−0.767355	−0.0384158
$400$	11.1866	0.559328
$401$	12.2313	0.610800	0.305400	−	0.952224i	$-0.401210\pi$
$401$	12.2313	0.610800	0.305400	+	0.952224i	$0.401210\pi$
$402$	−39.1379	−1.95202
$403$	−0.883921	−0.0440313
$404$	2.30943	0.114898
$405$	−1.68842	−0.0838981
$406$	−2.00561	−0.0995365
$407$	0	0
$408$	−7.33314	−0.363044
$409$	−27.8419	−1.37669	−0.688347	−	0.725381i	$-0.741663\pi$
$409$	−27.8419	−1.37669	−0.688347	+	0.725381i	$0.741663\pi$
$410$	−49.6576	−2.45242
$411$	−3.09007	−0.152422
$412$	10.3403	0.509428
$413$	−2.07022	−0.101869
$414$	19.3909	0.953011
$415$	63.5464	3.11937
$416$	0.597016	0.0292711
$417$	41.5313	2.03380
$418$	0	0
$419$	2.74637	0.134169	0.0670846	−	0.997747i	$-0.478630\pi$
$419$	2.74637	0.134169	0.0670846	+	0.997747i	$0.478630\pi$
$420$	3.08726	0.150643
$421$	3.45765	0.168516	0.0842579	−	0.996444i	$-0.473148\pi$
$421$	3.45765	0.168516	0.0842579	+	0.996444i	$0.473148\pi$
$422$	18.7715	0.913782
$423$	−43.6328	−2.12150
$424$	7.30127	0.354581
$425$	−29.3894	−1.42560
$426$	−26.8467	−1.30073
$427$	1.32931	0.0643299
$428$	−9.00544	−0.435294
$429$	0	0
$430$	22.4671	1.08346
$431$	33.1455	1.59656	0.798281	−	0.602285i	$-0.205743\pi$
$431$	33.1455	1.59656	0.798281	+	0.602285i	$0.205743\pi$
$432$	4.99894	0.240512
$433$	−17.0841	−0.821008	−0.410504	−	0.911859i	$-0.634647\pi$
$433$	−17.0841	−0.821008	−0.410504	+	0.911859i	$0.634647\pi$
$434$	−0.407032	−0.0195382
$435$	−81.9251	−3.92801
$436$	16.8995	0.809337
$437$	−4.04740	−0.193614
$438$	−8.80980	−0.420949
$439$	36.1437	1.72505	0.862523	−	0.506018i	$-0.168883\pi$
$439$	36.1437	1.72505	0.862523	+	0.506018i	$0.168883\pi$
$440$	0	0
$441$	−33.1745	−1.57974
$442$	−1.56849	−0.0746053
$443$	19.4900	0.925996	0.462998	−	0.886359i	$-0.346774\pi$
$443$	19.4900	0.925996	0.462998	+	0.886359i	$0.346774\pi$
$444$	−23.1994	−1.10100
$445$	6.02969	0.285835
$446$	−14.6688	−0.694590
$447$	58.4974	2.76683
$448$	0.274917	0.0129886
$449$	−12.8197	−0.604998	−0.302499	−	0.953150i	$-0.597821\pi$
$449$	−12.8197	−0.604998	−0.302499	+	0.953150i	$0.597821\pi$
$450$	53.5942	2.52646
$451$	0	0
$452$	2.84546	0.133839
$453$	−11.3871	−0.535014
$454$	3.54422	0.166338
$455$	0.660335	0.0309570
$456$	−2.79123	−0.130711
$457$	2.20055	0.102937	0.0514687	−	0.998675i	$-0.483610\pi$
$457$	2.20055	0.102937	0.0514687	+	0.998675i	$0.483610\pi$
$458$	−16.7749	−0.783841
$459$	−13.1333	−0.613008
$460$	16.2837	0.759233
$461$	−3.39457	−0.158101	−0.0790505	−	0.996871i	$-0.525189\pi$
$461$	−3.39457	−0.158101	−0.0790505	+	0.996871i	$0.525189\pi$
$462$	0	0
$463$	18.5198	0.860690	0.430345	−	0.902665i	$-0.358392\pi$
$463$	18.5198	0.860690	0.430345	+	0.902665i	$0.358392\pi$
$464$	−7.29532	−0.338677
$465$	−16.6265	−0.771034
$466$	25.7392	1.19234
$467$	29.7909	1.37856	0.689280	−	0.724495i	$-0.257927\pi$
$467$	29.7909	1.37856	0.689280	+	0.724495i	$0.257927\pi$
$468$	2.86027	0.132216
$469$	−3.85481	−0.177999
$470$	−36.6411	−1.69013
$471$	55.0321	2.53574
$472$	−7.53037	−0.346613
$473$	0	0
$474$	−6.75773	−0.310393
$475$	−11.1866	−0.513275
$476$	−0.722264	−0.0331049
$477$	34.9800	1.60163
$478$	3.83627	0.175467
$479$	25.3380	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$479$	25.3380	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$480$	11.2298	0.512568
$481$	−4.96213	−0.226254
$482$	−10.9064	−0.496771
$483$	3.10579	0.141319
$484$	0	0
$485$	36.2470	1.64589
$486$	−16.1682	−0.733405
$487$	−1.08718	−0.0492650	−0.0246325	−	0.999697i	$-0.507842\pi$
$487$	−1.08718	−0.0492650	−0.0246325	+	0.999697i	$0.507842\pi$
$488$	4.83533	0.218885
$489$	47.2148	2.13513
$490$	−27.8587	−1.25853
$491$	17.1850	0.775550	0.387775	−	0.921754i	$-0.373244\pi$
$491$	17.1850	0.775550	0.387775	+	0.921754i	$0.373244\pi$
$492$	−34.4512	−1.55318
$493$	19.1663	0.863209
$494$	−0.597016	−0.0268610
$495$	0	0
$496$	−1.48056	−0.0664793
$497$	−2.64421	−0.118609
$498$	44.0868	1.97558
$499$	−8.60896	−0.385390	−0.192695	−	0.981259i	$-0.561723\pi$
$499$	−8.60896	−0.385390	−0.192695	+	0.981259i	$0.561723\pi$
$500$	24.8901	1.11312
$501$	−64.6033	−2.88626
$502$	13.9463	0.622454
$503$	−7.29741	−0.325376	−0.162688	−	0.986678i	$-0.552016\pi$
$503$	−7.29741	−0.325376	−0.162688	+	0.986678i	$0.552016\pi$
$504$	1.31711	0.0586688
$505$	9.29141	0.413462
$506$	0	0
$507$	−35.2911	−1.56733
$508$	5.59695	0.248324
$509$	3.57411	0.158420	0.0792098	−	0.996858i	$-0.474760\pi$
$509$	3.57411	0.158420	0.0792098	+	0.996858i	$0.474760\pi$
$510$	−29.5031	−1.30642
$511$	−0.867705	−0.0383850
$512$	1.00000	0.0441942
$513$	−4.99894	−0.220709
$514$	16.8311	0.742388
$515$	41.6015	1.83318
$516$	15.5871	0.686184
$517$	0	0
$518$	−2.28498	−0.100396
$519$	−65.5960	−2.87935
$520$	2.40195	0.105332
$521$	20.7089	0.907275	0.453638	−	0.891186i	$-0.350126\pi$
$521$	20.7089	0.907275	0.453638	+	0.891186i	$0.350126\pi$
$522$	−34.9515	−1.52979
$523$	9.17755	0.401306	0.200653	−	0.979662i	$-0.435694\pi$
$523$	9.17755	0.401306	0.200653	+	0.979662i	$0.435694\pi$
$524$	−7.73690	−0.337988
$525$	8.58406	0.374639
$526$	−1.71132	−0.0746171
$527$	3.88975	0.169440
$528$	0	0
$529$	−6.61852	−0.287762
$530$	29.3749	1.27596
$531$	−36.0776	−1.56563
$532$	−0.274917	−0.0119191
$533$	−7.36877	−0.319177
$534$	4.18324	0.181027
$535$	−36.2312	−1.56641
$536$	−14.0217	−0.605647
$537$	21.0016	0.906286
$538$	22.3017	0.961495
$539$	0	0
$540$	20.1120	0.865483
$541$	−18.0117	−0.774383	−0.387191	−	0.921999i	$-0.626555\pi$
$541$	−18.0117	−0.774383	−0.387191	+	0.921999i	$0.626555\pi$
$542$	−2.26292	−0.0972008
$543$	54.7788	2.35078
$544$	−2.62721	−0.112641
$545$	67.9908	2.91240
$546$	0.458123	0.0196059
$547$	−18.2006	−0.778200	−0.389100	−	0.921196i	$-0.627214\pi$
$547$	−18.2006	−0.778200	−0.389100	+	0.921196i	$0.627214\pi$
$548$	−1.10706	−0.0472914
$549$	23.1658	0.988692
$550$	0	0
$551$	7.29532	0.310791
$552$	11.2972	0.480842
$553$	−0.665590	−0.0283038
$554$	9.83937	0.418035
$555$	−93.3371	−3.96194
$556$	14.8792	0.631020
$557$	−31.3931	−1.33017	−0.665083	−	0.746769i	$-0.731604\pi$
$557$	−31.3931	−1.33017	−0.665083	+	0.746769i	$0.731604\pi$
$558$	−7.09331	−0.300284
$559$	3.33393	0.141010
$560$	1.10606	0.0467395
$561$	0	0
$562$	17.9598	0.757590
$563$	−11.9362	−0.503051	−0.251526	−	0.967851i	$-0.580932\pi$
$563$	−11.9362	−0.503051	−0.251526	+	0.967851i	$0.580932\pi$
$564$	−25.4206	−1.07040
$565$	11.4480	0.481621
$566$	26.5193	1.11469
$567$	−0.115373	−0.00484520
$568$	−9.61823	−0.403572
$569$	−4.74045	−0.198730	−0.0993649	−	0.995051i	$-0.531681\pi$
$569$	−4.74045	−0.198730	−0.0993649	+	0.995051i	$0.531681\pi$
$570$	−11.2298	−0.470365
$571$	10.4663	0.438001	0.219001	−	0.975725i	$-0.429720\pi$
$571$	10.4663	0.438001	0.219001	+	0.975725i	$0.429720\pi$
$572$	0	0
$573$	58.4265	2.44080
$574$	−3.39320	−0.141630
$575$	45.2765	1.88816
$576$	4.79095	0.199623
$577$	−27.8884	−1.16101	−0.580504	−	0.814258i	$-0.697144\pi$
$577$	−27.8884	−1.16101	−0.580504	+	0.814258i	$0.697144\pi$
$578$	−10.0978	−0.420012
$579$	5.30113	0.220308
$580$	−29.3509	−1.21873
$581$	4.34225	0.180147
$582$	25.1472	1.04239
$583$	0	0
$584$	−3.15625	−0.130606
$585$	11.5076	0.475781
$586$	−12.3885	−0.511765
$587$	−0.355712	−0.0146818	−0.00734089	−	0.999973i	$-0.502337\pi$
$587$	−0.355712	−0.0146818	−0.00734089	+	0.999973i	$0.502337\pi$
$588$	−19.3276	−0.797058
$589$	1.48056	0.0610056
$590$	−30.2966	−1.24729
$591$	−3.91783	−0.161158
$592$	−8.31155	−0.341603
$593$	−34.4326	−1.41398	−0.706990	−	0.707224i	$-0.749947\pi$
$593$	−34.4326	−1.41398	−0.706990	+	0.707224i	$0.749947\pi$
$594$	0	0
$595$	−2.90585	−0.119128
$596$	20.9576	0.858457
$597$	−10.0597	−0.411716
$598$	2.41637	0.0988126
$599$	9.20766	0.376215	0.188107	−	0.982148i	$-0.439765\pi$
$599$	9.20766	0.376215	0.188107	+	0.982148i	$0.439765\pi$
$600$	31.2242	1.27472
$601$	−40.2925	−1.64357	−0.821783	−	0.569801i	$-0.807020\pi$
$601$	−40.2925	−1.64357	−0.821783	+	0.569801i	$0.807020\pi$
$602$	1.53522	0.0625710
$603$	−67.1774	−2.73568
$604$	−4.07961	−0.165997
$605$	0	0
$606$	6.44614	0.261856
$607$	21.8513	0.886916	0.443458	−	0.896295i	$-0.353751\pi$
$607$	21.8513	0.886916	0.443458	+	0.896295i	$0.353751\pi$
$608$	−1.00000	−0.0405554
$609$	−5.59810	−0.226847
$610$	19.4537	0.787659
$611$	−5.43723	−0.219967
$612$	−12.5868	−0.508792
$613$	18.0805	0.730264	0.365132	−	0.930956i	$-0.381024\pi$
$613$	18.0805	0.730264	0.365132	+	0.930956i	$0.381024\pi$
$614$	−29.2289	−1.17958
$615$	−138.606	−5.58912
$616$	0	0
$617$	−45.2047	−1.81987	−0.909936	−	0.414749i	$-0.863870\pi$
$617$	−45.2047	−1.81987	−0.909936	+	0.414749i	$0.863870\pi$
$618$	28.8620	1.16100
$619$	18.8902	0.759263	0.379631	−	0.925138i	$-0.376051\pi$
$619$	18.8902	0.759263	0.379631	+	0.925138i	$0.376051\pi$
$620$	−5.95669	−0.239226
$621$	20.2327	0.811912
$622$	10.9986	0.441004
$623$	0.412021	0.0165073
$624$	1.66641	0.0667097
$625$	44.2063	1.76825
$626$	15.5213	0.620355
$627$	0	0
$628$	19.7161	0.786758
$629$	21.8362	0.870666
$630$	5.29907	0.211120
$631$	−6.89416	−0.274452	−0.137226	−	0.990540i	$-0.543819\pi$
$631$	−6.89416	−0.274452	−0.137226	+	0.990540i	$0.543819\pi$
$632$	−2.42106	−0.0963046
$633$	52.3955	2.08253
$634$	−23.9485	−0.951116
$635$	22.5179	0.893597
$636$	20.3795	0.808100
$637$	−4.13399	−0.163795
$638$	0	0
$639$	−46.0804	−1.82291
$640$	4.02325	0.159033
$641$	−15.7499	−0.622085	−0.311043	−	0.950396i	$-0.600678\pi$
$641$	−15.7499	−0.622085	−0.311043	+	0.950396i	$0.600678\pi$
$642$	−25.1362	−0.992048
$643$	40.9900	1.61649	0.808245	−	0.588847i	$-0.200418\pi$
$643$	40.9900	1.61649	0.808245	+	0.588847i	$0.200418\pi$
$644$	1.11270	0.0438465
$645$	62.7108	2.46924
$646$	2.62721	0.103366
$647$	−5.82684	−0.229077	−0.114538	−	0.993419i	$-0.536539\pi$
$647$	−5.82684	−0.229077	−0.114538	+	0.993419i	$0.536539\pi$
$648$	−0.419665	−0.0164860
$649$	0	0
$650$	6.67856	0.261955
$651$	−1.13612	−0.0445280
$652$	16.9154	0.662460
$653$	18.8227	0.736591	0.368295	−	0.929709i	$-0.379942\pi$
$653$	18.8227	0.736591	0.368295	+	0.929709i	$0.379942\pi$
$654$	47.1702	1.84450
$655$	−31.1275	−1.21625
$656$	−12.3427	−0.481900
$657$	−15.1214	−0.589943
$658$	−2.50376	−0.0976066
$659$	29.6469	1.15488	0.577440	−	0.816433i	$-0.304052\pi$
$659$	29.6469	1.15488	0.577440	+	0.816433i	$0.304052\pi$
$660$	0	0
$661$	26.1657	1.01773	0.508864	−	0.860847i	$-0.330066\pi$
$661$	26.1657	1.01773	0.508864	+	0.860847i	$0.330066\pi$
$662$	25.6584	0.997241
$663$	−4.37800	−0.170028
$664$	15.7948	0.612957
$665$	−1.10606	−0.0428911
$666$	−39.8202	−1.54300
$667$	−29.5271	−1.14329
$668$	−23.1451	−0.895512
$669$	−40.9441	−1.58299
$670$	−56.4130	−2.17942
$671$	0	0
$672$	0.767355	0.0296014
$673$	30.9303	1.19228	0.596138	−	0.802882i	$-0.296701\pi$
$673$	30.9303	1.19228	0.596138	+	0.802882i	$0.296701\pi$
$674$	−2.94204	−0.113323
$675$	55.9210	2.15240
$676$	−12.6436	−0.486291
$677$	−21.2288	−0.815888	−0.407944	−	0.913007i	$-0.633754\pi$
$677$	−21.2288	−0.815888	−0.407944	+	0.913007i	$0.633754\pi$
$678$	7.94233	0.305023
$679$	2.47683	0.0950520
$680$	−10.5699	−0.405338
$681$	9.89271	0.379090
$682$	0	0
$683$	−8.46842	−0.324035	−0.162017	−	0.986788i	$-0.551800\pi$
$683$	−8.46842	−0.324035	−0.162017	+	0.986788i	$0.551800\pi$
$684$	−4.79095	−0.183186
$685$	−4.45400	−0.170179
$686$	−3.82806	−0.146156
$687$	−46.8226	−1.78639
$688$	5.58432	0.212900
$689$	4.35898	0.166064
$690$	45.4516	1.73031
$691$	0.920788	0.0350284	0.0175142	−	0.999847i	$-0.494425\pi$
$691$	0.920788	0.0350284	0.0175142	+	0.999847i	$0.494425\pi$
$692$	−23.5008	−0.893366
$693$	0	0
$694$	−6.33884	−0.240619
$695$	59.8629	2.27073
$696$	−20.3629	−0.771854
$697$	32.4268	1.22825
$698$	−10.5789	−0.400418
$699$	71.8439	2.71738
$700$	3.07537	0.116238
$701$	−10.4383	−0.394249	−0.197124	−	0.980379i	$-0.563160\pi$
$701$	−10.4383	−0.394249	−0.197124	+	0.980379i	$0.563160\pi$
$702$	2.98445	0.112641
$703$	8.31155	0.313476
$704$	0	0
$705$	−102.274	−3.85185
$706$	−35.1642	−1.32342
$707$	0.634900	0.0238779
$708$	−21.0190	−0.789941
$709$	−13.2648	−0.498170	−0.249085	−	0.968482i	$-0.580130\pi$
$709$	−13.2648	−0.498170	−0.249085	+	0.968482i	$0.580130\pi$
$710$	−38.6966	−1.45226
$711$	−11.5992	−0.435003
$712$	1.49871	0.0561666
$713$	−5.99244	−0.224419
$714$	−2.01600	−0.0754470
$715$	0	0
$716$	7.52415	0.281191
$717$	10.7079	0.399894
$718$	24.1939	0.902909
$719$	−44.0301	−1.64205	−0.821023	−	0.570895i	$-0.806596\pi$
$719$	−44.0301	−1.64205	−0.821023	+	0.570895i	$0.806596\pi$
$720$	19.2752	0.718344
$721$	2.84271	0.105868
$722$	1.00000	0.0372161
$723$	−30.4421	−1.13215
$724$	19.6253	0.729370
$725$	−81.6096	−3.03090
$726$	0	0
$727$	−14.8909	−0.552271	−0.276136	−	0.961119i	$-0.589054\pi$
$727$	−14.8909	−0.552271	−0.276136	+	0.961119i	$0.589054\pi$
$728$	0.164130	0.00608305
$729$	−43.8701	−1.62482
$730$	−12.6984	−0.469988
$731$	−14.6712	−0.542633
$732$	13.4965	0.498845
$733$	19.1078	0.705763	0.352882	−	0.935668i	$-0.385202\pi$
$733$	19.1078	0.705763	0.352882	+	0.935668i	$0.385202\pi$
$734$	−23.2519	−0.858242
$735$	−77.7599	−2.86822
$736$	4.04740	0.149189
$737$	0	0
$738$	−59.1330	−2.17672
$739$	−18.8804	−0.694527	−0.347264	−	0.937768i	$-0.612889\pi$
$739$	−18.8804	−0.694527	−0.347264	+	0.937768i	$0.612889\pi$
$740$	−33.4395	−1.22926
$741$	−1.66641	−0.0612170
$742$	2.00724	0.0736882
$743$	27.1802	0.997147	0.498573	−	0.866848i	$-0.333857\pi$
$743$	27.1802	0.997147	0.498573	+	0.866848i	$0.333857\pi$
$744$	−4.13259	−0.151508
$745$	84.3178	3.08916
$746$	8.15845	0.298702
$747$	75.6720	2.76869
$748$	0	0
$749$	−2.47575	−0.0904618
$750$	69.4739	2.53683
$751$	12.7321	0.464601	0.232300	−	0.972644i	$-0.425375\pi$
$751$	12.7321	0.464601	0.232300	+	0.972644i	$0.425375\pi$
$752$	−9.10733	−0.332110
$753$	38.9273	1.41859
$754$	−4.35543	−0.158615
$755$	−16.4133	−0.597341
$756$	1.37429	0.0499825
$757$	36.4140	1.32349	0.661745	−	0.749729i	$-0.269816\pi$
$757$	36.4140	1.32349	0.661745	+	0.749729i	$0.269816\pi$
$758$	−18.9997	−0.690102
$759$	0	0
$760$	−4.02325	−0.145939
$761$	19.2127	0.696461	0.348230	−	0.937409i	$-0.386783\pi$
$761$	19.2127	0.696461	0.348230	+	0.937409i	$0.386783\pi$
$762$	15.6224	0.565938
$763$	4.64594	0.168194
$764$	20.9322	0.757300
$765$	−50.6400	−1.83089
$766$	12.1817	0.440143
$767$	−4.49575	−0.162332
$768$	2.79123	0.100720
$769$	−15.0316	−0.542052	−0.271026	−	0.962572i	$-0.587363\pi$
$769$	−15.0316	−0.542052	−0.271026	+	0.962572i	$0.587363\pi$
$770$	0	0
$771$	46.9794	1.69192
$772$	1.89921	0.0683542
$773$	−25.2426	−0.907914	−0.453957	−	0.891023i	$-0.649988\pi$
$773$	−25.2426	−0.907914	−0.453957	+	0.891023i	$0.649988\pi$
$774$	26.7542	0.961659
$775$	−16.5624	−0.594940
$776$	9.00939	0.323418
$777$	−6.37791	−0.228806
$778$	−24.1433	−0.865579
$779$	12.3427	0.442222
$780$	6.70438	0.240055
$781$	0	0
$782$	−10.6334	−0.380249
$783$	−36.4689	−1.30329
$784$	−6.92442	−0.247301
$785$	79.3228	2.83115
$786$	−21.5954	−0.770284
$787$	−32.2538	−1.14972	−0.574862	−	0.818250i	$-0.694944\pi$
$787$	−32.2538	−1.14972	−0.574862	+	0.818250i	$0.694944\pi$
$788$	−1.40362	−0.0500020
$789$	−4.77668	−0.170054
$790$	−9.74054	−0.346553
$791$	0.782265	0.0278141
$792$	0	0
$793$	2.88677	0.102512
$794$	−10.1918	−0.361692
$795$	81.9919	2.90795
$796$	−3.60404	−0.127742
$797$	−17.7608	−0.629121	−0.314561	−	0.949237i	$-0.601857\pi$
$797$	−17.7608	−0.629121	−0.314561	+	0.949237i	$0.601857\pi$
$798$	−0.767355	−0.0271641
$799$	23.9269	0.846472
$800$	11.1866	0.395505
$801$	7.18025	0.253701
$802$	12.2313	0.431901
$803$	0	0
$804$	−39.1379	−1.38029
$805$	4.47667	0.157782
$806$	−0.883921	−0.0311348
$807$	62.2492	2.19127
$808$	2.30943	0.0812454
$809$	21.3809	0.751714	0.375857	−	0.926678i	$-0.377348\pi$
$809$	21.3809	0.751714	0.375857	+	0.926678i	$0.377348\pi$
$810$	−1.68842	−0.0593249
$811$	−9.48316	−0.332999	−0.166499	−	0.986042i	$-0.553246\pi$
$811$	−9.48316	−0.332999	−0.166499	+	0.986042i	$0.553246\pi$
$812$	−2.00561	−0.0703830
$813$	−6.31633	−0.221523
$814$	0	0
$815$	68.0551	2.38387
$816$	−7.33314	−0.256711
$817$	−5.58432	−0.195371
$818$	−27.8419	−0.973470
$819$	0.786337	0.0274768
$820$	−49.6576	−1.73412
$821$	−3.84674	−0.134252	−0.0671261	−	0.997744i	$-0.521383\pi$
$821$	−3.84674	−0.134252	−0.0671261	+	0.997744i	$0.521383\pi$
$822$	−3.09007	−0.107778
$823$	−15.9227	−0.555031	−0.277516	−	0.960721i	$-0.589511\pi$
$823$	−15.9227	−0.555031	−0.277516	+	0.960721i	$0.589511\pi$
$824$	10.3403	0.360220
$825$	0	0
$826$	−2.07022	−0.0720323
$827$	21.3561	0.742624	0.371312	−	0.928508i	$-0.378908\pi$
$827$	21.3561	0.742624	0.371312	+	0.928508i	$0.378908\pi$
$828$	19.3909	0.673880
$829$	22.3416	0.775957	0.387978	−	0.921668i	$-0.373174\pi$
$829$	22.3416	0.775957	0.387978	+	0.921668i	$0.373174\pi$
$830$	63.5464	2.20573
$831$	27.4639	0.952712
$832$	0.597016	0.0206978
$833$	18.1919	0.630312
$834$	41.5313	1.43811
$835$	−93.1187	−3.22250
$836$	0	0
$837$	−7.40126	−0.255825
$838$	2.74637	0.0948719
$839$	0.807131	0.0278653	0.0139326	−	0.999903i	$-0.495565\pi$
$839$	0.807131	0.0278653	0.0139326	+	0.999903i	$0.495565\pi$
$840$	3.08726	0.106521
$841$	24.2217	0.835233
$842$	3.45765	0.119159
$843$	50.1300	1.72657
$844$	18.7715	0.646141
$845$	−50.8683	−1.74992
$846$	−43.6328	−1.50013
$847$	0	0
$848$	7.30127	0.250727
$849$	74.0215	2.54041
$850$	−29.3894	−1.00805
$851$	−33.6402	−1.15317
$852$	−26.8467	−0.919752
$853$	−35.6981	−1.22228	−0.611139	−	0.791523i	$-0.709289\pi$
$853$	−35.6981	−1.22228	−0.611139	+	0.791523i	$0.709289\pi$
$854$	1.32931	0.0454881
$855$	−19.2752	−0.659198
$856$	−9.00544	−0.307800
$857$	53.2489	1.81895	0.909474	−	0.415760i	$-0.136484\pi$
$857$	53.2489	1.81895	0.909474	+	0.415760i	$0.136484\pi$
$858$	0	0
$859$	−57.5833	−1.96472	−0.982358	−	0.187009i	$-0.940121\pi$
$859$	−57.5833	−1.96472	−0.982358	+	0.187009i	$0.940121\pi$
$860$	22.4671	0.766123
$861$	−9.47120	−0.322778
$862$	33.1455	1.12894
$863$	−41.2077	−1.40273	−0.701364	−	0.712804i	$-0.747425\pi$
$863$	−41.2077	−1.40273	−0.701364	+	0.712804i	$0.747425\pi$
$864$	4.99894	0.170067
$865$	−94.5496	−3.21478
$866$	−17.0841	−0.580540
$867$	−28.1852	−0.957218
$868$	−0.407032	−0.0138156
$869$	0	0
$870$	−81.9251	−2.77752
$871$	−8.37121	−0.283647
$872$	16.8995	0.572288
$873$	43.1635	1.46086
$874$	−4.04740	−0.136905
$875$	6.84270	0.231326
$876$	−8.80980	−0.297656
$877$	−29.3504	−0.991092	−0.495546	−	0.868582i	$-0.665032\pi$
$877$	−29.3504	−0.991092	−0.495546	+	0.868582i	$0.665032\pi$
$878$	36.1437	1.21979
$879$	−34.5792	−1.16633
$880$	0	0
$881$	1.36463	0.0459757	0.0229878	−	0.999736i	$-0.492682\pi$
$881$	1.36463	0.0459757	0.0229878	+	0.999736i	$0.492682\pi$
$882$	−33.1745	−1.11704
$883$	11.8574	0.399034	0.199517	−	0.979894i	$-0.436063\pi$
$883$	11.8574	0.399034	0.199517	+	0.979894i	$0.436063\pi$
$884$	−1.56849	−0.0527539
$885$	−84.5646	−2.84261
$886$	19.4900	0.654778
$887$	−28.7149	−0.964152	−0.482076	−	0.876129i	$-0.660117\pi$
$887$	−28.7149	−0.964152	−0.482076	+	0.876129i	$0.660117\pi$
$888$	−23.1994	−0.778521
$889$	1.53869	0.0516061
$890$	6.02969	0.202116
$891$	0	0
$892$	−14.6688	−0.491149
$893$	9.10733	0.304765
$894$	58.4974	1.95645
$895$	30.2716	1.01187
$896$	0.274917	0.00918432
$897$	6.74463	0.225196
$898$	−12.8197	−0.427798
$899$	10.8012	0.360240
$900$	53.5942	1.78647
$901$	−19.1820	−0.639044
$902$	0	0
$903$	4.28515	0.142601
$904$	2.84546	0.0946386
$905$	78.9577	2.62464
$906$	−11.3871	−0.378312
$907$	20.8425	0.692063	0.346031	−	0.938223i	$-0.387529\pi$
$907$	20.8425	0.692063	0.346031	+	0.938223i	$0.387529\pi$
$908$	3.54422	0.117619
$909$	11.0644	0.366981
$910$	0.660335	0.0218899
$911$	−33.3467	−1.10483	−0.552413	−	0.833571i	$-0.686293\pi$
$911$	−33.3467	−1.10483	−0.552413	+	0.833571i	$0.686293\pi$
$912$	−2.79123	−0.0924268
$913$	0	0
$914$	2.20055	0.0727877
$915$	54.2998	1.79510
$916$	−16.7749	−0.554259
$917$	−2.12700	−0.0702398
$918$	−13.1333	−0.433462
$919$	−15.9480	−0.526076	−0.263038	−	0.964786i	$-0.584724\pi$
$919$	−15.9480	−0.526076	−0.263038	+	0.964786i	$0.584724\pi$
$920$	16.2837	0.536859
$921$	−81.5845	−2.68830
$922$	−3.39457	−0.111794
$923$	−5.74224	−0.189008
$924$	0	0
$925$	−92.9776	−3.05709
$926$	18.5198	0.608600
$927$	49.5397	1.62710
$928$	−7.29532	−0.239481
$929$	−34.2521	−1.12377	−0.561887	−	0.827214i	$-0.689924\pi$
$929$	−34.2521	−1.12377	−0.561887	+	0.827214i	$0.689924\pi$
$930$	−16.6265	−0.545203
$931$	6.92442	0.226939
$932$	25.7392	0.843115
$933$	30.6996	1.00506
$934$	29.7909	0.974789
$935$	0	0
$936$	2.86027	0.0934910
$937$	32.5123	1.06213	0.531065	−	0.847331i	$-0.321792\pi$
$937$	32.5123	1.06213	0.531065	+	0.847331i	$0.321792\pi$
$938$	−3.85481	−0.125864
$939$	43.3234	1.41381
$940$	−36.6411	−1.19510
$941$	12.8788	0.419838	0.209919	−	0.977719i	$-0.432680\pi$
$941$	12.8788	0.419838	0.209919	+	0.977719i	$0.432680\pi$
$942$	55.0321	1.79304
$943$	−49.9557	−1.62678
$944$	−7.53037	−0.245093
$945$	5.52912	0.179862
$946$	0	0
$947$	−27.4064	−0.890589	−0.445295	−	0.895384i	$-0.646901\pi$
$947$	−27.4064	−0.890589	−0.445295	+	0.895384i	$0.646901\pi$
$948$	−6.75773	−0.219481
$949$	−1.88433	−0.0611680
$950$	−11.1866	−0.362940
$951$	−66.8457	−2.16762
$952$	−0.722264	−0.0234087
$953$	13.5962	0.440423	0.220212	−	0.975452i	$-0.429325\pi$
$953$	13.5962	0.440423	0.220212	+	0.975452i	$0.429325\pi$
$954$	34.9800	1.13252
$955$	84.2155	2.72515
$956$	3.83627	0.124074
$957$	0	0
$958$	25.3380	0.818632
$959$	−0.304350	−0.00982798
$960$	11.2298	0.362441
$961$	−28.8079	−0.929288
$962$	−4.96213	−0.159985
$963$	−43.1446	−1.39031
$964$	−10.9064	−0.351270
$965$	7.64101	0.245973
$966$	3.10579	0.0999273
$967$	−19.4593	−0.625768	−0.312884	−	0.949791i	$-0.601295\pi$
$967$	−19.4593	−0.625768	−0.312884	+	0.949791i	$0.601295\pi$
$968$	0	0
$969$	7.33314	0.235574
$970$	36.2470	1.16382
$971$	−54.0585	−1.73482	−0.867410	−	0.497594i	$-0.834217\pi$
$971$	−54.0585	−1.73482	−0.867410	+	0.497594i	$0.834217\pi$
$972$	−16.1682	−0.518595
$973$	4.09055	0.131137
$974$	−1.08718	−0.0348356
$975$	18.6414	0.597002
$976$	4.83533	0.154775
$977$	−34.0503	−1.08937	−0.544684	−	0.838642i	$-0.683350\pi$
$977$	−34.0503	−1.08937	−0.544684	+	0.838642i	$0.683350\pi$
$978$	47.2148	1.50976
$979$	0	0
$980$	−27.8587	−0.889913
$981$	80.9644	2.58499
$982$	17.1850	0.548397
$983$	51.6148	1.64626	0.823129	−	0.567855i	$-0.192226\pi$
$983$	51.6148	1.64626	0.823129	+	0.567855i	$0.192226\pi$
$984$	−34.4512	−1.09826
$985$	−5.64713	−0.179932
$986$	19.1663	0.610381
$987$	−6.98856	−0.222448
$988$	−0.597016	−0.0189936
$989$	22.6020	0.718702
$990$	0	0
$991$	7.22913	0.229641	0.114820	−	0.993386i	$-0.463371\pi$
$991$	7.22913	0.229641	0.114820	+	0.993386i	$0.463371\pi$
$992$	−1.48056	−0.0470080
$993$	71.6183	2.27274
$994$	−2.64421	−0.0838693
$995$	−14.5000	−0.459679
$996$	44.0868	1.39695
$997$	40.4932	1.28243	0.641216	−	0.767360i	$-0.278430\pi$
$997$	40.4932	1.28243	0.641216	+	0.767360i	$0.278430\pi$
$998$	−8.60896	−0.272512
$999$	−41.5489	−1.31455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cb.1.6	yes	8
11.10	odd	2		4598.2.a.by.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.by.1.6	✓	8	11.10	odd	2
4598.2.a.cb.1.6	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.79123 q^{3} +1.00000 q^{4} +4.02325 q^{5} +2.79123 q^{6} +0.274917 q^{7} +1.00000 q^{8} +4.79095 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.79123 q^{3} +1.00000 q^{4} +4.02325 q^{5} +2.79123 q^{6} +0.274917 q^{7} +1.00000 q^{8} +4.79095 q^{9} +4.02325 q^{10} +2.79123 q^{12} +0.597016 q^{13} +0.274917 q^{14} +11.2298 q^{15} +1.00000 q^{16} -2.62721 q^{17} +4.79095 q^{18} -1.00000 q^{19} +4.02325 q^{20} +0.767355 q^{21} +4.04740 q^{23} +2.79123 q^{24} +11.1866 q^{25} +0.597016 q^{26} +4.99894 q^{27} +0.274917 q^{28} -7.29532 q^{29} +11.2298 q^{30} -1.48056 q^{31} +1.00000 q^{32} -2.62721 q^{34} +1.10606 q^{35} +4.79095 q^{36} -8.31155 q^{37} -1.00000 q^{38} +1.66641 q^{39} +4.02325 q^{40} -12.3427 q^{41} +0.767355 q^{42} +5.58432 q^{43} +19.2752 q^{45} +4.04740 q^{46} -9.10733 q^{47} +2.79123 q^{48} -6.92442 q^{49} +11.1866 q^{50} -7.33314 q^{51} +0.597016 q^{52} +7.30127 q^{53} +4.99894 q^{54} +0.274917 q^{56} -2.79123 q^{57} -7.29532 q^{58} -7.53037 q^{59} +11.2298 q^{60} +4.83533 q^{61} -1.48056 q^{62} +1.31711 q^{63} +1.00000 q^{64} +2.40195 q^{65} -14.0217 q^{67} -2.62721 q^{68} +11.2972 q^{69} +1.10606 q^{70} -9.61823 q^{71} +4.79095 q^{72} -3.15625 q^{73} -8.31155 q^{74} +31.2242 q^{75} -1.00000 q^{76} +1.66641 q^{78} -2.42106 q^{79} +4.02325 q^{80} -0.419665 q^{81} -12.3427 q^{82} +15.7948 q^{83} +0.767355 q^{84} -10.5699 q^{85} +5.58432 q^{86} -20.3629 q^{87} +1.49871 q^{89} +19.2752 q^{90} +0.164130 q^{91} +4.04740 q^{92} -4.13259 q^{93} -9.10733 q^{94} -4.02325 q^{95} +2.79123 q^{96} +9.00939 q^{97} -6.92442 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9 + 8 * q^12 - 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 + 22 * q^18 - 8 * q^19 - 20 * q^21 + 14 * q^23 + 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 + 4 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^32 - 4 * q^34 + 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 + 16 * q^39 + 8 * q^41 - 20 * q^42 + 8 * q^43 + 16 * q^45 + 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 + 36 * q^50 + 18 * q^51 - 12 * q^52 + 36 * q^53 + 32 * q^54 + 4 * q^56 - 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 + 12 * q^61 + 24 * q^63 + 8 * q^64 + 16 * q^65 + 16 * q^67 - 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 + 22 * q^72 - 20 * q^73 + 24 * q^74 + 40 * q^75 - 8 * q^76 + 16 * q^78 - 12 * q^79 + 40 * q^81 + 8 * q^82 + 20 * q^83 - 20 * q^84 + 12 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 - 16 * q^94 + 8 * q^96 + 4 * q^97 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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