LMFDB - Embedded newform 6027.2.a.be.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 $ x^10 - 4x^9 - 11x^8 + 56x^7 + 26x^6 - 266x^5 + 52x^4 + 526x^3 - 255x^2 - 372*x + 239
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.58399$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58399 q^{2} +1.00000 q^{3} +4.67700 q^{4} +0.798812 q^{5} -2.58399 q^{6} -6.91733 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58399 q^{2} +1.00000 q^{3} +4.67700 q^{4} +0.798812 q^{5} -2.58399 q^{6} -6.91733 q^{8} +1.00000 q^{9} -2.06412 q^{10} -1.79345 q^{11} +4.67700 q^{12} -3.77324 q^{13} +0.798812 q^{15} +8.52031 q^{16} +3.97884 q^{17} -2.58399 q^{18} -0.225138 q^{19} +3.73604 q^{20} +4.63426 q^{22} +5.53029 q^{23} -6.91733 q^{24} -4.36190 q^{25} +9.75000 q^{26} +1.00000 q^{27} +2.98276 q^{29} -2.06412 q^{30} +3.70251 q^{31} -8.18171 q^{32} -1.79345 q^{33} -10.2813 q^{34} +4.67700 q^{36} +6.88914 q^{37} +0.581755 q^{38} -3.77324 q^{39} -5.52565 q^{40} +1.00000 q^{41} +3.64753 q^{43} -8.38798 q^{44} +0.798812 q^{45} -14.2902 q^{46} +5.75596 q^{47} +8.52031 q^{48} +11.2711 q^{50} +3.97884 q^{51} -17.6474 q^{52} -10.2383 q^{53} -2.58399 q^{54} -1.43263 q^{55} -0.225138 q^{57} -7.70742 q^{58} +6.34098 q^{59} +3.73604 q^{60} -7.82495 q^{61} -9.56724 q^{62} +4.10084 q^{64} -3.01411 q^{65} +4.63426 q^{66} -3.89105 q^{67} +18.6090 q^{68} +5.53029 q^{69} +7.49365 q^{71} -6.91733 q^{72} -14.4571 q^{73} -17.8015 q^{74} -4.36190 q^{75} -1.05297 q^{76} +9.75000 q^{78} -0.117510 q^{79} +6.80613 q^{80} +1.00000 q^{81} -2.58399 q^{82} +5.66269 q^{83} +3.17835 q^{85} -9.42519 q^{86} +2.98276 q^{87} +12.4059 q^{88} -2.28446 q^{89} -2.06412 q^{90} +25.8651 q^{92} +3.70251 q^{93} -14.8733 q^{94} -0.179843 q^{95} -8.18171 q^{96} -0.883263 q^{97} -1.79345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * 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 $

$2$	−2.58399	−1.82716	−0.913578	−	0.406664i	$-0.866692\pi$
$2$	−2.58399	−1.82716	−0.913578	+	0.406664i	$0.866692\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.67700	2.33850
$5$	0.798812	0.357240	0.178620	−	0.983918i	$-0.442837\pi$
$5$	0.798812	0.357240	0.178620	+	0.983918i	$0.442837\pi$
$6$	−2.58399	−1.05491
$7$	0	0
$7$	0	0
$8$	−6.91733	−2.44565
$9$	1.00000	0.333333
$10$	−2.06412	−0.652733
$11$	−1.79345	−0.540747	−0.270373	−	0.962756i	$-0.587147\pi$
$11$	−1.79345	−0.540747	−0.270373	+	0.962756i	$0.587147\pi$
$12$	4.67700	1.35013
$13$	−3.77324	−1.04651	−0.523254	−	0.852177i	$-0.675282\pi$
$13$	−3.77324	−1.04651	−0.523254	+	0.852177i	$0.675282\pi$
$14$	0	0
$15$	0.798812	0.206252
$16$	8.52031	2.13008
$17$	3.97884	0.965010	0.482505	−	0.875893i	$-0.339727\pi$
$17$	3.97884	0.965010	0.482505	+	0.875893i	$0.339727\pi$
$18$	−2.58399	−0.609052
$19$	−0.225138	−0.0516502	−0.0258251	−	0.999666i	$-0.508221\pi$
$19$	−0.225138	−0.0516502	−0.0258251	+	0.999666i	$0.508221\pi$
$20$	3.73604	0.835405
$21$	0	0
$22$	4.63426	0.988028
$23$	5.53029	1.15314	0.576572	−	0.817046i	$-0.304390\pi$
$23$	5.53029	1.15314	0.576572	+	0.817046i	$0.304390\pi$
$24$	−6.91733	−1.41199
$25$	−4.36190	−0.872380
$26$	9.75000	1.91213
$27$	1.00000	0.192450
$28$	0	0
$29$	2.98276	0.553885	0.276942	−	0.960887i	$-0.410679\pi$
$29$	2.98276	0.553885	0.276942	+	0.960887i	$0.410679\pi$
$30$	−2.06412	−0.376855
$31$	3.70251	0.664990	0.332495	−	0.943105i	$-0.392109\pi$
$31$	3.70251	0.664990	0.332495	+	0.943105i	$0.392109\pi$
$32$	−8.18171	−1.44634
$33$	−1.79345	−0.312200
$34$	−10.2813	−1.76322
$35$	0	0
$36$	4.67700	0.779499
$37$	6.88914	1.13257	0.566284	−	0.824210i	$-0.308381\pi$
$37$	6.88914	1.13257	0.566284	+	0.824210i	$0.308381\pi$
$38$	0.581755	0.0943731
$39$	−3.77324	−0.604201
$40$	−5.52565	−0.873682
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	3.64753	0.556244	0.278122	−	0.960546i	$-0.410288\pi$
$43$	3.64753	0.556244	0.278122	+	0.960546i	$0.410288\pi$
$44$	−8.38798	−1.26454
$45$	0.798812	0.119080
$46$	−14.2902	−2.10697
$47$	5.75596	0.839593	0.419796	−	0.907618i	$-0.362102\pi$
$47$	5.75596	0.839593	0.419796	+	0.907618i	$0.362102\pi$
$48$	8.52031	1.22980
$49$	0	0
$50$	11.2711	1.59397
$51$	3.97884	0.557149
$52$	−17.6474	−2.44726
$53$	−10.2383	−1.40633	−0.703166	−	0.711025i	$-0.748231\pi$
$53$	−10.2383	−1.40633	−0.703166	+	0.711025i	$0.748231\pi$
$54$	−2.58399	−0.351636
$55$	−1.43263	−0.193176
$56$	0	0
$57$	−0.225138	−0.0298203
$58$	−7.70742	−1.01203
$59$	6.34098	0.825525	0.412763	−	0.910839i	$-0.364564\pi$
$59$	6.34098	0.825525	0.412763	+	0.910839i	$0.364564\pi$
$60$	3.73604	0.482321
$61$	−7.82495	−1.00188	−0.500941	−	0.865481i	$-0.667013\pi$
$61$	−7.82495	−1.00188	−0.500941	+	0.865481i	$0.667013\pi$
$62$	−9.56724	−1.21504
$63$	0	0
$64$	4.10084	0.512605
$65$	−3.01411	−0.373854
$66$	4.63426	0.570438
$67$	−3.89105	−0.475367	−0.237684	−	0.971343i	$-0.576388\pi$
$67$	−3.89105	−0.475367	−0.237684	+	0.971343i	$0.576388\pi$
$68$	18.6090	2.25667
$69$	5.53029	0.665768
$70$	0	0
$71$	7.49365	0.889333	0.444666	−	0.895696i	$-0.353322\pi$
$71$	7.49365	0.889333	0.444666	+	0.895696i	$0.353322\pi$
$72$	−6.91733	−0.815215
$73$	−14.4571	−1.69207	−0.846035	−	0.533127i	$-0.821017\pi$
$73$	−14.4571	−1.69207	−0.846035	+	0.533127i	$0.821017\pi$
$74$	−17.8015	−2.06938
$75$	−4.36190	−0.503669
$76$	−1.05297	−0.120784
$77$	0	0
$78$	9.75000	1.10397
$79$	−0.117510	−0.0132209	−0.00661047	−	0.999978i	$-0.502104\pi$
$79$	−0.117510	−0.0132209	−0.00661047	+	0.999978i	$0.502104\pi$
$80$	6.80613	0.760948
$81$	1.00000	0.111111
$82$	−2.58399	−0.285354
$83$	5.66269	0.621561	0.310781	−	0.950482i	$-0.399410\pi$
$83$	5.66269	0.621561	0.310781	+	0.950482i	$0.399410\pi$
$84$	0	0
$85$	3.17835	0.344740
$86$	−9.42519	−1.01634
$87$	2.98276	0.319786
$88$	12.4059	1.32247
$89$	−2.28446	−0.242152	−0.121076	−	0.992643i	$-0.538635\pi$
$89$	−2.28446	−0.242152	−0.121076	+	0.992643i	$0.538635\pi$
$90$	−2.06412	−0.217578
$91$	0	0
$92$	25.8651	2.69663
$93$	3.70251	0.383932
$94$	−14.8733	−1.53407
$95$	−0.179843	−0.0184515
$96$	−8.18171	−0.835043
$97$	−0.883263	−0.0896818	−0.0448409	−	0.998994i	$-0.514278\pi$
$97$	−0.883263	−0.0896818	−0.0448409	+	0.998994i	$0.514278\pi$
$98$	0	0
$99$	−1.79345	−0.180249
$100$	−20.4006	−2.04006
$101$	−4.09760	−0.407727	−0.203863	−	0.978999i	$-0.565350\pi$
$101$	−4.09760	−0.407727	−0.203863	+	0.978999i	$0.565350\pi$
$102$	−10.2813	−1.01800
$103$	−3.75803	−0.370290	−0.185145	−	0.982711i	$-0.559275\pi$
$103$	−3.75803	−0.370290	−0.185145	+	0.982711i	$0.559275\pi$
$104$	26.1007	2.55939
$105$	0	0
$106$	26.4555	2.56959
$107$	−4.22708	−0.408648	−0.204324	−	0.978903i	$-0.565500\pi$
$107$	−4.22708	−0.408648	−0.204324	+	0.978903i	$0.565500\pi$
$108$	4.67700	0.450044
$109$	−4.83517	−0.463125	−0.231563	−	0.972820i	$-0.574384\pi$
$109$	−4.83517	−0.463125	−0.231563	+	0.972820i	$0.574384\pi$
$110$	3.70191	0.352963
$111$	6.88914	0.653888
$112$	0	0
$113$	−1.01892	−0.0958517	−0.0479258	−	0.998851i	$-0.515261\pi$
$113$	−1.01892	−0.0958517	−0.0479258	+	0.998851i	$0.515261\pi$
$114$	0.581755	0.0544863
$115$	4.41766	0.411949
$116$	13.9504	1.29526
$117$	−3.77324	−0.348836
$118$	−16.3850	−1.50836
$119$	0	0
$120$	−5.52565	−0.504420
$121$	−7.78352	−0.707593
$122$	20.2196	1.83060
$123$	1.00000	0.0901670
$124$	17.3166	1.55508
$125$	−7.47840	−0.668889
$126$	0	0
$127$	9.98511	0.886036	0.443018	−	0.896513i	$-0.353908\pi$
$127$	9.98511	0.886036	0.443018	+	0.896513i	$0.353908\pi$
$128$	5.76690	0.509726
$129$	3.64753	0.321147
$130$	7.78842	0.683090
$131$	20.3135	1.77480	0.887398	−	0.461005i	$-0.152511\pi$
$131$	20.3135	1.77480	0.887398	+	0.461005i	$0.152511\pi$
$132$	−8.38798	−0.730080
$133$	0	0
$134$	10.0544	0.868570
$135$	0.798812	0.0687508
$136$	−27.5229	−2.36007
$137$	8.53622	0.729299	0.364649	−	0.931145i	$-0.381189\pi$
$137$	8.53622	0.729299	0.364649	+	0.931145i	$0.381189\pi$
$138$	−14.2902	−1.21646
$139$	0.613414	0.0520291	0.0260145	−	0.999662i	$-0.491718\pi$
$139$	0.613414	0.0520291	0.0260145	+	0.999662i	$0.491718\pi$
$140$	0	0
$141$	5.75596	0.484739
$142$	−19.3635	−1.62495
$143$	6.76712	0.565895
$144$	8.52031	0.710025
$145$	2.38267	0.197870
$146$	37.3569	3.09168
$147$	0	0
$148$	32.2205	2.64851
$149$	−1.37174	−0.112377	−0.0561887	−	0.998420i	$-0.517895\pi$
$149$	−1.37174	−0.112377	−0.0561887	+	0.998420i	$0.517895\pi$
$150$	11.2711	0.920281
$151$	−6.20983	−0.505349	−0.252674	−	0.967551i	$-0.581310\pi$
$151$	−6.20983	−0.505349	−0.252674	+	0.967551i	$0.581310\pi$
$152$	1.55736	0.126318
$153$	3.97884	0.321670
$154$	0	0
$155$	2.95761	0.237561
$156$	−17.6474	−1.41292
$157$	10.9903	0.877120	0.438560	−	0.898702i	$-0.355489\pi$
$157$	10.9903	0.877120	0.438560	+	0.898702i	$0.355489\pi$
$158$	0.303645	0.0241567
$159$	−10.2383	−0.811947
$160$	−6.53565	−0.516689
$161$	0	0
$162$	−2.58399	−0.203017
$163$	12.8342	1.00526	0.502628	−	0.864503i	$-0.332367\pi$
$163$	12.8342	1.00526	0.502628	+	0.864503i	$0.332367\pi$
$164$	4.67700	0.365212
$165$	−1.43263	−0.111530
$166$	−14.6323	−1.13569
$167$	−1.98043	−0.153251	−0.0766253	−	0.997060i	$-0.524415\pi$
$167$	−1.98043	−0.153251	−0.0766253	+	0.997060i	$0.524415\pi$
$168$	0	0
$169$	1.23731	0.0951776
$170$	−8.21281	−0.629894
$171$	−0.225138	−0.0172167
$172$	17.0595	1.30078
$173$	2.45273	0.186477	0.0932386	−	0.995644i	$-0.470278\pi$
$173$	2.45273	0.186477	0.0932386	+	0.995644i	$0.470278\pi$
$174$	−7.70742	−0.584298
$175$	0	0
$176$	−15.2808	−1.15183
$177$	6.34098	0.476617
$178$	5.90302	0.442450
$179$	16.9991	1.27057	0.635286	−	0.772277i	$-0.280882\pi$
$179$	16.9991	1.27057	0.635286	+	0.772277i	$0.280882\pi$
$180$	3.73604	0.278468
$181$	6.88971	0.512108	0.256054	−	0.966662i	$-0.417577\pi$
$181$	6.88971	0.512108	0.256054	+	0.966662i	$0.417577\pi$
$182$	0	0
$183$	−7.82495	−0.578437
$184$	−38.2548	−2.82018
$185$	5.50313	0.404598
$186$	−9.56724	−0.701504
$187$	−7.13586	−0.521826
$188$	26.9206	1.96339
$189$	0	0
$190$	0.464713	0.0337138
$191$	4.33811	0.313894	0.156947	−	0.987607i	$-0.449835\pi$
$191$	4.33811	0.313894	0.156947	+	0.987607i	$0.449835\pi$
$192$	4.10084	0.295953
$193$	18.8386	1.35603	0.678017	−	0.735046i	$-0.262840\pi$
$193$	18.8386	1.35603	0.678017	+	0.735046i	$0.262840\pi$
$194$	2.28234	0.163863
$195$	−3.01411	−0.215845
$196$	0	0
$197$	23.3402	1.66292	0.831461	−	0.555583i	$-0.187505\pi$
$197$	23.3402	1.66292	0.831461	+	0.555583i	$0.187505\pi$
$198$	4.63426	0.329343
$199$	−26.3459	−1.86761	−0.933806	−	0.357781i	$-0.883533\pi$
$199$	−26.3459	−1.86761	−0.933806	+	0.357781i	$0.883533\pi$
$200$	30.1727	2.13353
$201$	−3.89105	−0.274454
$202$	10.5882	0.744981
$203$	0	0
$204$	18.6090	1.30289
$205$	0.798812	0.0557915
$206$	9.71071	0.676577
$207$	5.53029	0.384381
$208$	−32.1491	−2.22914
$209$	0.403775	0.0279297
$210$	0	0
$211$	0.754748	0.0519590	0.0259795	−	0.999662i	$-0.491730\pi$
$211$	0.754748	0.0519590	0.0259795	+	0.999662i	$0.491730\pi$
$212$	−47.8843	−3.28871
$213$	7.49365	0.513456
$214$	10.9227	0.746663
$215$	2.91370	0.198712
$216$	−6.91733	−0.470665
$217$	0	0
$218$	12.4940	0.846202
$219$	−14.4571	−0.976917
$220$	−6.70042	−0.451742
$221$	−15.0131	−1.00989
$222$	−17.8015	−1.19476
$223$	17.8842	1.19761	0.598806	−	0.800894i	$-0.295642\pi$
$223$	17.8842	1.19761	0.598806	+	0.800894i	$0.295642\pi$
$224$	0	0
$225$	−4.36190	−0.290793
$226$	2.63287	0.175136
$227$	−16.8205	−1.11642	−0.558209	−	0.829700i	$-0.688511\pi$
$227$	−16.8205	−1.11642	−0.558209	+	0.829700i	$0.688511\pi$
$228$	−1.05297	−0.0697347
$229$	24.3602	1.60977	0.804885	−	0.593430i	$-0.202227\pi$
$229$	24.3602	1.60977	0.804885	+	0.593430i	$0.202227\pi$
$230$	−11.4152	−0.752695
$231$	0	0
$232$	−20.6327	−1.35461
$233$	23.8878	1.56494	0.782471	−	0.622687i	$-0.213959\pi$
$233$	23.8878	1.56494	0.782471	+	0.622687i	$0.213959\pi$
$234$	9.75000	0.637377
$235$	4.59793	0.299936
$236$	29.6567	1.93049
$237$	−0.117510	−0.00763312
$238$	0	0
$239$	−15.6876	−1.01474	−0.507372	−	0.861727i	$-0.669383\pi$
$239$	−15.6876	−1.01474	−0.507372	+	0.861727i	$0.669383\pi$
$240$	6.80613	0.439334
$241$	22.3732	1.44119	0.720593	−	0.693358i	$-0.243870\pi$
$241$	22.3732	1.44119	0.720593	+	0.693358i	$0.243870\pi$
$242$	20.1125	1.29288
$243$	1.00000	0.0641500
$244$	−36.5973	−2.34290
$245$	0	0
$246$	−2.58399	−0.164749
$247$	0.849500	0.0540524
$248$	−25.6115	−1.62633
$249$	5.66269	0.358859
$250$	19.3241	1.22216
$251$	9.85728	0.622186	0.311093	−	0.950379i	$-0.399305\pi$
$251$	9.85728	0.622186	0.311093	+	0.950379i	$0.399305\pi$
$252$	0	0
$253$	−9.91831	−0.623559
$254$	−25.8014	−1.61893
$255$	3.17835	0.199036
$256$	−23.1033	−1.44395
$257$	9.38566	0.585461	0.292731	−	0.956195i	$-0.405436\pi$
$257$	9.38566	0.585461	0.292731	+	0.956195i	$0.405436\pi$
$258$	−9.42519	−0.586786
$259$	0	0
$260$	−14.0970	−0.874257
$261$	2.98276	0.184628
$262$	−52.4897	−3.24283
$263$	−7.08960	−0.437163	−0.218582	−	0.975819i	$-0.570143\pi$
$263$	−7.08960	−0.437163	−0.218582	+	0.975819i	$0.570143\pi$
$264$	12.4059	0.763531
$265$	−8.17845	−0.502398
$266$	0	0
$267$	−2.28446	−0.139807
$268$	−18.1984	−1.11165
$269$	2.37006	0.144505	0.0722525	−	0.997386i	$-0.476981\pi$
$269$	2.37006	0.144505	0.0722525	+	0.997386i	$0.476981\pi$
$270$	−2.06412	−0.125618
$271$	25.9789	1.57811	0.789054	−	0.614324i	$-0.210571\pi$
$271$	25.9789	1.57811	0.789054	+	0.614324i	$0.210571\pi$
$272$	33.9009	2.05554
$273$	0	0
$274$	−22.0575	−1.33254
$275$	7.82286	0.471736
$276$	25.8651	1.55690
$277$	−19.0352	−1.14371	−0.571856	−	0.820354i	$-0.693777\pi$
$277$	−19.0352	−1.14371	−0.571856	+	0.820354i	$0.693777\pi$
$278$	−1.58505	−0.0950652
$279$	3.70251	0.221663
$280$	0	0
$281$	4.58121	0.273292	0.136646	−	0.990620i	$-0.456368\pi$
$281$	4.58121	0.273292	0.136646	+	0.990620i	$0.456368\pi$
$282$	−14.8733	−0.885694
$283$	−9.25972	−0.550433	−0.275216	−	0.961382i	$-0.588750\pi$
$283$	−9.25972	−0.550433	−0.275216	+	0.961382i	$0.588750\pi$
$284$	35.0478	2.07970
$285$	−0.179843	−0.0106530
$286$	−17.4862	−1.03398
$287$	0	0
$288$	−8.18171	−0.482112
$289$	−1.16885	−0.0687560
$290$	−6.15678	−0.361539
$291$	−0.883263	−0.0517778
$292$	−67.6156	−3.95690
$293$	14.7376	0.860982	0.430491	−	0.902595i	$-0.358340\pi$
$293$	14.7376	0.860982	0.430491	+	0.902595i	$0.358340\pi$
$294$	0	0
$295$	5.06525	0.294910
$296$	−47.6544	−2.76986
$297$	−1.79345	−0.104067
$298$	3.54456	0.205331
$299$	−20.8671	−1.20677
$300$	−20.4006	−1.17783
$301$	0	0
$302$	16.0461	0.923351
$303$	−4.09760	−0.235401
$304$	−1.91825	−0.110019
$305$	−6.25067	−0.357912
$306$	−10.2813	−0.587741
$307$	−10.9285	−0.623723	−0.311861	−	0.950128i	$-0.600952\pi$
$307$	−10.9285	−0.623723	−0.311861	+	0.950128i	$0.600952\pi$
$308$	0	0
$309$	−3.75803	−0.213787
$310$	−7.64243	−0.434061
$311$	15.7597	0.893653	0.446826	−	0.894621i	$-0.352554\pi$
$311$	15.7597	0.893653	0.446826	+	0.894621i	$0.352554\pi$
$312$	26.1007	1.47766
$313$	20.3002	1.14744	0.573718	−	0.819053i	$-0.305501\pi$
$313$	20.3002	1.14744	0.573718	+	0.819053i	$0.305501\pi$
$314$	−28.3987	−1.60263
$315$	0	0
$316$	−0.549595	−0.0309172
$317$	−1.76929	−0.0993735	−0.0496867	−	0.998765i	$-0.515822\pi$
$317$	−1.76929	−0.0993735	−0.0496867	+	0.998765i	$0.515822\pi$
$318$	26.4555	1.48355
$319$	−5.34944	−0.299511
$320$	3.27580	0.183123
$321$	−4.22708	−0.235933
$322$	0	0
$323$	−0.895788	−0.0498430
$324$	4.67700	0.259833
$325$	16.4585	0.912952
$326$	−33.1635	−1.83676
$327$	−4.83517	−0.267385
$328$	−6.91733	−0.381946
$329$	0	0
$330$	3.70191	0.203783
$331$	8.23405	0.452584	0.226292	−	0.974059i	$-0.427340\pi$
$331$	8.23405	0.452584	0.226292	+	0.974059i	$0.427340\pi$
$332$	26.4844	1.45352
$333$	6.88914	0.377522
$334$	5.11742	0.280013
$335$	−3.10822	−0.169820
$336$	0	0
$337$	−6.72820	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$337$	−6.72820	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$338$	−3.19719	−0.173904
$339$	−1.01892	−0.0553400
$340$	14.8651	0.806174
$341$	−6.64028	−0.359591
$342$	0.581755	0.0314577
$343$	0	0
$344$	−25.2312	−1.36037
$345$	4.41766	0.237839
$346$	−6.33781	−0.340723
$347$	−1.66517	−0.0893908	−0.0446954	−	0.999001i	$-0.514232\pi$
$347$	−1.66517	−0.0893908	−0.0446954	+	0.999001i	$0.514232\pi$
$348$	13.9504	0.747818
$349$	−30.7020	−1.64344	−0.821721	−	0.569891i	$-0.806986\pi$
$349$	−30.7020	−1.64344	−0.821721	+	0.569891i	$0.806986\pi$
$350$	0	0
$351$	−3.77324	−0.201400
$352$	14.6735	0.782101
$353$	−16.6549	−0.886453	−0.443226	−	0.896410i	$-0.646166\pi$
$353$	−16.6549	−0.886453	−0.443226	+	0.896410i	$0.646166\pi$
$354$	−16.3850	−0.870854
$355$	5.98602	0.317705
$356$	−10.6844	−0.566273
$357$	0	0
$358$	−43.9255	−2.32153
$359$	−24.4875	−1.29240	−0.646200	−	0.763168i	$-0.723643\pi$
$359$	−24.4875	−1.29240	−0.646200	+	0.763168i	$0.723643\pi$
$360$	−5.52565	−0.291227
$361$	−18.9493	−0.997332
$362$	−17.8029	−0.935702
$363$	−7.78352	−0.408529
$364$	0	0
$365$	−11.5485	−0.604475
$366$	20.2196	1.05689
$367$	14.8736	0.776393	0.388197	−	0.921577i	$-0.373098\pi$
$367$	14.8736	0.776393	0.388197	+	0.921577i	$0.373098\pi$
$368$	47.1197	2.45629
$369$	1.00000	0.0520579
$370$	−14.2200	−0.739264
$371$	0	0
$372$	17.3166	0.897825
$373$	7.77771	0.402715	0.201357	−	0.979518i	$-0.435465\pi$
$373$	7.77771	0.402715	0.201357	+	0.979518i	$0.435465\pi$
$374$	18.4390	0.953457
$375$	−7.47840	−0.386183
$376$	−39.8158	−2.05335
$377$	−11.2547	−0.579645
$378$	0	0
$379$	13.1541	0.675679	0.337840	−	0.941204i	$-0.390304\pi$
$379$	13.1541	0.675679	0.337840	+	0.941204i	$0.390304\pi$
$380$	−0.841126	−0.0431489
$381$	9.98511	0.511553
$382$	−11.2096	−0.573534
$383$	23.4481	1.19814	0.599071	−	0.800696i	$-0.295537\pi$
$383$	23.4481	1.19814	0.599071	+	0.800696i	$0.295537\pi$
$384$	5.76690	0.294291
$385$	0	0
$386$	−48.6788	−2.47769
$387$	3.64753	0.185415
$388$	−4.13102	−0.209721
$389$	29.2190	1.48146	0.740731	−	0.671802i	$-0.234479\pi$
$389$	29.2190	1.48146	0.740731	+	0.671802i	$0.234479\pi$
$390$	7.78842	0.394382
$391$	22.0041	1.11280
$392$	0	0
$393$	20.3135	1.02468
$394$	−60.3109	−3.03842
$395$	−0.0938687	−0.00472305
$396$	−8.38798	−0.421512
$397$	−21.7173	−1.08996	−0.544980	−	0.838449i	$-0.683463\pi$
$397$	−21.7173	−1.08996	−0.544980	+	0.838449i	$0.683463\pi$
$398$	68.0775	3.41242
$399$	0	0
$400$	−37.1647	−1.85824
$401$	27.5093	1.37375	0.686875	−	0.726776i	$-0.258982\pi$
$401$	27.5093	1.37375	0.686875	+	0.726776i	$0.258982\pi$
$402$	10.0544	0.501469
$403$	−13.9704	−0.695917
$404$	−19.1645	−0.953469
$405$	0.798812	0.0396933
$406$	0	0
$407$	−12.3554	−0.612432
$408$	−27.5229	−1.36259
$409$	24.5063	1.21176	0.605880	−	0.795556i	$-0.292821\pi$
$409$	24.5063	1.21176	0.605880	+	0.795556i	$0.292821\pi$
$410$	−2.06412	−0.101940
$411$	8.53622	0.421061
$412$	−17.5763	−0.865922
$413$	0	0
$414$	−14.2902	−0.702325
$415$	4.52343	0.222046
$416$	30.8715	1.51360
$417$	0.613414	0.0300390
$418$	−1.04335	−0.0510319
$419$	−10.0724	−0.492068	−0.246034	−	0.969261i	$-0.579127\pi$
$419$	−10.0724	−0.492068	−0.246034	+	0.969261i	$0.579127\pi$
$420$	0	0
$421$	12.4098	0.604817	0.302409	−	0.953178i	$-0.402209\pi$
$421$	12.4098	0.604817	0.302409	+	0.953178i	$0.402209\pi$
$422$	−1.95026	−0.0949372
$423$	5.75596	0.279864
$424$	70.8214	3.43939
$425$	−17.3553	−0.841855
$426$	−19.3635	−0.938165
$427$	0	0
$428$	−19.7701	−0.955622
$429$	6.76712	0.326720
$430$	−7.52896	−0.363078
$431$	−16.9511	−0.816507	−0.408254	−	0.912869i	$-0.633862\pi$
$431$	−16.9511	−0.816507	−0.408254	+	0.912869i	$0.633862\pi$
$432$	8.52031	0.409933
$433$	−0.771219	−0.0370624	−0.0185312	−	0.999828i	$-0.505899\pi$
$433$	−0.771219	−0.0370624	−0.0185312	+	0.999828i	$0.505899\pi$
$434$	0	0
$435$	2.38267	0.114240
$436$	−22.6141	−1.08302
$437$	−1.24508	−0.0595602
$438$	37.3569	1.78498
$439$	−21.0993	−1.00701	−0.503507	−	0.863991i	$-0.667957\pi$
$439$	−21.0993	−1.00701	−0.503507	+	0.863991i	$0.667957\pi$
$440$	9.90999	0.472440
$441$	0	0
$442$	38.7937	1.84523
$443$	15.4980	0.736330	0.368165	−	0.929760i	$-0.379986\pi$
$443$	15.4980	0.736330	0.368165	+	0.929760i	$0.379986\pi$
$444$	32.2205	1.52912
$445$	−1.82486	−0.0865065
$446$	−46.2125	−2.18822
$447$	−1.37174	−0.0648811
$448$	0	0
$449$	−5.19479	−0.245157	−0.122579	−	0.992459i	$-0.539116\pi$
$449$	−5.19479	−0.245157	−0.122579	+	0.992459i	$0.539116\pi$
$450$	11.2711	0.531325
$451$	−1.79345	−0.0844504
$452$	−4.76547	−0.224149
$453$	−6.20983	−0.291763
$454$	43.4641	2.03987
$455$	0	0
$456$	1.55736	0.0729298
$457$	38.7667	1.81343	0.906714	−	0.421745i	$-0.138582\pi$
$457$	38.7667	1.81343	0.906714	+	0.421745i	$0.138582\pi$
$458$	−62.9466	−2.94130
$459$	3.97884	0.185716
$460$	20.6614	0.963342
$461$	12.2468	0.570391	0.285195	−	0.958469i	$-0.407942\pi$
$461$	12.2468	0.570391	0.285195	+	0.958469i	$0.407942\pi$
$462$	0	0
$463$	19.6235	0.911982	0.455991	−	0.889984i	$-0.349285\pi$
$463$	19.6235	0.911982	0.455991	+	0.889984i	$0.349285\pi$
$464$	25.4140	1.17982
$465$	2.95761	0.137156
$466$	−61.7258	−2.85939
$467$	29.9077	1.38397	0.691983	−	0.721914i	$-0.256738\pi$
$467$	29.9077	1.38397	0.691983	+	0.721914i	$0.256738\pi$
$468$	−17.6474	−0.815752
$469$	0	0
$470$	−11.8810	−0.548030
$471$	10.9903	0.506405
$472$	−43.8626	−2.01894
$473$	−6.54168	−0.300787
$474$	0.303645	0.0139469
$475$	0.982030	0.0450586
$476$	0	0
$477$	−10.2383	−0.468778
$478$	40.5365	1.85410
$479$	−43.5239	−1.98866	−0.994329	−	0.106350i	$-0.966084\pi$
$479$	−43.5239	−1.98866	−0.994329	+	0.106350i	$0.966084\pi$
$480$	−6.53565	−0.298310
$481$	−25.9943	−1.18524
$482$	−57.8122	−2.63327
$483$	0	0
$484$	−36.4035	−1.65471
$485$	−0.705562	−0.0320379
$486$	−2.58399	−0.117212
$487$	38.0430	1.72389	0.861947	−	0.506999i	$-0.169245\pi$
$487$	38.0430	1.72389	0.861947	+	0.506999i	$0.169245\pi$
$488$	54.1278	2.45025
$489$	12.8342	0.580384
$490$	0	0
$491$	−3.46301	−0.156283	−0.0781416	−	0.996942i	$-0.524899\pi$
$491$	−3.46301	−0.156283	−0.0781416	+	0.996942i	$0.524899\pi$
$492$	4.67700	0.210855
$493$	11.8679	0.534504
$494$	−2.19510	−0.0987621
$495$	−1.43263	−0.0643921
$496$	31.5465	1.41648
$497$	0	0
$498$	−14.6323	−0.655690
$499$	22.1088	0.989726	0.494863	−	0.868971i	$-0.335218\pi$
$499$	22.1088	0.989726	0.494863	+	0.868971i	$0.335218\pi$
$500$	−34.9765	−1.56419
$501$	−1.98043	−0.0884793
$502$	−25.4711	−1.13683
$503$	−26.9611	−1.20214	−0.601068	−	0.799198i	$-0.705258\pi$
$503$	−26.9611	−1.20214	−0.601068	+	0.799198i	$0.705258\pi$
$504$	0	0
$505$	−3.27322	−0.145656
$506$	25.6288	1.13934
$507$	1.23731	0.0549508
$508$	46.7004	2.07199
$509$	−10.5158	−0.466104	−0.233052	−	0.972464i	$-0.574871\pi$
$509$	−10.5158	−0.466104	−0.233052	+	0.972464i	$0.574871\pi$
$510$	−8.21281	−0.363669
$511$	0	0
$512$	48.1648	2.12860
$513$	−0.225138	−0.00994010
$514$	−24.2524	−1.06973
$515$	−3.00196	−0.132282
$516$	17.0595	0.751003
$517$	−10.3230	−0.454007
$518$	0	0
$519$	2.45273	0.107663
$520$	20.8496	0.914314
$521$	−43.7619	−1.91724	−0.958622	−	0.284681i	$-0.908112\pi$
$521$	−43.7619	−1.91724	−0.958622	+	0.284681i	$0.908112\pi$
$522$	−7.70742	−0.337345
$523$	19.6354	0.858594	0.429297	−	0.903163i	$-0.358761\pi$
$523$	19.6354	0.858594	0.429297	+	0.903163i	$0.358761\pi$
$524$	95.0060	4.15036
$525$	0	0
$526$	18.3194	0.798766
$527$	14.7317	0.641722
$528$	−15.2808	−0.665010
$529$	7.58406	0.329742
$530$	21.1330	0.917960
$531$	6.34098	0.275175
$532$	0	0
$533$	−3.77324	−0.163437
$534$	5.90302	0.255449
$535$	−3.37665	−0.145985
$536$	26.9157	1.16258
$537$	16.9991	0.733565
$538$	−6.12420	−0.264033
$539$	0	0
$540$	3.73604	0.160774
$541$	5.08235	0.218507	0.109254	−	0.994014i	$-0.465154\pi$
$541$	5.08235	0.218507	0.109254	+	0.994014i	$0.465154\pi$
$542$	−67.1293	−2.88345
$543$	6.88971	0.295666
$544$	−32.5537	−1.39573
$545$	−3.86239	−0.165447
$546$	0	0
$547$	2.73903	0.117112	0.0585561	−	0.998284i	$-0.481350\pi$
$547$	2.73903	0.117112	0.0585561	+	0.998284i	$0.481350\pi$
$548$	39.9239	1.70546
$549$	−7.82495	−0.333961
$550$	−20.2142	−0.861936
$551$	−0.671534	−0.0286083
$552$	−38.2548	−1.62823
$553$	0	0
$554$	49.1867	2.08974
$555$	5.50313	0.233595
$556$	2.86893	0.121670
$557$	12.8563	0.544739	0.272370	−	0.962193i	$-0.412193\pi$
$557$	12.8563	0.544739	0.272370	+	0.962193i	$0.412193\pi$
$558$	−9.56724	−0.405014
$559$	−13.7630	−0.582113
$560$	0	0
$561$	−7.13586	−0.301276
$562$	−11.8378	−0.499347
$563$	5.70746	0.240541	0.120270	−	0.992741i	$-0.461624\pi$
$563$	5.70746	0.240541	0.120270	+	0.992741i	$0.461624\pi$
$564$	26.9206	1.13356
$565$	−0.813924	−0.0342420
$566$	23.9270	1.00573
$567$	0	0
$568$	−51.8360	−2.17499
$569$	18.4143	0.771966	0.385983	−	0.922506i	$-0.373862\pi$
$569$	18.4143	0.771966	0.385983	+	0.922506i	$0.373862\pi$
$570$	0.464713	0.0194647
$571$	8.17270	0.342017	0.171008	−	0.985270i	$-0.445297\pi$
$571$	8.17270	0.342017	0.171008	+	0.985270i	$0.445297\pi$
$572$	31.6498	1.32335
$573$	4.33811	0.181227
$574$	0	0
$575$	−24.1225	−1.00598
$576$	4.10084	0.170868
$577$	−2.64105	−0.109948	−0.0549742	−	0.998488i	$-0.517508\pi$
$577$	−2.64105	−0.109948	−0.0549742	+	0.998488i	$0.517508\pi$
$578$	3.02030	0.125628
$579$	18.8386	0.782907
$580$	11.1437	0.462718
$581$	0	0
$582$	2.28234	0.0946061
$583$	18.3618	0.760470
$584$	100.004	4.13820
$585$	−3.01411	−0.124618
$586$	−38.0819	−1.57315
$587$	22.6999	0.936926	0.468463	−	0.883483i	$-0.344808\pi$
$587$	22.6999	0.936926	0.468463	+	0.883483i	$0.344808\pi$
$588$	0	0
$589$	−0.833577	−0.0343469
$590$	−13.0886	−0.538847
$591$	23.3402	0.960089
$592$	58.6976	2.41246
$593$	−28.7347	−1.17999	−0.589997	−	0.807405i	$-0.700871\pi$
$593$	−28.7347	−1.17999	−0.589997	+	0.807405i	$0.700871\pi$
$594$	4.63426	0.190146
$595$	0	0
$596$	−6.41563	−0.262794
$597$	−26.3459	−1.07827
$598$	53.9203	2.20496
$599$	−22.4134	−0.915788	−0.457894	−	0.889007i	$-0.651396\pi$
$599$	−22.4134	−0.915788	−0.457894	+	0.889007i	$0.651396\pi$
$600$	30.1727	1.23179
$601$	−20.6781	−0.843476	−0.421738	−	0.906718i	$-0.638580\pi$
$601$	−20.6781	−0.843476	−0.421738	+	0.906718i	$0.638580\pi$
$602$	0	0
$603$	−3.89105	−0.158456
$604$	−29.0434	−1.18176
$605$	−6.21758	−0.252780
$606$	10.5882	0.430115
$607$	−37.2732	−1.51287	−0.756436	−	0.654067i	$-0.773061\pi$
$607$	−37.2732	−1.51287	−0.756436	+	0.654067i	$0.773061\pi$
$608$	1.84202	0.0747036
$609$	0	0
$610$	16.1517	0.653962
$611$	−21.7186	−0.878640
$612$	18.6090	0.752225
$613$	20.5784	0.831155	0.415577	−	0.909558i	$-0.363580\pi$
$613$	20.5784	0.831155	0.415577	+	0.909558i	$0.363580\pi$
$614$	28.2391	1.13964
$615$	0.798812	0.0322112
$616$	0	0
$617$	40.0044	1.61052	0.805259	−	0.592924i	$-0.202026\pi$
$617$	40.0044	1.61052	0.805259	+	0.592924i	$0.202026\pi$
$618$	9.71071	0.390622
$619$	20.5044	0.824141	0.412071	−	0.911152i	$-0.364806\pi$
$619$	20.5044	0.824141	0.412071	+	0.911152i	$0.364806\pi$
$620$	13.8327	0.555536
$621$	5.53029	0.221923
$622$	−40.7230	−1.63284
$623$	0	0
$624$	−32.1491	−1.28699
$625$	15.8357	0.633426
$626$	−52.4555	−2.09654
$627$	0.403775	0.0161252
$628$	51.4015	2.05114
$629$	27.4108	1.09294
$630$	0	0
$631$	−4.59735	−0.183017	−0.0915087	−	0.995804i	$-0.529169\pi$
$631$	−4.59735	−0.183017	−0.0915087	+	0.995804i	$0.529169\pi$
$632$	0.812858	0.0323337
$633$	0.754748	0.0299985
$634$	4.57184	0.181571
$635$	7.97623	0.316527
$636$	−47.8843	−1.89874
$637$	0	0
$638$	13.8229	0.547254
$639$	7.49365	0.296444
$640$	4.60667	0.182095
$641$	5.94306	0.234737	0.117368	−	0.993088i	$-0.462554\pi$
$641$	5.94306	0.234737	0.117368	+	0.993088i	$0.462554\pi$
$642$	10.9227	0.431086
$643$	−41.3341	−1.63006	−0.815029	−	0.579421i	$-0.803279\pi$
$643$	−41.3341	−1.63006	−0.815029	+	0.579421i	$0.803279\pi$
$644$	0	0
$645$	2.91370	0.114727
$646$	2.31471	0.0910709
$647$	−50.3361	−1.97891	−0.989457	−	0.144825i	$-0.953738\pi$
$647$	−50.3361	−1.97891	−0.989457	+	0.144825i	$0.953738\pi$
$648$	−6.91733	−0.271738
$649$	−11.3722	−0.446400
$650$	−42.5285	−1.66811
$651$	0	0
$652$	60.0257	2.35079
$653$	38.2547	1.49702	0.748512	−	0.663122i	$-0.230769\pi$
$653$	38.2547	1.49702	0.748512	+	0.663122i	$0.230769\pi$
$654$	12.4940	0.488555
$655$	16.2266	0.634027
$656$	8.52031	0.332662
$657$	−14.4571	−0.564024
$658$	0	0
$659$	−0.0500476	−0.00194958	−0.000974788	−	1.00000i	$-0.500310\pi$
$659$	−0.0500476	−0.00194958	−0.000974788		1.00000i	$0.500310\pi$
$660$	−6.70042	−0.260814
$661$	35.6249	1.38565	0.692824	−	0.721106i	$-0.256366\pi$
$661$	35.6249	1.38565	0.692824	+	0.721106i	$0.256366\pi$
$662$	−21.2767	−0.826942
$663$	−15.0131	−0.583060
$664$	−39.1707	−1.52012
$665$	0	0
$666$	−17.8015	−0.689792
$667$	16.4955	0.638709
$668$	−9.26249	−0.358376
$669$	17.8842	0.691441
$670$	8.03160	0.310288
$671$	14.0337	0.541765
$672$	0	0
$673$	43.9784	1.69524	0.847621	−	0.530603i	$-0.178034\pi$
$673$	43.9784	1.69524	0.847621	+	0.530603i	$0.178034\pi$
$674$	17.3856	0.669668
$675$	−4.36190	−0.167890
$676$	5.78689	0.222573
$677$	47.4455	1.82348	0.911740	−	0.410768i	$-0.134739\pi$
$677$	47.4455	1.82348	0.911740	+	0.410768i	$0.134739\pi$
$678$	2.63287	0.101115
$679$	0	0
$680$	−21.9857	−0.843112
$681$	−16.8205	−0.644565
$682$	17.1584	0.657029
$683$	8.15620	0.312088	0.156044	−	0.987750i	$-0.450126\pi$
$683$	8.15620	0.312088	0.156044	+	0.987750i	$0.450126\pi$
$684$	−1.05297	−0.0402613
$685$	6.81884	0.260535
$686$	0	0
$687$	24.3602	0.929401
$688$	31.0781	1.18484
$689$	38.6314	1.47174
$690$	−11.4152	−0.434569
$691$	−8.27386	−0.314753	−0.157376	−	0.987539i	$-0.550304\pi$
$691$	−8.27386	−0.314753	−0.157376	+	0.987539i	$0.550304\pi$
$692$	11.4714	0.436077
$693$	0	0
$694$	4.30277	0.163331
$695$	0.490002	0.0185869
$696$	−20.6327	−0.782082
$697$	3.97884	0.150709
$698$	79.3337	3.00282
$699$	23.8878	0.903520
$700$	0	0
$701$	22.0119	0.831379	0.415689	−	0.909507i	$-0.363540\pi$
$701$	22.0119	0.831379	0.415689	+	0.909507i	$0.363540\pi$
$702$	9.75000	0.367990
$703$	−1.55101	−0.0584974
$704$	−7.35467	−0.277190
$705$	4.59793	0.173168
$706$	43.0362	1.61969
$707$	0	0
$708$	29.6567	1.11457
$709$	18.7203	0.703056	0.351528	−	0.936177i	$-0.385662\pi$
$709$	18.7203	0.703056	0.351528	+	0.936177i	$0.385662\pi$
$710$	−15.4678	−0.580497
$711$	−0.117510	−0.00440698
$712$	15.8024	0.592219
$713$	20.4759	0.766830
$714$	0	0
$715$	5.40566	0.202160
$716$	79.5047	2.97123
$717$	−15.6876	−0.585863
$718$	63.2754	2.36142
$719$	0.324325	0.0120953	0.00604763	−	0.999982i	$-0.498075\pi$
$719$	0.324325	0.0120953	0.00604763	+	0.999982i	$0.498075\pi$
$720$	6.80613	0.253649
$721$	0	0
$722$	48.9648	1.82228
$723$	22.3732	0.832069
$724$	32.2232	1.19756
$725$	−13.0105	−0.483198
$726$	20.1125	0.746446
$727$	22.9912	0.852698	0.426349	−	0.904559i	$-0.359800\pi$
$727$	22.9912	0.852698	0.426349	+	0.904559i	$0.359800\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	29.8411	1.10447
$731$	14.5129	0.536781
$732$	−36.5973	−1.35267
$733$	−50.2211	−1.85496	−0.927480	−	0.373873i	$-0.878029\pi$
$733$	−50.2211	−1.85496	−0.927480	+	0.373873i	$0.878029\pi$
$734$	−38.4331	−1.41859
$735$	0	0
$736$	−45.2472	−1.66783
$737$	6.97842	0.257053
$738$	−2.58399	−0.0951179
$739$	−33.8797	−1.24629	−0.623143	−	0.782108i	$-0.714145\pi$
$739$	−33.8797	−1.24629	−0.623143	+	0.782108i	$0.714145\pi$
$740$	25.7381	0.946152
$741$	0.849500	0.0312071
$742$	0	0
$743$	27.4005	1.00523	0.502613	−	0.864511i	$-0.332372\pi$
$743$	27.4005	1.00523	0.502613	+	0.864511i	$0.332372\pi$
$744$	−25.6115	−0.938963
$745$	−1.09576	−0.0401457
$746$	−20.0975	−0.735823
$747$	5.66269	0.207187
$748$	−33.3744	−1.22029
$749$	0	0
$750$	19.3241	0.705616
$751$	−48.6440	−1.77505	−0.887523	−	0.460764i	$-0.847576\pi$
$751$	−48.6440	−1.77505	−0.887523	+	0.460764i	$0.847576\pi$
$752$	49.0425	1.78840
$753$	9.85728	0.359219
$754$	29.0819	1.05910
$755$	−4.96049	−0.180531
$756$	0	0
$757$	41.4199	1.50543	0.752717	−	0.658345i	$-0.228743\pi$
$757$	41.4199	1.50543	0.752717	+	0.658345i	$0.228743\pi$
$758$	−33.9900	−1.23457
$759$	−9.91831	−0.360012
$760$	1.24403	0.0451259
$761$	−26.6605	−0.966443	−0.483221	−	0.875498i	$-0.660533\pi$
$761$	−26.6605	−0.966443	−0.483221	+	0.875498i	$0.660533\pi$
$762$	−25.8014	−0.934687
$763$	0	0
$764$	20.2893	0.734041
$765$	3.17835	0.114913
$766$	−60.5896	−2.18919
$767$	−23.9260	−0.863918
$768$	−23.1033	−0.833668
$769$	4.67995	0.168763	0.0843817	−	0.996434i	$-0.473108\pi$
$769$	4.67995	0.168763	0.0843817	+	0.996434i	$0.473108\pi$
$770$	0	0
$771$	9.38566	0.338016
$772$	88.1082	3.17108
$773$	−22.0136	−0.791774	−0.395887	−	0.918299i	$-0.629563\pi$
$773$	−22.0136	−0.791774	−0.395887	+	0.918299i	$0.629563\pi$
$774$	−9.42519	−0.338781
$775$	−16.1500	−0.580124
$776$	6.10982	0.219330
$777$	0	0
$778$	−75.5015	−2.70686
$779$	−0.225138	−0.00806641
$780$	−14.0970	−0.504753
$781$	−13.4395	−0.480904
$782$	−56.8584	−2.03325
$783$	2.98276	0.106595
$784$	0	0
$785$	8.77917	0.313342
$786$	−52.4897	−1.87225
$787$	3.76492	0.134205	0.0671024	−	0.997746i	$-0.478625\pi$
$787$	3.76492	0.134205	0.0671024	+	0.997746i	$0.478625\pi$
$788$	109.162	3.88874
$789$	−7.08960	−0.252396
$790$	0.242556	0.00862975
$791$	0	0
$792$	12.4059	0.440825
$793$	29.5254	1.04848
$794$	56.1172	1.99153
$795$	−8.17845	−0.290060
$796$	−123.220	−4.36741
$797$	45.2886	1.60421	0.802103	−	0.597186i	$-0.203715\pi$
$797$	45.2886	1.60421	0.802103	+	0.597186i	$0.203715\pi$
$798$	0	0
$799$	22.9020	0.810215
$800$	35.6878	1.26175
$801$	−2.28446	−0.0807174
$802$	−71.0838	−2.51006
$803$	25.9281	0.914981
$804$	−18.1984	−0.641809
$805$	0	0
$806$	36.0995	1.27155
$807$	2.37006	0.0834300
$808$	28.3445	0.997155
$809$	8.72459	0.306740	0.153370	−	0.988169i	$-0.450987\pi$
$809$	8.72459	0.306740	0.153370	+	0.988169i	$0.450987\pi$
$810$	−2.06412	−0.0725259
$811$	−2.02312	−0.0710415	−0.0355207	−	0.999369i	$-0.511309\pi$
$811$	−2.02312	−0.0710415	−0.0355207	+	0.999369i	$0.511309\pi$
$812$	0	0
$813$	25.9789	0.911121
$814$	31.9261	1.11901
$815$	10.2522	0.359117
$816$	33.9009	1.18677
$817$	−0.821199	−0.0287301
$818$	−63.3241	−2.21408
$819$	0	0
$820$	3.73604	0.130468
$821$	32.9480	1.14989	0.574946	−	0.818191i	$-0.305023\pi$
$821$	32.9480	1.14989	0.574946	+	0.818191i	$0.305023\pi$
$822$	−22.0575	−0.769344
$823$	39.2922	1.36964	0.684820	−	0.728712i	$-0.259881\pi$
$823$	39.2922	1.36964	0.684820	+	0.728712i	$0.259881\pi$
$824$	25.9955	0.905598
$825$	7.82286	0.272357
$826$	0	0
$827$	−12.5928	−0.437893	−0.218947	−	0.975737i	$-0.570262\pi$
$827$	−12.5928	−0.437893	−0.218947	+	0.975737i	$0.570262\pi$
$828$	25.8651	0.898875
$829$	−53.1252	−1.84512	−0.922558	−	0.385859i	$-0.873905\pi$
$829$	−53.1252	−1.84512	−0.922558	+	0.385859i	$0.873905\pi$
$830$	−11.6885	−0.405713
$831$	−19.0352	−0.660323
$832$	−15.4734	−0.536445
$833$	0	0
$834$	−1.58505	−0.0548859
$835$	−1.58200	−0.0547472
$836$	1.88845	0.0653136
$837$	3.70251	0.127977
$838$	26.0269	0.899085
$839$	−40.9155	−1.41256	−0.706279	−	0.707933i	$-0.749628\pi$
$839$	−40.9155	−1.41256	−0.706279	+	0.707933i	$0.749628\pi$
$840$	0	0
$841$	−20.1031	−0.693212
$842$	−32.0668	−1.10510
$843$	4.58121	0.157785
$844$	3.52995	0.121506
$845$	0.988377	0.0340012
$846$	−14.8733	−0.511355
$847$	0	0
$848$	−87.2331	−2.99560
$849$	−9.25972	−0.317793
$850$	44.8459	1.53820
$851$	38.0989	1.30601
$852$	35.0478	1.20072
$853$	55.1504	1.88831	0.944157	−	0.329497i	$-0.106879\pi$
$853$	55.1504	1.88831	0.944157	+	0.329497i	$0.106879\pi$
$854$	0	0
$855$	−0.179843	−0.00615051
$856$	29.2401	0.999407
$857$	−27.2799	−0.931863	−0.465931	−	0.884821i	$-0.654281\pi$
$857$	−27.2799	−0.931863	−0.465931	+	0.884821i	$0.654281\pi$
$858$	−17.4862	−0.596968
$859$	−14.3493	−0.489592	−0.244796	−	0.969575i	$-0.578721\pi$
$859$	−14.3493	−0.489592	−0.244796	+	0.969575i	$0.578721\pi$
$860$	13.6273	0.464689
$861$	0	0
$862$	43.8015	1.49189
$863$	46.2324	1.57377	0.786885	−	0.617100i	$-0.211692\pi$
$863$	46.2324	1.57377	0.786885	+	0.617100i	$0.211692\pi$
$864$	−8.18171	−0.278348
$865$	1.95927	0.0666171
$866$	1.99282	0.0677188
$867$	−1.16885	−0.0396963
$868$	0	0
$869$	0.210749	0.00714918
$870$	−6.15678	−0.208735
$871$	14.6819	0.497476
$872$	33.4465	1.13264
$873$	−0.883263	−0.0298939
$874$	3.21727	0.108826
$875$	0	0
$876$	−67.6156	−2.28452
$877$	−14.8051	−0.499932	−0.249966	−	0.968255i	$-0.580419\pi$
$877$	−14.8051	−0.499932	−0.249966	+	0.968255i	$0.580419\pi$
$878$	54.5203	1.83997
$879$	14.7376	0.497088
$880$	−12.2065	−0.411480
$881$	−3.19091	−0.107504	−0.0537522	−	0.998554i	$-0.517118\pi$
$881$	−3.19091	−0.107504	−0.0537522	+	0.998554i	$0.517118\pi$
$882$	0	0
$883$	−5.54532	−0.186615	−0.0933074	−	0.995637i	$-0.529744\pi$
$883$	−5.54532	−0.186615	−0.0933074	+	0.995637i	$0.529744\pi$
$884$	−70.2162	−2.36163
$885$	5.06525	0.170267
$886$	−40.0466	−1.34539
$887$	48.4105	1.62546	0.812732	−	0.582638i	$-0.197979\pi$
$887$	48.4105	1.62546	0.812732	+	0.582638i	$0.197979\pi$
$888$	−47.6544	−1.59918
$889$	0	0
$890$	4.71541	0.158061
$891$	−1.79345	−0.0600830
$892$	83.6441	2.80061
$893$	−1.29589	−0.0433652
$894$	3.54456	0.118548
$895$	13.5791	0.453899
$896$	0	0
$897$	−20.8671	−0.696731
$898$	13.4233	0.447941
$899$	11.0437	0.368328
$900$	−20.4006	−0.680020
$901$	−40.7364	−1.35713
$902$	4.63426	0.154304
$903$	0	0
$904$	7.04818	0.234419
$905$	5.50359	0.182945
$906$	16.0461	0.533097
$907$	29.5080	0.979797	0.489899	−	0.871779i	$-0.337034\pi$
$907$	29.5080	0.979797	0.489899	+	0.871779i	$0.337034\pi$
$908$	−78.6696	−2.61074
$909$	−4.09760	−0.135909
$910$	0	0
$911$	−4.53682	−0.150312	−0.0751558	−	0.997172i	$-0.523945\pi$
$911$	−4.53682	−0.150312	−0.0751558	+	0.997172i	$0.523945\pi$
$912$	−1.91825	−0.0635195
$913$	−10.1558	−0.336107
$914$	−100.173	−3.31342
$915$	−6.25067	−0.206641
$916$	113.933	3.76445
$917$	0	0
$918$	−10.2813	−0.339332
$919$	−43.7804	−1.44418	−0.722091	−	0.691798i	$-0.756819\pi$
$919$	−43.7804	−1.44418	−0.722091	+	0.691798i	$0.756819\pi$
$920$	−30.5584	−1.00748
$921$	−10.9285	−0.360106
$922$	−31.6456	−1.04219
$923$	−28.2753	−0.930693
$924$	0	0
$925$	−30.0497	−0.988029
$926$	−50.7069	−1.66633
$927$	−3.75803	−0.123430
$928$	−24.4041	−0.801104
$929$	33.7361	1.10685	0.553423	−	0.832900i	$-0.313321\pi$
$929$	33.7361	1.10685	0.553423	+	0.832900i	$0.313321\pi$
$930$	−7.64243	−0.250605
$931$	0	0
$932$	111.723	3.65961
$933$	15.7597	0.515951
$934$	−77.2813	−2.52872
$935$	−5.70021	−0.186417
$936$	26.1007	0.853129
$937$	−12.2270	−0.399439	−0.199720	−	0.979853i	$-0.564003\pi$
$937$	−12.2270	−0.399439	−0.199720	+	0.979853i	$0.564003\pi$
$938$	0	0
$939$	20.3002	0.662472
$940$	21.5045	0.701400
$941$	−26.7854	−0.873179	−0.436590	−	0.899661i	$-0.643814\pi$
$941$	−26.7854	−0.873179	−0.436590	+	0.899661i	$0.643814\pi$
$942$	−28.3987	−0.925281
$943$	5.53029	0.180091
$944$	54.0271	1.75843
$945$	0	0
$946$	16.9036	0.549585
$947$	57.7008	1.87503	0.937513	−	0.347951i	$-0.113122\pi$
$947$	57.7008	1.87503	0.937513	+	0.347951i	$0.113122\pi$
$948$	−0.549595	−0.0178500
$949$	54.5499	1.77076
$950$	−2.53755	−0.0823291
$951$	−1.76929	−0.0573733
$952$	0	0
$953$	21.5944	0.699512	0.349756	−	0.936841i	$-0.386265\pi$
$953$	21.5944	0.699512	0.349756	+	0.936841i	$0.386265\pi$
$954$	26.4555	0.856530
$955$	3.46533	0.112136
$956$	−73.3707	−2.37298
$957$	−5.34944	−0.172923
$958$	112.465	3.63359
$959$	0	0
$960$	3.27580	0.105726
$961$	−17.2914	−0.557788
$962$	67.1691	2.16562
$963$	−4.22708	−0.136216
$964$	104.640	3.37021
$965$	15.0485	0.484429
$966$	0	0
$967$	8.88307	0.285660	0.142830	−	0.989747i	$-0.454380\pi$
$967$	8.88307	0.285660	0.142830	+	0.989747i	$0.454380\pi$
$968$	53.8412	1.73052
$969$	−0.895788	−0.0287769
$970$	1.82316	0.0585383
$971$	−41.5535	−1.33352	−0.666758	−	0.745274i	$-0.732318\pi$
$971$	−41.5535	−1.33352	−0.666758	+	0.745274i	$0.732318\pi$
$972$	4.67700	0.150015
$973$	0	0
$974$	−98.3027	−3.14982
$975$	16.4585	0.527093
$976$	−66.6710	−2.13409
$977$	29.3250	0.938191	0.469095	−	0.883148i	$-0.344580\pi$
$977$	29.3250	0.938191	0.469095	+	0.883148i	$0.344580\pi$
$978$	−33.1635	−1.06045
$979$	4.09707	0.130943
$980$	0	0
$981$	−4.83517	−0.154375
$982$	8.94837	0.285554
$983$	6.38836	0.203757	0.101878	−	0.994797i	$-0.467515\pi$
$983$	6.38836	0.203757	0.101878	+	0.994797i	$0.467515\pi$
$984$	−6.91733	−0.220516
$985$	18.6445	0.594062
$986$	−30.6666	−0.976623
$987$	0	0
$988$	3.97311	0.126401
$989$	20.1719	0.641429
$990$	3.70191	0.117654
$991$	−10.8483	−0.344607	−0.172303	−	0.985044i	$-0.555121\pi$
$991$	−10.8483	−0.344607	−0.172303	+	0.985044i	$0.555121\pi$
$992$	−30.2929	−0.961800
$993$	8.23405	0.261300
$994$	0	0
$995$	−21.0454	−0.667185
$996$	26.4844	0.839190
$997$	10.7429	0.340231	0.170116	−	0.985424i	$-0.445586\pi$
$997$	10.7429	0.340231	0.170116	+	0.985424i	$0.445586\pi$
$998$	−57.1289	−1.80838
$999$	6.88914	0.217963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.be.1.1	yes	10
7.6	odd	2		6027.2.a.bd.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bd.1.1	✓	10	7.6	odd	2
6027.2.a.be.1.1	yes	10	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58399 q^{2} +1.00000 q^{3} +4.67700 q^{4} +0.798812 q^{5} -2.58399 q^{6} -6.91733 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58399 q^{2} +1.00000 q^{3} +4.67700 q^{4} +0.798812 q^{5} -2.58399 q^{6} -6.91733 q^{8} +1.00000 q^{9} -2.06412 q^{10} -1.79345 q^{11} +4.67700 q^{12} -3.77324 q^{13} +0.798812 q^{15} +8.52031 q^{16} +3.97884 q^{17} -2.58399 q^{18} -0.225138 q^{19} +3.73604 q^{20} +4.63426 q^{22} +5.53029 q^{23} -6.91733 q^{24} -4.36190 q^{25} +9.75000 q^{26} +1.00000 q^{27} +2.98276 q^{29} -2.06412 q^{30} +3.70251 q^{31} -8.18171 q^{32} -1.79345 q^{33} -10.2813 q^{34} +4.67700 q^{36} +6.88914 q^{37} +0.581755 q^{38} -3.77324 q^{39} -5.52565 q^{40} +1.00000 q^{41} +3.64753 q^{43} -8.38798 q^{44} +0.798812 q^{45} -14.2902 q^{46} +5.75596 q^{47} +8.52031 q^{48} +11.2711 q^{50} +3.97884 q^{51} -17.6474 q^{52} -10.2383 q^{53} -2.58399 q^{54} -1.43263 q^{55} -0.225138 q^{57} -7.70742 q^{58} +6.34098 q^{59} +3.73604 q^{60} -7.82495 q^{61} -9.56724 q^{62} +4.10084 q^{64} -3.01411 q^{65} +4.63426 q^{66} -3.89105 q^{67} +18.6090 q^{68} +5.53029 q^{69} +7.49365 q^{71} -6.91733 q^{72} -14.4571 q^{73} -17.8015 q^{74} -4.36190 q^{75} -1.05297 q^{76} +9.75000 q^{78} -0.117510 q^{79} +6.80613 q^{80} +1.00000 q^{81} -2.58399 q^{82} +5.66269 q^{83} +3.17835 q^{85} -9.42519 q^{86} +2.98276 q^{87} +12.4059 q^{88} -2.28446 q^{89} -2.06412 q^{90} +25.8651 q^{92} +3.70251 q^{93} -14.8733 q^{94} -0.179843 q^{95} -8.18171 q^{96} -0.883263 q^{97} -1.79345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more