LMFDB - Embedded newform 6027.2.a.ba.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:	$1$
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} - 2x^{7} - 8x^{6} + 14x^{5} + 18x^{4} - 24x^{3} - 10x^{2} + 10x - 1 $ x^8 - 2x^7 - 8x^6 + 14x^5 + 18x^4 - 24x^3 - 10x^2 + 10*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.39346$ 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)

$f(q)$	$=$	$q-2.39346 q^{2} +1.00000 q^{3} +3.72866 q^{4} +2.51820 q^{5} -2.39346 q^{6} -4.13748 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.39346 q^{2} +1.00000 q^{3} +3.72866 q^{4} +2.51820 q^{5} -2.39346 q^{6} -4.13748 q^{8} +1.00000 q^{9} -6.02722 q^{10} +5.25918 q^{11} +3.72866 q^{12} +0.497250 q^{13} +2.51820 q^{15} +2.44558 q^{16} -7.20978 q^{17} -2.39346 q^{18} -5.61255 q^{19} +9.38952 q^{20} -12.5877 q^{22} -4.64090 q^{23} -4.13748 q^{24} +1.34134 q^{25} -1.19015 q^{26} +1.00000 q^{27} +2.78973 q^{29} -6.02722 q^{30} +5.51517 q^{31} +2.42156 q^{32} +5.25918 q^{33} +17.2563 q^{34} +3.72866 q^{36} -9.17233 q^{37} +13.4334 q^{38} +0.497250 q^{39} -10.4190 q^{40} -1.00000 q^{41} -11.4053 q^{43} +19.6097 q^{44} +2.51820 q^{45} +11.1078 q^{46} -8.72055 q^{47} +2.44558 q^{48} -3.21046 q^{50} -7.20978 q^{51} +1.85408 q^{52} -10.5938 q^{53} -2.39346 q^{54} +13.2437 q^{55} -5.61255 q^{57} -6.67711 q^{58} -1.20856 q^{59} +9.38952 q^{60} +9.52693 q^{61} -13.2003 q^{62} -10.6871 q^{64} +1.25218 q^{65} -12.5877 q^{66} -4.94710 q^{67} -26.8828 q^{68} -4.64090 q^{69} -5.28897 q^{71} -4.13748 q^{72} +0.0721771 q^{73} +21.9536 q^{74} +1.34134 q^{75} -20.9273 q^{76} -1.19015 q^{78} +7.85274 q^{79} +6.15846 q^{80} +1.00000 q^{81} +2.39346 q^{82} -9.86047 q^{83} -18.1557 q^{85} +27.2982 q^{86} +2.78973 q^{87} -21.7598 q^{88} -15.8029 q^{89} -6.02722 q^{90} -17.3043 q^{92} +5.51517 q^{93} +20.8723 q^{94} -14.1335 q^{95} +2.42156 q^{96} -5.21641 q^{97} +5.25918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 4 q^{13} - 2 q^{15} - 8 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{20} - 14 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} - 4 q^{29} + 2 q^{30} + 10 q^{31} - 4 q^{32} - 2 q^{33} - 4 q^{34} + 4 q^{36} - 20 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 8 q^{41} - 8 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 24 q^{47} - 22 q^{50} - 8 q^{51} + 30 q^{52} - 36 q^{53} - 2 q^{54} - 4 q^{55} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 4 q^{60} + 22 q^{61} - 30 q^{62} - 24 q^{64} + 8 q^{65} - 14 q^{66} - 14 q^{67} - 38 q^{68} - 12 q^{69} - 10 q^{71} - 6 q^{72} + 12 q^{73} - 2 q^{74} - 4 q^{75} - 32 q^{76} - 4 q^{78} + 16 q^{79} + 14 q^{80} + 8 q^{81} + 2 q^{82} - 24 q^{83} - 44 q^{85} + 36 q^{86} - 4 q^{87} - 34 q^{88} - 2 q^{89} + 2 q^{90} - 48 q^{92} + 10 q^{93} + 34 q^{94} - 24 q^{95} - 4 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 - 4 * q^13 - 2 * q^15 - 8 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^20 - 14 * q^22 - 12 * q^23 - 6 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 - 4 * q^29 + 2 * q^30 + 10 * q^31 - 4 * q^32 - 2 * q^33 - 4 * q^34 + 4 * q^36 - 20 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 8 * q^41 - 8 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 24 * q^47 - 22 * q^50 - 8 * q^51 + 30 * q^52 - 36 * q^53 - 2 * q^54 - 4 * q^55 - 6 * q^57 + 14 * q^58 - 10 * q^59 - 4 * q^60 + 22 * q^61 - 30 * q^62 - 24 * q^64 + 8 * q^65 - 14 * q^66 - 14 * q^67 - 38 * q^68 - 12 * q^69 - 10 * q^71 - 6 * q^72 + 12 * q^73 - 2 * q^74 - 4 * q^75 - 32 * q^76 - 4 * q^78 + 16 * q^79 + 14 * q^80 + 8 * q^81 + 2 * q^82 - 24 * q^83 - 44 * q^85 + 36 * q^86 - 4 * q^87 - 34 * q^88 - 2 * q^89 + 2 * q^90 - 48 * q^92 + 10 * q^93 + 34 * q^94 - 24 * q^95 - 4 * 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 $

$2$	−2.39346	−1.69243	−0.846216	−	0.532839i	$-0.821125\pi$
$2$	−2.39346	−1.69243	−0.846216	+	0.532839i	$0.821125\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.72866	1.86433
$5$	2.51820	1.12617	0.563087	−	0.826397i	$-0.309614\pi$
$5$	2.51820	1.12617	0.563087	+	0.826397i	$0.309614\pi$
$6$	−2.39346	−0.977127
$7$	0	0
$7$	0	0
$8$	−4.13748	−1.46282
$9$	1.00000	0.333333
$10$	−6.02722	−1.90597
$11$	5.25918	1.58570	0.792852	−	0.609415i	$-0.208596\pi$
$11$	5.25918	1.58570	0.792852	+	0.609415i	$0.208596\pi$
$12$	3.72866	1.07637
$13$	0.497250	0.137912	0.0689562	−	0.997620i	$-0.478033\pi$
$13$	0.497250	0.137912	0.0689562	+	0.997620i	$0.478033\pi$
$14$	0	0
$15$	2.51820	0.650197
$16$	2.44558	0.611395
$17$	−7.20978	−1.74863	−0.874314	−	0.485360i	$-0.838688\pi$
$17$	−7.20978	−1.74863	−0.874314	+	0.485360i	$0.838688\pi$
$18$	−2.39346	−0.564144
$19$	−5.61255	−1.28761	−0.643804	−	0.765191i	$-0.722645\pi$
$19$	−5.61255	−1.28761	−0.643804	+	0.765191i	$0.722645\pi$
$20$	9.38952	2.09956
$21$	0	0
$22$	−12.5877	−2.68370
$23$	−4.64090	−0.967695	−0.483848	−	0.875152i	$-0.660761\pi$
$23$	−4.64090	−0.967695	−0.483848	+	0.875152i	$0.660761\pi$
$24$	−4.13748	−0.844559
$25$	1.34134	0.268269
$26$	−1.19015	−0.233407
$27$	1.00000	0.192450
$28$	0	0
$29$	2.78973	0.518040	0.259020	−	0.965872i	$-0.416600\pi$
$29$	2.78973	0.518040	0.259020	+	0.965872i	$0.416600\pi$
$30$	−6.02722	−1.10042
$31$	5.51517	0.990553	0.495277	−	0.868735i	$-0.335067\pi$
$31$	5.51517	0.990553	0.495277	+	0.868735i	$0.335067\pi$
$32$	2.42156	0.428075
$33$	5.25918	0.915506
$34$	17.2563	2.95944
$35$	0	0
$36$	3.72866	0.621443
$37$	−9.17233	−1.50792	−0.753961	−	0.656919i	$-0.771859\pi$
$37$	−9.17233	−1.50792	−0.753961	+	0.656919i	$0.771859\pi$
$38$	13.4334	2.17919
$39$	0.497250	0.0796237
$40$	−10.4190	−1.64739
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−11.4053	−1.73930	−0.869648	−	0.493673i	$-0.835654\pi$
$43$	−11.4053	−1.73930	−0.869648	+	0.493673i	$0.835654\pi$
$44$	19.6097	2.95627
$45$	2.51820	0.375391
$46$	11.1078	1.63776
$47$	−8.72055	−1.27202	−0.636011	−	0.771680i	$-0.719417\pi$
$47$	−8.72055	−1.27202	−0.636011	+	0.771680i	$0.719417\pi$
$48$	2.44558	0.352989
$49$	0	0
$50$	−3.21046	−0.454027
$51$	−7.20978	−1.00957
$52$	1.85408	0.257114
$53$	−10.5938	−1.45518	−0.727588	−	0.686014i	$-0.759359\pi$
$53$	−10.5938	−1.45518	−0.727588	+	0.686014i	$0.759359\pi$
$54$	−2.39346	−0.325709
$55$	13.2437	1.78578
$56$	0	0
$57$	−5.61255	−0.743400
$58$	−6.67711	−0.876747
$59$	−1.20856	−0.157341	−0.0786707	−	0.996901i	$-0.525068\pi$
$59$	−1.20856	−0.157341	−0.0786707	+	0.996901i	$0.525068\pi$
$60$	9.38952	1.21218
$61$	9.52693	1.21980	0.609900	−	0.792479i	$-0.291210\pi$
$61$	9.52693	1.21980	0.609900	+	0.792479i	$0.291210\pi$
$62$	−13.2003	−1.67644
$63$	0	0
$64$	−10.6871	−1.33588
$65$	1.25218	0.155313
$66$	−12.5877	−1.54943
$67$	−4.94710	−0.604384	−0.302192	−	0.953247i	$-0.597718\pi$
$67$	−4.94710	−0.604384	−0.302192	+	0.953247i	$0.597718\pi$
$68$	−26.8828	−3.26002
$69$	−4.64090	−0.558699
$70$	0	0
$71$	−5.28897	−0.627685	−0.313843	−	0.949475i	$-0.601616\pi$
$71$	−5.28897	−0.627685	−0.313843	+	0.949475i	$0.601616\pi$
$72$	−4.13748	−0.487607
$73$	0.0721771	0.00844769	0.00422385	−	0.999991i	$-0.498656\pi$
$73$	0.0721771	0.00844769	0.00422385	+	0.999991i	$0.498656\pi$
$74$	21.9536	2.55206
$75$	1.34134	0.154885
$76$	−20.9273	−2.40052
$77$	0	0
$78$	−1.19015	−0.134758
$79$	7.85274	0.883503	0.441751	−	0.897138i	$-0.354357\pi$
$79$	7.85274	0.883503	0.441751	+	0.897138i	$0.354357\pi$
$80$	6.15846	0.688537
$81$	1.00000	0.111111
$82$	2.39346	0.264314
$83$	−9.86047	−1.08233	−0.541164	−	0.840917i	$-0.682016\pi$
$83$	−9.86047	−1.08233	−0.541164	+	0.840917i	$0.682016\pi$
$84$	0	0
$85$	−18.1557	−1.96926
$86$	27.2982	2.94364
$87$	2.78973	0.299090
$88$	−21.7598	−2.31960
$89$	−15.8029	−1.67511	−0.837553	−	0.546356i	$-0.816014\pi$
$89$	−15.8029	−1.67511	−0.837553	+	0.546356i	$0.816014\pi$
$90$	−6.02722	−0.635325
$91$	0	0
$92$	−17.3043	−1.80410
$93$	5.51517	0.571896
$94$	20.8723	2.15281
$95$	−14.1335	−1.45007
$96$	2.42156	0.247149
$97$	−5.21641	−0.529647	−0.264823	−	0.964297i	$-0.585314\pi$
$97$	−5.21641	−0.529647	−0.264823	+	0.964297i	$0.585314\pi$
$98$	0	0
$99$	5.25918	0.528568
$100$	5.00142	0.500142
$101$	6.88021	0.684606	0.342303	−	0.939590i	$-0.388793\pi$
$101$	6.88021	0.684606	0.342303	+	0.939590i	$0.388793\pi$
$102$	17.2563	1.70863
$103$	4.06158	0.400200	0.200100	−	0.979776i	$-0.435873\pi$
$103$	4.06158	0.400200	0.200100	+	0.979776i	$0.435873\pi$
$104$	−2.05736	−0.201741
$105$	0	0
$106$	25.3560	2.46279
$107$	−14.1186	−1.36489	−0.682447	−	0.730935i	$-0.739084\pi$
$107$	−14.1186	−1.36489	−0.682447	+	0.730935i	$0.739084\pi$
$108$	3.72866	0.358790
$109$	5.39356	0.516609	0.258304	−	0.966064i	$-0.416836\pi$
$109$	5.39356	0.516609	0.258304	+	0.966064i	$0.416836\pi$
$110$	−31.6983	−3.02231
$111$	−9.17233	−0.870599
$112$	0	0
$113$	−16.6666	−1.56786	−0.783932	−	0.620846i	$-0.786789\pi$
$113$	−16.6666	−1.56786	−0.783932	+	0.620846i	$0.786789\pi$
$114$	13.4334	1.25816
$115$	−11.6867	−1.08979
$116$	10.4019	0.965797
$117$	0.497250	0.0459708
$118$	2.89265	0.266290
$119$	0	0
$120$	−10.4190	−0.951121
$121$	16.6590	1.51446
$122$	−22.8024	−2.06443
$123$	−1.00000	−0.0901670
$124$	20.5642	1.84672
$125$	−9.21324	−0.824057
$126$	0	0
$127$	−8.08043	−0.717023	−0.358511	−	0.933525i	$-0.616716\pi$
$127$	−8.08043	−0.717023	−0.358511	+	0.933525i	$0.616716\pi$
$128$	20.7360	1.83282
$129$	−11.4053	−1.00418
$130$	−2.99704	−0.262857
$131$	−0.687445	−0.0600624	−0.0300312	−	0.999549i	$-0.509561\pi$
$131$	−0.687445	−0.0600624	−0.0300312	+	0.999549i	$0.509561\pi$
$132$	19.6097	1.70681
$133$	0	0
$134$	11.8407	1.02288
$135$	2.51820	0.216732
$136$	29.8303	2.55793
$137$	14.0142	1.19731	0.598655	−	0.801007i	$-0.295702\pi$
$137$	14.0142	1.19731	0.598655	+	0.801007i	$0.295702\pi$
$138$	11.1078	0.945561
$139$	0.130705	0.0110862	0.00554312	−	0.999985i	$-0.498236\pi$
$139$	0.130705	0.0110862	0.00554312	+	0.999985i	$0.498236\pi$
$140$	0	0
$141$	−8.72055	−0.734403
$142$	12.6589	1.06231
$143$	2.61513	0.218688
$144$	2.44558	0.203798
$145$	7.02510	0.583403
$146$	−0.172753	−0.0142972
$147$	0	0
$148$	−34.2005	−2.81126
$149$	−15.7438	−1.28978	−0.644891	−	0.764275i	$-0.723097\pi$
$149$	−15.7438	−1.28978	−0.644891	+	0.764275i	$0.723097\pi$
$150$	−3.21046	−0.262133
$151$	16.9699	1.38099	0.690496	−	0.723336i	$-0.257392\pi$
$151$	16.9699	1.38099	0.690496	+	0.723336i	$0.257392\pi$
$152$	23.2218	1.88354
$153$	−7.20978	−0.582876
$154$	0	0
$155$	13.8883	1.11554
$156$	1.85408	0.148445
$157$	−14.7623	−1.17816	−0.589081	−	0.808074i	$-0.700510\pi$
$157$	−14.7623	−1.17816	−0.589081	+	0.808074i	$0.700510\pi$
$158$	−18.7952	−1.49527
$159$	−10.5938	−0.840146
$160$	6.09797	0.482087
$161$	0	0
$162$	−2.39346	−0.188048
$163$	10.8608	0.850681	0.425340	−	0.905033i	$-0.360154\pi$
$163$	10.8608	0.850681	0.425340	+	0.905033i	$0.360154\pi$
$164$	−3.72866	−0.291159
$165$	13.2437	1.03102
$166$	23.6007	1.83177
$167$	13.7966	1.06761	0.533807	−	0.845607i	$-0.320761\pi$
$167$	13.7966	1.06761	0.533807	+	0.845607i	$0.320761\pi$
$168$	0	0
$169$	−12.7527	−0.980980
$170$	43.4549	3.33284
$171$	−5.61255	−0.429202
$172$	−42.5266	−3.24262
$173$	21.1538	1.60829	0.804146	−	0.594432i	$-0.202623\pi$
$173$	21.1538	1.60829	0.804146	+	0.594432i	$0.202623\pi$
$174$	−6.67711	−0.506190
$175$	0	0
$176$	12.8617	0.969491
$177$	−1.20856	−0.0908411
$178$	37.8237	2.83500
$179$	−15.7738	−1.17899	−0.589496	−	0.807772i	$-0.700673\pi$
$179$	−15.7738	−1.17899	−0.589496	+	0.807772i	$0.700673\pi$
$180$	9.38952	0.699853
$181$	−4.14541	−0.308126	−0.154063	−	0.988061i	$-0.549236\pi$
$181$	−4.14541	−0.308126	−0.154063	+	0.988061i	$0.549236\pi$
$182$	0	0
$183$	9.52693	0.704251
$184$	19.2016	1.41556
$185$	−23.0978	−1.69818
$186$	−13.2003	−0.967896
$187$	−37.9176	−2.77281
$188$	−32.5160	−2.37147
$189$	0	0
$190$	33.8281	2.45415
$191$	−11.7296	−0.848727	−0.424363	−	0.905492i	$-0.639502\pi$
$191$	−11.7296	−0.848727	−0.424363	+	0.905492i	$0.639502\pi$
$192$	−10.6871	−0.771272
$193$	−1.58800	−0.114307	−0.0571533	−	0.998365i	$-0.518202\pi$
$193$	−1.58800	−0.114307	−0.0571533	+	0.998365i	$0.518202\pi$
$194$	12.4853	0.896391
$195$	1.25218	0.0896702
$196$	0	0
$197$	9.03301	0.643576	0.321788	−	0.946812i	$-0.395716\pi$
$197$	9.03301	0.643576	0.321788	+	0.946812i	$0.395716\pi$
$198$	−12.5877	−0.894566
$199$	−4.76713	−0.337933	−0.168966	−	0.985622i	$-0.554043\pi$
$199$	−4.76713	−0.337933	−0.168966	+	0.985622i	$0.554043\pi$
$200$	−5.54978	−0.392429
$201$	−4.94710	−0.348941
$202$	−16.4675	−1.15865
$203$	0	0
$204$	−26.8828	−1.88217
$205$	−2.51820	−0.175879
$206$	−9.72124	−0.677311
$207$	−4.64090	−0.322565
$208$	1.21606	0.0843189
$209$	−29.5174	−2.04176
$210$	0	0
$211$	−16.2495	−1.11866	−0.559331	−	0.828944i	$-0.688942\pi$
$211$	−16.2495	−1.11866	−0.559331	+	0.828944i	$0.688942\pi$
$212$	−39.5008	−2.71293
$213$	−5.28897	−0.362394
$214$	33.7923	2.30999
$215$	−28.7209	−1.95875
$216$	−4.13748	−0.281520
$217$	0	0
$218$	−12.9093	−0.874326
$219$	0.0721771	0.00487728
$220$	49.3812	3.32928
$221$	−3.58506	−0.241157
$222$	21.9536	1.47343
$223$	20.7357	1.38857	0.694283	−	0.719702i	$-0.255722\pi$
$223$	20.7357	1.38857	0.694283	+	0.719702i	$0.255722\pi$
$224$	0	0
$225$	1.34134	0.0894230
$226$	39.8909	2.65351
$227$	7.73757	0.513560	0.256780	−	0.966470i	$-0.417338\pi$
$227$	7.73757	0.513560	0.256780	+	0.966470i	$0.417338\pi$
$228$	−20.9273	−1.38594
$229$	23.1868	1.53223	0.766115	−	0.642704i	$-0.222187\pi$
$229$	23.1868	1.53223	0.766115	+	0.642704i	$0.222187\pi$
$230$	27.9718	1.84440
$231$	0	0
$232$	−11.5424	−0.757799
$233$	−0.659793	−0.0432245	−0.0216122	−	0.999766i	$-0.506880\pi$
$233$	−0.659793	−0.0432245	−0.0216122	+	0.999766i	$0.506880\pi$
$234$	−1.19015	−0.0778025
$235$	−21.9601	−1.43252
$236$	−4.50632	−0.293336
$237$	7.85274	0.510091
$238$	0	0
$239$	5.00053	0.323457	0.161729	−	0.986835i	$-0.448293\pi$
$239$	5.00053	0.323457	0.161729	+	0.986835i	$0.448293\pi$
$240$	6.15846	0.397527
$241$	11.4412	0.736993	0.368497	−	0.929629i	$-0.379873\pi$
$241$	11.4412	0.736993	0.368497	+	0.929629i	$0.379873\pi$
$242$	−39.8727	−2.56311
$243$	1.00000	0.0641500
$244$	35.5227	2.27411
$245$	0	0
$246$	2.39346	0.152602
$247$	−2.79084	−0.177577
$248$	−22.8189	−1.44900
$249$	−9.86047	−0.624882
$250$	22.0515	1.39466
$251$	−25.3274	−1.59865	−0.799325	−	0.600899i	$-0.794809\pi$
$251$	−25.3274	−1.59865	−0.799325	+	0.600899i	$0.794809\pi$
$252$	0	0
$253$	−24.4074	−1.53448
$254$	19.3402	1.21351
$255$	−18.1557	−1.13695
$256$	−28.2566	−1.76604
$257$	−0.971771	−0.0606174	−0.0303087	−	0.999541i	$-0.509649\pi$
$257$	−0.971771	−0.0606174	−0.0303087	+	0.999541i	$0.509649\pi$
$258$	27.2982	1.69951
$259$	0	0
$260$	4.66894	0.289555
$261$	2.78973	0.172680
$262$	1.64537	0.101652
$263$	27.8674	1.71838	0.859189	−	0.511659i	$-0.170969\pi$
$263$	27.8674	1.71838	0.859189	+	0.511659i	$0.170969\pi$
$264$	−21.7598	−1.33922
$265$	−26.6774	−1.63878
$266$	0	0
$267$	−15.8029	−0.967123
$268$	−18.4460	−1.12677
$269$	−16.1446	−0.984352	−0.492176	−	0.870496i	$-0.663798\pi$
$269$	−16.1446	−0.984352	−0.492176	+	0.870496i	$0.663798\pi$
$270$	−6.02722	−0.366805
$271$	6.35019	0.385747	0.192873	−	0.981224i	$-0.438219\pi$
$271$	6.35019	0.385747	0.192873	+	0.981224i	$0.438219\pi$
$272$	−17.6321	−1.06910
$273$	0	0
$274$	−33.5424	−2.02637
$275$	7.05438	0.425395
$276$	−17.3043	−1.04160
$277$	22.1536	1.33108	0.665540	−	0.746362i	$-0.268201\pi$
$277$	22.1536	1.33108	0.665540	+	0.746362i	$0.268201\pi$
$278$	−0.312837	−0.0187627
$279$	5.51517	0.330184
$280$	0	0
$281$	−6.22779	−0.371519	−0.185759	−	0.982595i	$-0.559474\pi$
$281$	−6.22779	−0.371519	−0.185759	+	0.982595i	$0.559474\pi$
$282$	20.8723	1.24293
$283$	8.46365	0.503112	0.251556	−	0.967843i	$-0.419058\pi$
$283$	8.46365	0.503112	0.251556	+	0.967843i	$0.419058\pi$
$284$	−19.7208	−1.17021
$285$	−14.1335	−0.837198
$286$	−6.25921	−0.370115
$287$	0	0
$288$	2.42156	0.142692
$289$	34.9809	2.05770
$290$	−16.8143	−0.987371
$291$	−5.21641	−0.305792
$292$	0.269124	0.0157493
$293$	−0.387257	−0.0226238	−0.0113119	−	0.999936i	$-0.503601\pi$
$293$	−0.387257	−0.0226238	−0.0113119	+	0.999936i	$0.503601\pi$
$294$	0	0
$295$	−3.04340	−0.177194
$296$	37.9503	2.20582
$297$	5.25918	0.305169
$298$	37.6822	2.18287
$299$	−2.30769	−0.133457
$300$	5.00142	0.288757
$301$	0	0
$302$	−40.6169	−2.33724
$303$	6.88021	0.395258
$304$	−13.7259	−0.787236
$305$	23.9908	1.37371
$306$	17.2563	0.986479
$307$	32.8283	1.87361	0.936806	−	0.349849i	$-0.113767\pi$
$307$	32.8283	1.87361	0.936806	+	0.349849i	$0.113767\pi$
$308$	0	0
$309$	4.06158	0.231055
$310$	−33.2411	−1.88797
$311$	31.0785	1.76230	0.881149	−	0.472839i	$-0.156771\pi$
$311$	31.0785	1.76230	0.881149	+	0.472839i	$0.156771\pi$
$312$	−2.05736	−0.116475
$313$	0.922696	0.0521539	0.0260769	−	0.999660i	$-0.491699\pi$
$313$	0.922696	0.0521539	0.0260769	+	0.999660i	$0.491699\pi$
$314$	35.3331	1.99396
$315$	0	0
$316$	29.2802	1.64714
$317$	13.0974	0.735626	0.367813	−	0.929900i	$-0.380107\pi$
$317$	13.0974	0.735626	0.367813	+	0.929900i	$0.380107\pi$
$318$	25.3560	1.42189
$319$	14.6717	0.821457
$320$	−26.9122	−1.50444
$321$	−14.1186	−0.788022
$322$	0	0
$323$	40.4652	2.25155
$324$	3.72866	0.207148
$325$	0.666983	0.0369976
$326$	−25.9948	−1.43972
$327$	5.39356	0.298264
$328$	4.13748	0.228454
$329$	0	0
$330$	−31.6983	−1.74493
$331$	−0.599497	−0.0329513	−0.0164757	−	0.999864i	$-0.505245\pi$
$331$	−0.599497	−0.0329513	−0.0164757	+	0.999864i	$0.505245\pi$
$332$	−36.7663	−2.01781
$333$	−9.17233	−0.502641
$334$	−33.0216	−1.80686
$335$	−12.4578	−0.680642
$336$	0	0
$337$	32.7505	1.78403	0.892017	−	0.452003i	$-0.149290\pi$
$337$	32.7505	1.78403	0.892017	+	0.452003i	$0.149290\pi$
$338$	30.5232	1.66024
$339$	−16.6666	−0.905207
$340$	−67.6964	−3.67135
$341$	29.0053	1.57072
$342$	13.4334	0.726396
$343$	0	0
$344$	47.1893	2.54428
$345$	−11.6867	−0.629193
$346$	−50.6307	−2.72193
$347$	15.2913	0.820881	0.410440	−	0.911887i	$-0.365375\pi$
$347$	15.2913	0.820881	0.410440	+	0.911887i	$0.365375\pi$
$348$	10.4019	0.557603
$349$	−13.5287	−0.724177	−0.362089	−	0.932144i	$-0.617936\pi$
$349$	−13.5287	−0.724177	−0.362089	+	0.932144i	$0.617936\pi$
$350$	0	0
$351$	0.497250	0.0265412
$352$	12.7354	0.678800
$353$	24.3569	1.29639	0.648194	−	0.761475i	$-0.275524\pi$
$353$	24.3569	1.29639	0.648194	+	0.761475i	$0.275524\pi$
$354$	2.89265	0.153742
$355$	−13.3187	−0.706883
$356$	−58.9237	−3.12295
$357$	0	0
$358$	37.7540	1.99536
$359$	−24.0430	−1.26894	−0.634471	−	0.772947i	$-0.718782\pi$
$359$	−24.0430	−1.26894	−0.634471	+	0.772947i	$0.718782\pi$
$360$	−10.4190	−0.549130
$361$	12.5007	0.657932
$362$	9.92189	0.521483
$363$	16.6590	0.874371
$364$	0	0
$365$	0.181757	0.00951358
$366$	−22.8024	−1.19190
$367$	−17.4554	−0.911162	−0.455581	−	0.890194i	$-0.650569\pi$
$367$	−17.4554	−0.911162	−0.455581	+	0.890194i	$0.650569\pi$
$368$	−11.3497	−0.591644
$369$	−1.00000	−0.0520579
$370$	55.2837	2.87406
$371$	0	0
$372$	20.5642	1.06620
$373$	−34.3287	−1.77747	−0.888736	−	0.458419i	$-0.848416\pi$
$373$	−34.3287	−1.77747	−0.888736	+	0.458419i	$0.848416\pi$
$374$	90.7542	4.69279
$375$	−9.21324	−0.475769
$376$	36.0811	1.86074
$377$	1.38719	0.0714441
$378$	0	0
$379$	24.6055	1.26390	0.631950	−	0.775009i	$-0.282255\pi$
$379$	24.6055	1.26390	0.631950	+	0.775009i	$0.282255\pi$
$380$	−52.6991	−2.70341
$381$	−8.08043	−0.413973
$382$	28.0744	1.43641
$383$	−3.99256	−0.204010	−0.102005	−	0.994784i	$-0.532526\pi$
$383$	−3.99256	−0.204010	−0.102005	+	0.994784i	$0.532526\pi$
$384$	20.7360	1.05818
$385$	0	0
$386$	3.80081	0.193456
$387$	−11.4053	−0.579765
$388$	−19.4502	−0.987436
$389$	5.50852	0.279293	0.139647	−	0.990201i	$-0.455403\pi$
$389$	5.50852	0.279293	0.139647	+	0.990201i	$0.455403\pi$
$390$	−2.99704	−0.151761
$391$	33.4599	1.69214
$392$	0	0
$393$	−0.687445	−0.0346770
$394$	−21.6202	−1.08921
$395$	19.7748	0.994978
$396$	19.6097	0.985424
$397$	8.65336	0.434300	0.217150	−	0.976138i	$-0.430324\pi$
$397$	8.65336	0.434300	0.217150	+	0.976138i	$0.430324\pi$
$398$	11.4099	0.571928
$399$	0	0
$400$	3.28036	0.164018
$401$	1.91824	0.0957923	0.0478962	−	0.998852i	$-0.484748\pi$
$401$	1.91824	0.0957923	0.0478962	+	0.998852i	$0.484748\pi$
$402$	11.8407	0.590560
$403$	2.74242	0.136609
$404$	25.6540	1.27633
$405$	2.51820	0.125130
$406$	0	0
$407$	−48.2390	−2.39112
$408$	29.8303	1.47682
$409$	35.7749	1.76896	0.884478	−	0.466583i	$-0.154515\pi$
$409$	35.7749	1.76896	0.884478	+	0.466583i	$0.154515\pi$
$410$	6.02722	0.297663
$411$	14.0142	0.691268
$412$	15.1443	0.746104
$413$	0	0
$414$	11.1078	0.545920
$415$	−24.8307	−1.21889
$416$	1.20412	0.0590368
$417$	0.130705	0.00640064
$418$	70.6488	3.45555
$419$	−35.8765	−1.75268	−0.876342	−	0.481690i	$-0.840023\pi$
$419$	−35.8765	−1.75268	−0.876342	+	0.481690i	$0.840023\pi$
$420$	0	0
$421$	27.4895	1.33976	0.669879	−	0.742470i	$-0.266346\pi$
$421$	27.4895	1.33976	0.669879	+	0.742470i	$0.266346\pi$
$422$	38.8926	1.89326
$423$	−8.72055	−0.424008
$424$	43.8318	2.12866
$425$	−9.67080	−0.469103
$426$	12.6589	0.613328
$427$	0	0
$428$	−52.6433	−2.54461
$429$	2.61513	0.126260
$430$	68.7424	3.31505
$431$	27.0955	1.30515	0.652573	−	0.757726i	$-0.273690\pi$
$431$	27.0955	1.30515	0.652573	+	0.757726i	$0.273690\pi$
$432$	2.44558	0.117663
$433$	24.0559	1.15605	0.578026	−	0.816018i	$-0.303823\pi$
$433$	24.0559	1.15605	0.578026	+	0.816018i	$0.303823\pi$
$434$	0	0
$435$	7.02510	0.336828
$436$	20.1107	0.963129
$437$	26.0473	1.24601
$438$	−0.172753	−0.00825447
$439$	21.7513	1.03813	0.519066	−	0.854734i	$-0.326280\pi$
$439$	21.7513	1.03813	0.519066	+	0.854734i	$0.326280\pi$
$440$	−54.7955	−2.61227
$441$	0	0
$442$	8.58071	0.408143
$443$	−16.2083	−0.770079	−0.385040	−	0.922900i	$-0.625812\pi$
$443$	−16.2083	−0.770079	−0.385040	+	0.922900i	$0.625812\pi$
$444$	−34.2005	−1.62308
$445$	−39.7949	−1.88646
$446$	−49.6301	−2.35005
$447$	−15.7438	−0.744656
$448$	0	0
$449$	3.74204	0.176598	0.0882988	−	0.996094i	$-0.471857\pi$
$449$	3.74204	0.176598	0.0882988	+	0.996094i	$0.471857\pi$
$450$	−3.21046	−0.151342
$451$	−5.25918	−0.247645
$452$	−62.1442	−2.92302
$453$	16.9699	0.797316
$454$	−18.5196	−0.869167
$455$	0	0
$456$	23.2218	1.08746
$457$	−5.82968	−0.272701	−0.136350	−	0.990661i	$-0.543537\pi$
$457$	−5.82968	−0.272701	−0.136350	+	0.990661i	$0.543537\pi$
$458$	−55.4968	−2.59320
$459$	−7.20978	−0.336524
$460$	−43.5758	−2.03173
$461$	−3.02842	−0.141047	−0.0705237	−	0.997510i	$-0.522467\pi$
$461$	−3.02842	−0.141047	−0.0705237	+	0.997510i	$0.522467\pi$
$462$	0	0
$463$	24.8828	1.15640	0.578202	−	0.815894i	$-0.303755\pi$
$463$	24.8828	1.15640	0.578202	+	0.815894i	$0.303755\pi$
$464$	6.82250	0.316727
$465$	13.8883	0.644055
$466$	1.57919	0.0731546
$467$	21.3830	0.989489	0.494744	−	0.869039i	$-0.335262\pi$
$467$	21.3830	0.989489	0.494744	+	0.869039i	$0.335262\pi$
$468$	1.85408	0.0857047
$469$	0	0
$470$	52.5607	2.42444
$471$	−14.7623	−0.680213
$472$	5.00040	0.230162
$473$	−59.9827	−2.75801
$474$	−18.7952	−0.863294
$475$	−7.52836	−0.345425
$476$	0	0
$477$	−10.5938	−0.485059
$478$	−11.9686	−0.547430
$479$	22.5359	1.02969	0.514845	−	0.857283i	$-0.327849\pi$
$479$	22.5359	1.02969	0.514845	+	0.857283i	$0.327849\pi$
$480$	6.09797	0.278333
$481$	−4.56094	−0.207961
$482$	−27.3841	−1.24731
$483$	0	0
$484$	62.1157	2.82344
$485$	−13.1360	−0.596475
$486$	−2.39346	−0.108570
$487$	−14.1669	−0.641962	−0.320981	−	0.947086i	$-0.604013\pi$
$487$	−14.1669	−0.641962	−0.320981	+	0.947086i	$0.604013\pi$
$488$	−39.4175	−1.78435
$489$	10.8608	0.491141
$490$	0	0
$491$	−12.5590	−0.566781	−0.283391	−	0.959005i	$-0.591459\pi$
$491$	−12.5590	−0.566781	−0.283391	+	0.959005i	$0.591459\pi$
$492$	−3.72866	−0.168101
$493$	−20.1133	−0.905859
$494$	6.67977	0.300537
$495$	13.2437	0.595260
$496$	13.4878	0.605619
$497$	0	0
$498$	23.6007	1.05757
$499$	7.96632	0.356621	0.178311	−	0.983974i	$-0.442937\pi$
$499$	7.96632	0.356621	0.178311	+	0.983974i	$0.442937\pi$
$500$	−34.3530	−1.53631
$501$	13.7966	0.616387
$502$	60.6201	2.70561
$503$	−10.0853	−0.449683	−0.224841	−	0.974395i	$-0.572186\pi$
$503$	−10.0853	−0.449683	−0.224841	+	0.974395i	$0.572186\pi$
$504$	0	0
$505$	17.3258	0.770986
$506$	58.4181	2.59700
$507$	−12.7527	−0.566369
$508$	−30.1292	−1.33677
$509$	−27.8467	−1.23428	−0.617141	−	0.786852i	$-0.711709\pi$
$509$	−27.8467	−1.23428	−0.617141	+	0.786852i	$0.711709\pi$
$510$	43.4549	1.92422
$511$	0	0
$512$	26.1592	1.15608
$513$	−5.61255	−0.247800
$514$	2.32590	0.102591
$515$	10.2279	0.450695
$516$	−42.5266	−1.87213
$517$	−45.8630	−2.01705
$518$	0	0
$519$	21.1538	0.928547
$520$	−5.18085	−0.227195
$521$	−12.0067	−0.526025	−0.263012	−	0.964792i	$-0.584716\pi$
$521$	−12.0067	−0.526025	−0.263012	+	0.964792i	$0.584716\pi$
$522$	−6.67711	−0.292249
$523$	−3.68147	−0.160979	−0.0804897	−	0.996755i	$-0.525648\pi$
$523$	−3.68147	−0.160979	−0.0804897	+	0.996755i	$0.525648\pi$
$524$	−2.56325	−0.111976
$525$	0	0
$526$	−66.6995	−2.90824
$527$	−39.7631	−1.73211
$528$	12.8617	0.559736
$529$	−1.46202	−0.0635660
$530$	63.8514	2.77353
$531$	−1.20856	−0.0524471
$532$	0	0
$533$	−0.497250	−0.0215383
$534$	37.8237	1.63679
$535$	−35.5534	−1.53711
$536$	20.4685	0.884105
$537$	−15.7738	−0.680691
$538$	38.6414	1.66595
$539$	0	0
$540$	9.38952	0.404061
$541$	−15.7106	−0.675450	−0.337725	−	0.941245i	$-0.609657\pi$
$541$	−15.7106	−0.675450	−0.337725	+	0.941245i	$0.609657\pi$
$542$	−15.1989	−0.652851
$543$	−4.14541	−0.177897
$544$	−17.4589	−0.748544
$545$	13.5821	0.581792
$546$	0	0
$547$	−6.81188	−0.291255	−0.145627	−	0.989340i	$-0.546520\pi$
$547$	−6.81188	−0.291255	−0.145627	+	0.989340i	$0.546520\pi$
$548$	52.2540	2.23218
$549$	9.52693	0.406600
$550$	−16.8844	−0.719952
$551$	−15.6575	−0.667032
$552$	19.2016	0.817276
$553$	0	0
$554$	−53.0238	−2.25276
$555$	−23.0978	−0.980447
$556$	0.487354	0.0206684
$557$	−24.1728	−1.02423	−0.512117	−	0.858916i	$-0.671138\pi$
$557$	−24.1728	−1.02423	−0.512117	+	0.858916i	$0.671138\pi$
$558$	−13.2003	−0.558815
$559$	−5.67130	−0.239870
$560$	0	0
$561$	−37.9176	−1.60088
$562$	14.9060	0.628770
$563$	−35.1654	−1.48204	−0.741022	−	0.671480i	$-0.765659\pi$
$563$	−35.1654	−1.48204	−0.741022	+	0.671480i	$0.765659\pi$
$564$	−32.5160	−1.36917
$565$	−41.9699	−1.76569
$566$	−20.2574	−0.851483
$567$	0	0
$568$	21.8830	0.918190
$569$	−0.747079	−0.0313192	−0.0156596	−	0.999877i	$-0.504985\pi$
$569$	−0.747079	−0.0313192	−0.0156596	+	0.999877i	$0.504985\pi$
$570$	33.8281	1.41690
$571$	−0.0973672	−0.00407469	−0.00203735	−	0.999998i	$-0.500649\pi$
$571$	−0.0973672	−0.00407469	−0.00203735	+	0.999998i	$0.500649\pi$
$572$	9.75092	0.407707
$573$	−11.7296	−0.490013
$574$	0	0
$575$	−6.22505	−0.259602
$576$	−10.6871	−0.445294
$577$	11.2693	0.469145	0.234573	−	0.972099i	$-0.424631\pi$
$577$	11.2693	0.469145	0.234573	+	0.972099i	$0.424631\pi$
$578$	−83.7255	−3.48252
$579$	−1.58800	−0.0659949
$580$	26.1942	1.08766
$581$	0	0
$582$	12.4853	0.517532
$583$	−55.7149	−2.30748
$584$	−0.298631	−0.0123575
$585$	1.25218	0.0517711
$586$	0.926885	0.0382893
$587$	−2.11295	−0.0872109	−0.0436055	−	0.999049i	$-0.513884\pi$
$587$	−2.11295	−0.0872109	−0.0436055	+	0.999049i	$0.513884\pi$
$588$	0	0
$589$	−30.9541	−1.27544
$590$	7.28427	0.299889
$591$	9.03301	0.371569
$592$	−22.4317	−0.921936
$593$	6.83968	0.280872	0.140436	−	0.990090i	$-0.455150\pi$
$593$	6.83968	0.280872	0.140436	+	0.990090i	$0.455150\pi$
$594$	−12.5877	−0.516478
$595$	0	0
$596$	−58.7032	−2.40458
$597$	−4.76713	−0.195106
$598$	5.52337	0.225867
$599$	−3.92815	−0.160500	−0.0802498	−	0.996775i	$-0.525572\pi$
$599$	−3.92815	−0.160500	−0.0802498	+	0.996775i	$0.525572\pi$
$600$	−5.54978	−0.226569
$601$	−4.08570	−0.166659	−0.0833296	−	0.996522i	$-0.526555\pi$
$601$	−4.08570	−0.166659	−0.0833296	+	0.996522i	$0.526555\pi$
$602$	0	0
$603$	−4.94710	−0.201461
$604$	63.2751	2.57463
$605$	41.9508	1.70554
$606$	−16.4675	−0.668947
$607$	9.05306	0.367452	0.183726	−	0.982977i	$-0.441184\pi$
$607$	9.05306	0.367452	0.183726	+	0.982977i	$0.441184\pi$
$608$	−13.5911	−0.551192
$609$	0	0
$610$	−57.4209	−2.32491
$611$	−4.33629	−0.175428
$612$	−26.8828	−1.08667
$613$	−14.3384	−0.579122	−0.289561	−	0.957160i	$-0.593509\pi$
$613$	−14.3384	−0.579122	−0.289561	+	0.957160i	$0.593509\pi$
$614$	−78.5734	−3.17096
$615$	−2.51820	−0.101544
$616$	0	0
$617$	15.6801	0.631259	0.315630	−	0.948883i	$-0.397784\pi$
$617$	15.6801	0.631259	0.315630	+	0.948883i	$0.397784\pi$
$618$	−9.72124	−0.391046
$619$	1.07080	0.0430392	0.0215196	−	0.999768i	$-0.493150\pi$
$619$	1.07080	0.0430392	0.0215196	+	0.999768i	$0.493150\pi$
$620$	51.7848	2.07973
$621$	−4.64090	−0.186233
$622$	−74.3851	−2.98257
$623$	0	0
$624$	1.21606	0.0486815
$625$	−29.9075	−1.19630
$626$	−2.20844	−0.0882669
$627$	−29.5174	−1.17881
$628$	−55.0437	−2.19648
$629$	66.1305	2.63680
$630$	0	0
$631$	−32.7757	−1.30478	−0.652390	−	0.757883i	$-0.726234\pi$
$631$	−32.7757	−1.30478	−0.652390	+	0.757883i	$0.726234\pi$
$632$	−32.4906	−1.29241
$633$	−16.2495	−0.645860
$634$	−31.3482	−1.24500
$635$	−20.3482	−0.807492
$636$	−39.5008	−1.56631
$637$	0	0
$638$	−35.1161	−1.39026
$639$	−5.28897	−0.209228
$640$	52.2174	2.06407
$641$	14.3930	0.568491	0.284245	−	0.958752i	$-0.408257\pi$
$641$	14.3930	0.568491	0.284245	+	0.958752i	$0.408257\pi$
$642$	33.7923	1.33367
$643$	40.1711	1.58419	0.792097	−	0.610396i	$-0.208990\pi$
$643$	40.1711	1.58419	0.792097	+	0.610396i	$0.208990\pi$
$644$	0	0
$645$	−28.7209	−1.13089
$646$	−96.8520	−3.81059
$647$	10.9072	0.428805	0.214402	−	0.976745i	$-0.431220\pi$
$647$	10.9072	0.428805	0.214402	+	0.976745i	$0.431220\pi$
$648$	−4.13748	−0.162536
$649$	−6.35605	−0.249497
$650$	−1.59640	−0.0626159
$651$	0	0
$652$	40.4961	1.58595
$653$	−25.3109	−0.990493	−0.495247	−	0.868752i	$-0.664922\pi$
$653$	−25.3109	−0.990493	−0.495247	+	0.868752i	$0.664922\pi$
$654$	−12.9093	−0.504792
$655$	−1.73113	−0.0676407
$656$	−2.44558	−0.0954838
$657$	0.0721771	0.00281590
$658$	0	0
$659$	−3.89920	−0.151891	−0.0759456	−	0.997112i	$-0.524198\pi$
$659$	−3.89920	−0.151891	−0.0759456	+	0.997112i	$0.524198\pi$
$660$	49.3812	1.92216
$661$	−17.3899	−0.676390	−0.338195	−	0.941076i	$-0.609816\pi$
$661$	−17.3899	−0.676390	−0.338195	+	0.941076i	$0.609816\pi$
$662$	1.43487	0.0557679
$663$	−3.58506	−0.139232
$664$	40.7975	1.58325
$665$	0	0
$666$	21.9536	0.850686
$667$	−12.9469	−0.501305
$668$	51.4428	1.99038
$669$	20.7357	0.801689
$670$	29.8173	1.15194
$671$	50.1039	1.93424
$672$	0	0
$673$	6.09592	0.234980	0.117490	−	0.993074i	$-0.462515\pi$
$673$	6.09592	0.234980	0.117490	+	0.993074i	$0.462515\pi$
$674$	−78.3871	−3.01936
$675$	1.34134	0.0516284
$676$	−47.5506	−1.82887
$677$	10.2213	0.392835	0.196417	−	0.980520i	$-0.437069\pi$
$677$	10.2213	0.392835	0.196417	+	0.980520i	$0.437069\pi$
$678$	39.8909	1.53200
$679$	0	0
$680$	75.1188	2.88067
$681$	7.73757	0.296504
$682$	−69.4230	−2.65834
$683$	−40.5757	−1.55259	−0.776293	−	0.630372i	$-0.782902\pi$
$683$	−40.5757	−1.55259	−0.776293	+	0.630372i	$0.782902\pi$
$684$	−20.9273	−0.800175
$685$	35.2905	1.34838
$686$	0	0
$687$	23.1868	0.884633
$688$	−27.8926	−1.06340
$689$	−5.26779	−0.200687
$690$	27.9718	1.06487
$691$	10.9695	0.417298	0.208649	−	0.977991i	$-0.433093\pi$
$691$	10.9695	0.417298	0.208649	+	0.977991i	$0.433093\pi$
$692$	78.8752	2.99838
$693$	0	0
$694$	−36.5992	−1.38929
$695$	0.329141	0.0124850
$696$	−11.5424	−0.437515
$697$	7.20978	0.273090
$698$	32.3805	1.22562
$699$	−0.659793	−0.0249557
$700$	0	0
$701$	39.8587	1.50544	0.752721	−	0.658340i	$-0.228741\pi$
$701$	39.8587	1.50544	0.752721	+	0.658340i	$0.228741\pi$
$702$	−1.19015	−0.0449193
$703$	51.4802	1.94161
$704$	−56.2052	−2.11831
$705$	−21.9601	−0.827066
$706$	−58.2974	−2.19405
$707$	0	0
$708$	−4.50632	−0.169358
$709$	−0.986837	−0.0370614	−0.0185307	−	0.999828i	$-0.505899\pi$
$709$	−0.986837	−0.0370614	−0.0185307	+	0.999828i	$0.505899\pi$
$710$	31.8778	1.19635
$711$	7.85274	0.294501
$712$	65.3842	2.45038
$713$	−25.5954	−0.958553
$714$	0	0
$715$	6.58542	0.246281
$716$	−58.8152	−2.19803
$717$	5.00053	0.186748
$718$	57.5460	2.14760
$719$	−36.6383	−1.36638	−0.683189	−	0.730242i	$-0.739407\pi$
$719$	−36.6383	−1.36638	−0.683189	+	0.730242i	$0.739407\pi$
$720$	6.15846	0.229512
$721$	0	0
$722$	−29.9200	−1.11351
$723$	11.4412	0.425503
$724$	−15.4568	−0.574449
$725$	3.74199	0.138974
$726$	−39.8727	−1.47981
$727$	−7.38034	−0.273722	−0.136861	−	0.990590i	$-0.543701\pi$
$727$	−7.38034	−0.273722	−0.136861	+	0.990590i	$0.543701\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.435027	−0.0161011
$731$	82.2299	3.04138
$732$	35.5227	1.31296
$733$	15.4382	0.570223	0.285112	−	0.958494i	$-0.407969\pi$
$733$	15.4382	0.570223	0.285112	+	0.958494i	$0.407969\pi$
$734$	41.7787	1.54208
$735$	0	0
$736$	−11.2382	−0.414246
$737$	−26.0177	−0.958374
$738$	2.39346	0.0881045
$739$	−21.6801	−0.797516	−0.398758	−	0.917056i	$-0.630559\pi$
$739$	−21.6801	−0.797516	−0.398758	+	0.917056i	$0.630559\pi$
$740$	−86.1238	−3.16597
$741$	−2.79084	−0.102524
$742$	0	0
$743$	−3.73922	−0.137179	−0.0685894	−	0.997645i	$-0.521850\pi$
$743$	−3.73922	−0.137179	−0.0685894	+	0.997645i	$0.521850\pi$
$744$	−22.8189	−0.836581
$745$	−39.6461	−1.45252
$746$	82.1644	3.00825
$747$	−9.86047	−0.360776
$748$	−141.382	−5.16942
$749$	0	0
$750$	22.0515	0.805208
$751$	−6.22805	−0.227265	−0.113632	−	0.993523i	$-0.536249\pi$
$751$	−6.22805	−0.227265	−0.113632	+	0.993523i	$0.536249\pi$
$752$	−21.3268	−0.777708
$753$	−25.3274	−0.922981
$754$	−3.32019	−0.120914
$755$	42.7337	1.55524
$756$	0	0
$757$	−52.3343	−1.90212	−0.951061	−	0.309002i	$-0.900005\pi$
$757$	−52.3343	−1.90212	−0.951061	+	0.309002i	$0.900005\pi$
$758$	−58.8924	−2.13907
$759$	−24.4074	−0.885931
$760$	58.4772	2.12119
$761$	20.6592	0.748896	0.374448	−	0.927248i	$-0.377832\pi$
$761$	20.6592	0.748896	0.374448	+	0.927248i	$0.377832\pi$
$762$	19.3402	0.700622
$763$	0	0
$764$	−43.7358	−1.58231
$765$	−18.1557	−0.656420
$766$	9.55605	0.345274
$767$	−0.600958	−0.0216993
$768$	−28.2566	−1.01962
$769$	−35.7715	−1.28995	−0.644977	−	0.764202i	$-0.723133\pi$
$769$	−35.7715	−1.28995	−0.644977	+	0.764202i	$0.723133\pi$
$770$	0	0
$771$	−0.971771	−0.0349975
$772$	−5.92110	−0.213105
$773$	−4.28156	−0.153997	−0.0769984	−	0.997031i	$-0.524534\pi$
$773$	−4.28156	−0.153997	−0.0769984	+	0.997031i	$0.524534\pi$
$774$	27.2982	0.981214
$775$	7.39774	0.265735
$776$	21.5828	0.774778
$777$	0	0
$778$	−13.1844	−0.472685
$779$	5.61255	0.201090
$780$	4.66894	0.167175
$781$	−27.8157	−0.995322
$782$	−80.0850	−2.86383
$783$	2.78973	0.0996968
$784$	0	0
$785$	−37.1746	−1.32682
$786$	1.64537	0.0586885
$787$	−22.9874	−0.819412	−0.409706	−	0.912218i	$-0.634369\pi$
$787$	−22.9874	−0.819412	−0.409706	+	0.912218i	$0.634369\pi$
$788$	33.6810	1.19984
$789$	27.8674	0.992106
$790$	−47.3302	−1.68393
$791$	0	0
$792$	−21.7598	−0.773199
$793$	4.73727	0.168225
$794$	−20.7115	−0.735023
$795$	−26.6774	−0.946151
$796$	−17.7750	−0.630018
$797$	55.4679	1.96477	0.982386	−	0.186862i	$-0.0598316\pi$
$797$	55.4679	1.96477	0.982386	+	0.186862i	$0.0598316\pi$
$798$	0	0
$799$	62.8733	2.22430
$800$	3.24814	0.114839
$801$	−15.8029	−0.558369
$802$	−4.59123	−0.162122
$803$	0.379593	0.0133955
$804$	−18.4460	−0.650542
$805$	0	0
$806$	−6.56387	−0.231202
$807$	−16.1446	−0.568316
$808$	−28.4667	−1.00146
$809$	13.1865	0.463614	0.231807	−	0.972762i	$-0.425536\pi$
$809$	13.1865	0.463614	0.231807	+	0.972762i	$0.425536\pi$
$810$	−6.02722	−0.211775
$811$	35.1813	1.23538	0.617691	−	0.786421i	$-0.288068\pi$
$811$	35.1813	1.23538	0.617691	+	0.786421i	$0.288068\pi$
$812$	0	0
$813$	6.35019	0.222711
$814$	115.458	4.04681
$815$	27.3496	0.958015
$816$	−17.6321	−0.617247
$817$	64.0129	2.23953
$818$	−85.6259	−2.99384
$819$	0	0
$820$	−9.38952	−0.327896
$821$	−44.4381	−1.55090	−0.775451	−	0.631408i	$-0.782477\pi$
$821$	−44.4381	−1.55090	−0.775451	+	0.631408i	$0.782477\pi$
$822$	−33.5424	−1.16992
$823$	5.04465	0.175845	0.0879227	−	0.996127i	$-0.471977\pi$
$823$	5.04465	0.175845	0.0879227	+	0.996127i	$0.471977\pi$
$824$	−16.8047	−0.585420
$825$	7.05438	0.245602
$826$	0	0
$827$	−51.3758	−1.78651	−0.893255	−	0.449550i	$-0.851584\pi$
$827$	−51.3758	−1.78651	−0.893255	+	0.449550i	$0.851584\pi$
$828$	−17.3043	−0.601368
$829$	−34.1487	−1.18603	−0.593016	−	0.805190i	$-0.702063\pi$
$829$	−34.1487	−1.18603	−0.593016	+	0.805190i	$0.702063\pi$
$830$	59.4312	2.06289
$831$	22.1536	0.768500
$832$	−5.31414	−0.184235
$833$	0	0
$834$	−0.312837	−0.0108327
$835$	34.7426	1.20232
$836$	−110.060	−3.80652
$837$	5.51517	0.190632
$838$	85.8691	2.96630
$839$	−42.0682	−1.45236	−0.726178	−	0.687506i	$-0.758705\pi$
$839$	−42.0682	−1.45236	−0.726178	+	0.687506i	$0.758705\pi$
$840$	0	0
$841$	−21.2174	−0.731635
$842$	−65.7951	−2.26745
$843$	−6.22779	−0.214496
$844$	−60.5889	−2.08556
$845$	−32.1140	−1.10475
$846$	20.8723	0.717605
$847$	0	0
$848$	−25.9081	−0.889687
$849$	8.46365	0.290472
$850$	23.1467	0.793925
$851$	42.5679	1.45921
$852$	−19.7208	−0.675622
$853$	25.9346	0.887983	0.443991	−	0.896031i	$-0.353562\pi$
$853$	25.9346	0.887983	0.443991	+	0.896031i	$0.353562\pi$
$854$	0	0
$855$	−14.1335	−0.483357
$856$	58.4153	1.99659
$857$	−23.4889	−0.802367	−0.401183	−	0.915998i	$-0.631401\pi$
$857$	−23.4889	−0.802367	−0.401183	+	0.915998i	$0.631401\pi$
$858$	−6.25921	−0.213686
$859$	−15.2574	−0.520575	−0.260288	−	0.965531i	$-0.583817\pi$
$859$	−15.2574	−0.520575	−0.260288	+	0.965531i	$0.583817\pi$
$860$	−107.091	−3.65176
$861$	0	0
$862$	−64.8521	−2.20887
$863$	−7.64927	−0.260384	−0.130192	−	0.991489i	$-0.541559\pi$
$863$	−7.64927	−0.260384	−0.130192	+	0.991489i	$0.541559\pi$
$864$	2.42156	0.0823831
$865$	53.2695	1.81122
$866$	−57.5768	−1.95654
$867$	34.9809	1.18801
$868$	0	0
$869$	41.2990	1.40097
$870$	−16.8143	−0.570059
$871$	−2.45994	−0.0833521
$872$	−22.3157	−0.755706
$873$	−5.21641	−0.176549
$874$	−62.3432	−2.10879
$875$	0	0
$876$	0.269124	0.00909285
$877$	10.1637	0.343205	0.171602	−	0.985166i	$-0.445106\pi$
$877$	10.1637	0.343205	0.171602	+	0.985166i	$0.445106\pi$
$878$	−52.0608	−1.75697
$879$	−0.387257	−0.0130619
$880$	32.3885	1.09182
$881$	16.2339	0.546933	0.273466	−	0.961882i	$-0.411830\pi$
$881$	16.2339	0.546933	0.273466	+	0.961882i	$0.411830\pi$
$882$	0	0
$883$	−52.4381	−1.76468	−0.882342	−	0.470610i	$-0.844034\pi$
$883$	−52.4381	−1.76468	−0.882342	+	0.470610i	$0.844034\pi$
$884$	−13.3675	−0.449597
$885$	−3.04340	−0.102303
$886$	38.7939	1.30331
$887$	32.0724	1.07689	0.538443	−	0.842662i	$-0.319013\pi$
$887$	32.0724	1.07689	0.538443	+	0.842662i	$0.319013\pi$
$888$	37.9503	1.27353
$889$	0	0
$890$	95.2477	3.19271
$891$	5.25918	0.176189
$892$	77.3164	2.58874
$893$	48.9445	1.63787
$894$	37.6822	1.26028
$895$	−39.7217	−1.32775
$896$	0	0
$897$	−2.30769	−0.0770515
$898$	−8.95642	−0.298880
$899$	15.3858	0.513146
$900$	5.00142	0.166714
$901$	76.3793	2.54456
$902$	12.5877	0.419123
$903$	0	0
$904$	68.9578	2.29350
$905$	−10.4390	−0.347004
$906$	−40.6169	−1.34940
$907$	13.0826	0.434399	0.217200	−	0.976127i	$-0.430308\pi$
$907$	13.0826	0.434399	0.217200	+	0.976127i	$0.430308\pi$
$908$	28.8508	0.957446
$909$	6.88021	0.228202
$910$	0	0
$911$	8.35938	0.276959	0.138479	−	0.990365i	$-0.455779\pi$
$911$	8.35938	0.276959	0.138479	+	0.990365i	$0.455779\pi$
$912$	−13.7259	−0.454511
$913$	−51.8580	−1.71625
$914$	13.9531	0.461528
$915$	23.9908	0.793110
$916$	86.4558	2.85658
$917$	0	0
$918$	17.2563	0.569544
$919$	−29.4836	−0.972575	−0.486288	−	0.873799i	$-0.661649\pi$
$919$	−29.4836	−0.972575	−0.486288	+	0.873799i	$0.661649\pi$
$920$	48.3536	1.59417
$921$	32.8283	1.08173
$922$	7.24840	0.238713
$923$	−2.62994	−0.0865655
$924$	0	0
$925$	−12.3033	−0.404529
$926$	−59.5561	−1.95714
$927$	4.06158	0.133400
$928$	6.75549	0.221760
$929$	25.0807	0.822870	0.411435	−	0.911439i	$-0.365028\pi$
$929$	25.0807	0.822870	0.411435	+	0.911439i	$0.365028\pi$
$930$	−33.2411	−1.09002
$931$	0	0
$932$	−2.46014	−0.0805847
$933$	31.0785	1.01746
$934$	−51.1795	−1.67464
$935$	−95.4841	−3.12266
$936$	−2.05736	−0.0672470
$937$	−47.2185	−1.54256	−0.771281	−	0.636495i	$-0.780384\pi$
$937$	−47.2185	−1.54256	−0.771281	+	0.636495i	$0.780384\pi$
$938$	0	0
$939$	0.922696	0.0301110
$940$	−81.8818	−2.67069
$941$	51.7575	1.68725	0.843623	−	0.536936i	$-0.180418\pi$
$941$	51.7575	1.68725	0.843623	+	0.536936i	$0.180418\pi$
$942$	35.3331	1.15121
$943$	4.64090	0.151129
$944$	−2.95563	−0.0961977
$945$	0	0
$946$	143.566	4.66774
$947$	−13.3493	−0.433794	−0.216897	−	0.976195i	$-0.569594\pi$
$947$	−13.3493	−0.433794	−0.216897	+	0.976195i	$0.569594\pi$
$948$	29.2802	0.950977
$949$	0.0358901	0.00116504
$950$	18.0188	0.584608
$951$	13.0974	0.424714
$952$	0	0
$953$	11.5662	0.374665	0.187332	−	0.982297i	$-0.440016\pi$
$953$	11.5662	0.374665	0.187332	+	0.982297i	$0.440016\pi$
$954$	25.3560	0.820929
$955$	−29.5376	−0.955814
$956$	18.6453	0.603031
$957$	14.6717	0.474269
$958$	−53.9387	−1.74268
$959$	0	0
$960$	−26.9122	−0.868587
$961$	−0.582944	−0.0188046
$962$	10.9164	0.351960
$963$	−14.1186	−0.454965
$964$	42.6604	1.37400
$965$	−3.99890	−0.128729
$966$	0	0
$967$	25.0152	0.804433	0.402217	−	0.915545i	$-0.368240\pi$
$967$	25.0152	0.804433	0.402217	+	0.915545i	$0.368240\pi$
$968$	−68.9263	−2.21537
$969$	40.4652	1.29993
$970$	31.4405	1.00949
$971$	−21.9103	−0.703135	−0.351568	−	0.936162i	$-0.614351\pi$
$971$	−21.9103	−0.703135	−0.351568	+	0.936162i	$0.614351\pi$
$972$	3.72866	0.119597
$973$	0	0
$974$	33.9079	1.08648
$975$	0.666983	0.0213606
$976$	23.2989	0.745779
$977$	−13.9825	−0.447341	−0.223671	−	0.974665i	$-0.571804\pi$
$977$	−13.9825	−0.447341	−0.223671	+	0.974665i	$0.571804\pi$
$978$	−25.9948	−0.831223
$979$	−83.1104	−2.65622
$980$	0	0
$981$	5.39356	0.172203
$982$	30.0596	0.959239
$983$	20.8099	0.663733	0.331866	−	0.943326i	$-0.392322\pi$
$983$	20.8099	0.663733	0.331866	+	0.943326i	$0.392322\pi$
$984$	4.13748	0.131898
$985$	22.7470	0.724778
$986$	48.1405	1.53311
$987$	0	0
$988$	−10.4061	−0.331062
$989$	52.9310	1.68311
$990$	−31.6983	−1.00744
$991$	33.1799	1.05399	0.526996	−	0.849867i	$-0.323318\pi$
$991$	33.1799	1.05399	0.526996	+	0.849867i	$0.323318\pi$
$992$	13.3553	0.424031
$993$	−0.599497	−0.0190245
$994$	0	0
$995$	−12.0046	−0.380571
$996$	−36.7663	−1.16499
$997$	−11.2405	−0.355991	−0.177996	−	0.984031i	$-0.556961\pi$
$997$	−11.2405	−0.355991	−0.177996	+	0.984031i	$0.556961\pi$
$998$	−19.0671	−0.603558
$999$	−9.17233	−0.290200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.ba.1.1	yes	8
7.6	odd	2		6027.2.a.z.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.z.1.1	✓	8	7.6	odd	2
6027.2.a.ba.1.1	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39346 q^{2} +1.00000 q^{3} +3.72866 q^{4} +2.51820 q^{5} -2.39346 q^{6} -4.13748 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.39346 q^{2} +1.00000 q^{3} +3.72866 q^{4} +2.51820 q^{5} -2.39346 q^{6} -4.13748 q^{8} +1.00000 q^{9} -6.02722 q^{10} +5.25918 q^{11} +3.72866 q^{12} +0.497250 q^{13} +2.51820 q^{15} +2.44558 q^{16} -7.20978 q^{17} -2.39346 q^{18} -5.61255 q^{19} +9.38952 q^{20} -12.5877 q^{22} -4.64090 q^{23} -4.13748 q^{24} +1.34134 q^{25} -1.19015 q^{26} +1.00000 q^{27} +2.78973 q^{29} -6.02722 q^{30} +5.51517 q^{31} +2.42156 q^{32} +5.25918 q^{33} +17.2563 q^{34} +3.72866 q^{36} -9.17233 q^{37} +13.4334 q^{38} +0.497250 q^{39} -10.4190 q^{40} -1.00000 q^{41} -11.4053 q^{43} +19.6097 q^{44} +2.51820 q^{45} +11.1078 q^{46} -8.72055 q^{47} +2.44558 q^{48} -3.21046 q^{50} -7.20978 q^{51} +1.85408 q^{52} -10.5938 q^{53} -2.39346 q^{54} +13.2437 q^{55} -5.61255 q^{57} -6.67711 q^{58} -1.20856 q^{59} +9.38952 q^{60} +9.52693 q^{61} -13.2003 q^{62} -10.6871 q^{64} +1.25218 q^{65} -12.5877 q^{66} -4.94710 q^{67} -26.8828 q^{68} -4.64090 q^{69} -5.28897 q^{71} -4.13748 q^{72} +0.0721771 q^{73} +21.9536 q^{74} +1.34134 q^{75} -20.9273 q^{76} -1.19015 q^{78} +7.85274 q^{79} +6.15846 q^{80} +1.00000 q^{81} +2.39346 q^{82} -9.86047 q^{83} -18.1557 q^{85} +27.2982 q^{86} +2.78973 q^{87} -21.7598 q^{88} -15.8029 q^{89} -6.02722 q^{90} -17.3043 q^{92} +5.51517 q^{93} +20.8723 q^{94} -14.1335 q^{95} +2.42156 q^{96} -5.21641 q^{97} +5.25918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 4 q^{13} - 2 q^{15} - 8 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{20} - 14 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} - 4 q^{29} + 2 q^{30} + 10 q^{31} - 4 q^{32} - 2 q^{33} - 4 q^{34} + 4 q^{36} - 20 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 8 q^{41} - 8 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 24 q^{47} - 22 q^{50} - 8 q^{51} + 30 q^{52} - 36 q^{53} - 2 q^{54} - 4 q^{55} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 4 q^{60} + 22 q^{61} - 30 q^{62} - 24 q^{64} + 8 q^{65} - 14 q^{66} - 14 q^{67} - 38 q^{68} - 12 q^{69} - 10 q^{71} - 6 q^{72} + 12 q^{73} - 2 q^{74} - 4 q^{75} - 32 q^{76} - 4 q^{78} + 16 q^{79} + 14 q^{80} + 8 q^{81} + 2 q^{82} - 24 q^{83} - 44 q^{85} + 36 q^{86} - 4 q^{87} - 34 q^{88} - 2 q^{89} + 2 q^{90} - 48 q^{92} + 10 q^{93} + 34 q^{94} - 24 q^{95} - 4 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 - 4 * q^13 - 2 * q^15 - 8 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^20 - 14 * q^22 - 12 * q^23 - 6 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 - 4 * q^29 + 2 * q^30 + 10 * q^31 - 4 * q^32 - 2 * q^33 - 4 * q^34 + 4 * q^36 - 20 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 8 * q^41 - 8 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 24 * q^47 - 22 * q^50 - 8 * q^51 + 30 * q^52 - 36 * q^53 - 2 * q^54 - 4 * q^55 - 6 * q^57 + 14 * q^58 - 10 * q^59 - 4 * q^60 + 22 * q^61 - 30 * q^62 - 24 * q^64 + 8 * q^65 - 14 * q^66 - 14 * q^67 - 38 * q^68 - 12 * q^69 - 10 * q^71 - 6 * q^72 + 12 * q^73 - 2 * q^74 - 4 * q^75 - 32 * q^76 - 4 * q^78 + 16 * q^79 + 14 * q^80 + 8 * q^81 + 2 * q^82 - 24 * q^83 - 44 * q^85 + 36 * q^86 - 4 * q^87 - 34 * q^88 - 2 * q^89 + 2 * q^90 - 48 * q^92 + 10 * q^93 + 34 * q^94 - 24 * q^95 - 4 * q^96 - 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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