LMFDB - Embedded newform 7935.2.a.bi.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.54080$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54080 q^{2} +1.00000 q^{3} +4.45566 q^{4} +1.00000 q^{5} +2.54080 q^{6} +1.14270 q^{7} +6.23934 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54080 q^{2} +1.00000 q^{3} +4.45566 q^{4} +1.00000 q^{5} +2.54080 q^{6} +1.14270 q^{7} +6.23934 q^{8} +1.00000 q^{9} +2.54080 q^{10} +3.34647 q^{11} +4.45566 q^{12} -2.70486 q^{13} +2.90338 q^{14} +1.00000 q^{15} +6.94159 q^{16} +6.70638 q^{17} +2.54080 q^{18} +1.16406 q^{19} +4.45566 q^{20} +1.14270 q^{21} +8.50270 q^{22} +6.23934 q^{24} +1.00000 q^{25} -6.87251 q^{26} +1.00000 q^{27} +5.09149 q^{28} -4.73310 q^{29} +2.54080 q^{30} -9.58374 q^{31} +5.15851 q^{32} +3.34647 q^{33} +17.0396 q^{34} +1.14270 q^{35} +4.45566 q^{36} -7.96889 q^{37} +2.95765 q^{38} -2.70486 q^{39} +6.23934 q^{40} +3.24920 q^{41} +2.90338 q^{42} +11.8178 q^{43} +14.9107 q^{44} +1.00000 q^{45} -1.14258 q^{47} +6.94159 q^{48} -5.69423 q^{49} +2.54080 q^{50} +6.70638 q^{51} -12.0519 q^{52} -6.62445 q^{53} +2.54080 q^{54} +3.34647 q^{55} +7.12971 q^{56} +1.16406 q^{57} -12.0259 q^{58} +4.14480 q^{59} +4.45566 q^{60} +12.2675 q^{61} -24.3504 q^{62} +1.14270 q^{63} -0.776446 q^{64} -2.70486 q^{65} +8.50270 q^{66} -3.54763 q^{67} +29.8814 q^{68} +2.90338 q^{70} +2.64731 q^{71} +6.23934 q^{72} +14.2342 q^{73} -20.2473 q^{74} +1.00000 q^{75} +5.18666 q^{76} +3.82402 q^{77} -6.87251 q^{78} +4.83548 q^{79} +6.94159 q^{80} +1.00000 q^{81} +8.25556 q^{82} -15.3783 q^{83} +5.09149 q^{84} +6.70638 q^{85} +30.0266 q^{86} -4.73310 q^{87} +20.8798 q^{88} -5.33955 q^{89} +2.54080 q^{90} -3.09085 q^{91} -9.58374 q^{93} -2.90306 q^{94} +1.16406 q^{95} +5.15851 q^{96} -5.42866 q^{97} -14.4679 q^{98} +3.34647 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * 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 $

$2$	2.54080	1.79662	0.898308	−	0.439366i	$-0.144797\pi$
$2$	2.54080	1.79662	0.898308	+	0.439366i	$0.144797\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.45566	2.22783
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.54080	1.03728
$7$	1.14270	0.431901	0.215950	−	0.976404i	$-0.430715\pi$
$7$	1.14270	0.431901	0.215950	+	0.976404i	$0.430715\pi$
$8$	6.23934	2.20594
$9$	1.00000	0.333333
$10$	2.54080	0.803471
$11$	3.34647	1.00900	0.504499	−	0.863412i	$-0.331677\pi$
$11$	3.34647	1.00900	0.504499	+	0.863412i	$0.331677\pi$
$12$	4.45566	1.28624
$13$	−2.70486	−0.750193	−0.375097	−	0.926986i	$-0.622390\pi$
$13$	−2.70486	−0.750193	−0.375097	+	0.926986i	$0.622390\pi$
$14$	2.90338	0.775960
$15$	1.00000	0.258199
$16$	6.94159	1.73540
$17$	6.70638	1.62654	0.813269	−	0.581888i	$-0.197686\pi$
$17$	6.70638	1.62654	0.813269	+	0.581888i	$0.197686\pi$
$18$	2.54080	0.598872
$19$	1.16406	0.267054	0.133527	−	0.991045i	$-0.457370\pi$
$19$	1.16406	0.267054	0.133527	+	0.991045i	$0.457370\pi$
$20$	4.45566	0.996316
$21$	1.14270	0.249358
$22$	8.50270	1.81278
$23$	0	0
$23$	0	0
$24$	6.23934	1.27360
$25$	1.00000	0.200000
$26$	−6.87251	−1.34781
$27$	1.00000	0.192450
$28$	5.09149	0.962202
$29$	−4.73310	−0.878915	−0.439457	−	0.898263i	$-0.644829\pi$
$29$	−4.73310	−0.878915	−0.439457	+	0.898263i	$0.644829\pi$
$30$	2.54080	0.463884
$31$	−9.58374	−1.72129	−0.860646	−	0.509204i	$-0.829940\pi$
$31$	−9.58374	−1.72129	−0.860646	+	0.509204i	$0.829940\pi$
$32$	5.15851	0.911904
$33$	3.34647	0.582545
$34$	17.0396	2.92226
$35$	1.14270	0.193152
$36$	4.45566	0.742610
$37$	−7.96889	−1.31008	−0.655038	−	0.755596i	$-0.727348\pi$
$37$	−7.96889	−1.31008	−0.655038	+	0.755596i	$0.727348\pi$
$38$	2.95765	0.479794
$39$	−2.70486	−0.433124
$40$	6.23934	0.986527
$41$	3.24920	0.507440	0.253720	−	0.967278i	$-0.418346\pi$
$41$	3.24920	0.507440	0.253720	+	0.967278i	$0.418346\pi$
$42$	2.90338	0.448001
$43$	11.8178	1.80219	0.901097	−	0.433617i	$-0.142763\pi$
$43$	11.8178	1.80219	0.901097	+	0.433617i	$0.142763\pi$
$44$	14.9107	2.24788
$45$	1.00000	0.149071
$46$	0	0
$47$	−1.14258	−0.166662	−0.0833311	−	0.996522i	$-0.526556\pi$
$47$	−1.14258	−0.166662	−0.0833311	+	0.996522i	$0.526556\pi$
$48$	6.94159	1.00193
$49$	−5.69423	−0.813462
$50$	2.54080	0.359323
$51$	6.70638	0.939082
$52$	−12.0519	−1.67130
$53$	−6.62445	−0.909938	−0.454969	−	0.890507i	$-0.650350\pi$
$53$	−6.62445	−0.909938	−0.454969	+	0.890507i	$0.650350\pi$
$54$	2.54080	0.345759
$55$	3.34647	0.451238
$56$	7.12971	0.952747
$57$	1.16406	0.154184
$58$	−12.0259	−1.57907
$59$	4.14480	0.539607	0.269804	−	0.962915i	$-0.413041\pi$
$59$	4.14480	0.539607	0.269804	+	0.962915i	$0.413041\pi$
$60$	4.45566	0.575223
$61$	12.2675	1.57069	0.785346	−	0.619058i	$-0.212485\pi$
$61$	12.2675	1.57069	0.785346	+	0.619058i	$0.212485\pi$
$62$	−24.3504	−3.09250
$63$	1.14270	0.143967
$64$	−0.776446	−0.0970557
$65$	−2.70486	−0.335497
$66$	8.50270	1.04661
$67$	−3.54763	−0.433412	−0.216706	−	0.976237i	$-0.569531\pi$
$67$	−3.54763	−0.433412	−0.216706	+	0.976237i	$0.569531\pi$
$68$	29.8814	3.62365
$69$	0	0
$70$	2.90338	0.347020
$71$	2.64731	0.314178	0.157089	−	0.987584i	$-0.449789\pi$
$71$	2.64731	0.314178	0.157089	+	0.987584i	$0.449789\pi$
$72$	6.23934	0.735313
$73$	14.2342	1.66599	0.832994	−	0.553282i	$-0.186625\pi$
$73$	14.2342	1.66599	0.832994	+	0.553282i	$0.186625\pi$
$74$	−20.2473	−2.35371
$75$	1.00000	0.115470
$76$	5.18666	0.594951
$77$	3.82402	0.435787
$78$	−6.87251	−0.778158
$79$	4.83548	0.544034	0.272017	−	0.962292i	$-0.412309\pi$
$79$	4.83548	0.544034	0.272017	+	0.962292i	$0.412309\pi$
$80$	6.94159	0.776094
$81$	1.00000	0.111111
$82$	8.25556	0.911675
$83$	−15.3783	−1.68798	−0.843992	−	0.536355i	$-0.819801\pi$
$83$	−15.3783	−1.68798	−0.843992	+	0.536355i	$0.819801\pi$
$84$	5.09149	0.555527
$85$	6.70638	0.727410
$86$	30.0266	3.23785
$87$	−4.73310	−0.507442
$88$	20.8798	2.22579
$89$	−5.33955	−0.565992	−0.282996	−	0.959121i	$-0.591328\pi$
$89$	−5.33955	−0.565992	−0.282996	+	0.959121i	$0.591328\pi$
$90$	2.54080	0.267824
$91$	−3.09085	−0.324009
$92$	0	0
$93$	−9.58374	−0.993788
$94$	−2.90306	−0.299428
$95$	1.16406	0.119430
$96$	5.15851	0.526488
$97$	−5.42866	−0.551197	−0.275598	−	0.961273i	$-0.588876\pi$
$97$	−5.42866	−0.551197	−0.275598	+	0.961273i	$0.588876\pi$
$98$	−14.4679	−1.46148
$99$	3.34647	0.336333
$100$	4.45566	0.445566
$101$	−0.384952	−0.0383041	−0.0191521	−	0.999817i	$-0.506097\pi$
$101$	−0.384952	−0.0383041	−0.0191521	+	0.999817i	$0.506097\pi$
$102$	17.0396	1.68717
$103$	−7.90770	−0.779169	−0.389584	−	0.920991i	$-0.627381\pi$
$103$	−7.90770	−0.779169	−0.389584	+	0.920991i	$0.627381\pi$
$104$	−16.8765	−1.65488
$105$	1.14270	0.111516
$106$	−16.8314	−1.63481
$107$	−7.97908	−0.771367	−0.385683	−	0.922631i	$-0.626034\pi$
$107$	−7.97908	−0.771367	−0.385683	+	0.922631i	$0.626034\pi$
$108$	4.45566	0.428746
$109$	−12.0846	−1.15749	−0.578747	−	0.815507i	$-0.696458\pi$
$109$	−12.0846	−1.15749	−0.578747	+	0.815507i	$0.696458\pi$
$110$	8.50270	0.810701
$111$	−7.96889	−0.756373
$112$	7.93217	0.749520
$113$	−2.01474	−0.189530	−0.0947652	−	0.995500i	$-0.530210\pi$
$113$	−2.01474	−0.189530	−0.0947652	+	0.995500i	$0.530210\pi$
$114$	2.95765	0.277009
$115$	0	0
$116$	−21.0891	−1.95807
$117$	−2.70486	−0.250064
$118$	10.5311	0.969467
$119$	7.66340	0.702503
$120$	6.23934	0.569571
$121$	0.198843	0.0180766
$122$	31.1692	2.82193
$123$	3.24920	0.292970
$124$	−42.7019	−3.83474
$125$	1.00000	0.0894427
$126$	2.90338	0.258653
$127$	14.6913	1.30364	0.651820	−	0.758374i	$-0.274006\pi$
$127$	14.6913	1.30364	0.651820	+	0.758374i	$0.274006\pi$
$128$	−12.2898	−1.08628
$129$	11.8178	1.04050
$130$	−6.87251	−0.602759
$131$	−15.2758	−1.33465	−0.667327	−	0.744765i	$-0.732562\pi$
$131$	−15.2758	−1.33465	−0.667327	+	0.744765i	$0.732562\pi$
$132$	14.9107	1.29781
$133$	1.33018	0.115341
$134$	−9.01381	−0.778675
$135$	1.00000	0.0860663
$136$	41.8434	3.58804
$137$	18.3702	1.56947	0.784737	−	0.619829i	$-0.212798\pi$
$137$	18.3702	1.56947	0.784737	+	0.619829i	$0.212798\pi$
$138$	0	0
$139$	−5.35951	−0.454588	−0.227294	−	0.973826i	$-0.572988\pi$
$139$	−5.35951	−0.454588	−0.227294	+	0.973826i	$0.572988\pi$
$140$	5.09149	0.430310
$141$	−1.14258	−0.0962224
$142$	6.72629	0.564458
$143$	−9.05173	−0.756943
$144$	6.94159	0.578466
$145$	−4.73310	−0.393063
$146$	36.1663	2.99314
$147$	−5.69423	−0.469652
$148$	−35.5067	−2.91863
$149$	−2.67776	−0.219371	−0.109685	−	0.993966i	$-0.534984\pi$
$149$	−2.67776	−0.219371	−0.109685	+	0.993966i	$0.534984\pi$
$150$	2.54080	0.207455
$151$	−3.66170	−0.297985	−0.148993	−	0.988838i	$-0.547603\pi$
$151$	−3.66170	−0.297985	−0.148993	+	0.988838i	$0.547603\pi$
$152$	7.26298	0.589105
$153$	6.70638	0.542179
$154$	9.71606	0.782942
$155$	−9.58374	−0.769785
$156$	−12.0519	−0.964928
$157$	10.3476	0.825826	0.412913	−	0.910770i	$-0.364511\pi$
$157$	10.3476	0.825826	0.412913	+	0.910770i	$0.364511\pi$
$158$	12.2860	0.977421
$159$	−6.62445	−0.525353
$160$	5.15851	0.407816
$161$	0	0
$162$	2.54080	0.199624
$163$	23.8249	1.86611	0.933057	−	0.359730i	$-0.117131\pi$
$163$	23.8249	1.86611	0.933057	+	0.359730i	$0.117131\pi$
$164$	14.4773	1.13049
$165$	3.34647	0.260522
$166$	−39.0731	−3.03266
$167$	−12.9928	−1.00541	−0.502705	−	0.864458i	$-0.667662\pi$
$167$	−12.9928	−1.00541	−0.502705	+	0.864458i	$0.667662\pi$
$168$	7.12971	0.550069
$169$	−5.68373	−0.437210
$170$	17.0396	1.30688
$171$	1.16406	0.0890180
$172$	52.6560	4.01498
$173$	−24.6185	−1.87171	−0.935854	−	0.352389i	$-0.885370\pi$
$173$	−24.6185	−1.87171	−0.935854	+	0.352389i	$0.885370\pi$
$174$	−12.0259	−0.911678
$175$	1.14270	0.0863802
$176$	23.2298	1.75101
$177$	4.14480	0.311542
$178$	−13.5667	−1.01687
$179$	−12.9283	−0.966305	−0.483153	−	0.875536i	$-0.660508\pi$
$179$	−12.9283	−0.966305	−0.483153	+	0.875536i	$0.660508\pi$
$180$	4.45566	0.332105
$181$	13.9312	1.03550	0.517749	−	0.855532i	$-0.326770\pi$
$181$	13.9312	1.03550	0.517749	+	0.855532i	$0.326770\pi$
$182$	−7.85323	−0.582120
$183$	12.2675	0.906839
$184$	0	0
$185$	−7.96889	−0.585884
$186$	−24.3504	−1.78546
$187$	22.4427	1.64117
$188$	−5.09094	−0.371295
$189$	1.14270	0.0831194
$190$	2.95765	0.214570
$191$	4.15119	0.300370	0.150185	−	0.988658i	$-0.452013\pi$
$191$	4.15119	0.300370	0.150185	+	0.988658i	$0.452013\pi$
$192$	−0.776446	−0.0560351
$193$	−25.3470	−1.82452	−0.912259	−	0.409613i	$-0.865664\pi$
$193$	−25.3470	−1.82452	−0.912259	+	0.409613i	$0.865664\pi$
$194$	−13.7931	−0.990290
$195$	−2.70486	−0.193699
$196$	−25.3716	−1.81225
$197$	3.99436	0.284586	0.142293	−	0.989825i	$-0.454552\pi$
$197$	3.99436	0.284586	0.142293	+	0.989825i	$0.454552\pi$
$198$	8.50270	0.604261
$199$	−17.8647	−1.26640	−0.633198	−	0.773990i	$-0.718258\pi$
$199$	−17.8647	−1.26640	−0.633198	+	0.773990i	$0.718258\pi$
$200$	6.23934	0.441188
$201$	−3.54763	−0.250230
$202$	−0.978085	−0.0688179
$203$	−5.40852	−0.379604
$204$	29.8814	2.09211
$205$	3.24920	0.226934
$206$	−20.0919	−1.39987
$207$	0	0
$208$	−18.7760	−1.30188
$209$	3.89549	0.269457
$210$	2.90338	0.200352
$211$	23.1119	1.59109	0.795545	−	0.605895i	$-0.207185\pi$
$211$	23.1119	1.59109	0.795545	+	0.605895i	$0.207185\pi$
$212$	−29.5163	−2.02719
$213$	2.64731	0.181391
$214$	−20.2732	−1.38585
$215$	11.8178	0.805966
$216$	6.23934	0.424533
$217$	−10.9514	−0.743427
$218$	−30.7045	−2.07957
$219$	14.2342	0.961859
$220$	14.9107	1.00528
$221$	−18.1398	−1.22022
$222$	−20.2473	−1.35891
$223$	28.4412	1.90456	0.952280	−	0.305224i	$-0.0987315\pi$
$223$	28.4412	1.90456	0.952280	+	0.305224i	$0.0987315\pi$
$224$	5.89464	0.393852
$225$	1.00000	0.0666667
$226$	−5.11904	−0.340513
$227$	15.6868	1.04117	0.520585	−	0.853810i	$-0.325714\pi$
$227$	15.6868	1.04117	0.520585	+	0.853810i	$0.325714\pi$
$228$	5.18666	0.343495
$229$	10.9953	0.726589	0.363295	−	0.931674i	$-0.381652\pi$
$229$	10.9953	0.726589	0.363295	+	0.931674i	$0.381652\pi$
$230$	0	0
$231$	3.82402	0.251602
$232$	−29.5314	−1.93883
$233$	11.6794	0.765141	0.382571	−	0.923926i	$-0.375039\pi$
$233$	11.6794	0.765141	0.382571	+	0.923926i	$0.375039\pi$
$234$	−6.87251	−0.449270
$235$	−1.14258	−0.0745336
$236$	18.4678	1.20215
$237$	4.83548	0.314098
$238$	19.4712	1.26213
$239$	−10.2263	−0.661487	−0.330744	−	0.943721i	$-0.607300\pi$
$239$	−10.2263	−0.661487	−0.330744	+	0.943721i	$0.607300\pi$
$240$	6.94159	0.448078
$241$	5.23642	0.337307	0.168654	−	0.985675i	$-0.446058\pi$
$241$	5.23642	0.337307	0.168654	+	0.985675i	$0.446058\pi$
$242$	0.505220	0.0324768
$243$	1.00000	0.0641500
$244$	54.6598	3.49923
$245$	−5.69423	−0.363791
$246$	8.25556	0.526356
$247$	−3.14862	−0.200342
$248$	−59.7962	−3.79707
$249$	−15.3783	−0.974558
$250$	2.54080	0.160694
$251$	17.2095	1.08626	0.543128	−	0.839650i	$-0.317240\pi$
$251$	17.2095	1.08626	0.543128	+	0.839650i	$0.317240\pi$
$252$	5.09149	0.320734
$253$	0	0
$254$	37.3276	2.34214
$255$	6.70638	0.419970
$256$	−29.6731	−1.85457
$257$	−17.9546	−1.11998	−0.559988	−	0.828501i	$-0.689194\pi$
$257$	−17.9546	−1.11998	−0.559988	+	0.828501i	$0.689194\pi$
$258$	30.0266	1.86937
$259$	−9.10606	−0.565823
$260$	−12.0519	−0.747430
$261$	−4.73310	−0.292972
$262$	−38.8128	−2.39786
$263$	28.9246	1.78357	0.891784	−	0.452461i	$-0.149454\pi$
$263$	28.9246	1.78357	0.891784	+	0.452461i	$0.149454\pi$
$264$	20.8798	1.28506
$265$	−6.62445	−0.406937
$266$	3.37971	0.207223
$267$	−5.33955	−0.326775
$268$	−15.8070	−0.965568
$269$	6.58384	0.401424	0.200712	−	0.979650i	$-0.435674\pi$
$269$	6.58384	0.401424	0.200712	+	0.979650i	$0.435674\pi$
$270$	2.54080	0.154628
$271$	2.33083	0.141588	0.0707940	−	0.997491i	$-0.477447\pi$
$271$	2.33083	0.141588	0.0707940	+	0.997491i	$0.477447\pi$
$272$	46.5530	2.82269
$273$	−3.09085	−0.187067
$274$	46.6750	2.81974
$275$	3.34647	0.201800
$276$	0	0
$277$	13.5890	0.816481	0.408241	−	0.912874i	$-0.366142\pi$
$277$	13.5890	0.816481	0.408241	+	0.912874i	$0.366142\pi$
$278$	−13.6174	−0.816720
$279$	−9.58374	−0.573764
$280$	7.12971	0.426082
$281$	1.82642	0.108955	0.0544776	−	0.998515i	$-0.482651\pi$
$281$	1.82642	0.108955	0.0544776	+	0.998515i	$0.482651\pi$
$282$	−2.90306	−0.172875
$283$	22.1962	1.31942	0.659712	−	0.751518i	$-0.270678\pi$
$283$	22.1962	1.31942	0.659712	+	0.751518i	$0.270678\pi$
$284$	11.7955	0.699936
$285$	1.16406	0.0689530
$286$	−22.9986	−1.35994
$287$	3.71287	0.219164
$288$	5.15851	0.303968
$289$	27.9756	1.64562
$290$	−12.0259	−0.706183
$291$	−5.42866	−0.318234
$292$	63.4228	3.71154
$293$	−18.8976	−1.10401	−0.552005	−	0.833841i	$-0.686137\pi$
$293$	−18.8976	−1.10401	−0.552005	+	0.833841i	$0.686137\pi$
$294$	−14.4679	−0.843785
$295$	4.14480	0.241320
$296$	−49.7206	−2.88995
$297$	3.34647	0.194182
$298$	−6.80365	−0.394125
$299$	0	0
$300$	4.45566	0.257248
$301$	13.5042	0.778369
$302$	−9.30366	−0.535365
$303$	−0.384952	−0.0221149
$304$	8.08044	0.463445
$305$	12.2675	0.702434
$306$	17.0396	0.974088
$307$	−28.5629	−1.63017	−0.815084	−	0.579342i	$-0.803309\pi$
$307$	−28.5629	−1.63017	−0.815084	+	0.579342i	$0.803309\pi$
$308$	17.0385	0.970860
$309$	−7.90770	−0.449853
$310$	−24.3504	−1.38301
$311$	21.5145	1.21998	0.609988	−	0.792411i	$-0.291174\pi$
$311$	21.5145	1.21998	0.609988	+	0.792411i	$0.291174\pi$
$312$	−16.8765	−0.955446
$313$	28.9364	1.63558	0.817792	−	0.575514i	$-0.195198\pi$
$313$	28.9364	1.63558	0.817792	+	0.575514i	$0.195198\pi$
$314$	26.2911	1.48369
$315$	1.14270	0.0643840
$316$	21.5453	1.21202
$317$	6.46416	0.363063	0.181532	−	0.983385i	$-0.441895\pi$
$317$	6.46416	0.363063	0.181532	+	0.983385i	$0.441895\pi$
$318$	−16.8314	−0.943858
$319$	−15.8392	−0.886823
$320$	−0.776446	−0.0434046
$321$	−7.97908	−0.445349
$322$	0	0
$323$	7.80664	0.434373
$324$	4.45566	0.247537
$325$	−2.70486	−0.150039
$326$	60.5344	3.35269
$327$	−12.0846	−0.668279
$328$	20.2729	1.11938
$329$	−1.30563	−0.0719815
$330$	8.50270	0.468058
$331$	29.6022	1.62708	0.813542	−	0.581506i	$-0.197536\pi$
$331$	29.6022	1.62708	0.813542	+	0.581506i	$0.197536\pi$
$332$	−68.5204	−3.76054
$333$	−7.96889	−0.436692
$334$	−33.0120	−1.80634
$335$	−3.54763	−0.193828
$336$	7.93217	0.432736
$337$	−13.3817	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$337$	−13.3817	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$338$	−14.4412	−0.785499
$339$	−2.01474	−0.109425
$340$	29.8814	1.62055
$341$	−32.0717	−1.73678
$342$	2.95765	0.159931
$343$	−14.5057	−0.783236
$344$	73.7352	3.97553
$345$	0	0
$346$	−62.5506	−3.36274
$347$	−30.5155	−1.63816	−0.819080	−	0.573679i	$-0.805516\pi$
$347$	−30.5155	−1.63816	−0.819080	+	0.573679i	$0.805516\pi$
$348$	−21.0891	−1.13049
$349$	−12.1561	−0.650698	−0.325349	−	0.945594i	$-0.605482\pi$
$349$	−12.1561	−0.650698	−0.325349	+	0.945594i	$0.605482\pi$
$350$	2.90338	0.155192
$351$	−2.70486	−0.144375
$352$	17.2628	0.920110
$353$	15.2717	0.812830	0.406415	−	0.913689i	$-0.366779\pi$
$353$	15.2717	0.812830	0.406415	+	0.913689i	$0.366779\pi$
$354$	10.5311	0.559722
$355$	2.64731	0.140505
$356$	−23.7912	−1.26093
$357$	7.66340	0.405590
$358$	−32.8482	−1.73608
$359$	12.3073	0.649556	0.324778	−	0.945790i	$-0.394710\pi$
$359$	12.3073	0.649556	0.324778	+	0.945790i	$0.394710\pi$
$360$	6.23934	0.328842
$361$	−17.6450	−0.928682
$362$	35.3964	1.86039
$363$	0.198843	0.0104366
$364$	−13.7718	−0.721837
$365$	14.2342	0.745053
$366$	31.1692	1.62924
$367$	−26.7798	−1.39789	−0.698946	−	0.715174i	$-0.746347\pi$
$367$	−26.7798	−1.39789	−0.698946	+	0.715174i	$0.746347\pi$
$368$	0	0
$369$	3.24920	0.169147
$370$	−20.2473	−1.05261
$371$	−7.56977	−0.393003
$372$	−42.7019	−2.21399
$373$	−6.29562	−0.325975	−0.162988	−	0.986628i	$-0.552113\pi$
$373$	−6.29562	−0.325975	−0.162988	+	0.986628i	$0.552113\pi$
$374$	57.0224	2.94856
$375$	1.00000	0.0516398
$376$	−7.12894	−0.367647
$377$	12.8024	0.659356
$378$	2.90338	0.149334
$379$	−26.7523	−1.37417	−0.687086	−	0.726576i	$-0.741111\pi$
$379$	−26.7523	−1.37417	−0.687086	+	0.726576i	$0.741111\pi$
$380$	5.18666	0.266070
$381$	14.6913	0.752657
$382$	10.5473	0.539649
$383$	−1.14031	−0.0582670	−0.0291335	−	0.999576i	$-0.509275\pi$
$383$	−1.14031	−0.0582670	−0.0291335	+	0.999576i	$0.509275\pi$
$384$	−12.2898	−0.627162
$385$	3.82402	0.194890
$386$	−64.4017	−3.27796
$387$	11.8178	0.600731
$388$	−24.1883	−1.22797
$389$	−22.1919	−1.12518	−0.562588	−	0.826738i	$-0.690194\pi$
$389$	−22.1919	−1.12518	−0.562588	+	0.826738i	$0.690194\pi$
$390$	−6.87251	−0.348003
$391$	0	0
$392$	−35.5283	−1.79445
$393$	−15.2758	−0.770563
$394$	10.1489	0.511293
$395$	4.83548	0.243299
$396$	14.9107	0.749292
$397$	−27.2906	−1.36968	−0.684838	−	0.728696i	$-0.740127\pi$
$397$	−27.2906	−1.36968	−0.684838	+	0.728696i	$0.740127\pi$
$398$	−45.3906	−2.27523
$399$	1.33018	0.0665921
$400$	6.94159	0.347080
$401$	5.36590	0.267960	0.133980	−	0.990984i	$-0.457224\pi$
$401$	5.36590	0.267960	0.133980	+	0.990984i	$0.457224\pi$
$402$	−9.01381	−0.449568
$403$	25.9227	1.29130
$404$	−1.71522	−0.0853351
$405$	1.00000	0.0496904
$406$	−13.7420	−0.682003
$407$	−26.6676	−1.32186
$408$	41.8434	2.07156
$409$	−19.6317	−0.970724	−0.485362	−	0.874313i	$-0.661312\pi$
$409$	−19.6317	−0.970724	−0.485362	+	0.874313i	$0.661312\pi$
$410$	8.25556	0.407713
$411$	18.3702	0.906136
$412$	−35.2340	−1.73586
$413$	4.73627	0.233057
$414$	0	0
$415$	−15.3783	−0.754890
$416$	−13.9531	−0.684105
$417$	−5.35951	−0.262457
$418$	9.89767	0.484111
$419$	−7.35133	−0.359136	−0.179568	−	0.983746i	$-0.557470\pi$
$419$	−7.35133	−0.359136	−0.179568	+	0.983746i	$0.557470\pi$
$420$	5.09149	0.248439
$421$	−15.8645	−0.773187	−0.386594	−	0.922250i	$-0.626348\pi$
$421$	−15.8645	−0.773187	−0.386594	+	0.922250i	$0.626348\pi$
$422$	58.7227	2.85858
$423$	−1.14258	−0.0555541
$424$	−41.3322	−2.00727
$425$	6.70638	0.325307
$426$	6.72629	0.325890
$427$	14.0181	0.678383
$428$	−35.5521	−1.71847
$429$	−9.05173	−0.437022
$430$	30.0266	1.44801
$431$	5.21500	0.251198	0.125599	−	0.992081i	$-0.459915\pi$
$431$	5.21500	0.251198	0.125599	+	0.992081i	$0.459915\pi$
$432$	6.94159	0.333978
$433$	−0.968377	−0.0465372	−0.0232686	−	0.999729i	$-0.507407\pi$
$433$	−0.968377	−0.0465372	−0.0232686	+	0.999729i	$0.507407\pi$
$434$	−27.8252	−1.33565
$435$	−4.73310	−0.226935
$436$	−53.8448	−2.57870
$437$	0	0
$438$	36.1663	1.72809
$439$	−21.6424	−1.03294	−0.516468	−	0.856307i	$-0.672753\pi$
$439$	−21.6424	−1.03294	−0.516468	+	0.856307i	$0.672753\pi$
$440$	20.8798	0.995403
$441$	−5.69423	−0.271154
$442$	−46.0897	−2.19226
$443$	−34.9269	−1.65943	−0.829714	−	0.558188i	$-0.811497\pi$
$443$	−34.9269	−1.65943	−0.829714	+	0.558188i	$0.811497\pi$
$444$	−35.5067	−1.68507
$445$	−5.33955	−0.253119
$446$	72.2633	3.42177
$447$	−2.67776	−0.126654
$448$	−0.887246	−0.0419184
$449$	31.2124	1.47300	0.736502	−	0.676435i	$-0.236476\pi$
$449$	31.2124	1.47300	0.736502	+	0.676435i	$0.236476\pi$
$450$	2.54080	0.119774
$451$	10.8733	0.512006
$452$	−8.97698	−0.422242
$453$	−3.66170	−0.172042
$454$	39.8571	1.87058
$455$	−3.09085	−0.144901
$456$	7.26298	0.340120
$457$	−18.0905	−0.846239	−0.423119	−	0.906074i	$-0.639065\pi$
$457$	−18.0905	−0.846239	−0.423119	+	0.906074i	$0.639065\pi$
$458$	27.9368	1.30540
$459$	6.70638	0.313027
$460$	0	0
$461$	−33.6563	−1.56753	−0.783764	−	0.621058i	$-0.786703\pi$
$461$	−33.6563	−1.56753	−0.783764	+	0.621058i	$0.786703\pi$
$462$	9.71606	0.452032
$463$	−27.8490	−1.29425	−0.647126	−	0.762383i	$-0.724029\pi$
$463$	−27.8490	−1.29425	−0.647126	+	0.762383i	$0.724029\pi$
$464$	−32.8553	−1.52527
$465$	−9.58374	−0.444435
$466$	29.6750	1.37467
$467$	15.2836	0.707242	0.353621	−	0.935389i	$-0.384950\pi$
$467$	15.2836	0.707242	0.353621	+	0.935389i	$0.384950\pi$
$468$	−12.0519	−0.557101
$469$	−4.05388	−0.187191
$470$	−2.90306	−0.133908
$471$	10.3476	0.476791
$472$	25.8608	1.19034
$473$	39.5478	1.81841
$474$	12.2860	0.564314
$475$	1.16406	0.0534108
$476$	34.1455	1.56506
$477$	−6.62445	−0.303313
$478$	−25.9831	−1.18844
$479$	5.70082	0.260477	0.130239	−	0.991483i	$-0.458426\pi$
$479$	5.70082	0.260477	0.130239	+	0.991483i	$0.458426\pi$
$480$	5.15851	0.235453
$481$	21.5547	0.982811
$482$	13.3047	0.606012
$483$	0	0
$484$	0.885977	0.0402717
$485$	−5.42866	−0.246503
$486$	2.54080	0.115253
$487$	3.21993	0.145909	0.0729544	−	0.997335i	$-0.476757\pi$
$487$	3.21993	0.145909	0.0729544	+	0.997335i	$0.476757\pi$
$488$	76.5411	3.46485
$489$	23.8249	1.07740
$490$	−14.4679	−0.653593
$491$	−16.6006	−0.749177	−0.374588	−	0.927191i	$-0.622216\pi$
$491$	−16.6006	−0.749177	−0.374588	+	0.927191i	$0.622216\pi$
$492$	14.4773	0.652689
$493$	−31.7420	−1.42959
$494$	−8.00002	−0.359938
$495$	3.34647	0.150413
$496$	−66.5264	−2.98713
$497$	3.02509	0.135694
$498$	−39.0731	−1.75091
$499$	−9.87362	−0.442004	−0.221002	−	0.975273i	$-0.570933\pi$
$499$	−9.87362	−0.442004	−0.221002	+	0.975273i	$0.570933\pi$
$500$	4.45566	0.199263
$501$	−12.9928	−0.580474
$502$	43.7260	1.95159
$503$	−7.22581	−0.322183	−0.161092	−	0.986939i	$-0.551501\pi$
$503$	−7.22581	−0.322183	−0.161092	+	0.986939i	$0.551501\pi$
$504$	7.12971	0.317582
$505$	−0.384952	−0.0171301
$506$	0	0
$507$	−5.68373	−0.252423
$508$	65.4593	2.90429
$509$	41.2728	1.82939	0.914693	−	0.404150i	$-0.132433\pi$
$509$	41.2728	1.82939	0.914693	+	0.404150i	$0.132433\pi$
$510$	17.0396	0.754525
$511$	16.2655	0.719542
$512$	−50.8137	−2.24567
$513$	1.16406	0.0513946
$514$	−45.6190	−2.01217
$515$	−7.90770	−0.348455
$516$	52.6560	2.31805
$517$	−3.82360	−0.168162
$518$	−23.1367	−1.01657
$519$	−24.6185	−1.08063
$520$	−16.8765	−0.740086
$521$	22.9594	1.00587	0.502934	−	0.864325i	$-0.332254\pi$
$521$	22.9594	1.00587	0.502934	+	0.864325i	$0.332254\pi$
$522$	−12.0259	−0.526357
$523$	−20.2177	−0.884060	−0.442030	−	0.897000i	$-0.645742\pi$
$523$	−20.2177	−0.884060	−0.442030	+	0.897000i	$0.645742\pi$
$524$	−68.0638	−2.97338
$525$	1.14270	0.0498716
$526$	73.4917	3.20439
$527$	−64.2723	−2.79974
$528$	23.2298	1.01095
$529$	0	0
$530$	−16.8314	−0.731109
$531$	4.14480	0.179869
$532$	5.92681	0.256960
$533$	−8.78863	−0.380678
$534$	−13.5667	−0.587090
$535$	−7.97908	−0.344966
$536$	−22.1349	−0.956081
$537$	−12.9283	−0.557897
$538$	16.7282	0.721205
$539$	−19.0556	−0.820781
$540$	4.45566	0.191741
$541$	16.7282	0.719200	0.359600	−	0.933107i	$-0.382913\pi$
$541$	16.7282	0.719200	0.359600	+	0.933107i	$0.382913\pi$
$542$	5.92218	0.254379
$543$	13.9312	0.597845
$544$	34.5950	1.48325
$545$	−12.0846	−0.517647
$546$	−7.85323	−0.336087
$547$	−2.44447	−0.104518	−0.0522589	−	0.998634i	$-0.516642\pi$
$547$	−2.44447	−0.104518	−0.0522589	+	0.998634i	$0.516642\pi$
$548$	81.8515	3.49652
$549$	12.2675	0.523564
$550$	8.50270	0.362556
$551$	−5.50962	−0.234718
$552$	0	0
$553$	5.52551	0.234969
$554$	34.5268	1.46690
$555$	−7.96889	−0.338260
$556$	−23.8802	−1.01275
$557$	−5.42576	−0.229897	−0.114948	−	0.993371i	$-0.536670\pi$
$557$	−5.42576	−0.229897	−0.114948	+	0.993371i	$0.536670\pi$
$558$	−24.3504	−1.03083
$559$	−31.9654	−1.35199
$560$	7.93217	0.335195
$561$	22.4427	0.947531
$562$	4.64057	0.195751
$563$	19.7506	0.832391	0.416195	−	0.909275i	$-0.363363\pi$
$563$	19.7506	0.832391	0.416195	+	0.909275i	$0.363363\pi$
$564$	−5.09094	−0.214367
$565$	−2.01474	−0.0847606
$566$	56.3960	2.37050
$567$	1.14270	0.0479890
$568$	16.5175	0.693059
$569$	5.80927	0.243537	0.121769	−	0.992559i	$-0.461143\pi$
$569$	5.80927	0.243537	0.121769	+	0.992559i	$0.461143\pi$
$570$	2.95765	0.123882
$571$	−28.4182	−1.18927	−0.594633	−	0.803997i	$-0.702703\pi$
$571$	−28.4182	−1.18927	−0.594633	+	0.803997i	$0.702703\pi$
$572$	−40.3314	−1.68634
$573$	4.15119	0.173418
$574$	9.43365	0.393753
$575$	0	0
$576$	−0.776446	−0.0323519
$577$	5.76810	0.240129	0.120065	−	0.992766i	$-0.461690\pi$
$577$	5.76810	0.240129	0.120065	+	0.992766i	$0.461690\pi$
$578$	71.0804	2.95655
$579$	−25.3470	−1.05339
$580$	−21.0891	−0.875677
$581$	−17.5728	−0.729042
$582$	−13.7931	−0.571744
$583$	−22.1685	−0.918126
$584$	88.8121	3.67507
$585$	−2.70486	−0.111832
$586$	−48.0150	−1.98348
$587$	33.2982	1.37437	0.687183	−	0.726485i	$-0.258847\pi$
$587$	33.2982	1.37437	0.687183	+	0.726485i	$0.258847\pi$
$588$	−25.3716	−1.04631
$589$	−11.1561	−0.459678
$590$	10.5311	0.433559
$591$	3.99436	0.164306
$592$	−55.3168	−2.27350
$593$	−30.3323	−1.24560	−0.622798	−	0.782382i	$-0.714004\pi$
$593$	−30.3323	−1.24560	−0.622798	+	0.782382i	$0.714004\pi$
$594$	8.50270	0.348870
$595$	7.66340	0.314169
$596$	−11.9312	−0.488721
$597$	−17.8647	−0.731154
$598$	0	0
$599$	−3.76631	−0.153887	−0.0769436	−	0.997035i	$-0.524516\pi$
$599$	−3.76631	−0.153887	−0.0769436	+	0.997035i	$0.524516\pi$
$600$	6.23934	0.254720
$601$	22.8156	0.930666	0.465333	−	0.885136i	$-0.345935\pi$
$601$	22.8156	0.930666	0.465333	+	0.885136i	$0.345935\pi$
$602$	34.3115	1.39843
$603$	−3.54763	−0.144471
$604$	−16.3153	−0.663861
$605$	0.198843	0.00808412
$606$	−0.978085	−0.0397320
$607$	13.0820	0.530981	0.265490	−	0.964114i	$-0.414466\pi$
$607$	13.0820	0.530981	0.265490	+	0.964114i	$0.414466\pi$
$608$	6.00482	0.243528
$609$	−5.40852	−0.219164
$610$	31.1692	1.26201
$611$	3.09051	0.125029
$612$	29.8814	1.20788
$613$	33.4417	1.35070	0.675349	−	0.737498i	$-0.263993\pi$
$613$	33.4417	1.35070	0.675349	+	0.737498i	$0.263993\pi$
$614$	−72.5725	−2.92879
$615$	3.24920	0.131020
$616$	23.8593	0.961320
$617$	10.8178	0.435508	0.217754	−	0.976004i	$-0.430127\pi$
$617$	10.8178	0.435508	0.217754	+	0.976004i	$0.430127\pi$
$618$	−20.0919	−0.808214
$619$	2.23161	0.0896961	0.0448480	−	0.998994i	$-0.485720\pi$
$619$	2.23161	0.0896961	0.0448480	+	0.998994i	$0.485720\pi$
$620$	−42.7019	−1.71495
$621$	0	0
$622$	54.6640	2.19183
$623$	−6.10152	−0.244452
$624$	−18.7760	−0.751643
$625$	1.00000	0.0400000
$626$	73.5217	2.93852
$627$	3.89549	0.155571
$628$	46.1053	1.83980
$629$	−53.4424	−2.13089
$630$	2.90338	0.115673
$631$	1.68143	0.0669369	0.0334684	−	0.999440i	$-0.489345\pi$
$631$	1.68143	0.0669369	0.0334684	+	0.999440i	$0.489345\pi$
$632$	30.1702	1.20011
$633$	23.1119	0.918616
$634$	16.4241	0.652285
$635$	14.6913	0.583005
$636$	−29.5163	−1.17040
$637$	15.4021	0.610254
$638$	−40.2441	−1.59328
$639$	2.64731	0.104726
$640$	−12.2898	−0.485798
$641$	−4.59817	−0.181617	−0.0908084	−	0.995868i	$-0.528945\pi$
$641$	−4.59817	−0.181617	−0.0908084	+	0.995868i	$0.528945\pi$
$642$	−20.2732	−0.800121
$643$	8.29563	0.327148	0.163574	−	0.986531i	$-0.447698\pi$
$643$	8.29563	0.327148	0.163574	+	0.986531i	$0.447698\pi$
$644$	0	0
$645$	11.8178	0.465325
$646$	19.8351	0.780402
$647$	19.0943	0.750673	0.375336	−	0.926889i	$-0.377527\pi$
$647$	19.0943	0.750673	0.375336	+	0.926889i	$0.377527\pi$
$648$	6.23934	0.245104
$649$	13.8704	0.544462
$650$	−6.87251	−0.269562
$651$	−10.9514	−0.429218
$652$	106.156	4.15738
$653$	−37.6589	−1.47371	−0.736853	−	0.676054i	$-0.763689\pi$
$653$	−37.6589	−1.47371	−0.736853	+	0.676054i	$0.763689\pi$
$654$	−30.7045	−1.20064
$655$	−15.2758	−0.596875
$656$	22.5546	0.880610
$657$	14.2342	0.555330
$658$	−3.31734	−0.129323
$659$	48.1036	1.87385	0.936924	−	0.349532i	$-0.113659\pi$
$659$	48.1036	1.87385	0.936924	+	0.349532i	$0.113659\pi$
$660$	14.9107	0.580399
$661$	−13.5929	−0.528704	−0.264352	−	0.964426i	$-0.585158\pi$
$661$	−13.5929	−0.528704	−0.264352	+	0.964426i	$0.585158\pi$
$662$	75.2133	2.92325
$663$	−18.1398	−0.704493
$664$	−95.9503	−3.72359
$665$	1.33018	0.0515820
$666$	−20.2473	−0.784568
$667$	0	0
$668$	−57.8913	−2.23988
$669$	28.4412	1.09960
$670$	−9.01381	−0.348234
$671$	41.0528	1.58482
$672$	5.89464	0.227391
$673$	−18.9142	−0.729087	−0.364544	−	0.931186i	$-0.618775\pi$
$673$	−18.9142	−0.729087	−0.364544	+	0.931186i	$0.618775\pi$
$674$	−34.0002	−1.30964
$675$	1.00000	0.0384900
$676$	−25.3248	−0.974030
$677$	38.6657	1.48604	0.743022	−	0.669267i	$-0.233392\pi$
$677$	38.6657	1.48604	0.743022	+	0.669267i	$0.233392\pi$
$678$	−5.11904	−0.196595
$679$	−6.20334	−0.238062
$680$	41.8434	1.60462
$681$	15.6868	0.601120
$682$	−81.4877	−3.12033
$683$	−21.3678	−0.817615	−0.408807	−	0.912621i	$-0.634055\pi$
$683$	−21.3678	−0.817615	−0.408807	+	0.912621i	$0.634055\pi$
$684$	5.18666	0.198317
$685$	18.3702	0.701890
$686$	−36.8561	−1.40717
$687$	10.9953	0.419497
$688$	82.0342	3.12752
$689$	17.9182	0.682630
$690$	0	0
$691$	−3.45212	−0.131325	−0.0656623	−	0.997842i	$-0.520916\pi$
$691$	−3.45212	−0.131325	−0.0656623	+	0.997842i	$0.520916\pi$
$692$	−109.692	−4.16985
$693$	3.82402	0.145262
$694$	−77.5339	−2.94315
$695$	−5.35951	−0.203298
$696$	−29.5314	−1.11939
$697$	21.7904	0.825370
$698$	−30.8861	−1.16906
$699$	11.6794	0.441755
$700$	5.09149	0.192440
$701$	−20.7828	−0.784956	−0.392478	−	0.919761i	$-0.628382\pi$
$701$	−20.7828	−0.784956	−0.392478	+	0.919761i	$0.628382\pi$
$702$	−6.87251	−0.259386
$703$	−9.27627	−0.349861
$704$	−2.59835	−0.0979290
$705$	−1.14258	−0.0430320
$706$	38.8023	1.46034
$707$	−0.439885	−0.0165436
$708$	18.4678	0.694063
$709$	−52.2980	−1.96409	−0.982046	−	0.188640i	$-0.939592\pi$
$709$	−52.2980	−1.96409	−0.982046	+	0.188640i	$0.939592\pi$
$710$	6.72629	0.252433
$711$	4.83548	0.181345
$712$	−33.3153	−1.24854
$713$	0	0
$714$	19.4712	0.728690
$715$	−9.05173	−0.338515
$716$	−57.6041	−2.15276
$717$	−10.2263	−0.381910
$718$	31.2705	1.16700
$719$	−25.9527	−0.967871	−0.483935	−	0.875104i	$-0.660793\pi$
$719$	−25.9527	−0.967871	−0.483935	+	0.875104i	$0.660793\pi$
$720$	6.94159	0.258698
$721$	−9.03615	−0.336524
$722$	−44.8323	−1.66849
$723$	5.23642	0.194744
$724$	62.0727	2.30691
$725$	−4.73310	−0.175783
$726$	0.505220	0.0187505
$727$	22.7831	0.844978	0.422489	−	0.906368i	$-0.361156\pi$
$727$	22.7831	0.844978	0.422489	+	0.906368i	$0.361156\pi$
$728$	−19.2849	−0.714745
$729$	1.00000	0.0370370
$730$	36.1663	1.33857
$731$	79.2546	2.93134
$732$	54.6598	2.02028
$733$	17.9865	0.664348	0.332174	−	0.943218i	$-0.392218\pi$
$733$	17.9865	0.664348	0.332174	+	0.943218i	$0.392218\pi$
$734$	−68.0420	−2.51148
$735$	−5.69423	−0.210035
$736$	0	0
$737$	−11.8720	−0.437312
$738$	8.25556	0.303892
$739$	10.3741	0.381617	0.190809	−	0.981627i	$-0.438889\pi$
$739$	10.3741	0.381617	0.190809	+	0.981627i	$0.438889\pi$
$740$	−35.5067	−1.30525
$741$	−3.14862	−0.115668
$742$	−19.2333	−0.706076
$743$	−5.58723	−0.204975	−0.102488	−	0.994734i	$-0.532680\pi$
$743$	−5.58723	−0.204975	−0.102488	+	0.994734i	$0.532680\pi$
$744$	−59.7962	−2.19224
$745$	−2.67776	−0.0981056
$746$	−15.9959	−0.585652
$747$	−15.3783	−0.562662
$748$	99.9970	3.65625
$749$	−9.11771	−0.333154
$750$	2.54080	0.0927769
$751$	−20.9405	−0.764128	−0.382064	−	0.924136i	$-0.624787\pi$
$751$	−20.9405	−0.764128	−0.382064	+	0.924136i	$0.624787\pi$
$752$	−7.93131	−0.289225
$753$	17.2095	0.627150
$754$	32.5283	1.18461
$755$	−3.66170	−0.133263
$756$	5.09149	0.185176
$757$	−12.7649	−0.463947	−0.231973	−	0.972722i	$-0.574518\pi$
$757$	−12.7649	−0.463947	−0.231973	+	0.972722i	$0.574518\pi$
$758$	−67.9722	−2.46886
$759$	0	0
$760$	7.26298	0.263456
$761$	17.6304	0.639102	0.319551	−	0.947569i	$-0.396468\pi$
$761$	17.6304	0.639102	0.319551	+	0.947569i	$0.396468\pi$
$762$	37.3276	1.35224
$763$	−13.8091	−0.499923
$764$	18.4963	0.669172
$765$	6.70638	0.242470
$766$	−2.89729	−0.104683
$767$	−11.2111	−0.404810
$768$	−29.6731	−1.07073
$769$	51.4934	1.85690	0.928450	−	0.371458i	$-0.121142\pi$
$769$	51.4934	1.85690	0.928450	+	0.371458i	$0.121142\pi$
$770$	9.71606	0.350142
$771$	−17.9546	−0.646619
$772$	−112.938	−4.06472
$773$	20.6301	0.742013	0.371007	−	0.928630i	$-0.379013\pi$
$773$	20.6301	0.742013	0.371007	+	0.928630i	$0.379013\pi$
$774$	30.0266	1.07928
$775$	−9.58374	−0.344258
$776$	−33.8713	−1.21591
$777$	−9.10606	−0.326678
$778$	−56.3852	−2.02151
$779$	3.78227	0.135514
$780$	−12.0519	−0.431529
$781$	8.85915	0.317005
$782$	0	0
$783$	−4.73310	−0.169147
$784$	−39.5270	−1.41168
$785$	10.3476	0.369321
$786$	−38.8128	−1.38441
$787$	−14.1858	−0.505670	−0.252835	−	0.967509i	$-0.581363\pi$
$787$	−14.1858	−0.505670	−0.252835	+	0.967509i	$0.581363\pi$
$788$	17.7975	0.634010
$789$	28.9246	1.02974
$790$	12.2860	0.437116
$791$	−2.30224	−0.0818583
$792$	20.8798	0.741930
$793$	−33.1819	−1.17832
$794$	−69.3399	−2.46078
$795$	−6.62445	−0.234945
$796$	−79.5991	−2.82131
$797$	48.0072	1.70050	0.850251	−	0.526377i	$-0.176450\pi$
$797$	48.0072	1.70050	0.850251	+	0.526377i	$0.176450\pi$
$798$	3.37971	0.119640
$799$	−7.66257	−0.271082
$800$	5.15851	0.182381
$801$	−5.33955	−0.188664
$802$	13.6337	0.481422
$803$	47.6343	1.68098
$804$	−15.8070	−0.557471
$805$	0	0
$806$	65.8644	2.31997
$807$	6.58384	0.231762
$808$	−2.40185	−0.0844967
$809$	44.7675	1.57394	0.786971	−	0.616990i	$-0.211648\pi$
$809$	44.7675	1.57394	0.786971	+	0.616990i	$0.211648\pi$
$810$	2.54080	0.0892746
$811$	26.0077	0.913253	0.456627	−	0.889658i	$-0.349058\pi$
$811$	26.0077	0.913253	0.456627	+	0.889658i	$0.349058\pi$
$812$	−24.0985	−0.845693
$813$	2.33083	0.0817459
$814$	−67.7571	−2.37488
$815$	23.8249	0.834551
$816$	46.5530	1.62968
$817$	13.7566	0.481283
$818$	−49.8802	−1.74402
$819$	−3.09085	−0.108003
$820$	14.4773	0.505570
$821$	14.4511	0.504348	0.252174	−	0.967682i	$-0.418855\pi$
$821$	14.4511	0.504348	0.252174	+	0.967682i	$0.418855\pi$
$822$	46.6750	1.62798
$823$	−3.16235	−0.110233	−0.0551163	−	0.998480i	$-0.517553\pi$
$823$	−3.16235	−0.110233	−0.0551163	+	0.998480i	$0.517553\pi$
$824$	−49.3388	−1.71880
$825$	3.34647	0.116509
$826$	12.0339	0.418714
$827$	12.5956	0.437992	0.218996	−	0.975726i	$-0.429722\pi$
$827$	12.5956	0.437992	0.218996	+	0.975726i	$0.429722\pi$
$828$	0	0
$829$	−33.0780	−1.14885	−0.574423	−	0.818559i	$-0.694773\pi$
$829$	−33.0780	−1.14885	−0.574423	+	0.818559i	$0.694773\pi$
$830$	−39.0731	−1.35625
$831$	13.5890	0.471396
$832$	2.10018	0.0728105
$833$	−38.1877	−1.32313
$834$	−13.6174	−0.471534
$835$	−12.9928	−0.449633
$836$	17.3570	0.600304
$837$	−9.58374	−0.331263
$838$	−18.6782	−0.645229
$839$	49.5135	1.70940	0.854698	−	0.519125i	$-0.173742\pi$
$839$	49.5135	1.70940	0.854698	+	0.519125i	$0.173742\pi$
$840$	7.12971	0.245998
$841$	−6.59776	−0.227509
$842$	−40.3084	−1.38912
$843$	1.82642	0.0629054
$844$	102.979	3.54468
$845$	−5.68373	−0.195526
$846$	−2.90306	−0.0998093
$847$	0.227218	0.00780731
$848$	−45.9842	−1.57911
$849$	22.1962	0.761770
$850$	17.0396	0.584453
$851$	0	0
$852$	11.7955	0.404108
$853$	−28.4976	−0.975738	−0.487869	−	0.872917i	$-0.662226\pi$
$853$	−28.4976	−0.975738	−0.487869	+	0.872917i	$0.662226\pi$
$854$	35.6172	1.21879
$855$	1.16406	0.0398101
$856$	−49.7842	−1.70159
$857$	3.13669	0.107147	0.0535737	−	0.998564i	$-0.482939\pi$
$857$	3.13669	0.107147	0.0535737	+	0.998564i	$0.482939\pi$
$858$	−22.9986	−0.785160
$859$	17.8445	0.608847	0.304424	−	0.952537i	$-0.401536\pi$
$859$	17.8445	0.608847	0.304424	+	0.952537i	$0.401536\pi$
$860$	52.6560	1.79556
$861$	3.71287	0.126534
$862$	13.2503	0.451306
$863$	−13.8466	−0.471343	−0.235671	−	0.971833i	$-0.575729\pi$
$863$	−13.8466	−0.471343	−0.235671	+	0.971833i	$0.575729\pi$
$864$	5.15851	0.175496
$865$	−24.6185	−0.837053
$866$	−2.46045	−0.0836096
$867$	27.9756	0.950101
$868$	−48.7956	−1.65623
$869$	16.1818	0.548929
$870$	−12.0259	−0.407715
$871$	9.59584	0.325143
$872$	−75.3999	−2.55336
$873$	−5.42866	−0.183732
$874$	0	0
$875$	1.14270	0.0386304
$876$	63.4228	2.14286
$877$	18.2493	0.616234	0.308117	−	0.951348i	$-0.400301\pi$
$877$	18.2493	0.616234	0.308117	+	0.951348i	$0.400301\pi$
$878$	−54.9890	−1.85579
$879$	−18.8976	−0.637400
$880$	23.2298	0.783077
$881$	−11.8649	−0.399739	−0.199869	−	0.979823i	$-0.564052\pi$
$881$	−11.8649	−0.399739	−0.199869	+	0.979823i	$0.564052\pi$
$882$	−14.4679	−0.487160
$883$	7.28931	0.245305	0.122652	−	0.992450i	$-0.460860\pi$
$883$	7.28931	0.245305	0.122652	+	0.992450i	$0.460860\pi$
$884$	−80.8250	−2.71844
$885$	4.14480	0.139326
$886$	−88.7423	−2.98136
$887$	−8.35652	−0.280584	−0.140292	−	0.990110i	$-0.544804\pi$
$887$	−8.35652	−0.280584	−0.140292	+	0.990110i	$0.544804\pi$
$888$	−49.7206	−1.66851
$889$	16.7877	0.563043
$890$	−13.5667	−0.454758
$891$	3.34647	0.112111
$892$	126.724	4.24304
$893$	−1.33003	−0.0445078
$894$	−6.80365	−0.227548
$895$	−12.9283	−0.432145
$896$	−14.0436	−0.469164
$897$	0	0
$898$	79.3045	2.64642
$899$	45.3608	1.51287
$900$	4.45566	0.148522
$901$	−44.4261	−1.48005
$902$	27.6270	0.919878
$903$	13.5042	0.449392
$904$	−12.5706	−0.418093
$905$	13.9312	0.463089
$906$	−9.30366	−0.309093
$907$	19.4144	0.644644	0.322322	−	0.946630i	$-0.395537\pi$
$907$	19.4144	0.644644	0.322322	+	0.946630i	$0.395537\pi$
$908$	69.8952	2.31955
$909$	−0.384952	−0.0127680
$910$	−7.85323	−0.260332
$911$	−33.4386	−1.10787	−0.553935	−	0.832560i	$-0.686874\pi$
$911$	−33.4386	−1.10787	−0.553935	+	0.832560i	$0.686874\pi$
$912$	8.08044	0.267570
$913$	−51.4629	−1.70317
$914$	−45.9644	−1.52037
$915$	12.2675	0.405551
$916$	48.9913	1.61872
$917$	−17.4557	−0.576438
$918$	17.0396	0.562390
$919$	−1.15159	−0.0379873	−0.0189937	−	0.999820i	$-0.506046\pi$
$919$	−1.15159	−0.0379873	−0.0189937	+	0.999820i	$0.506046\pi$
$920$	0	0
$921$	−28.5629	−0.941178
$922$	−85.5138	−2.81625
$923$	−7.16062	−0.235695
$924$	17.0385	0.560526
$925$	−7.96889	−0.262015
$926$	−70.7586	−2.32527
$927$	−7.90770	−0.259723
$928$	−24.4157	−0.801486
$929$	−38.6827	−1.26914	−0.634568	−	0.772867i	$-0.718822\pi$
$929$	−38.6827	−1.26914	−0.634568	+	0.772867i	$0.718822\pi$
$930$	−24.3504	−0.798480
$931$	−6.62843	−0.217238
$932$	52.0393	1.70461
$933$	21.5145	0.704353
$934$	38.8326	1.27064
$935$	22.4427	0.733955
$936$	−16.8765	−0.551627
$937$	−38.7902	−1.26722	−0.633610	−	0.773653i	$-0.718427\pi$
$937$	−38.7902	−1.26722	−0.633610	+	0.773653i	$0.718427\pi$
$938$	−10.3001	−0.336310
$939$	28.9364	0.944305
$940$	−5.09094	−0.166048
$941$	−37.3129	−1.21637	−0.608183	−	0.793797i	$-0.708101\pi$
$941$	−37.3129	−1.21637	−0.608183	+	0.793797i	$0.708101\pi$
$942$	26.2911	0.856610
$943$	0	0
$944$	28.7715	0.936433
$945$	1.14270	0.0371721
$946$	100.483	3.26699
$947$	−0.261210	−0.00848819	−0.00424410	−	0.999991i	$-0.501351\pi$
$947$	−0.261210	−0.00848819	−0.00424410	+	0.999991i	$0.501351\pi$
$948$	21.5453	0.699758
$949$	−38.5016	−1.24981
$950$	2.95765	0.0959587
$951$	6.46416	0.209615
$952$	47.8146	1.54968
$953$	−0.0175517	−0.000568555 0	−0.000284278	−	1.00000i	$-0.500090\pi$
$953$	−0.0175517	−0.000568555 0	−0.000284278		1.00000i	$0.500090\pi$
$954$	−16.8314	−0.544937
$955$	4.15119	0.134329
$956$	−45.5651	−1.47368
$957$	−15.8392	−0.512007
$958$	14.4846	0.467977
$959$	20.9917	0.677857
$960$	−0.776446	−0.0250597
$961$	60.8481	1.96284
$962$	54.7662	1.76573
$963$	−7.97908	−0.257122
$964$	23.3317	0.751463
$965$	−25.3470	−0.815950
$966$	0	0
$967$	−15.1684	−0.487783	−0.243892	−	0.969802i	$-0.578424\pi$
$967$	−15.1684	−0.487783	−0.243892	+	0.969802i	$0.578424\pi$
$968$	1.24065	0.0398760
$969$	7.80664	0.250785
$970$	−13.7931	−0.442871
$971$	10.1767	0.326587	0.163294	−	0.986578i	$-0.447788\pi$
$971$	10.1767	0.326587	0.163294	+	0.986578i	$0.447788\pi$
$972$	4.45566	0.142915
$973$	−6.12433	−0.196337
$974$	8.18119	0.262142
$975$	−2.70486	−0.0866249
$976$	85.1559	2.72577
$977$	−17.0140	−0.544325	−0.272162	−	0.962251i	$-0.587739\pi$
$977$	−17.0140	−0.544325	−0.272162	+	0.962251i	$0.587739\pi$
$978$	60.5344	1.93568
$979$	−17.8686	−0.571084
$980$	−25.3716	−0.810465
$981$	−12.0846	−0.385831
$982$	−42.1789	−1.34598
$983$	−12.5803	−0.401248	−0.200624	−	0.979668i	$-0.564297\pi$
$983$	−12.5803	−0.401248	−0.200624	+	0.979668i	$0.564297\pi$
$984$	20.2729	0.646275
$985$	3.99436	0.127271
$986$	−80.6500	−2.56842
$987$	−1.30563	−0.0415586
$988$	−14.0292	−0.446328
$989$	0	0
$990$	8.50270	0.270234
$991$	−9.24309	−0.293617	−0.146808	−	0.989165i	$-0.546900\pi$
$991$	−9.24309	−0.293617	−0.146808	+	0.989165i	$0.546900\pi$
$992$	−49.4378	−1.56965
$993$	29.6022	0.939398
$994$	7.68615	0.243790
$995$	−17.8647	−0.566349
$996$	−68.5204	−2.17115
$997$	36.2821	1.14907	0.574533	−	0.818481i	$-0.305184\pi$
$997$	36.2821	1.14907	0.574533	+	0.818481i	$0.305184\pi$
$998$	−25.0869	−0.794112
$999$	−7.96889	−0.252124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bi.1.8	yes	8
23.22	odd	2		7935.2.a.bh.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.8	✓	8	23.22	odd	2
7935.2.a.bi.1.8	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54080 q^{2} +1.00000 q^{3} +4.45566 q^{4} +1.00000 q^{5} +2.54080 q^{6} +1.14270 q^{7} +6.23934 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54080 q^{2} +1.00000 q^{3} +4.45566 q^{4} +1.00000 q^{5} +2.54080 q^{6} +1.14270 q^{7} +6.23934 q^{8} +1.00000 q^{9} +2.54080 q^{10} +3.34647 q^{11} +4.45566 q^{12} -2.70486 q^{13} +2.90338 q^{14} +1.00000 q^{15} +6.94159 q^{16} +6.70638 q^{17} +2.54080 q^{18} +1.16406 q^{19} +4.45566 q^{20} +1.14270 q^{21} +8.50270 q^{22} +6.23934 q^{24} +1.00000 q^{25} -6.87251 q^{26} +1.00000 q^{27} +5.09149 q^{28} -4.73310 q^{29} +2.54080 q^{30} -9.58374 q^{31} +5.15851 q^{32} +3.34647 q^{33} +17.0396 q^{34} +1.14270 q^{35} +4.45566 q^{36} -7.96889 q^{37} +2.95765 q^{38} -2.70486 q^{39} +6.23934 q^{40} +3.24920 q^{41} +2.90338 q^{42} +11.8178 q^{43} +14.9107 q^{44} +1.00000 q^{45} -1.14258 q^{47} +6.94159 q^{48} -5.69423 q^{49} +2.54080 q^{50} +6.70638 q^{51} -12.0519 q^{52} -6.62445 q^{53} +2.54080 q^{54} +3.34647 q^{55} +7.12971 q^{56} +1.16406 q^{57} -12.0259 q^{58} +4.14480 q^{59} +4.45566 q^{60} +12.2675 q^{61} -24.3504 q^{62} +1.14270 q^{63} -0.776446 q^{64} -2.70486 q^{65} +8.50270 q^{66} -3.54763 q^{67} +29.8814 q^{68} +2.90338 q^{70} +2.64731 q^{71} +6.23934 q^{72} +14.2342 q^{73} -20.2473 q^{74} +1.00000 q^{75} +5.18666 q^{76} +3.82402 q^{77} -6.87251 q^{78} +4.83548 q^{79} +6.94159 q^{80} +1.00000 q^{81} +8.25556 q^{82} -15.3783 q^{83} +5.09149 q^{84} +6.70638 q^{85} +30.0266 q^{86} -4.73310 q^{87} +20.8798 q^{88} -5.33955 q^{89} +2.54080 q^{90} -3.09085 q^{91} -9.58374 q^{93} -2.90306 q^{94} +1.16406 q^{95} +5.15851 q^{96} -5.42866 q^{97} -14.4679 q^{98} +3.34647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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