LMFDB - Embedded newform 1859.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.28561300.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 $ x^6 - 9x^4 - x^3 + 22x^2 + 4*x - 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.35258$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53464 q^{2} -2.99024 q^{3} +4.42441 q^{4} +3.35258 q^{5} +7.57919 q^{6} -1.91841 q^{7} -6.14501 q^{8} +5.94153 q^{9} +O(q^{10})$	\(q-2.53464 q^{2} -2.99024 q^{3} +4.42441 q^{4} +3.35258 q^{5} +7.57919 q^{6} -1.91841 q^{7} -6.14501 q^{8} +5.94153 q^{9} -8.49760 q^{10} +1.00000 q^{11} -13.2300 q^{12} +4.86248 q^{14} -10.0250 q^{15} +6.72659 q^{16} -1.97271 q^{17} -15.0596 q^{18} +2.82126 q^{19} +14.8332 q^{20} +5.73650 q^{21} -2.53464 q^{22} -0.439850 q^{23} +18.3751 q^{24} +6.23981 q^{25} -8.79587 q^{27} -8.48783 q^{28} +2.49845 q^{29} +25.4098 q^{30} +4.63180 q^{31} -4.75947 q^{32} -2.99024 q^{33} +5.00013 q^{34} -6.43163 q^{35} +26.2878 q^{36} +7.79007 q^{37} -7.15087 q^{38} -20.6017 q^{40} +9.71084 q^{41} -14.5400 q^{42} -6.59493 q^{43} +4.42441 q^{44} +19.9195 q^{45} +1.11486 q^{46} +0.104554 q^{47} -20.1141 q^{48} -3.31970 q^{49} -15.8157 q^{50} +5.89889 q^{51} +0.381991 q^{53} +22.2944 q^{54} +3.35258 q^{55} +11.7887 q^{56} -8.43623 q^{57} -6.33267 q^{58} +1.03254 q^{59} -44.3548 q^{60} -5.73635 q^{61} -11.7399 q^{62} -11.3983 q^{63} -1.38963 q^{64} +7.57919 q^{66} +7.25193 q^{67} -8.72810 q^{68} +1.31526 q^{69} +16.3019 q^{70} -11.2672 q^{71} -36.5108 q^{72} -0.808179 q^{73} -19.7450 q^{74} -18.6585 q^{75} +12.4824 q^{76} -1.91841 q^{77} -7.04501 q^{79} +22.5514 q^{80} +8.47718 q^{81} -24.6135 q^{82} -8.70830 q^{83} +25.3807 q^{84} -6.61369 q^{85} +16.7158 q^{86} -7.47095 q^{87} -6.14501 q^{88} -10.3321 q^{89} -50.4887 q^{90} -1.94608 q^{92} -13.8502 q^{93} -0.265006 q^{94} +9.45849 q^{95} +14.2319 q^{96} +19.3846 q^{97} +8.41426 q^{98} +5.94153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	$ 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} - 3 q^{10} + 6 q^{11} - 17 q^{12} + 12 q^{14} - 4 q^{15} + 8 q^{16} + 2 q^{17} - 6 q^{18} + 10 q^{19} + 15 q^{20} + 12 q^{21} + 3 q^{23} + 14 q^{24} - 6 q^{25} + 10 q^{27} + 16 q^{28} + 3 q^{29} + 19 q^{30} + 5 q^{31} - q^{32} + q^{33} - 5 q^{34} - 13 q^{35} + 20 q^{36} + 25 q^{37} - 27 q^{38} - 8 q^{40} + 24 q^{41} + 13 q^{42} - 8 q^{43} + 8 q^{44} + 27 q^{45} + 18 q^{46} + 10 q^{47} - 28 q^{48} - q^{49} - 26 q^{50} - 17 q^{51} + 10 q^{53} + 47 q^{54} + 6 q^{55} + 15 q^{56} + 6 q^{58} - 4 q^{59} - 61 q^{60} - 21 q^{61} - 5 q^{62} + 6 q^{63} - 27 q^{64} + 12 q^{66} + 21 q^{67} + 14 q^{68} + 5 q^{69} + 31 q^{70} - 3 q^{71} - 50 q^{72} + 13 q^{73} - 38 q^{74} - 23 q^{75} + 8 q^{76} + 3 q^{77} - 4 q^{79} + 44 q^{80} + 34 q^{81} - 33 q^{82} + 8 q^{83} + 47 q^{84} - 13 q^{85} - 11 q^{86} - 51 q^{87} - 3 q^{88} - 9 q^{89} - 70 q^{90} + 15 q^{92} - 21 q^{93} + 10 q^{94} + 27 q^{95} - 19 q^{96} + 15 q^{97} + 21 q^{98} + 7 q^{99}+O(q^{100}) $ 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 - 3 * q^10 + 6 * q^11 - 17 * q^12 + 12 * q^14 - 4 * q^15 + 8 * q^16 + 2 * q^17 - 6 * q^18 + 10 * q^19 + 15 * q^20 + 12 * q^21 + 3 * q^23 + 14 * q^24 - 6 * q^25 + 10 * q^27 + 16 * q^28 + 3 * q^29 + 19 * q^30 + 5 * q^31 - q^32 + q^33 - 5 * q^34 - 13 * q^35 + 20 * q^36 + 25 * q^37 - 27 * q^38 - 8 * q^40 + 24 * q^41 + 13 * q^42 - 8 * q^43 + 8 * q^44 + 27 * q^45 + 18 * q^46 + 10 * q^47 - 28 * q^48 - q^49 - 26 * q^50 - 17 * q^51 + 10 * q^53 + 47 * q^54 + 6 * q^55 + 15 * q^56 + 6 * q^58 - 4 * q^59 - 61 * q^60 - 21 * q^61 - 5 * q^62 + 6 * q^63 - 27 * q^64 + 12 * q^66 + 21 * q^67 + 14 * q^68 + 5 * q^69 + 31 * q^70 - 3 * q^71 - 50 * q^72 + 13 * q^73 - 38 * q^74 - 23 * q^75 + 8 * q^76 + 3 * q^77 - 4 * q^79 + 44 * q^80 + 34 * q^81 - 33 * q^82 + 8 * q^83 + 47 * q^84 - 13 * q^85 - 11 * q^86 - 51 * q^87 - 3 * q^88 - 9 * q^89 - 70 * q^90 + 15 * q^92 - 21 * q^93 + 10 * q^94 + 27 * q^95 - 19 * q^96 + 15 * q^97 + 21 * q^98 + 7 * 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 $

$2$	−2.53464	−1.79226	−0.896131	−	0.443789i	$-0.853634\pi$
$2$	−2.53464	−1.79226	−0.896131	+	0.443789i	$0.853634\pi$
$3$	−2.99024	−1.72642	−0.863208	−	0.504849i	$-0.831548\pi$
$3$	−2.99024	−1.72642	−0.863208	+	0.504849i	$0.831548\pi$
$4$	4.42441	2.21221
$5$	3.35258	1.49932	0.749660	−	0.661823i	$-0.230217\pi$
$5$	3.35258	1.49932	0.749660	+	0.661823i	$0.230217\pi$
$6$	7.57919	3.09419
$7$	−1.91841	−0.725091	−0.362545	−	0.931966i	$-0.618092\pi$
$7$	−1.91841	−0.725091	−0.362545	+	0.931966i	$0.618092\pi$
$8$	−6.14501	−2.17259
$9$	5.94153	1.98051
$10$	−8.49760	−2.68718
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−13.2300	−3.81919
$13$	0	0
$13$	0	0
$14$	4.86248	1.29955
$15$	−10.0250	−2.58845
$16$	6.72659	1.68165
$17$	−1.97271	−0.478454	−0.239227	−	0.970964i	$-0.576894\pi$
$17$	−1.97271	−0.478454	−0.239227	+	0.970964i	$0.576894\pi$
$18$	−15.0596	−3.54959
$19$	2.82126	0.647240	0.323620	−	0.946187i	$-0.395100\pi$
$19$	2.82126	0.647240	0.323620	+	0.946187i	$0.395100\pi$
$20$	14.8332	3.31680
$21$	5.73650	1.25181
$22$	−2.53464	−0.540388
$23$	−0.439850	−0.0917150	−0.0458575	−	0.998948i	$-0.514602\pi$
$23$	−0.439850	−0.0917150	−0.0458575	+	0.998948i	$0.514602\pi$
$24$	18.3751	3.75079
$25$	6.23981	1.24796
$26$	0	0
$27$	−8.79587	−1.69277
$28$	−8.48783	−1.60405
$29$	2.49845	0.463950	0.231975	−	0.972722i	$-0.425481\pi$
$29$	2.49845	0.463950	0.231975	+	0.972722i	$0.425481\pi$
$30$	25.4098	4.63918
$31$	4.63180	0.831895	0.415948	−	0.909389i	$-0.363450\pi$
$31$	4.63180	0.831895	0.415948	+	0.909389i	$0.363450\pi$
$32$	−4.75947	−0.841363
$33$	−2.99024	−0.520534
$34$	5.00013	0.857514
$35$	−6.43163	−1.08714
$36$	26.2878	4.38129
$37$	7.79007	1.28068	0.640340	−	0.768092i	$-0.278794\pi$
$37$	7.79007	1.28068	0.640340	+	0.768092i	$0.278794\pi$
$38$	−7.15087	−1.16002
$39$	0	0
$40$	−20.6017	−3.25741
$41$	9.71084	1.51658	0.758289	−	0.651918i	$-0.226035\pi$
$41$	9.71084	1.51658	0.758289	+	0.651918i	$0.226035\pi$
$42$	−14.5400	−2.24357
$43$	−6.59493	−1.00572	−0.502859	−	0.864369i	$-0.667718\pi$
$43$	−6.59493	−1.00572	−0.502859	+	0.864369i	$0.667718\pi$
$44$	4.42441	0.667005
$45$	19.9195	2.96942
$46$	1.11486	0.164377
$47$	0.104554	0.0152507	0.00762536	−	0.999971i	$-0.497573\pi$
$47$	0.104554	0.0152507	0.00762536	+	0.999971i	$0.497573\pi$
$48$	−20.1141	−2.90322
$49$	−3.31970	−0.474243
$50$	−15.8157	−2.23667
$51$	5.89889	0.826010
$52$	0	0
$53$	0.381991	0.0524705	0.0262352	−	0.999656i	$-0.491648\pi$
$53$	0.381991	0.0524705	0.0262352	+	0.999656i	$0.491648\pi$
$54$	22.2944	3.03388
$55$	3.35258	0.452062
$56$	11.7887	1.57533
$57$	−8.43623	−1.11741
$58$	−6.33267	−0.831520
$59$	1.03254	0.134426	0.0672128	−	0.997739i	$-0.478589\pi$
$59$	1.03254	0.134426	0.0672128	+	0.997739i	$0.478589\pi$
$60$	−44.3548	−5.72618
$61$	−5.73635	−0.734464	−0.367232	−	0.930129i	$-0.619695\pi$
$61$	−5.73635	−0.734464	−0.367232	+	0.930129i	$0.619695\pi$
$62$	−11.7399	−1.49097
$63$	−11.3983	−1.43605
$64$	−1.38963	−0.173704
$65$	0	0
$66$	7.57919	0.932933
$67$	7.25193	0.885964	0.442982	−	0.896530i	$-0.353921\pi$
$67$	7.25193	0.885964	0.442982	+	0.896530i	$0.353921\pi$
$68$	−8.72810	−1.05844
$69$	1.31526	0.158338
$70$	16.3019	1.94845
$71$	−11.2672	−1.33717	−0.668586	−	0.743635i	$-0.733100\pi$
$71$	−11.2672	−1.33717	−0.668586	+	0.743635i	$0.733100\pi$
$72$	−36.5108	−4.30284
$73$	−0.808179	−0.0945902	−0.0472951	−	0.998881i	$-0.515060\pi$
$73$	−0.808179	−0.0945902	−0.0472951	+	0.998881i	$0.515060\pi$
$74$	−19.7450	−2.29531
$75$	−18.6585	−2.15450
$76$	12.4824	1.43183
$77$	−1.91841	−0.218623
$78$	0	0
$79$	−7.04501	−0.792625	−0.396313	−	0.918116i	$-0.629710\pi$
$79$	−7.04501	−0.792625	−0.396313	+	0.918116i	$0.629710\pi$
$80$	22.5514	2.52133
$81$	8.47718	0.941908
$82$	−24.6135	−2.71811
$83$	−8.70830	−0.955860	−0.477930	−	0.878398i	$-0.658613\pi$
$83$	−8.70830	−0.955860	−0.477930	+	0.878398i	$0.658613\pi$
$84$	25.3807	2.76926
$85$	−6.61369	−0.717355
$86$	16.7158	1.80251
$87$	−7.47095	−0.800970
$88$	−6.14501	−0.655061
$89$	−10.3321	−1.09520	−0.547599	−	0.836741i	$-0.684458\pi$
$89$	−10.3321	−1.09520	−0.547599	+	0.836741i	$0.684458\pi$
$90$	−50.4887	−5.32198
$91$	0	0
$92$	−1.94608	−0.202892
$93$	−13.8502	−1.43620
$94$	−0.265006	−0.0273333
$95$	9.45849	0.970421
$96$	14.2319	1.45254
$97$	19.3846	1.96821	0.984106	−	0.177583i	$-0.0568278\pi$
$97$	19.3846	1.96821	0.984106	+	0.177583i	$0.0568278\pi$
$98$	8.41426	0.849968
$99$	5.94153	0.597146
$100$	27.6075	2.76075
$101$	3.34654	0.332993	0.166497	−	0.986042i	$-0.446755\pi$
$101$	3.34654	0.332993	0.166497	+	0.986042i	$0.446755\pi$
$102$	−14.9516	−1.48043
$103$	18.4647	1.81939	0.909693	−	0.415282i	$-0.136317\pi$
$103$	18.4647	1.81939	0.909693	+	0.415282i	$0.136317\pi$
$104$	0	0
$105$	19.2321	1.87686
$106$	−0.968210	−0.0940409
$107$	−12.3949	−1.19826	−0.599132	−	0.800650i	$-0.704488\pi$
$107$	−12.3949	−1.19826	−0.599132	+	0.800650i	$0.704488\pi$
$108$	−38.9166	−3.74475
$109$	3.51113	0.336305	0.168153	−	0.985761i	$-0.446220\pi$
$109$	3.51113	0.336305	0.168153	+	0.985761i	$0.446220\pi$
$110$	−8.49760	−0.810214
$111$	−23.2942	−2.21098
$112$	−12.9044	−1.21935
$113$	17.0302	1.60206	0.801031	−	0.598623i	$-0.204285\pi$
$113$	17.0302	1.60206	0.801031	+	0.598623i	$0.204285\pi$
$114$	21.3828	2.00268
$115$	−1.47463	−0.137510
$116$	11.0542	1.02635
$117$	0	0
$118$	−2.61712	−0.240926
$119$	3.78448	0.346922
$120$	61.6039	5.62364
$121$	1.00000	0.0909091
$122$	14.5396	1.31635
$123$	−29.0377	−2.61824
$124$	20.4930	1.84032
$125$	4.15655	0.371773
$126$	28.8906	2.57378
$127$	2.56073	0.227228	0.113614	−	0.993525i	$-0.463757\pi$
$127$	2.56073	0.227228	0.113614	+	0.993525i	$0.463757\pi$
$128$	13.0411	1.15269
$129$	19.7204	1.73629
$130$	0	0
$131$	−12.1666	−1.06300	−0.531499	−	0.847059i	$-0.678371\pi$
$131$	−12.1666	−1.06300	−0.531499	+	0.847059i	$0.678371\pi$
$132$	−13.2300	−1.15153
$133$	−5.41233	−0.469308
$134$	−18.3810	−1.58788
$135$	−29.4889	−2.53800
$136$	12.1224	1.03948
$137$	−10.9394	−0.934620	−0.467310	−	0.884094i	$-0.654777\pi$
$137$	−10.9394	−0.934620	−0.467310	+	0.884094i	$0.654777\pi$
$138$	−3.33370	−0.283784
$139$	−6.00780	−0.509575	−0.254788	−	0.966997i	$-0.582006\pi$
$139$	−6.00780	−0.509575	−0.254788	+	0.966997i	$0.582006\pi$
$140$	−28.4562	−2.40498
$141$	−0.312640	−0.0263291
$142$	28.5584	2.39656
$143$	0	0
$144$	39.9662	3.33052
$145$	8.37625	0.695609
$146$	2.04844	0.169530
$147$	9.92670	0.818741
$148$	34.4665	2.83313
$149$	13.4382	1.10090	0.550448	−	0.834869i	$-0.314457\pi$
$149$	13.4382	1.10090	0.550448	+	0.834869i	$0.314457\pi$
$150$	47.2926	3.86143
$151$	7.46127	0.607190	0.303595	−	0.952801i	$-0.401813\pi$
$151$	7.46127	0.607190	0.303595	+	0.952801i	$0.401813\pi$
$152$	−17.3367	−1.40619
$153$	−11.7209	−0.947582
$154$	4.86248	0.391830
$155$	15.5285	1.24728
$156$	0	0
$157$	13.7742	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$157$	13.7742	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$158$	17.8566	1.42059
$159$	−1.14224	−0.0905858
$160$	−15.9565	−1.26147
$161$	0.843812	0.0665017
$162$	−21.4866	−1.68815
$163$	15.8386	1.24058	0.620289	−	0.784374i	$-0.287015\pi$
$163$	15.8386	1.24058	0.620289	+	0.784374i	$0.287015\pi$
$164$	42.9648	3.35498
$165$	−10.0250	−0.780447
$166$	22.0724	1.71315
$167$	−19.2946	−1.49306	−0.746530	−	0.665352i	$-0.768281\pi$
$167$	−19.2946	−1.49306	−0.746530	+	0.665352i	$0.768281\pi$
$168$	−35.2509	−2.71967
$169$	0	0
$170$	16.7633	1.28569
$171$	16.7626	1.28187
$172$	−29.1787	−2.22485
$173$	−16.0251	−1.21837	−0.609185	−	0.793028i	$-0.708503\pi$
$173$	−16.0251	−1.21837	−0.609185	+	0.793028i	$0.708503\pi$
$174$	18.9362	1.43555
$175$	−11.9705	−0.904885
$176$	6.72659	0.507036
$177$	−3.08755	−0.232074
$178$	26.1881	1.96288
$179$	10.0656	0.752339	0.376169	−	0.926551i	$-0.377241\pi$
$179$	10.0656	0.752339	0.376169	+	0.926551i	$0.377241\pi$
$180$	88.1319	6.56896
$181$	−9.77673	−0.726698	−0.363349	−	0.931653i	$-0.618367\pi$
$181$	−9.77673	−0.726698	−0.363349	+	0.931653i	$0.618367\pi$
$182$	0	0
$183$	17.1531	1.26799
$184$	2.70288	0.199259
$185$	26.1168	1.92015
$186$	35.1052	2.57404
$187$	−1.97271	−0.144259
$188$	0.462588	0.0337377
$189$	16.8741	1.22741
$190$	−23.9739	−1.73925
$191$	−1.02585	−0.0742276	−0.0371138	−	0.999311i	$-0.511816\pi$
$191$	−1.02585	−0.0742276	−0.0371138	+	0.999311i	$0.511816\pi$
$192$	4.15532	0.299884
$193$	20.8263	1.49911	0.749554	−	0.661944i	$-0.230268\pi$
$193$	20.8263	1.49911	0.749554	+	0.661944i	$0.230268\pi$
$194$	−49.1331	−3.52755
$195$	0	0
$196$	−14.6877	−1.04912
$197$	−8.05501	−0.573896	−0.286948	−	0.957946i	$-0.592641\pi$
$197$	−8.05501	−0.573896	−0.286948	+	0.957946i	$0.592641\pi$
$198$	−15.0596	−1.07024
$199$	19.0290	1.34893	0.674466	−	0.738306i	$-0.264374\pi$
$199$	19.0290	1.34893	0.674466	+	0.738306i	$0.264374\pi$
$200$	−38.3437	−2.71131
$201$	−21.6850	−1.52954
$202$	−8.48228	−0.596811
$203$	−4.79305	−0.336406
$204$	26.0991	1.82730
$205$	32.5564	2.27384
$206$	−46.8015	−3.26082
$207$	−2.61338	−0.181642
$208$	0	0
$209$	2.82126	0.195150
$210$	−48.7465	−3.36383
$211$	18.5614	1.27782	0.638909	−	0.769282i	$-0.279386\pi$
$211$	18.5614	1.27782	0.638909	+	0.769282i	$0.279386\pi$
$212$	1.69008	0.116075
$213$	33.6917	2.30852
$214$	31.4167	2.14760
$215$	−22.1101	−1.50789
$216$	54.0508	3.67769
$217$	−8.88569	−0.603200
$218$	−8.89946	−0.602748
$219$	2.41665	0.163302
$220$	14.8332	1.00005
$221$	0	0
$222$	59.0424	3.96267
$223$	−2.55638	−0.171188	−0.0855938	−	0.996330i	$-0.527279\pi$
$223$	−2.55638	−0.171188	−0.0855938	+	0.996330i	$0.527279\pi$
$224$	9.13061	0.610065
$225$	37.0740	2.47160
$226$	−43.1654	−2.87132
$227$	−10.1765	−0.675440	−0.337720	−	0.941247i	$-0.609656\pi$
$227$	−10.1765	−0.675440	−0.337720	+	0.941247i	$0.609656\pi$
$228$	−37.3253	−2.47193
$229$	−23.7436	−1.56902	−0.784510	−	0.620117i	$-0.787085\pi$
$229$	−23.7436	−1.56902	−0.784510	+	0.620117i	$0.787085\pi$
$230$	3.73766	0.246454
$231$	5.73650	0.377434
$232$	−15.3530	−1.00797
$233$	12.7702	0.836607	0.418303	−	0.908307i	$-0.362625\pi$
$233$	12.7702	0.836607	0.418303	+	0.908307i	$0.362625\pi$
$234$	0	0
$235$	0.350525	0.0228657
$236$	4.56839	0.297377
$237$	21.0663	1.36840
$238$	−9.59229	−0.621776
$239$	28.0301	1.81312	0.906558	−	0.422081i	$-0.138700\pi$
$239$	28.0301	1.81312	0.906558	+	0.422081i	$0.138700\pi$
$240$	−67.4342	−4.35286
$241$	6.06670	0.390790	0.195395	−	0.980725i	$-0.437401\pi$
$241$	6.06670	0.390790	0.195395	+	0.980725i	$0.437401\pi$
$242$	−2.53464	−0.162933
$243$	1.03884	0.0666415
$244$	−25.3800	−1.62479
$245$	−11.1296	−0.711042
$246$	73.6003	4.69258
$247$	0	0
$248$	−28.4625	−1.80737
$249$	26.0399	1.65021
$250$	−10.5354	−0.666315
$251$	16.3142	1.02974	0.514870	−	0.857268i	$-0.327840\pi$
$251$	16.3142	1.02974	0.514870	+	0.857268i	$0.327840\pi$
$252$	−50.4307	−3.17684
$253$	−0.439850	−0.0276531
$254$	−6.49052	−0.407252
$255$	19.7765	1.23845
$256$	−30.2754	−1.89221
$257$	12.5358	0.781964	0.390982	−	0.920398i	$-0.372135\pi$
$257$	12.5358	0.781964	0.390982	+	0.920398i	$0.372135\pi$
$258$	−49.9842	−3.11188
$259$	−14.9445	−0.928609
$260$	0	0
$261$	14.8446	0.918857
$262$	30.8379	1.90517
$263$	−13.5122	−0.833199	−0.416599	−	0.909090i	$-0.636778\pi$
$263$	−13.5122	−0.833199	−0.416599	+	0.909090i	$0.636778\pi$
$264$	18.3751	1.13091
$265$	1.28066	0.0786701
$266$	13.7183	0.841124
$267$	30.8954	1.89077
$268$	32.0855	1.95993
$269$	−11.9388	−0.727924	−0.363962	−	0.931414i	$-0.618576\pi$
$269$	−11.9388	−0.727924	−0.363962	+	0.931414i	$0.618576\pi$
$270$	74.7438	4.54876
$271$	−0.798793	−0.0485232	−0.0242616	−	0.999706i	$-0.507723\pi$
$271$	−0.798793	−0.0485232	−0.0242616	+	0.999706i	$0.507723\pi$
$272$	−13.2696	−0.804590
$273$	0	0
$274$	27.7276	1.67508
$275$	6.23981	0.376274
$276$	5.81923	0.350276
$277$	14.4989	0.871155	0.435578	−	0.900151i	$-0.356544\pi$
$277$	14.4989	0.871155	0.435578	+	0.900151i	$0.356544\pi$
$278$	15.2276	0.913292
$279$	27.5200	1.64758
$280$	39.5224	2.36192
$281$	−12.0278	−0.717520	−0.358760	−	0.933430i	$-0.616800\pi$
$281$	−12.0278	−0.717520	−0.358760	+	0.933430i	$0.616800\pi$
$282$	0.792432	0.0471886
$283$	13.0157	0.773701	0.386850	−	0.922143i	$-0.373563\pi$
$283$	13.0157	0.773701	0.386850	+	0.922143i	$0.373563\pi$
$284$	−49.8508	−2.95810
$285$	−28.2832	−1.67535
$286$	0	0
$287$	−18.6294	−1.09966
$288$	−28.2785	−1.66633
$289$	−13.1084	−0.771082
$290$	−21.2308	−1.24671
$291$	−57.9647	−3.39795
$292$	−3.57571	−0.209253
$293$	9.35716	0.546651	0.273326	−	0.961922i	$-0.411876\pi$
$293$	9.35716	0.546651	0.273326	+	0.961922i	$0.411876\pi$
$294$	−25.1606	−1.46740
$295$	3.46168	0.201547
$296$	−47.8701	−2.78239
$297$	−8.79587	−0.510388
$298$	−34.0609	−1.97310
$299$	0	0
$300$	−82.5529	−4.76619
$301$	12.6518	0.729237
$302$	−18.9117	−1.08824
$303$	−10.0070	−0.574884
$304$	18.9774	1.08843
$305$	−19.2316	−1.10120
$306$	29.7084	1.69832
$307$	14.3957	0.821604	0.410802	−	0.911725i	$-0.365249\pi$
$307$	14.3957	0.821604	0.410802	+	0.911725i	$0.365249\pi$
$308$	−8.48783	−0.483639
$309$	−55.2140	−3.14102
$310$	−39.3591	−2.23545
$311$	18.9376	1.07385	0.536926	−	0.843629i	$-0.319585\pi$
$311$	18.9376	1.07385	0.536926	+	0.843629i	$0.319585\pi$
$312$	0	0
$313$	−15.9761	−0.903024	−0.451512	−	0.892265i	$-0.649115\pi$
$313$	−15.9761	−0.903024	−0.451512	+	0.892265i	$0.649115\pi$
$314$	−34.9126	−1.97023
$315$	−38.2137	−2.15310
$316$	−31.1700	−1.75345
$317$	−12.0125	−0.674691	−0.337346	−	0.941381i	$-0.609529\pi$
$317$	−12.0125	−0.674691	−0.337346	+	0.941381i	$0.609529\pi$
$318$	2.89518	0.162354
$319$	2.49845	0.139886
$320$	−4.65884	−0.260437
$321$	37.0638	2.06870
$322$	−2.13876	−0.119189
$323$	−5.56553	−0.309675
$324$	37.5065	2.08369
$325$	0	0
$326$	−40.1453	−2.22344
$327$	−10.4991	−0.580603
$328$	−59.6733	−3.29490
$329$	−0.200577	−0.0110582
$330$	25.4098	1.39877
$331$	21.1500	1.16251	0.581256	−	0.813721i	$-0.302562\pi$
$331$	21.1500	1.16251	0.581256	+	0.813721i	$0.302562\pi$
$332$	−38.5291	−2.11456
$333$	46.2849	2.53640
$334$	48.9048	2.67595
$335$	24.3127	1.32834
$336$	38.5871	2.10510
$337$	6.26056	0.341034	0.170517	−	0.985355i	$-0.445456\pi$
$337$	6.26056	0.341034	0.170517	+	0.985355i	$0.445456\pi$
$338$	0	0
$339$	−50.9242	−2.76582
$340$	−29.2617	−1.58694
$341$	4.63180	0.250826
$342$	−42.4871	−2.29744
$343$	19.7974	1.06896
$344$	40.5260	2.18501
$345$	4.40950	0.237400
$346$	40.6180	2.18364
$347$	−10.4099	−0.558834	−0.279417	−	0.960170i	$-0.590141\pi$
$347$	−10.4099	−0.558834	−0.279417	+	0.960170i	$0.590141\pi$
$348$	−33.0546	−1.77191
$349$	27.5513	1.47479	0.737394	−	0.675462i	$-0.236056\pi$
$349$	27.5513	1.47479	0.737394	+	0.675462i	$0.236056\pi$
$350$	30.3410	1.62179
$351$	0	0
$352$	−4.75947	−0.253681
$353$	5.28628	0.281360	0.140680	−	0.990055i	$-0.455071\pi$
$353$	5.28628	0.281360	0.140680	+	0.990055i	$0.455071\pi$
$354$	7.82583	0.415938
$355$	−37.7743	−2.00485
$356$	−45.7134	−2.42280
$357$	−11.3165	−0.598932
$358$	−25.5127	−1.34839
$359$	−23.0174	−1.21481	−0.607407	−	0.794391i	$-0.707790\pi$
$359$	−23.0174	−1.21481	−0.607407	+	0.794391i	$0.707790\pi$
$360$	−122.405	−6.45133
$361$	−11.0405	−0.581080
$362$	24.7805	1.30243
$363$	−2.99024	−0.156947
$364$	0	0
$365$	−2.70949	−0.141821
$366$	−43.4769	−2.27257
$367$	18.6338	0.972677	0.486339	−	0.873770i	$-0.338332\pi$
$367$	18.6338	0.972677	0.486339	+	0.873770i	$0.338332\pi$
$368$	−2.95869	−0.154232
$369$	57.6972	3.00360
$370$	−66.1969	−3.44141
$371$	−0.732815	−0.0380459
$372$	−61.2789	−3.17716
$373$	0.434255	0.0224849	0.0112424	−	0.999937i	$-0.496421\pi$
$373$	0.434255	0.0224849	0.0112424	+	0.999937i	$0.496421\pi$
$374$	5.00013	0.258550
$375$	−12.4291	−0.641835
$376$	−0.642484	−0.0331336
$377$	0	0
$378$	−42.7698	−2.19984
$379$	−19.1999	−0.986231	−0.493115	−	0.869964i	$-0.664142\pi$
$379$	−19.1999	−0.986231	−0.493115	+	0.869964i	$0.664142\pi$
$380$	41.8483	2.14677
$381$	−7.65718	−0.392289
$382$	2.60015	0.133035
$383$	−5.79295	−0.296006	−0.148003	−	0.988987i	$-0.547284\pi$
$383$	−5.79295	−0.296006	−0.148003	+	0.988987i	$0.547284\pi$
$384$	−38.9961	−1.99001
$385$	−6.43163	−0.327786
$386$	−52.7871	−2.68679
$387$	−39.1840	−1.99183
$388$	85.7656	4.35409
$389$	22.3481	1.13309	0.566546	−	0.824030i	$-0.308279\pi$
$389$	22.3481	1.13309	0.566546	+	0.824030i	$0.308279\pi$
$390$	0	0
$391$	0.867698	0.0438814
$392$	20.3996	1.03034
$393$	36.3809	1.83518
$394$	20.4166	1.02857
$395$	−23.6190	−1.18840
$396$	26.2878	1.32101
$397$	32.7283	1.64259	0.821294	−	0.570506i	$-0.193253\pi$
$397$	32.7283	1.64259	0.821294	+	0.570506i	$0.193253\pi$
$398$	−48.2318	−2.41764
$399$	16.1841	0.810221
$400$	41.9726	2.09863
$401$	18.2188	0.909801	0.454901	−	0.890542i	$-0.349675\pi$
$401$	18.2188	0.909801	0.454901	+	0.890542i	$0.349675\pi$
$402$	54.9637	2.74134
$403$	0	0
$404$	14.8065	0.736649
$405$	28.4204	1.41222
$406$	12.1487	0.602928
$407$	7.79007	0.386139
$408$	−36.2487	−1.79458
$409$	39.2971	1.94312	0.971558	−	0.236802i	$-0.0760994\pi$
$409$	39.2971	1.94312	0.971558	+	0.236802i	$0.0760994\pi$
$410$	−82.5188	−4.07531
$411$	32.7116	1.61354
$412$	81.6956	4.02486
$413$	−1.98084	−0.0974707
$414$	6.62398	0.325551
$415$	−29.1953	−1.43314
$416$	0	0
$417$	17.9648	0.879738
$418$	−7.15087	−0.349761
$419$	−1.57695	−0.0770388	−0.0385194	−	0.999258i	$-0.512264\pi$
$419$	−1.57695	−0.0770388	−0.0385194	+	0.999258i	$0.512264\pi$
$420$	85.0907	4.15200
$421$	10.0373	0.489189	0.244595	−	0.969625i	$-0.421345\pi$
$421$	10.0373	0.489189	0.244595	+	0.969625i	$0.421345\pi$
$422$	−47.0465	−2.29019
$423$	0.621209	0.0302042
$424$	−2.34734	−0.113997
$425$	−12.3094	−0.597092
$426$	−85.3963	−4.13747
$427$	11.0047	0.532553
$428$	−54.8403	−2.65081
$429$	0	0
$430$	56.0411	2.70254
$431$	1.00444	0.0483821	0.0241911	−	0.999707i	$-0.492299\pi$
$431$	1.00444	0.0483821	0.0241911	+	0.999707i	$0.492299\pi$
$432$	−59.1662	−2.84664
$433$	−4.11273	−0.197645	−0.0988225	−	0.995105i	$-0.531508\pi$
$433$	−4.11273	−0.197645	−0.0988225	+	0.995105i	$0.531508\pi$
$434$	22.5220	1.08109
$435$	−25.0470	−1.20091
$436$	15.5347	0.743977
$437$	−1.24093	−0.0593616
$438$	−6.12534	−0.292680
$439$	4.14317	0.197743	0.0988713	−	0.995100i	$-0.468477\pi$
$439$	4.14317	0.197743	0.0988713	+	0.995100i	$0.468477\pi$
$440$	−20.6017	−0.982146
$441$	−19.7241	−0.939243
$442$	0	0
$443$	−10.3516	−0.491821	−0.245911	−	0.969293i	$-0.579087\pi$
$443$	−10.3516	−0.491821	−0.245911	+	0.969293i	$0.579087\pi$
$444$	−103.063	−4.89115
$445$	−34.6392	−1.64205
$446$	6.47950	0.306813
$447$	−40.1833	−1.90061
$448$	2.66588	0.125951
$449$	−9.13794	−0.431246	−0.215623	−	0.976477i	$-0.569178\pi$
$449$	−9.13794	−0.431246	−0.215623	+	0.976477i	$0.569178\pi$
$450$	−93.9693	−4.42975
$451$	9.71084	0.457266
$452$	75.3484	3.54409
$453$	−22.3110	−1.04826
$454$	25.7939	1.21057
$455$	0	0
$456$	51.8407	2.42767
$457$	1.43933	0.0673288	0.0336644	−	0.999433i	$-0.489282\pi$
$457$	1.43933	0.0673288	0.0336644	+	0.999433i	$0.489282\pi$
$458$	60.1814	2.81209
$459$	17.3517	0.809910
$460$	−6.52438	−0.304201
$461$	25.1927	1.17334	0.586671	−	0.809825i	$-0.300438\pi$
$461$	25.1927	1.17334	0.586671	+	0.809825i	$0.300438\pi$
$462$	−14.5400	−0.676461
$463$	−14.1428	−0.657271	−0.328635	−	0.944457i	$-0.606589\pi$
$463$	−14.1428	−0.657271	−0.328635	+	0.944457i	$0.606589\pi$
$464$	16.8060	0.780200
$465$	−46.4339	−2.15332
$466$	−32.3680	−1.49942
$467$	18.4384	0.853228	0.426614	−	0.904434i	$-0.359706\pi$
$467$	18.4384	0.853228	0.426614	+	0.904434i	$0.359706\pi$
$468$	0	0
$469$	−13.9122	−0.642405
$470$	−0.888455	−0.0409814
$471$	−41.1881	−1.89785
$472$	−6.34499	−0.292052
$473$	−6.59493	−0.303235
$474$	−53.3954	−2.45253
$475$	17.6041	0.807731
$476$	16.7441	0.767463
$477$	2.26961	0.103918
$478$	−71.0462	−3.24958
$479$	28.2221	1.28950	0.644750	−	0.764394i	$-0.276962\pi$
$479$	28.2221	1.28950	0.644750	+	0.764394i	$0.276962\pi$
$480$	47.7138	2.17783
$481$	0	0
$482$	−15.3769	−0.700399
$483$	−2.52320	−0.114810
$484$	4.42441	0.201110
$485$	64.9886	2.95098
$486$	−2.63308	−0.119439
$487$	−12.1754	−0.551720	−0.275860	−	0.961198i	$-0.588963\pi$
$487$	−12.1754	−0.551720	−0.275860	+	0.961198i	$0.588963\pi$
$488$	35.2499	1.59569
$489$	−47.3613	−2.14175
$490$	28.2095	1.27437
$491$	35.0308	1.58092	0.790458	−	0.612516i	$-0.209842\pi$
$491$	35.0308	1.58092	0.790458	+	0.612516i	$0.209842\pi$
$492$	−128.475	−5.79209
$493$	−4.92872	−0.221978
$494$	0	0
$495$	19.9195	0.895313
$496$	31.1562	1.39895
$497$	21.6151	0.969572
$498$	−66.0018	−2.95761
$499$	7.22186	0.323295	0.161648	−	0.986849i	$-0.448319\pi$
$499$	7.22186	0.323295	0.161648	+	0.986849i	$0.448319\pi$
$500$	18.3903	0.822439
$501$	57.6954	2.57764
$502$	−41.3505	−1.84556
$503$	15.4630	0.689460	0.344730	−	0.938702i	$-0.387970\pi$
$503$	15.4630	0.689460	0.344730	+	0.938702i	$0.387970\pi$
$504$	70.0426	3.11995
$505$	11.2195	0.499263
$506$	1.11486	0.0495616
$507$	0	0
$508$	11.3297	0.502674
$509$	33.2042	1.47175	0.735876	−	0.677117i	$-0.236771\pi$
$509$	33.2042	1.47175	0.735876	+	0.677117i	$0.236771\pi$
$510$	−50.1264	−2.21963
$511$	1.55042	0.0685865
$512$	50.6550	2.23865
$513$	−24.8154	−1.09563
$514$	−31.7739	−1.40149
$515$	61.9046	2.72784
$516$	87.2513	3.84102
$517$	0.104554	0.00459826
$518$	37.8791	1.66431
$519$	47.9190	2.10341
$520$	0	0
$521$	−22.0340	−0.965325	−0.482663	−	0.875806i	$-0.660330\pi$
$521$	−22.0340	−0.965325	−0.482663	+	0.875806i	$0.660330\pi$
$522$	−37.6257	−1.64683
$523$	28.8453	1.26132	0.630658	−	0.776061i	$-0.282785\pi$
$523$	28.8453	1.26132	0.630658	+	0.776061i	$0.282785\pi$
$524$	−53.8299	−2.35157
$525$	35.7947	1.56221
$526$	34.2486	1.49331
$527$	−9.13721	−0.398023
$528$	−20.1141	−0.875354
$529$	−22.8065	−0.991588
$530$	−3.24600	−0.140997
$531$	6.13488	0.266231
$532$	−23.9464	−1.03821
$533$	0	0
$534$	−78.3088	−3.38875
$535$	−41.5551	−1.79658
$536$	−44.5632	−1.92484
$537$	−30.0986	−1.29885
$538$	30.2607	1.30463
$539$	−3.31970	−0.142990
$540$	−130.471	−5.61458
$541$	19.3752	0.833007	0.416503	−	0.909134i	$-0.363255\pi$
$541$	19.3752	0.833007	0.416503	+	0.909134i	$0.363255\pi$
$542$	2.02465	0.0869664
$543$	29.2347	1.25458
$544$	9.38907	0.402553
$545$	11.7714	0.504230
$546$	0	0
$547$	31.4512	1.34475	0.672377	−	0.740209i	$-0.265273\pi$
$547$	31.4512	1.34475	0.672377	+	0.740209i	$0.265273\pi$
$548$	−48.4006	−2.06757
$549$	−34.0827	−1.45461
$550$	−15.8157	−0.674383
$551$	7.04876	0.300287
$552$	−8.08226	−0.344004
$553$	13.5152	0.574725
$554$	−36.7496	−1.56134
$555$	−78.0956	−3.31497
$556$	−26.5810	−1.12728
$557$	24.1266	1.02228	0.511138	−	0.859499i	$-0.329224\pi$
$557$	24.1266	1.02228	0.511138	+	0.859499i	$0.329224\pi$
$558$	−69.7532	−2.95289
$559$	0	0
$560$	−43.2629	−1.82819
$561$	5.89889	0.249051
$562$	30.4863	1.28598
$563$	−7.74375	−0.326360	−0.163180	−	0.986596i	$-0.552175\pi$
$563$	−7.74375	−0.326360	−0.163180	+	0.986596i	$0.552175\pi$
$564$	−1.38325	−0.0582453
$565$	57.0950	2.40200
$566$	−32.9900	−1.38667
$567$	−16.2627	−0.682969
$568$	69.2372	2.90513
$569$	−18.3952	−0.771167	−0.385583	−	0.922673i	$-0.626000\pi$
$569$	−18.3952	−0.771167	−0.385583	+	0.922673i	$0.626000\pi$
$570$	71.6877	3.00267
$571$	−9.57839	−0.400843	−0.200422	−	0.979710i	$-0.564231\pi$
$571$	−9.57839	−0.400843	−0.200422	+	0.979710i	$0.564231\pi$
$572$	0	0
$573$	3.06752	0.128148
$574$	47.2188	1.97087
$575$	−2.74458	−0.114457
$576$	−8.25652	−0.344022
$577$	−12.1259	−0.504808	−0.252404	−	0.967622i	$-0.581221\pi$
$577$	−12.1259	−0.504808	−0.252404	+	0.967622i	$0.581221\pi$
$578$	33.2251	1.38198
$579$	−62.2755	−2.58808
$580$	37.0600	1.53883
$581$	16.7061	0.693085
$582$	146.920	6.09002
$583$	0.381991	0.0158204
$584$	4.96627	0.205506
$585$	0	0
$586$	−23.7171	−0.979742
$587$	25.3026	1.04435	0.522175	−	0.852838i	$-0.325121\pi$
$587$	25.3026	1.04435	0.522175	+	0.852838i	$0.325121\pi$
$588$	43.9198	1.81122
$589$	13.0675	0.538436
$590$	−8.77413	−0.361225
$591$	24.0864	0.990783
$592$	52.4006	2.15365
$593$	2.55502	0.104922	0.0524610	−	0.998623i	$-0.483293\pi$
$593$	2.55502	0.104922	0.0524610	+	0.998623i	$0.483293\pi$
$594$	22.2944	0.914750
$595$	12.6878	0.520148
$596$	59.4559	2.43541
$597$	−56.9013	−2.32882
$598$	0	0
$599$	43.3849	1.77266	0.886329	−	0.463055i	$-0.153247\pi$
$599$	43.3849	1.77266	0.886329	+	0.463055i	$0.153247\pi$
$600$	114.657	4.68084
$601$	9.55136	0.389608	0.194804	−	0.980842i	$-0.437593\pi$
$601$	9.55136	0.389608	0.194804	+	0.980842i	$0.437593\pi$
$602$	−32.0677	−1.30698
$603$	43.0875	1.75466
$604$	33.0117	1.34323
$605$	3.35258	0.136302
$606$	25.3640	1.03034
$607$	3.77022	0.153028	0.0765142	−	0.997068i	$-0.475621\pi$
$607$	3.77022	0.153028	0.0765142	+	0.997068i	$0.475621\pi$
$608$	−13.4277	−0.544564
$609$	14.3324	0.580776
$610$	48.7452	1.97363
$611$	0	0
$612$	−51.8583	−2.09625
$613$	−39.3763	−1.59039	−0.795197	−	0.606352i	$-0.792632\pi$
$613$	−39.3763	−1.59039	−0.795197	+	0.606352i	$0.792632\pi$
$614$	−36.4879	−1.47253
$615$	−97.3514	−3.92559
$616$	11.7887	0.474979
$617$	26.9832	1.08630	0.543152	−	0.839635i	$-0.317231\pi$
$617$	26.9832	1.08630	0.543152	+	0.839635i	$0.317231\pi$
$618$	139.948	5.62952
$619$	19.3050	0.775932	0.387966	−	0.921674i	$-0.373178\pi$
$619$	19.3050	0.775932	0.387966	+	0.921674i	$0.373178\pi$
$620$	68.7044	2.75923
$621$	3.86886	0.155252
$622$	−48.0000	−1.92463
$623$	19.8212	0.794119
$624$	0	0
$625$	−17.2638	−0.690554
$626$	40.4938	1.61846
$627$	−8.43623	−0.336911
$628$	60.9426	2.43188
$629$	−15.3676	−0.612746
$630$	96.8580	3.85892
$631$	−15.3139	−0.609636	−0.304818	−	0.952411i	$-0.598596\pi$
$631$	−15.3139	−0.609636	−0.304818	+	0.952411i	$0.598596\pi$
$632$	43.2917	1.72205
$633$	−55.5030	−2.20604
$634$	30.4475	1.20922
$635$	8.58504	0.340687
$636$	−5.05376	−0.200395
$637$	0	0
$638$	−6.33267	−0.250713
$639$	−66.9445	−2.64828
$640$	43.7215	1.72824
$641$	29.3891	1.16080	0.580400	−	0.814332i	$-0.302896\pi$
$641$	29.3891	1.16080	0.580400	+	0.814332i	$0.302896\pi$
$642$	−93.9436	−3.70766
$643$	−44.7293	−1.76395	−0.881976	−	0.471295i	$-0.843787\pi$
$643$	−44.7293	−1.76395	−0.881976	+	0.471295i	$0.843787\pi$
$644$	3.73337	0.147115
$645$	66.1143	2.60325
$646$	14.1066	0.555018
$647$	16.1126	0.633452	0.316726	−	0.948517i	$-0.397416\pi$
$647$	16.1126	0.633452	0.316726	+	0.948517i	$0.397416\pi$
$648$	−52.0924	−2.04638
$649$	1.03254	0.0405308
$650$	0	0
$651$	26.5703	1.04137
$652$	70.0766	2.74441
$653$	−38.5815	−1.50981	−0.754905	−	0.655835i	$-0.772317\pi$
$653$	−38.5815	−1.50981	−0.754905	+	0.655835i	$0.772317\pi$
$654$	26.6115	1.04059
$655$	−40.7894	−1.59377
$656$	65.3208	2.55035
$657$	−4.80182	−0.187337
$658$	0.508390	0.0198191
$659$	−18.5716	−0.723447	−0.361723	−	0.932285i	$-0.617812\pi$
$659$	−18.5716	−0.723447	−0.361723	+	0.932285i	$0.617812\pi$
$660$	−44.3548	−1.72651
$661$	12.0249	0.467714	0.233857	−	0.972271i	$-0.424865\pi$
$661$	12.0249	0.467714	0.233857	+	0.972271i	$0.424865\pi$
$662$	−53.6078	−2.08353
$663$	0	0
$664$	53.5126	2.07669
$665$	−18.1453	−0.703643
$666$	−117.316	−4.54589
$667$	−1.09894	−0.0425512
$668$	−85.3671	−3.30295
$669$	7.64417	0.295541
$670$	−61.6240	−2.38074
$671$	−5.73635	−0.221449
$672$	−27.3027	−1.05323
$673$	−39.9547	−1.54014	−0.770071	−	0.637958i	$-0.779779\pi$
$673$	−39.9547	−1.54014	−0.770071	+	0.637958i	$0.779779\pi$
$674$	−15.8683	−0.611223
$675$	−54.8845	−2.11251
$676$	0	0
$677$	−1.34058	−0.0515226	−0.0257613	−	0.999668i	$-0.508201\pi$
$677$	−1.34058	−0.0515226	−0.0257613	+	0.999668i	$0.508201\pi$
$678$	129.075	4.95708
$679$	−37.1877	−1.42713
$680$	40.6412	1.55852
$681$	30.4303	1.16609
$682$	−11.7399	−0.449546
$683$	−17.6692	−0.676092	−0.338046	−	0.941130i	$-0.609766\pi$
$683$	−17.6692	−0.676092	−0.338046	+	0.941130i	$0.609766\pi$
$684$	74.1645	2.83575
$685$	−36.6754	−1.40129
$686$	−50.1794	−1.91586
$687$	70.9989	2.70878
$688$	−44.3614	−1.69126
$689$	0	0
$690$	−11.1765	−0.425482
$691$	−21.4216	−0.814915	−0.407458	−	0.913224i	$-0.633585\pi$
$691$	−21.4216	−0.814915	−0.407458	+	0.913224i	$0.633585\pi$
$692$	−70.9018	−2.69528
$693$	−11.3983	−0.432985
$694$	26.3854	1.00158
$695$	−20.1416	−0.764016
$696$	45.9091	1.74018
$697$	−19.1567	−0.725612
$698$	−69.8328	−2.64321
$699$	−38.1861	−1.44433
$700$	−52.9624	−2.00179
$701$	7.83629	0.295972	0.147986	−	0.988989i	$-0.452721\pi$
$701$	7.83629	0.295972	0.147986	+	0.988989i	$0.452721\pi$
$702$	0	0
$703$	21.9778	0.828908
$704$	−1.38963	−0.0523736
$705$	−1.04815	−0.0394757
$706$	−13.3988	−0.504272
$707$	−6.42003	−0.241450
$708$	−13.6606	−0.513396
$709$	−5.09790	−0.191456	−0.0957279	−	0.995408i	$-0.530518\pi$
$709$	−5.09790	−0.191456	−0.0957279	+	0.995408i	$0.530518\pi$
$710$	95.7443	3.59322
$711$	−41.8581	−1.56980
$712$	63.4908	2.37942
$713$	−2.03729	−0.0762972
$714$	28.6832	1.07344
$715$	0	0
$716$	44.5344	1.66433
$717$	−83.8167	−3.13019
$718$	58.3410	2.17727
$719$	−19.0066	−0.708827	−0.354413	−	0.935089i	$-0.615319\pi$
$719$	−19.0066	−0.708827	−0.354413	+	0.935089i	$0.615319\pi$
$720$	133.990	4.99351
$721$	−35.4230	−1.31922
$722$	27.9838	1.04145
$723$	−18.1409	−0.674666
$724$	−43.2563	−1.60761
$725$	15.5898	0.578991
$726$	7.57919	0.281290
$727$	4.60308	0.170719	0.0853595	−	0.996350i	$-0.472796\pi$
$727$	4.60308	0.170719	0.0853595	+	0.996350i	$0.472796\pi$
$728$	0	0
$729$	−28.5379	−1.05696
$730$	6.86758	0.254180
$731$	13.0099	0.481189
$732$	75.8922	2.80506
$733$	−22.9104	−0.846213	−0.423107	−	0.906080i	$-0.639060\pi$
$733$	−22.9104	−0.846213	−0.423107	+	0.906080i	$0.639060\pi$
$734$	−47.2300	−1.74329
$735$	33.2801	1.22755
$736$	2.09345	0.0771656
$737$	7.25193	0.267128
$738$	−146.242	−5.38324
$739$	−2.63363	−0.0968797	−0.0484398	−	0.998826i	$-0.515425\pi$
$739$	−2.63363	−0.0968797	−0.0484398	+	0.998826i	$0.515425\pi$
$740$	115.552	4.24776
$741$	0	0
$742$	1.85742	0.0681882
$743$	−6.05846	−0.222263	−0.111132	−	0.993806i	$-0.535448\pi$
$743$	−6.05846	−0.222263	−0.111132	+	0.993806i	$0.535448\pi$
$744$	85.1095	3.12027
$745$	45.0525	1.65060
$746$	−1.10068	−0.0402988
$747$	−51.7406	−1.89309
$748$	−8.72810	−0.319131
$749$	23.7786	0.868851
$750$	31.5033	1.15034
$751$	−12.7774	−0.466255	−0.233127	−	0.972446i	$-0.574896\pi$
$751$	−12.7774	−0.466255	−0.233127	+	0.972446i	$0.574896\pi$
$752$	0.703290	0.0256463
$753$	−48.7832	−1.77776
$754$	0	0
$755$	25.0145	0.910372
$756$	74.6579	2.71528
$757$	38.7827	1.40958	0.704791	−	0.709415i	$-0.251041\pi$
$757$	38.7827	1.40958	0.704791	+	0.709415i	$0.251041\pi$
$758$	48.6648	1.76758
$759$	1.31526	0.0477407
$760$	−58.1226	−2.10833
$761$	−40.5551	−1.47012	−0.735061	−	0.678001i	$-0.762846\pi$
$761$	−40.5551	−1.47012	−0.735061	+	0.678001i	$0.762846\pi$
$762$	19.4082	0.703086
$763$	−6.73579	−0.243852
$764$	−4.53876	−0.164207
$765$	−39.2954	−1.42073
$766$	14.6830	0.530520
$767$	0	0
$768$	90.5306	3.26674
$769$	−26.4805	−0.954910	−0.477455	−	0.878656i	$-0.658441\pi$
$769$	−26.4805	−0.954910	−0.477455	+	0.878656i	$0.658441\pi$
$770$	16.3019	0.587479
$771$	−37.4852	−1.34999
$772$	92.1439	3.31633
$773$	14.2498	0.512530	0.256265	−	0.966607i	$-0.417508\pi$
$773$	14.2498	0.512530	0.256265	+	0.966607i	$0.417508\pi$
$774$	99.3174	3.56989
$775$	28.9015	1.03817
$776$	−119.119	−4.27612
$777$	44.6878	1.60316
$778$	−56.6444	−2.03080
$779$	27.3968	0.981591
$780$	0	0
$781$	−11.2672	−0.403173
$782$	−2.19930	−0.0786469
$783$	−21.9760	−0.785359
$784$	−22.3303	−0.797510
$785$	46.1791	1.64820
$786$	−92.2126	−3.28912
$787$	−54.1394	−1.92986	−0.964931	−	0.262503i	$-0.915452\pi$
$787$	−54.1394	−1.92986	−0.964931	+	0.262503i	$0.915452\pi$
$788$	−35.6387	−1.26958
$789$	40.4047	1.43845
$790$	59.8656	2.12992
$791$	−32.6708	−1.16164
$792$	−36.5108	−1.29735
$793$	0	0
$794$	−82.9546	−2.94395
$795$	−3.82947	−0.135817
$796$	84.1922	2.98411
$797$	−19.7774	−0.700553	−0.350276	−	0.936646i	$-0.613912\pi$
$797$	−19.7774	−0.700553	−0.350276	+	0.936646i	$0.613912\pi$
$798$	−41.0210	−1.45213
$799$	−0.206255	−0.00729676
$800$	−29.6982	−1.04999
$801$	−61.3884	−2.16905
$802$	−46.1780	−1.63060
$803$	−0.808179	−0.0285200
$804$	−95.9433	−3.38366
$805$	2.82895	0.0997073
$806$	0	0
$807$	35.7000	1.25670
$808$	−20.5645	−0.723458
$809$	7.57611	0.266362	0.133181	−	0.991092i	$-0.457481\pi$
$809$	7.57611	0.266362	0.133181	+	0.991092i	$0.457481\pi$
$810$	−72.0356	−2.53107
$811$	36.2578	1.27318	0.636592	−	0.771201i	$-0.280343\pi$
$811$	36.2578	1.27318	0.636592	+	0.771201i	$0.280343\pi$
$812$	−21.2064	−0.744199
$813$	2.38858	0.0837712
$814$	−19.7450	−0.692063
$815$	53.1003	1.86002
$816$	39.6794	1.38906
$817$	−18.6060	−0.650941
$818$	−99.6040	−3.48257
$819$	0	0
$820$	144.043	5.03019
$821$	−28.6271	−0.999093	−0.499547	−	0.866287i	$-0.666500\pi$
$821$	−28.6271	−0.999093	−0.499547	+	0.866287i	$0.666500\pi$
$822$	−82.9121	−2.89189
$823$	−19.5200	−0.680424	−0.340212	−	0.940349i	$-0.610499\pi$
$823$	−19.5200	−0.680424	−0.340212	+	0.940349i	$0.610499\pi$
$824$	−113.466	−3.95278
$825$	−18.6585	−0.649606
$826$	5.02072	0.174693
$827$	−4.68925	−0.163061	−0.0815306	−	0.996671i	$-0.525981\pi$
$827$	−4.68925	−0.163061	−0.0815306	+	0.996671i	$0.525981\pi$
$828$	−11.5627	−0.401830
$829$	−20.9053	−0.726071	−0.363036	−	0.931775i	$-0.618260\pi$
$829$	−20.9053	−0.726071	−0.363036	+	0.931775i	$0.618260\pi$
$830$	73.9996	2.56856
$831$	−43.3552	−1.50398
$832$	0	0
$833$	6.54883	0.226903
$834$	−45.5342	−1.57672
$835$	−64.6867	−2.23857
$836$	12.4824	0.431713
$837$	−40.7407	−1.40820
$838$	3.99699	0.138074
$839$	47.0179	1.62324	0.811618	−	0.584188i	$-0.198587\pi$
$839$	47.0179	1.62324	0.811618	+	0.584188i	$0.198587\pi$
$840$	−118.182	−4.07765
$841$	−22.7578	−0.784751
$842$	−25.4410	−0.876756
$843$	35.9661	1.23874
$844$	82.1232	2.82680
$845$	0	0
$846$	−1.57454	−0.0541338
$847$	−1.91841	−0.0659174
$848$	2.56950	0.0882369
$849$	−38.9199	−1.33573
$850$	31.1998	1.07014
$851$	−3.42646	−0.117458
$852$	149.066	5.10691
$853$	48.7942	1.67068	0.835340	−	0.549733i	$-0.185271\pi$
$853$	48.7942	1.67068	0.835340	+	0.549733i	$0.185271\pi$
$854$	−27.8929	−0.954476
$855$	56.1979	1.92193
$856$	76.1671	2.60334
$857$	−48.2335	−1.64762	−0.823812	−	0.566863i	$-0.808157\pi$
$857$	−48.2335	−1.64762	−0.823812	+	0.566863i	$0.808157\pi$
$858$	0	0
$859$	26.2337	0.895082	0.447541	−	0.894263i	$-0.352300\pi$
$859$	26.2337	0.895082	0.447541	+	0.894263i	$0.352300\pi$
$860$	−97.8240	−3.33577
$861$	55.7063	1.89847
$862$	−2.54589	−0.0867135
$863$	28.5207	0.970857	0.485428	−	0.874276i	$-0.338664\pi$
$863$	28.5207	0.970857	0.485428	+	0.874276i	$0.338664\pi$
$864$	41.8637	1.42423
$865$	−53.7256	−1.82673
$866$	10.4243	0.354232
$867$	39.1972	1.33121
$868$	−39.3139	−1.33440
$869$	−7.04501	−0.238985
$870$	63.4851	2.15235
$871$	0	0
$872$	−21.5760	−0.730654
$873$	115.174	3.89806
$874$	3.14531	0.106392
$875$	−7.97397	−0.269569
$876$	10.6922	0.361257
$877$	−0.365718	−0.0123494	−0.00617472	−	0.999981i	$-0.501965\pi$
$877$	−0.365718	−0.0123494	−0.00617472	+	0.999981i	$0.501965\pi$
$878$	−10.5014	−0.354407
$879$	−27.9801	−0.943747
$880$	22.5514	0.760209
$881$	8.48901	0.286002	0.143001	−	0.989723i	$-0.454325\pi$
$881$	8.48901	0.286002	0.143001	+	0.989723i	$0.454325\pi$
$882$	49.9936	1.68337
$883$	−12.2202	−0.411244	−0.205622	−	0.978632i	$-0.565922\pi$
$883$	−12.2202	−0.411244	−0.205622	+	0.978632i	$0.565922\pi$
$884$	0	0
$885$	−10.3513	−0.347954
$886$	26.2377	0.881473
$887$	−17.1979	−0.577447	−0.288724	−	0.957412i	$-0.593231\pi$
$887$	−17.1979	−0.577447	−0.288724	+	0.957412i	$0.593231\pi$
$888$	143.143	4.80356
$889$	−4.91252	−0.164761
$890$	87.7979	2.94299
$891$	8.47718	0.283996
$892$	−11.3105	−0.378702
$893$	0.294973	0.00987088
$894$	101.850	3.40638
$895$	33.7458	1.12800
$896$	−25.0183	−0.835802
$897$	0	0
$898$	23.1614	0.772906
$899$	11.5723	0.385958
$900$	164.031	5.46768
$901$	−0.753559	−0.0251047
$902$	−24.6135	−0.819540
$903$	−37.8319	−1.25897
$904$	−104.651	−3.48063
$905$	−32.7773	−1.08955
$906$	56.5504	1.87876
$907$	−4.69802	−0.155995	−0.0779976	−	0.996954i	$-0.524853\pi$
$907$	−4.69802	−0.155995	−0.0779976	+	0.996954i	$0.524853\pi$
$908$	−45.0252	−1.49421
$909$	19.8836	0.659496
$910$	0	0
$911$	−30.8968	−1.02366	−0.511828	−	0.859088i	$-0.671032\pi$
$911$	−30.8968	−1.02366	−0.511828	+	0.859088i	$0.671032\pi$
$912$	−56.7470	−1.87908
$913$	−8.70830	−0.288203
$914$	−3.64817	−0.120671
$915$	57.5070	1.90112
$916$	−105.051	−3.47099
$917$	23.3405	0.770770
$918$	−43.9805	−1.45157
$919$	52.6196	1.73576	0.867880	−	0.496773i	$-0.165482\pi$
$919$	52.6196	1.73576	0.867880	+	0.496773i	$0.165482\pi$
$920$	9.06163	0.298753
$921$	−43.0465	−1.41843
$922$	−63.8545	−2.10294
$923$	0	0
$924$	25.3807	0.834962
$925$	48.6085	1.59824
$926$	35.8469	1.17800
$927$	109.709	3.60331
$928$	−11.8913	−0.390350
$929$	12.3906	0.406522	0.203261	−	0.979125i	$-0.434846\pi$
$929$	12.3906	0.406522	0.203261	+	0.979125i	$0.434846\pi$
$930$	117.693	3.85931
$931$	−9.36573	−0.306949
$932$	56.5008	1.85075
$933$	−56.6279	−1.85392
$934$	−46.7348	−1.52921
$935$	−6.61369	−0.216291
$936$	0	0
$937$	18.5056	0.604551	0.302275	−	0.953221i	$-0.402254\pi$
$937$	18.5056	0.604551	0.302275	+	0.953221i	$0.402254\pi$
$938$	35.2624	1.15136
$939$	47.7725	1.55900
$940$	1.55087	0.0505837
$941$	−40.0842	−1.30671	−0.653353	−	0.757053i	$-0.726638\pi$
$941$	−40.0842	−1.30671	−0.653353	+	0.757053i	$0.726638\pi$
$942$	104.397	3.40144
$943$	−4.27131	−0.139093
$944$	6.94549	0.226056
$945$	56.5718	1.84028
$946$	16.7158	0.543477
$947$	28.6413	0.930716	0.465358	−	0.885123i	$-0.345926\pi$
$947$	28.6413	0.930716	0.465358	+	0.885123i	$0.345926\pi$
$948$	93.2058	3.02718
$949$	0	0
$950$	−44.6201	−1.44767
$951$	35.9203	1.16480
$952$	−23.2557	−0.753720
$953$	18.6739	0.604907	0.302453	−	0.953164i	$-0.402194\pi$
$953$	18.6739	0.604907	0.302453	+	0.953164i	$0.402194\pi$
$954$	−5.75265	−0.186249
$955$	−3.43923	−0.111291
$956$	124.017	4.01098
$957$	−7.47095	−0.241502
$958$	−71.5329	−2.31112
$959$	20.9863	0.677684
$960$	13.9311	0.449623
$961$	−9.54646	−0.307950
$962$	0	0
$963$	−73.6449	−2.37317
$964$	26.8416	0.864508
$965$	69.8218	2.24764
$966$	6.39541	0.205769
$967$	0.163454	0.00525631	0.00262816	−	0.999997i	$-0.499163\pi$
$967$	0.163454	0.00525631	0.00262816	+	0.999997i	$0.499163\pi$
$968$	−6.14501	−0.197508
$969$	16.6423	0.534627
$970$	−164.723	−5.28893
$971$	−24.4462	−0.784514	−0.392257	−	0.919856i	$-0.628306\pi$
$971$	−24.4462	−0.784514	−0.392257	+	0.919856i	$0.628306\pi$
$972$	4.59624	0.147425
$973$	11.5254	0.369488
$974$	30.8603	0.988826
$975$	0	0
$976$	−38.5861	−1.23511
$977$	11.6592	0.373012	0.186506	−	0.982454i	$-0.440284\pi$
$977$	11.6592	0.373012	0.186506	+	0.982454i	$0.440284\pi$
$978$	120.044	3.83858
$979$	−10.3321	−0.330215
$980$	−49.2418	−1.57297
$981$	20.8615	0.666056
$982$	−88.7905	−2.83342
$983$	−32.6779	−1.04226	−0.521132	−	0.853476i	$-0.674490\pi$
$983$	−32.6779	−1.04226	−0.521132	+	0.853476i	$0.674490\pi$
$984$	178.437	5.68837
$985$	−27.0051	−0.860454
$986$	12.4925	0.397844
$987$	0.599773	0.0190910
$988$	0	0
$989$	2.90078	0.0922394
$990$	−50.4887	−1.60464
$991$	42.7697	1.35862	0.679312	−	0.733850i	$-0.262278\pi$
$991$	42.7697	1.35862	0.679312	+	0.733850i	$0.262278\pi$
$992$	−22.0449	−0.699926
$993$	−63.2437	−2.00698
$994$	−54.7867	−1.73773
$995$	63.7964	2.02248
$996$	115.211	3.65061
$997$	30.9571	0.980422	0.490211	−	0.871604i	$-0.336920\pi$
$997$	30.9571	0.980422	0.490211	+	0.871604i	$0.336920\pi$
$998$	−18.3048	−0.579430
$999$	−68.5205	−2.16789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.l.1.1		6
13.4	even	6		143.2.e.c.133.1	yes	12
13.10	even	6		143.2.e.c.100.1	✓	12
13.12	even	2		1859.2.a.k.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.1	✓	12	13.10	even	6
143.2.e.c.133.1	yes	12	13.4	even	6
1859.2.a.k.1.6		6	13.12	even	2
1859.2.a.l.1.1		6	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53464 q^{2} -2.99024 q^{3} +4.42441 q^{4} +3.35258 q^{5} +7.57919 q^{6} -1.91841 q^{7} -6.14501 q^{8} +5.94153 q^{9} +O(q^{10})\)	\(q-2.53464 q^{2} -2.99024 q^{3} +4.42441 q^{4} +3.35258 q^{5} +7.57919 q^{6} -1.91841 q^{7} -6.14501 q^{8} +5.94153 q^{9} -8.49760 q^{10} +1.00000 q^{11} -13.2300 q^{12} +4.86248 q^{14} -10.0250 q^{15} +6.72659 q^{16} -1.97271 q^{17} -15.0596 q^{18} +2.82126 q^{19} +14.8332 q^{20} +5.73650 q^{21} -2.53464 q^{22} -0.439850 q^{23} +18.3751 q^{24} +6.23981 q^{25} -8.79587 q^{27} -8.48783 q^{28} +2.49845 q^{29} +25.4098 q^{30} +4.63180 q^{31} -4.75947 q^{32} -2.99024 q^{33} +5.00013 q^{34} -6.43163 q^{35} +26.2878 q^{36} +7.79007 q^{37} -7.15087 q^{38} -20.6017 q^{40} +9.71084 q^{41} -14.5400 q^{42} -6.59493 q^{43} +4.42441 q^{44} +19.9195 q^{45} +1.11486 q^{46} +0.104554 q^{47} -20.1141 q^{48} -3.31970 q^{49} -15.8157 q^{50} +5.89889 q^{51} +0.381991 q^{53} +22.2944 q^{54} +3.35258 q^{55} +11.7887 q^{56} -8.43623 q^{57} -6.33267 q^{58} +1.03254 q^{59} -44.3548 q^{60} -5.73635 q^{61} -11.7399 q^{62} -11.3983 q^{63} -1.38963 q^{64} +7.57919 q^{66} +7.25193 q^{67} -8.72810 q^{68} +1.31526 q^{69} +16.3019 q^{70} -11.2672 q^{71} -36.5108 q^{72} -0.808179 q^{73} -19.7450 q^{74} -18.6585 q^{75} +12.4824 q^{76} -1.91841 q^{77} -7.04501 q^{79} +22.5514 q^{80} +8.47718 q^{81} -24.6135 q^{82} -8.70830 q^{83} +25.3807 q^{84} -6.61369 q^{85} +16.7158 q^{86} -7.47095 q^{87} -6.14501 q^{88} -10.3321 q^{89} -50.4887 q^{90} -1.94608 q^{92} -13.8502 q^{93} -0.265006 q^{94} +9.45849 q^{95} +14.2319 q^{96} +19.3846 q^{97} +8.41426 q^{98} +5.94153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	\( 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} - 3 q^{10} + 6 q^{11} - 17 q^{12} + 12 q^{14} - 4 q^{15} + 8 q^{16} + 2 q^{17} - 6 q^{18} + 10 q^{19} + 15 q^{20} + 12 q^{21} + 3 q^{23} + 14 q^{24} - 6 q^{25} + 10 q^{27} + 16 q^{28} + 3 q^{29} + 19 q^{30} + 5 q^{31} - q^{32} + q^{33} - 5 q^{34} - 13 q^{35} + 20 q^{36} + 25 q^{37} - 27 q^{38} - 8 q^{40} + 24 q^{41} + 13 q^{42} - 8 q^{43} + 8 q^{44} + 27 q^{45} + 18 q^{46} + 10 q^{47} - 28 q^{48} - q^{49} - 26 q^{50} - 17 q^{51} + 10 q^{53} + 47 q^{54} + 6 q^{55} + 15 q^{56} + 6 q^{58} - 4 q^{59} - 61 q^{60} - 21 q^{61} - 5 q^{62} + 6 q^{63} - 27 q^{64} + 12 q^{66} + 21 q^{67} + 14 q^{68} + 5 q^{69} + 31 q^{70} - 3 q^{71} - 50 q^{72} + 13 q^{73} - 38 q^{74} - 23 q^{75} + 8 q^{76} + 3 q^{77} - 4 q^{79} + 44 q^{80} + 34 q^{81} - 33 q^{82} + 8 q^{83} + 47 q^{84} - 13 q^{85} - 11 q^{86} - 51 q^{87} - 3 q^{88} - 9 q^{89} - 70 q^{90} + 15 q^{92} - 21 q^{93} + 10 q^{94} + 27 q^{95} - 19 q^{96} + 15 q^{97} + 21 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 - 3 * q^10 + 6 * q^11 - 17 * q^12 + 12 * q^14 - 4 * q^15 + 8 * q^16 + 2 * q^17 - 6 * q^18 + 10 * q^19 + 15 * q^20 + 12 * q^21 + 3 * q^23 + 14 * q^24 - 6 * q^25 + 10 * q^27 + 16 * q^28 + 3 * q^29 + 19 * q^30 + 5 * q^31 - q^32 + q^33 - 5 * q^34 - 13 * q^35 + 20 * q^36 + 25 * q^37 - 27 * q^38 - 8 * q^40 + 24 * q^41 + 13 * q^42 - 8 * q^43 + 8 * q^44 + 27 * q^45 + 18 * q^46 + 10 * q^47 - 28 * q^48 - q^49 - 26 * q^50 - 17 * q^51 + 10 * q^53 + 47 * q^54 + 6 * q^55 + 15 * q^56 + 6 * q^58 - 4 * q^59 - 61 * q^60 - 21 * q^61 - 5 * q^62 + 6 * q^63 - 27 * q^64 + 12 * q^66 + 21 * q^67 + 14 * q^68 + 5 * q^69 + 31 * q^70 - 3 * q^71 - 50 * q^72 + 13 * q^73 - 38 * q^74 - 23 * q^75 + 8 * q^76 + 3 * q^77 - 4 * q^79 + 44 * q^80 + 34 * q^81 - 33 * q^82 + 8 * q^83 + 47 * q^84 - 13 * q^85 - 11 * q^86 - 51 * q^87 - 3 * q^88 - 9 * q^89 - 70 * q^90 + 15 * q^92 - 21 * q^93 + 10 * q^94 + 27 * q^95 - 19 * q^96 + 15 * q^97 + 21 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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