LMFDB - Embedded newform 1815.4.a.bj.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 76 x^{10} + 86 x^{9} + 2070 x^{8} - 2627 x^{7} - 23872 x^{6} + 33784 x^{5} + \cdots + 9680 $ x^12 - x^11 - 76x^10 + 86x^9 + 2070x^8 - 2627x^7 - 23872x^6 + 33784x^5 + 101637x^4 - 160162x^3 - 65064x^2 + 93280x + 9680
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 11^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-4.86542$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.86542 q^{2} -3.00000 q^{3} +15.6724 q^{4} -5.00000 q^{5} -14.5963 q^{6} +19.6520 q^{7} +37.3293 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.86542 q^{2} -3.00000 q^{3} +15.6724 q^{4} -5.00000 q^{5} -14.5963 q^{6} +19.6520 q^{7} +37.3293 q^{8} +9.00000 q^{9} -24.3271 q^{10} -47.0171 q^{12} -1.18777 q^{13} +95.6154 q^{14} +15.0000 q^{15} +56.2438 q^{16} +9.08200 q^{17} +43.7888 q^{18} +39.4878 q^{19} -78.3618 q^{20} -58.9560 q^{21} +13.8319 q^{23} -111.988 q^{24} +25.0000 q^{25} -5.77899 q^{26} -27.0000 q^{27} +307.993 q^{28} +226.962 q^{29} +72.9814 q^{30} +252.880 q^{31} -24.9839 q^{32} +44.1878 q^{34} -98.2601 q^{35} +141.051 q^{36} -267.026 q^{37} +192.125 q^{38} +3.56330 q^{39} -186.646 q^{40} -419.371 q^{41} -286.846 q^{42} +305.460 q^{43} -45.0000 q^{45} +67.2981 q^{46} +89.7736 q^{47} -168.732 q^{48} +43.2017 q^{49} +121.636 q^{50} -27.2460 q^{51} -18.6151 q^{52} +33.2058 q^{53} -131.366 q^{54} +733.595 q^{56} -118.464 q^{57} +1104.26 q^{58} +835.898 q^{59} +235.085 q^{60} +53.9581 q^{61} +1230.37 q^{62} +176.868 q^{63} -571.508 q^{64} +5.93883 q^{65} +634.651 q^{67} +142.336 q^{68} -41.4957 q^{69} -478.077 q^{70} -606.279 q^{71} +335.963 q^{72} +397.374 q^{73} -1299.19 q^{74} -75.0000 q^{75} +618.868 q^{76} +17.3370 q^{78} +177.947 q^{79} -281.219 q^{80} +81.0000 q^{81} -2040.42 q^{82} +1161.84 q^{83} -923.980 q^{84} -45.4100 q^{85} +1486.19 q^{86} -680.885 q^{87} +1384.58 q^{89} -218.944 q^{90} -23.3420 q^{91} +216.778 q^{92} -758.639 q^{93} +436.787 q^{94} -197.439 q^{95} +74.9517 q^{96} +588.598 q^{97} +210.195 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 36 q^{3} + 57 q^{4} - 60 q^{5} + 3 q^{6} + 51 q^{7} + 45 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - q^2 - 36 * q^3 + 57 * q^4 - 60 * q^5 + 3 * q^6 + 51 * q^7 + 45 * q^8 + 108 * q^9	\( 12 q - q^{2} - 36 q^{3} + 57 q^{4} - 60 q^{5} + 3 q^{6} + 51 q^{7} + 45 q^{8} + 108 q^{9} + 5 q^{10} - 171 q^{12} + 132 q^{13} + 178 q^{14} + 180 q^{15} + 329 q^{16} + 189 q^{17} - 9 q^{18} + 85 q^{19} - 285 q^{20} - 153 q^{21} + 444 q^{23} - 135 q^{24} + 300 q^{25} - 308 q^{26} - 324 q^{27} + 858 q^{28} - 439 q^{29} - 15 q^{30} + 75 q^{31} - 56 q^{32} + 866 q^{34} - 255 q^{35} + 513 q^{36} - 138 q^{37} + 660 q^{38} - 396 q^{39} - 225 q^{40} - 379 q^{41} - 534 q^{42} + 1221 q^{43} - 540 q^{45} - 595 q^{46} - 696 q^{47} - 987 q^{48} + 731 q^{49} - 25 q^{50} - 567 q^{51} + 373 q^{52} - 915 q^{53} + 27 q^{54} + 2181 q^{56} - 255 q^{57} - 1182 q^{58} + 868 q^{59} + 855 q^{60} - 84 q^{61} - 1809 q^{62} + 459 q^{63} - 425 q^{64} - 660 q^{65} + 1569 q^{67} + 1182 q^{68} - 1332 q^{69} - 890 q^{70} - 604 q^{71} + 405 q^{72} + 3156 q^{73} - 2273 q^{74} - 900 q^{75} - 146 q^{76} + 924 q^{78} + 1061 q^{79} - 1645 q^{80} + 972 q^{81} - 3030 q^{82} - 314 q^{83} - 2574 q^{84} - 945 q^{85} - 4975 q^{86} + 1317 q^{87} + 3943 q^{89} + 45 q^{90} + 2726 q^{91} + 1842 q^{92} - 225 q^{93} + 1683 q^{94} - 425 q^{95} + 168 q^{96} + 194 q^{97} + 4008 q^{98}+O(q^{100}) \) 12 * q - q^2 - 36 * q^3 + 57 * q^4 - 60 * q^5 + 3 * q^6 + 51 * q^7 + 45 * q^8 + 108 * q^9 + 5 * q^10 - 171 * q^12 + 132 * q^13 + 178 * q^14 + 180 * q^15 + 329 * q^16 + 189 * q^17 - 9 * q^18 + 85 * q^19 - 285 * q^20 - 153 * q^21 + 444 * q^23 - 135 * q^24 + 300 * q^25 - 308 * q^26 - 324 * q^27 + 858 * q^28 - 439 * q^29 - 15 * q^30 + 75 * q^31 - 56 * q^32 + 866 * q^34 - 255 * q^35 + 513 * q^36 - 138 * q^37 + 660 * q^38 - 396 * q^39 - 225 * q^40 - 379 * q^41 - 534 * q^42 + 1221 * q^43 - 540 * q^45 - 595 * q^46 - 696 * q^47 - 987 * q^48 + 731 * q^49 - 25 * q^50 - 567 * q^51 + 373 * q^52 - 915 * q^53 + 27 * q^54 + 2181 * q^56 - 255 * q^57 - 1182 * q^58 + 868 * q^59 + 855 * q^60 - 84 * q^61 - 1809 * q^62 + 459 * q^63 - 425 * q^64 - 660 * q^65 + 1569 * q^67 + 1182 * q^68 - 1332 * q^69 - 890 * q^70 - 604 * q^71 + 405 * q^72 + 3156 * q^73 - 2273 * q^74 - 900 * q^75 - 146 * q^76 + 924 * q^78 + 1061 * q^79 - 1645 * q^80 + 972 * q^81 - 3030 * q^82 - 314 * q^83 - 2574 * q^84 - 945 * q^85 - 4975 * q^86 + 1317 * q^87 + 3943 * q^89 + 45 * q^90 + 2726 * q^91 + 1842 * q^92 - 225 * q^93 + 1683 * q^94 - 425 * q^95 + 168 * q^96 + 194 * q^97 + 4008 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.86542	1.72019	0.860094	−	0.510136i	$-0.170405\pi$
$2$	4.86542	1.72019	0.860094	+	0.510136i	$0.170405\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	15.6724	1.95904
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−14.5963	−0.993151
$7$	19.6520	1.06111	0.530555	−	0.847651i	$-0.321984\pi$
$7$	19.6520	1.06111	0.530555	+	0.847651i	$0.321984\pi$
$8$	37.3293	1.64974
$9$	9.00000	0.333333
$10$	−24.3271	−0.769291
$11$	0	0
$11$	0	0
$12$	−47.0171	−1.13105
$13$	−1.18777	−0.0253406	−0.0126703	−	0.999920i	$-0.504033\pi$
$13$	−1.18777	−0.0253406	−0.0126703	+	0.999920i	$0.504033\pi$
$14$	95.6154	1.82531
$15$	15.0000	0.258199
$16$	56.2438	0.878810
$17$	9.08200	0.129571	0.0647856	−	0.997899i	$-0.479364\pi$
$17$	9.08200	0.129571	0.0647856	+	0.997899i	$0.479364\pi$
$18$	43.7888	0.573396
$19$	39.4878	0.476797	0.238398	−	0.971167i	$-0.423378\pi$
$19$	39.4878	0.476797	0.238398	+	0.971167i	$0.423378\pi$
$20$	−78.3618	−0.876111
$21$	−58.9560	−0.612632
$22$	0	0
$23$	13.8319	0.125398	0.0626989	−	0.998032i	$-0.480029\pi$
$23$	13.8319	0.125398	0.0626989	+	0.998032i	$0.480029\pi$
$24$	−111.988	−0.952475
$25$	25.0000	0.200000
$26$	−5.77899	−0.0435905
$27$	−27.0000	−0.192450
$28$	307.993	2.07876
$29$	226.962	1.45330	0.726650	−	0.687008i	$-0.241076\pi$
$29$	226.962	1.45330	0.726650	+	0.687008i	$0.241076\pi$
$30$	72.9814	0.444150
$31$	252.880	1.46511	0.732557	−	0.680706i	$-0.238327\pi$
$31$	252.880	1.46511	0.732557	+	0.680706i	$0.238327\pi$
$32$	−24.9839	−0.138018
$33$	0	0
$34$	44.1878	0.222887
$35$	−98.2601	−0.474542
$36$	141.051	0.653015
$37$	−267.026	−1.18645	−0.593227	−	0.805035i	$-0.702146\pi$
$37$	−267.026	−1.18645	−0.593227	+	0.805035i	$0.702146\pi$
$38$	192.125	0.820179
$39$	3.56330	0.0146304
$40$	−186.646	−0.737784
$41$	−419.371	−1.59743	−0.798715	−	0.601709i	$-0.794487\pi$
$41$	−419.371	−1.59743	−0.798715	+	0.601709i	$0.794487\pi$
$42$	−286.846	−1.05384
$43$	305.460	1.08331	0.541653	−	0.840602i	$-0.317799\pi$
$43$	305.460	1.08331	0.541653	+	0.840602i	$0.317799\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	67.2981	0.215708
$47$	89.7736	0.278613	0.139307	−	0.990249i	$-0.455513\pi$
$47$	89.7736	0.278613	0.139307	+	0.990249i	$0.455513\pi$
$48$	−168.732	−0.507381
$49$	43.2017	0.125952
$50$	121.636	0.344037
$51$	−27.2460	−0.0748079
$52$	−18.6151	−0.0496433
$53$	33.2058	0.0860597	0.0430298	−	0.999074i	$-0.486299\pi$
$53$	33.2058	0.0860597	0.0430298	+	0.999074i	$0.486299\pi$
$54$	−131.366	−0.331050
$55$	0	0
$56$	733.595	1.75055
$57$	−118.464	−0.275279
$58$	1104.26	2.49995
$59$	835.898	1.84449	0.922243	−	0.386610i	$-0.126354\pi$
$59$	835.898	1.84449	0.922243	+	0.386610i	$0.126354\pi$
$60$	235.085	0.505823
$61$	53.9581	0.113256	0.0566280	−	0.998395i	$-0.481965\pi$
$61$	53.9581	0.113256	0.0566280	+	0.998395i	$0.481965\pi$
$62$	1230.37	2.52027
$63$	176.868	0.353703
$64$	−571.508	−1.11623
$65$	5.93883	0.0113326
$66$	0	0
$67$	634.651	1.15724	0.578619	−	0.815598i	$-0.303592\pi$
$67$	634.651	1.15724	0.578619	+	0.815598i	$0.303592\pi$
$68$	142.336	0.253836
$69$	−41.4957	−0.0723985
$70$	−478.077	−0.816302
$71$	−606.279	−1.01341	−0.506705	−	0.862120i	$-0.669137\pi$
$71$	−606.279	−1.01341	−0.506705	+	0.862120i	$0.669137\pi$
$72$	335.963	0.549912
$73$	397.374	0.637111	0.318555	−	0.947904i	$-0.396802\pi$
$73$	397.374	0.637111	0.318555	+	0.947904i	$0.396802\pi$
$74$	−1299.19	−2.04092
$75$	−75.0000	−0.115470
$76$	618.868	0.934065
$77$	0	0
$78$	17.3370	0.0251670
$79$	177.947	0.253426	0.126713	−	0.991939i	$-0.459557\pi$
$79$	177.947	0.253426	0.126713	+	0.991939i	$0.459557\pi$
$80$	−281.219	−0.393016
$81$	81.0000	0.111111
$82$	−2040.42	−2.74788
$83$	1161.84	1.53649	0.768244	−	0.640158i	$-0.221131\pi$
$83$	1161.84	1.53649	0.768244	+	0.640158i	$0.221131\pi$
$84$	−923.980	−1.20017
$85$	−45.4100	−0.0579460
$86$	1486.19	1.86349
$87$	−680.885	−0.839063
$88$	0	0
$89$	1384.58	1.64904	0.824521	−	0.565832i	$-0.191445\pi$
$89$	1384.58	1.64904	0.824521	+	0.565832i	$0.191445\pi$
$90$	−218.944	−0.256430
$91$	−23.3420	−0.0268891
$92$	216.778	0.245660
$93$	−758.639	−0.845884
$94$	436.787	0.479267
$95$	−197.439	−0.213230
$96$	74.9517	0.0796847
$97$	588.598	0.616114	0.308057	−	0.951368i	$-0.400321\pi$
$97$	588.598	0.616114	0.308057	+	0.951368i	$0.400321\pi$
$98$	210.195	0.216662
$99$	0	0
$100$	391.809	0.391809
$101$	−1258.66	−1.24001	−0.620007	−	0.784596i	$-0.712870\pi$
$101$	−1258.66	−1.24001	−0.620007	+	0.784596i	$0.712870\pi$
$102$	−132.563	−0.128684
$103$	−332.381	−0.317965	−0.158983	−	0.987281i	$-0.550821\pi$
$103$	−332.381	−0.317965	−0.158983	+	0.987281i	$0.550821\pi$
$104$	−44.3384	−0.0418052
$105$	294.780	0.273977
$106$	161.560	0.148039
$107$	546.363	0.493634	0.246817	−	0.969062i	$-0.420615\pi$
$107$	546.363	0.493634	0.246817	+	0.969062i	$0.420615\pi$
$108$	−423.154	−0.377018
$109$	−98.0957	−0.0862006	−0.0431003	−	0.999071i	$-0.513724\pi$
$109$	−98.0957	−0.0862006	−0.0431003	+	0.999071i	$0.513724\pi$
$110$	0	0
$111$	801.078	0.685000
$112$	1105.30	0.932513
$113$	−428.333	−0.356586	−0.178293	−	0.983977i	$-0.557057\pi$
$113$	−428.333	−0.356586	−0.178293	+	0.983977i	$0.557057\pi$
$114$	−576.375	−0.473531
$115$	−69.1595	−0.0560796
$116$	3557.02	2.84708
$117$	−10.6899	−0.00844685
$118$	4067.00	3.17286
$119$	178.480	0.137489
$120$	559.939	0.425960
$121$	0	0
$122$	262.529	0.194822
$123$	1258.11	0.922277
$124$	3963.22	2.87022
$125$	−125.000	−0.0894427
$126$	860.539	0.608435
$127$	1330.31	0.929499	0.464749	−	0.885442i	$-0.346144\pi$
$127$	1330.31	0.929499	0.464749	+	0.885442i	$0.346144\pi$
$128$	−2580.76	−1.78210
$129$	−916.380	−0.625447
$130$	28.8949	0.0194943
$131$	252.966	0.168715	0.0843577	−	0.996436i	$-0.473116\pi$
$131$	252.966	0.168715	0.0843577	+	0.996436i	$0.473116\pi$
$132$	0	0
$133$	776.016	0.505933
$134$	3087.85	1.99067
$135$	135.000	0.0860663
$136$	339.024	0.213758
$137$	3151.59	1.96539	0.982694	−	0.185236i	$-0.0593049\pi$
$137$	3151.59	1.96539	0.982694	+	0.185236i	$0.0593049\pi$
$138$	−201.894	−0.124539
$139$	−1752.26	−1.06924	−0.534621	−	0.845092i	$-0.679546\pi$
$139$	−1752.26	−1.06924	−0.534621	+	0.845092i	$0.679546\pi$
$140$	−1539.97	−0.929650
$141$	−269.321	−0.160857
$142$	−2949.80	−1.74325
$143$	0	0
$144$	506.195	0.292937
$145$	−1134.81	−0.649936
$146$	1933.39	1.09595
$147$	−129.605	−0.0727187
$148$	−4184.93	−2.32432
$149$	−3224.64	−1.77297	−0.886486	−	0.462755i	$-0.846861\pi$
$149$	−3224.64	−1.77297	−0.886486	+	0.462755i	$0.846861\pi$
$150$	−364.907	−0.198630
$151$	748.445	0.403362	0.201681	−	0.979451i	$-0.435360\pi$
$151$	748.445	0.403362	0.201681	+	0.979451i	$0.435360\pi$
$152$	1474.05	0.786588
$153$	81.7380	0.0431904
$154$	0	0
$155$	−1264.40	−0.655219
$156$	55.8453	0.0286615
$157$	−1544.92	−0.785337	−0.392668	−	0.919680i	$-0.628448\pi$
$157$	−1544.92	−0.785337	−0.392668	+	0.919680i	$0.628448\pi$
$158$	865.789	0.435940
$159$	−99.6173	−0.0496866
$160$	124.920	0.0617235
$161$	271.825	0.133061
$162$	394.099	0.191132
$163$	2945.00	1.41515	0.707576	−	0.706637i	$-0.249789\pi$
$163$	2945.00	1.41515	0.707576	+	0.706637i	$0.249789\pi$
$164$	−6572.52	−3.12944
$165$	0	0
$166$	5652.84	2.64305
$167$	−2840.94	−1.31640	−0.658200	−	0.752843i	$-0.728682\pi$
$167$	−2840.94	−1.31640	−0.658200	+	0.752843i	$0.728682\pi$
$168$	−2200.79	−1.01068
$169$	−2195.59	−0.999358
$170$	−220.939	−0.0996779
$171$	355.391	0.158932
$172$	4787.27	2.12225
$173$	−1490.94	−0.655226	−0.327613	−	0.944812i	$-0.606244\pi$
$173$	−1490.94	−0.655226	−0.327613	+	0.944812i	$0.606244\pi$
$174$	−3312.79	−1.44335
$175$	491.300	0.212222
$176$	0	0
$177$	−2507.70	−1.06491
$178$	6736.55	2.83666
$179$	3015.34	1.25909	0.629545	−	0.776964i	$-0.283241\pi$
$179$	3015.34	1.25909	0.629545	+	0.776964i	$0.283241\pi$
$180$	−705.256	−0.292037
$181$	3653.01	1.50015	0.750073	−	0.661355i	$-0.230018\pi$
$181$	3653.01	1.50015	0.750073	+	0.661355i	$0.230018\pi$
$182$	−113.569	−0.0462543
$183$	−161.874	−0.0653884
$184$	516.334	0.206873
$185$	1335.13	0.530599
$186$	−3691.10	−1.45508
$187$	0	0
$188$	1406.96	0.545816
$189$	−530.604	−0.204211
$190$	−960.626	−0.366795
$191$	1115.58	0.422619	0.211310	−	0.977419i	$-0.432227\pi$
$191$	1115.58	0.422619	0.211310	+	0.977419i	$0.432227\pi$
$192$	1714.52	0.644454
$193$	2426.83	0.905115	0.452558	−	0.891735i	$-0.350512\pi$
$193$	2426.83	0.905115	0.452558	+	0.891735i	$0.350512\pi$
$194$	2863.78	1.05983
$195$	−17.8165	−0.00654290
$196$	677.072	0.246746
$197$	−3756.88	−1.35871	−0.679357	−	0.733808i	$-0.737741\pi$
$197$	−3756.88	−1.35871	−0.679357	+	0.733808i	$0.737741\pi$
$198$	0	0
$199$	3438.06	1.22471	0.612356	−	0.790582i	$-0.290222\pi$
$199$	3438.06	1.22471	0.612356	+	0.790582i	$0.290222\pi$
$200$	933.231	0.329947
$201$	−1903.95	−0.668132
$202$	−6123.92	−2.13306
$203$	4460.25	1.54211
$204$	−427.009	−0.146552
$205$	2096.85	0.714393
$206$	−1617.17	−0.546960
$207$	124.487	0.0417993
$208$	−66.8045	−0.0222695
$209$	0	0
$210$	1434.23	0.471292
$211$	−122.014	−0.0398094	−0.0199047	−	0.999802i	$-0.506336\pi$
$211$	−122.014	−0.0398094	−0.0199047	+	0.999802i	$0.506336\pi$
$212$	520.413	0.168595
$213$	1818.84	0.585092
$214$	2658.29	0.849143
$215$	−1527.30	−0.484470
$216$	−1007.89	−0.317492
$217$	4969.60	1.55465
$218$	−477.277	−0.148281
$219$	−1192.12	−0.367836
$220$	0	0
$221$	−10.7873	−0.00328340
$222$	3897.58	1.17833
$223$	−4936.89	−1.48251	−0.741253	−	0.671226i	$-0.765768\pi$
$223$	−4936.89	−1.48251	−0.741253	+	0.671226i	$0.765768\pi$
$224$	−490.984	−0.146452
$225$	225.000	0.0666667
$226$	−2084.02	−0.613394
$227$	3018.48	0.882571	0.441286	−	0.897367i	$-0.354523\pi$
$227$	3018.48	0.882571	0.441286	+	0.897367i	$0.354523\pi$
$228$	−1856.60	−0.539283
$229$	5025.86	1.45030	0.725148	−	0.688593i	$-0.241771\pi$
$229$	5025.86	1.45030	0.725148	+	0.688593i	$0.241771\pi$
$230$	−336.490	−0.0964674
$231$	0	0
$232$	8472.31	2.39756
$233$	2597.70	0.730391	0.365195	−	0.930931i	$-0.381002\pi$
$233$	2597.70	0.730391	0.365195	+	0.930931i	$0.381002\pi$
$234$	−52.0109	−0.0145302
$235$	−448.868	−0.124600
$236$	13100.5	3.61343
$237$	−533.842	−0.146315
$238$	868.379	0.236507
$239$	−3285.55	−0.889223	−0.444612	−	0.895723i	$-0.646658\pi$
$239$	−3285.55	−0.889223	−0.444612	+	0.895723i	$0.646658\pi$
$240$	843.658	0.226908
$241$	4894.55	1.30824	0.654119	−	0.756391i	$-0.273039\pi$
$241$	4894.55	1.30824	0.654119	+	0.756391i	$0.273039\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	845.650	0.221874
$245$	−216.008	−0.0563277
$246$	6121.25	1.58649
$247$	−46.9023	−0.0120823
$248$	9439.81	2.41705
$249$	−3485.52	−0.887091
$250$	−608.178	−0.153858
$251$	−838.141	−0.210769	−0.105384	−	0.994432i	$-0.533607\pi$
$251$	−838.141	−0.210769	−0.105384	+	0.994432i	$0.533607\pi$
$252$	2771.94	0.692920
$253$	0	0
$254$	6472.55	1.59891
$255$	136.230	0.0334551
$256$	−7984.42	−1.94932
$257$	−4307.29	−1.04545	−0.522726	−	0.852501i	$-0.675085\pi$
$257$	−4307.29	−1.04545	−0.522726	+	0.852501i	$0.675085\pi$
$258$	−4458.58	−1.07589
$259$	−5247.60	−1.25896
$260$	93.0755	0.0222011
$261$	2042.65	0.484433
$262$	1230.78	0.290222
$263$	−8312.88	−1.94903	−0.974513	−	0.224329i	$-0.927981\pi$
$263$	−8312.88	−1.94903	−0.974513	+	0.224329i	$0.927981\pi$
$264$	0	0
$265$	−166.029	−0.0384871
$266$	3775.65	0.870300
$267$	−4153.73	−0.952075
$268$	9946.48	2.26708
$269$	−3597.39	−0.815379	−0.407689	−	0.913121i	$-0.633665\pi$
$269$	−3597.39	−0.815379	−0.407689	+	0.913121i	$0.633665\pi$
$270$	656.832	0.148050
$271$	7117.13	1.59533	0.797666	−	0.603100i	$-0.206068\pi$
$271$	7117.13	1.59533	0.797666	+	0.603100i	$0.206068\pi$
$272$	510.807	0.113868
$273$	70.0260	0.0155244
$274$	15333.8	3.38084
$275$	0	0
$276$	−650.335	−0.141832
$277$	−3864.58	−0.838267	−0.419133	−	0.907925i	$-0.637666\pi$
$277$	−3864.58	−0.838267	−0.419133	+	0.907925i	$0.637666\pi$
$278$	−8525.48	−1.83930
$279$	2275.92	0.488371
$280$	−3667.98	−0.782869
$281$	5923.13	1.25745	0.628726	−	0.777627i	$-0.283577\pi$
$281$	5923.13	1.25745	0.628726	+	0.777627i	$0.283577\pi$
$282$	−1310.36	−0.276705
$283$	4750.40	0.997817	0.498909	−	0.866655i	$-0.333734\pi$
$283$	4750.40	0.997817	0.498909	+	0.866655i	$0.333734\pi$
$284$	−9501.82	−1.98531
$285$	592.318	0.123108
$286$	0	0
$287$	−8241.48	−1.69505
$288$	−224.855	−0.0460060
$289$	−4830.52	−0.983211
$290$	−5521.32	−1.11801
$291$	−1765.79	−0.355713
$292$	6227.78	1.24813
$293$	−2423.72	−0.483259	−0.241630	−	0.970369i	$-0.577682\pi$
$293$	−2423.72	−0.483259	−0.241630	+	0.970369i	$0.577682\pi$
$294$	−630.584	−0.125090
$295$	−4179.49	−0.824879
$296$	−9967.88	−1.95734
$297$	0	0
$298$	−15689.2	−3.04985
$299$	−16.4291	−0.00317765
$300$	−1175.43	−0.226211
$301$	6002.90	1.14951
$302$	3641.50	0.693857
$303$	3775.98	0.715922
$304$	2220.95	0.419014
$305$	−269.790	−0.0506497
$306$	397.690	0.0742956
$307$	−3693.03	−0.686555	−0.343278	−	0.939234i	$-0.611537\pi$
$307$	−3693.03	−0.686555	−0.343278	+	0.939234i	$0.611537\pi$
$308$	0	0
$309$	997.142	0.183577
$310$	−6151.84	−1.12710
$311$	6.12485	0.00111675	0.000558374	−	1.00000i	$-0.499822\pi$
$311$	6.12485	0.00111675	0.000558374		1.00000i	$0.499822\pi$
$312$	133.015	0.0241362
$313$	−5160.35	−0.931886	−0.465943	−	0.884815i	$-0.654285\pi$
$313$	−5160.35	−0.931886	−0.465943	+	0.884815i	$0.654285\pi$
$314$	−7516.68	−1.35093
$315$	−884.341	−0.158181
$316$	2788.85	0.496472
$317$	−8456.64	−1.49833	−0.749167	−	0.662381i	$-0.769546\pi$
$317$	−8456.64	−1.49833	−0.749167	+	0.662381i	$0.769546\pi$
$318$	−484.680	−0.0854702
$319$	0	0
$320$	2857.54	0.499192
$321$	−1639.09	−0.285000
$322$	1322.54	0.228889
$323$	358.629	0.0617791
$324$	1269.46	0.217672
$325$	−29.6942	−0.00506811
$326$	14328.7	2.43433
$327$	294.287	0.0497679
$328$	−15654.8	−2.63534
$329$	1764.23	0.295639
$330$	0	0
$331$	−7051.37	−1.17093	−0.585466	−	0.810697i	$-0.699088\pi$
$331$	−7051.37	−1.17093	−0.585466	+	0.810697i	$0.699088\pi$
$332$	18208.8	3.01005
$333$	−2403.23	−0.395485
$334$	−13822.4	−2.26446
$335$	−3173.26	−0.517533
$336$	−3315.91	−0.538387
$337$	−289.275	−0.0467591	−0.0233796	−	0.999727i	$-0.507443\pi$
$337$	−289.275	−0.0467591	−0.0233796	+	0.999727i	$0.507443\pi$
$338$	−10682.5	−1.71908
$339$	1285.00	0.205875
$340$	−711.682	−0.113519
$341$	0	0
$342$	1729.13	0.273393
$343$	−5891.64	−0.927460
$344$	11402.6	1.78717
$345$	207.478	0.0323776
$346$	−7254.06	−1.12711
$347$	−5933.05	−0.917876	−0.458938	−	0.888468i	$-0.651770\pi$
$347$	−5933.05	−0.917876	−0.458938	+	0.888468i	$0.651770\pi$
$348$	−10671.1	−1.64376
$349$	253.141	0.0388261	0.0194130	−	0.999812i	$-0.493820\pi$
$349$	253.141	0.0388261	0.0194130	+	0.999812i	$0.493820\pi$
$350$	2390.38	0.365061
$351$	32.0697	0.00487679
$352$	0	0
$353$	−5163.53	−0.778547	−0.389274	−	0.921122i	$-0.627274\pi$
$353$	−5163.53	−0.778547	−0.389274	+	0.921122i	$0.627274\pi$
$354$	−12201.0	−1.83185
$355$	3031.39	0.453210
$356$	21699.6	3.23055
$357$	−535.439	−0.0793794
$358$	14670.9	2.16587
$359$	10273.0	1.51027	0.755137	−	0.655567i	$-0.227570\pi$
$359$	10273.0	1.51027	0.755137	+	0.655567i	$0.227570\pi$
$360$	−1679.82	−0.245928
$361$	−5299.71	−0.772665
$362$	17773.5	2.58053
$363$	0	0
$364$	−365.824	−0.0526769
$365$	−1986.87	−0.284925
$366$	−787.586	−0.112480
$367$	8725.06	1.24099	0.620497	−	0.784209i	$-0.286931\pi$
$367$	8725.06	1.24099	0.620497	+	0.784209i	$0.286931\pi$
$368$	777.959	0.110201
$369$	−3774.33	−0.532477
$370$	6495.97	0.912729
$371$	652.560	0.0913187
$372$	−11889.7	−1.65712
$373$	2352.65	0.326584	0.163292	−	0.986578i	$-0.447789\pi$
$373$	2352.65	0.326584	0.163292	+	0.986578i	$0.447789\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	3351.18	0.459638
$377$	−269.577	−0.0368274
$378$	−2581.62	−0.351280
$379$	−4030.33	−0.546237	−0.273119	−	0.961980i	$-0.588055\pi$
$379$	−4030.33	−0.546237	−0.273119	+	0.961980i	$0.588055\pi$
$380$	−3094.34	−0.417727
$381$	−3990.94	−0.536646
$382$	5427.75	0.726984
$383$	−2215.92	−0.295634	−0.147817	−	0.989015i	$-0.547225\pi$
$383$	−2215.92	−0.295634	−0.147817	+	0.989015i	$0.547225\pi$
$384$	7742.27	1.02890
$385$	0	0
$386$	11807.6	1.55697
$387$	2749.14	0.361102
$388$	9224.71	1.20699
$389$	−13572.7	−1.76905	−0.884527	−	0.466488i	$-0.845519\pi$
$389$	−13572.7	−1.76905	−0.884527	+	0.466488i	$0.845519\pi$
$390$	−86.6848	−0.0112550
$391$	125.621	0.0162479
$392$	1612.69	0.207788
$393$	−758.897	−0.0974078
$394$	−18278.8	−2.33724
$395$	−889.737	−0.113335
$396$	0	0
$397$	13206.3	1.66953	0.834767	−	0.550603i	$-0.185602\pi$
$397$	13206.3	1.66953	0.834767	+	0.550603i	$0.185602\pi$
$398$	16727.6	2.10673
$399$	−2328.05	−0.292101
$400$	1406.10	0.175762
$401$	−3884.30	−0.483723	−0.241861	−	0.970311i	$-0.577758\pi$
$401$	−3884.30	−0.483723	−0.241861	+	0.970311i	$0.577758\pi$
$402$	−9263.54	−1.14931
$403$	−300.362	−0.0371268
$404$	−19726.2	−2.42924
$405$	−405.000	−0.0496904
$406$	21701.0	2.65272
$407$	0	0
$408$	−1017.07	−0.123413
$409$	−3209.61	−0.388031	−0.194016	−	0.980998i	$-0.562151\pi$
$409$	−3209.61	−0.388031	−0.194016	+	0.980998i	$0.562151\pi$
$410$	10202.1	1.22889
$411$	−9454.76	−1.13472
$412$	−5209.19	−0.622908
$413$	16427.1	1.95720
$414$	605.683	0.0719026
$415$	−5809.20	−0.687138
$416$	29.6751	0.00349745
$417$	5256.77	0.617327
$418$	0	0
$419$	−4224.94	−0.492606	−0.246303	−	0.969193i	$-0.579216\pi$
$419$	−4224.94	−0.492606	−0.246303	+	0.969193i	$0.579216\pi$
$420$	4619.90	0.536733
$421$	−8309.45	−0.961943	−0.480971	−	0.876736i	$-0.659716\pi$
$421$	−8309.45	−0.961943	−0.480971	+	0.876736i	$0.659716\pi$
$422$	−593.649	−0.0684796
$423$	807.962	0.0928711
$424$	1239.55	0.141976
$425$	227.050	0.0259142
$426$	8849.41	1.00647
$427$	1060.38	0.120177
$428$	8562.79	0.967051
$429$	0	0
$430$	−7430.96	−0.833378
$431$	17.6425	0.00197172	0.000985859	−	1.00000i	$-0.499686\pi$
$431$	17.6425	0.00197172	0.000985859		1.00000i	$0.499686\pi$
$432$	−1518.58	−0.169127
$433$	−7980.13	−0.885683	−0.442842	−	0.896600i	$-0.646030\pi$
$433$	−7980.13	−0.885683	−0.442842	+	0.896600i	$0.646030\pi$
$434$	24179.2	2.67428
$435$	3404.42	0.375241
$436$	−1537.39	−0.168871
$437$	546.192	0.0597893
$438$	−5800.18	−0.632747
$439$	−13110.9	−1.42539	−0.712696	−	0.701473i	$-0.752526\pi$
$439$	−13110.9	−1.42539	−0.712696	+	0.701473i	$0.752526\pi$
$440$	0	0
$441$	388.815	0.0419842
$442$	−52.4848	−0.00564807
$443$	−4104.39	−0.440193	−0.220097	−	0.975478i	$-0.570637\pi$
$443$	−4104.39	−0.440193	−0.220097	+	0.975478i	$0.570637\pi$
$444$	12554.8	1.34194
$445$	−6922.88	−0.737474
$446$	−24020.1	−2.55019
$447$	9673.92	1.02363
$448$	−11231.3	−1.18444
$449$	−13103.9	−1.37731	−0.688654	−	0.725090i	$-0.741798\pi$
$449$	−13103.9	−1.37731	−0.688654	+	0.725090i	$0.741798\pi$
$450$	1094.72	0.114679
$451$	0	0
$452$	−6712.99	−0.698567
$453$	−2245.34	−0.232881
$454$	14686.2	1.51819
$455$	116.710	0.0120252
$456$	−4422.16	−0.454137
$457$	2792.27	0.285813	0.142907	−	0.989736i	$-0.454355\pi$
$457$	2792.27	0.285813	0.142907	+	0.989736i	$0.454355\pi$
$458$	24452.9	2.49478
$459$	−245.214	−0.0249360
$460$	−1083.89	−0.109862
$461$	41.4014	0.00418277	0.00209139	−	0.999998i	$-0.499334\pi$
$461$	41.4014	0.00418277	0.00209139	+	0.999998i	$0.499334\pi$
$462$	0	0
$463$	−8644.45	−0.867692	−0.433846	−	0.900987i	$-0.642844\pi$
$463$	−8644.45	−0.867692	−0.433846	+	0.900987i	$0.642844\pi$
$464$	12765.2	1.27717
$465$	3793.20	0.378291
$466$	12638.9	1.25641
$467$	12790.5	1.26739	0.633697	−	0.773581i	$-0.281536\pi$
$467$	12790.5	1.26739	0.633697	+	0.773581i	$0.281536\pi$
$468$	−167.536	−0.0165478
$469$	12472.2	1.22796
$470$	−2183.93	−0.214335
$471$	4634.75	0.453414
$472$	31203.5	3.04292
$473$	0	0
$474$	−2597.37	−0.251690
$475$	987.196	0.0953593
$476$	2797.20	0.269347
$477$	298.852	0.0286866
$478$	−15985.6	−1.52963
$479$	2551.04	0.243340	0.121670	−	0.992571i	$-0.461175\pi$
$479$	2551.04	0.243340	0.121670	+	0.992571i	$0.461175\pi$
$480$	−374.759	−0.0356361
$481$	317.165	0.0300654
$482$	23814.0	2.25042
$483$	−815.474	−0.0768227
$484$	0	0
$485$	−2942.99	−0.275534
$486$	−1182.30	−0.110350
$487$	−14076.7	−1.30980	−0.654902	−	0.755714i	$-0.727290\pi$
$487$	−14076.7	−1.30980	−0.654902	+	0.755714i	$0.727290\pi$
$488$	2014.21	0.186843
$489$	−8834.99	−0.817039
$490$	−1050.97	−0.0968941
$491$	10220.1	0.939358	0.469679	−	0.882837i	$-0.344370\pi$
$491$	10220.1	0.939358	0.469679	+	0.882837i	$0.344370\pi$
$492$	19717.6	1.80678
$493$	2061.27	0.188306
$494$	−228.200	−0.0207838
$495$	0	0
$496$	14222.9	1.28756
$497$	−11914.6	−1.07534
$498$	−16958.5	−1.52596
$499$	1918.08	0.172074	0.0860372	−	0.996292i	$-0.472580\pi$
$499$	1918.08	0.172074	0.0860372	+	0.996292i	$0.472580\pi$
$500$	−1959.04	−0.175222
$501$	8522.83	0.760024
$502$	−4077.91	−0.362562
$503$	−13269.4	−1.17625	−0.588126	−	0.808769i	$-0.700134\pi$
$503$	−13269.4	−1.17625	−0.588126	+	0.808769i	$0.700134\pi$
$504$	6602.36	0.583516
$505$	6293.30	0.554551
$506$	0	0
$507$	6586.77	0.576980
$508$	20849.2	1.82093
$509$	−12662.0	−1.10262	−0.551311	−	0.834300i	$-0.685872\pi$
$509$	−12662.0	−1.10262	−0.551311	+	0.834300i	$0.685872\pi$
$510$	662.817	0.0575491
$511$	7809.20	0.676044
$512$	−18201.5	−1.57110
$513$	−1066.17	−0.0917595
$514$	−20956.8	−1.79837
$515$	1661.90	0.142198
$516$	−14361.8	−1.22528
$517$	0	0
$518$	−25531.8	−2.16564
$519$	4472.82	0.378295
$520$	221.692	0.0186959
$521$	8402.59	0.706573	0.353286	−	0.935515i	$-0.385064\pi$
$521$	8402.59	0.706573	0.353286	+	0.935515i	$0.385064\pi$
$522$	9938.38	0.833316
$523$	11797.0	0.986321	0.493160	−	0.869938i	$-0.335842\pi$
$523$	11797.0	0.986321	0.493160	+	0.869938i	$0.335842\pi$
$524$	3964.57	0.330521
$525$	−1473.90	−0.122526
$526$	−40445.7	−3.35269
$527$	2296.66	0.189837
$528$	0	0
$529$	−11975.7	−0.984275
$530$	−807.801	−0.0662049
$531$	7523.09	0.614829
$532$	12162.0	0.991145
$533$	498.114	0.0404798
$534$	−20209.6	−1.63775
$535$	−2731.81	−0.220760
$536$	23691.1	1.90914
$537$	−9046.02	−0.726936
$538$	−17502.8	−1.40260
$539$	0	0
$540$	2115.77	0.168608
$541$	−18252.0	−1.45049	−0.725245	−	0.688490i	$-0.758274\pi$
$541$	−18252.0	−1.45049	−0.725245	+	0.688490i	$0.758274\pi$
$542$	34627.9	2.74427
$543$	−10959.0	−0.866110
$544$	−226.904	−0.0178831
$545$	490.479	0.0385501
$546$	340.706	0.0267049
$547$	−11378.3	−0.889399	−0.444699	−	0.895680i	$-0.646690\pi$
$547$	−11378.3	−0.889399	−0.444699	+	0.895680i	$0.646690\pi$
$548$	49392.8	3.85028
$549$	485.622	0.0377520
$550$	0	0
$551$	8962.22	0.692929
$552$	−1549.00	−0.119438
$553$	3497.02	0.268912
$554$	−18802.8	−1.44198
$555$	−4005.39	−0.306341
$556$	−27462.0	−2.09469
$557$	−13070.1	−0.994255	−0.497127	−	0.867678i	$-0.665612\pi$
$557$	−13070.1	−0.994255	−0.497127	+	0.867678i	$0.665612\pi$
$558$	11073.3	0.840090
$559$	−362.815	−0.0274516
$560$	−5526.52	−0.417033
$561$	0	0
$562$	28818.5	2.16305
$563$	−3319.20	−0.248468	−0.124234	−	0.992253i	$-0.539647\pi$
$563$	−3319.20	−0.248468	−0.124234	+	0.992253i	$0.539647\pi$
$564$	−4220.89	−0.315127
$565$	2141.67	0.159470
$566$	23112.7	1.71643
$567$	1591.81	0.117901
$568$	−22631.9	−1.67186
$569$	−5668.88	−0.417665	−0.208833	−	0.977951i	$-0.566966\pi$
$569$	−5668.88	−0.417665	−0.208833	+	0.977951i	$0.566966\pi$
$570$	2881.88	0.211769
$571$	−12027.0	−0.881460	−0.440730	−	0.897640i	$-0.645280\pi$
$571$	−12027.0	−0.881460	−0.440730	+	0.897640i	$0.645280\pi$
$572$	0	0
$573$	−3346.73	−0.243999
$574$	−40098.3	−2.91580
$575$	345.797	0.0250796
$576$	−5143.57	−0.372076
$577$	8141.91	0.587439	0.293719	−	0.955892i	$-0.405107\pi$
$577$	8141.91	0.587439	0.293719	+	0.955892i	$0.405107\pi$
$578$	−23502.5	−1.69131
$579$	−7280.50	−0.522569
$580$	−17785.1	−1.27325
$581$	22832.5	1.63038
$582$	−8591.33	−0.611894
$583$	0	0
$584$	14833.7	1.05106
$585$	53.4495	0.00377755
$586$	−11792.4	−0.831296
$587$	8144.26	0.572657	0.286329	−	0.958132i	$-0.407565\pi$
$587$	8144.26	0.572657	0.286329	+	0.958132i	$0.407565\pi$
$588$	−2031.22	−0.142459
$589$	9985.68	0.698561
$590$	−20335.0	−1.41895
$591$	11270.6	0.784454
$592$	−15018.6	−1.04267
$593$	9223.74	0.638741	0.319371	−	0.947630i	$-0.396529\pi$
$593$	9223.74	0.638741	0.319371	+	0.947630i	$0.396529\pi$
$594$	0	0
$595$	−892.398	−0.0614870
$596$	−50537.7	−3.47333
$597$	−10314.2	−0.707087
$598$	−79.9344	−0.00546615
$599$	11291.1	0.770189	0.385095	−	0.922877i	$-0.374169\pi$
$599$	11291.1	0.770189	0.385095	+	0.922877i	$0.374169\pi$
$600$	−2799.69	−0.190495
$601$	−9863.58	−0.669457	−0.334728	−	0.942315i	$-0.608645\pi$
$601$	−9863.58	−0.669457	−0.334728	+	0.942315i	$0.608645\pi$
$602$	29206.7	1.97737
$603$	5711.86	0.385746
$604$	11729.9	0.790203
$605$	0	0
$606$	18371.7	1.23152
$607$	26398.5	1.76521	0.882605	−	0.470116i	$-0.155788\pi$
$607$	26398.5	1.76521	0.882605	+	0.470116i	$0.155788\pi$
$608$	−986.561	−0.0658065
$609$	−13380.8	−0.890338
$610$	−1312.64	−0.0871269
$611$	−106.630	−0.00706022
$612$	1281.03	0.0846119
$613$	13380.0	0.881585	0.440792	−	0.897609i	$-0.354698\pi$
$613$	13380.0	0.881585	0.440792	+	0.897609i	$0.354698\pi$
$614$	−17968.2	−1.18100
$615$	−6290.56	−0.412455
$616$	0	0
$617$	−24979.8	−1.62990	−0.814949	−	0.579533i	$-0.803235\pi$
$617$	−24979.8	−1.62990	−0.814949	+	0.579533i	$0.803235\pi$
$618$	4851.52	0.315787
$619$	−16061.0	−1.04288	−0.521441	−	0.853287i	$-0.674605\pi$
$619$	−16061.0	−1.04288	−0.521441	+	0.853287i	$0.674605\pi$
$620$	−19816.1	−1.28360
$621$	−373.461	−0.0241328
$622$	29.8000	0.00192102
$623$	27209.7	1.74981
$624$	200.414	0.0128573
$625$	625.000	0.0400000
$626$	−25107.3	−1.60302
$627$	0	0
$628$	−24212.5	−1.53851
$629$	−2425.13	−0.153730
$630$	−4302.69	−0.272101
$631$	−13190.7	−0.832193	−0.416097	−	0.909320i	$-0.636602\pi$
$631$	−13190.7	−0.832193	−0.416097	+	0.909320i	$0.636602\pi$
$632$	6642.64	0.418086
$633$	366.042	0.0229840
$634$	−41145.1	−2.57742
$635$	−6651.57	−0.415685
$636$	−1561.24	−0.0973382
$637$	−51.3135	−0.00319170
$638$	0	0
$639$	−5456.51	−0.337803
$640$	12903.8	0.796980
$641$	−26376.9	−1.62531	−0.812655	−	0.582746i	$-0.801978\pi$
$641$	−26376.9	−1.62531	−0.812655	+	0.582746i	$0.801978\pi$
$642$	−7974.86	−0.490253
$643$	−274.560	−0.0168392	−0.00841958	−	0.999965i	$-0.502680\pi$
$643$	−274.560	−0.0168392	−0.00841958	+	0.999965i	$0.502680\pi$
$644$	4260.13	0.260672
$645$	4581.90	0.279709
$646$	1744.88	0.106272
$647$	25759.8	1.56526	0.782629	−	0.622488i	$-0.213878\pi$
$647$	25759.8	1.56526	0.782629	+	0.622488i	$0.213878\pi$
$648$	3023.67	0.183304
$649$	0	0
$650$	−144.475	−0.00871810
$651$	−14908.8	−0.897575
$652$	46155.0	2.77235
$653$	−22401.9	−1.34250	−0.671252	−	0.741229i	$-0.734243\pi$
$653$	−22401.9	−1.34250	−0.671252	+	0.741229i	$0.734243\pi$
$654$	1431.83	0.0856102
$655$	−1264.83	−0.0754518
$656$	−23587.0	−1.40384
$657$	3576.37	0.212370
$658$	8583.74	0.508555
$659$	−9620.91	−0.568706	−0.284353	−	0.958720i	$-0.591779\pi$
$659$	−9620.91	−0.568706	−0.284353	+	0.958720i	$0.591779\pi$
$660$	0	0
$661$	6231.23	0.366667	0.183333	−	0.983051i	$-0.441311\pi$
$661$	6231.23	0.366667	0.183333	+	0.983051i	$0.441311\pi$
$662$	−34307.9	−2.01422
$663$	32.3619	0.00189567
$664$	43370.6	2.53480
$665$	−3880.08	−0.226260
$666$	−11692.8	−0.680308
$667$	3139.31	0.182241
$668$	−44524.3	−2.57889
$669$	14810.7	0.855925
$670$	−15439.2	−0.890253
$671$	0	0
$672$	1472.95	0.0845541
$673$	18088.9	1.03607	0.518034	−	0.855360i	$-0.326664\pi$
$673$	18088.9	1.03607	0.518034	+	0.855360i	$0.326664\pi$
$674$	−1407.45	−0.0804345
$675$	−675.000	−0.0384900
$676$	−34410.1	−1.95779
$677$	−21109.0	−1.19835	−0.599176	−	0.800617i	$-0.704505\pi$
$677$	−21109.0	−1.19835	−0.599176	+	0.800617i	$0.704505\pi$
$678$	6252.07	0.354143
$679$	11567.1	0.653764
$680$	−1695.12	−0.0955956
$681$	−9055.45	−0.509553
$682$	0	0
$683$	−26782.8	−1.50046	−0.750231	−	0.661176i	$-0.770058\pi$
$683$	−26782.8	−1.50046	−0.750231	+	0.661176i	$0.770058\pi$
$684$	5569.81	0.311355
$685$	−15757.9	−0.878948
$686$	−28665.3	−1.59540
$687$	−15077.6	−0.837329
$688$	17180.2	0.952021
$689$	−39.4407	−0.00218080
$690$	1009.47	0.0556955
$691$	−25558.6	−1.40708	−0.703542	−	0.710653i	$-0.748399\pi$
$691$	−25558.6	−1.40708	−0.703542	+	0.710653i	$0.748399\pi$
$692$	−23366.5	−1.28362
$693$	0	0
$694$	−28866.8	−1.57892
$695$	8761.29	0.478179
$696$	−25416.9	−1.38423
$697$	−3808.73	−0.206981
$698$	1231.64	0.0667881
$699$	−7793.10	−0.421691
$700$	7699.83	0.415752
$701$	19187.4	1.03381	0.516903	−	0.856044i	$-0.327085\pi$
$701$	19187.4	1.03381	0.516903	+	0.856044i	$0.327085\pi$
$702$	156.033	0.00838899
$703$	−10544.3	−0.565697
$704$	0	0
$705$	1346.60	0.0719377
$706$	−25122.8	−1.33925
$707$	−24735.2	−1.31579
$708$	−39301.5	−2.08622
$709$	−7266.23	−0.384893	−0.192446	−	0.981307i	$-0.561642\pi$
$709$	−7266.23	−0.384893	−0.192446	+	0.981307i	$0.561642\pi$
$710$	14749.0	0.779607
$711$	1601.53	0.0844753
$712$	51685.2	2.72048
$713$	3497.81	0.183722
$714$	−2605.14	−0.136547
$715$	0	0
$716$	47257.5	2.46661
$717$	9856.64	0.513393
$718$	49982.5	2.59796
$719$	25642.6	1.33005	0.665027	−	0.746819i	$-0.268420\pi$
$719$	25642.6	1.33005	0.665027	+	0.746819i	$0.268420\pi$
$720$	−2530.97	−0.131005
$721$	−6531.95	−0.337396
$722$	−25785.3	−1.32913
$723$	−14683.6	−0.755312
$724$	57251.3	2.93885
$725$	5674.04	0.290660
$726$	0	0
$727$	−1726.65	−0.0880853	−0.0440426	−	0.999030i	$-0.514024\pi$
$727$	−1726.65	−0.0880853	−0.0440426	+	0.999030i	$0.514024\pi$
$728$	−871.340	−0.0443599
$729$	729.000	0.0370370
$730$	−9666.96	−0.490124
$731$	2774.19	0.140365
$732$	−2536.95	−0.128099
$733$	−17440.1	−0.878804	−0.439402	−	0.898291i	$-0.644810\pi$
$733$	−17440.1	−0.878804	−0.439402	+	0.898291i	$0.644810\pi$
$734$	42451.1	2.13474
$735$	648.025	0.0325208
$736$	−345.575	−0.0173071
$737$	0	0
$738$	−18363.7	−0.915960
$739$	−10802.1	−0.537704	−0.268852	−	0.963181i	$-0.586644\pi$
$739$	−10802.1	−0.537704	−0.268852	+	0.963181i	$0.586644\pi$
$740$	20924.6	1.03947
$741$	140.707	0.00697571
$742$	3174.98	0.157085
$743$	38626.0	1.90720	0.953602	−	0.301071i	$-0.0973441\pi$
$743$	38626.0	1.90720	0.953602	+	0.301071i	$0.0973441\pi$
$744$	−28319.4	−1.39549
$745$	16123.2	0.792897
$746$	11446.6	0.561785
$747$	10456.6	0.512162
$748$	0	0
$749$	10737.1	0.523800
$750$	1824.53	0.0888301
$751$	16596.0	0.806385	0.403192	−	0.915115i	$-0.367901\pi$
$751$	16596.0	0.806385	0.403192	+	0.915115i	$0.367901\pi$
$752$	5049.21	0.244848
$753$	2514.42	0.121688
$754$	−1311.61	−0.0633501
$755$	−3742.23	−0.180389
$756$	−8315.82	−0.400057
$757$	11499.3	0.552114	0.276057	−	0.961141i	$-0.410972\pi$
$757$	11499.3	0.552114	0.276057	+	0.961141i	$0.410972\pi$
$758$	−19609.2	−0.939630
$759$	0	0
$760$	−7370.26	−0.351773
$761$	39815.1	1.89658	0.948289	−	0.317408i	$-0.102812\pi$
$761$	39815.1	1.89658	0.948289	+	0.317408i	$0.102812\pi$
$762$	−19417.6	−0.923132
$763$	−1927.78	−0.0914682
$764$	17483.7	0.827930
$765$	−408.690	−0.0193153
$766$	−10781.4	−0.508547
$767$	−992.852	−0.0467403
$768$	23953.3	1.12544
$769$	−25944.4	−1.21662	−0.608308	−	0.793701i	$-0.708152\pi$
$769$	−25944.4	−1.21662	−0.608308	+	0.793701i	$0.708152\pi$
$770$	0	0
$771$	12921.9	0.603592
$772$	38034.2	1.77316
$773$	6725.54	0.312938	0.156469	−	0.987683i	$-0.449989\pi$
$773$	6725.54	0.312938	0.156469	+	0.987683i	$0.449989\pi$
$774$	13375.7	0.621164
$775$	6321.99	0.293023
$776$	21971.9	1.01642
$777$	15742.8	0.726859
$778$	−66036.9	−3.04311
$779$	−16560.0	−0.761650
$780$	−279.226	−0.0128178
$781$	0	0
$782$	611.201	0.0279495
$783$	−6127.96	−0.279688
$784$	2429.83	0.110688
$785$	7724.59	0.351213
$786$	−3692.35	−0.167560
$787$	19072.0	0.863842	0.431921	−	0.901911i	$-0.357836\pi$
$787$	19072.0	0.863842	0.431921	+	0.901911i	$0.357836\pi$
$788$	−58879.2	−2.66178
$789$	24938.6	1.12527
$790$	−4328.95	−0.194958
$791$	−8417.61	−0.378376
$792$	0	0
$793$	−64.0896	−0.00286997
$794$	64254.3	2.87191
$795$	498.087	0.0222205
$796$	53882.5	2.39926
$797$	−65.9857	−0.00293267	−0.00146633	−	0.999999i	$-0.500467\pi$
$797$	−65.9857	−0.00293267	−0.00146633	+	0.999999i	$0.500467\pi$
$798$	−11326.9	−0.502468
$799$	815.324	0.0361003
$800$	−624.598	−0.0276036
$801$	12461.2	0.549681
$802$	−18898.8	−0.832094
$803$	0	0
$804$	−29839.4	−1.30890
$805$	−1359.12	−0.0595066
$806$	−1461.39	−0.0638651
$807$	10792.2	0.470759
$808$	−46984.9	−2.04569
$809$	38313.7	1.66507	0.832533	−	0.553975i	$-0.186890\pi$
$809$	38313.7	1.66507	0.832533	+	0.553975i	$0.186890\pi$
$810$	−1970.50	−0.0854768
$811$	−10687.9	−0.462767	−0.231384	−	0.972863i	$-0.574325\pi$
$811$	−10687.9	−0.462767	−0.231384	+	0.972863i	$0.574325\pi$
$812$	69902.7	3.02106
$813$	−21351.4	−0.921065
$814$	0	0
$815$	−14725.0	−0.632875
$816$	−1532.42	−0.0657420
$817$	12062.0	0.516517
$818$	−15616.1	−0.667486
$819$	−210.078	−0.00896303
$820$	32862.6	1.39953
$821$	13770.6	0.585379	0.292689	−	0.956208i	$-0.405450\pi$
$821$	13770.6	0.585379	0.292689	+	0.956208i	$0.405450\pi$
$822$	−46001.4	−1.95193
$823$	15611.8	0.661231	0.330616	−	0.943766i	$-0.392744\pi$
$823$	15611.8	0.661231	0.330616	+	0.943766i	$0.392744\pi$
$824$	−12407.5	−0.524559
$825$	0	0
$826$	79924.8	3.36675
$827$	−43013.8	−1.80863	−0.904315	−	0.426865i	$-0.859618\pi$
$827$	−43013.8	−1.80863	−0.904315	+	0.426865i	$0.859618\pi$
$828$	1951.01	0.0818866
$829$	3425.84	0.143528	0.0717638	−	0.997422i	$-0.477137\pi$
$829$	3425.84	0.143528	0.0717638	+	0.997422i	$0.477137\pi$
$830$	−28264.2	−1.18201
$831$	11593.7	0.483973
$832$	678.818	0.0282858
$833$	392.358	0.0163198
$834$	25576.4	1.06192
$835$	14204.7	0.588712
$836$	0	0
$837$	−6827.75	−0.281961
$838$	−20556.1	−0.847374
$839$	477.119	0.0196329	0.00981643	−	0.999952i	$-0.496875\pi$
$839$	477.119	0.0196329	0.00981643	+	0.999952i	$0.496875\pi$
$840$	11003.9	0.451990
$841$	27122.6	1.11208
$842$	−40429.0	−1.65472
$843$	−17769.4	−0.725991
$844$	−1912.25	−0.0779884
$845$	10977.9	0.446926
$846$	3931.08	0.159756
$847$	0	0
$848$	1867.62	0.0756301
$849$	−14251.2	−0.576090
$850$	1104.70	0.0445773
$851$	−3693.48	−0.148779
$852$	28505.4	1.14622
$853$	18062.0	0.725008	0.362504	−	0.931982i	$-0.381922\pi$
$853$	18062.0	0.725008	0.362504	+	0.931982i	$0.381922\pi$
$854$	5159.22	0.206727
$855$	−1776.95	−0.0710766
$856$	20395.3	0.814366
$857$	35396.5	1.41088	0.705439	−	0.708771i	$-0.250750\pi$
$857$	35396.5	1.41088	0.705439	+	0.708771i	$0.250750\pi$
$858$	0	0
$859$	22228.2	0.882907	0.441454	−	0.897284i	$-0.354463\pi$
$859$	22228.2	0.882907	0.441454	+	0.897284i	$0.354463\pi$
$860$	−23936.4	−0.949097
$861$	24724.4	0.978637
$862$	85.8383	0.00339172
$863$	−4432.27	−0.174828	−0.0874138	−	0.996172i	$-0.527860\pi$
$863$	−4432.27	−0.174828	−0.0874138	+	0.996172i	$0.527860\pi$
$864$	674.566	0.0265616
$865$	7454.70	0.293026
$866$	−38826.7	−1.52354
$867$	14491.6	0.567657
$868$	77885.3	3.04562
$869$	0	0
$870$	16564.0	0.645484
$871$	−753.817	−0.0293251
$872$	−3661.84	−0.142208
$873$	5297.38	0.205371
$874$	2657.46	0.102849
$875$	−2456.50	−0.0949085
$876$	−18683.4	−0.720607
$877$	−18025.3	−0.694039	−0.347019	−	0.937858i	$-0.612806\pi$
$877$	−18025.3	−0.694039	−0.347019	+	0.937858i	$0.612806\pi$
$878$	−63789.9	−2.45194
$879$	7271.15	0.279010
$880$	0	0
$881$	−4141.52	−0.158378	−0.0791892	−	0.996860i	$-0.525233\pi$
$881$	−4141.52	−0.158378	−0.0791892	+	0.996860i	$0.525233\pi$
$882$	1891.75	0.0722206
$883$	28122.5	1.07180	0.535898	−	0.844283i	$-0.319973\pi$
$883$	28122.5	1.07180	0.535898	+	0.844283i	$0.319973\pi$
$884$	−169.062	−0.00643233
$885$	12538.5	0.476244
$886$	−19969.6	−0.757215
$887$	2108.77	0.0798260	0.0399130	−	0.999203i	$-0.487292\pi$
$887$	2108.77	0.0798260	0.0399130	+	0.999203i	$0.487292\pi$
$888$	29903.6	1.13007
$889$	26143.4	0.986300
$890$	−33682.7	−1.26859
$891$	0	0
$892$	−77372.7	−2.90429
$893$	3544.97	0.132842
$894$	47067.7	1.76083
$895$	−15076.7	−0.563082
$896$	−50717.1	−1.89100
$897$	49.2872	0.00183462
$898$	−63756.0	−2.36923
$899$	57394.0	2.12925
$900$	3526.28	0.130603
$901$	301.575	0.0111509
$902$	0	0
$903$	−18008.7	−0.663668
$904$	−15989.4	−0.588272
$905$	−18265.1	−0.670886
$906$	−10924.5	−0.400599
$907$	41134.2	1.50588	0.752942	−	0.658087i	$-0.228634\pi$
$907$	41134.2	1.50588	0.752942	+	0.658087i	$0.228634\pi$
$908$	47306.7	1.72900
$909$	−11327.9	−0.413338
$910$	567.844	0.0206855
$911$	−4295.17	−0.156208	−0.0781039	−	0.996945i	$-0.524887\pi$
$911$	−4295.17	−0.156208	−0.0781039	+	0.996945i	$0.524887\pi$
$912$	−6662.84	−0.241918
$913$	0	0
$914$	13585.6	0.491652
$915$	809.371	0.0292426
$916$	78767.0	2.84119
$917$	4971.28	0.179025
$918$	−1193.07	−0.0428946
$919$	38022.1	1.36478	0.682390	−	0.730988i	$-0.260941\pi$
$919$	38022.1	1.36478	0.682390	+	0.730988i	$0.260941\pi$
$920$	−2581.67	−0.0925165
$921$	11079.1	0.396383
$922$	201.436	0.00719515
$923$	720.118	0.0256804
$924$	0	0
$925$	−6675.65	−0.237291
$926$	−42058.9	−1.49259
$927$	−2991.43	−0.105988
$928$	−5670.39	−0.200581
$929$	−8431.33	−0.297764	−0.148882	−	0.988855i	$-0.547568\pi$
$929$	−8431.33	−0.297764	−0.148882	+	0.988855i	$0.547568\pi$
$930$	18455.5	0.650731
$931$	1705.94	0.0600537
$932$	40712.1	1.43087
$933$	−18.3746	−0.000644755 0
$934$	62231.2	2.18016
$935$	0	0
$936$	−399.046	−0.0139351
$937$	−32766.6	−1.14241	−0.571205	−	0.820807i	$-0.693524\pi$
$937$	−32766.6	−1.14241	−0.571205	+	0.820807i	$0.693524\pi$
$938$	60682.4	2.11231
$939$	15481.1	0.538025
$940$	−7034.82	−0.244096
$941$	−37000.0	−1.28179	−0.640895	−	0.767628i	$-0.721437\pi$
$941$	−37000.0	−1.28179	−0.640895	+	0.767628i	$0.721437\pi$
$942$	22550.0	0.779957
$943$	−5800.69	−0.200314
$944$	47014.1	1.62095
$945$	2653.02	0.0913257
$946$	0	0
$947$	−10812.3	−0.371018	−0.185509	−	0.982643i	$-0.559393\pi$
$947$	−10812.3	−0.371018	−0.185509	+	0.982643i	$0.559393\pi$
$948$	−8366.56	−0.286638
$949$	−471.987	−0.0161447
$950$	4803.13	0.164036
$951$	25369.9	0.865064
$952$	6662.51	0.226821
$953$	13238.6	0.449990	0.224995	−	0.974360i	$-0.427763\pi$
$953$	13238.6	0.449990	0.224995	+	0.974360i	$0.427763\pi$
$954$	1454.04	0.0493463
$955$	−5577.88	−0.189001
$956$	−51492.3	−1.74203
$957$	0	0
$958$	12411.9	0.418591
$959$	61935.0	2.08549
$960$	−8572.62	−0.288208
$961$	34157.2	1.14656
$962$	1543.14	0.0517181
$963$	4917.26	0.164545
$964$	76709.1	2.56290
$965$	−12134.2	−0.404780
$966$	−3967.63	−0.132149
$967$	47639.4	1.58426	0.792130	−	0.610353i	$-0.208972\pi$
$967$	47639.4	1.58426	0.792130	+	0.610353i	$0.208972\pi$
$968$	0	0
$969$	−1075.89	−0.0356682
$970$	−14318.9	−0.473971
$971$	−11595.5	−0.383230	−0.191615	−	0.981470i	$-0.561373\pi$
$971$	−11595.5	−0.383230	−0.191615	+	0.981470i	$0.561373\pi$
$972$	−3808.38	−0.125673
$973$	−34435.4	−1.13458
$974$	−68489.0	−2.25311
$975$	89.0825	0.00292607
$976$	3034.81	0.0995306
$977$	−9355.54	−0.306356	−0.153178	−	0.988199i	$-0.548951\pi$
$977$	−9355.54	−0.306356	−0.153178	+	0.988199i	$0.548951\pi$
$978$	−42986.0	−1.40546
$979$	0	0
$980$	−3385.36	−0.110348
$981$	−882.861	−0.0287335
$982$	49724.9	1.61587
$983$	7183.76	0.233089	0.116544	−	0.993185i	$-0.462818\pi$
$983$	7183.76	0.233089	0.116544	+	0.993185i	$0.462818\pi$
$984$	46964.4	1.52151
$985$	18784.4	0.607636
$986$	10028.9	0.323921
$987$	−5292.70	−0.170687
$988$	−735.070	−0.0236697
$989$	4225.09	0.135844
$990$	0	0
$991$	17622.3	0.564874	0.282437	−	0.959286i	$-0.408857\pi$
$991$	17622.3	0.564874	0.282437	+	0.959286i	$0.408857\pi$
$992$	−6317.93	−0.202212
$993$	21154.1	0.676038
$994$	−57969.6	−1.84978
$995$	−17190.3	−0.547708
$996$	−54626.3	−1.73785
$997$	33898.4	1.07680	0.538402	−	0.842688i	$-0.319028\pi$
$997$	33898.4	1.07680	0.538402	+	0.842688i	$0.319028\pi$
$998$	9332.28	0.296000
$999$	7209.70	0.228333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bj.1.11		12
11.3	even	5		165.4.m.b.31.6	yes	24
11.4	even	5		165.4.m.b.16.6	✓	24
11.10	odd	2		1815.4.a.bm.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.b.16.6	✓	24	11.4	even	5
165.4.m.b.31.6	yes	24	11.3	even	5
1815.4.a.bj.1.11		12	1.1	even	1	trivial
1815.4.a.bm.1.2		12	11.10	odd	2

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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+4.86542 q^{2} -3.00000 q^{3} +15.6724 q^{4} -5.00000 q^{5} -14.5963 q^{6} +19.6520 q^{7} +37.3293 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.86542 q^{2} -3.00000 q^{3} +15.6724 q^{4} -5.00000 q^{5} -14.5963 q^{6} +19.6520 q^{7} +37.3293 q^{8} +9.00000 q^{9} -24.3271 q^{10} -47.0171 q^{12} -1.18777 q^{13} +95.6154 q^{14} +15.0000 q^{15} +56.2438 q^{16} +9.08200 q^{17} +43.7888 q^{18} +39.4878 q^{19} -78.3618 q^{20} -58.9560 q^{21} +13.8319 q^{23} -111.988 q^{24} +25.0000 q^{25} -5.77899 q^{26} -27.0000 q^{27} +307.993 q^{28} +226.962 q^{29} +72.9814 q^{30} +252.880 q^{31} -24.9839 q^{32} +44.1878 q^{34} -98.2601 q^{35} +141.051 q^{36} -267.026 q^{37} +192.125 q^{38} +3.56330 q^{39} -186.646 q^{40} -419.371 q^{41} -286.846 q^{42} +305.460 q^{43} -45.0000 q^{45} +67.2981 q^{46} +89.7736 q^{47} -168.732 q^{48} +43.2017 q^{49} +121.636 q^{50} -27.2460 q^{51} -18.6151 q^{52} +33.2058 q^{53} -131.366 q^{54} +733.595 q^{56} -118.464 q^{57} +1104.26 q^{58} +835.898 q^{59} +235.085 q^{60} +53.9581 q^{61} +1230.37 q^{62} +176.868 q^{63} -571.508 q^{64} +5.93883 q^{65} +634.651 q^{67} +142.336 q^{68} -41.4957 q^{69} -478.077 q^{70} -606.279 q^{71} +335.963 q^{72} +397.374 q^{73} -1299.19 q^{74} -75.0000 q^{75} +618.868 q^{76} +17.3370 q^{78} +177.947 q^{79} -281.219 q^{80} +81.0000 q^{81} -2040.42 q^{82} +1161.84 q^{83} -923.980 q^{84} -45.4100 q^{85} +1486.19 q^{86} -680.885 q^{87} +1384.58 q^{89} -218.944 q^{90} -23.3420 q^{91} +216.778 q^{92} -758.639 q^{93} +436.787 q^{94} -197.439 q^{95} +74.9517 q^{96} +588.598 q^{97} +210.195 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 36 q^{3} + 57 q^{4} - 60 q^{5} + 3 q^{6} + 51 q^{7} + 45 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - q^2 - 36 * q^3 + 57 * q^4 - 60 * q^5 + 3 * q^6 + 51 * q^7 + 45 * q^8 + 108 * q^9	\( 12 q - q^{2} - 36 q^{3} + 57 q^{4} - 60 q^{5} + 3 q^{6} + 51 q^{7} + 45 q^{8} + 108 q^{9} + 5 q^{10} - 171 q^{12} + 132 q^{13} + 178 q^{14} + 180 q^{15} + 329 q^{16} + 189 q^{17} - 9 q^{18} + 85 q^{19} - 285 q^{20} - 153 q^{21} + 444 q^{23} - 135 q^{24} + 300 q^{25} - 308 q^{26} - 324 q^{27} + 858 q^{28} - 439 q^{29} - 15 q^{30} + 75 q^{31} - 56 q^{32} + 866 q^{34} - 255 q^{35} + 513 q^{36} - 138 q^{37} + 660 q^{38} - 396 q^{39} - 225 q^{40} - 379 q^{41} - 534 q^{42} + 1221 q^{43} - 540 q^{45} - 595 q^{46} - 696 q^{47} - 987 q^{48} + 731 q^{49} - 25 q^{50} - 567 q^{51} + 373 q^{52} - 915 q^{53} + 27 q^{54} + 2181 q^{56} - 255 q^{57} - 1182 q^{58} + 868 q^{59} + 855 q^{60} - 84 q^{61} - 1809 q^{62} + 459 q^{63} - 425 q^{64} - 660 q^{65} + 1569 q^{67} + 1182 q^{68} - 1332 q^{69} - 890 q^{70} - 604 q^{71} + 405 q^{72} + 3156 q^{73} - 2273 q^{74} - 900 q^{75} - 146 q^{76} + 924 q^{78} + 1061 q^{79} - 1645 q^{80} + 972 q^{81} - 3030 q^{82} - 314 q^{83} - 2574 q^{84} - 945 q^{85} - 4975 q^{86} + 1317 q^{87} + 3943 q^{89} + 45 q^{90} + 2726 q^{91} + 1842 q^{92} - 225 q^{93} + 1683 q^{94} - 425 q^{95} + 168 q^{96} + 194 q^{97} + 4008 q^{98}+O(q^{100}) \) 12 * q - q^2 - 36 * q^3 + 57 * q^4 - 60 * q^5 + 3 * q^6 + 51 * q^7 + 45 * q^8 + 108 * q^9 + 5 * q^10 - 171 * q^12 + 132 * q^13 + 178 * q^14 + 180 * q^15 + 329 * q^16 + 189 * q^17 - 9 * q^18 + 85 * q^19 - 285 * q^20 - 153 * q^21 + 444 * q^23 - 135 * q^24 + 300 * q^25 - 308 * q^26 - 324 * q^27 + 858 * q^28 - 439 * q^29 - 15 * q^30 + 75 * q^31 - 56 * q^32 + 866 * q^34 - 255 * q^35 + 513 * q^36 - 138 * q^37 + 660 * q^38 - 396 * q^39 - 225 * q^40 - 379 * q^41 - 534 * q^42 + 1221 * q^43 - 540 * q^45 - 595 * q^46 - 696 * q^47 - 987 * q^48 + 731 * q^49 - 25 * q^50 - 567 * q^51 + 373 * q^52 - 915 * q^53 + 27 * q^54 + 2181 * q^56 - 255 * q^57 - 1182 * q^58 + 868 * q^59 + 855 * q^60 - 84 * q^61 - 1809 * q^62 + 459 * q^63 - 425 * q^64 - 660 * q^65 + 1569 * q^67 + 1182 * q^68 - 1332 * q^69 - 890 * q^70 - 604 * q^71 + 405 * q^72 + 3156 * q^73 - 2273 * q^74 - 900 * q^75 - 146 * q^76 + 924 * q^78 + 1061 * q^79 - 1645 * q^80 + 972 * q^81 - 3030 * q^82 - 314 * q^83 - 2574 * q^84 - 945 * q^85 - 4975 * q^86 + 1317 * q^87 + 3943 * q^89 + 45 * q^90 + 2726 * q^91 + 1842 * q^92 - 225 * q^93 + 1683 * q^94 - 425 * q^95 + 168 * q^96 + 194 * q^97 + 4008 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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