LMFDB - Embedded newform 1815.4.a.bi.1.2

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:	$1$
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} - 72 x^{10} + 68 x^{9} + 1852 x^{8} - 1711 x^{7} - 20848 x^{6} + 20766 x^{5} + \cdots + 56080 $ x^12 - x^11 - 72x^10 + 68x^9 + 1852x^8 - 1711x^7 - 20848x^6 + 20766x^5 + 98931x^4 - 106938x^3 - 137664x^2 + 117840x + 56080
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 11^{3} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.90341$ 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)

$f(q)$	$=$	$q-4.90341 q^{2} -3.00000 q^{3} +16.0434 q^{4} +5.00000 q^{5} +14.7102 q^{6} +0.166503 q^{7} -39.4401 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.90341 q^{2} -3.00000 q^{3} +16.0434 q^{4} +5.00000 q^{5} +14.7102 q^{6} +0.166503 q^{7} -39.4401 q^{8} +9.00000 q^{9} -24.5170 q^{10} -48.1302 q^{12} -27.6851 q^{13} -0.816430 q^{14} -15.0000 q^{15} +65.0437 q^{16} -4.79353 q^{17} -44.1307 q^{18} +11.2232 q^{19} +80.2170 q^{20} -0.499508 q^{21} +107.716 q^{23} +118.320 q^{24} +25.0000 q^{25} +135.751 q^{26} -27.0000 q^{27} +2.67127 q^{28} -123.007 q^{29} +73.5511 q^{30} -75.8131 q^{31} -3.41483 q^{32} +23.5047 q^{34} +0.832513 q^{35} +144.391 q^{36} +351.397 q^{37} -55.0319 q^{38} +83.0553 q^{39} -197.201 q^{40} -355.049 q^{41} +2.44929 q^{42} +313.261 q^{43} +45.0000 q^{45} -528.176 q^{46} +160.565 q^{47} -195.131 q^{48} -342.972 q^{49} -122.585 q^{50} +14.3806 q^{51} -444.164 q^{52} +335.490 q^{53} +132.392 q^{54} -6.56688 q^{56} -33.6696 q^{57} +603.154 q^{58} +25.2343 q^{59} -240.651 q^{60} -461.486 q^{61} +371.743 q^{62} +1.49852 q^{63} -503.605 q^{64} -138.426 q^{65} -627.489 q^{67} -76.9046 q^{68} -323.148 q^{69} -4.08215 q^{70} +119.453 q^{71} -354.961 q^{72} -631.455 q^{73} -1723.04 q^{74} -75.0000 q^{75} +180.058 q^{76} -407.254 q^{78} -949.514 q^{79} +325.218 q^{80} +81.0000 q^{81} +1740.95 q^{82} -43.2803 q^{83} -8.01381 q^{84} -23.9677 q^{85} -1536.05 q^{86} +369.021 q^{87} +380.904 q^{89} -220.653 q^{90} -4.60964 q^{91} +1728.13 q^{92} +227.439 q^{93} -787.316 q^{94} +56.1160 q^{95} +10.2445 q^{96} +1698.20 q^{97} +1681.73 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 36 q^{3} + 49 q^{4} + 60 q^{5} + 3 q^{6} + 5 q^{7} + 3 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - q^2 - 36 * q^3 + 49 * q^4 + 60 * q^5 + 3 * q^6 + 5 * q^7 + 3 * q^8 + 108 * q^9	\( 12 q - q^{2} - 36 q^{3} + 49 q^{4} + 60 q^{5} + 3 q^{6} + 5 q^{7} + 3 q^{8} + 108 q^{9} - 5 q^{10} - 147 q^{12} - 34 q^{13} - 134 q^{14} - 180 q^{15} + 265 q^{16} - 169 q^{17} - 9 q^{18} - 203 q^{19} + 245 q^{20} - 15 q^{21} + 116 q^{23} - 9 q^{24} + 300 q^{25} + 216 q^{26} - 324 q^{27} - 80 q^{28} - 409 q^{29} + 15 q^{30} - 645 q^{31} - 532 q^{32} - 1442 q^{34} + 25 q^{35} + 441 q^{36} + 40 q^{37} + 404 q^{38} + 102 q^{39} + 15 q^{40} - 1071 q^{41} + 402 q^{42} + 101 q^{43} + 540 q^{45} - 1539 q^{46} - 572 q^{47} - 795 q^{48} + 1563 q^{49} - 25 q^{50} + 507 q^{51} - 1081 q^{52} + 611 q^{53} + 27 q^{54} - 3221 q^{56} + 609 q^{57} - 354 q^{58} + 958 q^{59} - 735 q^{60} - 2620 q^{61} - 1049 q^{62} + 45 q^{63} + 2931 q^{64} - 170 q^{65} - 1027 q^{67} - 1896 q^{68} - 348 q^{69} - 670 q^{70} + 1020 q^{71} + 27 q^{72} - 2244 q^{73} + 283 q^{74} - 900 q^{75} - 4958 q^{76} - 648 q^{78} - 2199 q^{79} + 1325 q^{80} + 972 q^{81} + 362 q^{82} + 602 q^{83} + 240 q^{84} - 845 q^{85} - 1589 q^{86} + 1227 q^{87} - 2413 q^{89} - 45 q^{90} + 302 q^{91} + 3030 q^{92} + 1935 q^{93} - 2885 q^{94} - 1015 q^{95} + 1596 q^{96} + 886 q^{97} + 1236 q^{98}+O(q^{100}) \) 12 * q - q^2 - 36 * q^3 + 49 * q^4 + 60 * q^5 + 3 * q^6 + 5 * q^7 + 3 * q^8 + 108 * q^9 - 5 * q^10 - 147 * q^12 - 34 * q^13 - 134 * q^14 - 180 * q^15 + 265 * q^16 - 169 * q^17 - 9 * q^18 - 203 * q^19 + 245 * q^20 - 15 * q^21 + 116 * q^23 - 9 * q^24 + 300 * q^25 + 216 * q^26 - 324 * q^27 - 80 * q^28 - 409 * q^29 + 15 * q^30 - 645 * q^31 - 532 * q^32 - 1442 * q^34 + 25 * q^35 + 441 * q^36 + 40 * q^37 + 404 * q^38 + 102 * q^39 + 15 * q^40 - 1071 * q^41 + 402 * q^42 + 101 * q^43 + 540 * q^45 - 1539 * q^46 - 572 * q^47 - 795 * q^48 + 1563 * q^49 - 25 * q^50 + 507 * q^51 - 1081 * q^52 + 611 * q^53 + 27 * q^54 - 3221 * q^56 + 609 * q^57 - 354 * q^58 + 958 * q^59 - 735 * q^60 - 2620 * q^61 - 1049 * q^62 + 45 * q^63 + 2931 * q^64 - 170 * q^65 - 1027 * q^67 - 1896 * q^68 - 348 * q^69 - 670 * q^70 + 1020 * q^71 + 27 * q^72 - 2244 * q^73 + 283 * q^74 - 900 * q^75 - 4958 * q^76 - 648 * q^78 - 2199 * q^79 + 1325 * q^80 + 972 * q^81 + 362 * q^82 + 602 * q^83 + 240 * q^84 - 845 * q^85 - 1589 * q^86 + 1227 * q^87 - 2413 * q^89 - 45 * q^90 + 302 * q^91 + 3030 * q^92 + 1935 * q^93 - 2885 * q^94 - 1015 * q^95 + 1596 * q^96 + 886 * q^97 + 1236 * 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 $

$2$	−4.90341	−1.73362	−0.866808	−	0.498642i	$-0.833832\pi$
$2$	−4.90341	−1.73362	−0.866808	+	0.498642i	$0.833832\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	16.0434	2.00543
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	14.7102	1.00090
$7$	0.166503	0.00899030	0.00449515	−	0.999990i	$-0.498569\pi$
$7$	0.166503	0.00899030	0.00449515	+	0.999990i	$0.498569\pi$
$8$	−39.4401	−1.74302
$9$	9.00000	0.333333
$10$	−24.5170	−0.775297
$11$	0	0
$11$	0	0
$12$	−48.1302	−1.15783
$13$	−27.6851	−0.590651	−0.295326	−	0.955397i	$-0.595428\pi$
$13$	−27.6851	−0.590651	−0.295326	+	0.955397i	$0.595428\pi$
$14$	−0.816430	−0.0155857
$15$	−15.0000	−0.258199
$16$	65.0437	1.01631
$17$	−4.79353	−0.0683884	−0.0341942	−	0.999415i	$-0.510886\pi$
$17$	−4.79353	−0.0683884	−0.0341942	+	0.999415i	$0.510886\pi$
$18$	−44.1307	−0.577872
$19$	11.2232	0.135515	0.0677573	−	0.997702i	$-0.478416\pi$
$19$	11.2232	0.135515	0.0677573	+	0.997702i	$0.478416\pi$
$20$	80.2170	0.896854
$21$	−0.499508	−0.00519055
$22$	0	0
$23$	107.716	0.976537	0.488268	−	0.872694i	$-0.337629\pi$
$23$	107.716	0.976537	0.488268	+	0.872694i	$0.337629\pi$
$24$	118.320	1.00633
$25$	25.0000	0.200000
$26$	135.751	1.02396
$27$	−27.0000	−0.192450
$28$	2.67127	0.0180294
$29$	−123.007	−0.787650	−0.393825	−	0.919185i	$-0.628848\pi$
$29$	−123.007	−0.787650	−0.393825	+	0.919185i	$0.628848\pi$
$30$	73.5511	0.447618
$31$	−75.8131	−0.439240	−0.219620	−	0.975585i	$-0.570482\pi$
$31$	−75.8131	−0.439240	−0.219620	+	0.975585i	$0.570482\pi$
$32$	−3.41483	−0.0188645
$33$	0	0
$34$	23.5047	0.118559
$35$	0.832513	0.00402058
$36$	144.391	0.668475
$37$	351.397	1.56133	0.780667	−	0.624947i	$-0.214880\pi$
$37$	351.397	1.56133	0.780667	+	0.624947i	$0.214880\pi$
$38$	−55.0319	−0.234930
$39$	83.0553	0.341013
$40$	−197.201	−0.779504
$41$	−355.049	−1.35242	−0.676211	−	0.736708i	$-0.736379\pi$
$41$	−355.049	−1.35242	−0.676211	+	0.736708i	$0.736379\pi$
$42$	2.44929	0.00899842
$43$	313.261	1.11097	0.555486	−	0.831526i	$-0.312532\pi$
$43$	313.261	1.11097	0.555486	+	0.831526i	$0.312532\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	−528.176	−1.69294
$47$	160.565	0.498315	0.249158	−	0.968463i	$-0.419846\pi$
$47$	160.565	0.498315	0.249158	+	0.968463i	$0.419846\pi$
$48$	−195.131	−0.586765
$49$	−342.972	−0.999919
$50$	−122.585	−0.346723
$51$	14.3806	0.0394841
$52$	−444.164	−1.18451
$53$	335.490	0.869491	0.434746	−	0.900553i	$-0.356838\pi$
$53$	335.490	0.869491	0.434746	+	0.900553i	$0.356838\pi$
$54$	132.392	0.333635
$55$	0	0
$56$	−6.56688	−0.0156703
$57$	−33.6696	−0.0782394
$58$	603.154	1.36548
$59$	25.2343	0.0556818	0.0278409	−	0.999612i	$-0.491137\pi$
$59$	25.2343	0.0556818	0.0278409	+	0.999612i	$0.491137\pi$
$60$	−240.651	−0.517799
$61$	−461.486	−0.968642	−0.484321	−	0.874890i	$-0.660933\pi$
$61$	−461.486	−0.968642	−0.484321	+	0.874890i	$0.660933\pi$
$62$	371.743	0.761474
$63$	1.49852	0.00299677
$64$	−503.605	−0.983604
$65$	−138.426	−0.264147
$66$	0	0
$67$	−627.489	−1.14418	−0.572089	−	0.820191i	$-0.693867\pi$
$67$	−627.489	−1.14418	−0.572089	+	0.820191i	$0.693867\pi$
$68$	−76.9046	−0.137148
$69$	−323.148	−0.563804
$70$	−4.08215	−0.00697015
$71$	119.453	0.199668	0.0998342	−	0.995004i	$-0.468169\pi$
$71$	119.453	0.199668	0.0998342	+	0.995004i	$0.468169\pi$
$72$	−354.961	−0.581008
$73$	−631.455	−1.01241	−0.506207	−	0.862412i	$-0.668953\pi$
$73$	−631.455	−1.01241	−0.506207	+	0.862412i	$0.668953\pi$
$74$	−1723.04	−2.70675
$75$	−75.0000	−0.115470
$76$	180.058	0.271764
$77$	0	0
$78$	−407.254	−0.591185
$79$	−949.514	−1.35226	−0.676131	−	0.736781i	$-0.736345\pi$
$79$	−949.514	−1.35226	−0.676131	+	0.736781i	$0.736345\pi$
$80$	325.218	0.454507
$81$	81.0000	0.111111
$82$	1740.95	2.34458
$83$	−43.2803	−0.0572364	−0.0286182	−	0.999590i	$-0.509111\pi$
$83$	−43.2803	−0.0572364	−0.0286182	+	0.999590i	$0.509111\pi$
$84$	−8.01381	−0.0104093
$85$	−23.9677	−0.0305842
$86$	−1536.05	−1.92600
$87$	369.021	0.454750
$88$	0	0
$89$	380.904	0.453660	0.226830	−	0.973934i	$-0.427164\pi$
$89$	380.904	0.453660	0.226830	+	0.973934i	$0.427164\pi$
$90$	−220.653	−0.258432
$91$	−4.60964	−0.00531013
$92$	1728.13	1.95837
$93$	227.439	0.253595
$94$	−787.316	−0.863887
$95$	56.1160	0.0606040
$96$	10.2445	0.0108914
$97$	1698.20	1.77759	0.888796	−	0.458303i	$-0.151543\pi$
$97$	1698.20	1.77759	0.888796	+	0.458303i	$0.151543\pi$
$98$	1681.73	1.73348
$99$	0	0
$100$	401.085	0.401085
$101$	584.343	0.575686	0.287843	−	0.957678i	$-0.407062\pi$
$101$	584.343	0.575686	0.287843	+	0.957678i	$0.407062\pi$
$102$	−70.5140	−0.0684502
$103$	−2078.91	−1.98875	−0.994373	−	0.105938i	$-0.966215\pi$
$103$	−2078.91	−1.98875	−0.994373	+	0.105938i	$0.966215\pi$
$104$	1091.90	1.02952
$105$	−2.49754	−0.00232128
$106$	−1645.04	−1.50736
$107$	−466.970	−0.421904	−0.210952	−	0.977496i	$-0.567656\pi$
$107$	−466.970	−0.421904	−0.210952	+	0.977496i	$0.567656\pi$
$108$	−433.172	−0.385944
$109$	1472.70	1.29412	0.647059	−	0.762440i	$-0.275999\pi$
$109$	1472.70	1.29412	0.647059	+	0.762440i	$0.275999\pi$
$110$	0	0
$111$	−1054.19	−0.901436
$112$	10.8299	0.00913691
$113$	990.341	0.824455	0.412227	−	0.911081i	$-0.364751\pi$
$113$	990.341	0.824455	0.412227	+	0.911081i	$0.364751\pi$
$114$	165.096	0.135637
$115$	538.580	0.436720
$116$	−1973.45	−1.57957
$117$	−249.166	−0.196884
$118$	−123.734	−0.0965309
$119$	−0.798136	−0.000614832 0
$120$	591.602	0.450047
$121$	0	0
$122$	2262.85	1.67925
$123$	1065.15	0.780821
$124$	−1216.30	−0.880864
$125$	125.000	0.0894427
$126$	−7.34787	−0.00519524
$127$	−1128.50	−0.788489	−0.394244	−	0.919006i	$-0.628994\pi$
$127$	−1128.50	−0.788489	−0.394244	+	0.919006i	$0.628994\pi$
$128$	2496.70	1.72406
$129$	−939.782	−0.641420
$130$	678.757	0.457930
$131$	265.042	0.176769	0.0883847	−	0.996086i	$-0.471830\pi$
$131$	265.042	0.176769	0.0883847	+	0.996086i	$0.471830\pi$
$132$	0	0
$133$	1.86869	0.00121832
$134$	3076.83	1.98357
$135$	−135.000	−0.0860663
$136$	189.058	0.119203
$137$	2408.25	1.50183	0.750913	−	0.660401i	$-0.229614\pi$
$137$	2408.25	1.50183	0.750913	+	0.660401i	$0.229614\pi$
$138$	1584.53	0.977419
$139$	−2828.87	−1.72620	−0.863101	−	0.505032i	$-0.831481\pi$
$139$	−2828.87	−1.72620	−0.863101	+	0.505032i	$0.831481\pi$
$140$	13.3564	0.00806298
$141$	−481.695	−0.287702
$142$	−585.727	−0.346149
$143$	0	0
$144$	585.393	0.338769
$145$	−615.035	−0.352248
$146$	3096.28	1.75514
$147$	1028.92	0.577304
$148$	5637.61	3.13114
$149$	3185.55	1.75148	0.875741	−	0.482782i	$-0.160374\pi$
$149$	3185.55	1.75148	0.875741	+	0.482782i	$0.160374\pi$
$150$	367.756	0.200181
$151$	553.261	0.298170	0.149085	−	0.988824i	$-0.452367\pi$
$151$	553.261	0.298170	0.149085	+	0.988824i	$0.452367\pi$
$152$	−442.644	−0.236205
$153$	−43.1418	−0.0227961
$154$	0	0
$155$	−379.066	−0.196434
$156$	1332.49	0.683876
$157$	−1173.99	−0.596783	−0.298392	−	0.954444i	$-0.596450\pi$
$157$	−1173.99	−0.596783	−0.298392	+	0.954444i	$0.596450\pi$
$158$	4655.86	2.34430
$159$	−1006.47	−0.502001
$160$	−17.0742	−0.00843644
$161$	17.9350	0.00877936
$162$	−397.176	−0.192624
$163$	−2561.03	−1.23065	−0.615324	−	0.788275i	$-0.710975\pi$
$163$	−2561.03	−1.23065	−0.615324	+	0.788275i	$0.710975\pi$
$164$	−5696.19	−2.71218
$165$	0	0
$166$	212.221	0.0992260
$167$	2593.23	1.20162	0.600809	−	0.799393i	$-0.294845\pi$
$167$	2593.23	1.20162	0.600809	+	0.799393i	$0.294845\pi$
$168$	19.7006	0.00904725
$169$	−1430.53	−0.651131
$170$	117.523	0.0530213
$171$	101.009	0.0451715
$172$	5025.77	2.22797
$173$	−1035.91	−0.455252	−0.227626	−	0.973749i	$-0.573096\pi$
$173$	−1035.91	−0.455252	−0.227626	+	0.973749i	$0.573096\pi$
$174$	−1809.46	−0.788362
$175$	4.16257	0.00179806
$176$	0	0
$177$	−75.7029	−0.0321479
$178$	−1867.73	−0.786472
$179$	1947.18	0.813067	0.406533	−	0.913636i	$-0.366737\pi$
$179$	1947.18	0.813067	0.406533	+	0.913636i	$0.366737\pi$
$180$	721.953	0.298951
$181$	2301.83	0.945269	0.472635	−	0.881258i	$-0.343303\pi$
$181$	2301.83	0.945269	0.472635	+	0.881258i	$0.343303\pi$
$182$	22.6030	0.00920573
$183$	1384.46	0.559246
$184$	−4248.33	−1.70213
$185$	1756.99	0.698250
$186$	−1115.23	−0.439637
$187$	0	0
$188$	2576.01	0.999334
$189$	−4.49557	−0.00173018
$190$	−275.159	−0.105064
$191$	1168.89	0.442815	0.221407	−	0.975181i	$-0.428935\pi$
$191$	1168.89	0.442815	0.221407	+	0.975181i	$0.428935\pi$
$192$	1510.82	0.567884
$193$	1588.69	0.592519	0.296259	−	0.955107i	$-0.404261\pi$
$193$	1588.69	0.592519	0.296259	+	0.955107i	$0.404261\pi$
$194$	−8326.98	−3.08166
$195$	415.277	0.152506
$196$	−5502.44	−2.00526
$197$	−4979.50	−1.80089	−0.900443	−	0.434973i	$-0.856758\pi$
$197$	−4979.50	−1.80089	−0.900443	+	0.434973i	$0.856758\pi$
$198$	0	0
$199$	5497.61	1.95837	0.979185	−	0.202972i	$-0.0650600\pi$
$199$	5497.61	1.95837	0.979185	+	0.202972i	$0.0650600\pi$
$200$	−986.003	−0.348605
$201$	1882.47	0.660592
$202$	−2865.27	−0.998018
$203$	−20.4810	−0.00708121
$204$	230.714	0.0791824
$205$	−1775.24	−0.604822
$206$	10193.7	3.44772
$207$	969.444	0.325512
$208$	−1800.74	−0.600284
$209$	0	0
$210$	12.2465	0.00402422
$211$	30.8223	0.0100564	0.00502818	−	0.999987i	$-0.498399\pi$
$211$	30.8223	0.0100564	0.00502818	+	0.999987i	$0.498399\pi$
$212$	5382.40	1.74370
$213$	−358.359	−0.115279
$214$	2289.75	0.731419
$215$	1566.30	0.496842
$216$	1064.88	0.335445
$217$	−12.6231	−0.00394890
$218$	−7221.24	−2.24351
$219$	1894.36	0.584517
$220$	0	0
$221$	132.710	0.0403937
$222$	5169.13	1.56275
$223$	3745.21	1.12465	0.562327	−	0.826915i	$-0.309906\pi$
$223$	3745.21	1.12465	0.562327	+	0.826915i	$0.309906\pi$
$224$	−0.568579	−0.000169597 0
$225$	225.000	0.0666667
$226$	−4856.04	−1.42929
$227$	1015.58	0.296944	0.148472	−	0.988917i	$-0.452565\pi$
$227$	1015.58	0.296944	0.148472	+	0.988917i	$0.452565\pi$
$228$	−540.175	−0.156903
$229$	−2826.34	−0.815590	−0.407795	−	0.913074i	$-0.633702\pi$
$229$	−2826.34	−0.815590	−0.407795	+	0.913074i	$0.633702\pi$
$230$	−2640.88	−0.757106
$231$	0	0
$232$	4851.41	1.37289
$233$	−3873.04	−1.08898	−0.544488	−	0.838768i	$-0.683276\pi$
$233$	−3873.04	−1.08898	−0.544488	+	0.838768i	$0.683276\pi$
$234$	1221.76	0.341321
$235$	802.825	0.222853
$236$	404.844	0.111666
$237$	2848.54	0.780729
$238$	3.91359	0.00106588
$239$	761.703	0.206153	0.103076	−	0.994673i	$-0.467131\pi$
$239$	761.703	0.206153	0.103076	+	0.994673i	$0.467131\pi$
$240$	−975.655	−0.262410
$241$	4258.07	1.13812	0.569058	−	0.822297i	$-0.307308\pi$
$241$	4258.07	1.13812	0.569058	+	0.822297i	$0.307308\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	−7403.80	−1.94254
$245$	−1714.86	−0.447177
$246$	−5222.85	−1.35364
$247$	−310.715	−0.0800419
$248$	2990.08	0.765606
$249$	129.841	0.0330455
$250$	−612.926	−0.155059
$251$	−3721.50	−0.935851	−0.467926	−	0.883768i	$-0.654999\pi$
$251$	−3721.50	−0.935851	−0.467926	+	0.883768i	$0.654999\pi$
$252$	24.0414	0.00600979
$253$	0	0
$254$	5533.49	1.36694
$255$	71.9030	0.0176578
$256$	−8213.50	−2.00525
$257$	−1014.08	−0.246135	−0.123068	−	0.992398i	$-0.539273\pi$
$257$	−1014.08	−0.246135	−0.123068	+	0.992398i	$0.539273\pi$
$258$	4608.14	1.11198
$259$	58.5086	0.0140369
$260$	−2220.82	−0.529728
$261$	−1107.06	−0.262550
$262$	−1299.61	−0.306450
$263$	4953.06	1.16129	0.580644	−	0.814158i	$-0.302801\pi$
$263$	4953.06	1.16129	0.580644	+	0.814158i	$0.302801\pi$
$264$	0	0
$265$	1677.45	0.388848
$266$	−9.16296	−0.00211209
$267$	−1142.71	−0.261920
$268$	−10067.1	−2.29456
$269$	−7881.62	−1.78643	−0.893217	−	0.449625i	$-0.851558\pi$
$269$	−7881.62	−1.78643	−0.893217	+	0.449625i	$0.851558\pi$
$270$	661.960	0.149206
$271$	−4001.28	−0.896901	−0.448451	−	0.893808i	$-0.648024\pi$
$271$	−4001.28	−0.896901	−0.448451	+	0.893808i	$0.648024\pi$
$272$	−311.789	−0.0695037
$273$	13.8289	0.00306581
$274$	−11808.6	−2.60359
$275$	0	0
$276$	−5184.40	−1.13067
$277$	−3459.06	−0.750306	−0.375153	−	0.926963i	$-0.622410\pi$
$277$	−3459.06	−0.750306	−0.375153	+	0.926963i	$0.622410\pi$
$278$	13871.1	2.99257
$279$	−682.318	−0.146413
$280$	−32.8344	−0.00700797
$281$	6651.23	1.41202	0.706012	−	0.708200i	$-0.250492\pi$
$281$	6651.23	1.41202	0.706012	+	0.708200i	$0.250492\pi$
$282$	2361.95	0.498766
$283$	1620.51	0.340386	0.170193	−	0.985411i	$-0.445561\pi$
$283$	1620.51	0.340386	0.170193	+	0.985411i	$0.445561\pi$
$284$	1916.43	0.400420
$285$	−168.348	−0.0349897
$286$	0	0
$287$	−59.1166	−0.0121587
$288$	−30.7335	−0.00628815
$289$	−4890.02	−0.995323
$290$	3015.77	0.610662
$291$	−5094.61	−1.02629
$292$	−10130.7	−2.03032
$293$	−1802.82	−0.359460	−0.179730	−	0.983716i	$-0.557522\pi$
$293$	−1802.82	−0.359460	−0.179730	+	0.983716i	$0.557522\pi$
$294$	−5045.20	−1.00082
$295$	126.172	0.0249017
$296$	−13859.1	−2.72144
$297$	0	0
$298$	−15620.1	−3.03640
$299$	−2982.13	−0.576793
$300$	−1203.26	−0.231567
$301$	52.1588	0.00998797
$302$	−2712.86	−0.516913
$303$	−1753.03	−0.332372
$304$	729.998	0.137724
$305$	−2307.43	−0.433190
$306$	211.542	0.0395198
$307$	1708.47	0.317614	0.158807	−	0.987310i	$-0.449235\pi$
$307$	1708.47	0.317614	0.158807	+	0.987310i	$0.449235\pi$
$308$	0	0
$309$	6236.72	1.14820
$310$	1858.71	0.340541
$311$	−6551.77	−1.19459	−0.597294	−	0.802022i	$-0.703757\pi$
$311$	−6551.77	−1.19459	−0.597294	+	0.802022i	$0.703757\pi$
$312$	−3275.71	−0.594393
$313$	389.791	0.0703908	0.0351954	−	0.999380i	$-0.488795\pi$
$313$	389.791	0.0703908	0.0351954	+	0.999380i	$0.488795\pi$
$314$	5756.58	1.03459
$315$	7.49262	0.00134019
$316$	−15233.4	−2.71186
$317$	−5891.92	−1.04392	−0.521961	−	0.852970i	$-0.674799\pi$
$317$	−5891.92	−1.04392	−0.521961	+	0.852970i	$0.674799\pi$
$318$	4935.13	0.870277
$319$	0	0
$320$	−2518.03	−0.439881
$321$	1400.91	0.243586
$322$	−87.9426	−0.0152200
$323$	−53.7988	−0.00926763
$324$	1299.52	0.222825
$325$	−692.128	−0.118130
$326$	12557.8	2.13347
$327$	−4418.10	−0.747160
$328$	14003.2	2.35730
$329$	26.7345	0.00448000
$330$	0	0
$331$	−1523.64	−0.253012	−0.126506	−	0.991966i	$-0.540376\pi$
$331$	−1523.64	−0.253012	−0.126506	+	0.991966i	$0.540376\pi$
$332$	−694.363	−0.114783
$333$	3162.57	0.520445
$334$	−12715.7	−2.08314
$335$	−3137.44	−0.511692
$336$	−32.4898	−0.00527520
$337$	4355.84	0.704087	0.352044	−	0.935984i	$-0.385487\pi$
$337$	4355.84	0.704087	0.352044	+	0.935984i	$0.385487\pi$
$338$	7014.49	1.12881
$339$	−2971.02	−0.475999
$340$	−384.523	−0.0613344
$341$	0	0
$342$	−495.287	−0.0783101
$343$	−114.216	−0.0179799
$344$	−12355.0	−1.93645
$345$	−1615.74	−0.252141
$346$	5079.48	0.789233
$347$	4969.24	0.768770	0.384385	−	0.923173i	$-0.374414\pi$
$347$	4969.24	0.768770	0.384385	+	0.923173i	$0.374414\pi$
$348$	5920.36	0.911967
$349$	−10747.3	−1.64840	−0.824200	−	0.566299i	$-0.808375\pi$
$349$	−10747.3	−1.64840	−0.824200	+	0.566299i	$0.808375\pi$
$350$	−20.4108	−0.00311715
$351$	747.498	0.113671
$352$	0	0
$353$	−9901.44	−1.49292	−0.746460	−	0.665431i	$-0.768248\pi$
$353$	−9901.44	−1.49292	−0.746460	+	0.665431i	$0.768248\pi$
$354$	371.202	0.0557321
$355$	597.265	0.0892944
$356$	6110.99	0.909781
$357$	2.39441	0.000354973 0
$358$	−9547.81	−1.40955
$359$	−5886.54	−0.865404	−0.432702	−	0.901537i	$-0.642440\pi$
$359$	−5886.54	−0.865404	−0.432702	+	0.901537i	$0.642440\pi$
$360$	−1774.81	−0.259835
$361$	−6733.04	−0.981636
$362$	−11286.8	−1.63873
$363$	0	0
$364$	−73.9544	−0.0106491
$365$	−3157.27	−0.452765
$366$	−6788.56	−0.969518
$367$	−5945.05	−0.845584	−0.422792	−	0.906227i	$-0.638950\pi$
$367$	−5945.05	−0.845584	−0.422792	+	0.906227i	$0.638950\pi$
$368$	7006.25	0.992462
$369$	−3195.44	−0.450807
$370$	−8615.22	−1.21050
$371$	55.8599	0.00781699
$372$	3648.90	0.508567
$373$	1021.68	0.141825	0.0709123	−	0.997483i	$-0.477409\pi$
$373$	1021.68	0.141825	0.0709123	+	0.997483i	$0.477409\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−6332.70	−0.868575
$377$	3405.46	0.465226
$378$	22.0436	0.00299947
$379$	−12345.9	−1.67327	−0.836633	−	0.547764i	$-0.815479\pi$
$379$	−12345.9	−1.67327	−0.836633	+	0.547764i	$0.815479\pi$
$380$	900.291	0.121537
$381$	3385.50	0.455234
$382$	−5731.53	−0.767671
$383$	10077.6	1.34449	0.672244	−	0.740330i	$-0.265331\pi$
$383$	10077.6	1.34449	0.672244	+	0.740330i	$0.265331\pi$
$384$	−7490.10	−0.995384
$385$	0	0
$386$	−7789.98	−1.02720
$387$	2819.35	0.370324
$388$	27245.0	3.56483
$389$	5494.70	0.716175	0.358088	−	0.933688i	$-0.383429\pi$
$389$	5494.70	0.716175	0.358088	+	0.933688i	$0.383429\pi$
$390$	−2036.27	−0.264386
$391$	−516.340	−0.0667838
$392$	13526.9	1.74288
$393$	−795.125	−0.102058
$394$	24416.5	3.12205
$395$	−4747.57	−0.604750
$396$	0	0
$397$	−9079.56	−1.14783	−0.573917	−	0.818914i	$-0.694577\pi$
$397$	−9079.56	−1.14783	−0.573917	+	0.818914i	$0.694577\pi$
$398$	−26957.0	−3.39506
$399$	−5.60607	−0.000703395 0
$400$	1626.09	0.203262
$401$	−8661.16	−1.07860	−0.539299	−	0.842114i	$-0.681311\pi$
$401$	−8661.16	−1.07860	−0.539299	+	0.842114i	$0.681311\pi$
$402$	−9230.50	−1.14521
$403$	2098.90	0.259438
$404$	9374.85	1.15450
$405$	405.000	0.0496904
$406$	100.427	0.0122761
$407$	0	0
$408$	−567.173	−0.0688216
$409$	−5425.07	−0.655874	−0.327937	−	0.944700i	$-0.606353\pi$
$409$	−5425.07	−0.655874	−0.327937	+	0.944700i	$0.606353\pi$
$410$	8704.75	1.04853
$411$	−7224.74	−0.867080
$412$	−33352.8	−3.98828
$413$	4.20158	0.000500596 0
$414$	−4753.58	−0.564313
$415$	−216.401	−0.0255969
$416$	94.5400	0.0111423
$417$	8486.62	0.996623
$418$	0	0
$419$	13057.1	1.52239	0.761195	−	0.648523i	$-0.224613\pi$
$419$	13057.1	1.52239	0.761195	+	0.648523i	$0.224613\pi$
$420$	−40.0691	−0.00465517
$421$	59.4078	0.00687734	0.00343867	−	0.999994i	$-0.498905\pi$
$421$	59.4078	0.00687734	0.00343867	+	0.999994i	$0.498905\pi$
$422$	−151.134	−0.0174339
$423$	1445.09	0.166105
$424$	−13231.7	−1.51554
$425$	−119.838	−0.0136777
$426$	1757.18	0.199849
$427$	−76.8386	−0.00870838
$428$	−7491.79	−0.846097
$429$	0	0
$430$	−7680.23	−0.861334
$431$	−5456.29	−0.609792	−0.304896	−	0.952386i	$-0.598622\pi$
$431$	−5456.29	−0.609792	−0.304896	+	0.952386i	$0.598622\pi$
$432$	−1756.18	−0.195588
$433$	−6513.69	−0.722928	−0.361464	−	0.932386i	$-0.617723\pi$
$433$	−6513.69	−0.722928	−0.361464	+	0.932386i	$0.617723\pi$
$434$	61.8962	0.00684588
$435$	1845.11	0.203370
$436$	23627.1	2.59526
$437$	1208.92	0.132335
$438$	−9288.84	−1.01333
$439$	−12553.6	−1.36480	−0.682402	−	0.730977i	$-0.739065\pi$
$439$	−12553.6	−1.36480	−0.682402	+	0.730977i	$0.739065\pi$
$440$	0	0
$441$	−3086.75	−0.333306
$442$	−650.729	−0.0700272
$443$	7186.84	0.770784	0.385392	−	0.922753i	$-0.374066\pi$
$443$	7186.84	0.770784	0.385392	+	0.922753i	$0.374066\pi$
$444$	−16912.8	−1.80776
$445$	1904.52	0.202883
$446$	−18364.3	−1.94972
$447$	−9556.66	−1.01122
$448$	−83.8516	−0.00884289
$449$	8712.97	0.915792	0.457896	−	0.889006i	$-0.348603\pi$
$449$	8712.97	0.915792	0.457896	+	0.889006i	$0.348603\pi$
$450$	−1103.27	−0.115574
$451$	0	0
$452$	15888.4	1.65338
$453$	−1659.78	−0.172149
$454$	−4979.79	−0.514787
$455$	−23.0482	−0.00237476
$456$	1327.93	0.136373
$457$	16046.2	1.64247	0.821234	−	0.570592i	$-0.193286\pi$
$457$	16046.2	1.64247	0.821234	+	0.570592i	$0.193286\pi$
$458$	13858.7	1.41392
$459$	129.425	0.0131614
$460$	8640.66	0.875811
$461$	−19543.2	−1.97444	−0.987219	−	0.159371i	$-0.949054\pi$
$461$	−19543.2	−1.97444	−0.987219	+	0.159371i	$0.949054\pi$
$462$	0	0
$463$	−4735.80	−0.475359	−0.237679	−	0.971344i	$-0.576387\pi$
$463$	−4735.80	−0.475359	−0.237679	+	0.971344i	$0.576387\pi$
$464$	−8000.83	−0.800494
$465$	1137.20	0.113411
$466$	18991.1	1.88787
$467$	−13632.6	−1.35084	−0.675419	−	0.737434i	$-0.736037\pi$
$467$	−13632.6	−1.35084	−0.675419	+	0.737434i	$0.736037\pi$
$468$	−3997.47	−0.394836
$469$	−104.479	−0.0102865
$470$	−3936.58	−0.386342
$471$	3521.98	0.344553
$472$	−995.244	−0.0970547
$473$	0	0
$474$	−13967.6	−1.35348
$475$	280.580	0.0271029
$476$	−12.8048	−0.00123300
$477$	3019.41	0.289830
$478$	−3734.94	−0.357390
$479$	−1396.23	−0.133184	−0.0665921	−	0.997780i	$-0.521213\pi$
$479$	−1396.23	−0.133184	−0.0665921	+	0.997780i	$0.521213\pi$
$480$	51.2225	0.00487078
$481$	−9728.47	−0.922204
$482$	−20879.0	−1.97306
$483$	−53.8050	−0.00506876
$484$	0	0
$485$	8491.02	0.794963
$486$	1191.53	0.111212
$487$	−9150.78	−0.851460	−0.425730	−	0.904850i	$-0.639983\pi$
$487$	−9150.78	−0.851460	−0.425730	+	0.904850i	$0.639983\pi$
$488$	18201.0	1.68837
$489$	7683.10	0.710515
$490$	8408.66	0.775234
$491$	7447.84	0.684554	0.342277	−	0.939599i	$-0.388802\pi$
$491$	7447.84	0.684554	0.342277	+	0.939599i	$0.388802\pi$
$492$	17088.6	1.56588
$493$	589.639	0.0538661
$494$	1523.56	0.138762
$495$	0	0
$496$	−4931.17	−0.446403
$497$	19.8892	0.00179508
$498$	−636.662	−0.0572882
$499$	7681.18	0.689092	0.344546	−	0.938770i	$-0.388033\pi$
$499$	7681.18	0.689092	0.344546	+	0.938770i	$0.388033\pi$
$500$	2005.43	0.179371
$501$	−7779.69	−0.693754
$502$	18248.0	1.62241
$503$	4531.61	0.401699	0.200849	−	0.979622i	$-0.435630\pi$
$503$	4531.61	0.401699	0.200849	+	0.979622i	$0.435630\pi$
$504$	−59.1019	−0.00522343
$505$	2921.71	0.257455
$506$	0	0
$507$	4291.60	0.375931
$508$	−18105.0	−1.58126
$509$	−7728.17	−0.672977	−0.336488	−	0.941688i	$-0.609239\pi$
$509$	−7728.17	−0.672977	−0.336488	+	0.941688i	$0.609239\pi$
$510$	−352.570	−0.0306119
$511$	−105.139	−0.00910190
$512$	20300.5	1.75228
$513$	−303.026	−0.0260798
$514$	4972.47	0.426704
$515$	−10394.5	−0.889394
$516$	−15077.3	−1.28632
$517$	0	0
$518$	−286.891	−0.0243345
$519$	3107.73	0.262840
$520$	5459.52	0.460415
$521$	−10150.6	−0.853563	−0.426782	−	0.904355i	$-0.640353\pi$
$521$	−10150.6	−0.853563	−0.426782	+	0.904355i	$0.640353\pi$
$522$	5428.39	0.455161
$523$	21882.1	1.82951	0.914757	−	0.404004i	$-0.132382\pi$
$523$	21882.1	1.82951	0.914757	+	0.404004i	$0.132382\pi$
$524$	4252.17	0.354498
$525$	−12.4877	−0.00103811
$526$	−24286.9	−2.01323
$527$	363.413	0.0300389
$528$	0	0
$529$	−564.259	−0.0463762
$530$	−8225.21	−0.674114
$531$	227.109	0.0185606
$532$	29.9802	0.00244324
$533$	9829.57	0.798810
$534$	5603.18	0.454070
$535$	−2334.85	−0.188681
$536$	24748.2	1.99433
$537$	−5841.54	−0.469424
$538$	38646.8	3.09699
$539$	0	0
$540$	−2165.86	−0.172600
$541$	22774.3	1.80988	0.904940	−	0.425540i	$-0.139916\pi$
$541$	22774.3	1.80988	0.904940	+	0.425540i	$0.139916\pi$
$542$	19619.9	1.55488
$543$	−6905.49	−0.545752
$544$	16.3691	0.00129011
$545$	7363.49	0.578747
$546$	−67.8089	−0.00531493
$547$	2852.46	0.222966	0.111483	−	0.993766i	$-0.464440\pi$
$547$	2852.46	0.222966	0.111483	+	0.993766i	$0.464440\pi$
$548$	38636.5	3.01180
$549$	−4153.37	−0.322881
$550$	0	0
$551$	−1380.53	−0.106738
$552$	12745.0	0.982723
$553$	−158.097	−0.0121572
$554$	16961.2	1.30074
$555$	−5270.96	−0.403135
$556$	−45384.8	−3.46177
$557$	−22651.6	−1.72312	−0.861561	−	0.507655i	$-0.830513\pi$
$557$	−22651.6	−1.72312	−0.861561	+	0.507655i	$0.830513\pi$
$558$	3345.69	0.253825
$559$	−8672.66	−0.656198
$560$	54.1497	0.00408615
$561$	0	0
$562$	−32613.7	−2.44791
$563$	19911.2	1.49051	0.745255	−	0.666779i	$-0.232328\pi$
$563$	19911.2	1.49051	0.745255	+	0.666779i	$0.232328\pi$
$564$	−7728.03	−0.576966
$565$	4951.70	0.368707
$566$	−7946.02	−0.590099
$567$	13.4867	0.000998922 0
$568$	−4711.24	−0.348027
$569$	12466.5	0.918493	0.459246	−	0.888309i	$-0.348119\pi$
$569$	12466.5	0.918493	0.459246	+	0.888309i	$0.348119\pi$
$570$	825.478	0.0606587
$571$	6373.47	0.467113	0.233557	−	0.972343i	$-0.424964\pi$
$571$	6373.47	0.467113	0.233557	+	0.972343i	$0.424964\pi$
$572$	0	0
$573$	−3506.66	−0.255659
$574$	289.873	0.0210785
$575$	2692.90	0.195307
$576$	−4532.45	−0.327868
$577$	−24898.4	−1.79642	−0.898209	−	0.439569i	$-0.855131\pi$
$577$	−24898.4	−1.79642	−0.898209	+	0.439569i	$0.855131\pi$
$578$	23977.8	1.72551
$579$	−4766.06	−0.342091
$580$	−9867.26	−0.706407
$581$	−7.20628	−0.000514573 0
$582$	24981.0	1.77920
$583$	0	0
$584$	24904.6	1.76466
$585$	−1245.83	−0.0880491
$586$	8839.95	0.623165
$587$	−18909.9	−1.32964	−0.664818	−	0.747006i	$-0.731491\pi$
$587$	−18909.9	−1.32964	−0.664818	+	0.747006i	$0.731491\pi$
$588$	16507.3	1.15774
$589$	−850.866	−0.0595234
$590$	−618.670	−0.0431699
$591$	14938.5	1.03974
$592$	22856.2	1.58680
$593$	−1200.67	−0.0831460	−0.0415730	−	0.999135i	$-0.513237\pi$
$593$	−1200.67	−0.0831460	−0.0415730	+	0.999135i	$0.513237\pi$
$594$	0	0
$595$	−3.99068	−0.000274961 0
$596$	51107.1	3.51247
$597$	−16492.8	−1.13066
$598$	14622.6	0.999937
$599$	−8975.45	−0.612232	−0.306116	−	0.951994i	$-0.599029\pi$
$599$	−8975.45	−0.612232	−0.306116	+	0.951994i	$0.599029\pi$
$600$	2958.01	0.201267
$601$	−16122.6	−1.09427	−0.547133	−	0.837046i	$-0.684281\pi$
$601$	−16122.6	−1.09427	−0.547133	+	0.837046i	$0.684281\pi$
$602$	−255.756	−0.0173153
$603$	−5647.40	−0.381393
$604$	8876.19	0.597959
$605$	0	0
$606$	8595.81	0.576206
$607$	12952.9	0.866134	0.433067	−	0.901362i	$-0.357431\pi$
$607$	12952.9	0.866134	0.433067	+	0.901362i	$0.357431\pi$
$608$	−38.3253	−0.00255641
$609$	61.4430	0.00408834
$610$	11314.3	0.750985
$611$	−4445.26	−0.294331
$612$	−692.142	−0.0457160
$613$	−21971.1	−1.44764	−0.723820	−	0.689989i	$-0.757615\pi$
$613$	−21971.1	−1.44764	−0.723820	+	0.689989i	$0.757615\pi$
$614$	−8377.32	−0.550621
$615$	5325.73	0.349194
$616$	0	0
$617$	10162.0	0.663055	0.331527	−	0.943446i	$-0.392436\pi$
$617$	10162.0	0.663055	0.331527	+	0.943446i	$0.392436\pi$
$618$	−30581.2	−1.99054
$619$	200.915	0.0130459	0.00652297	−	0.999979i	$-0.497924\pi$
$619$	200.915	0.0130459	0.00652297	+	0.999979i	$0.497924\pi$
$620$	−6081.51	−0.393934
$621$	−2908.33	−0.187935
$622$	32126.0	2.07096
$623$	63.4215	0.00407853
$624$	5402.23	0.346574
$625$	625.000	0.0400000
$626$	−1911.31	−0.122031
$627$	0	0
$628$	−18834.9	−1.19680
$629$	−1684.43	−0.106777
$630$	−36.7394	−0.00232338
$631$	−16137.0	−1.01807	−0.509037	−	0.860745i	$-0.669998\pi$
$631$	−16137.0	−1.01807	−0.509037	+	0.860745i	$0.669998\pi$
$632$	37449.0	2.35702
$633$	−92.4668	−0.00580604
$634$	28890.5	1.80976
$635$	−5642.49	−0.352623
$636$	−16147.2	−1.00673
$637$	9495.23	0.590604
$638$	0	0
$639$	1075.08	0.0665562
$640$	12483.5	0.771021
$641$	−9016.93	−0.555612	−0.277806	−	0.960637i	$-0.589607\pi$
$641$	−9016.93	−0.555612	−0.277806	+	0.960637i	$0.589607\pi$
$642$	−6869.24	−0.422285
$643$	4974.88	0.305117	0.152558	−	0.988294i	$-0.451249\pi$
$643$	4974.88	0.305117	0.152558	+	0.988294i	$0.451249\pi$
$644$	287.739	0.0176063
$645$	−4698.91	−0.286852
$646$	263.797	0.0160665
$647$	−15701.8	−0.954095	−0.477048	−	0.878877i	$-0.658293\pi$
$647$	−15701.8	−0.954095	−0.477048	+	0.878877i	$0.658293\pi$
$648$	−3194.65	−0.193669
$649$	0	0
$650$	3393.78	0.204793
$651$	37.8693	0.00227990
$652$	−41087.7	−2.46797
$653$	−21330.1	−1.27827	−0.639136	−	0.769093i	$-0.720708\pi$
$653$	−21330.1	−1.27827	−0.639136	+	0.769093i	$0.720708\pi$
$654$	21663.7	1.29529
$655$	1325.21	0.0790537
$656$	−23093.7	−1.37448
$657$	−5683.09	−0.337471
$658$	−131.090	−0.00776661
$659$	18697.3	1.10523	0.552613	−	0.833438i	$-0.313631\pi$
$659$	18697.3	1.10523	0.552613	+	0.833438i	$0.313631\pi$
$660$	0	0
$661$	11179.8	0.657858	0.328929	−	0.944355i	$-0.393312\pi$
$661$	11179.8	0.657858	0.328929	+	0.944355i	$0.393312\pi$
$662$	7471.04	0.438626
$663$	−398.129	−0.0233213
$664$	1706.98	0.0997644
$665$	9.34346	0.000544848 0
$666$	−15507.4	−0.902251
$667$	−13249.8	−0.769169
$668$	41604.3	2.40976
$669$	−11235.6	−0.649320
$670$	15384.2	0.887078
$671$	0	0
$672$	1.70574	9.79169e−5 0
$673$	2312.58	0.132457	0.0662283	−	0.997804i	$-0.478903\pi$
$673$	2312.58	0.132457	0.0662283	+	0.997804i	$0.478903\pi$
$674$	−21358.4	−1.22062
$675$	−675.000	−0.0384900
$676$	−22950.6	−1.30579
$677$	−13255.1	−0.752489	−0.376244	−	0.926520i	$-0.622785\pi$
$677$	−13255.1	−0.752489	−0.376244	+	0.926520i	$0.622785\pi$
$678$	14568.1	0.825200
$679$	282.755	0.0159811
$680$	945.288	0.0533090
$681$	−3046.73	−0.171441
$682$	0	0
$683$	21588.0	1.20943	0.604715	−	0.796442i	$-0.293287\pi$
$683$	21588.0	1.20943	0.604715	+	0.796442i	$0.293287\pi$
$684$	1620.52	0.0905882
$685$	12041.2	0.671637
$686$	560.049	0.0311702
$687$	8479.03	0.470881
$688$	20375.6	1.12909
$689$	−9288.07	−0.513566
$690$	7922.63	0.437115
$691$	−17127.2	−0.942907	−0.471453	−	0.881891i	$-0.656270\pi$
$691$	−17127.2	−0.942907	−0.471453	+	0.881891i	$0.656270\pi$
$692$	−16619.5	−0.912975
$693$	0	0
$694$	−24366.2	−1.33275
$695$	−14144.4	−0.771981
$696$	−14554.2	−0.792639
$697$	1701.94	0.0924900
$698$	52698.6	2.85769
$699$	11619.1	0.628721
$700$	66.7818	0.00360588
$701$	−18025.7	−0.971213	−0.485607	−	0.874177i	$-0.661401\pi$
$701$	−18025.7	−0.971213	−0.485607	+	0.874177i	$0.661401\pi$
$702$	−3665.29	−0.197062
$703$	3943.80	0.211583
$704$	0	0
$705$	−2408.48	−0.128664
$706$	48550.8	2.58815
$707$	97.2946	0.00517559
$708$	−1214.53	−0.0644702
$709$	15228.6	0.806662	0.403331	−	0.915054i	$-0.367852\pi$
$709$	15228.6	0.806662	0.403331	+	0.915054i	$0.367852\pi$
$710$	−2928.63	−0.154802
$711$	−8545.63	−0.450754
$712$	−15022.9	−0.790739
$713$	−8166.29	−0.428934
$714$	−11.7408	−0.000615388 0
$715$	0	0
$716$	31239.4	1.63055
$717$	−2285.11	−0.119022
$718$	28864.1	1.50028
$719$	−7521.45	−0.390129	−0.195064	−	0.980790i	$-0.562492\pi$
$719$	−7521.45	−0.390129	−0.195064	+	0.980790i	$0.562492\pi$
$720$	2926.97	0.151502
$721$	−346.143	−0.0178794
$722$	33014.8	1.70178
$723$	−12774.2	−0.657092
$724$	36929.2	1.89567
$725$	−3075.18	−0.157530
$726$	0	0
$727$	9747.30	0.497259	0.248629	−	0.968599i	$-0.420020\pi$
$727$	9747.30	0.497259	0.248629	+	0.968599i	$0.420020\pi$
$728$	181.805	0.00925568
$729$	729.000	0.0370370
$730$	15481.4	0.784921
$731$	−1501.63	−0.0759776
$732$	22211.4	1.12153
$733$	−13465.3	−0.678517	−0.339258	−	0.940693i	$-0.610176\pi$
$733$	−13465.3	−0.678517	−0.339258	+	0.940693i	$0.610176\pi$
$734$	29151.0	1.46592
$735$	5144.58	0.258178
$736$	−367.832	−0.0184218
$737$	0	0
$738$	15668.5	0.781527
$739$	11883.8	0.591549	0.295774	−	0.955258i	$-0.404422\pi$
$739$	11883.8	0.591549	0.295774	+	0.955258i	$0.404422\pi$
$740$	28188.0	1.40029
$741$	932.146	0.0462122
$742$	−273.904	−0.0135517
$743$	32944.7	1.62668	0.813339	−	0.581790i	$-0.197647\pi$
$743$	32944.7	1.62668	0.813339	+	0.581790i	$0.197647\pi$
$744$	−8970.24	−0.442023
$745$	15927.8	0.783286
$746$	−5009.71	−0.245869
$747$	−389.522	−0.0190788
$748$	0	0
$749$	−77.7518	−0.00379304
$750$	1838.78	0.0895236
$751$	−13359.2	−0.649114	−0.324557	−	0.945866i	$-0.605215\pi$
$751$	−13359.2	−0.649114	−0.324557	+	0.945866i	$0.605215\pi$
$752$	10443.7	0.506442
$753$	11164.5	0.540314
$754$	−16698.4	−0.806524
$755$	2766.31	0.133346
$756$	−72.1243	−0.00346976
$757$	−37918.6	−1.82057	−0.910287	−	0.413977i	$-0.864139\pi$
$757$	−37918.6	−1.82057	−0.910287	+	0.413977i	$0.864139\pi$
$758$	60537.1	2.90080
$759$	0	0
$760$	−2213.22	−0.105634
$761$	−10938.1	−0.521032	−0.260516	−	0.965470i	$-0.583893\pi$
$761$	−10938.1	−0.521032	−0.260516	+	0.965470i	$0.583893\pi$
$762$	−16600.5	−0.789201
$763$	245.208	0.0116345
$764$	18752.9	0.888033
$765$	−215.709	−0.0101947
$766$	−49414.3	−2.33083
$767$	−698.615	−0.0328885
$768$	24640.5	1.15773
$769$	−36398.8	−1.70686	−0.853429	−	0.521209i	$-0.825481\pi$
$769$	−36398.8	−1.70686	−0.853429	+	0.521209i	$0.825481\pi$
$770$	0	0
$771$	3042.25	0.142106
$772$	25487.9	1.18825
$773$	−11179.5	−0.520179	−0.260089	−	0.965585i	$-0.583752\pi$
$773$	−11179.5	−0.520179	−0.260089	+	0.965585i	$0.583752\pi$
$774$	−13824.4	−0.642000
$775$	−1895.33	−0.0878480
$776$	−66977.3	−3.09838
$777$	−175.526	−0.00810418
$778$	−26942.7	−1.24157
$779$	−3984.78	−0.183273
$780$	6662.45	0.305839
$781$	0	0
$782$	2531.83	0.115777
$783$	3321.19	0.151583
$784$	−22308.2	−1.01623
$785$	−5869.97	−0.266890
$786$	3898.82	0.176929
$787$	−30162.0	−1.36615	−0.683075	−	0.730348i	$-0.739358\pi$
$787$	−30162.0	−1.36615	−0.683075	+	0.730348i	$0.739358\pi$
$788$	−79888.2	−3.61155
$789$	−14859.2	−0.670470
$790$	23279.3	1.04840
$791$	164.894	0.00741210
$792$	0	0
$793$	12776.3	0.572130
$794$	44520.8	1.98990
$795$	−5032.34	−0.224502
$796$	88200.4	3.92736
$797$	8471.90	0.376524	0.188262	−	0.982119i	$-0.439715\pi$
$797$	8471.90	0.376524	0.188262	+	0.982119i	$0.439715\pi$
$798$	27.4889	0.00121942
$799$	−769.674	−0.0340790
$800$	−85.3708	−0.00377289
$801$	3428.13	0.151220
$802$	42469.2	1.86988
$803$	0	0
$804$	30201.2	1.32477
$805$	89.6750	0.00392625
$806$	−10291.7	−0.449766
$807$	23644.9	1.03140
$808$	−23046.5	−1.00343
$809$	5284.01	0.229636	0.114818	−	0.993387i	$-0.463371\pi$
$809$	5284.01	0.229636	0.114818	+	0.993387i	$0.463371\pi$
$810$	−1985.88	−0.0861441
$811$	−23277.7	−1.00788	−0.503939	−	0.863739i	$-0.668116\pi$
$811$	−23277.7	−1.00788	−0.503939	+	0.863739i	$0.668116\pi$
$812$	−328.585	−0.0142008
$813$	12003.8	0.517826
$814$	0	0
$815$	−12805.2	−0.550362
$816$	935.367	0.0401280
$817$	3515.79	0.150553
$818$	26601.3	1.13703
$819$	−41.4868	−0.00177004
$820$	−28481.0	−1.21292
$821$	−2460.25	−0.104584	−0.0522919	−	0.998632i	$-0.516653\pi$
$821$	−2460.25	−0.104584	−0.0522919	+	0.998632i	$0.516653\pi$
$822$	35425.8	1.50318
$823$	25658.1	1.08674	0.543368	−	0.839494i	$-0.317149\pi$
$823$	25658.1	1.08674	0.543368	+	0.839494i	$0.317149\pi$
$824$	81992.3	3.46643
$825$	0	0
$826$	−20.6021	−0.000867842 0
$827$	−36299.0	−1.52629	−0.763144	−	0.646229i	$-0.776345\pi$
$827$	−36299.0	−1.52629	−0.763144	+	0.646229i	$0.776345\pi$
$828$	15553.2	0.652791
$829$	22131.5	0.927213	0.463606	−	0.886041i	$-0.346555\pi$
$829$	22131.5	0.927213	0.463606	+	0.886041i	$0.346555\pi$
$830$	1061.10	0.0443752
$831$	10377.2	0.433189
$832$	13942.4	0.580967
$833$	1644.05	0.0683829
$834$	−41613.4	−1.72776
$835$	12966.2	0.537380
$836$	0	0
$837$	2046.95	0.0845318
$838$	−64024.3	−2.63924
$839$	13759.0	0.566168	0.283084	−	0.959095i	$-0.408642\pi$
$839$	13759.0	0.566168	0.283084	+	0.959095i	$0.408642\pi$
$840$	98.5032	0.00404605
$841$	−9258.26	−0.379608
$842$	−291.301	−0.0119227
$843$	−19953.7	−0.815233
$844$	494.494	0.0201673
$845$	−7152.67	−0.291195
$846$	−7085.84	−0.287962
$847$	0	0
$848$	21821.5	0.883671
$849$	−4861.53	−0.196522
$850$	587.616	0.0237119
$851$	37851.1	1.52470
$852$	−5749.30	−0.231183
$853$	21503.2	0.863136	0.431568	−	0.902080i	$-0.357960\pi$
$853$	21503.2	0.863136	0.431568	+	0.902080i	$0.357960\pi$
$854$	376.771	0.0150970
$855$	505.044	0.0202013
$856$	18417.4	0.735388
$857$	−36588.3	−1.45838	−0.729191	−	0.684310i	$-0.760103\pi$
$857$	−36588.3	−1.45838	−0.729191	+	0.684310i	$0.760103\pi$
$858$	0	0
$859$	7601.81	0.301945	0.150972	−	0.988538i	$-0.451760\pi$
$859$	7601.81	0.301945	0.150972	+	0.988538i	$0.451760\pi$
$860$	25128.9	0.996380
$861$	177.350	0.00701982
$862$	26754.4	1.05715
$863$	−38540.2	−1.52019	−0.760094	−	0.649813i	$-0.774847\pi$
$863$	−38540.2	−1.52019	−0.760094	+	0.649813i	$0.774847\pi$
$864$	92.2005	0.00363047
$865$	−5179.54	−0.203595
$866$	31939.3	1.25328
$867$	14670.1	0.574650
$868$	−202.517	−0.00791923
$869$	0	0
$870$	−9047.31	−0.352566
$871$	17372.1	0.675811
$872$	−58083.4	−2.25568
$873$	15283.8	0.592531
$874$	−5927.82	−0.229418
$875$	20.8128	0.000804117 0
$876$	30392.0	1.17221
$877$	21809.4	0.839740	0.419870	−	0.907584i	$-0.362076\pi$
$877$	21809.4	0.839740	0.419870	+	0.907584i	$0.362076\pi$
$878$	61555.2	2.36605
$879$	5408.45	0.207534
$880$	0	0
$881$	1554.67	0.0594530	0.0297265	−	0.999558i	$-0.490536\pi$
$881$	1554.67	0.0594530	0.0297265	+	0.999558i	$0.490536\pi$
$882$	15135.6	0.577825
$883$	21444.0	0.817270	0.408635	−	0.912698i	$-0.366005\pi$
$883$	21444.0	0.817270	0.408635	+	0.912698i	$0.366005\pi$
$884$	2129.11	0.0810066
$885$	−378.515	−0.0143770
$886$	−35240.0	−1.33624
$887$	126.181	0.00477650	0.00238825	−	0.999997i	$-0.499240\pi$
$887$	126.181	0.00477650	0.00238825	+	0.999997i	$0.499240\pi$
$888$	41577.4	1.57122
$889$	−187.898	−0.00708875
$890$	−9338.63	−0.351721
$891$	0	0
$892$	60086.0	2.25541
$893$	1802.05	0.0675290
$894$	46860.2	1.75306
$895$	9735.89	0.363615
$896$	415.707	0.0154998
$897$	8946.39	0.333011
$898$	−42723.2	−1.58763
$899$	9325.55	0.345967
$900$	3609.77	0.133695
$901$	−1608.18	−0.0594631
$902$	0	0
$903$	−156.476	−0.00576656
$904$	−39059.1	−1.43704
$905$	11509.2	0.422737
$906$	8138.59	0.298440
$907$	−20342.8	−0.744732	−0.372366	−	0.928086i	$-0.621453\pi$
$907$	−20342.8	−0.744732	−0.372366	+	0.928086i	$0.621453\pi$
$908$	16293.3	0.595499
$909$	5259.08	0.191895
$910$	113.015	0.00411693
$911$	2644.66	0.0961818	0.0480909	−	0.998843i	$-0.484686\pi$
$911$	2644.66	0.0961818	0.0480909	+	0.998843i	$0.484686\pi$
$912$	−2189.99	−0.0795153
$913$	0	0
$914$	−78680.9	−2.84741
$915$	6922.28	0.250102
$916$	−45344.2	−1.63560
$917$	44.1301	0.00158921
$918$	−634.626	−0.0228167
$919$	26851.8	0.963828	0.481914	−	0.876218i	$-0.339942\pi$
$919$	26851.8	0.963828	0.481914	+	0.876218i	$0.339942\pi$
$920$	−21241.7	−0.761214
$921$	−5125.41	−0.183374
$922$	95828.1	3.42292
$923$	−3307.07	−0.117934
$924$	0	0
$925$	8784.93	0.312267
$926$	23221.5	0.824090
$927$	−18710.2	−0.662915
$928$	420.048	0.0148586
$929$	−14199.2	−0.501466	−0.250733	−	0.968056i	$-0.580672\pi$
$929$	−14199.2	−0.501466	−0.250733	+	0.968056i	$0.580672\pi$
$930$	−5576.14	−0.196612
$931$	−3849.24	−0.135504
$932$	−62136.8	−2.18386
$933$	19655.3	0.689696
$934$	66846.2	2.34184
$935$	0	0
$936$	9827.14	0.343173
$937$	−30395.8	−1.05975	−0.529877	−	0.848075i	$-0.677762\pi$
$937$	−30395.8	−1.05975	−0.529877	+	0.848075i	$0.677762\pi$
$938$	512.301	0.0178329
$939$	−1169.37	−0.0406401
$940$	12880.1	0.446916
$941$	−19937.8	−0.690705	−0.345352	−	0.938473i	$-0.612241\pi$
$941$	−19937.8	−0.690705	−0.345352	+	0.938473i	$0.612241\pi$
$942$	−17269.7	−0.597323
$943$	−38244.4	−1.32069
$944$	1641.33	0.0565898
$945$	−22.4779	−0.000773762 0
$946$	0	0
$947$	−41403.0	−1.42071	−0.710357	−	0.703841i	$-0.751467\pi$
$947$	−41403.0	−1.42071	−0.710357	+	0.703841i	$0.751467\pi$
$948$	45700.3	1.56569
$949$	17481.9	0.597983
$950$	−1375.80	−0.0469861
$951$	17675.8	0.602708
$952$	31.4786	0.00107167
$953$	−48624.0	−1.65276	−0.826382	−	0.563109i	$-0.809605\pi$
$953$	−48624.0	−1.65276	−0.826382	+	0.563109i	$0.809605\pi$
$954$	−14805.4	−0.502455
$955$	5844.43	0.198033
$956$	12220.3	0.413424
$957$	0	0
$958$	6846.27	0.230890
$959$	400.979	0.0135019
$960$	7554.08	0.253965
$961$	−24043.4	−0.807068
$962$	47702.7	1.59875
$963$	−4202.73	−0.140635
$964$	68313.9	2.28241
$965$	7943.43	0.264983
$966$	263.828	0.00878729
$967$	17359.9	0.577308	0.288654	−	0.957433i	$-0.406792\pi$
$967$	17359.9	0.577308	0.288654	+	0.957433i	$0.406792\pi$
$968$	0	0
$969$	161.396	0.00535067
$970$	−41634.9	−1.37816
$971$	−56025.3	−1.85164	−0.925818	−	0.377971i	$-0.876622\pi$
$971$	−56025.3	−1.85164	−0.925818	+	0.377971i	$0.876622\pi$
$972$	−3898.55	−0.128648
$973$	−471.015	−0.0155191
$974$	44870.0	1.47611
$975$	2076.38	0.0682026
$976$	−30016.7	−0.984438
$977$	5107.98	0.167266	0.0836330	−	0.996497i	$-0.473348\pi$
$977$	5107.98	0.167266	0.0836330	+	0.996497i	$0.473348\pi$
$978$	−37673.4	−1.23176
$979$	0	0
$980$	−27512.2	−0.896781
$981$	13254.3	0.431373
$982$	−36519.8	−1.18675
$983$	12210.9	0.396202	0.198101	−	0.980182i	$-0.436523\pi$
$983$	12210.9	0.396202	0.198101	+	0.980182i	$0.436523\pi$
$984$	−42009.5	−1.36099
$985$	−24897.5	−0.805381
$986$	−2891.24	−0.0933832
$987$	−80.2035	−0.00258653
$988$	−4984.93	−0.160518
$989$	33743.2	1.08491
$990$	0	0
$991$	23722.0	0.760398	0.380199	−	0.924905i	$-0.375856\pi$
$991$	23722.0	0.760398	0.380199	+	0.924905i	$0.375856\pi$
$992$	258.889	0.00828603
$993$	4570.93	0.146077
$994$	−97.5250	−0.00311198
$995$	27488.1	0.875809
$996$	2083.09	0.0662703
$997$	−6963.79	−0.221209	−0.110605	−	0.993864i	$-0.535279\pi$
$997$	−6963.79	−0.221209	−0.110605	+	0.993864i	$0.535279\pi$
$998$	−37663.9	−1.19462
$999$	−9487.72	−0.300479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bi.1.2		12
11.5	even	5		165.4.m.c.91.6	✓	24
11.9	even	5		165.4.m.c.136.6	yes	24
11.10	odd	2		1815.4.a.bl.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.c.91.6	✓	24	11.5	even	5
165.4.m.c.136.6	yes	24	11.9	even	5
1815.4.a.bi.1.2		12	1.1	even	1	trivial
1815.4.a.bl.1.11		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)

\(f(q)\)	\(=\)	\(q-4.90341 q^{2} -3.00000 q^{3} +16.0434 q^{4} +5.00000 q^{5} +14.7102 q^{6} +0.166503 q^{7} -39.4401 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.90341 q^{2} -3.00000 q^{3} +16.0434 q^{4} +5.00000 q^{5} +14.7102 q^{6} +0.166503 q^{7} -39.4401 q^{8} +9.00000 q^{9} -24.5170 q^{10} -48.1302 q^{12} -27.6851 q^{13} -0.816430 q^{14} -15.0000 q^{15} +65.0437 q^{16} -4.79353 q^{17} -44.1307 q^{18} +11.2232 q^{19} +80.2170 q^{20} -0.499508 q^{21} +107.716 q^{23} +118.320 q^{24} +25.0000 q^{25} +135.751 q^{26} -27.0000 q^{27} +2.67127 q^{28} -123.007 q^{29} +73.5511 q^{30} -75.8131 q^{31} -3.41483 q^{32} +23.5047 q^{34} +0.832513 q^{35} +144.391 q^{36} +351.397 q^{37} -55.0319 q^{38} +83.0553 q^{39} -197.201 q^{40} -355.049 q^{41} +2.44929 q^{42} +313.261 q^{43} +45.0000 q^{45} -528.176 q^{46} +160.565 q^{47} -195.131 q^{48} -342.972 q^{49} -122.585 q^{50} +14.3806 q^{51} -444.164 q^{52} +335.490 q^{53} +132.392 q^{54} -6.56688 q^{56} -33.6696 q^{57} +603.154 q^{58} +25.2343 q^{59} -240.651 q^{60} -461.486 q^{61} +371.743 q^{62} +1.49852 q^{63} -503.605 q^{64} -138.426 q^{65} -627.489 q^{67} -76.9046 q^{68} -323.148 q^{69} -4.08215 q^{70} +119.453 q^{71} -354.961 q^{72} -631.455 q^{73} -1723.04 q^{74} -75.0000 q^{75} +180.058 q^{76} -407.254 q^{78} -949.514 q^{79} +325.218 q^{80} +81.0000 q^{81} +1740.95 q^{82} -43.2803 q^{83} -8.01381 q^{84} -23.9677 q^{85} -1536.05 q^{86} +369.021 q^{87} +380.904 q^{89} -220.653 q^{90} -4.60964 q^{91} +1728.13 q^{92} +227.439 q^{93} -787.316 q^{94} +56.1160 q^{95} +10.2445 q^{96} +1698.20 q^{97} +1681.73 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 36 q^{3} + 49 q^{4} + 60 q^{5} + 3 q^{6} + 5 q^{7} + 3 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - q^2 - 36 * q^3 + 49 * q^4 + 60 * q^5 + 3 * q^6 + 5 * q^7 + 3 * q^8 + 108 * q^9	\( 12 q - q^{2} - 36 q^{3} + 49 q^{4} + 60 q^{5} + 3 q^{6} + 5 q^{7} + 3 q^{8} + 108 q^{9} - 5 q^{10} - 147 q^{12} - 34 q^{13} - 134 q^{14} - 180 q^{15} + 265 q^{16} - 169 q^{17} - 9 q^{18} - 203 q^{19} + 245 q^{20} - 15 q^{21} + 116 q^{23} - 9 q^{24} + 300 q^{25} + 216 q^{26} - 324 q^{27} - 80 q^{28} - 409 q^{29} + 15 q^{30} - 645 q^{31} - 532 q^{32} - 1442 q^{34} + 25 q^{35} + 441 q^{36} + 40 q^{37} + 404 q^{38} + 102 q^{39} + 15 q^{40} - 1071 q^{41} + 402 q^{42} + 101 q^{43} + 540 q^{45} - 1539 q^{46} - 572 q^{47} - 795 q^{48} + 1563 q^{49} - 25 q^{50} + 507 q^{51} - 1081 q^{52} + 611 q^{53} + 27 q^{54} - 3221 q^{56} + 609 q^{57} - 354 q^{58} + 958 q^{59} - 735 q^{60} - 2620 q^{61} - 1049 q^{62} + 45 q^{63} + 2931 q^{64} - 170 q^{65} - 1027 q^{67} - 1896 q^{68} - 348 q^{69} - 670 q^{70} + 1020 q^{71} + 27 q^{72} - 2244 q^{73} + 283 q^{74} - 900 q^{75} - 4958 q^{76} - 648 q^{78} - 2199 q^{79} + 1325 q^{80} + 972 q^{81} + 362 q^{82} + 602 q^{83} + 240 q^{84} - 845 q^{85} - 1589 q^{86} + 1227 q^{87} - 2413 q^{89} - 45 q^{90} + 302 q^{91} + 3030 q^{92} + 1935 q^{93} - 2885 q^{94} - 1015 q^{95} + 1596 q^{96} + 886 q^{97} + 1236 q^{98}+O(q^{100}) \) 12 * q - q^2 - 36 * q^3 + 49 * q^4 + 60 * q^5 + 3 * q^6 + 5 * q^7 + 3 * q^8 + 108 * q^9 - 5 * q^10 - 147 * q^12 - 34 * q^13 - 134 * q^14 - 180 * q^15 + 265 * q^16 - 169 * q^17 - 9 * q^18 - 203 * q^19 + 245 * q^20 - 15 * q^21 + 116 * q^23 - 9 * q^24 + 300 * q^25 + 216 * q^26 - 324 * q^27 - 80 * q^28 - 409 * q^29 + 15 * q^30 - 645 * q^31 - 532 * q^32 - 1442 * q^34 + 25 * q^35 + 441 * q^36 + 40 * q^37 + 404 * q^38 + 102 * q^39 + 15 * q^40 - 1071 * q^41 + 402 * q^42 + 101 * q^43 + 540 * q^45 - 1539 * q^46 - 572 * q^47 - 795 * q^48 + 1563 * q^49 - 25 * q^50 + 507 * q^51 - 1081 * q^52 + 611 * q^53 + 27 * q^54 - 3221 * q^56 + 609 * q^57 - 354 * q^58 + 958 * q^59 - 735 * q^60 - 2620 * q^61 - 1049 * q^62 + 45 * q^63 + 2931 * q^64 - 170 * q^65 - 1027 * q^67 - 1896 * q^68 - 348 * q^69 - 670 * q^70 + 1020 * q^71 + 27 * q^72 - 2244 * q^73 + 283 * q^74 - 900 * q^75 - 4958 * q^76 - 648 * q^78 - 2199 * q^79 + 1325 * q^80 + 972 * q^81 + 362 * q^82 + 602 * q^83 + 240 * q^84 - 845 * q^85 - 1589 * q^86 + 1227 * q^87 - 2413 * q^89 - 45 * q^90 + 302 * q^91 + 3030 * q^92 + 1935 * q^93 - 2885 * q^94 - 1015 * q^95 + 1596 * q^96 + 886 * q^97 + 1236 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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