LMFDB - Embedded newform 1815.4.a.bd.1.7

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 52x^{5} + 37x^{4} + 765x^{3} - 296x^{2} - 2962x + 1692 $ x^7 - x^6 - 52x^5 + 37x^4 + 765x^3 - 296x^2 - 2962*x + 1692
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$5.46553$ 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)

$f(q)$	$=$	$q+5.46553 q^{2} -3.00000 q^{3} +21.8720 q^{4} +5.00000 q^{5} -16.3966 q^{6} +24.1442 q^{7} +75.8177 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.46553 q^{2} -3.00000 q^{3} +21.8720 q^{4} +5.00000 q^{5} -16.3966 q^{6} +24.1442 q^{7} +75.8177 q^{8} +9.00000 q^{9} +27.3276 q^{10} -65.6160 q^{12} +89.3509 q^{13} +131.961 q^{14} -15.0000 q^{15} +239.408 q^{16} -107.012 q^{17} +49.1897 q^{18} +26.2757 q^{19} +109.360 q^{20} -72.4327 q^{21} -147.519 q^{23} -227.453 q^{24} +25.0000 q^{25} +488.350 q^{26} -27.0000 q^{27} +528.082 q^{28} +264.656 q^{29} -81.9829 q^{30} +137.295 q^{31} +701.949 q^{32} -584.879 q^{34} +120.721 q^{35} +196.848 q^{36} -244.946 q^{37} +143.611 q^{38} -268.053 q^{39} +379.089 q^{40} +25.3785 q^{41} -395.883 q^{42} -48.1433 q^{43} +45.0000 q^{45} -806.269 q^{46} -329.264 q^{47} -718.224 q^{48} +239.943 q^{49} +136.638 q^{50} +321.037 q^{51} +1954.28 q^{52} -414.267 q^{53} -147.569 q^{54} +1830.56 q^{56} -78.8272 q^{57} +1446.49 q^{58} -590.701 q^{59} -328.080 q^{60} +171.942 q^{61} +750.392 q^{62} +217.298 q^{63} +1921.26 q^{64} +446.754 q^{65} +369.231 q^{67} -2340.57 q^{68} +442.557 q^{69} +659.804 q^{70} -255.837 q^{71} +682.359 q^{72} -590.167 q^{73} -1338.76 q^{74} -75.0000 q^{75} +574.703 q^{76} -1465.05 q^{78} -227.037 q^{79} +1197.04 q^{80} +81.0000 q^{81} +138.707 q^{82} -510.712 q^{83} -1584.25 q^{84} -535.062 q^{85} -263.128 q^{86} -793.969 q^{87} -177.062 q^{89} +245.949 q^{90} +2157.31 q^{91} -3226.53 q^{92} -411.886 q^{93} -1799.60 q^{94} +131.379 q^{95} -2105.85 q^{96} +391.649 q^{97} +1311.42 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 21 q^{3} + 49 q^{4} + 35 q^{5} - 3 q^{6} - 16 q^{7} + 30 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + q^2 - 21 * q^3 + 49 * q^4 + 35 * q^5 - 3 * q^6 - 16 * q^7 + 30 * q^8 + 63 * q^9	\( 7 q + q^{2} - 21 q^{3} + 49 q^{4} + 35 q^{5} - 3 q^{6} - 16 q^{7} + 30 q^{8} + 63 q^{9} + 5 q^{10} - 147 q^{12} + 90 q^{13} + 68 q^{14} - 105 q^{15} + 337 q^{16} - 67 q^{17} + 9 q^{18} + 270 q^{19} + 245 q^{20} + 48 q^{21} - 241 q^{23} - 90 q^{24} + 175 q^{25} + 36 q^{26} - 189 q^{27} - 236 q^{28} - 26 q^{29} - 15 q^{30} + 797 q^{31} + 351 q^{32} + 457 q^{34} - 80 q^{35} + 441 q^{36} - 310 q^{37} + 22 q^{38} - 270 q^{39} + 150 q^{40} + 108 q^{41} - 204 q^{42} + 812 q^{43} + 315 q^{45} - 2099 q^{46} + 671 q^{47} - 1011 q^{48} + 835 q^{49} + 25 q^{50} + 201 q^{51} + 1396 q^{52} + 347 q^{53} - 27 q^{54} + 2698 q^{56} - 810 q^{57} + 1212 q^{58} - 888 q^{59} - 735 q^{60} + q^{61} - 43 q^{62} - 144 q^{63} + 3316 q^{64} + 450 q^{65} - 118 q^{67} - 3975 q^{68} + 723 q^{69} + 340 q^{70} - 622 q^{71} + 270 q^{72} - 252 q^{73} + 458 q^{74} - 525 q^{75} + 5016 q^{76} - 108 q^{78} - 459 q^{79} + 1685 q^{80} + 567 q^{81} - 944 q^{82} - 1144 q^{83} + 708 q^{84} - 335 q^{85} + 2596 q^{86} + 78 q^{87} + 2072 q^{89} + 45 q^{90} + 3244 q^{91} - 1267 q^{92} - 2391 q^{93} - 2419 q^{94} + 1350 q^{95} - 1053 q^{96} + 2388 q^{97} + 5417 q^{98}+O(q^{100}) \) 7 * q + q^2 - 21 * q^3 + 49 * q^4 + 35 * q^5 - 3 * q^6 - 16 * q^7 + 30 * q^8 + 63 * q^9 + 5 * q^10 - 147 * q^12 + 90 * q^13 + 68 * q^14 - 105 * q^15 + 337 * q^16 - 67 * q^17 + 9 * q^18 + 270 * q^19 + 245 * q^20 + 48 * q^21 - 241 * q^23 - 90 * q^24 + 175 * q^25 + 36 * q^26 - 189 * q^27 - 236 * q^28 - 26 * q^29 - 15 * q^30 + 797 * q^31 + 351 * q^32 + 457 * q^34 - 80 * q^35 + 441 * q^36 - 310 * q^37 + 22 * q^38 - 270 * q^39 + 150 * q^40 + 108 * q^41 - 204 * q^42 + 812 * q^43 + 315 * q^45 - 2099 * q^46 + 671 * q^47 - 1011 * q^48 + 835 * q^49 + 25 * q^50 + 201 * q^51 + 1396 * q^52 + 347 * q^53 - 27 * q^54 + 2698 * q^56 - 810 * q^57 + 1212 * q^58 - 888 * q^59 - 735 * q^60 + q^61 - 43 * q^62 - 144 * q^63 + 3316 * q^64 + 450 * q^65 - 118 * q^67 - 3975 * q^68 + 723 * q^69 + 340 * q^70 - 622 * q^71 + 270 * q^72 - 252 * q^73 + 458 * q^74 - 525 * q^75 + 5016 * q^76 - 108 * q^78 - 459 * q^79 + 1685 * q^80 + 567 * q^81 - 944 * q^82 - 1144 * q^83 + 708 * q^84 - 335 * q^85 + 2596 * q^86 + 78 * q^87 + 2072 * q^89 + 45 * q^90 + 3244 * q^91 - 1267 * q^92 - 2391 * q^93 - 2419 * q^94 + 1350 * q^95 - 1053 * q^96 + 2388 * q^97 + 5417 * 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 $

$2$	5.46553	1.93236	0.966178	−	0.257877i	$-0.0830229\pi$
$2$	5.46553	1.93236	0.966178	+	0.257877i	$0.0830229\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	21.8720	2.73400
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−16.3966	−1.11565
$7$	24.1442	1.30367	0.651833	−	0.758363i	$-0.274000\pi$
$7$	24.1442	1.30367	0.651833	+	0.758363i	$0.274000\pi$
$8$	75.8177	3.35070
$9$	9.00000	0.333333
$10$	27.3276	0.864176
$11$	0	0
$11$	0	0
$12$	−65.6160	−1.57847
$13$	89.3509	1.90627	0.953134	−	0.302549i	$-0.0978376\pi$
$13$	89.3509	1.90627	0.953134	+	0.302549i	$0.0978376\pi$
$14$	131.961	2.51914
$15$	−15.0000	−0.258199
$16$	239.408	3.74075
$17$	−107.012	−1.52672	−0.763362	−	0.645971i	$-0.776453\pi$
$17$	−107.012	−1.52672	−0.763362	+	0.645971i	$0.776453\pi$
$18$	49.1897	0.644119
$19$	26.2757	0.317267	0.158633	−	0.987338i	$-0.449291\pi$
$19$	26.2757	0.317267	0.158633	+	0.987338i	$0.449291\pi$
$20$	109.360	1.22268
$21$	−72.4327	−0.752671
$22$	0	0
$23$	−147.519	−1.33738	−0.668692	−	0.743539i	$-0.733146\pi$
$23$	−147.519	−1.33738	−0.668692	+	0.743539i	$0.733146\pi$
$24$	−227.453	−1.93453
$25$	25.0000	0.200000
$26$	488.350	3.68359
$27$	−27.0000	−0.192450
$28$	528.082	3.56422
$29$	264.656	1.69467	0.847335	−	0.531058i	$-0.178205\pi$
$29$	264.656	1.69467	0.847335	+	0.531058i	$0.178205\pi$
$30$	−81.9829	−0.498932
$31$	137.295	0.795451	0.397725	−	0.917504i	$-0.369800\pi$
$31$	137.295	0.795451	0.397725	+	0.917504i	$0.369800\pi$
$32$	701.949	3.87775
$33$	0	0
$34$	−584.879	−2.95017
$35$	120.721	0.583017
$36$	196.848	0.911333
$37$	−244.946	−1.08835	−0.544175	−	0.838972i	$-0.683157\pi$
$37$	−244.946	−1.08835	−0.544175	+	0.838972i	$0.683157\pi$
$38$	143.611	0.613072
$39$	−268.053	−1.10058
$40$	379.089	1.49848
$41$	25.3785	0.0966695	0.0483348	−	0.998831i	$-0.484609\pi$
$41$	25.3785	0.0966695	0.0483348	+	0.998831i	$0.484609\pi$
$42$	−395.883	−1.45443
$43$	−48.1433	−0.170739	−0.0853696	−	0.996349i	$-0.527207\pi$
$43$	−48.1433	−0.170739	−0.0853696	+	0.996349i	$0.527207\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	−806.269	−2.58430
$47$	−329.264	−1.02187	−0.510937	−	0.859618i	$-0.670702\pi$
$47$	−329.264	−1.02187	−0.510937	+	0.859618i	$0.670702\pi$
$48$	−718.224	−2.15972
$49$	239.943	0.699543
$50$	136.638	0.386471
$51$	321.037	0.881454
$52$	1954.28	5.21173
$53$	−414.267	−1.07366	−0.536830	−	0.843690i	$-0.680378\pi$
$53$	−414.267	−1.07366	−0.536830	+	0.843690i	$0.680378\pi$
$54$	−147.569	−0.371882
$55$	0	0
$56$	1830.56	4.36819
$57$	−78.8272	−0.183174
$58$	1446.49	3.27471
$59$	−590.701	−1.30344	−0.651719	−	0.758461i	$-0.725952\pi$
$59$	−590.701	−1.30344	−0.651719	+	0.758461i	$0.725952\pi$
$60$	−328.080	−0.705915
$61$	171.942	0.360900	0.180450	−	0.983584i	$-0.442245\pi$
$61$	171.942	0.360900	0.180450	+	0.983584i	$0.442245\pi$
$62$	750.392	1.53709
$63$	217.298	0.434555
$64$	1921.26	3.75245
$65$	446.754	0.852509
$66$	0	0
$67$	369.231	0.673264	0.336632	−	0.941636i	$-0.390712\pi$
$67$	369.231	0.673264	0.336632	+	0.941636i	$0.390712\pi$
$68$	−2340.57	−4.17406
$69$	442.557	0.772139
$70$	659.804	1.12660
$71$	−255.837	−0.427637	−0.213818	−	0.976873i	$-0.568590\pi$
$71$	−255.837	−0.427637	−0.213818	+	0.976873i	$0.568590\pi$
$72$	682.359	1.11690
$73$	−590.167	−0.946217	−0.473108	−	0.881004i	$-0.656868\pi$
$73$	−590.167	−0.946217	−0.473108	+	0.881004i	$0.656868\pi$
$74$	−1338.76	−2.10308
$75$	−75.0000	−0.115470
$76$	574.703	0.867407
$77$	0	0
$78$	−1465.05	−2.12672
$79$	−227.037	−0.323338	−0.161669	−	0.986845i	$-0.551688\pi$
$79$	−227.037	−0.323338	−0.161669	+	0.986845i	$0.551688\pi$
$80$	1197.04	1.67291
$81$	81.0000	0.111111
$82$	138.707	0.186800
$83$	−510.712	−0.675397	−0.337698	−	0.941254i	$-0.609648\pi$
$83$	−510.712	−0.675397	−0.337698	+	0.941254i	$0.609648\pi$
$84$	−1584.25	−2.05780
$85$	−535.062	−0.682771
$86$	−263.128	−0.329929
$87$	−793.969	−0.978419
$88$	0	0
$89$	−177.062	−0.210883	−0.105441	−	0.994426i	$-0.533626\pi$
$89$	−177.062	−0.210883	−0.105441	+	0.994426i	$0.533626\pi$
$90$	245.949	0.288059
$91$	2157.31	2.48513
$92$	−3226.53	−3.65641
$93$	−411.886	−0.459254
$94$	−1799.60	−1.97463
$95$	131.379	0.141886
$96$	−2105.85	−2.23882
$97$	391.649	0.409959	0.204979	−	0.978766i	$-0.434287\pi$
$97$	391.649	0.409959	0.204979	+	0.978766i	$0.434287\pi$
$98$	1311.42	1.35177
$99$	0	0
$100$	546.800	0.546800
$101$	555.457	0.547228	0.273614	−	0.961840i	$-0.411781\pi$
$101$	555.457	0.547228	0.273614	+	0.961840i	$0.411781\pi$
$102$	1754.64	1.70328
$103$	−470.820	−0.450401	−0.225201	−	0.974312i	$-0.572304\pi$
$103$	−470.820	−0.450401	−0.225201	+	0.974312i	$0.572304\pi$
$104$	6774.38	6.38733
$105$	−362.163	−0.336605
$106$	−2264.19	−2.07469
$107$	275.416	0.248836	0.124418	−	0.992230i	$-0.460294\pi$
$107$	275.416	0.248836	0.124418	+	0.992230i	$0.460294\pi$
$108$	−590.544	−0.526158
$109$	1268.57	1.11475	0.557373	−	0.830262i	$-0.311809\pi$
$109$	1268.57	1.11475	0.557373	+	0.830262i	$0.311809\pi$
$110$	0	0
$111$	734.839	0.628359
$112$	5780.32	4.87668
$113$	−978.467	−0.814570	−0.407285	−	0.913301i	$-0.633524\pi$
$113$	−978.467	−0.814570	−0.407285	+	0.913301i	$0.633524\pi$
$114$	−430.832	−0.353957
$115$	−737.595	−0.598096
$116$	5788.56	4.63323
$117$	804.158	0.635423
$118$	−3228.49	−2.51870
$119$	−2583.73	−1.99034
$120$	−1137.27	−0.865147
$121$	0	0
$122$	939.753	0.697387
$123$	−76.1354	−0.0558122
$124$	3002.92	2.17476
$125$	125.000	0.0894427
$126$	1187.65	0.839715
$127$	−232.505	−0.162453	−0.0812263	−	0.996696i	$-0.525884\pi$
$127$	−232.505	−0.162453	−0.0812263	+	0.996696i	$0.525884\pi$
$128$	4885.09	3.37332
$129$	144.430	0.0985763
$130$	2441.75	1.64735
$131$	1859.92	1.24047	0.620236	−	0.784415i	$-0.287037\pi$
$131$	1859.92	1.24047	0.620236	+	0.784415i	$0.287037\pi$
$132$	0	0
$133$	634.407	0.413610
$134$	2018.04	1.30099
$135$	−135.000	−0.0860663
$136$	−8113.43	−5.11559
$137$	−1452.02	−0.905506	−0.452753	−	0.891636i	$-0.649558\pi$
$137$	−1452.02	−0.905506	−0.452753	+	0.891636i	$0.649558\pi$
$138$	2418.81	1.49205
$139$	2963.69	1.80847	0.904235	−	0.427035i	$-0.140442\pi$
$139$	2963.69	1.80847	0.904235	+	0.427035i	$0.140442\pi$
$140$	2640.41	1.59397
$141$	987.793	0.589980
$142$	−1398.28	−0.826347
$143$	0	0
$144$	2154.67	1.24692
$145$	1323.28	0.757880
$146$	−3225.57	−1.82843
$147$	−719.830	−0.403881
$148$	−5357.46	−2.97554
$149$	−671.158	−0.369016	−0.184508	−	0.982831i	$-0.559069\pi$
$149$	−671.158	−0.369016	−0.184508	+	0.982831i	$0.559069\pi$
$150$	−409.915	−0.223129
$151$	−1235.41	−0.665803	−0.332902	−	0.942962i	$-0.608028\pi$
$151$	−1235.41	−0.665803	−0.332902	+	0.942962i	$0.608028\pi$
$152$	1992.17	1.06307
$153$	−963.111	−0.508908
$154$	0	0
$155$	686.477	0.355736
$156$	−5862.84	−3.00900
$157$	1861.39	0.946210	0.473105	−	0.881006i	$-0.343133\pi$
$157$	1861.39	0.946210	0.473105	+	0.881006i	$0.343133\pi$
$158$	−1240.88	−0.624804
$159$	1242.80	0.619878
$160$	3509.74	1.73418
$161$	−3561.73	−1.74350
$162$	442.708	0.214706
$163$	−1211.63	−0.582220	−0.291110	−	0.956690i	$-0.594025\pi$
$163$	−1211.63	−0.582220	−0.291110	+	0.956690i	$0.594025\pi$
$164$	555.078	0.264294
$165$	0	0
$166$	−2791.31	−1.30511
$167$	628.170	0.291073	0.145537	−	0.989353i	$-0.453509\pi$
$167$	628.170	0.291073	0.145537	+	0.989353i	$0.453509\pi$
$168$	−5491.68	−2.52198
$169$	5786.58	2.63386
$170$	−2924.39	−1.31936
$171$	236.482	0.105756
$172$	−1052.99	−0.466800
$173$	3718.63	1.63423	0.817115	−	0.576474i	$-0.195572\pi$
$173$	3718.63	1.63423	0.817115	+	0.576474i	$0.195572\pi$
$174$	−4339.46	−1.89065
$175$	603.605	0.260733
$176$	0	0
$177$	1772.10	0.752540
$178$	−967.738	−0.407500
$179$	−2033.53	−0.849124	−0.424562	−	0.905399i	$-0.639572\pi$
$179$	−2033.53	−0.849124	−0.424562	+	0.905399i	$0.639572\pi$
$180$	984.239	0.407560
$181$	4250.78	1.74562	0.872811	−	0.488058i	$-0.162294\pi$
$181$	4250.78	1.74562	0.872811	+	0.488058i	$0.162294\pi$
$182$	11790.8	4.80216
$183$	−515.825	−0.208366
$184$	−11184.6	−4.48118
$185$	−1224.73	−0.486725
$186$	−2251.17	−0.887442
$187$	0	0
$188$	−7201.66	−2.79380
$189$	−651.894	−0.250890
$190$	718.054	0.274174
$191$	1546.61	0.585912	0.292956	−	0.956126i	$-0.405361\pi$
$191$	1546.61	0.585912	0.292956	+	0.956126i	$0.405361\pi$
$192$	−5763.77	−2.16648
$193$	2300.07	0.857837	0.428919	−	0.903343i	$-0.358895\pi$
$193$	2300.07	0.857837	0.428919	+	0.903343i	$0.358895\pi$
$194$	2140.57	0.792186
$195$	−1340.26	−0.492196
$196$	5248.03	1.91255
$197$	974.866	0.352570	0.176285	−	0.984339i	$-0.443592\pi$
$197$	974.866	0.352570	0.176285	+	0.984339i	$0.443592\pi$
$198$	0	0
$199$	−4080.21	−1.45346	−0.726729	−	0.686924i	$-0.758960\pi$
$199$	−4080.21	−1.45346	−0.726729	+	0.686924i	$0.758960\pi$
$200$	1895.44	0.670140
$201$	−1107.69	−0.388709
$202$	3035.87	1.05744
$203$	6389.92	2.20928
$204$	7021.72	2.40989
$205$	126.892	0.0432319
$206$	−2573.28	−0.870335
$207$	−1327.67	−0.445795
$208$	21391.3	7.13087
$209$	0	0
$210$	−1979.41	−0.650440
$211$	4563.58	1.48896	0.744478	−	0.667647i	$-0.232698\pi$
$211$	4563.58	1.48896	0.744478	+	0.667647i	$0.232698\pi$
$212$	−9060.85	−2.93538
$213$	767.510	0.246896
$214$	1505.29	0.480840
$215$	−240.716	−0.0763568
$216$	−2047.08	−0.644843
$217$	3314.89	1.03700
$218$	6933.42	2.15409
$219$	1770.50	0.546298
$220$	0	0
$221$	−9561.65	−2.91034
$222$	4016.28	1.21421
$223$	−2048.91	−0.615271	−0.307636	−	0.951504i	$-0.599538\pi$
$223$	−2048.91	−0.615271	−0.307636	+	0.951504i	$0.599538\pi$
$224$	16948.0	5.05529
$225$	225.000	0.0666667
$226$	−5347.84	−1.57404
$227$	1483.83	0.433855	0.216928	−	0.976188i	$-0.430396\pi$
$227$	1483.83	0.433855	0.216928	+	0.976188i	$0.430396\pi$
$228$	−1724.11	−0.500797
$229$	−3393.92	−0.979375	−0.489687	−	0.871898i	$-0.662889\pi$
$229$	−3393.92	−0.979375	−0.489687	+	0.871898i	$0.662889\pi$
$230$	−4031.35	−1.15574
$231$	0	0
$232$	20065.6	5.67834
$233$	−6114.76	−1.71928	−0.859638	−	0.510904i	$-0.829311\pi$
$233$	−6114.76	−1.71928	−0.859638	+	0.510904i	$0.829311\pi$
$234$	4395.15	1.22786
$235$	−1646.32	−0.456996
$236$	−12919.8	−3.56359
$237$	681.112	0.186679
$238$	−14121.4	−3.84604
$239$	−2945.25	−0.797122	−0.398561	−	0.917142i	$-0.630490\pi$
$239$	−2945.25	−0.797122	−0.398561	+	0.917142i	$0.630490\pi$
$240$	−3591.12	−0.965857
$241$	−1283.80	−0.343141	−0.171570	−	0.985172i	$-0.554884\pi$
$241$	−1283.80	−0.343141	−0.171570	+	0.985172i	$0.554884\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	3760.71	0.986700
$245$	1199.72	0.312845
$246$	−416.120	−0.107849
$247$	2347.76	0.604795
$248$	10409.4	2.66532
$249$	1532.14	0.389940
$250$	683.191	0.172835
$251$	1242.88	0.312550	0.156275	−	0.987714i	$-0.450051\pi$
$251$	1242.88	0.312550	0.156275	+	0.987714i	$0.450051\pi$
$252$	4752.74	1.18807
$253$	0	0
$254$	−1270.76	−0.313916
$255$	1605.18	0.394198
$256$	11329.5	2.76600
$257$	260.329	0.0631864	0.0315932	−	0.999501i	$-0.489942\pi$
$257$	260.329	0.0631864	0.0315932	+	0.999501i	$0.489942\pi$
$258$	789.385	0.190484
$259$	−5914.04	−1.41884
$260$	9771.41	2.33076
$261$	2381.91	0.564890
$262$	10165.4	2.39703
$263$	3450.76	0.809060	0.404530	−	0.914525i	$-0.367435\pi$
$263$	3450.76	0.809060	0.404530	+	0.914525i	$0.367435\pi$
$264$	0	0
$265$	−2071.34	−0.480155
$266$	3467.37	0.799241
$267$	531.186	0.121753
$268$	8075.81	1.84070
$269$	−1741.92	−0.394821	−0.197410	−	0.980321i	$-0.563253\pi$
$269$	−1741.92	−0.394821	−0.197410	+	0.980321i	$0.563253\pi$
$270$	−737.846	−0.166311
$271$	−5242.96	−1.17523	−0.587614	−	0.809141i	$-0.699933\pi$
$271$	−5242.96	−1.17523	−0.587614	+	0.809141i	$0.699933\pi$
$272$	−25619.6	−5.71109
$273$	−6471.92	−1.43479
$274$	−7936.05	−1.74976
$275$	0	0
$276$	9679.60	2.11103
$277$	−4666.16	−1.01214	−0.506069	−	0.862493i	$-0.668902\pi$
$277$	−4666.16	−1.01214	−0.506069	+	0.862493i	$0.668902\pi$
$278$	16198.2	3.49461
$279$	1235.66	0.265150
$280$	9152.80	1.95352
$281$	−2760.80	−0.586106	−0.293053	−	0.956096i	$-0.594671\pi$
$281$	−2760.80	−0.586106	−0.293053	+	0.956096i	$0.594671\pi$
$282$	5398.81	1.14005
$283$	5010.38	1.05242	0.526212	−	0.850353i	$-0.323612\pi$
$283$	5010.38	1.05242	0.526212	+	0.850353i	$0.323612\pi$
$284$	−5595.66	−1.16916
$285$	−394.136	−0.0819179
$286$	0	0
$287$	612.743	0.126025
$288$	6317.54	1.29258
$289$	6538.64	1.33088
$290$	7232.43	1.46449
$291$	−1174.95	−0.236690
$292$	−12908.1	−2.58695
$293$	−4431.86	−0.883659	−0.441829	−	0.897099i	$-0.645670\pi$
$293$	−4431.86	−0.883659	−0.441829	+	0.897099i	$0.645670\pi$
$294$	−3934.25	−0.780442
$295$	−2953.51	−0.582915
$296$	−18571.3	−3.64673
$297$	0	0
$298$	−3668.23	−0.713071
$299$	−13181.0	−2.54941
$300$	−1640.40	−0.315695
$301$	−1162.38	−0.222587
$302$	−6752.17	−1.28657
$303$	−1666.37	−0.315942
$304$	6290.62	1.18681
$305$	859.709	0.161399
$306$	−5263.91	−0.983391
$307$	589.509	0.109593	0.0547966	−	0.998498i	$-0.482549\pi$
$307$	589.509	0.109593	0.0547966	+	0.998498i	$0.482549\pi$
$308$	0	0
$309$	1412.46	0.260039
$310$	3751.96	0.687409
$311$	−9615.09	−1.75312	−0.876562	−	0.481289i	$-0.840169\pi$
$311$	−9615.09	−1.75312	−0.876562	+	0.481289i	$0.840169\pi$
$312$	−20323.1	−3.68773
$313$	98.2869	0.0177492	0.00887460	−	0.999961i	$-0.497175\pi$
$313$	98.2869	0.0177492	0.00887460	+	0.999961i	$0.497175\pi$
$314$	10173.5	1.82841
$315$	1086.49	0.194339
$316$	−4965.76	−0.884005
$317$	−3389.34	−0.600519	−0.300259	−	0.953858i	$-0.597073\pi$
$317$	−3389.34	−0.600519	−0.300259	+	0.953858i	$0.597073\pi$
$318$	6792.57	1.19782
$319$	0	0
$320$	9606.28	1.67815
$321$	−826.248	−0.143666
$322$	−19466.7	−3.36906
$323$	−2811.83	−0.484378
$324$	1771.63	0.303778
$325$	2233.77	0.381254
$326$	−6622.18	−1.12506
$327$	−3805.72	−0.643599
$328$	1924.14	0.323911
$329$	−7949.83	−1.33218
$330$	0	0
$331$	−7326.02	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$331$	−7326.02	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$332$	−11170.3	−1.84653
$333$	−2204.52	−0.362783
$334$	3433.28	0.562457
$335$	1846.15	0.301093
$336$	−17340.9	−2.81555
$337$	−7829.00	−1.26550	−0.632749	−	0.774357i	$-0.718074\pi$
$337$	−7829.00	−1.26550	−0.632749	+	0.774357i	$0.718074\pi$
$338$	31626.7	5.08955
$339$	2935.40	0.470292
$340$	−11702.9	−1.86670
$341$	0	0
$342$	1292.50	0.204357
$343$	−2488.23	−0.391695
$344$	−3650.11	−0.572096
$345$	2212.79	0.345311
$346$	20324.2	3.15791
$347$	−5231.07	−0.809275	−0.404638	−	0.914477i	$-0.632602\pi$
$347$	−5231.07	−0.809275	−0.404638	+	0.914477i	$0.632602\pi$
$348$	−17365.7	−2.67499
$349$	−7074.42	−1.08506	−0.542528	−	0.840037i	$-0.682533\pi$
$349$	−7074.42	−1.08506	−0.542528	+	0.840037i	$0.682533\pi$
$350$	3299.02	0.503829
$351$	−2412.47	−0.366861
$352$	0	0
$353$	10099.0	1.52271	0.761353	−	0.648337i	$-0.224535\pi$
$353$	10099.0	1.52271	0.761353	+	0.648337i	$0.224535\pi$
$354$	9685.48	1.45417
$355$	−1279.18	−0.191245
$356$	−3872.70	−0.576553
$357$	7751.19	1.14912
$358$	−11114.3	−1.64081
$359$	11106.5	1.63281	0.816405	−	0.577480i	$-0.195964\pi$
$359$	11106.5	1.63281	0.816405	+	0.577480i	$0.195964\pi$
$360$	3411.80	0.499493
$361$	−6168.59	−0.899342
$362$	23232.7	3.37316
$363$	0	0
$364$	47184.6	6.79435
$365$	−2950.83	−0.423161
$366$	−2819.26	−0.402636
$367$	−7276.74	−1.03499	−0.517497	−	0.855685i	$-0.673136\pi$
$367$	−7276.74	−1.03499	−0.517497	+	0.855685i	$0.673136\pi$
$368$	−35317.2	−5.00282
$369$	228.406	0.0322232
$370$	−6693.80	−0.940525
$371$	−10002.2	−1.39969
$372$	−9008.77	−1.25560
$373$	3937.08	0.546526	0.273263	−	0.961939i	$-0.411897\pi$
$373$	3937.08	0.546526	0.273263	+	0.961939i	$0.411897\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−24964.1	−3.42400
$377$	23647.3	3.23050
$378$	−3562.94	−0.484810
$379$	−0.0136316	−1.84752e−6 0	−9.23760e−7	−	1.00000i	$-0.500000\pi$
$379$	−0.0136316	−1.84752e−6 0	−9.23760e−7		1.00000i	$0.500000\pi$
$380$	2873.51	0.387916
$381$	697.515	0.0937921
$382$	8453.07	1.13219
$383$	9782.29	1.30510	0.652548	−	0.757747i	$-0.273700\pi$
$383$	9782.29	1.30510	0.652548	+	0.757747i	$0.273700\pi$
$384$	−14655.3	−1.94759
$385$	0	0
$386$	12571.1	1.65765
$387$	−433.290	−0.0569130
$388$	8566.15	1.12083
$389$	5355.40	0.698019	0.349010	−	0.937119i	$-0.386518\pi$
$389$	5355.40	0.698019	0.349010	+	0.937119i	$0.386518\pi$
$390$	−7325.25	−0.951098
$391$	15786.4	2.04182
$392$	18191.9	2.34396
$393$	−5579.76	−0.716187
$394$	5328.16	0.681291
$395$	−1135.19	−0.144601
$396$	0	0
$397$	−9328.64	−1.17932	−0.589661	−	0.807651i	$-0.700739\pi$
$397$	−9328.64	−1.17932	−0.589661	+	0.807651i	$0.700739\pi$
$398$	−22300.5	−2.80860
$399$	−1903.22	−0.238798
$400$	5985.20	0.748150
$401$	−11547.6	−1.43806	−0.719028	−	0.694982i	$-0.755413\pi$
$401$	−11547.6	−1.43806	−0.719028	+	0.694982i	$0.755413\pi$
$402$	−6054.12	−0.751125
$403$	12267.5	1.51634
$404$	12149.0	1.49612
$405$	405.000	0.0496904
$406$	34924.3	4.26912
$407$	0	0
$408$	24340.3	2.95349
$409$	10739.8	1.29841	0.649206	−	0.760613i	$-0.275101\pi$
$409$	10739.8	1.29841	0.649206	+	0.760613i	$0.275101\pi$
$410$	693.534	0.0835395
$411$	4356.06	0.522794
$412$	−10297.8	−1.23140
$413$	−14262.0	−1.69925
$414$	−7256.42	−0.861434
$415$	−2553.56	−0.302047
$416$	62719.7	7.39204
$417$	−8891.08	−1.04412
$418$	0	0
$419$	−11604.1	−1.35297	−0.676486	−	0.736456i	$-0.736498\pi$
$419$	−11604.1	−1.35297	−0.676486	+	0.736456i	$0.736498\pi$
$420$	−7921.23	−0.920277
$421$	13352.5	1.54575	0.772874	−	0.634559i	$-0.218818\pi$
$421$	13352.5	1.54575	0.772874	+	0.634559i	$0.218818\pi$
$422$	24942.4	2.87719
$423$	−2963.38	−0.340625
$424$	−31408.8	−3.59751
$425$	−2675.31	−0.305345
$426$	4194.85	0.477091
$427$	4151.40	0.470493
$428$	6023.90	0.680318
$429$	0	0
$430$	−1315.64	−0.147549
$431$	−12856.1	−1.43679	−0.718393	−	0.695637i	$-0.755122\pi$
$431$	−12856.1	−1.43679	−0.718393	+	0.695637i	$0.755122\pi$
$432$	−6464.01	−0.719907
$433$	11837.1	1.31376	0.656878	−	0.753997i	$-0.271877\pi$
$433$	11837.1	1.31376	0.656878	+	0.753997i	$0.271877\pi$
$434$	18117.6	2.00386
$435$	−3969.84	−0.437562
$436$	27746.2	3.04771
$437$	−3876.17	−0.424308
$438$	9676.72	1.05564
$439$	−7742.56	−0.841759	−0.420879	−	0.907117i	$-0.638278\pi$
$439$	−7742.56	−0.841759	−0.420879	+	0.907117i	$0.638278\pi$
$440$	0	0
$441$	2159.49	0.233181
$442$	−52259.4	−5.62382
$443$	−9709.15	−1.04130	−0.520650	−	0.853770i	$-0.674310\pi$
$443$	−9709.15	−1.04130	−0.520650	+	0.853770i	$0.674310\pi$
$444$	16072.4	1.71793
$445$	−885.311	−0.0943096
$446$	−11198.4	−1.18892
$447$	2013.47	0.213052
$448$	46387.2	4.89194
$449$	9301.57	0.977657	0.488829	−	0.872380i	$-0.337424\pi$
$449$	9301.57	0.977657	0.488829	+	0.872380i	$0.337424\pi$
$450$	1229.74	0.128824
$451$	0	0
$452$	−21401.0	−2.22703
$453$	3706.23	0.384402
$454$	8109.90	0.838362
$455$	10786.5	1.11139
$456$	−5976.50	−0.613761
$457$	−15425.8	−1.57897	−0.789486	−	0.613769i	$-0.789653\pi$
$457$	−15425.8	−1.57897	−0.789486	+	0.613769i	$0.789653\pi$
$458$	−18549.6	−1.89250
$459$	2889.33	0.293818
$460$	−16132.7	−1.63519
$461$	3861.35	0.390110	0.195055	−	0.980792i	$-0.437511\pi$
$461$	3861.35	0.390110	0.195055	+	0.980792i	$0.437511\pi$
$462$	0	0
$463$	−3929.21	−0.394397	−0.197199	−	0.980364i	$-0.563184\pi$
$463$	−3929.21	−0.394397	−0.197199	+	0.980364i	$0.563184\pi$
$464$	63360.8	6.33934
$465$	−2059.43	−0.205385
$466$	−33420.4	−3.32225
$467$	14947.4	1.48113	0.740563	−	0.671987i	$-0.234559\pi$
$467$	14947.4	1.48113	0.740563	+	0.671987i	$0.234559\pi$
$468$	17588.5	1.73724
$469$	8914.79	0.877711
$470$	−8998.01	−0.883079
$471$	−5584.16	−0.546295
$472$	−44785.6	−4.36743
$473$	0	0
$474$	3722.63	0.360731
$475$	656.893	0.0634533
$476$	−56511.3	−5.44158
$477$	−3728.40	−0.357887
$478$	−16097.3	−1.54032
$479$	−4942.19	−0.471429	−0.235714	−	0.971822i	$-0.575743\pi$
$479$	−4942.19	−0.471429	−0.235714	+	0.971822i	$0.575743\pi$
$480$	−10529.2	−1.00123
$481$	−21886.2	−2.07468
$482$	−7016.65	−0.663070
$483$	10685.2	1.00661
$484$	0	0
$485$	1958.25	0.183339
$486$	−1328.12	−0.123961
$487$	1206.73	0.112283	0.0561416	−	0.998423i	$-0.482120\pi$
$487$	1206.73	0.112283	0.0561416	+	0.998423i	$0.482120\pi$
$488$	13036.2	1.20927
$489$	3634.88	0.336145
$490$	6557.08	0.604528
$491$	15077.8	1.38585	0.692924	−	0.721011i	$-0.256322\pi$
$491$	15077.8	1.38585	0.692924	+	0.721011i	$0.256322\pi$
$492$	−1665.23	−0.152590
$493$	−28321.5	−2.58729
$494$	12831.7	1.16868
$495$	0	0
$496$	32869.6	2.97558
$497$	−6176.98	−0.557495
$498$	8373.93	0.753503
$499$	19610.9	1.75933	0.879666	−	0.475592i	$-0.157766\pi$
$499$	19610.9	1.75933	0.879666	+	0.475592i	$0.157766\pi$
$500$	2734.00	0.244536
$501$	−1884.51	−0.168051
$502$	6793.01	0.603958
$503$	−5704.92	−0.505705	−0.252853	−	0.967505i	$-0.581369\pi$
$503$	−5704.92	−0.505705	−0.252853	+	0.967505i	$0.581369\pi$
$504$	16475.0	1.45606
$505$	2777.29	0.244728
$506$	0	0
$507$	−17359.7	−1.52066
$508$	−5085.35	−0.444145
$509$	−1354.70	−0.117968	−0.0589842	−	0.998259i	$-0.518786\pi$
$509$	−1354.70	−0.117968	−0.0589842	+	0.998259i	$0.518786\pi$
$510$	8773.18	0.761731
$511$	−14249.1	−1.23355
$512$	22841.2	1.97157
$513$	−709.445	−0.0610580
$514$	1422.84	0.122099
$515$	−2354.10	−0.201425
$516$	3158.97	0.269507
$517$	0	0
$518$	−32323.3	−2.74171
$519$	−11155.9	−0.943523
$520$	33871.9	2.85650
$521$	−1606.23	−0.135068	−0.0675338	−	0.997717i	$-0.521513\pi$
$521$	−1606.23	−0.135068	−0.0675338	+	0.997717i	$0.521513\pi$
$522$	13018.4	1.09157
$523$	6095.62	0.509642	0.254821	−	0.966988i	$-0.417983\pi$
$523$	6095.62	0.509642	0.254821	+	0.966988i	$0.417983\pi$
$524$	40680.1	3.39145
$525$	−1810.82	−0.150534
$526$	18860.2	1.56339
$527$	−14692.3	−1.21443
$528$	0	0
$529$	9594.86	0.788597
$530$	−11320.9	−0.927831
$531$	−5316.31	−0.434479
$532$	13875.7	1.13081
$533$	2267.59	0.184278
$534$	2903.21	0.235270
$535$	1377.08	0.111283
$536$	27994.2	2.25591
$537$	6100.59	0.490242
$538$	−9520.52	−0.762934
$539$	0	0
$540$	−2952.72	−0.235305
$541$	−6638.07	−0.527529	−0.263764	−	0.964587i	$-0.584964\pi$
$541$	−6638.07	−0.527529	−0.263764	+	0.964587i	$0.584964\pi$
$542$	−28655.5	−2.27096
$543$	−12752.3	−1.00784
$544$	−75117.1	−5.92026
$545$	6342.87	0.498530
$546$	−35372.5	−2.77253
$547$	−5548.72	−0.433722	−0.216861	−	0.976202i	$-0.569582\pi$
$547$	−5548.72	−0.433722	−0.216861	+	0.976202i	$0.569582\pi$
$548$	−31758.5	−2.47565
$549$	1547.48	0.120300
$550$	0	0
$551$	6954.04	0.537663
$552$	33553.7	2.58721
$553$	−5481.64	−0.421524
$554$	−25503.0	−1.95581
$555$	3674.19	0.281011
$556$	64821.9	4.94435
$557$	8838.29	0.672335	0.336167	−	0.941802i	$-0.390869\pi$
$557$	8838.29	0.672335	0.336167	+	0.941802i	$0.390869\pi$
$558$	6753.52	0.512365
$559$	−4301.65	−0.325474
$560$	28901.6	2.18092
$561$	0	0
$562$	−15089.2	−1.13256
$563$	23920.8	1.79066	0.895331	−	0.445401i	$-0.146939\pi$
$563$	23920.8	1.79066	0.895331	+	0.445401i	$0.146939\pi$
$564$	21605.0	1.61300
$565$	−4892.33	−0.364287
$566$	27384.4	2.03366
$567$	1955.68	0.144852
$568$	−19397.0	−1.43288
$569$	21101.7	1.55471	0.777353	−	0.629065i	$-0.216562\pi$
$569$	21101.7	1.55471	0.777353	+	0.629065i	$0.216562\pi$
$570$	−2154.16	−0.158295
$571$	−17832.6	−1.30696	−0.653478	−	0.756945i	$-0.726691\pi$
$571$	−17832.6	−1.30696	−0.653478	+	0.756945i	$0.726691\pi$
$572$	0	0
$573$	−4639.84	−0.338276
$574$	3348.97	0.243525
$575$	−3687.98	−0.267477
$576$	17291.3	1.25082
$577$	10520.6	0.759064	0.379532	−	0.925179i	$-0.376085\pi$
$577$	10520.6	0.759064	0.379532	+	0.925179i	$0.376085\pi$
$578$	35737.1	2.57174
$579$	−6900.21	−0.495273
$580$	28942.8	2.07204
$581$	−12330.7	−0.880491
$582$	−6421.71	−0.457369
$583$	0	0
$584$	−44745.1	−3.17049
$585$	4020.79	0.284170
$586$	−24222.4	−1.70754
$587$	8837.65	0.621412	0.310706	−	0.950506i	$-0.399435\pi$
$587$	8837.65	0.621412	0.310706	+	0.950506i	$0.399435\pi$
$588$	−15744.1	−1.10421
$589$	3607.54	0.252370
$590$	−16142.5	−1.12640
$591$	−2924.60	−0.203556
$592$	−58642.1	−4.07124
$593$	1393.01	0.0964652	0.0482326	−	0.998836i	$-0.484641\pi$
$593$	1393.01	0.0964652	0.0482326	+	0.998836i	$0.484641\pi$
$594$	0	0
$595$	−12918.6	−0.890105
$596$	−14679.6	−1.00889
$597$	12240.6	0.839154
$598$	−72040.9	−4.92637
$599$	16273.3	1.11003	0.555016	−	0.831840i	$-0.312712\pi$
$599$	16273.3	1.11003	0.555016	+	0.831840i	$0.312712\pi$
$600$	−5686.33	−0.386906
$601$	−24237.7	−1.64505	−0.822526	−	0.568727i	$-0.807436\pi$
$601$	−24237.7	−1.64505	−0.822526	+	0.568727i	$0.807436\pi$
$602$	−6353.03	−0.430117
$603$	3323.08	0.224421
$604$	−27020.9	−1.82031
$605$	0	0
$606$	−9107.60	−0.610513
$607$	−13265.3	−0.887024	−0.443512	−	0.896269i	$-0.646268\pi$
$607$	−13265.3	−0.887024	−0.443512	+	0.896269i	$0.646268\pi$
$608$	18444.2	1.23028
$609$	−19169.8	−1.27553
$610$	4698.76	0.311881
$611$	−29420.0	−1.94797
$612$	−21065.1	−1.39135
$613$	−16831.9	−1.10903	−0.554513	−	0.832175i	$-0.687095\pi$
$613$	−16831.9	−1.10903	−0.554513	+	0.832175i	$0.687095\pi$
$614$	3221.98	0.211773
$615$	−380.677	−0.0249600
$616$	0	0
$617$	112.134	0.00731662	0.00365831	−	0.999993i	$-0.498836\pi$
$617$	112.134	0.00731662	0.00365831	+	0.999993i	$0.498836\pi$
$618$	7719.84	0.502488
$619$	−17187.2	−1.11601	−0.558007	−	0.829837i	$-0.688434\pi$
$619$	−17187.2	−1.11601	−0.558007	+	0.829837i	$0.688434\pi$
$620$	15014.6	0.972583
$621$	3983.01	0.257380
$622$	−52551.5	−3.38766
$623$	−4275.03	−0.274920
$624$	−64173.9	−4.11701
$625$	625.000	0.0400000
$626$	537.189	0.0342978
$627$	0	0
$628$	40712.3	2.58694
$629$	26212.3	1.66161
$630$	5938.24	0.375532
$631$	8198.25	0.517222	0.258611	−	0.965982i	$-0.416735\pi$
$631$	8198.25	0.517222	0.258611	+	0.965982i	$0.416735\pi$
$632$	−17213.4	−1.08341
$633$	−13690.7	−0.859649
$634$	−18524.5	−1.16042
$635$	−1162.52	−0.0726510
$636$	27182.5	1.69474
$637$	21439.1	1.33352
$638$	0	0
$639$	−2302.53	−0.142546
$640$	24425.4	1.50859
$641$	−9328.55	−0.574813	−0.287407	−	0.957809i	$-0.592793\pi$
$641$	−9328.55	−0.574813	−0.287407	+	0.957809i	$0.592793\pi$
$642$	−4515.88	−0.277613
$643$	−7312.03	−0.448458	−0.224229	−	0.974537i	$-0.571986\pi$
$643$	−7312.03	−0.448458	−0.224229	+	0.974537i	$0.571986\pi$
$644$	−77902.1	−4.76673
$645$	722.149	0.0440846
$646$	−15368.1	−0.935992
$647$	−6738.90	−0.409480	−0.204740	−	0.978816i	$-0.565635\pi$
$647$	−6738.90	−0.409480	−0.204740	+	0.978816i	$0.565635\pi$
$648$	6141.24	0.372300
$649$	0	0
$650$	12208.7	0.736717
$651$	−9944.67	−0.598713
$652$	−26500.7	−1.59179
$653$	11951.6	0.716233	0.358117	−	0.933677i	$-0.383419\pi$
$653$	11951.6	0.716233	0.358117	+	0.933677i	$0.383419\pi$
$654$	−20800.3	−1.24366
$655$	9299.59	0.554756
$656$	6075.81	0.361616
$657$	−5311.50	−0.315406
$658$	−43450.0	−2.57425
$659$	5455.59	0.322488	0.161244	−	0.986915i	$-0.448449\pi$
$659$	5455.59	0.322488	0.161244	+	0.986915i	$0.448449\pi$
$660$	0	0
$661$	7632.26	0.449108	0.224554	−	0.974462i	$-0.427907\pi$
$661$	7632.26	0.449108	0.224554	+	0.974462i	$0.427907\pi$
$662$	−40040.6	−2.35079
$663$	28684.9	1.68029
$664$	−38721.0	−2.26305
$665$	3172.04	0.184972
$666$	−12048.8	−0.701026
$667$	−39041.8	−2.26643
$668$	13739.3	0.795794
$669$	6146.74	0.355227
$670$	10090.2	0.581819
$671$	0	0
$672$	−50844.0	−2.91868
$673$	−26062.0	−1.49274	−0.746372	−	0.665529i	$-0.768206\pi$
$673$	−26062.0	−1.49274	−0.746372	+	0.665529i	$0.768206\pi$
$674$	−42789.6	−2.44539
$675$	−675.000	−0.0384900
$676$	126564.	7.20096
$677$	23123.5	1.31272	0.656358	−	0.754450i	$-0.272096\pi$
$677$	23123.5	1.31272	0.656358	+	0.754450i	$0.272096\pi$
$678$	16043.5	0.908772
$679$	9456.07	0.534449
$680$	−40567.1	−2.28776
$681$	−4451.48	−0.250486
$682$	0	0
$683$	−16877.7	−0.945544	−0.472772	−	0.881185i	$-0.656747\pi$
$683$	−16877.7	−0.945544	−0.472772	+	0.881185i	$0.656747\pi$
$684$	5172.32	0.289136
$685$	−7260.10	−0.404955
$686$	−13599.5	−0.756895
$687$	10181.8	0.565442
$688$	−11525.9	−0.638692
$689$	−37015.1	−2.04668
$690$	12094.0	0.667264
$691$	−946.926	−0.0521314	−0.0260657	−	0.999660i	$-0.508298\pi$
$691$	−946.926	−0.0521314	−0.0260657	+	0.999660i	$0.508298\pi$
$692$	81333.7	4.46798
$693$	0	0
$694$	−28590.6	−1.56381
$695$	14818.5	0.808772
$696$	−60196.9	−3.27839
$697$	−2715.81	−0.147588
$698$	−38665.4	−2.09672
$699$	18344.3	0.992624
$700$	13202.0	0.712844
$701$	−23877.0	−1.28648	−0.643241	−	0.765664i	$-0.722411\pi$
$701$	−23877.0	−1.28648	−0.643241	+	0.765664i	$0.722411\pi$
$702$	−13185.4	−0.708907
$703$	−6436.14	−0.345297
$704$	0	0
$705$	4938.96	0.263847
$706$	55196.3	2.94241
$707$	13411.1	0.713403
$708$	38759.4	2.05744
$709$	31868.3	1.68807	0.844033	−	0.536291i	$-0.180175\pi$
$709$	31868.3	1.68807	0.844033	+	0.536291i	$0.180175\pi$
$710$	−6991.41	−0.369553
$711$	−2043.34	−0.107779
$712$	−13424.4	−0.706605
$713$	−20253.7	−1.06382
$714$	42364.3	2.22051
$715$	0	0
$716$	−44477.3	−2.32150
$717$	8835.74	0.460218
$718$	60702.9	3.15517
$719$	33887.2	1.75769	0.878846	−	0.477106i	$-0.158314\pi$
$719$	33887.2	1.75769	0.878846	+	0.477106i	$0.158314\pi$
$720$	10773.4	0.557638
$721$	−11367.6	−0.587172
$722$	−33714.6	−1.73785
$723$	3851.40	0.198112
$724$	92972.9	4.77253
$725$	6616.41	0.338934
$726$	0	0
$727$	−1623.03	−0.0827988	−0.0413994	−	0.999143i	$-0.513182\pi$
$727$	−1623.03	−0.0827988	−0.0413994	+	0.999143i	$0.513182\pi$
$728$	163562.	8.32694
$729$	729.000	0.0370370
$730$	−16127.9	−0.817697
$731$	5151.92	0.260671
$732$	−11282.1	−0.569671
$733$	−15083.1	−0.760039	−0.380019	−	0.924978i	$-0.624083\pi$
$733$	−15083.1	−0.760039	−0.380019	+	0.924978i	$0.624083\pi$
$734$	−39771.2	−1.99998
$735$	−3599.15	−0.180621
$736$	−103551.	−5.18605
$737$	0	0
$738$	1248.36	0.0622666
$739$	−26548.9	−1.32154	−0.660769	−	0.750590i	$-0.729770\pi$
$739$	−26548.9	−1.32154	−0.660769	+	0.750590i	$0.729770\pi$
$740$	−26787.3	−1.33070
$741$	−7043.28	−0.349179
$742$	−54667.1	−2.70470
$743$	−8097.57	−0.399827	−0.199913	−	0.979814i	$-0.564066\pi$
$743$	−8097.57	−0.399827	−0.199913	+	0.979814i	$0.564066\pi$
$744$	−31228.3	−1.53882
$745$	−3355.79	−0.165029
$746$	21518.2	1.05608
$747$	−4596.41	−0.225132
$748$	0	0
$749$	6649.71	0.324399
$750$	−2049.57	−0.0997864
$751$	9234.47	0.448696	0.224348	−	0.974509i	$-0.427975\pi$
$751$	9234.47	0.448696	0.224348	+	0.974509i	$0.427975\pi$
$752$	−78828.4	−3.82258
$753$	−3728.65	−0.180451
$754$	129245.	6.24247
$755$	−6177.05	−0.297756
$756$	−14258.2	−0.685934
$757$	−4905.86	−0.235544	−0.117772	−	0.993041i	$-0.537575\pi$
$757$	−4905.86	−0.235544	−0.117772	+	0.993041i	$0.537575\pi$
$758$	−0.0745041	−3.57007e−6 0
$759$	0	0
$760$	9960.83	0.475418
$761$	−1361.53	−0.0648559	−0.0324280	−	0.999474i	$-0.510324\pi$
$761$	−1361.53	−0.0648559	−0.0324280	+	0.999474i	$0.510324\pi$
$762$	3812.29	0.181240
$763$	30628.7	1.45326
$764$	33827.5	1.60188
$765$	−4815.55	−0.227590
$766$	53465.4	2.52191
$767$	−52779.7	−2.48470
$768$	−33988.6	−1.59695
$769$	−586.382	−0.0274974	−0.0137487	−	0.999905i	$-0.504376\pi$
$769$	−586.382	−0.0274974	−0.0137487	+	0.999905i	$0.504376\pi$
$770$	0	0
$771$	−780.988	−0.0364807
$772$	50307.1	2.34533
$773$	−15151.8	−0.705010	−0.352505	−	0.935810i	$-0.614670\pi$
$773$	−15151.8	−0.705010	−0.352505	+	0.935810i	$0.614670\pi$
$774$	−2368.16	−0.109976
$775$	3432.38	0.159090
$776$	29694.0	1.37365
$777$	17742.1	0.819169
$778$	29270.1	1.34882
$779$	666.838	0.0306700
$780$	−29314.2	−1.34566
$781$	0	0
$782$	86280.7	3.94551
$783$	−7145.72	−0.326140
$784$	57444.3	2.61681
$785$	9306.94	0.423158
$786$	−30496.3	−1.38393
$787$	41854.5	1.89575	0.947873	−	0.318650i	$-0.103229\pi$
$787$	41854.5	1.89575	0.947873	+	0.318650i	$0.103229\pi$
$788$	21322.3	0.963926
$789$	−10352.3	−0.467111
$790$	−6204.39	−0.279421
$791$	−23624.3	−1.06193
$792$	0	0
$793$	15363.2	0.687972
$794$	−50985.9	−2.27887
$795$	6214.01	0.277218
$796$	−89242.2	−3.97375
$797$	14816.2	0.658489	0.329245	−	0.944245i	$-0.393206\pi$
$797$	14816.2	0.658489	0.329245	+	0.944245i	$0.393206\pi$
$798$	−10402.1	−0.461442
$799$	35235.3	1.56012
$800$	17548.7	0.775551
$801$	−1593.56	−0.0702942
$802$	−63113.8	−2.77883
$803$	0	0
$804$	−24227.4	−1.06273
$805$	−17808.7	−0.779718
$806$	67048.2	2.93011
$807$	5225.76	0.227950
$808$	42113.5	1.83360
$809$	−14673.9	−0.637711	−0.318856	−	0.947803i	$-0.603299\pi$
$809$	−14673.9	−0.637711	−0.318856	+	0.947803i	$0.603299\pi$
$810$	2213.54	0.0960195
$811$	−1961.72	−0.0849385	−0.0424693	−	0.999098i	$-0.513522\pi$
$811$	−1961.72	−0.0849385	−0.0424693	+	0.999098i	$0.513522\pi$
$812$	139760.	6.04018
$813$	15728.9	0.678518
$814$	0	0
$815$	−6058.13	−0.260377
$816$	76858.8	3.29730
$817$	−1265.00	−0.0541698
$818$	58698.9	2.50899
$819$	19415.8	0.828378
$820$	2775.39	0.118196
$821$	25819.1	1.09756	0.548778	−	0.835968i	$-0.315093\pi$
$821$	25819.1	1.09756	0.548778	+	0.835968i	$0.315093\pi$
$822$	23808.1	1.01022
$823$	−25848.7	−1.09481	−0.547405	−	0.836868i	$-0.684384\pi$
$823$	−25848.7	−1.09481	−0.547405	+	0.836868i	$0.684384\pi$
$824$	−35696.5	−1.50916
$825$	0	0
$826$	−77949.5	−3.28355
$827$	−9345.74	−0.392966	−0.196483	−	0.980507i	$-0.562952\pi$
$827$	−9345.74	−0.392966	−0.196483	+	0.980507i	$0.562952\pi$
$828$	−29038.8	−1.21880
$829$	14612.6	0.612201	0.306101	−	0.951999i	$-0.400976\pi$
$829$	14612.6	0.612201	0.306101	+	0.951999i	$0.400976\pi$
$830$	−13956.5	−0.583661
$831$	13998.5	0.584358
$832$	171666.	7.15318
$833$	−25676.9	−1.06801
$834$	−48594.5	−2.01761
$835$	3140.85	0.130172
$836$	0	0
$837$	−3706.98	−0.153085
$838$	−63422.3	−2.61442
$839$	−12245.8	−0.503900	−0.251950	−	0.967740i	$-0.581072\pi$
$839$	−12245.8	−0.503900	−0.251950	+	0.967740i	$0.581072\pi$
$840$	−27458.4	−1.12786
$841$	45654.0	1.87191
$842$	72978.4	2.98694
$843$	8282.41	0.338388
$844$	99814.6	4.07080
$845$	28932.9	1.17790
$846$	−16196.4	−0.658209
$847$	0	0
$848$	−99178.8	−4.01629
$849$	−15031.1	−0.607617
$850$	−14622.0	−0.590035
$851$	36134.2	1.45554
$852$	16787.0	0.675014
$853$	774.159	0.0310747	0.0155373	−	0.999879i	$-0.495054\pi$
$853$	774.159	0.0310747	0.0155373	+	0.999879i	$0.495054\pi$
$854$	22689.6	0.909159
$855$	1182.41	0.0472953
$856$	20881.4	0.833776
$857$	−22567.1	−0.899505	−0.449753	−	0.893153i	$-0.648488\pi$
$857$	−22567.1	−0.899505	−0.449753	+	0.893153i	$0.648488\pi$
$858$	0	0
$859$	31366.1	1.24586	0.622932	−	0.782276i	$-0.285941\pi$
$859$	31366.1	1.24586	0.622932	+	0.782276i	$0.285941\pi$
$860$	−5264.95	−0.208759
$861$	−1838.23	−0.0727604
$862$	−70265.2	−2.77638
$863$	18019.5	0.710766	0.355383	−	0.934721i	$-0.384350\pi$
$863$	18019.5	0.710766	0.355383	+	0.934721i	$0.384350\pi$
$864$	−18952.6	−0.746274
$865$	18593.1	0.730850
$866$	64696.1	2.53864
$867$	−19615.9	−0.768387
$868$	72503.2	2.83516
$869$	0	0
$870$	−21697.3	−0.845526
$871$	32991.1	1.28342
$872$	96180.4	3.73518
$873$	3524.85	0.136653
$874$	−21185.3	−0.819913
$875$	3018.03	0.116603
$876$	38724.4	1.49358
$877$	24565.3	0.945850	0.472925	−	0.881103i	$-0.343198\pi$
$877$	24565.3	0.945850	0.472925	+	0.881103i	$0.343198\pi$
$878$	−42317.2	−1.62658
$879$	13295.6	0.510180
$880$	0	0
$881$	14654.9	0.560425	0.280213	−	0.959938i	$-0.409595\pi$
$881$	14654.9	0.560425	0.280213	+	0.959938i	$0.409595\pi$
$882$	11802.7	0.450589
$883$	21906.9	0.834911	0.417455	−	0.908697i	$-0.362922\pi$
$883$	21906.9	0.834911	0.417455	+	0.908697i	$0.362922\pi$
$884$	−209132.	−7.95687
$885$	8860.52	0.336546
$886$	−53065.6	−2.01216
$887$	19138.1	0.724457	0.362229	−	0.932089i	$-0.382016\pi$
$887$	19138.1	0.724457	0.362229	+	0.932089i	$0.382016\pi$
$888$	55713.8	2.10544
$889$	−5613.65	−0.211784
$890$	−4838.69	−0.182240
$891$	0	0
$892$	−44813.8	−1.68215
$893$	−8651.66	−0.324207
$894$	11004.7	0.411692
$895$	−10167.6	−0.379740
$896$	117947.	4.39768
$897$	39542.9	1.47190
$898$	50838.0	1.88918
$899$	36336.1	1.34803
$900$	4921.20	0.182267
$901$	44331.7	1.63918
$902$	0	0
$903$	3487.15	0.128510
$904$	−74185.1	−2.72938
$905$	21253.9	0.780666
$906$	20256.5	0.742801
$907$	−35415.8	−1.29654	−0.648271	−	0.761410i	$-0.724508\pi$
$907$	−35415.8	−1.29654	−0.648271	+	0.761410i	$0.724508\pi$
$908$	32454.3	1.18616
$909$	4999.12	0.182409
$910$	58954.1	2.14759
$911$	−30302.1	−1.10203	−0.551017	−	0.834494i	$-0.685760\pi$
$911$	−30302.1	−1.10203	−0.551017	+	0.834494i	$0.685760\pi$
$912$	−18871.9	−0.685208
$913$	0	0
$914$	−84310.3	−3.05113
$915$	−2579.13	−0.0931839
$916$	−74231.9	−2.67761
$917$	44906.3	1.61716
$918$	15791.7	0.567761
$919$	−21012.5	−0.754230	−0.377115	−	0.926166i	$-0.623084\pi$
$919$	−21012.5	−0.754230	−0.377115	+	0.926166i	$0.623084\pi$
$920$	−55922.8	−2.00404
$921$	−1768.53	−0.0632736
$922$	21104.3	0.753832
$923$	−22859.2	−0.815191
$924$	0	0
$925$	−6123.66	−0.217670
$926$	−21475.2	−0.762116
$927$	−4237.38	−0.150134
$928$	185775.	6.57152
$929$	−18059.2	−0.637785	−0.318893	−	0.947791i	$-0.603311\pi$
$929$	−18059.2	−0.637785	−0.318893	+	0.947791i	$0.603311\pi$
$930$	−11255.9	−0.396876
$931$	6304.68	0.221942
$932$	−133742.	−4.70050
$933$	28845.3	1.01217
$934$	81695.7	2.86206
$935$	0	0
$936$	60969.4	2.12911
$937$	22768.8	0.793835	0.396917	−	0.917854i	$-0.370080\pi$
$937$	22768.8	0.793835	0.396917	+	0.917854i	$0.370080\pi$
$938$	48724.0	1.69605
$939$	−294.861	−0.0102475
$940$	−36008.3	−1.24943
$941$	−11156.0	−0.386476	−0.193238	−	0.981152i	$-0.561899\pi$
$941$	−11156.0	−0.386476	−0.193238	+	0.981152i	$0.561899\pi$
$942$	−30520.4	−1.05564
$943$	−3743.81	−0.129284
$944$	−141419.	−4.87583
$945$	−3259.47	−0.112202
$946$	0	0
$947$	8012.92	0.274958	0.137479	−	0.990505i	$-0.456100\pi$
$947$	8012.92	0.274958	0.137479	+	0.990505i	$0.456100\pi$
$948$	14897.3	0.510381
$949$	−52731.9	−1.80374
$950$	3590.27	0.122614
$951$	10168.0	0.346710
$952$	−195892.	−6.66902
$953$	−38789.4	−1.31848	−0.659241	−	0.751932i	$-0.729122\pi$
$953$	−38789.4	−1.31848	−0.659241	+	0.751932i	$0.729122\pi$
$954$	−20377.7	−0.691564
$955$	7733.07	0.262028
$956$	−64418.4	−2.17933
$957$	0	0
$958$	−27011.7	−0.910968
$959$	−35057.9	−1.18048
$960$	−28818.8	−0.968879
$961$	−10941.0	−0.367258
$962$	−119619.	−4.00903
$963$	2478.75	0.0829454
$964$	−28079.3	−0.938146
$965$	11500.3	0.383637
$966$	58400.2	1.94513
$967$	1352.75	0.0449859	0.0224930	−	0.999747i	$-0.492840\pi$
$967$	1352.75	0.0449859	0.0224930	+	0.999747i	$0.492840\pi$
$968$	0	0
$969$	8435.48	0.279656
$970$	10702.9	0.354276
$971$	23491.3	0.776387	0.388194	−	0.921578i	$-0.373099\pi$
$971$	23491.3	0.776387	0.388194	+	0.921578i	$0.373099\pi$
$972$	−5314.89	−0.175386
$973$	71556.1	2.35764
$974$	6595.39	0.216971
$975$	−6701.32	−0.220117
$976$	41164.2	1.35004
$977$	50287.2	1.64670	0.823352	−	0.567531i	$-0.192101\pi$
$977$	50287.2	1.64670	0.823352	+	0.567531i	$0.192101\pi$
$978$	19866.5	0.649552
$979$	0	0
$980$	26240.2	0.855318
$981$	11417.2	0.371582
$982$	82408.1	2.67795
$983$	−21791.5	−0.707061	−0.353531	−	0.935423i	$-0.615019\pi$
$983$	−21791.5	−0.707061	−0.353531	+	0.935423i	$0.615019\pi$
$984$	−5772.41	−0.187010
$985$	4874.33	0.157674
$986$	−154792.	−4.99957
$987$	23849.5	0.769136
$988$	51350.2	1.65351
$989$	7102.05	0.228344
$990$	0	0
$991$	−26145.6	−0.838086	−0.419043	−	0.907966i	$-0.637634\pi$
$991$	−26145.6	−0.838086	−0.419043	+	0.907966i	$0.637634\pi$
$992$	96374.3	3.08456
$993$	21978.1	0.702369
$994$	−33760.4	−1.07728
$995$	−20401.0	−0.650006
$996$	33510.9	1.06610
$997$	58479.6	1.85764	0.928820	−	0.370532i	$-0.120825\pi$
$997$	58479.6	1.85764	0.928820	+	0.370532i	$0.120825\pi$
$998$	107184.	3.39966
$999$	6613.55	0.209453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bd.1.7	yes	7
11.10	odd	2		1815.4.a.bc.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.4.a.bc.1.1	✓	7	11.10	odd	2
1815.4.a.bd.1.7	yes	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+5.46553 q^{2} -3.00000 q^{3} +21.8720 q^{4} +5.00000 q^{5} -16.3966 q^{6} +24.1442 q^{7} +75.8177 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.46553 q^{2} -3.00000 q^{3} +21.8720 q^{4} +5.00000 q^{5} -16.3966 q^{6} +24.1442 q^{7} +75.8177 q^{8} +9.00000 q^{9} +27.3276 q^{10} -65.6160 q^{12} +89.3509 q^{13} +131.961 q^{14} -15.0000 q^{15} +239.408 q^{16} -107.012 q^{17} +49.1897 q^{18} +26.2757 q^{19} +109.360 q^{20} -72.4327 q^{21} -147.519 q^{23} -227.453 q^{24} +25.0000 q^{25} +488.350 q^{26} -27.0000 q^{27} +528.082 q^{28} +264.656 q^{29} -81.9829 q^{30} +137.295 q^{31} +701.949 q^{32} -584.879 q^{34} +120.721 q^{35} +196.848 q^{36} -244.946 q^{37} +143.611 q^{38} -268.053 q^{39} +379.089 q^{40} +25.3785 q^{41} -395.883 q^{42} -48.1433 q^{43} +45.0000 q^{45} -806.269 q^{46} -329.264 q^{47} -718.224 q^{48} +239.943 q^{49} +136.638 q^{50} +321.037 q^{51} +1954.28 q^{52} -414.267 q^{53} -147.569 q^{54} +1830.56 q^{56} -78.8272 q^{57} +1446.49 q^{58} -590.701 q^{59} -328.080 q^{60} +171.942 q^{61} +750.392 q^{62} +217.298 q^{63} +1921.26 q^{64} +446.754 q^{65} +369.231 q^{67} -2340.57 q^{68} +442.557 q^{69} +659.804 q^{70} -255.837 q^{71} +682.359 q^{72} -590.167 q^{73} -1338.76 q^{74} -75.0000 q^{75} +574.703 q^{76} -1465.05 q^{78} -227.037 q^{79} +1197.04 q^{80} +81.0000 q^{81} +138.707 q^{82} -510.712 q^{83} -1584.25 q^{84} -535.062 q^{85} -263.128 q^{86} -793.969 q^{87} -177.062 q^{89} +245.949 q^{90} +2157.31 q^{91} -3226.53 q^{92} -411.886 q^{93} -1799.60 q^{94} +131.379 q^{95} -2105.85 q^{96} +391.649 q^{97} +1311.42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 21 q^{3} + 49 q^{4} + 35 q^{5} - 3 q^{6} - 16 q^{7} + 30 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + q^2 - 21 * q^3 + 49 * q^4 + 35 * q^5 - 3 * q^6 - 16 * q^7 + 30 * q^8 + 63 * q^9	\( 7 q + q^{2} - 21 q^{3} + 49 q^{4} + 35 q^{5} - 3 q^{6} - 16 q^{7} + 30 q^{8} + 63 q^{9} + 5 q^{10} - 147 q^{12} + 90 q^{13} + 68 q^{14} - 105 q^{15} + 337 q^{16} - 67 q^{17} + 9 q^{18} + 270 q^{19} + 245 q^{20} + 48 q^{21} - 241 q^{23} - 90 q^{24} + 175 q^{25} + 36 q^{26} - 189 q^{27} - 236 q^{28} - 26 q^{29} - 15 q^{30} + 797 q^{31} + 351 q^{32} + 457 q^{34} - 80 q^{35} + 441 q^{36} - 310 q^{37} + 22 q^{38} - 270 q^{39} + 150 q^{40} + 108 q^{41} - 204 q^{42} + 812 q^{43} + 315 q^{45} - 2099 q^{46} + 671 q^{47} - 1011 q^{48} + 835 q^{49} + 25 q^{50} + 201 q^{51} + 1396 q^{52} + 347 q^{53} - 27 q^{54} + 2698 q^{56} - 810 q^{57} + 1212 q^{58} - 888 q^{59} - 735 q^{60} + q^{61} - 43 q^{62} - 144 q^{63} + 3316 q^{64} + 450 q^{65} - 118 q^{67} - 3975 q^{68} + 723 q^{69} + 340 q^{70} - 622 q^{71} + 270 q^{72} - 252 q^{73} + 458 q^{74} - 525 q^{75} + 5016 q^{76} - 108 q^{78} - 459 q^{79} + 1685 q^{80} + 567 q^{81} - 944 q^{82} - 1144 q^{83} + 708 q^{84} - 335 q^{85} + 2596 q^{86} + 78 q^{87} + 2072 q^{89} + 45 q^{90} + 3244 q^{91} - 1267 q^{92} - 2391 q^{93} - 2419 q^{94} + 1350 q^{95} - 1053 q^{96} + 2388 q^{97} + 5417 q^{98}+O(q^{100}) \) 7 * q + q^2 - 21 * q^3 + 49 * q^4 + 35 * q^5 - 3 * q^6 - 16 * q^7 + 30 * q^8 + 63 * q^9 + 5 * q^10 - 147 * q^12 + 90 * q^13 + 68 * q^14 - 105 * q^15 + 337 * q^16 - 67 * q^17 + 9 * q^18 + 270 * q^19 + 245 * q^20 + 48 * q^21 - 241 * q^23 - 90 * q^24 + 175 * q^25 + 36 * q^26 - 189 * q^27 - 236 * q^28 - 26 * q^29 - 15 * q^30 + 797 * q^31 + 351 * q^32 + 457 * q^34 - 80 * q^35 + 441 * q^36 - 310 * q^37 + 22 * q^38 - 270 * q^39 + 150 * q^40 + 108 * q^41 - 204 * q^42 + 812 * q^43 + 315 * q^45 - 2099 * q^46 + 671 * q^47 - 1011 * q^48 + 835 * q^49 + 25 * q^50 + 201 * q^51 + 1396 * q^52 + 347 * q^53 - 27 * q^54 + 2698 * q^56 - 810 * q^57 + 1212 * q^58 - 888 * q^59 - 735 * q^60 + q^61 - 43 * q^62 - 144 * q^63 + 3316 * q^64 + 450 * q^65 - 118 * q^67 - 3975 * q^68 + 723 * q^69 + 340 * q^70 - 622 * q^71 + 270 * q^72 - 252 * q^73 + 458 * q^74 - 525 * q^75 + 5016 * q^76 - 108 * q^78 - 459 * q^79 + 1685 * q^80 + 567 * q^81 - 944 * q^82 - 1144 * q^83 + 708 * q^84 - 335 * q^85 + 2596 * q^86 + 78 * q^87 + 2072 * q^89 + 45 * q^90 + 3244 * q^91 - 1267 * q^92 - 2391 * q^93 - 2419 * q^94 + 1350 * q^95 - 1053 * q^96 + 2388 * q^97 + 5417 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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