LMFDB - Embedded newform 1815.4.a.bn.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$107.088466660$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 59 x^{10} + 269 x^{9} + 1318 x^{8} - 5253 x^{7} - 13369 x^{6} + 44853 x^{5} + \cdots + 17600 $ x^12 - 5x^11 - 59x^10 + 269x^9 + 1318x^8 - 5253x^7 - 13369x^6 + 44853x^5 + 57849x^4 - 151000x^3 - 76540x^2 + 100800*x + 17600
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-3.77011$ 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)

$f(q)$	$=$	$q+4.77011 q^{2} +3.00000 q^{3} +14.7539 q^{4} +5.00000 q^{5} +14.3103 q^{6} -30.6111 q^{7} +32.2168 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.77011 q^{2} +3.00000 q^{3} +14.7539 q^{4} +5.00000 q^{5} +14.3103 q^{6} -30.6111 q^{7} +32.2168 q^{8} +9.00000 q^{9} +23.8505 q^{10} +44.2617 q^{12} +56.2726 q^{13} -146.018 q^{14} +15.0000 q^{15} +35.6464 q^{16} +124.169 q^{17} +42.9309 q^{18} -46.6234 q^{19} +73.7695 q^{20} -91.8333 q^{21} +155.630 q^{23} +96.6505 q^{24} +25.0000 q^{25} +268.426 q^{26} +27.0000 q^{27} -451.633 q^{28} +107.001 q^{29} +71.5516 q^{30} -93.6551 q^{31} -87.6974 q^{32} +592.299 q^{34} -153.055 q^{35} +132.785 q^{36} +162.865 q^{37} -222.399 q^{38} +168.818 q^{39} +161.084 q^{40} +355.195 q^{41} -438.054 q^{42} +116.195 q^{43} +45.0000 q^{45} +742.371 q^{46} -474.877 q^{47} +106.939 q^{48} +594.039 q^{49} +119.253 q^{50} +372.507 q^{51} +830.241 q^{52} -276.676 q^{53} +128.793 q^{54} -986.192 q^{56} -139.870 q^{57} +510.404 q^{58} -443.269 q^{59} +221.309 q^{60} +261.592 q^{61} -446.745 q^{62} -275.500 q^{63} -703.497 q^{64} +281.363 q^{65} -117.384 q^{67} +1831.98 q^{68} +466.890 q^{69} -730.091 q^{70} +967.379 q^{71} +289.951 q^{72} +773.718 q^{73} +776.882 q^{74} +75.0000 q^{75} -687.877 q^{76} +805.279 q^{78} -383.586 q^{79} +178.232 q^{80} +81.0000 q^{81} +1694.32 q^{82} +1079.86 q^{83} -1354.90 q^{84} +620.845 q^{85} +554.265 q^{86} +321.002 q^{87} -960.079 q^{89} +214.655 q^{90} -1722.57 q^{91} +2296.15 q^{92} -280.965 q^{93} -2265.21 q^{94} -233.117 q^{95} -263.092 q^{96} +1588.52 q^{97} +2833.63 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9} + 35 q^{10} + 147 q^{12} + 172 q^{13} - 30 q^{14} + 180 q^{15} + 161 q^{16} + 317 q^{17} + 63 q^{18} + 237 q^{19} + 245 q^{20} + 231 q^{21} + 210 q^{23} + 333 q^{24} + 300 q^{25} + 8 q^{26} + 324 q^{27} + 542 q^{28} + 759 q^{29} + 105 q^{30} - 193 q^{31} + 410 q^{32} - 78 q^{34} + 385 q^{35} + 441 q^{36} + 286 q^{37} - 168 q^{38} + 516 q^{39} + 555 q^{40} + 1189 q^{41} - 90 q^{42} + 775 q^{43} + 540 q^{45} + 529 q^{46} + 382 q^{47} + 483 q^{48} + 1195 q^{49} + 175 q^{50} + 951 q^{51} + 1741 q^{52} + 275 q^{53} + 189 q^{54} - 419 q^{56} + 711 q^{57} - 418 q^{58} + 646 q^{59} + 735 q^{60} + 1340 q^{61} + 983 q^{62} + 693 q^{63} - 1489 q^{64} + 860 q^{65} - 185 q^{67} + 3322 q^{68} + 630 q^{69} - 150 q^{70} - 932 q^{71} + 999 q^{72} + 2860 q^{73} + 4187 q^{74} + 900 q^{75} + 1594 q^{76} + 24 q^{78} + 1429 q^{79} + 805 q^{80} + 972 q^{81} - 30 q^{82} + 2590 q^{83} + 1626 q^{84} + 1585 q^{85} - 3195 q^{86} + 2277 q^{87} - 473 q^{89} + 315 q^{90} - 4302 q^{91} + 5462 q^{92} - 579 q^{93} + 2875 q^{94} + 1185 q^{95} + 1230 q^{96} + 318 q^{97} - 194 q^{98}+O(q^{100}) \) 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9 + 35 * q^10 + 147 * q^12 + 172 * q^13 - 30 * q^14 + 180 * q^15 + 161 * q^16 + 317 * q^17 + 63 * q^18 + 237 * q^19 + 245 * q^20 + 231 * q^21 + 210 * q^23 + 333 * q^24 + 300 * q^25 + 8 * q^26 + 324 * q^27 + 542 * q^28 + 759 * q^29 + 105 * q^30 - 193 * q^31 + 410 * q^32 - 78 * q^34 + 385 * q^35 + 441 * q^36 + 286 * q^37 - 168 * q^38 + 516 * q^39 + 555 * q^40 + 1189 * q^41 - 90 * q^42 + 775 * q^43 + 540 * q^45 + 529 * q^46 + 382 * q^47 + 483 * q^48 + 1195 * q^49 + 175 * q^50 + 951 * q^51 + 1741 * q^52 + 275 * q^53 + 189 * q^54 - 419 * q^56 + 711 * q^57 - 418 * q^58 + 646 * q^59 + 735 * q^60 + 1340 * q^61 + 983 * q^62 + 693 * q^63 - 1489 * q^64 + 860 * q^65 - 185 * q^67 + 3322 * q^68 + 630 * q^69 - 150 * q^70 - 932 * q^71 + 999 * q^72 + 2860 * q^73 + 4187 * q^74 + 900 * q^75 + 1594 * q^76 + 24 * q^78 + 1429 * q^79 + 805 * q^80 + 972 * q^81 - 30 * q^82 + 2590 * q^83 + 1626 * q^84 + 1585 * q^85 - 3195 * q^86 + 2277 * q^87 - 473 * q^89 + 315 * q^90 - 4302 * q^91 + 5462 * q^92 - 579 * q^93 + 2875 * q^94 + 1185 * q^95 + 1230 * q^96 + 318 * q^97 - 194 * 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 $

$2$	4.77011	1.68649	0.843243	−	0.537532i	$-0.180643\pi$
$2$	4.77011	1.68649	0.843243	+	0.537532i	$0.180643\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.7539	1.84424
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	14.3103	0.973694
$7$	−30.6111	−1.65284	−0.826422	−	0.563052i	$-0.809627\pi$
$7$	−30.6111	−1.65284	−0.826422	+	0.563052i	$0.809627\pi$
$8$	32.2168	1.42380
$9$	9.00000	0.333333
$10$	23.8505	0.754220
$11$	0	0
$11$	0	0
$12$	44.2617	1.06477
$13$	56.2726	1.20056	0.600278	−	0.799792i	$-0.295057\pi$
$13$	56.2726	1.20056	0.600278	+	0.799792i	$0.295057\pi$
$14$	−146.018	−2.78750
$15$	15.0000	0.258199
$16$	35.6464	0.556975
$17$	124.169	1.77149	0.885747	−	0.464168i	$-0.153647\pi$
$17$	124.169	1.77149	0.885747	+	0.464168i	$0.153647\pi$
$18$	42.9309	0.562162
$19$	−46.6234	−0.562955	−0.281477	−	0.959568i	$-0.590824\pi$
$19$	−46.6234	−0.562955	−0.281477	+	0.959568i	$0.590824\pi$
$20$	73.7695	0.824768
$21$	−91.8333	−0.954270
$22$	0	0
$23$	155.630	1.41092	0.705458	−	0.708751i	$-0.250741\pi$
$23$	155.630	1.41092	0.705458	+	0.708751i	$0.250741\pi$
$24$	96.6505	0.822029
$25$	25.0000	0.200000
$26$	268.426	2.02472
$27$	27.0000	0.192450
$28$	−451.633	−3.04824
$29$	107.001	0.685155	0.342578	−	0.939490i	$-0.388700\pi$
$29$	107.001	0.685155	0.342578	+	0.939490i	$0.388700\pi$
$30$	71.5516	0.435449
$31$	−93.6551	−0.542611	−0.271306	−	0.962493i	$-0.587455\pi$
$31$	−93.6551	−0.542611	−0.271306	+	0.962493i	$0.587455\pi$
$32$	−87.6974	−0.484464
$33$	0	0
$34$	592.299	2.98760
$35$	−153.055	−0.739174
$36$	132.785	0.614746
$37$	162.865	0.723644	0.361822	−	0.932247i	$-0.382155\pi$
$37$	162.865	0.723644	0.361822	+	0.932247i	$0.382155\pi$
$38$	−222.399	−0.949416
$39$	168.818	0.693141
$40$	161.084	0.636741
$41$	355.195	1.35298	0.676489	−	0.736452i	$-0.263500\pi$
$41$	355.195	1.35298	0.676489	+	0.736452i	$0.263500\pi$
$42$	−438.054	−1.60936
$43$	116.195	0.412085	0.206042	−	0.978543i	$-0.433942\pi$
$43$	116.195	0.412085	0.206042	+	0.978543i	$0.433942\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	742.371	2.37949
$47$	−474.877	−1.47379	−0.736893	−	0.676010i	$-0.763708\pi$
$47$	−474.877	−1.47379	−0.736893	+	0.676010i	$0.763708\pi$
$48$	106.939	0.321570
$49$	594.039	1.73189
$50$	119.253	0.337297
$51$	372.507	1.02277
$52$	830.241	2.21411
$53$	−276.676	−0.717065	−0.358532	−	0.933517i	$-0.616723\pi$
$53$	−276.676	−0.717065	−0.358532	+	0.933517i	$0.616723\pi$
$54$	128.793	0.324565
$55$	0	0
$56$	−986.192	−2.35331
$57$	−139.870	−0.325022
$58$	510.404	1.15551
$59$	−443.269	−0.978115	−0.489057	−	0.872252i	$-0.662659\pi$
$59$	−443.269	−0.978115	−0.489057	+	0.872252i	$0.662659\pi$
$60$	221.309	0.476180
$61$	261.592	0.549071	0.274536	−	0.961577i	$-0.411476\pi$
$61$	261.592	0.549071	0.274536	+	0.961577i	$0.411476\pi$
$62$	−446.745	−0.915107
$63$	−275.500	−0.550948
$64$	−703.497	−1.37402
$65$	281.363	0.536905
$66$	0	0
$67$	−117.384	−0.214042	−0.107021	−	0.994257i	$-0.534131\pi$
$67$	−117.384	−0.214042	−0.107021	+	0.994257i	$0.534131\pi$
$68$	1831.98	3.26706
$69$	466.890	0.814593
$70$	−730.091	−1.24661
$71$	967.379	1.61700	0.808498	−	0.588499i	$-0.200281\pi$
$71$	967.379	1.61700	0.808498	+	0.588499i	$0.200281\pi$
$72$	289.951	0.474599
$73$	773.718	1.24050	0.620252	−	0.784403i	$-0.287030\pi$
$73$	773.718	1.24050	0.620252	+	0.784403i	$0.287030\pi$
$74$	776.882	1.22042
$75$	75.0000	0.115470
$76$	−687.877	−1.03822
$77$	0	0
$78$	805.279	1.16897
$79$	−383.586	−0.546289	−0.273144	−	0.961973i	$-0.588064\pi$
$79$	−383.586	−0.546289	−0.273144	+	0.961973i	$0.588064\pi$
$80$	178.232	0.249087
$81$	81.0000	0.111111
$82$	1694.32	2.28178
$83$	1079.86	1.42807	0.714035	−	0.700110i	$-0.246866\pi$
$83$	1079.86	1.42807	0.714035	+	0.700110i	$0.246866\pi$
$84$	−1354.90	−1.75990
$85$	620.845	0.792236
$86$	554.265	0.694976
$87$	321.002	0.395575
$88$	0	0
$89$	−960.079	−1.14346	−0.571731	−	0.820441i	$-0.693728\pi$
$89$	−960.079	−1.14346	−0.571731	+	0.820441i	$0.693728\pi$
$90$	214.655	0.251407
$91$	−1722.57	−1.98433
$92$	2296.15	2.60207
$93$	−280.965	−0.313277
$94$	−2265.21	−2.48552
$95$	−233.117	−0.251761
$96$	−263.092	−0.279706
$97$	1588.52	1.66279	0.831393	−	0.555685i	$-0.187544\pi$
$97$	1588.52	1.66279	0.831393	+	0.555685i	$0.187544\pi$
$98$	2833.63	2.92081
$99$	0	0
$100$	368.848	0.368848
$101$	1005.89	0.990984	0.495492	−	0.868613i	$-0.334988\pi$
$101$	1005.89	0.990984	0.495492	+	0.868613i	$0.334988\pi$
$102$	1776.90	1.72489
$103$	−556.871	−0.532720	−0.266360	−	0.963874i	$-0.585821\pi$
$103$	−556.871	−0.532720	−0.266360	+	0.963874i	$0.585821\pi$
$104$	1812.93	1.70935
$105$	−459.166	−0.426762
$106$	−1319.78	−1.20932
$107$	−56.3252	−0.0508894	−0.0254447	−	0.999676i	$-0.508100\pi$
$107$	−56.3252	−0.0508894	−0.0254447	+	0.999676i	$0.508100\pi$
$108$	398.355	0.354924
$109$	1147.22	1.00811	0.504053	−	0.863673i	$-0.331842\pi$
$109$	1147.22	1.00811	0.504053	+	0.863673i	$0.331842\pi$
$110$	0	0
$111$	488.595	0.417796
$112$	−1091.18	−0.920593
$113$	−908.737	−0.756520	−0.378260	−	0.925699i	$-0.623478\pi$
$113$	−908.737	−0.756520	−0.378260	+	0.925699i	$0.623478\pi$
$114$	−667.196	−0.548146
$115$	778.150	0.630981
$116$	1578.68	1.26359
$117$	506.454	0.400185
$118$	−2114.44	−1.64958
$119$	−3800.95	−2.92800
$120$	483.252	0.367623
$121$	0	0
$122$	1247.82	0.926002
$123$	1065.58	0.781143
$124$	−1381.78	−1.00070
$125$	125.000	0.0894427
$126$	−1314.16	−0.929166
$127$	554.663	0.387546	0.193773	−	0.981046i	$-0.437927\pi$
$127$	554.663	0.387546	0.193773	+	0.981046i	$0.437927\pi$
$128$	−2654.18	−1.83280
$129$	348.586	0.237917
$130$	1342.13	0.905483
$131$	912.163	0.608367	0.304183	−	0.952614i	$-0.401616\pi$
$131$	912.163	0.608367	0.304183	+	0.952614i	$0.401616\pi$
$132$	0	0
$133$	1427.19	0.930476
$134$	−559.936	−0.360978
$135$	135.000	0.0860663
$136$	4000.33	2.52225
$137$	−688.149	−0.429143	−0.214571	−	0.976708i	$-0.568835\pi$
$137$	−688.149	−0.429143	−0.214571	+	0.976708i	$0.568835\pi$
$138$	2227.11	1.37380
$139$	−2841.40	−1.73384	−0.866921	−	0.498445i	$-0.833904\pi$
$139$	−2841.40	−1.73384	−0.866921	+	0.498445i	$0.833904\pi$
$140$	−2258.17	−1.36321
$141$	−1424.63	−0.850890
$142$	4614.50	2.72704
$143$	0	0
$144$	320.818	0.185658
$145$	535.003	0.306411
$146$	3690.71	2.09209
$147$	1782.12	0.999908
$148$	2402.89	1.33457
$149$	79.6417	0.0437886	0.0218943	−	0.999760i	$-0.493030\pi$
$149$	79.6417	0.0437886	0.0218943	+	0.999760i	$0.493030\pi$
$150$	357.758	0.194739
$151$	111.746	0.0602238	0.0301119	−	0.999547i	$-0.490414\pi$
$151$	111.746	0.0602238	0.0301119	+	0.999547i	$0.490414\pi$
$152$	−1502.06	−0.801533
$153$	1117.52	0.590498
$154$	0	0
$155$	−468.276	−0.242663
$156$	2490.72	1.27832
$157$	493.983	0.251109	0.125554	−	0.992087i	$-0.459929\pi$
$157$	493.983	0.251109	0.125554	+	0.992087i	$0.459929\pi$
$158$	−1829.75	−0.921309
$159$	−830.029	−0.413998
$160$	−438.487	−0.216659
$161$	−4764.00	−2.33202
$162$	386.379	0.187387
$163$	1183.83	0.568862	0.284431	−	0.958696i	$-0.408195\pi$
$163$	1183.83	0.568862	0.284431	+	0.958696i	$0.408195\pi$
$164$	5240.51	2.49521
$165$	0	0
$166$	5151.03	2.40842
$167$	2109.81	0.977619	0.488810	−	0.872391i	$-0.337431\pi$
$167$	2109.81	0.977619	0.488810	+	0.872391i	$0.337431\pi$
$168$	−2958.58	−1.35869
$169$	969.611	0.441334
$170$	2961.50	1.33610
$171$	−419.611	−0.187652
$172$	1714.34	0.759982
$173$	−2617.16	−1.15017	−0.575083	−	0.818095i	$-0.695030\pi$
$173$	−2617.16	−1.15017	−0.575083	+	0.818095i	$0.695030\pi$
$174$	1531.21	0.667131
$175$	−765.277	−0.330569
$176$	0	0
$177$	−1329.81	−0.564715
$178$	−4579.68	−1.92843
$179$	−1460.14	−0.609700	−0.304850	−	0.952400i	$-0.598606\pi$
$179$	−1460.14	−0.609700	−0.304850	+	0.952400i	$0.598606\pi$
$180$	663.926	0.274923
$181$	233.327	0.0958178	0.0479089	−	0.998852i	$-0.484744\pi$
$181$	233.327	0.0958178	0.0479089	+	0.998852i	$0.484744\pi$
$182$	−8216.83	−3.34655
$183$	784.775	0.317007
$184$	5013.90	2.00886
$185$	814.324	0.323623
$186$	−1340.23	−0.528337
$187$	0	0
$188$	−7006.29	−2.71801
$189$	−826.499	−0.318090
$190$	−1111.99	−0.424592
$191$	−1550.54	−0.587400	−0.293700	−	0.955898i	$-0.594887\pi$
$191$	−1550.54	−0.587400	−0.293700	+	0.955898i	$0.594887\pi$
$192$	−2110.49	−0.793290
$193$	610.399	0.227655	0.113828	−	0.993501i	$-0.463689\pi$
$193$	610.399	0.227655	0.113828	+	0.993501i	$0.463689\pi$
$194$	7577.43	2.80427
$195$	844.090	0.309982
$196$	8764.39	3.19402
$197$	−4191.64	−1.51595	−0.757974	−	0.652284i	$-0.773811\pi$
$197$	−4191.64	−1.51595	−0.757974	+	0.652284i	$0.773811\pi$
$198$	0	0
$199$	−3807.81	−1.35643	−0.678213	−	0.734865i	$-0.737245\pi$
$199$	−3807.81	−1.35643	−0.678213	+	0.734865i	$0.737245\pi$
$200$	805.421	0.284759
$201$	−352.153	−0.123577
$202$	4798.18	1.67128
$203$	−3275.40	−1.13245
$204$	5495.93	1.88624
$205$	1775.97	0.605070
$206$	−2656.33	−0.898425
$207$	1400.67	0.470306
$208$	2005.92	0.668680
$209$	0	0
$210$	−2190.27	−0.719729
$211$	−2005.84	−0.654444	−0.327222	−	0.944947i	$-0.606113\pi$
$211$	−2005.84	−0.654444	−0.327222	+	0.944947i	$0.606113\pi$
$212$	−4082.06	−1.32244
$213$	2902.14	0.933573
$214$	−268.677	−0.0858243
$215$	580.977	0.184290
$216$	869.854	0.274010
$217$	2866.88	0.896852
$218$	5472.35	1.70016
$219$	2321.15	0.716205
$220$	0	0
$221$	6987.32	2.12678
$222$	2330.65	0.704607
$223$	118.849	0.0356893	0.0178446	−	0.999841i	$-0.494320\pi$
$223$	118.849	0.0356893	0.0178446	+	0.999841i	$0.494320\pi$
$224$	2684.51	0.800744
$225$	225.000	0.0666667
$226$	−4334.77	−1.27586
$227$	−3094.24	−0.904723	−0.452361	−	0.891835i	$-0.649418\pi$
$227$	−3094.24	−0.904723	−0.452361	+	0.891835i	$0.649418\pi$
$228$	−2063.63	−0.599418
$229$	−4777.06	−1.37850	−0.689251	−	0.724522i	$-0.742060\pi$
$229$	−4777.06	−1.37850	−0.689251	+	0.724522i	$0.742060\pi$
$230$	3711.86	1.06414
$231$	0	0
$232$	3447.22	0.975521
$233$	−1280.20	−0.359953	−0.179976	−	0.983671i	$-0.557602\pi$
$233$	−1280.20	−0.359953	−0.179976	+	0.983671i	$0.557602\pi$
$234$	2415.84	0.674907
$235$	−2374.38	−0.659097
$236$	−6539.95	−1.80388
$237$	−1150.76	−0.315400
$238$	−18130.9	−4.93804
$239$	−5352.78	−1.44871	−0.724357	−	0.689425i	$-0.757863\pi$
$239$	−5352.78	−1.44871	−0.724357	+	0.689425i	$0.757863\pi$
$240$	534.696	0.143810
$241$	−4086.24	−1.09219	−0.546095	−	0.837723i	$-0.683886\pi$
$241$	−4086.24	−1.09219	−0.546095	+	0.837723i	$0.683886\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	3859.50	1.01262
$245$	2970.19	0.774525
$246$	5082.95	1.31739
$247$	−2623.62	−0.675859
$248$	−3017.27	−0.772568
$249$	3239.57	0.824496
$250$	596.263	0.150844
$251$	−5085.21	−1.27879	−0.639394	−	0.768879i	$-0.720815\pi$
$251$	−5085.21	−1.27879	−0.639394	+	0.768879i	$0.720815\pi$
$252$	−4064.70	−1.01608
$253$	0	0
$254$	2645.80	0.653591
$255$	1862.53	0.457398
$256$	−7032.72	−1.71697
$257$	24.5605	0.00596126	0.00298063	−	0.999996i	$-0.499051\pi$
$257$	24.5605	0.00596126	0.00298063	+	0.999996i	$0.499051\pi$
$258$	1662.79	0.401244
$259$	−4985.47	−1.19607
$260$	4151.21	0.990180
$261$	963.005	0.228385
$262$	4351.11	1.02600
$263$	1597.08	0.374449	0.187224	−	0.982317i	$-0.440051\pi$
$263$	1597.08	0.374449	0.187224	+	0.982317i	$0.440051\pi$
$264$	0	0
$265$	−1383.38	−0.320681
$266$	6807.86	1.56924
$267$	−2880.24	−0.660179
$268$	−1731.88	−0.394743
$269$	−3317.70	−0.751985	−0.375992	−	0.926623i	$-0.622698\pi$
$269$	−3317.70	−0.751985	−0.375992	+	0.926623i	$0.622698\pi$
$270$	643.964	0.145150
$271$	4533.49	1.01620	0.508099	−	0.861298i	$-0.330348\pi$
$271$	4533.49	1.01620	0.508099	+	0.861298i	$0.330348\pi$
$272$	4426.18	0.986679
$273$	−5167.70	−1.14565
$274$	−3282.54	−0.723744
$275$	0	0
$276$	6888.45	1.50230
$277$	−6791.06	−1.47305	−0.736526	−	0.676409i	$-0.763535\pi$
$277$	−6791.06	−1.47305	−0.736526	+	0.676409i	$0.763535\pi$
$278$	−13553.8	−2.92410
$279$	−842.896	−0.180870
$280$	−4930.96	−1.05243
$281$	−2304.40	−0.489214	−0.244607	−	0.969622i	$-0.578659\pi$
$281$	−2304.40	−0.489214	−0.244607	+	0.969622i	$0.578659\pi$
$282$	−6795.64	−1.43502
$283$	−1775.83	−0.373012	−0.186506	−	0.982454i	$-0.559716\pi$
$283$	−1775.83	−0.373012	−0.186506	+	0.982454i	$0.559716\pi$
$284$	14272.6	2.98213
$285$	−699.351	−0.145354
$286$	0	0
$287$	−10872.9	−2.23626
$288$	−789.277	−0.161488
$289$	10504.9	2.13819
$290$	2552.02	0.516758
$291$	4765.57	0.960010
$292$	11415.4	2.28778
$293$	−4633.20	−0.923803	−0.461901	−	0.886931i	$-0.652833\pi$
$293$	−4633.20	−0.923803	−0.461901	+	0.886931i	$0.652833\pi$
$294$	8500.88	1.68633
$295$	−2216.35	−0.437426
$296$	5246.99	1.03032
$297$	0	0
$298$	379.899	0.0738489
$299$	8757.71	1.69388
$300$	1106.54	0.212954
$301$	−3556.87	−0.681112
$302$	533.043	0.101567
$303$	3017.66	0.572145
$304$	−1661.96	−0.313552
$305$	1307.96	0.245552
$306$	5330.69	0.995867
$307$	2771.13	0.515168	0.257584	−	0.966256i	$-0.417074\pi$
$307$	2771.13	0.515168	0.257584	+	0.966256i	$0.417074\pi$
$308$	0	0
$309$	−1670.61	−0.307566
$310$	−2233.72	−0.409248
$311$	−9864.73	−1.79864	−0.899321	−	0.437289i	$-0.855939\pi$
$311$	−9864.73	−1.79864	−0.899321	+	0.437289i	$0.855939\pi$
$312$	5438.78	0.986892
$313$	2301.48	0.415615	0.207808	−	0.978170i	$-0.433367\pi$
$313$	2301.48	0.415615	0.207808	+	0.978170i	$0.433367\pi$
$314$	2356.35	0.423492
$315$	−1377.50	−0.246391
$316$	−5659.39	−1.00749
$317$	2329.40	0.412721	0.206360	−	0.978476i	$-0.433838\pi$
$317$	2329.40	0.412721	0.206360	+	0.978476i	$0.433838\pi$
$318$	−3959.33	−0.698201
$319$	0	0
$320$	−3517.49	−0.614480
$321$	−168.976	−0.0293810
$322$	−22724.8	−3.93293
$323$	−5789.18	−0.997271
$324$	1195.07	0.204915
$325$	1406.82	0.240111
$326$	5646.98	0.959379
$327$	3441.65	0.582030
$328$	11443.3	1.92637
$329$	14536.5	2.43594
$330$	0	0
$331$	−129.762	−0.0215480	−0.0107740	−	0.999942i	$-0.503430\pi$
$331$	−129.762	−0.0215480	−0.0107740	+	0.999942i	$0.503430\pi$
$332$	15932.1	2.63370
$333$	1465.78	0.241215
$334$	10064.0	1.64874
$335$	−586.922	−0.0957223
$336$	−3273.53	−0.531505
$337$	1448.36	0.234117	0.117058	−	0.993125i	$-0.462654\pi$
$337$	1448.36	0.234117	0.117058	+	0.993125i	$0.462654\pi$
$338$	4625.14	0.744304
$339$	−2726.21	−0.436777
$340$	9159.89	1.46107
$341$	0	0
$342$	−2001.59	−0.316472
$343$	−7684.57	−1.20970
$344$	3743.45	0.586725
$345$	2334.45	0.364297
$346$	−12484.1	−1.93974
$347$	4375.83	0.676965	0.338483	−	0.940973i	$-0.390086\pi$
$347$	4375.83	0.676965	0.338483	+	0.940973i	$0.390086\pi$
$348$	4736.03	0.729533
$349$	−734.973	−0.112728	−0.0563642	−	0.998410i	$-0.517951\pi$
$349$	−734.973	−0.112728	−0.0563642	+	0.998410i	$0.517951\pi$
$350$	−3650.45	−0.557500
$351$	1519.36	0.231047
$352$	0	0
$353$	8217.01	1.23894	0.619472	−	0.785018i	$-0.287347\pi$
$353$	8217.01	1.23894	0.619472	+	0.785018i	$0.287347\pi$
$354$	−6343.33	−0.952384
$355$	4836.89	0.723143
$356$	−14164.9	−2.10882
$357$	−11402.8	−1.69048
$358$	−6965.04	−1.02825
$359$	6252.36	0.919184	0.459592	−	0.888130i	$-0.347996\pi$
$359$	6252.36	0.919184	0.459592	+	0.888130i	$0.347996\pi$
$360$	1449.76	0.212247
$361$	−4685.26	−0.683082
$362$	1112.99	0.161596
$363$	0	0
$364$	−25414.6	−3.65958
$365$	3868.59	0.554770
$366$	3743.46	0.534627
$367$	−6046.64	−0.860033	−0.430017	−	0.902821i	$-0.641492\pi$
$367$	−6046.64	−0.860033	−0.430017	+	0.902821i	$0.641492\pi$
$368$	5547.65	0.785846
$369$	3196.75	0.450993
$370$	3884.41	0.545786
$371$	8469.37	1.18520
$372$	−4145.34	−0.577757
$373$	4300.69	0.597000	0.298500	−	0.954410i	$-0.403514\pi$
$373$	4300.69	0.597000	0.298500	+	0.954410i	$0.403514\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	−15299.0	−2.09837
$377$	6021.20	0.822567
$378$	−3942.49	−0.536454
$379$	4421.89	0.599307	0.299654	−	0.954048i	$-0.403129\pi$
$379$	4421.89	0.599307	0.299654	+	0.954048i	$0.403129\pi$
$380$	−3439.39	−0.464307
$381$	1663.99	0.223750
$382$	−7396.26	−0.990643
$383$	7075.44	0.943964	0.471982	−	0.881608i	$-0.343539\pi$
$383$	7075.44	0.943964	0.471982	+	0.881608i	$0.343539\pi$
$384$	−7962.53	−1.05817
$385$	0	0
$386$	2911.67	0.383938
$387$	1045.76	0.137362
$388$	23436.9	3.06657
$389$	−13244.2	−1.72624	−0.863122	−	0.504996i	$-0.831494\pi$
$389$	−13244.2	−1.72624	−0.863122	+	0.504996i	$0.831494\pi$
$390$	4026.40	0.522781
$391$	19324.4	2.49943
$392$	19138.0	2.46586
$393$	2736.49	0.351241
$394$	−19994.6	−2.55663
$395$	−1917.93	−0.244308
$396$	0	0
$397$	11266.6	1.42432	0.712162	−	0.702015i	$-0.247716\pi$
$397$	11266.6	1.42432	0.712162	+	0.702015i	$0.247716\pi$
$398$	−18163.7	−2.28759
$399$	4281.58	0.537211
$400$	891.161	0.111395
$401$	−2452.55	−0.305422	−0.152711	−	0.988271i	$-0.548800\pi$
$401$	−2452.55	−0.305422	−0.152711	+	0.988271i	$0.548800\pi$
$402$	−1679.81	−0.208411
$403$	−5270.22	−0.651435
$404$	14840.7	1.82761
$405$	405.000	0.0496904
$406$	−15624.0	−1.90987
$407$	0	0
$408$	12001.0	1.45622
$409$	−644.955	−0.0779730	−0.0389865	−	0.999240i	$-0.512413\pi$
$409$	−644.955	−0.0779730	−0.0389865	+	0.999240i	$0.512413\pi$
$410$	8471.59	1.02044
$411$	−2064.45	−0.247766
$412$	−8216.02	−0.982462
$413$	13569.0	1.61667
$414$	6681.34	0.793164
$415$	5399.29	0.638652
$416$	−4934.97	−0.581626
$417$	−8524.19	−1.00103
$418$	0	0
$419$	−10785.2	−1.25750	−0.628749	−	0.777608i	$-0.716433\pi$
$419$	−10785.2	−1.25750	−0.628749	+	0.777608i	$0.716433\pi$
$420$	−6774.50	−0.787051
$421$	−2085.76	−0.241458	−0.120729	−	0.992686i	$-0.538523\pi$
$421$	−2085.76	−0.241458	−0.120729	+	0.992686i	$0.538523\pi$
$422$	−9568.07	−1.10371
$423$	−4273.89	−0.491262
$424$	−8913.64	−1.02095
$425$	3104.22	0.354299
$426$	13843.5	1.57446
$427$	−8007.60	−0.907529
$428$	−831.017	−0.0938521
$429$	0	0
$430$	2771.32	0.310803
$431$	14138.9	1.58015	0.790077	−	0.613007i	$-0.210040\pi$
$431$	14138.9	1.58015	0.790077	+	0.613007i	$0.210040\pi$
$432$	962.453	0.107190
$433$	8611.23	0.955726	0.477863	−	0.878434i	$-0.341412\pi$
$433$	8611.23	0.955726	0.477863	+	0.878434i	$0.341412\pi$
$434$	13675.3	1.51253
$435$	1605.01	0.176906
$436$	16925.9	1.85919
$437$	−7256.00	−0.794283
$438$	11072.1	1.20787
$439$	3469.04	0.377149	0.188574	−	0.982059i	$-0.439613\pi$
$439$	3469.04	0.377149	0.188574	+	0.982059i	$0.439613\pi$
$440$	0	0
$441$	5346.35	0.577297
$442$	33330.2	3.58678
$443$	964.877	0.103482	0.0517412	−	0.998661i	$-0.483523\pi$
$443$	964.877	0.103482	0.0517412	+	0.998661i	$0.483523\pi$
$444$	7208.68	0.770515
$445$	−4800.40	−0.511372
$446$	566.922	0.0601895
$447$	238.925	0.0252814
$448$	21534.8	2.27104
$449$	14799.5	1.55553	0.777764	−	0.628556i	$-0.216354\pi$
$449$	14799.5	1.55553	0.777764	+	0.628556i	$0.216354\pi$
$450$	1073.27	0.112432
$451$	0	0
$452$	−13407.4	−1.39520
$453$	335.239	0.0347703
$454$	−14759.9	−1.52580
$455$	−8612.83	−0.887420
$456$	−4506.17	−0.462765
$457$	7910.39	0.809699	0.404849	−	0.914383i	$-0.367324\pi$
$457$	7910.39	0.809699	0.404849	+	0.914383i	$0.367324\pi$
$458$	−22787.1	−2.32483
$459$	3352.56	0.340924
$460$	11480.7	1.16368
$461$	4733.02	0.478175	0.239087	−	0.970998i	$-0.423152\pi$
$461$	4733.02	0.478175	0.239087	+	0.970998i	$0.423152\pi$
$462$	0	0
$463$	5718.63	0.574011	0.287006	−	0.957929i	$-0.407340\pi$
$463$	5718.63	0.574011	0.287006	+	0.957929i	$0.407340\pi$
$464$	3814.19	0.381615
$465$	−1404.83	−0.140102
$466$	−6106.71	−0.607055
$467$	4319.01	0.427965	0.213983	−	0.976837i	$-0.431356\pi$
$467$	4319.01	0.427965	0.213983	+	0.976837i	$0.431356\pi$
$468$	7472.17	0.738037
$469$	3593.26	0.353777
$470$	−11326.1	−1.11156
$471$	1481.95	0.144978
$472$	−14280.7	−1.39264
$473$	0	0
$474$	−5489.24	−0.531918
$475$	−1165.59	−0.112591
$476$	−56078.8	−5.39993
$477$	−2490.09	−0.239022
$478$	−25533.3	−2.44324
$479$	−15592.1	−1.48731	−0.743656	−	0.668562i	$-0.766910\pi$
$479$	−15592.1	−1.48731	−0.743656	+	0.668562i	$0.766910\pi$
$480$	−1315.46	−0.125088
$481$	9164.84	0.868774
$482$	−19491.8	−1.84196
$483$	−14292.0	−1.34640
$484$	0	0
$485$	7942.62	0.743620
$486$	1159.14	0.108188
$487$	16177.0	1.50523	0.752617	−	0.658458i	$-0.228791\pi$
$487$	16177.0	1.50523	0.752617	+	0.658458i	$0.228791\pi$
$488$	8427.65	0.781766
$489$	3551.48	0.328433
$490$	14168.1	1.30623
$491$	−7871.14	−0.723461	−0.361731	−	0.932283i	$-0.617814\pi$
$491$	−7871.14	−0.723461	−0.361731	+	0.932283i	$0.617814\pi$
$492$	15721.5	1.44061
$493$	13286.1	1.21375
$494$	−12515.0	−1.13983
$495$	0	0
$496$	−3338.47	−0.302221
$497$	−29612.5	−2.67264
$498$	15453.1	1.39050
$499$	−10729.4	−0.962554	−0.481277	−	0.876569i	$-0.659827\pi$
$499$	−10729.4	−0.962554	−0.481277	+	0.876569i	$0.659827\pi$
$500$	1844.24	0.164954
$501$	6329.44	0.564429
$502$	−24257.0	−2.15666
$503$	−21474.4	−1.90357	−0.951785	−	0.306765i	$-0.900754\pi$
$503$	−21474.4	−1.90357	−0.951785	+	0.306765i	$0.900754\pi$
$504$	−8875.73	−0.784437
$505$	5029.43	0.443181
$506$	0	0
$507$	2908.83	0.254804
$508$	8183.44	0.714727
$509$	−9529.46	−0.829835	−0.414917	−	0.909859i	$-0.636190\pi$
$509$	−9529.46	−0.829835	−0.414917	+	0.909859i	$0.636190\pi$
$510$	8884.49	0.771395
$511$	−23684.3	−2.05036
$512$	−12313.4	−1.06285
$513$	−1258.83	−0.108341
$514$	117.156	0.0100536
$515$	−2784.36	−0.238240
$516$	5143.01	0.438776
$517$	0	0
$518$	−23781.2	−2.01716
$519$	−7851.47	−0.664048
$520$	9064.63	0.764443
$521$	2629.09	0.221079	0.110540	−	0.993872i	$-0.464742\pi$
$521$	2629.09	0.221079	0.110540	+	0.993872i	$0.464742\pi$
$522$	4593.63	0.385168
$523$	5017.51	0.419503	0.209752	−	0.977755i	$-0.432734\pi$
$523$	5017.51	0.419503	0.209752	+	0.977755i	$0.432734\pi$
$524$	13458.0	1.12197
$525$	−2295.83	−0.190854
$526$	7618.23	0.631503
$527$	−11629.1	−0.961233
$528$	0	0
$529$	12053.7	0.990686
$530$	−6598.88	−0.540825
$531$	−3989.43	−0.326038
$532$	21056.7	1.71602
$533$	19987.8	1.62433
$534$	−13739.0	−1.11338
$535$	−281.626	−0.0227584
$536$	−3781.75	−0.304751
$537$	−4380.43	−0.352011
$538$	−15825.8	−1.26821
$539$	0	0
$540$	1991.78	0.158727
$541$	12314.5	0.978639	0.489319	−	0.872105i	$-0.337245\pi$
$541$	12314.5	0.978639	0.489319	+	0.872105i	$0.337245\pi$
$542$	21625.2	1.71381
$543$	699.980	0.0553205
$544$	−10889.3	−0.858226
$545$	5736.09	0.450839
$546$	−24650.5	−1.93213
$547$	−17167.7	−1.34193	−0.670966	−	0.741489i	$-0.734120\pi$
$547$	−17167.7	−1.34193	−0.670966	+	0.741489i	$0.734120\pi$
$548$	−10152.9	−0.791441
$549$	2354.32	0.183024
$550$	0	0
$551$	−4988.73	−0.385711
$552$	15041.7	1.15981
$553$	11742.0	0.902930
$554$	−32394.1	−2.48428
$555$	2442.97	0.186844
$556$	−41921.7	−3.19762
$557$	−3175.46	−0.241560	−0.120780	−	0.992679i	$-0.538540\pi$
$557$	−3175.46	−0.241560	−0.120780	+	0.992679i	$0.538540\pi$
$558$	−4020.70	−0.305036
$559$	6538.63	0.494731
$560$	−5455.88	−0.411702
$561$	0	0
$562$	−10992.2	−0.825053
$563$	−2783.87	−0.208394	−0.104197	−	0.994557i	$-0.533227\pi$
$563$	−2783.87	−0.208394	−0.104197	+	0.994557i	$0.533227\pi$
$564$	−21018.9	−1.56924
$565$	−4543.69	−0.338326
$566$	−8470.92	−0.629080
$567$	−2479.50	−0.183649
$568$	31165.9	2.30227
$569$	19484.7	1.43557	0.717786	−	0.696264i	$-0.245156\pi$
$569$	19484.7	1.43557	0.717786	+	0.696264i	$0.245156\pi$
$570$	−3335.98	−0.245138
$571$	1680.30	0.123150	0.0615749	−	0.998102i	$-0.480388\pi$
$571$	1680.30	0.123150	0.0615749	+	0.998102i	$0.480388\pi$
$572$	0	0
$573$	−4651.63	−0.339136
$574$	−51864.9	−3.77143
$575$	3890.75	0.282183
$576$	−6331.48	−0.458006
$577$	−24595.5	−1.77456	−0.887282	−	0.461228i	$-0.847409\pi$
$577$	−24595.5	−1.77456	−0.887282	+	0.461228i	$0.847409\pi$
$578$	50109.7	3.60603
$579$	1831.20	0.131437
$580$	7893.38	0.565094
$581$	−33055.6	−2.36038
$582$	22732.3	1.61904
$583$	0	0
$584$	24926.7	1.76622
$585$	2532.27	0.178968
$586$	−22100.8	−1.55798
$587$	−20379.8	−1.43299	−0.716496	−	0.697592i	$-0.754255\pi$
$587$	−20379.8	−1.43299	−0.716496	+	0.697592i	$0.754255\pi$
$588$	26293.2	1.84407
$589$	4366.52	0.305466
$590$	−10572.2	−0.737714
$591$	−12574.9	−0.875233
$592$	5805.55	0.403052
$593$	18109.5	1.25408	0.627038	−	0.778989i	$-0.284267\pi$
$593$	18109.5	1.25408	0.627038	+	0.778989i	$0.284267\pi$
$594$	0	0
$595$	−19004.7	−1.30944
$596$	1175.03	0.0807566
$597$	−11423.4	−0.783133
$598$	41775.2	2.85671
$599$	14069.1	0.959676	0.479838	−	0.877357i	$-0.340695\pi$
$599$	14069.1	0.959676	0.479838	+	0.877357i	$0.340695\pi$
$600$	2416.26	0.164406
$601$	27060.7	1.83665	0.918326	−	0.395824i	$-0.129541\pi$
$601$	27060.7	1.83665	0.918326	+	0.395824i	$0.129541\pi$
$602$	−16966.6	−1.14869
$603$	−1056.46	−0.0713472
$604$	1648.70	0.111067
$605$	0	0
$606$	14394.5	0.964915
$607$	11875.6	0.794097	0.397048	−	0.917798i	$-0.370034\pi$
$607$	11875.6	0.794097	0.397048	+	0.917798i	$0.370034\pi$
$608$	4088.75	0.272732
$609$	−9826.21	−0.653823
$610$	6239.10	0.414121
$611$	−26722.6	−1.76936
$612$	16487.8	1.08902
$613$	−18552.4	−1.22239	−0.611193	−	0.791482i	$-0.709310\pi$
$613$	−18552.4	−1.22239	−0.611193	+	0.791482i	$0.709310\pi$
$614$	13218.6	0.868824
$615$	5327.92	0.349338
$616$	0	0
$617$	−21094.4	−1.37638	−0.688192	−	0.725529i	$-0.741595\pi$
$617$	−21094.4	−1.37638	−0.688192	+	0.725529i	$0.741595\pi$
$618$	−7969.00	−0.518706
$619$	13118.8	0.851839	0.425919	−	0.904761i	$-0.359951\pi$
$619$	13118.8	0.851839	0.425919	+	0.904761i	$0.359951\pi$
$620$	−6908.89	−0.447529
$621$	4202.01	0.271531
$622$	−47055.8	−3.03339
$623$	29389.1	1.88996
$624$	6017.76	0.386063
$625$	625.000	0.0400000
$626$	10978.3	0.700930
$627$	0	0
$628$	7288.17	0.463105
$629$	20222.8	1.28193
$630$	−6570.81	−0.415536
$631$	15747.5	0.993500	0.496750	−	0.867894i	$-0.334527\pi$
$631$	15747.5	0.993500	0.496750	+	0.867894i	$0.334527\pi$
$632$	−12357.9	−0.777804
$633$	−6017.52	−0.377843
$634$	11111.5	0.696048
$635$	2773.31	0.173316
$636$	−12246.2	−0.763510
$637$	33428.1	2.07923
$638$	0	0
$639$	8706.41	0.538999
$640$	−13270.9	−0.819653
$641$	15363.2	0.946662	0.473331	−	0.880885i	$-0.343051\pi$
$641$	15363.2	0.946662	0.473331	+	0.880885i	$0.343051\pi$
$642$	−806.031	−0.0495507
$643$	14115.2	0.865705	0.432852	−	0.901465i	$-0.357507\pi$
$643$	14115.2	0.865705	0.432852	+	0.901465i	$0.357507\pi$
$644$	−70287.6	−4.30081
$645$	1742.93	0.106400
$646$	−27615.0	−1.68189
$647$	−26134.1	−1.58800	−0.794002	−	0.607915i	$-0.792006\pi$
$647$	−26134.1	−1.58800	−0.794002	+	0.607915i	$0.792006\pi$
$648$	2609.56	0.158200
$649$	0	0
$650$	6710.66	0.404944
$651$	8600.65	0.517798
$652$	17466.1	1.04912
$653$	16762.6	1.00455	0.502276	−	0.864707i	$-0.332496\pi$
$653$	16762.6	1.00455	0.502276	+	0.864707i	$0.332496\pi$
$654$	16417.0	0.981586
$655$	4560.81	0.272070
$656$	12661.4	0.753576
$657$	6963.46	0.413501
$658$	69340.6	4.10818
$659$	25431.8	1.50331	0.751654	−	0.659557i	$-0.229256\pi$
$659$	25431.8	1.50331	0.751654	+	0.659557i	$0.229256\pi$
$660$	0	0
$661$	−31227.5	−1.83753	−0.918767	−	0.394799i	$-0.870814\pi$
$661$	−31227.5	−1.83753	−0.918767	+	0.394799i	$0.870814\pi$
$662$	−618.981	−0.0363404
$663$	20962.0	1.22790
$664$	34789.6	2.03328
$665$	7135.97	0.416122
$666$	6991.94	0.406805
$667$	16652.5	0.966697
$668$	31128.0	1.80296
$669$	356.547	0.0206052
$670$	−2799.68	−0.161434
$671$	0	0
$672$	8053.54	0.462310
$673$	−9402.00	−0.538515	−0.269258	−	0.963068i	$-0.586778\pi$
$673$	−9402.00	−0.538515	−0.269258	+	0.963068i	$0.586778\pi$
$674$	6908.85	0.394835
$675$	675.000	0.0384900
$676$	14305.5	0.813925
$677$	−10215.2	−0.579916	−0.289958	−	0.957039i	$-0.593641\pi$
$677$	−10215.2	−0.579916	−0.289958	+	0.957039i	$0.593641\pi$
$678$	−13004.3	−0.736619
$679$	−48626.4	−2.74832
$680$	20001.7	1.12798
$681$	−9282.73	−0.522342
$682$	0	0
$683$	−6511.48	−0.364795	−0.182397	−	0.983225i	$-0.558386\pi$
$683$	−6511.48	−0.364795	−0.182397	+	0.983225i	$0.558386\pi$
$684$	−6190.90	−0.346074
$685$	−3440.75	−0.191918
$686$	−36656.2	−2.04015
$687$	−14331.2	−0.795879
$688$	4141.95	0.229521
$689$	−15569.3	−0.860876
$690$	11135.6	0.614382
$691$	−2247.52	−0.123733	−0.0618667	−	0.998084i	$-0.519705\pi$
$691$	−2247.52	−0.123733	−0.0618667	+	0.998084i	$0.519705\pi$
$692$	−38613.3	−2.12118
$693$	0	0
$694$	20873.2	1.14169
$695$	−14207.0	−0.775398
$696$	10341.7	0.563217
$697$	44104.2	2.39679
$698$	−3505.90	−0.190115
$699$	−3840.61	−0.207819
$700$	−11290.8	−0.609647
$701$	−10157.4	−0.547273	−0.273636	−	0.961833i	$-0.588226\pi$
$701$	−10157.4	−0.547273	−0.273636	+	0.961833i	$0.588226\pi$
$702$	7247.51	0.389658
$703$	−7593.31	−0.407379
$704$	0	0
$705$	−7123.15	−0.380530
$706$	39196.0	2.08946
$707$	−30791.3	−1.63794
$708$	−19619.9	−1.04147
$709$	16805.5	0.890190	0.445095	−	0.895483i	$-0.353170\pi$
$709$	16805.5	0.890190	0.445095	+	0.895483i	$0.353170\pi$
$710$	23072.5	1.21957
$711$	−3452.27	−0.182096
$712$	−30930.7	−1.62806
$713$	−14575.5	−0.765580
$714$	−54392.8	−2.85098
$715$	0	0
$716$	−21542.8	−1.12443
$717$	−16058.3	−0.836415
$718$	29824.4	1.55019
$719$	16644.4	0.863329	0.431664	−	0.902034i	$-0.357927\pi$
$719$	16644.4	0.863329	0.431664	+	0.902034i	$0.357927\pi$
$720$	1604.09	0.0830290
$721$	17046.4	0.880502
$722$	−22349.2	−1.15201
$723$	−12258.7	−0.630576
$724$	3442.48	0.176711
$725$	2675.01	0.137031
$726$	0	0
$727$	−31009.4	−1.58195	−0.790973	−	0.611851i	$-0.790425\pi$
$727$	−31009.4	−1.58195	−0.790973	+	0.611851i	$0.790425\pi$
$728$	−55495.6	−2.82528
$729$	729.000	0.0370370
$730$	18453.6	0.935613
$731$	14427.9	0.730006
$732$	11578.5	0.584636
$733$	−32051.2	−1.61506	−0.807530	−	0.589827i	$-0.799196\pi$
$733$	−32051.2	−1.61506	−0.807530	+	0.589827i	$0.799196\pi$
$734$	−28843.1	−1.45043
$735$	8910.58	0.447172
$736$	−13648.3	−0.683539
$737$	0	0
$738$	15248.9	0.760594
$739$	25967.0	1.29257	0.646286	−	0.763095i	$-0.276321\pi$
$739$	25967.0	1.29257	0.646286	+	0.763095i	$0.276321\pi$
$740$	12014.5	0.596838
$741$	−7870.87	−0.390207
$742$	40399.8	1.99882
$743$	8688.42	0.429000	0.214500	−	0.976724i	$-0.431188\pi$
$743$	8688.42	0.429000	0.214500	+	0.976724i	$0.431188\pi$
$744$	−9051.81	−0.446042
$745$	398.209	0.0195829
$746$	20514.7	1.00683
$747$	9718.72	0.476023
$748$	0	0
$749$	1724.18	0.0841122
$750$	1788.79	0.0870898
$751$	7853.29	0.381585	0.190793	−	0.981630i	$-0.438894\pi$
$751$	7853.29	0.381585	0.190793	+	0.981630i	$0.438894\pi$
$752$	−16927.7	−0.820862
$753$	−15255.6	−0.738308
$754$	28721.8	1.38725
$755$	558.732	0.0269329
$756$	−12194.1	−0.586633
$757$	−7895.28	−0.379074	−0.189537	−	0.981874i	$-0.560699\pi$
$757$	−7895.28	−0.379074	−0.189537	+	0.981874i	$0.560699\pi$
$758$	21092.9	1.01072
$759$	0	0
$760$	−7510.29	−0.358456
$761$	−26204.6	−1.24825	−0.624124	−	0.781325i	$-0.714544\pi$
$761$	−26204.6	−1.24825	−0.624124	+	0.781325i	$0.714544\pi$
$762$	7937.40	0.377351
$763$	−35117.6	−1.66624
$764$	−22876.6	−1.08331
$765$	5587.60	0.264079
$766$	33750.6	1.59198
$767$	−24943.9	−1.17428
$768$	−21098.2	−0.991295
$769$	−21014.1	−0.985419	−0.492710	−	0.870194i	$-0.663993\pi$
$769$	−21014.1	−0.985419	−0.492710	+	0.870194i	$0.663993\pi$
$770$	0	0
$771$	73.6816	0.00344173
$772$	9005.76	0.419850
$773$	34961.9	1.62677	0.813385	−	0.581726i	$-0.197622\pi$
$773$	34961.9	1.62677	0.813385	+	0.581726i	$0.197622\pi$
$774$	4988.38	0.231659
$775$	−2341.38	−0.108522
$776$	51177.2	2.36747
$777$	−14956.4	−0.690551
$778$	−63176.3	−2.91129
$779$	−16560.4	−0.761666
$780$	12453.6	0.571681
$781$	0	0
$782$	92179.5	4.21526
$783$	2889.01	0.131858
$784$	21175.4	0.964621
$785$	2469.91	0.112299
$786$	13053.3	0.592363
$787$	−20980.3	−0.950277	−0.475138	−	0.879911i	$-0.657602\pi$
$787$	−20980.3	−0.950277	−0.475138	+	0.879911i	$0.657602\pi$
$788$	−61843.0	−2.79577
$789$	4791.23	0.216188
$790$	−9148.73	−0.412022
$791$	27817.4	1.25041
$792$	0	0
$793$	14720.4	0.659191
$794$	53743.1	2.40210
$795$	−4150.15	−0.185145
$796$	−56180.1	−2.50157
$797$	−10634.2	−0.472627	−0.236314	−	0.971677i	$-0.575939\pi$
$797$	−10634.2	−0.472627	−0.236314	+	0.971677i	$0.575939\pi$
$798$	20423.6	0.905999
$799$	−58965.0	−2.61080
$800$	−2192.44	−0.0968929
$801$	−8640.71	−0.381154
$802$	−11698.9	−0.515091
$803$	0	0
$804$	−5195.63	−0.227905
$805$	−23820.0	−1.04291
$806$	−25139.5	−1.09864
$807$	−9953.11	−0.434159
$808$	32406.4	1.41096
$809$	5429.52	0.235960	0.117980	−	0.993016i	$-0.462358\pi$
$809$	5429.52	0.235960	0.117980	+	0.993016i	$0.462358\pi$
$810$	1931.89	0.0838022
$811$	14403.7	0.623653	0.311827	−	0.950139i	$-0.399059\pi$
$811$	14403.7	0.623653	0.311827	+	0.950139i	$0.399059\pi$
$812$	−48325.0	−2.08851
$813$	13600.5	0.586703
$814$	0	0
$815$	5919.14	0.254403
$816$	13278.5	0.569659
$817$	−5417.43	−0.231985
$818$	−3076.50	−0.131500
$819$	−15503.1	−0.661443
$820$	26202.6	1.11589
$821$	−13996.1	−0.594967	−0.297483	−	0.954727i	$-0.596147\pi$
$821$	−13996.1	−0.594967	−0.297483	+	0.954727i	$0.596147\pi$
$822$	−9847.63	−0.417854
$823$	−35108.6	−1.48701	−0.743506	−	0.668729i	$-0.766838\pi$
$823$	−35108.6	−1.48701	−0.743506	+	0.668729i	$0.766838\pi$
$824$	−17940.6	−0.758484
$825$	0	0
$826$	64725.4	2.72649
$827$	34410.8	1.44689	0.723446	−	0.690381i	$-0.242557\pi$
$827$	34410.8	1.44689	0.723446	+	0.690381i	$0.242557\pi$
$828$	20665.3	0.867355
$829$	−6979.26	−0.292400	−0.146200	−	0.989255i	$-0.546704\pi$
$829$	−6979.26	−0.292400	−0.146200	+	0.989255i	$0.546704\pi$
$830$	25755.2	1.07708
$831$	−20373.2	−0.850467
$832$	−39587.7	−1.64959
$833$	73761.2	3.06804
$834$	−40661.3	−1.68823
$835$	10549.1	0.437205
$836$	0	0
$837$	−2528.69	−0.104426
$838$	−51446.6	−2.12076
$839$	−3307.00	−0.136079	−0.0680396	−	0.997683i	$-0.521674\pi$
$839$	−3307.00	−0.136079	−0.0680396	+	0.997683i	$0.521674\pi$
$840$	−14792.9	−0.607622
$841$	−12939.9	−0.530562
$842$	−9949.30	−0.407215
$843$	−6913.21	−0.282448
$844$	−29594.0	−1.20695
$845$	4848.05	0.197371
$846$	−20386.9	−0.828507
$847$	0	0
$848$	−9862.53	−0.399387
$849$	−5327.50	−0.215359
$850$	14807.5	0.597520
$851$	25346.6	1.02100
$852$	42817.8	1.72173
$853$	1700.66	0.0682643	0.0341322	−	0.999417i	$-0.489133\pi$
$853$	1700.66	0.0682643	0.0341322	+	0.999417i	$0.489133\pi$
$854$	−38197.1	−1.53054
$855$	−2098.05	−0.0839204
$856$	−1814.62	−0.0724561
$857$	−24431.0	−0.973802	−0.486901	−	0.873457i	$-0.661873\pi$
$857$	−24431.0	−0.973802	−0.486901	+	0.873457i	$0.661873\pi$
$858$	0	0
$859$	−21579.4	−0.857136	−0.428568	−	0.903510i	$-0.640982\pi$
$859$	−21579.4	−0.857136	−0.428568	+	0.903510i	$0.640982\pi$
$860$	8571.68	0.339874
$861$	−32618.7	−1.29111
$862$	67444.0	2.66491
$863$	19337.8	0.762766	0.381383	−	0.924417i	$-0.375448\pi$
$863$	19337.8	0.762766	0.381383	+	0.924417i	$0.375448\pi$
$864$	−2367.83	−0.0932352
$865$	−13085.8	−0.514370
$866$	41076.5	1.61182
$867$	31514.8	1.23449
$868$	42297.7	1.65401
$869$	0	0
$870$	7656.06	0.298350
$871$	−6605.53	−0.256969
$872$	36959.7	1.43534
$873$	14296.7	0.554262
$874$	−34611.9	−1.33955
$875$	−3826.39	−0.147835
$876$	34246.1	1.32085
$877$	35085.8	1.35093	0.675463	−	0.737394i	$-0.263944\pi$
$877$	35085.8	1.35093	0.675463	+	0.737394i	$0.263944\pi$
$878$	16547.7	0.636057
$879$	−13899.6	−0.533358
$880$	0	0
$881$	25965.8	0.992974	0.496487	−	0.868044i	$-0.334623\pi$
$881$	25965.8	0.992974	0.496487	+	0.868044i	$0.334623\pi$
$882$	25502.6	0.973604
$883$	17452.1	0.665130	0.332565	−	0.943080i	$-0.392086\pi$
$883$	17452.1	0.665130	0.332565	+	0.943080i	$0.392086\pi$
$884$	103090.	3.92228
$885$	−6649.04	−0.252548
$886$	4602.57	0.174522
$887$	45061.5	1.70577	0.852885	−	0.522099i	$-0.174851\pi$
$887$	45061.5	1.70577	0.852885	+	0.522099i	$0.174851\pi$
$888$	15741.0	0.594856
$889$	−16978.8	−0.640553
$890$	−22898.4	−0.862422
$891$	0	0
$892$	1753.49	0.0658196
$893$	22140.4	0.829675
$894$	1139.70	0.0426367
$895$	−7300.72	−0.272666
$896$	81247.2	3.02933
$897$	26273.1	0.977965
$898$	70595.2	2.62338
$899$	−10021.1	−0.371773
$900$	3319.63	0.122949
$901$	−34354.6	−1.27028
$902$	0	0
$903$	−10670.6	−0.393240
$904$	−29276.6	−1.07713
$905$	1166.63	0.0428510
$906$	1599.13	0.0586396
$907$	−4493.80	−0.164514	−0.0822570	−	0.996611i	$-0.526213\pi$
$907$	−4493.80	−0.164514	−0.0822570	+	0.996611i	$0.526213\pi$
$908$	−45652.2	−1.66852
$909$	9052.97	0.330328
$910$	−41084.1	−1.49662
$911$	4498.37	0.163598	0.0817989	−	0.996649i	$-0.473933\pi$
$911$	4498.37	0.163598	0.0817989	+	0.996649i	$0.473933\pi$
$912$	−4985.87	−0.181029
$913$	0	0
$914$	37733.4	1.36555
$915$	3923.87	0.141770
$916$	−70480.3	−2.54229
$917$	−27922.3	−1.00553
$918$	15992.1	0.574964
$919$	47753.3	1.71408	0.857039	−	0.515252i	$-0.172302\pi$
$919$	47753.3	1.71408	0.857039	+	0.515252i	$0.172302\pi$
$920$	25069.5	0.898389
$921$	8313.38	0.297432
$922$	22577.0	0.806435
$923$	54437.0	1.94129
$924$	0	0
$925$	4071.62	0.144729
$926$	27278.5	0.968063
$927$	−5011.84	−0.177573
$928$	−9383.67	−0.331933
$929$	12314.9	0.434918	0.217459	−	0.976069i	$-0.430223\pi$
$929$	12314.9	0.434918	0.217459	+	0.976069i	$0.430223\pi$
$930$	−6701.17	−0.236280
$931$	−27696.1	−0.974977
$932$	−18888.0	−0.663838
$933$	−29594.2	−1.03845
$934$	20602.1	0.721758
$935$	0	0
$936$	16316.3	0.569782
$937$	8980.00	0.313088	0.156544	−	0.987671i	$-0.449965\pi$
$937$	8980.00	0.313088	0.156544	+	0.987671i	$0.449965\pi$
$938$	17140.2	0.596640
$939$	6904.45	0.239956
$940$	−35031.4	−1.21553
$941$	330.635	0.0114542	0.00572710	−	0.999984i	$-0.498177\pi$
$941$	330.635	0.0114542	0.00572710	+	0.999984i	$0.498177\pi$
$942$	7069.05	0.244503
$943$	55279.0	1.90894
$944$	−15801.0	−0.544786
$945$	−4132.50	−0.142254
$946$	0	0
$947$	3986.42	0.136791	0.0683955	−	0.997658i	$-0.478212\pi$
$947$	3986.42	0.136791	0.0683955	+	0.997658i	$0.478212\pi$
$948$	−16978.2	−0.581672
$949$	43539.1	1.48929
$950$	−5559.96	−0.189883
$951$	6988.21	0.238284
$952$	−122454.	−4.16888
$953$	−55751.9	−1.89505	−0.947524	−	0.319685i	$-0.896423\pi$
$953$	−55751.9	−1.89505	−0.947524	+	0.319685i	$0.896423\pi$
$954$	−11878.0	−0.403107
$955$	−7752.72	−0.262693
$956$	−78974.4	−2.67177
$957$	0	0
$958$	−74376.1	−2.50833
$959$	21065.0	0.709306
$960$	−10552.5	−0.354770
$961$	−21019.7	−0.705573
$962$	43717.2	1.46518
$963$	−506.927	−0.0169631
$964$	−60288.0	−2.01426
$965$	3051.99	0.101811
$966$	−68174.4	−2.27068
$967$	173.237	0.00576105	0.00288052	−	0.999996i	$-0.499083\pi$
$967$	173.237	0.00576105	0.00288052	+	0.999996i	$0.499083\pi$
$968$	0	0
$969$	−17367.5	−0.575775
$970$	37887.1	1.25411
$971$	50825.3	1.67978	0.839888	−	0.542760i	$-0.182621\pi$
$971$	50825.3	1.67978	0.839888	+	0.542760i	$0.182621\pi$
$972$	3585.20	0.118308
$973$	86978.2	2.86577
$974$	77165.9	2.53856
$975$	4220.45	0.138628
$976$	9324.80	0.305819
$977$	−55092.6	−1.80406	−0.902030	−	0.431672i	$-0.857924\pi$
$977$	−55092.6	−1.80406	−0.902030	+	0.431672i	$0.857924\pi$
$978$	16940.9	0.553898
$979$	0	0
$980$	43821.9	1.42841
$981$	10325.0	0.336035
$982$	−37546.2	−1.22011
$983$	48234.0	1.56503	0.782515	−	0.622631i	$-0.213936\pi$
$983$	48234.0	1.56503	0.782515	+	0.622631i	$0.213936\pi$
$984$	34329.8	1.11219
$985$	−20958.2	−0.677953
$986$	63376.3	2.04697
$987$	43609.5	1.40639
$988$	−38708.7	−1.24644
$989$	18083.5	0.581417
$990$	0	0
$991$	−23735.4	−0.760827	−0.380413	−	0.924817i	$-0.624218\pi$
$991$	−23735.4	−0.760827	−0.380413	+	0.924817i	$0.624218\pi$
$992$	8213.31	0.262876
$993$	−389.287	−0.0124407
$994$	−141255.	−4.50738
$995$	−19039.1	−0.606612
$996$	47796.3	1.52057
$997$	51305.7	1.62976	0.814879	−	0.579631i	$-0.196803\pi$
$997$	51305.7	1.62976	0.814879	+	0.579631i	$0.196803\pi$
$998$	−51180.4	−1.62333
$999$	4397.35	0.139265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bn.1.10		12
11.5	even	5		165.4.m.a.91.2	✓	24
11.9	even	5		165.4.m.a.136.2	yes	24
11.10	odd	2		1815.4.a.bh.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.a.91.2	✓	24	11.5	even	5
165.4.m.a.136.2	yes	24	11.9	even	5
1815.4.a.bh.1.3		12	11.10	odd	2
1815.4.a.bn.1.10		12	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)

\(f(q)\)	\(=\)	\(q+4.77011 q^{2} +3.00000 q^{3} +14.7539 q^{4} +5.00000 q^{5} +14.3103 q^{6} -30.6111 q^{7} +32.2168 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.77011 q^{2} +3.00000 q^{3} +14.7539 q^{4} +5.00000 q^{5} +14.3103 q^{6} -30.6111 q^{7} +32.2168 q^{8} +9.00000 q^{9} +23.8505 q^{10} +44.2617 q^{12} +56.2726 q^{13} -146.018 q^{14} +15.0000 q^{15} +35.6464 q^{16} +124.169 q^{17} +42.9309 q^{18} -46.6234 q^{19} +73.7695 q^{20} -91.8333 q^{21} +155.630 q^{23} +96.6505 q^{24} +25.0000 q^{25} +268.426 q^{26} +27.0000 q^{27} -451.633 q^{28} +107.001 q^{29} +71.5516 q^{30} -93.6551 q^{31} -87.6974 q^{32} +592.299 q^{34} -153.055 q^{35} +132.785 q^{36} +162.865 q^{37} -222.399 q^{38} +168.818 q^{39} +161.084 q^{40} +355.195 q^{41} -438.054 q^{42} +116.195 q^{43} +45.0000 q^{45} +742.371 q^{46} -474.877 q^{47} +106.939 q^{48} +594.039 q^{49} +119.253 q^{50} +372.507 q^{51} +830.241 q^{52} -276.676 q^{53} +128.793 q^{54} -986.192 q^{56} -139.870 q^{57} +510.404 q^{58} -443.269 q^{59} +221.309 q^{60} +261.592 q^{61} -446.745 q^{62} -275.500 q^{63} -703.497 q^{64} +281.363 q^{65} -117.384 q^{67} +1831.98 q^{68} +466.890 q^{69} -730.091 q^{70} +967.379 q^{71} +289.951 q^{72} +773.718 q^{73} +776.882 q^{74} +75.0000 q^{75} -687.877 q^{76} +805.279 q^{78} -383.586 q^{79} +178.232 q^{80} +81.0000 q^{81} +1694.32 q^{82} +1079.86 q^{83} -1354.90 q^{84} +620.845 q^{85} +554.265 q^{86} +321.002 q^{87} -960.079 q^{89} +214.655 q^{90} -1722.57 q^{91} +2296.15 q^{92} -280.965 q^{93} -2265.21 q^{94} -233.117 q^{95} -263.092 q^{96} +1588.52 q^{97} +2833.63 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9} + 35 q^{10} + 147 q^{12} + 172 q^{13} - 30 q^{14} + 180 q^{15} + 161 q^{16} + 317 q^{17} + 63 q^{18} + 237 q^{19} + 245 q^{20} + 231 q^{21} + 210 q^{23} + 333 q^{24} + 300 q^{25} + 8 q^{26} + 324 q^{27} + 542 q^{28} + 759 q^{29} + 105 q^{30} - 193 q^{31} + 410 q^{32} - 78 q^{34} + 385 q^{35} + 441 q^{36} + 286 q^{37} - 168 q^{38} + 516 q^{39} + 555 q^{40} + 1189 q^{41} - 90 q^{42} + 775 q^{43} + 540 q^{45} + 529 q^{46} + 382 q^{47} + 483 q^{48} + 1195 q^{49} + 175 q^{50} + 951 q^{51} + 1741 q^{52} + 275 q^{53} + 189 q^{54} - 419 q^{56} + 711 q^{57} - 418 q^{58} + 646 q^{59} + 735 q^{60} + 1340 q^{61} + 983 q^{62} + 693 q^{63} - 1489 q^{64} + 860 q^{65} - 185 q^{67} + 3322 q^{68} + 630 q^{69} - 150 q^{70} - 932 q^{71} + 999 q^{72} + 2860 q^{73} + 4187 q^{74} + 900 q^{75} + 1594 q^{76} + 24 q^{78} + 1429 q^{79} + 805 q^{80} + 972 q^{81} - 30 q^{82} + 2590 q^{83} + 1626 q^{84} + 1585 q^{85} - 3195 q^{86} + 2277 q^{87} - 473 q^{89} + 315 q^{90} - 4302 q^{91} + 5462 q^{92} - 579 q^{93} + 2875 q^{94} + 1185 q^{95} + 1230 q^{96} + 318 q^{97} - 194 q^{98}+O(q^{100}) \) 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9 + 35 * q^10 + 147 * q^12 + 172 * q^13 - 30 * q^14 + 180 * q^15 + 161 * q^16 + 317 * q^17 + 63 * q^18 + 237 * q^19 + 245 * q^20 + 231 * q^21 + 210 * q^23 + 333 * q^24 + 300 * q^25 + 8 * q^26 + 324 * q^27 + 542 * q^28 + 759 * q^29 + 105 * q^30 - 193 * q^31 + 410 * q^32 - 78 * q^34 + 385 * q^35 + 441 * q^36 + 286 * q^37 - 168 * q^38 + 516 * q^39 + 555 * q^40 + 1189 * q^41 - 90 * q^42 + 775 * q^43 + 540 * q^45 + 529 * q^46 + 382 * q^47 + 483 * q^48 + 1195 * q^49 + 175 * q^50 + 951 * q^51 + 1741 * q^52 + 275 * q^53 + 189 * q^54 - 419 * q^56 + 711 * q^57 - 418 * q^58 + 646 * q^59 + 735 * q^60 + 1340 * q^61 + 983 * q^62 + 693 * q^63 - 1489 * q^64 + 860 * q^65 - 185 * q^67 + 3322 * q^68 + 630 * q^69 - 150 * q^70 - 932 * q^71 + 999 * q^72 + 2860 * q^73 + 4187 * q^74 + 900 * q^75 + 1594 * q^76 + 24 * q^78 + 1429 * q^79 + 805 * q^80 + 972 * q^81 - 30 * q^82 + 2590 * q^83 + 1626 * q^84 + 1585 * q^85 - 3195 * q^86 + 2277 * q^87 - 473 * q^89 + 315 * q^90 - 4302 * q^91 + 5462 * q^92 - 579 * q^93 + 2875 * q^94 + 1185 * q^95 + 1230 * q^96 + 318 * q^97 - 194 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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