LMFDB - Embedded newform 1815.4.a.bn.1.6

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			1.6
Root			$0.843186$ 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)

$f(q)$	$=$	$q+0.156814 q^{2} +3.00000 q^{3} -7.97541 q^{4} +5.00000 q^{5} +0.470441 q^{6} +3.41884 q^{7} -2.50516 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.156814 q^{2} +3.00000 q^{3} -7.97541 q^{4} +5.00000 q^{5} +0.470441 q^{6} +3.41884 q^{7} -2.50516 q^{8} +9.00000 q^{9} +0.784068 q^{10} -23.9262 q^{12} +62.9512 q^{13} +0.536121 q^{14} +15.0000 q^{15} +63.4104 q^{16} +30.3789 q^{17} +1.41132 q^{18} -150.881 q^{19} -39.8770 q^{20} +10.2565 q^{21} -94.0884 q^{23} -7.51549 q^{24} +25.0000 q^{25} +9.87161 q^{26} +27.0000 q^{27} -27.2667 q^{28} +12.7700 q^{29} +2.35220 q^{30} +191.099 q^{31} +29.9849 q^{32} +4.76383 q^{34} +17.0942 q^{35} -71.7787 q^{36} +109.563 q^{37} -23.6602 q^{38} +188.854 q^{39} -12.5258 q^{40} +354.800 q^{41} +1.60836 q^{42} +47.2313 q^{43} +45.0000 q^{45} -14.7543 q^{46} +277.497 q^{47} +190.231 q^{48} -331.312 q^{49} +3.92034 q^{50} +91.1368 q^{51} -502.062 q^{52} +500.218 q^{53} +4.23397 q^{54} -8.56476 q^{56} -452.643 q^{57} +2.00252 q^{58} -228.086 q^{59} -119.631 q^{60} -405.766 q^{61} +29.9670 q^{62} +30.7696 q^{63} -502.581 q^{64} +314.756 q^{65} -826.423 q^{67} -242.284 q^{68} -282.265 q^{69} +2.68061 q^{70} -895.191 q^{71} -22.5465 q^{72} +855.850 q^{73} +17.1810 q^{74} +75.0000 q^{75} +1203.34 q^{76} +29.6148 q^{78} +561.960 q^{79} +317.052 q^{80} +81.0000 q^{81} +55.6374 q^{82} -1243.62 q^{83} -81.8000 q^{84} +151.895 q^{85} +7.40652 q^{86} +38.3101 q^{87} -149.639 q^{89} +7.05661 q^{90} +215.220 q^{91} +750.394 q^{92} +573.298 q^{93} +43.5154 q^{94} -754.405 q^{95} +89.9547 q^{96} +848.781 q^{97} -51.9542 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.156814	0.0554420	0.0277210	−	0.999616i	$-0.491175\pi$
$2$	0.156814	0.0554420	0.0277210	+	0.999616i	$0.491175\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.97541	−0.996926
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0.470441	0.0320094
$7$	3.41884	0.184600	0.0923001	−	0.995731i	$-0.470578\pi$
$7$	3.41884	0.184600	0.0923001	+	0.995731i	$0.470578\pi$
$8$	−2.50516	−0.110714
$9$	9.00000	0.333333
$10$	0.784068	0.0247944
$11$	0	0
$11$	0	0
$12$	−23.9262	−0.575576
$13$	62.9512	1.34304	0.671520	−	0.740986i	$-0.265642\pi$
$13$	62.9512	1.34304	0.671520	+	0.740986i	$0.265642\pi$
$14$	0.536121	0.0102346
$15$	15.0000	0.258199
$16$	63.4104	0.990788
$17$	30.3789	0.433410	0.216705	−	0.976237i	$-0.430469\pi$
$17$	30.3789	0.433410	0.216705	+	0.976237i	$0.430469\pi$
$18$	1.41132	0.0184807
$19$	−150.881	−1.82181	−0.910907	−	0.412612i	$-0.864617\pi$
$19$	−150.881	−1.82181	−0.910907	+	0.412612i	$0.864617\pi$
$20$	−39.8770	−0.445839
$21$	10.2565	0.106579
$22$	0	0
$23$	−94.0884	−0.852991	−0.426496	−	0.904490i	$-0.640252\pi$
$23$	−94.0884	−0.852991	−0.426496	+	0.904490i	$0.640252\pi$
$24$	−7.51549	−0.0639205
$25$	25.0000	0.200000
$26$	9.87161	0.0744608
$27$	27.0000	0.192450
$28$	−27.2667	−0.184033
$29$	12.7700	0.0817702	0.0408851	−	0.999164i	$-0.486982\pi$
$29$	12.7700	0.0817702	0.0408851	+	0.999164i	$0.486982\pi$
$30$	2.35220	0.0143151
$31$	191.099	1.10718	0.553588	−	0.832791i	$-0.313258\pi$
$31$	191.099	1.10718	0.553588	+	0.832791i	$0.313258\pi$
$32$	29.9849	0.165645
$33$	0	0
$34$	4.76383	0.0240291
$35$	17.0942	0.0825557
$36$	−71.7787	−0.332309
$37$	109.563	0.486814	0.243407	−	0.969924i	$-0.421735\pi$
$37$	109.563	0.486814	0.243407	+	0.969924i	$0.421735\pi$
$38$	−23.6602	−0.101005
$39$	188.854	0.775405
$40$	−12.5258	−0.0495126
$41$	354.800	1.35147	0.675737	−	0.737143i	$-0.263826\pi$
$41$	354.800	1.35147	0.675737	+	0.737143i	$0.263826\pi$
$42$	1.60836	0.00590895
$43$	47.2313	0.167505	0.0837525	−	0.996487i	$-0.473309\pi$
$43$	47.2313	0.167505	0.0837525	+	0.996487i	$0.473309\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	−14.7543	−0.0472915
$47$	277.497	0.861216	0.430608	−	0.902539i	$-0.358299\pi$
$47$	277.497	0.861216	0.430608	+	0.902539i	$0.358299\pi$
$48$	190.231	0.572032
$49$	−331.312	−0.965923
$50$	3.92034	0.0110884
$51$	91.1368	0.250229
$52$	−502.062	−1.33891
$53$	500.218	1.29642	0.648209	−	0.761462i	$-0.275518\pi$
$53$	500.218	1.29642	0.648209	+	0.761462i	$0.275518\pi$
$54$	4.23397	0.0106698
$55$	0	0
$56$	−8.56476	−0.0204377
$57$	−452.643	−1.05182
$58$	2.00252	0.00453351
$59$	−228.086	−0.503293	−0.251647	−	0.967819i	$-0.580972\pi$
$59$	−228.086	−0.503293	−0.251647	+	0.967819i	$0.580972\pi$
$60$	−119.631	−0.257405
$61$	−405.766	−0.851689	−0.425845	−	0.904796i	$-0.640023\pi$
$61$	−405.766	−0.851689	−0.425845	+	0.904796i	$0.640023\pi$
$62$	29.9670	0.0613840
$63$	30.7696	0.0615334
$64$	−502.581	−0.981604
$65$	314.756	0.600626
$66$	0	0
$67$	−826.423	−1.50692	−0.753460	−	0.657494i	$-0.771617\pi$
$67$	−826.423	−1.50692	−0.753460	+	0.657494i	$0.771617\pi$
$68$	−242.284	−0.432078
$69$	−282.265	−0.492475
$70$	2.68061	0.00457705
$71$	−895.191	−1.49633	−0.748167	−	0.663511i	$-0.769066\pi$
$71$	−895.191	−1.49633	−0.748167	+	0.663511i	$0.769066\pi$
$72$	−22.5465	−0.0369045
$73$	855.850	1.37219	0.686094	−	0.727513i	$-0.259324\pi$
$73$	855.850	1.37219	0.686094	+	0.727513i	$0.259324\pi$
$74$	17.1810	0.0269899
$75$	75.0000	0.115470
$76$	1203.34	1.81621
$77$	0	0
$78$	29.6148	0.0429900
$79$	561.960	0.800322	0.400161	−	0.916445i	$-0.368954\pi$
$79$	561.960	0.800322	0.400161	+	0.916445i	$0.368954\pi$
$80$	317.052	0.443094
$81$	81.0000	0.111111
$82$	55.6374	0.0749284
$83$	−1243.62	−1.64464	−0.822321	−	0.569023i	$-0.807321\pi$
$83$	−1243.62	−1.64464	−0.822321	+	0.569023i	$0.807321\pi$
$84$	−81.8000	−0.106251
$85$	151.895	0.193827
$86$	7.40652	0.00928681
$87$	38.3101	0.0472101
$88$	0	0
$89$	−149.639	−0.178222	−0.0891108	−	0.996022i	$-0.528403\pi$
$89$	−149.639	−0.178222	−0.0891108	+	0.996022i	$0.528403\pi$
$90$	7.05661	0.00826480
$91$	215.220	0.247926
$92$	750.394	0.850369
$93$	573.298	0.639228
$94$	43.5154	0.0477475
$95$	−754.405	−0.814740
$96$	89.9547	0.0956351
$97$	848.781	0.888461	0.444230	−	0.895913i	$-0.353477\pi$
$97$	848.781	0.888461	0.444230	+	0.895913i	$0.353477\pi$
$98$	−51.9542	−0.0535527
$99$	0	0
$100$	−199.385	−0.199385
$101$	485.490	0.478298	0.239149	−	0.970983i	$-0.423132\pi$
$101$	485.490	0.478298	0.239149	+	0.970983i	$0.423132\pi$
$102$	14.2915	0.0138732
$103$	926.432	0.886253	0.443126	−	0.896459i	$-0.353869\pi$
$103$	926.432	0.886253	0.443126	+	0.896459i	$0.353869\pi$
$104$	−157.703	−0.148693
$105$	51.2827	0.0476636
$106$	78.4410	0.0718760
$107$	267.854	0.242004	0.121002	−	0.992652i	$-0.461389\pi$
$107$	267.854	0.242004	0.121002	+	0.992652i	$0.461389\pi$
$108$	−215.336	−0.191859
$109$	358.485	0.315015	0.157508	−	0.987518i	$-0.449654\pi$
$109$	358.485	0.315015	0.157508	+	0.987518i	$0.449654\pi$
$110$	0	0
$111$	328.690	0.281062
$112$	216.790	0.182900
$113$	−241.393	−0.200959	−0.100479	−	0.994939i	$-0.532038\pi$
$113$	−241.393	−0.200959	−0.100479	+	0.994939i	$0.532038\pi$
$114$	−70.9806	−0.0583153
$115$	−470.442	−0.381469
$116$	−101.846	−0.0815189
$117$	566.561	0.447680
$118$	−35.7670	−0.0279036
$119$	103.861	0.0800076
$120$	−37.5774	−0.0285861
$121$	0	0
$122$	−63.6297	−0.0472193
$123$	1064.40	0.780273
$124$	−1524.10	−1.10377
$125$	125.000	0.0894427
$126$	4.82509	0.00341153
$127$	2611.11	1.82440	0.912201	−	0.409744i	$-0.134382\pi$
$127$	2611.11	1.82440	0.912201	+	0.409744i	$0.134382\pi$
$128$	−318.691	−0.220067
$129$	141.694	0.0967090
$130$	49.3581	0.0332999
$131$	1954.36	1.30346	0.651730	−	0.758451i	$-0.274043\pi$
$131$	1954.36	1.30346	0.651730	+	0.758451i	$0.274043\pi$
$132$	0	0
$133$	−515.838	−0.336307
$134$	−129.594	−0.0835467
$135$	135.000	0.0860663
$136$	−76.1041	−0.0479844
$137$	3004.16	1.87345	0.936726	−	0.350064i	$-0.113840\pi$
$137$	3004.16	1.87345	0.936726	+	0.350064i	$0.113840\pi$
$138$	−44.2630	−0.0273038
$139$	−955.718	−0.583187	−0.291593	−	0.956542i	$-0.594185\pi$
$139$	−955.718	−0.583187	−0.291593	+	0.956542i	$0.594185\pi$
$140$	−136.333	−0.0823020
$141$	832.492	0.497223
$142$	−140.378	−0.0829597
$143$	0	0
$144$	570.694	0.330263
$145$	63.8502	0.0365688
$146$	134.209	0.0760768
$147$	−993.935	−0.557676
$148$	−873.813	−0.485318
$149$	−393.487	−0.216347	−0.108174	−	0.994132i	$-0.534500\pi$
$149$	−393.487	−0.216347	−0.108174	+	0.994132i	$0.534500\pi$
$150$	11.7610	0.00640189
$151$	2422.26	1.30543	0.652717	−	0.757602i	$-0.273629\pi$
$151$	2422.26	1.30543	0.652717	+	0.757602i	$0.273629\pi$
$152$	377.981	0.201700
$153$	273.410	0.144470
$154$	0	0
$155$	955.497	0.495144
$156$	−1506.19	−0.773021
$157$	243.157	0.123605	0.0618026	−	0.998088i	$-0.480315\pi$
$157$	243.157	0.123605	0.0618026	+	0.998088i	$0.480315\pi$
$158$	88.1230	0.0443714
$159$	1500.65	0.748488
$160$	149.925	0.0740786
$161$	−321.674	−0.157462
$162$	12.7019	0.00616022
$163$	−802.608	−0.385676	−0.192838	−	0.981231i	$-0.561769\pi$
$163$	−802.608	−0.385676	−0.192838	+	0.981231i	$0.561769\pi$
$164$	−2829.67	−1.34732
$165$	0	0
$166$	−195.017	−0.0911823
$167$	2126.83	0.985505	0.492752	−	0.870170i	$-0.335991\pi$
$167$	2126.83	0.985505	0.492752	+	0.870170i	$0.335991\pi$
$168$	−25.6943	−0.0117997
$169$	1765.86	0.803758
$170$	23.8191	0.0107461
$171$	−1357.93	−0.607271
$172$	−376.689	−0.166990
$173$	1579.11	0.693974	0.346987	−	0.937870i	$-0.387205\pi$
$173$	1579.11	0.693974	0.346987	+	0.937870i	$0.387205\pi$
$174$	6.00755	0.00261742
$175$	85.4711	0.0369200
$176$	0	0
$177$	−684.258	−0.290576
$178$	−23.4655	−0.00988096
$179$	−3490.09	−1.45733	−0.728663	−	0.684872i	$-0.759858\pi$
$179$	−3490.09	−1.45733	−0.728663	+	0.684872i	$0.759858\pi$
$180$	−358.893	−0.148613
$181$	−1617.56	−0.664268	−0.332134	−	0.943232i	$-0.607769\pi$
$181$	−1617.56	−0.664268	−0.332134	+	0.943232i	$0.607769\pi$
$182$	33.7495	0.0137455
$183$	−1217.30	−0.491723
$184$	235.707	0.0944377
$185$	547.817	0.217710
$186$	89.9010	0.0354401
$187$	0	0
$188$	−2213.15	−0.858569
$189$	92.3088	0.0355263
$190$	−118.301	−0.0451708
$191$	−2051.27	−0.777092	−0.388546	−	0.921429i	$-0.627023\pi$
$191$	−2051.27	−0.777092	−0.388546	+	0.921429i	$0.627023\pi$
$192$	−1507.74	−0.566730
$193$	1888.53	0.704350	0.352175	−	0.935934i	$-0.385442\pi$
$193$	1888.53	0.704350	0.352175	+	0.935934i	$0.385442\pi$
$194$	133.100	0.0492580
$195$	944.268	0.346772
$196$	2642.34	0.962954
$197$	4352.38	1.57408	0.787041	−	0.616901i	$-0.211612\pi$
$197$	4352.38	1.57408	0.787041	+	0.616901i	$0.211612\pi$
$198$	0	0
$199$	2655.86	0.946076	0.473038	−	0.881042i	$-0.343157\pi$
$199$	2655.86	0.946076	0.473038	+	0.881042i	$0.343157\pi$
$200$	−62.6290	−0.0221427
$201$	−2479.27	−0.870021
$202$	76.1315	0.0265178
$203$	43.6588	0.0150948
$204$	−726.853	−0.249460
$205$	1774.00	0.604397
$206$	145.277	0.0491356
$207$	−846.796	−0.284330
$208$	3991.76	1.33067
$209$	0	0
$210$	8.04182	0.00264256
$211$	3295.47	1.07521	0.537605	−	0.843197i	$-0.319329\pi$
$211$	3295.47	1.07521	0.537605	+	0.843197i	$0.319329\pi$
$212$	−3989.44	−1.29243
$213$	−2685.57	−0.863908
$214$	42.0032	0.0134172
$215$	236.157	0.0749105
$216$	−67.6394	−0.0213068
$217$	653.339	0.204385
$218$	56.2154	0.0174651
$219$	2567.55	0.792233
$220$	0	0
$221$	1912.39	0.582087
$222$	51.5431	0.0155826
$223$	362.868	0.108966	0.0544831	−	0.998515i	$-0.482649\pi$
$223$	362.868	0.108966	0.0544831	+	0.998515i	$0.482649\pi$
$224$	102.514	0.0305781
$225$	225.000	0.0666667
$226$	−37.8537	−0.0111415
$227$	−663.967	−0.194137	−0.0970684	−	0.995278i	$-0.530947\pi$
$227$	−663.967	−0.194137	−0.0970684	+	0.995278i	$0.530947\pi$
$228$	3610.01	1.04859
$229$	5468.56	1.57805	0.789024	−	0.614363i	$-0.210587\pi$
$229$	5468.56	1.57805	0.789024	+	0.614363i	$0.210587\pi$
$230$	−73.7717	−0.0211494
$231$	0	0
$232$	−31.9910	−0.00905308
$233$	−261.376	−0.0734907	−0.0367454	−	0.999325i	$-0.511699\pi$
$233$	−261.376	−0.0734907	−0.0367454	+	0.999325i	$0.511699\pi$
$234$	88.8445	0.0248203
$235$	1387.49	0.385147
$236$	1819.08	0.501746
$237$	1685.88	0.462066
$238$	16.2868	0.00443578
$239$	4504.25	1.21906	0.609531	−	0.792762i	$-0.291358\pi$
$239$	4504.25	1.21906	0.609531	+	0.792762i	$0.291358\pi$
$240$	951.156	0.255820
$241$	1169.87	0.312689	0.156345	−	0.987703i	$-0.450029\pi$
$241$	1169.87	0.312689	0.156345	+	0.987703i	$0.450029\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	3236.15	0.849071
$245$	−1656.56	−0.431974
$246$	166.912	0.0432599
$247$	−9498.14	−2.44677
$248$	−478.735	−0.122579
$249$	−3730.87	−0.949535
$250$	19.6017	0.00495888
$251$	−7367.68	−1.85276	−0.926382	−	0.376585i	$-0.877098\pi$
$251$	−7367.68	−1.85276	−0.926382	+	0.376585i	$0.877098\pi$
$252$	−245.400	−0.0613443
$253$	0	0
$254$	409.458	0.101148
$255$	455.684	0.111906
$256$	3970.68	0.969403
$257$	8131.20	1.97358	0.986790	−	0.162005i	$-0.0517959\pi$
$257$	8131.20	1.97358	0.986790	+	0.162005i	$0.0517959\pi$
$258$	22.2196	0.00536174
$259$	374.580	0.0898660
$260$	−2510.31	−0.598780
$261$	114.930	0.0272567
$262$	306.470	0.0722664
$263$	2836.71	0.665091	0.332545	−	0.943087i	$-0.392093\pi$
$263$	2836.71	0.665091	0.332545	+	0.943087i	$0.392093\pi$
$264$	0	0
$265$	2501.09	0.579776
$266$	−80.8905	−0.0186455
$267$	−448.918	−0.102896
$268$	6591.06	1.50229
$269$	−829.542	−0.188023	−0.0940113	−	0.995571i	$-0.529969\pi$
$269$	−829.542	−0.188023	−0.0940113	+	0.995571i	$0.529969\pi$
$270$	21.1698	0.00477169
$271$	1808.11	0.405295	0.202648	−	0.979252i	$-0.435045\pi$
$271$	1808.11	0.405295	0.202648	+	0.979252i	$0.435045\pi$
$272$	1926.34	0.429417
$273$	645.661	0.143140
$274$	471.094	0.103868
$275$	0	0
$276$	2251.18	0.490961
$277$	4686.64	1.01658	0.508290	−	0.861186i	$-0.330278\pi$
$277$	4686.64	1.01658	0.508290	+	0.861186i	$0.330278\pi$
$278$	−149.870	−0.0323330
$279$	1719.89	0.369059
$280$	−42.8238	−0.00914004
$281$	7808.89	1.65779	0.828896	−	0.559403i	$-0.188969\pi$
$281$	7808.89	1.65779	0.828896	+	0.559403i	$0.188969\pi$
$282$	130.546	0.0275670
$283$	64.2115	0.0134876	0.00674378	−	0.999977i	$-0.497853\pi$
$283$	64.2115	0.0134876	0.00674378	+	0.999977i	$0.497853\pi$
$284$	7139.52	1.49173
$285$	−2263.21	−0.470390
$286$	0	0
$287$	1213.00	0.249482
$288$	269.864	0.0552149
$289$	−3990.12	−0.812156
$290$	10.0126	0.00202745
$291$	2546.34	0.512953
$292$	−6825.75	−1.36797
$293$	1695.85	0.338133	0.169066	−	0.985605i	$-0.445925\pi$
$293$	1695.85	0.338133	0.169066	+	0.985605i	$0.445925\pi$
$294$	−155.862	−0.0309187
$295$	−1140.43	−0.225079
$296$	−274.474	−0.0538969
$297$	0	0
$298$	−61.7041	−0.0119947
$299$	−5922.98	−1.14560
$300$	−598.156	−0.115115
$301$	161.477	0.0309214
$302$	379.843	0.0723759
$303$	1456.47	0.276146
$304$	−9567.43	−1.80503
$305$	−2028.83	−0.380887
$306$	42.8745	0.00800970
$307$	1504.42	0.279680	0.139840	−	0.990174i	$-0.455341\pi$
$307$	1504.42	0.279680	0.139840	+	0.990174i	$0.455341\pi$
$308$	0	0
$309$	2779.30	0.511678
$310$	149.835	0.0274518
$311$	−5052.07	−0.921146	−0.460573	−	0.887622i	$-0.652356\pi$
$311$	−5052.07	−0.921146	−0.460573	+	0.887622i	$0.652356\pi$
$312$	−473.109	−0.0858478
$313$	5534.59	0.999467	0.499734	−	0.866179i	$-0.333431\pi$
$313$	5534.59	0.999467	0.499734	+	0.866179i	$0.333431\pi$
$314$	38.1303	0.00685291
$315$	153.848	0.0275186
$316$	−4481.86	−0.797862
$317$	2538.09	0.449696	0.224848	−	0.974394i	$-0.427811\pi$
$317$	2538.09	0.449696	0.224848	+	0.974394i	$0.427811\pi$
$318$	235.323	0.0414976
$319$	0	0
$320$	−2512.91	−0.438987
$321$	803.562	0.139721
$322$	−50.4428	−0.00873002
$323$	−4583.60	−0.789593
$324$	−646.008	−0.110770
$325$	1573.78	0.268608
$326$	−125.860	−0.0213826
$327$	1075.46	0.181874
$328$	−888.831	−0.149626
$329$	948.720	0.158981
$330$	0	0
$331$	−10597.8	−1.75985	−0.879925	−	0.475113i	$-0.842407\pi$
$331$	−10597.8	−1.75985	−0.879925	+	0.475113i	$0.842407\pi$
$332$	9918.40	1.63959
$333$	986.071	0.162271
$334$	333.516	0.0546383
$335$	−4132.12	−0.673915
$336$	650.371	0.105597
$337$	−1679.44	−0.271469	−0.135735	−	0.990745i	$-0.543339\pi$
$337$	−1679.44	−0.271469	−0.135735	+	0.990745i	$0.543339\pi$
$338$	276.910	0.0445620
$339$	−724.178	−0.116023
$340$	−1211.42	−0.193231
$341$	0	0
$342$	−212.942	−0.0336683
$343$	−2305.37	−0.362910
$344$	−118.322	−0.0185451
$345$	−1411.33	−0.220241
$346$	247.626	0.0384753
$347$	−7759.20	−1.20039	−0.600195	−	0.799854i	$-0.704910\pi$
$347$	−7759.20	−1.20039	−0.600195	+	0.799854i	$0.704910\pi$
$348$	−305.539	−0.0470650
$349$	−6870.83	−1.05383	−0.526916	−	0.849918i	$-0.676652\pi$
$349$	−6870.83	−1.05383	−0.526916	+	0.849918i	$0.676652\pi$
$350$	13.4030	0.00204692
$351$	1699.68	0.258468
$352$	0	0
$353$	−733.283	−0.110563	−0.0552815	−	0.998471i	$-0.517606\pi$
$353$	−733.283	−0.110563	−0.0552815	+	0.998471i	$0.517606\pi$
$354$	−107.301	−0.0161101
$355$	−4475.96	−0.669181
$356$	1193.43	0.177674
$357$	311.582	0.0461924
$358$	−547.293	−0.0807971
$359$	−6215.33	−0.913740	−0.456870	−	0.889533i	$-0.651030\pi$
$359$	−6215.33	−0.913740	−0.456870	+	0.889533i	$0.651030\pi$
$360$	−112.732	−0.0165042
$361$	15906.1	2.31901
$362$	−253.656	−0.0368284
$363$	0	0
$364$	−1716.47	−0.247164
$365$	4279.25	0.613661
$366$	−190.889	−0.0272621
$367$	2567.48	0.365181	0.182590	−	0.983189i	$-0.441552\pi$
$367$	2567.48	0.365181	0.182590	+	0.983189i	$0.441552\pi$
$368$	−5966.19	−0.845133
$369$	3193.20	0.450491
$370$	85.9052	0.0120703
$371$	1710.17	0.239319
$372$	−4572.29	−0.637264
$373$	10284.9	1.42770	0.713848	−	0.700300i	$-0.246951\pi$
$373$	10284.9	1.42770	0.713848	+	0.700300i	$0.246951\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	−695.176	−0.0953483
$377$	803.890	0.109821
$378$	14.4753	0.00196965
$379$	−10876.1	−1.47406	−0.737028	−	0.675862i	$-0.763771\pi$
$379$	−10876.1	−1.47406	−0.737028	+	0.675862i	$0.763771\pi$
$380$	6016.69	0.812236
$381$	7833.34	1.05332
$382$	−321.667	−0.0430835
$383$	13466.3	1.79659	0.898297	−	0.439388i	$-0.144805\pi$
$383$	13466.3	1.79659	0.898297	+	0.439388i	$0.144805\pi$
$384$	−956.073	−0.127056
$385$	0	0
$386$	296.148	0.0390505
$387$	425.082	0.0558350
$388$	−6769.38	−0.885730
$389$	−3123.59	−0.407127	−0.203564	−	0.979062i	$-0.565252\pi$
$389$	−3123.59	−0.407127	−0.203564	+	0.979062i	$0.565252\pi$
$390$	148.074	0.0192257
$391$	−2858.30	−0.369695
$392$	829.989	0.106941
$393$	5863.08	0.752553
$394$	682.512	0.0872702
$395$	2809.80	0.357915
$396$	0	0
$397$	−12194.7	−1.54165	−0.770823	−	0.637050i	$-0.780155\pi$
$397$	−12194.7	−1.54165	−0.770823	+	0.637050i	$0.780155\pi$
$398$	416.475	0.0524523
$399$	−1547.52	−0.194167
$400$	1585.26	0.198158
$401$	964.771	0.120146	0.0600728	−	0.998194i	$-0.480867\pi$
$401$	964.771	0.120146	0.0600728	+	0.998194i	$0.480867\pi$
$402$	−388.783	−0.0482357
$403$	12029.9	1.48698
$404$	−3871.99	−0.476828
$405$	405.000	0.0496904
$406$	6.84629	0.000836886 0
$407$	0	0
$408$	−228.312	−0.0277038
$409$	−11358.5	−1.37321	−0.686603	−	0.727032i	$-0.740899\pi$
$409$	−11358.5	−1.37321	−0.686603	+	0.727032i	$0.740899\pi$
$410$	278.187	0.0335090
$411$	9012.49	1.08164
$412$	−7388.67	−0.883529
$413$	−779.791	−0.0929080
$414$	−132.789	−0.0157638
$415$	−6218.11	−0.735507
$416$	1887.59	0.222468
$417$	−2867.15	−0.336703
$418$	0	0
$419$	7613.80	0.887729	0.443865	−	0.896094i	$-0.353607\pi$
$419$	7613.80	0.887729	0.443865	+	0.896094i	$0.353607\pi$
$420$	−409.000	−0.0475171
$421$	−11449.2	−1.32542	−0.662709	−	0.748877i	$-0.730593\pi$
$421$	−11449.2	−1.32542	−0.662709	+	0.748877i	$0.730593\pi$
$422$	516.774	0.0596118
$423$	2497.48	0.287072
$424$	−1253.13	−0.143531
$425$	759.473	0.0866820
$426$	−421.135	−0.0478968
$427$	−1387.25	−0.157222
$428$	−2136.25	−0.241260
$429$	0	0
$430$	37.0326	0.00415319
$431$	−126.476	−0.0141349	−0.00706744	−	0.999975i	$-0.502250\pi$
$431$	−126.476	−0.0141349	−0.00706744	+	0.999975i	$0.502250\pi$
$432$	1712.08	0.190677
$433$	189.484	0.0210301	0.0105150	−	0.999945i	$-0.496653\pi$
$433$	189.484	0.0210301	0.0105150	+	0.999945i	$0.496653\pi$
$434$	102.452	0.0113315
$435$	191.551	0.0211130
$436$	−2859.07	−0.314047
$437$	14196.2	1.55399
$438$	402.627	0.0439230
$439$	5554.02	0.603825	0.301912	−	0.953336i	$-0.402375\pi$
$439$	5554.02	0.603825	0.301912	+	0.953336i	$0.402375\pi$
$440$	0	0
$441$	−2981.80	−0.321974
$442$	299.889	0.0322721
$443$	12557.2	1.34675	0.673377	−	0.739299i	$-0.264843\pi$
$443$	12557.2	1.34675	0.673377	+	0.739299i	$0.264843\pi$
$444$	−2621.44	−0.280198
$445$	−748.196	−0.0797031
$446$	56.9027	0.00604130
$447$	−1180.46	−0.124908
$448$	−1718.25	−0.181204
$449$	−13257.3	−1.39343	−0.696714	−	0.717349i	$-0.745355\pi$
$449$	−13257.3	−1.39343	−0.696714	+	0.717349i	$0.745355\pi$
$450$	35.2831	0.00369613
$451$	0	0
$452$	1925.21	0.200341
$453$	7266.78	0.753693
$454$	−104.119	−0.0107633
$455$	1076.10	0.110876
$456$	1133.94	0.116451
$457$	−497.390	−0.0509123	−0.0254561	−	0.999676i	$-0.508104\pi$
$457$	−497.390	−0.0509123	−0.0254561	+	0.999676i	$0.508104\pi$
$458$	857.545	0.0874901
$459$	820.231	0.0834098
$460$	3751.97	0.380297
$461$	11090.5	1.12047	0.560235	−	0.828333i	$-0.310711\pi$
$461$	11090.5	1.12047	0.560235	+	0.828333i	$0.310711\pi$
$462$	0	0
$463$	−4013.08	−0.402815	−0.201408	−	0.979508i	$-0.564552\pi$
$463$	−4013.08	−0.402815	−0.201408	+	0.979508i	$0.564552\pi$
$464$	809.754	0.0810170
$465$	2866.49	0.285872
$466$	−40.9874	−0.00407447
$467$	−7547.03	−0.747826	−0.373913	−	0.927464i	$-0.621984\pi$
$467$	−7547.03	−0.747826	−0.373913	+	0.927464i	$0.621984\pi$
$468$	−4518.56	−0.446304
$469$	−2825.41	−0.278178
$470$	217.577	0.0213533
$471$	729.470	0.0713635
$472$	571.393	0.0557214
$473$	0	0
$474$	264.369	0.0256179
$475$	−3772.02	−0.364363
$476$	−828.332	−0.0797616
$477$	4501.96	0.432140
$478$	706.328	0.0675872
$479$	−4945.07	−0.471704	−0.235852	−	0.971789i	$-0.575788\pi$
$479$	−4945.07	−0.471704	−0.235852	+	0.971789i	$0.575788\pi$
$480$	449.774	0.0427693
$481$	6897.15	0.653811
$482$	183.452	0.0173361
$483$	−965.021	−0.0909109
$484$	0	0
$485$	4243.91	0.397332
$486$	38.1057	0.00355661
$487$	18167.5	1.69045	0.845223	−	0.534414i	$-0.179468\pi$
$487$	18167.5	1.69045	0.845223	+	0.534414i	$0.179468\pi$
$488$	1016.51	0.0942935
$489$	−2407.82	−0.222670
$490$	−259.771	−0.0239495
$491$	11290.7	1.03777	0.518884	−	0.854845i	$-0.326348\pi$
$491$	11290.7	1.03777	0.518884	+	0.854845i	$0.326348\pi$
$492$	−8489.02	−0.777875
$493$	387.940	0.0354400
$494$	−1489.44	−0.135654
$495$	0	0
$496$	12117.7	1.09698
$497$	−3060.52	−0.276223
$498$	−585.051	−0.0526441
$499$	−1012.50	−0.0908329	−0.0454164	−	0.998968i	$-0.514461\pi$
$499$	−1012.50	−0.0908329	−0.0454164	+	0.998968i	$0.514461\pi$
$500$	−996.926	−0.0891678
$501$	6380.50	0.568981
$502$	−1155.35	−0.102721
$503$	12451.1	1.10371	0.551857	−	0.833939i	$-0.313919\pi$
$503$	12451.1	1.10371	0.551857	+	0.833939i	$0.313919\pi$
$504$	−77.0828	−0.00681258
$505$	2427.45	0.213901
$506$	0	0
$507$	5297.57	0.464050
$508$	−20824.7	−1.81879
$509$	−651.996	−0.0567765	−0.0283882	−	0.999597i	$-0.509037\pi$
$509$	−651.996	−0.0567765	−0.0283882	+	0.999597i	$0.509037\pi$
$510$	71.4574	0.00620429
$511$	2926.02	0.253306
$512$	3172.18	0.273813
$513$	−4073.79	−0.350608
$514$	1275.08	0.109419
$515$	4632.16	0.396344
$516$	−1130.07	−0.0964118
$517$	0	0
$518$	58.7393	0.00498235
$519$	4737.33	0.400666
$520$	−788.515	−0.0664975
$521$	−14746.2	−1.24000	−0.620002	−	0.784600i	$-0.712868\pi$
$521$	−14746.2	−1.24000	−0.620002	+	0.784600i	$0.712868\pi$
$522$	18.0226	0.00151117
$523$	−16966.9	−1.41857	−0.709284	−	0.704923i	$-0.750982\pi$
$523$	−16966.9	−1.41857	−0.709284	+	0.704923i	$0.750982\pi$
$524$	−15586.8	−1.29945
$525$	256.413	0.0213158
$526$	444.834	0.0368739
$527$	5805.39	0.479861
$528$	0	0
$529$	−3314.37	−0.272406
$530$	392.205	0.0321439
$531$	−2052.78	−0.167764
$532$	4114.02	0.335274
$533$	22335.1	1.81508
$534$	−70.3964	−0.00570478
$535$	1339.27	0.108227
$536$	2070.32	0.166837
$537$	−10470.3	−0.841388
$538$	−130.084	−0.0104243
$539$	0	0
$540$	−1076.68	−0.0858017
$541$	−8957.54	−0.711857	−0.355929	−	0.934513i	$-0.615835\pi$
$541$	−8957.54	−0.711857	−0.355929	+	0.934513i	$0.615835\pi$
$542$	283.537	0.0224704
$543$	−4852.69	−0.383516
$544$	910.909	0.0717921
$545$	1792.43	0.140879
$546$	101.248	0.00793596
$547$	−19479.0	−1.52260	−0.761299	−	0.648401i	$-0.775438\pi$
$547$	−19479.0	−1.52260	−0.761299	+	0.648401i	$0.775438\pi$
$548$	−23959.4	−1.86769
$549$	−3651.90	−0.283896
$550$	0	0
$551$	−1926.76	−0.148970
$552$	707.120	0.0545236
$553$	1921.25	0.147740
$554$	734.929	0.0563612
$555$	1643.45	0.125695
$556$	7622.24	0.581394
$557$	9272.70	0.705380	0.352690	−	0.935740i	$-0.385267\pi$
$557$	9272.70	0.705380	0.352690	+	0.935740i	$0.385267\pi$
$558$	269.703	0.0204613
$559$	2973.27	0.224966
$560$	1083.95	0.0817952
$561$	0	0
$562$	1224.54	0.0919113
$563$	17645.9	1.32093	0.660467	−	0.750855i	$-0.270358\pi$
$563$	17645.9	1.32093	0.660467	+	0.750855i	$0.270358\pi$
$564$	−6639.46	−0.495695
$565$	−1206.96	−0.0898714
$566$	10.0692	0.000747777 0
$567$	276.926	0.0205111
$568$	2242.60	0.165664
$569$	−8772.48	−0.646330	−0.323165	−	0.946343i	$-0.604747\pi$
$569$	−8772.48	−0.646330	−0.323165	+	0.946343i	$0.604747\pi$
$570$	−354.903	−0.0260794
$571$	5985.60	0.438686	0.219343	−	0.975648i	$-0.429609\pi$
$571$	5985.60	0.438686	0.219343	+	0.975648i	$0.429609\pi$
$572$	0	0
$573$	−6153.81	−0.448654
$574$	190.216	0.0138318
$575$	−2352.21	−0.170598
$576$	−4523.23	−0.327201
$577$	24964.8	1.80121	0.900607	−	0.434635i	$-0.143123\pi$
$577$	24964.8	1.80121	0.900607	+	0.434635i	$0.143123\pi$
$578$	−625.705	−0.0450275
$579$	5665.60	0.406656
$580$	−509.232	−0.0364564
$581$	−4251.75	−0.303601
$582$	399.301	0.0284391
$583$	0	0
$584$	−2144.04	−0.151920
$585$	2832.81	0.200209
$586$	265.933	0.0187467
$587$	2876.77	0.202277	0.101139	−	0.994872i	$-0.467751\pi$
$587$	2876.77	0.202277	0.101139	+	0.994872i	$0.467751\pi$
$588$	7927.03	0.555962
$589$	−28833.3	−2.01707
$590$	−178.835	−0.0124789
$591$	13057.1	0.908797
$592$	6947.46	0.482329
$593$	−8490.12	−0.587938	−0.293969	−	0.955815i	$-0.594976\pi$
$593$	−8490.12	−0.587938	−0.293969	+	0.955815i	$0.594976\pi$
$594$	0	0
$595$	519.304	0.0357805
$596$	3138.22	0.215682
$597$	7967.59	0.546217
$598$	−928.804	−0.0635144
$599$	21683.0	1.47904	0.739520	−	0.673135i	$-0.235053\pi$
$599$	21683.0	1.47904	0.739520	+	0.673135i	$0.235053\pi$
$600$	−187.887	−0.0127841
$601$	−9359.70	−0.635258	−0.317629	−	0.948215i	$-0.602887\pi$
$601$	−9359.70	−0.635258	−0.317629	+	0.948215i	$0.602887\pi$
$602$	25.3217	0.00171435
$603$	−7437.81	−0.502307
$604$	−19318.5	−1.30142
$605$	0	0
$606$	228.395	0.0153101
$607$	−4717.04	−0.315418	−0.157709	−	0.987486i	$-0.550411\pi$
$607$	−4717.04	−0.315418	−0.157709	+	0.987486i	$0.550411\pi$
$608$	−4524.15	−0.301774
$609$	130.976	0.00871499
$610$	−318.148	−0.0211171
$611$	17468.8	1.15665
$612$	−2180.56	−0.144026
$613$	−13744.3	−0.905589	−0.452795	−	0.891615i	$-0.649573\pi$
$613$	−13744.3	−0.905589	−0.452795	+	0.891615i	$0.649573\pi$
$614$	235.914	0.0155060
$615$	5321.99	0.348949
$616$	0	0
$617$	−25101.5	−1.63784	−0.818921	−	0.573907i	$-0.805427\pi$
$617$	−25101.5	−1.63784	−0.818921	+	0.573907i	$0.805427\pi$
$618$	435.831	0.0283685
$619$	4014.06	0.260644	0.130322	−	0.991472i	$-0.458399\pi$
$619$	4014.06	0.260644	0.130322	+	0.991472i	$0.458399\pi$
$620$	−7620.48	−0.493622
$621$	−2540.39	−0.164158
$622$	−792.233	−0.0510702
$623$	−511.593	−0.0328997
$624$	11975.3	0.768262
$625$	625.000	0.0400000
$626$	867.898	0.0554125
$627$	0	0
$628$	−1939.27	−0.123225
$629$	3328.42	0.210990
$630$	24.1255	0.00152568
$631$	−16546.7	−1.04392	−0.521959	−	0.852971i	$-0.674799\pi$
$631$	−16546.7	−1.04392	−0.521959	+	0.852971i	$0.674799\pi$
$632$	−1407.80	−0.0886065
$633$	9886.40	0.620772
$634$	398.008	0.0249320
$635$	13055.6	0.815897
$636$	−11968.3	−0.746187
$637$	−20856.5	−1.29727
$638$	0	0
$639$	−8056.72	−0.498778
$640$	−1593.45	−0.0984169
$641$	10095.1	0.622047	0.311024	−	0.950402i	$-0.399328\pi$
$641$	10095.1	0.622047	0.311024	+	0.950402i	$0.399328\pi$
$642$	126.009	0.00774641
$643$	−21625.4	−1.32632	−0.663160	−	0.748478i	$-0.730785\pi$
$643$	−21625.4	−1.32632	−0.663160	+	0.748478i	$0.730785\pi$
$644$	2565.48	0.156978
$645$	708.470	0.0432496
$646$	−718.771	−0.0437766
$647$	1595.49	0.0969477	0.0484738	−	0.998824i	$-0.484564\pi$
$647$	1595.49	0.0969477	0.0484738	+	0.998824i	$0.484564\pi$
$648$	−202.918	−0.0123015
$649$	0	0
$650$	246.790	0.0148922
$651$	1960.02	0.118002
$652$	6401.13	0.384490
$653$	−11595.9	−0.694921	−0.347461	−	0.937695i	$-0.612956\pi$
$653$	−11595.9	−0.694921	−0.347461	+	0.937695i	$0.612956\pi$
$654$	168.646	0.0100835
$655$	9771.81	0.582925
$656$	22498.0	1.33902
$657$	7702.65	0.457396
$658$	148.772	0.00881420
$659$	−32754.4	−1.93616	−0.968080	−	0.250643i	$-0.919358\pi$
$659$	−32754.4	−1.93616	−0.968080	+	0.250643i	$0.919358\pi$
$660$	0	0
$661$	19728.5	1.16089	0.580447	−	0.814298i	$-0.302878\pi$
$661$	19728.5	1.16089	0.580447	+	0.814298i	$0.302878\pi$
$662$	−1661.89	−0.0975696
$663$	5737.17	0.336068
$664$	3115.48	0.182084
$665$	−2579.19	−0.150401
$666$	154.629	0.00899665
$667$	−1201.51	−0.0697493
$668$	−16962.4	−0.982475
$669$	1088.61	0.0629117
$670$	−647.972	−0.0373632
$671$	0	0
$672$	307.541	0.0176543
$673$	−834.102	−0.0477745	−0.0238873	−	0.999715i	$-0.507604\pi$
$673$	−834.102	−0.0477745	−0.0238873	+	0.999715i	$0.507604\pi$
$674$	−263.359	−0.0150508
$675$	675.000	0.0384900
$676$	−14083.4	−0.801288
$677$	18030.8	1.02361	0.511803	−	0.859103i	$-0.328978\pi$
$677$	18030.8	1.02361	0.511803	+	0.859103i	$0.328978\pi$
$678$	−113.561	−0.00643257
$679$	2901.85	0.164010
$680$	−380.521	−0.0214593
$681$	−1991.90	−0.112085
$682$	0	0
$683$	11137.0	0.623931	0.311966	−	0.950093i	$-0.399013\pi$
$683$	11137.0	0.623931	0.311966	+	0.950093i	$0.399013\pi$
$684$	10830.0	0.605405
$685$	15020.8	0.837833
$686$	−361.513	−0.0201204
$687$	16405.7	0.911086
$688$	2994.96	0.165962
$689$	31489.3	1.74114
$690$	−221.315	−0.0122106
$691$	147.291	0.00810887	0.00405443	−	0.999992i	$-0.498709\pi$
$691$	147.291	0.00810887	0.00405443	+	0.999992i	$0.498709\pi$
$692$	−12594.0	−0.691840
$693$	0	0
$694$	−1216.75	−0.0665520
$695$	−4778.59	−0.260809
$696$	−95.9731	−0.00522680
$697$	10778.4	0.585742
$698$	−1077.44	−0.0584265
$699$	−784.129	−0.0424299
$700$	−681.667	−0.0368066
$701$	3627.58	0.195452	0.0977260	−	0.995213i	$-0.468843\pi$
$701$	3627.58	0.195452	0.0977260	+	0.995213i	$0.468843\pi$
$702$	266.533	0.0143300
$703$	−16531.0	−0.886885
$704$	0	0
$705$	4162.46	0.222365
$706$	−114.989	−0.00612983
$707$	1659.82	0.0882939
$708$	5457.24	0.289683
$709$	4994.01	0.264533	0.132267	−	0.991214i	$-0.457774\pi$
$709$	4994.01	0.264533	0.132267	+	0.991214i	$0.457774\pi$
$710$	−701.891	−0.0371007
$711$	5057.64	0.266774
$712$	374.870	0.0197315
$713$	−17980.2	−0.944411
$714$	48.8604	0.00256100
$715$	0	0
$716$	27834.9	1.45285
$717$	13512.8	0.703826
$718$	−974.649	−0.0506596
$719$	6580.64	0.341330	0.170665	−	0.985329i	$-0.445408\pi$
$719$	6580.64	0.341330	0.170665	+	0.985329i	$0.445408\pi$
$720$	2853.47	0.147698
$721$	3167.33	0.163602
$722$	2494.29	0.128570
$723$	3509.62	0.180531
$724$	12900.7	0.662227
$725$	319.251	0.0163540
$726$	0	0
$727$	−15359.8	−0.783581	−0.391790	−	0.920055i	$-0.628144\pi$
$727$	−15359.8	−0.783581	−0.391790	+	0.920055i	$0.628144\pi$
$728$	−539.162	−0.0274487
$729$	729.000	0.0370370
$730$	671.045	0.0340226
$731$	1434.84	0.0725983
$732$	9708.46	0.490212
$733$	−20852.9	−1.05078	−0.525388	−	0.850863i	$-0.676080\pi$
$733$	−20852.9	−1.05078	−0.525388	+	0.850863i	$0.676080\pi$
$734$	402.616	0.0202463
$735$	−4969.67	−0.249400
$736$	−2821.23	−0.141294
$737$	0	0
$738$	500.737	0.0249761
$739$	−20359.7	−1.01346	−0.506729	−	0.862106i	$-0.669145\pi$
$739$	−20359.7	−1.01346	−0.506729	+	0.862106i	$0.669145\pi$
$740$	−4369.07	−0.217041
$741$	−28494.4	−1.41264
$742$	268.177	0.0132683
$743$	11595.0	0.572515	0.286257	−	0.958153i	$-0.407589\pi$
$743$	11595.0	0.572515	0.286257	+	0.958153i	$0.407589\pi$
$744$	−1436.20	−0.0707713
$745$	−1967.44	−0.0967534
$746$	1612.81	0.0791544
$747$	−11192.6	−0.548214
$748$	0	0
$749$	915.751	0.0446740
$750$	58.8051	0.00286301
$751$	22660.9	1.10107	0.550537	−	0.834811i	$-0.314423\pi$
$751$	22660.9	1.10107	0.550537	+	0.834811i	$0.314423\pi$
$752$	17596.2	0.853282
$753$	−22103.0	−1.06969
$754$	126.061	0.00608868
$755$	12111.3	0.583808
$756$	−736.200	−0.0354171
$757$	−23449.2	−1.12586	−0.562931	−	0.826504i	$-0.690326\pi$
$757$	−23449.2	−1.12586	−0.562931	+	0.826504i	$0.690326\pi$
$758$	−1705.52	−0.0817246
$759$	0	0
$760$	1889.91	0.0902028
$761$	−17965.0	−0.855758	−0.427879	−	0.903836i	$-0.640739\pi$
$761$	−17965.0	−0.855758	−0.427879	+	0.903836i	$0.640739\pi$
$762$	1228.38	0.0583981
$763$	1225.60	0.0581519
$764$	16359.7	0.774703
$765$	1367.05	0.0646090
$766$	2111.70	0.0996068
$767$	−14358.3	−0.675943
$768$	11912.0	0.559685
$769$	23205.3	1.08817	0.544087	−	0.839029i	$-0.316876\pi$
$769$	23205.3	1.08817	0.544087	+	0.839029i	$0.316876\pi$
$770$	0	0
$771$	24393.6	1.13945
$772$	−15061.8	−0.702185
$773$	−6334.00	−0.294719	−0.147360	−	0.989083i	$-0.547078\pi$
$773$	−6334.00	−0.294719	−0.147360	+	0.989083i	$0.547078\pi$
$774$	66.6587	0.00309560
$775$	4777.48	0.221435
$776$	−2126.33	−0.0983646
$777$	1123.74	0.0518841
$778$	−489.822	−0.0225719
$779$	−53532.5	−2.46213
$780$	−7530.93	−0.345706
$781$	0	0
$782$	−448.221	−0.0204966
$783$	344.791	0.0157367
$784$	−21008.6	−0.957025
$785$	1215.78	0.0552779
$786$	919.411	0.0417231
$787$	−43343.1	−1.96317	−0.981584	−	0.191029i	$-0.938818\pi$
$787$	−43343.1	−1.96317	−0.981584	+	0.191029i	$0.938818\pi$
$788$	−34712.0	−1.56924
$789$	8510.12	0.383990
$790$	440.615	0.0198435
$791$	−825.284	−0.0370970
$792$	0	0
$793$	−25543.5	−1.14385
$794$	−1912.29	−0.0854719
$795$	7503.27	0.334734
$796$	−21181.6	−0.943168
$797$	−24002.6	−1.06677	−0.533386	−	0.845872i	$-0.679081\pi$
$797$	−24002.6	−1.06677	−0.533386	+	0.845872i	$0.679081\pi$
$798$	−242.671	−0.0107650
$799$	8430.07	0.373260
$800$	749.623	0.0331290
$801$	−1346.75	−0.0594072
$802$	151.289	0.00666111
$803$	0	0
$804$	19773.2	0.867347
$805$	−1608.37	−0.0704193
$806$	1886.46	0.0824413
$807$	−2488.63	−0.108555
$808$	−1216.23	−0.0529541
$809$	−10485.3	−0.455678	−0.227839	−	0.973699i	$-0.573166\pi$
$809$	−10485.3	−0.455678	−0.227839	+	0.973699i	$0.573166\pi$
$810$	63.5095	0.00275493
$811$	−38528.5	−1.66821	−0.834106	−	0.551604i	$-0.814016\pi$
$811$	−38528.5	−1.66821	−0.834106	+	0.551604i	$0.814016\pi$
$812$	−348.197	−0.0150484
$813$	5424.34	0.233997
$814$	0	0
$815$	−4013.04	−0.172479
$816$	5779.02	0.247924
$817$	−7126.31	−0.305163
$818$	−1781.17	−0.0761333
$819$	1936.98	0.0826419
$820$	−14148.4	−0.602539
$821$	94.0122	0.00399640	0.00199820	−	0.999998i	$-0.499364\pi$
$821$	94.0122	0.00399640	0.00199820	+	0.999998i	$0.499364\pi$
$822$	1413.28	0.0599682
$823$	−317.906	−0.0134648	−0.00673238	−	0.999977i	$-0.502143\pi$
$823$	−317.906	−0.0134648	−0.00673238	+	0.999977i	$0.502143\pi$
$824$	−2320.86	−0.0981202
$825$	0	0
$826$	−122.282	−0.00515100
$827$	45494.2	1.91292	0.956462	−	0.291857i	$-0.0942733\pi$
$827$	45494.2	1.91292	0.956462	+	0.291857i	$0.0942733\pi$
$828$	6753.54	0.283456
$829$	2268.53	0.0950415	0.0475208	−	0.998870i	$-0.484868\pi$
$829$	2268.53	0.0950415	0.0475208	+	0.998870i	$0.484868\pi$
$830$	−975.085	−0.0407779
$831$	14059.9	0.586923
$832$	−31638.1	−1.31833
$833$	−10064.9	−0.418641
$834$	−449.609	−0.0186675
$835$	10634.2	0.440731
$836$	0	0
$837$	5159.68	0.213076
$838$	1193.95	0.0492175
$839$	32836.0	1.35116	0.675582	−	0.737285i	$-0.263893\pi$
$839$	32836.0	1.35116	0.675582	+	0.737285i	$0.263893\pi$
$840$	−128.471	−0.00527700
$841$	−24225.9	−0.993314
$842$	−1795.39	−0.0734838
$843$	23426.7	0.957127
$844$	−26282.7	−1.07190
$845$	8829.29	0.359452
$846$	391.638	0.0159158
$847$	0	0
$848$	31719.0	1.28448
$849$	192.634	0.00778704
$850$	119.096	0.00480582
$851$	−10308.7	−0.415248
$852$	21418.6	0.861253
$853$	−20888.1	−0.838445	−0.419222	−	0.907884i	$-0.637697\pi$
$853$	−20888.1	−0.838445	−0.419222	+	0.907884i	$0.637697\pi$
$854$	−217.540	−0.00871670
$855$	−6789.64	−0.271580
$856$	−671.018	−0.0267931
$857$	−1800.87	−0.0717813	−0.0358907	−	0.999356i	$-0.511427\pi$
$857$	−1800.87	−0.0717813	−0.0358907	+	0.999356i	$0.511427\pi$
$858$	0	0
$859$	−26088.2	−1.03622	−0.518112	−	0.855313i	$-0.673365\pi$
$859$	−26088.2	−1.03622	−0.518112	+	0.855313i	$0.673365\pi$
$860$	−1883.45	−0.0746802
$861$	3639.01	0.144039
$862$	−19.8331	−0.000783665 0
$863$	41057.1	1.61947	0.809733	−	0.586799i	$-0.199612\pi$
$863$	41057.1	1.61947	0.809733	+	0.586799i	$0.199612\pi$
$864$	809.593	0.0318784
$865$	7895.55	0.310354
$866$	29.7137	0.00116595
$867$	−11970.4	−0.468898
$868$	−5210.64	−0.203757
$869$	0	0
$870$	30.0377	0.00117055
$871$	−52024.4	−2.02386
$872$	−898.064	−0.0348765
$873$	7639.03	0.296154
$874$	2226.15	0.0861564
$875$	427.355	0.0165111
$876$	−20477.3	−0.789797
$877$	−47000.6	−1.80969	−0.904845	−	0.425741i	$-0.860013\pi$
$877$	−47000.6	−1.80969	−0.904845	+	0.425741i	$0.860013\pi$
$878$	870.947	0.0334773
$879$	5087.56	0.195221
$880$	0	0
$881$	10193.9	0.389830	0.194915	−	0.980820i	$-0.437557\pi$
$881$	10193.9	0.389830	0.194915	+	0.980820i	$0.437557\pi$
$882$	−467.587	−0.0178509
$883$	15504.6	0.590907	0.295454	−	0.955357i	$-0.404529\pi$
$883$	15504.6	0.590907	0.295454	+	0.955357i	$0.404529\pi$
$884$	−15252.1	−0.580298
$885$	−3421.29	−0.129950
$886$	1969.14	0.0746667
$887$	−37461.0	−1.41806	−0.709029	−	0.705179i	$-0.750867\pi$
$887$	−37461.0	−1.41806	−0.709029	+	0.705179i	$0.750867\pi$
$888$	−823.422	−0.0311174
$889$	8926.99	0.336785
$890$	−117.327	−0.00441890
$891$	0	0
$892$	−2894.02	−0.108631
$893$	−41869.1	−1.56898
$894$	−185.112	−0.00692515
$895$	−17450.4	−0.651736
$896$	−1089.55	−0.0406244
$897$	−17768.9	−0.661413
$898$	−2078.92	−0.0772544
$899$	2440.35	0.0905341
$900$	−1794.47	−0.0664617
$901$	15196.1	0.561881
$902$	0	0
$903$	484.430	0.0178525
$904$	604.728	0.0222488
$905$	−8087.82	−0.297070
$906$	1139.53	0.0417862
$907$	−6747.41	−0.247017	−0.123508	−	0.992344i	$-0.539415\pi$
$907$	−6747.41	−0.247017	−0.123508	+	0.992344i	$0.539415\pi$
$908$	5295.41	0.193540
$909$	4369.41	0.159433
$910$	168.747	0.00614717
$911$	42639.7	1.55073	0.775366	−	0.631512i	$-0.217565\pi$
$911$	42639.7	1.55073	0.775366	+	0.631512i	$0.217565\pi$
$912$	−28702.3	−1.04214
$913$	0	0
$914$	−77.9975	−0.00282268
$915$	−6086.49	−0.219905
$916$	−43614.0	−1.57320
$917$	6681.66	0.240619
$918$	128.623	0.00462441
$919$	20125.4	0.722391	0.361195	−	0.932490i	$-0.382369\pi$
$919$	20125.4	0.722391	0.361195	+	0.932490i	$0.382369\pi$
$920$	1178.53	0.0422338
$921$	4513.27	0.161474
$922$	1739.15	0.0621211
$923$	−56353.4	−2.00964
$924$	0	0
$925$	2739.09	0.0973628
$926$	−629.305	−0.0223329
$927$	8337.89	0.295418
$928$	382.909	0.0135448
$929$	5615.72	0.198327	0.0991636	−	0.995071i	$-0.468383\pi$
$929$	5615.72	0.198327	0.0991636	+	0.995071i	$0.468383\pi$
$930$	449.505	0.0158493
$931$	49988.6	1.75973
$932$	2084.58	0.0732648
$933$	−15156.2	−0.531824
$934$	−1183.48	−0.0414610
$935$	0	0
$936$	−1419.33	−0.0495643
$937$	−21943.4	−0.765058	−0.382529	−	0.923943i	$-0.624947\pi$
$937$	−21943.4	−0.765058	−0.382529	+	0.923943i	$0.624947\pi$
$938$	−443.063	−0.0154227
$939$	16603.8	0.577043
$940$	−11065.8	−0.383964
$941$	2722.24	0.0943066	0.0471533	−	0.998888i	$-0.484985\pi$
$941$	2722.24	0.0943066	0.0471533	+	0.998888i	$0.484985\pi$
$942$	114.391	0.00395653
$943$	−33382.5	−1.15279
$944$	−14463.0	−0.498657
$945$	461.544	0.0158879
$946$	0	0
$947$	−26690.9	−0.915879	−0.457939	−	0.888983i	$-0.651412\pi$
$947$	−26690.9	−0.915879	−0.457939	+	0.888983i	$0.651412\pi$
$948$	−13445.6	−0.460646
$949$	53876.8	1.84290
$950$	−591.505	−0.0202010
$951$	7614.28	0.259632
$952$	−260.188	−0.00885792
$953$	11714.0	0.398169	0.199084	−	0.979982i	$-0.436203\pi$
$953$	11714.0	0.398169	0.199084	+	0.979982i	$0.436203\pi$
$954$	705.969	0.0239587
$955$	−10256.3	−0.347526
$956$	−35923.3	−1.21532
$957$	0	0
$958$	−775.455	−0.0261522
$959$	10270.8	0.345840
$960$	−7538.72	−0.253449
$961$	6727.97	0.225839
$962$	1081.57	0.0362486
$963$	2410.69	0.0806680
$964$	−9330.21	−0.311728
$965$	9442.66	0.314995
$966$	−151.328	−0.00504028
$967$	−46878.1	−1.55894	−0.779472	−	0.626437i	$-0.784512\pi$
$967$	−46878.1	−1.55894	−0.779472	+	0.626437i	$0.784512\pi$
$968$	0	0
$969$	−13750.8	−0.455871
$970$	665.502	0.0220289
$971$	17315.9	0.572289	0.286145	−	0.958186i	$-0.407626\pi$
$971$	17315.9	0.572289	0.286145	+	0.958186i	$0.407626\pi$
$972$	−1938.02	−0.0639528
$973$	−3267.45	−0.107656
$974$	2848.91	0.0937217
$975$	4721.34	0.155081
$976$	−25729.8	−0.843843
$977$	−46689.4	−1.52889	−0.764446	−	0.644688i	$-0.776987\pi$
$977$	−46689.4	−1.52889	−0.764446	+	0.644688i	$0.776987\pi$
$978$	−377.580	−0.0123453
$979$	0	0
$980$	13211.7	0.430646
$981$	3226.37	0.105005
$982$	1770.54	0.0575359
$983$	8591.26	0.278758	0.139379	−	0.990239i	$-0.455489\pi$
$983$	8591.26	0.278758	0.139379	+	0.990239i	$0.455489\pi$
$984$	−2666.49	−0.0863868
$985$	21761.9	0.703951
$986$	60.8343	0.00196487
$987$	2846.16	0.0917875
$988$	75751.6	2.43925
$989$	−4443.92	−0.142880
$990$	0	0
$991$	3222.97	0.103311	0.0516554	−	0.998665i	$-0.483550\pi$
$991$	3222.97	0.103311	0.0516554	+	0.998665i	$0.483550\pi$
$992$	5730.10	0.183398
$993$	−31793.5	−1.01605
$994$	−479.931	−0.0153144
$995$	13279.3	0.423098
$996$	29755.2	0.946616
$997$	35074.3	1.11416	0.557078	−	0.830460i	$-0.311922\pi$
$997$	35074.3	1.11416	0.557078	+	0.830460i	$0.311922\pi$
$998$	−158.773	−0.00503595
$999$	2958.21	0.0936874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bn.1.6		12
11.5	even	5		165.4.m.a.91.4	✓	24
11.9	even	5		165.4.m.a.136.4	yes	24
11.10	odd	2		1815.4.a.bh.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.a.91.4	✓	24	11.5	even	5
165.4.m.a.136.4	yes	24	11.9	even	5
1815.4.a.bh.1.7		12	11.10	odd	2
1815.4.a.bn.1.6		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)

\(f(q)\)	\(=\)	\(q+0.156814 q^{2} +3.00000 q^{3} -7.97541 q^{4} +5.00000 q^{5} +0.470441 q^{6} +3.41884 q^{7} -2.50516 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.156814 q^{2} +3.00000 q^{3} -7.97541 q^{4} +5.00000 q^{5} +0.470441 q^{6} +3.41884 q^{7} -2.50516 q^{8} +9.00000 q^{9} +0.784068 q^{10} -23.9262 q^{12} +62.9512 q^{13} +0.536121 q^{14} +15.0000 q^{15} +63.4104 q^{16} +30.3789 q^{17} +1.41132 q^{18} -150.881 q^{19} -39.8770 q^{20} +10.2565 q^{21} -94.0884 q^{23} -7.51549 q^{24} +25.0000 q^{25} +9.87161 q^{26} +27.0000 q^{27} -27.2667 q^{28} +12.7700 q^{29} +2.35220 q^{30} +191.099 q^{31} +29.9849 q^{32} +4.76383 q^{34} +17.0942 q^{35} -71.7787 q^{36} +109.563 q^{37} -23.6602 q^{38} +188.854 q^{39} -12.5258 q^{40} +354.800 q^{41} +1.60836 q^{42} +47.2313 q^{43} +45.0000 q^{45} -14.7543 q^{46} +277.497 q^{47} +190.231 q^{48} -331.312 q^{49} +3.92034 q^{50} +91.1368 q^{51} -502.062 q^{52} +500.218 q^{53} +4.23397 q^{54} -8.56476 q^{56} -452.643 q^{57} +2.00252 q^{58} -228.086 q^{59} -119.631 q^{60} -405.766 q^{61} +29.9670 q^{62} +30.7696 q^{63} -502.581 q^{64} +314.756 q^{65} -826.423 q^{67} -242.284 q^{68} -282.265 q^{69} +2.68061 q^{70} -895.191 q^{71} -22.5465 q^{72} +855.850 q^{73} +17.1810 q^{74} +75.0000 q^{75} +1203.34 q^{76} +29.6148 q^{78} +561.960 q^{79} +317.052 q^{80} +81.0000 q^{81} +55.6374 q^{82} -1243.62 q^{83} -81.8000 q^{84} +151.895 q^{85} +7.40652 q^{86} +38.3101 q^{87} -149.639 q^{89} +7.05661 q^{90} +215.220 q^{91} +750.394 q^{92} +573.298 q^{93} +43.5154 q^{94} -754.405 q^{95} +89.9547 q^{96} +848.781 q^{97} -51.9542 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9}+O(q^{10}) \) 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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