LMFDB - Embedded newform 475.4.b.a.324.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,4,Mod(324,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("475.324");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	475.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$28.0259072527$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	475.324
Dual form			475.4.b.a.324.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.00000i q^{2} +4.00000i q^{3} -17.0000 q^{4} +20.0000 q^{6} +32.0000i q^{7} +45.0000i q^{8} +11.0000 q^{9} +O(q^{10})$	\(q-5.00000i q^{2} +4.00000i q^{3} -17.0000 q^{4} +20.0000 q^{6} +32.0000i q^{7} +45.0000i q^{8} +11.0000 q^{9} -12.0000 q^{11} -68.0000i q^{12} -42.0000i q^{13} +160.000 q^{14} +89.0000 q^{16} -114.000i q^{17} -55.0000i q^{18} -19.0000 q^{19} -128.000 q^{21} +60.0000i q^{22} +160.000i q^{23} -180.000 q^{24} -210.000 q^{26} +152.000i q^{27} -544.000i q^{28} -214.000 q^{29} -144.000 q^{31} -85.0000i q^{32} -48.0000i q^{33} -570.000 q^{34} -187.000 q^{36} -94.0000i q^{37} +95.0000i q^{38} +168.000 q^{39} -6.00000 q^{41} +640.000i q^{42} -308.000i q^{43} +204.000 q^{44} +800.000 q^{46} -184.000i q^{47} +356.000i q^{48} -681.000 q^{49} +456.000 q^{51} +714.000i q^{52} -274.000i q^{53} +760.000 q^{54} -1440.00 q^{56} -76.0000i q^{57} +1070.00i q^{58} -276.000 q^{59} -826.000 q^{61} +720.000i q^{62} +352.000i q^{63} +287.000 q^{64} -240.000 q^{66} -52.0000i q^{67} +1938.00i q^{68} -640.000 q^{69} -344.000 q^{71} +495.000i q^{72} -166.000i q^{73} -470.000 q^{74} +323.000 q^{76} -384.000i q^{77} -840.000i q^{78} +688.000 q^{79} -311.000 q^{81} +30.0000i q^{82} +996.000i q^{83} +2176.00 q^{84} -1540.00 q^{86} -856.000i q^{87} -540.000i q^{88} -1578.00 q^{89} +1344.00 q^{91} -2720.00i q^{92} -576.000i q^{93} -920.000 q^{94} +340.000 q^{96} -786.000i q^{97} +3405.00i q^{98} -132.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 34 q^{4} + 40 q^{6} + 22 q^{9}+O(q^{10}) $ 2 * q - 34 * q^4 + 40 * q^6 + 22 * q^9	$ 2 q - 34 q^{4} + 40 q^{6} + 22 q^{9} - 24 q^{11} + 320 q^{14} + 178 q^{16} - 38 q^{19} - 256 q^{21} - 360 q^{24} - 420 q^{26} - 428 q^{29} - 288 q^{31} - 1140 q^{34} - 374 q^{36} + 336 q^{39} - 12 q^{41} + 408 q^{44} + 1600 q^{46} - 1362 q^{49} + 912 q^{51} + 1520 q^{54} - 2880 q^{56} - 552 q^{59} - 1652 q^{61} + 574 q^{64} - 480 q^{66} - 1280 q^{69} - 688 q^{71} - 940 q^{74} + 646 q^{76} + 1376 q^{79} - 622 q^{81} + 4352 q^{84} - 3080 q^{86} - 3156 q^{89} + 2688 q^{91} - 1840 q^{94} + 680 q^{96} - 264 q^{99}+O(q^{100}) $ 2 * q - 34 * q^4 + 40 * q^6 + 22 * q^9 - 24 * q^11 + 320 * q^14 + 178 * q^16 - 38 * q^19 - 256 * q^21 - 360 * q^24 - 420 * q^26 - 428 * q^29 - 288 * q^31 - 1140 * q^34 - 374 * q^36 + 336 * q^39 - 12 * q^41 + 408 * q^44 + 1600 * q^46 - 1362 * q^49 + 912 * q^51 + 1520 * q^54 - 2880 * q^56 - 552 * q^59 - 1652 * q^61 + 574 * q^64 - 480 * q^66 - 1280 * q^69 - 688 * q^71 - 940 * q^74 + 646 * q^76 + 1376 * q^79 - 622 * q^81 + 4352 * q^84 - 3080 * q^86 - 3156 * q^89 + 2688 * q^91 - 1840 * q^94 + 680 * q^96 - 264 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	− 5.00000i	− 1.76777i	−0.467707	−	0.883883i	$-0.654920\pi$
$2$	− 5.00000i	− 1.76777i	0.467707	−	0.883883i	$-0.345080\pi$
$3$	4.00000i	0.769800i	0.922958	+	0.384900i	$0.125764\pi$
$3$	4.00000i	0.769800i	−0.922958	+	0.384900i	$0.874236\pi$
$4$	−17.0000	−2.12500
$5$	0	0
$5$	0	0
$6$	20.0000	1.36083
$7$	32.0000i	1.72784i	0.503631	+	0.863919i	$0.331997\pi$
$7$	32.0000i	1.72784i	−0.503631	+	0.863919i	$0.668003\pi$
$8$	45.0000i	1.98874i
$9$	11.0000	0.407407
$10$	0	0
$11$	−12.0000	−0.328921	−0.164461	−	0.986384i	$-0.552588\pi$
$11$	−12.0000	−0.328921	−0.164461	+	0.986384i	$0.552588\pi$
$12$	− 68.0000i	− 1.63583i
$13$	− 42.0000i	− 0.896054i	−0.894020	−	0.448027i	$-0.852127\pi$
$13$	− 42.0000i	− 0.896054i	0.894020	−	0.448027i	$-0.147873\pi$
$14$	160.000	3.05441
$15$	0	0
$16$	89.0000	1.39062
$17$	− 114.000i	− 1.62642i	−0.581974	−	0.813208i	$-0.697719\pi$
$17$	− 114.000i	− 1.62642i	0.581974	−	0.813208i	$-0.302281\pi$
$18$	− 55.0000i	− 0.720201i
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	−128.000	−1.33009
$22$	60.0000i	0.581456i
$23$	160.000i	1.45054i	0.688467	+	0.725268i	$0.258284\pi$
$23$	160.000i	1.45054i	−0.688467	+	0.725268i	$0.741716\pi$
$24$	−180.000	−1.53093
$25$	0	0
$26$	−210.000	−1.58401
$27$	152.000i	1.08342i
$28$	− 544.000i	− 3.67165i
$29$	−214.000	−1.37030	−0.685152	−	0.728400i	$-0.740264\pi$
$29$	−214.000	−1.37030	−0.685152	+	0.728400i	$0.740264\pi$
$30$	0	0
$31$	−144.000	−0.834296	−0.417148	−	0.908839i	$-0.636970\pi$
$31$	−144.000	−0.834296	−0.417148	+	0.908839i	$0.636970\pi$
$32$	− 85.0000i	− 0.469563i
$33$	− 48.0000i	− 0.253204i
$34$	−570.000	−2.87512
$35$	0	0
$36$	−187.000	−0.865741
$37$	− 94.0000i	− 0.417662i	−0.977952	−	0.208831i	$-0.933034\pi$
$37$	− 94.0000i	− 0.417662i	0.977952	−	0.208831i	$-0.0669659\pi$
$38$	95.0000i	0.405554i
$39$	168.000	0.689783
$40$	0	0
$41$	−6.00000	−0.0228547	−0.0114273	−	0.999935i	$-0.503638\pi$
$41$	−6.00000	−0.0228547	−0.0114273	+	0.999935i	$0.503638\pi$
$42$	640.000i	2.35129i
$43$	− 308.000i	− 1.09232i	−0.837682	−	0.546158i	$-0.816090\pi$
$43$	− 308.000i	− 1.09232i	0.837682	−	0.546158i	$-0.183910\pi$
$44$	204.000	0.698958
$45$	0	0
$46$	800.000	2.56421
$47$	− 184.000i	− 0.571046i	−0.958372	−	0.285523i	$-0.907833\pi$
$47$	− 184.000i	− 0.571046i	0.958372	−	0.285523i	$-0.0921673\pi$
$48$	356.000i	1.07050i
$49$	−681.000	−1.98542
$50$	0	0
$51$	456.000	1.25202
$52$	714.000i	1.90412i
$53$	− 274.000i	− 0.710128i	−0.934842	−	0.355064i	$-0.884459\pi$
$53$	− 274.000i	− 0.710128i	0.934842	−	0.355064i	$-0.115541\pi$
$54$	760.000	1.91524
$55$	0	0
$56$	−1440.00	−3.43622
$57$	− 76.0000i	− 0.176604i
$58$	1070.00i	2.42238i
$59$	−276.000	−0.609019	−0.304510	−	0.952509i	$-0.598493\pi$
$59$	−276.000	−0.609019	−0.304510	+	0.952509i	$0.598493\pi$
$60$	0	0
$61$	−826.000	−1.73375	−0.866873	−	0.498530i	$-0.833873\pi$
$61$	−826.000	−1.73375	−0.866873	+	0.498530i	$0.833873\pi$
$62$	720.000i	1.47484i
$63$	352.000i	0.703934i
$64$	287.000	0.560547
$65$	0	0
$66$	−240.000	−0.447605
$67$	− 52.0000i	− 0.0948181i	−0.998876	−	0.0474090i	$-0.984904\pi$
$67$	− 52.0000i	− 0.0948181i	0.998876	−	0.0474090i	$-0.0150964\pi$
$68$	1938.00i	3.45613i
$69$	−640.000	−1.11662
$70$	0	0
$71$	−344.000	−0.575004	−0.287502	−	0.957780i	$-0.592825\pi$
$71$	−344.000	−0.575004	−0.287502	+	0.957780i	$0.592825\pi$
$72$	495.000i	0.810227i
$73$	− 166.000i	− 0.266148i	−0.991106	−	0.133074i	$-0.957515\pi$
$73$	− 166.000i	− 0.266148i	0.991106	−	0.133074i	$-0.0424849\pi$
$74$	−470.000	−0.738330
$75$	0	0
$76$	323.000	0.487508
$77$	− 384.000i	− 0.568323i
$78$	− 840.000i	− 1.21938i
$79$	688.000	0.979823	0.489912	−	0.871772i	$-0.337029\pi$
$79$	688.000	0.979823	0.489912	+	0.871772i	$0.337029\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	30.0000i	0.0404018i
$83$	996.000i	1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$	996.000i	1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$	2176.00	2.82644
$85$	0	0
$86$	−1540.00	−1.93096
$87$	− 856.000i	− 1.05486i
$88$	− 540.000i	− 0.654139i
$89$	−1578.00	−1.87941	−0.939706	−	0.341983i	$-0.888901\pi$
$89$	−1578.00	−1.87941	−0.939706	+	0.341983i	$0.888901\pi$
$90$	0	0
$91$	1344.00	1.54824
$92$	− 2720.00i	− 3.08239i
$93$	− 576.000i	− 0.642241i
$94$	−920.000	−1.00948
$95$	0	0
$96$	340.000	0.361470
$97$	− 786.000i	− 0.822744i	−0.911467	−	0.411372i	$-0.865050\pi$
$97$	− 786.000i	− 0.822744i	0.911467	−	0.411372i	$-0.134950\pi$
$98$	3405.00i	3.50976i
$99$	−132.000	−0.134005
$100$	0	0
$101$	126.000	0.124133	0.0620667	−	0.998072i	$-0.480231\pi$
$101$	126.000	0.124133	0.0620667	+	0.998072i	$0.480231\pi$
$102$	− 2280.00i	− 2.21327i
$103$	− 368.000i	− 0.352040i	−0.984387	−	0.176020i	$-0.943678\pi$
$103$	− 368.000i	− 0.352040i	0.984387	−	0.176020i	$-0.0563223\pi$
$104$	1890.00	1.78202
$105$	0	0
$106$	−1370.00	−1.25534
$107$	− 204.000i	− 0.184312i	−0.995745	−	0.0921562i	$-0.970624\pi$
$107$	− 204.000i	− 0.184312i	0.995745	−	0.0921562i	$-0.0293759\pi$
$108$	− 2584.00i	− 2.30227i
$109$	1434.00	1.26011	0.630056	−	0.776549i	$-0.283032\pi$
$109$	1434.00	1.26011	0.630056	+	0.776549i	$0.283032\pi$
$110$	0	0
$111$	376.000	0.321517
$112$	2848.00i	2.40277i
$113$	1218.00i	1.01398i	0.861952	+	0.506990i	$0.169242\pi$
$113$	1218.00i	1.01398i	−0.861952	+	0.506990i	$0.830758\pi$
$114$	−380.000	−0.312195
$115$	0	0
$116$	3638.00	2.91190
$117$	− 462.000i	− 0.365059i
$118$	1380.00i	1.07660i
$119$	3648.00	2.81018
$120$	0	0
$121$	−1187.00	−0.891811
$122$	4130.00i	3.06486i
$123$	− 24.0000i	− 0.0175936i
$124$	2448.00	1.77288
$125$	0	0
$126$	1760.00	1.24439
$127$	− 904.000i	− 0.631630i	−0.948821	−	0.315815i	$-0.897722\pi$
$127$	− 904.000i	− 0.631630i	0.948821	−	0.315815i	$-0.102278\pi$
$128$	− 2115.00i	− 1.46048i
$129$	1232.00	0.840865
$130$	0	0
$131$	−2180.00	−1.45395	−0.726975	−	0.686664i	$-0.759074\pi$
$131$	−2180.00	−1.45395	−0.726975	+	0.686664i	$0.759074\pi$
$132$	816.000i	0.538058i
$133$	− 608.000i	− 0.396393i
$134$	−260.000	−0.167616
$135$	0	0
$136$	5130.00	3.23451
$137$	2566.00i	1.60021i	0.599863	+	0.800103i	$0.295222\pi$
$137$	2566.00i	1.60021i	−0.599863	+	0.800103i	$0.704778\pi$
$138$	3200.00i	1.97393i
$139$	−1988.00	−1.21309	−0.606547	−	0.795048i	$-0.707446\pi$
$139$	−1988.00	−1.21309	−0.606547	+	0.795048i	$0.707446\pi$
$140$	0	0
$141$	736.000	0.439591
$142$	1720.00i	1.01647i
$143$	504.000i	0.294731i
$144$	979.000	0.566551
$145$	0	0
$146$	−830.000	−0.470488
$147$	− 2724.00i	− 1.52838i
$148$	1598.00i	0.887532i
$149$	−1134.00	−0.623496	−0.311748	−	0.950165i	$-0.600914\pi$
$149$	−1134.00	−0.623496	−0.311748	+	0.950165i	$0.600914\pi$
$150$	0	0
$151$	−2440.00	−1.31500	−0.657498	−	0.753456i	$-0.728385\pi$
$151$	−2440.00	−1.31500	−0.657498	+	0.753456i	$0.728385\pi$
$152$	− 855.000i	− 0.456248i
$153$	− 1254.00i	− 0.662614i
$154$	−1920.00	−1.00466
$155$	0	0
$156$	−2856.00	−1.46579
$157$	− 3238.00i	− 1.64599i	−0.568048	−	0.822995i	$-0.692301\pi$
$157$	− 3238.00i	− 1.64599i	0.568048	−	0.822995i	$-0.307699\pi$
$158$	− 3440.00i	− 1.73210i
$159$	1096.00	0.546657
$160$	0	0
$161$	−5120.00	−2.50629
$162$	1555.00i	0.754150i
$163$	− 1420.00i	− 0.682350i	−0.940000	−	0.341175i	$-0.889175\pi$
$163$	− 1420.00i	− 0.682350i	0.940000	−	0.341175i	$-0.110825\pi$
$164$	102.000	0.0485662
$165$	0	0
$166$	4980.00	2.32845
$167$	2336.00i	1.08243i	0.840886	+	0.541213i	$0.182035\pi$
$167$	2336.00i	1.08243i	−0.840886	+	0.541213i	$0.817965\pi$
$168$	− 5760.00i	− 2.64520i
$169$	433.000	0.197087
$170$	0	0
$171$	−209.000	−0.0934657
$172$	5236.00i	2.32117i
$173$	1206.00i	0.530003i	0.964248	+	0.265001i	$0.0853724\pi$
$173$	1206.00i	0.530003i	−0.964248	+	0.265001i	$0.914628\pi$
$174$	−4280.00	−1.86475
$175$	0	0
$176$	−1068.00	−0.457406
$177$	− 1104.00i	− 0.468823i
$178$	7890.00i	3.32236i
$179$	1412.00	0.589597	0.294798	−	0.955559i	$-0.404747\pi$
$179$	1412.00	0.589597	0.294798	+	0.955559i	$0.404747\pi$
$180$	0	0
$181$	3742.00	1.53669	0.768344	−	0.640037i	$-0.221081\pi$
$181$	3742.00	1.53669	0.768344	+	0.640037i	$0.221081\pi$
$182$	− 6720.00i	− 2.73692i
$183$	− 3304.00i	− 1.33464i
$184$	−7200.00	−2.88473
$185$	0	0
$186$	−2880.00	−1.13533
$187$	1368.00i	0.534963i
$188$	3128.00i	1.21347i
$189$	−4864.00	−1.87198
$190$	0	0
$191$	−1472.00	−0.557645	−0.278822	−	0.960343i	$-0.589944\pi$
$191$	−1472.00	−0.557645	−0.278822	+	0.960343i	$0.589944\pi$
$192$	1148.00i	0.431509i
$193$	1458.00i	0.543778i	0.962329	+	0.271889i	$0.0876483\pi$
$193$	1458.00i	0.543778i	−0.962329	+	0.271889i	$0.912352\pi$
$194$	−3930.00	−1.45442
$195$	0	0
$196$	11577.0	4.21902
$197$	− 2046.00i	− 0.739957i	−0.929040	−	0.369978i	$-0.879365\pi$
$197$	− 2046.00i	− 0.739957i	0.929040	−	0.369978i	$-0.120635\pi$
$198$	660.000i	0.236890i
$199$	1496.00	0.532908	0.266454	−	0.963848i	$-0.414148\pi$
$199$	1496.00	0.532908	0.266454	+	0.963848i	$0.414148\pi$
$200$	0	0
$201$	208.000	0.0729910
$202$	− 630.000i	− 0.219439i
$203$	− 6848.00i	− 2.36766i
$204$	−7752.00	−2.66053
$205$	0	0
$206$	−1840.00	−0.622325
$207$	1760.00i	0.590959i
$208$	− 3738.00i	− 1.24608i
$209$	228.000	0.0754598
$210$	0	0
$211$	844.000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	844.000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	4658.00i	1.50902i
$213$	− 1376.00i	− 0.442638i
$214$	−1020.00	−0.325821
$215$	0	0
$216$	−6840.00	−2.15464
$217$	− 4608.00i	− 1.44153i
$218$	− 7170.00i	− 2.22759i
$219$	664.000	0.204881
$220$	0	0
$221$	−4788.00	−1.45736
$222$	− 1880.00i	− 0.568366i
$223$	− 3400.00i	− 1.02099i	−0.859881	−	0.510495i	$-0.829462\pi$
$223$	− 3400.00i	− 1.02099i	0.859881	−	0.510495i	$-0.170538\pi$
$224$	2720.00	0.811329
$225$	0	0
$226$	6090.00	1.79248
$227$	− 1844.00i	− 0.539166i	−0.962977	−	0.269583i	$-0.913114\pi$
$227$	− 1844.00i	− 0.539166i	0.962977	−	0.269583i	$-0.0868858\pi$
$228$	1292.00i	0.375284i
$229$	1090.00	0.314538	0.157269	−	0.987556i	$-0.449731\pi$
$229$	1090.00	0.314538	0.157269	+	0.987556i	$0.449731\pi$
$230$	0	0
$231$	1536.00	0.437495
$232$	− 9630.00i	− 2.72517i
$233$	2842.00i	0.799080i	0.916716	+	0.399540i	$0.130830\pi$
$233$	2842.00i	0.799080i	−0.916716	+	0.399540i	$0.869170\pi$
$234$	−2310.00	−0.645339
$235$	0	0
$236$	4692.00	1.29417
$237$	2752.00i	0.754268i
$238$	− 18240.0i	− 4.96775i
$239$	2400.00	0.649553	0.324776	−	0.945791i	$-0.394711\pi$
$239$	2400.00	0.649553	0.324776	+	0.945791i	$0.394711\pi$
$240$	0	0
$241$	2130.00	0.569317	0.284658	−	0.958629i	$-0.408120\pi$
$241$	2130.00	0.569317	0.284658	+	0.958629i	$0.408120\pi$
$242$	5935.00i	1.57651i
$243$	2860.00i	0.755017i
$244$	14042.0	3.68421
$245$	0	0
$246$	−120.000	−0.0311013
$247$	798.000i	0.205569i
$248$	− 6480.00i	− 1.65920i
$249$	−3984.00	−1.01396
$250$	0	0
$251$	−2364.00	−0.594480	−0.297240	−	0.954803i	$-0.596066\pi$
$251$	−2364.00	−0.594480	−0.297240	+	0.954803i	$0.596066\pi$
$252$	− 5984.00i	− 1.49586i
$253$	− 1920.00i	− 0.477112i
$254$	−4520.00	−1.11657
$255$	0	0
$256$	−8279.00	−2.02124
$257$	− 6290.00i	− 1.52669i	−0.645991	−	0.763345i	$-0.723556\pi$
$257$	− 6290.00i	− 1.52669i	0.645991	−	0.763345i	$-0.276444\pi$
$258$	− 6160.00i	− 1.48645i
$259$	3008.00	0.721653
$260$	0	0
$261$	−2354.00	−0.558272
$262$	10900.0i	2.57025i
$263$	8112.00i	1.90193i	0.309300	+	0.950965i	$0.399905\pi$
$263$	8112.00i	1.90193i	−0.309300	+	0.950965i	$0.600095\pi$
$264$	2160.00	0.503556
$265$	0	0
$266$	−3040.00	−0.700731
$267$	− 6312.00i	− 1.44677i
$268$	884.000i	0.201488i
$269$	4794.00	1.08660	0.543300	−	0.839539i	$-0.317175\pi$
$269$	4794.00	1.08660	0.543300	+	0.839539i	$0.317175\pi$
$270$	0	0
$271$	304.000	0.0681427	0.0340714	−	0.999419i	$-0.489153\pi$
$271$	304.000	0.0681427	0.0340714	+	0.999419i	$0.489153\pi$
$272$	− 10146.0i	− 2.26173i
$273$	5376.00i	1.19183i
$274$	12830.0	2.82879
$275$	0	0
$276$	10880.0	2.37282
$277$	− 2062.00i	− 0.447269i	−0.974673	−	0.223635i	$-0.928208\pi$
$277$	− 2062.00i	− 0.447269i	0.974673	−	0.223635i	$-0.0717922\pi$
$278$	9940.00i	2.14447i
$279$	−1584.00	−0.339898
$280$	0	0
$281$	−4054.00	−0.860645	−0.430323	−	0.902675i	$-0.641600\pi$
$281$	−4054.00	−0.860645	−0.430323	+	0.902675i	$0.641600\pi$
$282$	− 3680.00i	− 0.777095i
$283$	7996.00i	1.67955i	0.542934	+	0.839775i	$0.317313\pi$
$283$	7996.00i	1.67955i	−0.542934	+	0.839775i	$0.682687\pi$
$284$	5848.00	1.22188
$285$	0	0
$286$	2520.00	0.521017
$287$	− 192.000i	− 0.0394892i
$288$	− 935.000i	− 0.191303i
$289$	−8083.00	−1.64523
$290$	0	0
$291$	3144.00	0.633349
$292$	2822.00i	0.565565i
$293$	− 3906.00i	− 0.778809i	−0.921067	−	0.389404i	$-0.872681\pi$
$293$	− 3906.00i	− 0.778809i	0.921067	−	0.389404i	$-0.127319\pi$
$294$	−13620.0	−2.70182
$295$	0	0
$296$	4230.00	0.830621
$297$	− 1824.00i	− 0.356361i
$298$	5670.00i	1.10220i
$299$	6720.00	1.29976
$300$	0	0
$301$	9856.00	1.88734
$302$	12200.0i	2.32461i
$303$	504.000i	0.0955579i
$304$	−1691.00	−0.319031
$305$	0	0
$306$	−6270.00	−1.17135
$307$	1820.00i	0.338348i	0.985586	+	0.169174i	$0.0541100\pi$
$307$	1820.00i	0.338348i	−0.985586	+	0.169174i	$0.945890\pi$
$308$	6528.00i	1.20769i
$309$	1472.00	0.271000
$310$	0	0
$311$	712.000	0.129819	0.0649097	−	0.997891i	$-0.479324\pi$
$311$	712.000	0.129819	0.0649097	+	0.997891i	$0.479324\pi$
$312$	7560.00i	1.37180i
$313$	9130.00i	1.64875i	0.566046	+	0.824374i	$0.308473\pi$
$313$	9130.00i	1.64875i	−0.566046	+	0.824374i	$0.691527\pi$
$314$	−16190.0	−2.90973
$315$	0	0
$316$	−11696.0	−2.08212
$317$	− 6342.00i	− 1.12367i	−0.827251	−	0.561833i	$-0.810096\pi$
$317$	− 6342.00i	− 1.12367i	0.827251	−	0.561833i	$-0.189904\pi$
$318$	− 5480.00i	− 0.966362i
$319$	2568.00	0.450722
$320$	0	0
$321$	816.000	0.141884
$322$	25600.0i	4.43053i
$323$	2166.00i	0.373125i
$324$	5287.00	0.906550
$325$	0	0
$326$	−7100.00	−1.20624
$327$	5736.00i	0.970035i
$328$	− 270.000i	− 0.0454520i
$329$	5888.00	0.986675
$330$	0	0
$331$	−4748.00	−0.788440	−0.394220	−	0.919016i	$-0.628985\pi$
$331$	−4748.00	−0.788440	−0.394220	+	0.919016i	$0.628985\pi$
$332$	− 16932.0i	− 2.79899i
$333$	− 1034.00i	− 0.170159i
$334$	11680.0	1.91348
$335$	0	0
$336$	−11392.0	−1.84966
$337$	− 5154.00i	− 0.833105i	−0.909112	−	0.416552i	$-0.863238\pi$
$337$	− 5154.00i	− 0.833105i	0.909112	−	0.416552i	$-0.136762\pi$
$338$	− 2165.00i	− 0.348404i
$339$	−4872.00	−0.780563
$340$	0	0
$341$	1728.00	0.274418
$342$	1045.00i	0.165226i
$343$	− 10816.0i	− 1.70265i
$344$	13860.0	2.17233
$345$	0	0
$346$	6030.00	0.936921
$347$	12148.0i	1.87936i	0.342051	+	0.939681i	$0.388878\pi$
$347$	12148.0i	1.87936i	−0.342051	+	0.939681i	$0.611122\pi$
$348$	14552.0i	2.24158i
$349$	602.000	0.0923333	0.0461666	−	0.998934i	$-0.485299\pi$
$349$	602.000	0.0923333	0.0461666	+	0.998934i	$0.485299\pi$
$350$	0	0
$351$	6384.00	0.970805
$352$	1020.00i	0.154449i
$353$	2.00000i	0 0.000301556i	1.00000		0.000150778i	$4.79941e-5\pi$
$353$	2.00000i	0 0.000301556i	−1.00000		0.000150778i	$0.999952\pi$
$354$	−5520.00	−0.828770
$355$	0	0
$356$	26826.0	3.99375
$357$	14592.0i	2.16328i
$358$	− 7060.00i	− 1.04227i
$359$	−1960.00	−0.288147	−0.144074	−	0.989567i	$-0.546020\pi$
$359$	−1960.00	−0.288147	−0.144074	+	0.989567i	$0.546020\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	− 18710.0i	− 2.71651i
$363$	− 4748.00i	− 0.686516i
$364$	−22848.0	−3.29000
$365$	0	0
$366$	−16520.0	−2.35933
$367$	5864.00i	0.834055i	0.908894	+	0.417028i	$0.136928\pi$
$367$	5864.00i	0.834055i	−0.908894	+	0.417028i	$0.863072\pi$
$368$	14240.0i	2.01715i
$369$	−66.0000	−0.00931117
$370$	0	0
$371$	8768.00	1.22699
$372$	9792.00i	1.36476i
$373$	558.000i	0.0774588i	0.999250	+	0.0387294i	$0.0123310\pi$
$373$	558.000i	0.0774588i	−0.999250	+	0.0387294i	$0.987669\pi$
$374$	6840.00	0.945690
$375$	0	0
$376$	8280.00	1.13566
$377$	8988.00i	1.22787i
$378$	24320.0i	3.30922i
$379$	4876.00	0.660853	0.330427	−	0.943832i	$-0.392807\pi$
$379$	4876.00	0.660853	0.330427	+	0.943832i	$0.392807\pi$
$380$	0	0
$381$	3616.00	0.486229
$382$	7360.00i	0.985786i
$383$	− 424.000i	− 0.0565676i	−0.999600	−	0.0282838i	$-0.990996\pi$
$383$	− 424.000i	− 0.0565676i	0.999600	−	0.0282838i	$-0.00900421\pi$
$384$	8460.00	1.12428
$385$	0	0
$386$	7290.00	0.961273
$387$	− 3388.00i	− 0.445017i
$388$	13362.0i	1.74833i
$389$	9890.00	1.28906	0.644528	−	0.764581i	$-0.277054\pi$
$389$	9890.00	1.28906	0.644528	+	0.764581i	$0.277054\pi$
$390$	0	0
$391$	18240.0	2.35917
$392$	− 30645.0i	− 3.94849i
$393$	− 8720.00i	− 1.11925i
$394$	−10230.0	−1.30807
$395$	0	0
$396$	2244.00	0.284761
$397$	234.000i	0.0295822i	0.999891	+	0.0147911i	$0.00470832\pi$
$397$	234.000i	0.0295822i	−0.999891	+	0.0147911i	$0.995292\pi$
$398$	− 7480.00i	− 0.942057i
$399$	2432.00	0.305144
$400$	0	0
$401$	11602.0	1.44483	0.722414	−	0.691461i	$-0.243032\pi$
$401$	11602.0	1.44483	0.722414	+	0.691461i	$0.243032\pi$
$402$	− 1040.00i	− 0.129031i
$403$	6048.00i	0.747574i
$404$	−2142.00	−0.263783
$405$	0	0
$406$	−34240.0	−4.18547
$407$	1128.00i	0.137378i
$408$	20520.0i	2.48993i
$409$	14806.0	1.79000	0.894999	−	0.446067i	$-0.147176\pi$
$409$	14806.0	1.79000	0.894999	+	0.446067i	$0.147176\pi$
$410$	0	0
$411$	−10264.0	−1.23184
$412$	6256.00i	0.748085i
$413$	− 8832.00i	− 1.05229i
$414$	8800.00	1.04468
$415$	0	0
$416$	−3570.00	−0.420754
$417$	− 7952.00i	− 0.933840i
$418$	− 1140.00i	− 0.133395i
$419$	−6252.00	−0.728950	−0.364475	−	0.931213i	$-0.618752\pi$
$419$	−6252.00	−0.728950	−0.364475	+	0.931213i	$0.618752\pi$
$420$	0	0
$421$	−10482.0	−1.21345	−0.606724	−	0.794913i	$-0.707517\pi$
$421$	−10482.0	−1.21345	−0.606724	+	0.794913i	$0.707517\pi$
$422$	− 4220.00i	− 0.486792i
$423$	− 2024.00i	− 0.232648i
$424$	12330.0	1.41226
$425$	0	0
$426$	−6880.00	−0.782481
$427$	− 26432.0i	− 2.99563i
$428$	3468.00i	0.391664i
$429$	−2016.00	−0.226884
$430$	0	0
$431$	3936.00	0.439885	0.219943	−	0.975513i	$-0.429413\pi$
$431$	3936.00	0.439885	0.219943	+	0.975513i	$0.429413\pi$
$432$	13528.0i	1.50663i
$433$	10946.0i	1.21485i	0.794376	+	0.607426i	$0.207798\pi$
$433$	10946.0i	1.21485i	−0.794376	+	0.607426i	$0.792202\pi$
$434$	−23040.0	−2.54828
$435$	0	0
$436$	−24378.0	−2.67774
$437$	− 3040.00i	− 0.332776i
$438$	− 3320.00i	− 0.362182i
$439$	7800.00	0.848004	0.424002	−	0.905661i	$-0.360625\pi$
$439$	7800.00	0.848004	0.424002	+	0.905661i	$0.360625\pi$
$440$	0	0
$441$	−7491.00	−0.808876
$442$	23940.0i	2.57627i
$443$	− 11364.0i	− 1.21878i	−0.792870	−	0.609390i	$-0.791414\pi$
$443$	− 11364.0i	− 1.21878i	0.792870	−	0.609390i	$-0.208586\pi$
$444$	−6392.00	−0.683223
$445$	0	0
$446$	−17000.0	−1.80487
$447$	− 4536.00i	− 0.479967i
$448$	9184.00i	0.968534i
$449$	−7330.00	−0.770432	−0.385216	−	0.922826i	$-0.625873\pi$
$449$	−7330.00	−0.770432	−0.385216	+	0.922826i	$0.625873\pi$
$450$	0	0
$451$	72.0000	0.00751740
$452$	− 20706.0i	− 2.15471i
$453$	− 9760.00i	− 1.01228i
$454$	−9220.00	−0.953119
$455$	0	0
$456$	3420.00	0.351220
$457$	12774.0i	1.30753i	0.756696	+	0.653766i	$0.226812\pi$
$457$	12774.0i	1.30753i	−0.756696	+	0.653766i	$0.773188\pi$
$458$	− 5450.00i	− 0.556030i
$459$	17328.0	1.76210
$460$	0	0
$461$	−3786.00	−0.382498	−0.191249	−	0.981542i	$-0.561254\pi$
$461$	−3786.00	−0.382498	−0.191249	+	0.981542i	$0.561254\pi$
$462$	− 7680.00i	− 0.773389i
$463$	− 19448.0i	− 1.95211i	−0.217532	−	0.976053i	$-0.569801\pi$
$463$	− 19448.0i	− 1.95211i	0.217532	−	0.976053i	$-0.430199\pi$
$464$	−19046.0	−1.90558
$465$	0	0
$466$	14210.0	1.41259
$467$	− 4596.00i	− 0.455412i	−0.973730	−	0.227706i	$-0.926877\pi$
$467$	− 4596.00i	− 0.455412i	0.973730	−	0.227706i	$-0.0731225\pi$
$468$	7854.00i	0.775751i
$469$	1664.00	0.163830
$470$	0	0
$471$	12952.0	1.26708
$472$	− 12420.0i	− 1.21118i
$473$	3696.00i	0.359286i
$474$	13760.0	1.33337
$475$	0	0
$476$	−62016.0	−5.97164
$477$	− 3014.00i	− 0.289311i
$478$	− 12000.0i	− 1.14826i
$479$	−12432.0	−1.18587	−0.592936	−	0.805250i	$-0.702031\pi$
$479$	−12432.0	−1.18587	−0.592936	+	0.805250i	$0.702031\pi$
$480$	0	0
$481$	−3948.00	−0.374248
$482$	− 10650.0i	− 1.00642i
$483$	− 20480.0i	− 1.92934i
$484$	20179.0	1.89510
$485$	0	0
$486$	14300.0	1.33469
$487$	18016.0i	1.67635i	0.545401	+	0.838175i	$0.316378\pi$
$487$	18016.0i	1.67635i	−0.545401	+	0.838175i	$0.683622\pi$
$488$	− 37170.0i	− 3.44796i
$489$	5680.00	0.525273
$490$	0	0
$491$	1972.00	0.181253	0.0906264	−	0.995885i	$-0.471113\pi$
$491$	1972.00	0.181253	0.0906264	+	0.995885i	$0.471113\pi$
$492$	408.000i	0.0373863i
$493$	24396.0i	2.22868i
$494$	3990.00	0.363398
$495$	0	0
$496$	−12816.0	−1.16019
$497$	− 11008.0i	− 0.993514i
$498$	19920.0i	1.79244i
$499$	−18780.0	−1.68479	−0.842393	−	0.538864i	$-0.818854\pi$
$499$	−18780.0	−1.68479	−0.842393	+	0.538864i	$0.818854\pi$
$500$	0	0
$501$	−9344.00	−0.833252
$502$	11820.0i	1.05090i
$503$	8256.00i	0.731843i	0.930646	+	0.365921i	$0.119246\pi$
$503$	8256.00i	0.731843i	−0.930646	+	0.365921i	$0.880754\pi$
$504$	−15840.0	−1.39994
$505$	0	0
$506$	−9600.00	−0.843423
$507$	1732.00i	0.151718i
$508$	15368.0i	1.34221i
$509$	13290.0	1.15731	0.578653	−	0.815574i	$-0.303579\pi$
$509$	13290.0	1.15731	0.578653	+	0.815574i	$0.303579\pi$
$510$	0	0
$511$	5312.00	0.459861
$512$	24475.0i	2.11260i
$513$	− 2888.00i	− 0.248554i
$514$	−31450.0	−2.69883
$515$	0	0
$516$	−20944.0	−1.78684
$517$	2208.00i	0.187829i
$518$	− 15040.0i	− 1.27571i
$519$	−4824.00	−0.407996
$520$	0	0
$521$	7610.00	0.639924	0.319962	−	0.947430i	$-0.396330\pi$
$521$	7610.00	0.639924	0.319962	+	0.947430i	$0.396330\pi$
$522$	11770.0i	0.986894i
$523$	− 13636.0i	− 1.14008i	−0.821618	−	0.570039i	$-0.806928\pi$
$523$	− 13636.0i	− 1.14008i	0.821618	−	0.570039i	$-0.193072\pi$
$524$	37060.0	3.08964
$525$	0	0
$526$	40560.0	3.36217
$527$	16416.0i	1.35691i
$528$	− 4272.00i	− 0.352112i
$529$	−13433.0	−1.10405
$530$	0	0
$531$	−3036.00	−0.248119
$532$	10336.0i	0.842335i
$533$	252.000i	0.0204790i
$534$	−31560.0	−2.55756
$535$	0	0
$536$	2340.00	0.188568
$537$	5648.00i	0.453872i
$538$	− 23970.0i	− 1.92086i
$539$	8172.00	0.653048
$540$	0	0
$541$	1350.00	0.107285	0.0536424	−	0.998560i	$-0.482917\pi$
$541$	1350.00	0.107285	0.0536424	+	0.998560i	$0.482917\pi$
$542$	− 1520.00i	− 0.120460i
$543$	14968.0i	1.18294i
$544$	−9690.00	−0.763705
$545$	0	0
$546$	26880.0	2.10688
$547$	20396.0i	1.59428i	0.603796	+	0.797139i	$0.293654\pi$
$547$	20396.0i	1.59428i	−0.603796	+	0.797139i	$0.706346\pi$
$548$	− 43622.0i	− 3.40044i
$549$	−9086.00	−0.706341
$550$	0	0
$551$	4066.00	0.314369
$552$	− 28800.0i	− 2.22067i
$553$	22016.0i	1.69298i
$554$	−10310.0	−0.790668
$555$	0	0
$556$	33796.0	2.57782
$557$	4458.00i	0.339123i	0.985520	+	0.169562i	$0.0542351\pi$
$557$	4458.00i	0.339123i	−0.985520	+	0.169562i	$0.945765\pi$
$558$	7920.00i	0.600861i
$559$	−12936.0	−0.978774
$560$	0	0
$561$	−5472.00	−0.411815
$562$	20270.0i	1.52142i
$563$	18228.0i	1.36451i	0.731115	+	0.682255i	$0.239000\pi$
$563$	18228.0i	1.36451i	−0.731115	+	0.682255i	$0.761000\pi$
$564$	−12512.0	−0.934132
$565$	0	0
$566$	39980.0	2.96905
$567$	− 9952.00i	− 0.737116i
$568$	− 15480.0i	− 1.14353i
$569$	8246.00	0.607540	0.303770	−	0.952745i	$-0.401755\pi$
$569$	8246.00	0.607540	0.303770	+	0.952745i	$0.401755\pi$
$570$	0	0
$571$	−924.000	−0.0677201	−0.0338601	−	0.999427i	$-0.510780\pi$
$571$	−924.000	−0.0677201	−0.0338601	+	0.999427i	$0.510780\pi$
$572$	− 8568.00i	− 0.626304i
$573$	− 5888.00i	− 0.429275i
$574$	−960.000	−0.0698077
$575$	0	0
$576$	3157.00	0.228371
$577$	− 16322.0i	− 1.17763i	−0.808267	−	0.588816i	$-0.799594\pi$
$577$	− 16322.0i	− 1.17763i	0.808267	−	0.588816i	$-0.200406\pi$
$578$	40415.0i	2.90838i
$579$	−5832.00	−0.418600
$580$	0	0
$581$	−31872.0	−2.27586
$582$	− 15720.0i	− 1.11961i
$583$	3288.00i	0.233576i
$584$	7470.00	0.529299
$585$	0	0
$586$	−19530.0	−1.37675
$587$	− 17500.0i	− 1.23050i	−0.788333	−	0.615249i	$-0.789055\pi$
$587$	− 17500.0i	− 1.23050i	0.788333	−	0.615249i	$-0.210945\pi$
$588$	46308.0i	3.24781i
$589$	2736.00	0.191401
$590$	0	0
$591$	8184.00	0.569619
$592$	− 8366.00i	− 0.580812i
$593$	− 1486.00i	− 0.102905i	−0.998675	−	0.0514525i	$-0.983615\pi$
$593$	− 1486.00i	− 0.102905i	0.998675	−	0.0514525i	$-0.0163851\pi$
$594$	−9120.00	−0.629963
$595$	0	0
$596$	19278.0	1.32493
$597$	5984.00i	0.410233i
$598$	− 33600.0i	− 2.29767i
$599$	−24616.0	−1.67910	−0.839551	−	0.543280i	$-0.817182\pi$
$599$	−24616.0	−1.67910	−0.839551	+	0.543280i	$0.817182\pi$
$600$	0	0
$601$	−13334.0	−0.905000	−0.452500	−	0.891764i	$-0.649468\pi$
$601$	−13334.0	−0.905000	−0.452500	+	0.891764i	$0.649468\pi$
$602$	− 49280.0i	− 3.33638i
$603$	− 572.000i	− 0.0386296i
$604$	41480.0	2.79437
$605$	0	0
$606$	2520.00	0.168924
$607$	12056.0i	0.806158i	0.915165	+	0.403079i	$0.132060\pi$
$607$	12056.0i	0.806158i	−0.915165	+	0.403079i	$0.867940\pi$
$608$	1615.00i	0.107725i
$609$	27392.0	1.82263
$610$	0	0
$611$	−7728.00	−0.511688
$612$	21318.0i	1.40805i
$613$	− 98.0000i	− 0.00645707i	−0.999995	−	0.00322853i	$-0.998972\pi$
$613$	− 98.0000i	− 0.00645707i	0.999995	−	0.00322853i	$-0.00102768\pi$
$614$	9100.00	0.598121
$615$	0	0
$616$	17280.0	1.13025
$617$	− 2938.00i	− 0.191701i	−0.995396	−	0.0958504i	$-0.969443\pi$
$617$	− 2938.00i	− 0.191701i	0.995396	−	0.0958504i	$-0.0305571\pi$
$618$	− 7360.00i	− 0.479066i
$619$	−25316.0	−1.64384	−0.821919	−	0.569604i	$-0.807097\pi$
$619$	−25316.0	−1.64384	−0.821919	+	0.569604i	$0.807097\pi$
$620$	0	0
$621$	−24320.0	−1.57154
$622$	− 3560.00i	− 0.229490i
$623$	− 50496.0i	− 3.24732i
$624$	14952.0	0.959229
$625$	0	0
$626$	45650.0	2.91460
$627$	912.000i	0.0580890i
$628$	55046.0i	3.49773i
$629$	−10716.0	−0.679292
$630$	0	0
$631$	1256.00	0.0792402	0.0396201	−	0.999215i	$-0.487385\pi$
$631$	1256.00	0.0792402	0.0396201	+	0.999215i	$0.487385\pi$
$632$	30960.0i	1.94861i
$633$	3376.00i	0.211981i
$634$	−31710.0	−1.98638
$635$	0	0
$636$	−18632.0	−1.16165
$637$	28602.0i	1.77905i
$638$	− 12840.0i	− 0.796772i
$639$	−3784.00	−0.234261
$640$	0	0
$641$	20290.0	1.25024	0.625122	−	0.780527i	$-0.285049\pi$
$641$	20290.0	1.25024	0.625122	+	0.780527i	$0.285049\pi$
$642$	− 4080.00i	− 0.250817i
$643$	10676.0i	0.654775i	0.944890	+	0.327388i	$0.106168\pi$
$643$	10676.0i	0.654775i	−0.944890	+	0.327388i	$0.893832\pi$
$644$	87040.0	5.32586
$645$	0	0
$646$	10830.0	0.659599
$647$	− 11264.0i	− 0.684441i	−0.939620	−	0.342221i	$-0.888821\pi$
$647$	− 11264.0i	− 0.684441i	0.939620	−	0.342221i	$-0.111179\pi$
$648$	− 13995.0i	− 0.848419i
$649$	3312.00	0.200320
$650$	0	0
$651$	18432.0	1.10969
$652$	24140.0i	1.44999i
$653$	25878.0i	1.55082i	0.631459	+	0.775409i	$0.282456\pi$
$653$	25878.0i	1.55082i	−0.631459	+	0.775409i	$0.717544\pi$
$654$	28680.0	1.71480
$655$	0	0
$656$	−534.000	−0.0317823
$657$	− 1826.00i	− 0.108431i
$658$	− 29440.0i	− 1.74421i
$659$	−1500.00	−0.0886672	−0.0443336	−	0.999017i	$-0.514116\pi$
$659$	−1500.00	−0.0886672	−0.0443336	+	0.999017i	$0.514116\pi$
$660$	0	0
$661$	−7618.00	−0.448269	−0.224135	−	0.974558i	$-0.571956\pi$
$661$	−7618.00	−0.448269	−0.224135	+	0.974558i	$0.571956\pi$
$662$	23740.0i	1.39378i
$663$	− 19152.0i	− 1.12187i
$664$	−44820.0	−2.61951
$665$	0	0
$666$	−5170.00	−0.300801
$667$	− 34240.0i	− 1.98767i
$668$	− 39712.0i	− 2.30015i
$669$	13600.0	0.785959
$670$	0	0
$671$	9912.00	0.570266
$672$	10880.0i	0.624561i
$673$	− 4110.00i	− 0.235407i	−0.993049	−	0.117703i	$-0.962447\pi$
$673$	− 4110.00i	− 0.235407i	0.993049	−	0.117703i	$-0.0375532\pi$
$674$	−25770.0	−1.47273
$675$	0	0
$676$	−7361.00	−0.418810
$677$	21474.0i	1.21907i	0.792758	+	0.609537i	$0.208645\pi$
$677$	21474.0i	1.21907i	−0.792758	+	0.609537i	$0.791355\pi$
$678$	24360.0i	1.37985i
$679$	25152.0	1.42157
$680$	0	0
$681$	7376.00	0.415050
$682$	− 8640.00i	− 0.485107i
$683$	4668.00i	0.261517i	0.991414	+	0.130758i	$0.0417412\pi$
$683$	4668.00i	0.261517i	−0.991414	+	0.130758i	$0.958259\pi$
$684$	3553.00	0.198615
$685$	0	0
$686$	−54080.0	−3.00989
$687$	4360.00i	0.242132i
$688$	− 27412.0i	− 1.51900i
$689$	−11508.0	−0.636313
$690$	0	0
$691$	13292.0	0.731768	0.365884	−	0.930661i	$-0.380767\pi$
$691$	13292.0	0.731768	0.365884	+	0.930661i	$0.380767\pi$
$692$	− 20502.0i	− 1.12626i
$693$	− 4224.00i	− 0.231539i
$694$	60740.0	3.32228
$695$	0	0
$696$	38520.0	2.09784
$697$	684.000i	0.0371712i
$698$	− 3010.00i	− 0.163224i
$699$	−11368.0	−0.615132
$700$	0	0
$701$	7206.00	0.388255	0.194128	−	0.980976i	$-0.437812\pi$
$701$	7206.00	0.388255	0.194128	+	0.980976i	$0.437812\pi$
$702$	− 31920.0i	− 1.71616i
$703$	1786.00i	0.0958183i
$704$	−3444.00	−0.184376
$705$	0	0
$706$	10.0000	0.000533081 0
$707$	4032.00i	0.214482i
$708$	18768.0i	0.996249i
$709$	5666.00	0.300128	0.150064	−	0.988676i	$-0.452052\pi$
$709$	5666.00	0.300128	0.150064	+	0.988676i	$0.452052\pi$
$710$	0	0
$711$	7568.00	0.399187
$712$	− 71010.0i	− 3.73766i
$713$	− 23040.0i	− 1.21018i
$714$	72960.0	3.82417
$715$	0	0
$716$	−24004.0	−1.25289
$717$	9600.00i	0.500026i
$718$	9800.00i	0.509377i
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	11776.0	0.608268
$722$	− 1805.00i	− 0.0930404i
$723$	8520.00i	0.438260i
$724$	−63614.0	−3.26546
$725$	0	0
$726$	−23740.0	−1.21360
$727$	4048.00i	0.206509i	0.994655	+	0.103254i	$0.0329256\pi$
$727$	4048.00i	0.206509i	−0.994655	+	0.103254i	$0.967074\pi$
$728$	60480.0i	3.07904i
$729$	−19837.0	−1.00782
$730$	0	0
$731$	−35112.0	−1.77656
$732$	56168.0i	2.83611i
$733$	12134.0i	0.611432i	0.952123	+	0.305716i	$0.0988958\pi$
$733$	12134.0i	0.611432i	−0.952123	+	0.305716i	$0.901104\pi$
$734$	29320.0	1.47442
$735$	0	0
$736$	13600.0	0.681118
$737$	624.000i	0.0311877i
$738$	330.000i	0.0164600i
$739$	13556.0	0.674784	0.337392	−	0.941364i	$-0.390455\pi$
$739$	13556.0	0.674784	0.337392	+	0.941364i	$0.390455\pi$
$740$	0	0
$741$	−3192.00	−0.158247
$742$	− 43840.0i	− 2.16903i
$743$	4368.00i	0.215675i	0.994169	+	0.107837i	$0.0343926\pi$
$743$	4368.00i	0.215675i	−0.994169	+	0.107837i	$0.965607\pi$
$744$	25920.0	1.27725
$745$	0	0
$746$	2790.00	0.136929
$747$	10956.0i	0.536625i
$748$	− 23256.0i	− 1.13680i
$749$	6528.00	0.318462
$750$	0	0
$751$	3872.00	0.188138	0.0940688	−	0.995566i	$-0.470013\pi$
$751$	3872.00	0.188138	0.0940688	+	0.995566i	$0.470013\pi$
$752$	− 16376.0i	− 0.794111i
$753$	− 9456.00i	− 0.457631i
$754$	44940.0	2.17058
$755$	0	0
$756$	82688.0	3.97795
$757$	− 6190.00i	− 0.297199i	−0.988897	−	0.148599i	$-0.952524\pi$
$757$	− 6190.00i	− 0.297199i	0.988897	−	0.148599i	$-0.0474765\pi$
$758$	− 24380.0i	− 1.16823i
$759$	7680.00	0.367281
$760$	0	0
$761$	−7062.00	−0.336396	−0.168198	−	0.985753i	$-0.553795\pi$
$761$	−7062.00	−0.336396	−0.168198	+	0.985753i	$0.553795\pi$
$762$	− 18080.0i	− 0.859540i
$763$	45888.0i	2.17727i
$764$	25024.0	1.18500
$765$	0	0
$766$	−2120.00	−0.0999983
$767$	11592.0i	0.545714i
$768$	− 33116.0i	− 1.55595i
$769$	5438.00	0.255006	0.127503	−	0.991838i	$-0.459304\pi$
$769$	5438.00	0.255006	0.127503	+	0.991838i	$0.459304\pi$
$770$	0	0
$771$	25160.0	1.17525
$772$	− 24786.0i	− 1.15553i
$773$	1182.00i	0.0549982i	0.999622	+	0.0274991i	$0.00875433\pi$
$773$	1182.00i	0.0549982i	−0.999622	+	0.0274991i	$0.991246\pi$
$774$	−16940.0	−0.786687
$775$	0	0
$776$	35370.0	1.63622
$777$	12032.0i	0.555528i
$778$	− 49450.0i	− 2.27875i
$779$	114.000	0.00524323
$780$	0	0
$781$	4128.00	0.189131
$782$	− 91200.0i	− 4.17047i
$783$	− 32528.0i	− 1.48462i
$784$	−60609.0	−2.76098
$785$	0	0
$786$	−43600.0	−1.97858
$787$	− 12452.0i	− 0.563997i	−0.959415	−	0.281999i	$-0.909003\pi$
$787$	− 12452.0i	− 0.563997i	0.959415	−	0.281999i	$-0.0909974\pi$
$788$	34782.0i	1.57241i
$789$	−32448.0	−1.46411
$790$	0	0
$791$	−38976.0	−1.75199
$792$	− 5940.00i	− 0.266501i
$793$	34692.0i	1.55353i
$794$	1170.00	0.0522944
$795$	0	0
$796$	−25432.0	−1.13243
$797$	− 15526.0i	− 0.690037i	−0.938596	−	0.345018i	$-0.887873\pi$
$797$	− 15526.0i	− 0.690037i	0.938596	−	0.345018i	$-0.112127\pi$
$798$	− 12160.0i	− 0.539423i
$799$	−20976.0	−0.928758
$800$	0	0
$801$	−17358.0	−0.765686
$802$	− 58010.0i	− 2.55412i
$803$	1992.00i	0.0875419i
$804$	−3536.00	−0.155106
$805$	0	0
$806$	30240.0	1.32154
$807$	19176.0i	0.836465i
$808$	5670.00i	0.246869i
$809$	−31034.0	−1.34870	−0.674349	−	0.738412i	$-0.735576\pi$
$809$	−31034.0	−1.34870	−0.674349	+	0.738412i	$0.735576\pi$
$810$	0	0
$811$	−34636.0	−1.49967	−0.749836	−	0.661623i	$-0.769868\pi$
$811$	−34636.0	−1.49967	−0.749836	+	0.661623i	$0.769868\pi$
$812$	116416.i	5.03128i
$813$	1216.00i	0.0524563i
$814$	5640.00	0.242852
$815$	0	0
$816$	40584.0	1.74108
$817$	5852.00i	0.250594i
$818$	− 74030.0i	− 3.16430i
$819$	14784.0	0.630763
$820$	0	0
$821$	−20082.0	−0.853674	−0.426837	−	0.904328i	$-0.640372\pi$
$821$	−20082.0	−0.853674	−0.426837	+	0.904328i	$0.640372\pi$
$822$	51320.0i	2.17760i
$823$	33568.0i	1.42176i	0.703314	+	0.710879i	$0.251703\pi$
$823$	33568.0i	1.42176i	−0.703314	+	0.710879i	$0.748297\pi$
$824$	16560.0	0.700115
$825$	0	0
$826$	−44160.0	−1.86020
$827$	− 19644.0i	− 0.825984i	−0.910735	−	0.412992i	$-0.864484\pi$
$827$	− 19644.0i	− 0.825984i	0.910735	−	0.412992i	$-0.135516\pi$
$828$	− 29920.0i	− 1.25579i
$829$	−726.000	−0.0304162	−0.0152081	−	0.999884i	$-0.504841\pi$
$829$	−726.000	−0.0304162	−0.0152081	+	0.999884i	$0.504841\pi$
$830$	0	0
$831$	8248.00	0.344308
$832$	− 12054.0i	− 0.502280i
$833$	77634.0i	3.22912i
$834$	−39760.0	−1.65081
$835$	0	0
$836$	−3876.00	−0.160352
$837$	− 21888.0i	− 0.903895i
$838$	31260.0i	1.28861i
$839$	−3512.00	−0.144515	−0.0722573	−	0.997386i	$-0.523020\pi$
$839$	−3512.00	−0.144515	−0.0722573	+	0.997386i	$0.523020\pi$
$840$	0	0
$841$	21407.0	0.877732
$842$	52410.0i	2.14509i
$843$	− 16216.0i	− 0.662525i
$844$	−14348.0	−0.585164
$845$	0	0
$846$	−10120.0	−0.411268
$847$	− 37984.0i	− 1.54090i
$848$	− 24386.0i	− 0.987522i
$849$	−31984.0	−1.29292
$850$	0	0
$851$	15040.0	0.605834
$852$	23392.0i	0.940606i
$853$	− 39442.0i	− 1.58320i	−0.611041	−	0.791599i	$-0.709249\pi$
$853$	− 39442.0i	− 1.58320i	0.611041	−	0.791599i	$-0.290751\pi$
$854$	−132160.	−5.29558
$855$	0	0
$856$	9180.00	0.366549
$857$	40454.0i	1.61246i	0.591599	+	0.806232i	$0.298497\pi$
$857$	40454.0i	1.61246i	−0.591599	+	0.806232i	$0.701503\pi$
$858$	10080.0i	0.401079i
$859$	3436.00	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	3436.00	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	768.000	0.0303988
$862$	− 19680.0i	− 0.777614i
$863$	− 10056.0i	− 0.396651i	−0.980136	−	0.198326i	$-0.936450\pi$
$863$	− 10056.0i	− 0.396651i	0.980136	−	0.198326i	$-0.0635504\pi$
$864$	12920.0	0.508735
$865$	0	0
$866$	54730.0	2.14758
$867$	− 32332.0i	− 1.26650i
$868$	78336.0i	3.06325i
$869$	−8256.00	−0.322285
$870$	0	0
$871$	−2184.00	−0.0849621
$872$	64530.0i	2.50603i
$873$	− 8646.00i	− 0.335192i
$874$	−15200.0	−0.588270
$875$	0	0
$876$	−11288.0	−0.435372
$877$	44394.0i	1.70933i	0.519183	+	0.854663i	$0.326236\pi$
$877$	44394.0i	1.70933i	−0.519183	+	0.854663i	$0.673764\pi$
$878$	− 39000.0i	− 1.49907i
$879$	15624.0	0.599527
$880$	0	0
$881$	−18222.0	−0.696839	−0.348419	−	0.937339i	$-0.613281\pi$
$881$	−18222.0	−0.696839	−0.348419	+	0.937339i	$0.613281\pi$
$882$	37455.0i	1.42990i
$883$	− 29404.0i	− 1.12064i	−0.828277	−	0.560319i	$-0.810679\pi$
$883$	− 29404.0i	− 1.12064i	0.828277	−	0.560319i	$-0.189321\pi$
$884$	81396.0	3.09688
$885$	0	0
$886$	−56820.0	−2.15452
$887$	− 18576.0i	− 0.703180i	−0.936154	−	0.351590i	$-0.885641\pi$
$887$	− 18576.0i	− 0.703180i	0.936154	−	0.351590i	$-0.114359\pi$
$888$	16920.0i	0.639412i
$889$	28928.0	1.09135
$890$	0	0
$891$	3732.00	0.140322
$892$	57800.0i	2.16960i
$893$	3496.00i	0.131007i
$894$	−22680.0	−0.848471
$895$	0	0
$896$	67680.0	2.52347
$897$	26880.0i	1.00055i
$898$	36650.0i	1.36194i
$899$	30816.0	1.14324
$900$	0	0
$901$	−31236.0	−1.15496
$902$	− 360.000i	− 0.0132890i
$903$	39424.0i	1.45288i
$904$	−54810.0	−2.01654
$905$	0	0
$906$	−48800.0	−1.78948
$907$	2644.00i	0.0967945i	0.998828	+	0.0483972i	$0.0154113\pi$
$907$	2644.00i	0.0967945i	−0.998828	+	0.0483972i	$0.984589\pi$
$908$	31348.0i	1.14573i
$909$	1386.00	0.0505728
$910$	0	0
$911$	39744.0	1.44542	0.722710	−	0.691151i	$-0.242896\pi$
$911$	39744.0	1.44542	0.722710	+	0.691151i	$0.242896\pi$
$912$	− 6764.00i	− 0.245590i
$913$	− 11952.0i	− 0.433246i
$914$	63870.0	2.31141
$915$	0	0
$916$	−18530.0	−0.668393
$917$	− 69760.0i	− 2.51219i
$918$	− 86640.0i	− 3.11497i
$919$	19720.0	0.707838	0.353919	−	0.935276i	$-0.384849\pi$
$919$	19720.0	0.707838	0.353919	+	0.935276i	$0.384849\pi$
$920$	0	0
$921$	−7280.00	−0.260461
$922$	18930.0i	0.676167i
$923$	14448.0i	0.515235i
$924$	−26112.0	−0.929677
$925$	0	0
$926$	−97240.0	−3.45087
$927$	− 4048.00i	− 0.143424i
$928$	18190.0i	0.643444i
$929$	−36258.0	−1.28050	−0.640251	−	0.768166i	$-0.721170\pi$
$929$	−36258.0	−1.28050	−0.640251	+	0.768166i	$0.721170\pi$
$930$	0	0
$931$	12939.0	0.455487
$932$	− 48314.0i	− 1.69804i
$933$	2848.00i	0.0999350i
$934$	−22980.0	−0.805063
$935$	0	0
$936$	20790.0	0.726007
$937$	− 14586.0i	− 0.508542i	−0.967133	−	0.254271i	$-0.918164\pi$
$937$	− 14586.0i	− 0.508542i	0.967133	−	0.254271i	$-0.0818355\pi$
$938$	− 8320.00i	− 0.289614i
$939$	−36520.0	−1.26921
$940$	0	0
$941$	30182.0	1.04560	0.522798	−	0.852457i	$-0.324888\pi$
$941$	30182.0	1.04560	0.522798	+	0.852457i	$0.324888\pi$
$942$	− 64760.0i	− 2.23991i
$943$	− 960.000i	− 0.0331515i
$944$	−24564.0	−0.846917
$945$	0	0
$946$	18480.0	0.635134
$947$	− 15828.0i	− 0.543127i	−0.962421	−	0.271563i	$-0.912459\pi$
$947$	− 15828.0i	− 0.543127i	0.962421	−	0.271563i	$-0.0875406\pi$
$948$	− 46784.0i	− 1.60282i
$949$	−6972.00	−0.238483
$950$	0	0
$951$	25368.0	0.864999
$952$	164160.i	5.58871i
$953$	22746.0i	0.773153i	0.922257	+	0.386577i	$0.126343\pi$
$953$	22746.0i	0.773153i	−0.922257	+	0.386577i	$0.873657\pi$
$954$	−15070.0	−0.511435
$955$	0	0
$956$	−40800.0	−1.38030
$957$	10272.0i	0.346966i
$958$	62160.0i	2.09634i
$959$	−82112.0	−2.76490
$960$	0	0
$961$	−9055.00	−0.303951
$962$	19740.0i	0.661583i
$963$	− 2244.00i	− 0.0750902i
$964$	−36210.0	−1.20980
$965$	0	0
$966$	−102400.	−3.41063
$967$	− 16480.0i	− 0.548047i	−0.961723	−	0.274023i	$-0.911645\pi$
$967$	− 16480.0i	− 0.548047i	0.961723	−	0.274023i	$-0.0883545\pi$
$968$	− 53415.0i	− 1.77358i
$969$	−8664.00	−0.287232
$970$	0	0
$971$	−16940.0	−0.559867	−0.279933	−	0.960019i	$-0.590312\pi$
$971$	−16940.0	−0.559867	−0.279933	+	0.960019i	$0.590312\pi$
$972$	− 48620.0i	− 1.60441i
$973$	− 63616.0i	− 2.09603i
$974$	90080.0	2.96340
$975$	0	0
$976$	−73514.0	−2.41099
$977$	40062.0i	1.31187i	0.754817	+	0.655935i	$0.227725\pi$
$977$	40062.0i	1.31187i	−0.754817	+	0.655935i	$0.772275\pi$
$978$	− 28400.0i	− 0.928560i
$979$	18936.0	0.618179
$980$	0	0
$981$	15774.0	0.513379
$982$	− 9860.00i	− 0.320413i
$983$	4832.00i	0.156782i	0.996923	+	0.0783911i	$0.0249783\pi$
$983$	4832.00i	0.156782i	−0.996923	+	0.0783911i	$0.975022\pi$
$984$	1080.00	0.0349890
$985$	0	0
$986$	121980.	3.93979
$987$	23552.0i	0.759542i
$988$	− 13566.0i	− 0.436834i
$989$	49280.0	1.58444
$990$	0	0
$991$	−4144.00	−0.132834	−0.0664170	−	0.997792i	$-0.521157\pi$
$991$	−4144.00	−0.132834	−0.0664170	+	0.997792i	$0.521157\pi$
$992$	12240.0i	0.391754i
$993$	− 18992.0i	− 0.606941i
$994$	−55040.0	−1.75630
$995$	0	0
$996$	67728.0	2.15466
$997$	− 35294.0i	− 1.12114i	−0.828109	−	0.560568i	$-0.810583\pi$
$997$	− 35294.0i	− 1.12114i	0.828109	−	0.560568i	$-0.189417\pi$
$998$	93900.0i	2.97831i
$999$	14288.0	0.452505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.4.b.a.324.1		2
5.2	odd	4		95.4.a.d.1.1	✓	1
5.3	odd	4		475.4.a.a.1.1		1
5.4	even	2	inner	475.4.b.a.324.2		2
15.2	even	4		855.4.a.a.1.1		1
20.7	even	4		1520.4.a.c.1.1		1
95.37	even	4		1805.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.a.d.1.1	✓	1	5.2	odd	4
475.4.a.a.1.1		1	5.3	odd	4
475.4.b.a.324.1		2	1.1	even	1	trivial
475.4.b.a.324.2		2	5.4	even	2	inner
855.4.a.a.1.1		1	15.2	even	4
1520.4.a.c.1.1		1	20.7	even	4
1805.4.a.a.1.1		1	95.37	even	4

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	475.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-5.00000i q^{2} +4.00000i q^{3} -17.0000 q^{4} +20.0000 q^{6} +32.0000i q^{7} +45.0000i q^{8} +11.0000 q^{9} +O(q^{10})\)	\(q-5.00000i q^{2} +4.00000i q^{3} -17.0000 q^{4} +20.0000 q^{6} +32.0000i q^{7} +45.0000i q^{8} +11.0000 q^{9} -12.0000 q^{11} -68.0000i q^{12} -42.0000i q^{13} +160.000 q^{14} +89.0000 q^{16} -114.000i q^{17} -55.0000i q^{18} -19.0000 q^{19} -128.000 q^{21} +60.0000i q^{22} +160.000i q^{23} -180.000 q^{24} -210.000 q^{26} +152.000i q^{27} -544.000i q^{28} -214.000 q^{29} -144.000 q^{31} -85.0000i q^{32} -48.0000i q^{33} -570.000 q^{34} -187.000 q^{36} -94.0000i q^{37} +95.0000i q^{38} +168.000 q^{39} -6.00000 q^{41} +640.000i q^{42} -308.000i q^{43} +204.000 q^{44} +800.000 q^{46} -184.000i q^{47} +356.000i q^{48} -681.000 q^{49} +456.000 q^{51} +714.000i q^{52} -274.000i q^{53} +760.000 q^{54} -1440.00 q^{56} -76.0000i q^{57} +1070.00i q^{58} -276.000 q^{59} -826.000 q^{61} +720.000i q^{62} +352.000i q^{63} +287.000 q^{64} -240.000 q^{66} -52.0000i q^{67} +1938.00i q^{68} -640.000 q^{69} -344.000 q^{71} +495.000i q^{72} -166.000i q^{73} -470.000 q^{74} +323.000 q^{76} -384.000i q^{77} -840.000i q^{78} +688.000 q^{79} -311.000 q^{81} +30.0000i q^{82} +996.000i q^{83} +2176.00 q^{84} -1540.00 q^{86} -856.000i q^{87} -540.000i q^{88} -1578.00 q^{89} +1344.00 q^{91} -2720.00i q^{92} -576.000i q^{93} -920.000 q^{94} +340.000 q^{96} -786.000i q^{97} +3405.00i q^{98} -132.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 34 q^{4} + 40 q^{6} + 22 q^{9}+O(q^{10}) \) 2 * q - 34 * q^4 + 40 * q^6 + 22 * q^9	\( 2 q - 34 q^{4} + 40 q^{6} + 22 q^{9} - 24 q^{11} + 320 q^{14} + 178 q^{16} - 38 q^{19} - 256 q^{21} - 360 q^{24} - 420 q^{26} - 428 q^{29} - 288 q^{31} - 1140 q^{34} - 374 q^{36} + 336 q^{39} - 12 q^{41} + 408 q^{44} + 1600 q^{46} - 1362 q^{49} + 912 q^{51} + 1520 q^{54} - 2880 q^{56} - 552 q^{59} - 1652 q^{61} + 574 q^{64} - 480 q^{66} - 1280 q^{69} - 688 q^{71} - 940 q^{74} + 646 q^{76} + 1376 q^{79} - 622 q^{81} + 4352 q^{84} - 3080 q^{86} - 3156 q^{89} + 2688 q^{91} - 1840 q^{94} + 680 q^{96} - 264 q^{99}+O(q^{100}) \) 2 * q - 34 * q^4 + 40 * q^6 + 22 * q^9 - 24 * q^11 + 320 * q^14 + 178 * q^16 - 38 * q^19 - 256 * q^21 - 360 * q^24 - 420 * q^26 - 428 * q^29 - 288 * q^31 - 1140 * q^34 - 374 * q^36 + 336 * q^39 - 12 * q^41 + 408 * q^44 + 1600 * q^46 - 1362 * q^49 + 912 * q^51 + 1520 * q^54 - 2880 * q^56 - 552 * q^59 - 1652 * q^61 + 574 * q^64 - 480 * q^66 - 1280 * q^69 - 688 * q^71 - 940 * q^74 + 646 * q^76 + 1376 * q^79 - 622 * q^81 + 4352 * q^84 - 3080 * q^86 - 3156 * q^89 + 2688 * q^91 - 1840 * q^94 + 680 * q^96 - 264 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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