LMFDB - Embedded newform 990.4.c.b.199.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,4,Mod(199,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.199"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	990.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-8,20,0,0,0,0,20,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$58.4118909057$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	990.199
Dual form			990.4.c.b.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -4.00000 q^{4} +(10.0000 - 5.00000i) q^{5} +5.00000i q^{7} -8.00000i q^{8} +(10.0000 + 20.0000i) q^{10} -11.0000 q^{11} -36.0000i q^{13} -10.0000 q^{14} +16.0000 q^{16} +17.0000i q^{17} -41.0000 q^{19} +(-40.0000 + 20.0000i) q^{20} -22.0000i q^{22} -44.0000i q^{23} +(75.0000 - 100.000i) q^{25} +72.0000 q^{26} -20.0000i q^{28} +285.000 q^{29} -323.000 q^{31} +32.0000i q^{32} -34.0000 q^{34} +(25.0000 + 50.0000i) q^{35} +29.0000i q^{37} -82.0000i q^{38} +(-40.0000 - 80.0000i) q^{40} -208.000 q^{41} -430.000i q^{43} +44.0000 q^{44} +88.0000 q^{46} -336.000i q^{47} +318.000 q^{49} +(200.000 + 150.000i) q^{50} +144.000i q^{52} +725.000i q^{53} +(-110.000 + 55.0000i) q^{55} +40.0000 q^{56} +570.000i q^{58} -648.000 q^{59} -565.000 q^{61} -646.000i q^{62} -64.0000 q^{64} +(-180.000 - 360.000i) q^{65} -748.000i q^{67} -68.0000i q^{68} +(-100.000 + 50.0000i) q^{70} +265.000 q^{71} -602.000i q^{73} -58.0000 q^{74} +164.000 q^{76} -55.0000i q^{77} -8.00000 q^{79} +(160.000 - 80.0000i) q^{80} -416.000i q^{82} -708.000i q^{83} +(85.0000 + 170.000i) q^{85} +860.000 q^{86} +88.0000i q^{88} +137.000 q^{89} +180.000 q^{91} +176.000i q^{92} +672.000 q^{94} +(-410.000 + 205.000i) q^{95} +44.0000i q^{97} +636.000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 20 q^{5} + 20 q^{10} - 22 q^{11} - 20 q^{14} + 32 q^{16} - 82 q^{19} - 80 q^{20} + 150 q^{25} + 144 q^{26} + 570 q^{29} - 646 q^{31} - 68 q^{34} + 50 q^{35} - 80 q^{40} - 416 q^{41} + 88 q^{44}+ \cdots - 820 q^{95}+O(q^{100}) $ 2 * q - 8 * q^4 + 20 * q^5 + 20 * q^10 - 22 * q^11 - 20 * q^14 + 32 * q^16 - 82 * q^19 - 80 * q^20 + 150 * q^25 + 144 * q^26 + 570 * q^29 - 646 * q^31 - 68 * q^34 + 50 * q^35 - 80 * q^40 - 416 * q^41 + 88 * q^44 + 176 * q^46 + 636 * q^49 + 400 * q^50 - 220 * q^55 + 80 * q^56 - 1296 * q^59 - 1130 * q^61 - 128 * q^64 - 360 * q^65 - 200 * q^70 + 530 * q^71 - 116 * q^74 + 328 * q^76 - 16 * q^79 + 320 * q^80 + 170 * q^85 + 1720 * q^86 + 274 * q^89 + 360 * q^91 + 1344 * q^94 - 820 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	10.0000	−	5.00000i	0.894427	−	0.447214i
$5$	10.0000	−	5.00000i	0.894427	−	0.447214i
$6$		0			0
$7$			5.00000i			0.269975i	0.990847	+	0.134987i	$0.0430994\pi$
$7$			5.00000i			0.269975i	−0.990847	+	0.134987i	$0.956901\pi$
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	10.0000	+	20.0000i	0.316228	+	0.632456i
$11$	−11.0000			−0.301511
$11$	−11.0000			−0.301511
$12$		0			0
$13$		−	36.0000i		−	0.768046i	−0.923323	−	0.384023i	$-0.874538\pi$
$13$		−	36.0000i		−	0.768046i	0.923323	−	0.384023i	$-0.125462\pi$
$14$	−10.0000			−0.190901
$15$		0			0
$16$	16.0000			0.250000
$17$			17.0000i			0.242536i	0.992620	+	0.121268i	$0.0386960\pi$
$17$			17.0000i			0.242536i	−0.992620	+	0.121268i	$0.961304\pi$
$18$		0			0
$19$	−41.0000			−0.495055			−0.247528	−	0.968881i	$-0.579618\pi$
$19$	−41.0000			−0.495055			−0.247528	+	0.968881i	$0.579618\pi$
$20$	−40.0000	+	20.0000i	−0.447214	+	0.223607i
$21$		0			0
$22$		−	22.0000i		−	0.213201i
$23$		−	44.0000i		−	0.398897i	−0.979908	−	0.199449i	$-0.936085\pi$
$23$		−	44.0000i		−	0.398897i	0.979908	−	0.199449i	$-0.0639151\pi$
$24$		0			0
$25$	75.0000	−	100.000i	0.600000	−	0.800000i
$26$	72.0000			0.543091
$27$		0			0
$28$		−	20.0000i		−	0.134987i
$29$	285.000			1.82494			0.912468	−	0.409147i	$-0.134174\pi$
$29$	285.000			1.82494			0.912468	+	0.409147i	$0.134174\pi$
$30$		0			0
$31$	−323.000			−1.87137			−0.935686	−	0.352835i	$-0.885218\pi$
$31$	−323.000			−1.87137			−0.935686	+	0.352835i	$0.885218\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	−34.0000			−0.171499
$35$	25.0000	+	50.0000i	0.120736	+	0.241473i
$36$		0			0
$37$			29.0000i			0.128853i	0.997922	+	0.0644266i	$0.0205218\pi$
$37$			29.0000i			0.128853i	−0.997922	+	0.0644266i	$0.979478\pi$
$38$		−	82.0000i		−	0.350057i
$39$		0			0
$40$	−40.0000	−	80.0000i	−0.158114	−	0.316228i
$41$	−208.000			−0.792296			−0.396148	−	0.918187i	$-0.629653\pi$
$41$	−208.000			−0.792296			−0.396148	+	0.918187i	$0.629653\pi$
$42$		0			0
$43$		−	430.000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	430.000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$	44.0000			0.150756
$45$		0			0
$46$	88.0000			0.282063
$47$		−	336.000i		−	1.04278i	−0.853319	−	0.521390i	$-0.825414\pi$
$47$		−	336.000i		−	1.04278i	0.853319	−	0.521390i	$-0.174586\pi$
$48$		0			0
$49$	318.000			0.927114
$50$	200.000	+	150.000i	0.565685	+	0.424264i
$51$		0			0
$52$			144.000i			0.384023i
$53$			725.000i			1.87899i	0.342564	+	0.939494i	$0.388705\pi$
$53$			725.000i			1.87899i	−0.342564	+	0.939494i	$0.611295\pi$
$54$		0			0
$55$	−110.000	+	55.0000i	−0.269680	+	0.134840i
$56$	40.0000			0.0954504
$57$		0			0
$58$			570.000i			1.29043i
$59$	−648.000			−1.42987			−0.714936	−	0.699190i	$-0.753544\pi$
$59$	−648.000			−1.42987			−0.714936	+	0.699190i	$0.753544\pi$
$60$		0			0
$61$	−565.000			−1.18592			−0.592958	−	0.805234i	$-0.702040\pi$
$61$	−565.000			−1.18592			−0.592958	+	0.805234i	$0.702040\pi$
$62$		−	646.000i		−	1.32326i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−180.000	−	360.000i	−0.343481	−	0.686962i
$66$		0			0
$67$		−	748.000i		−	1.36392i	−0.731389	−	0.681961i	$-0.761127\pi$
$67$		−	748.000i		−	1.36392i	0.731389	−	0.681961i	$-0.238873\pi$
$68$		−	68.0000i		−	0.121268i
$69$		0			0
$70$	−100.000	+	50.0000i	−0.170747	+	0.0853735i
$71$	265.000			0.442954			0.221477	−	0.975166i	$-0.428912\pi$
$71$	265.000			0.442954			0.221477	+	0.975166i	$0.428912\pi$
$72$		0			0
$73$		−	602.000i		−	0.965189i	−0.875844	−	0.482594i	$-0.839695\pi$
$73$		−	602.000i		−	0.965189i	0.875844	−	0.482594i	$-0.160305\pi$
$74$	−58.0000			−0.0911130
$75$		0			0
$76$	164.000			0.247528
$77$		−	55.0000i		−	0.0814004i
$78$		0			0
$79$	−8.00000			−0.0113933			−0.00569665	−	0.999984i	$-0.501813\pi$
$79$	−8.00000			−0.0113933			−0.00569665	+	0.999984i	$0.501813\pi$
$80$	160.000	−	80.0000i	0.223607	−	0.111803i
$81$		0			0
$82$		−	416.000i		−	0.560238i
$83$		−	708.000i		−	0.936302i	−0.883648	−	0.468151i	$-0.844920\pi$
$83$		−	708.000i		−	0.936302i	0.883648	−	0.468151i	$-0.155080\pi$
$84$		0			0
$85$	85.0000	+	170.000i	0.108465	+	0.216930i
$86$	860.000			1.07833
$87$		0			0
$88$			88.0000i			0.106600i
$89$	137.000			0.163168			0.0815841	−	0.996666i	$-0.474002\pi$
$89$	137.000			0.163168			0.0815841	+	0.996666i	$0.474002\pi$
$90$		0			0
$91$	180.000			0.207353
$92$			176.000i			0.199449i
$93$		0			0
$94$	672.000			0.737356
$95$	−410.000	+	205.000i	−0.442791	+	0.221395i
$96$		0			0
$97$			44.0000i			0.0460569i	0.999735	+	0.0230285i	$0.00733084\pi$
$97$			44.0000i			0.0460569i	−0.999735	+	0.0230285i	$0.992669\pi$
$98$			636.000i			0.655568i
$99$		0			0
$100$	−300.000	+	400.000i	−0.300000	+	0.400000i
$101$	−1722.00			−1.69649			−0.848245	−	0.529605i	$-0.822340\pi$
$101$	−1722.00			−1.69649			−0.848245	+	0.529605i	$0.822340\pi$
$102$		0			0
$103$		−	1612.00i		−	1.54209i	−0.636782	−	0.771044i	$-0.719735\pi$
$103$		−	1612.00i		−	1.54209i	0.636782	−	0.771044i	$-0.280265\pi$
$104$	−288.000			−0.271545
$105$		0			0
$106$	−1450.00			−1.32865
$107$		−	516.000i		−	0.466202i	−0.972453	−	0.233101i	$-0.925113\pi$
$107$		−	516.000i		−	0.466202i	0.972453	−	0.233101i	$-0.0748873\pi$
$108$		0			0
$109$	2.00000			0.00175748			0.000878740	−	1.00000i	$-0.499720\pi$
$109$	2.00000			0.00175748			0.000878740		1.00000i	$0.499720\pi$
$110$	−110.000	−	220.000i	−0.0953463	−	0.190693i
$111$		0			0
$112$			80.0000i			0.0674937i
$113$		−	126.000i		−	0.104895i	−0.998624	−	0.0524473i	$-0.983298\pi$
$113$		−	126.000i		−	0.104895i	0.998624	−	0.0524473i	$-0.0167021\pi$
$114$		0			0
$115$	−220.000	−	440.000i	−0.178392	−	0.356784i
$116$	−1140.00			−0.912468
$117$		0			0
$118$		−	1296.00i		−	1.01107i
$119$	−85.0000			−0.0654785
$120$		0			0
$121$	121.000			0.0909091
$122$		−	1130.00i		−	0.838569i
$123$		0			0
$124$	1292.00			0.935686
$125$	250.000	−	1375.00i	0.178885	−	0.983870i
$126$		0			0
$127$			88.0000i			0.0614861i	0.999527	+	0.0307431i	$0.00978736\pi$
$127$			88.0000i			0.0614861i	−0.999527	+	0.0307431i	$0.990213\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	720.000	−	360.000i	0.485755	−	0.242878i
$131$	1603.00			1.06912			0.534560	−	0.845130i	$-0.320477\pi$
$131$	1603.00			1.06912			0.534560	+	0.845130i	$0.320477\pi$
$132$		0			0
$133$		−	205.000i		−	0.133652i
$134$	1496.00			0.964438
$135$		0			0
$136$	136.000			0.0857493
$137$		−	204.000i		−	0.127218i	−0.997975	−	0.0636091i	$-0.979739\pi$
$137$		−	204.000i		−	0.127218i	0.997975	−	0.0636091i	$-0.0202611\pi$
$138$		0			0
$139$	1668.00			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	1668.00			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$	−100.000	−	200.000i	−0.0603682	−	0.120736i
$141$		0			0
$142$			530.000i			0.313216i
$143$			396.000i			0.231575i
$144$		0			0
$145$	2850.00	−	1425.00i	1.63227	−	0.816137i
$146$	1204.00			0.682491
$147$		0			0
$148$		−	116.000i		−	0.0644266i
$149$	−701.000			−0.385424			−0.192712	−	0.981255i	$-0.561728\pi$
$149$	−701.000			−0.385424			−0.192712	+	0.981255i	$0.561728\pi$
$150$		0			0
$151$	1278.00			0.688756			0.344378	−	0.938831i	$-0.388090\pi$
$151$	1278.00			0.688756			0.344378	+	0.938831i	$0.388090\pi$
$152$			328.000i			0.175028i
$153$		0			0
$154$	110.000			0.0575588
$155$	−3230.00	+	1615.00i	−1.67381	+	0.836903i
$156$		0			0
$157$		−	2623.00i		−	1.33336i	−0.745342	−	0.666682i	$-0.767714\pi$
$157$		−	2623.00i		−	1.33336i	0.745342	−	0.666682i	$-0.232286\pi$
$158$		−	16.0000i		−	0.00805628i
$159$		0			0
$160$	160.000	+	320.000i	0.0790569	+	0.158114i
$161$	220.000			0.107692
$162$		0			0
$163$		−	2053.00i		−	0.986524i	−0.869881	−	0.493262i	$-0.835804\pi$
$163$		−	2053.00i		−	0.986524i	0.869881	−	0.493262i	$-0.164196\pi$
$164$	832.000			0.396148
$165$		0			0
$166$	1416.00			0.662066
$167$		−	3305.00i		−	1.53143i	−0.643181	−	0.765714i	$-0.722386\pi$
$167$		−	3305.00i		−	1.53143i	0.643181	−	0.765714i	$-0.277614\pi$
$168$		0			0
$169$	901.000			0.410105
$170$	−340.000	+	170.000i	−0.153393	+	0.0766965i
$171$		0			0
$172$			1720.00i			0.762493i
$173$		−	2186.00i		−	0.960685i	−0.877081	−	0.480342i	$-0.840512\pi$
$173$		−	2186.00i		−	0.960685i	0.877081	−	0.480342i	$-0.159488\pi$
$174$		0			0
$175$	500.000	+	375.000i	0.215980	+	0.161985i
$176$	−176.000			−0.0753778
$177$		0			0
$178$			274.000i			0.115377i
$179$	246.000			0.102720			0.0513601	−	0.998680i	$-0.483644\pi$
$179$	246.000			0.102720			0.0513601	+	0.998680i	$0.483644\pi$
$180$		0			0
$181$	2854.00			1.17202			0.586011	−	0.810303i	$-0.300697\pi$
$181$	2854.00			1.17202			0.586011	+	0.810303i	$0.300697\pi$
$182$			360.000i			0.146621i
$183$		0			0
$184$	−352.000			−0.141031
$185$	145.000	+	290.000i	0.0576249	+	0.115250i
$186$		0			0
$187$		−	187.000i		−	0.0731272i
$188$			1344.00i			0.521390i
$189$		0			0
$190$	−410.000	−	820.000i	−0.156550	−	0.313100i
$191$	3264.00			1.23652			0.618259	−	0.785975i	$-0.287838\pi$
$191$	3264.00			1.23652			0.618259	+	0.785975i	$0.287838\pi$
$192$		0			0
$193$			3925.00i			1.46387i	0.681372	+	0.731937i	$0.261383\pi$
$193$			3925.00i			1.46387i	−0.681372	+	0.731937i	$0.738617\pi$
$194$	−88.0000			−0.0325672
$195$		0			0
$196$	−1272.00			−0.463557
$197$			3534.00i			1.27811i	0.769162	+	0.639053i	$0.220674\pi$
$197$			3534.00i			1.27811i	−0.769162	+	0.639053i	$0.779326\pi$
$198$		0			0
$199$	−1043.00			−0.371539			−0.185770	−	0.982593i	$-0.559478\pi$
$199$	−1043.00			−0.371539			−0.185770	+	0.982593i	$0.559478\pi$
$200$	−800.000	−	600.000i	−0.282843	−	0.212132i
$201$		0			0
$202$		−	3444.00i		−	1.19960i
$203$			1425.00i			0.492687i
$204$		0			0
$205$	−2080.00	+	1040.00i	−0.708651	+	0.354326i
$206$	3224.00			1.09042
$207$		0			0
$208$		−	576.000i		−	0.192012i
$209$	451.000			0.149265
$210$		0			0
$211$	−3767.00			−1.22906			−0.614528	−	0.788895i	$-0.710654\pi$
$211$	−3767.00			−1.22906			−0.614528	+	0.788895i	$0.710654\pi$
$212$		−	2900.00i		−	0.939494i
$213$		0			0
$214$	1032.00			0.329655
$215$	−2150.00	−	4300.00i	−0.681994	−	1.36399i
$216$		0			0
$217$		−	1615.00i		−	0.505223i
$218$			4.00000i			0.00124273i
$219$		0			0
$220$	440.000	−	220.000i	0.134840	−	0.0674200i
$221$	612.000			0.186279
$222$		0			0
$223$			1462.00i			0.439026i	0.975610	+	0.219513i	$0.0704468\pi$
$223$			1462.00i			0.439026i	−0.975610	+	0.219513i	$0.929553\pi$
$224$	−160.000			−0.0477252
$225$		0			0
$226$	252.000			0.0741716
$227$		−	4572.00i		−	1.33680i	−0.743801	−	0.668402i	$-0.766979\pi$
$227$		−	4572.00i		−	1.33680i	0.743801	−	0.668402i	$-0.233021\pi$
$228$		0			0
$229$	3744.00			1.08040			0.540198	−	0.841538i	$-0.318350\pi$
$229$	3744.00			1.08040			0.540198	+	0.841538i	$0.318350\pi$
$230$	880.000	−	440.000i	0.252285	−	0.126142i
$231$		0			0
$232$		−	2280.00i		−	0.645213i
$233$			6255.00i			1.75871i	0.476170	+	0.879353i	$0.342025\pi$
$233$			6255.00i			1.75871i	−0.476170	+	0.879353i	$0.657975\pi$
$234$		0			0
$235$	−1680.00	−	3360.00i	−0.466345	−	0.932690i
$236$	2592.00			0.714936
$237$		0			0
$238$		−	170.000i		−	0.0463003i
$239$	5208.00			1.40953			0.704765	−	0.709441i	$-0.251053\pi$
$239$	5208.00			1.40953			0.704765	+	0.709441i	$0.251053\pi$
$240$		0			0
$241$	−5352.00			−1.43051			−0.715254	−	0.698864i	$-0.753689\pi$
$241$	−5352.00			−1.43051			−0.715254	+	0.698864i	$0.753689\pi$
$242$			242.000i			0.0642824i
$243$		0			0
$244$	2260.00			0.592958
$245$	3180.00	−	1590.00i	0.829236	−	0.414618i
$246$		0			0
$247$			1476.00i			0.380225i
$248$			2584.00i			0.661630i
$249$		0			0
$250$	2750.00	+	500.000i	0.695701	+	0.126491i
$251$	−2750.00			−0.691548			−0.345774	−	0.938318i	$-0.612384\pi$
$251$	−2750.00			−0.691548			−0.345774	+	0.938318i	$0.612384\pi$
$252$		0			0
$253$			484.000i			0.120272i
$254$	−176.000			−0.0434773
$255$		0			0
$256$	256.000			0.0625000
$257$			1564.00i			0.379609i	0.981822	+	0.189805i	$0.0607855\pi$
$257$			1564.00i			0.379609i	−0.981822	+	0.189805i	$0.939215\pi$
$258$		0			0
$259$	−145.000			−0.0347871
$260$	720.000	+	1440.00i	0.171740	+	0.343481i
$261$		0			0
$262$			3206.00i			0.755982i
$263$		−	3649.00i		−	0.855540i	−0.903888	−	0.427770i	$-0.859299\pi$
$263$		−	3649.00i		−	0.855540i	0.903888	−	0.427770i	$-0.140701\pi$
$264$		0			0
$265$	3625.00	+	7250.00i	0.840309	+	1.68062i
$266$	410.000			0.0945064
$267$		0			0
$268$			2992.00i			0.681961i
$269$	−4728.00			−1.07164			−0.535820	−	0.844332i	$-0.679997\pi$
$269$	−4728.00			−1.07164			−0.535820	+	0.844332i	$0.679997\pi$
$270$		0			0
$271$	−7198.00			−1.61346			−0.806729	−	0.590921i	$-0.798764\pi$
$271$	−7198.00			−1.61346			−0.806729	+	0.590921i	$0.798764\pi$
$272$			272.000i			0.0606339i
$273$		0			0
$274$	408.000			0.0899569
$275$	−825.000	+	1100.00i	−0.180907	+	0.241209i
$276$		0			0
$277$		−	5644.00i		−	1.22424i	−0.790764	−	0.612121i	$-0.790316\pi$
$277$		−	5644.00i		−	1.22424i	0.790764	−	0.612121i	$-0.209684\pi$
$278$			3336.00i			0.719712i
$279$		0			0
$280$	400.000	−	200.000i	0.0853735	−	0.0426867i
$281$	2738.00			0.581265			0.290632	−	0.956835i	$-0.406134\pi$
$281$	2738.00			0.581265			0.290632	+	0.956835i	$0.406134\pi$
$282$		0			0
$283$			4736.00i			0.994791i	0.867524	+	0.497396i	$0.165710\pi$
$283$			4736.00i			0.994791i	−0.867524	+	0.497396i	$0.834290\pi$
$284$	−1060.00			−0.221477
$285$		0			0
$286$	−792.000			−0.163748
$287$		−	1040.00i		−	0.213900i
$288$		0			0
$289$	4624.00			0.941176
$290$	2850.00	+	5700.00i	0.577096	+	1.15419i
$291$		0			0
$292$			2408.00i			0.482594i
$293$		−	992.000i		−	0.197793i	−0.995098	−	0.0988963i	$-0.968469\pi$
$293$		−	992.000i		−	0.197793i	0.995098	−	0.0988963i	$-0.0315312\pi$
$294$		0			0
$295$	−6480.00	+	3240.00i	−1.27892	+	0.639458i
$296$	232.000			0.0455565
$297$		0			0
$298$		−	1402.00i		−	0.272536i
$299$	−1584.00			−0.306372
$300$		0			0
$301$	2150.00			0.411707
$302$			2556.00i			0.487024i
$303$		0			0
$304$	−656.000			−0.123764
$305$	−5650.00	+	2825.00i	−1.06071	+	0.530357i
$306$		0			0
$307$		−	3272.00i		−	0.608283i	−0.952627	−	0.304142i	$-0.901630\pi$
$307$		−	3272.00i		−	0.608283i	0.952627	−	0.304142i	$-0.0983696\pi$
$308$			220.000i			0.0407002i
$309$		0			0
$310$	−3230.00	−	6460.00i	−0.591780	−	1.18356i
$311$	743.000			0.135472			0.0677358	−	0.997703i	$-0.478423\pi$
$311$	743.000			0.135472			0.0677358	+	0.997703i	$0.478423\pi$
$312$		0			0
$313$		−	4998.00i		−	0.902568i	−0.892380	−	0.451284i	$-0.850966\pi$
$313$		−	4998.00i		−	0.902568i	0.892380	−	0.451284i	$-0.149034\pi$
$314$	5246.00			0.942831
$315$		0			0
$316$	32.0000			0.00569665
$317$			4669.00i			0.827247i	0.910448	+	0.413623i	$0.135737\pi$
$317$			4669.00i			0.827247i	−0.910448	+	0.413623i	$0.864263\pi$
$318$		0			0
$319$	−3135.00			−0.550239
$320$	−640.000	+	320.000i	−0.111803	+	0.0559017i
$321$		0			0
$322$			440.000i			0.0761498i
$323$		−	697.000i		−	0.120068i
$324$		0			0
$325$	−3600.00	−	2700.00i	−0.614437	−	0.460828i
$326$	4106.00			0.697578
$327$		0			0
$328$			1664.00i			0.280119i
$329$	1680.00			0.281524
$330$		0			0
$331$	−3998.00			−0.663897			−0.331949	−	0.943297i	$-0.607706\pi$
$331$	−3998.00			−0.663897			−0.331949	+	0.943297i	$0.607706\pi$
$332$			2832.00i			0.468151i
$333$		0			0
$334$	6610.00			1.08288
$335$	−3740.00	−	7480.00i	−0.609964	−	1.21993i
$336$		0			0
$337$		−	4835.00i		−	0.781541i	−0.920488	−	0.390770i	$-0.872209\pi$
$337$		−	4835.00i		−	0.781541i	0.920488	−	0.390770i	$-0.127791\pi$
$338$			1802.00i			0.289988i
$339$		0			0
$340$	−340.000	−	680.000i	−0.0542326	−	0.108465i
$341$	3553.00			0.564240
$342$		0			0
$343$			3305.00i			0.520272i
$344$	−3440.00			−0.539164
$345$		0			0
$346$	4372.00			0.679307
$347$			2506.00i			0.387692i	0.981032	+	0.193846i	$0.0620962\pi$
$347$			2506.00i			0.387692i	−0.981032	+	0.193846i	$0.937904\pi$
$348$		0			0
$349$	−6254.00			−0.959223			−0.479612	−	0.877481i	$-0.659222\pi$
$349$	−6254.00			−0.959223			−0.479612	+	0.877481i	$0.659222\pi$
$350$	−750.000	+	1000.00i	−0.114541	+	0.152721i
$351$		0			0
$352$		−	352.000i		−	0.0533002i
$353$			3526.00i			0.531643i	0.964022	+	0.265822i	$0.0856432\pi$
$353$			3526.00i			0.531643i	−0.964022	+	0.265822i	$0.914357\pi$
$354$		0			0
$355$	2650.00	−	1325.00i	0.396190	−	0.198095i
$356$	−548.000			−0.0815841
$357$		0			0
$358$			492.000i			0.0726341i
$359$	−9352.00			−1.37487			−0.687437	−	0.726244i	$-0.741264\pi$
$359$	−9352.00			−1.37487			−0.687437	+	0.726244i	$0.741264\pi$
$360$		0			0
$361$	−5178.00			−0.754921
$362$			5708.00i			0.828745i
$363$		0			0
$364$	−720.000			−0.103677
$365$	−3010.00	−	6020.00i	−0.431645	−	0.863291i
$366$		0			0
$367$			2288.00i			0.325430i	0.986673	+	0.162715i	$0.0520250\pi$
$367$			2288.00i			0.325430i	−0.986673	+	0.162715i	$0.947975\pi$
$368$		−	704.000i		−	0.0997243i
$369$		0			0
$370$	−580.000	+	290.000i	−0.0814940	+	0.0407470i
$371$	−3625.00			−0.507279
$372$		0			0
$373$		−	3892.00i		−	0.540268i	−0.962823	−	0.270134i	$-0.912932\pi$
$373$		−	3892.00i		−	0.540268i	0.962823	−	0.270134i	$-0.0870681\pi$
$374$	374.000			0.0517088
$375$		0			0
$376$	−2688.00			−0.368678
$377$		−	10260.0i		−	1.40164i
$378$		0			0
$379$	12526.0			1.69767			0.848836	−	0.528657i	$-0.177304\pi$
$379$	12526.0			1.69767			0.848836	+	0.528657i	$0.177304\pi$
$380$	1640.00	−	820.000i	0.221395	−	0.110698i
$381$		0			0
$382$			6528.00i			0.874350i
$383$			2566.00i			0.342341i	0.985241	+	0.171170i	$0.0547548\pi$
$383$			2566.00i			0.342341i	−0.985241	+	0.171170i	$0.945245\pi$
$384$		0			0
$385$	−275.000	−	550.000i	−0.0364034	−	0.0728067i
$386$	−7850.00			−1.03512
$387$		0			0
$388$		−	176.000i		−	0.0230285i
$389$	5906.00			0.769784			0.384892	−	0.922962i	$-0.374239\pi$
$389$	5906.00			0.769784			0.384892	+	0.922962i	$0.374239\pi$
$390$		0			0
$391$	748.000			0.0967468
$392$		−	2544.00i		−	0.327784i
$393$		0			0
$394$	−7068.00			−0.903758
$395$	−80.0000	+	40.0000i	−0.0101905	+	0.00509524i
$396$		0			0
$397$			7346.00i			0.928678i	0.885658	+	0.464339i	$0.153708\pi$
$397$			7346.00i			0.928678i	−0.885658	+	0.464339i	$0.846292\pi$
$398$		−	2086.00i		−	0.262718i
$399$		0			0
$400$	1200.00	−	1600.00i	0.150000	−	0.200000i
$401$	−7475.00			−0.930882			−0.465441	−	0.885079i	$-0.654104\pi$
$401$	−7475.00			−0.930882			−0.465441	+	0.885079i	$0.654104\pi$
$402$		0			0
$403$			11628.0i			1.43730i
$404$	6888.00			0.848245
$405$		0			0
$406$	−2850.00			−0.348382
$407$		−	319.000i		−	0.0388507i
$408$		0			0
$409$	−8788.00			−1.06244			−0.531221	−	0.847233i	$-0.678267\pi$
$409$	−8788.00			−1.06244			−0.531221	+	0.847233i	$0.678267\pi$
$410$	−2080.00	−	4160.00i	−0.250546	−	0.501092i
$411$		0			0
$412$			6448.00i			0.771044i
$413$		−	3240.00i		−	0.386029i
$414$		0			0
$415$	−3540.00	−	7080.00i	−0.418727	−	0.837454i
$416$	1152.00			0.135773
$417$		0			0
$418$			902.000i			0.105546i
$419$	2700.00			0.314806			0.157403	−	0.987534i	$-0.449688\pi$
$419$	2700.00			0.314806			0.157403	+	0.987534i	$0.449688\pi$
$420$		0			0
$421$	2052.00			0.237550			0.118775	−	0.992921i	$-0.462103\pi$
$421$	2052.00			0.237550			0.118775	+	0.992921i	$0.462103\pi$
$422$		−	7534.00i		−	0.869074i
$423$		0			0
$424$	5800.00			0.664323
$425$	1700.00	+	1275.00i	0.194029	+	0.145521i
$426$		0			0
$427$		−	2825.00i		−	0.320167i
$428$			2064.00i			0.233101i
$429$		0			0
$430$	8600.00	−	4300.00i	0.964486	−	0.482243i
$431$	−2632.00			−0.294151			−0.147075	−	0.989125i	$-0.546986\pi$
$431$	−2632.00			−0.294151			−0.147075	+	0.989125i	$0.546986\pi$
$432$		0			0
$433$			4658.00i			0.516973i	0.966015	+	0.258486i	$0.0832237\pi$
$433$			4658.00i			0.516973i	−0.966015	+	0.258486i	$0.916776\pi$
$434$	3230.00			0.357246
$435$		0			0
$436$	−8.00000			−0.000878740
$437$			1804.00i			0.197476i
$438$		0			0
$439$	−7894.00			−0.858223			−0.429112	−	0.903251i	$-0.641173\pi$
$439$	−7894.00			−0.858223			−0.429112	+	0.903251i	$0.641173\pi$
$440$	440.000	+	880.000i	0.0476731	+	0.0953463i
$441$		0			0
$442$			1224.00i			0.131719i
$443$		−	3548.00i		−	0.380520i	−0.981734	−	0.190260i	$-0.939067\pi$
$443$		−	3548.00i		−	0.380520i	0.981734	−	0.190260i	$-0.0609332\pi$
$444$		0			0
$445$	1370.00	−	685.000i	0.145942	−	0.0729710i
$446$	−2924.00			−0.310438
$447$		0			0
$448$		−	320.000i		−	0.0337468i
$449$	−8258.00			−0.867971			−0.433986	−	0.900920i	$-0.642893\pi$
$449$	−8258.00			−0.867971			−0.433986	+	0.900920i	$0.642893\pi$
$450$		0			0
$451$	2288.00			0.238886
$452$			504.000i			0.0524473i
$453$		0			0
$454$	9144.00			0.945263
$455$	1800.00	−	900.000i	0.185462	−	0.0927311i
$456$		0			0
$457$			9969.00i			1.02042i	0.860051	+	0.510208i	$0.170432\pi$
$457$			9969.00i			1.02042i	−0.860051	+	0.510208i	$0.829568\pi$
$458$			7488.00i			0.763955i
$459$		0			0
$460$	880.000	+	1760.00i	0.0891961	+	0.178392i
$461$	−8147.00			−0.823088			−0.411544	−	0.911390i	$-0.635010\pi$
$461$	−8147.00			−0.823088			−0.411544	+	0.911390i	$0.635010\pi$
$462$		0			0
$463$			13488.0i			1.35387i	0.736044	+	0.676934i	$0.236692\pi$
$463$			13488.0i			1.35387i	−0.736044	+	0.676934i	$0.763308\pi$
$464$	4560.00			0.456234
$465$		0			0
$466$	−12510.0			−1.24359
$467$			4883.00i			0.483851i	0.970295	+	0.241925i	$0.0777789\pi$
$467$			4883.00i			0.483851i	−0.970295	+	0.241925i	$0.922221\pi$
$468$		0			0
$469$	3740.00			0.368224
$470$	6720.00	−	3360.00i	0.659512	−	0.329756i
$471$		0			0
$472$			5184.00i			0.505536i
$473$			4730.00i			0.459800i
$474$		0			0
$475$	−3075.00	+	4100.00i	−0.297033	+	0.396044i
$476$	340.000			0.0327392
$477$		0			0
$478$			10416.0i			0.996688i
$479$	−15006.0			−1.43140			−0.715701	−	0.698407i	$-0.753893\pi$
$479$	−15006.0			−1.43140			−0.715701	+	0.698407i	$0.753893\pi$
$480$		0			0
$481$	1044.00			0.0989653
$482$		−	10704.0i		−	1.01152i
$483$		0			0
$484$	−484.000			−0.0454545
$485$	220.000	+	440.000i	0.0205973	+	0.0411946i
$486$		0			0
$487$		−	7074.00i		−	0.658221i	−0.944291	−	0.329110i	$-0.893251\pi$
$487$		−	7074.00i		−	0.658221i	0.944291	−	0.329110i	$-0.106749\pi$
$488$			4520.00i			0.419284i
$489$		0			0
$490$	3180.00	+	6360.00i	0.293179	+	0.586358i
$491$	4099.00			0.376752			0.188376	−	0.982097i	$-0.439678\pi$
$491$	4099.00			0.376752			0.188376	+	0.982097i	$0.439678\pi$
$492$		0			0
$493$			4845.00i			0.442612i
$494$	−2952.00			−0.268860
$495$		0			0
$496$	−5168.00			−0.467843
$497$			1325.00i			0.119586i
$498$		0			0
$499$	10520.0			0.943767			0.471884	−	0.881661i	$-0.343574\pi$
$499$	10520.0			0.943767			0.471884	+	0.881661i	$0.343574\pi$
$500$	−1000.00	+	5500.00i	−0.0894427	+	0.491935i
$501$		0			0
$502$		−	5500.00i		−	0.488998i
$503$			14040.0i			1.24456i	0.782796	+	0.622279i	$0.213793\pi$
$503$			14040.0i			1.24456i	−0.782796	+	0.622279i	$0.786207\pi$
$504$		0			0
$505$	−17220.0	+	8610.00i	−1.51739	+	0.758693i
$506$	−968.000			−0.0850452
$507$		0			0
$508$		−	352.000i		−	0.0307431i
$509$	−4836.00			−0.421124			−0.210562	−	0.977581i	$-0.567529\pi$
$509$	−4836.00			−0.421124			−0.210562	+	0.977581i	$0.567529\pi$
$510$		0			0
$511$	3010.00			0.260576
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−3128.00			−0.268424
$515$	−8060.00	−	16120.0i	−0.689643	−	1.37929i
$516$		0			0
$517$			3696.00i			0.314410i
$518$		−	290.000i		−	0.0245982i
$519$		0			0
$520$	−2880.00	+	1440.00i	−0.242878	+	0.121439i
$521$	15498.0			1.30322			0.651612	−	0.758552i	$-0.274093\pi$
$521$	15498.0			1.30322			0.651612	+	0.758552i	$0.274093\pi$
$522$		0			0
$523$			16288.0i			1.36181i	0.732374	+	0.680903i	$0.238412\pi$
$523$			16288.0i			1.36181i	−0.732374	+	0.680903i	$0.761588\pi$
$524$	−6412.00			−0.534560
$525$		0			0
$526$	7298.00			0.604958
$527$		−	5491.00i		−	0.453874i
$528$		0			0
$529$	10231.0			0.840881
$530$	−14500.0	+	7250.00i	−1.18838	+	0.594188i
$531$		0			0
$532$			820.000i			0.0668261i
$533$			7488.00i			0.608520i
$534$		0			0
$535$	−2580.00	−	5160.00i	−0.208492	−	0.416984i
$536$	−5984.00			−0.482219
$537$		0			0
$538$		−	9456.00i		−	0.757764i
$539$	−3498.00			−0.279535
$540$		0			0
$541$	8313.00			0.660635			0.330318	−	0.943870i	$-0.392844\pi$
$541$	8313.00			0.660635			0.330318	+	0.943870i	$0.392844\pi$
$542$		−	14396.0i		−	1.14089i
$543$		0			0
$544$	−544.000			−0.0428746
$545$	20.0000	−	10.0000i	0.00157194	−	0.000785969i
$546$		0			0
$547$		−	5888.00i		−	0.460243i	−0.973162	−	0.230121i	$-0.926088\pi$
$547$		−	5888.00i		−	0.460243i	0.973162	−	0.230121i	$-0.0739123\pi$
$548$			816.000i			0.0636091i
$549$		0			0
$550$	−2200.00	−	1650.00i	−0.170561	−	0.127920i
$551$	−11685.0			−0.903444
$552$		0			0
$553$		−	40.0000i		−	0.00307590i
$554$	11288.0			0.865670
$555$		0			0
$556$	−6672.00			−0.508913
$557$			16844.0i			1.28133i	0.767819	+	0.640667i	$0.221342\pi$
$557$			16844.0i			1.28133i	−0.767819	+	0.640667i	$0.778658\pi$
$558$		0			0
$559$	−15480.0			−1.17126
$560$	400.000	+	800.000i	0.0301841	+	0.0603682i
$561$		0			0
$562$			5476.00i			0.411016i
$563$		−	9132.00i		−	0.683602i	−0.939772	−	0.341801i	$-0.888963\pi$
$563$		−	9132.00i		−	0.683602i	0.939772	−	0.341801i	$-0.111037\pi$
$564$		0			0
$565$	−630.000	−	1260.00i	−0.0469103	−	0.0938205i
$566$	−9472.00			−0.703424
$567$		0			0
$568$		−	2120.00i		−	0.156608i
$569$	6444.00			0.474774			0.237387	−	0.971415i	$-0.423709\pi$
$569$	6444.00			0.474774			0.237387	+	0.971415i	$0.423709\pi$
$570$		0			0
$571$	−17713.0			−1.29819			−0.649095	−	0.760708i	$-0.724852\pi$
$571$	−17713.0			−1.29819			−0.649095	+	0.760708i	$0.724852\pi$
$572$		−	1584.00i		−	0.115787i
$573$		0			0
$574$	2080.00			0.151250
$575$	−4400.00	−	3300.00i	−0.319118	−	0.239338i
$576$		0			0
$577$		−	7352.00i		−	0.530447i	−0.964187	−	0.265223i	$-0.914554\pi$
$577$		−	7352.00i		−	0.530447i	0.964187	−	0.265223i	$-0.0854457\pi$
$578$			9248.00i			0.665512i
$579$		0			0
$580$	−11400.0	+	5700.00i	−0.816137	+	0.408068i
$581$	3540.00			0.252778
$582$		0			0
$583$		−	7975.00i		−	0.566536i
$584$	−4816.00			−0.341246
$585$		0			0
$586$	1984.00			0.139861
$587$			4521.00i			0.317890i	0.987287	+	0.158945i	$0.0508093\pi$
$587$			4521.00i			0.317890i	−0.987287	+	0.158945i	$0.949191\pi$
$588$		0			0
$589$	13243.0			0.926432
$590$	−6480.00	−	12960.0i	−0.452165	−	0.904330i
$591$		0			0
$592$			464.000i			0.0322133i
$593$			27514.0i			1.90534i	0.304012	+	0.952668i	$0.401674\pi$
$593$			27514.0i			1.90534i	−0.304012	+	0.952668i	$0.598326\pi$
$594$		0			0
$595$	−850.000	+	425.000i	−0.0585657	+	0.0292829i
$596$	2804.00			0.192712
$597$		0			0
$598$		−	3168.00i		−	0.216637i
$599$	−5047.00			−0.344265			−0.172133	−	0.985074i	$-0.555066\pi$
$599$	−5047.00			−0.344265			−0.172133	+	0.985074i	$0.555066\pi$
$600$		0			0
$601$	8026.00			0.544738			0.272369	−	0.962193i	$-0.412193\pi$
$601$	8026.00			0.544738			0.272369	+	0.962193i	$0.412193\pi$
$602$			4300.00i			0.291121i
$603$		0			0
$604$	−5112.00			−0.344378
$605$	1210.00	−	605.000i	0.0813116	−	0.0406558i
$606$		0			0
$607$			27231.0i			1.82088i	0.413645	+	0.910438i	$0.364256\pi$
$607$			27231.0i			1.82088i	−0.413645	+	0.910438i	$0.635744\pi$
$608$		−	1312.00i		−	0.0875142i
$609$		0			0
$610$	−5650.00	−	11300.0i	−0.375019	−	0.750039i
$611$	−12096.0			−0.800903
$612$		0			0
$613$		−	1258.00i		−	0.0828877i	−0.999141	−	0.0414438i	$-0.986804\pi$
$613$		−	1258.00i		−	0.0828877i	0.999141	−	0.0414438i	$-0.0131958\pi$
$614$	6544.00			0.430121
$615$		0			0
$616$	−440.000			−0.0287794
$617$			24572.0i			1.60329i	0.597799	+	0.801646i	$0.296042\pi$
$617$			24572.0i			1.60329i	−0.597799	+	0.801646i	$0.703958\pi$
$618$		0			0
$619$	−14604.0			−0.948278			−0.474139	−	0.880450i	$-0.657241\pi$
$619$	−14604.0			−0.948278			−0.474139	+	0.880450i	$0.657241\pi$
$620$	12920.0	−	6460.00i	0.836903	−	0.418451i
$621$		0			0
$622$			1486.00i			0.0957929i
$623$			685.000i			0.0440513i
$624$		0			0
$625$	−4375.00	−	15000.0i	−0.280000	−	0.960000i
$626$	9996.00			0.638212
$627$		0			0
$628$			10492.0i			0.666682i
$629$	−493.000			−0.0312515
$630$		0			0
$631$	11535.0			0.727735			0.363868	−	0.931451i	$-0.381456\pi$
$631$	11535.0			0.727735			0.363868	+	0.931451i	$0.381456\pi$
$632$			64.0000i			0.00402814i
$633$		0			0
$634$	−9338.00			−0.584952
$635$	440.000	+	880.000i	0.0274974	+	0.0549949i
$636$		0			0
$637$		−	11448.0i		−	0.712066i
$638$		−	6270.00i		−	0.389078i
$639$		0			0
$640$	−640.000	−	1280.00i	−0.0395285	−	0.0790569i
$641$	1073.00			0.0661169			0.0330585	−	0.999453i	$-0.489475\pi$
$641$	1073.00			0.0661169			0.0330585	+	0.999453i	$0.489475\pi$
$642$		0			0
$643$			9943.00i			0.609819i	0.952381	+	0.304910i	$0.0986262\pi$
$643$			9943.00i			0.609819i	−0.952381	+	0.304910i	$0.901374\pi$
$644$	−880.000			−0.0538461
$645$		0			0
$646$	1394.00			0.0849012
$647$			3540.00i			0.215103i	0.994200	+	0.107552i	$0.0343011\pi$
$647$			3540.00i			0.215103i	−0.994200	+	0.107552i	$0.965699\pi$
$648$		0			0
$649$	7128.00			0.431122
$650$	5400.00	−	7200.00i	0.325855	−	0.434473i
$651$		0			0
$652$			8212.00i			0.493262i
$653$			8503.00i			0.509568i	0.966998	+	0.254784i	$0.0820044\pi$
$653$			8503.00i			0.509568i	−0.966998	+	0.254784i	$0.917996\pi$
$654$		0			0
$655$	16030.0	−	8015.00i	0.956250	−	0.478125i
$656$	−3328.00			−0.198074
$657$		0			0
$658$			3360.00i			0.199068i
$659$	27847.0			1.64608			0.823039	−	0.567985i	$-0.192277\pi$
$659$	27847.0			1.64608			0.823039	+	0.567985i	$0.192277\pi$
$660$		0			0
$661$	9748.00			0.573606			0.286803	−	0.957990i	$-0.407408\pi$
$661$	9748.00			0.573606			0.286803	+	0.957990i	$0.407408\pi$
$662$		−	7996.00i		−	0.469446i
$663$		0			0
$664$	−5664.00			−0.331033
$665$	−1025.00	−	2050.00i	−0.0597711	−	0.119542i
$666$		0			0
$667$		−	12540.0i		−	0.727962i
$668$			13220.0i			0.765714i
$669$		0			0
$670$	14960.0	−	7480.00i	0.862620	−	0.431310i
$671$	6215.00			0.357567
$672$		0			0
$673$		−	12595.0i		−	0.721399i	−0.932682	−	0.360700i	$-0.882538\pi$
$673$		−	12595.0i		−	0.721399i	0.932682	−	0.360700i	$-0.117462\pi$
$674$	9670.00			0.552633
$675$		0			0
$676$	−3604.00			−0.205052
$677$		−	27312.0i		−	1.55050i	−0.631657	−	0.775248i	$-0.717625\pi$
$677$		−	27312.0i		−	1.55050i	0.631657	−	0.775248i	$-0.282375\pi$
$678$		0			0
$679$	−220.000			−0.0124342
$680$	1360.00	−	680.000i	0.0766965	−	0.0383482i
$681$		0			0
$682$			7106.00i			0.398978i
$683$			21503.0i			1.20467i	0.798244	+	0.602335i	$0.205763\pi$
$683$			21503.0i			1.20467i	−0.798244	+	0.602335i	$0.794237\pi$
$684$		0			0
$685$	−1020.00	−	2040.00i	−0.0568937	−	0.113787i
$686$	−6610.00			−0.367888
$687$		0			0
$688$		−	6880.00i		−	0.381246i
$689$	26100.0			1.44315
$690$		0			0
$691$	8920.00			0.491075			0.245537	−	0.969387i	$-0.421036\pi$
$691$	8920.00			0.491075			0.245537	+	0.969387i	$0.421036\pi$
$692$			8744.00i			0.480342i
$693$		0			0
$694$	−5012.00			−0.274140
$695$	16680.0	−	8340.00i	0.910372	−	0.455186i
$696$		0			0
$697$		−	3536.00i		−	0.192160i
$698$		−	12508.0i		−	0.678273i
$699$		0			0
$700$	−2000.00	−	1500.00i	−0.107990	−	0.0809924i
$701$	−7651.00			−0.412232			−0.206116	−	0.978528i	$-0.566082\pi$
$701$	−7651.00			−0.412232			−0.206116	+	0.978528i	$0.566082\pi$
$702$		0			0
$703$		−	1189.00i		−	0.0637895i
$704$	704.000			0.0376889
$705$		0			0
$706$	−7052.00			−0.375929
$707$		−	8610.00i		−	0.458009i
$708$		0			0
$709$	4374.00			0.231691			0.115846	−	0.993267i	$-0.463042\pi$
$709$	4374.00			0.231691			0.115846	+	0.993267i	$0.463042\pi$
$710$	2650.00	+	5300.00i	0.140074	+	0.280149i
$711$		0			0
$712$		−	1096.00i		−	0.0576887i
$713$			14212.0i			0.746485i
$714$		0			0
$715$	1980.00	+	3960.00i	0.103563	+	0.207127i
$716$	−984.000			−0.0513601
$717$		0			0
$718$		−	18704.0i		−	0.972183i
$719$	34509.0			1.78994			0.894971	−	0.446124i	$-0.147196\pi$
$719$	34509.0			1.78994			0.894971	+	0.446124i	$0.147196\pi$
$720$		0			0
$721$	8060.00			0.416325
$722$		−	10356.0i		−	0.533809i
$723$		0			0
$724$	−11416.0			−0.586011
$725$	21375.0	−	28500.0i	1.09496	−	1.45995i
$726$		0			0
$727$		−	10770.0i		−	0.549432i	−0.961525	−	0.274716i	$-0.911416\pi$
$727$		−	10770.0i		−	0.549432i	0.961525	−	0.274716i	$-0.0885839\pi$
$728$		−	1440.00i		−	0.0733104i
$729$		0			0
$730$	12040.0	−	6020.00i	0.610439	−	0.305219i
$731$	7310.00			0.369863
$732$		0			0
$733$		−	7950.00i		−	0.400600i	−0.979735	−	0.200300i	$-0.935808\pi$
$733$		−	7950.00i		−	0.400600i	0.979735	−	0.200300i	$-0.0641917\pi$
$734$	−4576.00			−0.230113
$735$		0			0
$736$	1408.00			0.0705157
$737$			8228.00i			0.411238i
$738$		0			0
$739$	−8792.00			−0.437644			−0.218822	−	0.975765i	$-0.570221\pi$
$739$	−8792.00			−0.437644			−0.218822	+	0.975765i	$0.570221\pi$
$740$	−580.000	−	1160.00i	−0.0288125	−	0.0576249i
$741$		0			0
$742$		−	7250.00i		−	0.358701i
$743$		−	1791.00i		−	0.0884326i	−0.999022	−	0.0442163i	$-0.985921\pi$
$743$		−	1791.00i		−	0.0884326i	0.999022	−	0.0442163i	$-0.0140791\pi$
$744$		0			0
$745$	−7010.00	+	3505.00i	−0.344734	+	0.172367i
$746$	7784.00			0.382027
$747$		0			0
$748$			748.000i			0.0365636i
$749$	2580.00			0.125863
$750$		0			0
$751$	37745.0			1.83400			0.917000	−	0.398886i	$-0.130603\pi$
$751$	37745.0			1.83400			0.917000	+	0.398886i	$0.130603\pi$
$752$		−	5376.00i		−	0.260695i
$753$		0			0
$754$	20520.0			0.991107
$755$	12780.0	−	6390.00i	0.616042	−	0.308021i
$756$		0			0
$757$		−	15686.0i		−	0.753127i	−0.926391	−	0.376564i	$-0.877106\pi$
$757$		−	15686.0i		−	0.753127i	0.926391	−	0.376564i	$-0.122894\pi$
$758$			25052.0i			1.20043i
$759$		0			0
$760$	1640.00	+	3280.00i	0.0782751	+	0.156550i
$761$	−452.000			−0.0215309			−0.0107654	−	0.999942i	$-0.503427\pi$
$761$	−452.000			−0.0215309			−0.0107654	+	0.999942i	$0.503427\pi$
$762$		0			0
$763$			10.0000i			0.000474475i
$764$	−13056.0			−0.618259
$765$		0			0
$766$	−5132.00			−0.242071
$767$			23328.0i			1.09821i
$768$		0			0
$769$	6610.00			0.309964			0.154982	−	0.987917i	$-0.450468\pi$
$769$	6610.00			0.309964			0.154982	+	0.987917i	$0.450468\pi$
$770$	1100.00	−	550.000i	0.0514821	−	0.0257411i
$771$		0			0
$772$		−	15700.0i		−	0.731937i
$773$			26601.0i			1.23774i	0.785494	+	0.618869i	$0.212409\pi$
$773$			26601.0i			1.23774i	−0.785494	+	0.618869i	$0.787591\pi$
$774$		0			0
$775$	−24225.0	+	32300.0i	−1.12282	+	1.49710i
$776$	352.000			0.0162836
$777$		0			0
$778$			11812.0i			0.544320i
$779$	8528.00			0.392230
$780$		0			0
$781$	−2915.00			−0.133556
$782$			1496.00i			0.0684103i
$783$		0			0
$784$	5088.00			0.231778
$785$	−13115.0	−	26230.0i	−0.596299	−	1.19260i
$786$		0			0
$787$		−	35166.0i		−	1.59280i	−0.604771	−	0.796399i	$-0.706735\pi$
$787$		−	35166.0i		−	1.59280i	0.604771	−	0.796399i	$-0.293265\pi$
$788$		−	14136.0i		−	0.639053i
$789$		0			0
$790$	−80.0000	−	160.000i	−0.00360288	−	0.00720575i
$791$	630.000			0.0283189
$792$		0			0
$793$			20340.0i			0.910838i
$794$	−14692.0			−0.656675
$795$		0			0
$796$	4172.00			0.185770
$797$		−	42026.0i		−	1.86780i	−0.357533	−	0.933900i	$-0.616382\pi$
$797$		−	42026.0i		−	1.86780i	0.357533	−	0.933900i	$-0.383618\pi$
$798$		0			0
$799$	5712.00			0.252911
$800$	3200.00	+	2400.00i	0.141421	+	0.106066i
$801$		0			0
$802$		−	14950.0i		−	0.658233i
$803$			6622.00i			0.291015i
$804$		0			0
$805$	2200.00	−	1100.00i	0.0963227	−	0.0481614i
$806$	−23256.0			−1.01632
$807$		0			0
$808$			13776.0i			0.599799i
$809$	31666.0			1.37616			0.688082	−	0.725633i	$-0.258453\pi$
$809$	31666.0			1.37616			0.688082	+	0.725633i	$0.258453\pi$
$810$		0			0
$811$	3143.00			0.136086			0.0680429	−	0.997682i	$-0.478325\pi$
$811$	3143.00			0.136086			0.0680429	+	0.997682i	$0.478325\pi$
$812$		−	5700.00i		−	0.246343i
$813$		0			0
$814$	638.000			0.0274716
$815$	−10265.0	−	20530.0i	−0.441187	−	0.882374i
$816$		0			0
$817$			17630.0i			0.754952i
$818$		−	17576.0i		−	0.751260i
$819$		0			0
$820$	8320.00	−	4160.00i	0.354326	−	0.177163i
$821$	1282.00			0.0544971			0.0272485	−	0.999629i	$-0.491325\pi$
$821$	1282.00			0.0544971			0.0272485	+	0.999629i	$0.491325\pi$
$822$		0			0
$823$		−	6778.00i		−	0.287079i	−0.989645	−	0.143540i	$-0.954152\pi$
$823$		−	6778.00i		−	0.287079i	0.989645	−	0.143540i	$-0.0458485\pi$
$824$	−12896.0			−0.545210
$825$		0			0
$826$	6480.00			0.272964
$827$		−	10158.0i		−	0.427120i	−0.976930	−	0.213560i	$-0.931494\pi$
$827$		−	10158.0i		−	0.427120i	0.976930	−	0.213560i	$-0.0685059\pi$
$828$		0			0
$829$	−45716.0			−1.91530			−0.957649	−	0.287938i	$-0.907030\pi$
$829$	−45716.0			−1.91530			−0.957649	+	0.287938i	$0.907030\pi$
$830$	14160.0	−	7080.00i	0.592170	−	0.296085i
$831$		0			0
$832$			2304.00i			0.0960058i
$833$			5406.00i			0.224858i
$834$		0			0
$835$	−16525.0	−	33050.0i	−0.684876	−	1.36975i
$836$	−1804.00			−0.0746324
$837$		0			0
$838$			5400.00i			0.222601i
$839$	2184.00			0.0898690			0.0449345	−	0.998990i	$-0.485692\pi$
$839$	2184.00			0.0898690			0.0449345	+	0.998990i	$0.485692\pi$
$840$		0			0
$841$	56836.0			2.33039
$842$			4104.00i			0.167973i
$843$		0			0
$844$	15068.0			0.614528
$845$	9010.00	−	4505.00i	0.366809	−	0.183404i
$846$		0			0
$847$			605.000i			0.0245431i
$848$			11600.0i			0.469747i
$849$		0			0
$850$	−2550.00	+	3400.00i	−0.102899	+	0.137199i
$851$	1276.00			0.0513992
$852$		0			0
$853$		−	16292.0i		−	0.653960i	−0.945031	−	0.326980i	$-0.893969\pi$
$853$		−	16292.0i		−	0.653960i	0.945031	−	0.326980i	$-0.106031\pi$
$854$	5650.00			0.226392
$855$		0			0
$856$	−4128.00			−0.164827
$857$		−	20443.0i		−	0.814842i	−0.913240	−	0.407421i	$-0.866428\pi$
$857$		−	20443.0i		−	0.814842i	0.913240	−	0.407421i	$-0.133572\pi$
$858$		0			0
$859$	24350.0			0.967184			0.483592	−	0.875293i	$-0.339332\pi$
$859$	24350.0			0.967184			0.483592	+	0.875293i	$0.339332\pi$
$860$	8600.00	+	17200.0i	0.340997	+	0.681994i
$861$		0			0
$862$		−	5264.00i		−	0.207996i
$863$			11988.0i			0.472858i	0.971649	+	0.236429i	$0.0759770\pi$
$863$			11988.0i			0.472858i	−0.971649	+	0.236429i	$0.924023\pi$
$864$		0			0
$865$	−10930.0	−	21860.0i	−0.429631	−	0.859263i
$866$	−9316.00			−0.365555
$867$		0			0
$868$			6460.00i			0.252611i
$869$	88.0000			0.00343521
$870$		0			0
$871$	−26928.0			−1.04756
$872$		−	16.0000i		−	0.000621363i
$873$		0			0
$874$	−3608.00			−0.139637
$875$	6875.00	+	1250.00i	0.265620	+	0.0482945i
$876$		0			0
$877$		−	12314.0i		−	0.474133i	−0.971493	−	0.237066i	$-0.923814\pi$
$877$		−	12314.0i		−	0.474133i	0.971493	−	0.237066i	$-0.0761859\pi$
$878$		−	15788.0i		−	0.606856i
$879$		0			0
$880$	−1760.00	+	880.000i	−0.0674200	+	0.0337100i
$881$	24882.0			0.951528			0.475764	−	0.879573i	$-0.342172\pi$
$881$	24882.0			0.951528			0.475764	+	0.879573i	$0.342172\pi$
$882$		0			0
$883$		−	15175.0i		−	0.578346i	−0.957277	−	0.289173i	$-0.906620\pi$
$883$		−	15175.0i		−	0.578346i	0.957277	−	0.289173i	$-0.0933803\pi$
$884$	−2448.00			−0.0931393
$885$		0			0
$886$	7096.00			0.269069
$887$		−	1472.00i		−	0.0557214i	−0.999612	−	0.0278607i	$-0.991131\pi$
$887$		−	1472.00i		−	0.0557214i	0.999612	−	0.0278607i	$-0.00886949\pi$
$888$		0			0
$889$	−440.000			−0.0165997
$890$	1370.00	+	2740.00i	0.0515983	+	0.103197i
$891$		0			0
$892$		−	5848.00i		−	0.219513i
$893$			13776.0i			0.516233i
$894$		0			0
$895$	2460.00	−	1230.00i	0.0918757	−	0.0459378i
$896$	640.000			0.0238626
$897$		0			0
$898$		−	16516.0i		−	0.613748i
$899$	−92055.0			−3.41513
$900$		0			0
$901$	−12325.0			−0.455722
$902$			4576.00i			0.168918i
$903$		0			0
$904$	−1008.00			−0.0370858
$905$	28540.0	−	14270.0i	1.04829	−	0.524145i
$906$		0			0
$907$		−	9335.00i		−	0.341746i	−0.985293	−	0.170873i	$-0.945341\pi$
$907$		−	9335.00i		−	0.341746i	0.985293	−	0.170873i	$-0.0546588\pi$
$908$			18288.0i			0.668402i
$909$		0			0
$910$	1800.00	+	3600.00i	0.0655708	+	0.131142i
$911$	16137.0			0.586874			0.293437	−	0.955978i	$-0.405201\pi$
$911$	16137.0			0.586874			0.293437	+	0.955978i	$0.405201\pi$
$912$		0			0
$913$			7788.00i			0.282306i
$914$	−19938.0			−0.721543
$915$		0			0
$916$	−14976.0			−0.540198
$917$			8015.00i			0.288635i
$918$		0			0
$919$	4658.00			0.167196			0.0835981	−	0.996500i	$-0.473359\pi$
$919$	4658.00			0.167196			0.0835981	+	0.996500i	$0.473359\pi$
$920$	−3520.00	+	1760.00i	−0.126142	+	0.0630712i
$921$		0			0
$922$		−	16294.0i		−	0.582011i
$923$		−	9540.00i		−	0.340209i
$924$		0			0
$925$	2900.00	+	2175.00i	0.103083	+	0.0773120i
$926$	−26976.0			−0.957329
$927$		0			0
$928$			9120.00i			0.322606i
$929$	−25105.0			−0.886618			−0.443309	−	0.896369i	$-0.646196\pi$
$929$	−25105.0			−0.886618			−0.443309	+	0.896369i	$0.646196\pi$
$930$		0			0
$931$	−13038.0			−0.458972
$932$		−	25020.0i		−	0.879353i
$933$		0			0
$934$	−9766.00			−0.342134
$935$	−935.000	−	1870.00i	−0.0327035	−	0.0654070i
$936$		0			0
$937$			15094.0i			0.526253i	0.964761	+	0.263127i	$0.0847537\pi$
$937$			15094.0i			0.526253i	−0.964761	+	0.263127i	$0.915246\pi$
$938$			7480.00i			0.260374i
$939$		0			0
$940$	6720.00	+	13440.0i	0.233173	+	0.466345i
$941$	18167.0			0.629359			0.314680	−	0.949198i	$-0.398103\pi$
$941$	18167.0			0.629359			0.314680	+	0.949198i	$0.398103\pi$
$942$		0			0
$943$			9152.00i			0.316045i
$944$	−10368.0			−0.357468
$945$		0			0
$946$	−9460.00			−0.325128
$947$			17781.0i			0.610142i	0.952330	+	0.305071i	$0.0986803\pi$
$947$			17781.0i			0.610142i	−0.952330	+	0.305071i	$0.901320\pi$
$948$		0			0
$949$	−21672.0			−0.741310
$950$	−8200.00	−	6150.00i	−0.280045	−	0.210034i
$951$		0			0
$952$			680.000i			0.0231501i
$953$		−	28327.0i		−	0.962856i	−0.876486	−	0.481428i	$-0.840118\pi$
$953$		−	28327.0i		−	0.962856i	0.876486	−	0.481428i	$-0.159882\pi$
$954$		0			0
$955$	32640.0	−	16320.0i	1.10597	−	0.552987i
$956$	−20832.0			−0.704765
$957$		0			0
$958$		−	30012.0i		−	1.01215i
$959$	1020.00			0.0343457
$960$		0			0
$961$	74538.0			2.50203
$962$			2088.00i			0.0699790i
$963$		0			0
$964$	21408.0			0.715254
$965$	19625.0	+	39250.0i	0.654664	+	1.30933i
$966$		0			0
$967$			34867.0i			1.15951i	0.814791	+	0.579755i	$0.196852\pi$
$967$			34867.0i			1.15951i	−0.814791	+	0.579755i	$0.803148\pi$
$968$		−	968.000i		−	0.0321412i
$969$		0			0
$970$	−880.000	+	440.000i	−0.0291290	+	0.0145645i
$971$	−38780.0			−1.28168			−0.640839	−	0.767675i	$-0.721413\pi$
$971$	−38780.0			−1.28168			−0.640839	+	0.767675i	$0.721413\pi$
$972$		0			0
$973$			8340.00i			0.274787i
$974$	14148.0			0.465432
$975$		0			0
$976$	−9040.00			−0.296479
$977$		−	33940.0i		−	1.11140i	−0.831383	−	0.555699i	$-0.812451\pi$
$977$		−	33940.0i		−	1.11140i	0.831383	−	0.555699i	$-0.187549\pi$
$978$		0			0
$979$	−1507.00			−0.0491971
$980$	−12720.0	+	6360.00i	−0.414618	+	0.207309i
$981$		0			0
$982$			8198.00i			0.266404i
$983$		−	39254.0i		−	1.27366i	−0.771004	−	0.636830i	$-0.780245\pi$
$983$		−	39254.0i		−	1.27366i	0.771004	−	0.636830i	$-0.219755\pi$
$984$		0			0
$985$	17670.0	+	35340.0i	0.571587	+	1.14317i
$986$	−9690.00			−0.312974
$987$		0			0
$988$		−	5904.00i		−	0.190113i
$989$	−18920.0			−0.608312
$990$		0			0
$991$	21840.0			0.700071			0.350036	−	0.936736i	$-0.386170\pi$
$991$	21840.0			0.700071			0.350036	+	0.936736i	$0.386170\pi$
$992$		−	10336.0i		−	0.330815i
$993$		0			0
$994$	−2650.00			−0.0845603
$995$	−10430.0	+	5215.00i	−0.332315	+	0.166157i
$996$		0			0
$997$		−	10226.0i		−	0.324835i	−0.986722	−	0.162418i	$-0.948071\pi$
$997$		−	10226.0i		−	0.324835i	0.986722	−	0.162418i	$-0.0519292\pi$
$998$			21040.0i			0.667344i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.4.c.b.199.2		2
3.2	odd	2		110.4.b.a.89.1	✓	2
5.4	even	2	inner	990.4.c.b.199.1		2
12.11	even	2		880.4.b.a.529.2		2
15.2	even	4		550.4.a.i.1.1		1
15.8	even	4		550.4.a.h.1.1		1
15.14	odd	2		110.4.b.a.89.2	yes	2
60.59	even	2		880.4.b.a.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.b.a.89.1	✓	2	3.2	odd	2
110.4.b.a.89.2	yes	2	15.14	odd	2
550.4.a.h.1.1		1	15.8	even	4
550.4.a.i.1.1		1	15.2	even	4
880.4.b.a.529.1		2	60.59	even	2
880.4.b.a.529.2		2	12.11	even	2
990.4.c.b.199.1		2	5.4	even	2	inner
990.4.c.b.199.2		2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	990.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(10.0000 - 5.00000i) q^{5} +5.00000i q^{7} -8.00000i q^{8} +(10.0000 + 20.0000i) q^{10} -11.0000 q^{11} -36.0000i q^{13} -10.0000 q^{14} +16.0000 q^{16} +17.0000i q^{17} -41.0000 q^{19} +(-40.0000 + 20.0000i) q^{20} -22.0000i q^{22} -44.0000i q^{23} +(75.0000 - 100.000i) q^{25} +72.0000 q^{26} -20.0000i q^{28} +285.000 q^{29} -323.000 q^{31} +32.0000i q^{32} -34.0000 q^{34} +(25.0000 + 50.0000i) q^{35} +29.0000i q^{37} -82.0000i q^{38} +(-40.0000 - 80.0000i) q^{40} -208.000 q^{41} -430.000i q^{43} +44.0000 q^{44} +88.0000 q^{46} -336.000i q^{47} +318.000 q^{49} +(200.000 + 150.000i) q^{50} +144.000i q^{52} +725.000i q^{53} +(-110.000 + 55.0000i) q^{55} +40.0000 q^{56} +570.000i q^{58} -648.000 q^{59} -565.000 q^{61} -646.000i q^{62} -64.0000 q^{64} +(-180.000 - 360.000i) q^{65} -748.000i q^{67} -68.0000i q^{68} +(-100.000 + 50.0000i) q^{70} +265.000 q^{71} -602.000i q^{73} -58.0000 q^{74} +164.000 q^{76} -55.0000i q^{77} -8.00000 q^{79} +(160.000 - 80.0000i) q^{80} -416.000i q^{82} -708.000i q^{83} +(85.0000 + 170.000i) q^{85} +860.000 q^{86} +88.0000i q^{88} +137.000 q^{89} +180.000 q^{91} +176.000i q^{92} +672.000 q^{94} +(-410.000 + 205.000i) q^{95} +44.0000i q^{97} +636.000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 20 q^{5} + 20 q^{10} - 22 q^{11} - 20 q^{14} + 32 q^{16} - 82 q^{19} - 80 q^{20} + 150 q^{25} + 144 q^{26} + 570 q^{29} - 646 q^{31} - 68 q^{34} + 50 q^{35} - 80 q^{40} - 416 q^{41} + 88 q^{44}+ \cdots - 820 q^{95}+O(q^{100}) \) 2 * q - 8 * q^4 + 20 * q^5 + 20 * q^10 - 22 * q^11 - 20 * q^14 + 32 * q^16 - 82 * q^19 - 80 * q^20 + 150 * q^25 + 144 * q^26 + 570 * q^29 - 646 * q^31 - 68 * q^34 + 50 * q^35 - 80 * q^40 - 416 * q^41 + 88 * q^44 + 176 * q^46 + 636 * q^49 + 400 * q^50 - 220 * q^55 + 80 * q^56 - 1296 * q^59 - 1130 * q^61 - 128 * q^64 - 360 * q^65 - 200 * q^70 + 530 * q^71 - 116 * q^74 + 328 * q^76 - 16 * q^79 + 320 * q^80 + 170 * q^85 + 1720 * q^86 + 274 * q^89 + 360 * q^91 + 1344 * q^94 - 820 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more