LMFDB - Embedded newform 3330.2.d.r.1999.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3330,2,Mod(1999,3330)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3330.1999"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3330, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,4,0,0,0,0,-6,-12,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 20x^{12} + 154x^{10} + 580x^{8} + 1105x^{6} + 960x^{4} + 256x^{2} + 16 $ x^14 + 20x^12 + 154x^10 + 580x^8 + 1105x^6 + 960x^4 + 256x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.8
Root			$-2.64550i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.r.1999.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.17297 + 0.527467i) q^{5} -4.99866i q^{7} -1.00000i q^{8} +(-0.527467 - 2.17297i) q^{10} -2.41083 q^{11} -3.44356i q^{13} +4.99866 q^{14} +1.00000 q^{16} +1.84744i q^{17} -0.288789 q^{19} +(2.17297 - 0.527467i) q^{20} -2.41083i q^{22} +0.170297i q^{23} +(4.44356 - 2.29234i) q^{25} +3.44356 q^{26} +4.99866i q^{28} +6.81364 q^{29} +3.19979 q^{31} +1.00000i q^{32} -1.84744 q^{34} +(2.63663 + 10.8619i) q^{35} -1.00000i q^{37} -0.288789i q^{38} +(0.527467 + 2.17297i) q^{40} -3.43306 q^{41} -8.57489i q^{43} +2.41083 q^{44} -0.170297 q^{46} -1.88658i q^{47} -17.9866 q^{49} +(2.29234 + 4.44356i) q^{50} +3.44356i q^{52} -3.73718i q^{53} +(5.23865 - 1.27163i) q^{55} -4.99866 q^{56} +6.81364i q^{58} -13.5430 q^{59} -2.14293 q^{61} +3.19979i q^{62} -1.00000 q^{64} +(1.81636 + 7.48273i) q^{65} +9.08723i q^{67} -1.84744i q^{68} +(-10.8619 + 2.63663i) q^{70} -2.43273 q^{71} +13.2347i q^{73} +1.00000 q^{74} +0.288789 q^{76} +12.0509i q^{77} -12.6555 q^{79} +(-2.17297 + 0.527467i) q^{80} -3.43306i q^{82} -3.21967i q^{83} +(-0.974464 - 4.01442i) q^{85} +8.57489 q^{86} +2.41083i q^{88} -4.27078 q^{89} -17.2132 q^{91} -0.170297i q^{92} +1.88658 q^{94} +(0.627528 - 0.152327i) q^{95} -7.95362i q^{97} -17.9866i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} + 4 q^{5} - 6 q^{10} - 12 q^{11} + 12 q^{14} + 14 q^{16} + 4 q^{19} - 4 q^{20} + 10 q^{25} - 4 q^{26} + 16 q^{29} + 12 q^{31} - 12 q^{34} + 8 q^{35} + 6 q^{40} - 56 q^{41} + 12 q^{44} - 8 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) $ 14 * q - 14 * q^4 + 4 * q^5 - 6 * q^10 - 12 * q^11 + 12 * q^14 + 14 * q^16 + 4 * q^19 - 4 * q^20 + 10 * q^25 - 4 * q^26 + 16 * q^29 + 12 * q^31 - 12 * q^34 + 8 * q^35 + 6 * q^40 - 56 * q^41 + 12 * q^44 - 8 * q^46 + 18 * q^49 + 24 * q^50 - 12 * q^56 + 28 * q^59 + 12 * q^61 - 14 * q^64 - 12 * q^65 - 16 * q^70 - 48 * q^71 + 14 * q^74 - 4 * q^76 - 20 * q^79 + 4 * q^80 + 12 * q^85 - 12 * q^86 + 36 * q^89 - 32 * q^91 + 32 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.17297	+	0.527467i	−0.971780	+	0.235891i
$5$	−2.17297	+	0.527467i	−0.971780	+	0.235891i
$6$		0			0
$7$		−	4.99866i		−	1.88932i	−0.328058	−	0.944658i	$-0.606394\pi$
$7$		−	4.99866i		−	1.88932i	0.328058	−	0.944658i	$-0.393606\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.527467	−	2.17297i	−0.166800	−	0.687152i
$11$	−2.41083			−0.726892			−0.363446	−	0.931615i	$-0.618400\pi$
$11$	−2.41083			−0.726892			−0.363446	+	0.931615i	$0.618400\pi$
$12$		0			0
$13$		−	3.44356i		−	0.955071i	−0.878613	−	0.477535i	$-0.841530\pi$
$13$		−	3.44356i		−	0.955071i	0.878613	−	0.477535i	$-0.158470\pi$
$14$	4.99866			1.33595
$15$		0			0
$16$	1.00000			0.250000
$17$			1.84744i			0.448070i	0.974581	+	0.224035i	$0.0719230\pi$
$17$			1.84744i			0.448070i	−0.974581	+	0.224035i	$0.928077\pi$
$18$		0			0
$19$	−0.288789			−0.0662527			−0.0331263	−	0.999451i	$-0.510546\pi$
$19$	−0.288789			−0.0662527			−0.0331263	+	0.999451i	$0.510546\pi$
$20$	2.17297	−	0.527467i	0.485890	−	0.117945i
$21$		0			0
$22$		−	2.41083i		−	0.513990i
$23$			0.170297i			0.0355093i	0.999842	+	0.0177547i	$0.00565178\pi$
$23$			0.170297i			0.0355093i	−0.999842	+	0.0177547i	$0.994348\pi$
$24$		0			0
$25$	4.44356	−	2.29234i	0.888711	−	0.458467i
$26$	3.44356			0.675337
$27$		0			0
$28$			4.99866i			0.944658i
$29$	6.81364			1.26526			0.632630	−	0.774454i	$-0.281975\pi$
$29$	6.81364			1.26526			0.632630	+	0.774454i	$0.281975\pi$
$30$		0			0
$31$	3.19979			0.574698			0.287349	−	0.957826i	$-0.407226\pi$
$31$	3.19979			0.574698			0.287349	+	0.957826i	$0.407226\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.84744			−0.316833
$35$	2.63663	+	10.8619i	0.445672	+	1.83600i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	0.288789i		−	0.0468477i
$39$		0			0
$40$	0.527467	+	2.17297i	0.0833999	+	0.343576i
$41$	−3.43306			−0.536154			−0.268077	−	0.963397i	$-0.586388\pi$
$41$	−3.43306			−0.536154			−0.268077	+	0.963397i	$0.586388\pi$
$42$		0			0
$43$		−	8.57489i		−	1.30766i	−0.756642	−	0.653830i	$-0.773161\pi$
$43$		−	8.57489i		−	1.30766i	0.756642	−	0.653830i	$-0.226839\pi$
$44$	2.41083			0.363446
$45$		0			0
$46$	−0.170297			−0.0251089
$47$		−	1.88658i		−	0.275186i	−0.990489	−	0.137593i	$-0.956063\pi$
$47$		−	1.88658i		−	0.275186i	0.990489	−	0.137593i	$-0.0439366\pi$
$48$		0			0
$49$	−17.9866			−2.56951
$50$	2.29234	+	4.44356i	0.324185	+	0.628414i
$51$		0			0
$52$			3.44356i			0.477535i
$53$		−	3.73718i		−	0.513341i	−0.966499	−	0.256670i	$-0.917375\pi$
$53$		−	3.73718i		−	0.513341i	0.966499	−	0.256670i	$-0.0826255\pi$
$54$		0			0
$55$	5.23865	−	1.27163i	0.706379	−	0.171467i
$56$	−4.99866			−0.667974
$57$		0			0
$58$			6.81364i			0.894675i
$59$	−13.5430			−1.76315			−0.881576	−	0.472041i	$-0.843517\pi$
$59$	−13.5430			−1.76315			−0.881576	+	0.472041i	$0.843517\pi$
$60$		0			0
$61$	−2.14293			−0.274374			−0.137187	−	0.990545i	$-0.543806\pi$
$61$	−2.14293			−0.274374			−0.137187	+	0.990545i	$0.543806\pi$
$62$			3.19979i			0.406373i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.81636	+	7.48273i	0.225292	+	0.928118i
$66$		0			0
$67$			9.08723i			1.11018i	0.831790	+	0.555091i	$0.187317\pi$
$67$			9.08723i			1.11018i	−0.831790	+	0.555091i	$0.812683\pi$
$68$		−	1.84744i		−	0.224035i
$69$		0			0
$70$	−10.8619	+	2.63663i	−1.29825	+	0.315138i
$71$	−2.43273			−0.288712			−0.144356	−	0.989526i	$-0.546111\pi$
$71$	−2.43273			−0.288712			−0.144356	+	0.989526i	$0.546111\pi$
$72$		0			0
$73$			13.2347i			1.54901i	0.632570	+	0.774503i	$0.282000\pi$
$73$			13.2347i			1.54901i	−0.632570	+	0.774503i	$0.718000\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	0.288789			0.0331263
$77$			12.0509i			1.37333i
$78$		0			0
$79$	−12.6555			−1.42385			−0.711926	−	0.702255i	$-0.752177\pi$
$79$	−12.6555			−1.42385			−0.711926	+	0.702255i	$0.752177\pi$
$80$	−2.17297	+	0.527467i	−0.242945	+	0.0589727i
$81$		0			0
$82$		−	3.43306i		−	0.379118i
$83$		−	3.21967i		−	0.353404i	−0.984264	−	0.176702i	$-0.943457\pi$
$83$		−	3.21967i		−	0.353404i	0.984264	−	0.176702i	$-0.0565429\pi$
$84$		0			0
$85$	−0.974464	−	4.01442i	−0.105695	−	0.435425i
$86$	8.57489			0.924655
$87$		0			0
$88$			2.41083i			0.256995i
$89$	−4.27078			−0.452702			−0.226351	−	0.974046i	$-0.572680\pi$
$89$	−4.27078			−0.452702			−0.226351	+	0.974046i	$0.572680\pi$
$90$		0			0
$91$	−17.2132			−1.80443
$92$		−	0.170297i		−	0.0177547i
$93$		0			0
$94$	1.88658			0.194586
$95$	0.627528	−	0.152327i	0.0643830	−	0.0156284i
$96$		0			0
$97$		−	7.95362i		−	0.807567i	−0.914855	−	0.403784i	$-0.867695\pi$
$97$		−	7.95362i		−	0.807567i	0.914855	−	0.403784i	$-0.132305\pi$
$98$		−	17.9866i		−	1.81692i
$99$		0			0
$100$	−4.44356	+	2.29234i	−0.444356	+	0.229234i
$101$	−9.14260			−0.909722			−0.454861	−	0.890562i	$-0.650311\pi$
$101$	−9.14260			−0.909722			−0.454861	+	0.890562i	$0.650311\pi$
$102$		0			0
$103$			15.0650i			1.48440i	0.670178	+	0.742201i	$0.266218\pi$
$103$			15.0650i			1.48440i	−0.670178	+	0.742201i	$0.733782\pi$
$104$	−3.44356			−0.337668
$105$		0			0
$106$	3.73718			0.362987
$107$		−	3.15153i		−	0.304670i	−0.988329	−	0.152335i	$-0.951321\pi$
$107$		−	3.15153i		−	0.304670i	0.988329	−	0.152335i	$-0.0486792\pi$
$108$		0			0
$109$	14.9899			1.43577			0.717885	−	0.696162i	$-0.245110\pi$
$109$	14.9899			1.43577			0.717885	+	0.696162i	$0.245110\pi$
$110$	1.27163	+	5.23865i	0.121246	+	0.499485i
$111$		0			0
$112$		−	4.99866i		−	0.472329i
$113$			9.39655i			0.883953i	0.897027	+	0.441977i	$0.145723\pi$
$113$			9.39655i			0.883953i	−0.897027	+	0.441977i	$0.854277\pi$
$114$		0			0
$115$	−0.0898259	−	0.370049i	−0.00837631	−	0.0345072i
$116$	−6.81364			−0.632630
$117$		0			0
$118$		−	13.5430i		−	1.24674i
$119$	9.23472			0.846545
$120$		0			0
$121$	−5.18790			−0.471628
$122$		−	2.14293i		−	0.194012i
$123$		0			0
$124$	−3.19979			−0.287349
$125$	−8.44656	+	7.32500i	−0.755483	+	0.655168i
$126$		0			0
$127$			0.310541i			0.0275560i	0.999905	+	0.0137780i	$0.00438582\pi$
$127$			0.310541i			0.0275560i	−0.999905	+	0.0137780i	$0.995614\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−7.48273	+	1.81636i	−0.656279	+	0.159306i
$131$	−6.58514			−0.575346			−0.287673	−	0.957729i	$-0.592882\pi$
$131$	−6.58514			−0.575346			−0.287673	+	0.957729i	$0.592882\pi$
$132$		0			0
$133$			1.44356i			0.125172i
$134$	−9.08723			−0.785017
$135$		0			0
$136$	1.84744			0.158417
$137$			19.3362i			1.65200i	0.563667	+	0.826002i	$0.309390\pi$
$137$			19.3362i			1.65200i	−0.563667	+	0.826002i	$0.690610\pi$
$138$		0			0
$139$	−7.69153			−0.652387			−0.326193	−	0.945303i	$-0.605766\pi$
$139$	−7.69153			−0.652387			−0.326193	+	0.945303i	$0.605766\pi$
$140$	−2.63663	−	10.8619i	−0.222836	−	0.917999i
$141$		0			0
$142$		−	2.43273i		−	0.204150i
$143$			8.30182i			0.694233i
$144$		0			0
$145$	−14.8058	+	3.59397i	−1.22955	+	0.298463i
$146$	−13.2347			−1.09531
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	19.1926			1.57232			0.786161	−	0.618022i	$-0.212066\pi$
$149$	19.1926			1.57232			0.786161	+	0.618022i	$0.212066\pi$
$150$		0			0
$151$	−15.3170			−1.24648			−0.623240	−	0.782031i	$-0.714184\pi$
$151$	−15.3170			−1.24648			−0.623240	+	0.782031i	$0.714184\pi$
$152$			0.288789i			0.0234239i
$153$		0			0
$154$	−12.0509			−0.971090
$155$	−6.95302	+	1.68778i	−0.558480	+	0.135566i
$156$		0			0
$157$		−	3.86579i		−	0.308524i	−0.988030	−	0.154262i	$-0.950700\pi$
$157$		−	3.86579i		−	0.308524i	0.988030	−	0.154262i	$-0.0492999\pi$
$158$		−	12.6555i		−	1.00681i
$159$		0			0
$160$	−0.527467	−	2.17297i	−0.0417000	−	0.171788i
$161$	0.851255			0.0670883
$162$		0			0
$163$			9.27619i			0.726567i	0.931679	+	0.363284i	$0.118344\pi$
$163$			9.27619i			0.726567i	−0.931679	+	0.363284i	$0.881656\pi$
$164$	3.43306			0.268077
$165$		0			0
$166$	3.21967			0.249895
$167$		−	15.1512i		−	1.17243i	−0.810154	−	0.586217i	$-0.800617\pi$
$167$		−	15.1512i		−	1.17243i	0.810154	−	0.586217i	$-0.199383\pi$
$168$		0			0
$169$	1.14192			0.0878401
$170$	4.01442	−	0.974464i	0.307892	−	0.0747380i
$171$		0			0
$172$			8.57489i			0.653830i
$173$			13.2051i			1.00396i	0.864878	+	0.501982i	$0.167396\pi$
$173$			13.2051i			1.00396i	−0.864878	+	0.501982i	$0.832604\pi$
$174$		0			0
$175$	−11.4586	−	22.2118i	−0.866189	−	1.67906i
$176$	−2.41083			−0.181723
$177$		0			0
$178$		−	4.27078i		−	0.320108i
$179$	12.8119			0.957605			0.478802	−	0.877923i	$-0.341071\pi$
$179$	12.8119			0.957605			0.478802	+	0.877923i	$0.341071\pi$
$180$		0			0
$181$	−8.80834			−0.654718			−0.327359	−	0.944900i	$-0.606159\pi$
$181$	−8.80834			−0.654718			−0.327359	+	0.944900i	$0.606159\pi$
$182$		−	17.2132i		−	1.27592i
$183$		0			0
$184$	0.170297			0.0125544
$185$	0.527467	+	2.17297i	0.0387802	+	0.159760i
$186$		0			0
$187$		−	4.45386i		−	0.325699i
$188$			1.88658i			0.137593i
$189$		0			0
$190$	0.152327	+	0.627528i	0.0110509	+	0.0455257i
$191$	−10.2136			−0.739027			−0.369514	−	0.929225i	$-0.620476\pi$
$191$	−10.2136			−0.739027			−0.369514	+	0.929225i	$0.620476\pi$
$192$		0			0
$193$		−	15.1989i		−	1.09404i	−0.837119	−	0.547020i	$-0.815762\pi$
$193$		−	15.1989i		−	1.09404i	0.837119	−	0.547020i	$-0.184238\pi$
$194$	7.95362			0.571036
$195$		0			0
$196$	17.9866			1.28476
$197$		−	7.11984i		−	0.507268i	−0.967300	−	0.253634i	$-0.918374\pi$
$197$		−	7.11984i		−	0.507268i	0.967300	−	0.253634i	$-0.0816258\pi$
$198$		0			0
$199$	−1.07977			−0.0765427			−0.0382713	−	0.999267i	$-0.512185\pi$
$199$	−1.07977			−0.0765427			−0.0382713	+	0.999267i	$0.512185\pi$
$200$	−2.29234	−	4.44356i	−0.162093	−	0.314207i
$201$		0			0
$202$		−	9.14260i		−	0.643271i
$203$		−	34.0591i		−	2.39048i
$204$		0			0
$205$	7.45993	−	1.81083i	0.521024	−	0.126474i
$206$	−15.0650			−1.04963
$207$		0			0
$208$		−	3.44356i		−	0.238768i
$209$	0.696220			0.0481586
$210$		0			0
$211$	−16.7884			−1.15576			−0.577881	−	0.816121i	$-0.696120\pi$
$211$	−16.7884			−1.15576			−0.577881	+	0.816121i	$0.696120\pi$
$212$			3.73718i			0.256670i
$213$		0			0
$214$	3.15153			0.215434
$215$	4.52298	+	18.6329i	0.308465	+	1.27076i
$216$		0			0
$217$		−	15.9946i		−	1.08579i
$218$			14.9899i			1.01524i
$219$		0			0
$220$	−5.23865	+	1.27163i	−0.353190	+	0.0857335i
$221$	6.36176			0.427938
$222$		0			0
$223$		−	7.49275i		−	0.501751i	−0.968019	−	0.250876i	$-0.919281\pi$
$223$		−	7.49275i		−	0.501751i	0.968019	−	0.250876i	$-0.0807185\pi$
$224$	4.99866			0.333987
$225$		0			0
$226$	−9.39655			−0.625049
$227$			4.44353i			0.294927i	0.989067	+	0.147464i	$0.0471110\pi$
$227$			4.44353i			0.294927i	−0.989067	+	0.147464i	$0.952889\pi$
$228$		0			0
$229$	4.02673			0.266094			0.133047	−	0.991110i	$-0.457524\pi$
$229$	4.02673			0.266094			0.133047	+	0.991110i	$0.457524\pi$
$230$	0.370049	−	0.0898259i	0.0244003	−	0.00592295i
$231$		0			0
$232$		−	6.81364i		−	0.447337i
$233$		−	30.1146i		−	1.97287i	−0.164144	−	0.986436i	$-0.552486\pi$
$233$		−	30.1146i		−	1.97287i	0.164144	−	0.986436i	$-0.447514\pi$
$234$		0			0
$235$	0.995111	+	4.09948i	0.0649139	+	0.267420i
$236$	13.5430			0.881576
$237$		0			0
$238$			9.23472i			0.598598i
$239$	−19.1950			−1.24162			−0.620809	−	0.783962i	$-0.713196\pi$
$239$	−19.1950			−1.24162			−0.620809	+	0.783962i	$0.713196\pi$
$240$		0			0
$241$	−1.03560			−0.0667092			−0.0333546	−	0.999444i	$-0.510619\pi$
$241$	−1.03560			−0.0667092			−0.0333546	+	0.999444i	$0.510619\pi$
$242$		−	5.18790i		−	0.333491i
$243$		0			0
$244$	2.14293			0.137187
$245$	39.0842	−	9.48734i	2.49700	−	0.606124i
$246$		0			0
$247$			0.994460i			0.0632760i
$248$		−	3.19979i		−	0.203187i
$249$		0			0
$250$	−7.32500	−	8.44656i	−0.463274	−	0.534207i
$251$	−3.99357			−0.252072			−0.126036	−	0.992026i	$-0.540226\pi$
$251$	−3.99357			−0.252072			−0.126036	+	0.992026i	$0.540226\pi$
$252$		0			0
$253$		−	0.410556i		−	0.0258114i
$254$	−0.310541			−0.0194851
$255$		0			0
$256$	1.00000			0.0625000
$257$			16.5532i			1.03256i	0.856419	+	0.516281i	$0.172684\pi$
$257$			16.5532i			1.03256i	−0.856419	+	0.516281i	$0.827316\pi$
$258$		0			0
$259$	−4.99866			−0.310602
$260$	−1.81636	−	7.48273i	−0.112646	−	0.464059i
$261$		0			0
$262$		−	6.58514i		−	0.406831i
$263$			26.4909i			1.63350i	0.576992	+	0.816750i	$0.304226\pi$
$263$			26.4909i			1.63350i	−0.576992	+	0.816750i	$0.695774\pi$
$264$		0			0
$265$	1.97124	+	8.12076i	0.121092	+	0.498854i
$266$	−1.44356			−0.0885101
$267$		0			0
$268$		−	9.08723i		−	0.555091i
$269$	29.5153			1.79958			0.899791	−	0.436321i	$-0.143719\pi$
$269$	29.5153			1.79958			0.899791	+	0.436321i	$0.143719\pi$
$270$		0			0
$271$	1.03452			0.0628424			0.0314212	−	0.999506i	$-0.489997\pi$
$271$	1.03452			0.0628424			0.0314212	+	0.999506i	$0.489997\pi$
$272$			1.84744i			0.112017i
$273$		0			0
$274$	−19.3362			−1.16814
$275$	−10.7127	+	5.52643i	−0.645997	+	0.333256i
$276$		0			0
$277$			3.42257i			0.205642i	0.994700	+	0.102821i	$0.0327869\pi$
$277$			3.42257i			0.205642i	−0.994700	+	0.102821i	$0.967213\pi$
$278$		−	7.69153i		−	0.461307i
$279$		0			0
$280$	10.8619	−	2.63663i	0.649123	−	0.157569i
$281$	−5.71617			−0.340998			−0.170499	−	0.985358i	$-0.554538\pi$
$281$	−5.71617			−0.340998			−0.170499	+	0.985358i	$0.554538\pi$
$282$		0			0
$283$		−	16.4185i		−	0.975979i	−0.872849	−	0.487990i	$-0.837730\pi$
$283$		−	16.4185i		−	0.975979i	0.872849	−	0.487990i	$-0.162270\pi$
$284$	2.43273			0.144356
$285$		0			0
$286$	−8.30182			−0.490897
$287$			17.1607i			1.01296i
$288$		0			0
$289$	13.5870			0.799233
$290$	−3.59397	−	14.8058i	−0.211045	−	0.869426i
$291$		0			0
$292$		−	13.2347i		−	0.774503i
$293$			4.25371i			0.248505i	0.992251	+	0.124252i	$0.0396532\pi$
$293$			4.25371i			0.248505i	−0.992251	+	0.124252i	$0.960347\pi$
$294$		0			0
$295$	29.4285	−	7.14351i	1.71340	−	0.415911i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$			19.1926i			1.11180i
$299$	0.586426			0.0339139
$300$		0			0
$301$	−42.8630			−2.47058
$302$		−	15.3170i		−	0.881394i
$303$		0			0
$304$	−0.288789			−0.0165632
$305$	4.65652	−	1.13033i	0.266631	−	0.0647223i
$306$		0			0
$307$			29.4057i			1.67827i	0.543922	+	0.839136i	$0.316939\pi$
$307$			29.4057i			1.67827i	−0.543922	+	0.839136i	$0.683061\pi$
$308$		−	12.0509i		−	0.686664i
$309$		0			0
$310$	−1.68778	−	6.95302i	−0.0958596	−	0.394905i
$311$	−18.0328			−1.02255			−0.511273	−	0.859418i	$-0.670826\pi$
$311$	−18.0328			−1.02255			−0.511273	+	0.859418i	$0.670826\pi$
$312$		0			0
$313$			13.2327i			0.747958i	0.927437	+	0.373979i	$0.122007\pi$
$313$			13.2327i			0.747958i	−0.927437	+	0.373979i	$0.877993\pi$
$314$	3.86579			0.218159
$315$		0			0
$316$	12.6555			0.711926
$317$			29.9410i			1.68165i	0.541303	+	0.840827i	$0.317931\pi$
$317$			29.9410i			1.68165i	−0.541303	+	0.840827i	$0.682069\pi$
$318$		0			0
$319$	−16.4265			−0.919708
$320$	2.17297	−	0.527467i	0.121472	−	0.0294863i
$321$		0			0
$322$			0.851255i			0.0474386i
$323$		−	0.533520i		−	0.0296858i
$324$		0			0
$325$	−7.89379	−	15.3016i	−0.437869	−	0.848782i
$326$	−9.27619			−0.513761
$327$		0			0
$328$			3.43306i			0.189559i
$329$	−9.43038			−0.519914
$330$		0			0
$331$	18.4123			1.01203			0.506014	−	0.862525i	$-0.331118\pi$
$331$	18.4123			1.01203			0.506014	+	0.862525i	$0.331118\pi$
$332$			3.21967i			0.176702i
$333$		0			0
$334$	15.1512			0.829036
$335$	−4.79322	−	19.7462i	−0.261882	−	1.07885i
$336$		0			0
$337$		−	8.69446i		−	0.473617i	−0.971556	−	0.236809i	$-0.923899\pi$
$337$		−	8.69446i		−	0.473617i	0.971556	−	0.236809i	$-0.0761015\pi$
$338$			1.14192i			0.0621123i
$339$		0			0
$340$	0.974464	+	4.01442i	0.0528477	+	0.217713i
$341$	−7.71414			−0.417744
$342$		0			0
$343$			54.9182i			2.96530i
$344$	−8.57489			−0.462327
$345$		0			0
$346$	−13.2051			−0.709909
$347$			2.34430i			0.125849i	0.998018	+	0.0629243i	$0.0200427\pi$
$347$			2.34430i			0.125849i	−0.998018	+	0.0629243i	$0.979957\pi$
$348$		0			0
$349$	25.8033			1.38122			0.690610	−	0.723228i	$-0.257342\pi$
$349$	25.8033			1.38122			0.690610	+	0.723228i	$0.257342\pi$
$350$	22.2118	−	11.4586i	1.18727	−	0.612488i
$351$		0			0
$352$		−	2.41083i		−	0.128498i
$353$			12.5607i			0.668539i	0.942477	+	0.334270i	$0.108490\pi$
$353$			12.5607i			0.668539i	−0.942477	+	0.334270i	$0.891510\pi$
$354$		0			0
$355$	5.28623	−	1.28318i	0.280564	−	0.0681043i
$356$	4.27078			0.226351
$357$		0			0
$358$			12.8119i			0.677129i
$359$	9.61865			0.507653			0.253826	−	0.967250i	$-0.418311\pi$
$359$	9.61865			0.507653			0.253826	+	0.967250i	$0.418311\pi$
$360$		0			0
$361$	−18.9166			−0.995611
$362$		−	8.80834i		−	0.462956i
$363$		0			0
$364$	17.2132			0.902215
$365$	−6.98088	−	28.7586i	−0.365396	−	1.50529i
$366$		0			0
$367$			16.0992i			0.840371i	0.907438	+	0.420186i	$0.138035\pi$
$367$			16.0992i			0.840371i	−0.907438	+	0.420186i	$0.861965\pi$
$368$			0.170297i			0.00887733i
$369$		0			0
$370$	−2.17297	+	0.527467i	−0.112967	+	0.0274217i
$371$	−18.6809			−0.969863
$372$		0			0
$373$		−	19.1756i		−	0.992877i	−0.868072	−	0.496438i	$-0.834641\pi$
$373$		−	19.1756i		−	0.992877i	0.868072	−	0.496438i	$-0.165359\pi$
$374$	4.45386			0.230304
$375$		0			0
$376$	−1.88658			−0.0972930
$377$		−	23.4631i		−	1.20841i
$378$		0			0
$379$	−4.84571			−0.248907			−0.124454	−	0.992225i	$-0.539718\pi$
$379$	−4.84571			−0.248907			−0.124454	+	0.992225i	$0.539718\pi$
$380$	−0.627528	+	0.152327i	−0.0321915	+	0.00781419i
$381$		0			0
$382$		−	10.2136i		−	0.522571i
$383$		−	29.3127i		−	1.49781i	−0.662678	−	0.748904i	$-0.730580\pi$
$383$		−	29.3127i		−	1.49781i	0.662678	−	0.748904i	$-0.269420\pi$
$384$		0			0
$385$	−6.35646	−	26.1862i	−0.323955	−	1.33457i
$386$	15.1989			0.773603
$387$		0			0
$388$			7.95362i			0.403784i
$389$	−0.432598			−0.0219336			−0.0109668	−	0.999940i	$-0.503491\pi$
$389$	−0.432598			−0.0219336			−0.0109668	+	0.999940i	$0.503491\pi$
$390$		0			0
$391$	−0.314613			−0.0159107
$392$			17.9866i			0.908460i
$393$		0			0
$394$	7.11984			0.358692
$395$	27.4999	−	6.67535i	1.38367	−	0.335873i
$396$		0			0
$397$			4.21228i			0.211408i	0.994398	+	0.105704i	$0.0337097\pi$
$397$			4.21228i			0.211408i	−0.994398	+	0.105704i	$0.966290\pi$
$398$		−	1.07977i		−	0.0541238i
$399$		0			0
$400$	4.44356	−	2.29234i	0.222178	−	0.114617i
$401$	−31.3490			−1.56550			−0.782748	−	0.622339i	$-0.786182\pi$
$401$	−31.3490			−1.56550			−0.782748	+	0.622339i	$0.786182\pi$
$402$		0			0
$403$		−	11.0186i		−	0.548878i
$404$	9.14260			0.454861
$405$		0			0
$406$	34.0591			1.69032
$407$			2.41083i			0.119500i
$408$		0			0
$409$	0.0295145			0.00145940			0.000729699	−	1.00000i	$-0.499768\pi$
$409$	0.0295145			0.00145940			0.000729699		1.00000i	$0.499768\pi$
$410$	1.81083	+	7.45993i	0.0894305	+	0.368419i
$411$		0			0
$412$		−	15.0650i		−	0.742201i
$413$			67.6970i			3.33115i
$414$		0			0
$415$	1.69827	+	6.99622i	0.0833647	+	0.343431i
$416$	3.44356			0.168834
$417$		0			0
$418$			0.696220i			0.0340532i
$419$	11.9707			0.584808			0.292404	−	0.956295i	$-0.405545\pi$
$419$	11.9707			0.584808			0.292404	+	0.956295i	$0.405545\pi$
$420$		0			0
$421$	−2.45820			−0.119805			−0.0599027	−	0.998204i	$-0.519079\pi$
$421$	−2.45820			−0.119805			−0.0599027	+	0.998204i	$0.519079\pi$
$422$		−	16.7884i		−	0.817247i
$423$		0			0
$424$	−3.73718			−0.181493
$425$	4.23495	+	8.20920i	0.205425	+	0.398205i
$426$		0			0
$427$			10.7118i			0.518380i
$428$			3.15153i			0.152335i
$429$		0			0
$430$	−18.6329	+	4.52298i	−0.898561	+	0.218117i
$431$	5.92658			0.285473			0.142737	−	0.989761i	$-0.454410\pi$
$431$	5.92658			0.285473			0.142737	+	0.989761i	$0.454410\pi$
$432$		0			0
$433$			5.13974i			0.247000i	0.992345	+	0.123500i	$0.0394119\pi$
$433$			5.13974i			0.247000i	−0.992345	+	0.123500i	$0.960588\pi$
$434$	15.9946			0.767767
$435$		0			0
$436$	−14.9899			−0.717885
$437$		−	0.0491797i		−	0.00235259i
$438$		0			0
$439$	−24.9687			−1.19169			−0.595846	−	0.803099i	$-0.703183\pi$
$439$	−24.9687			−1.19169			−0.595846	+	0.803099i	$0.703183\pi$
$440$	−1.27163	−	5.23865i	−0.0606228	−	0.249743i
$441$		0			0
$442$			6.36176i			0.302598i
$443$		−	8.11812i		−	0.385704i	−0.981228	−	0.192852i	$-0.938226\pi$
$443$		−	8.11812i		−	0.385704i	0.981228	−	0.192852i	$-0.0617736\pi$
$444$		0			0
$445$	9.28026	−	2.25270i	0.439926	−	0.106788i
$446$	7.49275			0.354792
$447$		0			0
$448$			4.99866i			0.236164i
$449$	14.6825			0.692912			0.346456	−	0.938066i	$-0.387385\pi$
$449$	14.6825			0.692912			0.346456	+	0.938066i	$0.387385\pi$
$450$		0			0
$451$	8.27653			0.389726
$452$		−	9.39655i		−	0.441977i
$453$		0			0
$454$	−4.44353			−0.208545
$455$	37.4036	−	9.07938i	1.75351	−	0.425648i
$456$		0			0
$457$			19.6738i			0.920304i	0.887840	+	0.460152i	$0.152205\pi$
$457$			19.6738i			0.920304i	−0.887840	+	0.460152i	$0.847795\pi$
$458$			4.02673i			0.188157i
$459$		0			0
$460$	0.0898259	+	0.370049i	0.00418816	+	0.0172536i
$461$	23.3382			1.08697			0.543485	−	0.839419i	$-0.317104\pi$
$461$	23.3382			1.08697			0.543485	+	0.839419i	$0.317104\pi$
$462$		0			0
$463$			19.0971i			0.887520i	0.896146	+	0.443760i	$0.146356\pi$
$463$			19.0971i			0.887520i	−0.896146	+	0.443760i	$0.853644\pi$
$464$	6.81364			0.316315
$465$		0			0
$466$	30.1146			1.39503
$467$		−	38.7494i		−	1.79311i	−0.442934	−	0.896554i	$-0.646062\pi$
$467$		−	38.7494i		−	1.79311i	0.442934	−	0.896554i	$-0.353938\pi$
$468$		0			0
$469$	45.4240			2.09748
$470$	−4.09948	+	0.995111i	−0.189095	+	0.0459010i
$471$		0			0
$472$			13.5430i			0.623369i
$473$			20.6726i			0.950527i
$474$		0			0
$475$	−1.28325	+	0.662001i	−0.0588795	+	0.0303747i
$476$	−9.23472			−0.423273
$477$		0			0
$478$		−	19.1950i		−	0.877957i
$479$	−18.4527			−0.843127			−0.421563	−	0.906799i	$-0.638519\pi$
$479$	−18.4527			−0.843127			−0.421563	+	0.906799i	$0.638519\pi$
$480$		0			0
$481$	−3.44356			−0.157013
$482$		−	1.03560i		−	0.0471705i
$483$		0			0
$484$	5.18790			0.235814
$485$	4.19527	+	17.2829i	0.190498	+	0.784777i
$486$		0			0
$487$			18.9340i			0.857981i	0.903309	+	0.428990i	$0.141131\pi$
$487$			18.9340i			0.857981i	−0.903309	+	0.428990i	$0.858869\pi$
$488$			2.14293i			0.0970060i
$489$		0			0
$490$	9.48734	+	39.0842i	0.428594	+	1.76565i
$491$	−38.7713			−1.74973			−0.874863	−	0.484370i	$-0.839049\pi$
$491$	−38.7713			−1.74973			−0.874863	+	0.484370i	$0.839049\pi$
$492$		0			0
$493$			12.5878i			0.566925i
$494$	−0.994460			−0.0447429
$495$		0			0
$496$	3.19979			0.143675
$497$			12.1604i			0.545467i
$498$		0			0
$499$	40.2106			1.80007			0.900036	−	0.435815i	$-0.143540\pi$
$499$	40.2106			1.80007			0.900036	+	0.435815i	$0.143540\pi$
$500$	8.44656	−	7.32500i	0.377742	−	0.327584i
$501$		0			0
$502$		−	3.99357i		−	0.178242i
$503$			21.5210i			0.959576i	0.877385	+	0.479788i	$0.159286\pi$
$503$			21.5210i			0.959576i	−0.877385	+	0.479788i	$0.840714\pi$
$504$		0			0
$505$	19.8665	−	4.82242i	0.884050	−	0.214595i
$506$	0.410556			0.0182514
$507$		0			0
$508$		−	0.310541i		−	0.0137780i
$509$	−17.0571			−0.756043			−0.378022	−	0.925797i	$-0.623396\pi$
$509$	−17.0571			−0.756043			−0.378022	+	0.925797i	$0.623396\pi$
$510$		0			0
$511$	66.1558			2.92656
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−16.5532			−0.730132
$515$	−7.94631	−	32.7358i	−0.350156	−	1.44251i
$516$		0			0
$517$			4.54823i			0.200031i
$518$		−	4.99866i		−	0.219628i
$519$		0			0
$520$	7.48273	−	1.81636i	0.328139	−	0.0796528i
$521$	−28.1974			−1.23535			−0.617676	−	0.786433i	$-0.711926\pi$
$521$	−28.1974			−1.23535			−0.617676	+	0.786433i	$0.711926\pi$
$522$		0			0
$523$		−	25.3083i		−	1.10666i	−0.832963	−	0.553328i	$-0.813358\pi$
$523$		−	25.3083i		−	1.10666i	0.832963	−	0.553328i	$-0.186642\pi$
$524$	6.58514			0.287673
$525$		0			0
$526$	−26.4909			−1.15506
$527$			5.91141i			0.257505i
$528$		0			0
$529$	22.9710			0.998739
$530$	−8.12076	+	1.97124i	−0.352743	+	0.0856252i
$531$		0			0
$532$		−	1.44356i		−	0.0625861i
$533$			11.8219i			0.512065i
$534$		0			0
$535$	1.66233	+	6.84816i	0.0718687	+	0.296072i
$536$	9.08723			0.392509
$537$		0			0
$538$			29.5153i			1.27250i
$539$	43.3626			1.86776
$540$		0			0
$541$	−34.5346			−1.48476			−0.742379	−	0.669980i	$-0.766302\pi$
$541$	−34.5346			−1.48476			−0.742379	+	0.669980i	$0.766302\pi$
$542$			1.03452i			0.0444363i
$543$		0			0
$544$	−1.84744			−0.0792083
$545$	−32.5725	+	7.90667i	−1.39525	+	0.338685i
$546$		0			0
$547$		−	41.8293i		−	1.78849i	−0.447575	−	0.894247i	$-0.647712\pi$
$547$		−	41.8293i		−	1.78849i	0.447575	−	0.894247i	$-0.352288\pi$
$548$		−	19.3362i		−	0.826002i
$549$		0			0
$550$	−5.52643	−	10.7127i	−0.235648	−	0.456789i
$551$	−1.96770			−0.0838269
$552$		0			0
$553$			63.2604i			2.69010i
$554$	−3.42257			−0.145411
$555$		0			0
$556$	7.69153			0.326193
$557$		−	25.5381i		−	1.08208i	−0.840996	−	0.541042i	$-0.818030\pi$
$557$		−	25.5381i		−	1.08208i	0.840996	−	0.541042i	$-0.181970\pi$
$558$		0			0
$559$	−29.5281			−1.24891
$560$	2.63663	+	10.8619i	0.111418	+	0.459000i
$561$		0			0
$562$		−	5.71617i		−	0.241122i
$563$		−	14.7140i		−	0.620122i	−0.950717	−	0.310061i	$-0.899651\pi$
$563$		−	14.7140i		−	0.620122i	0.950717	−	0.310061i	$-0.100349\pi$
$564$		0			0
$565$	−4.95638	−	20.4184i	−0.208516	−	0.859008i
$566$	16.4185			0.690122
$567$		0			0
$568$			2.43273i			0.102075i
$569$	−15.7693			−0.661082			−0.330541	−	0.943792i	$-0.607231\pi$
$569$	−15.7693			−0.661082			−0.330541	+	0.943792i	$0.607231\pi$
$570$		0			0
$571$	27.6667			1.15781			0.578907	−	0.815394i	$-0.303479\pi$
$571$	27.6667			1.15781			0.578907	+	0.815394i	$0.303479\pi$
$572$		−	8.30182i		−	0.347117i
$573$		0			0
$574$	−17.1607			−0.716274
$575$	0.390377	+	0.756723i	0.0162799	+	0.0315575i
$576$		0			0
$577$			22.9753i			0.956475i	0.878231	+	0.478237i	$0.158724\pi$
$577$			22.9753i			0.956475i	−0.878231	+	0.478237i	$0.841276\pi$
$578$			13.5870i			0.565143i
$579$		0			0
$580$	14.8058	−	3.59397i	0.614777	−	0.149232i
$581$	−16.0940			−0.667692
$582$		0			0
$583$			9.00970i			0.373143i
$584$	13.2347			0.547657
$585$		0			0
$586$	−4.25371			−0.175719
$587$		−	37.8905i		−	1.56391i	−0.623335	−	0.781955i	$-0.714223\pi$
$587$		−	37.8905i		−	1.56391i	0.623335	−	0.781955i	$-0.285777\pi$
$588$		0			0
$589$	−0.924062			−0.0380753
$590$	7.14351	+	29.4285i	0.294094	+	1.21155i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$			39.3179i			1.61459i	0.590146	+	0.807296i	$0.299070\pi$
$593$			39.3179i			1.61459i	−0.590146	+	0.807296i	$0.700930\pi$
$594$		0			0
$595$	−20.0667	+	4.87101i	−0.822656	+	0.199692i
$596$	−19.1926			−0.786161
$597$		0			0
$598$			0.586426i			0.0239807i
$599$	26.4050			1.07888			0.539440	−	0.842024i	$-0.318636\pi$
$599$	26.4050			1.07888			0.539440	+	0.842024i	$0.318636\pi$
$600$		0			0
$601$	41.0745			1.67547			0.837733	−	0.546080i	$-0.183881\pi$
$601$	41.0745			1.67547			0.837733	+	0.546080i	$0.183881\pi$
$602$		−	42.8630i		−	1.74696i
$603$		0			0
$604$	15.3170			0.623240
$605$	11.2731	−	2.73645i	0.458318	−	0.111253i
$606$		0			0
$607$		−	28.2417i		−	1.14629i	−0.819453	−	0.573147i	$-0.805722\pi$
$607$		−	28.2417i		−	1.14629i	0.819453	−	0.573147i	$-0.194278\pi$
$608$		−	0.288789i		−	0.0117119i
$609$		0			0
$610$	1.13033	+	4.65652i	0.0457656	+	0.188537i
$611$	−6.49655			−0.262822
$612$		0			0
$613$		−	24.6764i		−	0.996671i	−0.866984	−	0.498335i	$-0.833945\pi$
$613$		−	24.6764i		−	0.996671i	0.866984	−	0.498335i	$-0.166055\pi$
$614$	−29.4057			−1.18672
$615$		0			0
$616$	12.0509			0.485545
$617$		−	38.5546i		−	1.55215i	−0.630640	−	0.776075i	$-0.717208\pi$
$617$		−	38.5546i		−	1.55215i	0.630640	−	0.776075i	$-0.282792\pi$
$618$		0			0
$619$	−30.0442			−1.20758			−0.603789	−	0.797144i	$-0.706343\pi$
$619$	−30.0442			−1.20758			−0.603789	+	0.797144i	$0.706343\pi$
$620$	6.95302	−	1.68778i	0.279240	−	0.0677830i
$621$		0			0
$622$		−	18.0328i		−	0.723049i
$623$			21.3482i			0.855296i
$624$		0			0
$625$	14.4904	−	20.3723i	0.579615	−	0.814890i
$626$	−13.2327			−0.528886
$627$		0			0
$628$			3.86579i			0.154262i
$629$	1.84744			0.0736622
$630$		0			0
$631$	2.76916			0.110238			0.0551192	−	0.998480i	$-0.482446\pi$
$631$	2.76916			0.110238			0.0551192	+	0.998480i	$0.482446\pi$
$632$			12.6555i			0.503407i
$633$		0			0
$634$	−29.9410			−1.18911
$635$	−0.163800	−	0.674794i	−0.00650021	−	0.0267784i
$636$		0			0
$637$			61.9378i			2.45407i
$638$		−	16.4265i		−	0.650332i
$639$		0			0
$640$	0.527467	+	2.17297i	0.0208500	+	0.0858940i
$641$	−49.6368			−1.96054			−0.980268	−	0.197675i	$-0.936661\pi$
$641$	−49.6368			−1.96054			−0.980268	+	0.197675i	$0.936661\pi$
$642$		0			0
$643$			12.9550i			0.510896i	0.966823	+	0.255448i	$0.0822230\pi$
$643$			12.9550i			0.510896i	−0.966823	+	0.255448i	$0.917777\pi$
$644$	−0.851255			−0.0335441
$645$		0			0
$646$	0.533520			0.0209910
$647$		−	19.6591i		−	0.772878i	−0.922315	−	0.386439i	$-0.873705\pi$
$647$		−	19.6591i		−	0.772878i	0.922315	−	0.386439i	$-0.126295\pi$
$648$		0			0
$649$	32.6499			1.28162
$650$	15.3016	−	7.89379i	0.600180	−	0.309620i
$651$		0			0
$652$		−	9.27619i		−	0.363284i
$653$			3.07313i			0.120261i	0.998191	+	0.0601304i	$0.0191516\pi$
$653$			3.07313i			0.120261i	−0.998191	+	0.0601304i	$0.980848\pi$
$654$		0			0
$655$	14.3093	−	3.47345i	0.559110	−	0.135719i
$656$	−3.43306			−0.134039
$657$		0			0
$658$		−	9.43038i		−	0.367634i
$659$	−33.8785			−1.31972			−0.659859	−	0.751390i	$-0.729384\pi$
$659$	−33.8785			−1.31972			−0.659859	+	0.751390i	$0.729384\pi$
$660$		0			0
$661$	−16.7825			−0.652762			−0.326381	−	0.945238i	$-0.605829\pi$
$661$	−16.7825			−0.652762			−0.326381	+	0.945238i	$0.605829\pi$
$662$			18.4123i			0.715612i
$663$		0			0
$664$	−3.21967			−0.124947
$665$	−0.761429	−	3.13680i	−0.0295269	−	0.121640i
$666$		0			0
$667$			1.16034i			0.0449285i
$668$			15.1512i			0.586217i
$669$		0			0
$670$	19.7462	−	4.79322i	0.762864	−	0.185178i
$671$	5.16624			0.199441
$672$		0			0
$673$		−	23.3945i		−	0.901791i	−0.892577	−	0.450895i	$-0.851105\pi$
$673$		−	23.3945i		−	0.901791i	0.892577	−	0.450895i	$-0.148895\pi$
$674$	8.69446			0.334898
$675$		0			0
$676$	−1.14192			−0.0439200
$677$			10.1163i			0.388800i	0.980922	+	0.194400i	$0.0622761\pi$
$677$			10.1163i			0.388800i	−0.980922	+	0.194400i	$0.937724\pi$
$678$		0			0
$679$	−39.7574			−1.52575
$680$	−4.01442	+	0.974464i	−0.153946	+	0.0373690i
$681$		0			0
$682$		−	7.71414i		−	0.295390i
$683$			15.8875i			0.607918i	0.952685	+	0.303959i	$0.0983085\pi$
$683$			15.8875i			0.607918i	−0.952685	+	0.303959i	$0.901691\pi$
$684$		0			0
$685$	−10.1992	−	42.0169i	−0.389692	−	1.60538i
$686$	−54.9182			−2.09679
$687$		0			0
$688$		−	8.57489i		−	0.326915i
$689$	−12.8692			−0.490277
$690$		0			0
$691$	50.4451			1.91902			0.959510	−	0.281673i	$-0.0908893\pi$
$691$	50.4451			1.91902			0.959510	+	0.281673i	$0.0908893\pi$
$692$		−	13.2051i		−	0.501982i
$693$		0			0
$694$	−2.34430			−0.0889884
$695$	16.7134	−	4.05703i	0.633976	−	0.153892i
$696$		0			0
$697$		−	6.34237i		−	0.240235i
$698$			25.8033i			0.976670i
$699$		0			0
$700$	11.4586	+	22.2118i	0.433095	+	0.839528i
$701$	−32.4597			−1.22599			−0.612994	−	0.790088i	$-0.710035\pi$
$701$	−32.4597			−1.22599			−0.612994	+	0.790088i	$0.710035\pi$
$702$		0			0
$703$			0.288789i			0.0108919i
$704$	2.41083			0.0908615
$705$		0			0
$706$	−12.5607			−0.472729
$707$			45.7007i			1.71875i
$708$		0			0
$709$	32.7296			1.22919			0.614593	−	0.788844i	$-0.289320\pi$
$709$	32.7296			1.22919			0.614593	+	0.788844i	$0.289320\pi$
$710$	1.28318	+	5.28623i	0.0481570	+	0.198389i
$711$		0			0
$712$			4.27078i			0.160054i
$713$			0.544913i			0.0204071i
$714$		0			0
$715$	−4.37894	−	18.0396i	−0.163763	−	0.674642i
$716$	−12.8119			−0.478802
$717$		0			0
$718$			9.61865i			0.358965i
$719$	−42.7154			−1.59302			−0.796509	−	0.604627i	$-0.793322\pi$
$719$	−42.7154			−1.59302			−0.796509	+	0.604627i	$0.793322\pi$
$720$		0			0
$721$	75.3049			2.80450
$722$		−	18.9166i		−	0.704003i
$723$		0			0
$724$	8.80834			0.327359
$725$	30.2768	−	15.6192i	1.12445	−	0.580081i
$726$		0			0
$727$			7.32006i			0.271486i	0.990744	+	0.135743i	$0.0433421\pi$
$727$			7.32006i			0.271486i	−0.990744	+	0.135743i	$0.956658\pi$
$728$			17.2132i			0.637962i
$729$		0			0
$730$	28.7586	−	6.98088i	1.06440	−	0.258374i
$731$	15.8416			0.585923
$732$		0			0
$733$		−	20.9087i		−	0.772280i	−0.922440	−	0.386140i	$-0.873808\pi$
$733$		−	20.9087i		−	0.772280i	0.922440	−	0.386140i	$-0.126192\pi$
$734$	−16.0992			−0.594232
$735$		0			0
$736$	−0.170297			−0.00627722
$737$		−	21.9078i		−	0.806983i
$738$		0			0
$739$	42.5665			1.56583			0.782917	−	0.622126i	$-0.213731\pi$
$739$	42.5665			1.56583			0.782917	+	0.622126i	$0.213731\pi$
$740$	−0.527467	−	2.17297i	−0.0193901	−	0.0798798i
$741$		0			0
$742$		−	18.6809i		−	0.685797i
$743$		−	22.8670i		−	0.838907i	−0.907777	−	0.419454i	$-0.862222\pi$
$743$		−	22.8670i		−	0.838907i	0.907777	−	0.419454i	$-0.137778\pi$
$744$		0			0
$745$	−41.7049	+	10.1235i	−1.52795	+	0.370896i
$746$	19.1756			0.702070
$747$		0			0
$748$			4.45386i			0.162849i
$749$	−15.7534			−0.575617
$750$		0			0
$751$	−32.0864			−1.17085			−0.585424	−	0.810727i	$-0.699072\pi$
$751$	−32.0864			−1.17085			−0.585424	+	0.810727i	$0.699072\pi$
$752$		−	1.88658i		−	0.0687966i
$753$		0			0
$754$	23.4631			0.854477
$755$	33.2833	−	8.07922i	1.21130	−	0.294033i
$756$		0			0
$757$		−	28.0202i		−	1.01841i	−0.860644	−	0.509206i	$-0.829939\pi$
$757$		−	28.0202i		−	1.01841i	0.860644	−	0.509206i	$-0.170061\pi$
$758$		−	4.84571i		−	0.176004i
$759$		0			0
$760$	−0.152327	−	0.627528i	−0.00552547	−	0.0227628i
$761$	−47.5310			−1.72300			−0.861499	−	0.507759i	$-0.830474\pi$
$761$	−47.5310			−1.72300			−0.861499	+	0.507759i	$0.830474\pi$
$762$		0			0
$763$		−	74.9293i		−	2.71262i
$764$	10.2136			0.369514
$765$		0			0
$766$	29.3127			1.05911
$767$			46.6362i			1.68394i
$768$		0			0
$769$	−36.2676			−1.30784			−0.653922	−	0.756562i	$-0.726878\pi$
$769$	−36.2676			−1.30784			−0.653922	+	0.756562i	$0.726878\pi$
$770$	26.1862	−	6.35646i	0.943686	−	0.229071i
$771$		0			0
$772$			15.1989i			0.547020i
$773$			39.2967i			1.41340i	0.707512	+	0.706701i	$0.249818\pi$
$773$			39.2967i			1.41340i	−0.707512	+	0.706701i	$0.750182\pi$
$774$		0			0
$775$	14.2184	−	7.33499i	0.510741	−	0.263480i
$776$	−7.95362			−0.285518
$777$		0			0
$778$		−	0.432598i		−	0.0155094i
$779$	0.991430			0.0355217
$780$		0			0
$781$	5.86489			0.209862
$782$		−	0.314613i		−	0.0112505i
$783$		0			0
$784$	−17.9866			−0.642378
$785$	2.03908	+	8.40023i	0.0727778	+	0.299817i
$786$		0			0
$787$		−	37.6379i		−	1.34164i	−0.741618	−	0.670822i	$-0.765941\pi$
$787$		−	37.6379i		−	1.34164i	0.741618	−	0.670822i	$-0.234059\pi$
$788$			7.11984i			0.253634i
$789$		0			0
$790$	6.67535	+	27.4999i	0.237498	+	0.978402i
$791$	46.9702			1.67007
$792$		0			0
$793$			7.37931i			0.262047i
$794$	−4.21228			−0.149488
$795$		0			0
$796$	1.07977			0.0382713
$797$			34.0691i			1.20679i	0.797442	+	0.603396i	$0.206186\pi$
$797$			34.0691i			1.20679i	−0.797442	+	0.603396i	$0.793814\pi$
$798$		0			0
$799$	3.48535			0.123303
$800$	2.29234	+	4.44356i	0.0810463	+	0.157103i
$801$		0			0
$802$		−	31.3490i		−	1.10697i
$803$		−	31.9066i		−	1.12596i
$804$		0			0
$805$	−1.84975	+	0.449009i	−0.0651950	+	0.0158255i
$806$	11.0186			0.388115
$807$		0			0
$808$			9.14260i			0.321635i
$809$	−52.5581			−1.84785			−0.923923	−	0.382578i	$-0.875036\pi$
$809$	−52.5581			−1.84785			−0.923923	+	0.382578i	$0.875036\pi$
$810$		0			0
$811$	26.6557			0.936008			0.468004	−	0.883726i	$-0.344973\pi$
$811$	26.6557			0.936008			0.468004	+	0.883726i	$0.344973\pi$
$812$			34.0591i			1.19524i
$813$		0			0
$814$	−2.41083			−0.0844995
$815$	−4.89289	−	20.1568i	−0.171390	−	0.706063i
$816$		0			0
$817$			2.47633i			0.0866359i
$818$			0.0295145i			0.00103195i
$819$		0			0
$820$	−7.45993	+	1.81083i	−0.260512	+	0.0632369i
$821$	39.6834			1.38496			0.692480	−	0.721437i	$-0.256518\pi$
$821$	39.6834			1.38496			0.692480	+	0.721437i	$0.256518\pi$
$822$		0			0
$823$			13.4315i			0.468192i	0.972214	+	0.234096i	$0.0752130\pi$
$823$			13.4315i			0.468192i	−0.972214	+	0.234096i	$0.924787\pi$
$824$	15.0650			0.524815
$825$		0			0
$826$	−67.6970			−2.35548
$827$		−	15.7576i		−	0.547947i	−0.961737	−	0.273973i	$-0.911662\pi$
$827$		−	15.7576i		−	0.547947i	0.961737	−	0.273973i	$-0.0883380\pi$
$828$		0			0
$829$	5.68708			0.197521			0.0987603	−	0.995111i	$-0.468512\pi$
$829$	5.68708			0.197521			0.0987603	+	0.995111i	$0.468512\pi$
$830$	−6.99622	+	1.69827i	−0.242842	+	0.0589478i
$831$		0			0
$832$			3.44356i			0.119384i
$833$		−	33.2291i		−	1.15132i
$834$		0			0
$835$	7.99176	+	32.9230i	0.276566	+	1.13935i
$836$	−0.696220			−0.0240793
$837$		0			0
$838$			11.9707i			0.413521i
$839$	50.8699			1.75622			0.878111	−	0.478457i	$-0.158804\pi$
$839$	50.8699			1.75622			0.878111	+	0.478457i	$0.158804\pi$
$840$		0			0
$841$	17.4257			0.600885
$842$		−	2.45820i		−	0.0847152i
$843$		0			0
$844$	16.7884			0.577881
$845$	−2.48135	+	0.602326i	−0.0853612	+	0.0207206i
$846$		0			0
$847$			25.9326i			0.891053i
$848$		−	3.73718i		−	0.128335i
$849$		0			0
$850$	−8.20920	+	4.23495i	−0.281573	+	0.145258i
$851$	0.170297			0.00583769
$852$		0			0
$853$			37.9664i			1.29994i	0.759958	+	0.649972i	$0.225220\pi$
$853$			37.9664i			1.29994i	−0.759958	+	0.649972i	$0.774780\pi$
$854$	−10.7118			−0.366550
$855$		0			0
$856$	−3.15153			−0.107717
$857$			30.9464i			1.05711i	0.848899	+	0.528555i	$0.177266\pi$
$857$			30.9464i			1.05711i	−0.848899	+	0.528555i	$0.822734\pi$
$858$		0			0
$859$	−26.2307			−0.894978			−0.447489	−	0.894289i	$-0.647682\pi$
$859$	−26.2307			−0.894978			−0.447489	+	0.894289i	$0.647682\pi$
$860$	−4.52298	−	18.6329i	−0.154232	−	0.635378i
$861$		0			0
$862$			5.92658i			0.201860i
$863$			3.73171i			0.127029i	0.997981	+	0.0635145i	$0.0202309\pi$
$863$			3.73171i			0.127029i	−0.997981	+	0.0635145i	$0.979769\pi$
$864$		0			0
$865$	−6.96525	−	28.6942i	−0.236826	−	0.975631i
$866$	−5.13974			−0.174655
$867$		0			0
$868$			15.9946i			0.542893i
$869$	30.5102			1.03499
$870$		0			0
$871$	31.2924			1.06030
$872$		−	14.9899i		−	0.507621i
$873$		0			0
$874$	0.0491797			0.00166353
$875$	36.6152	+	42.2215i	1.23782	+	1.42735i
$876$		0			0
$877$		−	12.2050i		−	0.412132i	−0.978538	−	0.206066i	$-0.933934\pi$
$877$		−	12.2050i		−	0.412132i	0.978538	−	0.206066i	$-0.0660661\pi$
$878$		−	24.9687i		−	0.842654i
$879$		0			0
$880$	5.23865	−	1.27163i	0.176595	−	0.0428668i
$881$	−36.3657			−1.22519			−0.612596	−	0.790397i	$-0.709875\pi$
$881$	−36.3657			−1.22519			−0.612596	+	0.790397i	$0.709875\pi$
$882$		0			0
$883$		−	21.1849i		−	0.712930i	−0.934309	−	0.356465i	$-0.883982\pi$
$883$		−	21.1849i		−	0.712930i	0.934309	−	0.356465i	$-0.116018\pi$
$884$	−6.36176			−0.213969
$885$		0			0
$886$	8.11812			0.272734
$887$			16.6151i			0.557880i	0.960309	+	0.278940i	$0.0899830\pi$
$887$			16.6151i			0.557880i	−0.960309	+	0.278940i	$0.910017\pi$
$888$		0			0
$889$	1.55229			0.0520620
$890$	2.25270	+	9.28026i	0.0755106	+	0.311075i
$891$		0			0
$892$			7.49275i			0.250876i
$893$			0.544824i			0.0182318i
$894$		0			0
$895$	−27.8398	+	6.75785i	−0.930581	+	0.225890i
$896$	−4.99866			−0.166993
$897$		0			0
$898$			14.6825i			0.489963i
$899$	21.8022			0.727143
$900$		0			0
$901$	6.90421			0.230013
$902$			8.27653i			0.275578i
$903$		0			0
$904$	9.39655			0.312525
$905$	19.1402	−	4.64611i	0.636242	−	0.154442i
$906$		0			0
$907$			32.6208i			1.08316i	0.840650	+	0.541578i	$0.182173\pi$
$907$			32.6208i			1.08316i	−0.840650	+	0.541578i	$0.817827\pi$
$908$		−	4.44353i		−	0.147464i
$909$		0			0
$910$	9.07938	+	37.4036i	0.300979	+	1.23992i
$911$	−43.7539			−1.44963			−0.724816	−	0.688943i	$-0.758075\pi$
$911$	−43.7539			−1.44963			−0.724816	+	0.688943i	$0.758075\pi$
$912$		0			0
$913$			7.76206i			0.256887i
$914$	−19.6738			−0.650753
$915$		0			0
$916$	−4.02673			−0.133047
$917$			32.9169i			1.08701i
$918$		0			0
$919$	20.7488			0.684438			0.342219	−	0.939620i	$-0.388821\pi$
$919$	20.7488			0.684438			0.342219	+	0.939620i	$0.388821\pi$
$920$	−0.370049	+	0.0898259i	−0.0122001	+	0.00296147i
$921$		0			0
$922$			23.3382i			0.768604i
$923$			8.37723i			0.275740i
$924$		0			0
$925$	−2.29234	−	4.44356i	−0.0753716	−	0.146103i
$926$	−19.0971			−0.627571
$927$		0			0
$928$			6.81364i			0.223669i
$929$	27.9190			0.915992			0.457996	−	0.888954i	$-0.348567\pi$
$929$	27.9190			0.915992			0.457996	+	0.888954i	$0.348567\pi$
$930$		0			0
$931$	5.19432			0.170237
$932$			30.1146i			0.986436i
$933$		0			0
$934$	38.7494			1.26792
$935$	2.34927	+	9.67808i	0.0768292	+	0.316507i
$936$		0			0
$937$		−	0.763669i		−	0.0249480i	−0.999922	−	0.0124740i	$-0.996029\pi$
$937$		−	0.763669i		−	0.0249480i	0.999922	−	0.0124740i	$-0.00397070\pi$
$938$			45.4240i			1.48315i
$939$		0			0
$940$	−0.995111	−	4.09948i	−0.0324569	−	0.133710i
$941$	31.8565			1.03849			0.519247	−	0.854624i	$-0.326213\pi$
$941$	31.8565			1.03849			0.519247	+	0.854624i	$0.326213\pi$
$942$		0			0
$943$		−	0.584639i		−	0.0190385i
$944$	−13.5430			−0.440788
$945$		0			0
$946$	−20.6726			−0.672124
$947$		−	11.5491i		−	0.375295i	−0.982236	−	0.187648i	$-0.939914\pi$
$947$		−	11.5491i		−	0.375295i	0.982236	−	0.187648i	$-0.0600863\pi$
$948$		0			0
$949$	45.5745			1.47941
$950$	−0.662001	−	1.28325i	−0.0214781	−	0.0416341i
$951$		0			0
$952$		−	9.23472i		−	0.299299i
$953$		−	4.29656i		−	0.139179i	−0.997576	−	0.0695896i	$-0.977831\pi$
$953$		−	4.29656i		−	0.139179i	0.997576	−	0.0695896i	$-0.0221690\pi$
$954$		0			0
$955$	22.1937	−	5.38732i	0.718172	−	0.174330i
$956$	19.1950			0.620809
$957$		0			0
$958$		−	18.4527i		−	0.596181i
$959$	96.6551			3.12116
$960$		0			0
$961$	−20.7614			−0.669722
$962$		−	3.44356i		−	0.111025i
$963$		0			0
$964$	1.03560			0.0333546
$965$	8.01692	+	33.0267i	0.258074	+	1.06317i
$966$		0			0
$967$			20.9828i			0.674762i	0.941368	+	0.337381i	$0.109541\pi$
$967$			20.9828i			0.674762i	−0.941368	+	0.337381i	$0.890459\pi$
$968$			5.18790i			0.166746i
$969$		0			0
$970$	−17.2829	+	4.19527i	−0.554921	+	0.134702i
$971$	−6.56444			−0.210663			−0.105331	−	0.994437i	$-0.533590\pi$
$971$	−6.56444			−0.210663			−0.105331	+	0.994437i	$0.533590\pi$
$972$		0			0
$973$			38.4473i			1.23256i
$974$	−18.9340			−0.606684
$975$		0			0
$976$	−2.14293			−0.0685936
$977$			35.6698i			1.14118i	0.821236	+	0.570589i	$0.193285\pi$
$977$			35.6698i			1.14118i	−0.821236	+	0.570589i	$0.806715\pi$
$978$		0			0
$979$	10.2961			0.329065
$980$	−39.0842	+	9.48734i	−1.24850	+	0.303062i
$981$		0			0
$982$		−	38.7713i		−	1.23724i
$983$			3.01990i			0.0963197i	0.998840	+	0.0481599i	$0.0153357\pi$
$983$			3.01990i			0.0963197i	−0.998840	+	0.0481599i	$0.984664\pi$
$984$		0			0
$985$	3.75548	+	15.4712i	0.119660	+	0.492952i
$986$	−12.5878			−0.400877
$987$		0			0
$988$		−	0.994460i		−	0.0316380i
$989$	1.46028			0.0464341
$990$		0			0
$991$	13.3694			0.424692			0.212346	−	0.977195i	$-0.431890\pi$
$991$	13.3694			0.424692			0.212346	+	0.977195i	$0.431890\pi$
$992$			3.19979i			0.101593i
$993$		0			0
$994$	−12.1604			−0.385704
$995$	2.34630	−	0.569542i	0.0743826	−	0.0180557i
$996$		0			0
$997$			11.1903i			0.354402i	0.984175	+	0.177201i	$0.0567042\pi$
$997$			11.1903i			0.354402i	−0.984175	+	0.177201i	$0.943296\pi$
$998$			40.2106i			1.27284i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.r.1999.8	yes	14
3.2	odd	2		3330.2.d.q.1999.7	✓	14
5.4	even	2	inner	3330.2.d.r.1999.1	yes	14
15.14	odd	2		3330.2.d.q.1999.14	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3330.2.d.q.1999.7	✓	14	3.2	odd	2
3330.2.d.q.1999.14	yes	14	15.14	odd	2
3330.2.d.r.1999.1	yes	14	5.4	even	2	inner
3330.2.d.r.1999.8	yes	14	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:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.17297 + 0.527467i) q^{5} -4.99866i q^{7} -1.00000i q^{8} +(-0.527467 - 2.17297i) q^{10} -2.41083 q^{11} -3.44356i q^{13} +4.99866 q^{14} +1.00000 q^{16} +1.84744i q^{17} -0.288789 q^{19} +(2.17297 - 0.527467i) q^{20} -2.41083i q^{22} +0.170297i q^{23} +(4.44356 - 2.29234i) q^{25} +3.44356 q^{26} +4.99866i q^{28} +6.81364 q^{29} +3.19979 q^{31} +1.00000i q^{32} -1.84744 q^{34} +(2.63663 + 10.8619i) q^{35} -1.00000i q^{37} -0.288789i q^{38} +(0.527467 + 2.17297i) q^{40} -3.43306 q^{41} -8.57489i q^{43} +2.41083 q^{44} -0.170297 q^{46} -1.88658i q^{47} -17.9866 q^{49} +(2.29234 + 4.44356i) q^{50} +3.44356i q^{52} -3.73718i q^{53} +(5.23865 - 1.27163i) q^{55} -4.99866 q^{56} +6.81364i q^{58} -13.5430 q^{59} -2.14293 q^{61} +3.19979i q^{62} -1.00000 q^{64} +(1.81636 + 7.48273i) q^{65} +9.08723i q^{67} -1.84744i q^{68} +(-10.8619 + 2.63663i) q^{70} -2.43273 q^{71} +13.2347i q^{73} +1.00000 q^{74} +0.288789 q^{76} +12.0509i q^{77} -12.6555 q^{79} +(-2.17297 + 0.527467i) q^{80} -3.43306i q^{82} -3.21967i q^{83} +(-0.974464 - 4.01442i) q^{85} +8.57489 q^{86} +2.41083i q^{88} -4.27078 q^{89} -17.2132 q^{91} -0.170297i q^{92} +1.88658 q^{94} +(0.627528 - 0.152327i) q^{95} -7.95362i q^{97} -17.9866i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} + 4 q^{5} - 6 q^{10} - 12 q^{11} + 12 q^{14} + 14 q^{16} + 4 q^{19} - 4 q^{20} + 10 q^{25} - 4 q^{26} + 16 q^{29} + 12 q^{31} - 12 q^{34} + 8 q^{35} + 6 q^{40} - 56 q^{41} + 12 q^{44} - 8 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) \) 14 * q - 14 * q^4 + 4 * q^5 - 6 * q^10 - 12 * q^11 + 12 * q^14 + 14 * q^16 + 4 * q^19 - 4 * q^20 + 10 * q^25 - 4 * q^26 + 16 * q^29 + 12 * q^31 - 12 * q^34 + 8 * q^35 + 6 * q^40 - 56 * q^41 + 12 * q^44 - 8 * q^46 + 18 * q^49 + 24 * q^50 - 12 * q^56 + 28 * q^59 + 12 * q^61 - 14 * q^64 - 12 * q^65 - 16 * q^70 - 48 * q^71 + 14 * q^74 - 4 * q^76 - 20 * q^79 + 4 * q^80 + 12 * q^85 - 12 * q^86 + 36 * q^89 - 32 * q^91 + 32 * q^94 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more