LMFDB - Embedded newform 1305.2.c.k.784.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 $ x^12 + 20x^10 + 148x^8 + 502x^6 + 792x^4 + 496*x^2 + 45
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.1
Root			$-2.62500i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.k.784.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.62500i q^{2} -4.89062 q^{4} +(1.48188 - 1.67452i) q^{5} +1.33988i q^{7} +7.58789i q^{8} +(-4.39562 - 3.88994i) q^{10} -4.65602 q^{11} -6.90089i q^{13} +3.51717 q^{14} +10.1370 q^{16} +6.12899i q^{17} -3.89699 q^{19} +(-7.24733 + 8.18946i) q^{20} +12.2221i q^{22} +2.21197i q^{23} +(-0.608053 - 4.96289i) q^{25} -18.1148 q^{26} -6.55283i q^{28} -1.00000 q^{29} -6.88700 q^{31} -11.4337i q^{32} +16.0886 q^{34} +(2.24365 + 1.98554i) q^{35} -5.79075i q^{37} +10.2296i q^{38} +(12.7061 + 11.2444i) q^{40} -7.05434 q^{41} +11.9077i q^{43} +22.7709 q^{44} +5.80642 q^{46} +6.12899i q^{47} +5.20473 q^{49} +(-13.0276 + 1.59614i) q^{50} +33.7497i q^{52} +1.31265i q^{53} +(-6.89968 + 7.79662i) q^{55} -10.1668 q^{56} +2.62500i q^{58} +6.20611 q^{59} -14.2242 q^{61} +18.0784i q^{62} -9.73965 q^{64} +(-11.5557 - 10.2263i) q^{65} -3.00997i q^{67} -29.9746i q^{68} +(5.21204 - 5.88959i) q^{70} +6.04971 q^{71} -4.47120i q^{73} -15.2007 q^{74} +19.0587 q^{76} -6.23849i q^{77} +1.31186 q^{79} +(15.0218 - 16.9746i) q^{80} +18.5176i q^{82} +4.20110i q^{83} +(10.2631 + 9.08244i) q^{85} +31.2578 q^{86} -35.3294i q^{88} +0.232864 q^{89} +9.24634 q^{91} -10.8179i q^{92} +16.0886 q^{94} +(-5.77488 + 6.52560i) q^{95} -2.99879i q^{97} -13.6624i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) $ 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	2.62500i		−	1.85616i	−0.372387	−	0.928078i	$-0.621461\pi$
$2$		−	2.62500i		−	1.85616i	0.372387	−	0.928078i	$-0.378539\pi$
$3$		0			0
$3$		0			0
$4$	−4.89062			−2.44531
$5$	1.48188	−	1.67452i	0.662718	−	0.748869i
$5$	1.48188	−	1.67452i	0.662718	−	0.748869i
$6$		0			0
$7$			1.33988i			0.506425i	0.967411	+	0.253213i	$0.0814873\pi$
$7$			1.33988i			0.506425i	−0.967411	+	0.253213i	$0.918513\pi$
$8$			7.58789i			2.68272i
$9$		0			0
$10$	−4.39562	−	3.88994i	−1.39002	−	1.23011i
$11$	−4.65602			−1.40384			−0.701922	−	0.712254i	$-0.747674\pi$
$11$	−4.65602			−1.40384			−0.701922	+	0.712254i	$0.747674\pi$
$12$		0			0
$13$		−	6.90089i		−	1.91396i	−0.290150	−	0.956981i	$-0.593705\pi$
$13$		−	6.90089i		−	1.91396i	0.290150	−	0.956981i	$-0.406295\pi$
$14$	3.51717			0.940004
$15$		0			0
$16$	10.1370			2.53424
$17$			6.12899i			1.48650i	0.669015	+	0.743249i	$0.266716\pi$
$17$			6.12899i			1.48650i	−0.669015	+	0.743249i	$0.733284\pi$
$18$		0			0
$19$	−3.89699			−0.894031			−0.447016	−	0.894526i	$-0.647513\pi$
$19$	−3.89699			−0.894031			−0.447016	+	0.894526i	$0.647513\pi$
$20$	−7.24733	+	8.18946i	−1.62055	+	1.83122i
$21$		0			0
$22$			12.2221i			2.60575i
$23$			2.21197i			0.461227i	0.973045	+	0.230614i	$0.0740734\pi$
$23$			2.21197i			0.461227i	−0.973045	+	0.230614i	$0.925927\pi$
$24$		0			0
$25$	−0.608053	−	4.96289i	−0.121611	−	0.992578i
$26$	−18.1148			−3.55261
$27$		0			0
$28$		−	6.55283i		−	1.23837i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	−6.88700			−1.23694			−0.618471	−	0.785808i	$-0.712247\pi$
$31$	−6.88700			−1.23694			−0.618471	+	0.785808i	$0.712247\pi$
$32$		−	11.4337i		−	2.02122i
$33$		0			0
$34$	16.0886			2.75917
$35$	2.24365	+	1.98554i	0.379246	+	0.335617i
$36$		0			0
$37$		−	5.79075i		−	0.951993i	−0.879447	−	0.475996i	$-0.842088\pi$
$37$		−	5.79075i		−	0.951993i	0.879447	−	0.475996i	$-0.157912\pi$
$38$			10.2296i			1.65946i
$39$		0			0
$40$	12.7061	+	11.2444i	2.00901	+	1.77789i
$41$	−7.05434			−1.10170			−0.550851	−	0.834603i	$-0.685697\pi$
$41$	−7.05434			−1.10170			−0.550851	+	0.834603i	$0.685697\pi$
$42$		0			0
$43$			11.9077i			1.81591i	0.419067	+	0.907955i	$0.362357\pi$
$43$			11.9077i			1.81591i	−0.419067	+	0.907955i	$0.637643\pi$
$44$	22.7709			3.43284
$45$		0			0
$46$	5.80642			0.856110
$47$			6.12899i			0.894005i	0.894533	+	0.447002i	$0.147508\pi$
$47$			6.12899i			0.894005i	−0.894533	+	0.447002i	$0.852492\pi$
$48$		0			0
$49$	5.20473			0.743533
$50$	−13.0276	+	1.59614i	−1.84238	+	0.225728i
$51$		0			0
$52$			33.7497i			4.68024i
$53$			1.31265i			0.180306i	0.995928	+	0.0901531i	$0.0287356\pi$
$53$			1.31265i			0.180306i	−0.995928	+	0.0901531i	$0.971264\pi$
$54$		0			0
$55$	−6.89968	+	7.79662i	−0.930352	+	1.05130i
$56$	−10.1668			−1.35860
$57$		0			0
$58$			2.62500i			0.344679i
$59$	6.20611			0.807967			0.403983	−	0.914766i	$-0.367625\pi$
$59$	6.20611			0.807967			0.403983	+	0.914766i	$0.367625\pi$
$60$		0			0
$61$	−14.2242			−1.82122			−0.910612	−	0.413263i	$-0.864389\pi$
$61$	−14.2242			−1.82122			−0.910612	+	0.413263i	$0.864389\pi$
$62$			18.0784i			2.29595i
$63$		0			0
$64$	−9.73965			−1.21746
$65$	−11.5557	−	10.2263i	−1.43331	−	1.26842i
$66$		0			0
$67$		−	3.00997i		−	0.367726i	−0.982952	−	0.183863i	$-0.941140\pi$
$67$		−	3.00997i		−	0.367726i	0.982952	−	0.183863i	$-0.0588603\pi$
$68$		−	29.9746i		−	3.63495i
$69$		0			0
$70$	5.21204	−	5.88959i	0.622957	−	0.703940i
$71$	6.04971			0.717968			0.358984	−	0.933344i	$-0.383123\pi$
$71$	6.04971			0.717968			0.358984	+	0.933344i	$0.383123\pi$
$72$		0			0
$73$		−	4.47120i		−	0.523315i	−0.965161	−	0.261657i	$-0.915731\pi$
$73$		−	4.47120i		−	0.523315i	0.965161	−	0.261657i	$-0.0842690\pi$
$74$	−15.2007			−1.76705
$75$		0			0
$76$	19.0587			2.18619
$77$		−	6.23849i		−	0.710942i
$78$		0			0
$79$	1.31186			0.147596			0.0737978	−	0.997273i	$-0.476488\pi$
$79$	1.31186			0.147596			0.0737978	+	0.997273i	$0.476488\pi$
$80$	15.0218	−	16.9746i	1.67949	−	1.89781i
$81$		0			0
$82$			18.5176i			2.04493i
$83$			4.20110i			0.461131i	0.973057	+	0.230565i	$0.0740576\pi$
$83$			4.20110i			0.461131i	−0.973057	+	0.230565i	$0.925942\pi$
$84$		0			0
$85$	10.2631	+	9.08244i	1.11319	+	0.985129i
$86$	31.2578			3.37061
$87$		0			0
$88$		−	35.3294i		−	3.76613i
$89$	0.232864			0.0246835			0.0123418	−	0.999924i	$-0.496071\pi$
$89$	0.232864			0.0246835			0.0123418	+	0.999924i	$0.496071\pi$
$90$		0			0
$91$	9.24634			0.969279
$92$		−	10.8179i		−	1.12785i
$93$		0			0
$94$	16.0886			1.65941
$95$	−5.77488	+	6.52560i	−0.592490	+	0.669513i
$96$		0			0
$97$		−	2.99879i		−	0.304481i	−0.988343	−	0.152240i	$-0.951351\pi$
$97$		−	2.99879i		−	0.304481i	0.988343	−	0.152240i	$-0.0486488\pi$
$98$		−	13.6624i		−	1.38011i
$99$		0			0
$100$	2.97376	+	24.2716i	0.297376	+	2.42716i
$101$	−15.4724			−1.53956			−0.769782	−	0.638306i	$-0.779635\pi$
$101$	−15.4724			−1.53956			−0.769782	+	0.638306i	$0.779635\pi$
$102$		0			0
$103$		−	11.5085i		−	1.13397i	−0.823728	−	0.566985i	$-0.808110\pi$
$103$		−	11.5085i		−	1.13397i	0.823728	−	0.566985i	$-0.191890\pi$
$104$	52.3632			5.13463
$105$		0			0
$106$	3.44570			0.334676
$107$		−	16.5277i		−	1.59779i	−0.601471	−	0.798895i	$-0.705418\pi$
$107$		−	16.5277i		−	1.59779i	0.601471	−	0.798895i	$-0.294582\pi$
$108$		0			0
$109$	−3.89730			−0.373293			−0.186647	−	0.982427i	$-0.559762\pi$
$109$	−3.89730			−0.373293			−0.186647	+	0.982427i	$0.559762\pi$
$110$	20.4661	+	18.1116i	1.95137	+	1.72688i
$111$		0			0
$112$			13.5823i			1.28340i
$113$		−	8.11123i		−	0.763040i	−0.924361	−	0.381520i	$-0.875401\pi$
$113$		−	8.11123i		−	0.763040i	0.924361	−	0.381520i	$-0.124599\pi$
$114$		0			0
$115$	3.70399	+	3.27788i	0.345399	+	0.305664i
$116$	4.89062			0.454083
$117$		0			0
$118$		−	16.2910i		−	1.49971i
$119$	−8.21208			−0.752800
$120$		0			0
$121$	10.6785			0.970777
$122$			37.3386i			3.38047i
$123$		0			0
$124$	33.6817			3.02471
$125$	−9.21153	−	6.33622i	−0.823905	−	0.566728i
$126$		0			0
$127$		−	6.07606i		−	0.539163i	−0.962978	−	0.269582i	$-0.913115\pi$
$127$		−	6.07606i		−	0.539163i	0.962978	−	0.269582i	$-0.0868854\pi$
$128$			2.69909i			0.238568i
$129$		0			0
$130$	−26.8440	+	30.3337i	−2.35438	+	2.66044i
$131$	1.40292			0.122574			0.0612870	−	0.998120i	$-0.480479\pi$
$131$	1.40292			0.122574			0.0612870	+	0.998120i	$0.480479\pi$
$132$		0			0
$133$		−	5.22149i		−	0.452760i
$134$	−7.90117			−0.682557
$135$		0			0
$136$	−46.5061			−3.98786
$137$			5.98153i			0.511037i	0.966804	+	0.255518i	$0.0822461\pi$
$137$			5.98153i			0.511037i	−0.966804	+	0.255518i	$0.917754\pi$
$138$		0			0
$139$	5.24634			0.444988			0.222494	−	0.974934i	$-0.428580\pi$
$139$	5.24634			0.444988			0.222494	+	0.974934i	$0.428580\pi$
$140$	−10.9729	−	9.71052i	−0.927376	−	0.820689i
$141$		0			0
$142$		−	15.8805i		−	1.33266i
$143$			32.1307i			2.68690i
$144$		0			0
$145$	−1.48188	+	1.67452i	−0.123064	+	0.139062i
$146$	−11.7369			−0.971353
$147$		0			0
$148$			28.3204i			2.32792i
$149$	7.74964			0.634875			0.317438	−	0.948279i	$-0.397178\pi$
$149$	7.74964			0.634875			0.317438	+	0.948279i	$0.397178\pi$
$150$		0			0
$151$	−12.7704			−1.03924			−0.519619	−	0.854398i	$-0.673926\pi$
$151$	−12.7704			−1.03924			−0.519619	+	0.854398i	$0.673926\pi$
$152$		−	29.5699i		−	2.39844i
$153$		0			0
$154$	−16.3760			−1.31962
$155$	−10.2057	+	11.5324i	−0.819743	+	0.926307i
$156$		0			0
$157$		−	19.2823i		−	1.53889i	−0.638710	−	0.769447i	$-0.720532\pi$
$157$		−	19.2823i		−	1.53889i	0.638710	−	0.769447i	$-0.279468\pi$
$158$		−	3.44363i		−	0.273960i
$159$		0			0
$160$	−19.1461	−	16.9435i	−1.51363	−	1.33950i
$161$	−2.96376			−0.233577
$162$		0			0
$163$		−	7.46999i		−	0.585095i	−0.956251	−	0.292547i	$-0.905497\pi$
$163$		−	7.46999i		−	0.585095i	0.956251	−	0.292547i	$-0.0945030\pi$
$164$	34.5001			2.69401
$165$		0			0
$166$	11.0279			0.855930
$167$			6.07493i			0.470092i	0.971984	+	0.235046i	$0.0755242\pi$
$167$			6.07493i			0.470092i	−0.971984	+	0.235046i	$0.924476\pi$
$168$		0			0
$169$	−34.6223			−2.66325
$170$	23.8414	−	26.9407i	1.82855	−	2.06626i
$171$		0			0
$172$		−	58.2362i		−	4.44047i
$173$			22.7580i			1.73026i	0.501550	+	0.865128i	$0.332763\pi$
$173$			22.7580i			1.73026i	−0.501550	+	0.865128i	$0.667237\pi$
$174$		0			0
$175$	6.64966	−	0.814715i	0.502667	−	0.0615867i
$176$	−47.1979			−3.55768
$177$		0			0
$178$		−	0.611267i		−	0.0458164i
$179$	1.87173			0.139900			0.0699498	−	0.997551i	$-0.477716\pi$
$179$	1.87173			0.139900			0.0699498	+	0.997551i	$0.477716\pi$
$180$		0			0
$181$	18.9013			1.40492			0.702461	−	0.711722i	$-0.252084\pi$
$181$	18.9013			1.40492			0.702461	+	0.711722i	$0.252084\pi$
$182$		−	24.2716i		−	1.79913i
$183$		0			0
$184$	−16.7842			−1.23735
$185$	−9.69674	−	8.58120i	−0.712918	−	0.630903i
$186$		0			0
$187$		−	28.5367i		−	2.08681i
$188$		−	29.9746i		−	2.18612i
$189$		0			0
$190$	17.1297	+	15.1591i	1.24272	+	1.09975i
$191$	−10.3997			−0.752495			−0.376248	−	0.926519i	$-0.622786\pi$
$191$	−10.3997			−0.752495			−0.376248	+	0.926519i	$0.622786\pi$
$192$		0			0
$193$		−	5.32409i		−	0.383237i	−0.981470	−	0.191618i	$-0.938626\pi$
$193$		−	5.32409i		−	0.383237i	0.981470	−	0.191618i	$-0.0613736\pi$
$194$	−7.87182			−0.565164
$195$		0			0
$196$	−25.4544			−1.81817
$197$			13.3489i			0.951071i	0.879697	+	0.475535i	$0.157746\pi$
$197$			13.3489i			0.951071i	−0.879697	+	0.475535i	$0.842254\pi$
$198$		0			0
$199$	−20.6404			−1.46316			−0.731580	−	0.681755i	$-0.761217\pi$
$199$	−20.6404			−1.46316			−0.731580	+	0.681755i	$0.761217\pi$
$200$	37.6579	−	4.61384i	2.66281	−	0.326248i
$201$		0			0
$202$			40.6151i			2.85767i
$203$		−	1.33988i		−	0.0940408i
$204$		0			0
$205$	−10.4537	+	11.8126i	−0.730118	+	0.825031i
$206$	−30.2099			−2.10482
$207$		0			0
$208$		−	69.9540i		−	4.85044i
$209$	18.1445			1.25508
$210$		0			0
$211$	−11.0541			−0.760998			−0.380499	−	0.924781i	$-0.624248\pi$
$211$	−11.0541			−0.760998			−0.380499	+	0.924781i	$0.624248\pi$
$212$		−	6.41967i		−	0.440905i
$213$		0			0
$214$	−43.3851			−2.96575
$215$	19.9398	+	17.6458i	1.35988	+	1.20344i
$216$		0			0
$217$		−	9.22772i		−	0.626418i
$218$			10.2304i			0.692891i
$219$		0			0
$220$	33.7437	−	38.1303i	2.27500	−	2.57075i
$221$	42.2955			2.84510
$222$		0			0
$223$			23.4495i			1.57030i	0.619307	+	0.785149i	$0.287413\pi$
$223$			23.4495i			1.57030i	−0.619307	+	0.785149i	$0.712587\pi$
$224$	15.3198			1.02360
$225$		0			0
$226$	−21.2920			−1.41632
$227$		−	4.66282i		−	0.309482i	−0.987955	−	0.154741i	$-0.950546\pi$
$227$		−	4.66282i		−	0.309482i	0.987955	−	0.154741i	$-0.0494544\pi$
$228$		0			0
$229$	9.77936			0.646238			0.323119	−	0.946358i	$-0.395269\pi$
$229$	9.77936			0.646238			0.323119	+	0.946358i	$0.395269\pi$
$230$	8.60443	−	9.72298i	0.567359	−	0.641114i
$231$		0			0
$232$		−	7.58789i		−	0.498169i
$233$		−	9.39163i		−	0.615266i	−0.951505	−	0.307633i	$-0.900463\pi$
$233$		−	9.39163i		−	0.615266i	0.951505	−	0.307633i	$-0.0995370\pi$
$234$		0			0
$235$	10.2631	+	9.08244i	0.669493	+	0.592473i
$236$	−30.3518			−1.97573
$237$		0			0
$238$			21.5567i			1.39731i
$239$	−22.9585			−1.48506			−0.742530	−	0.669813i	$-0.766374\pi$
$239$	−22.9585			−1.48506			−0.742530	+	0.669813i	$0.766374\pi$
$240$		0			0
$241$	1.04624			0.0673944			0.0336972	−	0.999432i	$-0.489272\pi$
$241$	1.04624			0.0673944			0.0336972	+	0.999432i	$0.489272\pi$
$242$		−	28.0312i		−	1.80191i
$243$		0			0
$244$	69.5653			4.45346
$245$	7.71280	−	8.71544i	0.492753	−	0.556809i
$246$		0			0
$247$			26.8927i			1.71114i
$248$		−	52.2578i		−	3.31837i
$249$		0			0
$250$	−16.6326	+	24.1803i	−1.05194	+	1.52929i
$251$	−1.08079			−0.0682188			−0.0341094	−	0.999418i	$-0.510859\pi$
$251$	−1.08079			−0.0682188			−0.0341094	+	0.999418i	$0.510859\pi$
$252$		0			0
$253$		−	10.2990i		−	0.647491i
$254$	−15.9497			−1.00077
$255$		0			0
$256$	−12.3942			−0.774636
$257$		−	11.4142i		−	0.712001i	−0.934486	−	0.356000i	$-0.884140\pi$
$257$		−	11.4142i		−	0.712001i	0.934486	−	0.356000i	$-0.115860\pi$
$258$		0			0
$259$	7.75888			0.482113
$260$	56.5146	+	50.0130i	3.50489	+	3.10168i
$261$		0			0
$262$		−	3.68268i		−	0.227517i
$263$		−	0.662105i		−	0.0408271i	−0.999792	−	0.0204136i	$-0.993502\pi$
$263$		−	0.662105i		−	0.0408271i	0.999792	−	0.0204136i	$-0.00649829\pi$
$264$		0			0
$265$	2.19806	+	1.94519i	0.135026	+	0.119492i
$266$	−13.7064			−0.840393
$267$		0			0
$268$			14.7206i			0.899206i
$269$	−22.3008			−1.35970			−0.679851	−	0.733350i	$-0.737956\pi$
$269$	−22.3008			−1.35970			−0.679851	+	0.733350i	$0.737956\pi$
$270$		0			0
$271$	5.53607			0.336292			0.168146	−	0.985762i	$-0.446222\pi$
$271$	5.53607			0.336292			0.168146	+	0.985762i	$0.446222\pi$
$272$			62.1293i			3.76714i
$273$		0			0
$274$	15.7015			0.948564
$275$	2.83111	+	23.1073i	0.170722	+	1.39342i
$276$		0			0
$277$		−	12.6054i		−	0.757383i	−0.925523	−	0.378692i	$-0.876374\pi$
$277$		−	12.6054i		−	0.757383i	0.925523	−	0.378692i	$-0.123626\pi$
$278$		−	13.7716i		−	0.825967i
$279$		0			0
$280$	−15.0660	+	17.0246i	−0.900368	+	1.01741i
$281$	−3.34566			−0.199585			−0.0997926	−	0.995008i	$-0.531818\pi$
$281$	−3.34566			−0.199585			−0.0997926	+	0.995008i	$0.531818\pi$
$282$		0			0
$283$		−	4.86489i		−	0.289188i	−0.989491	−	0.144594i	$-0.953812\pi$
$283$		−	4.86489i		−	0.289188i	0.989491	−	0.144594i	$-0.0461876\pi$
$284$	−29.5869			−1.75566
$285$		0			0
$286$	84.3431			4.98731
$287$		−	9.45194i		−	0.557930i
$288$		0			0
$289$	−20.5645			−1.20968
$290$	4.39562	+	3.88994i	0.258120	+	0.228425i
$291$		0			0
$292$			21.8670i			1.27967i
$293$		−	4.13296i		−	0.241450i	−0.992686	−	0.120725i	$-0.961478\pi$
$293$		−	4.13296i		−	0.241450i	0.992686	−	0.120725i	$-0.0385219\pi$
$294$		0			0
$295$	9.19672	−	10.3923i	0.535454	−	0.605062i
$296$	43.9395			2.55393
$297$		0			0
$298$		−	20.3428i		−	1.17843i
$299$	15.2646			0.882772
$300$		0			0
$301$	−15.9549			−0.919623
$302$			33.5222i			1.92899i
$303$		0			0
$304$	−39.5037			−2.26569
$305$	−21.0786	+	23.8188i	−1.20696	+	1.36386i
$306$		0			0
$307$		−	15.7578i		−	0.899344i	−0.893194	−	0.449672i	$-0.851541\pi$
$307$		−	15.7578i		−	0.899344i	0.893194	−	0.449672i	$-0.148459\pi$
$308$			30.5101i			1.73848i
$309$		0			0
$310$	30.2726	+	26.7900i	1.71937	+	1.52157i
$311$	−22.0419			−1.24988			−0.624940	−	0.780673i	$-0.714877\pi$
$311$	−22.0419			−1.24988			−0.624940	+	0.780673i	$0.714877\pi$
$312$		0			0
$313$		−	9.68896i		−	0.547653i	−0.961779	−	0.273826i	$-0.911711\pi$
$313$		−	9.68896i		−	0.547653i	0.961779	−	0.273826i	$-0.0882893\pi$
$314$	−50.6160			−2.85643
$315$		0			0
$316$	−6.41581			−0.360917
$317$			4.64549i			0.260917i	0.991454	+	0.130458i	$0.0416449\pi$
$317$			4.64549i			0.260917i	−0.991454	+	0.130458i	$0.958355\pi$
$318$		0			0
$319$	4.65602			0.260687
$320$	−14.4330	+	16.3093i	−0.806830	+	0.911715i
$321$		0			0
$322$			7.77988i			0.433556i
$323$		−	23.8846i		−	1.32898i
$324$		0			0
$325$	−34.2484	+	4.19611i	−1.89976	+	0.232758i
$326$	−19.6087			−1.08603
$327$		0			0
$328$		−	53.5275i		−	2.95556i
$329$	−8.21208			−0.452747
$330$		0			0
$331$	−6.38231			−0.350804			−0.175402	−	0.984497i	$-0.556122\pi$
$331$	−6.38231			−0.350804			−0.175402	+	0.984497i	$0.556122\pi$
$332$		−	20.5460i		−	1.12761i
$333$		0			0
$334$	15.9467			0.872565
$335$	−5.04026	−	4.46042i	−0.275379	−	0.243699i
$336$		0			0
$337$			8.44947i			0.460272i	0.973159	+	0.230136i	$0.0739171\pi$
$337$			8.44947i			0.460272i	−0.973159	+	0.230136i	$0.926083\pi$
$338$			90.8835i			4.94341i
$339$		0			0
$340$	−50.1931	−	44.4188i	−2.72210	−	2.40895i
$341$	32.0660			1.73647
$342$		0			0
$343$			16.3528i			0.882970i
$344$	−90.3545			−4.87159
$345$		0			0
$346$	59.7397			3.21163
$347$		−	15.3895i		−	0.826150i	−0.910697	−	0.413075i	$-0.864455\pi$
$347$		−	15.3895i		−	0.826150i	0.910697	−	0.413075i	$-0.135545\pi$
$348$		0			0
$349$	−1.89930			−0.101667			−0.0508336	−	0.998707i	$-0.516188\pi$
$349$	−1.89930			−0.101667			−0.0508336	+	0.998707i	$0.516188\pi$
$350$	−2.13863	−	17.4553i	−0.114314	−	0.933027i
$351$		0			0
$352$			53.2358i			2.83748i
$353$		−	17.8674i		−	0.950985i	−0.879720	−	0.475492i	$-0.842270\pi$
$353$		−	17.8674i		−	0.950985i	0.879720	−	0.475492i	$-0.157730\pi$
$354$		0			0
$355$	8.96495	−	10.1304i	0.475810	−	0.537664i
$356$	−1.13885			−0.0603589
$357$		0			0
$358$		−	4.91329i		−	0.259675i
$359$	−24.7905			−1.30839			−0.654197	−	0.756324i	$-0.726993\pi$
$359$	−24.7905			−1.30839			−0.654197	+	0.756324i	$0.726993\pi$
$360$		0			0
$361$	−3.81345			−0.200708
$362$		−	49.6159i		−	2.60775i
$363$		0			0
$364$	−45.2204			−2.37019
$365$	−7.48713	−	6.62579i	−0.391894	−	0.346810i
$366$		0			0
$367$		−	20.5944i		−	1.07502i	−0.843258	−	0.537509i	$-0.819365\pi$
$367$		−	20.5944i		−	1.07502i	0.843258	−	0.537509i	$-0.180635\pi$
$368$			22.4226i			1.16886i
$369$		0			0
$370$	−22.5257	+	25.4539i	−1.17105	+	1.32329i
$371$	−1.75879			−0.0913116
$372$		0			0
$373$			7.55956i			0.391419i	0.980662	+	0.195710i	$0.0627010\pi$
$373$			7.55956i			0.391419i	−0.980662	+	0.195710i	$0.937299\pi$
$374$	−74.9089			−3.87345
$375$		0			0
$376$	−46.5061			−2.39837
$377$			6.90089i			0.355414i
$378$		0			0
$379$	29.0454			1.49196			0.745980	−	0.665968i	$-0.231981\pi$
$379$	29.0454			1.49196			0.745980	+	0.665968i	$0.231981\pi$
$380$	28.2428	−	31.9143i	1.44882	−	1.63717i
$381$		0			0
$382$			27.2992i			1.39675i
$383$			9.20227i			0.470214i	0.971969	+	0.235107i	$0.0755441\pi$
$383$			9.20227i			0.470214i	−0.971969	+	0.235107i	$0.924456\pi$
$384$		0			0
$385$	−10.4465	−	9.24471i	−0.532403	−	0.471154i
$386$	−13.9757			−0.711347
$387$		0			0
$388$			14.6660i			0.744551i
$389$	12.7690			0.647414			0.323707	−	0.946157i	$-0.395071\pi$
$389$	12.7690			0.647414			0.323707	+	0.946157i	$0.395071\pi$
$390$		0			0
$391$	−13.5571			−0.685614
$392$			39.4929i			1.99469i
$393$		0			0
$394$	35.0409			1.76534
$395$	1.94402	−	2.19674i	0.0978142	−	0.110530i
$396$		0			0
$397$			24.2689i			1.21802i	0.793163	+	0.609009i	$0.208433\pi$
$397$			24.2689i			1.21802i	−0.793163	+	0.609009i	$0.791567\pi$
$398$			54.1811i			2.71585i
$399$		0			0
$400$	−6.16381	−	50.3086i	−0.308190	−	2.51543i
$401$	3.50670			0.175116			0.0875581	−	0.996159i	$-0.472094\pi$
$401$	3.50670			0.175116			0.0875581	+	0.996159i	$0.472094\pi$
$402$		0			0
$403$			47.5264i			2.36746i
$404$	75.6699			3.76472
$405$		0			0
$406$	−3.51717			−0.174554
$407$			26.9618i			1.33645i
$408$		0			0
$409$	−15.0852			−0.745913			−0.372956	−	0.927849i	$-0.621656\pi$
$409$	−15.0852			−0.745913			−0.372956	+	0.927849i	$0.621656\pi$
$410$	31.0082	+	27.4409i	1.53139	+	1.35521i
$411$		0			0
$412$			56.2839i			2.77291i
$413$			8.31542i			0.409175i
$414$		0			0
$415$	7.03484	+	6.22553i	0.345327	+	0.305599i
$416$	−78.9030			−3.86854
$417$		0			0
$418$		−	47.6293i		−	2.32962i
$419$	35.1725			1.71829			0.859144	−	0.511734i	$-0.170997\pi$
$419$	35.1725			1.71829			0.859144	+	0.511734i	$0.170997\pi$
$420$		0			0
$421$	24.4390			1.19108			0.595541	−	0.803325i	$-0.296938\pi$
$421$	24.4390			1.19108			0.595541	+	0.803325i	$0.296938\pi$
$422$			29.0171i			1.41253i
$423$		0			0
$424$	−9.96023			−0.483712
$425$	30.4175	−	3.72675i	1.47547	−	0.180774i
$426$		0			0
$427$		−	19.0587i		−	0.922314i
$428$			80.8306i			3.90710i
$429$		0			0
$430$	46.3203	−	52.3418i	2.23376	−	2.52415i
$431$	−38.0385			−1.83225			−0.916125	−	0.400892i	$-0.868700\pi$
$431$	−38.0385			−1.83225			−0.916125	+	0.400892i	$0.868700\pi$
$432$		0			0
$433$		−	19.3627i		−	0.930513i	−0.885176	−	0.465256i	$-0.845962\pi$
$433$		−	19.3627i		−	0.930513i	0.885176	−	0.465256i	$-0.154038\pi$
$434$	−24.2228			−1.16273
$435$		0			0
$436$	19.0602			0.912819
$437$		−	8.62003i		−	0.412352i
$438$		0			0
$439$	−11.4598			−0.546946			−0.273473	−	0.961880i	$-0.588172\pi$
$439$	−11.4598			−0.546946			−0.273473	+	0.961880i	$0.588172\pi$
$440$	−59.1599	−	52.3540i	−2.82034	−	2.49588i
$441$		0			0
$442$		−	111.026i		−	5.28095i
$443$		−	14.4767i		−	0.687811i	−0.939004	−	0.343905i	$-0.888250\pi$
$443$		−	14.4767i		−	0.687811i	0.939004	−	0.343905i	$-0.111750\pi$
$444$		0			0
$445$	0.345076	−	0.389936i	0.0163582	−	0.0184847i
$446$	61.5550			2.91472
$447$		0			0
$448$		−	13.0499i		−	0.616551i
$449$	13.4544			0.634955			0.317477	−	0.948266i	$-0.397164\pi$
$449$	13.4544			0.634955			0.317477	+	0.948266i	$0.397164\pi$
$450$		0			0
$451$	32.8452			1.54662
$452$			39.6690i			1.86587i
$453$		0			0
$454$	−12.2399			−0.574447
$455$	13.7020	−	15.4832i	0.642359	−	0.725864i
$456$		0			0
$457$		−	8.41068i		−	0.393435i	−0.980460	−	0.196717i	$-0.936972\pi$
$457$		−	8.41068i		−	0.393435i	0.980460	−	0.196717i	$-0.0630282\pi$
$458$		−	25.6708i		−	1.19952i
$459$		0			0
$460$	−18.1148	−	16.0309i	−0.844609	−	0.747443i
$461$	23.6845			1.10310			0.551549	−	0.834142i	$-0.314037\pi$
$461$	23.6845			1.10310			0.551549	+	0.834142i	$0.314037\pi$
$462$		0			0
$463$		−	8.12644i		−	0.377668i	−0.982009	−	0.188834i	$-0.939529\pi$
$463$		−	8.12644i		−	0.377668i	0.982009	−	0.188834i	$-0.0604707\pi$
$464$	−10.1370			−0.470597
$465$		0			0
$466$	−24.6530			−1.14203
$467$		−	7.02702i		−	0.325172i	−0.986694	−	0.162586i	$-0.948017\pi$
$467$		−	7.02702i		−	0.325172i	0.986694	−	0.162586i	$-0.0519835\pi$
$468$		0			0
$469$	4.03298			0.186226
$470$	23.8414	−	26.9407i	1.09972	−	1.24268i
$471$		0			0
$472$			47.0913i			2.16755i
$473$		−	55.4426i		−	2.54925i
$474$		0			0
$475$	2.36958	+	19.3403i	0.108724	+	0.887396i
$476$	40.1622			1.84083
$477$		0			0
$478$			60.2660i			2.75650i
$479$	27.7993			1.27018			0.635090	−	0.772438i	$-0.280963\pi$
$479$	27.7993			1.27018			0.635090	+	0.772438i	$0.280963\pi$
$480$		0			0
$481$	−39.9613			−1.82208
$482$		−	2.74639i		−	0.125094i
$483$		0			0
$484$	−52.2248			−2.37385
$485$	−5.02154	−	4.44385i	−0.228016	−	0.201785i
$486$		0			0
$487$			6.76082i			0.306362i	0.988198	+	0.153181i	$0.0489517\pi$
$487$			6.76082i			0.306362i	−0.988198	+	0.153181i	$0.951048\pi$
$488$		−	107.932i		−	4.88584i
$489$		0			0
$490$	−22.8780	−	20.2461i	−1.03352	−	0.914625i
$491$	23.3110			1.05201			0.526006	−	0.850481i	$-0.323689\pi$
$491$	23.3110			1.05201			0.526006	+	0.850481i	$0.323689\pi$
$492$		0			0
$493$		−	6.12899i		−	0.276036i
$494$	70.5934			3.17615
$495$		0			0
$496$	−69.8132			−3.13471
$497$			8.10586i			0.363597i
$498$		0			0
$499$	12.7385			0.570253			0.285126	−	0.958490i	$-0.407964\pi$
$499$	12.7385			0.570253			0.285126	+	0.958490i	$0.407964\pi$
$500$	45.0502	+	30.9881i	2.01470	+	1.38583i
$501$		0			0
$502$			2.83707i			0.126625i
$503$		−	28.1328i		−	1.25438i	−0.778867	−	0.627190i	$-0.784205\pi$
$503$		−	28.1328i		−	1.25438i	0.778867	−	0.627190i	$-0.215795\pi$
$504$		0			0
$505$	−22.9283	+	25.9089i	−1.02030	+	1.15293i
$506$	−27.0348			−1.20184
$507$		0			0
$508$			29.7157i			1.31842i
$509$	−19.5447			−0.866305			−0.433152	−	0.901321i	$-0.642599\pi$
$509$	−19.5447			−0.866305			−0.433152	+	0.901321i	$0.642599\pi$
$510$		0			0
$511$	5.99086			0.265020
$512$			37.9329i			1.67641i
$513$		0			0
$514$	−29.9624			−1.32158
$515$	−19.2713	−	17.0543i	−0.849195	−	0.751501i
$516$		0			0
$517$		−	28.5367i		−	1.25504i
$518$		−	20.3671i		−	0.894877i
$519$		0			0
$520$	77.5961	−	87.6834i	3.40281	−	3.84517i
$521$	−20.4477			−0.895831			−0.447915	−	0.894076i	$-0.647833\pi$
$521$	−20.4477			−0.895831			−0.447915	+	0.894076i	$0.647833\pi$
$522$		0			0
$523$			5.82433i			0.254680i	0.991859	+	0.127340i	$0.0406439\pi$
$523$			5.82433i			0.254680i	−0.991859	+	0.127340i	$0.959356\pi$
$524$	−6.86118			−0.299732
$525$		0			0
$526$	−1.73802			−0.0757815
$527$		−	42.2103i		−	1.83871i
$528$		0			0
$529$	18.1072			0.787269
$530$	5.10612	−	5.76991i	0.221796	−	0.250629i
$531$		0			0
$532$			25.5363i			1.10714i
$533$			48.6812i			2.10862i
$534$		0			0
$535$	−27.6760	−	24.4921i	−1.19654	−	1.05888i
$536$	22.8393			0.986508
$537$		0			0
$538$			58.5395i			2.52382i
$539$	−24.2334			−1.04380
$540$		0			0
$541$	−27.8021			−1.19531			−0.597653	−	0.801755i	$-0.703900\pi$
$541$	−27.8021			−1.19531			−0.597653	+	0.801755i	$0.703900\pi$
$542$		−	14.5322i		−	0.624211i
$543$		0			0
$544$	70.0773			3.00454
$545$	−5.77533	+	6.52611i	−0.247388	+	0.279548i
$546$		0			0
$547$		−	14.9066i		−	0.637360i	−0.947862	−	0.318680i	$-0.896760\pi$
$547$		−	14.9066i		−	0.637360i	0.947862	−	0.318680i	$-0.103240\pi$
$548$		−	29.2534i		−	1.24964i
$549$		0			0
$550$	60.6567	−	7.43166i	2.58641	−	0.316887i
$551$	3.89699			0.166017
$552$		0			0
$553$			1.75773i			0.0747462i
$554$	−33.0891			−1.40582
$555$		0			0
$556$	−25.6579			−1.08814
$557$			10.3968i			0.440529i	0.975440	+	0.220264i	$0.0706920\pi$
$557$			10.3968i			0.440529i	−0.975440	+	0.220264i	$0.929308\pi$
$558$		0			0
$559$	82.1739			3.47558
$560$	22.7438	+	20.1273i	0.961102	+	0.850534i
$561$		0			0
$562$			8.78235i			0.370461i
$563$		−	40.1299i		−	1.69127i	−0.533759	−	0.845636i	$-0.679221\pi$
$563$		−	40.1299i		−	1.69127i	0.533759	−	0.845636i	$-0.320779\pi$
$564$		0			0
$565$	−13.5824	−	12.0199i	−0.571417	−	0.505680i
$566$	−12.7703			−0.536778
$567$		0			0
$568$			45.9045i			1.92611i
$569$	28.0544			1.17610			0.588051	−	0.808824i	$-0.299895\pi$
$569$	28.0544			1.17610			0.588051	+	0.808824i	$0.299895\pi$
$570$		0			0
$571$	−16.5985			−0.694626			−0.347313	−	0.937749i	$-0.612906\pi$
$571$	−16.5985			−0.694626			−0.347313	+	0.937749i	$0.612906\pi$
$572$		−	157.139i		−	6.57032i
$573$		0			0
$574$	−24.8113			−1.03560
$575$	10.9778	−	1.34499i	0.457804	−	0.0560901i
$576$		0			0
$577$			11.9936i			0.499302i	0.968336	+	0.249651i	$0.0803159\pi$
$577$			11.9936i			0.499302i	−0.968336	+	0.249651i	$0.919684\pi$
$578$			53.9818i			2.24535i
$579$		0			0
$580$	7.24733	−	8.18946i	0.300929	−	0.340049i
$581$	−5.62895			−0.233528
$582$		0			0
$583$		−	6.11172i		−	0.253122i
$584$	33.9270			1.40391
$585$		0			0
$586$	−10.8490			−0.448169
$587$			8.58663i			0.354408i	0.984174	+	0.177204i	$0.0567053\pi$
$587$			8.58663i			0.354408i	−0.984174	+	0.177204i	$0.943295\pi$
$588$		0			0
$589$	26.8386			1.10586
$590$	−27.2797	−	24.1414i	−1.12309	−	0.993886i
$591$		0			0
$592$		−	58.7006i		−	2.41258i
$593$			16.1445i			0.662976i	0.943459	+	0.331488i	$0.107551\pi$
$593$			16.1445i			0.662976i	−0.943459	+	0.331488i	$0.892449\pi$
$594$		0			0
$595$	−12.1693	+	13.7513i	−0.498894	+	0.563749i
$596$	−37.9006			−1.55247
$597$		0			0
$598$		−	40.0695i		−	1.63856i
$599$	32.8519			1.34229			0.671146	−	0.741326i	$-0.265803\pi$
$599$	32.8519			1.34229			0.671146	+	0.741326i	$0.265803\pi$
$600$		0			0
$601$	30.9385			1.26201			0.631004	−	0.775780i	$-0.282643\pi$
$601$	30.9385			1.26201			0.631004	+	0.775780i	$0.282643\pi$
$602$			41.8815i			1.70696i
$603$		0			0
$604$	62.4551			2.54126
$605$	15.8243	−	17.8815i	0.643351	−	0.726985i
$606$		0			0
$607$			11.3258i			0.459699i	0.973226	+	0.229849i	$0.0738234\pi$
$607$			11.3258i			0.459699i	−0.973226	+	0.229849i	$0.926177\pi$
$608$			44.5572i			1.80703i
$609$		0			0
$610$	62.5243	+	55.3313i	2.53153	+	2.24030i
$611$	42.2955			1.71109
$612$		0			0
$613$		−	22.7537i		−	0.919015i	−0.888174	−	0.459508i	$-0.848026\pi$
$613$		−	22.7537i		−	0.919015i	0.888174	−	0.459508i	$-0.151974\pi$
$614$	−41.3642			−1.66932
$615$		0			0
$616$	47.3370			1.90726
$617$		−	12.2226i		−	0.492062i	−0.969262	−	0.246031i	$-0.920873\pi$
$617$		−	12.2226i		−	0.492062i	0.969262	−	0.246031i	$-0.0791265\pi$
$618$		0			0
$619$	−15.3131			−0.615486			−0.307743	−	0.951469i	$-0.599574\pi$
$619$	−15.3131			−0.615486			−0.307743	+	0.951469i	$0.599574\pi$
$620$	49.9123	−	56.4008i	2.00453	−	2.26511i
$621$		0			0
$622$			57.8599i			2.31997i
$623$			0.312008i			0.0125004i
$624$		0			0
$625$	−24.2605	+	6.03540i	−0.970422	+	0.241416i
$626$	−25.4335			−1.01653
$627$		0			0
$628$			94.3025i			3.76308i
$629$	35.4914			1.41514
$630$		0			0
$631$	−7.63898			−0.304103			−0.152051	−	0.988373i	$-0.548588\pi$
$631$	−7.63898			−0.304103			−0.152051	+	0.988373i	$0.548588\pi$
$632$			9.95424i			0.395958i
$633$		0			0
$634$	12.1944			0.484302
$635$	−10.1745	−	9.00401i	−0.403763	−	0.357313i
$636$		0			0
$637$		−	35.9173i		−	1.42309i
$638$		−	12.2221i		−	0.483876i
$639$		0			0
$640$	4.51969	+	3.99974i	0.178657	+	0.158103i
$641$	−30.6857			−1.21201			−0.606007	−	0.795459i	$-0.707230\pi$
$641$	−30.6857			−1.21201			−0.606007	+	0.795459i	$0.707230\pi$
$642$		0			0
$643$			22.1507i			0.873539i	0.899574	+	0.436769i	$0.143877\pi$
$643$			22.1507i			0.873539i	−0.899574	+	0.436769i	$0.856123\pi$
$644$	14.4947			0.571169
$645$		0			0
$646$	−62.6971			−2.46679
$647$			33.6116i			1.32141i	0.750647	+	0.660704i	$0.229742\pi$
$647$			33.6116i			1.32141i	−0.750647	+	0.660704i	$0.770258\pi$
$648$		0			0
$649$	−28.8958			−1.13426
$650$	11.0148	+	89.9019i	0.432035	+	3.52624i
$651$		0			0
$652$			36.5329i			1.43074i
$653$		−	23.8816i		−	0.934558i	−0.884110	−	0.467279i	$-0.845234\pi$
$653$		−	23.8816i		−	0.934558i	0.884110	−	0.467279i	$-0.154766\pi$
$654$		0			0
$655$	2.07897	−	2.34923i	0.0812320	−	0.0917920i
$656$	−71.5095			−2.79198
$657$		0			0
$658$			21.5567i			0.840368i
$659$	14.3592			0.559355			0.279678	−	0.960094i	$-0.409772\pi$
$659$	14.3592			0.559355			0.279678	+	0.960094i	$0.409772\pi$
$660$		0			0
$661$	26.0880			1.01471			0.507353	−	0.861738i	$-0.330624\pi$
$661$	26.0880			1.01471			0.507353	+	0.861738i	$0.330624\pi$
$662$			16.7536i			0.651146i
$663$		0			0
$664$	−31.8775			−1.23709
$665$	−8.74350	−	7.73762i	−0.339058	−	0.300052i
$666$		0			0
$667$		−	2.21197i		−	0.0856478i
$668$		−	29.7102i		−	1.14952i
$669$		0			0
$670$	−11.7086	+	13.2307i	−0.452343	+	0.511146i
$671$	66.2283			2.55671
$672$		0			0
$673$		−	21.3205i		−	0.821846i	−0.911670	−	0.410923i	$-0.865207\pi$
$673$		−	21.3205i		−	0.821846i	0.911670	−	0.410923i	$-0.134793\pi$
$674$	22.1798			0.854336
$675$		0			0
$676$	169.325			6.51248
$677$			3.63342i			0.139644i	0.997559	+	0.0698218i	$0.0222431\pi$
$677$			3.63342i			0.139644i	−0.997559	+	0.0698218i	$0.977757\pi$
$678$		0			0
$679$	4.01801			0.154197
$680$	−68.9165	+	77.8755i	−2.64283	+	2.98639i
$681$		0			0
$682$		−	84.1733i		−	3.22316i
$683$		−	39.7305i		−	1.52025i	−0.649779	−	0.760123i	$-0.725139\pi$
$683$		−	39.7305i		−	1.52025i	0.649779	−	0.760123i	$-0.274861\pi$
$684$		0			0
$685$	10.0162	+	8.86392i	0.382700	+	0.338673i
$686$	42.9262			1.63893
$687$		0			0
$688$			120.708i			4.60195i
$689$	9.05844			0.345099
$690$		0			0
$691$	8.88067			0.337837			0.168918	−	0.985630i	$-0.445973\pi$
$691$	8.88067			0.337837			0.168918	+	0.985630i	$0.445973\pi$
$692$		−	111.301i		−	4.23102i
$693$		0			0
$694$	−40.3973			−1.53346
$695$	7.77445	−	8.78511i	0.294902	−	0.333238i
$696$		0			0
$697$		−	43.2360i		−	1.63768i
$698$			4.98567i			0.188710i
$699$		0			0
$700$	−32.5210	+	3.98447i	−1.22918	+	0.150599i
$701$	−45.6880			−1.72561			−0.862806	−	0.505536i	$-0.831295\pi$
$701$	−45.6880			−1.72561			−0.862806	+	0.505536i	$0.831295\pi$
$702$		0			0
$703$			22.5665i			0.851112i
$704$	45.3480			1.70912
$705$		0			0
$706$	−46.9019			−1.76518
$707$		−	20.7311i		−	0.779675i
$708$		0			0
$709$	35.5852			1.33643			0.668215	−	0.743969i	$-0.267059\pi$
$709$	35.5852			1.33643			0.668215	+	0.743969i	$0.267059\pi$
$710$	−26.5922	−	23.5330i	−0.997989	−	0.883178i
$711$		0			0
$712$			1.76694i			0.0662190i
$713$		−	15.2338i		−	0.570511i
$714$		0			0
$715$	53.8036	+	47.6139i	2.01214	+	1.78066i
$716$	−9.15392			−0.342098
$717$		0			0
$718$			65.0751i			2.42858i
$719$	23.1553			0.863545			0.431773	−	0.901983i	$-0.357888\pi$
$719$	23.1553			0.863545			0.431773	+	0.901983i	$0.357888\pi$
$720$		0			0
$721$	15.4200			0.574271
$722$			10.0103i			0.372545i
$723$		0			0
$724$	−92.4391			−3.43547
$725$	0.608053	+	4.96289i	0.0225825	+	0.184317i
$726$		0			0
$727$		−	34.1200i		−	1.26544i	−0.774380	−	0.632720i	$-0.781938\pi$
$727$		−	34.1200i		−	1.26544i	0.774380	−	0.632720i	$-0.218062\pi$
$728$			70.1602i			2.60031i
$729$		0			0
$730$	−17.3927	+	19.6537i	−0.643733	+	0.727417i
$731$	−72.9823			−2.69935
$732$		0			0
$733$			10.3872i			0.383660i	0.981428	+	0.191830i	$0.0614423\pi$
$733$			10.3872i			0.383660i	−0.981428	+	0.191830i	$0.938558\pi$
$734$	−54.0603			−1.99540
$735$		0			0
$736$	25.2911			0.932242
$737$			14.0145i			0.516230i
$738$		0			0
$739$	32.0193			1.17785			0.588925	−	0.808188i	$-0.299551\pi$
$739$	32.0193			1.17785			0.588925	+	0.808188i	$0.299551\pi$
$740$	47.4231	+	41.9674i	1.74331	+	1.54275i
$741$		0			0
$742$			4.61681i			0.169489i
$743$			51.2195i			1.87906i	0.342465	+	0.939531i	$0.388738\pi$
$743$			51.2195i			1.87906i	−0.342465	+	0.939531i	$0.611262\pi$
$744$		0			0
$745$	11.4841	−	12.9770i	0.420743	−	0.475439i
$746$	19.8439			0.726535
$747$		0			0
$748$			139.562i			5.10290i
$749$	22.1450			0.809161
$750$		0			0
$751$	−39.4419			−1.43925			−0.719627	−	0.694361i	$-0.755687\pi$
$751$	−39.4419			−1.43925			−0.719627	+	0.694361i	$0.755687\pi$
$752$			62.1293i			2.26562i
$753$		0			0
$754$	18.1148			0.659703
$755$	−18.9242	+	21.3843i	−0.688721	+	0.778253i
$756$		0			0
$757$		−	50.3776i		−	1.83100i	−0.402313	−	0.915502i	$-0.631794\pi$
$757$		−	50.3776i		−	1.83100i	0.402313	−	0.915502i	$-0.368206\pi$
$758$		−	76.2441i		−	2.76931i
$759$		0			0
$760$	−49.5155	−	43.8192i	−1.79612	−	1.58949i
$761$	46.2866			1.67789			0.838945	−	0.544217i	$-0.183173\pi$
$761$	46.2866			1.67789			0.838945	+	0.544217i	$0.183173\pi$
$762$		0			0
$763$		−	5.22189i		−	0.189045i
$764$	50.8610			1.84009
$765$		0			0
$766$	24.1560			0.872790
$767$		−	42.8277i		−	1.54642i
$768$		0			0
$769$	−53.5564			−1.93129			−0.965647	−	0.259856i	$-0.916325\pi$
$769$	−53.5564			−1.93129			−0.965647	+	0.259856i	$0.916325\pi$
$770$	−24.2674	+	27.4221i	−0.874535	+	0.988222i
$771$		0			0
$772$			26.0381i			0.937133i
$773$		−	7.80587i		−	0.280758i	−0.990098	−	0.140379i	$-0.955168\pi$
$773$		−	7.80587i		−	0.280758i	0.990098	−	0.140379i	$-0.0448320\pi$
$774$		0			0
$775$	4.18766	+	34.1794i	0.150425	+	1.22776i
$776$	22.7545			0.816838
$777$		0			0
$778$		−	33.5186i		−	1.20170i
$779$	27.4907			0.984956
$780$		0			0
$781$	−28.1676			−1.00792
$782$			35.5875i			1.27261i
$783$		0			0
$784$	52.7602			1.88429
$785$	−32.2886	−	28.5741i	−1.15243	−	1.01985i
$786$		0			0
$787$			31.5089i			1.12317i	0.827419	+	0.561585i	$0.189808\pi$
$787$			31.5089i			1.12317i	−0.827419	+	0.561585i	$0.810192\pi$
$788$		−	65.2845i		−	2.32567i
$789$		0			0
$790$	−5.76644	−	5.10305i	−0.205161	−	0.181558i
$791$	10.8680			0.386423
$792$		0			0
$793$			98.1597i			3.48575i
$794$	63.7057			2.26083
$795$		0			0
$796$	100.945			3.57788
$797$			25.6334i			0.907983i	0.891006	+	0.453992i	$0.150000\pi$
$797$			25.6334i			0.907983i	−0.891006	+	0.453992i	$0.850000\pi$
$798$		0			0
$799$	−37.5645			−1.32894
$800$	−56.7444	+	6.95232i	−2.00622	+	0.245802i
$801$		0			0
$802$		−	9.20509i		−	0.325043i
$803$			20.8180i			0.734652i
$804$		0			0
$805$	−4.39195	+	4.96289i	−0.154796	+	0.174919i
$806$	124.757			4.39437
$807$		0			0
$808$		−	117.403i		−	4.13023i
$809$	24.1633			0.849535			0.424767	−	0.905303i	$-0.360356\pi$
$809$	24.1633			0.849535			0.424767	+	0.905303i	$0.360356\pi$
$810$		0			0
$811$	56.1745			1.97255			0.986277	−	0.165099i	$-0.0527944\pi$
$811$	56.1745			1.97255			0.986277	+	0.165099i	$0.0527944\pi$
$812$			6.55283i			0.229959i
$813$		0			0
$814$	70.7749			2.48066
$815$	−12.5087	−	11.0696i	−0.438160	−	0.387753i
$816$		0			0
$817$		−	46.4043i		−	1.62348i
$818$			39.5985i			1.38453i
$819$		0			0
$820$	51.1251	−	57.7712i	1.78537	−	2.01746i
$821$	29.0885			1.01520			0.507598	−	0.861594i	$-0.330533\pi$
$821$	29.0885			1.01520			0.507598	+	0.861594i	$0.330533\pi$
$822$		0			0
$823$			46.8596i			1.63342i	0.577047	+	0.816711i	$0.304205\pi$
$823$			46.8596i			1.63342i	−0.577047	+	0.816711i	$0.695795\pi$
$824$	87.3254			3.04213
$825$		0			0
$826$	21.8280			0.759492
$827$		−	21.6577i		−	0.753113i	−0.926394	−	0.376556i	$-0.877108\pi$
$827$		−	21.6577i		−	0.753113i	0.926394	−	0.376556i	$-0.122892\pi$
$828$		0			0
$829$	−20.1844			−0.701035			−0.350517	−	0.936556i	$-0.613994\pi$
$829$	−20.1844			−0.701035			−0.350517	+	0.936556i	$0.613994\pi$
$830$	16.3420	−	18.4665i	0.567240	−	0.640980i
$831$		0			0
$832$			67.2122i			2.33016i
$833$			31.8997i			1.10526i
$834$		0			0
$835$	10.1726	+	9.00233i	0.352038	+	0.311539i
$836$	−88.7379			−3.06906
$837$		0			0
$838$		−	92.3277i		−	3.18941i
$839$	25.5393			0.881716			0.440858	−	0.897577i	$-0.354674\pi$
$839$	25.5393			0.881716			0.440858	+	0.897577i	$0.354674\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		−	64.1522i		−	2.21083i
$843$		0			0
$844$	54.0616			1.86088
$845$	−51.3061	+	57.9758i	−1.76498	+	1.99443i
$846$		0			0
$847$			14.3079i			0.491626i
$848$			13.3063i			0.456939i
$849$		0			0
$850$	−9.78272	−	79.8459i	−0.335544	−	2.73869i
$851$	12.8090			0.439085
$852$		0			0
$853$			26.9472i			0.922655i	0.887230	+	0.461328i	$0.152627\pi$
$853$			26.9472i			0.922655i	−0.887230	+	0.461328i	$0.847373\pi$
$854$	−50.0290			−1.71196
$855$		0			0
$856$	125.410			4.28643
$857$			18.9777i			0.648267i	0.946011	+	0.324134i	$0.105073\pi$
$857$			18.9777i			0.648267i	−0.946011	+	0.324134i	$0.894927\pi$
$858$		0			0
$859$	−34.1724			−1.16595			−0.582973	−	0.812491i	$-0.698111\pi$
$859$	−34.1724			−1.16595			−0.582973	+	0.812491i	$0.698111\pi$
$860$	−97.5178	−	86.2992i	−3.32533	−	2.94278i
$861$		0			0
$862$			99.8511i			3.40094i
$863$			17.6589i			0.601117i	0.953763	+	0.300558i	$0.0971730\pi$
$863$			17.6589i			0.601117i	−0.953763	+	0.300558i	$0.902827\pi$
$864$		0			0
$865$	38.1088	+	33.7246i	1.29574	+	1.14667i
$866$	−50.8271			−1.72718
$867$		0			0
$868$			45.1293i			1.53179i
$869$	−6.10804			−0.207201
$870$		0			0
$871$	−20.7715			−0.703814
$872$		−	29.5723i		−	1.00144i
$873$		0			0
$874$	−22.6276			−0.765389
$875$	8.48974	−	12.3423i	0.287006	−	0.417246i
$876$		0			0
$877$		−	13.4119i		−	0.452888i	−0.974024	−	0.226444i	$-0.927290\pi$
$877$		−	13.4119i		−	0.452888i	0.974024	−	0.226444i	$-0.0727100\pi$
$878$			30.0820i			1.01522i
$879$		0			0
$880$	−69.9417	+	79.0340i	−2.35774	+	2.66423i
$881$	−19.3105			−0.650588			−0.325294	−	0.945613i	$-0.605463\pi$
$881$	−19.3105			−0.650588			−0.325294	+	0.945613i	$0.605463\pi$
$882$		0			0
$883$		−	7.59663i		−	0.255647i	−0.991797	−	0.127823i	$-0.959201\pi$
$883$		−	7.59663i		−	0.255647i	0.991797	−	0.127823i	$-0.0407991\pi$
$884$	−206.851			−6.95716
$885$		0			0
$886$	−38.0014			−1.27668
$887$			37.4220i			1.25651i	0.778009	+	0.628253i	$0.216230\pi$
$887$			37.4220i			1.25651i	−0.778009	+	0.628253i	$0.783770\pi$
$888$		0			0
$889$	8.14117			0.273046
$890$	−1.02358	−	0.905826i	−0.0343105	−	0.0303633i
$891$		0			0
$892$		−	114.683i		−	3.83987i
$893$		−	23.8846i		−	0.799268i
$894$		0			0
$895$	2.77368	−	3.13425i	0.0927139	−	0.104766i
$896$	−3.61645			−0.120817
$897$		0			0
$898$		−	35.3179i		−	1.17857i
$899$	6.88700			0.229694
$900$		0			0
$901$	−8.04521			−0.268025
$902$		−	86.2185i		−	2.87076i
$903$		0			0
$904$	61.5471			2.04703
$905$	28.0095	−	31.6507i	0.931067	−	1.05210i
$906$		0			0
$907$			27.9154i			0.926916i	0.886119	+	0.463458i	$0.153392\pi$
$907$			27.9154i			0.926916i	−0.886119	+	0.463458i	$0.846608\pi$
$908$			22.8041i			0.756781i
$909$		0			0
$910$	−40.6434	−	35.9677i	−1.34732	−	1.19232i
$911$	−2.76946			−0.0917562			−0.0458781	−	0.998947i	$-0.514609\pi$
$911$	−2.76946			−0.0917562			−0.0458781	+	0.998947i	$0.514609\pi$
$912$		0			0
$913$		−	19.5604i		−	0.647355i
$914$	−22.0780			−0.730276
$915$		0			0
$916$	−47.8272			−1.58025
$917$			1.87974i			0.0620746i
$918$		0			0
$919$	−24.9275			−0.822283			−0.411141	−	0.911572i	$-0.634870\pi$
$919$	−24.9275			−0.822283			−0.411141	+	0.911572i	$0.634870\pi$
$920$	−24.8722	+	28.1055i	−0.820011	+	0.926610i
$921$		0			0
$922$		−	62.1719i		−	2.04752i
$923$		−	41.7484i		−	1.37416i
$924$		0			0
$925$	−28.7388	+	3.52108i	−0.944927	+	0.115772i
$926$	−21.3319			−0.701010
$927$		0			0
$928$			11.4337i			0.375331i
$929$	−45.2284			−1.48389			−0.741947	−	0.670458i	$-0.766097\pi$
$929$	−45.2284			−1.48389			−0.741947	+	0.670458i	$0.766097\pi$
$930$		0			0
$931$	−20.2828			−0.664742
$932$			45.9310i			1.50452i
$933$		0			0
$934$	−18.4459			−0.603569
$935$	−47.7854	−	42.2880i	−1.56275	−	1.38297i
$936$		0			0
$937$		−	39.2167i		−	1.28115i	−0.767895	−	0.640576i	$-0.778696\pi$
$937$		−	39.2167i		−	1.28115i	0.767895	−	0.640576i	$-0.221304\pi$
$938$		−	10.5866i		−	0.345664i
$939$		0			0
$940$	−50.1931	−	44.4188i	−1.63712	−	1.44878i
$941$	−8.43823			−0.275078			−0.137539	−	0.990496i	$-0.543919\pi$
$941$	−8.43823			−0.275078			−0.137539	+	0.990496i	$0.543919\pi$
$942$		0			0
$943$		−	15.6040i		−	0.508135i
$944$	62.9111			2.04758
$945$		0			0
$946$	−145.537			−4.73181
$947$			20.8288i			0.676844i	0.940994	+	0.338422i	$0.109893\pi$
$947$			20.8288i			0.676844i	−0.940994	+	0.338422i	$0.890107\pi$
$948$		0			0
$949$	−30.8553			−1.00160
$950$	50.7684	−	6.22014i	1.64714	−	0.201808i
$951$		0			0
$952$		−	62.3124i		−	2.01956i
$953$			59.9085i			1.94063i	0.241850	+	0.970314i	$0.422246\pi$
$953$			59.9085i			1.94063i	−0.241850	+	0.970314i	$0.577754\pi$
$954$		0			0
$955$	−15.4111	+	17.4145i	−0.498692	+	0.563521i
$956$	112.281			3.63144
$957$		0			0
$958$		−	72.9731i		−	2.35765i
$959$	−8.01451			−0.258802
$960$		0			0
$961$	16.4307			0.530024
$962$			104.898i			3.38206i
$963$		0			0
$964$	−5.11678			−0.164800
$965$	−8.91531	−	7.88968i	−0.286994	−	0.253978i
$966$		0			0
$967$		−	35.8015i		−	1.15130i	−0.817696	−	0.575650i	$-0.804749\pi$
$967$		−	35.8015i		−	1.15130i	0.817696	−	0.575650i	$-0.195251\pi$
$968$			81.0276i			2.60433i
$969$		0			0
$970$	−11.6651	+	13.1815i	−0.374544	+	0.423234i
$971$	−45.0783			−1.44663			−0.723316	−	0.690517i	$-0.757383\pi$
$971$	−45.0783			−1.44663			−0.723316	+	0.690517i	$0.757383\pi$
$972$		0			0
$973$			7.02944i			0.225353i
$974$	17.7471			0.568655
$975$		0			0
$976$	−144.190			−4.61542
$977$			32.5779i			1.04226i	0.853478	+	0.521129i	$0.174489\pi$
$977$			32.5779i			1.04226i	−0.853478	+	0.521129i	$0.825511\pi$
$978$		0			0
$979$	−1.08422			−0.0346518
$980$	−37.7204	+	42.6240i	−1.20493	+	1.36157i
$981$		0			0
$982$		−	61.1915i		−	1.95270i
$983$			36.0502i			1.14982i	0.818215	+	0.574912i	$0.194964\pi$
$983$			36.0502i			1.14982i	−0.818215	+	0.574912i	$0.805036\pi$
$984$		0			0
$985$	22.3531	+	19.7815i	0.712228	+	0.630292i
$986$	−16.0886			−0.512365
$987$		0			0
$988$		−	131.522i		−	4.18428i
$989$	−26.3395			−0.837548
$990$		0			0
$991$	−49.5150			−1.57289			−0.786447	−	0.617657i	$-0.788082\pi$
$991$	−49.5150			−1.57289			−0.786447	+	0.617657i	$0.788082\pi$
$992$			78.7441i			2.50013i
$993$		0			0
$994$	21.2779			0.674893
$995$	−30.5867	+	34.5629i	−0.969662	+	1.09572i
$996$		0			0
$997$			23.3377i			0.739112i	0.929209	+	0.369556i	$0.120490\pi$
$997$			23.3377i			0.739112i	−0.929209	+	0.369556i	$0.879510\pi$
$998$		−	33.4385i		−	1.05848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.k.784.1	✓	12
3.2	odd	2		1305.2.c.l.784.12	yes	12
5.2	odd	4		6525.2.a.ce.1.12		12
5.3	odd	4		6525.2.a.ce.1.1		12
5.4	even	2	inner	1305.2.c.k.784.12	yes	12
15.2	even	4		6525.2.a.cf.1.1		12
15.8	even	4		6525.2.a.cf.1.12		12
15.14	odd	2		1305.2.c.l.784.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.c.k.784.1	✓	12	1.1	even	1	trivial
1305.2.c.k.784.12	yes	12	5.4	even	2	inner
1305.2.c.l.784.1	yes	12	15.14	odd	2
1305.2.c.l.784.12	yes	12	3.2	odd	2
6525.2.a.ce.1.1		12	5.3	odd	4
6525.2.a.ce.1.12		12	5.2	odd	4
6525.2.a.cf.1.1		12	15.2	even	4
6525.2.a.cf.1.12		12	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.62500i q^{2} -4.89062 q^{4} +(1.48188 - 1.67452i) q^{5} +1.33988i q^{7} +7.58789i q^{8} +(-4.39562 - 3.88994i) q^{10} -4.65602 q^{11} -6.90089i q^{13} +3.51717 q^{14} +10.1370 q^{16} +6.12899i q^{17} -3.89699 q^{19} +(-7.24733 + 8.18946i) q^{20} +12.2221i q^{22} +2.21197i q^{23} +(-0.608053 - 4.96289i) q^{25} -18.1148 q^{26} -6.55283i q^{28} -1.00000 q^{29} -6.88700 q^{31} -11.4337i q^{32} +16.0886 q^{34} +(2.24365 + 1.98554i) q^{35} -5.79075i q^{37} +10.2296i q^{38} +(12.7061 + 11.2444i) q^{40} -7.05434 q^{41} +11.9077i q^{43} +22.7709 q^{44} +5.80642 q^{46} +6.12899i q^{47} +5.20473 q^{49} +(-13.0276 + 1.59614i) q^{50} +33.7497i q^{52} +1.31265i q^{53} +(-6.89968 + 7.79662i) q^{55} -10.1668 q^{56} +2.62500i q^{58} +6.20611 q^{59} -14.2242 q^{61} +18.0784i q^{62} -9.73965 q^{64} +(-11.5557 - 10.2263i) q^{65} -3.00997i q^{67} -29.9746i q^{68} +(5.21204 - 5.88959i) q^{70} +6.04971 q^{71} -4.47120i q^{73} -15.2007 q^{74} +19.0587 q^{76} -6.23849i q^{77} +1.31186 q^{79} +(15.0218 - 16.9746i) q^{80} +18.5176i q^{82} +4.20110i q^{83} +(10.2631 + 9.08244i) q^{85} +31.2578 q^{86} -35.3294i q^{88} +0.232864 q^{89} +9.24634 q^{91} -10.8179i q^{92} +16.0886 q^{94} +(-5.77488 + 6.52560i) q^{95} -2.99879i q^{97} -13.6624i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) \) 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

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