LMFDB - Embedded newform 1305.2.c.l.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.l.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	$-0.918513\pi$
$7$		−	1.33988i		−	0.506425i	0.967411	−	0.253213i	$-0.0814873\pi$
$8$			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	$-0.252326\pi$
$11$	4.65602			1.40384			0.701922	+	0.712254i	$0.252326\pi$
$12$		0			0
$13$			6.90089i			1.91396i	0.290150	+	0.956981i	$0.406295\pi$
$13$			6.90089i			1.91396i	−0.290150	+	0.956981i	$0.593705\pi$
$14$	−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	$0.157912\pi$
$37$			5.79075i			0.951993i	−0.879447	+	0.475996i	$0.842088\pi$
$38$			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	$-0.314303\pi$
$41$	7.05434			1.10170			0.550851	+	0.834603i	$0.314303\pi$
$42$		0			0
$43$		−	11.9077i		−	1.81591i	−0.419067	−	0.907955i	$-0.637643\pi$
$43$		−	11.9077i		−	1.81591i	0.419067	−	0.907955i	$-0.362357\pi$
$44$	−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	$-0.632375\pi$
$59$	−6.20611			−0.807967			−0.403983	+	0.914766i	$0.632375\pi$
$60$		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	$0.0588603\pi$
$67$			3.00997i			0.367726i	−0.982952	+	0.183863i	$0.941140\pi$
$68$		−	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	$-0.616877\pi$
$71$	−6.04971			−0.717968			−0.358984	+	0.933344i	$0.616877\pi$
$72$		0			0
$73$			4.47120i			0.523315i	0.965161	+	0.261657i	$0.0842690\pi$
$73$			4.47120i			0.523315i	−0.965161	+	0.261657i	$0.915731\pi$
$74$	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	$-0.503929\pi$
$89$	−0.232864			−0.0246835			−0.0123418	+	0.999924i	$0.503929\pi$
$90$		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	$0.0486488\pi$
$97$			2.99879i			0.304481i	−0.988343	+	0.152240i	$0.951351\pi$
$98$		−	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	$-0.220365\pi$
$101$	15.4724			1.53956			0.769782	+	0.638306i	$0.220365\pi$
$102$		0			0
$103$			11.5085i			1.13397i	0.823728	+	0.566985i	$0.191890\pi$
$103$			11.5085i			1.13397i	−0.823728	+	0.566985i	$0.808110\pi$
$104$	−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	$0.0868854\pi$
$127$			6.07606i			0.539163i	−0.962978	+	0.269582i	$0.913115\pi$
$128$			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	$-0.519521\pi$
$131$	−1.40292			−0.122574			−0.0612870	+	0.998120i	$0.519521\pi$
$132$		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	$-0.602822\pi$
$149$	−7.74964			−0.634875			−0.317438	+	0.948279i	$0.602822\pi$
$150$		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	$0.279468\pi$
$157$			19.2823i			1.53889i	−0.638710	+	0.769447i	$0.720532\pi$
$158$		−	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	$0.0945030\pi$
$163$			7.46999i			0.585095i	−0.956251	+	0.292547i	$0.905497\pi$
$164$	−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	$-0.522284\pi$
$179$	−1.87173			−0.139900			−0.0699498	+	0.997551i	$0.522284\pi$
$180$		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	$-0.377214\pi$
$191$	10.3997			0.752495			0.376248	+	0.926519i	$0.377214\pi$
$192$		0			0
$193$			5.32409i			0.383237i	0.981470	+	0.191618i	$0.0613736\pi$
$193$			5.32409i			0.383237i	−0.981470	+	0.191618i	$0.938626\pi$
$194$	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	$-0.712587\pi$
$223$		−	23.4495i		−	1.57030i	0.619307	−	0.785149i	$-0.287413\pi$
$224$	−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	$-0.233626\pi$
$239$	22.9585			1.48506			0.742530	+	0.669813i	$0.233626\pi$
$240$		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	$-0.489141\pi$
$251$	1.08079			0.0682188			0.0341094	+	0.999418i	$0.489141\pi$
$252$		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	$-0.262044\pi$
$269$	22.3008			1.35970			0.679851	+	0.733350i	$0.262044\pi$
$270$		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	$0.123626\pi$
$277$			12.6054i			0.757383i	−0.925523	+	0.378692i	$0.876374\pi$
$278$		−	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	$-0.468182\pi$
$281$	3.34566			0.199585			0.0997926	+	0.995008i	$0.468182\pi$
$282$		0			0
$283$			4.86489i			0.289188i	0.989491	+	0.144594i	$0.0461876\pi$
$283$			4.86489i			0.289188i	−0.989491	+	0.144594i	$0.953812\pi$
$284$	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	$0.148459\pi$
$307$			15.7578i			0.899344i	−0.893194	+	0.449672i	$0.851541\pi$
$308$			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	$-0.285123\pi$
$311$	22.0419			1.24988			0.624940	+	0.780673i	$0.285123\pi$
$312$		0			0
$313$			9.68896i			0.547653i	0.961779	+	0.273826i	$0.0882893\pi$
$313$			9.68896i			0.547653i	−0.961779	+	0.273826i	$0.911711\pi$
$314$	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	$-0.926083\pi$
$337$		−	8.44947i		−	0.460272i	0.973159	−	0.230136i	$-0.0739171\pi$
$338$			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	$-0.273007\pi$
$359$	24.7905			1.30839			0.654197	+	0.756324i	$0.273007\pi$
$360$		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	$0.180635\pi$
$367$			20.5944i			1.07502i	−0.843258	+	0.537509i	$0.819365\pi$
$368$			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	$-0.937299\pi$
$373$		−	7.55956i		−	0.391419i	0.980662	−	0.195710i	$-0.0627010\pi$
$374$	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	$-0.604929\pi$
$389$	−12.7690			−0.647414			−0.323707	+	0.946157i	$0.604929\pi$
$390$		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	$-0.791567\pi$
$397$		−	24.2689i		−	1.21802i	0.793163	−	0.609009i	$-0.208433\pi$
$398$			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	$-0.527906\pi$
$401$	−3.50670			−0.175116			−0.0875581	+	0.996159i	$0.527906\pi$
$402$		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	$-0.829003\pi$
$419$	−35.1725			−1.71829			−0.859144	+	0.511734i	$0.829003\pi$
$420$		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	$-0.131300\pi$
$431$	38.0385			1.83225			0.916125	+	0.400892i	$0.131300\pi$
$432$		0			0
$433$			19.3627i			0.930513i	0.885176	+	0.465256i	$0.154038\pi$
$433$			19.3627i			0.930513i	−0.885176	+	0.465256i	$0.845962\pi$
$434$	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	$-0.602836\pi$
$449$	−13.4544			−0.634955			−0.317477	+	0.948266i	$0.602836\pi$
$450$		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	$0.0630282\pi$
$457$			8.41068i			0.393435i	−0.980460	+	0.196717i	$0.936972\pi$
$458$		−	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	$-0.685963\pi$
$461$	−23.6845			−1.10310			−0.551549	+	0.834142i	$0.685963\pi$
$462$		0			0
$463$			8.12644i			0.377668i	0.982009	+	0.188834i	$0.0604707\pi$
$463$			8.12644i			0.377668i	−0.982009	+	0.188834i	$0.939529\pi$
$464$	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	$-0.719037\pi$
$479$	−27.7993			−1.27018			−0.635090	+	0.772438i	$0.719037\pi$
$480$		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	$-0.951048\pi$
$487$		−	6.76082i		−	0.306362i	0.988198	−	0.153181i	$-0.0489517\pi$
$488$		−	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	$-0.676311\pi$
$491$	−23.3110			−1.05201			−0.526006	+	0.850481i	$0.676311\pi$
$492$		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	$-0.357401\pi$
$509$	19.5447			0.866305			0.433152	+	0.901321i	$0.357401\pi$
$510$		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	$-0.352167\pi$
$521$	20.4477			0.895831			0.447915	+	0.894076i	$0.352167\pi$
$522$		0			0
$523$		−	5.82433i		−	0.254680i	−0.991859	−	0.127340i	$-0.959356\pi$
$523$		−	5.82433i		−	0.254680i	0.991859	−	0.127340i	$-0.0406439\pi$
$524$	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	$0.103240\pi$
$547$			14.9066i			0.637360i	−0.947862	+	0.318680i	$0.896760\pi$
$548$		−	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	$-0.700105\pi$
$569$	−28.0544			−1.17610			−0.588051	+	0.808824i	$0.700105\pi$
$570$		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	$-0.919684\pi$
$577$		−	11.9936i		−	0.499302i	0.968336	−	0.249651i	$-0.0803159\pi$
$578$			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	$-0.734197\pi$
$599$	−32.8519			−1.34229			−0.671146	+	0.741326i	$0.734197\pi$
$600$		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	$-0.926177\pi$
$607$		−	11.3258i		−	0.459699i	0.973226	−	0.229849i	$-0.0738234\pi$
$608$			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	$0.151974\pi$
$613$			22.7537i			0.919015i	−0.888174	+	0.459508i	$0.848026\pi$
$614$	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	$-0.292770\pi$
$641$	30.6857			1.21201			0.606007	+	0.795459i	$0.292770\pi$
$642$		0			0
$643$		−	22.1507i		−	0.873539i	−0.899574	−	0.436769i	$-0.856123\pi$
$643$		−	22.1507i		−	0.873539i	0.899574	−	0.436769i	$-0.143877\pi$
$644$	−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	$-0.590228\pi$
$659$	−14.3592			−0.559355			−0.279678	+	0.960094i	$0.590228\pi$
$660$		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	$0.134793\pi$
$673$			21.3205i			0.821846i	−0.911670	+	0.410923i	$0.865207\pi$
$674$	−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	$-0.168705\pi$
$701$	45.6880			1.72561			0.862806	+	0.505536i	$0.168705\pi$
$702$		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	$-0.642112\pi$
$719$	−23.1553			−0.863545			−0.431773	+	0.901983i	$0.642112\pi$
$720$		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	$0.218062\pi$
$727$			34.1200i			1.26544i	−0.774380	+	0.632720i	$0.781938\pi$
$728$			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	$-0.938558\pi$
$733$		−	10.3872i		−	0.383660i	0.981428	−	0.191830i	$-0.0614423\pi$
$734$	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	$0.368206\pi$
$757$			50.3776i			1.83100i	−0.402313	+	0.915502i	$0.631794\pi$
$758$		−	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	$-0.816827\pi$
$761$	−46.2866			−1.67789			−0.838945	+	0.544217i	$0.816827\pi$
$762$		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	$-0.810192\pi$
$787$		−	31.5089i		−	1.12317i	0.827419	−	0.561585i	$-0.189808\pi$
$788$		−	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	$-0.639644\pi$
$809$	−24.1633			−0.849535			−0.424767	+	0.905303i	$0.639644\pi$
$810$		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	$-0.669467\pi$
$821$	−29.0885			−1.01520			−0.507598	+	0.861594i	$0.669467\pi$
$822$		0			0
$823$		−	46.8596i		−	1.63342i	−0.577047	−	0.816711i	$-0.695795\pi$
$823$		−	46.8596i		−	1.63342i	0.577047	−	0.816711i	$-0.304205\pi$
$824$	−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	$-0.645326\pi$
$839$	−25.5393			−0.881716			−0.440858	+	0.897577i	$0.645326\pi$
$840$		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	$-0.847373\pi$
$853$		−	26.9472i		−	0.922655i	0.887230	−	0.461328i	$-0.152627\pi$
$854$	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	$0.0727100\pi$
$877$			13.4119i			0.452888i	−0.974024	+	0.226444i	$0.927290\pi$
$878$			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	$-0.394537\pi$
$881$	19.3105			0.650588			0.325294	+	0.945613i	$0.394537\pi$
$882$		0			0
$883$			7.59663i			0.255647i	0.991797	+	0.127823i	$0.0407991\pi$
$883$			7.59663i			0.255647i	−0.991797	+	0.127823i	$0.959201\pi$
$884$	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	$-0.846608\pi$
$907$		−	27.9154i		−	0.926916i	0.886119	−	0.463458i	$-0.153392\pi$
$908$			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	$-0.485391\pi$
$911$	2.76946			0.0917562			0.0458781	+	0.998947i	$0.485391\pi$
$912$		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	$-0.233903\pi$
$929$	45.2284			1.48389			0.741947	+	0.670458i	$0.233903\pi$
$930$		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	$0.221304\pi$
$937$			39.2167i			1.28115i	−0.767895	+	0.640576i	$0.778696\pi$
$938$		−	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	$-0.456081\pi$
$941$	8.43823			0.275078			0.137539	+	0.990496i	$0.456081\pi$
$942$		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	$0.195251\pi$
$967$			35.8015i			1.15130i	−0.817696	+	0.575650i	$0.804749\pi$
$968$			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	$-0.242617\pi$
$971$	45.0783			1.44663			0.723316	+	0.690517i	$0.242617\pi$
$972$		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	$-0.879510\pi$
$997$		−	23.3377i		−	0.739112i	0.929209	−	0.369556i	$-0.120490\pi$
$998$		−	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.l.784.1	yes	12
3.2	odd	2		1305.2.c.k.784.12	yes	12
5.2	odd	4		6525.2.a.cf.1.12		12
5.3	odd	4		6525.2.a.cf.1.1		12
5.4	even	2	inner	1305.2.c.l.784.12	yes	12
15.2	even	4		6525.2.a.ce.1.1		12
15.8	even	4		6525.2.a.ce.1.12		12
15.14	odd	2		1305.2.c.k.784.1	✓	12

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