LMFDB - Embedded newform 1665.2.g.e.739.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1665,2,Mod(739,1665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1665, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1665.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1665 = 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1665.g (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:	$13.2950919365$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 555)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.27
Character	$\chi$	$=$	1665.739
Dual form			1665.2.g.e.739.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39280 q^{2} -0.0601015 q^{4} +(-2.20287 + 0.383884i) q^{5} +0.344118i q^{7} -2.86931 q^{8} +O(q^{10})$	\(q+1.39280 q^{2} -0.0601015 q^{4} +(-2.20287 + 0.383884i) q^{5} +0.344118i q^{7} -2.86931 q^{8} +(-3.06816 + 0.534675i) q^{10} +1.00065 q^{11} +4.37110 q^{13} +0.479288i q^{14} -3.87618 q^{16} +0.428787 q^{17} -5.70197i q^{19} +(0.132396 - 0.0230720i) q^{20} +1.39371 q^{22} -2.35097 q^{23} +(4.70527 - 1.69129i) q^{25} +6.08808 q^{26} -0.0206820i q^{28} -7.62547i q^{29} -4.55060i q^{31} +0.339869 q^{32} +0.597215 q^{34} +(-0.132101 - 0.758047i) q^{35} +(1.95109 + 5.76136i) q^{37} -7.94172i q^{38} +(6.32072 - 1.10148i) q^{40} -2.50995 q^{41} +8.58272 q^{43} -0.0601408 q^{44} -3.27443 q^{46} -7.01935i q^{47} +6.88158 q^{49} +(6.55351 - 2.35564i) q^{50} -0.262710 q^{52} -7.41870i q^{53} +(-2.20431 + 0.384136i) q^{55} -0.987382i q^{56} -10.6208i q^{58} -3.94753i q^{59} +2.18574i q^{61} -6.33808i q^{62} +8.22574 q^{64} +(-9.62897 + 1.67800i) q^{65} -10.2635i q^{67} -0.0257707 q^{68} +(-0.183991 - 1.05581i) q^{70} -1.92267 q^{71} +9.22636i q^{73} +(2.71748 + 8.02444i) q^{74} +0.342697i q^{76} +0.344343i q^{77} -14.3679i q^{79} +(8.53873 - 1.48801i) q^{80} -3.49587 q^{82} +0.402746i q^{83} +(-0.944561 + 0.164604i) q^{85} +11.9540 q^{86} -2.87119 q^{88} -7.34498i q^{89} +1.50417i q^{91} +0.141297 q^{92} -9.77657i q^{94} +(2.18890 + 12.5607i) q^{95} -9.66376 q^{97} +9.58469 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4}+O(q^{10}) $ 40 * q + 44 * q^4	$ 40 q + 44 q^{4} + 4 q^{10} - 8 q^{11} + 52 q^{16} + 8 q^{25} + 16 q^{26} - 32 q^{34} - 28 q^{40} - 8 q^{41} - 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} + 48 q^{65} - 56 q^{70} - 24 q^{71} + 68 q^{74} - 64 q^{85} - 80 q^{86} - 32 q^{95}+O(q^{100}) $ 40 * q + 44 * q^4 + 4 * q^10 - 8 * q^11 + 52 * q^16 + 8 * q^25 + 16 * q^26 - 32 * q^34 - 28 * q^40 - 8 * q^41 - 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 + 48 * q^65 - 56 * q^70 - 24 * q^71 + 68 * q^74 - 64 * q^85 - 80 * q^86 - 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1665\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.39280			0.984860			0.492430	−	0.870352i	$-0.336109\pi$
$2$	1.39280			0.984860			0.492430	+	0.870352i	$0.336109\pi$
$3$		0			0
$3$		0			0
$4$	−0.0601015			−0.0300507
$5$	−2.20287	+	0.383884i	−0.985153	+	0.171678i
$5$	−2.20287	+	0.383884i	−0.985153	+	0.171678i
$6$		0			0
$7$			0.344118i			0.130064i	0.997883	+	0.0650322i	$0.0207150\pi$
$7$			0.344118i			0.130064i	−0.997883	+	0.0650322i	$0.979285\pi$
$8$	−2.86931			−1.01446
$9$		0			0
$10$	−3.06816	+	0.534675i	−0.970238	+	0.169079i
$11$	1.00065			0.301709			0.150854	−	0.988556i	$-0.451798\pi$
$11$	1.00065			0.301709			0.150854	+	0.988556i	$0.451798\pi$
$12$		0			0
$13$	4.37110			1.21233			0.606163	−	0.795340i	$-0.292708\pi$
$13$	4.37110			1.21233			0.606163	+	0.795340i	$0.292708\pi$
$14$			0.479288i			0.128095i
$15$		0			0
$16$	−3.87618			−0.969046
$17$	0.428787			0.103996			0.0519980	−	0.998647i	$-0.483441\pi$
$17$	0.428787			0.103996			0.0519980	+	0.998647i	$0.483441\pi$
$18$		0			0
$19$		−	5.70197i		−	1.30812i	−0.756442	−	0.654061i	$-0.773064\pi$
$19$		−	5.70197i		−	1.30812i	0.756442	−	0.654061i	$-0.226936\pi$
$20$	0.132396	−	0.0230720i	0.0296046	−	0.00515906i
$21$		0			0
$22$	1.39371			0.297141
$23$	−2.35097			−0.490211			−0.245105	−	0.969496i	$-0.578823\pi$
$23$	−2.35097			−0.490211			−0.245105	+	0.969496i	$0.578823\pi$
$24$		0			0
$25$	4.70527	−	1.69129i	0.941053	−	0.338259i
$26$	6.08808			1.19397
$27$		0			0
$28$		−	0.0206820i		−	0.00390853i
$29$		−	7.62547i		−	1.41601i	−0.706206	−	0.708007i	$-0.749595\pi$
$29$		−	7.62547i		−	1.41601i	0.706206	−	0.708007i	$-0.250405\pi$
$30$		0			0
$31$		−	4.55060i		−	0.817311i	−0.912689	−	0.408656i	$-0.865998\pi$
$31$		−	4.55060i		−	0.817311i	0.912689	−	0.408656i	$-0.134002\pi$
$32$	0.339869			0.0600809
$33$		0			0
$34$	0.597215			0.102422
$35$	−0.132101	−	0.758047i	−0.0223292	−	0.128133i
$36$		0			0
$37$	1.95109	+	5.76136i	0.320757	+	0.947162i
$37$	1.95109	+	5.76136i	0.320757	+	0.947162i
$38$		−	7.94172i		−	1.28832i
$39$		0			0
$40$	6.32072	−	1.10148i	0.999394	−	0.174160i
$41$	−2.50995			−0.391988			−0.195994	−	0.980605i	$-0.562793\pi$
$41$	−2.50995			−0.391988			−0.195994	+	0.980605i	$0.562793\pi$
$42$		0			0
$43$	8.58272			1.30885			0.654426	−	0.756126i	$-0.272910\pi$
$43$	8.58272			1.30885			0.654426	+	0.756126i	$0.272910\pi$
$44$	−0.0601408			−0.00906657
$45$		0			0
$46$	−3.27443			−0.482789
$47$		−	7.01935i		−	1.02388i	−0.859022	−	0.511939i	$-0.828928\pi$
$47$		−	7.01935i		−	1.02388i	0.859022	−	0.511939i	$-0.171072\pi$
$48$		0			0
$49$	6.88158			0.983083
$50$	6.55351	−	2.35564i	0.926806	−	0.333138i
$51$		0			0
$52$	−0.262710			−0.0364313
$53$		−	7.41870i		−	1.01904i	−0.860460	−	0.509518i	$-0.829824\pi$
$53$		−	7.41870i		−	1.01904i	0.860460	−	0.509518i	$-0.170176\pi$
$54$		0			0
$55$	−2.20431	+	0.384136i	−0.297229	+	0.0517968i
$56$		−	0.987382i		−	0.131944i
$57$		0			0
$58$		−	10.6208i		−	1.39457i
$59$		−	3.94753i		−	0.513924i	−0.966422	−	0.256962i	$-0.917278\pi$
$59$		−	3.94753i		−	0.513924i	0.966422	−	0.256962i	$-0.0827215\pi$
$60$		0			0
$61$			2.18574i			0.279855i	0.990162	+	0.139927i	$0.0446869\pi$
$61$			2.18574i			0.279855i	−0.990162	+	0.139927i	$0.955313\pi$
$62$		−	6.33808i		−	0.804937i
$63$		0			0
$64$	8.22574			1.02822
$65$	−9.62897	+	1.67800i	−1.19433	+	0.208130i
$66$		0			0
$67$		−	10.2635i		−	1.25389i	−0.779064	−	0.626944i	$-0.784305\pi$
$67$		−	10.2635i		−	1.25389i	0.779064	−	0.626944i	$-0.215695\pi$
$68$	−0.0257707			−0.00312516
$69$		0			0
$70$	−0.183991	−	1.05581i	−0.0219912	−	0.126193i
$71$	−1.92267			−0.228179			−0.114090	−	0.993470i	$-0.536395\pi$
$71$	−1.92267			−0.228179			−0.114090	+	0.993470i	$0.536395\pi$
$72$		0			0
$73$			9.22636i			1.07986i	0.841709	+	0.539932i	$0.181550\pi$
$73$			9.22636i			1.07986i	−0.841709	+	0.539932i	$0.818450\pi$
$74$	2.71748	+	8.02444i	0.315900	+	0.932822i
$75$		0			0
$76$			0.342697i			0.0393101i
$77$			0.344343i			0.0392415i
$78$		0			0
$79$		−	14.3679i		−	1.61652i	−0.588828	−	0.808258i	$-0.700411\pi$
$79$		−	14.3679i		−	1.61652i	0.588828	−	0.808258i	$-0.299589\pi$
$80$	8.53873	−	1.48801i	0.954659	−	0.166364i
$81$		0			0
$82$	−3.49587			−0.386054
$83$			0.402746i			0.0442071i	0.999756	+	0.0221035i	$0.00703635\pi$
$83$			0.402746i			0.0442071i	−0.999756	+	0.0221035i	$0.992964\pi$
$84$		0			0
$85$	−0.944561	+	0.164604i	−0.102452	+	0.0178539i
$86$	11.9540			1.28904
$87$		0			0
$88$	−2.87119			−0.306070
$89$		−	7.34498i		−	0.778566i	−0.921118	−	0.389283i	$-0.872723\pi$
$89$		−	7.34498i		−	0.778566i	0.921118	−	0.389283i	$-0.127277\pi$
$90$		0			0
$91$			1.50417i			0.157680i
$92$	0.141297			0.0147312
$93$		0			0
$94$		−	9.77657i		−	1.00838i
$95$	2.18890	+	12.5607i	0.224576	+	1.28870i
$96$		0			0
$97$	−9.66376			−0.981206			−0.490603	−	0.871383i	$-0.663224\pi$
$97$	−9.66376			−0.981206			−0.490603	+	0.871383i	$0.663224\pi$
$98$	9.58469			0.968199
$99$		0			0
$100$	−0.282793	+	0.101649i	−0.0282793	+	0.0101649i
$101$	9.43463			0.938781			0.469391	−	0.882991i	$-0.344474\pi$
$101$	9.43463			0.938781			0.469391	+	0.882991i	$0.344474\pi$
$102$		0			0
$103$	3.60566			0.355276			0.177638	−	0.984096i	$-0.443154\pi$
$103$	3.60566			0.355276			0.177638	+	0.984096i	$0.443154\pi$
$104$	−12.5421			−1.22985
$105$		0			0
$106$		−	10.3328i		−	1.00361i
$107$			14.5128i			1.40300i	0.712669	+	0.701500i	$0.247486\pi$
$107$			14.5128i			1.40300i	−0.712669	+	0.701500i	$0.752514\pi$
$108$		0			0
$109$		−	5.44298i		−	0.521343i	−0.965428	−	0.260671i	$-0.916056\pi$
$109$		−	5.44298i		−	0.521343i	0.965428	−	0.260671i	$-0.0839439\pi$
$110$	−3.07017	+	0.535025i	−0.292729	+	0.0510126i
$111$		0			0
$112$		−	1.33386i		−	0.126038i
$113$	−9.13297			−0.859157			−0.429579	−	0.903029i	$-0.641338\pi$
$113$	−9.13297			−0.859157			−0.429579	+	0.903029i	$0.641338\pi$
$114$		0			0
$115$	5.17887	−	0.902500i	0.482933	−	0.0841585i
$116$			0.458302i			0.0425522i
$117$		0			0
$118$		−	5.49812i		−	0.506143i
$119$			0.147553i			0.0135262i
$120$		0			0
$121$	−9.99869			−0.908972
$122$			3.04430i			0.275618i
$123$		0			0
$124$			0.273498i			0.0245608i
$125$	−9.71582	+	5.53198i	−0.869010	+	0.494795i
$126$		0			0
$127$			21.0161i			1.86487i	0.361332	+	0.932437i	$0.382322\pi$
$127$			21.0161i			1.86487i	−0.361332	+	0.932437i	$0.617678\pi$
$128$	10.7771			0.952569
$129$		0			0
$130$	−13.4113	+	2.33712i	−1.17624	+	0.204979i
$131$			6.86428i			0.599735i	0.953981	+	0.299868i	$0.0969425\pi$
$131$			6.86428i			0.599735i	−0.953981	+	0.299868i	$0.903057\pi$
$132$		0			0
$133$	1.96215			0.170140
$134$		−	14.2951i		−	1.23490i
$135$		0			0
$136$	−1.23032			−0.105499
$137$			10.1126i			0.863976i	0.901879	+	0.431988i	$0.142188\pi$
$137$			10.1126i			0.863976i	−0.901879	+	0.431988i	$0.857812\pi$
$138$		0			0
$139$	−3.55340			−0.301396			−0.150698	−	0.988580i	$-0.548152\pi$
$139$	−3.55340			−0.301396			−0.150698	+	0.988580i	$0.548152\pi$
$140$	0.00793949	+	0.0455597i	0.000671010	+	0.00385050i
$141$		0			0
$142$	−2.67790			−0.224724
$143$	4.37396			0.365769
$144$		0			0
$145$	2.92730	+	16.7979i	0.243099	+	1.39499i
$146$			12.8505i			1.06351i
$147$		0			0
$148$	−0.117263	−	0.346266i	−0.00963897	−	0.0284629i
$149$	15.4708			1.26742			0.633710	−	0.773571i	$-0.281531\pi$
$149$	15.4708			1.26742			0.633710	+	0.773571i	$0.281531\pi$
$150$		0			0
$151$	−9.11731			−0.741956			−0.370978	−	0.928642i	$-0.620977\pi$
$151$	−9.11731			−0.741956			−0.370978	+	0.928642i	$0.620977\pi$
$152$			16.3608i			1.32703i
$153$		0			0
$154$			0.479602i			0.0386474i
$155$	1.74690	+	10.0244i	0.140315	+	0.805177i
$156$		0			0
$157$		−	13.2988i		−	1.06136i	−0.847572	−	0.530680i	$-0.821937\pi$
$157$		−	13.2988i		−	1.06136i	0.847572	−	0.530680i	$-0.178063\pi$
$158$		−	20.0117i		−	1.59204i
$159$		0			0
$160$	−0.748687	+	0.130470i	−0.0591889	+	0.0103146i
$161$		−	0.809010i		−	0.0637589i
$162$		0			0
$163$	−19.7530			−1.54717			−0.773585	−	0.633692i	$-0.781539\pi$
$163$	−19.7530			−1.54717			−0.773585	+	0.633692i	$0.781539\pi$
$164$	0.150852			0.0117795
$165$		0			0
$166$			0.560945i			0.0435378i
$167$	7.51159			0.581265			0.290632	−	0.956835i	$-0.406134\pi$
$167$	7.51159			0.581265			0.290632	+	0.956835i	$0.406134\pi$
$168$		0			0
$169$	6.10655			0.469735
$170$	−1.31559	+	0.229261i	−0.100901	+	0.0175835i
$171$		0			0
$172$	−0.515834			−0.0393320
$173$			12.8334i			0.975706i	0.872926	+	0.487853i	$0.162220\pi$
$173$			12.8334i			0.975706i	−0.872926	+	0.487853i	$0.837780\pi$
$174$		0			0
$175$	0.582004	+	1.61917i	0.0439954	+	0.122397i
$176$	−3.87872			−0.292370
$177$		0			0
$178$		−	10.2301i		−	0.766779i
$179$		−	7.40603i		−	0.553553i	−0.960934	−	0.276777i	$-0.910734\pi$
$179$		−	7.40603i		−	0.553553i	0.960934	−	0.276777i	$-0.0892662\pi$
$180$		0			0
$181$	−14.6421			−1.08834			−0.544171	−	0.838974i	$-0.683156\pi$
$181$	−14.6421			−1.08834			−0.544171	+	0.838974i	$0.683156\pi$
$182$			2.09502i			0.155293i
$183$		0			0
$184$	6.74567			0.497297
$185$	−6.50968	−	11.9425i	−0.478601	−	0.878032i
$186$		0			0
$187$	0.429067			0.0313765
$188$			0.421873i			0.0307683i
$189$		0			0
$190$	3.04870	+	17.4946i	0.221176	+	1.26919i
$191$		−	4.01324i		−	0.290388i	−0.989403	−	0.145194i	$-0.953619\pi$
$191$		−	4.01324i		−	0.290388i	0.989403	−	0.145194i	$-0.0463807\pi$
$192$		0			0
$193$	24.0591			1.73181			0.865906	−	0.500207i	$-0.166743\pi$
$193$	24.0591			1.73181			0.865906	+	0.500207i	$0.166743\pi$
$194$	−13.4597			−0.966351
$195$		0			0
$196$	−0.413593			−0.0295424
$197$			4.81990i			0.343403i	0.985149	+	0.171702i	$0.0549265\pi$
$197$			4.81990i			0.343403i	−0.985149	+	0.171702i	$0.945073\pi$
$198$		0			0
$199$		−	27.1785i		−	1.92663i	−0.268372	−	0.963315i	$-0.586486\pi$
$199$		−	27.1785i		−	1.92663i	0.268372	−	0.963315i	$-0.413514\pi$
$200$	−13.5009	+	4.85285i	−0.954657	+	0.343149i
$201$		0			0
$202$	13.1406			0.924568
$203$	2.62406			0.184173
$204$		0			0
$205$	5.52909	−	0.963531i	0.386169	−	0.0672959i
$206$	5.02197			0.349897
$207$		0			0
$208$	−16.9432			−1.17480
$209$		−	5.70571i		−	0.394672i
$210$		0			0
$211$	9.18627			0.632409			0.316204	−	0.948691i	$-0.397591\pi$
$211$	9.18627			0.632409			0.316204	+	0.948691i	$0.397591\pi$
$212$			0.445875i			0.0306228i
$213$		0			0
$214$			20.2134i			1.38176i
$215$	−18.9066	+	3.29477i	−1.28942	+	0.224702i
$216$		0			0
$217$	1.56594			0.106303
$218$		−	7.58100i		−	0.513450i
$219$		0			0
$220$	0.132482	−	0.0230871i	0.00893196	−	0.00155653i
$221$	1.87427			0.126077
$222$		0			0
$223$			5.05112i			0.338248i	0.985595	+	0.169124i	$0.0540939\pi$
$223$			5.05112i			0.338248i	−0.985595	+	0.169124i	$0.945906\pi$
$224$			0.116955i			0.00781438i
$225$		0			0
$226$	−12.7204			−0.846150
$227$	−13.1231			−0.871011			−0.435506	−	0.900186i	$-0.643430\pi$
$227$	−13.1231			−0.871011			−0.435506	+	0.900186i	$0.643430\pi$
$228$		0			0
$229$	10.8507			0.717032			0.358516	−	0.933524i	$-0.383283\pi$
$229$	10.8507			0.717032			0.358516	+	0.933524i	$0.383283\pi$
$230$	7.21315	−	1.25700i	0.475621	−	0.0828844i
$231$		0			0
$232$			21.8799i			1.43648i
$233$		−	17.1449i		−	1.12320i	−0.827410	−	0.561598i	$-0.810187\pi$
$233$		−	17.1449i		−	1.12320i	0.827410	−	0.561598i	$-0.189813\pi$
$234$		0			0
$235$	2.69462	+	15.4627i	0.175778	+	1.00868i
$236$			0.237252i			0.0154438i
$237$		0			0
$238$			0.205512i			0.0133214i
$239$		−	1.53255i		−	0.0991323i	−0.998771	−	0.0495662i	$-0.984216\pi$
$239$		−	1.53255i		−	0.0991323i	0.998771	−	0.0495662i	$-0.0157839\pi$
$240$		0			0
$241$			3.84894i			0.247932i	0.992286	+	0.123966i	$0.0395614\pi$
$241$			3.84894i			0.247932i	−0.992286	+	0.123966i	$0.960439\pi$
$242$	−13.9262			−0.895210
$243$		0			0
$244$		−	0.131366i		−	0.00840984i
$245$	−15.1592	+	2.64173i	−0.968488	+	0.168774i
$246$		0			0
$247$		−	24.9239i		−	1.58587i
$248$			13.0571i			0.829126i
$249$		0			0
$250$	−13.5322	+	7.70495i	−0.855853	+	0.487304i
$251$			5.32686i			0.336229i	0.985767	+	0.168114i	$0.0537678\pi$
$251$			5.32686i			0.336229i	−0.985767	+	0.168114i	$0.946232\pi$
$252$		0			0
$253$	−2.35251			−0.147901
$254$			29.2712i			1.83664i
$255$		0			0
$256$	−1.44112			−0.0900700
$257$	5.23877			0.326786			0.163393	−	0.986561i	$-0.447756\pi$
$257$	5.23877			0.326786			0.163393	+	0.986561i	$0.447756\pi$
$258$		0			0
$259$	−1.98259	+	0.671404i	−0.123192	+	0.0417190i
$260$	0.578715	−	0.100850i	0.0358904	−	0.00625446i
$261$		0			0
$262$			9.56059i			0.590655i
$263$			7.96305i			0.491022i	0.969394	+	0.245511i	$0.0789558\pi$
$263$			7.96305i			0.491022i	−0.969394	+	0.245511i	$0.921044\pi$
$264$		0			0
$265$	2.84792	+	16.3424i	0.174946	+	1.00391i
$266$	2.73289			0.167564
$267$		0			0
$268$			0.616853i			0.0376803i
$269$	9.37825			0.571802			0.285901	−	0.958259i	$-0.407707\pi$
$269$	9.37825			0.571802			0.285901	+	0.958259i	$0.407707\pi$
$270$		0			0
$271$	26.6529			1.61905			0.809524	−	0.587087i	$-0.199725\pi$
$271$	26.6529			1.61905			0.809524	+	0.587087i	$0.199725\pi$
$272$	−1.66206			−0.100777
$273$		0			0
$274$			14.0848i			0.850895i
$275$	4.70834	−	1.69240i	0.283924	−	0.102056i
$276$		0			0
$277$	9.95700			0.598258			0.299129	−	0.954213i	$-0.403304\pi$
$277$	9.95700			0.598258			0.299129	+	0.954213i	$0.403304\pi$
$278$	−4.94919			−0.296833
$279$		0			0
$280$	0.379041	+	2.17507i	0.0226520	+	0.129986i
$281$			18.2638i			1.08953i	0.838589	+	0.544764i	$0.183381\pi$
$281$			18.2638i			1.08953i	−0.838589	+	0.544764i	$0.816619\pi$
$282$		0			0
$283$	−18.6227			−1.10700			−0.553501	−	0.832848i	$-0.686709\pi$
$283$	−18.6227			−1.10700			−0.553501	+	0.832848i	$0.686709\pi$
$284$	0.115555			0.00685695
$285$		0			0
$286$	6.09207			0.360232
$287$		−	0.863719i		−	0.0509837i
$288$		0			0
$289$	−16.8161			−0.989185
$290$	4.07715	+	23.3962i	0.239418	+	1.37387i
$291$		0			0
$292$		−	0.554518i		−	0.0324507i
$293$		−	29.8367i		−	1.74308i	−0.490327	−	0.871538i	$-0.663123\pi$
$293$		−	29.8367i		−	1.74308i	0.490327	−	0.871538i	$-0.336877\pi$
$294$		0			0
$295$	1.51539	+	8.69588i	0.0882296	+	0.506294i
$296$	−5.59828	−	16.5312i	−0.325393	−	0.960854i
$297$		0			0
$298$	21.5478			1.24823
$299$	−10.2763			−0.594295
$300$		0			0
$301$			2.95347i			0.170235i
$302$	−12.6986			−0.730723
$303$		0			0
$304$			22.1019i			1.26763i
$305$	−0.839070	−	4.81489i	−0.0480450	−	0.275700i
$306$		0			0
$307$			19.6530i			1.12166i	0.827932	+	0.560828i	$0.189517\pi$
$307$			19.6530i			1.12166i	−0.827932	+	0.560828i	$0.810483\pi$
$308$		−	0.0206955i		−	0.00117924i
$309$		0			0
$310$	2.43309	+	13.9620i	0.138190	+	0.792986i
$311$		−	23.0782i		−	1.30864i	−0.756217	−	0.654321i	$-0.772954\pi$
$311$		−	23.0782i		−	1.30864i	0.756217	−	0.654321i	$-0.227046\pi$
$312$		0			0
$313$	−12.0135			−0.679043			−0.339522	−	0.940598i	$-0.610265\pi$
$313$	−12.0135			−0.679043			−0.339522	+	0.940598i	$0.610265\pi$
$314$		−	18.5226i		−	1.04529i
$315$		0			0
$316$			0.863533i			0.0485775i
$317$		−	9.84245i		−	0.552807i	−0.961042	−	0.276404i	$-0.910857\pi$
$317$		−	9.84245i		−	0.552807i	0.961042	−	0.276404i	$-0.0891427\pi$
$318$		0			0
$319$		−	7.63045i		−	0.427223i
$320$	−18.1202	+	3.15773i	−1.01295	+	0.176523i
$321$		0			0
$322$		−	1.12679i		−	0.0627936i
$323$		−	2.44493i		−	0.136040i
$324$		0			0
$325$	20.5672	−	7.39282i	1.14086	−	0.410080i
$326$	−27.5120			−1.52375
$327$		0			0
$328$	7.20184			0.397655
$329$	2.41548			0.133170
$330$		0			0
$331$		−	12.5516i		−	0.689896i	−0.938622	−	0.344948i	$-0.887896\pi$
$331$		−	12.5516i		−	0.689896i	0.938622	−	0.344948i	$-0.112104\pi$
$332$		−	0.0242056i		−	0.00132846i
$333$		0			0
$334$	10.4622			0.572464
$335$	3.94000	+	22.6092i	0.215265	+	1.23527i
$336$		0			0
$337$		−	24.4199i		−	1.33024i	−0.746738	−	0.665118i	$-0.768381\pi$
$337$		−	24.4199i		−	1.33024i	0.746738	−	0.665118i	$-0.231619\pi$
$338$	8.50522			0.462623
$339$		0			0
$340$	0.0567695	−	0.00989297i	0.00307876	−	0.000536522i
$341$		−	4.55357i		−	0.246590i
$342$		0			0
$343$			4.77690i			0.257928i
$344$	−24.6265			−1.32777
$345$		0			0
$346$			17.8744i			0.960934i
$347$	4.91405			0.263800			0.131900	−	0.991263i	$-0.457892\pi$
$347$	4.91405			0.263800			0.131900	+	0.991263i	$0.457892\pi$
$348$		0			0
$349$	−7.69210			−0.411749			−0.205874	−	0.978578i	$-0.566004\pi$
$349$	−7.69210			−0.411749			−0.205874	+	0.978578i	$0.566004\pi$
$350$	0.810617	+	2.25518i	0.0433293	+	0.120544i
$351$		0			0
$352$	0.340091			0.0181269
$353$	5.78846			0.308089			0.154044	−	0.988064i	$-0.450770\pi$
$353$	5.78846			0.308089			0.154044	+	0.988064i	$0.450770\pi$
$354$		0			0
$355$	4.23539	−	0.738083i	0.224791	−	0.0391734i
$356$			0.441444i			0.0233965i
$357$		0			0
$358$		−	10.3151i		−	0.545172i
$359$	23.3366			1.23166			0.615830	−	0.787879i	$-0.288821\pi$
$359$	23.3366			1.23166			0.615830	+	0.787879i	$0.288821\pi$
$360$		0			0
$361$	−13.5125			−0.711185
$362$	−20.3936			−1.07186
$363$		0			0
$364$		−	0.0904031i		−	0.00473841i
$365$	−3.54185	−	20.3245i	−0.185389	−	1.06383i
$366$		0			0
$367$			0.996653i			0.0520249i	0.999662	+	0.0260124i	$0.00828095\pi$
$367$			0.996653i			0.0520249i	−0.999662	+	0.0260124i	$0.991719\pi$
$368$	9.11279			0.475037
$369$		0			0
$370$	−9.06670	−	16.6336i	−0.471355	−	0.864739i
$371$	2.55291			0.132540
$372$		0			0
$373$		−	25.4727i		−	1.31893i	−0.751737	−	0.659463i	$-0.770784\pi$
$373$		−	25.4727i		−	1.31893i	0.751737	−	0.659463i	$-0.229216\pi$
$374$	0.597606			0.0309015
$375$		0			0
$376$			20.1407i			1.03868i
$377$		−	33.3317i		−	1.71667i
$378$		0			0
$379$	−13.7468			−0.706124			−0.353062	−	0.935600i	$-0.614859\pi$
$379$	−13.7468			−0.706124			−0.353062	+	0.935600i	$0.614859\pi$
$380$	−0.131556	−	0.754917i	−0.00674868	−	0.0387264i
$381$		0			0
$382$		−	5.58966i		−	0.285992i
$383$	31.5653			1.61291			0.806456	−	0.591294i	$-0.201383\pi$
$383$	31.5653			1.61291			0.806456	+	0.591294i	$0.201383\pi$
$384$		0			0
$385$	−0.132188	−	0.758543i	−0.00673692	−	0.0386589i
$386$	33.5096			1.70559
$387$		0			0
$388$	0.580806			0.0294860
$389$			32.3554i			1.64049i	0.572016	+	0.820243i	$0.306162\pi$
$389$			32.3554i			1.64049i	−0.572016	+	0.820243i	$0.693838\pi$
$390$		0			0
$391$	−1.00806			−0.0509799
$392$	−19.7454			−0.997295
$393$		0			0
$394$			6.71316i			0.338204i
$395$	5.51562	+	31.6506i	0.277521	+	1.59252i
$396$		0			0
$397$			19.2972i			0.968501i	0.874929	+	0.484250i	$0.160908\pi$
$397$			19.2972i			0.968501i	−0.874929	+	0.484250i	$0.839092\pi$
$398$		−	37.8542i		−	1.89746i
$399$		0			0
$400$	−18.2385	+	6.55577i	−0.911924	+	0.327788i
$401$			27.7461i			1.38558i	0.721141	+	0.692788i	$0.243618\pi$
$401$			27.7461i			1.38558i	−0.721141	+	0.692788i	$0.756382\pi$
$402$		0			0
$403$		−	19.8911i		−	0.990848i
$404$	−0.567036			−0.0282111
$405$		0			0
$406$	3.65479			0.181384
$407$	1.95236	+	5.76513i	0.0967750	+	0.285767i
$408$		0			0
$409$		−	30.8229i		−	1.52409i	−0.647522	−	0.762047i	$-0.724194\pi$
$409$		−	30.8229i		−	1.52409i	0.647522	−	0.762047i	$-0.275806\pi$
$410$	7.70093	−	1.34201i	0.380322	−	0.0662771i
$411$		0			0
$412$	−0.216706			−0.0106763
$413$	1.35841			0.0668432
$414$		0			0
$415$	−0.154608	−	0.887196i	−0.00758940	−	0.0435508i
$416$	1.48560			0.0728377
$417$		0			0
$418$		−	7.94692i		−	0.388697i
$419$	29.0149			1.41747			0.708735	−	0.705475i	$-0.249266\pi$
$419$	29.0149			1.41747			0.708735	+	0.705475i	$0.249266\pi$
$420$		0			0
$421$			24.1020i			1.17466i	0.809348	+	0.587329i	$0.199820\pi$
$421$			24.1020i			1.17466i	−0.809348	+	0.587329i	$0.800180\pi$
$422$	12.7947			0.622834
$423$		0			0
$424$			21.2866i			1.03377i
$425$	2.01755	−	0.725204i	0.0978658	−	0.0351776i
$426$		0			0
$427$	−0.752151			−0.0363991
$428$		−	0.872238i		−	0.0421612i
$429$		0			0
$430$	−26.3332	+	4.58897i	−1.26990	+	0.221300i
$431$		−	19.5238i		−	0.940427i	−0.882553	−	0.470214i	$-0.844177\pi$
$431$		−	19.5238i		−	0.940427i	0.882553	−	0.470214i	$-0.155823\pi$
$432$		0			0
$433$		−	28.2340i		−	1.35684i	−0.734675	−	0.678419i	$-0.762665\pi$
$433$		−	28.2340i		−	1.35684i	0.734675	−	0.678419i	$-0.237335\pi$
$434$	2.18105			0.104694
$435$		0			0
$436$			0.327131i			0.0156667i
$437$			13.4052i			0.641256i
$438$		0			0
$439$		−	0.0399408i		−	0.00190627i	−1.00000		0.000953135i	$-0.999697\pi$
$439$		−	0.0399408i		−	0.00190627i	1.00000		0.000953135i	$-0.000303392\pi$
$440$	6.32486	−	1.10221i	0.301526	−	0.0525456i
$441$		0			0
$442$	2.61049			0.124168
$443$		−	32.6233i		−	1.54998i	−0.631973	−	0.774990i	$-0.717755\pi$
$443$		−	32.6233i		−	1.54998i	0.631973	−	0.774990i	$-0.282245\pi$
$444$		0			0
$445$	2.81962	+	16.1800i	0.133663	+	0.767007i
$446$			7.03522i			0.333127i
$447$		0			0
$448$			2.83062i			0.133734i
$449$		−	7.95302i		−	0.375326i	−0.982233	−	0.187663i	$-0.939909\pi$
$449$		−	7.95302i		−	0.375326i	0.982233	−	0.187663i	$-0.0600913\pi$
$450$		0			0
$451$	−2.51159			−0.118266
$452$	0.548905			0.0258183
$453$		0			0
$454$	−18.2779			−0.857824
$455$	−0.577429	−	3.31350i	−0.0270703	−	0.155339i
$456$		0			0
$457$	11.4750			0.536776			0.268388	−	0.963311i	$-0.413509\pi$
$457$	11.4750			0.536776			0.268388	+	0.963311i	$0.413509\pi$
$458$	15.1128			0.706176
$459$		0			0
$460$	−0.311258	+	0.0542416i	−0.0145125	+	0.00252903i
$461$			1.19985i			0.0558824i	0.999610	+	0.0279412i	$0.00889512\pi$
$461$			1.19985i			0.0558824i	−0.999610	+	0.0279412i	$0.991105\pi$
$462$		0			0
$463$	−10.2734			−0.477448			−0.238724	−	0.971088i	$-0.576729\pi$
$463$	−10.2734			−0.477448			−0.238724	+	0.971088i	$0.576729\pi$
$464$			29.5577i			1.37218i
$465$		0			0
$466$		−	23.8794i		−	1.10619i
$467$	37.1879			1.72085			0.860426	−	0.509575i	$-0.170197\pi$
$467$	37.1879			1.72085			0.860426	+	0.509575i	$0.170197\pi$
$468$		0			0
$469$	3.53186			0.163086
$470$	3.75307	+	21.5365i	0.173116	+	0.993405i
$471$		0			0
$472$			11.3267i			0.521353i
$473$	8.58834			0.394892
$474$		0			0
$475$	−9.64371	−	26.8293i	−0.442484	−	1.23101i
$476$		−	0.00886816i		−	0.000406471i
$477$		0			0
$478$		−	2.13454i		−	0.0976315i
$479$			9.73753i			0.444919i	0.974942	+	0.222460i	$0.0714086\pi$
$479$			9.73753i			0.444919i	−0.974942	+	0.222460i	$0.928591\pi$
$480$		0			0
$481$	8.52840	+	25.1835i	0.388862	+	1.14827i
$482$			5.36082i			0.244178i
$483$		0			0
$484$	0.600936			0.0273153
$485$	21.2880	−	3.70977i	0.966638	−	0.168452i
$486$		0			0
$487$	−35.6585			−1.61584			−0.807920	−	0.589293i	$-0.799407\pi$
$487$	−35.6585			−1.61584			−0.807920	+	0.589293i	$0.799407\pi$
$488$		−	6.27156i		−	0.283900i
$489$		0			0
$490$	−21.1138	+	3.67941i	−0.953825	+	0.166219i
$491$	−26.4591			−1.19408			−0.597041	−	0.802211i	$-0.703657\pi$
$491$	−26.4591			−1.19408			−0.597041	+	0.802211i	$0.703657\pi$
$492$		0			0
$493$		−	3.26970i		−	0.147260i
$494$		−	34.7141i		−	1.56186i
$495$		0			0
$496$			17.6390i			0.792013i
$497$		−	0.661625i		−	0.0296779i
$498$		0			0
$499$			15.1576i			0.678545i	0.940688	+	0.339273i	$0.110181\pi$
$499$			15.1576i			0.678545i	−0.940688	+	0.339273i	$0.889819\pi$
$500$	0.583935	−	0.332480i	0.0261144	−	0.0148690i
$501$		0			0
$502$			7.41927i			0.331138i
$503$	−9.89357			−0.441132			−0.220566	−	0.975372i	$-0.570790\pi$
$503$	−9.89357			−0.441132			−0.220566	+	0.975372i	$0.570790\pi$
$504$		0			0
$505$	−20.7833	+	3.62181i	−0.924843	+	0.161168i
$506$	−3.27658			−0.145662
$507$		0			0
$508$		−	1.26310i		−	0.0560409i
$509$	−36.1879			−1.60400			−0.802000	−	0.597324i	$-0.796231\pi$
$509$	−36.1879			−1.60400			−0.802000	+	0.597324i	$0.796231\pi$
$510$		0			0
$511$	−3.17495			−0.140452
$512$	−23.5614			−1.04128
$513$		0			0
$514$	7.29657			0.321838
$515$	−7.94280	+	1.38416i	−0.350002	+	0.0609932i
$516$		0			0
$517$		−	7.02394i		−	0.308913i
$518$	−2.76135	+	0.935133i	−0.121327	+	0.0410874i
$519$		0			0
$520$	27.6285	−	4.81470i	1.21159	−	0.211139i
$521$	−32.0406			−1.40373			−0.701863	−	0.712312i	$-0.747648\pi$
$521$	−32.0406			−1.40373			−0.701863	+	0.712312i	$0.747648\pi$
$522$		0			0
$523$	−3.11083			−0.136027			−0.0680136	−	0.997684i	$-0.521666\pi$
$523$	−3.11083			−0.136027			−0.0680136	+	0.997684i	$0.521666\pi$
$524$		−	0.412554i		−	0.0180225i
$525$		0			0
$526$			11.0909i			0.483588i
$527$		−	1.95123i		−	0.0849971i
$528$		0			0
$529$	−17.4730			−0.759694
$530$	3.96659	+	22.7618i	0.172298	+	0.988708i
$531$		0			0
$532$	−0.117928			−0.00511284
$533$	−10.9713			−0.475218
$534$		0			0
$535$	−5.57122	−	31.9697i	−0.240865	−	1.38217i
$536$			29.4493i			1.27201i
$537$		0			0
$538$	13.0620			0.563145
$539$	6.88609			0.296605
$540$		0			0
$541$			40.0599i			1.72231i	0.508341	+	0.861156i	$0.330259\pi$
$541$			40.0599i			1.72231i	−0.508341	+	0.861156i	$0.669741\pi$
$542$	37.1222			1.59453
$543$		0			0
$544$	0.145731			0.00624818
$545$	2.08947	+	11.9902i	0.0895033	+	0.513603i
$546$		0			0
$547$	−29.0324			−1.24134			−0.620669	−	0.784073i	$-0.713139\pi$
$547$	−29.0324			−1.24134			−0.620669	+	0.784073i	$0.713139\pi$
$548$		−	0.607781i		−	0.0259631i
$549$		0			0
$550$	6.55779	−	2.35718i	0.279625	−	0.100510i
$551$	−43.4802			−1.85232
$552$		0			0
$553$	4.94425			0.210251
$554$	13.8681			0.589201
$555$		0			0
$556$	0.213565			0.00905717
$557$	0.496954			0.0210566			0.0105283	−	0.999945i	$-0.496649\pi$
$557$	0.496954			0.0210566			0.0105283	+	0.999945i	$0.496649\pi$
$558$		0			0
$559$	37.5160			1.58676
$560$	0.512050	+	2.93833i	0.0216380	+	0.124167i
$561$		0			0
$562$			25.4379i			1.07303i
$563$	24.9566			1.05179			0.525897	−	0.850548i	$-0.323730\pi$
$563$	24.9566			1.05179			0.525897	+	0.850548i	$0.323730\pi$
$564$		0			0
$565$	20.1187	−	3.50600i	0.846402	−	0.147499i
$566$	−25.9377			−1.09024
$567$		0			0
$568$	5.51675			0.231478
$569$			24.1825i			1.01379i	0.862009	+	0.506893i	$0.169206\pi$
$569$			24.1825i			1.01379i	−0.862009	+	0.506893i	$0.830794\pi$
$570$		0			0
$571$	36.7544			1.53812			0.769062	−	0.639175i	$-0.220724\pi$
$571$	36.7544			1.53812			0.769062	+	0.639175i	$0.220724\pi$
$572$	−0.262882			−0.0109916
$573$		0			0
$574$		−	1.20299i		−	0.0502118i
$575$	−11.0619	+	3.97618i	−0.461314	+	0.165818i
$576$		0			0
$577$	−28.8512			−1.20109			−0.600545	−	0.799591i	$-0.705050\pi$
$577$	−28.8512			−1.20109			−0.600545	+	0.799591i	$0.705050\pi$
$578$	−23.4216			−0.974209
$579$		0			0
$580$	−0.175935	−	1.00958i	−0.00730530	−	0.0419205i
$581$	−0.138592			−0.00574977
$582$		0			0
$583$		−	7.42355i		−	0.307452i
$584$		−	26.4733i		−	1.09547i
$585$		0			0
$586$		−	41.5566i		−	1.71669i
$587$	11.1675			0.460933			0.230466	−	0.973080i	$-0.425975\pi$
$587$	11.1675			0.460933			0.230466	+	0.973080i	$0.425975\pi$
$588$		0			0
$589$	−25.9474			−1.06914
$590$	2.11064	+	12.1116i	0.0868938	+	0.498629i
$591$		0			0
$592$	−7.56277	−	22.3321i	−0.310828	−	0.917843i
$593$		−	3.72900i		−	0.153132i	−0.997065	−	0.0765658i	$-0.975604\pi$
$593$		−	3.72900i		−	0.153132i	0.997065	−	0.0765658i	$-0.0243955\pi$
$594$		0			0
$595$	−0.0566433	−	0.325040i	−0.00232215	−	0.0133253i
$596$	−0.929820			−0.0380869
$597$		0			0
$598$	−14.3129			−0.585298
$599$	20.9040			0.854113			0.427056	−	0.904225i	$-0.359551\pi$
$599$	20.9040			0.854113			0.427056	+	0.904225i	$0.359551\pi$
$600$		0			0
$601$	25.2037			1.02808			0.514041	−	0.857766i	$-0.328148\pi$
$601$	25.2037			1.02808			0.514041	+	0.857766i	$0.328148\pi$
$602$			4.11360i			0.167658i
$603$		0			0
$604$	0.547964			0.0222963
$605$	22.0258	−	3.83834i	0.895476	−	0.156051i
$606$		0			0
$607$	0.485148			0.0196916			0.00984578	−	0.999952i	$-0.496866\pi$
$607$	0.485148			0.0196916			0.00984578	+	0.999952i	$0.496866\pi$
$608$		−	1.93792i		−	0.0785932i
$609$		0			0
$610$	−1.16866	−	6.70619i	−0.0473176	−	0.271526i
$611$		−	30.6823i		−	1.24127i
$612$		0			0
$613$			39.1708i			1.58210i	0.611755	+	0.791048i	$0.290464\pi$
$613$			39.1708i			1.58210i	−0.611755	+	0.791048i	$0.709536\pi$
$614$			27.3727i			1.10467i
$615$		0			0
$616$		−	0.988028i		−	0.0398088i
$617$			27.8220i			1.12007i	0.828468	+	0.560036i	$0.189213\pi$
$617$			27.8220i			1.12007i	−0.828468	+	0.560036i	$0.810787\pi$
$618$		0			0
$619$	−0.946919			−0.0380599			−0.0190299	−	0.999819i	$-0.506058\pi$
$619$	−0.946919			−0.0380599			−0.0190299	+	0.999819i	$0.506058\pi$
$620$	−0.104991	−	0.602480i	−0.00421656	−	0.0241962i
$621$		0			0
$622$		−	32.1433i		−	1.28883i
$623$	2.52754			0.101264
$624$		0			0
$625$	19.2790	−	15.9160i	0.771162	−	0.636639i
$626$	−16.7324			−0.668762
$627$		0			0
$628$			0.799278i			0.0318947i
$629$	0.836599	+	2.47039i	0.0333574	+	0.0985010i
$630$		0			0
$631$			2.30783i			0.0918734i	0.998944	+	0.0459367i	$0.0146273\pi$
$631$			2.30783i			0.0918734i	−0.998944	+	0.0459367i	$0.985373\pi$
$632$			41.2261i			1.63988i
$633$		0			0
$634$		−	13.7086i		−	0.544438i
$635$	−8.06774	−	46.2957i	−0.320159	−	1.83719i
$636$		0			0
$637$	30.0801			1.19182
$638$		−	10.6277i		−	0.420755i
$639$		0			0
$640$	−23.7405	+	4.13716i	−0.938427	+	0.163535i
$641$	48.9069			1.93171			0.965853	−	0.259091i	$-0.0834228\pi$
$641$	48.9069			1.93171			0.965853	+	0.259091i	$0.0834228\pi$
$642$		0			0
$643$	24.4145			0.962814			0.481407	−	0.876497i	$-0.340126\pi$
$643$	24.4145			0.962814			0.481407	+	0.876497i	$0.340126\pi$
$644$			0.0486227i			0.00191600i
$645$		0			0
$646$		−	3.40530i		−	0.133980i
$647$	21.3926			0.841028			0.420514	−	0.907286i	$-0.361850\pi$
$647$	21.3926			0.841028			0.420514	+	0.907286i	$0.361850\pi$
$648$		0			0
$649$		−	3.95011i		−	0.155055i
$650$	28.6461	−	10.2967i	1.12359	−	0.403871i
$651$		0			0
$652$	1.18718			0.0464936
$653$	−28.7548			−1.12526			−0.562631	−	0.826708i	$-0.690211\pi$
$653$	−28.7548			−1.12526			−0.562631	+	0.826708i	$0.690211\pi$
$654$		0			0
$655$	−2.63509	−	15.1211i	−0.102962	−	0.590831i
$656$	9.72903			0.379855
$657$		0			0
$658$	3.36429			0.131154
$659$	−36.1968			−1.41003			−0.705014	−	0.709193i	$-0.749059\pi$
$659$	−36.1968			−1.41003			−0.705014	+	0.709193i	$0.749059\pi$
$660$		0			0
$661$		−	26.4419i		−	1.02847i	−0.857649	−	0.514235i	$-0.828076\pi$
$661$		−	26.4419i		−	1.02847i	0.857649	−	0.514235i	$-0.171924\pi$
$662$		−	17.4819i		−	0.679451i
$663$		0			0
$664$		−	1.15560i		−	0.0448461i
$665$	−4.32236	+	0.753239i	−0.167614	+	0.0292094i
$666$		0			0
$667$			17.9272i			0.694145i
$668$	−0.451458			−0.0174674
$669$		0			0
$670$	5.48765	+	31.4901i	0.212006	+	1.21657i
$671$			2.18717i			0.0844346i
$672$		0			0
$673$			12.6452i			0.487438i	0.969846	+	0.243719i	$0.0783674\pi$
$673$			12.6452i			0.487438i	−0.969846	+	0.243719i	$0.921633\pi$
$674$		−	34.0121i		−	1.31010i
$675$		0			0
$676$	−0.367013			−0.0141159
$677$		−	24.2473i		−	0.931900i	−0.884811	−	0.465950i	$-0.845713\pi$
$677$		−	24.2473i		−	0.931900i	0.884811	−	0.465950i	$-0.154287\pi$
$678$		0			0
$679$		−	3.32547i		−	0.127620i
$680$	2.71024	−	0.472302i	0.103933	−	0.0181119i
$681$		0			0
$682$		−	6.34223i		−	0.242857i
$683$	−13.8062			−0.528279			−0.264140	−	0.964484i	$-0.585088\pi$
$683$	−13.8062			−0.528279			−0.264140	+	0.964484i	$0.585088\pi$
$684$		0			0
$685$	−3.88206	−	22.2767i	−0.148326	−	0.851149i
$686$			6.65328i			0.254023i
$687$		0			0
$688$	−33.2682			−1.26834
$689$		−	32.4279i		−	1.23540i
$690$		0			0
$691$	19.4603			0.740303			0.370151	−	0.928971i	$-0.379306\pi$
$691$	19.4603			0.740303			0.370151	+	0.928971i	$0.379306\pi$
$692$		−	0.771307i		−	0.0293207i
$693$		0			0
$694$	6.84431			0.259806
$695$	7.82768	−	1.36410i	0.296921	−	0.0517431i
$696$		0			0
$697$	−1.07623			−0.0407652
$698$	−10.7136			−0.405515
$699$		0			0
$700$	−0.0349793	−	0.0973143i	−0.00132209	−	0.00367813i
$701$			33.8058i			1.27683i	0.769694	+	0.638413i	$0.220409\pi$
$701$			33.8058i			1.27683i	−0.769694	+	0.638413i	$0.779591\pi$
$702$		0			0
$703$	32.8511	−	11.1250i	1.23900	−	0.419589i
$704$	8.23112			0.310222
$705$		0			0
$706$	8.06218			0.303424
$707$			3.24663i			0.122102i
$708$		0			0
$709$			17.1515i			0.644137i	0.946716	+	0.322069i	$0.104378\pi$
$709$			17.1515i			0.644137i	−0.946716	+	0.322069i	$0.895622\pi$
$710$	5.89906	−	1.02800i	0.221388	−	0.0385803i
$711$		0			0
$712$			21.0751i			0.789821i
$713$			10.6983i			0.400655i
$714$		0			0
$715$	−9.63527	+	1.67910i	−0.360339	+	0.0627946i
$716$			0.445114i			0.0166347i
$717$		0			0
$718$	32.5033			1.21301
$719$	20.0146			0.746419			0.373209	−	0.927747i	$-0.378257\pi$
$719$	20.0146			0.746419			0.373209	+	0.927747i	$0.378257\pi$
$720$		0			0
$721$			1.24077i			0.0462088i
$722$	−18.8203			−0.700418
$723$		0			0
$724$	0.880015			0.0327055
$725$	−12.8969	−	35.8798i	−0.478979	−	1.33254i
$726$		0			0
$727$	20.5563			0.762390			0.381195	−	0.924495i	$-0.375513\pi$
$727$	20.5563			0.762390			0.381195	+	0.924495i	$0.375513\pi$
$728$		−	4.31595i		−	0.159960i
$729$		0			0
$730$	−4.93310	−	28.3079i	−0.182582	−	1.04772i
$731$	3.68015			0.136115
$732$		0			0
$733$			4.14889i			0.153243i	0.997060	+	0.0766213i	$0.0244132\pi$
$733$			4.14889i			0.153243i	−0.997060	+	0.0766213i	$0.975587\pi$
$734$			1.38814i			0.0512372i
$735$		0			0
$736$	−0.799021			−0.0294523
$737$		−	10.2702i		−	0.378309i
$738$		0			0
$739$	−47.3841			−1.74305			−0.871527	−	0.490348i	$-0.836870\pi$
$739$	−47.3841			−1.74305			−0.871527	+	0.490348i	$0.836870\pi$
$740$	0.391242	+	0.717764i	0.0143823	+	0.0263855i
$741$		0			0
$742$	3.55569			0.130534
$743$			7.43386i			0.272722i	0.990659	+	0.136361i	$0.0435407\pi$
$743$			7.43386i			0.272722i	−0.990659	+	0.136361i	$0.956459\pi$
$744$		0			0
$745$	−34.0802	+	5.93901i	−1.24860	+	0.217588i
$746$		−	35.4784i		−	1.29896i
$747$		0			0
$748$	−0.0257876			−0.000942887
$749$	−4.99410			−0.182480
$750$		0			0
$751$	2.00815			0.0732786			0.0366393	−	0.999329i	$-0.488335\pi$
$751$	2.00815			0.0732786			0.0366393	+	0.999329i	$0.488335\pi$
$752$			27.2083i			0.992184i
$753$		0			0
$754$		−	46.4245i		−	1.69068i
$755$	20.0842	−	3.49999i	0.730940	−	0.127378i
$756$		0			0
$757$	24.4281			0.887853			0.443926	−	0.896063i	$-0.353585\pi$
$757$	24.4281			0.887853			0.443926	+	0.896063i	$0.353585\pi$
$758$	−19.1465			−0.695433
$759$		0			0
$760$	−6.28064	−	36.0406i	−0.227823	−	1.30733i
$761$	−33.4813			−1.21370			−0.606848	−	0.794818i	$-0.707566\pi$
$761$	−33.4813			−1.21370			−0.606848	+	0.794818i	$0.707566\pi$
$762$		0			0
$763$	1.87303			0.0678081
$764$			0.241202i			0.00872638i
$765$		0			0
$766$	43.9642			1.58849
$767$		−	17.2550i		−	0.623044i
$768$		0			0
$769$			39.7615i			1.43384i	0.697158	+	0.716918i	$0.254448\pi$
$769$			39.7615i			1.43384i	−0.697158	+	0.716918i	$0.745552\pi$
$770$	−0.184112	−	1.05650i	−0.00663492	−	0.0380736i
$771$		0			0
$772$	−1.44599			−0.0520422
$773$			17.4578i			0.627912i	0.949437	+	0.313956i	$0.101655\pi$
$773$			17.4578i			0.627912i	−0.949437	+	0.313956i	$0.898345\pi$
$774$		0			0
$775$	−7.69640	−	21.4118i	−0.276463	−	0.769133i
$776$	27.7284			0.995390
$777$		0			0
$778$			45.0647i			1.61565i
$779$			14.3117i			0.512769i
$780$		0			0
$781$	−1.92393			−0.0688436
$782$	−1.40403			−0.0502081
$783$		0			0
$784$	−26.6743			−0.952653
$785$	5.10520	+	29.2955i	0.182212	+	1.04560i
$786$		0			0
$787$			2.56830i			0.0915499i	0.998952	+	0.0457749i	$0.0145757\pi$
$787$			2.56830i			0.0915499i	−0.998952	+	0.0457749i	$0.985424\pi$
$788$		−	0.289683i		−	0.0103195i
$789$		0			0
$790$	7.68216	+	44.0831i	0.273319	+	1.56841i
$791$		−	3.14282i		−	0.111746i
$792$		0			0
$793$			9.55408i			0.339275i
$794$			26.8772i			0.953838i
$795$		0			0
$796$			1.63347i			0.0578967i
$797$	−12.9875			−0.460040			−0.230020	−	0.973186i	$-0.573879\pi$
$797$	−12.9875			−0.460040			−0.230020	+	0.973186i	$0.573879\pi$
$798$		0			0
$799$		−	3.00980i		−	0.106479i
$800$	1.59917	−	0.574818i	0.0565393	−	0.0203229i
$801$		0			0
$802$			38.6449i			1.36460i
$803$			9.23239i			0.325804i
$804$		0			0
$805$	0.310566	+	1.78214i	0.0109460	+	0.0628123i
$806$		−	27.7044i		−	0.975847i
$807$		0			0
$808$	−27.0709			−0.952352
$809$			32.4055i			1.13932i	0.821882	+	0.569658i	$0.192924\pi$
$809$			32.4055i			1.13932i	−0.821882	+	0.569658i	$0.807076\pi$
$810$		0			0
$811$	−9.17716			−0.322254			−0.161127	−	0.986934i	$-0.551513\pi$
$811$	−9.17716			−0.322254			−0.161127	+	0.986934i	$0.551513\pi$
$812$	−0.157710			−0.00553453
$813$		0			0
$814$	2.71926	+	8.02969i	0.0953099	+	0.281440i
$815$	43.5132	−	7.58285i	1.52420	−	0.265616i
$816$		0			0
$817$		−	48.9384i		−	1.71214i
$818$		−	42.9302i		−	1.50102i
$819$		0			0
$820$	−0.332307	+	0.0579096i	−0.0116047	+	0.00202229i
$821$	−21.9824			−0.767190			−0.383595	−	0.923501i	$-0.625314\pi$
$821$	−21.9824			−0.767190			−0.383595	+	0.923501i	$0.625314\pi$
$822$		0			0
$823$		−	1.23098i		−	0.0429092i	−0.999770	−	0.0214546i	$-0.993170\pi$
$823$		−	1.23098i		−	0.0429092i	0.999770	−	0.0214546i	$-0.00682974\pi$
$824$	−10.3458			−0.360412
$825$		0			0
$826$	1.89200			0.0658312
$827$	−41.6469			−1.44820			−0.724102	−	0.689693i	$-0.757746\pi$
$827$	−41.6469			−1.44820			−0.724102	+	0.689693i	$0.757746\pi$
$828$		0			0
$829$			24.0119i			0.833969i	0.908914	+	0.416985i	$0.136913\pi$
$829$			24.0119i			0.833969i	−0.908914	+	0.416985i	$0.863087\pi$
$830$	−0.215338	−	1.23569i	−0.00747450	−	0.0428914i
$831$		0			0
$832$	35.9556			1.24653
$833$	2.95073			0.102237
$834$		0			0
$835$	−16.5471	+	2.88358i	−0.572635	+	0.0997905i
$836$			0.342921i			0.0118602i
$837$		0			0
$838$	40.4120			1.39601
$839$	47.1610			1.62818			0.814090	−	0.580739i	$-0.197236\pi$
$839$	47.1610			1.62818			0.814090	+	0.580739i	$0.197236\pi$
$840$		0			0
$841$	−29.1477			−1.00509
$842$			33.5693i			1.15687i
$843$		0			0
$844$	−0.552108			−0.0190043
$845$	−13.4519	+	2.34421i	−0.462761	+	0.0806432i
$846$		0			0
$847$		−	3.44073i		−	0.118225i
$848$			28.7562i			0.987493i
$849$		0			0
$850$	2.81005	−	1.01007i	0.0963841	−	0.0346450i
$851$	−4.58694	−	13.5448i	−0.157238	−	0.464309i
$852$		0			0
$853$	1.13310			0.0387967			0.0193983	−	0.999812i	$-0.493825\pi$
$853$	1.13310			0.0387967			0.0193983	+	0.999812i	$0.493825\pi$
$854$	−1.04760			−0.0358480
$855$		0			0
$856$		−	41.6416i		−	1.42328i
$857$	−34.5092			−1.17881			−0.589406	−	0.807837i	$-0.700638\pi$
$857$	−34.5092			−1.17881			−0.589406	+	0.807837i	$0.700638\pi$
$858$		0			0
$859$		−	3.75019i		−	0.127955i	−0.997951	−	0.0639774i	$-0.979621\pi$
$859$		−	3.75019i		−	0.127955i	0.997951	−	0.0639774i	$-0.0203785\pi$
$860$	1.13632	−	0.198021i	0.0387480	−	0.00675245i
$861$		0			0
$862$		−	27.1928i		−	0.926189i
$863$			9.79362i			0.333379i	0.986009	+	0.166689i	$0.0533077\pi$
$863$			9.79362i			0.333379i	−0.986009	+	0.166689i	$0.946692\pi$
$864$		0			0
$865$	−4.92655	−	28.2703i	−0.167508	−	0.961220i
$866$		−	39.3244i		−	1.33630i
$867$		0			0
$868$	−0.0941154			−0.00319449
$869$		−	14.3773i		−	0.487717i
$870$		0			0
$871$		−	44.8629i		−	1.52012i
$872$			15.6176i			0.528879i
$873$		0			0
$874$			18.6707i			0.631547i
$875$	−1.90365	−	3.34339i	−0.0643552	−	0.113027i
$876$		0			0
$877$			13.4128i			0.452919i	0.974021	+	0.226459i	$0.0727150\pi$
$877$			13.4128i			0.452919i	−0.974021	+	0.226459i	$0.927285\pi$
$878$		−	0.0556296i		−	0.00187741i
$879$		0			0
$880$	8.54432	−	1.48898i	0.288029	−	0.0501935i
$881$	−10.4429			−0.351832			−0.175916	−	0.984405i	$-0.556289\pi$
$881$	−10.4429			−0.351832			−0.175916	+	0.984405i	$0.556289\pi$
$882$		0			0
$883$	32.1571			1.08217			0.541086	−	0.840967i	$-0.318013\pi$
$883$	32.1571			1.08217			0.541086	+	0.840967i	$0.318013\pi$
$884$	−0.112646			−0.00378871
$885$		0			0
$886$		−	45.4378i		−	1.52651i
$887$		−	44.3996i		−	1.49079i	−0.666621	−	0.745397i	$-0.732260\pi$
$887$		−	44.3996i		−	1.49079i	0.666621	−	0.745397i	$-0.267740\pi$
$888$		0			0
$889$	−7.23200			−0.242554
$890$	3.92718	+	22.5356i	0.131639	+	0.755395i
$891$		0			0
$892$		−	0.303580i		−	0.0101646i
$893$	−40.0242			−1.33936
$894$		0			0
$895$	2.84306	+	16.3145i	0.0950330	+	0.545334i
$896$			3.70859i			0.123895i
$897$		0			0
$898$		−	11.0770i		−	0.369644i
$899$	−34.7004			−1.15732
$900$		0			0
$901$		−	3.18104i		−	0.105976i
$902$	−3.49815			−0.116476
$903$		0			0
$904$	26.2054			0.871577
$905$	32.2547	−	5.62089i	1.07218	−	0.186845i
$906$		0			0
$907$	3.69899			0.122823			0.0614115	−	0.998113i	$-0.480440\pi$
$907$	3.69899			0.122823			0.0614115	+	0.998113i	$0.480440\pi$
$908$	0.788718			0.0261745
$909$		0			0
$910$	−0.804245	−	4.61505i	−0.0266605	−	0.152987i
$911$		−	42.9518i		−	1.42306i	−0.702658	−	0.711528i	$-0.748003\pi$
$911$		−	42.9518i		−	1.42306i	0.702658	−	0.711528i	$-0.251997\pi$
$912$		0			0
$913$			0.403009i			0.0133377i
$914$	15.9824			0.528649
$915$		0			0
$916$	−0.652141			−0.0215473
$917$	−2.36212			−0.0780042
$918$		0			0
$919$		−	17.4354i		−	0.575142i	−0.957759	−	0.287571i	$-0.907152\pi$
$919$		−	17.4354i		−	0.575142i	0.957759	−	0.287571i	$-0.0928477\pi$
$920$	−14.8598	+	2.58956i	−0.489914	+	0.0853751i
$921$		0			0
$922$			1.67115i			0.0550363i
$923$	−8.40419			−0.276627
$924$		0			0
$925$	18.9245	+	23.8089i	0.622235	+	0.782831i
$926$	−14.3089			−0.470219
$927$		0			0
$928$		−	2.59166i		−	0.0850754i
$929$	47.5276			1.55933			0.779666	−	0.626196i	$-0.215389\pi$
$929$	47.5276			1.55933			0.779666	+	0.626196i	$0.215389\pi$
$930$		0			0
$931$		−	39.2386i		−	1.28599i
$932$			1.03043i			0.0337529i
$933$		0			0
$934$	51.7955			1.69480
$935$	−0.945179	+	0.164712i	−0.0309106	+	0.00538666i
$936$		0			0
$937$			40.3594i			1.31848i	0.751931	+	0.659241i	$0.229122\pi$
$937$			40.3594i			1.31848i	−0.751931	+	0.659241i	$0.770878\pi$
$938$	4.91918			0.160617
$939$		0			0
$940$	−0.161951	−	0.929332i	−0.00528224	−	0.0303115i
$941$	47.6850			1.55449			0.777244	−	0.629199i	$-0.216617\pi$
$941$	47.6850			1.55449			0.777244	+	0.629199i	$0.216617\pi$
$942$		0			0
$943$	5.90081			0.192157
$944$			15.3013i			0.498016i
$945$		0			0
$946$	11.9619			0.388913
$947$	33.1655			1.07773			0.538866	−	0.842391i	$-0.318853\pi$
$947$	33.1655			1.07773			0.538866	+	0.842391i	$0.318853\pi$
$948$		0			0
$949$			40.3294i			1.30915i
$950$	−13.4318	−	37.3679i	−0.435785	−	1.21238i
$951$		0			0
$952$		−	0.423376i		−	0.0137217i
$953$			35.1011i			1.13704i	0.822671	+	0.568518i	$0.192483\pi$
$953$			35.1011i			1.13704i	−0.822671	+	0.568518i	$0.807517\pi$
$954$		0			0
$955$	1.54062	+	8.84065i	0.0498533	+	0.286077i
$956$			0.0921085i			0.00297900i
$957$		0			0
$958$			13.5625i			0.438183i
$959$	−3.47992			−0.112372
$960$		0			0
$961$	10.2921			0.332002
$962$	11.8784	+	35.0756i	0.382974	+	1.13088i
$963$		0			0
$964$		−	0.231327i		−	0.00745054i
$965$	−52.9991	+	9.23591i	−1.70610	+	0.297315i
$966$		0			0
$967$	−23.1104			−0.743180			−0.371590	−	0.928397i	$-0.621187\pi$
$967$	−23.1104			−0.743180			−0.371590	+	0.928397i	$0.621187\pi$
$968$	28.6894			0.922112
$969$		0			0
$970$	29.6500	−	5.16697i	0.952003	−	0.165901i
$971$	31.6046			1.01424			0.507120	−	0.861875i	$-0.330710\pi$
$971$	31.6046			1.01424			0.507120	+	0.861875i	$0.330710\pi$
$972$		0			0
$973$		−	1.22279i		−	0.0392008i
$974$	−49.6652			−1.59138
$975$		0			0
$976$		−	8.47232i		−	0.271192i
$977$	19.9276			0.637539			0.318770	−	0.947832i	$-0.396730\pi$
$977$	19.9276			0.637539			0.318770	+	0.947832i	$0.396730\pi$
$978$		0			0
$979$		−	7.34979i		−	0.234900i
$980$	0.911092	−	0.158772i	0.0291038	−	0.00507179i
$981$		0			0
$982$	−36.8523			−1.17600
$983$		−	21.5507i		−	0.687361i	−0.939087	−	0.343680i	$-0.888326\pi$
$983$		−	21.5507i		−	0.687361i	0.939087	−	0.343680i	$-0.111674\pi$
$984$		0			0
$985$	−1.85028	−	10.6176i	−0.0589549	−	0.338305i
$986$		−	4.55404i		−	0.145030i
$987$		0			0
$988$			1.49796i			0.0476566i
$989$	−20.1777			−0.641613
$990$		0			0
$991$		−	12.5861i		−	0.399810i	−0.979815	−	0.199905i	$-0.935937\pi$
$991$		−	12.5861i		−	0.399810i	0.979815	−	0.199905i	$-0.0640633\pi$
$992$		−	1.54661i		−	0.0491048i
$993$		0			0
$994$		−	0.921513i		−	0.0292286i
$995$	10.4334	+	59.8706i	0.330761	+	1.89803i
$996$		0			0
$997$	57.5782			1.82352			0.911760	−	0.410723i	$-0.134724\pi$
$997$	57.5782			1.82352			0.911760	+	0.410723i	$0.134724\pi$
$998$			21.1115i			0.668272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1665.2.g.e.739.27		40
3.2	odd	2		555.2.g.a.184.14	yes	40
5.4	even	2	inner	1665.2.g.e.739.14		40
15.14	odd	2		555.2.g.a.184.27	yes	40
37.36	even	2	inner	1665.2.g.e.739.13		40
111.110	odd	2		555.2.g.a.184.28	yes	40
185.184	even	2	inner	1665.2.g.e.739.28		40
555.554	odd	2		555.2.g.a.184.13	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.13	✓	40	555.554	odd	2
555.2.g.a.184.14	yes	40	3.2	odd	2
555.2.g.a.184.27	yes	40	15.14	odd	2
555.2.g.a.184.28	yes	40	111.110	odd	2
1665.2.g.e.739.13		40	37.36	even	2	inner
1665.2.g.e.739.14		40	5.4	even	2	inner
1665.2.g.e.739.27		40	1.1	even	1	trivial
1665.2.g.e.739.28		40	185.184	even	2	inner

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:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.39280 q^{2} -0.0601015 q^{4} +(-2.20287 + 0.383884i) q^{5} +0.344118i q^{7} -2.86931 q^{8} +O(q^{10})\)	\(q+1.39280 q^{2} -0.0601015 q^{4} +(-2.20287 + 0.383884i) q^{5} +0.344118i q^{7} -2.86931 q^{8} +(-3.06816 + 0.534675i) q^{10} +1.00065 q^{11} +4.37110 q^{13} +0.479288i q^{14} -3.87618 q^{16} +0.428787 q^{17} -5.70197i q^{19} +(0.132396 - 0.0230720i) q^{20} +1.39371 q^{22} -2.35097 q^{23} +(4.70527 - 1.69129i) q^{25} +6.08808 q^{26} -0.0206820i q^{28} -7.62547i q^{29} -4.55060i q^{31} +0.339869 q^{32} +0.597215 q^{34} +(-0.132101 - 0.758047i) q^{35} +(1.95109 + 5.76136i) q^{37} -7.94172i q^{38} +(6.32072 - 1.10148i) q^{40} -2.50995 q^{41} +8.58272 q^{43} -0.0601408 q^{44} -3.27443 q^{46} -7.01935i q^{47} +6.88158 q^{49} +(6.55351 - 2.35564i) q^{50} -0.262710 q^{52} -7.41870i q^{53} +(-2.20431 + 0.384136i) q^{55} -0.987382i q^{56} -10.6208i q^{58} -3.94753i q^{59} +2.18574i q^{61} -6.33808i q^{62} +8.22574 q^{64} +(-9.62897 + 1.67800i) q^{65} -10.2635i q^{67} -0.0257707 q^{68} +(-0.183991 - 1.05581i) q^{70} -1.92267 q^{71} +9.22636i q^{73} +(2.71748 + 8.02444i) q^{74} +0.342697i q^{76} +0.344343i q^{77} -14.3679i q^{79} +(8.53873 - 1.48801i) q^{80} -3.49587 q^{82} +0.402746i q^{83} +(-0.944561 + 0.164604i) q^{85} +11.9540 q^{86} -2.87119 q^{88} -7.34498i q^{89} +1.50417i q^{91} +0.141297 q^{92} -9.77657i q^{94} +(2.18890 + 12.5607i) q^{95} -9.66376 q^{97} +9.58469 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4}+O(q^{10}) \) 40 * q + 44 * q^4	\( 40 q + 44 q^{4} + 4 q^{10} - 8 q^{11} + 52 q^{16} + 8 q^{25} + 16 q^{26} - 32 q^{34} - 28 q^{40} - 8 q^{41} - 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} + 48 q^{65} - 56 q^{70} - 24 q^{71} + 68 q^{74} - 64 q^{85} - 80 q^{86} - 32 q^{95}+O(q^{100}) \) 40 * q + 44 * q^4 + 4 * q^10 - 8 * q^11 + 52 * q^16 + 8 * q^25 + 16 * q^26 - 32 * q^34 - 28 * q^40 - 8 * q^41 - 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 + 48 * q^65 - 56 * q^70 - 24 * q^71 + 68 * q^74 - 64 * q^85 - 80 * q^86 - 32 * q^95

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