LMFDB - Embedded newform 3024.2.r.f.2017.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1009,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("3024.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.r (of order $3$, degree $2$, not 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2017.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	3024.2017
Dual form			3024.2.r.f.1009.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18614 + 3.78651i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(2.18614 + 3.78651i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.686141 - 1.18843i) q^{11} +(-1.00000 - 1.73205i) q^{13} -1.37228 q^{17} -5.00000 q^{19} +(0.813859 + 1.40965i) q^{23} +(-7.05842 + 12.2255i) q^{25} +(-4.37228 + 7.57301i) q^{29} +(1.00000 + 1.73205i) q^{31} +4.37228 q^{35} +2.00000 q^{37} +(2.31386 + 4.00772i) q^{41} +(-4.05842 + 7.02939i) q^{43} +(-0.500000 - 0.866025i) q^{49} +8.74456 q^{53} +6.00000 q^{55} +(5.05842 + 8.76144i) q^{59} +(-1.55842 + 2.69927i) q^{61} +(4.37228 - 7.57301i) q^{65} +(-1.05842 - 1.83324i) q^{67} -7.11684 q^{71} +12.1168 q^{73} +(-0.686141 - 1.18843i) q^{77} +(-2.55842 + 4.43132i) q^{79} +(-8.74456 + 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} -14.7446 q^{89} -2.00000 q^{91} +(-10.9307 - 18.9325i) q^{95} +(4.05842 - 7.02939i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q + 3 * q^5 + 2 * q^7	$ 4 q + 3 q^{5} + 2 q^{7} - 3 q^{11} - 4 q^{13} + 6 q^{17} - 20 q^{19} + 9 q^{23} - 11 q^{25} - 6 q^{29} + 4 q^{31} + 6 q^{35} + 8 q^{37} + 15 q^{41} + q^{43} - 2 q^{49} + 12 q^{53} + 24 q^{55} + 3 q^{59} + 11 q^{61} + 6 q^{65} + 13 q^{67} + 6 q^{71} + 14 q^{73} + 3 q^{77} + 7 q^{79} - 12 q^{83} - 12 q^{85} - 36 q^{89} - 8 q^{91} - 15 q^{95} - q^{97}+O(q^{100}) $ 4 * q + 3 * q^5 + 2 * q^7 - 3 * q^11 - 4 * q^13 + 6 * q^17 - 20 * q^19 + 9 * q^23 - 11 * q^25 - 6 * q^29 + 4 * q^31 + 6 * q^35 + 8 * q^37 + 15 * q^41 + q^43 - 2 * q^49 + 12 * q^53 + 24 * q^55 + 3 * q^59 + 11 * q^61 + 6 * q^65 + 13 * q^67 + 6 * q^71 + 14 * q^73 + 3 * q^77 + 7 * q^79 - 12 * q^83 - 12 * q^85 - 36 * q^89 - 8 * q^91 - 15 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.18614	+	3.78651i	0.977672	+	1.69338i	0.670820	+	0.741620i	$0.265942\pi$
$5$	2.18614	+	3.78651i	0.977672	+	1.69338i	0.306851	+	0.951757i	$0.400725\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	−0.743851	−	0.668346i	$-0.767003\pi$
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	0.950730	+	0.310021i	$0.100336\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.37228			−0.332827			−0.166414	−	0.986056i	$-0.553219\pi$
$17$	−1.37228			−0.332827			−0.166414	+	0.986056i	$0.553219\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.813859	+	1.40965i	0.169701	+	0.293931i	0.938315	−	0.345782i	$-0.112386\pi$
$23$	0.813859	+	1.40965i	0.169701	+	0.293931i	−0.768613	+	0.639713i	$0.779053\pi$
$24$		0			0
$25$	−7.05842	+	12.2255i	−1.41168	+	2.44511i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.37228	+	7.57301i	−0.811912	+	1.40627i	0.0996117	+	0.995026i	$0.468240\pi$
$29$	−4.37228	+	7.57301i	−0.811912	+	1.40627i	−0.911524	+	0.411247i	$0.865093\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.37228			0.739050
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.31386	+	4.00772i	0.361364	+	0.625901i	0.988186	−	0.153262i	$-0.0489778\pi$
$41$	2.31386	+	4.00772i	0.361364	+	0.625901i	−0.626821	+	0.779163i	$0.715644\pi$
$42$		0			0
$43$	−4.05842	+	7.02939i	−0.618904	+	1.07197i	0.370783	+	0.928720i	$0.379090\pi$
$43$	−4.05842	+	7.02939i	−0.618904	+	1.07197i	−0.989686	+	0.143253i	$0.954244\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.74456			1.20116			0.600579	−	0.799565i	$-0.294937\pi$
$53$	8.74456			1.20116			0.600579	+	0.799565i	$0.294937\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.05842	+	8.76144i	0.658550	+	1.14064i	0.980991	+	0.194053i	$0.0621634\pi$
$59$	5.05842	+	8.76144i	0.658550	+	1.14064i	−0.322441	+	0.946590i	$0.604503\pi$
$60$		0			0
$61$	−1.55842	+	2.69927i	−0.199535	+	0.345606i	−0.948378	−	0.317142i	$-0.897277\pi$
$61$	−1.55842	+	2.69927i	−0.199535	+	0.345606i	0.748842	+	0.662748i	$0.230610\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.37228	−	7.57301i	0.542315	−	0.939317i
$66$		0			0
$67$	−1.05842	−	1.83324i	−0.129307	−	0.223966i	0.794101	−	0.607785i	$-0.207942\pi$
$67$	−1.05842	−	1.83324i	−0.129307	−	0.223966i	−0.923408	+	0.383819i	$0.874609\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.11684			−0.844614			−0.422307	−	0.906453i	$-0.638780\pi$
$71$	−7.11684			−0.844614			−0.422307	+	0.906453i	$0.638780\pi$
$72$		0			0
$73$	12.1168			1.41817			0.709085	−	0.705123i	$-0.249108\pi$
$73$	12.1168			1.41817			0.709085	+	0.705123i	$0.249108\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.686141	−	1.18843i	−0.0781930	−	0.135434i
$78$		0			0
$79$	−2.55842	+	4.43132i	−0.287845	+	0.498562i	−0.973295	−	0.229557i	$-0.926272\pi$
$79$	−2.55842	+	4.43132i	−0.287845	+	0.498562i	0.685450	+	0.728120i	$0.259605\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.74456	+	15.1460i	−0.959840	+	1.66249i	−0.236960	+	0.971519i	$0.576151\pi$
$83$	−8.74456	+	15.1460i	−0.959840	+	1.66249i	−0.722881	+	0.690973i	$0.757182\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.7446			−1.56292			−0.781460	−	0.623955i	$-0.785525\pi$
$89$	−14.7446			−1.56292			−0.781460	+	0.623955i	$0.785525\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.9307	−	18.9325i	−1.12147	−	1.94244i
$96$		0			0
$97$	4.05842	−	7.02939i	0.412070	−	0.713727i	−0.583046	−	0.812439i	$-0.698139\pi$
$97$	4.05842	−	7.02939i	0.412070	−	0.713727i	0.995116	+	0.0987127i	$0.0314725\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.813859	−	1.40965i	0.0809820	−	0.140265i	−0.822690	−	0.568490i	$-0.807528\pi$
$101$	0.813859	−	1.40965i	0.0809820	−	0.140265i	0.903672	+	0.428225i	$0.140861\pi$
$102$		0			0
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.37228			−0.712705			−0.356353	−	0.934352i	$-0.615980\pi$
$107$	−7.37228			−0.712705			−0.356353	+	0.934352i	$0.615980\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.18614	−	3.78651i	−0.205655	−	0.356205i	0.744686	−	0.667415i	$-0.232599\pi$
$113$	−2.18614	−	3.78651i	−0.205655	−	0.356205i	−0.950341	+	0.311210i	$0.899266\pi$
$114$		0			0
$115$	−3.55842	+	6.16337i	−0.331825	+	0.574737i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.686141	+	1.18843i	−0.0628984	+	0.108943i
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−39.8614			−3.56531
$126$		0			0
$127$	−3.11684			−0.276575			−0.138288	−	0.990392i	$-0.544160\pi$
$127$	−3.11684			−0.276575			−0.138288	+	0.990392i	$0.544160\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.813859	+	1.40965i	0.0711072	+	0.123161i	0.899387	−	0.437154i	$-0.144013\pi$
$131$	0.813859	+	1.40965i	0.0711072	+	0.123161i	−0.828280	+	0.560315i	$0.810680\pi$
$132$		0			0
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.31386	−	9.20387i	0.453994	−	0.786340i	−0.544636	−	0.838672i	$-0.683332\pi$
$137$	5.31386	−	9.20387i	0.453994	−	0.786340i	0.998630	+	0.0523324i	$0.0166655\pi$
$138$		0			0
$139$	6.61684	+	11.4607i	0.561233	+	0.972085i	0.997389	+	0.0722136i	$0.0230063\pi$
$139$	6.61684	+	11.4607i	0.561233	+	0.972085i	−0.436156	+	0.899871i	$0.643660\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.74456			−0.229512
$144$		0			0
$145$	−38.2337			−3.17513
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.62772	+	2.81929i	0.133348	+	0.230965i	0.924965	−	0.380052i	$-0.124094\pi$
$149$	1.62772	+	2.81929i	0.133348	+	0.230965i	−0.791617	+	0.611017i	$0.790761\pi$
$150$		0			0
$151$	4.55842	−	7.89542i	0.370959	−	0.642520i	−0.618754	−	0.785585i	$-0.712362\pi$
$151$	4.55842	−	7.89542i	0.370959	−	0.642520i	0.989713	+	0.143065i	$0.0456957\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.37228	+	7.57301i	−0.351190	+	0.608279i
$156$		0			0
$157$	−4.55842	−	7.89542i	−0.363802	−	0.630123i	0.624781	−	0.780800i	$-0.285188\pi$
$157$	−4.55842	−	7.89542i	−0.363802	−	0.630123i	−0.988583	+	0.150677i	$0.951855\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.62772			0.128282
$162$		0			0
$163$	18.2337			1.42817			0.714086	−	0.700058i	$-0.246842\pi$
$163$	18.2337			1.42817			0.714086	+	0.700058i	$0.246842\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.74456	+	4.75372i	0.212381	+	0.367854i	0.952459	−	0.304666i	$-0.0985450\pi$
$167$	2.74456	+	4.75372i	0.212381	+	0.367854i	−0.740078	+	0.672521i	$0.765212\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	7.05842	+	12.2255i	0.533567	+	0.924164i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.25544			0.243323			0.121661	−	0.992572i	$-0.461178\pi$
$179$	3.25544			0.243323			0.121661	+	0.992572i	$0.461178\pi$
$180$		0			0
$181$	0.883156			0.0656445			0.0328222	−	0.999461i	$-0.489550\pi$
$181$	0.883156			0.0656445			0.0328222	+	0.999461i	$0.489550\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.37228	+	7.57301i	0.321457	+	0.556779i
$186$		0			0
$187$	−0.941578	+	1.63086i	−0.0688550	+	0.119260i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.55842	−	16.5557i	0.691623	−	1.19793i	−0.279683	−	0.960092i	$-0.590229\pi$
$191$	9.55842	−	16.5557i	0.691623	−	1.19793i	0.971306	−	0.237834i	$-0.0764374\pi$
$192$		0			0
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.37228	+	7.57301i	0.306874	+	0.531521i
$204$		0			0
$205$	−10.1168	+	17.5229i	−0.706591	+	1.22385i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.43070	+	5.94215i	−0.237307	+	0.411027i
$210$		0			0
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	0.447478	−	0.894295i	$-0.352322\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−35.4891			−2.42034
$216$		0			0
$217$	2.00000			0.135769
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.37228	+	2.37686i	0.0923096	+	0.159885i
$222$		0			0
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.12772	−	10.6135i	0.406711	−	0.704444i	−0.587808	−	0.809000i	$-0.700009\pi$
$227$	6.12772	−	10.6135i	0.406711	−	0.704444i	0.994519	+	0.104556i	$0.0333423\pi$
$228$		0			0
$229$	1.44158	+	2.49689i	0.0952622	+	0.164999i	0.909718	−	0.415227i	$-0.136298\pi$
$229$	1.44158	+	2.49689i	0.0952622	+	0.164999i	−0.814456	+	0.580226i	$0.802964\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.255437			0.0167343			0.00836713	−	0.999965i	$-0.497337\pi$
$233$	0.255437			0.0167343			0.00836713	+	0.999965i	$0.497337\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.93070	−	8.54023i	−0.318941	−	0.552421i	0.661327	−	0.750098i	$-0.269994\pi$
$239$	−4.93070	−	8.54023i	−0.318941	−	0.552421i	−0.980267	+	0.197677i	$0.936660\pi$
$240$		0			0
$241$	−9.05842	+	15.6896i	−0.583504	+	1.01066i	0.411556	+	0.911385i	$0.364986\pi$
$241$	−9.05842	+	15.6896i	−0.583504	+	1.01066i	−0.995060	+	0.0992745i	$0.968348\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.18614	−	3.78651i	0.139667	−	0.241911i
$246$		0			0
$247$	5.00000	+	8.66025i	0.318142	+	0.551039i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	2.23369			0.140431
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.43070	−	5.94215i	−0.214001	−	0.370661i	0.738962	−	0.673747i	$-0.235316\pi$
$257$	−3.43070	−	5.94215i	−0.214001	−	0.370661i	−0.952963	+	0.303086i	$0.901983\pi$
$258$		0			0
$259$	1.00000	−	1.73205i	0.0621370	−	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.81386	+	6.60580i	−0.235173	+	0.407331i	−0.959323	−	0.282311i	$-0.908899\pi$
$263$	−3.81386	+	6.60580i	−0.235173	+	0.407331i	0.724150	+	0.689642i	$0.242232\pi$
$264$		0			0
$265$	19.1168	+	33.1113i	1.17434	+	2.03401i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.62772			0.0992438			0.0496219	−	0.998768i	$-0.484198\pi$
$269$	1.62772			0.0992438			0.0496219	+	0.998768i	$0.484198\pi$
$270$		0			0
$271$	−16.2337			−0.986126			−0.493063	−	0.869994i	$-0.664123\pi$
$271$	−16.2337			−0.986126			−0.493063	+	0.869994i	$0.664123\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.68614	+	16.7769i	0.584096	+	1.01168i
$276$		0			0
$277$	6.11684	−	10.5947i	0.367526	−	0.636573i	−0.621652	−	0.783293i	$-0.713538\pi$
$277$	6.11684	−	10.5947i	0.367526	−	0.636573i	0.989178	+	0.146720i	$0.0468717\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.18614	−	14.1788i	0.488344	−	0.845837i	−0.511566	−	0.859244i	$-0.670934\pi$
$281$	8.18614	−	14.1788i	0.488344	−	0.845837i	0.999910	+	0.0134071i	$0.00426773\pi$
$282$		0			0
$283$	13.5584	+	23.4839i	0.805965	+	1.39597i	0.915638	+	0.402004i	$0.131686\pi$
$283$	13.5584	+	23.4839i	0.805965	+	1.39597i	−0.109673	+	0.993968i	$0.534981\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.62772			0.273166
$288$		0			0
$289$	−15.1168			−0.889226
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.18614	−	8.98266i	−0.302978	−	0.524773i	0.673831	−	0.738885i	$-0.264647\pi$
$293$	−5.18614	−	8.98266i	−0.302978	−	0.524773i	−0.976809	+	0.214113i	$0.931314\pi$
$294$		0			0
$295$	−22.1168	+	38.3075i	−1.28769	+	2.23035i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.62772	−	2.81929i	0.0941334	−	0.163044i
$300$		0			0
$301$	4.05842	+	7.02939i	0.233924	+	0.405167i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−13.6277			−0.780321
$306$		0			0
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.11684	−	7.13058i	−0.233445	−	0.404338i	0.725375	−	0.688354i	$-0.241666\pi$
$311$	−4.11684	−	7.13058i	−0.233445	−	0.404338i	−0.958820	+	0.284016i	$0.908333\pi$
$312$		0			0
$313$	10.0584	−	17.4217i	0.568536	−	0.984733i	−0.428175	−	0.903696i	$-0.640843\pi$
$313$	10.0584	−	17.4217i	0.568536	−	0.984733i	0.996711	−	0.0810370i	$-0.0258232\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.86141			0.381779
$324$		0			0
$325$	28.2337			1.56612
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.1168	−	19.2549i	0.611037	−	1.05835i	−0.380029	−	0.924975i	$-0.624086\pi$
$331$	11.1168	−	19.2549i	0.611037	−	1.05835i	0.991066	−	0.133373i	$-0.0425807\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.62772	−	8.01544i	0.252839	−	0.437930i
$336$		0			0
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	0.955135	−	0.296171i	$-0.0957097\pi$
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	−0.734059	+	0.679086i	$0.762376\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.74456			0.148626
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.05842	+	8.76144i	0.271550	+	0.470339i	0.969259	−	0.246043i	$-0.0791303\pi$
$347$	5.05842	+	8.76144i	0.271550	+	0.470339i	−0.697709	+	0.716382i	$0.745797\pi$
$348$		0			0
$349$	11.0000	−	19.0526i	0.588817	−	1.01986i	−0.405571	−	0.914063i	$-0.632927\pi$
$349$	11.0000	−	19.0526i	0.588817	−	1.01986i	0.994388	−	0.105797i	$-0.0337393\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.68614	+	11.5807i	−0.355867	+	0.616380i	−0.987266	−	0.159078i	$-0.949148\pi$
$353$	−6.68614	+	11.5807i	−0.355867	+	0.616380i	0.631399	+	0.775458i	$0.282481\pi$
$354$		0			0
$355$	−15.5584	−	26.9480i	−0.825755	−	1.43025i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	21.8614			1.15380			0.576900	−	0.816814i	$-0.304262\pi$
$359$	21.8614			1.15380			0.576900	+	0.816814i	$0.304262\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$		0			0
$363$		0			0
$364$		0			0
$365$	26.4891	+	45.8805i	1.38650	+	2.40150i
$366$		0			0
$367$	−6.11684	+	10.5947i	−0.319297	+	0.553038i	−0.980341	−	0.197308i	$-0.936780\pi$
$367$	−6.11684	+	10.5947i	−0.319297	+	0.553038i	0.661045	+	0.750346i	$0.270113\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.37228	−	7.57301i	0.226998	−	0.393171i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.4891			0.900736
$378$		0			0
$379$	8.11684			0.416934			0.208467	−	0.978029i	$-0.433153\pi$
$379$	8.11684			0.416934			0.208467	+	0.978029i	$0.433153\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.3723	+	28.3576i	0.836584	+	1.44901i	0.892734	+	0.450584i	$0.148784\pi$
$383$	16.3723	+	28.3576i	0.836584	+	1.44901i	−0.0561493	+	0.998422i	$0.517882\pi$
$384$		0			0
$385$	3.00000	−	5.19615i	0.152894	−	0.264820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5.48913	−	9.50744i	0.278310	−	0.482047i	−0.692655	−	0.721269i	$-0.743559\pi$
$389$	5.48913	−	9.50744i	0.278310	−	0.482047i	0.970965	+	0.239222i	$0.0768925\pi$
$390$		0			0
$391$	−1.11684	−	1.93443i	−0.0564812	−	0.0978284i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.3723			−1.12567
$396$		0			0
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.87228	−	10.1711i	−0.293248	−	0.507920i	0.681328	−	0.731978i	$-0.261403\pi$
$401$	−5.87228	−	10.1711i	−0.293248	−	0.507920i	−0.974576	+	0.224058i	$0.928069\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.37228	−	2.37686i	0.0680215	−	0.117817i
$408$		0			0
$409$	11.1753	+	19.3561i	0.552581	+	0.957099i	0.998087	+	0.0618200i	$0.0196905\pi$
$409$	11.1753	+	19.3561i	0.552581	+	0.957099i	−0.445506	+	0.895279i	$0.646976\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.1168			0.497817
$414$		0			0
$415$	−76.4674			−3.75364
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.30298	+	10.9171i	0.307921	+	0.533335i	0.977907	−	0.209039i	$-0.0670334\pi$
$419$	6.30298	+	10.9171i	0.307921	+	0.533335i	−0.669986	+	0.742373i	$0.733700\pi$
$420$		0			0
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	0.0604368	+	0.998172i	$0.480751\pi$
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	−0.894661	+	0.446746i	$0.852583\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.68614	−	16.7769i	0.469847	−	0.813799i
$426$		0			0
$427$	1.55842	+	2.69927i	0.0754173	+	0.130627i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.51087			−0.313618			−0.156809	−	0.987629i	$-0.550121\pi$
$431$	−6.51087			−0.313618			−0.156809	+	0.987629i	$0.550121\pi$
$432$		0			0
$433$	−20.1168			−0.966754			−0.483377	−	0.875412i	$-0.660590\pi$
$433$	−20.1168			−0.966754			−0.483377	+	0.875412i	$0.660590\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.06930	−	7.04823i	−0.194661	−	0.337162i
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	20.0584	−	34.7422i	0.953004	−	1.65065i	0.214134	−	0.976804i	$-0.431307\pi$
$443$	20.0584	−	34.7422i	0.953004	−	1.65065i	0.738870	−	0.673848i	$-0.235360\pi$
$444$		0			0
$445$	−32.2337	−	55.8304i	−1.52802	−	2.64661i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	6.35053			0.299035
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.37228	−	7.57301i	−0.204976	−	0.355028i
$456$		0			0
$457$	17.7337	−	30.7156i	0.829547	−	1.43682i	−0.0688472	−	0.997627i	$-0.521932\pi$
$457$	17.7337	−	30.7156i	0.829547	−	1.43682i	0.898394	−	0.439190i	$-0.144735\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.06930	−	1.85208i	0.0498021	−	0.0862598i	−0.840050	−	0.542509i	$-0.817474\pi$
$461$	1.06930	−	1.85208i	0.0498021	−	0.0862598i	0.889852	+	0.456250i	$0.150808\pi$
$462$		0			0
$463$	−11.5584	−	20.0198i	−0.537165	−	0.930398i	−0.999055	−	0.0434604i	$-0.986162\pi$
$463$	−11.5584	−	20.0198i	−0.537165	−	0.930398i	0.461890	−	0.886937i	$-0.347172\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	33.0951			1.53146			0.765729	−	0.643163i	$-0.222378\pi$
$467$	33.0951			1.53146			0.765729	+	0.643163i	$0.222378\pi$
$468$		0			0
$469$	−2.11684			−0.0977468
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.56930	+	9.64630i	0.256077	+	0.443538i
$474$		0			0
$475$	35.2921	−	61.1277i	1.61931	−	2.80473i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.3723	+	28.3576i	−0.748069	+	1.29569i	0.200679	+	0.979657i	$0.435685\pi$
$479$	−16.3723	+	28.3576i	−0.748069	+	1.29569i	−0.948747	+	0.316036i	$0.897648\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	35.4891			1.61148
$486$		0			0
$487$	−35.3505			−1.60189			−0.800943	−	0.598741i	$-0.795668\pi$
$487$	−35.3505			−1.60189			−0.800943	+	0.598741i	$0.795668\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.6861	+	21.9730i	0.572518	+	0.991629i	0.996306	+	0.0858685i	$0.0273665\pi$
$491$	12.6861	+	21.9730i	0.572518	+	0.991629i	−0.423789	+	0.905761i	$0.639300\pi$
$492$		0			0
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.55842	+	6.16337i	−0.159617	+	0.276465i
$498$		0			0
$499$	9.05842	+	15.6896i	0.405511	+	0.702365i	0.994381	−	0.105863i	$-0.0337604\pi$
$499$	9.05842	+	15.6896i	0.405511	+	0.702365i	−0.588870	+	0.808228i	$0.700427\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−32.2337			−1.43723			−0.718615	−	0.695409i	$-0.755223\pi$
$503$	−32.2337			−1.43723			−0.718615	+	0.695409i	$0.755223\pi$
$504$		0			0
$505$	7.11684			0.316695
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.4891	−	25.0959i	−0.642219	−	1.11236i	−0.984936	−	0.172918i	$-0.944681\pi$
$509$	−14.4891	−	25.0959i	−0.642219	−	1.11236i	0.342717	−	0.939439i	$-0.388653\pi$
$510$		0			0
$511$	6.05842	−	10.4935i	0.268009	−	0.464205i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.8614	−	37.8651i	0.963329	−	1.66853i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	24.8614			1.08920			0.544599	−	0.838697i	$-0.316682\pi$
$521$	24.8614			1.08920			0.544599	+	0.838697i	$0.316682\pi$
$522$		0			0
$523$	35.1168			1.53555			0.767776	−	0.640718i	$-0.221363\pi$
$523$	35.1168			1.53555			0.767776	+	0.640718i	$0.221363\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.37228	−	2.37686i	−0.0597775	−	0.103538i
$528$		0			0
$529$	10.1753	−	17.6241i	0.442403	−	0.766264i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.62772	−	8.01544i	0.200449	−	0.347187i
$534$		0			0
$535$	−16.1168	−	27.9152i	−0.696792	−	1.20688i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.37228			−0.0591083
$540$		0			0
$541$	−6.23369			−0.268007			−0.134004	−	0.990981i	$-0.542783\pi$
$541$	−6.23369			−0.268007			−0.134004	+	0.990981i	$0.542783\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	30.6060	+	53.0111i	1.31102	+	2.27075i
$546$		0			0
$547$	9.05842	−	15.6896i	0.387310	−	0.670841i	−0.604777	−	0.796395i	$-0.706738\pi$
$547$	9.05842	−	15.6896i	0.387310	−	0.670841i	0.992087	+	0.125554i	$0.0400709\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	21.8614	−	37.8651i	0.931327	−	1.61311i
$552$		0			0
$553$	2.55842	+	4.43132i	0.108795	+	0.188439i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−29.4891			−1.24949			−0.624747	−	0.780827i	$-0.714798\pi$
$557$	−29.4891			−1.24949			−0.624747	+	0.780827i	$0.714798\pi$
$558$		0			0
$559$	16.2337			0.686612
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	0.832684	−	0.553748i	$-0.186803\pi$
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	−0.895902	+	0.444252i	$0.853470\pi$
$564$		0			0
$565$	9.55842	−	16.5557i	0.402126	−	0.696502i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.05842	−	13.9576i	0.337827	−	0.585133i	−0.646197	−	0.763171i	$-0.723642\pi$
$569$	8.05842	−	13.9576i	0.337827	−	0.585133i	0.984024	+	0.178038i	$0.0569749\pi$
$570$		0			0
$571$	−11.1753	−	19.3561i	−0.467670	−	0.810029i	0.531647	−	0.846966i	$-0.321573\pi$
$571$	−11.1753	−	19.3561i	−0.467670	−	0.810029i	−0.999318	+	0.0369371i	$0.988240\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−22.9783			−0.958259
$576$		0			0
$577$	9.88316			0.411441			0.205721	−	0.978611i	$-0.434046\pi$
$577$	9.88316			0.411441			0.205721	+	0.978611i	$0.434046\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.74456	+	15.1460i	0.362786	+	0.628363i
$582$		0			0
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.24456	+	12.5480i	−0.299015	+	0.517909i	−0.975911	−	0.218170i	$-0.929991\pi$
$587$	−7.24456	+	12.5480i	−0.299015	+	0.517909i	0.676896	+	0.736079i	$0.263325\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.7446			−0.605487			−0.302743	−	0.953072i	$-0.597902\pi$
$593$	−14.7446			−0.605487			−0.302743	+	0.953072i	$0.597902\pi$
$594$		0			0
$595$	−6.00000			−0.245976
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	−12.0584	+	20.8858i	−0.491873	+	0.851950i	−0.999956	−	0.00935863i	$-0.997021\pi$
$601$	−12.0584	+	20.8858i	−0.491873	+	0.851950i	0.508083	+	0.861308i	$0.330354\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.9307	+	34.5210i	−0.810298	+	1.40348i
$606$		0			0
$607$	11.1168	+	19.2549i	0.451219	+	0.781534i	0.998462	−	0.0554398i	$-0.0176561\pi$
$607$	11.1168	+	19.2549i	0.451219	+	0.781534i	−0.547243	+	0.836974i	$0.684323\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−36.2337			−1.46346			−0.731732	−	0.681592i	$-0.761288\pi$
$613$	−36.2337			−1.46346			−0.731732	+	0.681592i	$0.761288\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.43070	+	16.3345i	0.379666	+	0.657600i	0.991014	−	0.133762i	$-0.0427056\pi$
$617$	9.43070	+	16.3345i	0.379666	+	0.657600i	−0.611348	+	0.791362i	$0.709372\pi$
$618$		0			0
$619$	22.7337	−	39.3759i	0.913744	−	1.58265i	0.105014	−	0.994471i	$-0.466511\pi$
$619$	22.7337	−	39.3759i	0.913744	−	1.58265i	0.808730	−	0.588180i	$-0.200156\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.37228	+	12.7692i	−0.295364	+	0.511586i
$624$		0			0
$625$	−51.8505	−	89.8078i	−2.07402	−	3.59231i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.74456			−0.109433
$630$		0			0
$631$	37.3505			1.48690			0.743451	−	0.668791i	$-0.233188\pi$
$631$	37.3505			1.48690			0.743451	+	0.668791i	$0.233188\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.81386	−	11.8020i	−0.270400	−	0.468346i
$636$		0			0
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.1060	−	29.6284i	0.675645	−	1.17025i	−0.300635	−	0.953739i	$-0.597198\pi$
$641$	17.1060	−	29.6284i	0.675645	−	1.17025i	0.976280	−	0.216512i	$-0.0694682\pi$
$642$		0			0
$643$	13.1753	+	22.8202i	0.519582	+	0.899942i	0.999741	+	0.0227606i	$0.00724556\pi$
$643$	13.1753	+	22.8202i	0.519582	+	0.899942i	−0.480159	+	0.877181i	$0.659421\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.48913			0.215800			0.107900	−	0.994162i	$-0.465587\pi$
$647$	5.48913			0.215800			0.107900	+	0.994162i	$0.465587\pi$
$648$		0			0
$649$	13.8832			0.544962
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.3723	−	23.1615i	−0.523298	−	0.906378i	−0.999632	−	0.0271143i	$-0.991368\pi$
$653$	−13.3723	−	23.1615i	−0.523298	−	0.906378i	0.476335	−	0.879264i	$-0.341965\pi$
$654$		0			0
$655$	−3.55842	+	6.16337i	−0.139039	+	0.240823i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.3723	−	17.9653i	0.404047	−	0.699829i	−0.590163	−	0.807284i	$-0.700937\pi$
$659$	10.3723	−	17.9653i	0.404047	−	0.699829i	0.994210	+	0.107454i	$0.0342700\pi$
$660$		0			0
$661$	−13.5584	−	23.4839i	−0.527361	−	0.913417i	−0.999491	−	0.0318879i	$-0.989848\pi$
$661$	−13.5584	−	23.4839i	−0.527361	−	0.913417i	0.472130	−	0.881529i	$-0.343485\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−21.8614			−0.847749
$666$		0			0
$667$	−14.2337			−0.551131
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.13859	+	3.70415i	0.0825595	+	0.142997i
$672$		0			0
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	−0.836903	−	0.547351i	$-0.815636\pi$
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	0.892472	+	0.451103i	$0.148969\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.2337	−	29.8496i	0.662344	−	1.14721i	−0.317654	−	0.948207i	$-0.602895\pi$
$677$	17.2337	−	29.8496i	0.662344	−	1.14721i	0.979998	−	0.199007i	$-0.0637718\pi$
$678$		0			0
$679$	−4.05842	−	7.02939i	−0.155748	−	0.269763i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	29.8397			1.14178			0.570891	−	0.821026i	$-0.306598\pi$
$683$	29.8397			1.14178			0.570891	+	0.821026i	$0.306598\pi$
$684$		0			0
$685$	46.4674			1.77543
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.74456	−	15.1460i	−0.333141	−	0.577018i
$690$		0			0
$691$	−11.5584	+	20.0198i	−0.439703	+	0.761588i	−0.997666	−	0.0682775i	$-0.978250\pi$
$691$	−11.5584	+	20.0198i	−0.439703	+	0.761588i	0.557963	+	0.829866i	$0.311583\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.9307	+	50.1094i	−1.09740	+	1.90076i
$696$		0			0
$697$	−3.17527	−	5.49972i	−0.120272	−	0.208317i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	38.2337			1.44407			0.722033	−	0.691858i	$-0.243208\pi$
$701$	38.2337			1.44407			0.722033	+	0.691858i	$0.243208\pi$
$702$		0			0
$703$	−10.0000			−0.377157
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.813859	−	1.40965i	−0.0306083	−	0.0530152i
$708$		0			0
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	0.0747503	+	0.997202i	$0.476184\pi$
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	−0.900978	+	0.433865i	$0.857149\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.62772	+	2.81929i	−0.0609585	+	0.105583i
$714$		0			0
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.74456			0.102355			0.0511775	−	0.998690i	$-0.483703\pi$
$719$	2.74456			0.102355			0.0511775	+	0.998690i	$0.483703\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−61.7228	−	106.907i	−2.29233	−	3.97043i
$726$		0			0
$727$	−18.1168	+	31.3793i	−0.671917	+	1.16379i	0.305443	+	0.952210i	$0.401195\pi$
$727$	−18.1168	+	31.3793i	−0.671917	+	1.16379i	−0.977360	+	0.211583i	$0.932138\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.56930	−	9.64630i	0.205988	−	0.356781i
$732$		0			0
$733$	20.5584	+	35.6082i	0.759343	+	1.31522i	0.943186	+	0.332265i	$0.107813\pi$
$733$	20.5584	+	35.6082i	0.759343	+	1.31522i	−0.183844	+	0.982956i	$0.558854\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.90491			−0.107004
$738$		0			0
$739$	8.11684			0.298583			0.149291	−	0.988793i	$-0.452301\pi$
$739$	8.11684			0.298583			0.149291	+	0.988793i	$0.452301\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.86141	+	11.8843i	0.251721	+	0.435993i	0.964000	−	0.265904i	$-0.0856703\pi$
$743$	6.86141	+	11.8843i	0.251721	+	0.435993i	−0.712279	+	0.701896i	$0.752337\pi$
$744$		0			0
$745$	−7.11684	+	12.3267i	−0.260741	+	0.451617i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.68614	+	6.38458i	−0.134689	+	0.233288i
$750$		0			0
$751$	−8.55842	−	14.8236i	−0.312301	−	0.540922i	0.666559	−	0.745452i	$-0.267766\pi$
$751$	−8.55842	−	14.8236i	−0.312301	−	0.540922i	−0.978860	+	0.204531i	$0.934433\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	39.8614			1.45071
$756$		0			0
$757$	46.2337			1.68039			0.840196	−	0.542283i	$-0.182440\pi$
$757$	46.2337			1.68039			0.840196	+	0.542283i	$0.182440\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.7446	+	30.7345i	0.643240	+	1.11412i	0.984705	+	0.174230i	$0.0557435\pi$
$761$	17.7446	+	30.7345i	0.643240	+	1.11412i	−0.341465	+	0.939894i	$0.610923\pi$
$762$		0			0
$763$	7.00000	−	12.1244i	0.253417	−	0.438931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.1168	−	17.5229i	0.365298	−	0.632715i
$768$		0			0
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	0.941984	−	0.335657i	$-0.108958\pi$
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	−0.761680	+	0.647954i	$0.775625\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	39.8614			1.43372			0.716858	−	0.697220i	$-0.245580\pi$
$773$	39.8614			1.43372			0.716858	+	0.697220i	$0.245580\pi$
$774$		0			0
$775$	−28.2337			−1.01418
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.5693	−	20.0386i	−0.414513	−	0.717958i
$780$		0			0
$781$	−4.88316	+	8.45787i	−0.174733	+	0.302647i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	19.9307	−	34.5210i	0.711357	−	1.23211i
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.37228			−0.155460
$792$		0			0
$793$	6.23369			0.221365
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.06930	−	7.04823i	−0.144142	−	0.249661i	0.784911	−	0.619609i	$-0.212709\pi$
$797$	−4.06930	−	7.04823i	−0.144142	−	0.249661i	−0.929052	+	0.369948i	$0.879376\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.31386	−	14.4000i	0.293390	−	0.508166i
$804$		0			0
$805$	3.55842	+	6.16337i	0.125418	+	0.217230i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.86141			0.241234			0.120617	−	0.992699i	$-0.461513\pi$
$809$	6.86141			0.241234			0.120617	+	0.992699i	$0.461513\pi$
$810$		0			0
$811$	−42.1168			−1.47892			−0.739461	−	0.673199i	$-0.764920\pi$
$811$	−42.1168			−1.47892			−0.739461	+	0.673199i	$0.764920\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	39.8614	+	69.0420i	1.39628	+	2.41844i
$816$		0			0
$817$	20.2921	−	35.1470i	0.709931	−	1.22964i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.88316	+	3.26172i	−0.0657226	+	0.113835i	−0.897014	−	0.442002i	$-0.854269\pi$
$821$	−1.88316	+	3.26172i	−0.0657226	+	0.113835i	0.831292	+	0.555836i	$0.187602\pi$
$822$		0			0
$823$	−6.11684	−	10.5947i	−0.213220	−	0.369307i	0.739501	−	0.673156i	$-0.235062\pi$
$823$	−6.11684	−	10.5947i	−0.213220	−	0.369307i	−0.952720	+	0.303848i	$0.901728\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.686141	+	1.18843i	0.0237734	+	0.0411767i
$834$		0			0
$835$	−12.0000	+	20.7846i	−0.415277	+	0.719281i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.74456	+	4.75372i	−0.0947528	+	0.164117i	−0.909505	−	0.415692i	$-0.863539\pi$
$839$	−2.74456	+	4.75372i	−0.0947528	+	0.164117i	0.814753	+	0.579809i	$0.196873\pi$
$840$		0			0
$841$	−23.7337	−	41.1080i	−0.818403	−	1.41752i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	39.3505			1.35370
$846$		0			0
$847$	9.11684			0.313258
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.62772	+	2.81929i	0.0557975	+	0.0966441i
$852$		0			0
$853$	17.5584	−	30.4121i	0.601189	−	1.04129i	−0.391452	−	0.920198i	$-0.628027\pi$
$853$	17.5584	−	30.4121i	0.601189	−	1.04129i	0.992641	−	0.121091i	$-0.0386394\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.9783	+	34.6033i	−0.682444	+	1.18203i	0.291789	+	0.956483i	$0.405750\pi$
$857$	−19.9783	+	34.6033i	−0.682444	+	1.18203i	−0.974233	+	0.225545i	$0.927584\pi$
$858$		0			0
$859$	16.9416	+	29.3437i	0.578039	+	1.00119i	0.995704	+	0.0925921i	$0.0295153\pi$
$859$	16.9416	+	29.3437i	0.578039	+	1.00119i	−0.417665	+	0.908601i	$0.637151\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.86141			0.335686			0.167843	−	0.985814i	$-0.446320\pi$
$863$	9.86141			0.335686			0.167843	+	0.985814i	$0.446320\pi$
$864$		0			0
$865$	−26.2337			−0.891972
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.51087	+	6.08101i	0.119098	+	0.206284i
$870$		0			0
$871$	−2.11684	+	3.66648i	−0.0717265	+	0.124234i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−19.9307	+	34.5210i	−0.673781	+	1.16702i
$876$		0			0
$877$	29.3505	+	50.8366i	0.991097	+	1.71663i	0.610852	+	0.791744i	$0.290827\pi$
$877$	29.3505	+	50.8366i	0.991097	+	1.71663i	0.380245	+	0.924886i	$0.375840\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20.2337			0.681690			0.340845	−	0.940119i	$-0.389287\pi$
$881$	20.2337			0.681690			0.340845	+	0.940119i	$0.389287\pi$
$882$		0			0
$883$	40.3505			1.35790			0.678952	−	0.734183i	$-0.262435\pi$
$883$	40.3505			1.35790			0.678952	+	0.734183i	$0.262435\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.8614	−	22.2766i	−0.431844	−	0.747975i	0.565188	−	0.824962i	$-0.308803\pi$
$887$	−12.8614	−	22.2766i	−0.431844	−	0.747975i	−0.997032	+	0.0769865i	$0.975470\pi$
$888$		0			0
$889$	−1.55842	+	2.69927i	−0.0522678	+	0.0905305i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	7.11684	+	12.3267i	0.237890	+	0.412037i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.4891			−0.583295
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.93070	+	3.34408i	0.0641787	+	0.111161i
$906$		0			0
$907$	−13.0584	+	22.6179i	−0.433598	+	0.751013i	−0.997180	−	0.0750466i	$-0.976089\pi$
$907$	−13.0584	+	22.6179i	−0.433598	+	0.751013i	0.563582	+	0.826060i	$0.309423\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	18.8139	−	32.5866i	0.623331	−	1.07964i	−0.365530	−	0.930800i	$-0.619112\pi$
$911$	18.8139	−	32.5866i	0.623331	−	1.07964i	0.988861	−	0.148841i	$-0.0475544\pi$
$912$		0			0
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.62772			0.0537520
$918$		0			0
$919$	47.1168			1.55424			0.777121	−	0.629352i	$-0.216679\pi$
$919$	47.1168			1.55424			0.777121	+	0.629352i	$0.216679\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.11684	+	12.3267i	0.234254	+	0.405739i
$924$		0			0
$925$	−14.1168	+	24.4511i	−0.464159	+	0.803947i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	22.1168	−	38.3075i	0.725630	−	1.25683i	−0.233084	−	0.972457i	$-0.574882\pi$
$929$	22.1168	−	38.3075i	0.725630	−	1.25683i	0.958714	−	0.284372i	$-0.0917850\pi$
$930$		0			0
$931$	2.50000	+	4.33013i	0.0819342	+	0.141914i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.23369			−0.269270
$936$		0			0
$937$	30.4674			0.995326			0.497663	−	0.867371i	$-0.334192\pi$
$937$	30.4674			0.995326			0.497663	+	0.867371i	$0.334192\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.55842	+	16.5557i	0.311596	+	0.539699i	0.978708	−	0.205258i	$-0.0658032\pi$
$941$	9.55842	+	16.5557i	0.311596	+	0.539699i	−0.667112	+	0.744957i	$0.732470\pi$
$942$		0			0
$943$	−3.76631	+	6.52344i	−0.122648	+	0.212433i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.0584	+	29.5461i	−0.554324	+	0.960118i	0.443632	+	0.896209i	$0.353690\pi$
$947$	−17.0584	+	29.5461i	−0.554324	+	0.960118i	−0.997956	+	0.0639085i	$0.979643\pi$
$948$		0			0
$949$	−12.1168	−	20.9870i	−0.393329	−	0.681267i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−28.1168			−0.910794			−0.455397	−	0.890288i	$-0.650503\pi$
$953$	−28.1168			−0.910794			−0.455397	+	0.890288i	$0.650503\pi$
$954$		0			0
$955$	83.5842			2.70472
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.31386	−	9.20387i	−0.171593	−	0.297209i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−15.3030	+	26.5055i	−0.492621	+	0.853244i
$966$		0			0
$967$	15.4416	+	26.7456i	0.496568	+	0.860080i	0.999992	−	0.00395879i	$-0.00126012\pi$
$967$	15.4416	+	26.7456i	0.496568	+	0.860080i	−0.503424	+	0.864039i	$0.667927\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.62772			0.0522360			0.0261180	−	0.999659i	$-0.491685\pi$
$971$	1.62772			0.0522360			0.0261180	+	0.999659i	$0.491685\pi$
$972$		0			0
$973$	13.2337			0.424253
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.0584	+	34.7422i	0.641726	+	1.11150i	0.985047	+	0.172284i	$0.0551146\pi$
$977$	20.0584	+	34.7422i	0.641726	+	1.11150i	−0.343322	+	0.939218i	$0.611552\pi$
$978$		0			0
$979$	−10.1168	+	17.5229i	−0.323336	+	0.560034i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.6277	−	33.9962i	0.626027	−	1.08431i	−0.362314	−	0.932056i	$-0.618013\pi$
$983$	19.6277	−	33.9962i	0.626027	−	1.08431i	0.988341	−	0.152255i	$-0.0486534\pi$
$984$		0			0
$985$	13.1168	+	22.7190i	0.417937	+	0.723889i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.2119			−0.420115
$990$		0			0
$991$	−48.4674			−1.53962			−0.769808	−	0.638275i	$-0.779648\pi$
$991$	−48.4674			−1.53962			−0.769808	+	0.638275i	$0.779648\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	21.8614	+	37.8651i	0.693053	+	1.20040i
$996$		0			0
$997$	2.55842	−	4.43132i	0.0810260	−	0.140341i	−0.822665	−	0.568527i	$-0.807514\pi$
$997$	2.55842	−	4.43132i	0.0810260	−	0.140341i	0.903691	+	0.428185i	$0.140847\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.f.2017.2		4
3.2	odd	2		1008.2.r.f.673.2		4
4.3	odd	2		378.2.f.c.127.2		4
9.2	odd	6		9072.2.a.bm.1.2		2
9.4	even	3	inner	3024.2.r.f.1009.2		4
9.5	odd	6		1008.2.r.f.337.2		4
9.7	even	3		9072.2.a.bb.1.1		2
12.11	even	2		126.2.f.d.43.1	✓	4
28.3	even	6		2646.2.h.l.667.2		4
28.11	odd	6		2646.2.h.k.667.1		4
28.19	even	6		2646.2.e.m.2125.1		4
28.23	odd	6		2646.2.e.n.2125.2		4
28.27	even	2		2646.2.f.j.883.1		4
36.7	odd	6		1134.2.a.n.1.1		2
36.11	even	6		1134.2.a.k.1.2		2
36.23	even	6		126.2.f.d.85.1	yes	4
36.31	odd	6		378.2.f.c.253.2		4
84.11	even	6		882.2.h.m.79.2		4
84.23	even	6		882.2.e.l.655.1		4
84.47	odd	6		882.2.e.k.655.2		4
84.59	odd	6		882.2.h.n.79.1		4
84.83	odd	2		882.2.f.k.295.2		4
252.23	even	6		882.2.h.m.67.2		4
252.31	even	6		2646.2.e.m.1549.1		4
252.59	odd	6		882.2.e.k.373.1		4
252.67	odd	6		2646.2.e.n.1549.2		4
252.83	odd	6		7938.2.a.bh.1.1		2
252.95	even	6		882.2.e.l.373.2		4
252.103	even	6		2646.2.h.l.361.2		4
252.131	odd	6		882.2.h.n.67.1		4
252.139	even	6		2646.2.f.j.1765.1		4
252.167	odd	6		882.2.f.k.589.2		4
252.223	even	6		7938.2.a.bs.1.2		2
252.247	odd	6		2646.2.h.k.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.1	✓	4	12.11	even	2
126.2.f.d.85.1	yes	4	36.23	even	6
378.2.f.c.127.2		4	4.3	odd	2
378.2.f.c.253.2		4	36.31	odd	6
882.2.e.k.373.1		4	252.59	odd	6
882.2.e.k.655.2		4	84.47	odd	6
882.2.e.l.373.2		4	252.95	even	6
882.2.e.l.655.1		4	84.23	even	6
882.2.f.k.295.2		4	84.83	odd	2
882.2.f.k.589.2		4	252.167	odd	6
882.2.h.m.67.2		4	252.23	even	6
882.2.h.m.79.2		4	84.11	even	6
882.2.h.n.67.1		4	252.131	odd	6
882.2.h.n.79.1		4	84.59	odd	6
1008.2.r.f.337.2		4	9.5	odd	6
1008.2.r.f.673.2		4	3.2	odd	2
1134.2.a.k.1.2		2	36.11	even	6
1134.2.a.n.1.1		2	36.7	odd	6
2646.2.e.m.1549.1		4	252.31	even	6
2646.2.e.m.2125.1		4	28.19	even	6
2646.2.e.n.1549.2		4	252.67	odd	6
2646.2.e.n.2125.2		4	28.23	odd	6
2646.2.f.j.883.1		4	28.27	even	2
2646.2.f.j.1765.1		4	252.139	even	6
2646.2.h.k.361.1		4	252.247	odd	6
2646.2.h.k.667.1		4	28.11	odd	6
2646.2.h.l.361.2		4	252.103	even	6
2646.2.h.l.667.2		4	28.3	even	6
3024.2.r.f.1009.2		4	9.4	even	3	inner
3024.2.r.f.2017.2		4	1.1	even	1	trivial
7938.2.a.bh.1.1		2	252.83	odd	6
7938.2.a.bs.1.2		2	252.223	even	6
9072.2.a.bb.1.1		2	9.7	even	3
9072.2.a.bm.1.2		2	9.2	odd	6

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18614 + 3.78651i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(2.18614 + 3.78651i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.686141 - 1.18843i) q^{11} +(-1.00000 - 1.73205i) q^{13} -1.37228 q^{17} -5.00000 q^{19} +(0.813859 + 1.40965i) q^{23} +(-7.05842 + 12.2255i) q^{25} +(-4.37228 + 7.57301i) q^{29} +(1.00000 + 1.73205i) q^{31} +4.37228 q^{35} +2.00000 q^{37} +(2.31386 + 4.00772i) q^{41} +(-4.05842 + 7.02939i) q^{43} +(-0.500000 - 0.866025i) q^{49} +8.74456 q^{53} +6.00000 q^{55} +(5.05842 + 8.76144i) q^{59} +(-1.55842 + 2.69927i) q^{61} +(4.37228 - 7.57301i) q^{65} +(-1.05842 - 1.83324i) q^{67} -7.11684 q^{71} +12.1168 q^{73} +(-0.686141 - 1.18843i) q^{77} +(-2.55842 + 4.43132i) q^{79} +(-8.74456 + 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} -14.7446 q^{89} -2.00000 q^{91} +(-10.9307 - 18.9325i) q^{95} +(4.05842 - 7.02939i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q + 3 * q^5 + 2 * q^7	\( 4 q + 3 q^{5} + 2 q^{7} - 3 q^{11} - 4 q^{13} + 6 q^{17} - 20 q^{19} + 9 q^{23} - 11 q^{25} - 6 q^{29} + 4 q^{31} + 6 q^{35} + 8 q^{37} + 15 q^{41} + q^{43} - 2 q^{49} + 12 q^{53} + 24 q^{55} + 3 q^{59} + 11 q^{61} + 6 q^{65} + 13 q^{67} + 6 q^{71} + 14 q^{73} + 3 q^{77} + 7 q^{79} - 12 q^{83} - 12 q^{85} - 36 q^{89} - 8 q^{91} - 15 q^{95} - q^{97}+O(q^{100}) \) 4 * q + 3 * q^5 + 2 * q^7 - 3 * q^11 - 4 * q^13 + 6 * q^17 - 20 * q^19 + 9 * q^23 - 11 * q^25 - 6 * q^29 + 4 * q^31 + 6 * q^35 + 8 * q^37 + 15 * q^41 + q^43 - 2 * q^49 + 12 * q^53 + 24 * q^55 + 3 * q^59 + 11 * q^61 + 6 * q^65 + 13 * q^67 + 6 * q^71 + 14 * q^73 + 3 * q^77 + 7 * q^79 - 12 * q^83 - 12 * q^85 - 36 * q^89 - 8 * q^91 - 15 * q^95 - q^97

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