LMFDB - Embedded newform 2070.2.d.e.829.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(829,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2070.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.d (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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 690)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			829.4
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	2070.829
Dual form			2070.2.d.e.829.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-2.21432 - 0.311108i) q^{5} -0.622216i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.21432 - 0.311108i) q^{5} -0.622216i q^{7} -1.00000i q^{8} +(0.311108 - 2.21432i) q^{10} -4.42864 q^{11} +1.37778i q^{13} +0.622216 q^{14} +1.00000 q^{16} +6.42864i q^{17} +1.37778 q^{19} +(2.21432 + 0.311108i) q^{20} -4.42864i q^{22} -1.00000i q^{23} +(4.80642 + 1.37778i) q^{25} -1.37778 q^{26} +0.622216i q^{28} -4.23506 q^{29} -4.00000 q^{31} +1.00000i q^{32} -6.42864 q^{34} +(-0.193576 + 1.37778i) q^{35} -11.8064i q^{37} +1.37778i q^{38} +(-0.311108 + 2.21432i) q^{40} +10.8573 q^{41} -1.05086i q^{43} +4.42864 q^{44} +1.00000 q^{46} -11.6128i q^{47} +6.61285 q^{49} +(-1.37778 + 4.80642i) q^{50} -1.37778i q^{52} -3.37778i q^{53} +(9.80642 + 1.37778i) q^{55} -0.622216 q^{56} -4.23506i q^{58} +9.61285 q^{59} +8.66370 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(0.428639 - 3.05086i) q^{65} -11.8064i q^{67} -6.42864i q^{68} +(-1.37778 - 0.193576i) q^{70} +6.99063 q^{71} +2.75557i q^{73} +11.8064 q^{74} -1.37778 q^{76} +2.75557i q^{77} -12.0415 q^{79} +(-2.21432 - 0.311108i) q^{80} +10.8573i q^{82} -2.19358i q^{83} +(2.00000 - 14.2351i) q^{85} +1.05086 q^{86} +4.42864i q^{88} +2.75557 q^{89} +0.857279 q^{91} +1.00000i q^{92} +11.6128 q^{94} +(-3.05086 - 0.428639i) q^{95} +2.13335i q^{97} +6.61285i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4}+O(q^{10}) $ 6 * q - 6 * q^4	$ 6 q - 6 q^{4} + 2 q^{10} + 4 q^{14} + 6 q^{16} + 8 q^{19} + 2 q^{25} - 8 q^{26} + 28 q^{29} - 24 q^{31} - 12 q^{34} - 28 q^{35} - 2 q^{40} + 12 q^{41} + 6 q^{46} - 14 q^{49} - 8 q^{50} + 32 q^{55} - 4 q^{56} + 4 q^{59} - 28 q^{61} - 6 q^{64} - 24 q^{65} - 8 q^{70} - 12 q^{71} + 44 q^{74} - 8 q^{76} + 8 q^{79} + 12 q^{85} - 20 q^{86} + 16 q^{89} - 48 q^{91} + 16 q^{94} + 8 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^10 + 4 * q^14 + 6 * q^16 + 8 * q^19 + 2 * q^25 - 8 * q^26 + 28 * q^29 - 24 * q^31 - 12 * q^34 - 28 * q^35 - 2 * q^40 + 12 * q^41 + 6 * q^46 - 14 * q^49 - 8 * q^50 + 32 * q^55 - 4 * q^56 + 4 * q^59 - 28 * q^61 - 6 * q^64 - 24 * q^65 - 8 * q^70 - 12 * q^71 + 44 * q^74 - 8 * q^76 + 8 * q^79 + 12 * q^85 - 20 * q^86 + 16 * q^89 - 48 * q^91 + 16 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.21432	−	0.311108i	−0.990274	−	0.139132i
$5$	−2.21432	−	0.311108i	−0.990274	−	0.139132i
$6$		0			0
$7$		−	0.622216i		−	0.235175i	−0.993063	−	0.117588i	$-0.962484\pi$
$7$		−	0.622216i		−	0.235175i	0.993063	−	0.117588i	$-0.0375161\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.311108	−	2.21432i	0.0983809	−	0.700229i
$11$	−4.42864			−1.33529			−0.667643	−	0.744482i	$-0.732697\pi$
$11$	−4.42864			−1.33529			−0.667643	+	0.744482i	$0.732697\pi$
$12$		0			0
$13$			1.37778i			0.382129i	0.981578	+	0.191064i	$0.0611939\pi$
$13$			1.37778i			0.382129i	−0.981578	+	0.191064i	$0.938806\pi$
$14$	0.622216			0.166294
$15$		0			0
$16$	1.00000			0.250000
$17$			6.42864i			1.55917i	0.626294	+	0.779587i	$0.284571\pi$
$17$			6.42864i			1.55917i	−0.626294	+	0.779587i	$0.715429\pi$
$18$		0			0
$19$	1.37778			0.316085			0.158043	−	0.987432i	$-0.449482\pi$
$19$	1.37778			0.316085			0.158043	+	0.987432i	$0.449482\pi$
$20$	2.21432	+	0.311108i	0.495137	+	0.0695658i
$21$		0			0
$22$		−	4.42864i		−	0.944189i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$		0			0
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$	−1.37778			−0.270206
$27$		0			0
$28$			0.622216i			0.117588i
$29$	−4.23506			−0.786432			−0.393216	−	0.919446i	$-0.628637\pi$
$29$	−4.23506			−0.786432			−0.393216	+	0.919446i	$0.628637\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−6.42864			−1.10250
$35$	−0.193576	+	1.37778i	−0.0327203	+	0.232888i
$36$		0			0
$37$		−	11.8064i		−	1.94096i	−0.241173	−	0.970482i	$-0.577532\pi$
$37$		−	11.8064i		−	1.94096i	0.241173	−	0.970482i	$-0.422468\pi$
$38$			1.37778i			0.223506i
$39$		0			0
$40$	−0.311108	+	2.21432i	−0.0491905	+	0.350115i
$41$	10.8573			1.69562			0.847811	−	0.530298i	$-0.177920\pi$
$41$	10.8573			1.69562			0.847811	+	0.530298i	$0.177920\pi$
$42$		0			0
$43$		−	1.05086i		−	0.160254i	−0.996785	−	0.0801270i	$-0.974467\pi$
$43$		−	1.05086i		−	0.160254i	0.996785	−	0.0801270i	$-0.0255326\pi$
$44$	4.42864			0.667643
$45$		0			0
$46$	1.00000			0.147442
$47$		−	11.6128i		−	1.69391i	−0.531666	−	0.846954i	$-0.678434\pi$
$47$		−	11.6128i		−	1.69391i	0.531666	−	0.846954i	$-0.321566\pi$
$48$		0			0
$49$	6.61285			0.944693
$50$	−1.37778	+	4.80642i	−0.194848	+	0.679731i
$51$		0			0
$52$		−	1.37778i		−	0.191064i
$53$		−	3.37778i		−	0.463974i	−0.972719	−	0.231987i	$-0.925477\pi$
$53$		−	3.37778i		−	0.463974i	0.972719	−	0.231987i	$-0.0745227\pi$
$54$		0			0
$55$	9.80642	+	1.37778i	1.32230	+	0.185780i
$56$	−0.622216			−0.0831471
$57$		0			0
$58$		−	4.23506i		−	0.556091i
$59$	9.61285			1.25149			0.625743	−	0.780029i	$-0.284796\pi$
$59$	9.61285			1.25149			0.625743	+	0.780029i	$0.284796\pi$
$60$		0			0
$61$	8.66370			1.10927			0.554637	−	0.832093i	$-0.312857\pi$
$61$	8.66370			1.10927			0.554637	+	0.832093i	$0.312857\pi$
$62$		−	4.00000i		−	0.508001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.428639	−	3.05086i	0.0531662	−	0.378412i
$66$		0			0
$67$		−	11.8064i		−	1.44238i	−0.692735	−	0.721192i	$-0.743594\pi$
$67$		−	11.8064i		−	1.44238i	0.692735	−	0.721192i	$-0.256406\pi$
$68$		−	6.42864i		−	0.779587i
$69$		0			0
$70$	−1.37778	−	0.193576i	−0.164677	−	0.0231368i
$71$	6.99063			0.829635			0.414818	−	0.909905i	$-0.363845\pi$
$71$	6.99063			0.829635			0.414818	+	0.909905i	$0.363845\pi$
$72$		0			0
$73$			2.75557i			0.322515i	0.986912	+	0.161257i	$0.0515550\pi$
$73$			2.75557i			0.322515i	−0.986912	+	0.161257i	$0.948445\pi$
$74$	11.8064			1.37247
$75$		0			0
$76$	−1.37778			−0.158043
$77$			2.75557i			0.314026i
$78$		0			0
$79$	−12.0415			−1.35477			−0.677387	−	0.735627i	$-0.736888\pi$
$79$	−12.0415			−1.35477			−0.677387	+	0.735627i	$0.736888\pi$
$80$	−2.21432	−	0.311108i	−0.247568	−	0.0347829i
$81$		0			0
$82$			10.8573i			1.19899i
$83$		−	2.19358i		−	0.240776i	−0.992727	−	0.120388i	$-0.961586\pi$
$83$		−	2.19358i		−	0.240776i	0.992727	−	0.120388i	$-0.0384139\pi$
$84$		0			0
$85$	2.00000	−	14.2351i	0.216930	−	1.54401i
$86$	1.05086			0.113317
$87$		0			0
$88$			4.42864i			0.472095i
$89$	2.75557			0.292090			0.146045	−	0.989278i	$-0.453346\pi$
$89$	2.75557			0.292090			0.146045	+	0.989278i	$0.453346\pi$
$90$		0			0
$91$	0.857279			0.0898673
$92$			1.00000i			0.104257i
$93$		0			0
$94$	11.6128			1.19777
$95$	−3.05086	−	0.428639i	−0.313011	−	0.0439775i
$96$		0			0
$97$			2.13335i			0.216609i	0.994118	+	0.108305i	$0.0345422\pi$
$97$			2.13335i			0.216609i	−0.994118	+	0.108305i	$0.965458\pi$
$98$			6.61285i			0.667998i
$99$		0			0
$100$	−4.80642	−	1.37778i	−0.480642	−	0.137778i
$101$	−16.2351			−1.61545			−0.807725	−	0.589560i	$-0.799301\pi$
$101$	−16.2351			−1.61545			−0.807725	+	0.589560i	$0.799301\pi$
$102$		0			0
$103$			12.2351i			1.20556i	0.797909	+	0.602778i	$0.205940\pi$
$103$			12.2351i			1.20556i	−0.797909	+	0.602778i	$0.794060\pi$
$104$	1.37778			0.135103
$105$		0			0
$106$	3.37778			0.328079
$107$		−	10.6637i		−	1.03090i	−0.856920	−	0.515450i	$-0.827625\pi$
$107$		−	10.6637i		−	1.03090i	0.856920	−	0.515450i	$-0.172375\pi$
$108$		0			0
$109$	15.1526			1.45135			0.725676	−	0.688036i	$-0.241527\pi$
$109$	15.1526			1.45135			0.725676	+	0.688036i	$0.241527\pi$
$110$	−1.37778	+	9.80642i	−0.131367	+	0.935006i
$111$		0			0
$112$		−	0.622216i		−	0.0587939i
$113$		−	14.4286i		−	1.35733i	−0.734447	−	0.678666i	$-0.762558\pi$
$113$		−	14.4286i		−	1.35733i	0.734447	−	0.678666i	$-0.237442\pi$
$114$		0			0
$115$	−0.311108	+	2.21432i	−0.0290110	+	0.206486i
$116$	4.23506			0.393216
$117$		0			0
$118$			9.61285i			0.884934i
$119$	4.00000			0.366679
$120$		0			0
$121$	8.61285			0.782986
$122$			8.66370i			0.784375i
$123$		0			0
$124$	4.00000			0.359211
$125$	−10.2143	−	4.54617i	−0.913597	−	0.406622i
$126$		0			0
$127$			4.99063i			0.442847i	0.975178	+	0.221423i	$0.0710703\pi$
$127$			4.99063i			0.442847i	−0.975178	+	0.221423i	$0.928930\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	3.05086	+	0.428639i	0.267578	+	0.0375942i
$131$	−0.755569			−0.0660143			−0.0330072	−	0.999455i	$-0.510508\pi$
$131$	−0.755569			−0.0660143			−0.0330072	+	0.999455i	$0.510508\pi$
$132$		0			0
$133$		−	0.857279i		−	0.0743355i
$134$	11.8064			1.01992
$135$		0			0
$136$	6.42864			0.551251
$137$			12.9175i			1.10362i	0.833971	+	0.551808i	$0.186062\pi$
$137$			12.9175i			1.10362i	−0.833971	+	0.551808i	$0.813938\pi$
$138$		0			0
$139$	14.1017			1.19609			0.598046	−	0.801462i	$-0.295944\pi$
$139$	14.1017			1.19609			0.598046	+	0.801462i	$0.295944\pi$
$140$	0.193576	−	1.37778i	0.0163602	−	0.116444i
$141$		0			0
$142$			6.99063i			0.586641i
$143$		−	6.10171i		−	0.510251i
$144$		0			0
$145$	9.37778	+	1.31756i	0.778783	+	0.109418i
$146$	−2.75557			−0.228052
$147$		0			0
$148$			11.8064i			0.970482i
$149$	12.4286			1.01819			0.509097	−	0.860709i	$-0.329979\pi$
$149$	12.4286			1.01819			0.509097	+	0.860709i	$0.329979\pi$
$150$		0			0
$151$	−4.85728			−0.395280			−0.197640	−	0.980275i	$-0.563328\pi$
$151$	−4.85728			−0.395280			−0.197640	+	0.980275i	$0.563328\pi$
$152$		−	1.37778i		−	0.111753i
$153$		0			0
$154$	−2.75557			−0.222050
$155$	8.85728	+	1.24443i	0.711434	+	0.0999551i
$156$		0			0
$157$			9.90813i			0.790755i	0.918519	+	0.395378i	$0.129386\pi$
$157$			9.90813i			0.790755i	−0.918519	+	0.395378i	$0.870614\pi$
$158$		−	12.0415i		−	0.957969i
$159$		0			0
$160$	0.311108	−	2.21432i	0.0245952	−	0.175057i
$161$	−0.622216			−0.0490375
$162$		0			0
$163$			10.1017i			0.791227i	0.918417	+	0.395614i	$0.129468\pi$
$163$			10.1017i			0.791227i	−0.918417	+	0.395614i	$0.870532\pi$
$164$	−10.8573			−0.847811
$165$		0			0
$166$	2.19358			0.170255
$167$			1.89829i			0.146894i	0.997299	+	0.0734470i	$0.0234000\pi$
$167$			1.89829i			0.146894i	−0.997299	+	0.0734470i	$0.976600\pi$
$168$		0			0
$169$	11.1017			0.853978
$170$	14.2351	+	2.00000i	1.09178	+	0.153393i
$171$		0			0
$172$			1.05086i			0.0801270i
$173$		−	21.2257i		−	1.61376i	−0.590716	−	0.806880i	$-0.701154\pi$
$173$		−	21.2257i		−	1.61376i	0.590716	−	0.806880i	$-0.298846\pi$
$174$		0			0
$175$	0.857279	−	2.99063i	0.0648042	−	0.226071i
$176$	−4.42864			−0.333821
$177$		0			0
$178$			2.75557i			0.206539i
$179$	0.488863			0.0365393			0.0182697	−	0.999833i	$-0.494184\pi$
$179$	0.488863			0.0365393			0.0182697	+	0.999833i	$0.494184\pi$
$180$		0			0
$181$	−20.9304			−1.55575			−0.777873	−	0.628422i	$-0.783701\pi$
$181$	−20.9304			−1.55575			−0.777873	+	0.628422i	$0.783701\pi$
$182$			0.857279i			0.0635457i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	−3.67307	+	26.1432i	−0.270050	+	1.92209i
$186$		0			0
$187$		−	28.4701i		−	2.08194i
$188$			11.6128i			0.846954i
$189$		0			0
$190$	0.428639	−	3.05086i	0.0310968	−	0.221332i
$191$	−18.9590			−1.37182			−0.685912	−	0.727684i	$-0.740597\pi$
$191$	−18.9590			−1.37182			−0.685912	+	0.727684i	$0.740597\pi$
$192$		0			0
$193$		−	1.24443i		−	0.0895761i	−0.998997	−	0.0447881i	$-0.985739\pi$
$193$		−	1.24443i		−	0.0895761i	0.998997	−	0.0447881i	$-0.0142613\pi$
$194$	−2.13335			−0.153166
$195$		0			0
$196$	−6.61285			−0.472346
$197$		−	15.2444i		−	1.08612i	−0.839694	−	0.543060i	$-0.817265\pi$
$197$		−	15.2444i		−	1.08612i	0.839694	−	0.543060i	$-0.182735\pi$
$198$		0			0
$199$	14.5303			1.03003			0.515015	−	0.857181i	$-0.327786\pi$
$199$	14.5303			1.03003			0.515015	+	0.857181i	$0.327786\pi$
$200$	1.37778	−	4.80642i	0.0974241	−	0.339865i
$201$		0			0
$202$		−	16.2351i		−	1.14230i
$203$			2.63512i			0.184949i
$204$		0			0
$205$	−24.0415	−	3.37778i	−1.67913	−	0.235915i
$206$	−12.2351			−0.852457
$207$		0			0
$208$			1.37778i			0.0955322i
$209$	−6.10171			−0.422064
$210$		0			0
$211$	0.266706			0.0183608			0.00918041	−	0.999958i	$-0.497078\pi$
$211$	0.266706			0.0183608			0.00918041	+	0.999958i	$0.497078\pi$
$212$			3.37778i			0.231987i
$213$		0			0
$214$	10.6637			0.728956
$215$	−0.326929	+	2.32693i	−0.0222964	+	0.158695i
$216$		0			0
$217$			2.48886i			0.168955i
$218$			15.1526i			1.02626i
$219$		0			0
$220$	−9.80642	−	1.37778i	−0.661149	−	0.0928902i
$221$	−8.85728			−0.595805
$222$		0			0
$223$		−	0.990632i		−	0.0663376i	−0.999450	−	0.0331688i	$-0.989440\pi$
$223$		−	0.990632i		−	0.0663376i	0.999450	−	0.0331688i	$-0.0105599\pi$
$224$	0.622216			0.0415735
$225$		0			0
$226$	14.4286			0.959779
$227$		−	17.1526i		−	1.13846i	−0.822180	−	0.569228i	$-0.807242\pi$
$227$		−	17.1526i		−	1.13846i	0.822180	−	0.569228i	$-0.192758\pi$
$228$		0			0
$229$	−7.15257			−0.472655			−0.236327	−	0.971673i	$-0.575944\pi$
$229$	−7.15257			−0.472655			−0.236327	+	0.971673i	$0.575944\pi$
$230$	−2.21432	−	0.311108i	−0.146008	−	0.0205138i
$231$		0			0
$232$			4.23506i			0.278046i
$233$			3.71456i			0.243349i	0.992570	+	0.121674i	$0.0388264\pi$
$233$			3.71456i			0.243349i	−0.992570	+	0.121674i	$0.961174\pi$
$234$		0			0
$235$	−3.61285	+	25.7146i	−0.235676	+	1.67743i
$236$	−9.61285			−0.625743
$237$		0			0
$238$			4.00000i			0.259281i
$239$	27.8479			1.80133			0.900666	−	0.434512i	$-0.143079\pi$
$239$	27.8479			1.80133			0.900666	+	0.434512i	$0.143079\pi$
$240$		0			0
$241$	−7.12399			−0.458896			−0.229448	−	0.973321i	$-0.573692\pi$
$241$	−7.12399			−0.458896			−0.229448	+	0.973321i	$0.573692\pi$
$242$			8.61285i			0.553655i
$243$		0			0
$244$	−8.66370			−0.554637
$245$	−14.6430	−	2.05731i	−0.935504	−	0.131437i
$246$		0			0
$247$			1.89829i			0.120785i
$248$			4.00000i			0.254000i
$249$		0			0
$250$	4.54617	−	10.2143i	0.287525	−	0.646010i
$251$	22.4099			1.41450			0.707250	−	0.706963i	$-0.249935\pi$
$251$	22.4099			1.41450			0.707250	+	0.706963i	$0.249935\pi$
$252$		0			0
$253$			4.42864i			0.278426i
$254$	−4.99063			−0.313140
$255$		0			0
$256$	1.00000			0.0625000
$257$			11.7146i			0.730734i	0.930864	+	0.365367i	$0.119057\pi$
$257$			11.7146i			0.730734i	−0.930864	+	0.365367i	$0.880943\pi$
$258$		0			0
$259$	−7.34614			−0.456467
$260$	−0.428639	+	3.05086i	−0.0265831	+	0.189206i
$261$		0			0
$262$		−	0.755569i		−	0.0466792i
$263$		−	8.47013i		−	0.522290i	−0.965300	−	0.261145i	$-0.915900\pi$
$263$		−	8.47013i		−	0.522290i	0.965300	−	0.261145i	$-0.0841001\pi$
$264$		0			0
$265$	−1.05086	+	7.47949i	−0.0645535	+	0.459462i
$266$	0.857279			0.0525631
$267$		0			0
$268$			11.8064i			0.721192i
$269$	28.8256			1.75753			0.878765	−	0.477255i	$-0.158368\pi$
$269$	28.8256			1.75753			0.878765	+	0.477255i	$0.158368\pi$
$270$		0			0
$271$	−13.8350			−0.840417			−0.420208	−	0.907428i	$-0.638043\pi$
$271$	−13.8350			−0.840417			−0.420208	+	0.907428i	$0.638043\pi$
$272$			6.42864i			0.389794i
$273$		0			0
$274$	−12.9175			−0.780375
$275$	−21.2859	−	6.10171i	−1.28359	−	0.367947i
$276$		0			0
$277$			2.88892i			0.173578i	0.996227	+	0.0867892i	$0.0276607\pi$
$277$			2.88892i			0.173578i	−0.996227	+	0.0867892i	$0.972339\pi$
$278$			14.1017i			0.845764i
$279$		0			0
$280$	1.37778	+	0.193576i	0.0823384	+	0.0115684i
$281$	−5.51114			−0.328767			−0.164383	−	0.986397i	$-0.552563\pi$
$281$	−5.51114			−0.328767			−0.164383	+	0.986397i	$0.552563\pi$
$282$		0			0
$283$		−	8.19358i		−	0.487058i	−0.969894	−	0.243529i	$-0.921695\pi$
$283$		−	8.19358i		−	0.487058i	0.969894	−	0.243529i	$-0.0783050\pi$
$284$	−6.99063			−0.414818
$285$		0			0
$286$	6.10171			0.360802
$287$		−	6.75557i		−	0.398769i
$288$		0			0
$289$	−24.3274			−1.43102
$290$	−1.31756	+	9.37778i	−0.0773699	+	0.550682i
$291$		0			0
$292$		−	2.75557i		−	0.161257i
$293$			12.6222i			0.737398i	0.929549	+	0.368699i	$0.120197\pi$
$293$			12.6222i			0.737398i	−0.929549	+	0.368699i	$0.879803\pi$
$294$		0			0
$295$	−21.2859	−	2.99063i	−1.23931	−	0.174121i
$296$	−11.8064			−0.686234
$297$		0			0
$298$			12.4286i			0.719972i
$299$	1.37778			0.0796793
$300$		0			0
$301$	−0.653858			−0.0376878
$302$		−	4.85728i		−	0.279505i
$303$		0			0
$304$	1.37778			0.0790214
$305$	−19.1842	−	2.69535i	−1.09848	−	0.154335i
$306$		0			0
$307$		−	0.653858i		−	0.0373177i	−0.999826	−	0.0186588i	$-0.994060\pi$
$307$		−	0.653858i		−	0.0373177i	0.999826	−	0.0186588i	$-0.00593964\pi$
$308$		−	2.75557i		−	0.157013i
$309$		0			0
$310$	−1.24443	+	8.85728i	−0.0706789	+	0.503060i
$311$	13.0923			0.742399			0.371199	−	0.928553i	$-0.378947\pi$
$311$	13.0923			0.742399			0.371199	+	0.928553i	$0.378947\pi$
$312$		0			0
$313$		−	11.2573i		−	0.636302i	−0.948040	−	0.318151i	$-0.896938\pi$
$313$		−	11.2573i		−	0.636302i	0.948040	−	0.318151i	$-0.103062\pi$
$314$	−9.90813			−0.559148
$315$		0			0
$316$	12.0415			0.677387
$317$			22.4701i			1.26205i	0.775763	+	0.631024i	$0.217365\pi$
$317$			22.4701i			1.26205i	−0.775763	+	0.631024i	$0.782635\pi$
$318$		0			0
$319$	18.7556			1.05011
$320$	2.21432	+	0.311108i	0.123784	+	0.0173915i
$321$		0			0
$322$		−	0.622216i		−	0.0346747i
$323$			8.85728i			0.492832i
$324$		0			0
$325$	−1.89829	+	6.62222i	−0.105298	+	0.367334i
$326$	−10.1017			−0.559482
$327$		0			0
$328$		−	10.8573i		−	0.599493i
$329$	−7.22570			−0.398365
$330$		0			0
$331$	−29.4479			−1.61860			−0.809300	−	0.587395i	$-0.800153\pi$
$331$	−29.4479			−1.61860			−0.809300	+	0.587395i	$0.800153\pi$
$332$			2.19358i			0.120388i
$333$		0			0
$334$	−1.89829			−0.103870
$335$	−3.67307	+	26.1432i	−0.200681	+	1.42836i
$336$		0			0
$337$		−	24.6222i		−	1.34126i	−0.741793	−	0.670629i	$-0.766024\pi$
$337$		−	24.6222i		−	1.34126i	0.741793	−	0.670629i	$-0.233976\pi$
$338$			11.1017i			0.603853i
$339$		0			0
$340$	−2.00000	+	14.2351i	−0.108465	+	0.772005i
$341$	17.7146			0.959297
$342$		0			0
$343$		−	8.47013i		−	0.457344i
$344$	−1.05086			−0.0566583
$345$		0			0
$346$	21.2257			1.14110
$347$		−	26.1017i		−	1.40121i	−0.713548	−	0.700607i	$-0.752913\pi$
$347$		−	26.1017i		−	1.40121i	0.713548	−	0.700607i	$-0.247087\pi$
$348$		0			0
$349$	21.2257			1.13619			0.568093	−	0.822965i	$-0.307681\pi$
$349$	21.2257			1.13619			0.568093	+	0.822965i	$0.307681\pi$
$350$	2.99063	+	0.857279i	0.159856	+	0.0458235i
$351$		0			0
$352$		−	4.42864i		−	0.236047i
$353$		−	4.28544i		−	0.228091i	−0.993476	−	0.114046i	$-0.963619\pi$
$353$		−	4.28544i		−	0.228091i	0.993476	−	0.114046i	$-0.0363810\pi$
$354$		0			0
$355$	−15.4795	−	2.17484i	−0.821566	−	0.115429i
$356$	−2.75557			−0.146045
$357$		0			0
$358$			0.488863i			0.0258372i
$359$	−4.65386			−0.245621			−0.122811	−	0.992430i	$-0.539191\pi$
$359$	−4.65386			−0.245621			−0.122811	+	0.992430i	$0.539191\pi$
$360$		0			0
$361$	−17.1017			−0.900090
$362$		−	20.9304i		−	1.10008i
$363$		0			0
$364$	−0.857279			−0.0449336
$365$	0.857279	−	6.10171i	0.0448720	−	0.319378i
$366$		0			0
$367$			4.88892i			0.255200i	0.991826	+	0.127600i	$0.0407273\pi$
$367$			4.88892i			0.255200i	−0.991826	+	0.127600i	$0.959273\pi$
$368$		−	1.00000i		−	0.0521286i
$369$		0			0
$370$	−26.1432	−	3.67307i	−1.35912	−	0.190954i
$371$	−2.10171			−0.109115
$372$		0			0
$373$		−	23.4193i		−	1.21260i	−0.795235	−	0.606302i	$-0.792652\pi$
$373$		−	23.4193i		−	1.21260i	0.795235	−	0.606302i	$-0.207348\pi$
$374$	28.4701			1.47216
$375$		0			0
$376$	−11.6128			−0.598887
$377$		−	5.83500i		−	0.300518i
$378$		0			0
$379$	4.90766			0.252089			0.126045	−	0.992025i	$-0.459772\pi$
$379$	4.90766			0.252089			0.126045	+	0.992025i	$0.459772\pi$
$380$	3.05086	+	0.428639i	0.156506	+	0.0219887i
$381$		0			0
$382$		−	18.9590i		−	0.970026i
$383$		−	19.8796i		−	1.01580i	−0.861417	−	0.507899i	$-0.830422\pi$
$383$		−	19.8796i		−	1.01580i	0.861417	−	0.507899i	$-0.169578\pi$
$384$		0			0
$385$	0.857279	−	6.10171i	0.0436910	−	0.310972i
$386$	1.24443			0.0633399
$387$		0			0
$388$		−	2.13335i		−	0.108305i
$389$	−0.161933			−0.00821034			−0.00410517	−	0.999992i	$-0.501307\pi$
$389$	−0.161933			−0.00821034			−0.00410517	+	0.999992i	$0.501307\pi$
$390$		0			0
$391$	6.42864			0.325110
$392$		−	6.61285i		−	0.333999i
$393$		0			0
$394$	15.2444			0.768003
$395$	26.6637	+	3.74620i	1.34160	+	0.188492i
$396$		0			0
$397$			1.76494i			0.0885796i	0.999019	+	0.0442898i	$0.0141025\pi$
$397$			1.76494i			0.0885796i	−0.999019	+	0.0442898i	$0.985898\pi$
$398$			14.5303i			0.728341i
$399$		0			0
$400$	4.80642	+	1.37778i	0.240321	+	0.0688892i
$401$	31.3461			1.56535			0.782676	−	0.622430i	$-0.213854\pi$
$401$	31.3461			1.56535			0.782676	+	0.622430i	$0.213854\pi$
$402$		0			0
$403$		−	5.51114i		−	0.274529i
$404$	16.2351			0.807725
$405$		0			0
$406$	−2.63512			−0.130779
$407$			52.2864i			2.59174i
$408$		0			0
$409$	3.51114			0.173615			0.0868073	−	0.996225i	$-0.472334\pi$
$409$	3.51114			0.173615			0.0868073	+	0.996225i	$0.472334\pi$
$410$	3.37778	−	24.0415i	0.166817	−	1.18732i
$411$		0			0
$412$		−	12.2351i		−	0.602778i
$413$		−	5.98126i		−	0.294319i
$414$		0			0
$415$	−0.682439	+	4.85728i	−0.0334996	+	0.238434i
$416$	−1.37778			−0.0675514
$417$		0			0
$418$		−	6.10171i		−	0.298444i
$419$	−19.7748			−0.966061			−0.483031	−	0.875603i	$-0.660464\pi$
$419$	−19.7748			−0.966061			−0.483031	+	0.875603i	$0.660464\pi$
$420$		0			0
$421$	11.8064			0.575410			0.287705	−	0.957719i	$-0.407108\pi$
$421$	11.8064			0.575410			0.287705	+	0.957719i	$0.407108\pi$
$422$			0.266706i			0.0129831i
$423$		0			0
$424$	−3.37778			−0.164040
$425$	−8.85728	+	30.8988i	−0.429641	+	1.49881i
$426$		0			0
$427$		−	5.39069i		−	0.260874i
$428$			10.6637i			0.515450i
$429$		0			0
$430$	−2.32693	−	0.326929i	−0.112214	−	0.0157659i
$431$	−24.9403			−1.20133			−0.600665	−	0.799501i	$-0.705097\pi$
$431$	−24.9403			−1.20133			−0.600665	+	0.799501i	$0.705097\pi$
$432$		0			0
$433$			32.0513i			1.54029i	0.637870	+	0.770144i	$0.279816\pi$
$433$			32.0513i			1.54029i	−0.637870	+	0.770144i	$0.720184\pi$
$434$	−2.48886			−0.119469
$435$		0			0
$436$	−15.1526			−0.725676
$437$		−	1.37778i		−	0.0659084i
$438$		0			0
$439$	−0.470127			−0.0224379			−0.0112190	−	0.999937i	$-0.503571\pi$
$439$	−0.470127			−0.0224379			−0.0112190	+	0.999937i	$0.503571\pi$
$440$	1.37778	−	9.80642i	0.0656833	−	0.467503i
$441$		0			0
$442$		−	8.85728i		−	0.421298i
$443$		−	0.653858i		−	0.0310658i	−0.999879	−	0.0155329i	$-0.995056\pi$
$443$		−	0.653858i		−	0.0310658i	0.999879	−	0.0155329i	$-0.00494447\pi$
$444$		0			0
$445$	−6.10171	−	0.857279i	−0.289249	−	0.0406389i
$446$	0.990632			0.0469078
$447$		0			0
$448$			0.622216i			0.0293969i
$449$	17.1427			0.809015			0.404508	−	0.914535i	$-0.367443\pi$
$449$	17.1427			0.809015			0.404508	+	0.914535i	$0.367443\pi$
$450$		0			0
$451$	−48.0830			−2.26414
$452$			14.4286i			0.678666i
$453$		0			0
$454$	17.1526			0.805010
$455$	−1.89829	−	0.266706i	−0.0889932	−	0.0125034i
$456$		0			0
$457$			1.00937i			0.0472162i	0.999721	+	0.0236081i	$0.00751540\pi$
$457$			1.00937i			0.0472162i	−0.999721	+	0.0236081i	$0.992485\pi$
$458$		−	7.15257i		−	0.334217i
$459$		0			0
$460$	0.311108	−	2.21432i	0.0145055	−	0.103243i
$461$	−20.3180			−0.946305			−0.473153	−	0.880980i	$-0.656884\pi$
$461$	−20.3180			−0.946305			−0.473153	+	0.880980i	$0.656884\pi$
$462$		0			0
$463$		−	12.4572i		−	0.578936i	−0.957188	−	0.289468i	$-0.906522\pi$
$463$		−	12.4572i		−	0.578936i	0.957188	−	0.289468i	$-0.0934784\pi$
$464$	−4.23506			−0.196608
$465$		0			0
$466$	−3.71456			−0.172074
$467$			15.7877i			0.730567i	0.930896	+	0.365284i	$0.119028\pi$
$467$			15.7877i			0.730567i	−0.930896	+	0.365284i	$0.880972\pi$
$468$		0			0
$469$	−7.34614			−0.339213
$470$	−25.7146	−	3.61285i	−1.18612	−	0.166648i
$471$		0			0
$472$		−	9.61285i		−	0.442467i
$473$			4.65386i			0.213985i
$474$		0			0
$475$	6.62222	+	1.89829i	0.303848	+	0.0870995i
$476$	−4.00000			−0.183340
$477$		0			0
$478$			27.8479i			1.27373i
$479$	5.12399			0.234121			0.117060	−	0.993125i	$-0.462653\pi$
$479$	5.12399			0.234121			0.117060	+	0.993125i	$0.462653\pi$
$480$		0			0
$481$	16.2667			0.741698
$482$		−	7.12399i		−	0.324489i
$483$		0			0
$484$	−8.61285			−0.391493
$485$	0.663703	−	4.72393i	0.0301372	−	0.214502i
$486$		0			0
$487$		−	23.2128i		−	1.05187i	−0.850524	−	0.525936i	$-0.823715\pi$
$487$		−	23.2128i		−	1.05187i	0.850524	−	0.525936i	$-0.176285\pi$
$488$		−	8.66370i		−	0.392187i
$489$		0			0
$490$	2.05731	−	14.6430i	0.0929397	−	0.661501i
$491$	40.1847			1.81351			0.906755	−	0.421658i	$-0.138552\pi$
$491$	40.1847			1.81351			0.906755	+	0.421658i	$0.138552\pi$
$492$		0			0
$493$		−	27.2257i		−	1.22618i
$494$	−1.89829			−0.0854081
$495$		0			0
$496$	−4.00000			−0.179605
$497$		−	4.34968i		−	0.195110i
$498$		0			0
$499$	−30.5718			−1.36858			−0.684292	−	0.729208i	$-0.739888\pi$
$499$	−30.5718			−1.36858			−0.684292	+	0.729208i	$0.739888\pi$
$500$	10.2143	+	4.54617i	0.456798	+	0.203311i
$501$		0			0
$502$			22.4099i			1.00020i
$503$		−	23.4291i		−	1.04465i	−0.852746	−	0.522326i	$-0.825064\pi$
$503$		−	23.4291i		−	1.04465i	0.852746	−	0.522326i	$-0.174936\pi$
$504$		0			0
$505$	35.9496	+	5.05086i	1.59974	+	0.224760i
$506$	−4.42864			−0.196877
$507$		0			0
$508$		−	4.99063i		−	0.221423i
$509$	−17.2128			−0.762943			−0.381472	−	0.924381i	$-0.624583\pi$
$509$	−17.2128			−0.762943			−0.381472	+	0.924381i	$0.624583\pi$
$510$		0			0
$511$	1.71456			0.0758476
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−11.7146			−0.516707
$515$	3.80642	−	27.0923i	0.167731	−	1.19383i
$516$		0			0
$517$			51.4291i			2.26185i
$518$		−	7.34614i		−	0.322771i
$519$		0			0
$520$	−3.05086	−	0.428639i	−0.133789	−	0.0187971i
$521$	−22.3684			−0.979978			−0.489989	−	0.871729i	$-0.662999\pi$
$521$	−22.3684			−0.979978			−0.489989	+	0.871729i	$0.662999\pi$
$522$		0			0
$523$		−	30.2953i		−	1.32472i	−0.749186	−	0.662360i	$-0.769555\pi$
$523$		−	30.2953i		−	1.32472i	0.749186	−	0.662360i	$-0.230445\pi$
$524$	0.755569			0.0330072
$525$		0			0
$526$	8.47013			0.369315
$527$		−	25.7146i		−	1.12014i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$	−7.47949	−	1.05086i	−0.324888	−	0.0456462i
$531$		0			0
$532$			0.857279i			0.0371678i
$533$			14.9590i			0.647946i
$534$		0			0
$535$	−3.31756	+	23.6128i	−0.143431	+	1.02087i
$536$	−11.8064			−0.509960
$537$		0			0
$538$			28.8256i			1.24276i
$539$	−29.2859			−1.26143
$540$		0			0
$541$	31.4479			1.35205			0.676024	−	0.736879i	$-0.263701\pi$
$541$	31.4479			1.35205			0.676024	+	0.736879i	$0.263701\pi$
$542$		−	13.8350i		−	0.594264i
$543$		0			0
$544$	−6.42864			−0.275626
$545$	−33.5526	−	4.71408i	−1.43724	−	0.201929i
$546$		0			0
$547$			20.8573i			0.891793i	0.895085	+	0.445896i	$0.147115\pi$
$547$			20.8573i			0.891793i	−0.895085	+	0.445896i	$0.852885\pi$
$548$		−	12.9175i		−	0.551808i
$549$		0			0
$550$	6.10171	−	21.2859i	0.260178	−	0.907635i
$551$	−5.83500			−0.248580
$552$		0			0
$553$			7.49240i			0.318609i
$554$	−2.88892			−0.122739
$555$		0			0
$556$	−14.1017			−0.598046
$557$		−	36.3180i		−	1.53884i	−0.638740	−	0.769422i	$-0.720544\pi$
$557$		−	36.3180i		−	1.53884i	0.638740	−	0.769422i	$-0.279456\pi$
$558$		0			0
$559$	1.44785			0.0612376
$560$	−0.193576	+	1.37778i	−0.00818009	+	0.0582220i
$561$		0			0
$562$		−	5.51114i		−	0.232473i
$563$			2.58073i			0.108765i	0.998520	+	0.0543824i	$0.0173190\pi$
$563$			2.58073i			0.108765i	−0.998520	+	0.0543824i	$0.982681\pi$
$564$		0			0
$565$	−4.48886	+	31.9496i	−0.188848	+	1.34413i
$566$	8.19358			0.344402
$567$		0			0
$568$		−	6.99063i		−	0.293320i
$569$	−36.3497			−1.52386			−0.761929	−	0.647661i	$-0.775747\pi$
$569$	−36.3497			−1.52386			−0.761929	+	0.647661i	$0.775747\pi$
$570$		0			0
$571$	−45.9309			−1.92215			−0.961074	−	0.276292i	$-0.910894\pi$
$571$	−45.9309			−1.92215			−0.961074	+	0.276292i	$0.910894\pi$
$572$			6.10171i			0.255125i
$573$		0			0
$574$	6.75557			0.281972
$575$	1.37778	−	4.80642i	0.0574576	−	0.200442i
$576$		0			0
$577$			4.00000i			0.166522i	0.996528	+	0.0832611i	$0.0265335\pi$
$577$			4.00000i			0.166522i	−0.996528	+	0.0832611i	$0.973466\pi$
$578$		−	24.3274i		−	1.01189i
$579$		0			0
$580$	−9.37778	−	1.31756i	−0.389391	−	0.0547088i
$581$	−1.36488			−0.0566247
$582$		0			0
$583$			14.9590i			0.619538i
$584$	2.75557			0.114026
$585$		0			0
$586$	−12.6222			−0.521419
$587$		−	42.1847i		−	1.74115i	−0.492037	−	0.870574i	$-0.663748\pi$
$587$		−	42.1847i		−	1.74115i	0.492037	−	0.870574i	$-0.336252\pi$
$588$		0			0
$589$	−5.51114			−0.227082
$590$	2.99063	−	21.2859i	0.123122	−	0.876327i
$591$		0			0
$592$		−	11.8064i		−	0.485241i
$593$			18.7368i			0.769430i	0.923036	+	0.384715i	$0.125700\pi$
$593$			18.7368i			0.769430i	−0.923036	+	0.384715i	$0.874300\pi$
$594$		0			0
$595$	−8.85728	−	1.24443i	−0.363113	−	0.0510167i
$596$	−12.4286			−0.509097
$597$		0			0
$598$			1.37778i			0.0563418i
$599$	−41.5625			−1.69820			−0.849098	−	0.528235i	$-0.822854\pi$
$599$	−41.5625			−1.69820			−0.849098	+	0.528235i	$0.822854\pi$
$600$		0			0
$601$	23.7146			0.967337			0.483668	−	0.875251i	$-0.339304\pi$
$601$	23.7146			0.967337			0.483668	+	0.875251i	$0.339304\pi$
$602$		−	0.653858i		−	0.0266493i
$603$		0			0
$604$	4.85728			0.197640
$605$	−19.0716	−	2.67952i	−0.775371	−	0.108938i
$606$		0			0
$607$			2.74266i			0.111321i	0.998450	+	0.0556606i	$0.0177265\pi$
$607$			2.74266i			0.111321i	−0.998450	+	0.0556606i	$0.982274\pi$
$608$			1.37778i			0.0558765i
$609$		0			0
$610$	2.69535	−	19.1842i	0.109131	−	0.776746i
$611$	16.0000			0.647291
$612$		0			0
$613$			24.0731i			0.972305i	0.873874	+	0.486152i	$0.161600\pi$
$613$			24.0731i			0.972305i	−0.873874	+	0.486152i	$0.838400\pi$
$614$	0.653858			0.0263876
$615$		0			0
$616$	2.75557			0.111025
$617$			39.4893i			1.58978i	0.606753	+	0.794890i	$0.292472\pi$
$617$			39.4893i			1.58978i	−0.606753	+	0.794890i	$0.707528\pi$
$618$		0			0
$619$	22.6222			0.909264			0.454632	−	0.890679i	$-0.349771\pi$
$619$	22.6222			0.909264			0.454632	+	0.890679i	$0.349771\pi$
$620$	−8.85728	−	1.24443i	−0.355717	−	0.0499776i
$621$		0			0
$622$			13.0923i			0.524955i
$623$		−	1.71456i		−	0.0686923i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	11.2573			0.449934
$627$		0			0
$628$		−	9.90813i		−	0.395378i
$629$	75.8992			3.02630
$630$		0			0
$631$	5.93978			0.236459			0.118229	−	0.992986i	$-0.462278\pi$
$631$	5.93978			0.236459			0.118229	+	0.992986i	$0.462278\pi$
$632$			12.0415i			0.478985i
$633$		0			0
$634$	−22.4701			−0.892403
$635$	1.55262	−	11.0509i	0.0616140	−	0.438540i
$636$		0			0
$637$			9.11108i			0.360994i
$638$			18.7556i			0.742540i
$639$		0			0
$640$	−0.311108	+	2.21432i	−0.0122976	+	0.0875287i
$641$	−19.8163			−0.782696			−0.391348	−	0.920243i	$-0.627991\pi$
$641$	−19.8163			−0.782696			−0.391348	+	0.920243i	$0.627991\pi$
$642$		0			0
$643$		−	44.7467i		−	1.76464i	−0.470653	−	0.882318i	$-0.655982\pi$
$643$		−	44.7467i		−	1.76464i	0.470653	−	0.882318i	$-0.344018\pi$
$644$	0.622216			0.0245187
$645$		0			0
$646$	−8.85728			−0.348485
$647$		−	32.9403i		−	1.29501i	−0.762059	−	0.647507i	$-0.775811\pi$
$647$		−	32.9403i		−	1.29501i	0.762059	−	0.647507i	$-0.224189\pi$
$648$		0			0
$649$	−42.5718			−1.67109
$650$	−6.62222	−	1.89829i	−0.259745	−	0.0744571i
$651$		0			0
$652$		−	10.1017i		−	0.395614i
$653$			37.2257i			1.45675i	0.685177	+	0.728377i	$0.259725\pi$
$653$			37.2257i			1.45675i	−0.685177	+	0.728377i	$0.740275\pi$
$654$		0			0
$655$	1.67307	+	0.235063i	0.0653723	+	0.00918468i
$656$	10.8573			0.423906
$657$		0			0
$658$		−	7.22570i		−	0.281687i
$659$	24.6953			0.961994			0.480997	−	0.876722i	$-0.340275\pi$
$659$	24.6953			0.961994			0.480997	+	0.876722i	$0.340275\pi$
$660$		0			0
$661$	−14.8287			−0.576770			−0.288385	−	0.957515i	$-0.593118\pi$
$661$	−14.8287			−0.576770			−0.288385	+	0.957515i	$0.593118\pi$
$662$		−	29.4479i		−	1.14452i
$663$		0			0
$664$	−2.19358			−0.0851273
$665$	−0.266706	+	1.89829i	−0.0103424	+	0.0736125i
$666$		0			0
$667$			4.23506i			0.163982i
$668$		−	1.89829i		−	0.0734470i
$669$		0			0
$670$	−26.1432	−	3.67307i	−1.01000	−	0.141903i
$671$	−38.3684			−1.48120
$672$		0			0
$673$		−	8.77430i		−	0.338225i	−0.985597	−	0.169112i	$-0.945910\pi$
$673$		−	8.77430i		−	0.338225i	0.985597	−	0.169112i	$-0.0540901\pi$
$674$	24.6222			0.948412
$675$		0			0
$676$	−11.1017			−0.426989
$677$			12.8256i			0.492929i	0.969152	+	0.246465i	$0.0792689\pi$
$677$			12.8256i			0.492929i	−0.969152	+	0.246465i	$0.920731\pi$
$678$		0			0
$679$	1.32741			0.0509412
$680$	−14.2351	−	2.00000i	−0.545890	−	0.0766965i
$681$		0			0
$682$			17.7146i			0.678325i
$683$			8.47013i			0.324100i	0.986783	+	0.162050i	$0.0518106\pi$
$683$			8.47013i			0.324100i	−0.986783	+	0.162050i	$0.948189\pi$
$684$		0			0
$685$	4.01874	−	28.6035i	0.153548	−	1.09288i
$686$	8.47013			0.323391
$687$		0			0
$688$		−	1.05086i		−	0.0400635i
$689$	4.65386			0.177298
$690$		0			0
$691$	25.7975			0.981384			0.490692	−	0.871333i	$-0.336744\pi$
$691$	25.7975			0.981384			0.490692	+	0.871333i	$0.336744\pi$
$692$			21.2257i			0.806880i
$693$		0			0
$694$	26.1017			0.990807
$695$	−31.2257	−	4.38715i	−1.18446	−	0.166414i
$696$		0			0
$697$			69.7975i			2.64377i
$698$			21.2257i			0.803404i
$699$		0			0
$700$	−0.857279	+	2.99063i	−0.0324021	+	0.113035i
$701$	−7.45091			−0.281417			−0.140709	−	0.990051i	$-0.544938\pi$
$701$	−7.45091			−0.281417			−0.140709	+	0.990051i	$0.544938\pi$
$702$		0			0
$703$		−	16.2667i		−	0.613510i
$704$	4.42864			0.166911
$705$		0			0
$706$	4.28544			0.161285
$707$			10.1017i			0.379914i
$708$		0			0
$709$	−13.2543			−0.497775			−0.248887	−	0.968532i	$-0.580065\pi$
$709$	−13.2543			−0.497775			−0.248887	+	0.968532i	$0.580065\pi$
$710$	2.17484	−	15.4795i	0.0816203	−	0.580935i
$711$		0			0
$712$		−	2.75557i		−	0.103269i
$713$			4.00000i			0.149801i
$714$		0			0
$715$	−1.89829	+	13.5111i	−0.0709920	+	0.505288i
$716$	−0.488863			−0.0182697
$717$		0			0
$718$		−	4.65386i		−	0.173680i
$719$	−2.33677			−0.0871469			−0.0435735	−	0.999050i	$-0.513874\pi$
$719$	−2.33677			−0.0871469			−0.0435735	+	0.999050i	$0.513874\pi$
$720$		0			0
$721$	7.61285			0.283517
$722$		−	17.1017i		−	0.636460i
$723$		0			0
$724$	20.9304			0.777873
$725$	−20.3555	−	5.83500i	−0.755985	−	0.216707i
$726$		0			0
$727$		−	3.37778i		−	0.125275i	−0.998036	−	0.0626375i	$-0.980049\pi$
$727$		−	3.37778i		−	0.125275i	0.998036	−	0.0626375i	$-0.0199512\pi$
$728$		−	0.857279i		−	0.0317729i
$729$		0			0
$730$	6.10171	+	0.857279i	0.225834	+	0.0317293i
$731$	6.75557			0.249864
$732$		0			0
$733$		−	21.0509i		−	0.777531i	−0.921337	−	0.388766i	$-0.872902\pi$
$733$		−	21.0509i		−	0.777531i	0.921337	−	0.388766i	$-0.127098\pi$
$734$	−4.88892			−0.180453
$735$		0			0
$736$	1.00000			0.0368605
$737$			52.2864i			1.92599i
$738$		0			0
$739$	22.6351			0.832646			0.416323	−	0.909217i	$-0.363318\pi$
$739$	22.6351			0.832646			0.416323	+	0.909217i	$0.363318\pi$
$740$	3.67307	−	26.1432i	0.135025	−	0.961043i
$741$		0			0
$742$		−	2.10171i		−	0.0771562i
$743$		−	3.87955i		−	0.142327i	−0.997465	−	0.0711635i	$-0.977329\pi$
$743$		−	3.87955i		−	0.142327i	0.997465	−	0.0711635i	$-0.0226712\pi$
$744$		0			0
$745$	−27.5210	−	3.86665i	−1.00829	−	0.141663i
$746$	23.4193			0.857440
$747$		0			0
$748$			28.4701i			1.04097i
$749$	−6.63512			−0.242442
$750$		0			0
$751$	19.7748			0.721592			0.360796	−	0.932645i	$-0.382505\pi$
$751$	19.7748			0.721592			0.360796	+	0.932645i	$0.382505\pi$
$752$		−	11.6128i		−	0.423477i
$753$		0			0
$754$	5.83500			0.212498
$755$	10.7556	+	1.51114i	0.391435	+	0.0549959i
$756$		0			0
$757$			8.19358i			0.297801i	0.988852	+	0.148900i	$0.0475733\pi$
$757$			8.19358i			0.297801i	−0.988852	+	0.148900i	$0.952427\pi$
$758$			4.90766i			0.178254i
$759$		0			0
$760$	−0.428639	+	3.05086i	−0.0155484	+	0.110666i
$761$	45.1624			1.63714			0.818568	−	0.574410i	$-0.194768\pi$
$761$	45.1624			1.63714			0.818568	+	0.574410i	$0.194768\pi$
$762$		0			0
$763$		−	9.42816i		−	0.341322i
$764$	18.9590			0.685912
$765$		0			0
$766$	19.8796			0.718277
$767$			13.2444i			0.478229i
$768$		0			0
$769$	−29.4924			−1.06352			−0.531762	−	0.846894i	$-0.678470\pi$
$769$	−29.4924			−1.06352			−0.531762	+	0.846894i	$0.678470\pi$
$770$	6.10171	+	0.857279i	0.219890	+	0.0308942i
$771$		0			0
$772$			1.24443i			0.0447881i
$773$		−	41.0923i		−	1.47799i	−0.673712	−	0.738994i	$-0.735301\pi$
$773$		−	41.0923i		−	1.47799i	0.673712	−	0.738994i	$-0.264699\pi$
$774$		0			0
$775$	−19.2257	−	5.51114i	−0.690607	−	0.197966i
$776$	2.13335			0.0765829
$777$		0			0
$778$		−	0.161933i		−	0.00580559i
$779$	14.9590			0.535961
$780$		0			0
$781$	−30.9590			−1.10780
$782$			6.42864i			0.229888i
$783$		0			0
$784$	6.61285			0.236173
$785$	3.08250	−	21.9398i	0.110019	−	0.783064i
$786$		0			0
$787$			10.0919i			0.359736i	0.983691	+	0.179868i	$0.0575671\pi$
$787$			10.0919i			0.359736i	−0.983691	+	0.179868i	$0.942433\pi$
$788$			15.2444i			0.543060i
$789$		0			0
$790$	−3.74620	+	26.6637i	−0.133284	+	0.948652i
$791$	−8.97773			−0.319211
$792$		0			0
$793$			11.9367i			0.423885i
$794$	−1.76494			−0.0626353
$795$		0			0
$796$	−14.5303			−0.515015
$797$			25.2958i			0.896022i	0.894028	+	0.448011i	$0.147867\pi$
$797$			25.2958i			0.896022i	−0.894028	+	0.448011i	$0.852133\pi$
$798$		0			0
$799$	74.6548			2.64110
$800$	−1.37778	+	4.80642i	−0.0487120	+	0.169933i
$801$		0			0
$802$			31.3461i			1.10687i
$803$		−	12.2034i		−	0.430649i
$804$		0			0
$805$	1.37778	+	0.193576i	0.0485605	+	0.00682266i
$806$	5.51114			0.194122
$807$		0			0
$808$			16.2351i			0.571148i
$809$	43.4479			1.52755			0.763773	−	0.645485i	$-0.223345\pi$
$809$	43.4479			1.52755			0.763773	+	0.645485i	$0.223345\pi$
$810$		0			0
$811$	−8.65386			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$811$	−8.65386			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$812$		−	2.63512i		−	0.0924747i
$813$		0			0
$814$	−52.2864			−1.83264
$815$	3.14272	−	22.3684i	0.110085	−	0.783531i
$816$		0			0
$817$		−	1.44785i		−	0.0506539i
$818$			3.51114i			0.122764i
$819$		0			0
$820$	24.0415	+	3.37778i	0.839565	+	0.117957i
$821$	−2.78721			−0.0972744			−0.0486372	−	0.998817i	$-0.515488\pi$
$821$	−2.78721			−0.0972744			−0.0486372	+	0.998817i	$0.515488\pi$
$822$		0			0
$823$		−	29.9684i		−	1.04463i	−0.852752	−	0.522316i	$-0.825068\pi$
$823$		−	29.9684i		−	1.04463i	0.852752	−	0.522316i	$-0.174932\pi$
$824$	12.2351			0.426229
$825$		0			0
$826$	5.98126			0.208115
$827$		−	47.2543i		−	1.64319i	−0.570070	−	0.821596i	$-0.693084\pi$
$827$		−	47.2543i		−	1.64319i	0.570070	−	0.821596i	$-0.306916\pi$
$828$		0			0
$829$	53.1624			1.84641			0.923203	−	0.384312i	$-0.125561\pi$
$829$	53.1624			1.84641			0.923203	+	0.384312i	$0.125561\pi$
$830$	−4.85728	−	0.682439i	−0.168599	−	0.0236878i
$831$		0			0
$832$		−	1.37778i		−	0.0477661i
$833$			42.5116i			1.47294i
$834$		0			0
$835$	0.590573	−	4.20342i	0.0204376	−	0.145465i
$836$	6.10171			0.211032
$837$		0			0
$838$		−	19.7748i		−	0.683108i
$839$	−17.3274			−0.598208			−0.299104	−	0.954220i	$-0.596688\pi$
$839$	−17.3274			−0.598208			−0.299104	+	0.954220i	$0.596688\pi$
$840$		0			0
$841$	−11.0642			−0.381525
$842$			11.8064i			0.406876i
$843$		0			0
$844$	−0.266706			−0.00918041
$845$	−24.5827	−	3.45383i	−0.845672	−	0.118815i
$846$		0			0
$847$		−	5.35905i		−	0.184139i
$848$		−	3.37778i		−	0.115994i
$849$		0			0
$850$	−30.8988	−	8.85728i	−1.05982	−	0.303802i
$851$	−11.8064			−0.404719
$852$		0			0
$853$		−	17.7649i		−	0.608260i	−0.952631	−	0.304130i	$-0.901634\pi$
$853$		−	17.7649i		−	0.608260i	0.952631	−	0.304130i	$-0.0983657\pi$
$854$	5.39069			0.184466
$855$		0			0
$856$	−10.6637			−0.364478
$857$		−	10.0830i		−	0.344428i	−0.985060	−	0.172214i	$-0.944908\pi$
$857$		−	10.0830i		−	0.344428i	0.985060	−	0.172214i	$-0.0550920\pi$
$858$		0			0
$859$	−5.12399			−0.174828			−0.0874141	−	0.996172i	$-0.527860\pi$
$859$	−5.12399			−0.174828			−0.0874141	+	0.996172i	$0.527860\pi$
$860$	0.326929	−	2.32693i	0.0111482	−	0.0793476i
$861$		0			0
$862$		−	24.9403i		−	0.849468i
$863$			49.2070i			1.67502i	0.546419	+	0.837512i	$0.315991\pi$
$863$			49.2070i			1.67502i	−0.546419	+	0.837512i	$0.684009\pi$
$864$		0			0
$865$	−6.60348	+	47.0005i	−0.224525	+	1.59806i
$866$	−32.0513			−1.08915
$867$		0			0
$868$		−	2.48886i		−	0.0844775i
$869$	53.3274			1.80901
$870$		0			0
$871$	16.2667			0.551176
$872$		−	15.1526i		−	0.513131i
$873$		0			0
$874$	1.37778			0.0466043
$875$	−2.82870	+	6.35551i	−0.0956275	+	0.214855i
$876$		0			0
$877$		−	9.11108i		−	0.307659i	−0.988097	−	0.153830i	$-0.950839\pi$
$877$		−	9.11108i		−	0.307659i	0.988097	−	0.153830i	$-0.0491607\pi$
$878$		−	0.470127i		−	0.0158660i
$879$		0			0
$880$	9.80642	+	1.37778i	0.330574	+	0.0464451i
$881$	9.71456			0.327292			0.163646	−	0.986519i	$-0.447675\pi$
$881$	9.71456			0.327292			0.163646	+	0.986519i	$0.447675\pi$
$882$		0			0
$883$		−	33.3274i		−	1.12156i	−0.827966	−	0.560778i	$-0.810502\pi$
$883$		−	33.3274i		−	1.12156i	0.827966	−	0.560778i	$-0.189498\pi$
$884$	8.85728			0.297903
$885$		0			0
$886$	0.653858			0.0219668
$887$		−	53.5941i		−	1.79951i	−0.436391	−	0.899757i	$-0.643744\pi$
$887$		−	53.5941i		−	1.79951i	0.436391	−	0.899757i	$-0.356256\pi$
$888$		0			0
$889$	3.10525			0.104147
$890$	0.857279	−	6.10171i	0.0287361	−	0.204530i
$891$		0			0
$892$			0.990632i			0.0331688i
$893$		−	16.0000i		−	0.535420i
$894$		0			0
$895$	−1.08250	−	0.152089i	−0.0361839	−	0.00508377i
$896$	−0.622216			−0.0207868
$897$		0			0
$898$			17.1427i			0.572060i
$899$	16.9403			0.564989
$900$		0			0
$901$	21.7146			0.723417
$902$		−	48.0830i		−	1.60099i
$903$		0			0
$904$	−14.4286			−0.479889
$905$	46.3466	+	6.51161i	1.54061	+	0.216453i
$906$		0			0
$907$		−	2.56199i		−	0.0850696i	−0.999095	−	0.0425348i	$-0.986457\pi$
$907$		−	2.56199i		−	0.0850696i	0.999095	−	0.0425348i	$-0.0135433\pi$
$908$			17.1526i			0.569228i
$909$		0			0
$910$	0.266706	−	1.89829i	0.00884122	−	0.0629277i
$911$	−8.47013			−0.280628			−0.140314	−	0.990107i	$-0.544811\pi$
$911$	−8.47013			−0.280628			−0.140314	+	0.990107i	$0.544811\pi$
$912$		0			0
$913$			9.71456i			0.321505i
$914$	−1.00937			−0.0333869
$915$		0			0
$916$	7.15257			0.236327
$917$			0.470127i			0.0155250i
$918$		0			0
$919$	36.8988			1.21718			0.608589	−	0.793486i	$-0.291736\pi$
$919$	36.8988			1.21718			0.608589	+	0.793486i	$0.291736\pi$
$920$	2.21432	+	0.311108i	0.0730040	+	0.0102569i
$921$		0			0
$922$		−	20.3180i		−	0.669139i
$923$			9.63158i			0.317027i
$924$		0			0
$925$	16.2667	−	56.7467i	0.534846	−	1.86582i
$926$	12.4572			0.409370
$927$		0			0
$928$		−	4.23506i		−	0.139023i
$929$	−0.164996			−0.00541334			−0.00270667	−	0.999996i	$-0.500862\pi$
$929$	−0.164996			−0.00541334			−0.00270667	+	0.999996i	$0.500862\pi$
$930$		0			0
$931$	9.11108			0.298604
$932$		−	3.71456i		−	0.121674i
$933$		0			0
$934$	−15.7877			−0.516589
$935$	−8.85728	+	63.0420i	−0.289664	+	2.06169i
$936$		0			0
$937$			40.3180i			1.31713i	0.752523	+	0.658566i	$0.228837\pi$
$937$			40.3180i			1.31713i	−0.752523	+	0.658566i	$0.771163\pi$
$938$		−	7.34614i		−	0.239860i
$939$		0			0
$940$	3.61285	−	25.7146i	0.117838	−	0.838716i
$941$	−53.3689			−1.73978			−0.869888	−	0.493249i	$-0.835809\pi$
$941$	−53.3689			−1.73978			−0.869888	+	0.493249i	$0.835809\pi$
$942$		0			0
$943$		−	10.8573i		−	0.353562i
$944$	9.61285			0.312872
$945$		0			0
$946$	−4.65386			−0.151310
$947$			44.6735i			1.45170i	0.687856	+	0.725848i	$0.258552\pi$
$947$			44.6735i			1.45170i	−0.687856	+	0.725848i	$0.741448\pi$
$948$		0			0
$949$	−3.79658			−0.123242
$950$	−1.89829	+	6.62222i	−0.0615887	+	0.214853i
$951$		0			0
$952$		−	4.00000i		−	0.129641i
$953$			21.2672i			0.688912i	0.938803	+	0.344456i	$0.111937\pi$
$953$			21.2672i			0.688912i	−0.938803	+	0.344456i	$0.888063\pi$
$954$		0			0
$955$	41.9813	+	5.89829i	1.35848	+	0.190864i
$956$	−27.8479			−0.900666
$957$		0			0
$958$			5.12399i			0.165548i
$959$	8.03747			0.259543
$960$		0			0
$961$	−15.0000			−0.483871
$962$			16.2667i			0.524460i
$963$		0			0
$964$	7.12399			0.229448
$965$	−0.387152	+	2.75557i	−0.0124629	+	0.0887049i
$966$		0			0
$967$		−	10.9461i		−	0.352002i	−0.984390	−	0.176001i	$-0.943684\pi$
$967$		−	10.9461i		−	0.352002i	0.984390	−	0.176001i	$-0.0563162\pi$
$968$		−	8.61285i		−	0.276827i
$969$		0			0
$970$	4.72393	+	0.663703i	0.151676	+	0.0213102i
$971$	16.8988			0.542307			0.271154	−	0.962536i	$-0.412595\pi$
$971$	16.8988			0.542307			0.271154	+	0.962536i	$0.412595\pi$
$972$		0			0
$973$		−	8.77430i		−	0.281291i
$974$	23.2128			0.743786
$975$		0			0
$976$	8.66370			0.277318
$977$			59.2484i			1.89553i	0.318976	+	0.947763i	$0.396661\pi$
$977$			59.2484i			1.89553i	−0.318976	+	0.947763i	$0.603339\pi$
$978$		0			0
$979$	−12.2034			−0.390023
$980$	14.6430	+	2.05731i	0.467752	+	0.0657183i
$981$		0			0
$982$			40.1847i			1.28234i
$983$			23.8163i			0.759621i	0.925064	+	0.379810i	$0.124011\pi$
$983$			23.8163i			0.759621i	−0.925064	+	0.379810i	$0.875989\pi$
$984$		0			0
$985$	−4.74266	+	33.7560i	−0.151114	+	1.07556i
$986$	27.2257			0.867043
$987$		0			0
$988$		−	1.89829i		−	0.0603926i
$989$	−1.05086			−0.0334152
$990$		0			0
$991$	29.7146			0.943914			0.471957	−	0.881622i	$-0.343548\pi$
$991$	29.7146			0.943914			0.471957	+	0.881622i	$0.343548\pi$
$992$		−	4.00000i		−	0.127000i
$993$		0			0
$994$	4.34968			0.137963
$995$	−32.1748	−	4.52051i	−1.02001	−	0.143310i
$996$		0			0
$997$		−	22.7052i		−	0.719081i	−0.933130	−	0.359540i	$-0.882934\pi$
$997$		−	22.7052i		−	0.719081i	0.933130	−	0.359540i	$-0.117066\pi$
$998$		−	30.5718i		−	0.967735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.d.e.829.4		6
3.2	odd	2		690.2.d.c.139.3	✓	6
5.4	even	2	inner	2070.2.d.e.829.1		6
15.2	even	4		3450.2.a.bt.1.2		3
15.8	even	4		3450.2.a.bo.1.2		3
15.14	odd	2		690.2.d.c.139.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.c.139.3	✓	6	3.2	odd	2
690.2.d.c.139.6	yes	6	15.14	odd	2
2070.2.d.e.829.1		6	5.4	even	2	inner
2070.2.d.e.829.4		6	1.1	even	1	trivial
3450.2.a.bo.1.2		3	15.8	even	4
3450.2.a.bt.1.2		3	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.21432 - 0.311108i) q^{5} -0.622216i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.21432 - 0.311108i) q^{5} -0.622216i q^{7} -1.00000i q^{8} +(0.311108 - 2.21432i) q^{10} -4.42864 q^{11} +1.37778i q^{13} +0.622216 q^{14} +1.00000 q^{16} +6.42864i q^{17} +1.37778 q^{19} +(2.21432 + 0.311108i) q^{20} -4.42864i q^{22} -1.00000i q^{23} +(4.80642 + 1.37778i) q^{25} -1.37778 q^{26} +0.622216i q^{28} -4.23506 q^{29} -4.00000 q^{31} +1.00000i q^{32} -6.42864 q^{34} +(-0.193576 + 1.37778i) q^{35} -11.8064i q^{37} +1.37778i q^{38} +(-0.311108 + 2.21432i) q^{40} +10.8573 q^{41} -1.05086i q^{43} +4.42864 q^{44} +1.00000 q^{46} -11.6128i q^{47} +6.61285 q^{49} +(-1.37778 + 4.80642i) q^{50} -1.37778i q^{52} -3.37778i q^{53} +(9.80642 + 1.37778i) q^{55} -0.622216 q^{56} -4.23506i q^{58} +9.61285 q^{59} +8.66370 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(0.428639 - 3.05086i) q^{65} -11.8064i q^{67} -6.42864i q^{68} +(-1.37778 - 0.193576i) q^{70} +6.99063 q^{71} +2.75557i q^{73} +11.8064 q^{74} -1.37778 q^{76} +2.75557i q^{77} -12.0415 q^{79} +(-2.21432 - 0.311108i) q^{80} +10.8573i q^{82} -2.19358i q^{83} +(2.00000 - 14.2351i) q^{85} +1.05086 q^{86} +4.42864i q^{88} +2.75557 q^{89} +0.857279 q^{91} +1.00000i q^{92} +11.6128 q^{94} +(-3.05086 - 0.428639i) q^{95} +2.13335i q^{97} +6.61285i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 6 * q - 6 * q^4	\( 6 q - 6 q^{4} + 2 q^{10} + 4 q^{14} + 6 q^{16} + 8 q^{19} + 2 q^{25} - 8 q^{26} + 28 q^{29} - 24 q^{31} - 12 q^{34} - 28 q^{35} - 2 q^{40} + 12 q^{41} + 6 q^{46} - 14 q^{49} - 8 q^{50} + 32 q^{55} - 4 q^{56} + 4 q^{59} - 28 q^{61} - 6 q^{64} - 24 q^{65} - 8 q^{70} - 12 q^{71} + 44 q^{74} - 8 q^{76} + 8 q^{79} + 12 q^{85} - 20 q^{86} + 16 q^{89} - 48 q^{91} + 16 q^{94} + 8 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^10 + 4 * q^14 + 6 * q^16 + 8 * q^19 + 2 * q^25 - 8 * q^26 + 28 * q^29 - 24 * q^31 - 12 * q^34 - 28 * q^35 - 2 * q^40 + 12 * q^41 + 6 * q^46 - 14 * q^49 - 8 * q^50 + 32 * q^55 - 4 * q^56 + 4 * q^59 - 28 * q^61 - 6 * q^64 - 24 * q^65 - 8 * q^70 - 12 * q^71 + 44 * q^74 - 8 * q^76 + 8 * q^79 + 12 * q^85 - 20 * q^86 + 16 * q^89 - 48 * q^91 + 16 * q^94 + 8 * q^95

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