LMFDB - Embedded newform 2070.2.d.e.829.2

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			829.2
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	2070.829
Dual form			2070.2.d.e.829.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +4.34017i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +4.34017i q^{7} +1.00000i q^{8} +(2.17009 - 0.539189i) q^{10} +1.07838 q^{11} +2.34017i q^{13} +4.34017 q^{14} +1.00000 q^{16} -0.921622i q^{17} -2.34017 q^{19} +(-0.539189 - 2.17009i) q^{20} -1.07838i q^{22} +1.00000i q^{23} +(-4.41855 + 2.34017i) q^{25} +2.34017 q^{26} -4.34017i q^{28} +10.4969 q^{29} -4.00000 q^{31} -1.00000i q^{32} -0.921622 q^{34} +(-9.41855 + 2.34017i) q^{35} +2.58145i q^{37} +2.34017i q^{38} +(-2.17009 + 0.539189i) q^{40} -0.156755 q^{41} -0.738205i q^{43} -1.07838 q^{44} +1.00000 q^{46} -6.83710i q^{47} -11.8371 q^{49} +(2.34017 + 4.41855i) q^{50} -2.34017i q^{52} -0.340173i q^{53} +(0.581449 + 2.34017i) q^{55} -4.34017 q^{56} -10.4969i q^{58} -8.83710 q^{59} -11.5753 q^{61} +4.00000i q^{62} -1.00000 q^{64} +(-5.07838 + 1.26180i) q^{65} +2.58145i q^{67} +0.921622i q^{68} +(2.34017 + 9.41855i) q^{70} -15.1773 q^{71} +4.68035i q^{73} +2.58145 q^{74} +2.34017 q^{76} +4.68035i q^{77} +11.9155 q^{79} +(0.539189 + 2.17009i) q^{80} +0.156755i q^{82} +11.4186i q^{83} +(2.00000 - 0.496928i) q^{85} -0.738205 q^{86} +1.07838i q^{88} -4.68035 q^{89} -10.1568 q^{91} -1.00000i q^{92} -6.83710 q^{94} +(-1.26180 - 5.07838i) q^{95} +9.02052i q^{97} +11.8371i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.539189	+	2.17009i	0.241133	+	0.970492i
$5$	0.539189	+	2.17009i	0.241133	+	0.970492i
$6$		0			0
$7$			4.34017i			1.64043i	0.572055	+	0.820216i	$0.306147\pi$
$7$			4.34017i			1.64043i	−0.572055	+	0.820216i	$0.693853\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.17009	−	0.539189i	0.686242	−	0.170506i
$11$	1.07838			0.325143			0.162572	−	0.986697i	$-0.448021\pi$
$11$	1.07838			0.325143			0.162572	+	0.986697i	$0.448021\pi$
$12$		0			0
$13$			2.34017i			0.649047i	0.945878	+	0.324524i	$0.105204\pi$
$13$			2.34017i			0.649047i	−0.945878	+	0.324524i	$0.894796\pi$
$14$	4.34017			1.15996
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.921622i		−	0.223526i	−0.993735	−	0.111763i	$-0.964350\pi$
$17$		−	0.921622i		−	0.223526i	0.993735	−	0.111763i	$-0.0356498\pi$
$18$		0			0
$19$	−2.34017			−0.536873			−0.268436	−	0.963297i	$-0.586507\pi$
$19$	−2.34017			−0.536873			−0.268436	+	0.963297i	$0.586507\pi$
$20$	−0.539189	−	2.17009i	−0.120566	−	0.485246i
$21$		0			0
$22$		−	1.07838i		−	0.229911i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$		0			0
$25$	−4.41855	+	2.34017i	−0.883710	+	0.468035i
$26$	2.34017			0.458946
$27$		0			0
$28$		−	4.34017i		−	0.820216i
$29$	10.4969			1.94923			0.974615	−	0.223886i	$-0.0718743\pi$
$29$	10.4969			1.94923			0.974615	+	0.223886i	$0.0718743\pi$
$30$		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
$34$	−0.921622			−0.158057
$35$	−9.41855	+	2.34017i	−1.59203	+	0.395561i
$36$		0			0
$37$			2.58145i			0.424388i	0.977228	+	0.212194i	$0.0680608\pi$
$37$			2.58145i			0.424388i	−0.977228	+	0.212194i	$0.931939\pi$
$38$			2.34017i			0.379626i
$39$		0			0
$40$	−2.17009	+	0.539189i	−0.343121	+	0.0852532i
$41$	−0.156755			−0.0244811			−0.0122405	−	0.999925i	$-0.503896\pi$
$41$	−0.156755			−0.0244811			−0.0122405	+	0.999925i	$0.503896\pi$
$42$		0			0
$43$		−	0.738205i		−	0.112575i	−0.998415	−	0.0562876i	$-0.982074\pi$
$43$		−	0.738205i		−	0.112575i	0.998415	−	0.0562876i	$-0.0179264\pi$
$44$	−1.07838			−0.162572
$45$		0			0
$46$	1.00000			0.147442
$47$		−	6.83710i		−	0.997294i	−0.866805	−	0.498647i	$-0.833830\pi$
$47$		−	6.83710i		−	0.997294i	0.866805	−	0.498647i	$-0.166170\pi$
$48$		0			0
$49$	−11.8371			−1.69101
$50$	2.34017	+	4.41855i	0.330950	+	0.624877i
$51$		0			0
$52$		−	2.34017i		−	0.324524i
$53$		−	0.340173i		−	0.0467264i	−0.999727	−	0.0233632i	$-0.992563\pi$
$53$		−	0.340173i		−	0.0467264i	0.999727	−	0.0233632i	$-0.00743741\pi$
$54$		0			0
$55$	0.581449	+	2.34017i	0.0784026	+	0.315549i
$56$	−4.34017			−0.579980
$57$		0			0
$58$		−	10.4969i		−	1.37831i
$59$	−8.83710			−1.15049			−0.575246	−	0.817980i	$-0.695094\pi$
$59$	−8.83710			−1.15049			−0.575246	+	0.817980i	$0.695094\pi$
$60$		0			0
$61$	−11.5753			−1.48207			−0.741033	−	0.671469i	$-0.765664\pi$
$61$	−11.5753			−1.48207			−0.741033	+	0.671469i	$0.765664\pi$
$62$			4.00000i			0.508001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.07838	+	1.26180i	−0.629895	+	0.156506i
$66$		0			0
$67$			2.58145i			0.315374i	0.987489	+	0.157687i	$0.0504037\pi$
$67$			2.58145i			0.315374i	−0.987489	+	0.157687i	$0.949596\pi$
$68$			0.921622i			0.111763i
$69$		0			0
$70$	2.34017	+	9.41855i	0.279704	+	1.12573i
$71$	−15.1773			−1.80121			−0.900606	−	0.434637i	$-0.856877\pi$
$71$	−15.1773			−1.80121			−0.900606	+	0.434637i	$0.856877\pi$
$72$		0			0
$73$			4.68035i			0.547793i	0.961759	+	0.273897i	$0.0883126\pi$
$73$			4.68035i			0.547793i	−0.961759	+	0.273897i	$0.911687\pi$
$74$	2.58145			0.300087
$75$		0			0
$76$	2.34017			0.268436
$77$			4.68035i			0.533375i
$78$		0			0
$79$	11.9155			1.34060			0.670298	−	0.742092i	$-0.266166\pi$
$79$	11.9155			1.34060			0.670298	+	0.742092i	$0.266166\pi$
$80$	0.539189	+	2.17009i	0.0602831	+	0.242623i
$81$		0			0
$82$			0.156755i			0.0173107i
$83$			11.4186i			1.25335i	0.779281	+	0.626674i	$0.215584\pi$
$83$			11.4186i			1.25335i	−0.779281	+	0.626674i	$0.784416\pi$
$84$		0			0
$85$	2.00000	−	0.496928i	0.216930	−	0.0538995i
$86$	−0.738205			−0.0796027
$87$		0			0
$88$			1.07838i			0.114955i
$89$	−4.68035			−0.496116			−0.248058	−	0.968745i	$-0.579792\pi$
$89$	−4.68035			−0.496116			−0.248058	+	0.968745i	$0.579792\pi$
$90$		0			0
$91$	−10.1568			−1.06472
$92$		−	1.00000i		−	0.104257i
$93$		0			0
$94$	−6.83710			−0.705193
$95$	−1.26180	−	5.07838i	−0.129457	−	0.521031i
$96$		0			0
$97$			9.02052i			0.915895i	0.888979	+	0.457947i	$0.151415\pi$
$97$			9.02052i			0.915895i	−0.888979	+	0.457947i	$0.848585\pi$
$98$			11.8371i			1.19573i
$99$		0			0
$100$	4.41855	−	2.34017i	0.441855	−	0.234017i
$101$	−1.50307			−0.149561			−0.0747806	−	0.997200i	$-0.523826\pi$
$101$	−1.50307			−0.149561			−0.0747806	+	0.997200i	$0.523826\pi$
$102$		0			0
$103$			2.49693i			0.246030i	0.992405	+	0.123015i	$0.0392563\pi$
$103$			2.49693i			0.246030i	−0.992405	+	0.123015i	$0.960744\pi$
$104$	−2.34017			−0.229473
$105$		0			0
$106$	−0.340173			−0.0330405
$107$		−	9.57531i		−	0.925680i	−0.886442	−	0.462840i	$-0.846830\pi$
$107$		−	9.57531i		−	0.925680i	0.886442	−	0.462840i	$-0.153170\pi$
$108$		0			0
$109$	9.78539			0.937270			0.468635	−	0.883392i	$-0.344746\pi$
$109$	9.78539			0.937270			0.468635	+	0.883392i	$0.344746\pi$
$110$	2.34017	−	0.581449i	0.223127	−	0.0554390i
$111$		0			0
$112$			4.34017i			0.410108i
$113$			8.92162i			0.839276i	0.907692	+	0.419638i	$0.137843\pi$
$113$			8.92162i			0.839276i	−0.907692	+	0.419638i	$0.862157\pi$
$114$		0			0
$115$	−2.17009	+	0.539189i	−0.202362	+	0.0502796i
$116$	−10.4969			−0.974615
$117$		0			0
$118$			8.83710i			0.813521i
$119$	4.00000			0.366679
$120$		0			0
$121$	−9.83710			−0.894282
$122$			11.5753i			1.04798i
$123$		0			0
$124$	4.00000			0.359211
$125$	−7.46081	−	8.32684i	−0.667315	−	0.744775i
$126$		0			0
$127$			17.1773i			1.52424i	0.647438	+	0.762118i	$0.275841\pi$
$127$			17.1773i			1.52424i	−0.647438	+	0.762118i	$0.724159\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	1.26180	+	5.07838i	0.110667	+	0.445403i
$131$	6.68035			0.583665			0.291832	−	0.956470i	$-0.405735\pi$
$131$	6.68035			0.583665			0.291832	+	0.956470i	$0.405735\pi$
$132$		0			0
$133$		−	10.1568i		−	0.880702i
$134$	2.58145			0.223003
$135$		0			0
$136$	0.921622			0.0790285
$137$		−	22.2823i		−	1.90371i	−0.306554	−	0.951853i	$-0.599176\pi$
$137$		−	22.2823i		−	1.90371i	0.306554	−	0.951853i	$-0.400824\pi$
$138$		0			0
$139$	10.5236			0.892599			0.446300	−	0.894884i	$-0.352742\pi$
$139$	10.5236			0.892599			0.446300	+	0.894884i	$0.352742\pi$
$140$	9.41855	−	2.34017i	0.796013	−	0.197781i
$141$		0			0
$142$			15.1773i			1.27365i
$143$			2.52359i			0.211033i
$144$		0			0
$145$	5.65983	+	22.7792i	0.470023	+	1.89171i
$146$	4.68035			0.387348
$147$		0			0
$148$		−	2.58145i		−	0.212194i
$149$	6.92162			0.567041			0.283521	−	0.958966i	$-0.408498\pi$
$149$	6.92162			0.567041			0.283521	+	0.958966i	$0.408498\pi$
$150$		0			0
$151$	6.15676			0.501030			0.250515	−	0.968113i	$-0.419400\pi$
$151$	6.15676			0.501030			0.250515	+	0.968113i	$0.419400\pi$
$152$		−	2.34017i		−	0.189813i
$153$		0			0
$154$	4.68035			0.377153
$155$	−2.15676	−	8.68035i	−0.173235	−	0.697222i
$156$		0			0
$157$			2.89496i			0.231043i	0.993305	+	0.115521i	$0.0368539\pi$
$157$			2.89496i			0.231043i	−0.993305	+	0.115521i	$0.963146\pi$
$158$		−	11.9155i		−	0.947945i
$159$		0			0
$160$	2.17009	−	0.539189i	0.171560	−	0.0426266i
$161$	−4.34017			−0.342054
$162$		0			0
$163$		−	6.52359i		−	0.510967i	−0.966813	−	0.255484i	$-0.917765\pi$
$163$		−	6.52359i		−	0.510967i	0.966813	−	0.255484i	$-0.0822347\pi$
$164$	0.156755			0.0122405
$165$		0			0
$166$	11.4186			0.886251
$167$		−	5.47641i		−	0.423777i	−0.977294	−	0.211889i	$-0.932039\pi$
$167$		−	5.47641i		−	0.423777i	0.977294	−	0.211889i	$-0.0679614\pi$
$168$		0			0
$169$	7.52359			0.578738
$170$	−0.496928	−	2.00000i	−0.0381127	−	0.153393i
$171$		0			0
$172$			0.738205i			0.0562876i
$173$		−	15.6742i		−	1.19169i	−0.803100	−	0.595844i	$-0.796818\pi$
$173$		−	15.6742i		−	1.19169i	0.803100	−	0.595844i	$-0.203182\pi$
$174$		0			0
$175$	−10.1568	−	19.1773i	−0.767779	−	1.44967i
$176$	1.07838			0.0812858
$177$		0			0
$178$			4.68035i			0.350807i
$179$	15.3607			1.14811			0.574056	−	0.818816i	$-0.305369\pi$
$179$	15.3607			1.14811			0.574056	+	0.818816i	$0.305369\pi$
$180$		0			0
$181$	21.6163			1.60673			0.803365	−	0.595487i	$-0.203041\pi$
$181$	21.6163			1.60673			0.803365	+	0.595487i	$0.203041\pi$
$182$			10.1568i			0.752869i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	−5.60197	+	1.39189i	−0.411865	+	0.102334i
$186$		0			0
$187$		−	0.993857i		−	0.0726780i
$188$			6.83710i			0.498647i
$189$		0			0
$190$	−5.07838	+	1.26180i	−0.368424	+	0.0915402i
$191$	−4.36683			−0.315973			−0.157987	−	0.987441i	$-0.550500\pi$
$191$	−4.36683			−0.315973			−0.157987	+	0.987441i	$0.550500\pi$
$192$		0			0
$193$			8.68035i			0.624825i	0.949947	+	0.312412i	$0.101137\pi$
$193$			8.68035i			0.624825i	−0.949947	+	0.312412i	$0.898863\pi$
$194$	9.02052			0.647636
$195$		0			0
$196$	11.8371			0.845507
$197$			22.6803i			1.61591i	0.589246	+	0.807954i	$0.299425\pi$
$197$			22.6803i			1.61591i	−0.589246	+	0.807954i	$0.700575\pi$
$198$		0			0
$199$	5.44521			0.386001			0.193000	−	0.981199i	$-0.438178\pi$
$199$	5.44521			0.386001			0.193000	+	0.981199i	$0.438178\pi$
$200$	−2.34017	−	4.41855i	−0.165475	−	0.312439i
$201$		0			0
$202$			1.50307i			0.105756i
$203$			45.5585i			3.19758i
$204$		0			0
$205$	−0.0845208	−	0.340173i	−0.00590319	−	0.0237587i
$206$	2.49693			0.173969
$207$		0			0
$208$			2.34017i			0.162262i
$209$	−2.52359			−0.174560
$210$		0			0
$211$	−22.0410			−1.51737			−0.758684	−	0.651459i	$-0.774157\pi$
$211$	−22.0410			−1.51737			−0.758684	+	0.651459i	$0.774157\pi$
$212$			0.340173i			0.0233632i
$213$		0			0
$214$	−9.57531			−0.654554
$215$	1.60197	−	0.398032i	0.109253	−	0.0271455i
$216$		0			0
$217$		−	17.3607i		−	1.17852i
$218$		−	9.78539i		−	0.662750i
$219$		0			0
$220$	−0.581449	−	2.34017i	−0.0392013	−	0.157774i
$221$	2.15676			0.145079
$222$		0			0
$223$		−	21.1773i		−	1.41814i	−0.705141	−	0.709068i	$-0.749116\pi$
$223$		−	21.1773i		−	1.41814i	0.705141	−	0.709068i	$-0.250884\pi$
$224$	4.34017			0.289990
$225$		0			0
$226$	8.92162			0.593457
$227$			11.7854i			0.782224i	0.920343	+	0.391112i	$0.127909\pi$
$227$			11.7854i			0.782224i	−0.920343	+	0.391112i	$0.872091\pi$
$228$		0			0
$229$	−1.78539			−0.117982			−0.0589908	−	0.998259i	$-0.518788\pi$
$229$	−1.78539			−0.117982			−0.0589908	+	0.998259i	$0.518788\pi$
$230$	0.539189	+	2.17009i	0.0355531	+	0.143091i
$231$		0			0
$232$			10.4969i			0.689157i
$233$			18.3135i			1.19976i	0.800091	+	0.599879i	$0.204785\pi$
$233$			18.3135i			1.19976i	−0.800091	+	0.599879i	$0.795215\pi$
$234$		0			0
$235$	14.8371	−	3.68649i	0.967866	−	0.240480i
$236$	8.83710			0.575246
$237$		0			0
$238$		−	4.00000i		−	0.259281i
$239$	−5.33403			−0.345030			−0.172515	−	0.985007i	$-0.555189\pi$
$239$	−5.33403			−0.345030			−0.172515	+	0.985007i	$0.555189\pi$
$240$		0			0
$241$	26.1978			1.68755			0.843774	−	0.536698i	$-0.180329\pi$
$241$	26.1978			1.68755			0.843774	+	0.536698i	$0.180329\pi$
$242$			9.83710i			0.632353i
$243$		0			0
$244$	11.5753			0.741033
$245$	−6.38243	−	25.6875i	−0.407759	−	1.64112i
$246$		0			0
$247$		−	5.47641i		−	0.348456i
$248$		−	4.00000i		−	0.254000i
$249$		0			0
$250$	−8.32684	+	7.46081i	−0.526636	+	0.471863i
$251$	−27.4329			−1.73155			−0.865775	−	0.500433i	$-0.833174\pi$
$251$	−27.4329			−1.73155			−0.865775	+	0.500433i	$0.833174\pi$
$252$		0			0
$253$			1.07838i			0.0677970i
$254$	17.1773			1.07780
$255$		0			0
$256$	1.00000			0.0625000
$257$			10.3135i			0.643339i	0.946852	+	0.321670i	$0.104244\pi$
$257$			10.3135i			0.643339i	−0.946852	+	0.321670i	$0.895756\pi$
$258$		0			0
$259$	−11.2039			−0.696179
$260$	5.07838	−	1.26180i	0.314948	−	0.0782532i
$261$		0			0
$262$		−	6.68035i		−	0.412713i
$263$		−	20.9939i		−	1.29454i	−0.762262	−	0.647268i	$-0.775911\pi$
$263$		−	20.9939i		−	1.29454i	0.762262	−	0.647268i	$-0.224089\pi$
$264$		0			0
$265$	0.738205	−	0.183417i	0.0453476	−	0.0112672i
$266$	−10.1568			−0.622751
$267$		0			0
$268$		−	2.58145i		−	0.157687i
$269$	25.3874			1.54789			0.773947	−	0.633250i	$-0.218280\pi$
$269$	25.3874			1.54789			0.773947	+	0.633250i	$0.218280\pi$
$270$		0			0
$271$	−32.5646			−1.97816			−0.989080	−	0.147379i	$-0.952916\pi$
$271$	−32.5646			−1.97816			−0.989080	+	0.147379i	$0.952916\pi$
$272$		−	0.921622i		−	0.0558816i
$273$		0			0
$274$	−22.2823			−1.34612
$275$	−4.76487	+	2.52359i	−0.287332	+	0.152178i
$276$		0			0
$277$			15.7009i			0.943374i	0.881766	+	0.471687i	$0.156355\pi$
$277$			15.7009i			0.943374i	−0.881766	+	0.471687i	$0.843645\pi$
$278$		−	10.5236i		−	0.631163i
$279$		0			0
$280$	−2.34017	−	9.41855i	−0.139852	−	0.562866i
$281$	9.36069			0.558412			0.279206	−	0.960231i	$-0.409929\pi$
$281$	9.36069			0.558412			0.279206	+	0.960231i	$0.409929\pi$
$282$		0			0
$283$			17.4186i			1.03543i	0.855555	+	0.517713i	$0.173216\pi$
$283$			17.4186i			1.03543i	−0.855555	+	0.517713i	$0.826784\pi$
$284$	15.1773			0.900606
$285$		0			0
$286$	2.52359			0.149223
$287$		−	0.680346i		−	0.0401596i
$288$		0			0
$289$	16.1506			0.950036
$290$	22.7792	−	5.65983i	1.33764	−	0.332356i
$291$		0			0
$292$		−	4.68035i		−	0.273897i
$293$		−	16.3402i		−	0.954603i	−0.878740	−	0.477302i	$-0.841615\pi$
$293$		−	16.3402i		−	0.954603i	0.878740	−	0.477302i	$-0.158385\pi$
$294$		0			0
$295$	−4.76487	−	19.1773i	−0.277421	−	1.11654i
$296$	−2.58145			−0.150044
$297$		0			0
$298$		−	6.92162i		−	0.400959i
$299$	−2.34017			−0.135336
$300$		0			0
$301$	3.20394			0.184672
$302$		−	6.15676i		−	0.354281i
$303$		0			0
$304$	−2.34017			−0.134218
$305$	−6.24128	−	25.1194i	−0.357374	−	1.43833i
$306$		0			0
$307$		−	3.20394i		−	0.182858i	−0.995812	−	0.0914292i	$-0.970856\pi$
$307$		−	3.20394i		−	0.182858i	0.995812	−	0.0914292i	$-0.0291435\pi$
$308$		−	4.68035i		−	0.266687i
$309$		0			0
$310$	−8.68035	+	2.15676i	−0.493011	+	0.122495i
$311$	−12.6537			−0.717525			−0.358762	−	0.933429i	$-0.616801\pi$
$311$	−12.6537			−0.717525			−0.358762	+	0.933429i	$0.616801\pi$
$312$		0			0
$313$		−	33.2183i		−	1.87761i	−0.344449	−	0.938805i	$-0.611934\pi$
$313$		−	33.2183i		−	1.87761i	0.344449	−	0.938805i	$-0.388066\pi$
$314$	2.89496			0.163372
$315$		0			0
$316$	−11.9155			−0.670298
$317$			6.99386i			0.392814i	0.980522	+	0.196407i	$0.0629274\pi$
$317$			6.99386i			0.392814i	−0.980522	+	0.196407i	$0.937073\pi$
$318$		0			0
$319$	11.3197			0.633779
$320$	−0.539189	−	2.17009i	−0.0301416	−	0.121312i
$321$		0			0
$322$			4.34017i			0.241868i
$323$			2.15676i			0.120005i
$324$		0			0
$325$	−5.47641	−	10.3402i	−0.303777	−	0.573570i
$326$	−6.52359			−0.361308
$327$		0			0
$328$		−	0.156755i		−	0.00865537i
$329$	29.6742			1.63599
$330$		0			0
$331$	−29.7275			−1.63397			−0.816986	−	0.576657i	$-0.804357\pi$
$331$	−29.7275			−1.63397			−0.816986	+	0.576657i	$0.804357\pi$
$332$		−	11.4186i		−	0.626674i
$333$		0			0
$334$	−5.47641			−0.299656
$335$	−5.60197	+	1.39189i	−0.306068	+	0.0760470i
$336$		0			0
$337$			28.3402i			1.54379i	0.635751	+	0.771894i	$0.280690\pi$
$337$			28.3402i			1.54379i	−0.635751	+	0.771894i	$0.719310\pi$
$338$		−	7.52359i		−	0.409229i
$339$		0			0
$340$	−2.00000	+	0.496928i	−0.108465	+	0.0269497i
$341$	−4.31351			−0.233590
$342$		0			0
$343$		−	20.9939i		−	1.13356i
$344$	0.738205			0.0398013
$345$		0			0
$346$	−15.6742			−0.842650
$347$			22.5236i			1.20913i	0.796556	+	0.604565i	$0.206653\pi$
$347$			22.5236i			1.20913i	−0.796556	+	0.604565i	$0.793347\pi$
$348$		0			0
$349$	−15.6742			−0.839021			−0.419510	−	0.907751i	$-0.637798\pi$
$349$	−15.6742			−0.839021			−0.419510	+	0.907751i	$0.637798\pi$
$350$	−19.1773	+	10.1568i	−1.02507	+	0.542901i
$351$		0			0
$352$		−	1.07838i		−	0.0574777i
$353$			26.3135i			1.40053i	0.713885	+	0.700263i	$0.246934\pi$
$353$			26.3135i			1.40053i	−0.713885	+	0.700263i	$0.753066\pi$
$354$		0			0
$355$	−8.18342	−	32.9360i	−0.434331	−	1.74806i
$356$	4.68035			0.248058
$357$		0			0
$358$		−	15.3607i		−	0.811838i
$359$	−0.796064			−0.0420146			−0.0210073	−	0.999779i	$-0.506687\pi$
$359$	−0.796064			−0.0420146			−0.0210073	+	0.999779i	$0.506687\pi$
$360$		0			0
$361$	−13.5236			−0.711768
$362$		−	21.6163i		−	1.13613i
$363$		0			0
$364$	10.1568			0.532359
$365$	−10.1568	+	2.52359i	−0.531629	+	0.132091i
$366$		0			0
$367$			13.7009i			0.715179i	0.933879	+	0.357590i	$0.116401\pi$
$367$			13.7009i			0.715179i	−0.933879	+	0.357590i	$0.883599\pi$
$368$			1.00000i			0.0521286i
$369$		0			0
$370$	1.39189	+	5.60197i	0.0723608	+	0.291232i
$371$	1.47641			0.0766514
$372$		0			0
$373$		−	4.25565i		−	0.220349i	−0.993912	−	0.110175i	$-0.964859\pi$
$373$		−	4.25565i		−	0.220349i	0.993912	−	0.110175i	$-0.0351410\pi$
$374$	−0.993857			−0.0513911
$375$		0			0
$376$	6.83710			0.352597
$377$			24.5646i			1.26514i
$378$		0			0
$379$	30.6537			1.57457			0.787287	−	0.616587i	$-0.211485\pi$
$379$	30.6537			1.57457			0.787287	+	0.616587i	$0.211485\pi$
$380$	1.26180	+	5.07838i	0.0647287	+	0.260515i
$381$		0			0
$382$			4.36683i			0.223427i
$383$		−	20.8781i		−	1.06682i	−0.845856	−	0.533412i	$-0.820910\pi$
$383$		−	20.8781i		−	1.06682i	0.845856	−	0.533412i	$-0.179090\pi$
$384$		0			0
$385$	−10.1568	+	2.52359i	−0.517636	+	0.128614i
$386$	8.68035			0.441818
$387$		0			0
$388$		−	9.02052i		−	0.457947i
$389$	−16.9627			−0.860041			−0.430021	−	0.902819i	$-0.641494\pi$
$389$	−16.9627			−0.860041			−0.430021	+	0.902819i	$0.641494\pi$
$390$		0			0
$391$	0.921622			0.0466084
$392$		−	11.8371i		−	0.597864i
$393$		0			0
$394$	22.6803			1.14262
$395$	6.42469	+	25.8576i	0.323261	+	1.30104i
$396$		0			0
$397$		−	16.4969i		−	0.827957i	−0.910287	−	0.413979i	$-0.864139\pi$
$397$		−	16.4969i		−	0.827957i	0.910287	−	0.413979i	$-0.135861\pi$
$398$		−	5.44521i		−	0.272944i
$399$		0			0
$400$	−4.41855	+	2.34017i	−0.220928	+	0.117009i
$401$	35.2039			1.75800			0.879000	−	0.476821i	$-0.158211\pi$
$401$	35.2039			1.75800			0.879000	+	0.476821i	$0.158211\pi$
$402$		0			0
$403$		−	9.36069i		−	0.466289i
$404$	1.50307			0.0747806
$405$		0			0
$406$	45.5585			2.26103
$407$			2.78378i			0.137987i
$408$		0			0
$409$	−11.3607			−0.561750			−0.280875	−	0.959744i	$-0.590625\pi$
$409$	−11.3607			−0.561750			−0.280875	+	0.959744i	$0.590625\pi$
$410$	−0.340173	+	0.0845208i	−0.0167999	+	0.00417419i
$411$		0			0
$412$		−	2.49693i		−	0.123015i
$413$		−	38.3545i		−	1.88730i
$414$		0			0
$415$	−24.7792	+	6.15676i	−1.21637	+	0.302223i
$416$	2.34017			0.114736
$417$		0			0
$418$			2.52359i			0.123433i
$419$	−18.1256			−0.885491			−0.442746	−	0.896647i	$-0.645996\pi$
$419$	−18.1256			−0.885491			−0.442746	+	0.896647i	$0.645996\pi$
$420$		0			0
$421$	2.58145			0.125812			0.0629061	−	0.998019i	$-0.479963\pi$
$421$	2.58145			0.125812			0.0629061	+	0.998019i	$0.479963\pi$
$422$			22.0410i			1.07294i
$423$		0			0
$424$	0.340173			0.0165203
$425$	2.15676	+	4.07223i	0.104618	+	0.197532i
$426$		0			0
$427$		−	50.2388i		−	2.43123i
$428$			9.57531i			0.462840i
$429$		0			0
$430$	−0.398032	−	1.60197i	−0.0191948	−	0.0772538i
$431$	33.9877			1.63713			0.818565	−	0.574414i	$-0.194770\pi$
$431$	33.9877			1.63713			0.818565	+	0.574414i	$0.194770\pi$
$432$		0			0
$433$			8.28685i			0.398241i	0.979975	+	0.199120i	$0.0638084\pi$
$433$			8.28685i			0.398241i	−0.979975	+	0.199120i	$0.936192\pi$
$434$	−17.3607			−0.833340
$435$		0			0
$436$	−9.78539			−0.468635
$437$		−	2.34017i		−	0.111946i
$438$		0			0
$439$	28.9939			1.38380			0.691901	−	0.721993i	$-0.256774\pi$
$439$	28.9939			1.38380			0.691901	+	0.721993i	$0.256774\pi$
$440$	−2.34017	+	0.581449i	−0.111563	+	0.0277195i
$441$		0			0
$442$		−	2.15676i		−	0.102586i
$443$		−	3.20394i		−	0.152224i	−0.997099	−	0.0761118i	$-0.975749\pi$
$443$		−	3.20394i		−	0.152224i	0.997099	−	0.0761118i	$-0.0242506\pi$
$444$		0			0
$445$	−2.52359	−	10.1568i	−0.119630	−	0.481476i
$446$	−21.1773			−1.00277
$447$		0			0
$448$		−	4.34017i		−	0.205054i
$449$	28.1568			1.32880			0.664400	−	0.747377i	$-0.268687\pi$
$449$	28.1568			1.32880			0.664400	+	0.747377i	$0.268687\pi$
$450$		0			0
$451$	−0.169042			−0.00795986
$452$		−	8.92162i		−	0.419638i
$453$		0			0
$454$	11.7854			0.553116
$455$	−5.47641	−	22.0410i	−0.256738	−	1.03330i
$456$		0			0
$457$		−	23.1773i		−	1.08419i	−0.840318	−	0.542094i	$-0.817632\pi$
$457$		−	23.1773i		−	1.08419i	0.840318	−	0.542094i	$-0.182368\pi$
$458$			1.78539i			0.0834256i
$459$		0			0
$460$	2.17009	−	0.539189i	0.101181	−	0.0251398i
$461$	42.3279			1.97141			0.985703	−	0.168491i	$-0.0538896\pi$
$461$	42.3279			1.97141			0.985703	+	0.168491i	$0.0538896\pi$
$462$		0			0
$463$			34.9048i			1.62216i	0.584933	+	0.811082i	$0.301121\pi$
$463$			34.9048i			1.62216i	−0.584933	+	0.811082i	$0.698879\pi$
$464$	10.4969			0.487308
$465$		0			0
$466$	18.3135			0.848357
$467$			37.7731i			1.74793i	0.485988	+	0.873965i	$0.338460\pi$
$467$			37.7731i			1.74793i	−0.485988	+	0.873965i	$0.661540\pi$
$468$		0			0
$469$	−11.2039			−0.517350
$470$	−3.68649	−	14.8371i	−0.170045	−	0.684384i
$471$		0			0
$472$		−	8.83710i		−	0.406761i
$473$		−	0.796064i		−	0.0366030i
$474$		0			0
$475$	10.3402	−	5.47641i	0.474440	−	0.251275i
$476$	−4.00000			−0.183340
$477$		0			0
$478$			5.33403i			0.243973i
$479$	−28.1978			−1.28839			−0.644195	−	0.764861i	$-0.722807\pi$
$479$	−28.1978			−1.28839			−0.644195	+	0.764861i	$0.722807\pi$
$480$		0			0
$481$	−6.04104			−0.275448
$482$		−	26.1978i		−	1.19328i
$483$		0			0
$484$	9.83710			0.447141
$485$	−19.5753	+	4.86376i	−0.888869	+	0.220852i
$486$		0			0
$487$			38.2245i			1.73212i	0.499944	+	0.866058i	$0.333354\pi$
$487$			38.2245i			1.73212i	−0.499944	+	0.866058i	$0.666646\pi$
$488$		−	11.5753i		−	0.523989i
$489$		0			0
$490$	−25.6875	+	6.38243i	−1.16044	+	0.288329i
$491$	−11.3074			−0.510294			−0.255147	−	0.966902i	$-0.582124\pi$
$491$	−11.3074			−0.510294			−0.255147	+	0.966902i	$0.582124\pi$
$492$		0			0
$493$		−	9.67420i		−	0.435704i
$494$	−5.47641			−0.246395
$495$		0			0
$496$	−4.00000			−0.179605
$497$		−	65.8720i		−	2.95476i
$498$		0			0
$499$	2.47027			0.110584			0.0552922	−	0.998470i	$-0.482391\pi$
$499$	2.47027			0.110584			0.0552922	+	0.998470i	$0.482391\pi$
$500$	7.46081	+	8.32684i	0.333658	+	0.372388i
$501$		0			0
$502$			27.4329i			1.22439i
$503$		−	20.6270i		−	0.919713i	−0.887993	−	0.459857i	$-0.847901\pi$
$503$		−	20.6270i		−	0.919713i	0.887993	−	0.459857i	$-0.152099\pi$
$504$		0			0
$505$	−0.810439	−	3.26180i	−0.0360641	−	0.145148i
$506$	1.07838			0.0479397
$507$		0			0
$508$		−	17.1773i		−	0.762118i
$509$	−32.2245			−1.42832			−0.714162	−	0.699981i	$-0.753192\pi$
$509$	−32.2245			−1.42832			−0.714162	+	0.699981i	$0.753192\pi$
$510$		0			0
$511$	−20.3135			−0.898617
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	10.3135			0.454909
$515$	−5.41855	+	1.34632i	−0.238770	+	0.0593258i
$516$		0			0
$517$		−	7.37298i		−	0.324263i
$518$			11.2039i			0.492273i
$519$		0			0
$520$	−1.26180	−	5.07838i	−0.0553334	−	0.222702i
$521$	3.51745			0.154102			0.0770511	−	0.997027i	$-0.475450\pi$
$521$	3.51745			0.154102			0.0770511	+	0.997027i	$0.475450\pi$
$522$		0			0
$523$			35.9421i			1.57164i	0.618455	+	0.785820i	$0.287759\pi$
$523$			35.9421i			1.57164i	−0.618455	+	0.785820i	$0.712241\pi$
$524$	−6.68035			−0.291832
$525$		0			0
$526$	−20.9939			−0.915376
$527$			3.68649i			0.160586i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$	−0.183417	−	0.738205i	−0.00796715	−	0.0320656i
$531$		0			0
$532$			10.1568i			0.440351i
$533$		−	0.366835i		−	0.0158894i
$534$		0			0
$535$	20.7792	−	5.16290i	0.898365	−	0.223212i
$536$	−2.58145			−0.111502
$537$		0			0
$538$		−	25.3874i		−	1.09453i
$539$	−12.7649			−0.549822
$540$		0			0
$541$	31.7275			1.36407			0.682036	−	0.731318i	$-0.261095\pi$
$541$	31.7275			1.36407			0.682036	+	0.731318i	$0.261095\pi$
$542$			32.5646i			1.39877i
$543$		0			0
$544$	−0.921622			−0.0395142
$545$	5.27617	+	21.2351i	0.226006	+	0.909613i
$546$		0			0
$547$		−	9.84324i		−	0.420867i	−0.977608	−	0.210433i	$-0.932512\pi$
$547$		−	9.84324i		−	0.420867i	0.977608	−	0.210433i	$-0.0674875\pi$
$548$			22.2823i			0.951853i
$549$		0			0
$550$	2.52359	+	4.76487i	0.107606	+	0.203175i
$551$	−24.5646			−1.04649
$552$		0			0
$553$			51.7152i			2.19916i
$554$	15.7009			0.667066
$555$		0			0
$556$	−10.5236			−0.446300
$557$		−	26.3279i		−	1.11555i	−0.829993	−	0.557774i	$-0.811656\pi$
$557$		−	26.3279i		−	1.11555i	0.829993	−	0.557774i	$-0.188344\pi$
$558$		0			0
$559$	1.72753			0.0730666
$560$	−9.41855	+	2.34017i	−0.398006	+	0.0988904i
$561$		0			0
$562$		−	9.36069i		−	0.394857i
$563$		−	30.2557i		−	1.27512i	−0.770399	−	0.637562i	$-0.779943\pi$
$563$		−	30.2557i		−	1.27512i	0.770399	−	0.637562i	$-0.220057\pi$
$564$		0			0
$565$	−19.3607	+	4.81044i	−0.814510	+	0.202377i
$566$	17.4186			0.732156
$567$		0			0
$568$		−	15.1773i		−	0.636824i
$569$	33.8720			1.41999			0.709994	−	0.704208i	$-0.248698\pi$
$569$	33.8720			1.41999			0.709994	+	0.704208i	$0.248698\pi$
$570$		0			0
$571$	35.1650			1.47161			0.735804	−	0.677194i	$-0.236804\pi$
$571$	35.1650			1.47161			0.735804	+	0.677194i	$0.236804\pi$
$572$		−	2.52359i		−	0.105517i
$573$		0			0
$574$	−0.680346			−0.0283971
$575$	−2.34017	−	4.41855i	−0.0975920	−	0.184266i
$576$		0			0
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$		−	16.1506i		−	0.671777i
$579$		0			0
$580$	−5.65983	−	22.7792i	−0.235012	−	0.945857i
$581$	−49.5585			−2.05603
$582$		0			0
$583$		−	0.366835i		−	0.0151928i
$584$	−4.68035			−0.193674
$585$		0			0
$586$	−16.3402			−0.675006
$587$		−	9.30737i		−	0.384156i	−0.981380	−	0.192078i	$-0.938477\pi$
$587$		−	9.30737i		−	0.384156i	0.981380	−	0.192078i	$-0.0615227\pi$
$588$		0			0
$589$	9.36069			0.385701
$590$	−19.1773	+	4.76487i	−0.789516	+	0.196166i
$591$		0			0
$592$			2.58145i			0.106097i
$593$			33.0349i			1.35658i	0.734794	+	0.678290i	$0.237279\pi$
$593$			33.0349i			1.35658i	−0.734794	+	0.678290i	$0.762721\pi$
$594$		0			0
$595$	2.15676	+	8.68035i	0.0884184	+	0.355859i
$596$	−6.92162			−0.283521
$597$		0			0
$598$			2.34017i			0.0956968i
$599$	13.6475			0.557623			0.278812	−	0.960346i	$-0.410059\pi$
$599$	13.6475			0.557623			0.278812	+	0.960346i	$0.410059\pi$
$600$		0			0
$601$	1.68649			0.0687933			0.0343967	−	0.999408i	$-0.489049\pi$
$601$	1.68649			0.0687933			0.0343967	+	0.999408i	$0.489049\pi$
$602$		−	3.20394i		−	0.130583i
$603$		0			0
$604$	−6.15676			−0.250515
$605$	−5.30406	−	21.3474i	−0.215641	−	0.867894i
$606$		0			0
$607$		−	47.2183i		−	1.91653i	−0.285878	−	0.958266i	$-0.592285\pi$
$607$		−	47.2183i		−	1.91653i	0.285878	−	0.958266i	$-0.407715\pi$
$608$			2.34017i			0.0949065i
$609$		0			0
$610$	−25.1194	+	6.24128i	−1.01706	+	0.252702i
$611$	16.0000			0.647291
$612$		0			0
$613$			7.45959i			0.301290i	0.988588	+	0.150645i	$0.0481350\pi$
$613$			7.45959i			0.301290i	−0.988588	+	0.150645i	$0.951865\pi$
$614$	−3.20394			−0.129300
$615$		0			0
$616$	−4.68035			−0.188577
$617$		−	15.8120i		−	0.636569i	−0.947995	−	0.318285i	$-0.896893\pi$
$617$		−	15.8120i		−	0.636569i	0.947995	−	0.318285i	$-0.103107\pi$
$618$		0			0
$619$	26.3402			1.05870			0.529350	−	0.848403i	$-0.322436\pi$
$619$	26.3402			1.05870			0.529350	+	0.848403i	$0.322436\pi$
$620$	2.15676	+	8.68035i	0.0866174	+	0.348611i
$621$		0			0
$622$			12.6537i			0.507367i
$623$		−	20.3135i		−	0.813844i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	−33.2183			−1.32767
$627$		0			0
$628$		−	2.89496i		−	0.115521i
$629$	2.37912			0.0948618
$630$		0			0
$631$	−14.4391			−0.574810			−0.287405	−	0.957809i	$-0.592793\pi$
$631$	−14.4391			−0.574810			−0.287405	+	0.957809i	$0.592793\pi$
$632$			11.9155i			0.473972i
$633$		0			0
$634$	6.99386			0.277762
$635$	−37.2762	+	9.26180i	−1.47926	+	0.367543i
$636$		0			0
$637$		−	27.7009i		−	1.09755i
$638$		−	11.3197i		−	0.448149i
$639$		0			0
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	5.78992			0.228688			0.114344	−	0.993441i	$-0.463523\pi$
$641$	5.78992			0.228688			0.114344	+	0.993441i	$0.463523\pi$
$642$		0			0
$643$		−	23.4063i		−	0.923053i	−0.887126	−	0.461526i	$-0.847302\pi$
$643$		−	23.4063i		−	0.923053i	0.887126	−	0.461526i	$-0.152698\pi$
$644$	4.34017			0.171027
$645$		0			0
$646$	2.15676			0.0848564
$647$		−	25.9877i		−	1.02168i	−0.859675	−	0.510841i	$-0.829334\pi$
$647$		−	25.9877i		−	1.02168i	0.859675	−	0.510841i	$-0.170666\pi$
$648$		0			0
$649$	−9.52973			−0.374075
$650$	−10.3402	+	5.47641i	−0.405575	+	0.214802i
$651$		0			0
$652$			6.52359i			0.255484i
$653$		−	0.325797i		−	0.0127494i	−0.999980	−	0.00637471i	$-0.997971\pi$
$653$		−	0.325797i		−	0.0127494i	0.999980	−	0.00637471i	$-0.00202915\pi$
$654$		0			0
$655$	3.60197	+	14.4969i	0.140741	+	0.566442i
$656$	−0.156755			−0.00612027
$657$		0			0
$658$		−	29.6742i		−	1.15682i
$659$	−3.11942			−0.121515			−0.0607576	−	0.998153i	$-0.519352\pi$
$659$	−3.11942			−0.121515			−0.0607576	+	0.998153i	$0.519352\pi$
$660$		0			0
$661$	24.1399			0.938935			0.469467	−	0.882950i	$-0.344446\pi$
$661$	24.1399			0.938935			0.469467	+	0.882950i	$0.344446\pi$
$662$			29.7275i			1.15539i
$663$		0			0
$664$	−11.4186			−0.443126
$665$	22.0410	−	5.47641i	0.854715	−	0.212366i
$666$		0			0
$667$			10.4969i			0.406443i
$668$			5.47641i			0.211889i
$669$		0			0
$670$	1.39189	+	5.60197i	0.0537734	+	0.216423i
$671$	−12.4826			−0.481884
$672$		0			0
$673$			45.6742i			1.76061i	0.474407	+	0.880306i	$0.342662\pi$
$673$			45.6742i			1.76061i	−0.474407	+	0.880306i	$0.657338\pi$
$674$	28.3402			1.09162
$675$		0			0
$676$	−7.52359			−0.289369
$677$		−	9.38735i		−	0.360785i	−0.983595	−	0.180393i	$-0.942263\pi$
$677$		−	9.38735i		−	0.360785i	0.983595	−	0.180393i	$-0.0577368\pi$
$678$		0			0
$679$	−39.1506			−1.50246
$680$	0.496928	+	2.00000i	0.0190563	+	0.0766965i
$681$		0			0
$682$			4.31351i			0.165173i
$683$			20.9939i			0.803308i	0.915792	+	0.401654i	$0.131564\pi$
$683$			20.9939i			0.803308i	−0.915792	+	0.401654i	$0.868436\pi$
$684$		0			0
$685$	48.3545	−	12.0144i	1.84753	−	0.459046i
$686$	−20.9939			−0.801549
$687$		0			0
$688$		−	0.738205i		−	0.0281438i
$689$	0.796064			0.0303276
$690$		0			0
$691$	−44.1445			−1.67933			−0.839667	−	0.543101i	$-0.817250\pi$
$691$	−44.1445			−1.67933			−0.839667	+	0.543101i	$0.817250\pi$
$692$			15.6742i			0.595844i
$693$		0			0
$694$	22.5236			0.854984
$695$	5.67420	+	22.8371i	0.215235	+	0.866261i
$696$		0			0
$697$			0.144469i			0.00547217i
$698$			15.6742i			0.593277i
$699$		0			0
$700$	10.1568	+	19.1773i	0.383889	+	0.724833i
$701$	27.7998			1.04998			0.524991	−	0.851108i	$-0.324069\pi$
$701$	27.7998			1.04998			0.524991	+	0.851108i	$0.324069\pi$
$702$		0			0
$703$		−	6.04104i		−	0.227842i
$704$	−1.07838			−0.0406429
$705$		0			0
$706$	26.3135			0.990322
$707$		−	6.52359i		−	0.245345i
$708$		0			0
$709$	−4.30898			−0.161827			−0.0809135	−	0.996721i	$-0.525784\pi$
$709$	−4.30898			−0.161827			−0.0809135	+	0.996721i	$0.525784\pi$
$710$	−32.9360	+	8.18342i	−1.23607	+	0.307118i
$711$		0			0
$712$		−	4.68035i		−	0.175403i
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$	−5.47641	+	1.36069i	−0.204806	+	0.0508870i
$716$	−15.3607			−0.574056
$717$		0			0
$718$			0.796064i			0.0297088i
$719$	15.9733			0.595705			0.297852	−	0.954612i	$-0.403730\pi$
$719$	15.9733			0.595705			0.297852	+	0.954612i	$0.403730\pi$
$720$		0			0
$721$	−10.8371			−0.403595
$722$			13.5236i			0.503296i
$723$		0			0
$724$	−21.6163			−0.803365
$725$	−46.3812	+	24.5646i	−1.72255	+	0.912307i
$726$		0			0
$727$		−	0.340173i		−	0.0126163i	−0.999980	−	0.00630816i	$-0.997992\pi$
$727$		−	0.340173i		−	0.0126163i	0.999980	−	0.00630816i	$-0.00200796\pi$
$728$		−	10.1568i		−	0.376434i
$729$		0			0
$730$	2.52359	+	10.1568i	0.0934023	+	0.375918i
$731$	−0.680346			−0.0251635
$732$		0			0
$733$			19.2618i			0.711451i	0.934591	+	0.355725i	$0.115766\pi$
$733$			19.2618i			0.711451i	−0.934591	+	0.355725i	$0.884234\pi$
$734$	13.7009			0.505708
$735$		0			0
$736$	1.00000			0.0368605
$737$			2.78378i			0.102542i
$738$		0			0
$739$	−25.5585			−0.940184			−0.470092	−	0.882617i	$-0.655779\pi$
$739$	−25.5585			−0.940184			−0.470092	+	0.882617i	$0.655779\pi$
$740$	5.60197	−	1.39189i	0.205932	−	0.0511668i
$741$		0			0
$742$		−	1.47641i		−	0.0542007i
$743$		−	36.8781i		−	1.35293i	−0.736476	−	0.676464i	$-0.763511\pi$
$743$		−	36.8781i		−	1.35293i	0.736476	−	0.676464i	$-0.236489\pi$
$744$		0			0
$745$	3.73206	+	15.0205i	0.136732	+	0.550309i
$746$	−4.25565			−0.155810
$747$		0			0
$748$			0.993857i			0.0363390i
$749$	41.5585			1.51851
$750$		0			0
$751$	18.1256			0.661411			0.330706	−	0.943734i	$-0.392713\pi$
$751$	18.1256			0.661411			0.330706	+	0.943734i	$0.392713\pi$
$752$		−	6.83710i		−	0.249323i
$753$		0			0
$754$	24.5646			0.894591
$755$	3.31965	+	13.3607i	0.120815	+	0.486245i
$756$		0			0
$757$		−	17.4186i		−	0.633088i	−0.948578	−	0.316544i	$-0.897478\pi$
$757$		−	17.4186i		−	0.633088i	0.948578	−	0.316544i	$-0.102522\pi$
$758$		−	30.6537i		−	1.11339i
$759$		0			0
$760$	5.07838	−	1.26180i	0.184212	−	0.0457701i
$761$	23.4140			0.848757			0.424379	−	0.905485i	$-0.360493\pi$
$761$	23.4140			0.848757			0.424379	+	0.905485i	$0.360493\pi$
$762$		0			0
$763$			42.4703i			1.53753i
$764$	4.36683			0.157987
$765$		0			0
$766$	−20.8781			−0.754358
$767$		−	20.6803i		−	0.746724i
$768$		0			0
$769$	29.7152			1.07156			0.535779	−	0.844358i	$-0.320018\pi$
$769$	29.7152			1.07156			0.535779	+	0.844358i	$0.320018\pi$
$770$	2.52359	+	10.1568i	0.0909439	+	0.366024i
$771$		0			0
$772$		−	8.68035i		−	0.312412i
$773$			15.3463i			0.551969i	0.961162	+	0.275984i	$0.0890038\pi$
$773$			15.3463i			0.551969i	−0.961162	+	0.275984i	$0.910996\pi$
$774$		0			0
$775$	17.6742	−	9.36069i	0.634876	−	0.336246i
$776$	−9.02052			−0.323818
$777$		0			0
$778$			16.9627i			0.608141i
$779$	0.366835			0.0131432
$780$		0			0
$781$	−16.3668			−0.585651
$782$		−	0.921622i		−	0.0329571i
$783$		0			0
$784$	−11.8371			−0.422754
$785$	−6.28231	+	1.56093i	−0.224225	+	0.0557120i
$786$		0			0
$787$		−	22.8950i		−	0.816117i	−0.912956	−	0.408059i	$-0.866206\pi$
$787$		−	22.8950i		−	0.816117i	0.912956	−	0.408059i	$-0.133794\pi$
$788$		−	22.6803i		−	0.807954i
$789$		0			0
$790$	25.8576	−	6.42469i	0.919973	−	0.228580i
$791$	−38.7214			−1.37677
$792$		0			0
$793$		−	27.0882i		−	0.961931i
$794$	−16.4969			−0.585454
$795$		0			0
$796$	−5.44521			−0.193000
$797$			7.60650i			0.269436i	0.990884	+	0.134718i	$0.0430129\pi$
$797$			7.60650i			0.269436i	−0.990884	+	0.134718i	$0.956987\pi$
$798$		0			0
$799$	−6.30122			−0.222921
$800$	2.34017	+	4.41855i	0.0827376	+	0.156219i
$801$		0			0
$802$		−	35.2039i		−	1.24309i
$803$			5.04718i			0.178111i
$804$		0			0
$805$	−2.34017	−	9.41855i	−0.0824803	−	0.331960i
$806$	−9.36069			−0.329716
$807$		0			0
$808$		−	1.50307i		−	0.0528779i
$809$	43.7275			1.53738			0.768689	−	0.639623i	$-0.220909\pi$
$809$	43.7275			1.53738			0.768689	+	0.639623i	$0.220909\pi$
$810$		0			0
$811$	−4.79606			−0.168413			−0.0842063	−	0.996448i	$-0.526835\pi$
$811$	−4.79606			−0.168413			−0.0842063	+	0.996448i	$0.526835\pi$
$812$		−	45.5585i		−	1.59879i
$813$		0			0
$814$	2.78378			0.0975713
$815$	14.1568	−	3.51745i	0.495890	−	0.123211i
$816$		0			0
$817$			1.72753i			0.0604385i
$818$			11.3607i			0.397217i
$819$		0			0
$820$	0.0845208	+	0.340173i	0.00295159	+	0.0118794i
$821$	12.2245			0.426636			0.213318	−	0.976983i	$-0.431573\pi$
$821$	12.2245			0.426636			0.213318	+	0.976983i	$0.431573\pi$
$822$		0			0
$823$			37.5441i			1.30871i	0.756189	+	0.654353i	$0.227059\pi$
$823$			37.5441i			1.30871i	−0.756189	+	0.654353i	$0.772941\pi$
$824$	−2.49693			−0.0869846
$825$		0			0
$826$	−38.3545			−1.33453
$827$			38.3090i			1.33213i	0.745892	+	0.666067i	$0.232023\pi$
$827$			38.3090i			1.33213i	−0.745892	+	0.666067i	$0.767977\pi$
$828$		0			0
$829$	31.4140			1.09105			0.545527	−	0.838093i	$-0.316330\pi$
$829$	31.4140			1.09105			0.545527	+	0.838093i	$0.316330\pi$
$830$	6.15676	+	24.7792i	0.213704	+	0.860100i
$831$		0			0
$832$		−	2.34017i		−	0.0811309i
$833$			10.9093i			0.377986i
$834$		0			0
$835$	11.8843	−	2.95282i	0.411273	−	0.102187i
$836$	2.52359			0.0872802
$837$		0			0
$838$			18.1256i			0.626137i
$839$	23.1506			0.799248			0.399624	−	0.916679i	$-0.369141\pi$
$839$	23.1506			0.799248			0.399624	+	0.916679i	$0.369141\pi$
$840$		0			0
$841$	81.1855			2.79950
$842$		−	2.58145i		−	0.0889626i
$843$		0			0
$844$	22.0410			0.758684
$845$	4.05664	+	16.3268i	0.139553	+	0.561660i
$846$		0			0
$847$		−	42.6947i		−	1.46701i
$848$		−	0.340173i		−	0.0116816i
$849$		0			0
$850$	4.07223	−	2.15676i	0.139676	−	0.0739761i
$851$	−2.58145			−0.0884909
$852$		0			0
$853$			32.4969i			1.11267i	0.830957	+	0.556337i	$0.187794\pi$
$853$			32.4969i			1.11267i	−0.830957	+	0.556337i	$0.812206\pi$
$854$	−50.2388			−1.71914
$855$		0			0
$856$	9.57531			0.327277
$857$		−	37.8310i		−	1.29228i	−0.763219	−	0.646140i	$-0.776382\pi$
$857$		−	37.8310i		−	1.29228i	0.763219	−	0.646140i	$-0.223618\pi$
$858$		0			0
$859$	28.1978			0.962096			0.481048	−	0.876694i	$-0.340256\pi$
$859$	28.1978			0.962096			0.481048	+	0.876694i	$0.340256\pi$
$860$	−1.60197	+	0.398032i	−0.0546267	+	0.0135728i
$861$		0			0
$862$		−	33.9877i		−	1.15763i
$863$			32.0288i			1.09027i	0.838348	+	0.545136i	$0.183522\pi$
$863$			32.0288i			1.09027i	−0.838348	+	0.545136i	$0.816478\pi$
$864$		0			0
$865$	34.0144	−	8.45136i	1.15652	−	0.287355i
$866$	8.28685			0.281599
$867$		0			0
$868$			17.3607i			0.589260i
$869$	12.8494			0.435886
$870$		0			0
$871$	−6.04104			−0.204693
$872$			9.78539i			0.331375i
$873$		0			0
$874$	−2.34017			−0.0791575
$875$	36.1399	−	32.3812i	1.22175	−	1.09468i
$876$		0			0
$877$			27.7009i			0.935392i	0.883889	+	0.467696i	$0.154916\pi$
$877$			27.7009i			0.935392i	−0.883889	+	0.467696i	$0.845084\pi$
$878$		−	28.9939i		−	0.978495i
$879$		0			0
$880$	0.581449	+	2.34017i	0.0196007	+	0.0788872i
$881$	−12.3135			−0.414853			−0.207426	−	0.978251i	$-0.566509\pi$
$881$	−12.3135			−0.414853			−0.207426	+	0.978251i	$0.566509\pi$
$882$		0			0
$883$		−	7.15061i		−	0.240637i	−0.992735	−	0.120319i	$-0.961608\pi$
$883$		−	7.15061i		−	0.240637i	0.992735	−	0.120319i	$-0.0383916\pi$
$884$	−2.15676			−0.0725395
$885$		0			0
$886$	−3.20394			−0.107638
$887$		−	9.19165i		−	0.308625i	−0.988022	−	0.154313i	$-0.950684\pi$
$887$		−	9.19165i		−	0.308625i	0.988022	−	0.154313i	$-0.0493163\pi$
$888$		0			0
$889$	−74.5523			−2.50041
$890$	−10.1568	+	2.52359i	−0.340455	+	0.0845909i
$891$		0			0
$892$			21.1773i			0.709068i
$893$			16.0000i			0.535420i
$894$		0			0
$895$	8.28231	+	33.3340i	0.276847	+	1.11423i
$896$	−4.34017			−0.144995
$897$		0			0
$898$		−	28.1568i		−	0.939603i
$899$	−41.9877			−1.40037
$900$		0			0
$901$	−0.313511			−0.0104446
$902$			0.169042i			0.00562847i
$903$		0			0
$904$	−8.92162			−0.296729
$905$	11.6553	+	46.9093i	0.387435	+	1.55932i
$906$		0			0
$907$		−	14.0989i		−	0.468146i	−0.972219	−	0.234073i	$-0.924794\pi$
$907$		−	14.0989i		−	0.468146i	0.972219	−	0.234073i	$-0.0752055\pi$
$908$		−	11.7854i		−	0.391112i
$909$		0			0
$910$	−22.0410	+	5.47641i	−0.730653	+	0.181541i
$911$	20.9939			0.695558			0.347779	−	0.937577i	$-0.386936\pi$
$911$	20.9939			0.695558			0.347779	+	0.937577i	$0.386936\pi$
$912$		0			0
$913$			12.3135i			0.407518i
$914$	−23.1773			−0.766636
$915$		0			0
$916$	1.78539			0.0589908
$917$			28.9939i			0.957462i
$918$		0			0
$919$	1.92777			0.0635911			0.0317956	−	0.999494i	$-0.489877\pi$
$919$	1.92777			0.0635911			0.0317956	+	0.999494i	$0.489877\pi$
$920$	−0.539189	−	2.17009i	−0.0177765	−	0.0715456i
$921$		0			0
$922$		−	42.3279i		−	1.39399i
$923$		−	35.5174i		−	1.16907i
$924$		0			0
$925$	−6.04104	−	11.4063i	−0.198628	−	0.375036i
$926$	34.9048			1.14704
$927$		0			0
$928$		−	10.4969i		−	0.344579i
$929$	18.5646			0.609086			0.304543	−	0.952499i	$-0.401496\pi$
$929$	18.5646			0.609086			0.304543	+	0.952499i	$0.401496\pi$
$930$		0			0
$931$	27.7009			0.907859
$932$		−	18.3135i		−	0.599879i
$933$		0			0
$934$	37.7731			1.23597
$935$	2.15676	−	0.535877i	0.0705334	−	0.0175250i
$936$		0			0
$937$			22.3279i			0.729420i	0.931121	+	0.364710i	$0.118832\pi$
$937$			22.3279i			0.729420i	−0.931121	+	0.364710i	$0.881168\pi$
$938$			11.2039i			0.365821i
$939$		0			0
$940$	−14.8371	+	3.68649i	−0.483933	+	0.120240i
$941$	11.0661			0.360744			0.180372	−	0.983598i	$-0.442270\pi$
$941$	11.0661			0.360744			0.180372	+	0.983598i	$0.442270\pi$
$942$		0			0
$943$		−	0.156755i		−	0.00510466i
$944$	−8.83710			−0.287623
$945$		0			0
$946$	−0.796064			−0.0258823
$947$		−	8.05332i		−	0.261698i	−0.991402	−	0.130849i	$-0.958230\pi$
$947$		−	8.05332i		−	0.261698i	0.991402	−	0.130849i	$-0.0417703\pi$
$948$		0			0
$949$	−10.9528			−0.355544
$950$	−5.47641	−	10.3402i	−0.177678	−	0.335480i
$951$		0			0
$952$			4.00000i			0.129641i
$953$			39.5897i			1.28244i	0.767359	+	0.641218i	$0.221570\pi$
$953$			39.5897i			1.28244i	−0.767359	+	0.641218i	$0.778430\pi$
$954$		0			0
$955$	−2.35455	−	9.47641i	−0.0761914	−	0.306649i
$956$	5.33403			0.172515
$957$		0			0
$958$			28.1978i			0.911029i
$959$	96.7091			3.12290
$960$		0			0
$961$	−15.0000			−0.483871
$962$			6.04104i			0.194771i
$963$		0			0
$964$	−26.1978			−0.843774
$965$	−18.8371	+	4.68035i	−0.606388	+	0.150666i
$966$		0			0
$967$			48.2655i			1.55211i	0.630663	+	0.776057i	$0.282783\pi$
$967$			48.2655i			1.55211i	−0.630663	+	0.776057i	$0.717217\pi$
$968$		−	9.83710i		−	0.316176i
$969$		0			0
$970$	4.86376	+	19.5753i	0.156166	+	0.628525i
$971$	−18.0722			−0.579966			−0.289983	−	0.957032i	$-0.593650\pi$
$971$	−18.0722			−0.579966			−0.289983	+	0.957032i	$0.593650\pi$
$972$		0			0
$973$			45.6742i			1.46425i
$974$	38.2245			1.22479
$975$		0			0
$976$	−11.5753			−0.370517
$977$			45.9442i			1.46989i	0.678129	+	0.734943i	$0.262791\pi$
$977$			45.9442i			1.46989i	−0.678129	+	0.734943i	$0.737209\pi$
$978$		0			0
$979$	−5.04718			−0.161309
$980$	6.38243	+	25.6875i	0.203879	+	0.820558i
$981$		0			0
$982$			11.3074i			0.360833i
$983$			1.78992i			0.0570896i	0.999593	+	0.0285448i	$0.00908733\pi$
$983$			1.78992i			0.0570896i	−0.999593	+	0.0285448i	$0.990913\pi$
$984$		0			0
$985$	−49.2183	+	12.2290i	−1.56823	+	0.389648i
$986$	−9.67420			−0.308089
$987$		0			0
$988$			5.47641i			0.174228i
$989$	0.738205			0.0234735
$990$		0			0
$991$	7.68649			0.244169			0.122085	−	0.992520i	$-0.461042\pi$
$991$	7.68649			0.244169			0.122085	+	0.992520i	$0.461042\pi$
$992$			4.00000i			0.127000i
$993$		0			0
$994$	−65.8720			−2.08933
$995$	2.93600	+	11.8166i	0.0930774	+	0.374611i
$996$		0			0
$997$		−	21.4908i		−	0.680620i	−0.940313	−	0.340310i	$-0.889468\pi$
$997$		−	21.4908i		−	0.680620i	0.940313	−	0.340310i	$-0.110532\pi$
$998$		−	2.47027i		−	0.0781949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.d.e.829.2		6
3.2	odd	2		690.2.d.c.139.5	yes	6
5.4	even	2	inner	2070.2.d.e.829.5		6
15.2	even	4		3450.2.a.bo.1.1		3
15.8	even	4		3450.2.a.bt.1.3		3
15.14	odd	2		690.2.d.c.139.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.c.139.2	✓	6	15.14	odd	2
690.2.d.c.139.5	yes	6	3.2	odd	2
2070.2.d.e.829.2		6	1.1	even	1	trivial
2070.2.d.e.829.5		6	5.4	even	2	inner
3450.2.a.bo.1.1		3	15.2	even	4
3450.2.a.bt.1.3		3	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +4.34017i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +4.34017i q^{7} +1.00000i q^{8} +(2.17009 - 0.539189i) q^{10} +1.07838 q^{11} +2.34017i q^{13} +4.34017 q^{14} +1.00000 q^{16} -0.921622i q^{17} -2.34017 q^{19} +(-0.539189 - 2.17009i) q^{20} -1.07838i q^{22} +1.00000i q^{23} +(-4.41855 + 2.34017i) q^{25} +2.34017 q^{26} -4.34017i q^{28} +10.4969 q^{29} -4.00000 q^{31} -1.00000i q^{32} -0.921622 q^{34} +(-9.41855 + 2.34017i) q^{35} +2.58145i q^{37} +2.34017i q^{38} +(-2.17009 + 0.539189i) q^{40} -0.156755 q^{41} -0.738205i q^{43} -1.07838 q^{44} +1.00000 q^{46} -6.83710i q^{47} -11.8371 q^{49} +(2.34017 + 4.41855i) q^{50} -2.34017i q^{52} -0.340173i q^{53} +(0.581449 + 2.34017i) q^{55} -4.34017 q^{56} -10.4969i q^{58} -8.83710 q^{59} -11.5753 q^{61} +4.00000i q^{62} -1.00000 q^{64} +(-5.07838 + 1.26180i) q^{65} +2.58145i q^{67} +0.921622i q^{68} +(2.34017 + 9.41855i) q^{70} -15.1773 q^{71} +4.68035i q^{73} +2.58145 q^{74} +2.34017 q^{76} +4.68035i q^{77} +11.9155 q^{79} +(0.539189 + 2.17009i) q^{80} +0.156755i q^{82} +11.4186i q^{83} +(2.00000 - 0.496928i) q^{85} -0.738205 q^{86} +1.07838i q^{88} -4.68035 q^{89} -10.1568 q^{91} -1.00000i q^{92} -6.83710 q^{94} +(-1.26180 - 5.07838i) q^{95} +9.02052i q^{97} +11.8371i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 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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