LMFDB - Embedded newform 1620.3.t.a.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,3,Mod(269,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1620.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1620.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$44.1418028264$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.154550410641.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 15x^{6} + 221x^{4} - 60x^{2} + 16 $ x^8 - 15x^6 + 221x^4 - 60*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 540)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$3.32360 + 1.91888i$ of defining polynomial
Character	$\chi$	$=$	1620.269
Dual form			1620.3.t.a.1349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.29522 - 2.55951i) q^{5} +(2.42096 + 1.39774i) q^{7} +O(q^{10})$	$q+(-4.29522 - 2.55951i) q^{5} +(2.42096 + 1.39774i) q^{7} +(-15.7154 - 9.07327i) q^{11} +(19.9416 - 11.5133i) q^{13} -5.72842 q^{17} +23.1852 q^{19} +(0.135792 + 0.235199i) q^{23} +(11.8979 + 21.9873i) q^{25} +(34.4674 + 19.8997i) q^{29} +(-23.6852 - 41.0241i) q^{31} +(-6.82104 - 12.2001i) q^{35} +34.8712i q^{37} +(-11.4891 + 6.63325i) q^{41} +(-40.4571 - 23.3579i) q^{43} +(-20.4568 + 35.4323i) q^{47} +(-20.5926 - 35.6675i) q^{49} -91.3705 q^{53} +(44.2779 + 79.1953i) q^{55} +(68.2773 - 39.4199i) q^{59} +(-15.5926 + 27.0072i) q^{61} +(-115.122 - 1.58852i) q^{65} +(5.98970 - 3.45816i) q^{67} -81.5870i q^{71} -106.084i q^{73} +(-25.3642 - 43.9321i) q^{77} +(-31.7779 + 55.0409i) q^{79} +(-0.142081 + 0.246091i) q^{83} +(24.6048 + 14.6619i) q^{85} -28.5210i q^{89} +64.3705 q^{91} +(-99.5858 - 59.3428i) q^{95} +(-80.4657 - 46.4569i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{5}+O(q^{10}) $ 8 * q - 3 * q^5	$ 8 q - 3 q^{5} + 12 q^{17} + 12 q^{19} + 30 q^{23} - 9 q^{25} - 16 q^{31} + 90 q^{35} - 48 q^{47} - 78 q^{49} - 384 q^{53} + 94 q^{55} - 38 q^{61} - 138 q^{65} - 174 q^{77} + 6 q^{79} + 288 q^{83} + 100 q^{85} + 168 q^{91} - 318 q^{95}+O(q^{100}) $ 8 * q - 3 * q^5 + 12 * q^17 + 12 * q^19 + 30 * q^23 - 9 * q^25 - 16 * q^31 + 90 * q^35 - 48 * q^47 - 78 * q^49 - 384 * q^53 + 94 * q^55 - 38 * q^61 - 138 * q^65 - 174 * q^77 + 6 * q^79 + 288 * q^83 + 100 * q^85 + 168 * q^91 - 318 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−4.29522	−	2.55951i	−0.859044	−	0.511901i
$5$	−4.29522	−	2.55951i	−0.859044	−	0.511901i
$6$		0			0
$7$	2.42096	+	1.39774i	0.345852	+	0.199678i	0.662857	−	0.748746i	$-0.269344\pi$
$7$	2.42096	+	1.39774i	0.345852	+	0.199678i	−0.317005	+	0.948424i	$0.602677\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−15.7154	−	9.07327i	−1.42867	−	0.824843i	−0.431653	−	0.902040i	$-0.642070\pi$
$11$	−15.7154	−	9.07327i	−1.42867	−	0.824843i	−0.997016	+	0.0771971i	$0.975403\pi$
$12$		0			0
$13$	19.9416	−	11.5133i	1.53397	−	0.885637i	0.534796	−	0.844981i	$-0.320389\pi$
$13$	19.9416	−	11.5133i	1.53397	−	0.885637i	0.999173	−	0.0406560i	$-0.0129448\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.72842			−0.336966			−0.168483	−	0.985705i	$-0.553887\pi$
$17$	−5.72842			−0.336966			−0.168483	+	0.985705i	$0.553887\pi$
$18$		0			0
$19$	23.1852			1.22028			0.610138	−	0.792295i	$-0.291114\pi$
$19$	23.1852			1.22028			0.610138	+	0.792295i	$0.291114\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.135792	+	0.235199i	0.00590400	+	0.0102260i	0.868962	−	0.494878i	$-0.164787\pi$
$23$	0.135792	+	0.235199i	0.00590400	+	0.0102260i	−0.863058	+	0.505104i	$0.831454\pi$
$24$		0			0
$25$	11.8979	+	21.9873i	0.475914	+	0.879492i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	34.4674	+	19.8997i	1.18853	+	0.686198i	0.957972	−	0.286860i	$-0.0926116\pi$
$29$	34.4674	+	19.8997i	1.18853	+	0.686198i	0.230558	+	0.973059i	$0.425945\pi$
$30$		0			0
$31$	−23.6852	−	41.0241i	−0.764040	−	1.32336i	−0.940752	−	0.339094i	$-0.889880\pi$
$31$	−23.6852	−	41.0241i	−0.764040	−	1.32336i	0.176712	−	0.984263i	$-0.443454\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.82104	−	12.2001i	−0.194887	−	0.348574i
$36$		0			0
$37$			34.8712i			0.942465i	0.882009	+	0.471232i	$0.156191\pi$
$37$			34.8712i			0.942465i	−0.882009	+	0.471232i	$0.843809\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−11.4891	+	6.63325i	−0.280223	+	0.161787i	−0.633524	−	0.773723i	$-0.718392\pi$
$41$	−11.4891	+	6.63325i	−0.280223	+	0.161787i	0.353302	+	0.935509i	$0.385059\pi$
$42$		0			0
$43$	−40.4571	−	23.3579i	−0.940862	−	0.543207i	−0.0506318	−	0.998717i	$-0.516123\pi$
$43$	−40.4571	−	23.3579i	−0.940862	−	0.543207i	−0.890231	+	0.455510i	$0.849457\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−20.4568	+	35.4323i	−0.435252	+	0.753878i	−0.997316	−	0.0732153i	$-0.976674\pi$
$47$	−20.4568	+	35.4323i	−0.435252	+	0.753878i	0.562064	+	0.827093i	$0.310007\pi$
$48$		0			0
$49$	−20.5926	−	35.6675i	−0.420258	−	0.727908i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−91.3705			−1.72397			−0.861986	−	0.506932i	$-0.830779\pi$
$53$	−91.3705			−1.72397			−0.861986	+	0.506932i	$0.830779\pi$
$54$		0			0
$55$	44.2779	+	79.1953i	0.805052	+	1.43991i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	68.2773	−	39.4199i	1.15724	−	0.668134i	0.206600	−	0.978425i	$-0.433760\pi$
$59$	68.2773	−	39.4199i	1.15724	−	0.668134i	0.950641	+	0.310292i	$0.100427\pi$
$60$		0			0
$61$	−15.5926	+	27.0072i	−0.255617	+	0.442741i	−0.965063	−	0.262018i	$-0.915612\pi$
$61$	−15.5926	+	27.0072i	−0.255617	+	0.442741i	0.709446	+	0.704760i	$0.248945\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−115.122	−	1.58852i	−1.77111	−	0.0244388i
$66$		0			0
$67$	5.98970	−	3.45816i	0.0893986	−	0.0516143i	−0.454634	−	0.890678i	$-0.650230\pi$
$67$	5.98970	−	3.45816i	0.0893986	−	0.0516143i	0.544033	+	0.839064i	$0.316897\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	81.5870i		−	1.14911i	−0.818465	−	0.574556i	$-0.805175\pi$
$71$		−	81.5870i		−	1.14911i	0.818465	−	0.574556i	$-0.194825\pi$
$72$		0			0
$73$		−	106.084i		−	1.45320i	−0.687060	−	0.726601i	$-0.741099\pi$
$73$		−	106.084i		−	1.45320i	0.687060	−	0.726601i	$-0.258901\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−25.3642	−	43.9321i	−0.329405	−	0.570547i
$78$		0			0
$79$	−31.7779	+	55.0409i	−0.402252	+	0.696720i	−0.993997	−	0.109405i	$-0.965106\pi$
$79$	−31.7779	+	55.0409i	−0.402252	+	0.696720i	0.591746	+	0.806125i	$0.298439\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.142081	+	0.246091i	−0.00171182	+	0.00296495i	−0.866880	−	0.498517i	$-0.833878\pi$
$83$	−0.142081	+	0.246091i	−0.00171182	+	0.00296495i	0.865168	+	0.501482i	$0.167212\pi$
$84$		0			0
$85$	24.6048	+	14.6619i	0.289468	+	0.172493i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	28.5210i		−	0.320461i	−0.987080	−	0.160230i	$-0.948776\pi$
$89$		−	28.5210i		−	0.320461i	0.987080	−	0.160230i	$-0.0512237\pi$
$90$		0			0
$91$	64.3705			0.707368
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−99.5858	−	59.3428i	−1.04827	−	0.624661i
$96$		0			0
$97$	−80.4657	−	46.4569i	−0.829543	−	0.478937i	0.0241531	−	0.999708i	$-0.492311\pi$
$97$	−80.4657	−	46.4569i	−0.829543	−	0.478937i	−0.853696	+	0.520771i	$0.825644\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−40.4153	−	23.3338i	−0.400151	−	0.231027i	0.286398	−	0.958111i	$-0.407542\pi$
$101$	−40.4153	−	23.3338i	−0.400151	−	0.231027i	−0.686549	+	0.727083i	$0.740875\pi$
$102$		0			0
$103$	−9.68385	+	5.59098i	−0.0940180	+	0.0542813i	−0.546272	−	0.837608i	$-0.683953\pi$
$103$	−9.68385	+	5.59098i	−0.0940180	+	0.0542813i	0.452254	+	0.891889i	$0.350620\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−147.297			−1.37661			−0.688303	−	0.725424i	$-0.741644\pi$
$107$	−147.297			−1.37661			−0.688303	+	0.725424i	$0.741644\pi$
$108$		0			0
$109$	−121.556			−1.11519			−0.557595	−	0.830113i	$-0.688276\pi$
$109$	−121.556			−1.11519			−0.557595	+	0.830113i	$0.688276\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	48.8148	+	84.5496i	0.431989	+	0.748227i	0.997045	−	0.0768260i	$-0.0244786\pi$
$113$	48.8148	+	84.5496i	0.431989	+	0.748227i	−0.565056	+	0.825053i	$0.691145\pi$
$114$		0			0
$115$	0.0187356	−	1.35779i	0.000162918	−	0.0118069i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−13.8683	−	8.00686i	−0.116540	−	0.0672845i
$120$		0			0
$121$	104.148	+	180.390i	0.860730	+	1.49083i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.17267	−	124.893i	0.0413814	−	0.999143i
$126$		0			0
$127$		−	88.6481i		−	0.698017i	−0.937120	−	0.349008i	$-0.886518\pi$
$127$		−	88.6481i		−	0.698017i	0.937120	−	0.349008i	$-0.113482\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	77.9193	−	44.9867i	0.594804	−	0.343410i	−0.172191	−	0.985064i	$-0.555085\pi$
$131$	77.9193	−	44.9867i	0.594804	−	0.343410i	0.766995	+	0.641653i	$0.221751\pi$
$132$		0			0
$133$	56.1306	+	32.4070i	0.422035	+	0.243662i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−114.963	+	199.122i	−0.839147	+	1.45345i	0.0514620	+	0.998675i	$0.483612\pi$
$137$	−114.963	+	199.122i	−0.839147	+	1.45345i	−0.890609	+	0.454770i	$0.849721\pi$
$138$		0			0
$139$	−28.8148	−	49.9086i	−0.207300	−	0.359055i	0.743563	−	0.668666i	$-0.233134\pi$
$139$	−28.8148	−	49.9086i	−0.207300	−	0.359055i	−0.950863	+	0.309611i	$0.899801\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−417.852			−2.92205
$144$		0			0
$145$	−97.1115	−	173.693i	−0.669734	−	1.19788i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.64205	+	5.56684i	−0.0647117	+	0.0373613i	−0.532007	−	0.846740i	$-0.678562\pi$
$149$	−9.64205	+	5.56684i	−0.0647117	+	0.0373613i	0.467295	+	0.884101i	$0.345229\pi$
$150$		0			0
$151$	11.0926	−	19.2130i	0.0734611	−	0.127238i	−0.826955	−	0.562268i	$-0.809929\pi$
$151$	11.0926	−	19.2130i	0.0734611	−	0.127238i	0.900416	+	0.435030i	$0.143262\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.26792	+	236.830i	−0.0210834	+	1.52794i
$156$		0			0
$157$	−195.148	+	112.669i	−1.24298	+	0.717635i	−0.969700	−	0.244299i	$-0.921442\pi$
$157$	−195.148	+	112.669i	−1.24298	+	0.717635i	−0.273281	+	0.961934i	$0.588109\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			0.759209i			0.00471559i
$162$		0			0
$163$			302.948i			1.85858i	0.369352	+	0.929290i	$0.379580\pi$
$163$			302.948i			1.85858i	−0.369352	+	0.929290i	$0.620420\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−119.334	−	206.692i	−0.714573	−	1.23768i	−0.963124	−	0.269057i	$-0.913288\pi$
$167$	−119.334	−	206.692i	−0.714573	−	1.23768i	0.248552	−	0.968619i	$-0.420045\pi$
$168$		0			0
$169$	180.611	−	312.828i	1.06871	−	1.85105i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	54.4011	−	94.2254i	0.314457	−	0.544656i	−0.664865	−	0.746964i	$-0.731511\pi$
$173$	54.4011	−	94.2254i	0.314457	−	0.544656i	0.979322	+	0.202308i	$0.0648442\pi$
$174$		0			0
$175$	−1.92832	+	69.8606i	−0.0110190	+	0.399203i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	168.054i		−	0.938849i	−0.882973	−	0.469425i	$-0.844461\pi$
$179$		−	168.054i		−	0.938849i	0.882973	−	0.469425i	$-0.155539\pi$
$180$		0			0
$181$	−154.297			−0.852468			−0.426234	−	0.904613i	$-0.640160\pi$
$181$	−154.297			−0.852468			−0.426234	+	0.904613i	$0.640160\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	89.2530	−	149.779i	0.482449	−	0.809619i
$186$		0			0
$187$	90.0241	+	51.9755i	0.481412	+	0.277944i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−134.175	−	77.4662i	−0.702489	−	0.405582i	0.105785	−	0.994389i	$-0.466264\pi$
$191$	−134.175	−	77.4662i	−0.702489	−	0.405582i	−0.808274	+	0.588807i	$0.799598\pi$
$192$		0			0
$193$	−55.4313	+	32.0033i	−0.287209	+	0.165820i	−0.636683	−	0.771126i	$-0.719694\pi$
$193$	−55.4313	+	32.0033i	−0.287209	+	0.165820i	0.349473	+	0.936946i	$0.386360\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.56832			−0.0485702			−0.0242851	−	0.999705i	$-0.507731\pi$
$197$	−9.56832			−0.0485702			−0.0242851	+	0.999705i	$0.507731\pi$
$198$		0			0
$199$	−117.815			−0.592034			−0.296017	−	0.955183i	$-0.595658\pi$
$199$	−117.815			−0.592034			−0.296017	+	0.955183i	$0.595658\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	55.6295	+	96.3531i	0.274037	+	0.474646i
$204$		0			0
$205$	66.3262	+	0.915209i	0.323542	+	0.00446443i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−364.365	−	210.366i	−1.74337	−	1.00654i
$210$		0			0
$211$	24.4074	+	42.2748i	0.115675	+	0.200355i	0.918049	−	0.396466i	$-0.129764\pi$
$211$	24.4074	+	42.2748i	0.115675	+	0.200355i	−0.802375	+	0.596821i	$0.796430\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	113.987	+	203.878i	0.530174	+	0.948268i
$216$		0			0
$217$		−	132.424i		−	0.610247i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−114.234	+	65.9529i	−0.516895	+	0.298429i
$222$		0			0
$223$	276.887	+	159.861i	1.24164	+	0.716864i	0.969429	−	0.245372i	$-0.0789102\pi$
$223$	276.887	+	159.861i	1.24164	+	0.716864i	0.272216	+	0.962236i	$0.412244\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.13579	+	15.8237i	−0.0402458	+	0.0697077i	−0.885447	−	0.464741i	$-0.846147\pi$
$227$	−9.13579	+	15.8237i	−0.0402458	+	0.0697077i	0.845201	+	0.534449i	$0.179481\pi$
$228$		0			0
$229$	−67.0369	−	116.111i	−0.292737	−	0.507036i	0.681719	−	0.731615i	$-0.261233\pi$
$229$	−67.0369	−	116.111i	−0.292737	−	0.507036i	−0.974456	+	0.224578i	$0.927900\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−284.173			−1.21963			−0.609813	−	0.792546i	$-0.708755\pi$
$233$	−284.173			−1.21963			−0.609813	+	0.792546i	$0.708755\pi$
$234$		0			0
$235$	178.556	−	99.8301i	0.759812	−	0.424809i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−179.068	+	103.385i	−0.749237	+	0.432572i	−0.825418	−	0.564522i	$-0.809061\pi$
$239$	−179.068	+	103.385i	−0.749237	+	0.432572i	0.0761810	+	0.997094i	$0.475727\pi$
$240$		0			0
$241$	81.3336	−	140.874i	0.337484	−	0.584539i	−0.646475	−	0.762935i	$-0.723757\pi$
$241$	81.3336	−	140.874i	0.337484	−	0.584539i	0.983959	+	0.178396i	$0.0570908\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.84122	+	205.907i	−0.0115968	+	0.840435i
$246$		0			0
$247$	462.351	−	266.938i	1.87187	−	1.08072i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	347.387i		−	1.38401i	−0.721893	−	0.692005i	$-0.756728\pi$
$251$		−	347.387i		−	1.38401i	0.721893	−	0.692005i	$-0.243272\pi$
$252$		0			0
$253$		−	4.92831i		−	0.0194795i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.5189	+	18.2192i	0.0409294	+	0.0708919i	0.885764	−	0.464135i	$-0.153635\pi$
$257$	10.5189	+	18.2192i	0.0409294	+	0.0708919i	−0.844835	+	0.535027i	$0.820301\pi$
$258$		0			0
$259$	−48.7410	+	84.4219i	−0.188189	+	0.325953i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	107.728	−	186.591i	0.409614	−	0.709472i	−0.585233	−	0.810865i	$-0.698997\pi$
$263$	107.728	−	186.591i	0.409614	−	0.709472i	0.994846	+	0.101394i	$0.0323301\pi$
$264$		0			0
$265$	392.457	+	233.863i	1.48097	+	0.882503i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	180.237i		−	0.670024i	−0.942214	−	0.335012i	$-0.891260\pi$
$269$		−	180.237i		−	0.670024i	0.942214	−	0.335012i	$-0.108740\pi$
$270$		0			0
$271$	231.741			0.855133			0.427566	−	0.903984i	$-0.359371\pi$
$271$	231.741			0.855133			0.427566	+	0.903984i	$0.359371\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.5175	−	453.491i	0.0455180	−	1.64906i
$276$		0			0
$277$	91.4227	+	52.7829i	0.330046	+	0.190552i	0.655862	−	0.754881i	$-0.272306\pi$
$277$	91.4227	+	52.7829i	0.330046	+	0.190552i	−0.325816	+	0.945433i	$0.605639\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	436.993	+	252.298i	1.55514	+	0.897859i	0.997710	+	0.0676323i	$0.0215445\pi$
$281$	436.993	+	252.298i	1.55514	+	0.897859i	0.557426	+	0.830226i	$0.311789\pi$
$282$		0			0
$283$	−131.306	+	75.8095i	−0.463978	+	0.267878i	−0.713716	−	0.700436i	$-0.752989\pi$
$283$	−131.306	+	75.8095i	−0.463978	+	0.267878i	0.249737	+	0.968314i	$0.419656\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−37.0863			−0.129221
$288$		0			0
$289$	−256.185			−0.886454
$290$		0			0
$291$		0			0
$292$		0			0
$293$	274.519	+	475.481i	0.936924	+	1.62280i	0.771166	+	0.636634i	$0.219674\pi$
$293$	274.519	+	475.481i	0.936924	+	1.62280i	0.165759	+	0.986166i	$0.446993\pi$
$294$		0			0
$295$	−394.161	−	5.43888i	−1.33614	−	0.0184369i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.41582	+	3.12682i	0.0181131	+	0.0104576i
$300$		0			0
$301$	−65.2967	−	113.097i	−0.216933	−	0.375738i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	136.099	−	76.0926i	0.446226	−	0.249484i
$306$		0			0
$307$			146.401i			0.476876i	0.971158	+	0.238438i	$0.0766355\pi$
$307$			146.401i			0.476876i	−0.971158	+	0.238438i	$0.923365\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	422.468	−	243.912i	1.35842	−	0.784282i	0.369006	−	0.929427i	$-0.379698\pi$
$311$	422.468	−	243.912i	1.35842	−	0.784282i	0.989410	+	0.145144i	$0.0463647\pi$
$312$		0			0
$313$	−94.9915	−	54.8433i	−0.303487	−	0.175218i	0.340521	−	0.940237i	$-0.389396\pi$
$313$	−94.9915	−	54.8433i	−0.303487	−	0.175218i	−0.644008	+	0.765018i	$0.722730\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−181.784	+	314.859i	−0.573452	+	0.993247i	0.422756	+	0.906243i	$0.361063\pi$
$317$	−181.784	+	314.859i	−0.573452	+	0.993247i	−0.996208	+	0.0870039i	$0.972271\pi$
$318$		0			0
$319$	−361.111	−	625.463i	−1.13201	−	1.96070i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−132.815			−0.411191
$324$		0			0
$325$	490.408	+	301.478i	1.50895	+	0.927625i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−99.0505	+	57.1868i	−0.301065	+	0.173820i
$330$		0			0
$331$	−150.111	+	260.001i	−0.453509	+	0.785501i	−0.998601	−	0.0528755i	$-0.983161\pi$
$331$	−150.111	+	260.001i	−0.453509	+	0.785501i	0.545092	+	0.838376i	$0.316495\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−34.5783	−	0.477132i	−0.103219	−	0.00142427i
$336$		0			0
$337$	−323.334	+	186.677i	−0.959447	+	0.553937i	−0.896003	−	0.444049i	$-0.853542\pi$
$337$	−323.334	+	186.677i	−0.959447	+	0.553937i	−0.0634441	+	0.997985i	$0.520208\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			859.610i			2.52085i
$342$		0			0
$343$		−	252.112i		−	0.735020i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.72213	+	15.1072i	0.0251358	+	0.0435365i	0.878320	−	0.478074i	$-0.158665\pi$
$347$	8.72213	+	15.1072i	0.0251358	+	0.0435365i	−0.853184	+	0.521610i	$0.825332\pi$
$348$		0			0
$349$	−117.075	+	202.779i	−0.335457	+	0.581029i	−0.983573	−	0.180513i	$-0.942224\pi$
$349$	−117.075	+	202.779i	−0.335457	+	0.581029i	0.648115	+	0.761542i	$0.275558\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	190.642	−	330.202i	0.540063	−	0.935416i	−0.458837	−	0.888520i	$-0.651734\pi$
$353$	190.642	−	330.202i	0.540063	−	0.935416i	0.998900	−	0.0468954i	$-0.0149328\pi$
$354$		0			0
$355$	−208.822	+	350.434i	−0.588232	+	0.987139i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			222.024i			0.618451i	0.950989	+	0.309226i	$0.100070\pi$
$359$			222.024i			0.618451i	−0.950989	+	0.309226i	$0.899930\pi$
$360$		0			0
$361$	176.556			0.489074
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−271.522	+	455.653i	−0.743896	+	1.24836i
$366$		0			0
$367$	−389.023	−	224.602i	−1.06001	−	0.611995i	−0.134573	−	0.990904i	$-0.542966\pi$
$367$	−389.023	−	224.602i	−1.06001	−	0.611995i	−0.925434	+	0.378908i	$0.876300\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−221.205	−	127.713i	−0.596239	−	0.344239i
$372$		0			0
$373$	278.932	−	161.041i	0.747806	−	0.431746i	−0.0770948	−	0.997024i	$-0.524564\pi$
$373$	278.932	−	161.041i	0.747806	−	0.431746i	0.824901	+	0.565278i	$0.191231\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	916.446			2.43089
$378$		0			0
$379$	−216.074			−0.570115			−0.285058	−	0.958510i	$-0.592013\pi$
$379$	−216.074			−0.570115			−0.285058	+	0.958510i	$0.592013\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−186.988	−	323.873i	−0.488220	−	0.845622i	0.511688	−	0.859171i	$-0.329020\pi$
$383$	−186.988	−	323.873i	−0.488220	−	0.845622i	−0.999908	+	0.0135493i	$0.995687\pi$
$384$		0			0
$385$	−3.49957	+	253.618i	−0.00908980	+	0.658748i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	193.217	+	111.554i	0.496702	+	0.286771i	0.727351	−	0.686266i	$-0.240751\pi$
$389$	193.217	+	111.554i	0.496702	+	0.286771i	−0.230648	+	0.973037i	$0.574085\pi$
$390$		0			0
$391$	−0.777873	−	1.34731i	−0.00198944	−	0.00344582i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	277.370	−	155.077i	0.702204	−	0.392600i
$396$		0			0
$397$			610.535i			1.53787i	0.639325	+	0.768936i	$0.279214\pi$
$397$			610.535i			1.53787i	−0.639325	+	0.768936i	$0.720786\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−356.319	+	205.721i	−0.888575	+	0.513019i	−0.873476	−	0.486867i	$-0.838140\pi$
$401$	−356.319	+	205.721i	−0.888575	+	0.513019i	−0.0150992	+	0.999886i	$0.504806\pi$
$402$		0			0
$403$	−944.643	−	545.390i	−2.34403	−	1.35333i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	316.396	−	548.013i	0.777385	−	1.34647i
$408$		0			0
$409$	−295.315	−	511.500i	−0.722041	−	1.25061i	−0.960180	−	0.279381i	$-0.909871\pi$
$409$	−295.315	−	511.500i	−0.722041	−	1.25061i	0.238139	−	0.971231i	$-0.423462\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	220.396			0.533646
$414$		0			0
$415$	1.24014	−	0.693359i	0.00298829	−	0.00167074i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	207.462	−	119.778i	0.495135	−	0.285867i	−0.231567	−	0.972819i	$-0.574385\pi$
$419$	207.462	−	119.778i	0.495135	−	0.285867i	0.726702	+	0.686952i	$0.241052\pi$
$420$		0			0
$421$	−296.704	+	513.907i	−0.704760	+	1.22068i	0.262018	+	0.965063i	$0.415612\pi$
$421$	−296.704	+	513.907i	−0.704760	+	1.22068i	−0.966778	+	0.255618i	$0.917721\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−68.1559	−	125.952i	−0.160367	−	0.296358i
$426$		0			0
$427$	−75.4983	+	43.5890i	−0.176811	+	0.102082i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	436.566i		−	1.01291i	−0.862265	−	0.506457i	$-0.830955\pi$
$431$		−	436.566i		−	1.01291i	0.862265	−	0.506457i	$-0.169045\pi$
$432$		0			0
$433$		−	231.736i		−	0.535187i	−0.963532	−	0.267593i	$-0.913772\pi$
$433$		−	231.736i		−	0.535187i	0.963532	−	0.267593i	$-0.0862284\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.14837	+	5.45314i	0.00720451	+	0.0124786i
$438$		0			0
$439$	209.611	−	363.058i	0.477475	−	0.827011i	−0.522192	−	0.852828i	$-0.674885\pi$
$439$	209.611	−	363.058i	0.477475	−	0.827011i	0.999667	+	0.0258173i	$0.00821881\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	223.260	−	386.697i	0.503973	−	0.872906i	−0.496017	−	0.868313i	$-0.665205\pi$
$443$	223.260	−	386.697i	0.503973	−	0.872906i	0.999989	−	0.00459325i	$-0.00146208\pi$
$444$		0			0
$445$	−72.9997	+	122.504i	−0.164044	+	0.275290i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			495.776i			1.10418i	0.833785	+	0.552089i	$0.186169\pi$
$449$			495.776i			1.10418i	−0.833785	+	0.552089i	$0.813831\pi$
$450$		0			0
$451$	240.741			0.533794
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−276.486	−	164.757i	−0.607661	−	0.362103i
$456$		0			0
$457$	591.810	+	341.681i	1.29499	+	0.747662i	0.979534	−	0.201279i	$-0.0645097\pi$
$457$	591.810	+	341.681i	1.29499	+	0.747662i	0.315454	+	0.948941i	$0.397843\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−346.521	−	200.064i	−0.751672	−	0.433978i	0.0746257	−	0.997212i	$-0.476224\pi$
$461$	−346.521	−	200.064i	−0.751672	−	0.433978i	−0.826298	+	0.563234i	$0.809557\pi$
$462$		0			0
$463$	273.892	−	158.132i	0.591559	−	0.341537i	−0.174155	−	0.984718i	$-0.555719\pi$
$463$	273.892	−	158.132i	0.591559	−	0.341537i	0.765714	+	0.643181i	$0.222386\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−419.741			−0.898803			−0.449401	−	0.893330i	$-0.648363\pi$
$467$	−419.741			−0.898803			−0.449401	+	0.893330i	$0.648363\pi$
$468$		0			0
$469$	19.3345			0.0412249
$470$		0			0
$471$		0			0
$472$		0			0
$473$	423.865	+	734.156i	0.896121	+	1.55213i
$474$		0			0
$475$	275.855	+	509.781i	0.580747	+	1.07322i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	731.766	+	422.485i	1.52769	+	0.882015i	0.999458	+	0.0329177i	$0.0104799\pi$
$479$	731.766	+	422.485i	1.52769	+	0.882015i	0.528237	+	0.849097i	$0.322853\pi$
$480$		0			0
$481$	401.482	+	695.387i	0.834682	+	1.44571i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	226.711	+	405.495i	0.467446	+	0.836072i
$486$		0			0
$487$		−	546.384i		−	1.12194i	−0.827837	−	0.560969i	$-0.810429\pi$
$487$		−	546.384i		−	1.12194i	0.827837	−	0.560969i	$-0.189571\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−560.713	+	323.728i	−1.14198	+	0.659324i	−0.946921	−	0.321467i	$-0.895824\pi$
$491$	−560.713	+	323.728i	−1.14198	+	0.659324i	−0.195062	+	0.980791i	$0.562491\pi$
$492$		0			0
$493$	−197.443	−	113.994i	−0.400494	−	0.231225i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	114.038	−	197.519i	0.229452	−	0.397423i
$498$		0			0
$499$	−291.407	−	504.732i	−0.583983	−	1.01149i	−0.995001	−	0.0998608i	$-0.968160\pi$
$499$	−291.407	−	504.732i	−0.583983	−	1.01149i	0.411019	−	0.911627i	$-0.365173\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	752.520			1.49606			0.748032	−	0.663663i	$-0.230999\pi$
$503$	752.520			1.49606			0.748032	+	0.663663i	$0.230999\pi$
$504$		0			0
$505$	113.870	+	203.667i	0.225484	+	0.403301i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	252.479	−	145.769i	0.496030	−	0.286383i	−0.231042	−	0.972944i	$-0.574214\pi$
$509$	252.479	−	145.769i	0.496030	−	0.286383i	0.727073	+	0.686560i	$0.240880\pi$
$510$		0			0
$511$	148.278	−	256.825i	0.290172	−	0.502593i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	55.9044	+	0.771403i	0.108552	+	0.00149787i
$516$		0			0
$517$	642.973	−	371.221i	1.24366	−	0.718028i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	137.690i		−	0.264280i	−0.991231	−	0.132140i	$-0.957815\pi$
$521$		−	137.690i		−	0.264280i	0.991231	−	0.132140i	$-0.0421848\pi$
$522$		0			0
$523$		−	330.987i		−	0.632862i	−0.948616	−	0.316431i	$-0.897515\pi$
$523$		−	330.987i		−	0.632862i	0.948616	−	0.316431i	$-0.102485\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	135.679	+	235.003i	0.257455	+	0.445926i
$528$		0			0
$529$	264.463	−	458.064i	0.499930	−	0.865905i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−152.741	+	264.555i	−0.286568	+	0.496351i
$534$		0			0
$535$	632.672	+	377.007i	1.18256	+	0.704686i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			747.370i			1.38659i
$540$		0			0
$541$	556.593			1.02882			0.514412	−	0.857543i	$-0.328010\pi$
$541$	556.593			1.02882			0.514412	+	0.857543i	$0.328010\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	522.109	+	311.123i	0.957998	+	0.570867i
$546$		0			0
$547$	402.849	+	232.585i	0.736470	+	0.425201i	0.820784	−	0.571238i	$-0.193537\pi$
$547$	402.849	+	232.585i	0.736470	+	0.425201i	−0.0843144	+	0.996439i	$0.526870\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	799.135	+	461.381i	1.45034	+	0.837351i
$552$		0			0
$553$	−153.866	+	88.8347i	−0.278239	+	0.160641i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1059.37			1.90192			0.950962	−	0.309306i	$-0.100097\pi$
$557$	1059.37			1.90192			0.950962	+	0.309306i	$0.100097\pi$
$558$		0			0
$559$	−1075.70			−1.92434
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−193.080	−	334.424i	−0.342949	−	0.594004i	0.642030	−	0.766679i	$-0.278092\pi$
$563$	−193.080	−	334.424i	−0.342949	−	0.594004i	−0.984979	+	0.172675i	$0.944759\pi$
$564$		0			0
$565$	6.73511	−	488.101i	0.0119206	−	0.863896i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	594.147	+	343.031i	1.04420	+	0.602866i	0.921019	−	0.389518i	$-0.127359\pi$
$569$	594.147	+	343.031i	1.04420	+	0.602866i	0.123176	+	0.992385i	$0.460692\pi$
$570$		0			0
$571$	410.816	+	711.554i	0.719467	+	1.24615i	0.961211	+	0.275813i	$0.0889471\pi$
$571$	410.816	+	711.554i	0.719467	+	1.24615i	−0.241744	+	0.970340i	$0.577720\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.55575	+	5.78406i	−0.00618390	+	0.0100592i
$576$		0			0
$577$			183.840i			0.318613i	0.987229	+	0.159306i	$0.0509258\pi$
$577$			183.840i			0.318613i	−0.987229	+	0.159306i	$0.949074\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.687945	+	0.397185i	−0.00118407	+	0.000683623i
$582$		0			0
$583$	1435.92	+	829.029i	2.46299	+	1.42201i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	160.203	−	277.480i	0.272919	−	0.472709i	−0.696689	−	0.717373i	$-0.745344\pi$
$587$	160.203	−	277.480i	0.272919	−	0.472709i	0.969608	+	0.244664i	$0.0786777\pi$
$588$		0			0
$589$	−549.148	−	951.153i	−0.932340	−	1.61486i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1061.34			1.78977			0.894887	−	0.446292i	$-0.147256\pi$
$593$	1061.34			1.78977			0.894887	+	0.446292i	$0.147256\pi$
$594$		0			0
$595$	39.0738	+	69.8872i	0.0656702	+	0.117457i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	846.155	−	488.528i	1.41261	−	0.815573i	0.416979	−	0.908916i	$-0.363089\pi$
$599$	846.155	−	488.528i	1.41261	−	0.815573i	0.995634	+	0.0933433i	$0.0297554\pi$
$600$		0			0
$601$	130.908	−	226.740i	0.217817	−	0.377271i	−0.736323	−	0.676630i	$-0.763440\pi$
$601$	130.908	−	226.740i	0.217817	−	0.377271i	0.954140	+	0.299359i	$0.0967730\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.3697	−	1041.38i	0.0237515	−	1.72130i
$606$		0			0
$607$	−579.203	+	334.403i	−0.954206	+	0.550911i	−0.894385	−	0.447298i	$-0.852386\pi$
$607$	−579.203	+	334.403i	−0.954206	+	0.550911i	−0.0598212	+	0.998209i	$0.519053\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			942.101i			1.54190i
$612$		0			0
$613$			220.119i			0.359086i	0.983750	+	0.179543i	$0.0574618\pi$
$613$			220.119i			0.359086i	−0.983750	+	0.179543i	$0.942538\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	160.531	+	278.049i	0.260181	+	0.450646i	0.966290	−	0.257457i	$-0.0828846\pi$
$617$	160.531	+	278.049i	0.260181	+	0.450646i	−0.706109	+	0.708103i	$0.749551\pi$
$618$		0			0
$619$	445.593	−	771.791i	0.719860	−	1.24683i	−0.241195	−	0.970477i	$-0.577539\pi$
$619$	445.593	−	771.791i	0.719860	−	1.24683i	0.961055	−	0.276358i	$-0.0891275\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	39.8651	−	69.0483i	0.0639889	−	0.110832i
$624$		0			0
$625$	−341.882	+	523.203i	−0.547011	+	0.837125i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	199.757i		−	0.317578i
$630$		0			0
$631$	−583.669			−0.924990			−0.462495	−	0.886622i	$-0.653046\pi$
$631$	−583.669			−0.924990			−0.462495	+	0.886622i	$0.653046\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−226.895	+	380.763i	−0.357316	+	0.599627i
$636$		0			0
$637$	−821.300	−	474.178i	−1.28932	−	0.744392i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−603.006	−	348.146i	−0.940727	−	0.543129i	−0.0505391	−	0.998722i	$-0.516094\pi$
$641$	−603.006	−	348.146i	−0.940727	−	0.543129i	−0.890188	+	0.455593i	$0.849427\pi$
$642$		0			0
$643$	−694.262	+	400.832i	−1.07972	+	0.623378i	−0.930822	−	0.365474i	$-0.880907\pi$
$643$	−694.262	+	400.832i	−1.07972	+	0.623378i	−0.148901	+	0.988852i	$0.547574\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−216.221			−0.334191			−0.167095	−	0.985941i	$-0.553439\pi$
$647$	−216.221			−0.334191			−0.167095	+	0.985941i	$0.553439\pi$
$648$		0			0
$649$	−1430.67			−2.20442
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−219.401	−	380.014i	−0.335989	−	0.581951i	0.647685	−	0.761908i	$-0.275737\pi$
$653$	−219.401	−	380.014i	−0.335989	−	0.581951i	−0.983674	+	0.179958i	$0.942404\pi$
$654$		0			0
$655$	−449.825	−	6.20695i	−0.686755	−	0.00947626i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−317.063	−	183.056i	−0.481127	−	0.277779i	0.239759	−	0.970832i	$-0.422932\pi$
$659$	−317.063	−	183.056i	−0.481127	−	0.277779i	−0.720886	+	0.693054i	$0.756265\pi$
$660$		0			0
$661$	−79.0377	−	136.897i	−0.119573	−	0.207106i	0.800026	−	0.599966i	$-0.204819\pi$
$661$	−79.0377	−	136.897i	−0.119573	−	0.207106i	−0.919599	+	0.392859i	$0.871486\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−158.148	−	282.862i	−0.237816	−	0.425357i
$666$		0			0
$667$			10.8089i			0.0162052i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	490.087	−	282.952i	0.730384	−	0.421687i
$672$		0			0
$673$	561.683	+	324.288i	0.834595	+	0.481854i	0.855423	−	0.517929i	$-0.173297\pi$
$673$	561.683	+	324.288i	0.834595	+	0.481854i	−0.0208282	+	0.999783i	$0.506630\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−101.173	+	175.236i	−0.149443	+	0.258842i	−0.931022	−	0.364964i	$-0.881081\pi$
$677$	−101.173	+	175.236i	−0.149443	+	0.258842i	0.781579	+	0.623806i	$0.214415\pi$
$678$		0			0
$679$	−129.870	−	224.941i	−0.191266	−	0.331283i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−173.829			−0.254508			−0.127254	−	0.991870i	$-0.540616\pi$
$683$	−173.829			−0.254508			−0.127254	+	0.991870i	$0.540616\pi$
$684$		0			0
$685$	1003.45	−	561.024i	1.46488	−	0.819013i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1822.07	+	1051.97i	−2.64452	+	1.52681i
$690$		0			0
$691$	423.371	−	733.301i	0.612694	−	1.06122i	−0.378091	−	0.925769i	$-0.623419\pi$
$691$	423.371	−	733.301i	0.612694	−	1.06122i	0.990784	−	0.135448i	$-0.0432474\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.97566	+	288.120i	−0.00572037	+	0.414561i
$696$		0			0
$697$	65.8145	−	37.9980i	0.0944254	−	0.0545165i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	72.2614i		−	0.103083i	−0.998671	−	0.0515416i	$-0.983587\pi$
$701$		−	72.2614i		−	0.103083i	0.998671	−	0.0515416i	$-0.0164135\pi$
$702$		0			0
$703$			808.497i			1.15007i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−65.2293	−	112.980i	−0.0922621	−	0.159803i
$708$		0			0
$709$	−143.779	+	249.032i	−0.202791	+	0.351244i	−0.949427	−	0.313989i	$-0.898334\pi$
$709$	−143.779	+	249.032i	−0.202791	+	0.351244i	0.746636	+	0.665233i	$0.231668\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.43253	−	11.1415i	0.00902178	−	0.0156262i
$714$		0			0
$715$	1794.77	+	1069.50i	2.51017	+	1.49580i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	1015.27i		−	1.41205i	−0.708185	−	0.706027i	$-0.750486\pi$
$719$		−	1015.27i		−	1.41205i	0.708185	−	0.706027i	$-0.249514\pi$
$720$		0			0
$721$	−31.2590			−0.0433551
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−27.4536	+	994.609i	−0.0378671	+	1.37187i
$726$		0			0
$727$	269.696	+	155.709i	0.370971	+	0.214180i	0.673883	−	0.738838i	$-0.264625\pi$
$727$	269.696	+	155.709i	0.370971	+	0.214180i	−0.302911	+	0.953019i	$0.597959\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	231.755	+	133.804i	0.317038	+	0.183042i
$732$		0			0
$733$	−278.035	+	160.523i	−0.379310	+	0.218995i	−0.677518	−	0.735506i	$-0.736945\pi$
$733$	−278.035	+	160.523i	−0.379310	+	0.218995i	0.298208	+	0.954501i	$0.403611\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−125.507			−0.170295
$738$		0			0
$739$	−657.185			−0.889290			−0.444645	−	0.895707i	$-0.646670\pi$
$739$	−657.185			−0.889290			−0.444645	+	0.895707i	$0.646670\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−512.482	−	887.645i	−0.689747	−	1.19468i	−0.971920	−	0.235313i	$-0.924388\pi$
$743$	−512.482	−	887.645i	−0.689747	−	1.19468i	0.282173	−	0.959364i	$-0.408945\pi$
$744$		0			0
$745$	55.6631	+	0.768073i	0.0747156	+	0.00103097i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−356.600	−	205.883i	−0.476101	−	0.274877i
$750$		0			0
$751$	31.5738	+	54.6874i	0.0420423	+	0.0728194i	0.886281	−	0.463148i	$-0.153280\pi$
$751$	31.5738	+	54.6874i	0.0420423	+	0.0728194i	−0.844239	+	0.535968i	$0.819947\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−96.8210	+	54.1324i	−0.128240	+	0.0716986i
$756$		0			0
$757$		−	1452.21i		−	1.91837i	−0.282781	−	0.959185i	$-0.591257\pi$
$757$		−	1452.21i		−	1.91837i	0.282781	−	0.959185i	$-0.408743\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	422.468	−	243.912i	0.555148	−	0.320515i	−0.196048	−	0.980594i	$-0.562811\pi$
$761$	422.468	−	243.912i	0.555148	−	0.320515i	0.751196	+	0.660079i	$0.229477\pi$
$762$		0			0
$763$	−294.282	−	169.904i	−0.385691	−	0.222679i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	907.705	−	1572.19i	1.18345	−	2.04979i
$768$		0			0
$769$	−338.574	−	586.427i	−0.440278	−	0.762584i	0.557432	−	0.830223i	$-0.311787\pi$
$769$	−338.574	−	586.427i	−0.440278	−	0.762584i	−0.997710	+	0.0676389i	$0.978453\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	949.926			1.22888			0.614441	−	0.788963i	$-0.289381\pi$
$773$	949.926			1.22888			0.614441	+	0.788963i	$0.289381\pi$
$774$		0			0
$775$	620.204	−	1008.87i	0.800263	−	1.30177i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−266.378	+	153.794i	−0.341949	+	0.197424i
$780$		0			0
$781$	−740.261	+	1282.17i	−0.947837	+	1.64170i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1126.58	+	15.5452i	1.43513	+	0.0198028i
$786$		0			0
$787$	−991.018	+	572.164i	−1.25923	+	0.727020i	−0.972926	−	0.231118i	$-0.925762\pi$
$787$	−991.018	+	572.164i	−1.25923	+	0.727020i	−0.286309	+	0.958137i	$0.592428\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			272.922i			0.345034i
$792$		0			0
$793$			718.089i			0.905535i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	325.550	+	563.870i	0.408470	+	0.707490i	0.994718	−	0.102641i	$-0.0327292\pi$
$797$	325.550	+	563.870i	0.408470	+	0.707490i	−0.586249	+	0.810131i	$0.699396\pi$
$798$		0			0
$799$	117.185	−	202.971i	0.146665	−	0.254031i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−962.526	+	1667.14i	−1.19866	+	2.07614i
$804$		0			0
$805$	1.94320	−	3.26097i	0.00241391	−	0.00405090i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1296.03i			1.60202i	0.598653	+	0.801008i	$0.295703\pi$
$809$			1296.03i			1.60202i	−0.598653	+	0.801008i	$0.704297\pi$
$810$		0			0
$811$	69.9245			0.0862201			0.0431101	−	0.999070i	$-0.486273\pi$
$811$	69.9245			0.0862201			0.0431101	+	0.999070i	$0.486273\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	775.398	−	1301.23i	0.951409	−	1.59660i
$816$		0			0
$817$	−938.007	−	541.559i	−1.14811	−	0.662863i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	809.810	+	467.544i	0.986371	+	0.569481i	0.904187	−	0.427136i	$-0.140477\pi$
$821$	809.810	+	467.544i	0.986371	+	0.569481i	0.0821833	+	0.996617i	$0.473811\pi$
$822$		0			0
$823$	935.659	−	540.203i	1.13689	−	0.656383i	0.191230	−	0.981545i	$-0.438752\pi$
$823$	935.659	−	540.203i	1.13689	−	0.656383i	0.945658	+	0.325163i	$0.105419\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1105.43			−1.33668			−0.668339	−	0.743856i	$-0.732995\pi$
$827$	−1105.43			−1.33668			−0.668339	+	0.743856i	$0.732995\pi$
$828$		0			0
$829$	899.633			1.08520			0.542601	−	0.839990i	$-0.317439\pi$
$829$	899.633			1.08520			0.542601	+	0.839990i	$0.317439\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	117.963	+	204.318i	0.141612	+	0.245280i
$834$		0			0
$835$	−16.4648	+	1193.22i	−0.0197183	+	1.42901i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−987.814	−	570.315i	−1.17737	−	0.679755i	−0.221966	−	0.975054i	$-0.571247\pi$
$839$	−987.814	−	570.315i	−1.17737	−	0.679755i	−0.955405	+	0.295299i	$0.904581\pi$
$840$		0			0
$841$	371.500	+	643.457i	0.441736	+	0.765109i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1576.45	+	881.391i	−1.86562	+	1.04307i
$846$		0			0
$847$			582.291i			0.687475i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−8.20165	+	4.73523i	−0.00963766	+	0.00556431i
$852$		0			0
$853$	−1059.52	−	611.716i	−1.24211	−	0.717135i	−0.272590	−	0.962130i	$-0.587880\pi$
$853$	−1059.52	−	611.716i	−1.24211	−	0.717135i	−0.969524	+	0.244996i	$0.921213\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−835.039	+	1446.33i	−0.974374	+	1.68767i	−0.292389	+	0.956300i	$0.594450\pi$
$857$	−835.039	+	1446.33i	−0.974374	+	1.68767i	−0.681985	+	0.731366i	$0.738883\pi$
$858$		0			0
$859$	−218.111	−	377.779i	−0.253912	−	0.439789i	0.710687	−	0.703508i	$-0.248384\pi$
$859$	−218.111	−	377.779i	−0.253912	−	0.439789i	−0.964600	+	0.263719i	$0.915051\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	883.333			1.02356			0.511780	−	0.859116i	$-0.328986\pi$
$863$	883.333			1.02356			0.511780	+	0.859116i	$0.328986\pi$
$864$		0			0
$865$	−474.835	+	265.479i	−0.548943	+	0.306912i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	998.801	−	576.658i	1.14937	−	0.663588i
$870$		0			0
$871$	79.6295	−	137.922i	0.0914231	−	0.158349i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	187.091	−	295.131i	0.213818	−	0.337293i
$876$		0			0
$877$	1305.39	−	753.665i	1.48847	−	0.859367i	0.488554	−	0.872534i	$-0.337524\pi$
$877$	1305.39	−	753.665i	1.48847	−	0.859367i	0.999913	+	0.0131665i	$0.00419116\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	626.273i		−	0.710866i	−0.934702	−	0.355433i	$-0.884333\pi$
$881$		−	626.273i		−	0.710866i	0.934702	−	0.355433i	$-0.115667\pi$
$882$		0			0
$883$		−	23.3162i		−	0.0264057i	−0.999913	−	0.0132028i	$-0.995797\pi$
$883$		−	23.3162i		−	0.0264057i	0.999913	−	0.0132028i	$-0.00420271\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	264.666	+	458.416i	0.298384	+	0.516816i	0.975766	−	0.218815i	$-0.0702192\pi$
$887$	264.666	+	458.416i	0.298384	+	0.516816i	−0.677383	+	0.735631i	$0.736886\pi$
$888$		0			0
$889$	123.907	−	214.614i	0.139378	−	0.241410i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−474.297	+	821.506i	−0.531127	+	0.919940i
$894$		0			0
$895$	−430.135	+	721.829i	−0.480598	+	0.806513i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1885.32i		−	2.09713i
$900$		0			0
$901$	523.408			0.580919
$902$		0			0
$903$		0			0
$904$		0			0
$905$	662.739	+	394.923i	0.732308	+	0.436379i
$906$		0			0
$907$	−329.897	−	190.466i	−0.363723	−	0.209996i	0.306989	−	0.951713i	$-0.400678\pi$
$907$	−329.897	−	190.466i	−0.363723	−	0.209996i	−0.670713	+	0.741717i	$0.734012\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−99.7080	−	57.5664i	−0.109449	−	0.0631904i	0.444276	−	0.895890i	$-0.353461\pi$
$911$	−99.7080	−	57.5664i	−0.109449	−	0.0631904i	−0.553725	+	0.832699i	$0.686794\pi$
$912$		0			0
$913$	4.46570	−	2.57827i	0.00489124	−	0.00282396i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	251.520			0.274285
$918$		0			0
$919$	−31.5163			−0.0342941			−0.0171471	−	0.999853i	$-0.505458\pi$
$919$	−31.5163			−0.0342941			−0.0171471	+	0.999853i	$0.505458\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−939.334	−	1626.98i	−1.01770	−	1.76270i
$924$		0			0
$925$	−766.723	+	414.892i	−0.828890	+	0.448532i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−941.451	−	543.547i	−1.01340	−	0.585088i	−0.101216	−	0.994864i	$-0.532273\pi$
$929$	−941.451	−	543.547i	−1.01340	−	0.585088i	−0.912186	+	0.409776i	$0.865607\pi$
$930$		0			0
$931$	−477.445	−	826.959i	−0.512830	−	0.888248i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−253.642	−	453.663i	−0.271275	−	0.485201i
$936$		0			0
$937$		−	40.9800i		−	0.0437354i	−0.999761	−	0.0218677i	$-0.993039\pi$
$937$		−	40.9800i		−	0.0437354i	0.999761	−	0.0218677i	$-0.00696125\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1165.03	+	672.633i	−1.23808	+	0.714807i	−0.968702	−	0.248227i	$-0.920152\pi$
$941$	−1165.03	+	672.633i	−1.23808	+	0.714807i	−0.269380	+	0.963034i	$0.586819\pi$
$942$		0			0
$943$	−3.12026	−	1.80148i	−0.00330887	−	0.00191037i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−182.390	+	315.909i	−0.192598	+	0.333589i	−0.946110	−	0.323844i	$-0.895025\pi$
$947$	−182.390	+	315.909i	−0.192598	+	0.333589i	0.753513	+	0.657434i	$0.228358\pi$
$948$		0			0
$949$	−1221.37	−	2115.48i	−1.28701	−	2.22917i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1529.14			−1.60455			−0.802277	−	0.596952i	$-0.796378\pi$
$953$	−1529.14			−1.60455			−0.802277	+	0.596952i	$0.796378\pi$
$954$		0			0
$955$	378.038	+	676.157i	0.395851	+	0.708018i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−556.643	+	321.378i	−0.580441	+	0.335118i
$960$		0			0
$961$	−641.482	+	1111.08i	−0.667515	+	1.15617i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	320.003	+	4.41559i	0.331609	+	0.00457574i
$966$		0			0
$967$	−604.937	+	349.260i	−0.625581	+	0.361179i	−0.779039	−	0.626976i	$-0.784292\pi$
$967$	−604.937	+	349.260i	−0.625581	+	0.361179i	0.153458	+	0.988155i	$0.450959\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	554.481i		−	0.571041i	−0.958373	−	0.285521i	$-0.907834\pi$
$971$		−	554.481i		−	0.571041i	0.958373	−	0.285521i	$-0.0921665\pi$
$972$		0			0
$973$		−	161.103i		−	0.165573i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−785.223	−	1360.05i	−0.803708	−	1.39206i	−0.917160	−	0.398520i	$-0.869524\pi$
$977$	−785.223	−	1360.05i	−0.803708	−	1.39206i	0.113451	−	0.993544i	$-0.463809\pi$
$978$		0			0
$979$	−258.779	+	448.218i	−0.264330	+	0.457832i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	145.828	−	252.582i	0.148350	−	0.256950i	−0.782268	−	0.622942i	$-0.785937\pi$
$983$	145.828	−	252.582i	0.148350	−	0.256950i	0.930618	+	0.365992i	$0.119270\pi$
$984$		0			0
$985$	41.0981	+	24.4902i	0.0417239	+	0.0248631i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	12.6873i		−	0.0128284i
$990$		0			0
$991$	1554.11			1.56823			0.784114	−	0.620616i	$-0.213117\pi$
$991$	1554.11			1.56823			0.784114	+	0.620616i	$0.213117\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	506.040	+	301.548i	0.508583	+	0.303063i
$996$		0			0
$997$	771.337	+	445.332i	0.773658	+	0.446672i	0.834178	−	0.551495i	$-0.185943\pi$
$997$	771.337	+	445.332i	0.773658	+	0.446672i	−0.0605199	+	0.998167i	$0.519276\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.3.t.a.269.1		8
3.2	odd	2		1620.3.t.d.269.4		8
5.4	even	2		1620.3.t.d.269.2		8
9.2	odd	6		540.3.b.a.269.2	yes	4
9.4	even	3	inner	1620.3.t.a.1349.3		8
9.5	odd	6		1620.3.t.d.1349.2		8
9.7	even	3		540.3.b.b.269.3	yes	4
15.14	odd	2	inner	1620.3.t.a.269.3		8
36.7	odd	6		2160.3.c.l.1889.3		4
36.11	even	6		2160.3.c.h.1889.2		4
45.2	even	12		2700.3.g.s.701.5		8
45.4	even	6		1620.3.t.d.1349.4		8
45.7	odd	12		2700.3.g.s.701.6		8
45.14	odd	6	inner	1620.3.t.a.1349.1		8
45.29	odd	6		540.3.b.b.269.4	yes	4
45.34	even	6		540.3.b.a.269.1	✓	4
45.38	even	12		2700.3.g.s.701.3		8
45.43	odd	12		2700.3.g.s.701.4		8
180.79	odd	6		2160.3.c.h.1889.1		4
180.119	even	6		2160.3.c.l.1889.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.3.b.a.269.1	✓	4	45.34	even	6
540.3.b.a.269.2	yes	4	9.2	odd	6
540.3.b.b.269.3	yes	4	9.7	even	3
540.3.b.b.269.4	yes	4	45.29	odd	6
1620.3.t.a.269.1		8	1.1	even	1	trivial
1620.3.t.a.269.3		8	15.14	odd	2	inner
1620.3.t.a.1349.1		8	45.14	odd	6	inner
1620.3.t.a.1349.3		8	9.4	even	3	inner
1620.3.t.d.269.2		8	5.4	even	2
1620.3.t.d.269.4		8	3.2	odd	2
1620.3.t.d.1349.2		8	9.5	odd	6
1620.3.t.d.1349.4		8	45.4	even	6
2160.3.c.h.1889.1		4	180.79	odd	6
2160.3.c.h.1889.2		4	36.11	even	6
2160.3.c.l.1889.3		4	36.7	odd	6
2160.3.c.l.1889.4		4	180.119	even	6
2700.3.g.s.701.3		8	45.38	even	12
2700.3.g.s.701.4		8	45.43	odd	12
2700.3.g.s.701.5		8	45.2	even	12
2700.3.g.s.701.6		8	45.7	odd	12

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.29522 - 2.55951i) q^{5} +(2.42096 + 1.39774i) q^{7} +O(q^{10})\)	\(q+(-4.29522 - 2.55951i) q^{5} +(2.42096 + 1.39774i) q^{7} +(-15.7154 - 9.07327i) q^{11} +(19.9416 - 11.5133i) q^{13} -5.72842 q^{17} +23.1852 q^{19} +(0.135792 + 0.235199i) q^{23} +(11.8979 + 21.9873i) q^{25} +(34.4674 + 19.8997i) q^{29} +(-23.6852 - 41.0241i) q^{31} +(-6.82104 - 12.2001i) q^{35} +34.8712i q^{37} +(-11.4891 + 6.63325i) q^{41} +(-40.4571 - 23.3579i) q^{43} +(-20.4568 + 35.4323i) q^{47} +(-20.5926 - 35.6675i) q^{49} -91.3705 q^{53} +(44.2779 + 79.1953i) q^{55} +(68.2773 - 39.4199i) q^{59} +(-15.5926 + 27.0072i) q^{61} +(-115.122 - 1.58852i) q^{65} +(5.98970 - 3.45816i) q^{67} -81.5870i q^{71} -106.084i q^{73} +(-25.3642 - 43.9321i) q^{77} +(-31.7779 + 55.0409i) q^{79} +(-0.142081 + 0.246091i) q^{83} +(24.6048 + 14.6619i) q^{85} -28.5210i q^{89} +64.3705 q^{91} +(-99.5858 - 59.3428i) q^{95} +(-80.4657 - 46.4569i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{5}+O(q^{10}) \) 8 * q - 3 * q^5	\( 8 q - 3 q^{5} + 12 q^{17} + 12 q^{19} + 30 q^{23} - 9 q^{25} - 16 q^{31} + 90 q^{35} - 48 q^{47} - 78 q^{49} - 384 q^{53} + 94 q^{55} - 38 q^{61} - 138 q^{65} - 174 q^{77} + 6 q^{79} + 288 q^{83} + 100 q^{85} + 168 q^{91} - 318 q^{95}+O(q^{100}) \) 8 * q - 3 * q^5 + 12 * q^17 + 12 * q^19 + 30 * q^23 - 9 * q^25 - 16 * q^31 + 90 * q^35 - 48 * q^47 - 78 * q^49 - 384 * q^53 + 94 * q^55 - 38 * q^61 - 138 * q^65 - 174 * q^77 + 6 * q^79 + 288 * q^83 + 100 * q^85 + 168 * q^91 - 318 * q^95

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