LMFDB - Embedded newform 3024.2.q.k.2881.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.7
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.k.2305.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.170100 - 0.294622i) q^{5} +(2.63360 - 0.253251i) q^{7} +O(q^{10})$	$q+(0.170100 - 0.294622i) q^{5} +(2.63360 - 0.253251i) q^{7} +(0.335794 + 0.581612i) q^{11} +(1.62370 + 2.81233i) q^{13} +(1.10014 - 1.90550i) q^{17} +(-0.242085 - 0.419303i) q^{19} +(-2.09495 + 3.62856i) q^{23} +(2.44213 + 4.22990i) q^{25} +(-0.478868 + 0.829424i) q^{29} -2.08263 q^{31} +(0.373363 - 0.818995i) q^{35} +(4.81613 + 8.34178i) q^{37} +(3.90207 + 6.75858i) q^{41} +(3.66119 - 6.34136i) q^{43} -2.69901 q^{47} +(6.87173 - 1.33392i) q^{49} +(6.12335 - 10.6059i) q^{53} +0.228474 q^{55} -4.94297 q^{59} -3.52119 q^{61} +1.10477 q^{65} -12.3202 q^{67} -5.57304 q^{71} +(-3.71686 + 6.43779i) q^{73} +(1.03164 + 1.44669i) q^{77} +10.0127 q^{79} +(2.47376 - 4.28468i) q^{83} +(-0.374269 - 0.648252i) q^{85} +(8.52177 + 14.7601i) q^{89} +(4.98840 + 6.99536i) q^{91} -0.164714 q^{95} +(4.23657 - 7.33795i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 + 5 * q^7	$ 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.170100	−	0.294622i	0.0760711	−	0.131759i	−0.825480	−	0.564431i	$-0.809096\pi$
$5$	0.170100	−	0.294622i	0.0760711	−	0.131759i	0.901552	+	0.432672i	$0.142429\pi$
$6$		0			0
$7$	2.63360	−	0.253251i	0.995408	−	0.0957197i
$7$	2.63360	−	0.253251i	0.995408	−	0.0957197i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.335794	+	0.581612i	0.101246	+	0.175363i	0.912198	−	0.409749i	$-0.134384\pi$
$11$	0.335794	+	0.581612i	0.101246	+	0.175363i	−0.810952	+	0.585112i	$0.801051\pi$
$12$		0			0
$13$	1.62370	+	2.81233i	0.450333	+	0.780000i	0.998407	−	0.0564303i	$-0.0179719\pi$
$13$	1.62370	+	2.81233i	0.450333	+	0.780000i	−0.548073	+	0.836430i	$0.684639\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.10014	−	1.90550i	0.266824	−	0.462152i	−0.701216	−	0.712949i	$-0.747359\pi$
$17$	1.10014	−	1.90550i	0.266824	−	0.462152i	0.968040	+	0.250796i	$0.0806925\pi$
$18$		0			0
$19$	−0.242085	−	0.419303i	−0.0555380	−	0.0961946i	0.836920	−	0.547326i	$-0.184354\pi$
$19$	−0.242085	−	0.419303i	−0.0555380	−	0.0961946i	−0.892458	+	0.451131i	$0.851021\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.09495	+	3.62856i	−0.436827	+	0.756607i	−0.997443	−	0.0714692i	$-0.977231\pi$
$23$	−2.09495	+	3.62856i	−0.436827	+	0.756607i	0.560616	+	0.828076i	$0.310565\pi$
$24$		0			0
$25$	2.44213	+	4.22990i	0.488426	+	0.845979i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.478868	+	0.829424i	−0.0889235	+	0.154020i	−0.907056	−	0.421009i	$-0.861676\pi$
$29$	−0.478868	+	0.829424i	−0.0889235	+	0.154020i	0.818133	+	0.575029i	$0.195009\pi$
$30$		0			0
$31$	−2.08263			−0.374052			−0.187026	−	0.982355i	$-0.559885\pi$
$31$	−2.08263			−0.374052			−0.187026	+	0.982355i	$0.559885\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.373363	−	0.818995i	0.0631098	−	0.138435i
$36$		0			0
$37$	4.81613	+	8.34178i	0.791767	+	1.37138i	0.924872	+	0.380278i	$0.124172\pi$
$37$	4.81613	+	8.34178i	0.791767	+	1.37138i	−0.133105	+	0.991102i	$0.542495\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.90207	+	6.75858i	0.609400	+	1.05551i	0.991339	+	0.131325i	$0.0419231\pi$
$41$	3.90207	+	6.75858i	0.609400	+	1.05551i	−0.381939	+	0.924188i	$0.624744\pi$
$42$		0			0
$43$	3.66119	−	6.34136i	0.558326	−	0.967048i	−0.439311	−	0.898335i	$-0.644777\pi$
$43$	3.66119	−	6.34136i	0.558326	−	0.967048i	0.997636	−	0.0687132i	$-0.0218893\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.69901			−0.393692			−0.196846	−	0.980434i	$-0.563070\pi$
$47$	−2.69901			−0.393692			−0.196846	+	0.980434i	$0.563070\pi$
$48$		0			0
$49$	6.87173	−	1.33392i	0.981675	−	0.190560i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.12335	−	10.6059i	0.841107	−	1.45684i	−0.0478535	−	0.998854i	$-0.515238\pi$
$53$	6.12335	−	10.6059i	0.841107	−	1.45684i	0.888960	−	0.457985i	$-0.151429\pi$
$54$		0			0
$55$	0.228474			0.0308075
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.94297			−0.643520			−0.321760	−	0.946821i	$-0.604274\pi$
$59$	−4.94297			−0.643520			−0.321760	+	0.946821i	$0.604274\pi$
$60$		0			0
$61$	−3.52119			−0.450842			−0.225421	−	0.974261i	$-0.572376\pi$
$61$	−3.52119			−0.450842			−0.225421	+	0.974261i	$0.572376\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.10477			0.137029
$66$		0			0
$67$	−12.3202			−1.50516			−0.752579	−	0.658502i	$-0.771190\pi$
$67$	−12.3202			−1.50516			−0.752579	+	0.658502i	$0.771190\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.57304			−0.661398			−0.330699	−	0.943736i	$-0.607285\pi$
$71$	−5.57304			−0.661398			−0.330699	+	0.943736i	$0.607285\pi$
$72$		0			0
$73$	−3.71686	+	6.43779i	−0.435026	+	0.753487i	−0.997298	−	0.0734657i	$-0.976594\pi$
$73$	−3.71686	+	6.43779i	−0.435026	+	0.753487i	0.562272	+	0.826952i	$0.309927\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.03164	+	1.44669i	0.117566	+	0.164866i
$78$		0			0
$79$	10.0127			1.12652			0.563260	−	0.826279i	$-0.309547\pi$
$79$	10.0127			1.12652			0.563260	+	0.826279i	$0.309547\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.47376	−	4.28468i	0.271530	−	0.470305i	−0.697723	−	0.716367i	$-0.745804\pi$
$83$	2.47376	−	4.28468i	0.271530	−	0.470305i	0.969254	+	0.246063i	$0.0791369\pi$
$84$		0			0
$85$	−0.374269	−	0.648252i	−0.0405951	−	0.0703128i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.52177	+	14.7601i	0.903306	+	1.56457i	0.823175	+	0.567788i	$0.192201\pi$
$89$	8.52177	+	14.7601i	0.903306	+	1.56457i	0.0801310	+	0.996784i	$0.474466\pi$
$90$		0			0
$91$	4.98840	+	6.99536i	0.522927	+	0.733313i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.164714			−0.0168993
$96$		0			0
$97$	4.23657	−	7.33795i	0.430159	−	0.745056i	−0.566728	−	0.823905i	$-0.691791\pi$
$97$	4.23657	−	7.33795i	0.430159	−	0.745056i	0.996887	+	0.0788485i	$0.0251243\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.28693	−	3.96107i	−0.227558	−	0.394141i	0.729526	−	0.683953i	$-0.239741\pi$
$101$	−2.28693	−	3.96107i	−0.227558	−	0.394141i	−0.957084	+	0.289812i	$0.906407\pi$
$102$		0			0
$103$	−0.903563	+	1.56502i	−0.0890307	+	0.154206i	−0.907102	−	0.420912i	$-0.861710\pi$
$103$	−0.903563	+	1.56502i	−0.0890307	+	0.154206i	0.818071	+	0.575117i	$0.195044\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.88188	+	6.72361i	0.375275	+	0.649996i	0.990368	−	0.138459i	$-0.0442149\pi$
$107$	3.88188	+	6.72361i	0.375275	+	0.649996i	−0.615093	+	0.788454i	$0.710882\pi$
$108$		0			0
$109$	−1.07178	+	1.85638i	−0.102658	+	0.177809i	−0.912779	−	0.408454i	$-0.866068\pi$
$109$	−1.07178	+	1.85638i	−0.102658	+	0.177809i	0.810121	+	0.586263i	$0.199401\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.91006	+	13.7006i	0.744116	+	1.28885i	0.950607	+	0.310398i	$0.100462\pi$
$113$	7.91006	+	13.7006i	0.744116	+	1.28885i	−0.206491	+	0.978449i	$0.566204\pi$
$114$		0			0
$115$	0.712702	+	1.23444i	0.0664598	+	0.115112i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.41477	−	5.29695i	0.221362	−	0.485571i
$120$		0			0
$121$	5.27449	−	9.13568i	0.479499	−	0.830516i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.36263			0.300763
$126$		0			0
$127$	13.8820			1.23183			0.615915	−	0.787812i	$-0.288786\pi$
$127$	13.8820			1.23183			0.615915	+	0.787812i	$0.288786\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.08769	−	3.61599i	0.182402	−	0.315930i	−0.760296	−	0.649577i	$-0.774946\pi$
$131$	2.08769	−	3.61599i	0.182402	−	0.315930i	0.942698	+	0.333647i	$0.108279\pi$
$132$		0			0
$133$	−0.743743	−	1.04297i	−0.0644907	−	0.0904369i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.38043	−	11.0512i	−0.545117	−	0.944170i	−0.998600	−	0.0529051i	$-0.983152\pi$
$137$	−6.38043	−	11.0512i	−0.545117	−	0.944170i	0.453483	−	0.891265i	$-0.350181\pi$
$138$		0			0
$139$	−5.95986	−	10.3228i	−0.505509	−	0.875567i	−0.999980	−	0.00637264i	$-0.997972\pi$
$139$	−5.95986	−	10.3228i	−0.505509	−	0.875567i	0.494471	−	0.869194i	$-0.335362\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.09046	+	1.88873i	−0.0911885	+	0.157943i
$144$		0			0
$145$	0.162911	+	0.282170i	0.0135290	+	0.0234329i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.37548	+	9.31060i	−0.440376	+	0.762754i	−0.997717	−	0.0675295i	$-0.978488\pi$
$149$	−5.37548	+	9.31060i	−0.440376	+	0.762754i	0.557341	+	0.830284i	$0.311822\pi$
$150$		0			0
$151$	−1.29050	−	2.23521i	−0.105019	−	0.181899i	0.808727	−	0.588184i	$-0.200157\pi$
$151$	−1.29050	−	2.23521i	−0.105019	−	0.181899i	−0.913746	+	0.406286i	$0.866824\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.354256	+	0.613589i	−0.0284545	+	0.0492846i
$156$		0			0
$157$	7.99693			0.638224			0.319112	−	0.947717i	$-0.396615\pi$
$157$	7.99693			0.638224			0.319112	+	0.947717i	$0.396615\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.59833	+	10.0867i	−0.362399	+	0.794946i
$162$		0			0
$163$	−4.13306	−	7.15868i	−0.323727	−	0.560711i	0.657527	−	0.753431i	$-0.271602\pi$
$163$	−4.13306	−	7.15868i	−0.323727	−	0.560711i	−0.981254	+	0.192720i	$0.938269\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.99384	+	15.5778i	0.695964	+	1.20544i	0.969855	+	0.243684i	$0.0783560\pi$
$167$	8.99384	+	15.5778i	0.695964	+	1.20544i	−0.273891	+	0.961761i	$0.588311\pi$
$168$		0			0
$169$	1.22720	−	2.12557i	0.0944000	−	0.163506i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	16.9983			1.29236			0.646179	−	0.763186i	$-0.276366\pi$
$173$	16.9983			1.29236			0.646179	+	0.763186i	$0.276366\pi$
$174$		0			0
$175$	7.50283	+	10.5214i	0.567161	+	0.795343i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.65073	+	16.7156i	−0.721329	+	1.24938i	0.239138	+	0.970986i	$0.423135\pi$
$179$	−9.65073	+	16.7156i	−0.721329	+	1.24938i	−0.960467	+	0.278393i	$0.910198\pi$
$180$		0			0
$181$	21.9640			1.63257			0.816287	−	0.577646i	$-0.196029\pi$
$181$	21.9640			1.63257			0.816287	+	0.577646i	$0.196029\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.27690			0.240922
$186$		0			0
$187$	1.47768			0.108059
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.65744			0.481716			0.240858	−	0.970560i	$-0.422571\pi$
$191$	6.65744			0.481716			0.240858	+	0.970560i	$0.422571\pi$
$192$		0			0
$193$	6.34906			0.457015			0.228508	−	0.973542i	$-0.426615\pi$
$193$	6.34906			0.457015			0.228508	+	0.973542i	$0.426615\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−23.8112			−1.69648			−0.848239	−	0.529614i	$-0.822337\pi$
$197$	−23.8112			−1.69648			−0.848239	+	0.529614i	$0.822337\pi$
$198$		0			0
$199$	10.4771	−	18.1468i	0.742701	−	1.28640i	−0.208561	−	0.978009i	$-0.566878\pi$
$199$	10.4771	−	18.1468i	0.742701	−	1.28640i	0.951261	−	0.308386i	$-0.0997887\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.05110	+	2.30565i	−0.0737725	+	0.161825i
$204$		0			0
$205$	2.65497			0.185431
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.162581	−	0.281599i	0.0112460	−	0.0194786i
$210$		0			0
$211$	6.32431	+	10.9540i	0.435384	+	0.754106i	0.997327	−	0.0730693i	$-0.0232794\pi$
$211$	6.32431	+	10.9540i	0.435384	+	0.754106i	−0.561943	+	0.827176i	$0.689946\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.24554	−	2.15733i	−0.0849448	−	0.147129i
$216$		0			0
$217$	−5.48482	+	0.527427i	−0.372334	+	0.0358041i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.14520			0.480638
$222$		0			0
$223$	1.34432	−	2.32843i	0.0900225	−	0.155924i	−0.817498	−	0.575932i	$-0.804639\pi$
$223$	1.34432	−	2.32843i	0.0900225	−	0.155924i	0.907520	+	0.420008i	$0.137973\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.9942	−	24.2387i	−0.928829	−	1.60878i	−0.785284	−	0.619136i	$-0.787483\pi$
$227$	−13.9942	−	24.2387i	−0.928829	−	1.60878i	−0.143546	−	0.989644i	$-0.545850\pi$
$228$		0			0
$229$	−12.2695	+	21.2514i	−0.810790	+	1.40433i	0.101521	+	0.994833i	$0.467629\pi$
$229$	−12.2695	+	21.2514i	−0.810790	+	1.40433i	−0.912312	+	0.409497i	$0.865704\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.61844	+	7.99938i	0.302564	+	0.524057i	0.976716	−	0.214536i	$-0.0688240\pi$
$233$	4.61844	+	7.99938i	0.302564	+	0.524057i	−0.674152	+	0.738593i	$0.735491\pi$
$234$		0			0
$235$	−0.459103	+	0.795189i	−0.0299486	+	0.0518724i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.0126	+	24.2706i	0.906403	+	1.56994i	0.819023	+	0.573760i	$0.194516\pi$
$239$	14.0126	+	24.2706i	0.906403	+	1.56994i	0.0873796	+	0.996175i	$0.472151\pi$
$240$		0			0
$241$	−9.91411	−	17.1717i	−0.638624	−	1.10613i	−0.985735	−	0.168305i	$-0.946171\pi$
$241$	−9.91411	−	17.1717i	−0.638624	−	1.10613i	0.347111	−	0.937824i	$-0.387163\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.775879	−	2.25146i	0.0495691	−	0.143841i
$246$		0			0
$247$	0.786145	−	1.36164i	0.0500212	−	0.0866393i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	16.5759			1.04626			0.523132	−	0.852252i	$-0.324764\pi$
$251$	16.5759			1.04626			0.523132	+	0.852252i	$0.324764\pi$
$252$		0			0
$253$	−2.81389			−0.176907
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.64750	−	6.31766i	0.227525	−	0.394085i	−0.729549	−	0.683929i	$-0.760270\pi$
$257$	3.64750	−	6.31766i	0.227525	−	0.394085i	0.957074	+	0.289844i	$0.0936033\pi$
$258$		0			0
$259$	14.7963	+	20.7493i	0.919399	+	1.28930i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.3899	+	23.1920i	0.825657	+	1.43008i	0.901416	+	0.432954i	$0.142529\pi$
$263$	13.3899	+	23.1920i	0.825657	+	1.43008i	−0.0757586	+	0.997126i	$0.524138\pi$
$264$		0			0
$265$	−2.08316	−	3.60815i	−0.127968	−	0.221647i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.1791	+	17.6307i	−0.620630	+	1.07496i	0.368739	+	0.929533i	$0.379790\pi$
$269$	−10.1791	+	17.6307i	−0.620630	+	1.07496i	−0.989369	+	0.145429i	$0.953544\pi$
$270$		0			0
$271$	−5.45842	−	9.45427i	−0.331576	−	0.574306i	0.651245	−	0.758867i	$-0.274247\pi$
$271$	−5.45842	−	9.45427i	−0.331576	−	0.574306i	−0.982821	+	0.184561i	$0.940914\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.64011	+	2.84075i	−0.0989021	+	0.171303i
$276$		0			0
$277$	−8.83689	−	15.3059i	−0.530957	−	0.919645i	−0.999347	−	0.0361231i	$-0.988499\pi$
$277$	−8.83689	−	15.3059i	−0.530957	−	0.919645i	0.468390	−	0.883522i	$-0.344834\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.17614	+	12.4294i	−0.428092	+	0.741478i	−0.996704	−	0.0811286i	$-0.974148\pi$
$281$	−7.17614	+	12.4294i	−0.428092	+	0.741478i	0.568611	+	0.822606i	$0.307481\pi$
$282$		0			0
$283$	−9.72841			−0.578294			−0.289147	−	0.957285i	$-0.593372\pi$
$283$	−9.72841			−0.578294			−0.289147	+	0.957285i	$0.593372\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.9881	+	16.8112i	0.707636	+	0.992334i
$288$		0			0
$289$	6.07937	+	10.5298i	0.357610	+	0.619399i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.26345	−	10.8486i	−0.365915	−	0.633783i	0.623008	−	0.782216i	$-0.285911\pi$
$293$	−6.26345	−	10.8486i	−0.365915	−	0.633783i	−0.988923	+	0.148433i	$0.952577\pi$
$294$		0			0
$295$	−0.840799	+	1.45631i	−0.0489532	+	0.0847895i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.6063			−0.786871
$300$		0			0
$301$	8.03616	−	17.6278i	0.463196	−	1.01605i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.598954	+	1.03742i	−0.0342960	+	0.0594025i
$306$		0			0
$307$	−25.8747			−1.47675			−0.738375	−	0.674391i	$-0.764406\pi$
$307$	−25.8747			−1.47675			−0.738375	+	0.674391i	$0.764406\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	28.4001			1.61042			0.805211	−	0.592988i	$-0.202052\pi$
$311$	28.4001			1.61042			0.805211	+	0.592988i	$0.202052\pi$
$312$		0			0
$313$	−12.2015			−0.689668			−0.344834	−	0.938664i	$-0.612065\pi$
$313$	−12.2015			−0.689668			−0.344834	+	0.938664i	$0.612065\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.95219			0.221977			0.110988	−	0.993822i	$-0.464598\pi$
$317$	3.95219			0.221977			0.110988	+	0.993822i	$0.464598\pi$
$318$		0			0
$319$	−0.643204			−0.0360125
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.06531			−0.0592754
$324$		0			0
$325$	−7.93058	+	13.7362i	−0.439909	+	0.761945i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.10813	+	0.683527i	−0.391884	+	0.0376841i
$330$		0			0
$331$	8.88286			0.488246			0.244123	−	0.969744i	$-0.421500\pi$
$331$	8.88286			0.488246			0.244123	+	0.969744i	$0.421500\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.09567	+	3.62981i	−0.114499	+	0.198318i
$336$		0			0
$337$	−11.9741	−	20.7397i	−0.652269	−	1.12976i	−0.982571	−	0.185887i	$-0.940484\pi$
$337$	−11.9741	−	20.7397i	−0.652269	−	1.12976i	0.330302	−	0.943875i	$-0.392849\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.699335	−	1.21128i	−0.0378711	−	0.0655947i
$342$		0			0
$343$	17.7596	−	5.25329i	0.958928	−	0.283651i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.49059			0.509481			0.254741	−	0.967009i	$-0.418010\pi$
$347$	9.49059			0.509481			0.254741	+	0.967009i	$0.418010\pi$
$348$		0			0
$349$	4.26145	−	7.38104i	0.228110	−	0.395098i	−0.729138	−	0.684367i	$-0.760079\pi$
$349$	4.26145	−	7.38104i	0.228110	−	0.395098i	0.957248	+	0.289269i	$0.0934121\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.5872	−	32.1940i	−0.989297	−	1.71351i	−0.621018	−	0.783797i	$-0.713281\pi$
$353$	−18.5872	−	32.1940i	−0.989297	−	1.71351i	−0.368279	−	0.929715i	$-0.620053\pi$
$354$		0			0
$355$	−0.947975	+	1.64194i	−0.0503133	+	0.0871451i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.30964	−	9.19657i	−0.280232	−	0.485376i	0.691210	−	0.722654i	$-0.257078\pi$
$359$	−5.30964	−	9.19657i	−0.280232	−	0.485376i	−0.971442	+	0.237278i	$0.923745\pi$
$360$		0			0
$361$	9.38279	−	16.2515i	0.493831	−	0.855340i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.26448	+	2.19014i	0.0661857	+	0.114637i
$366$		0			0
$367$	11.1799	+	19.3642i	0.583586	+	1.01080i	0.995050	+	0.0993751i	$0.0316844\pi$
$367$	11.1799	+	19.3642i	0.583586	+	1.01080i	−0.411464	+	0.911426i	$0.634982\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.4405	−	29.4826i	0.697796	−	1.53066i
$372$		0			0
$373$	8.79264	−	15.2293i	0.455266	−	0.788544i	−0.543438	−	0.839450i	$-0.682878\pi$
$373$	8.79264	−	15.2293i	0.455266	−	0.788544i	0.998703	+	0.0509059i	$0.0162109\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.11015			−0.160181
$378$		0			0
$379$	−10.0443			−0.515939			−0.257969	−	0.966153i	$-0.583053\pi$
$379$	−10.0443			−0.515939			−0.257969	+	0.966153i	$0.583053\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.93619	−	6.81768i	0.201130	−	0.348367i	−0.747763	−	0.663966i	$-0.768872\pi$
$383$	3.93619	−	6.81768i	0.201130	−	0.348367i	0.948893	+	0.315599i	$0.102205\pi$
$384$		0			0
$385$	0.601710	−	0.0578612i	0.0306660	−	0.00294888i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.82417	−	3.15956i	−0.0924893	−	0.160196i	0.816069	−	0.577955i	$-0.196149\pi$
$389$	−1.82417	−	3.15956i	−0.0924893	−	0.160196i	−0.908558	+	0.417759i	$0.862816\pi$
$390$		0			0
$391$	4.60949	+	7.98387i	0.233112	+	0.403762i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.70317	−	2.94997i	0.0856956	−	0.148429i
$396$		0			0
$397$	6.56071	+	11.3635i	0.329272	+	0.570317i	0.982368	−	0.186959i	$-0.0598632\pi$
$397$	6.56071	+	11.3635i	0.329272	+	0.570317i	−0.653095	+	0.757276i	$0.726530\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.71872	−	9.90511i	0.285579	−	0.494638i	−0.687170	−	0.726496i	$-0.741147\pi$
$401$	5.71872	−	9.90511i	0.285579	−	0.494638i	0.972749	+	0.231859i	$0.0744807\pi$
$402$		0			0
$403$	−3.38157	−	5.85705i	−0.168448	−	0.291760i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.23445	+	5.60224i	−0.160326	+	0.277693i
$408$		0			0
$409$	−18.4821			−0.913882			−0.456941	−	0.889497i	$-0.651055\pi$
$409$	−18.4821			−0.913882			−0.456941	+	0.889497i	$0.651055\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.0178	+	1.25181i	−0.640565	+	0.0615975i
$414$		0			0
$415$	−0.841574	−	1.45765i	−0.0413112	−	0.0715531i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6290	−	18.4099i	−0.519260	−	0.899385i	−0.999749	−	0.0223843i	$-0.992874\pi$
$419$	−10.6290	−	18.4099i	−0.519260	−	0.899385i	0.480489	−	0.877001i	$-0.340459\pi$
$420$		0			0
$421$	−8.60478	+	14.9039i	−0.419371	+	0.726373i	−0.995876	−	0.0907211i	$-0.971083\pi$
$421$	−8.60478	+	14.9039i	−0.419371	+	0.726373i	0.576505	+	0.817094i	$0.304416\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.7468			0.521295
$426$		0			0
$427$	−9.27341	+	0.891743i	−0.448772	+	0.0431545i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.02962	−	5.24745i	0.145931	−	0.252761i	−0.783789	−	0.621028i	$-0.786715\pi$
$431$	3.02962	−	5.24745i	0.145931	−	0.252761i	0.929720	+	0.368267i	$0.120049\pi$
$432$		0			0
$433$	−17.6963			−0.850432			−0.425216	−	0.905092i	$-0.639802\pi$
$433$	−17.6963			−0.850432			−0.425216	+	0.905092i	$0.639802\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.02862			0.0970421
$438$		0			0
$439$	−27.3373			−1.30474			−0.652370	−	0.757901i	$-0.726225\pi$
$439$	−27.3373			−1.30474			−0.652370	+	0.757901i	$0.726225\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.91771			0.0911132			0.0455566	−	0.998962i	$-0.485494\pi$
$443$	1.91771			0.0911132			0.0455566	+	0.998962i	$0.485494\pi$
$444$		0			0
$445$	5.79822			0.274862
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.3249			−1.33674			−0.668368	−	0.743831i	$-0.733007\pi$
$449$	−28.3249			−1.33674			−0.668368	+	0.743831i	$0.733007\pi$
$450$		0			0
$451$	−2.62058	+	4.53898i	−0.123398	+	0.213732i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.90951	−	0.279782i	0.136400	−	0.0131164i
$456$		0			0
$457$	13.0085			0.608514			0.304257	−	0.952590i	$-0.401592\pi$
$457$	13.0085			0.608514			0.304257	+	0.952590i	$0.401592\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.8278	−	20.4863i	0.550875	−	0.954144i	−0.447336	−	0.894366i	$-0.647627\pi$
$461$	11.8278	−	20.4863i	0.550875	−	0.954144i	0.998212	−	0.0597782i	$-0.0190393\pi$
$462$		0			0
$463$	20.2403	+	35.0572i	0.940647	+	1.62925i	0.764241	+	0.644931i	$0.223114\pi$
$463$	20.2403	+	35.0572i	0.940647	+	1.62925i	0.176406	+	0.984317i	$0.443553\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.6010	−	32.2179i	−0.860753	−	1.49087i	−0.871203	−	0.490923i	$-0.836659\pi$
$467$	−18.6010	−	32.2179i	−0.860753	−	1.49087i	0.0104492	−	0.999945i	$-0.496674\pi$
$468$		0			0
$469$	−32.4466	+	3.12011i	−1.49825	+	0.144073i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.91761			0.226112
$474$		0			0
$475$	1.18240	−	2.04799i	0.0542525	−	0.0939680i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.2918	−	35.1463i	−0.927154	−	1.60588i	−0.788060	−	0.615598i	$-0.788914\pi$
$479$	−20.2918	−	35.1463i	−0.927154	−	1.60588i	−0.139094	−	0.990279i	$-0.544419\pi$
$480$		0			0
$481$	−15.6399	+	27.0891i	−0.713118	+	1.23516i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.44128	−	2.49637i	−0.0654452	−	0.113354i
$486$		0			0
$487$	−10.5255	+	18.2307i	−0.476956	+	0.826113i	−0.999651	−	0.0264072i	$-0.991593\pi$
$487$	−10.5255	+	18.2307i	−0.476956	+	0.826113i	0.522695	+	0.852520i	$0.324927\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.97925	−	8.62432i	−0.224711	−	0.389210i	0.731522	−	0.681818i	$-0.238810\pi$
$491$	−4.97925	−	8.62432i	−0.224711	−	0.389210i	−0.956233	+	0.292608i	$0.905477\pi$
$492$		0			0
$493$	1.05365	+	1.82497i	0.0474538	+	0.0821924i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.6772	+	1.41138i	−0.658361	+	0.0633088i
$498$		0			0
$499$	11.3150	−	19.5982i	0.506531	−	0.877337i	−0.493440	−	0.869780i	$-0.664261\pi$
$499$	11.3150	−	19.5982i	0.506531	−	0.877337i	0.999971	−	0.00755788i	$-0.00240577\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−43.4520			−1.93743			−0.968714	−	0.248179i	$-0.920168\pi$
$503$	−43.4520			−1.93743			−0.968714	+	0.248179i	$0.920168\pi$
$504$		0			0
$505$	−1.55602			−0.0692422
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.77739	+	8.27468i	−0.211754	+	0.366769i	−0.952264	−	0.305277i	$-0.901251\pi$
$509$	−4.77739	+	8.27468i	−0.211754	+	0.366769i	0.740510	+	0.672046i	$0.234584\pi$
$510$		0			0
$511$	−8.15836	+	17.8959i	−0.360905	+	0.791667i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.307392	+	0.532419i	0.0135453	+	0.0234612i
$516$		0			0
$517$	−0.906312	−	1.56978i	−0.0398596	−	0.0690388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.581462	+	1.00712i	−0.0254743	+	0.0441228i	−0.878482	−	0.477776i	$-0.841443\pi$
$521$	−0.581462	+	1.00712i	−0.0254743	+	0.0441228i	0.853007	+	0.521899i	$0.174776\pi$
$522$		0			0
$523$	3.20567	+	5.55239i	0.140174	+	0.242789i	0.927562	−	0.373669i	$-0.121900\pi$
$523$	3.20567	+	5.55239i	0.140174	+	0.242789i	−0.787388	+	0.616458i	$0.788567\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.29119	+	3.96846i	−0.0998059	+	0.172869i
$528$		0			0
$529$	2.72237	+	4.71528i	0.118364	+	0.205012i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.6716	+	21.9478i	−0.548866	+	0.950665i
$534$		0			0
$535$	2.64123			0.114190
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.08331	+	3.54876i	0.132808	+	0.152856i
$540$		0			0
$541$	−7.37443	−	12.7729i	−0.317052	−	0.549150i	0.662820	−	0.748779i	$-0.269360\pi$
$541$	−7.37443	−	12.7729i	−0.317052	−	0.549150i	−0.979871	+	0.199629i	$0.936026\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.364621	+	0.631542i	0.0156187	+	0.0270523i
$546$		0			0
$547$	−6.57905	+	11.3952i	−0.281300	+	0.487226i	−0.971705	−	0.236197i	$-0.924099\pi$
$547$	−6.57905	+	11.3952i	−0.281300	+	0.487226i	0.690405	+	0.723423i	$0.257432\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.463706			0.0197545
$552$		0			0
$553$	26.3696	−	2.53573i	1.12135	−	0.107830i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.1869	−	21.1083i	0.516374	−	0.894385i	−0.483446	−	0.875374i	$-0.660615\pi$
$557$	12.1869	−	21.1083i	0.516374	−	0.894385i	0.999819	−	0.0190111i	$-0.00605177\pi$
$558$		0			0
$559$	23.7787			1.00573
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.11965			−0.131478			−0.0657388	−	0.997837i	$-0.520940\pi$
$563$	−3.11965			−0.131478			−0.0657388	+	0.997837i	$0.520940\pi$
$564$		0			0
$565$	5.38201			0.226423
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.4769			0.900358			0.450179	−	0.892938i	$-0.351360\pi$
$569$	21.4769			0.900358			0.450179	+	0.892938i	$0.351360\pi$
$570$		0			0
$571$	−33.0460			−1.38293			−0.691466	−	0.722409i	$-0.743035\pi$
$571$	−33.0460			−1.38293			−0.691466	+	0.722409i	$0.743035\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.4646			−0.853432
$576$		0			0
$577$	0.904826	−	1.56720i	0.0376684	−	0.0652436i	−0.846577	−	0.532267i	$-0.821340\pi$
$577$	0.904826	−	1.56720i	0.0376684	−	0.0652436i	0.884245	+	0.467023i	$0.154674\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.42980	−	11.9106i	0.225266	−	0.494136i
$582$		0			0
$583$	8.22473			0.340633
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.65901	−	2.87349i	0.0684746	−	0.118601i	−0.829755	−	0.558127i	$-0.811520\pi$
$587$	1.65901	−	2.87349i	0.0684746	−	0.118601i	0.898230	+	0.439526i	$0.144853\pi$
$588$		0			0
$589$	0.504173	+	0.873253i	0.0207741	+	0.0359818i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.3784	−	26.6362i	−0.631516	−	1.09382i	−0.987242	−	0.159228i	$-0.949100\pi$
$593$	−15.3784	−	26.6362i	−0.631516	−	1.09382i	0.355726	−	0.934590i	$-0.384234\pi$
$594$		0			0
$595$	−1.14985	−	1.61246i	−0.0471391	−	0.0661042i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.9705			0.570817			0.285409	−	0.958406i	$-0.407871\pi$
$599$	13.9705			0.570817			0.285409	+	0.958406i	$0.407871\pi$
$600$		0			0
$601$	−7.50432	+	12.9979i	−0.306108	+	0.530194i	−0.977507	−	0.210901i	$-0.932360\pi$
$601$	−7.50432	+	12.9979i	−0.306108	+	0.530194i	0.671400	+	0.741096i	$0.265693\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.79438	−	3.10796i	−0.0729519	−	0.126356i
$606$		0			0
$607$	11.6644	−	20.2034i	0.473444	−	0.820030i	−0.526093	−	0.850427i	$-0.676344\pi$
$607$	11.6644	−	20.2034i	0.473444	−	0.820030i	0.999538	+	0.0303969i	$0.00967712\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.38239	−	7.59052i	−0.177292	−	0.307080i
$612$		0			0
$613$	22.3374	−	38.6895i	0.902198	−	1.56265i	0.0775635	−	0.996987i	$-0.475286\pi$
$613$	22.3374	−	38.6895i	0.902198	−	1.56265i	0.824635	−	0.565666i	$-0.191381\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.18488	+	2.05227i	0.0477013	+	0.0826212i	0.888890	−	0.458120i	$-0.151477\pi$
$617$	1.18488	+	2.05227i	0.0477013	+	0.0826212i	−0.841189	+	0.540741i	$0.818144\pi$
$618$		0			0
$619$	−11.3863	−	19.7217i	−0.457655	−	0.792682i	0.541181	−	0.840906i	$-0.317977\pi$
$619$	−11.3863	−	19.7217i	−0.457655	−	0.792682i	−0.998837	+	0.0482236i	$0.984644\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	26.1810	+	36.7142i	1.04892	+	1.47092i
$624$		0			0
$625$	−11.6387	+	20.1588i	−0.465547	+	0.806351i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.1937			0.845049
$630$		0			0
$631$	−17.8652			−0.711201			−0.355600	−	0.934638i	$-0.615724\pi$
$631$	−17.8652			−0.711201			−0.355600	+	0.934638i	$0.615724\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.36133	−	4.08995i	0.0937067	−	0.162305i
$636$		0			0
$637$	14.9091	+	17.1597i	0.590718	+	0.679891i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.7900	−	22.1529i	−0.505175	−	0.874988i	−0.999982	−	0.00598543i	$-0.998095\pi$
$641$	−12.7900	−	22.1529i	−0.505175	−	0.874988i	0.494808	−	0.869003i	$-0.335239\pi$
$642$		0			0
$643$	−7.99334	−	13.8449i	−0.315227	−	0.545989i	0.664259	−	0.747503i	$-0.268747\pi$
$643$	−7.99334	−	13.8449i	−0.315227	−	0.545989i	−0.979486	+	0.201514i	$0.935414\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.47306	−	12.9437i	0.293796	−	0.508870i	−0.680908	−	0.732369i	$-0.738415\pi$
$647$	7.47306	−	12.9437i	0.293796	−	0.508870i	0.974704	+	0.223499i	$0.0717479\pi$
$648$		0			0
$649$	−1.65982	−	2.87489i	−0.0651536	−	0.112849i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.82885	+	8.36381i	−0.188967	+	0.327301i	−0.944906	−	0.327341i	$-0.893847\pi$
$653$	−4.82885	+	8.36381i	−0.188967	+	0.327301i	0.755939	+	0.654642i	$0.227181\pi$
$654$		0			0
$655$	−0.710233	−	1.23016i	−0.0277511	−	0.0480663i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.80353	−	16.9802i	0.381891	−	0.661455i	−0.609441	−	0.792831i	$-0.708606\pi$
$659$	9.80353	−	16.9802i	0.381891	−	0.661455i	0.991333	+	0.131376i	$0.0419396\pi$
$660$		0			0
$661$	−10.2655			−0.399281			−0.199641	−	0.979869i	$-0.563977\pi$
$661$	−10.2655			−0.399281			−0.199641	+	0.979869i	$0.563977\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.433792	+	0.0417140i	−0.0168217	+	0.00161760i
$666$		0			0
$667$	−2.00641	−	3.47520i	−0.0776885	−	0.134560i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.18239	−	2.04797i	−0.0456458	−	0.0790608i
$672$		0			0
$673$	−17.1584	+	29.7191i	−0.661406	+	1.14559i	0.318840	+	0.947808i	$0.396707\pi$
$673$	−17.1584	+	29.7191i	−0.661406	+	1.14559i	−0.980246	+	0.197780i	$0.936627\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.47419			−0.287256			−0.143628	−	0.989632i	$-0.545877\pi$
$677$	−7.47419			−0.287256			−0.143628	+	0.989632i	$0.545877\pi$
$678$		0			0
$679$	9.29910	−	20.3982i	0.356867	−	0.782810i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−18.1577	+	31.4501i	−0.694786	+	1.20340i	0.275467	+	0.961310i	$0.411167\pi$
$683$	−18.1577	+	31.4501i	−0.694786	+	1.20340i	−0.970253	+	0.242094i	$0.922166\pi$
$684$		0			0
$685$	−4.34125			−0.165871
$686$		0			0
$687$		0			0
$688$		0			0
$689$	39.7699			1.51511
$690$		0			0
$691$	−50.9624			−1.93870			−0.969350	−	0.245684i	$-0.920987\pi$
$691$	−50.9624			−1.93870			−0.969350	+	0.245684i	$0.920987\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.05509			−0.153818
$696$		0			0
$697$	17.1713			0.650410
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−36.6075			−1.38265			−0.691324	−	0.722545i	$-0.742972\pi$
$701$	−36.6075			−1.38265			−0.691324	+	0.722545i	$0.742972\pi$
$702$		0			0
$703$	2.33182	−	4.03883i	0.0879463	−	0.152327i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.02600	−	9.85272i	−0.264240	−	0.370550i
$708$		0			0
$709$	−5.87578			−0.220670			−0.110335	−	0.993894i	$-0.535192\pi$
$709$	−5.87578			−0.220670			−0.110335	+	0.993894i	$0.535192\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.36301	−	7.55695i	0.163396	−	0.283010i
$714$		0			0
$715$	0.370973	+	0.642545i	0.0138736	+	0.0240298i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.09642	−	14.0234i	−0.301945	−	0.522985i	0.674631	−	0.738155i	$-0.264303\pi$
$719$	−8.09642	−	14.0234i	−0.301945	−	0.522985i	−0.976577	+	0.215170i	$0.930969\pi$
$720$		0			0
$721$	−1.98328	+	4.35046i	−0.0738614	+	0.162020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.67783			−0.173730
$726$		0			0
$727$	22.8771	−	39.6243i	0.848464	−	1.46958i	−0.0341138	−	0.999418i	$-0.510861\pi$
$727$	22.8771	−	39.6243i	0.848464	−	1.46958i	0.882578	−	0.470166i	$-0.155806\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.05565	−	13.9528i	−0.297949	−	0.516063i
$732$		0			0
$733$	−13.5916	+	23.5414i	−0.502019	+	0.869522i	0.497978	+	0.867189i	$0.334076\pi$
$733$	−13.5916	+	23.5414i	−0.502019	+	0.869522i	−0.999997	+	0.00233276i	$0.999257\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.13706	−	7.16560i	−0.152391	−	0.263948i
$738$		0			0
$739$	−12.1738	+	21.0856i	−0.447821	+	0.775648i	−0.998244	−	0.0592377i	$-0.981133\pi$
$739$	−12.1738	+	21.0856i	−0.447821	+	0.775648i	0.550423	+	0.834886i	$0.314466\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.0683178	−	0.118330i	−0.00250634	−	0.00434110i	0.864770	−	0.502169i	$-0.167464\pi$
$743$	−0.0683178	−	0.118330i	−0.00250634	−	0.00434110i	−0.867276	+	0.497828i	$0.834131\pi$
$744$		0			0
$745$	1.82874	+	3.16747i	0.0669998	+	0.116047i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.9261	+	16.7242i	0.435769	+	0.611090i
$750$		0			0
$751$	3.71446	−	6.43364i	0.135543	−	0.234767i	−0.790262	−	0.612769i	$-0.790056\pi$
$751$	3.71446	−	6.43364i	0.135543	−	0.234767i	0.925805	+	0.378002i	$0.123389\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.878055			−0.0319557
$756$		0			0
$757$	−14.0794			−0.511723			−0.255861	−	0.966713i	$-0.582359\pi$
$757$	−14.0794			−0.511723			−0.255861	+	0.966713i	$0.582359\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.3616	−	33.5353i	0.701858	−	1.21565i	−0.265955	−	0.963985i	$-0.585687\pi$
$761$	19.3616	−	33.5353i	0.701858	−	1.21565i	0.967813	−	0.251669i	$-0.0809793\pi$
$762$		0			0
$763$	−2.35252	+	5.16041i	−0.0851671	+	0.186819i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.02589	−	13.9013i	−0.289798	−	0.501945i
$768$		0			0
$769$	5.14295	+	8.90786i	0.185460	+	0.321226i	0.943731	−	0.330713i	$-0.107289\pi$
$769$	5.14295	+	8.90786i	0.185460	+	0.321226i	−0.758272	+	0.651939i	$0.773956\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.6768	−	39.2773i	0.815627	−	1.41271i	−0.0932501	−	0.995643i	$-0.529726\pi$
$773$	22.6768	−	39.2773i	0.815627	−	1.41271i	0.908877	−	0.417064i	$-0.136941\pi$
$774$		0			0
$775$	−5.08606	−	8.80931i	−0.182697	−	0.316440i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.88926	−	3.27229i	0.0676898	−	0.117242i
$780$		0			0
$781$	−1.87139	−	3.24135i	−0.0669637	−	0.115985i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.36028	−	2.35607i	0.0485504	−	0.0840917i
$786$		0			0
$787$	−26.1087			−0.930675			−0.465337	−	0.885133i	$-0.654067\pi$
$787$	−26.1087			−0.930675			−0.465337	+	0.885133i	$0.654067\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.3017	+	34.0788i	0.864067	+	1.21170i
$792$		0			0
$793$	−5.71735	−	9.90274i	−0.203029	−	0.351657i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.1618	+	27.9931i	0.572481	+	0.991567i	0.996310	+	0.0858244i	$0.0273524\pi$
$797$	16.1618	+	27.9931i	0.572481	+	0.991567i	−0.423829	+	0.905742i	$0.639314\pi$
$798$		0			0
$799$	−2.96930	+	5.14298i	−0.105046	+	0.181946i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.99240			−0.176178
$804$		0			0
$805$	2.18960	+	3.07052i	0.0771731	+	0.108222i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.4553	+	38.8938i	−0.789488	+	1.36743i	0.136793	+	0.990600i	$0.456320\pi$
$809$	−22.4553	+	38.8938i	−0.789488	+	1.36743i	−0.926281	+	0.376833i	$0.877013\pi$
$810$		0			0
$811$	−42.8204			−1.50363			−0.751813	−	0.659376i	$-0.770820\pi$
$811$	−42.8204			−1.50363			−0.751813	+	0.659376i	$0.770820\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.81214			−0.0985049
$816$		0			0
$817$	−3.54527			−0.124033
$818$		0			0
$819$		0			0
$820$		0			0
$821$	32.2200			1.12448			0.562242	−	0.826972i	$-0.309939\pi$
$821$	32.2200			1.12448			0.562242	+	0.826972i	$0.309939\pi$
$822$		0			0
$823$	−4.38841			−0.152970			−0.0764851	−	0.997071i	$-0.524370\pi$
$823$	−4.38841			−0.152970			−0.0764851	+	0.997071i	$0.524370\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−42.0996			−1.46395			−0.731973	−	0.681333i	$-0.761400\pi$
$827$	−42.0996			−1.46395			−0.731973	+	0.681333i	$0.761400\pi$
$828$		0			0
$829$	−5.55838	+	9.62739i	−0.193050	+	0.334373i	−0.946260	−	0.323408i	$-0.895171\pi$
$829$	−5.55838	+	9.62739i	−0.193050	+	0.334373i	0.753209	+	0.657781i	$0.228505\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.01809	−	14.5616i	0.173866	−	0.504530i
$834$		0			0
$835$	6.11941			0.211771
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−27.2669	+	47.2277i	−0.941360	+	1.63048i	−0.178479	+	0.983944i	$0.557118\pi$
$839$	−27.2669	+	47.2277i	−0.941360	+	1.63048i	−0.762881	+	0.646539i	$0.776216\pi$
$840$		0			0
$841$	14.0414	+	24.3204i	0.484185	+	0.838633i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.417494	−	0.723120i	−0.0143622	−	0.0248761i
$846$		0			0
$847$	11.5773	−	25.3955i	0.397800	−	0.872600i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−40.3582			−1.38346
$852$		0			0
$853$	−11.3669	+	19.6880i	−0.389194	+	0.674105i	−0.992341	−	0.123526i	$-0.960580\pi$
$853$	−11.3669	+	19.6880i	−0.389194	+	0.674105i	0.603147	+	0.797630i	$0.293913\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.61928	+	9.73288i	0.191951	+	0.332469i	0.945897	−	0.324468i	$-0.105185\pi$
$857$	5.61928	+	9.73288i	0.191951	+	0.332469i	−0.753946	+	0.656937i	$0.771852\pi$
$858$		0			0
$859$	25.4024	−	43.9983i	0.866720	−	1.50120i	0.00139066	−	0.999999i	$-0.499557\pi$
$859$	25.4024	−	43.9983i	0.866720	−	1.50120i	0.865329	−	0.501204i	$-0.167109\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.340985	−	0.590603i	−0.0116073	−	0.0201044i	0.860163	−	0.510018i	$-0.170361\pi$
$863$	−0.340985	−	0.590603i	−0.0116073	−	0.0201044i	−0.871771	+	0.489914i	$0.837028\pi$
$864$		0			0
$865$	2.89141	−	5.00807i	0.0983110	−	0.170280i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.36222	+	5.82353i	0.114055	+	0.197550i
$870$		0			0
$871$	−20.0044	−	34.6486i	−0.677822	−	1.17402i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.85583	−	0.851587i	0.299382	−	0.0287889i
$876$		0			0
$877$	12.6595	−	21.9269i	0.427480	−	0.740418i	−0.569168	−	0.822221i	$-0.692735\pi$
$877$	12.6595	−	21.9269i	0.427480	−	0.740418i	0.996648	+	0.0818035i	$0.0260680\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.9482			1.04267			0.521335	−	0.853352i	$-0.325434\pi$
$881$	30.9482			1.04267			0.521335	+	0.853352i	$0.325434\pi$
$882$		0			0
$883$	−9.48501			−0.319196			−0.159598	−	0.987182i	$-0.551020\pi$
$883$	−9.48501			−0.319196			−0.159598	+	0.987182i	$0.551020\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.97469	+	3.42026i	−0.0663036	+	0.114841i	−0.897272	−	0.441479i	$-0.854454\pi$
$887$	−1.97469	+	3.42026i	−0.0663036	+	0.114841i	0.830968	+	0.556320i	$0.187787\pi$
$888$		0			0
$889$	36.5597	−	3.51563i	1.22617	−	0.117910i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.653390	+	1.13170i	0.0218649	+	0.0378710i
$894$		0			0
$895$	3.28318	+	5.68663i	0.109745	+	0.190083i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.997305	−	1.72738i	0.0332620	−	0.0576115i
$900$		0			0
$901$	−13.4731	−	23.3361i	−0.448854	−	0.777439i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.73609	−	6.47109i	0.124192	−	0.215106i
$906$		0			0
$907$	−16.7531	−	29.0171i	−0.556276	−	0.963498i	−0.997803	−	0.0662505i	$-0.978896\pi$
$907$	−16.7531	−	29.0171i	−0.556276	−	0.963498i	0.441527	−	0.897248i	$-0.354437\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	5.26585	−	9.12072i	0.174465	−	0.302183i	−0.765511	−	0.643423i	$-0.777514\pi$
$911$	5.26585	−	9.12072i	0.174465	−	0.302183i	0.939976	+	0.341240i	$0.110847\pi$
$912$		0			0
$913$	3.32269			0.109965
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.58240	−	10.0518i	0.151324	−	0.331939i
$918$		0			0
$919$	−1.81600	−	3.14540i	−0.0599042	−	0.103757i	0.834518	−	0.550981i	$-0.185746\pi$
$919$	−1.81600	−	3.14540i	−0.0599042	−	0.103757i	−0.894422	+	0.447224i	$0.852413\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.04894	−	15.6732i	−0.297850	−	0.515891i
$924$		0			0
$925$	−23.5232	+	40.7435i	−0.773440	+	1.33964i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.6058			−0.446392			−0.223196	−	0.974774i	$-0.571649\pi$
$929$	−13.6058			−0.446392			−0.223196	+	0.974774i	$0.571649\pi$
$930$		0			0
$931$	−2.22286	−	2.55841i	−0.0728512	−	0.0838486i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.251354	−	0.435358i	0.00822016	−	0.0142377i
$936$		0			0
$937$	9.98770			0.326284			0.163142	−	0.986603i	$-0.447837\pi$
$937$	9.98770			0.326284			0.163142	+	0.986603i	$0.447837\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−34.6209			−1.12861			−0.564305	−	0.825566i	$-0.690856\pi$
$941$	−34.6209			−1.12861			−0.564305	+	0.825566i	$0.690856\pi$
$942$		0			0
$943$	−32.6985			−1.06481
$944$		0			0
$945$		0			0
$946$		0			0
$947$	49.2171			1.59934			0.799670	−	0.600440i	$-0.205008\pi$
$947$	49.2171			1.59934			0.799670	+	0.600440i	$0.205008\pi$
$948$		0			0
$949$	−24.1403			−0.783626
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.2310			−0.460987			−0.230494	−	0.973074i	$-0.574034\pi$
$953$	−14.2310			−0.460987			−0.230494	+	0.973074i	$0.574034\pi$
$954$		0			0
$955$	1.13243	−	1.96143i	0.0366446	−	0.0634704i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.6022	−	27.4887i	−0.632990	−	0.887656i
$960$		0			0
$961$	−26.6626			−0.860085
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.07998	−	1.87057i	0.0347657	−	0.0602159i
$966$		0			0
$967$	19.4246	+	33.6443i	0.624652	+	1.08193i	0.988608	+	0.150513i	$0.0480925\pi$
$967$	19.4246	+	33.6443i	0.624652	+	1.08193i	−0.363956	+	0.931416i	$0.618574\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.13629	−	7.16427i	−0.132740	−	0.229912i	0.791992	−	0.610532i	$-0.209044\pi$
$971$	−4.13629	−	7.16427i	−0.132740	−	0.229912i	−0.924732	+	0.380619i	$0.875711\pi$
$972$		0			0
$973$	−18.3102	−	25.6768i	−0.586997	−	0.823159i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.37473			−0.235938			−0.117969	−	0.993017i	$-0.537638\pi$
$977$	−7.37473			−0.235938			−0.117969	+	0.993017i	$0.537638\pi$
$978$		0			0
$979$	−5.72312	+	9.91273i	−0.182912	+	0.316812i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.39181	+	4.14274i	0.0762870	+	0.132133i	0.901645	−	0.432476i	$-0.142360\pi$
$983$	2.39181	+	4.14274i	0.0762870	+	0.132133i	−0.825358	+	0.564609i	$0.809027\pi$
$984$		0			0
$985$	−4.05029	+	7.01530i	−0.129053	+	0.223526i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.3400	+	26.5697i	0.487784	+	0.844866i
$990$		0			0
$991$	−18.4932	+	32.0312i	−0.587456	+	1.01750i	0.407108	+	0.913380i	$0.366537\pi$
$991$	−18.4932	+	32.0312i	−0.587456	+	1.01750i	−0.994564	+	0.104124i	$0.966796\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.56430	−	6.17356i	−0.112996	−	0.195715i
$996$		0			0
$997$	−24.3285	−	42.1382i	−0.770491	−	1.33453i	−0.937294	−	0.348539i	$-0.886678\pi$
$997$	−24.3285	−	42.1382i	−0.770491	−	1.33453i	0.166803	−	0.985990i	$-0.446656\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.k.2881.7		22
3.2	odd	2		1008.2.q.k.529.8		22
4.3	odd	2		1512.2.q.c.1369.7		22
7.2	even	3		3024.2.t.l.289.5		22
9.4	even	3		3024.2.t.l.1873.5		22
9.5	odd	6		1008.2.t.k.193.1		22
12.11	even	2		504.2.q.d.25.4	✓	22
21.2	odd	6		1008.2.t.k.961.1		22
28.23	odd	6		1512.2.t.d.289.5		22
36.23	even	6		504.2.t.d.193.11	yes	22
36.31	odd	6		1512.2.t.d.361.5		22
63.23	odd	6		1008.2.q.k.625.8		22
63.58	even	3	inner	3024.2.q.k.2305.7		22
84.23	even	6		504.2.t.d.457.11	yes	22
252.23	even	6		504.2.q.d.121.4	yes	22
252.247	odd	6		1512.2.q.c.793.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.4	✓	22	12.11	even	2
504.2.q.d.121.4	yes	22	252.23	even	6
504.2.t.d.193.11	yes	22	36.23	even	6
504.2.t.d.457.11	yes	22	84.23	even	6
1008.2.q.k.529.8		22	3.2	odd	2
1008.2.q.k.625.8		22	63.23	odd	6
1008.2.t.k.193.1		22	9.5	odd	6
1008.2.t.k.961.1		22	21.2	odd	6
1512.2.q.c.793.7		22	252.247	odd	6
1512.2.q.c.1369.7		22	4.3	odd	2
1512.2.t.d.289.5		22	28.23	odd	6
1512.2.t.d.361.5		22	36.31	odd	6
3024.2.q.k.2305.7		22	63.58	even	3	inner
3024.2.q.k.2881.7		22	1.1	even	1	trivial
3024.2.t.l.289.5		22	7.2	even	3
3024.2.t.l.1873.5		22	9.4	even	3

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.170100 - 0.294622i) q^{5} +(2.63360 - 0.253251i) q^{7} +O(q^{10})\)	\(q+(0.170100 - 0.294622i) q^{5} +(2.63360 - 0.253251i) q^{7} +(0.335794 + 0.581612i) q^{11} +(1.62370 + 2.81233i) q^{13} +(1.10014 - 1.90550i) q^{17} +(-0.242085 - 0.419303i) q^{19} +(-2.09495 + 3.62856i) q^{23} +(2.44213 + 4.22990i) q^{25} +(-0.478868 + 0.829424i) q^{29} -2.08263 q^{31} +(0.373363 - 0.818995i) q^{35} +(4.81613 + 8.34178i) q^{37} +(3.90207 + 6.75858i) q^{41} +(3.66119 - 6.34136i) q^{43} -2.69901 q^{47} +(6.87173 - 1.33392i) q^{49} +(6.12335 - 10.6059i) q^{53} +0.228474 q^{55} -4.94297 q^{59} -3.52119 q^{61} +1.10477 q^{65} -12.3202 q^{67} -5.57304 q^{71} +(-3.71686 + 6.43779i) q^{73} +(1.03164 + 1.44669i) q^{77} +10.0127 q^{79} +(2.47376 - 4.28468i) q^{83} +(-0.374269 - 0.648252i) q^{85} +(8.52177 + 14.7601i) q^{89} +(4.98840 + 6.99536i) q^{91} -0.164714 q^{95} +(4.23657 - 7.33795i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 + 5 * q^7	\( 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

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