LMFDB - Embedded newform 3024.2.q.a.2881.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(2305,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,0,0,0,-3,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.a.2305.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} +(1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.50000 + 2.59808i) q^{29} +4.00000 q^{31} +(1.50000 + 7.79423i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-4.50000 - 7.79423i) q^{41} +(5.50000 - 9.52628i) q^{43} +(1.00000 - 6.92820i) q^{49} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +12.0000 q^{59} +2.00000 q^{61} +15.0000 q^{65} +4.00000 q^{67} +(-5.50000 + 9.52628i) q^{73} +(7.50000 + 2.59808i) q^{77} -8.00000 q^{79} +(-1.50000 + 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} +(7.50000 + 12.9904i) q^{89} +(-12.5000 - 4.33013i) q^{91} -15.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} + 4 q^{7} + 3 q^{11} - 5 q^{13} + 3 q^{17} + 5 q^{19} + 3 q^{23} - 4 q^{25} - 3 q^{29} + 8 q^{31} + 3 q^{35} + 7 q^{37} - 9 q^{41} + 11 q^{43} + 2 q^{49} - 3 q^{53} - 18 q^{55} + 24 q^{59}+ \cdots + q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 + 4 * q^7 + 3 * q^11 - 5 * q^13 + 3 * q^17 + 5 * q^19 + 3 * q^23 - 4 * q^25 - 3 * q^29 + 8 * q^31 + 3 * q^35 + 7 * q^37 - 9 * q^41 + 11 * q^43 + 2 * q^49 - 3 * q^53 - 18 * q^55 + 24 * q^59 + 4 * q^61 + 30 * q^65 + 8 * q^67 - 11 * q^73 + 15 * q^77 - 16 * q^79 - 3 * q^83 + 9 * q^85 + 15 * q^89 - 25 * q^91 - 30 * q^95 + q^97

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
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	+	7.79423i	0.253546	+	1.31747i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	−0.0522047	−	0.998636i	$-0.516625\pi$
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	0.890947	−	0.454108i	$-0.150042\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$		0			0
$58$		0			0
$59$	12.0000			1.56227			0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000			1.56227			0.781133	+	0.624364i	$0.214642\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	15.0000			1.86052
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.50000	+	2.59808i	0.854704	+	0.296078i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$		0			0
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		0			0
$91$	−12.5000	−	4.33013i	−1.31036	−	0.453921i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−15.0000			−1.53897
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	−0.716173	−	0.697923i	$-0.754108\pi$
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	0.962505	+	0.271263i	$0.0874412\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	0.958952	+	0.283567i	$0.0915178\pi$
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	−0.233900	+	0.972261i	$0.575149\pi$
$108$		0			0
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.50000	−	7.79423i	−0.137505	−	0.714496i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$	12.5000	+	4.33013i	1.08389	+	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	0.998228	−	0.0595022i	$-0.0189513\pi$
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	−0.550645	+	0.834740i	$0.685618\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$		0			0
$163$	8.50000	+	14.7224i	0.665771	+	1.15315i	0.979076	+	0.203497i	$0.0652307\pi$
$163$	8.50000	+	14.7224i	0.665771	+	1.15315i	−0.313304	+	0.949653i	$0.601436\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	0.802135	−	0.597143i	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−21.0000			−1.54395
$186$		0			0
$187$	9.00000			0.658145
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	−0.963001	−	0.269498i	$-0.913142\pi$
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	0.714893	+	0.699234i	$0.246476\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$		0			0
$205$	27.0000			1.88576
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	16.5000	+	28.5788i	1.12529	+	1.94906i
$216$		0			0
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−15.0000			−1.00901
$222$		0			0
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	−0.427443	−	0.904042i	$-0.640586\pi$
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	0.996645	−	0.0818447i	$-0.0260811\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$		0			0
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	0.435653	+	0.900115i	$0.356518\pi$
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	−0.997349	+	0.0727709i	$0.976816\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.5000	+	23.3827i	0.884414	+	1.53185i	0.846383	+	0.532574i	$0.178775\pi$
$233$	13.5000	+	23.3827i	0.884414	+	1.53185i	0.0380310	+	0.999277i	$0.487891\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.858623	−	0.512607i	$-0.828680\pi$
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.0146191	−	0.999893i	$-0.504654\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	16.5000	+	12.9904i	1.05415	+	0.829925i
$246$		0			0
$247$	12.5000	−	21.6506i	0.795356	−	1.37760i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$	17.5000	+	6.06218i	1.08740	+	0.376685i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	−6.50000	−	11.2583i	−0.394847	−	0.683895i	0.598235	−	0.801321i	$-0.295869\pi$
$271$	−6.50000	−	11.2583i	−0.394847	−	0.683895i	−0.993082	+	0.117426i	$0.962536\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	−8.00000			−0.475551			−0.237775	−	0.971320i	$-0.576418\pi$
$283$	−8.00000			−0.475551			−0.237775	+	0.971320i	$0.576418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.5000	−	7.79423i	−1.32813	−	0.460079i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$		0			0
$295$	−18.0000	+	31.1769i	−1.04800	+	1.81519i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.0000			−0.867472
$300$		0			0
$301$	−5.50000	−	28.5788i	−0.317015	−	1.64726i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$		0			0
$319$	−9.00000			−0.503903
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.0000			0.834622
$324$		0			0
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	0.974701	+	0.223513i	$0.0717525\pi$
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	−0.293783	+	0.955872i	$0.594914\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		0			0
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	0.852680	−	0.522433i	$-0.174975\pi$
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	−0.878780	+	0.477227i	$0.841642\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.50000	+	7.79423i	0.0778761	+	0.404656i
$372$		0			0
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	−0.997697	−	0.0678218i	$-0.978395\pi$
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	0.557584	+	0.830120i	$0.311728\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	−18.0000	+	15.5885i	−0.917365	+	0.794461i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$		0			0
$391$	−4.50000	−	7.79423i	−0.227575	−	0.394171i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.0000	−	20.7846i	0.603786	−	1.04579i
$396$		0			0
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	−0.957839	−	0.287307i	$-0.907240\pi$
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	0.230105	−	0.973166i	$-0.426093\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$		0			0
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0000	−	20.7846i	1.18096	−	1.02274i
$414$		0			0
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	0.900337	−	0.435194i	$-0.143320\pi$
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	−0.827057	+	0.562118i	$0.809987\pi$
$420$		0			0
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	−0.189740	−	0.981834i	$-0.560764\pi$
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	0.945163	−	0.326598i	$-0.105902\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.0000			−0.582086
$426$		0			0
$427$	4.00000	−	3.46410i	0.193574	−	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.0000			0.717547
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−45.0000			−2.13320
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	13.5000	−	23.3827i	0.635690	−	1.10105i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	30.0000	−	25.9808i	1.40642	−	1.21800i
$456$		0			0
$457$	−34.0000			−1.59045			−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000			−1.59045			−0.795226	+	0.606313i	$0.792648\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	17.5000	+	30.3109i	0.813294	+	1.40867i	0.910546	+	0.413407i	$0.135661\pi$
$463$	17.5000	+	30.3109i	0.813294	+	1.40867i	−0.0972525	+	0.995260i	$0.531005\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$		0			0
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	33.0000			1.51734
$474$		0			0
$475$	10.0000	−	17.3205i	0.458831	−	0.794719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	0.950327	−	0.311253i	$-0.100749\pi$
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	−0.744717	+	0.667381i	$0.767415\pi$
$480$		0			0
$481$	17.5000	−	30.3109i	0.797931	−	1.38206i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.50000	+	2.59808i	0.0681115	+	0.117973i
$486$		0			0
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.851314	+	0.524656i	$0.175806\pi$
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.0287085	+	0.999588i	$0.490861\pi$
$492$		0			0
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	0.962472	+	0.271380i	$0.0874801\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	0.394684	+	0.918817i	$0.370854\pi$
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	−0.993061	+	0.117602i	$0.962479\pi$
$510$		0			0
$511$	5.50000	+	28.5788i	0.243306	+	1.26425i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.50000	+	12.9904i	0.330489	+	0.572425i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$		0			0
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	0.779301	−	0.626650i	$-0.215574\pi$
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	−0.932345	+	0.361569i	$0.882241\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−22.5000	+	38.9711i	−0.974583	+	1.68803i
$534$		0			0
$535$	−45.0000			−1.94552
$536$		0			0
$537$		0			0
$538$		0			0
$539$	19.5000	−	7.79423i	0.839924	−	0.335721i
$540$		0			0
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.5000	+	18.1865i	0.449771	+	0.779026i
$546$		0			0
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	−0.724157	−	0.689635i	$-0.757771\pi$
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	0.959320	+	0.282321i	$0.0911043\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−15.0000			−0.639021
$552$		0			0
$553$	−16.0000	+	13.8564i	−0.680389	+	0.589234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	−0.896053	−	0.443947i	$-0.853578\pi$
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	0.832496	+	0.554031i	$0.186911\pi$
$558$		0			0
$559$	−55.0000			−2.32625
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−45.0000			−1.89316
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$		0			0
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.50000	+	7.79423i	0.0622305	+	0.323359i
$582$		0			0
$583$	−9.00000			−0.372742
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	0.565792	−	0.824548i	$-0.308570\pi$
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	−0.996976	+	0.0777165i	$0.975237\pi$
$594$		0			0
$595$	22.5000	+	7.79423i	0.922410	+	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	−21.5000	+	37.2391i	−0.872658	+	1.51149i	−0.0134214	+	0.999910i	$0.504272\pi$
$607$	−21.5000	+	37.2391i	−0.872658	+	1.51149i	−0.859237	+	0.511578i	$0.829061\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	0.609488	−	0.792796i	$-0.291375\pi$
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	−0.991325	+	0.131434i	$0.958042\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	37.5000	+	12.9904i	1.50241	+	0.520449i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−24.0000	+	41.5692i	−0.952411	+	1.64962i
$636$		0			0
$637$	−32.5000	+	12.9904i	−1.28770	+	0.514698i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$		0			0
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	0.996379	+	0.0850262i	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$		0			0
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$		0			0
$655$	−4.50000	−	7.79423i	−0.175830	−	0.304546i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	0.183436	+	0.983032i	$0.441278\pi$
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	−0.943049	+	0.332655i	$0.892055\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−30.0000	+	25.9808i	−1.16335	+	1.00749i
$666$		0			0
$667$	4.50000	+	7.79423i	0.174241	+	0.301794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$		0			0
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	−0.500000	−	2.59808i	−0.0191882	−	0.0997050i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	−0.355920	−	0.934516i	$-0.615832\pi$
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	0.987275	−	0.159022i	$-0.0508342\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$		0			0
$688$		0			0
$689$	15.0000			0.571454
$690$		0			0
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.0000			−0.568982
$696$		0			0
$697$	−27.0000			−1.02270
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	−17.5000	+	30.3109i	−0.660025	+	1.14320i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.50000	−	2.59808i	−0.282067	−	0.0977107i
$708$		0			0
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	22.5000	+	38.9711i	0.841452	+	1.45744i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	−0.958051	−	0.286599i	$-0.907475\pi$
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	0.230823	−	0.972996i	$-0.425858\pi$
$720$		0			0
$721$	−2.50000	−	12.9904i	−0.0931049	−	0.483787i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	12.0000			0.445669
$726$		0			0
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	0.908655	+	0.417548i	$0.137111\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.5000	−	28.5788i	−0.610275	−	1.05703i
$732$		0			0
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$		0			0
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	−0.00311943	−	0.999995i	$-0.500993\pi$
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	0.867581	−	0.497296i	$-0.165674\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	0.837198	−	0.546899i	$-0.184192\pi$
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	−0.892228	+	0.451585i	$0.850859\pi$
$744$		0			0
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	37.5000	+	12.9904i	1.37022	+	0.474658i
$750$		0			0
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	−0.470311	−	0.882501i	$-0.655858\pi$
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	0.999424	−	0.0339490i	$-0.0108084\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.0000			−1.20099
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		0			0
$763$	−3.50000	−	18.1865i	−0.126709	−	0.658397i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−30.0000	−	51.9615i	−1.08324	−	1.87622i
$768$		0			0
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$		0			0
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	22.5000	−	38.9711i	0.806146	−	1.39629i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−21.0000	+	36.3731i	−0.749522	+	1.29821i
$786$		0			0
$787$	−44.0000			−1.56843			−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000			−1.56843			−0.784215	+	0.620489i	$0.786934\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	37.5000	+	12.9904i	1.33335	+	0.461885i
$792$		0			0
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−33.0000			−1.16454
$804$		0			0
$805$	22.5000	+	7.79423i	0.793021	+	0.274710i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	−0.287670	−	0.957730i	$-0.592880\pi$
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	0.973253	−	0.229736i	$-0.0737862\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−51.0000			−1.78645
$816$		0			0
$817$	55.0000			1.92421
$818$		0			0
$819$		0			0
$820$		0			0
$821$	54.0000			1.88461			0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000			1.88461			0.942306	+	0.334751i	$0.108652\pi$
$822$		0			0
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$	9.00000			0.311458
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	−0.303773	−	0.952745i	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$	−1.00000	−	5.19615i	−0.0343604	−	0.178542i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	21.0000			0.719871
$852$		0			0
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	−0.974055	−	0.226313i	$-0.927333\pi$
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	0.683020	+	0.730400i	$0.260666\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	5.50000	−	9.52628i	0.187658	−	0.325032i	−0.756811	−	0.653633i	$-0.773244\pi$
$859$	5.50000	−	9.52628i	0.187658	−	0.325032i	0.944469	+	0.328601i	$0.106577\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	0.709675	−	0.704529i	$-0.248842\pi$
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	−0.964978	+	0.262332i	$0.915509\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.00000	+	5.19615i	−0.202837	+	0.175662i
$876$		0			0
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	−0.232556	−	0.972583i	$-0.574709\pi$
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	0.958560	−	0.284892i	$-0.0919577\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.5000	−	33.7750i	0.654746	−	1.13405i	−0.327212	−	0.944951i	$-0.606109\pi$
$887$	19.5000	−	33.7750i	0.654746	−	1.13405i	0.981957	−	0.189102i	$-0.0605577\pi$
$888$		0			0
$889$	32.0000	−	27.7128i	1.07325	−	0.929458i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−4.50000	−	7.79423i	−0.150418	−	0.260532i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	4.50000	+	7.79423i	0.149917	+	0.259663i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.0000	−	25.9808i	0.498617	−	0.863630i
$906$		0			0
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	0.971936	−	0.235247i	$-0.0755899\pi$
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	−0.689698	+	0.724097i	$0.742257\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.50000	+	7.79423i	−0.149092	+	0.258234i	−0.930892	−	0.365295i	$-0.880968\pi$
$911$	−4.50000	+	7.79423i	−0.149092	+	0.258234i	0.781800	+	0.623529i	$0.214302\pi$
$912$		0			0
$913$	−9.00000			−0.297857
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.50000	+	7.79423i	0.0495344	+	0.257388i
$918$		0			0
$919$	−0.500000	−	0.866025i	−0.0164935	−	0.0285675i	0.857661	−	0.514216i	$-0.171917\pi$
$919$	−0.500000	−	0.866025i	−0.0164935	−	0.0285675i	−0.874154	+	0.485648i	$0.838584\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	14.0000	−	24.2487i	0.460317	−	0.797293i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$		0			0
$931$	32.5000	−	12.9904i	1.06514	−	0.425743i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−13.5000	+	23.3827i	−0.441497	+	0.764696i
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−54.0000			−1.76035			−0.880175	−	0.474650i	$-0.842575\pi$
$941$	−54.0000			−1.76035			−0.880175	+	0.474650i	$0.842575\pi$
$942$		0			0
$943$	−27.0000			−0.879241
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$		0			0
$949$	55.0000			1.78538
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.50000	+	2.59808i	0.242188	+	0.0838963i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$		0			0
$967$	−24.5000	−	42.4352i	−0.787867	−	1.36463i	−0.927271	−	0.374390i	$-0.877852\pi$
$967$	−24.5000	−	42.4352i	−0.787867	−	1.36463i	0.139404	−	0.990236i	$-0.455481\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	0.997150	−	0.0754473i	$-0.0240385\pi$
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	−0.563914	+	0.825833i	$0.690705\pi$
$972$		0			0
$973$	12.5000	+	4.33013i	0.400732	+	0.138817i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.00000			−0.191957			−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000			−0.191957			−0.0959785	+	0.995383i	$0.530598\pi$
$978$		0			0
$979$	−22.5000	+	38.9711i	−0.719103	+	1.24552i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	0.983465	−	0.181097i	$-0.0579648\pi$
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	−0.648567	+	0.761157i	$0.724631\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.5000	−	28.5788i	−0.524669	−	0.908754i
$990$		0			0
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	−0.538384	−	0.842700i	$-0.680965\pi$
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	0.998991	+	0.0449040i	$0.0142982\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.5000	−	18.1865i	−0.332872	−	0.576552i
$996$		0			0
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.a.2881.1		2
3.2	odd	2		1008.2.q.e.529.1		2
4.3	odd	2		378.2.e.a.235.1		2
7.2	even	3		3024.2.t.f.289.1		2
9.4	even	3		3024.2.t.f.1873.1		2
9.5	odd	6		1008.2.t.c.193.1		2
12.11	even	2		126.2.e.b.25.1	✓	2
21.2	odd	6		1008.2.t.c.961.1		2
28.3	even	6		2646.2.f.i.883.1		2
28.11	odd	6		2646.2.f.e.883.1		2
28.19	even	6		2646.2.h.f.667.1		2
28.23	odd	6		378.2.h.b.289.1		2
28.27	even	2		2646.2.e.e.2125.1		2
36.7	odd	6		1134.2.g.f.487.1		2
36.11	even	6		1134.2.g.d.487.1		2
36.23	even	6		126.2.h.a.67.1	yes	2
36.31	odd	6		378.2.h.b.361.1		2
63.23	odd	6		1008.2.q.e.625.1		2
63.58	even	3	inner	3024.2.q.a.2305.1		2
84.11	even	6		882.2.f.e.295.1		2
84.23	even	6		126.2.h.a.79.1	yes	2
84.47	odd	6		882.2.h.e.79.1		2
84.59	odd	6		882.2.f.a.295.1		2
84.83	odd	2		882.2.e.h.655.1		2
252.11	even	6		7938.2.a.r.1.1		1
252.23	even	6		126.2.e.b.121.1	yes	2
252.31	even	6		2646.2.f.i.1765.1		2
252.59	odd	6		882.2.f.a.589.1		2
252.67	odd	6		2646.2.f.e.1765.1		2
252.79	odd	6		1134.2.g.f.163.1		2
252.95	even	6		882.2.f.e.589.1		2
252.103	even	6		2646.2.e.e.1549.1		2
252.115	even	6		7938.2.a.c.1.1		1
252.131	odd	6		882.2.e.h.373.1		2
252.139	even	6		2646.2.h.f.361.1		2
252.151	odd	6		7938.2.a.o.1.1		1
252.167	odd	6		882.2.h.e.67.1		2
252.191	even	6		1134.2.g.d.163.1		2
252.227	odd	6		7938.2.a.bd.1.1		1
252.247	odd	6		378.2.e.a.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	12.11	even	2
126.2.e.b.121.1	yes	2	252.23	even	6
126.2.h.a.67.1	yes	2	36.23	even	6
126.2.h.a.79.1	yes	2	84.23	even	6
378.2.e.a.37.1		2	252.247	odd	6
378.2.e.a.235.1		2	4.3	odd	2
378.2.h.b.289.1		2	28.23	odd	6
378.2.h.b.361.1		2	36.31	odd	6
882.2.e.h.373.1		2	252.131	odd	6
882.2.e.h.655.1		2	84.83	odd	2
882.2.f.a.295.1		2	84.59	odd	6
882.2.f.a.589.1		2	252.59	odd	6
882.2.f.e.295.1		2	84.11	even	6
882.2.f.e.589.1		2	252.95	even	6
882.2.h.e.67.1		2	252.167	odd	6
882.2.h.e.79.1		2	84.47	odd	6
1008.2.q.e.529.1		2	3.2	odd	2
1008.2.q.e.625.1		2	63.23	odd	6
1008.2.t.c.193.1		2	9.5	odd	6
1008.2.t.c.961.1		2	21.2	odd	6
1134.2.g.d.163.1		2	252.191	even	6
1134.2.g.d.487.1		2	36.11	even	6
1134.2.g.f.163.1		2	252.79	odd	6
1134.2.g.f.487.1		2	36.7	odd	6
2646.2.e.e.1549.1		2	252.103	even	6
2646.2.e.e.2125.1		2	28.27	even	2
2646.2.f.e.883.1		2	28.11	odd	6
2646.2.f.e.1765.1		2	252.67	odd	6
2646.2.f.i.883.1		2	28.3	even	6
2646.2.f.i.1765.1		2	252.31	even	6
2646.2.h.f.361.1		2	252.139	even	6
2646.2.h.f.667.1		2	28.19	even	6
3024.2.q.a.2305.1		2	63.58	even	3	inner
3024.2.q.a.2881.1		2	1.1	even	1	trivial
3024.2.t.f.289.1		2	7.2	even	3
3024.2.t.f.1873.1		2	9.4	even	3
7938.2.a.c.1.1		1	252.115	even	6
7938.2.a.o.1.1		1	252.151	odd	6
7938.2.a.r.1.1		1	252.11	even	6
7938.2.a.bd.1.1		1	252.227	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} +(1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.50000 + 2.59808i) q^{29} +4.00000 q^{31} +(1.50000 + 7.79423i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-4.50000 - 7.79423i) q^{41} +(5.50000 - 9.52628i) q^{43} +(1.00000 - 6.92820i) q^{49} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +12.0000 q^{59} +2.00000 q^{61} +15.0000 q^{65} +4.00000 q^{67} +(-5.50000 + 9.52628i) q^{73} +(7.50000 + 2.59808i) q^{77} -8.00000 q^{79} +(-1.50000 + 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} +(7.50000 + 12.9904i) q^{89} +(-12.5000 - 4.33013i) q^{91} -15.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} + 4 q^{7} + 3 q^{11} - 5 q^{13} + 3 q^{17} + 5 q^{19} + 3 q^{23} - 4 q^{25} - 3 q^{29} + 8 q^{31} + 3 q^{35} + 7 q^{37} - 9 q^{41} + 11 q^{43} + 2 q^{49} - 3 q^{53} - 18 q^{55} + 24 q^{59}+ \cdots + q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 + 4 * q^7 + 3 * q^11 - 5 * q^13 + 3 * q^17 + 5 * q^19 + 3 * q^23 - 4 * q^25 - 3 * q^29 + 8 * q^31 + 3 * q^35 + 7 * q^37 - 9 * q^41 + 11 * q^43 + 2 * q^49 - 3 * q^53 - 18 * q^55 + 24 * q^59 + 4 * q^61 + 30 * q^65 + 8 * q^67 - 11 * q^73 + 15 * q^77 - 16 * q^79 - 3 * q^83 + 9 * q^85 + 15 * q^89 - 25 * q^91 - 30 * q^95 + q^97

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