LMFDB - Embedded newform 1512.2.t.c.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (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:	$12.0733807856$
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			361.4
Character	$\chi$	$=$	1512.361
Dual form			1512.2.t.c.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10440 q^{5} +(-1.78475 + 1.95312i) q^{7} +O(q^{10})$	$q-2.10440 q^{5} +(-1.78475 + 1.95312i) q^{7} -0.399064 q^{11} +(1.44292 - 2.49921i) q^{13} +(0.176596 - 0.305873i) q^{17} +(2.84888 + 4.93440i) q^{19} +0.877364 q^{23} -0.571513 q^{25} +(-0.874997 - 1.51554i) q^{29} +(-4.56745 - 7.91106i) q^{31} +(3.75582 - 4.11014i) q^{35} +(-3.39555 - 5.88127i) q^{37} +(-1.20377 + 2.08499i) q^{41} +(0.276745 + 0.479336i) q^{43} +(5.86859 - 10.1647i) q^{47} +(-0.629343 - 6.97165i) q^{49} +(2.07821 - 3.59956i) q^{53} +0.839790 q^{55} +(-4.66210 - 8.07500i) q^{59} +(5.03601 - 8.72262i) q^{61} +(-3.03648 + 5.25934i) q^{65} +(-0.601204 - 1.04132i) q^{67} +14.6826 q^{71} +(0.315636 - 0.546697i) q^{73} +(0.712229 - 0.779420i) q^{77} +(1.24364 - 2.15406i) q^{79} +(4.59366 + 7.95645i) q^{83} +(-0.371628 + 0.643678i) q^{85} +(-7.29358 - 12.6328i) q^{89} +(2.30601 + 7.27866i) q^{91} +(-5.99517 - 10.3839i) q^{95} +(-7.84245 - 13.5835i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.10440			−0.941115			−0.470558	−	0.882369i	$-0.655947\pi$
$5$	−2.10440			−0.941115			−0.470558	+	0.882369i	$0.655947\pi$
$6$		0			0
$7$	−1.78475	+	1.95312i	−0.674572	+	0.738209i
$7$	−1.78475	+	1.95312i	−0.674572	+	0.738209i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.399064			−0.120322			−0.0601612	−	0.998189i	$-0.519161\pi$
$11$	−0.399064			−0.120322			−0.0601612	+	0.998189i	$0.519161\pi$
$12$		0			0
$13$	1.44292	−	2.49921i	0.400194	−	0.693157i	−0.593555	−	0.804794i	$-0.702276\pi$
$13$	1.44292	−	2.49921i	0.400194	−	0.693157i	0.993749	+	0.111637i	$0.0356093\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.176596	−	0.305873i	0.0428308	−	0.0741851i	−0.843815	−	0.536634i	$-0.819696\pi$
$17$	0.176596	−	0.305873i	0.0428308	−	0.0741851i	0.886646	+	0.462449i	$0.153029\pi$
$18$		0			0
$19$	2.84888	+	4.93440i	0.653578	+	1.13203i	0.982248	+	0.187585i	$0.0600661\pi$
$19$	2.84888	+	4.93440i	0.653578	+	1.13203i	−0.328670	+	0.944445i	$0.606601\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.877364			0.182943			0.0914716	−	0.995808i	$-0.470843\pi$
$23$	0.877364			0.182943			0.0914716	+	0.995808i	$0.470843\pi$
$24$		0			0
$25$	−0.571513			−0.114303
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.874997	−	1.51554i	−0.162483	−	0.281429i	0.773276	−	0.634070i	$-0.218617\pi$
$29$	−0.874997	−	1.51554i	−0.162483	−	0.281429i	−0.935759	+	0.352641i	$0.885284\pi$
$30$		0			0
$31$	−4.56745	−	7.91106i	−0.820339	−	1.42087i	−0.905430	−	0.424495i	$-0.860452\pi$
$31$	−4.56745	−	7.91106i	−0.820339	−	1.42087i	0.0850916	−	0.996373i	$-0.472882\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.75582	−	4.11014i	0.634850	−	0.694740i
$36$		0			0
$37$	−3.39555	−	5.88127i	−0.558225	−	0.966874i	−0.997645	−	0.0685922i	$-0.978149\pi$
$37$	−3.39555	−	5.88127i	−0.558225	−	0.966874i	0.439420	−	0.898282i	$-0.355184\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.20377	+	2.08499i	−0.187997	+	0.325621i	−0.944582	−	0.328274i	$-0.893533\pi$
$41$	−1.20377	+	2.08499i	−0.187997	+	0.325621i	0.756585	+	0.653895i	$0.226866\pi$
$42$		0			0
$43$	0.276745	+	0.479336i	0.0422032	+	0.0730981i	0.886355	−	0.463005i	$-0.153229\pi$
$43$	0.276745	+	0.479336i	0.0422032	+	0.0730981i	−0.844152	+	0.536104i	$0.819896\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.86859	−	10.1647i	0.856023	−	1.48267i	−0.0196707	−	0.999807i	$-0.506262\pi$
$47$	5.86859	−	10.1647i	0.856023	−	1.48267i	0.875693	−	0.482868i	$-0.160405\pi$
$48$		0			0
$49$	−0.629343	−	6.97165i	−0.0899061	−	0.995950i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.07821	−	3.59956i	0.285464	−	0.494437i	−0.687258	−	0.726413i	$-0.741186\pi$
$53$	2.07821	−	3.59956i	0.285464	−	0.494437i	0.972721	+	0.231976i	$0.0745191\pi$
$54$		0			0
$55$	0.839790			0.113237
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.66210	−	8.07500i	−0.606954	−	1.05128i	−0.991739	−	0.128269i	$-0.959058\pi$
$59$	−4.66210	−	8.07500i	−0.606954	−	1.05128i	0.384785	−	0.923006i	$-0.374276\pi$
$60$		0			0
$61$	5.03601	−	8.72262i	0.644795	−	1.11682i	−0.339554	−	0.940586i	$-0.610276\pi$
$61$	5.03601	−	8.72262i	0.644795	−	1.11682i	0.984349	−	0.176231i	$-0.0563905\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.03648	+	5.25934i	−0.376629	+	0.652340i
$66$		0			0
$67$	−0.601204	−	1.04132i	−0.0734488	−	0.127217i	0.826962	−	0.562258i	$-0.190067\pi$
$67$	−0.601204	−	1.04132i	−0.0734488	−	0.127217i	−0.900411	+	0.435041i	$0.856734\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	14.6826			1.74250			0.871250	−	0.490840i	$-0.163310\pi$
$71$	14.6826			1.74250			0.871250	+	0.490840i	$0.163310\pi$
$72$		0			0
$73$	0.315636	−	0.546697i	0.0369423	−	0.0639860i	−0.846963	−	0.531652i	$-0.821572\pi$
$73$	0.315636	−	0.546697i	0.0369423	−	0.0639860i	0.883905	+	0.467666i	$0.154905\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.712229	−	0.779420i	0.0811661	−	0.0888231i
$78$		0			0
$79$	1.24364	−	2.15406i	0.139921	−	0.242350i	−0.787546	−	0.616256i	$-0.788648\pi$
$79$	1.24364	−	2.15406i	0.139921	−	0.242350i	0.927467	+	0.373906i	$0.121982\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.59366	+	7.95645i	0.504219	+	0.873333i	0.999988	+	0.00487885i	$0.00155299\pi$
$83$	4.59366	+	7.95645i	0.504219	+	0.873333i	−0.495769	+	0.868455i	$0.665114\pi$
$84$		0			0
$85$	−0.371628	+	0.643678i	−0.0403087	+	0.0698167i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.29358	−	12.6328i	−0.773118	−	1.33908i	−0.935846	−	0.352408i	$-0.885363\pi$
$89$	−7.29358	−	12.6328i	−0.773118	−	1.33908i	0.162729	−	0.986671i	$-0.447971\pi$
$90$		0			0
$91$	2.30601	+	7.27866i	0.241735	+	0.763011i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.99517	−	10.3839i	−0.615092	−	1.06537i
$96$		0			0
$97$	−7.84245	−	13.5835i	−0.796280	−	1.37920i	−0.922023	−	0.387134i	$-0.873465\pi$
$97$	−7.84245	−	13.5835i	−0.796280	−	1.37920i	0.125744	−	0.992063i	$-0.459868\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.0928571			0.00923962			0.00461981	−	0.999989i	$-0.498529\pi$
$101$	0.0928571			0.00923962			0.00461981	+	0.999989i	$0.498529\pi$
$102$		0			0
$103$	−19.9154			−1.96232			−0.981161	−	0.193193i	$-0.938116\pi$
$103$	−19.9154			−1.96232			−0.981161	+	0.193193i	$0.938116\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.89225	+	5.00953i	0.279605	+	0.484290i	0.971287	−	0.237913i	$-0.0764633\pi$
$107$	2.89225	+	5.00953i	0.279605	+	0.484290i	−0.691682	+	0.722202i	$0.743130\pi$
$108$		0			0
$109$	−6.25516	+	10.8343i	−0.599136	+	1.03773i	0.393813	+	0.919191i	$0.371156\pi$
$109$	−6.25516	+	10.8343i	−0.599136	+	1.03773i	−0.992949	+	0.118543i	$0.962178\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.69411	+	2.93428i	−0.159368	+	0.276034i	−0.934641	−	0.355593i	$-0.884279\pi$
$113$	−1.69411	+	2.93428i	−0.159368	+	0.276034i	0.775273	+	0.631627i	$0.217612\pi$
$114$		0			0
$115$	−1.84632			−0.172171
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.282227	+	0.890819i	0.0258717	+	0.0816613i
$120$		0			0
$121$	−10.8407			−0.985523
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.7247			1.04869
$126$		0			0
$127$	14.7348			1.30750			0.653752	−	0.756709i	$-0.273194\pi$
$127$	14.7348			1.30750			0.653752	+	0.756709i	$0.273194\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.9078			1.21513			0.607567	−	0.794268i	$-0.292146\pi$
$131$	13.9078			1.21513			0.607567	+	0.794268i	$0.292146\pi$
$132$		0			0
$133$	−14.7220	−	3.24247i	−1.27656	−	0.281158i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.5575			−1.24373			−0.621865	−	0.783124i	$-0.713625\pi$
$137$	−14.5575			−1.24373			−0.621865	+	0.783124i	$0.713625\pi$
$138$		0			0
$139$	−3.63996	+	6.30460i	−0.308737	+	0.534749i	−0.978086	−	0.208199i	$-0.933240\pi$
$139$	−3.63996	+	6.30460i	−0.308737	+	0.534749i	0.669349	+	0.742948i	$0.266573\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.575818	+	0.997347i	−0.0481523	+	0.0834023i
$144$		0			0
$145$	1.84134	+	3.18930i	0.152915	+	0.264857i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.721664			0.0591210			0.0295605	−	0.999563i	$-0.490589\pi$
$149$	0.721664			0.0591210			0.0295605	+	0.999563i	$0.490589\pi$
$150$		0			0
$151$	21.8044			1.77441			0.887207	−	0.461372i	$-0.152643\pi$
$151$	21.8044			1.77441			0.887207	+	0.461372i	$0.152643\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.61173	+	16.6480i	0.772033	+	1.33720i
$156$		0			0
$157$	−2.58986	−	4.48577i	−0.206694	−	0.358004i	0.743977	−	0.668205i	$-0.232937\pi$
$157$	−2.58986	−	4.48577i	−0.206694	−	0.358004i	−0.950671	+	0.310201i	$0.899604\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.56588	+	1.71360i	−0.123408	+	0.135050i
$162$		0			0
$163$	2.63906	+	4.57098i	0.206707	+	0.358027i	0.950675	−	0.310188i	$-0.100392\pi$
$163$	2.63906	+	4.57098i	0.206707	+	0.358027i	−0.743968	+	0.668215i	$0.767059\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.83710	−	11.8422i	0.529071	−	0.916378i	−0.470354	−	0.882478i	$-0.655874\pi$
$167$	6.83710	−	11.8422i	0.529071	−	0.916378i	0.999425	−	0.0339001i	$-0.0107928\pi$
$168$		0			0
$169$	2.33596	+	4.04599i	0.179689	+	0.311230i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.0912	−	17.4784i	0.767218	−	1.32886i	−0.171847	−	0.985124i	$-0.554974\pi$
$173$	10.0912	−	17.4784i	0.767218	−	1.32886i	0.939066	−	0.343738i	$-0.111693\pi$
$174$		0			0
$175$	1.02001	−	1.11623i	0.0771053	−	0.0843792i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.5968	+	21.8183i	−0.941528	+	1.63077i	−0.178971	+	0.983854i	$0.557277\pi$
$179$	−12.5968	+	21.8183i	−0.941528	+	1.63077i	−0.762557	+	0.646921i	$0.776056\pi$
$180$		0			0
$181$	−17.2815			−1.28453			−0.642263	−	0.766485i	$-0.722004\pi$
$181$	−17.2815			−1.28453			−0.642263	+	0.766485i	$0.722004\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.14559	+	12.3765i	0.525354	+	0.909940i
$186$		0			0
$187$	−0.0704731	+	0.122063i	−0.00515350	+	0.00892613i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.50949	+	4.34657i	−0.181580	+	0.314506i	−0.942419	−	0.334435i	$-0.891455\pi$
$191$	−2.50949	+	4.34657i	−0.181580	+	0.314506i	0.760839	+	0.648941i	$0.224788\pi$
$192$		0			0
$193$	2.71882	+	4.70914i	0.195705	+	0.338971i	0.947131	−	0.320846i	$-0.103967\pi$
$193$	2.71882	+	4.70914i	0.195705	+	0.338971i	−0.751426	+	0.659817i	$0.770634\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.95839			−0.424517			−0.212259	−	0.977214i	$-0.568082\pi$
$197$	−5.95839			−0.424517			−0.212259	+	0.977214i	$0.568082\pi$
$198$		0			0
$199$	5.62062	−	9.73520i	0.398435	−	0.690110i	−0.595098	−	0.803653i	$-0.702887\pi$
$199$	5.62062	−	9.73520i	0.398435	−	0.690110i	0.993533	+	0.113543i	$0.0362200\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.52168	+	0.995884i	0.317360	+	0.0698974i
$204$		0			0
$205$	2.53321	−	4.38765i	0.176927	−	0.306447i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.13689	−	1.96914i	−0.0786401	−	0.136209i
$210$		0			0
$211$	0.381084	−	0.660057i	0.0262349	−	0.0454402i	−0.852610	−	0.522548i	$-0.824982\pi$
$211$	0.381084	−	0.660057i	0.0262349	−	0.0454402i	0.878845	+	0.477108i	$0.158315\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.582381	−	1.00871i	−0.0397181	−	0.0687937i
$216$		0			0
$217$	23.6030	+	5.19848i	1.60228	+	0.352896i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.509628	−	0.882702i	−0.0342813	−	0.0593769i
$222$		0			0
$223$	−5.80556	−	10.0555i	−0.388769	−	0.673368i	0.603515	−	0.797352i	$-0.293766\pi$
$223$	−5.80556	−	10.0555i	−0.388769	−	0.673368i	−0.992284	+	0.123984i	$0.960433\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.3325			0.685790			0.342895	−	0.939374i	$-0.388592\pi$
$227$	10.3325			0.685790			0.342895	+	0.939374i	$0.388592\pi$
$228$		0			0
$229$	−3.72383			−0.246077			−0.123039	−	0.992402i	$-0.539264\pi$
$229$	−3.72383			−0.246077			−0.123039	+	0.992402i	$0.539264\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.3649	−	23.1488i	−0.875566	−	1.51653i	−0.856158	−	0.516714i	$-0.827155\pi$
$233$	−13.3649	−	23.1488i	−0.875566	−	1.51653i	−0.0194083	−	0.999812i	$-0.506178\pi$
$234$		0			0
$235$	−12.3499	+	21.3906i	−0.805616	+	1.39537i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.94164	+	12.0233i	−0.449018	+	0.777721i	−0.998322	−	0.0579007i	$-0.981559\pi$
$239$	−6.94164	+	12.0233i	−0.449018	+	0.777721i	0.549305	+	0.835622i	$0.314893\pi$
$240$		0			0
$241$	14.9056			0.960154			0.480077	−	0.877226i	$-0.340609\pi$
$241$	14.9056			0.960154			0.480077	+	0.877226i	$0.340609\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.32439	+	14.6711i	0.0846120	+	0.937304i
$246$		0			0
$247$	16.4428			1.04623
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−22.5515			−1.42344			−0.711720	−	0.702464i	$-0.752083\pi$
$251$	−22.5515			−1.42344			−0.711720	+	0.702464i	$0.752083\pi$
$252$		0			0
$253$	−0.350125			−0.0220122
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.8953			−0.742008			−0.371004	−	0.928631i	$-0.620986\pi$
$257$	−11.8953			−0.742008			−0.371004	+	0.928631i	$0.620986\pi$
$258$		0			0
$259$	17.5470	+	3.86467i	1.09032	+	0.240139i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−24.6059			−1.51727			−0.758633	−	0.651518i	$-0.774132\pi$
$263$	−24.6059			−1.51727			−0.758633	+	0.651518i	$0.774132\pi$
$264$		0			0
$265$	−4.37337	+	7.57490i	−0.268654	+	0.465322i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.75722	+	11.7039i	−0.411995	+	0.713597i	−0.995108	−	0.0987947i	$-0.968501\pi$
$269$	−6.75722	+	11.7039i	−0.411995	+	0.713597i	0.583113	+	0.812391i	$0.301835\pi$
$270$		0			0
$271$	−1.34195	−	2.32433i	−0.0815177	−	0.141193i	0.822384	−	0.568932i	$-0.192643\pi$
$271$	−1.34195	−	2.32433i	−0.0815177	−	0.141193i	−0.903902	+	0.427740i	$0.859310\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.228070			0.0137532
$276$		0			0
$277$	19.0524			1.14475			0.572373	−	0.819993i	$-0.306023\pi$
$277$	19.0524			1.14475			0.572373	+	0.819993i	$0.306023\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.2006	−	24.5962i	−0.847139	−	1.46729i	−0.883751	−	0.467958i	$-0.844990\pi$
$281$	−14.2006	−	24.5962i	−0.847139	−	1.46729i	0.0366118	−	0.999330i	$-0.488343\pi$
$282$		0			0
$283$	7.71105	+	13.3559i	0.458374	+	0.793928i	0.998875	−	0.0474156i	$-0.0150985\pi$
$283$	7.71105	+	13.3559i	0.458374	+	0.793928i	−0.540501	+	0.841344i	$0.681765\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.92381	−	6.07230i	−0.113559	−	0.358436i
$288$		0			0
$289$	8.43763	+	14.6144i	0.496331	+	0.859671i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.02253	+	15.6275i	−0.527102	+	0.912967i	0.472399	+	0.881385i	$0.343388\pi$
$293$	−9.02253	+	15.6275i	−0.527102	+	0.912967i	−0.999501	+	0.0315825i	$0.989945\pi$
$294$		0			0
$295$	9.81092	+	16.9930i	0.571214	+	0.989371i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.26597	−	2.19272i	0.0732128	−	0.126808i
$300$		0			0
$301$	−1.43012	−	0.314979i	−0.0824308	−	0.0181551i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.5978	+	18.3559i	−0.606826	+	1.05105i
$306$		0			0
$307$	−7.30860			−0.417124			−0.208562	−	0.978009i	$-0.566878\pi$
$307$	−7.30860			−0.417124			−0.208562	+	0.978009i	$0.566878\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.8896	−	20.5934i	−0.674197	−	1.16774i	−0.976703	−	0.214597i	$-0.931156\pi$
$311$	−11.8896	−	20.5934i	−0.674197	−	1.16774i	0.302505	−	0.953148i	$-0.402177\pi$
$312$		0			0
$313$	9.14534	−	15.8402i	0.516925	−	0.895341i	−0.482882	−	0.875686i	$-0.660410\pi$
$313$	9.14534	−	15.8402i	0.516925	−	0.895341i	0.999807	−	0.0196551i	$-0.00625681\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.34494	+	4.06155i	−0.131705	+	0.228120i	−0.924334	−	0.381585i	$-0.875378\pi$
$317$	−2.34494	+	4.06155i	−0.131705	+	0.228120i	0.792629	+	0.609704i	$0.208712\pi$
$318$		0			0
$319$	0.349180	+	0.604798i	0.0195503	+	0.0338622i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.01240			0.111973
$324$		0			0
$325$	−0.824648	+	1.42833i	−0.0457432	+	0.0792296i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.37890	+	29.6035i	0.517076	+	1.63209i
$330$		0			0
$331$	5.71433	−	9.89751i	0.314088	−	0.544016i	−0.665155	−	0.746705i	$-0.731635\pi$
$331$	5.71433	−	9.89751i	0.314088	−	0.544016i	0.979243	+	0.202689i	$0.0649680\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.26517	+	2.19134i	0.0691238	+	0.119726i
$336$		0			0
$337$	8.74160	−	15.1409i	0.476185	−	0.824777i	−0.523442	−	0.852061i	$-0.675353\pi$
$337$	8.74160	−	15.1409i	0.476185	−	0.824777i	0.999628	+	0.0272840i	$0.00868584\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.82271	+	3.15702i	0.0987051	+	0.170962i
$342$		0			0
$343$	14.7397	+	11.2135i	0.795868	+	0.605470i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.05929	+	12.2270i	0.378962	+	0.656382i	0.990912	−	0.134515i	$-0.0429476\pi$
$347$	7.05929	+	12.2270i	0.378962	+	0.656382i	−0.611949	+	0.790897i	$0.709614\pi$
$348$		0			0
$349$	10.7216	+	18.5704i	0.573916	+	0.994052i	0.996158	+	0.0875692i	$0.0279099\pi$
$349$	10.7216	+	18.5704i	0.573916	+	0.994052i	−0.422242	+	0.906483i	$0.638757\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	31.3760			1.66997			0.834987	−	0.550269i	$-0.185475\pi$
$353$	31.3760			1.66997			0.834987	+	0.550269i	$0.185475\pi$
$354$		0			0
$355$	−30.8979			−1.63989
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.313156	−	0.542402i	−0.0165277	−	0.0286269i	0.857643	−	0.514245i	$-0.171928\pi$
$359$	−0.313156	−	0.542402i	−0.0165277	−	0.0286269i	−0.874171	+	0.485618i	$0.838595\pi$
$360$		0			0
$361$	−6.73223	+	11.6606i	−0.354328	+	0.613714i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.664223	+	1.15047i	−0.0347670	+	0.0602182i
$366$		0			0
$367$	−3.24397			−0.169334			−0.0846670	−	0.996409i	$-0.526983\pi$
$367$	−3.24397			−0.169334			−0.0846670	+	0.996409i	$0.526983\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.32129	+	10.4833i	0.172433	+	0.544265i
$372$		0			0
$373$	−27.6027			−1.42921			−0.714606	−	0.699527i	$-0.753394\pi$
$373$	−27.6027			−1.42921			−0.714606	+	0.699527i	$0.753394\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.05021			−0.260099
$378$		0			0
$379$	−12.7800			−0.656463			−0.328231	−	0.944597i	$-0.606453\pi$
$379$	−12.7800			−0.656463			−0.328231	+	0.944597i	$0.606453\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.16557			0.263948			0.131974	−	0.991253i	$-0.457868\pi$
$383$	5.16557			0.263948			0.131974	+	0.991253i	$0.457868\pi$
$384$		0			0
$385$	−1.49881	+	1.64021i	−0.0763866	+	0.0835928i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−32.9413			−1.67019			−0.835095	−	0.550105i	$-0.814588\pi$
$389$	−32.9413			−1.67019			−0.835095	+	0.550105i	$0.814588\pi$
$390$		0			0
$391$	0.154939	−	0.268362i	0.00783560	−	0.0135717i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.61712	+	4.53299i	−0.131682	+	0.228079i
$396$		0			0
$397$	−0.411705	−	0.713095i	−0.0206629	−	0.0357892i	0.855509	−	0.517788i	$-0.173244\pi$
$397$	−0.411705	−	0.713095i	−0.0206629	−	0.0357892i	−0.876172	+	0.481999i	$0.839911\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.7385			0.985691			0.492846	−	0.870117i	$-0.335957\pi$
$401$	19.7385			0.985691			0.492846	+	0.870117i	$0.335957\pi$
$402$		0			0
$403$	−26.3619			−1.31318
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.35504	+	2.34700i	0.0671670	+	0.116337i
$408$		0			0
$409$	12.6276	+	21.8716i	0.624393	+	1.08148i	0.988658	+	0.150185i	$0.0479869\pi$
$409$	12.6276	+	21.8716i	0.624393	+	1.08148i	−0.364265	+	0.931295i	$0.618680\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0921	+	5.30621i	1.18550	+	0.261101i
$414$		0			0
$415$	−9.66688	−	16.7435i	−0.474528	−	0.821907i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.406717	+	0.704455i	−0.0198694	+	0.0344149i	−0.875789	−	0.482694i	$-0.839658\pi$
$419$	−0.406717	+	0.704455i	−0.0198694	+	0.0344149i	0.855920	+	0.517109i	$0.172992\pi$
$420$		0			0
$421$	5.12114	+	8.87008i	0.249589	+	0.432301i	0.963412	−	0.268025i	$-0.0863711\pi$
$421$	5.12114	+	8.87008i	0.249589	+	0.432301i	−0.713823	+	0.700326i	$0.753038\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.100927	+	0.174810i	−0.00489567	+	0.00847955i
$426$		0			0
$427$	8.04830	+	25.4036i	0.389485	+	1.22937i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.3348	+	28.2928i	−0.786822	+	1.36281i	0.141083	+	0.989998i	$0.454941\pi$
$431$	−16.3348	+	28.2928i	−0.786822	+	1.36281i	−0.927905	+	0.372817i	$0.878392\pi$
$432$		0			0
$433$	−14.3151			−0.687941			−0.343970	−	0.938980i	$-0.611772\pi$
$433$	−14.3151			−0.687941			−0.343970	+	0.938980i	$0.611772\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.49951	+	4.32927i	0.119568	+	0.207097i
$438$		0			0
$439$	4.93330	−	8.54472i	0.235453	−	0.407817i	−0.723951	−	0.689852i	$-0.757676\pi$
$439$	4.93330	−	8.54472i	0.235453	−	0.407817i	0.959404	+	0.282034i	$0.0910091\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.6400	−	32.2855i	0.885615	−	1.53393i	0.0406086	−	0.999175i	$-0.487070\pi$
$443$	18.6400	−	32.2855i	0.885615	−	1.53393i	0.845007	−	0.534756i	$-0.179596\pi$
$444$		0			0
$445$	15.3486	+	26.5845i	0.727593	+	1.26023i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	36.2926			1.71276			0.856378	−	0.516350i	$-0.172710\pi$
$449$	36.2926			1.71276			0.856378	+	0.516350i	$0.172710\pi$
$450$		0			0
$451$	0.480382	−	0.832046i	0.0226203	−	0.0391795i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.85275	−	15.3172i	−0.227501	−	0.718081i
$456$		0			0
$457$	6.59716	−	11.4266i	0.308602	−	0.534515i	−0.669455	−	0.742853i	$-0.733472\pi$
$457$	6.59716	−	11.4266i	0.308602	−	0.534515i	0.978057	+	0.208338i	$0.0668054\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1326	−	17.5502i	−0.471924	−	0.817396i	0.527560	−	0.849518i	$-0.323107\pi$
$461$	−10.1326	−	17.5502i	−0.471924	−	0.817396i	−0.999484	+	0.0321215i	$0.989774\pi$
$462$		0			0
$463$	12.7106	−	22.0154i	0.590712	−	1.02314i	−0.403424	−	0.915013i	$-0.632180\pi$
$463$	12.7106	−	22.0154i	0.590712	−	1.02314i	0.994137	−	0.108131i	$-0.0344866\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.40661	+	7.63248i	0.203914	+	0.353189i	0.949786	−	0.312900i	$-0.101300\pi$
$467$	4.40661	+	7.63248i	0.203914	+	0.353189i	−0.745872	+	0.666089i	$0.767967\pi$
$468$		0			0
$469$	3.10681	+	0.684265i	0.143459	+	0.0315964i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.110439	−	0.191286i	−0.00507799	−	0.00879534i
$474$		0			0
$475$	−1.62817	−	2.82008i	−0.0747056	−	0.129394i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−24.2687			−1.10887			−0.554433	−	0.832229i	$-0.687065\pi$
$479$	−24.2687			−1.10887			−0.554433	+	0.832229i	$0.687065\pi$
$480$		0			0
$481$	−19.5980			−0.893594
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.5036	+	28.5851i	0.749391	+	1.29798i
$486$		0			0
$487$	−5.37220	+	9.30492i	−0.243438	+	0.421646i	−0.961691	−	0.274135i	$-0.911608\pi$
$487$	−5.37220	+	9.30492i	−0.243438	+	0.421646i	0.718254	+	0.695781i	$0.244942\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.3934	+	19.7340i	−0.514179	+	0.890584i	0.485686	+	0.874134i	$0.338570\pi$
$491$	−11.3934	+	19.7340i	−0.514179	+	0.890584i	−0.999865	+	0.0164507i	$0.994763\pi$
$492$		0			0
$493$	−0.618084			−0.0278371
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−26.2047	+	28.6768i	−1.17544	+	1.28633i
$498$		0			0
$499$	23.1509			1.03638			0.518189	−	0.855266i	$-0.326606\pi$
$499$	23.1509			1.03638			0.518189	+	0.855266i	$0.326606\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.43360			−0.420623			−0.210312	−	0.977634i	$-0.567448\pi$
$503$	−9.43360			−0.420623			−0.210312	+	0.977634i	$0.567448\pi$
$504$		0			0
$505$	−0.195408			−0.00869555
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.45963			0.419291			0.209645	−	0.977777i	$-0.432769\pi$
$509$	9.45963			0.419291			0.209645	+	0.977777i	$0.432769\pi$
$510$		0			0
$511$	0.504433	+	1.59219i	0.0223148	+	0.0704343i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	41.9099			1.84677
$516$		0			0
$517$	−2.34195	+	4.05637i	−0.102999	+	0.178399i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.3368	−	24.8320i	0.628105	−	1.08791i	−0.359826	−	0.933019i	$-0.617164\pi$
$521$	14.3368	−	24.8320i	0.628105	−	1.08791i	0.987932	−	0.154891i	$-0.0495026\pi$
$522$		0			0
$523$	−13.5104	−	23.4006i	−0.590767	−	1.02324i	−0.994129	−	0.108198i	$-0.965492\pi$
$523$	−13.5104	−	23.4006i	−0.590767	−	1.02324i	0.403362	−	0.915040i	$-0.367841\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.22637			−0.140543
$528$		0			0
$529$	−22.2302			−0.966532
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.47389	+	6.01696i	0.150471	+	0.260624i
$534$		0			0
$535$	−6.08645	−	10.5420i	−0.263140	−	0.455772i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.251148	+	2.78214i	0.0108177	+	0.119835i
$540$		0			0
$541$	−1.52907	−	2.64842i	−0.0657397	−	0.113864i	0.831282	−	0.555851i	$-0.187607\pi$
$541$	−1.52907	−	2.64842i	−0.0657397	−	0.113864i	−0.897022	+	0.441986i	$0.854274\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.1633	−	22.7996i	0.563856	−	0.976627i
$546$		0			0
$547$	3.58144	+	6.20323i	0.153131	+	0.265231i	0.932377	−	0.361487i	$-0.117731\pi$
$547$	3.58144	+	6.20323i	0.153131	+	0.265231i	−0.779246	+	0.626719i	$0.784398\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.98552	−	8.63518i	0.212390	−	0.367871i
$552$		0			0
$553$	1.98753	+	6.27343i	0.0845185	+	0.266774i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.3518	−	24.8580i	0.608104	−	1.05327i	−0.383449	−	0.923562i	$-0.625264\pi$
$557$	14.3518	−	24.8580i	0.608104	−	1.05327i	0.991553	−	0.129704i	$-0.0414028\pi$
$558$		0			0
$559$	1.59729			0.0675580
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.8859	+	30.9794i	0.753803	+	1.30562i	0.945967	+	0.324262i	$0.105116\pi$
$563$	17.8859	+	30.9794i	0.753803	+	1.30562i	−0.192165	+	0.981363i	$0.561551\pi$
$564$		0			0
$565$	3.56508	−	6.17490i	0.149984	−	0.259780i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.6001	+	21.8240i	−0.528223	+	0.914909i	0.471235	+	0.882007i	$0.343808\pi$
$569$	−12.6001	+	21.8240i	−0.528223	+	0.914909i	−0.999459	+	0.0329018i	$0.989525\pi$
$570$		0			0
$571$	3.02469	+	5.23891i	0.126579	+	0.219242i	0.922349	−	0.386357i	$-0.126267\pi$
$571$	3.02469	+	5.23891i	0.126579	+	0.219242i	−0.795770	+	0.605599i	$0.792934\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.501425			−0.0209109
$576$		0			0
$577$	9.57977	−	16.5926i	0.398811	−	0.690761i	−0.594768	−	0.803897i	$-0.702756\pi$
$577$	9.57977	−	16.5926i	0.398811	−	0.690761i	0.993580	+	0.113136i	$0.0360896\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.7384	−	5.22830i	−0.984835	−	0.216907i
$582$		0			0
$583$	−0.829338	+	1.43645i	−0.0343477	+	0.0594919i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.4147	−	31.8953i	−0.760058	−	1.31646i	−0.942820	−	0.333301i	$-0.891837\pi$
$587$	−18.4147	−	31.8953i	−0.760058	−	1.31646i	0.182763	−	0.983157i	$-0.441496\pi$
$588$		0			0
$589$	26.0242	−	45.0753i	1.07231	−	1.85730i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.97285	−	15.5414i	−0.368471	−	0.638210i	0.620856	−	0.783925i	$-0.286785\pi$
$593$	−8.97285	−	15.5414i	−0.368471	−	0.638210i	−0.989327	+	0.145715i	$0.953452\pi$
$594$		0			0
$595$	−0.593918	−	1.87464i	−0.0243482	−	0.0768526i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.2457	−	35.0665i	−0.827215	−	1.43278i	−0.900214	−	0.435447i	$-0.856590\pi$
$599$	−20.2457	−	35.0665i	−0.827215	−	1.43278i	0.0729993	−	0.997332i	$-0.476743\pi$
$600$		0			0
$601$	13.2589	+	22.9651i	0.540841	+	0.936765i	0.998856	+	0.0478200i	$0.0152274\pi$
$601$	13.2589	+	22.9651i	0.540841	+	0.936765i	−0.458015	+	0.888945i	$0.651439\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	22.8132			0.927490
$606$		0			0
$607$	−42.1696			−1.71161			−0.855806	−	0.517297i	$-0.826938\pi$
$607$	−42.1696			−1.71161			−0.855806	+	0.517297i	$0.826938\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.9358	−	29.3337i	−0.685151	−	1.18672i
$612$		0			0
$613$	−0.700827	+	1.21387i	−0.0283061	+	0.0490277i	−0.879831	−	0.475286i	$-0.842345\pi$
$613$	−0.700827	+	1.21387i	−0.0283061	+	0.0490277i	0.851525	+	0.524313i	$0.175678\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.76787	−	11.7223i	0.272464	−	0.471922i	−0.697028	−	0.717044i	$-0.745495\pi$
$617$	6.76787	−	11.7223i	0.272464	−	0.471922i	0.969492	+	0.245122i	$0.0788280\pi$
$618$		0			0
$619$	−29.8245			−1.19875			−0.599374	−	0.800469i	$-0.704584\pi$
$619$	−29.8245			−1.19875			−0.599374	+	0.800469i	$0.704584\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	37.6907	+	8.30124i	1.51004	+	0.332582i
$624$		0			0
$625$	−21.8158			−0.872632
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.39856			−0.0956369
$630$		0			0
$631$	6.84708			0.272578			0.136289	−	0.990669i	$-0.456482\pi$
$631$	6.84708			0.272578			0.136289	+	0.990669i	$0.456482\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−31.0079			−1.23051
$636$		0			0
$637$	−18.3317	−	8.48668i	−0.726330	−	0.336255i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−32.2417			−1.27347			−0.636735	−	0.771082i	$-0.719716\pi$
$641$	−32.2417			−1.27347			−0.636735	+	0.771082i	$0.719716\pi$
$642$		0			0
$643$	1.16002	−	2.00921i	0.0457465	−	0.0792353i	−0.842245	−	0.539094i	$-0.818767\pi$
$643$	1.16002	−	2.00921i	0.0457465	−	0.0792353i	0.887992	+	0.459859i	$0.152100\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.06813	+	1.85005i	−0.0419924	+	0.0727329i	−0.886258	−	0.463193i	$-0.846704\pi$
$647$	−1.06813	+	1.85005i	−0.0419924	+	0.0727329i	0.844265	+	0.535925i	$0.180037\pi$
$648$		0			0
$649$	1.86048	+	3.22244i	0.0730302	+	0.126492i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.03865			−0.118912			−0.0594558	−	0.998231i	$-0.518937\pi$
$653$	−3.03865			−0.118912			−0.0594558	+	0.998231i	$0.518937\pi$
$654$		0			0
$655$	−29.2676			−1.14358
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.8000	+	34.2946i	0.771298	+	1.33593i	0.936852	+	0.349726i	$0.113725\pi$
$659$	19.8000	+	34.2946i	0.771298	+	1.33593i	−0.165554	+	0.986201i	$0.552941\pi$
$660$		0			0
$661$	−3.06199	−	5.30352i	−0.119098	−	0.206283i	0.800313	−	0.599583i	$-0.204667\pi$
$661$	−3.06199	−	5.30352i	−0.119098	−	0.206283i	−0.919410	+	0.393300i	$0.871333\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	30.9810	+	6.82345i	1.20139	+	0.264602i
$666$		0			0
$667$	−0.767691	−	1.32968i	−0.0297251	−	0.0514854i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.00969	+	3.48089i	−0.0775832	+	0.134378i
$672$		0			0
$673$	−4.36248	−	7.55603i	−0.168161	−	0.291264i	0.769612	−	0.638512i	$-0.220450\pi$
$673$	−4.36248	−	7.55603i	−0.168161	−	0.291264i	−0.937773	+	0.347248i	$0.887116\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.48007	−	12.9559i	0.287482	−	0.497934i	−0.685726	−	0.727860i	$-0.740515\pi$
$677$	7.48007	−	12.9559i	0.287482	−	0.497934i	0.973208	+	0.229926i	$0.0738484\pi$
$678$		0			0
$679$	40.5270	+	8.92594i	1.55528	+	0.342546i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.89558	−	15.4076i	0.340380	−	0.589555i	−0.644123	−	0.764922i	$-0.722778\pi$
$683$	8.89558	−	15.4076i	0.340380	−	0.589555i	0.984503	+	0.175366i	$0.0561110\pi$
$684$		0			0
$685$	30.6347			1.17049
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.99738	−	10.3878i	−0.228482	−	0.395742i
$690$		0			0
$691$	14.7694	−	25.5814i	0.561856	−	0.973164i	−0.435478	−	0.900199i	$-0.643421\pi$
$691$	14.7694	−	25.5814i	0.561856	−	0.973164i	0.997335	−	0.0729644i	$-0.0232459\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.65992	−	13.2674i	0.290557	−	0.503260i
$696$		0			0
$697$	0.425162	+	0.736402i	0.0161042	+	0.0278932i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−27.7740			−1.04901			−0.524504	−	0.851408i	$-0.675749\pi$
$701$	−27.7740			−1.04901			−0.524504	+	0.851408i	$0.675749\pi$
$702$		0			0
$703$	19.3470	−	33.5100i	0.729687	−	1.26385i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.165727	+	0.181361i	−0.00623279	+	0.00682078i
$708$		0			0
$709$	−23.5492	+	40.7884i	−0.884409	+	1.53184i	−0.0380203	+	0.999277i	$0.512105\pi$
$709$	−23.5492	+	40.7884i	−0.884409	+	1.53184i	−0.846389	+	0.532565i	$0.821228\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.00732	−	6.94088i	−0.150075	−	0.259938i
$714$		0			0
$715$	1.21175	−	2.09881i	0.0453169	−	0.0784912i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.63394	−	2.83007i	−0.0609357	−	0.105544i	0.833948	−	0.551843i	$-0.186075\pi$
$719$	−1.63394	−	2.83007i	−0.0609357	−	0.105544i	−0.894884	+	0.446299i	$0.852742\pi$
$720$		0			0
$721$	35.5440	−	38.8971i	1.32373	−	1.44860i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.500072	+	0.866150i	0.0185722	+	0.0321680i
$726$		0			0
$727$	−6.37047	−	11.0340i	−0.236268	−	0.409228i	0.723373	−	0.690458i	$-0.242591\pi$
$727$	−6.37047	−	11.0340i	−0.236268	−	0.409228i	−0.959640	+	0.281230i	$0.909258\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.195488			0.00723039
$732$		0			0
$733$	9.17716			0.338966			0.169483	−	0.985533i	$-0.445790\pi$
$733$	9.17716			0.338966			0.169483	+	0.985533i	$0.445790\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.239919	+	0.415552i	0.00883754	+	0.0153071i
$738$		0			0
$739$	−23.3467	+	40.4377i	−0.858823	+	1.48752i	0.0142303	+	0.999899i	$0.495470\pi$
$739$	−23.3467	+	40.4377i	−0.858823	+	1.48752i	−0.873053	+	0.487626i	$0.837863\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.62654	−	13.2095i	0.279790	−	0.484611i	−0.691542	−	0.722336i	$-0.743068\pi$
$743$	7.62654	−	13.2095i	0.279790	−	0.484611i	0.971333	+	0.237725i	$0.0764017\pi$
$744$		0			0
$745$	−1.51867			−0.0556396
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−14.9462	−	3.29184i	−0.546121	−	0.120281i
$750$		0			0
$751$	6.34887			0.231673			0.115837	−	0.993268i	$-0.463045\pi$
$751$	6.34887			0.231673			0.115837	+	0.993268i	$0.463045\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−45.8850			−1.66993
$756$		0			0
$757$	28.4278			1.03323			0.516614	−	0.856219i	$-0.327192\pi$
$757$	28.4278			1.03323			0.516614	+	0.856219i	$0.327192\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.0687			0.654991			0.327496	−	0.944853i	$-0.393795\pi$
$761$	18.0687			0.654991			0.327496	+	0.944853i	$0.393795\pi$
$762$		0			0
$763$	−9.99670	−	31.5535i	−0.361905	−	1.14231i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−26.9082			−0.971599
$768$		0			0
$769$	−1.72471	+	2.98728i	−0.0621946	+	0.107724i	−0.895446	−	0.445170i	$-0.853143\pi$
$769$	−1.72471	+	2.98728i	−0.0621946	+	0.107724i	0.833252	+	0.552894i	$0.186477\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.1837	−	34.9592i	0.725957	−	1.25740i	−0.232621	−	0.972567i	$-0.574730\pi$
$773$	20.1837	−	34.9592i	0.725957	−	1.25740i	0.958579	−	0.284828i	$-0.0919364\pi$
$774$		0			0
$775$	2.61036	+	4.52127i	0.0937668	+	0.162409i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13.7176			−0.491484
$780$		0			0
$781$	−5.85929			−0.209662
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.45010	+	9.43985i	0.194522	+	0.336923i
$786$		0			0
$787$	−9.16031	−	15.8661i	−0.326530	−	0.565566i	0.655291	−	0.755377i	$-0.272546\pi$
$787$	−9.16031	−	15.8661i	−0.326530	−	0.565566i	−0.981821	+	0.189810i	$0.939213\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.70744	−	8.54575i	−0.0962656	−	0.303852i
$792$		0			0
$793$	−14.5331	−	25.1721i	−0.516086	−	0.893888i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.86884	−	8.43307i	0.172463	−	0.298715i	−0.766817	−	0.641865i	$-0.778161\pi$
$797$	4.86884	−	8.43307i	0.172463	−	0.298715i	0.939280	+	0.343151i	$0.111494\pi$
$798$		0			0
$799$	−2.07274	−	3.59009i	−0.0733283	−	0.127008i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.125959	+	0.218167i	−0.00444499	+	0.00769895i
$804$		0			0
$805$	3.29522	−	3.60609i	0.116141	−	0.127098i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.98714	−	10.3700i	0.210497	−	0.364591i	−0.741373	−	0.671093i	$-0.765825\pi$
$809$	5.98714	−	10.3700i	0.210497	−	0.364591i	0.951870	+	0.306502i	$0.0991586\pi$
$810$		0			0
$811$	4.05517			0.142396			0.0711982	−	0.997462i	$-0.477318\pi$
$811$	4.05517			0.142396			0.0711982	+	0.997462i	$0.477318\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.55362	−	9.61916i	−0.194535	−	0.336944i
$816$		0			0
$817$	−1.57683	+	2.73114i	−0.0551662	+	0.0955506i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.99256	−	6.91532i	0.139341	−	0.241346i	−0.787906	−	0.615795i	$-0.788835\pi$
$821$	3.99256	−	6.91532i	0.139341	−	0.241346i	0.927248	+	0.374449i	$0.122168\pi$
$822$		0			0
$823$	−23.7901	−	41.2056i	−0.829270	−	1.43634i	−0.898611	−	0.438746i	$-0.855423\pi$
$823$	−23.7901	−	41.2056i	−0.829270	−	1.43634i	0.0693409	−	0.997593i	$-0.477910\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	29.2725			1.01790			0.508952	−	0.860795i	$-0.330033\pi$
$827$	29.2725			1.01790			0.508952	+	0.860795i	$0.330033\pi$
$828$		0			0
$829$	3.15249	−	5.46028i	0.109491	−	0.189643i	−0.806073	−	0.591816i	$-0.798411\pi$
$829$	3.15249	−	5.46028i	0.109491	−	0.189643i	0.915564	+	0.402172i	$0.131745\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.24358	−	1.03867i	−0.0777354	−	0.0359876i
$834$		0			0
$835$	−14.3880	+	24.9207i	−0.497917	+	0.862417i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.501711	+	0.868989i	0.0173210	+	0.0300008i	0.874556	−	0.484925i	$-0.161153\pi$
$839$	0.501711	+	0.868989i	0.0173210	+	0.0300008i	−0.857235	+	0.514925i	$0.827820\pi$
$840$		0			0
$841$	12.9688	−	22.4626i	0.447199	−	0.774571i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.91578	−	8.51438i	−0.169108	−	0.292904i
$846$		0			0
$847$	19.3480	−	21.1733i	0.664806	−	0.727522i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.97913	−	5.16001i	−0.102123	−	0.176883i
$852$		0			0
$853$	20.0519	+	34.7309i	0.686565	+	1.18916i	0.972942	+	0.231048i	$0.0742154\pi$
$853$	20.0519	+	34.7309i	0.686565	+	1.18916i	−0.286378	+	0.958117i	$0.592451\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	37.4776			1.28021			0.640106	−	0.768287i	$-0.278890\pi$
$857$	37.4776			1.28021			0.640106	+	0.768287i	$0.278890\pi$
$858$		0			0
$859$	24.5032			0.836039			0.418019	−	0.908438i	$-0.362724\pi$
$859$	24.5032			0.836039			0.418019	+	0.908438i	$0.362724\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.79806	−	16.9707i	−0.333530	−	0.577691i	0.649671	−	0.760215i	$-0.274906\pi$
$863$	−9.79806	−	16.9707i	−0.333530	−	0.577691i	−0.983201	+	0.182524i	$0.941573\pi$
$864$		0			0
$865$	−21.2359	+	36.7816i	−0.722041	+	1.25061i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.496294	+	0.859607i	−0.0168356	+	0.0291602i
$870$		0			0
$871$	−3.46996			−0.117575
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−20.9256	+	22.8997i	−0.707414	+	0.774150i
$876$		0			0
$877$	34.2269			1.15576			0.577880	−	0.816122i	$-0.303880\pi$
$877$	34.2269			1.15576			0.577880	+	0.816122i	$0.303880\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	25.2818			0.851764			0.425882	−	0.904779i	$-0.359964\pi$
$881$	25.2818			0.851764			0.425882	+	0.904779i	$0.359964\pi$
$882$		0			0
$883$	−45.4688			−1.53015			−0.765073	−	0.643943i	$-0.777297\pi$
$883$	−45.4688			−1.53015			−0.765073	+	0.643943i	$0.777297\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.8301			−0.363638			−0.181819	−	0.983332i	$-0.558199\pi$
$887$	−10.8301			−0.363638			−0.181819	+	0.983332i	$0.558199\pi$
$888$		0			0
$889$	−26.2980	+	28.7789i	−0.882005	+	0.965212i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	66.8757			2.23791
$894$		0			0
$895$	26.5087	−	45.9143i	0.886086	−	1.53475i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.99301	+	13.8443i	−0.266582	+	0.461733i
$900$		0			0
$901$	−0.734005	−	1.27133i	−0.0244533	−	0.0423543i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	36.3672			1.20889
$906$		0			0
$907$	4.01683			0.133377			0.0666883	−	0.997774i	$-0.478757\pi$
$907$	4.01683			0.133377			0.0666883	+	0.997774i	$0.478757\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.43681	+	14.6130i	0.279524	+	0.484150i	0.971266	−	0.237995i	$-0.0764901\pi$
$911$	8.43681	+	14.6130i	0.279524	+	0.484150i	−0.691743	+	0.722144i	$0.743157\pi$
$912$		0			0
$913$	−1.83316	−	3.17513i	−0.0606689	−	0.105082i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.8220	+	27.1637i	−0.819695	+	0.897023i
$918$		0			0
$919$	−16.9485	−	29.3557i	−0.559081	−	0.968356i	−0.997573	−	0.0696214i	$-0.977821\pi$
$919$	−16.9485	−	29.3557i	−0.559081	−	0.968356i	0.438493	−	0.898735i	$-0.355512\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	21.1858	−	36.6949i	0.697339	−	1.20783i
$924$		0			0
$925$	1.94060	+	3.36122i	0.0638065	+	0.110516i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.3050	+	33.4373i	−0.633377	+	1.09704i	0.353480	+	0.935442i	$0.384998\pi$
$929$	−19.3050	+	33.4373i	−0.633377	+	1.09704i	−0.986857	+	0.161599i	$0.948335\pi$
$930$		0			0
$931$	32.6080	−	22.9668i	1.06868	−	0.752707i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.148303	−	0.256869i	0.00485004	−	0.00840052i
$936$		0			0
$937$	−45.4955			−1.48627			−0.743136	−	0.669140i	$-0.766663\pi$
$937$	−45.4955			−1.48627			−0.743136	+	0.669140i	$0.766663\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.99460	−	15.5791i	−0.293216	−	0.507864i	0.681353	−	0.731955i	$-0.261392\pi$
$941$	−8.99460	−	15.5791i	−0.293216	−	0.507864i	−0.974568	+	0.224091i	$0.928059\pi$
$942$		0			0
$943$	−1.05615	+	1.82930i	−0.0343928	+	0.0595702i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.26121	−	14.3088i	0.268453	−	0.464975i	−0.700009	−	0.714134i	$-0.746821\pi$
$947$	8.26121	−	14.3088i	0.268453	−	0.464975i	0.968463	+	0.249159i	$0.0801542\pi$
$948$		0			0
$949$	−0.910875	−	1.57768i	−0.0295682	−	0.0512137i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	15.6799			0.507922			0.253961	−	0.967214i	$-0.418266\pi$
$953$	15.6799			0.507922			0.253961	+	0.967214i	$0.418266\pi$
$954$		0			0
$955$	5.28096	−	9.14690i	0.170888	−	0.295987i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	25.9815	−	28.4325i	0.838985	−	0.918133i
$960$		0			0
$961$	−26.2232	+	45.4200i	−0.845911	+	1.46516i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.72149	−	9.90991i	−0.184181	−	0.319011i
$966$		0			0
$967$	−25.3908	+	43.9782i	−0.816513	+	1.41424i	0.0917230	+	0.995785i	$0.470763\pi$
$967$	−25.3908	+	43.9782i	−0.816513	+	1.41424i	−0.908236	+	0.418458i	$0.862571\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.23027	+	15.9873i	0.296214	+	0.513057i	0.975266	−	0.221032i	$-0.0709427\pi$
$971$	9.23027	+	15.9873i	0.296214	+	0.513057i	−0.679053	+	0.734089i	$0.737609\pi$
$972$		0			0
$973$	−5.81721	−	18.3614i	−0.186491	−	0.588639i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.8151	+	27.3925i	0.505970	+	0.876365i	0.999976	+	0.00690692i	$0.00219856\pi$
$977$	15.8151	+	27.3925i	0.505970	+	0.876365i	−0.494007	+	0.869458i	$0.664468\pi$
$978$		0			0
$979$	2.91061	+	5.04132i	0.0930234	+	0.161121i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−40.4132			−1.28898			−0.644490	−	0.764613i	$-0.722930\pi$
$983$	−40.4132			−1.28898			−0.644490	+	0.764613i	$0.722930\pi$
$984$		0			0
$985$	12.5388			0.399520
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.242806	+	0.420553i	0.00772079	+	0.0133728i
$990$		0			0
$991$	16.6187	−	28.7845i	0.527911	−	0.914368i	−0.471560	−	0.881834i	$-0.656309\pi$
$991$	16.6187	−	28.7845i	0.527911	−	0.914368i	0.999471	−	0.0325343i	$-0.0103578\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.8280	+	20.4867i	−0.374973	+	0.649473i
$996$		0			0
$997$	−41.1185			−1.30223			−0.651117	−	0.758977i	$-0.725699\pi$
$997$	−41.1185			−1.30223			−0.651117	+	0.758977i	$0.725699\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.361.4		22
3.2	odd	2		504.2.t.c.193.11	yes	22
4.3	odd	2		3024.2.t.k.1873.4		22
7.2	even	3		1512.2.q.d.793.8		22
9.2	odd	6		504.2.q.c.25.5	✓	22
9.7	even	3		1512.2.q.d.1369.8		22
12.11	even	2		1008.2.t.l.193.1		22
21.2	odd	6		504.2.q.c.121.5	yes	22
28.23	odd	6		3024.2.q.l.2305.8		22
36.7	odd	6		3024.2.q.l.2881.8		22
36.11	even	6		1008.2.q.l.529.7		22
63.2	odd	6		504.2.t.c.457.11	yes	22
63.16	even	3	inner	1512.2.t.c.289.4		22
84.23	even	6		1008.2.q.l.625.7		22
252.79	odd	6		3024.2.t.k.289.4		22
252.191	even	6		1008.2.t.l.961.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.5	✓	22	9.2	odd	6
504.2.q.c.121.5	yes	22	21.2	odd	6
504.2.t.c.193.11	yes	22	3.2	odd	2
504.2.t.c.457.11	yes	22	63.2	odd	6
1008.2.q.l.529.7		22	36.11	even	6
1008.2.q.l.625.7		22	84.23	even	6
1008.2.t.l.193.1		22	12.11	even	2
1008.2.t.l.961.1		22	252.191	even	6
1512.2.q.d.793.8		22	7.2	even	3
1512.2.q.d.1369.8		22	9.7	even	3
1512.2.t.c.289.4		22	63.16	even	3	inner
1512.2.t.c.361.4		22	1.1	even	1	trivial
3024.2.q.l.2305.8		22	28.23	odd	6
3024.2.q.l.2881.8		22	36.7	odd	6
3024.2.t.k.289.4		22	252.79	odd	6
3024.2.t.k.1873.4		22	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.10440 q^{5} +(-1.78475 + 1.95312i) q^{7} +O(q^{10})\)	\(q-2.10440 q^{5} +(-1.78475 + 1.95312i) q^{7} -0.399064 q^{11} +(1.44292 - 2.49921i) q^{13} +(0.176596 - 0.305873i) q^{17} +(2.84888 + 4.93440i) q^{19} +0.877364 q^{23} -0.571513 q^{25} +(-0.874997 - 1.51554i) q^{29} +(-4.56745 - 7.91106i) q^{31} +(3.75582 - 4.11014i) q^{35} +(-3.39555 - 5.88127i) q^{37} +(-1.20377 + 2.08499i) q^{41} +(0.276745 + 0.479336i) q^{43} +(5.86859 - 10.1647i) q^{47} +(-0.629343 - 6.97165i) q^{49} +(2.07821 - 3.59956i) q^{53} +0.839790 q^{55} +(-4.66210 - 8.07500i) q^{59} +(5.03601 - 8.72262i) q^{61} +(-3.03648 + 5.25934i) q^{65} +(-0.601204 - 1.04132i) q^{67} +14.6826 q^{71} +(0.315636 - 0.546697i) q^{73} +(0.712229 - 0.779420i) q^{77} +(1.24364 - 2.15406i) q^{79} +(4.59366 + 7.95645i) q^{83} +(-0.371628 + 0.643678i) q^{85} +(-7.29358 - 12.6328i) q^{89} +(2.30601 + 7.27866i) q^{91} +(-5.99517 - 10.3839i) q^{95} +(-7.84245 - 13.5835i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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