LMFDB - Embedded newform 136.2.s.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(3,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 8, 1]))

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

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

chi := DirichletCharacter("136.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.s (of order $16$, degree $8$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{16}]$

Embedding invariants

Embedding label			11.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	136.11
Dual form			136.2.s.b.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30656 - 0.541196i) q^{2} +(0.675577 + 3.39635i) q^{3} +(1.41421 + 1.41421i) q^{4} +(0.955410 - 4.80317i) q^{6} +(-1.08239 - 2.61313i) q^{8} +(-8.30717 + 3.44094i) q^{9} +O(q^{10})$	\(q+(-1.30656 - 0.541196i) q^{2} +(0.675577 + 3.39635i) q^{3} +(1.41421 + 1.41421i) q^{4} +(0.955410 - 4.80317i) q^{6} +(-1.08239 - 2.61313i) q^{8} +(-8.30717 + 3.44094i) q^{9} +(1.57273 + 0.312835i) q^{11} +(-3.84776 + 5.75858i) q^{12} +4.00000i q^{16} +(-1.68925 - 3.76118i) q^{17} +12.7161 q^{18} +(6.84984 + 2.83730i) q^{19} +(-1.88556 - 1.25989i) q^{22} +(8.14386 - 5.44155i) q^{24} +(1.91342 + 4.61940i) q^{25} +(-11.5272 - 17.2516i) q^{27} +(2.16478 - 5.22625i) q^{32} +5.55288i q^{33} +(0.171573 + 5.82843i) q^{34} +(-16.6143 - 6.88189i) q^{36} +(-7.41421 - 7.41421i) q^{38} +(6.72817 - 4.49562i) q^{41} +(5.53553 - 2.29289i) q^{43} +(1.78176 + 2.66659i) q^{44} +(-13.5854 + 2.70231i) q^{48} +(2.67878 - 6.46716i) q^{49} -7.07107i q^{50} +(11.6331 - 8.27824i) q^{51} +(5.72445 + 28.7788i) q^{54} +(-5.00887 + 25.1813i) q^{57} +(4.19239 + 10.1213i) q^{59} +(-5.65685 + 5.65685i) q^{64} +(3.00520 - 7.25518i) q^{66} -2.48181i q^{67} +(2.93015 - 7.70806i) q^{68} +(17.9832 + 17.9832i) q^{72} +(-13.5150 - 9.03040i) q^{73} +(-14.3964 + 9.61940i) q^{75} +(5.67459 + 13.6997i) q^{76} +(31.7310 - 31.7310i) q^{81} +(-11.2238 + 2.23255i) q^{82} +(-3.63604 + 8.77817i) q^{83} -8.47343 q^{86} +(-0.884830 - 4.44834i) q^{88} +(-10.2283 - 10.2283i) q^{89} +(19.2127 + 3.82164i) q^{96} +(-0.618707 + 0.925961i) q^{97} +(-7.00000 + 7.00000i) q^{98} +(-14.1414 + 2.81289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 8 q^{6} - 16 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 - 8 * q^6 - 16 * q^9	$ 8 q + 8 q^{3} - 8 q^{6} - 16 q^{9} - 16 q^{12} + 24 q^{22} + 32 q^{24} - 16 q^{27} + 24 q^{34} - 32 q^{36} - 48 q^{38} + 32 q^{41} + 16 q^{43} + 16 q^{44} - 32 q^{48} + 40 q^{51} - 8 q^{54} - 40 q^{57} - 40 q^{59} + 56 q^{66} + 48 q^{72} - 48 q^{73} + 56 q^{81} - 80 q^{83} + 32 q^{96} - 56 q^{98} + 32 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 8 * q^6 - 16 * q^9 - 16 * q^12 + 24 * q^22 + 32 * q^24 - 16 * q^27 + 24 * q^34 - 32 * q^36 - 48 * q^38 + 32 * q^41 + 16 * q^43 + 16 * q^44 - 32 * q^48 + 40 * q^51 - 8 * q^54 - 40 * q^57 - 40 * q^59 + 56 * q^66 + 48 * q^72 - 48 * q^73 + 56 * q^81 - 80 * q^83 + 32 * q^96 - 56 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−1.30656	−	0.541196i	−0.923880	−	0.382683i
$2$	−1.30656	−	0.541196i	−0.923880	−	0.382683i
$3$	0.675577	+	3.39635i	0.390044	+	1.96089i	0.220942	+	0.975287i	$0.429087\pi$
$3$	0.675577	+	3.39635i	0.390044	+	1.96089i	0.169102	+	0.985599i	$0.445913\pi$
$4$	1.41421	+	1.41421i	0.707107	+	0.707107i
$5$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$5$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$6$	0.955410	−	4.80317i	0.390044	−	1.96089i
$7$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$7$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$8$	−1.08239	−	2.61313i	−0.382683	−	0.923880i
$9$	−8.30717	+	3.44094i	−2.76906	+	1.14698i
$10$		0			0
$11$	1.57273	+	0.312835i	0.474195	+	0.0943232i	0.426401	−	0.904534i	$-0.359781\pi$
$11$	1.57273	+	0.312835i	0.474195	+	0.0943232i	0.0477934	+	0.998857i	$0.484781\pi$
$12$	−3.84776	+	5.75858i	−1.11075	+	1.66236i
$13$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$13$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$14$		0			0
$15$		0			0
$16$			4.00000i			1.00000i
$17$	−1.68925	−	3.76118i	−0.409702	−	0.912219i
$17$	−1.68925	−	3.76118i	−0.409702	−	0.912219i
$18$	12.7161			2.99721
$19$	6.84984	+	2.83730i	1.57146	+	0.650921i	0.987032	−	0.160524i	$-0.0513185\pi$
$19$	6.84984	+	2.83730i	1.57146	+	0.650921i	0.584429	+	0.811445i	$0.301318\pi$
$20$		0			0
$21$		0			0
$22$	−1.88556	−	1.25989i	−0.402003	−	0.268610i
$23$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$23$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$24$	8.14386	−	5.44155i	1.66236	−	1.11075i
$25$	1.91342	+	4.61940i	0.382683	+	0.923880i
$26$		0			0
$27$	−11.5272	−	17.2516i	−2.21840	−	3.32007i
$28$		0			0
$29$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$29$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$30$		0			0
$31$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$31$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$32$	2.16478	−	5.22625i	0.382683	−	0.923880i
$33$			5.55288i			0.966632i
$34$	0.171573	+	5.82843i	0.0294245	+	0.999567i
$35$		0			0
$36$	−16.6143	−	6.88189i	−2.76906	−	1.14698i
$37$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$37$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$38$	−7.41421	−	7.41421i	−1.20274	−	1.20274i
$39$		0			0
$40$		0			0
$41$	6.72817	−	4.49562i	1.05076	−	0.702098i	0.0947747	−	0.995499i	$-0.469787\pi$
$41$	6.72817	−	4.49562i	1.05076	−	0.702098i	0.955990	+	0.293400i	$0.0947869\pi$
$42$		0			0
$43$	5.53553	−	2.29289i	0.844161	−	0.349663i	0.0816682	−	0.996660i	$-0.473975\pi$
$43$	5.53553	−	2.29289i	0.844161	−	0.349663i	0.762493	+	0.646997i	$0.223975\pi$
$44$	1.78176	+	2.66659i	0.268610	+	0.402003i
$45$		0			0
$46$		0			0
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$	−13.5854	+	2.70231i	−1.96089	+	0.390044i
$49$	2.67878	−	6.46716i	0.382683	−	0.923880i
$50$		−	7.07107i		−	1.00000i
$51$	11.6331	−	8.27824i	1.62896	−	1.15919i
$52$		0			0
$53$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$53$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$54$	5.72445	+	28.7788i	0.778999	+	3.91629i
$55$		0			0
$56$		0			0
$57$	−5.00887	+	25.1813i	−0.663441	+	3.33534i
$58$		0			0
$59$	4.19239	+	10.1213i	0.545802	+	1.31768i	0.920575	+	0.390567i	$0.127721\pi$
$59$	4.19239	+	10.1213i	0.545802	+	1.31768i	−0.374772	+	0.927117i	$0.622279\pi$
$60$		0			0
$61$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$61$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$62$		0			0
$63$		0			0
$64$	−5.65685	+	5.65685i	−0.707107	+	0.707107i
$65$		0			0
$66$	3.00520	−	7.25518i	0.369914	−	0.893051i
$67$		−	2.48181i		−	0.303201i	−0.988442	−	0.151601i	$-0.951557\pi$
$67$		−	2.48181i		−	0.303201i	0.988442	−	0.151601i	$-0.0484428\pi$
$68$	2.93015	−	7.70806i	0.355333	−	0.934740i
$69$		0			0
$70$		0			0
$71$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$71$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$72$	17.9832	+	17.9832i	2.11934	+	2.11934i
$73$	−13.5150	−	9.03040i	−1.58181	−	1.05693i	−0.962319	−	0.271921i	$-0.912341\pi$
$73$	−13.5150	−	9.03040i	−1.58181	−	1.05693i	−0.619486	−	0.785007i	$-0.712659\pi$
$74$		0			0
$75$	−14.3964	+	9.61940i	−1.66236	+	1.11075i
$76$	5.67459	+	13.6997i	0.650921	+	1.57146i
$77$		0			0
$78$		0			0
$79$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$79$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$80$		0			0
$81$	31.7310	−	31.7310i	3.52566	−	3.52566i
$82$	−11.2238	+	2.23255i	−1.23946	+	0.246544i
$83$	−3.63604	+	8.77817i	−0.399107	+	0.963530i	0.588771	+	0.808300i	$0.299612\pi$
$83$	−3.63604	+	8.77817i	−0.399107	+	0.963530i	−0.987878	+	0.155230i	$0.950388\pi$
$84$		0			0
$85$		0			0
$86$	−8.47343			−0.913713
$87$		0			0
$88$	−0.884830	−	4.44834i	−0.0943232	−	0.474195i
$89$	−10.2283	−	10.2283i	−1.08420	−	1.08420i	−0.996113	−	0.0880885i	$-0.971924\pi$
$89$	−10.2283	−	10.2283i	−1.08420	−	1.08420i	−0.0880885	−	0.996113i	$-0.528076\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	19.2127	+	3.82164i	1.96089	+	0.390044i
$97$	−0.618707	+	0.925961i	−0.0628202	+	0.0940171i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$	−0.618707	+	0.925961i	−0.0628202	+	0.0940171i	0.798730	+	0.601690i	$0.205506\pi$
$98$	−7.00000	+	7.00000i	−0.707107	+	0.707107i
$99$	−14.1414	+	2.81289i	−1.42126	+	0.282706i
$100$	−3.82683	+	9.23880i	−0.382683	+	0.923880i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	−19.6795	+	4.52027i	−1.94856	+	0.447574i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.99789	−	3.33948i	−0.483164	−	0.322840i	0.290021	−	0.957020i	$-0.406338\pi$
$107$	−4.99789	−	3.33948i	−0.483164	−	0.322840i	−0.773185	+	0.634180i	$0.781338\pi$
$108$	8.09560	−	40.6993i	0.778999	−	3.91629i
$109$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$109$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−8.51409	−	1.69356i	−0.800938	−	0.159317i	−0.222383	−	0.974959i	$-0.571383\pi$
$113$	−8.51409	−	1.69356i	−0.800938	−	0.159317i	−0.578556	+	0.815643i	$0.696383\pi$
$114$	20.1724	−	30.1902i	1.88932	−	2.82757i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		−	15.4930i		−	1.42625i
$119$		0			0
$120$		0			0
$121$	−7.78707	−	3.22551i	−0.707916	−	0.293228i
$122$		0			0
$123$	19.8141	+	19.8141i	1.78658	+	1.78658i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$127$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$128$	10.4525	−	4.32957i	0.923880	−	0.382683i
$129$	11.5272	+	17.2516i	1.01491	+	1.51892i
$130$		0			0
$131$	−8.27530	+	12.3849i	−0.723016	+	1.08207i	0.269858	+	0.962900i	$0.413023\pi$
$131$	−8.27530	+	12.3849i	−0.723016	+	1.08207i	−0.992874	+	0.119170i	$0.961977\pi$
$132$	−7.85295	+	7.85295i	−0.683512	+	0.683512i
$133$		0			0
$134$	−1.34315	+	3.24264i	−0.116030	+	0.280121i
$135$		0			0
$136$	−8.00000	+	8.48528i	−0.685994	+	0.727607i
$137$	11.7574			1.00450			0.502249	−	0.864723i	$-0.332506\pi$
$137$	11.7574			1.00450			0.502249	+	0.864723i	$0.332506\pi$
$138$		0			0
$139$	−2.64897	−	13.3173i	−0.224683	−	1.12956i	−0.914193	−	0.405279i	$-0.867174\pi$
$139$	−2.64897	−	13.3173i	−0.224683	−	1.12956i	0.689510	−	0.724276i	$-0.257826\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−13.7638	−	33.2287i	−1.14698	−	2.76906i
$145$		0			0
$146$	12.7709	+	19.1130i	1.05693	+	1.58181i
$147$	23.7745	+	4.72904i	1.96089	+	0.390044i
$148$		0			0
$149$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$149$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$150$	24.0158	−	4.77705i	1.96089	−	0.390044i
$151$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$151$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$152$		−	20.9706i		−	1.70094i
$153$	26.9749	+	25.4321i	2.18079	+	2.05607i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−58.6312	+	24.2858i	−4.60650	+	1.90807i
$163$	−8.78104	−	13.1418i	−0.687784	−	1.02934i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$	−8.78104	−	13.1418i	−0.687784	−	1.02934i	0.309144	−	0.951015i	$-0.399958\pi$
$164$	15.8728	+	3.15731i	1.23946	+	0.246544i
$165$		0			0
$166$	9.50143	−	9.50143i	0.737454	−	0.737454i
$167$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$167$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$168$		0			0
$169$		−	13.0000i		−	1.00000i
$170$		0			0
$171$	−66.6658			−5.09806
$172$	11.0711	+	4.58579i	0.844161	+	0.349663i
$173$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$173$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$174$		0			0
$175$		0			0
$176$	−1.25134	+	6.29090i	−0.0943232	+	0.474195i
$177$	−31.5433	+	21.0766i	−2.37094	+	1.58421i
$178$	7.82843	+	18.8995i	0.586765	+	1.41658i
$179$	−1.17525	+	0.486803i	−0.0878421	+	0.0363854i	−0.426172	−	0.904642i	$-0.640138\pi$
$179$	−1.17525	+	0.486803i	−0.0878421	+	0.0363854i	0.338330	+	0.941028i	$0.390138\pi$
$180$		0			0
$181$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$181$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.48010	−	6.44376i	−0.108235	−	0.471214i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−23.0343	−	15.3910i	−1.66236	−	1.11075i
$193$	0.368323	−	1.85169i	0.0265125	−	0.133287i	−0.965262	−	0.261283i	$-0.915854\pi$
$193$	0.368323	−	1.85169i	0.0265125	−	0.133287i	0.991775	+	0.127996i	$0.0408544\pi$
$194$	1.30951	−	0.874984i	0.0940171	−	0.0628202i
$195$		0			0
$196$	12.9343	−	5.35757i	0.923880	−	0.382683i
$197$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$197$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$198$	19.9989	+	3.97803i	1.42126	+	0.282706i
$199$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$199$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$200$	10.0000	−	10.0000i	0.707107	−	0.707107i
$201$	8.42910	−	1.67665i	0.594543	−	0.118262i
$202$		0			0
$203$		0			0
$204$	28.1588	+	4.74444i	1.97151	+	0.332177i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.88532	+	6.60516i	0.683782	+	0.456888i
$210$		0			0
$211$	23.0300	−	15.3882i	1.58545	−	1.05937i	0.625112	−	0.780535i	$-0.285053\pi$
$211$	23.0300	−	15.3882i	1.58545	−	1.05937i	0.960340	−	0.278831i	$-0.0899469\pi$
$212$		0			0
$213$		0			0
$214$	4.72274	+	7.06808i	0.322840	+	0.483164i
$215$		0			0
$216$	−32.6037	+	48.7949i	−2.21840	+	3.32007i
$217$		0			0
$218$		0			0
$219$	21.5401	−	52.0023i	1.45554	−	3.51399i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$223$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$224$		0			0
$225$	−31.7902	−	31.7902i	−2.11934	−	2.11934i
$226$	10.2077	+	6.82053i	0.679003	+	0.453695i
$227$	−4.55979	+	22.9236i	−0.302644	+	1.52149i	0.467714	+	0.883880i	$0.345078\pi$
$227$	−4.55979	+	22.9236i	−0.302644	+	1.52149i	−0.770357	+	0.637613i	$0.779922\pi$
$228$	−42.6953	+	28.5281i	−2.82757	+	1.88932i
$229$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$229$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.64662	−	9.94737i	0.435435	−	0.651674i	−0.547248	−	0.836971i	$-0.684325\pi$
$233$	6.64662	−	9.94737i	0.435435	−	0.651674i	0.982683	+	0.185296i	$0.0593245\pi$
$234$		0			0
$235$		0			0
$236$	−8.38478	+	20.2426i	−0.545802	+	1.31768i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	5.62079	+	28.2576i	0.362067	+	1.82023i	0.546585	+	0.837404i	$0.315928\pi$
$241$	5.62079	+	28.2576i	0.362067	+	1.82023i	−0.184518	+	0.982829i	$0.559072\pi$
$242$	8.42867	+	8.42867i	0.541815	+	0.541815i
$243$	77.4514	+	51.7514i	4.96851	+	3.31985i
$244$		0			0
$245$		0			0
$246$	−15.1651	−	36.6117i	−0.966890	−	2.33428i
$247$		0			0
$248$		0			0
$249$	−32.2702	−	6.41894i	−2.04504	−	0.406784i
$250$		0			0
$251$	−18.7018	+	18.7018i	−1.18044	+	1.18044i	−0.200816	+	0.979629i	$0.564359\pi$
$251$	−18.7018	+	18.7018i	−1.18044	+	1.18044i	−0.979629	+	0.200816i	$0.935641\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−16.0000			−1.00000
$257$	0.949747	+	0.393398i	0.0592436	+	0.0245395i	0.412108	−	0.911135i	$-0.364792\pi$
$257$	0.949747	+	0.393398i	0.0592436	+	0.0245395i	−0.352865	+	0.935674i	$0.614792\pi$
$258$	−5.72445	−	28.7788i	−0.356389	−	1.79169i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	17.5148	−	11.7030i	1.08207	−	0.723016i
$263$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$263$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$264$	14.5104	−	6.01039i	0.893051	−	0.369914i
$265$		0			0
$266$		0			0
$267$	27.8290	−	41.6491i	1.70311	−	2.54888i
$268$	3.50981	−	3.50981i	0.214396	−	0.214396i
$269$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$269$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	15.0447	−	6.75699i	0.912219	−	0.409702i
$273$		0			0
$274$	−15.3617	−	6.36304i	−0.928036	−	0.384405i
$275$	1.56417	+	7.86363i	0.0943232	+	0.474195i
$276$		0			0
$277$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$277$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$278$	−3.74621	+	18.8335i	−0.224683	+	1.12956i
$279$		0			0
$280$		0			0
$281$	30.2367	−	12.5244i	1.80377	−	0.747145i	0.818877	−	0.573969i	$-0.194597\pi$
$281$	30.2367	−	12.5244i	1.80377	−	0.747145i	0.984891	−	0.173176i	$-0.0554029\pi$
$282$		0			0
$283$	−26.0334	−	5.17837i	−1.54753	−	0.307822i	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−26.0334	−	5.17837i	−1.54753	−	0.307822i	−0.893645	+	0.448774i	$0.851861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$			50.8643i			2.99721i
$289$	−11.2929	+	12.7071i	−0.664288	+	0.747477i
$290$		0			0
$291$	−3.56287	−	1.47579i	−0.208859	−	0.0865124i
$292$	−6.34211	−	31.8840i	−0.371144	−	1.86587i
$293$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$293$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$294$	−28.5035	−	19.0454i	−1.66236	−	1.11075i
$295$		0			0
$296$		0			0
$297$	−12.7322	−	30.7381i	−0.738795	−	1.78361i
$298$		0			0
$299$		0			0
$300$	−33.9635	−	6.75577i	−1.96089	−	0.390044i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−11.3492	+	27.3994i	−0.650921	+	1.57146i
$305$		0			0
$306$	−21.4806	−	47.8274i	−1.22796	−	2.73411i
$307$	8.48528			0.484281			0.242140	−	0.970241i	$-0.422151\pi$
$307$	8.48528			0.484281			0.242140	+	0.970241i	$0.422151\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$311$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$312$		0			0
$313$	18.8455	−	12.5922i	1.06521	−	0.711752i	0.105979	−	0.994368i	$-0.466202\pi$
$313$	18.8455	−	12.5922i	1.06521	−	0.711752i	0.959233	+	0.282617i	$0.0912024\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$317$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	7.96561	−	19.2307i	0.444597	−	1.07335i
$322$		0			0
$323$	−0.899495	−	30.5563i	−0.0500492	−	1.70020i
$324$	89.7487			4.98604
$325$		0			0
$326$	4.36071	+	21.9228i	0.241518	+	1.21419i
$327$		0			0
$328$	−19.0302	−	12.7155i	−1.05076	−	0.702098i
$329$		0			0
$330$		0			0
$331$	12.8076	+	30.9203i	0.703970	+	1.69953i	0.714545	+	0.699590i	$0.246634\pi$
$331$	12.8076	+	30.9203i	0.703970	+	1.69953i	−0.0105746	+	0.999944i	$0.503366\pi$
$332$	−17.5563	+	7.27208i	−0.963530	+	0.399107i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−29.9113	+	5.94972i	−1.62937	+	0.324102i	−0.923312	−	0.384052i	$-0.874528\pi$
$337$	−29.9113	+	5.94972i	−1.62937	+	0.324102i	−0.706058	+	0.708154i	$0.749528\pi$
$338$	−7.03555	+	16.9853i	−0.382683	+	0.923880i
$339$		−	30.0610i		−	1.63269i
$340$		0			0
$341$		0			0
$342$	87.1030	+	36.0793i	4.70999	+	1.95094i
$343$		0			0
$344$	−11.9832	−	11.9832i	−0.646093	−	0.646093i
$345$		0			0
$346$		0			0
$347$	−1.07149	+	0.715948i	−0.0575207	+	0.0384341i	−0.583998	−	0.811755i	$-0.698512\pi$
$347$	−1.07149	+	0.715948i	−0.0575207	+	0.0384341i	0.526477	+	0.850189i	$0.323512\pi$
$348$		0			0
$349$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$349$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$350$		0			0
$351$		0			0
$352$	5.03957	−	7.54224i	0.268610	−	0.402003i
$353$	−25.7214	+	25.7214i	−1.36901	+	1.36901i	−0.507157	+	0.861853i	$0.669304\pi$
$353$	−25.7214	+	25.7214i	−1.36901	+	1.36901i	−0.861853	+	0.507157i	$0.830696\pi$
$354$	52.6199	−	10.4667i	2.79671	−	0.556301i
$355$		0			0
$356$		−	28.9301i		−	1.53329i
$357$		0			0
$358$	1.79899			0.0950796
$359$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$359$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$360$		0			0
$361$	25.4350	+	25.4350i	1.33869	+	1.33869i
$362$		0			0
$363$	5.69421	−	28.6267i	0.298869	−	1.50251i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$367$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$368$		0			0
$369$	−40.4229	+	60.4972i	−2.10433	+	3.14936i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$	−1.55350	+	9.22019i	−0.0803294	+	0.476765i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−29.6123	−	19.7863i	−1.52108	−	1.01636i	−0.985072	−	0.172145i	$-0.944930\pi$
$379$	−29.6123	−	19.7863i	−1.52108	−	1.01636i	−0.536011	−	0.844211i	$-0.680070\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$383$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$384$	21.7662	+	32.5754i	1.11075	+	1.66236i
$385$		0			0
$386$	−1.48336	+	2.22001i	−0.0755012	+	0.112995i
$387$	−38.0949	+	38.0949i	−1.93647	+	1.93647i
$388$	−2.18449	+	0.434522i	−0.110901	+	0.0220595i
$389$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$389$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$390$		0			0
$391$		0			0
$392$	−19.7990			−1.00000
$393$	−47.6539	−	19.7389i	−2.40382	−	0.995696i
$394$		0			0
$395$		0			0
$396$	−23.9769	−	16.0209i	−1.20489	−	0.805079i
$397$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$397$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$398$		0			0
$399$		0			0
$400$	−18.4776	+	7.65367i	−0.923880	+	0.382683i
$401$	16.4399	+	24.6041i	0.820971	+	1.22867i	0.970784	+	0.239956i	$0.0771329\pi$
$401$	16.4399	+	24.6041i	0.820971	+	1.22867i	−0.149813	+	0.988714i	$0.547867\pi$
$402$	−11.9206	−	2.37115i	−0.594543	−	0.118262i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−34.2236	−	21.4384i	−1.69432	−	1.06136i
$409$	22.9385			1.13423			0.567117	−	0.823637i	$-0.308059\pi$
$409$	22.9385			1.13423			0.567117	+	0.823637i	$0.308059\pi$
$410$		0			0
$411$	7.94300	+	39.9321i	0.391799	+	1.96971i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	43.4405	−	17.9937i	2.12729	−	0.881153i
$418$	−9.34110	−	13.9800i	−0.456888	−	0.683782i
$419$	−34.7144	−	6.90513i	−1.69591	−	0.337338i	−0.749919	−	0.661529i	$-0.769908\pi$
$419$	−34.7144	−	6.90513i	−1.69591	−	0.337338i	−0.945991	+	0.324192i	$0.894908\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	−38.4182	+	7.64186i	−1.87017	+	0.372000i
$423$		0			0
$424$		0			0
$425$	14.1421	−	15.0000i	0.685994	−	0.727607i
$426$		0			0
$427$		0			0
$428$	−2.34534	−	11.7908i	−0.113366	−	0.569931i
$429$		0			0
$430$		0			0
$431$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$431$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$432$	69.0064	−	46.1086i	3.32007	−	2.21840i
$433$	14.8749	+	35.9113i	0.714843	+	1.72578i	0.687528	+	0.726158i	$0.258696\pi$
$433$	14.8749	+	35.9113i	0.714843	+	1.72578i	0.0273152	+	0.999627i	$0.491304\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−56.2869	+	56.2869i	−2.68949	+	2.68949i
$439$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$439$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$440$		0			0
$441$			62.9413i			2.99721i
$442$		0			0
$443$	39.8853			1.89501			0.947505	−	0.319742i	$-0.103596\pi$
$443$	39.8853			1.89501			0.947505	+	0.319742i	$0.103596\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	31.6495	−	21.1475i	1.49363	−	0.998012i	0.502580	−	0.864531i	$-0.332384\pi$
$449$	31.6495	−	21.1475i	1.49363	−	0.998012i	0.991051	−	0.133482i	$-0.0426157\pi$
$450$	24.3311	+	58.7406i	1.14698	+	2.76906i
$451$	11.9880	−	4.96558i	0.564491	−	0.233820i
$452$	−9.64569	−	14.4358i	−0.453695	−	0.679003i
$453$		0			0
$454$	18.3638	−	27.4834i	0.861856	−	1.28986i
$455$		0			0
$456$	71.2234	−	14.1672i	3.33534	−	0.663441i
$457$	−2.14885	+	5.18779i	−0.100519	+	0.242675i	−0.966137	−	0.258031i	$-0.916926\pi$
$457$	−2.14885	+	5.18779i	−0.100519	+	0.242675i	0.865617	+	0.500706i	$0.166926\pi$
$458$		0			0
$459$	−45.4141	+	72.4979i	−2.11975	+	3.38391i
$460$		0			0
$461$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$461$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$462$		0			0
$463$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$463$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$464$		0			0
$465$		0			0
$466$	−14.0677	+	9.39974i	−0.651674	+	0.435435i
$467$	−16.5370	−	39.9238i	−0.765240	−	1.84745i	−0.399439	−	0.916760i	$-0.630795\pi$
$467$	−16.5370	−	39.9238i	−0.765240	−	1.84745i	−0.365801	−	0.930693i	$-0.619205\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	21.9105	−	21.9105i	1.00851	−	1.00851i
$473$	9.42318	−	1.87439i	0.433278	−	0.0861844i
$474$		0			0
$475$			37.0711i			1.70094i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$479$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$480$		0			0
$481$		0			0
$482$	7.94899	−	39.9623i	0.362067	−	1.82023i
$483$		0			0
$484$	−6.45102	−	15.5741i	−0.293228	−	0.707916i
$485$		0			0
$486$	−73.1875	−	109.533i	−3.31985	−	4.96851i
$487$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$487$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$488$		0			0
$489$	38.7018	−	38.7018i	1.75015	−	1.75015i
$490$		0			0
$491$	−7.53828	+	18.1990i	−0.340198	+	0.821311i	0.657497	+	0.753457i	$0.271615\pi$
$491$	−7.53828	+	18.1990i	−0.340198	+	0.821311i	−0.997695	+	0.0678537i	$0.978385\pi$
$492$			56.0428i			2.52660i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	38.6891	+	25.8513i	1.73370	+	1.15842i
$499$	−4.29354	+	21.5851i	−0.192205	+	0.966282i	0.757428	+	0.652919i	$0.226456\pi$
$499$	−4.29354	+	21.5851i	−0.192205	+	0.966282i	−0.949633	+	0.313363i	$0.898544\pi$
$500$		0			0
$501$		0			0
$502$	34.5563	−	14.3137i	1.54233	−	0.638852i
$503$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$503$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	44.1526	−	8.78250i	1.96089	−	0.390044i
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$		0			0
$512$	20.9050	+	8.65914i	0.923880	+	0.382683i
$513$	−30.0112	−	150.877i	−1.32503	−	6.66137i
$514$	−1.02800	−	1.02800i	−0.0453431	−	0.0453431i
$515$		0			0
$516$	−8.09560	+	40.6993i	−0.356389	+	1.79169i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−44.6805	−	8.88750i	−1.95749	−	0.389368i	−0.991325	−	0.131432i	$-0.958042\pi$
$521$	−44.6805	−	8.88750i	−1.95749	−	0.389368i	−0.966162	−	0.257936i	$-0.916958\pi$
$522$		0			0
$523$	31.7130	−	31.7130i	1.38671	−	1.38671i	0.554587	−	0.832126i	$-0.312876\pi$
$523$	31.7130	−	31.7130i	1.38671	−	1.38671i	0.832126	−	0.554587i	$-0.187124\pi$
$524$	−29.2179	+	5.81180i	−1.27639	+	0.253889i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−22.2115			−0.966632
$529$	−21.2492	−	8.80172i	−0.923880	−	0.382683i
$530$		0			0
$531$	−69.6538	−	69.6538i	−3.02272	−	3.02272i
$532$		0			0
$533$		0			0
$534$	−58.9007	+	39.3562i	−2.54888	+	1.70311i
$535$		0			0
$536$	−6.48528	+	2.68629i	−0.280121	+	0.116030i
$537$	−2.44732	−	3.66268i	−0.105610	−	0.158056i
$538$		0			0
$539$	6.23614	−	9.33305i	0.268610	−	0.402003i
$540$		0			0
$541$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$541$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$542$		0			0
$543$		0			0
$544$	−23.3137	+	0.686292i	−0.999567	+	0.0294245i
$545$		0			0
$546$		0			0
$547$	8.38143	+	42.1363i	0.358364	+	1.80162i	0.567104	+	0.823646i	$0.308064\pi$
$547$	8.38143	+	42.1363i	0.358364	+	1.80162i	−0.208741	+	0.977971i	$0.566936\pi$
$548$	16.6274	+	16.6274i	0.710288	+	0.710288i
$549$		0			0
$550$	2.21208	−	11.1209i	0.0943232	−	0.474195i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	15.0872	−	22.5797i	0.639842	−	0.957591i
$557$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$557$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	20.8854	−	9.38018i	0.881780	−	0.396031i
$562$	−46.2843			−1.95238
$563$	41.9914	+	17.3934i	1.76973	+	0.733044i	0.994900	+	0.100870i	$0.0321625\pi$
$563$	41.9914	+	17.3934i	1.76973	+	0.733044i	0.774826	+	0.632175i	$0.217837\pi$
$564$		0			0
$565$		0			0
$566$	31.2118	+	20.8551i	1.31193	+	0.876604i
$567$		0			0
$568$		0			0
$569$	−14.1508	−	34.1630i	−0.593231	−	1.43219i	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−14.1508	−	34.1630i	−0.593231	−	1.43219i	0.287135	−	0.957890i	$-0.407297\pi$
$570$		0			0
$571$	−20.7334	−	31.0298i	−0.867668	−	1.29856i	−0.953237	−	0.302224i	$-0.902271\pi$
$571$	−20.7334	−	31.0298i	−0.867668	−	1.29856i	0.0855694	−	0.996332i	$-0.472729\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	27.5275	−	66.4574i	1.14698	−	2.76906i
$577$			33.9411i			1.41299i	0.707719	+	0.706494i	$0.249724\pi$
$577$			33.9411i			1.41299i	−0.707719	+	0.706494i	$0.750276\pi$
$578$	21.6319	−	10.4910i	0.899769	−	0.436367i
$579$	6.53781			0.271702
$580$		0			0
$581$		0			0
$582$	3.85643	+	3.85643i	0.159854	+	0.159854i
$583$		0			0
$584$	−8.96910	+	45.0907i	−0.371144	+	1.86587i
$585$		0			0
$586$		0			0
$587$	−5.54328	+	2.29610i	−0.228796	+	0.0947702i	−0.494136	−	0.869385i	$-0.664516\pi$
$587$	−5.54328	+	2.29610i	−0.228796	+	0.0947702i	0.265341	+	0.964155i	$0.414516\pi$
$588$	26.9343	+	40.3100i	1.11075	+	1.66236i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.3640	−	32.2635i	0.548792	−	1.32490i	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	13.3640	−	32.2635i	0.548792	−	1.32490i	0.918378	−	0.395705i	$-0.129500\pi$
$594$			47.0519i			1.93056i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$599$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$600$	40.7193	+	27.2078i	1.66236	+	1.11075i
$601$	7.73860	−	38.9046i	0.315664	−	1.58695i	−0.418655	−	0.908145i	$-0.637498\pi$
$601$	7.73860	−	38.9046i	0.315664	−	1.58695i	0.734319	−	0.678804i	$-0.237502\pi$
$602$		0			0
$603$	8.53977	+	20.6168i	0.347766	+	0.839582i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$607$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$608$	29.6569	−	29.6569i	1.20274	−	1.20274i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	2.18173	+	74.1147i	0.0881913	+	2.99591i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−11.0866	−	4.59220i	−0.447417	−	0.185326i
$615$		0			0
$616$		0			0
$617$	18.0415	+	12.0550i	0.726325	+	0.485315i	0.862938	−	0.505310i	$-0.168622\pi$
$617$	18.0415	+	12.0550i	0.726325	+	0.485315i	−0.136613	+	0.990624i	$0.543622\pi$
$618$		0			0
$619$	−37.5733	+	25.1057i	−1.51020	+	1.00908i	−0.522514	+	0.852631i	$0.675006\pi$
$619$	−37.5733	+	25.1057i	−1.51020	+	1.00908i	−0.987685	+	0.156452i	$0.949994\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.6777	+	17.6777i	−0.707107	+	0.707107i
$626$	−31.4377	+	6.25335i	−1.25650	+	0.249934i
$627$	−15.7552	+	38.0363i	−0.629201	+	1.51902i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$631$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$632$		0			0
$633$	67.8222	+	67.8222i	2.69569	+	2.69569i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−19.9642	+	29.8785i	−0.788538	+	1.18013i	0.191534	+	0.981486i	$0.438654\pi$
$641$	−19.9642	+	29.8785i	−0.788538	+	1.18013i	−0.980072	+	0.198645i	$0.936346\pi$
$642$	−20.8151	+	20.8151i	−0.821508	+	0.821508i
$643$	−17.7294	+	3.52660i	−0.699180	+	0.139076i	−0.531866	−	0.846828i	$-0.678509\pi$
$643$	−17.7294	+	3.52660i	−0.699180	+	0.139076i	−0.167313	+	0.985904i	$0.553509\pi$
$644$		0			0
$645$		0			0
$646$	−15.3617	+	40.4106i	−0.604399	+	1.58993i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−117.262	−	48.5716i	−4.60650	−	1.90807i
$649$	3.42718	+	17.2296i	0.134529	+	0.676321i
$650$		0			0
$651$		0			0
$652$	6.16698	−	31.0035i	0.241518	−	1.21419i
$653$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$653$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$654$		0			0
$655$		0			0
$656$	17.9825	+	26.9127i	0.702098	+	1.05076i
$657$	143.344	+	28.5129i	5.59239	+	1.11240i
$658$		0			0
$659$	12.7279	−	12.7279i	0.495809	−	0.495809i	−0.414321	−	0.910131i	$-0.635981\pi$
$659$	12.7279	−	12.7279i	0.495809	−	0.495809i	0.910131	+	0.414321i	$0.135981\pi$
$660$		0			0
$661$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$661$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$662$		−	47.3308i		−	1.83956i
$663$		0			0
$664$	26.8741			1.04292
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−10.9671	−	16.4134i	−0.422750	−	0.632690i	0.557564	−	0.830134i	$-0.311736\pi$
$673$	−10.9671	−	16.4134i	−0.422750	−	0.632690i	−0.980314	+	0.197444i	$0.936736\pi$
$674$	42.3009	+	8.41417i	1.62937	+	0.324102i
$675$	57.6358	−	86.2580i	2.21840	−	3.32007i
$676$	18.3848	−	18.3848i	0.707107	−	0.707107i
$677$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$677$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$678$	−16.2689	+	39.2766i	−0.624803	+	1.50841i
$679$		0			0
$680$		0			0
$681$	−80.9371			−3.10152
$682$		0			0
$683$	−9.22051	−	46.3546i	−0.352813	−	1.77371i	−0.595247	−	0.803543i	$-0.702946\pi$
$683$	−9.22051	−	46.3546i	−0.352813	−	1.77371i	0.242434	−	0.970168i	$-0.422054\pi$
$684$	−94.2797	−	94.2797i	−3.60487	−	3.60487i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	9.17157	+	22.1421i	0.349663	+	0.844161i
$689$		0			0
$690$		0			0
$691$	39.3785	+	7.83286i	1.49803	+	0.297976i	0.874961	−	0.484193i	$-0.160887\pi$
$691$	39.3785	+	7.83286i	1.49803	+	0.297976i	0.623066	+	0.782169i	$0.285887\pi$
$692$		0			0
$693$		0			0
$694$	1.78744	−	0.355544i	0.0678503	−	0.0134963i
$695$		0			0
$696$		0			0
$697$	−28.2744	−	17.7116i	−1.07097	−	0.670876i
$698$		0			0
$699$	38.2751	+	15.8541i	1.44770	+	0.599656i
$700$		0			0
$701$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$701$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$702$		0			0
$703$		0			0
$704$	−10.6663	+	7.12702i	−0.402003	+	0.268610i
$705$		0			0
$706$	47.5269	−	19.6863i	1.78870	−	0.740903i
$707$		0			0
$708$	−74.4157	−	14.8022i	−2.79671	−	0.556301i
$709$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$709$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$710$		0			0
$711$		0			0
$712$	−15.6569	+	37.7990i	−0.586765	+	1.41658i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.35049	−	0.973606i	−0.0878421	−	0.0363854i
$717$		0			0
$718$		0			0
$719$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$719$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$720$		0			0
$721$		0			0
$722$	−19.4671	−	46.9978i	−0.724491	−	1.74908i
$723$	−92.1756	+	38.1804i	−3.42805	+	1.41994i
$724$		0			0
$725$		0			0
$726$	−22.9325	+	34.3209i	−0.851106	+	1.27377i
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$		0			0
$729$	−71.9236	+	173.639i	−2.66384	+	6.43107i
$730$		0			0
$731$	−17.9749	−	16.9469i	−0.664824	−	0.626802i
$732$		0			0
$733$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$733$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.776396	−	3.90321i	0.0285989	−	0.143776i
$738$	85.5559	−	57.1666i	3.14936	−	2.10433i
$739$	16.2359	+	39.1969i	0.597247	+	1.44188i	0.876376	+	0.481627i	$0.159954\pi$
$739$	16.2359	+	39.1969i	0.597247	+	1.44188i	−0.279129	+	0.960253i	$0.590046\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$743$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	85.4332i		−	3.12584i
$748$	7.01967	−	11.2060i	0.256665	−	0.409733i
$749$		0			0
$750$		0			0
$751$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$751$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$752$		0			0
$753$	−76.1523	−	50.8833i	−2.77514	−	1.85429i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$757$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$758$	27.9821	+	41.8782i	1.01636	+	1.52108i
$759$		0			0
$760$		0			0
$761$	−21.3431	+	21.3431i	−0.773688	+	0.773688i	−0.978749	−	0.205061i	$-0.934261\pi$
$761$	−21.3431	+	21.3431i	−0.773688	+	0.773688i	0.205061	+	0.978749i	$0.434261\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−10.8092	−	54.3417i	−0.390044	−	1.96089i
$769$	−14.4558	−	14.4558i	−0.521291	−	0.521291i	0.396670	−	0.917961i	$-0.370166\pi$
$769$	−14.4558	−	14.4558i	−0.521291	−	0.521291i	−0.917961	+	0.396670i	$0.870166\pi$
$770$		0			0
$771$	−0.694492	+	3.49145i	−0.0250115	+	0.125741i
$772$	3.13957	−	2.09779i	0.112995	−	0.0755012i
$773$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$773$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$774$	70.3902	−	29.1566i	2.53012	−	1.04801i
$775$		0			0
$776$	3.08934	+	0.614507i	0.110901	+	0.0220595i
$777$		0			0
$778$		0			0
$779$	58.8423	−	11.7045i	2.10825	−	0.419356i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	25.8686	+	10.7151i	0.923880	+	0.382683i
$785$		0			0
$786$	51.5803	+	51.5803i	1.83981	+	1.83981i
$787$	−5.49830	−	3.67385i	−0.195993	−	0.130959i	0.453701	−	0.891154i	$-0.350103\pi$
$787$	−5.49830	−	3.67385i	−0.195993	−	0.130959i	−0.649695	+	0.760195i	$0.725103\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	22.6569	+	33.9085i	0.805079	+	1.20489i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$797$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$798$		0			0
$799$		0			0
$800$	28.2843			1.00000
$801$	120.164	+	49.7734i	4.24577	+	1.75866i
$802$	−8.16416	−	41.0440i	−0.288287	−	1.44932i
$803$	−18.4303	−	18.4303i	−0.650391	−	0.650391i
$804$	14.2917	+	9.54941i	0.504029	+	0.336782i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−27.9832	−	41.8798i	−0.983837	−	1.47242i	−0.878363	−	0.477994i	$-0.841364\pi$
$809$	−27.9832	−	41.8798i	−0.983837	−	1.47242i	−0.105474	−	0.994422i	$-0.533636\pi$
$810$		0			0
$811$	7.86943	−	11.7774i	0.276333	−	0.413562i	−0.667180	−	0.744896i	$-0.732499\pi$
$811$	7.86943	−	11.7774i	0.276333	−	0.413562i	0.943513	+	0.331335i	$0.107499\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	33.1130	+	46.5323i	1.15919	+	1.62896i
$817$	44.4231			1.55417
$818$	−29.9706	−	12.4142i	−1.04790	−	0.434053i
$819$		0			0
$820$		0			0
$821$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$821$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$822$	11.2331	−	56.4726i	0.391799	−	1.96971i
$823$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$823$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$824$		0			0
$825$	−25.6509	+	10.6250i	−0.893051	+	0.369914i
$826$		0			0
$827$	−13.2784	−	2.64124i	−0.461735	−	0.0918448i	−0.0412591	−	0.999148i	$-0.513137\pi$
$827$	−13.2784	−	2.64124i	−0.461735	−	0.0918448i	−0.420476	+	0.907304i	$0.638137\pi$
$828$		0			0
$829$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$829$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−28.8492	+	0.849242i	−0.999567	+	0.0294245i
$834$	−66.4959			−2.30256
$835$		0			0
$836$	4.63885	+	23.3211i	0.160438	+	0.806576i
$837$		0			0
$838$	41.6196	+	27.8093i	1.43772	+	0.960656i
$839$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$839$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$840$		0			0
$841$	−11.0978	−	26.7925i	−0.382683	−	0.923880i
$842$		0			0
$843$	62.9646	+	94.2332i	2.16862	+	3.24556i
$844$	54.3315	+	10.8072i	1.87017	+	0.372000i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$		−	91.9171i		−	3.15459i
$850$	−26.5955	+	11.9448i	−0.912219	+	0.409702i
$851$		0			0
$852$		0			0
$853$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$853$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$854$		0			0
$855$		0			0
$856$	−3.31681	+	16.6747i	−0.113366	+	0.569931i
$857$	−27.2119	+	18.1824i	−0.929542	+	0.621100i	−0.925441	−	0.378892i	$-0.876305\pi$
$857$	−27.2119	+	18.1824i	−0.929542	+	0.621100i	−0.00410087	+	0.999992i	$0.501305\pi$
$858$		0			0
$859$	−52.5061	+	21.7487i	−1.79148	+	0.742057i	−0.802018	+	0.597300i	$0.796240\pi$
$859$	−52.5061	+	21.7487i	−1.79148	+	0.742057i	−0.989467	+	0.144757i	$0.953760\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$	−115.115	+	22.8978i	−3.91629	+	0.778999i
$865$		0			0
$866$		−	54.9706i		−	1.86798i
$867$	−50.7870	−	29.7700i	−1.72482	−	1.01104i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.95353	−	9.82105i	0.0661169	−	0.332392i
$874$		0			0
$875$		0			0
$876$	104.005	−	43.0801i	3.51399	−	1.45554i
$877$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$877$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−50.9714	+	10.1388i	−1.71727	+	0.341586i	−0.952921	−	0.303218i	$-0.901939\pi$
$881$	−50.9714	+	10.1388i	−1.71727	+	0.341586i	−0.764348	+	0.644804i	$0.776939\pi$
$882$	34.0636	−	82.2368i	1.14698	−	2.76906i
$883$			20.8825i			0.702751i	0.936235	+	0.351376i	$0.114286\pi$
$883$			20.8825i			0.702751i	−0.936235	+	0.351376i	$0.885714\pi$
$884$		0			0
$885$		0			0
$886$	−52.1127	−	21.5858i	−1.75076	−	0.725189i
$887$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$887$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	59.8307	−	39.9776i	2.00440	−	1.33930i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−52.7970	+	10.5020i	−1.76186	+	0.350455i
$899$		0			0
$900$		−	89.9162i		−	2.99721i
$901$		0			0
$902$	−18.3504			−0.611001
$903$		0			0
$904$	4.79011	+	24.0815i	0.159317	+	0.800938i
$905$		0			0
$906$		0			0
$907$	−11.7457	+	59.0497i	−0.390010	+	1.96071i	−0.166022	+	0.986122i	$0.553092\pi$
$907$	−11.7457	+	59.0497i	−0.390010	+	1.96071i	−0.223988	+	0.974592i	$0.571908\pi$
$908$	−38.8674	+	25.9704i	−1.28986	+	0.861856i
$909$		0			0
$910$		0			0
$911$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$911$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$912$	−100.725	−	20.0355i	−3.33534	−	0.663441i
$913$	−8.46461	+	12.6682i	−0.280138	+	0.419256i
$914$	5.61522	−	5.61522i	0.185735	−	0.185735i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	98.5720	−	70.1451i	3.25336	−	2.31513i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	5.73246	+	28.8190i	0.188891	+	0.949619i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−52.4900	−	10.4409i	−1.72214	−	0.342555i	−0.767666	−	0.640850i	$-0.778582\pi$
$929$	−52.4900	−	10.4409i	−1.72214	−	0.342555i	−0.954474	+	0.298295i	$0.903582\pi$
$930$		0			0
$931$	36.6985	−	36.6985i	1.20274	−	1.20274i
$932$	23.4675	−	4.66797i	0.768702	−	0.152904i
$933$		0			0
$934$			61.1127i			1.99967i
$935$		0			0
$936$		0			0
$937$	−47.0363	−	19.4831i	−1.53661	−	0.636484i	−0.555775	−	0.831333i	$-0.687578\pi$
$937$	−47.0363	−	19.4831i	−1.53661	−	0.636484i	−0.980833	+	0.194849i	$0.937578\pi$
$938$		0			0
$939$	55.4991	+	55.4991i	1.81114	+	1.81114i
$940$		0			0
$941$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$941$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$942$		0			0
$943$		0			0
$944$	−40.4853	+	16.7696i	−1.31768	+	0.545802i
$945$		0			0
$946$	−13.3264	−	2.65078i	−0.433278	−	0.0861844i
$947$	−15.5649	+	23.2946i	−0.505793	+	0.756972i	−0.993227	−	0.116187i	$-0.962933\pi$
$947$	−15.5649	+	23.2946i	−0.505793	+	0.756972i	0.487435	+	0.873160i	$0.337933\pi$
$948$		0			0
$949$		0			0
$950$	20.0627	−	48.4357i	0.650921	−	1.57146i
$951$		0			0
$952$		0			0
$953$	21.4847			0.695957			0.347978	−	0.937503i	$-0.386868\pi$
$953$	21.4847			0.695957			0.347978	+	0.937503i	$0.386868\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	28.6403	−	11.8632i	0.923880	−	0.382683i
$962$		0			0
$963$	53.0093	+	10.5442i	1.70820	+	0.339782i
$964$	−32.0133	+	47.9113i	−1.03108	+	1.54312i
$965$		0			0
$966$		0			0
$967$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$967$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$968$			23.8399i			0.766242i
$969$	103.172	−	23.6982i	3.31438	−	0.761295i
$970$		0			0
$971$	57.0919	+	23.6482i	1.83217	+	0.758908i	0.965694	+	0.259681i	$0.0836174\pi$
$971$	57.0919	+	23.6482i	1.83217	+	0.758908i	0.866471	+	0.499227i	$0.166383\pi$
$972$	36.3453	+	182.720i	1.16578	+	5.86076i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.2340	+	27.1213i	0.359408	+	0.867688i	0.995383	+	0.0959785i	$0.0305980\pi$
$977$	11.2340	+	27.1213i	0.359408	+	0.867688i	−0.635975	+	0.771709i	$0.719402\pi$
$978$	−71.5115	+	29.6210i	−2.28669	+	0.947177i
$979$	−12.8866	−	19.2861i	−0.411857	−	0.616388i
$980$		0			0
$981$		0			0
$982$	19.6985	−	19.6985i	0.628604	−	0.628604i
$983$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$983$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$984$	30.3301	−	73.2234i	0.966890	−	2.33428i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$991$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$992$		0			0
$993$	−96.3638	+	64.3882i	−3.05801	+	2.04330i
$994$		0			0
$995$		0			0
$996$	−36.5592	−	54.7147i	−1.15842	−	1.73370i
$997$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$997$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$998$	17.2916	−	25.8786i	0.547355	−	0.819174i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.b.11.1	✓	8
4.3	odd	2		544.2.cc.a.79.1		8
8.3	odd	2	CM	136.2.s.b.11.1	✓	8
8.5	even	2		544.2.cc.a.79.1		8
17.14	odd	16	inner	136.2.s.b.99.1	yes	8
68.31	even	16		544.2.cc.a.303.1		8
136.99	even	16	inner	136.2.s.b.99.1	yes	8
136.133	odd	16		544.2.cc.a.303.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.b.11.1	✓	8	1.1	even	1	trivial
136.2.s.b.11.1	✓	8	8.3	odd	2	CM
136.2.s.b.99.1	yes	8	17.14	odd	16	inner
136.2.s.b.99.1	yes	8	136.99	even	16	inner
544.2.cc.a.79.1		8	4.3	odd	2
544.2.cc.a.79.1		8	8.5	even	2
544.2.cc.a.303.1		8	68.31	even	16
544.2.cc.a.303.1		8	136.133	odd	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30656 - 0.541196i) q^{2} +(0.675577 + 3.39635i) q^{3} +(1.41421 + 1.41421i) q^{4} +(0.955410 - 4.80317i) q^{6} +(-1.08239 - 2.61313i) q^{8} +(-8.30717 + 3.44094i) q^{9} +O(q^{10})\)	\(q+(-1.30656 - 0.541196i) q^{2} +(0.675577 + 3.39635i) q^{3} +(1.41421 + 1.41421i) q^{4} +(0.955410 - 4.80317i) q^{6} +(-1.08239 - 2.61313i) q^{8} +(-8.30717 + 3.44094i) q^{9} +(1.57273 + 0.312835i) q^{11} +(-3.84776 + 5.75858i) q^{12} +4.00000i q^{16} +(-1.68925 - 3.76118i) q^{17} +12.7161 q^{18} +(6.84984 + 2.83730i) q^{19} +(-1.88556 - 1.25989i) q^{22} +(8.14386 - 5.44155i) q^{24} +(1.91342 + 4.61940i) q^{25} +(-11.5272 - 17.2516i) q^{27} +(2.16478 - 5.22625i) q^{32} +5.55288i q^{33} +(0.171573 + 5.82843i) q^{34} +(-16.6143 - 6.88189i) q^{36} +(-7.41421 - 7.41421i) q^{38} +(6.72817 - 4.49562i) q^{41} +(5.53553 - 2.29289i) q^{43} +(1.78176 + 2.66659i) q^{44} +(-13.5854 + 2.70231i) q^{48} +(2.67878 - 6.46716i) q^{49} -7.07107i q^{50} +(11.6331 - 8.27824i) q^{51} +(5.72445 + 28.7788i) q^{54} +(-5.00887 + 25.1813i) q^{57} +(4.19239 + 10.1213i) q^{59} +(-5.65685 + 5.65685i) q^{64} +(3.00520 - 7.25518i) q^{66} -2.48181i q^{67} +(2.93015 - 7.70806i) q^{68} +(17.9832 + 17.9832i) q^{72} +(-13.5150 - 9.03040i) q^{73} +(-14.3964 + 9.61940i) q^{75} +(5.67459 + 13.6997i) q^{76} +(31.7310 - 31.7310i) q^{81} +(-11.2238 + 2.23255i) q^{82} +(-3.63604 + 8.77817i) q^{83} -8.47343 q^{86} +(-0.884830 - 4.44834i) q^{88} +(-10.2283 - 10.2283i) q^{89} +(19.2127 + 3.82164i) q^{96} +(-0.618707 + 0.925961i) q^{97} +(-7.00000 + 7.00000i) q^{98} +(-14.1414 + 2.81289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 8 q^{6} - 16 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 - 8 * q^6 - 16 * q^9	\( 8 q + 8 q^{3} - 8 q^{6} - 16 q^{9} - 16 q^{12} + 24 q^{22} + 32 q^{24} - 16 q^{27} + 24 q^{34} - 32 q^{36} - 48 q^{38} + 32 q^{41} + 16 q^{43} + 16 q^{44} - 32 q^{48} + 40 q^{51} - 8 q^{54} - 40 q^{57} - 40 q^{59} + 56 q^{66} + 48 q^{72} - 48 q^{73} + 56 q^{81} - 80 q^{83} + 32 q^{96} - 56 q^{98} + 32 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 8 * q^6 - 16 * q^9 - 16 * q^12 + 24 * q^22 + 32 * q^24 - 16 * q^27 + 24 * q^34 - 32 * q^36 - 48 * q^38 + 32 * q^41 + 16 * q^43 + 16 * q^44 - 32 * q^48 + 40 * q^51 - 8 * q^54 - 40 * q^57 - 40 * q^59 + 56 * q^66 + 48 * q^72 - 48 * q^73 + 56 * q^81 - 80 * q^83 + 32 * q^96 - 56 * q^98 + 32 * q^99

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