LMFDB - Embedded newform 1127.2.c.c.1126.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1127,2,Mod(1126,1127)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1127, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1127.1126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1127 = 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1127.c (of order $2$, degree $1$, 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:	$8.99914030780$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 161)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1126.10
Character	$\chi$	$=$	1127.1126
Dual form			1127.2.c.c.1126.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.584306 q^{2} +0.589587i q^{3} -1.65859 q^{4} +3.53325 q^{5} -0.344500i q^{6} +2.13773 q^{8} +2.65239 q^{9} -2.06450 q^{10} -0.280969i q^{11} -0.977882i q^{12} -6.20533i q^{13} +2.08316i q^{15} +2.06808 q^{16} +3.79570 q^{17} -1.54981 q^{18} -3.85425 q^{19} -5.86020 q^{20} +0.164172i q^{22} +(-2.06808 - 4.32701i) q^{23} +1.26038i q^{24} +7.48386 q^{25} +3.62581i q^{26} +3.33258i q^{27} -2.64066 q^{29} -1.21720i q^{30} -5.30430i q^{31} -5.48386 q^{32} +0.165656 q^{33} -2.21785 q^{34} -4.39921 q^{36} -0.745680i q^{37} +2.25206 q^{38} +3.65859 q^{39} +7.55315 q^{40} +4.20999i q^{41} -7.90283i q^{43} +0.466011i q^{44} +9.37155 q^{45} +(1.20839 + 2.52830i) q^{46} +6.24816i q^{47} +1.21931i q^{48} -4.37287 q^{50} +2.23790i q^{51} +10.2921i q^{52} +1.32805i q^{53} -1.94725i q^{54} -0.992733i q^{55} -2.27242i q^{57} +1.54295 q^{58} +3.59592i q^{59} -3.45510i q^{60} +10.3536 q^{61} +3.09934i q^{62} -0.931905 q^{64} -21.9250i q^{65} -0.0967936 q^{66} -11.1972i q^{67} -6.29550 q^{68} +(2.55115 - 1.21931i) q^{69} +5.77682 q^{71} +5.67010 q^{72} +7.45389i q^{73} +0.435706i q^{74} +4.41239i q^{75} +6.39260 q^{76} -2.13773 q^{78} -7.14772i q^{79} +7.30705 q^{80} +5.99231 q^{81} -2.45992i q^{82} -10.3906 q^{83} +13.4112 q^{85} +4.61768i q^{86} -1.55690i q^{87} -0.600637i q^{88} +5.58545 q^{89} -5.47585 q^{90} +(3.43009 + 7.17672i) q^{92} +3.12735 q^{93} -3.65084i q^{94} -13.6180 q^{95} -3.23322i q^{96} +10.9371 q^{97} -0.745238i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 8 q^{2} + 24 q^{4} + 12 q^{8} - 8 q^{9} - 44 q^{18} + 44 q^{25} - 44 q^{29} + 12 q^{32} + 32 q^{39} - 36 q^{46} + 84 q^{50} - 28 q^{58} - 68 q^{64} + 16 q^{71} + 8 q^{72} - 12 q^{78} - 44 q^{81}+ \cdots - 112 q^{95}+O(q^{100}) $ 28 * q + 8 * q^2 + 24 * q^4 + 12 * q^8 - 8 * q^9 - 44 * q^18 + 44 * q^25 - 44 * q^29 + 12 * q^32 + 32 * q^39 - 36 * q^46 + 84 * q^50 - 28 * q^58 - 68 * q^64 + 16 * q^71 + 8 * q^72 - 12 * q^78 - 44 * q^81 - 52 * q^85 - 28 * q^92 + 20 * q^93 - 112 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1127\mathbb{Z}\right)^\times$.

$n$	$346$	$442$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.584306			−0.413167			−0.206583	−	0.978429i	$-0.566234\pi$
$2$	−0.584306			−0.413167			−0.206583	+	0.978429i	$0.566234\pi$
$3$			0.589587i			0.340399i	0.985410	+	0.170199i	$0.0544411\pi$
$3$			0.589587i			0.340399i	−0.985410	+	0.170199i	$0.945559\pi$
$4$	−1.65859			−0.829293
$5$	3.53325			1.58012			0.790059	−	0.613031i	$-0.210050\pi$
$5$	3.53325			1.58012			0.790059	+	0.613031i	$0.210050\pi$
$6$		−	0.344500i		−	0.140641i
$7$		0			0
$7$		0			0
$8$	2.13773			0.755803
$9$	2.65239			0.884129
$10$	−2.06450			−0.652852
$11$		−	0.280969i		−	0.0847153i	−0.999103	−	0.0423576i	$-0.986513\pi$
$11$		−	0.280969i		−	0.0847153i	0.999103	−	0.0423576i	$-0.0134869\pi$
$12$		−	0.977882i		−	0.282290i
$13$		−	6.20533i		−	1.72105i	−0.509409	−	0.860525i	$-0.670136\pi$
$13$		−	6.20533i		−	1.72105i	0.509409	−	0.860525i	$-0.329864\pi$
$14$		0			0
$15$			2.08316i			0.537870i
$16$	2.06808			0.517020
$17$	3.79570			0.920593			0.460296	−	0.887765i	$-0.347743\pi$
$17$	3.79570			0.920593			0.460296	+	0.887765i	$0.347743\pi$
$18$	−1.54981			−0.365293
$19$	−3.85425			−0.884225			−0.442113	−	0.896960i	$-0.645771\pi$
$19$	−3.85425			−0.884225			−0.442113	+	0.896960i	$0.645771\pi$
$20$	−5.86020			−1.31038
$21$		0			0
$22$			0.164172i			0.0350015i
$23$	−2.06808	−	4.32701i	−0.431225	−	0.902245i
$23$	−2.06808	−	4.32701i	−0.431225	−	0.902245i
$24$			1.26038i			0.257274i
$25$	7.48386			1.49677
$26$			3.62581i			0.711081i
$27$			3.33258i			0.641355i
$28$		0			0
$29$	−2.64066			−0.490358			−0.245179	−	0.969478i	$-0.578847\pi$
$29$	−2.64066			−0.490358			−0.245179	+	0.969478i	$0.578847\pi$
$30$		−	1.21720i		−	0.222230i
$31$		−	5.30430i		−	0.952681i	−0.879261	−	0.476340i	$-0.841963\pi$
$31$		−	5.30430i		−	0.952681i	0.879261	−	0.476340i	$-0.158037\pi$
$32$	−5.48386			−0.969419
$33$	0.165656			0.0288369
$34$	−2.21785			−0.380358
$35$		0			0
$36$	−4.39921			−0.733202
$37$		−	0.745680i		−	0.122589i	−0.998120	−	0.0612945i	$-0.980477\pi$
$37$		−	0.745680i		−	0.122589i	0.998120	−	0.0612945i	$-0.0195229\pi$
$38$	2.25206			0.365333
$39$	3.65859			0.585843
$40$	7.55315			1.19426
$41$			4.20999i			0.657490i	0.944419	+	0.328745i	$0.106626\pi$
$41$			4.20999i			0.657490i	−0.944419	+	0.328745i	$0.893374\pi$
$42$		0			0
$43$		−	7.90283i		−	1.20517i	−0.798054	−	0.602585i	$-0.794137\pi$
$43$		−	7.90283i		−	1.20517i	0.798054	−	0.602585i	$-0.205863\pi$
$44$			0.466011i			0.0702538i
$45$	9.37155			1.39703
$46$	1.20839	+	2.52830i	0.178168	+	0.372778i
$47$			6.24816i			0.911388i	0.890137	+	0.455694i	$0.150609\pi$
$47$			6.24816i			0.911388i	−0.890137	+	0.455694i	$0.849391\pi$
$48$			1.21931i			0.175993i
$49$		0			0
$50$	−4.37287			−0.618417
$51$			2.23790i			0.313368i
$52$			10.2921i			1.42725i
$53$			1.32805i			0.182421i	0.995832	+	0.0912105i	$0.0290736\pi$
$53$			1.32805i			0.182421i	−0.995832	+	0.0912105i	$0.970926\pi$
$54$		−	1.94725i		−	0.264987i
$55$		−	0.992733i		−	0.133860i
$56$		0			0
$57$		−	2.27242i		−	0.300989i
$58$	1.54295			0.202600
$59$			3.59592i			0.468149i	0.972219	+	0.234075i	$0.0752060\pi$
$59$			3.59592i			0.468149i	−0.972219	+	0.234075i	$0.924794\pi$
$60$		−	3.45510i		−	0.446052i
$61$	10.3536			1.32565			0.662824	−	0.748775i	$-0.269358\pi$
$61$	10.3536			1.32565			0.662824	+	0.748775i	$0.269358\pi$
$62$			3.09934i			0.393616i
$63$		0			0
$64$	−0.931905			−0.116488
$65$		−	21.9250i		−	2.71946i
$66$	−0.0967936			−0.0119145
$67$		−	11.1972i		−	1.36796i	−0.729500	−	0.683980i	$-0.760247\pi$
$67$		−	11.1972i		−	1.36796i	0.729500	−	0.683980i	$-0.239753\pi$
$68$	−6.29550			−0.763441
$69$	2.55115	−	1.21931i	0.307123	−	0.146788i
$70$		0			0
$71$	5.77682			0.685582			0.342791	−	0.939412i	$-0.388628\pi$
$71$	5.77682			0.685582			0.342791	+	0.939412i	$0.388628\pi$
$72$	5.67010			0.668228
$73$			7.45389i			0.872412i	0.899847	+	0.436206i	$0.143678\pi$
$73$			7.45389i			0.872412i	−0.899847	+	0.436206i	$0.856322\pi$
$74$			0.435706i			0.0506497i
$75$			4.41239i			0.509499i
$76$	6.39260			0.733282
$77$		0			0
$78$	−2.13773			−0.242051
$79$		−	7.14772i		−	0.804181i	−0.915600	−	0.402091i	$-0.868284\pi$
$79$		−	7.14772i		−	0.804181i	0.915600	−	0.402091i	$-0.131716\pi$
$80$	7.30705			0.816953
$81$	5.99231			0.665813
$82$		−	2.45992i		−	0.271653i
$83$	−10.3906			−1.14052			−0.570258	−	0.821465i	$-0.693157\pi$
$83$	−10.3906			−1.14052			−0.570258	+	0.821465i	$0.693157\pi$
$84$		0			0
$85$	13.4112			1.45464
$86$			4.61768i			0.497937i
$87$		−	1.55690i		−	0.166917i
$88$		−	0.600637i		−	0.0640281i
$89$	5.58545			0.592056			0.296028	−	0.955179i	$-0.404338\pi$
$89$	5.58545			0.592056			0.296028	+	0.955179i	$0.404338\pi$
$90$	−5.47585			−0.577206
$91$		0			0
$92$	3.43009	+	7.17672i	0.357612	+	0.748225i
$93$	3.12735			0.324291
$94$		−	3.65084i		−	0.376555i
$95$	−13.6180			−1.39718
$96$		−	3.23322i		−	0.329989i
$97$	10.9371			1.11049			0.555247	−	0.831686i	$-0.312624\pi$
$97$	10.9371			1.11049			0.555247	+	0.831686i	$0.312624\pi$
$98$		0			0
$99$		−	0.745238i		−	0.0748992i
$100$	−12.4126			−1.24126
$101$			7.32332i			0.728697i	0.931263	+	0.364349i	$0.118708\pi$
$101$			7.32332i			0.728697i	−0.931263	+	0.364349i	$0.881292\pi$
$102$		−	1.30762i		−	0.129473i
$103$	9.31856			0.918185			0.459093	−	0.888388i	$-0.348175\pi$
$103$	9.31856			0.918185			0.459093	+	0.888388i	$0.348175\pi$
$104$		−	13.2654i		−	1.30078i
$105$		0			0
$106$		−	0.775985i		−	0.0753704i
$107$			7.05049i			0.681597i	0.940136	+	0.340798i	$0.110697\pi$
$107$			7.05049i			0.681597i	−0.940136	+	0.340798i	$0.889303\pi$
$108$		−	5.52737i		−	0.531871i
$109$			15.5344i			1.48792i	0.668221	+	0.743962i	$0.267056\pi$
$109$			15.5344i			1.48792i	−0.668221	+	0.743962i	$0.732944\pi$
$110$			0.580060i			0.0553066i
$111$	0.439644			0.0417291
$112$		0			0
$113$		−	2.81523i		−	0.264834i	−0.991194	−	0.132417i	$-0.957726\pi$
$113$		−	2.81523i		−	0.264834i	0.991194	−	0.132417i	$-0.0422738\pi$
$114$			1.32779i			0.124359i
$115$	−7.30705	−	15.2884i	−0.681386	−	1.42565i
$116$	4.37976			0.406650
$117$		−	16.4589i		−	1.52163i
$118$		−	2.10112i		−	0.193424i
$119$		0			0
$120$			4.45325i			0.406524i
$121$	10.9211			0.992823
$122$	−6.04970			−0.547714
$123$	−2.48216			−0.223809
$124$			8.79764i			0.790051i
$125$	8.77611			0.784959
$126$		0			0
$127$	6.58438			0.584269			0.292135	−	0.956377i	$-0.405634\pi$
$127$	6.58438			0.584269			0.292135	+	0.956377i	$0.405634\pi$
$128$	11.5122			1.01755
$129$	4.65941			0.410238
$130$			12.8109i			1.12359i
$131$			7.90581i			0.690734i	0.938468	+	0.345367i	$0.112246\pi$
$131$			7.90581i			0.690734i	−0.938468	+	0.345367i	$0.887754\pi$
$132$	−0.274754			−0.0239143
$133$		0			0
$134$			6.54262i			0.565196i
$135$			11.7748i			1.01342i
$136$	8.11420			0.695787
$137$		−	21.1490i		−	1.80688i	−0.428713	−	0.903441i	$-0.641033\pi$
$137$		−	21.1490i		−	1.80688i	0.428713	−	0.903441i	$-0.358967\pi$
$138$	−1.49065	+	0.712453i	−0.126893	+	0.0606480i
$139$		−	0.0766084i		−	0.00649784i	−0.999995	−	0.00324892i	$-0.998966\pi$
$139$		−	0.0766084i		−	0.00649784i	0.999995	−	0.00324892i	$-0.00103416\pi$
$140$		0			0
$141$	−3.68384			−0.310235
$142$	−3.37543			−0.283260
$143$	−1.74350			−0.145799
$144$	5.48535			0.457112
$145$	−9.33010			−0.774823
$146$		−	4.35536i		−	0.360452i
$147$		0			0
$148$			1.23677i			0.101662i
$149$			22.3423i			1.83036i	0.403051	+	0.915178i	$0.367950\pi$
$149$			22.3423i			1.83036i	−0.403051	+	0.915178i	$0.632050\pi$
$150$		−	2.57819i		−	0.210508i
$151$	−14.8965			−1.21226			−0.606130	−	0.795366i	$-0.707279\pi$
$151$	−14.8965			−1.21226			−0.606130	+	0.795366i	$0.707279\pi$
$152$	−8.23936			−0.668300
$153$	10.0677			0.813922
$154$		0			0
$155$		−	18.7414i		−	1.50535i
$156$	−6.06808			−0.485835
$157$	−18.8796			−1.50676			−0.753378	−	0.657587i	$-0.771577\pi$
$157$	−18.8796			−1.50676			−0.753378	+	0.657587i	$0.771577\pi$
$158$			4.17646i			0.332261i
$159$	−0.782999			−0.0620959
$160$	−19.3759			−1.53180
$161$		0			0
$162$	−3.50135			−0.275092
$163$	0.919318			0.0720066			0.0360033	−	0.999352i	$-0.488537\pi$
$163$	0.919318			0.0720066			0.0360033	+	0.999352i	$0.488537\pi$
$164$		−	6.98263i		−	0.545252i
$165$	0.585303			0.0455658
$166$	6.07129			0.471224
$167$			24.9470i			1.93045i	0.261413	+	0.965227i	$0.415811\pi$
$167$			24.9470i			1.93045i	−0.261413	+	0.965227i	$0.584189\pi$
$168$		0			0
$169$	−25.5061			−1.96201
$170$	−7.83623			−0.601011
$171$	−10.2230			−0.781769
$172$			13.1075i			0.999440i
$173$			15.6615i			1.19072i	0.803457	+	0.595362i	$0.202992\pi$
$173$			15.6615i			1.19072i	−0.803457	+	0.595362i	$0.797008\pi$
$174$			0.909705i			0.0689646i
$175$		0			0
$176$		−	0.581066i		−	0.0437995i
$177$	−2.12011			−0.159357
$178$	−3.26361			−0.244618
$179$	3.10337			0.231957			0.115978	−	0.993252i	$-0.463000\pi$
$179$	3.10337			0.231957			0.115978	+	0.993252i	$0.463000\pi$
$180$	−15.5435			−1.15855
$181$	−2.83745			−0.210906			−0.105453	−	0.994424i	$-0.533629\pi$
$181$	−2.83745			−0.210906			−0.105453	+	0.994424i	$0.533629\pi$
$182$		0			0
$183$			6.10438i			0.451249i
$184$	−4.42101	−	9.25001i	−0.325921	−	0.681920i
$185$		−	2.63467i		−	0.193705i
$186$	−1.82733			−0.133986
$187$		−	1.06647i		−	0.0779882i
$188$		−	10.3631i		−	0.755807i
$189$		0			0
$190$	7.95710			0.577268
$191$		−	22.0554i		−	1.59587i	−0.602741	−	0.797937i	$-0.705925\pi$
$191$		−	22.0554i		−	1.59587i	0.602741	−	0.797937i	$-0.294075\pi$
$192$		−	0.549440i		−	0.0396524i
$193$	13.6199			0.980382			0.490191	−	0.871615i	$-0.336927\pi$
$193$	13.6199			0.980382			0.490191	+	0.871615i	$0.336927\pi$
$194$	−6.39061			−0.458819
$195$	12.9267			0.925700
$196$		0			0
$197$	2.26953			0.161697			0.0808486	−	0.996726i	$-0.474237\pi$
$197$	2.26953			0.161697			0.0808486	+	0.996726i	$0.474237\pi$
$198$			0.435447i			0.0309459i
$199$	−12.0736			−0.855876			−0.427938	−	0.903808i	$-0.640760\pi$
$199$	−12.0736			−0.855876			−0.427938	+	0.903808i	$0.640760\pi$
$200$	15.9985			1.13127
$201$	6.60175			0.465652
$202$		−	4.27906i		−	0.301074i
$203$		0			0
$204$		−	3.71175i		−	0.259874i
$205$			14.8749i			1.03891i
$206$	−5.44490			−0.379364
$207$	−5.48535	−	11.4769i	−0.381258	−	0.797701i
$208$		−	12.8331i		−	0.889817i
$209$			1.08292i			0.0749074i
$210$		0			0
$211$	−15.0034			−1.03287			−0.516437	−	0.856325i	$-0.672742\pi$
$211$	−15.0034			−1.03287			−0.516437	+	0.856325i	$0.672742\pi$
$212$		−	2.20268i		−	0.151281i
$213$			3.40594i			0.233371i
$214$		−	4.11965i		−	0.281613i
$215$		−	27.9227i		−	1.90431i
$216$			7.12417i			0.484738i
$217$		0			0
$218$		−	9.07684i		−	0.614761i
$219$	−4.39472			−0.296968
$220$			1.64653i			0.111009i
$221$		−	23.5536i		−	1.58439i
$222$	−0.256887			−0.0172411
$223$			13.7114i			0.918184i	0.888389	+	0.459092i	$0.151825\pi$
$223$			13.7114i			0.918184i	−0.888389	+	0.459092i	$0.848175\pi$
$224$		0			0
$225$	19.8501			1.32334
$226$			1.64495i			0.109421i
$227$	15.0410			0.998305			0.499153	−	0.866514i	$-0.333645\pi$
$227$	15.0410			0.998305			0.499153	+	0.866514i	$0.333645\pi$
$228$			3.76900i			0.249608i
$229$	−15.6285			−1.03276			−0.516379	−	0.856360i	$-0.672720\pi$
$229$	−15.6285			−1.03276			−0.516379	+	0.856360i	$0.672720\pi$
$230$	4.26955	+	8.93312i	0.281526	+	0.589033i
$231$		0			0
$232$	−5.64502			−0.370614
$233$	−22.4064			−1.46789			−0.733946	−	0.679208i	$-0.762323\pi$
$233$	−22.4064			−1.46789			−0.733946	+	0.679208i	$0.762323\pi$
$234$			9.61706i			0.628687i
$235$			22.0763i			1.44010i
$236$		−	5.96415i		−	0.388233i
$237$	4.21421			0.273742
$238$		0			0
$239$	6.47497			0.418831			0.209416	−	0.977827i	$-0.432844\pi$
$239$	6.47497			0.418831			0.209416	+	0.977827i	$0.432844\pi$
$240$			4.30814i			0.278089i
$241$	0.579409			0.0373230			0.0186615	−	0.999826i	$-0.494060\pi$
$241$	0.579409			0.0373230			0.0186615	+	0.999826i	$0.494060\pi$
$242$	−6.38124			−0.410202
$243$			13.5307i			0.867996i
$244$	−17.1724			−1.09935
$245$		0			0
$246$	1.45034			0.0924703
$247$			23.9169i			1.52179i
$248$		−	11.3392i		−	0.720039i
$249$		−	6.12617i		−	0.388230i
$250$	−5.12794			−0.324319
$251$	2.46315			0.155473			0.0777364	−	0.996974i	$-0.475231\pi$
$251$	2.46315			0.155473			0.0777364	+	0.996974i	$0.475231\pi$
$252$		0			0
$253$	−1.21576	+	0.581066i	−0.0764339	+	0.0365313i
$254$	−3.84729			−0.241401
$255$			7.90705i			0.495159i
$256$	−4.86287			−0.303929
$257$		−	19.7863i		−	1.23424i	−0.786870	−	0.617119i	$-0.788300\pi$
$257$		−	19.7863i		−	1.23424i	0.786870	−	0.617119i	$-0.211700\pi$
$258$	−2.72252			−0.169497
$259$		0			0
$260$			36.3645i			2.25523i
$261$	−7.00404			−0.433539
$262$		−	4.61942i		−	0.285389i
$263$			22.8976i			1.41192i	0.708250	+	0.705962i	$0.249485\pi$
$263$			22.8976i			1.41192i	−0.708250	+	0.705962i	$0.750515\pi$
$264$	0.354128			0.0217951
$265$			4.69232i			0.288247i
$266$		0			0
$267$			3.29311i			0.201535i
$268$			18.5716i			1.13444i
$269$			15.8009i			0.963396i	0.876337	+	0.481698i	$0.159980\pi$
$269$			15.8009i			0.963396i	−0.876337	+	0.481698i	$0.840020\pi$
$270$		−	6.88011i		−	0.418710i
$271$			14.4967i			0.880609i	0.897848	+	0.440305i	$0.145130\pi$
$271$			14.4967i			0.880609i	−0.897848	+	0.440305i	$0.854870\pi$
$272$	7.84981			0.475965
$273$		0			0
$274$			12.3575i			0.746544i
$275$		−	2.10273i		−	0.126799i
$276$	−4.23131	+	2.02234i	−0.254695	+	0.121730i
$277$	−23.3337			−1.40199			−0.700993	−	0.713168i	$-0.747259\pi$
$277$	−23.3337			−1.40199			−0.700993	+	0.713168i	$0.747259\pi$
$278$			0.0447628i			0.00268469i
$279$		−	14.0691i		−	0.842292i
$280$		0			0
$281$		−	16.7022i		−	0.996371i	−0.867070	−	0.498185i	$-0.834000\pi$
$281$		−	16.7022i		−	0.996371i	0.867070	−	0.498185i	$-0.166000\pi$
$282$	2.15249			0.128179
$283$	−12.2103			−0.725828			−0.362914	−	0.931823i	$-0.618218\pi$
$283$	−12.2103			−0.725828			−0.362914	+	0.931823i	$0.618218\pi$
$284$	−9.58135			−0.568548
$285$		−	8.02902i		−	0.475598i
$286$	1.01874			0.0602394
$287$		0			0
$288$	−14.5453			−0.857091
$289$	−2.59266			−0.152509
$290$	5.45164			0.320131
$291$			6.44837i			0.378010i
$292$		−	12.3629i		−	0.723485i
$293$	12.6527			0.739177			0.369588	−	0.929196i	$-0.379499\pi$
$293$	12.6527			0.739177			0.369588	+	0.929196i	$0.379499\pi$
$294$		0			0
$295$			12.7053i			0.739731i
$296$		−	1.59407i		−	0.0926532i
$297$	0.936350			0.0543325
$298$		−	13.0548i		−	0.756242i
$299$	−26.8506	+	12.8331i	−1.55281	+	0.742159i
$300$		−	7.31833i		−	0.422524i
$301$		0			0
$302$	8.70412			0.500866
$303$	−4.31774			−0.248047
$304$	−7.97089			−0.457162
$305$	36.5820			2.09468
$306$	−5.88260			−0.336286
$307$		−	1.54074i		−	0.0879346i	−0.999033	−	0.0439673i	$-0.986000\pi$
$307$		−	1.54074i		−	0.0879346i	0.999033	−	0.0439673i	$-0.0139997\pi$
$308$		0			0
$309$			5.49411i			0.312549i
$310$			10.9507i			0.621960i
$311$			5.82103i			0.330080i	0.986287	+	0.165040i	$0.0527754\pi$
$311$			5.82103i			0.330080i	−0.986287	+	0.165040i	$0.947225\pi$
$312$	7.82109			0.442782
$313$	−16.7462			−0.946554			−0.473277	−	0.880914i	$-0.656929\pi$
$313$	−16.7462			−0.946554			−0.473277	+	0.880914i	$0.656929\pi$
$314$	11.0315			0.622542
$315$		0			0
$316$			11.8551i			0.666902i
$317$	11.5813			0.650473			0.325236	−	0.945633i	$-0.394556\pi$
$317$	11.5813			0.650473			0.325236	+	0.945633i	$0.394556\pi$
$318$	0.457511			0.0256560
$319$			0.741942i			0.0415408i
$320$	−3.29266			−0.184065
$321$	−4.15688			−0.232015
$322$		0			0
$323$	−14.6296			−0.814011
$324$	−9.93877			−0.552154
$325$		−	46.4398i		−	2.57602i
$326$	−0.537163			−0.0297507
$327$	−9.15888			−0.506487
$328$			8.99984i			0.496933i
$329$		0			0
$330$	−0.341996			−0.0188263
$331$	24.6051			1.35242			0.676208	−	0.736711i	$-0.263622\pi$
$331$	24.6051			1.35242			0.676208	+	0.736711i	$0.263622\pi$
$332$	17.2337			0.945822
$333$		−	1.97783i		−	0.108385i
$334$		−	14.5767i		−	0.797600i
$335$		−	39.5627i		−	2.16154i
$336$		0			0
$337$		−	28.2320i		−	1.53789i	−0.639312	−	0.768947i	$-0.720781\pi$
$337$		−	28.2320i		−	1.53789i	0.639312	−	0.768947i	$-0.279219\pi$
$338$	14.9034			0.810638
$339$	1.65982			0.0901491
$340$	−22.2436			−1.20633
$341$	−1.49034			−0.0807066
$342$	5.97334			0.323001
$343$		0			0
$344$		−	16.8942i		−	0.910872i
$345$	9.01386	−	4.30814i	0.485290	−	0.231943i
$346$		−	9.15114i		−	0.491968i
$347$	10.1989			0.547507			0.273754	−	0.961800i	$-0.411735\pi$
$347$	10.1989			0.547507			0.273754	+	0.961800i	$0.411735\pi$
$348$			2.58225i			0.138423i
$349$		−	0.948313i		−	0.0507620i	−0.999678	−	0.0253810i	$-0.991920\pi$
$349$		−	0.948313i		−	0.0507620i	0.999678	−	0.0253810i	$-0.00807990\pi$
$350$		0			0
$351$	20.6797			1.10380
$352$			1.54079i			0.0821246i
$353$			10.9846i			0.584650i	0.956319	+	0.292325i	$0.0944289\pi$
$353$			10.9846i			0.584650i	−0.956319	+	0.292325i	$0.905571\pi$
$354$	1.23879			0.0658411
$355$	20.4109			1.08330
$356$	−9.26394			−0.490988
$357$		0			0
$358$	−1.81332			−0.0958369
$359$			10.5939i			0.559124i	0.960128	+	0.279562i	$0.0901892\pi$
$359$			10.5939i			0.559124i	−0.960128	+	0.279562i	$0.909811\pi$
$360$	20.0339			1.05588
$361$	−4.14478			−0.218146
$362$	1.65794			0.0871393
$363$			6.43892i			0.337956i
$364$		0			0
$365$			26.3365i			1.37851i
$366$		−	3.56683i		−	0.186441i
$367$	−11.5396			−0.602365			−0.301182	−	0.953567i	$-0.597381\pi$
$367$	−11.5396			−0.602365			−0.301182	+	0.953567i	$0.597381\pi$
$368$	−4.27696	−	8.94861i	−0.222952	−	0.466479i
$369$			11.1665i			0.581306i
$370$			1.53946i			0.0800326i
$371$		0			0
$372$	−5.18698			−0.268932
$373$			11.7192i			0.606796i	0.952864	+	0.303398i	$0.0981212\pi$
$373$			11.7192i			0.606796i	−0.952864	+	0.303398i	$0.901879\pi$
$374$			0.623147i			0.0322222i
$375$			5.17428i			0.267199i
$376$			13.3569i			0.688830i
$377$			16.3861i			0.843930i
$378$		0			0
$379$			14.9631i			0.768602i	0.923208	+	0.384301i	$0.125557\pi$
$379$			14.9631i			0.768602i	−0.923208	+	0.384301i	$0.874443\pi$
$380$	22.5867			1.15867
$381$			3.88207i			0.198884i
$382$			12.8871i			0.659362i
$383$	26.5424			1.35625			0.678126	−	0.734946i	$-0.262793\pi$
$383$	26.5424			1.35625			0.678126	+	0.734946i	$0.262793\pi$
$384$			6.78747i			0.346372i
$385$		0			0
$386$	−7.95819			−0.405061
$387$		−	20.9614i		−	1.06553i
$388$	−18.1401			−0.920924
$389$			11.4339i			0.579720i	0.957069	+	0.289860i	$0.0936088\pi$
$389$			11.4339i			0.579720i	−0.957069	+	0.289860i	$0.906391\pi$
$390$	−7.55315			−0.382469
$391$	−7.84981	−	16.4240i	−0.396982	−	0.830600i
$392$		0			0
$393$	−4.66117			−0.235125
$394$	−1.32610			−0.0668079
$395$		−	25.2547i		−	1.27070i
$396$			1.23604i			0.0621134i
$397$			12.2503i			0.614825i	0.951576	+	0.307412i	$0.0994631\pi$
$397$			12.2503i			0.614825i	−0.951576	+	0.307412i	$0.900537\pi$
$398$	7.05469			0.353620
$399$		0			0
$400$	15.4772			0.773861
$401$		−	8.54274i		−	0.426604i	−0.976986	−	0.213302i	$-0.931578\pi$
$401$		−	8.54274i		−	0.426604i	0.976986	−	0.213302i	$-0.0684219\pi$
$402$	−3.85745			−0.192392
$403$	−32.9149			−1.63961
$404$		−	12.1464i		−	0.604304i
$405$	21.1724			1.05206
$406$		0			0
$407$	−0.209513			−0.0103852
$408$			4.78403i			0.236845i
$409$		−	27.9808i		−	1.38356i	−0.722109	−	0.691780i	$-0.756827\pi$
$409$		−	27.9808i		−	1.38356i	0.722109	−	0.691780i	$-0.243173\pi$
$410$		−	8.69152i		−	0.429244i
$411$	12.4692			0.615060
$412$	−15.4556			−0.761445
$413$		0			0
$414$	3.20512	+	6.70603i	0.157523	+	0.329583i
$415$	−36.7126			−1.80215
$416$			34.0292i			1.66842i
$417$	0.0451673			0.00221185
$418$		−	0.632759i		−	0.0309492i
$419$	−15.6695			−0.765503			−0.382751	−	0.923851i	$-0.625023\pi$
$419$	−15.6695			−0.765503			−0.382751	+	0.923851i	$0.625023\pi$
$420$		0			0
$421$		−	34.7278i		−	1.69253i	−0.532764	−	0.846264i	$-0.678847\pi$
$421$		−	34.7278i		−	1.69253i	0.532764	−	0.846264i	$-0.321153\pi$
$422$	8.76657			0.426750
$423$			16.5725i			0.805784i
$424$			2.83901i			0.137874i
$425$	28.4065			1.37792
$426$		−	1.99011i		−	0.0964212i
$427$		0			0
$428$		−	11.6938i		−	0.565244i
$429$		−	1.02795i		−	0.0496298i
$430$			16.3154i			0.786799i
$431$			8.22776i			0.396317i	0.980170	+	0.198159i	$0.0634961\pi$
$431$			8.22776i			0.396317i	−0.980170	+	0.198159i	$0.936504\pi$
$432$			6.89204i			0.331593i
$433$	0.384659			0.0184855			0.00924276	−	0.999957i	$-0.497058\pi$
$433$	0.384659			0.0184855			0.00924276	+	0.999957i	$0.497058\pi$
$434$		0			0
$435$		−	5.50091i		−	0.263749i
$436$		−	25.7651i		−	1.23393i
$437$	7.97089	+	16.6774i	0.381300	+	0.797787i
$438$	2.56786			0.122697
$439$			4.85503i			0.231718i	0.993266	+	0.115859i	$0.0369620\pi$
$439$			4.85503i			0.231718i	−0.993266	+	0.115859i	$0.963038\pi$
$440$		−	2.12220i		−	0.101172i
$441$		0			0
$442$			13.7625i			0.654616i
$443$	−31.1431			−1.47965			−0.739827	−	0.672797i	$-0.765093\pi$
$443$	−31.1431			−1.47965			−0.739827	+	0.672797i	$0.765093\pi$
$444$	−0.729187			−0.0346057
$445$	19.7348			0.935519
$446$		−	8.01166i		−	0.379363i
$447$	−13.1728			−0.623050
$448$		0			0
$449$	−15.2127			−0.717931			−0.358965	−	0.933351i	$-0.616870\pi$
$449$	−15.2127			−0.717931			−0.358965	+	0.933351i	$0.616870\pi$
$450$	−11.5985			−0.546760
$451$	1.18288			0.0556994
$452$			4.66929i			0.219625i
$453$		−	8.78279i		−	0.412651i
$454$	−8.78854			−0.412467
$455$		0			0
$456$		−	4.85782i		−	0.227488i
$457$			8.34997i			0.390595i	0.980744	+	0.195298i	$0.0625673\pi$
$457$			8.34997i			0.390595i	−0.980744	+	0.195298i	$0.937433\pi$
$458$	9.13181			0.426701
$459$			12.6495i			0.590426i
$460$	12.1194	+	25.3572i	0.565068	+	1.18228i
$461$			3.94962i			0.183952i	0.995761	+	0.0919762i	$0.0293184\pi$
$461$			3.94962i			0.183952i	−0.995761	+	0.0919762i	$0.970682\pi$
$462$		0			0
$463$	24.9864			1.16121			0.580607	−	0.814184i	$-0.302815\pi$
$463$	24.9864			1.16121			0.580607	+	0.814184i	$0.302815\pi$
$464$	−5.46109			−0.253525
$465$	11.0497			0.512418
$466$	13.0922			0.606484
$467$	−3.83311			−0.177375			−0.0886876	−	0.996059i	$-0.528267\pi$
$467$	−3.83311			−0.177375			−0.0886876	+	0.996059i	$0.528267\pi$
$468$			27.2986i			1.26188i
$469$		0			0
$470$		−	12.8993i		−	0.595002i
$471$		−	11.1312i		−	0.512898i
$472$			7.68713i			0.353829i
$473$	−2.22045			−0.102096
$474$	−2.46239			−0.113101
$475$	−28.8447			−1.32348
$476$		0			0
$477$			3.52249i			0.161284i
$478$	−3.78337			−0.173047
$479$	0.605754			0.0276776			0.0138388	−	0.999904i	$-0.495595\pi$
$479$	0.605754			0.0276776			0.0138388	+	0.999904i	$0.495595\pi$
$480$		−	11.4238i		−	0.521421i
$481$	−4.62719			−0.210982
$482$	−0.338552			−0.0154206
$483$		0			0
$484$	−18.1135			−0.823342
$485$	38.6435			1.75471
$486$		−	7.90609i		−	0.358627i
$487$	20.2406			0.917188			0.458594	−	0.888646i	$-0.348353\pi$
$487$	20.2406			0.917188			0.458594	+	0.888646i	$0.348353\pi$
$488$	22.1333			1.00193
$489$			0.542019i			0.0245109i
$490$		0			0
$491$	9.16948			0.413813			0.206906	−	0.978361i	$-0.433660\pi$
$491$	9.16948			0.413813			0.206906	+	0.978361i	$0.433660\pi$
$492$	4.11687			0.185603
$493$	−10.0231			−0.451420
$494$		−	13.9748i		−	0.628755i
$495$		−	2.63311i		−	0.118350i
$496$		−	10.9697i		−	0.492555i
$497$		0			0
$498$			3.57956i			0.160404i
$499$	2.37066			0.106125			0.0530626	−	0.998591i	$-0.483102\pi$
$499$	2.37066			0.106125			0.0530626	+	0.998591i	$0.483102\pi$
$500$	−14.5559			−0.650961
$501$	−14.7084			−0.657124
$502$	−1.43924			−0.0642362
$503$	28.6649			1.27811			0.639053	−	0.769163i	$-0.279327\pi$
$503$	28.6649			1.27811			0.639053	+	0.769163i	$0.279327\pi$
$504$		0			0
$505$			25.8751i			1.15143i
$506$	0.710374	−	0.339520i	0.0315800	−	0.0150935i
$507$		−	15.0381i		−	0.667866i
$508$	−10.9208			−0.484530
$509$		−	15.1398i		−	0.671061i	−0.942029	−	0.335530i	$-0.891084\pi$
$509$		−	15.1398i		−	0.671061i	0.942029	−	0.335530i	$-0.108916\pi$
$510$		−	4.62014i		−	0.204583i
$511$		0			0
$512$	−20.1831			−0.891975
$513$		−	12.8446i		−	0.567102i
$514$			11.5613i			0.509946i
$515$	32.9248			1.45084
$516$	−7.72804			−0.340208
$517$	1.75554			0.0772084
$518$		0			0
$519$	−9.23385			−0.405321
$520$		−	46.8698i		−	2.05538i
$521$	−0.724384			−0.0317358			−0.0158679	−	0.999874i	$-0.505051\pi$
$521$	−0.724384			−0.0317358			−0.0158679	+	0.999874i	$0.505051\pi$
$522$	4.09251			0.179124
$523$	23.5559			1.03003			0.515014	−	0.857182i	$-0.327787\pi$
$523$	23.5559			1.03003			0.515014	+	0.857182i	$0.327787\pi$
$524$		−	13.1125i		−	0.572821i
$525$		0			0
$526$		−	13.3792i		−	0.583360i
$527$		−	20.1335i		−	0.877031i
$528$	0.342589			0.0149093
$529$	−14.4461	+	17.8972i	−0.628091	+	0.778140i
$530$		−	2.74175i		−	0.119094i
$531$			9.53777i			0.413904i
$532$		0			0
$533$	26.1244			1.13157
$534$		−	1.92418i		−	0.0832676i
$535$			24.9112i			1.07700i
$536$		−	23.9367i		−	1.03391i
$537$			1.82971i			0.0789578i
$538$		−	9.23255i		−	0.398043i
$539$		0			0
$540$		−	19.5296i		−	0.840419i
$541$	−19.5886			−0.842179			−0.421089	−	0.907019i	$-0.638352\pi$
$541$	−19.5886			−0.842179			−0.421089	+	0.907019i	$0.638352\pi$
$542$		−	8.47049i		−	0.363839i
$543$		−	1.67292i		−	0.0717920i
$544$	−20.8151			−0.892440
$545$			54.8869i			2.35110i
$546$		0			0
$547$	−5.60011			−0.239443			−0.119722	−	0.992808i	$-0.538200\pi$
$547$	−5.60011			−0.239443			−0.119722	+	0.992808i	$0.538200\pi$
$548$			35.0775i			1.49843i
$549$	27.4619			1.17204
$550$			1.22864i			0.0523894i
$551$	10.1777			0.433586
$552$	5.45369	−	2.60657i	0.232124	−	0.110943i
$553$		0			0
$554$	13.6340			0.579254
$555$	1.55337			0.0659369
$556$			0.127062i			0.00538861i
$557$		−	23.3410i		−	0.988991i	−0.869180	−	0.494495i	$-0.835353\pi$
$557$		−	23.3410i		−	0.988991i	0.869180	−	0.494495i	$-0.164647\pi$
$558$			8.22064i			0.348007i
$559$	−49.0397			−2.07416
$560$		0			0
$561$	0.628779			0.0265471
$562$			9.75921i			0.411668i
$563$	−10.4002			−0.438316			−0.219158	−	0.975689i	$-0.570331\pi$
$563$	−10.4002			−0.438316			−0.219158	+	0.975689i	$0.570331\pi$
$564$	6.10996			0.257276
$565$		−	9.94690i		−	0.418469i
$566$	7.13456			0.299888
$567$		0			0
$568$	12.3493			0.518165
$569$		−	16.6323i		−	0.697261i	−0.937260	−	0.348630i	$-0.886647\pi$
$569$		−	16.6323i		−	0.697261i	0.937260	−	0.348630i	$-0.113353\pi$
$570$			4.69140i			0.196501i
$571$			12.1423i			0.508141i	0.967186	+	0.254071i	$0.0817696\pi$
$571$			12.1423i			0.508141i	−0.967186	+	0.254071i	$0.918230\pi$
$572$	2.89175			0.120910
$573$	13.0036			0.543233
$574$		0			0
$575$	−15.4772	−	32.3828i	−0.645445	−	1.35045i
$576$	−2.47177			−0.102991
$577$			0.160752i			0.00669218i	0.999994	+	0.00334609i	$0.00106510\pi$
$577$			0.160752i			0.00669218i	−0.999994	+	0.00334609i	$0.998935\pi$
$578$	1.51491			0.0630118
$579$			8.03012i			0.333720i
$580$	15.4748			0.642555
$581$		0			0
$582$		−	3.76782i		−	0.156181i
$583$	0.373139			0.0154539
$584$			15.9344i			0.659372i
$585$		−	58.1536i		−	2.40435i
$586$	−7.39303			−0.305403
$587$		−	36.0106i		−	1.48632i	−0.669116	−	0.743158i	$-0.733327\pi$
$587$		−	36.0106i		−	1.48632i	0.669116	−	0.743158i	$-0.266673\pi$
$588$		0			0
$589$			20.4441i			0.842384i
$590$		−	7.42378i		−	0.305632i
$591$			1.33809i			0.0550415i
$592$		−	1.54213i		−	0.0633810i
$593$			36.2156i			1.48720i	0.668626	+	0.743599i	$0.266883\pi$
$593$			36.2156i			1.48720i	−0.668626	+	0.743599i	$0.733117\pi$
$594$	−0.547115			−0.0224484
$595$		0			0
$596$		−	37.0567i		−	1.51790i
$597$		−	7.11845i		−	0.291339i
$598$	15.6889	−	7.49848i	0.641569	−	0.306635i
$599$	−23.5453			−0.962036			−0.481018	−	0.876711i	$-0.659733\pi$
$599$	−23.5453			−0.962036			−0.481018	+	0.876711i	$0.659733\pi$
$600$			9.43252i			0.385081i
$601$			0.940529i			0.0383650i	0.999816	+	0.0191825i	$0.00610635\pi$
$601$			0.940529i			0.0383650i	−0.999816	+	0.0191825i	$0.993894\pi$
$602$		0			0
$603$		−	29.6994i		−	1.20945i
$604$	24.7071			1.00532
$605$	38.5868			1.56878
$606$	2.52288			0.102485
$607$			7.52999i			0.305633i	0.988255	+	0.152816i	$0.0488343\pi$
$607$			7.52999i			0.305633i	−0.988255	+	0.152816i	$0.951166\pi$
$608$	21.1362			0.857185
$609$		0			0
$610$	−21.3751			−0.865453
$611$	38.7719			1.56854
$612$	−16.6981			−0.674980
$613$		−	26.9736i		−	1.08945i	−0.838613	−	0.544727i	$-0.816633\pi$
$613$		−	26.9736i		−	1.08945i	0.838613	−	0.544727i	$-0.183367\pi$
$614$			0.900263i			0.0363317i
$615$	−8.77008			−0.353644
$616$		0			0
$617$		−	9.25381i		−	0.372544i	−0.982498	−	0.186272i	$-0.940359\pi$
$617$		−	9.25381i		−	0.372544i	0.982498	−	0.186272i	$-0.0596406\pi$
$618$		−	3.21024i		−	0.129135i
$619$	−31.5176			−1.26680			−0.633399	−	0.773825i	$-0.718341\pi$
$619$	−31.5176			−1.26680			−0.633399	+	0.773825i	$0.718341\pi$
$620$			31.0843i			1.24837i
$621$	14.4201	−	6.89204i	0.578659	−	0.276568i
$622$		−	3.40126i		−	0.136378i
$623$		0			0
$624$	7.56625			0.302892
$625$	−6.41112			−0.256445
$626$	9.78494			0.391085
$627$	−0.638478			−0.0254984
$628$	31.3135			1.24954
$629$		−	2.83038i		−	0.112855i
$630$		0			0
$631$			14.2570i			0.567562i	0.958889	+	0.283781i	$0.0915889\pi$
$631$			14.2570i			0.567562i	−0.958889	+	0.283781i	$0.908411\pi$
$632$		−	15.2799i		−	0.607803i
$633$		−	8.84580i		−	0.351589i
$634$	−6.76705			−0.268754
$635$	23.2643			0.923214
$636$	1.29867			0.0514957
$637$		0			0
$638$		−	0.433521i		−	0.0171633i
$639$	15.3224			0.606143
$640$	40.6756			1.60785
$641$			2.02889i			0.0801362i	0.999197	+	0.0400681i	$0.0127575\pi$
$641$			2.02889i			0.0801362i	−0.999197	+	0.0400681i	$0.987243\pi$
$642$	2.42889			0.0958607
$643$	42.6136			1.68052			0.840259	−	0.542186i	$-0.182403\pi$
$643$	42.6136			1.68052			0.840259	+	0.542186i	$0.182403\pi$
$644$		0			0
$645$	16.4629			0.648225
$646$	8.54815			0.336322
$647$		−	22.6729i		−	0.891364i	−0.895191	−	0.445682i	$-0.852961\pi$
$647$		−	22.6729i		−	0.891364i	0.895191	−	0.445682i	$-0.147039\pi$
$648$	12.8100			0.503224
$649$	1.01034			0.0396594
$650$			27.1351i			1.06433i
$651$		0			0
$652$	−1.52477			−0.0597145
$653$	23.1850			0.907301			0.453650	−	0.891180i	$-0.350122\pi$
$653$	23.1850			0.907301			0.453650	+	0.891180i	$0.350122\pi$
$654$	5.35159			0.209264
$655$			27.9332i			1.09144i
$656$			8.70659i			0.339935i
$657$			19.7706i			0.771325i
$658$		0			0
$659$			33.6441i			1.31059i	0.755375	+	0.655293i	$0.227455\pi$
$659$			33.6441i			1.31059i	−0.755375	+	0.655293i	$0.772545\pi$
$660$	−0.970775			−0.0377874
$661$	41.5145			1.61473			0.807363	−	0.590055i	$-0.200894\pi$
$661$	41.5145			1.61473			0.807363	+	0.590055i	$0.200894\pi$
$662$	−14.3769			−0.558774
$663$	13.8869			0.539322
$664$	−22.2123			−0.862006
$665$		0			0
$666$			1.15566i			0.0447809i
$667$	5.46109	+	11.4262i	0.211454	+	0.442422i
$668$		−	41.3767i		−	1.60091i
$669$	−8.08407			−0.312548
$670$			23.1167i			0.893077i
$671$		−	2.90905i		−	0.112303i
$672$		0			0
$673$	20.9048			0.805820			0.402910	−	0.915239i	$-0.367999\pi$
$673$	20.9048			0.805820			0.402910	+	0.915239i	$0.367999\pi$
$674$			16.4961i			0.635407i
$675$			24.9405i			0.959962i
$676$	42.3041			1.62708
$677$	−16.7782			−0.644838			−0.322419	−	0.946597i	$-0.604496\pi$
$677$	−16.7782			−0.644838			−0.322419	+	0.946597i	$0.604496\pi$
$678$	−0.969844			−0.0372466
$679$		0			0
$680$	28.6695			1.09943
$681$			8.86798i			0.339822i
$682$	0.870817			0.0333453
$683$	44.9654			1.72055			0.860276	−	0.509828i	$-0.170291\pi$
$683$	44.9654			1.72055			0.860276	+	0.509828i	$0.170291\pi$
$684$	16.9557			0.648315
$685$		−	74.7248i		−	2.85509i
$686$		0			0
$687$		−	9.21435i		−	0.351549i
$688$		−	16.3437i		−	0.623098i
$689$	8.24096			0.313956
$690$	−5.26686	+	2.51728i	−0.200506	+	0.0958310i
$691$			10.5467i			0.401215i	0.979672	+	0.200608i	$0.0642917\pi$
$691$			10.5467i			0.401215i	−0.979672	+	0.200608i	$0.935708\pi$
$692$		−	25.9760i		−	0.987460i
$693$		0			0
$694$	−5.95930			−0.226212
$695$		−	0.270677i		−	0.0102673i
$696$		−	3.32824i		−	0.126156i
$697$			15.9799i			0.605280i
$698$			0.554105i			0.0209732i
$699$		−	13.2105i		−	0.499668i
$700$		0			0
$701$			13.2757i			0.501417i	0.968063	+	0.250709i	$0.0806636\pi$
$701$			13.2757i			0.501417i	−0.968063	+	0.250709i	$0.919336\pi$
$702$	−12.0833			−0.456055
$703$			2.87404i			0.108396i
$704$			0.261836i			0.00986833i
$705$	−13.0159			−0.490208
$706$		−	6.41835i		−	0.241558i
$707$		0			0
$708$	3.51639			0.132154
$709$			16.9406i			0.636217i	0.948054	+	0.318109i	$0.103048\pi$
$709$			16.9406i			0.636217i	−0.948054	+	0.318109i	$0.896952\pi$
$710$	−11.9262			−0.447584
$711$		−	18.9585i		−	0.711000i
$712$	11.9402			0.447478
$713$	−22.9518	+	10.9697i	−0.859551	+	0.410819i
$714$		0			0
$715$	−6.16024			−0.230380
$716$	−5.14721			−0.192360
$717$			3.81756i			0.142570i
$718$		−	6.19007i		−	0.231012i
$719$		−	45.7999i		−	1.70805i	−0.520235	−	0.854023i	$-0.674155\pi$
$719$		−	45.7999i		−	1.70805i	0.520235	−	0.854023i	$-0.325845\pi$
$720$	19.3811			0.722291
$721$		0			0
$722$	2.42182			0.0901308
$723$			0.341612i			0.0127047i
$724$	4.70615			0.174903
$725$	−19.7623			−0.733954
$726$		−	3.76230i		−	0.139632i
$727$	27.5793			1.02286			0.511429	−	0.859325i	$-0.329116\pi$
$727$	27.5793			1.02286			0.511429	+	0.859325i	$0.329116\pi$
$728$		0			0
$729$	9.99940			0.370348
$730$		−	15.3886i		−	0.569556i
$731$		−	29.9968i		−	1.10947i
$732$		−	10.1246i		−	0.374217i
$733$	−13.0343			−0.481433			−0.240717	−	0.970595i	$-0.577382\pi$
$733$	−13.0343			−0.481433			−0.240717	+	0.970595i	$0.577382\pi$
$734$	6.74269			0.248877
$735$		0			0
$736$	11.3411	+	23.7287i	0.418037	+	0.874653i
$737$	−3.14608			−0.115887
$738$		−	6.52467i		−	0.240176i
$739$	−28.6649			−1.05445			−0.527227	−	0.849724i	$-0.676768\pi$
$739$	−28.6649			−1.05445			−0.527227	+	0.849724i	$0.676768\pi$
$740$			4.36984i			0.160638i
$741$	−14.1011			−0.518017
$742$		0			0
$743$		−	22.7481i		−	0.834547i	−0.908781	−	0.417274i	$-0.862986\pi$
$743$		−	22.7481i		−	0.834547i	0.908781	−	0.417274i	$-0.137014\pi$
$744$	6.68544			0.245100
$745$			78.9411i			2.89218i
$746$		−	6.84759i		−	0.250708i
$747$	−27.5599			−1.00836
$748$			1.76884i			0.0646751i
$749$		0			0
$750$		−	3.02337i		−	0.110398i
$751$		−	29.0873i		−	1.06141i	−0.847556	−	0.530705i	$-0.821927\pi$
$751$		−	29.0873i		−	1.06141i	0.847556	−	0.530705i	$-0.178073\pi$
$752$			12.9217i			0.471206i
$753$			1.45224i			0.0529227i
$754$		−	9.57453i		−	0.348684i
$755$	−52.6331			−1.91551
$756$		0			0
$757$			31.5963i			1.14839i	0.818720	+	0.574193i	$0.194684\pi$
$757$			31.5963i			1.14839i	−0.818720	+	0.574193i	$0.805316\pi$
$758$		−	8.74302i		−	0.317561i
$759$	−0.342589	−	0.716794i	−0.0124352	−	0.0260180i
$760$	−29.1117			−1.05599
$761$		−	3.04353i		−	0.110328i	−0.998477	−	0.0551640i	$-0.982432\pi$
$761$		−	3.04353i		−	0.110328i	0.998477	−	0.0551640i	$-0.0175682\pi$
$762$		−	2.26832i		−	0.0821725i
$763$		0			0
$764$			36.5808i			1.32345i
$765$	35.5716			1.28609
$766$	−15.5089			−0.560358
$767$	22.3139			0.805708
$768$		−	2.86708i		−	0.103457i
$769$	−44.5932			−1.60807			−0.804036	−	0.594580i	$-0.797318\pi$
$769$	−44.5932			−1.60807			−0.804036	+	0.594580i	$0.797318\pi$
$770$		0			0
$771$	11.6658			0.420133
$772$	−22.5898			−0.813024
$773$	−16.7044			−0.600817			−0.300408	−	0.953811i	$-0.597123\pi$
$773$	−16.7044			−0.600817			−0.300408	+	0.953811i	$0.597123\pi$
$774$			12.2479i			0.440240i
$775$		−	39.6967i		−	1.42595i
$776$	23.3806			0.839315
$777$		0			0
$778$		−	6.68088i		−	0.239521i
$779$		−	16.2263i		−	0.581369i
$780$	−21.4401			−0.767677
$781$		−	1.62310i		−	0.0580793i
$782$	4.58670	+	9.59667i	0.164020	+	0.343176i
$783$		−	8.80019i		−	0.314493i
$784$		0			0
$785$	−66.7064			−2.38085
$786$	2.72355			0.0971458
$787$	3.03184			0.108073			0.0540367	−	0.998539i	$-0.482791\pi$
$787$	3.03184			0.108073			0.0540367	+	0.998539i	$0.482791\pi$
$788$	−3.76421			−0.134094
$789$	−13.5001			−0.480617
$790$			14.7565i			0.525012i
$791$		0			0
$792$		−	1.59312i		−	0.0566091i
$793$		−	64.2478i		−	2.28151i
$794$		−	7.15793i		−	0.254025i
$795$	−2.76653			−0.0981188
$796$	20.0251			0.709772
$797$	2.93351			0.103910			0.0519551	−	0.998649i	$-0.483455\pi$
$797$	2.93351			0.103910			0.0519551	+	0.998649i	$0.483455\pi$
$798$		0			0
$799$			23.7161i			0.839017i
$800$	−41.0405			−1.45100
$801$	14.8148			0.523454
$802$			4.99158i			0.176259i
$803$	2.09431			0.0739066
$804$	−10.9496			−0.386162
$805$		0			0
$806$	19.2324			0.677433
$807$	−9.31599			−0.327938
$808$			15.6553i			0.550752i
$809$	−49.4454			−1.73841			−0.869203	−	0.494455i	$-0.835368\pi$
$809$	−49.4454			−1.73841			−0.869203	+	0.494455i	$0.835368\pi$
$810$	−12.3711			−0.434677
$811$			23.8421i			0.837210i	0.908168	+	0.418605i	$0.137481\pi$
$811$			23.8421i			0.837210i	−0.908168	+	0.418605i	$0.862519\pi$
$812$		0			0
$813$	−8.54705			−0.299758
$814$	0.122420			0.00429081
$815$	3.24818			0.113779
$816$			4.62815i			0.162018i
$817$			30.4595i			1.06564i
$818$			16.3493i			0.571641i
$819$		0			0
$820$		−	24.6714i		−	0.861562i
$821$	−31.8587			−1.11188			−0.555938	−	0.831224i	$-0.687641\pi$
$821$	−31.8587			−1.11188			−0.555938	+	0.831224i	$0.687641\pi$
$822$	−7.28583			−0.254122
$823$	−37.5306			−1.30823			−0.654117	−	0.756394i	$-0.726959\pi$
$823$	−37.5306			−1.30823			−0.654117	+	0.756394i	$0.726959\pi$
$824$	19.9206			0.693968
$825$	1.23974			0.0431624
$826$		0			0
$827$			13.6994i			0.476373i	0.971219	+	0.238187i	$0.0765530\pi$
$827$			13.6994i			0.476373i	−0.971219	+	0.238187i	$0.923447\pi$
$828$	9.09792	+	19.0354i	0.316175	+	0.661528i
$829$		−	11.5400i		−	0.400802i	−0.979714	−	0.200401i	$-0.935775\pi$
$829$		−	11.5400i		−	0.400802i	0.979714	−	0.200401i	$-0.0642245\pi$
$830$	21.4514			0.744589
$831$		−	13.7573i		−	0.477234i
$832$			5.78278i			0.200482i
$833$		0			0
$834$	−0.0263916			−0.000913865
$835$			88.1439i			3.05034i
$836$		−	1.79612i		−	0.0621201i
$837$	17.6770			0.611006
$838$	9.15576			0.316280
$839$	−25.1844			−0.869463			−0.434732	−	0.900560i	$-0.643157\pi$
$839$	−25.1844			−0.869463			−0.434732	+	0.900560i	$0.643157\pi$
$840$		0			0
$841$	−22.0269			−0.759549
$842$			20.2917i			0.699297i
$843$	9.84742			0.339163
$844$	24.8844			0.856556
$845$	−90.1196			−3.10021
$846$		−	9.68343i		−	0.332923i
$847$		0			0
$848$			2.74650i			0.0943154i
$849$		−	7.19905i		−	0.247071i
$850$	−16.5981			−0.569310
$851$	−3.22657	+	1.54213i	−0.110605	+	0.0528634i
$852$		−	5.64904i		−	0.193533i
$853$			6.71783i			0.230014i	0.993365	+	0.115007i	$0.0366891\pi$
$853$			6.71783i			0.230014i	−0.993365	+	0.115007i	$0.963311\pi$
$854$		0			0
$855$	−36.1203			−1.23529
$856$			15.0721i			0.515153i
$857$			51.7893i			1.76909i	0.466456	+	0.884544i	$0.345531\pi$
$857$			51.7893i			1.76909i	−0.466456	+	0.884544i	$0.654469\pi$
$858$			0.600637i			0.0205054i
$859$		−	45.4636i		−	1.55120i	−0.631227	−	0.775598i	$-0.717448\pi$
$859$		−	45.4636i		−	1.55120i	0.631227	−	0.775598i	$-0.282552\pi$
$860$			46.3122i			1.57923i
$861$		0			0
$862$		−	4.80753i		−	0.163745i
$863$	−13.9393			−0.474501			−0.237250	−	0.971449i	$-0.576246\pi$
$863$	−13.9393			−0.474501			−0.237250	+	0.971449i	$0.576246\pi$
$864$		−	18.2754i		−	0.621741i
$865$			55.3362i			1.88149i
$866$	−0.224759			−0.00763761
$867$		−	1.52860i		−	0.0519140i
$868$		0			0
$869$	−2.00829			−0.0681264
$870$			3.21422i			0.108972i
$871$	−69.4826			−2.35433
$872$			33.2084i			1.12458i
$873$	29.0094			0.981819
$874$	−4.65744	−	9.74470i	−0.157540	−	0.329619i
$875$		0			0
$876$	7.28902			0.246273
$877$	−30.3265			−1.02405			−0.512026	−	0.858970i	$-0.671105\pi$
$877$	−30.3265			−1.02405			−0.512026	+	0.858970i	$0.671105\pi$
$878$		−	2.83682i		−	0.0957381i
$879$			7.45985i			0.251615i
$880$		−	2.05305i		−	0.0692084i
$881$	−17.2441			−0.580968			−0.290484	−	0.956880i	$-0.593816\pi$
$881$	−17.2441			−0.580968			−0.290484	+	0.956880i	$0.593816\pi$
$882$		0			0
$883$	2.24713			0.0756221			0.0378110	−	0.999285i	$-0.487962\pi$
$883$	2.24713			0.0756221			0.0378110	+	0.999285i	$0.487962\pi$
$884$			39.0656i			1.31392i
$885$	−7.49088			−0.251803
$886$	18.1971			0.611344
$887$			41.4905i			1.39311i	0.717501	+	0.696557i	$0.245286\pi$
$887$			41.4905i			1.39311i	−0.717501	+	0.696557i	$0.754714\pi$
$888$	0.939842			0.0315390
$889$		0			0
$890$	−11.5312			−0.386525
$891$		−	1.68365i		−	0.0564045i
$892$		−	22.7415i		−	0.761443i
$893$		−	24.0819i		−	0.805872i
$894$	7.69693			0.257424
$895$	10.9650			0.366519
$896$		0			0
$897$	−7.56625	−	15.8308i	−0.252630	−	0.528573i
$898$	8.88887			0.296625
$899$			14.0068i			0.467154i
$900$	−32.9231			−1.09744
$901$			5.04086i			0.167935i
$902$	−0.691161			−0.0230132
$903$		0			0
$904$		−	6.01821i		−	0.200163i
$905$	−10.0254			−0.333256
$906$			5.13184i			0.170494i
$907$			39.9299i			1.32585i	0.748686	+	0.662925i	$0.230685\pi$
$907$			39.9299i			1.32585i	−0.748686	+	0.662925i	$0.769315\pi$
$908$	−24.9468			−0.827888
$909$			19.4243i			0.644262i
$910$		0			0
$911$			39.5814i			1.31139i	0.755026	+	0.655695i	$0.227624\pi$
$911$			39.5814i			1.31139i	−0.755026	+	0.655695i	$0.772376\pi$
$912$		−	4.69954i		−	0.155617i
$913$			2.91943i			0.0966192i
$914$		−	4.87894i		−	0.161381i
$915$			21.5683i			0.713026i
$916$	25.9212			0.856459
$917$		0			0
$918$		−	7.39116i		−	0.243945i
$919$			37.1480i			1.22540i	0.790316	+	0.612700i	$0.209916\pi$
$919$			37.1480i			1.22540i	−0.790316	+	0.612700i	$0.790084\pi$
$920$	−15.6205	−	32.6826i	−0.514994	−	1.07751i
$921$	0.908400			0.0299328
$922$		−	2.30779i		−	0.0760030i
$923$		−	35.8471i		−	1.17992i
$924$		0			0
$925$		−	5.58057i		−	0.183488i
$926$	−14.5997			−0.479776
$927$	24.7164			0.811794
$928$	14.4810			0.475362
$929$			29.1264i			0.955607i	0.878467	+	0.477803i	$0.158567\pi$
$929$			29.1264i			0.955607i	−0.878467	+	0.477803i	$0.841433\pi$
$930$	−6.45642			−0.211714
$931$		0			0
$932$	37.1629			1.21731
$933$	−3.43201			−0.112359
$934$	2.23971			0.0732855
$935$		−	3.76812i		−	0.123231i
$936$		−	35.1848i		−	1.15005i
$937$	8.29853			0.271101			0.135551	−	0.990770i	$-0.456720\pi$
$937$	8.29853			0.271101			0.135551	+	0.990770i	$0.456720\pi$
$938$		0			0
$939$		−	9.87338i		−	0.322206i
$940$		−	36.6155i		−	1.19426i
$941$	8.30935			0.270877			0.135439	−	0.990786i	$-0.456756\pi$
$941$	8.30935			0.270877			0.135439	+	0.990786i	$0.456756\pi$
$942$			6.50402i			0.211912i
$943$	18.2167	−	8.70659i	0.593217	−	0.283526i
$944$			7.43665i			0.242042i
$945$		0			0
$946$	1.29742			0.0421828
$947$	−3.84336			−0.124892			−0.0624462	−	0.998048i	$-0.519890\pi$
$947$	−3.84336			−0.124892			−0.0624462	+	0.998048i	$0.519890\pi$
$948$	−6.98962			−0.227012
$949$	46.2539			1.50146
$950$	16.8541			0.546820
$951$			6.82821i			0.221420i
$952$		0			0
$953$		−	31.2541i		−	1.01242i	−0.862411	−	0.506209i	$-0.831046\pi$
$953$		−	31.2541i		−	1.01242i	0.862411	−	0.506209i	$-0.168954\pi$
$954$		−	2.05821i		−	0.0666371i
$955$		−	77.9273i		−	2.52167i
$956$	−10.7393			−0.347334
$957$	−0.437440			−0.0141404
$958$	−0.353946			−0.0114355
$959$		0			0
$960$		−	1.94131i		−	0.0626555i
$961$	2.86439			0.0923996
$962$	2.70370			0.0871707
$963$			18.7006i			0.602619i
$964$	−0.960999			−0.0309517
$965$	48.1225			1.54912
$966$		0			0
$967$	−37.6191			−1.20975			−0.604874	−	0.796321i	$-0.706776\pi$
$967$	−37.6191			−1.20975			−0.604874	+	0.796321i	$0.706776\pi$
$968$	23.3463			0.750379
$969$		−	8.62541i		−	0.277088i
$970$	−22.5796			−0.724988
$971$	−49.3754			−1.58453			−0.792266	−	0.610176i	$-0.791099\pi$
$971$	−49.3754			−1.58453			−0.792266	+	0.610176i	$0.791099\pi$
$972$		−	22.4419i		−	0.719823i
$973$		0			0
$974$	−11.8267			−0.378952
$975$	27.3804			0.876873
$976$	21.4122			0.685387
$977$		−	52.7282i		−	1.68693i	−0.537188	−	0.843463i	$-0.680513\pi$
$977$		−	52.7282i		−	1.68693i	0.537188	−	0.843463i	$-0.319487\pi$
$978$		−	0.316705i		−	0.0101271i
$979$		−	1.56934i		−	0.0501562i
$980$		0			0
$981$			41.2032i			1.31552i
$982$	−5.35779			−0.170974
$983$	−31.9447			−1.01888			−0.509438	−	0.860507i	$-0.670147\pi$
$983$	−31.9447			−1.01888			−0.509438	+	0.860507i	$0.670147\pi$
$984$	−5.30619			−0.169155
$985$	8.01881			0.255501
$986$	5.85658			0.186512
$987$		0			0
$988$		−	39.6682i		−	1.26201i
$989$	−34.1957	+	16.3437i	−1.08736	+	0.519699i
$990$			1.53854i			0.0488981i
$991$	34.3595			1.09147			0.545733	−	0.837959i	$-0.316251\pi$
$991$	34.3595			1.09147			0.545733	+	0.837959i	$0.316251\pi$
$992$			29.0881i			0.923547i
$993$			14.5068i			0.460361i
$994$		0			0
$995$	−42.6591			−1.35239
$996$			10.1608i			0.321957i
$997$		−	8.66264i		−	0.274349i	−0.990547	−	0.137174i	$-0.956198\pi$
$997$		−	8.66264i		−	0.274349i	0.990547	−	0.137174i	$-0.0438020\pi$
$998$	−1.38519			−0.0438474
$999$	2.48504			0.0786231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1127.2.c.c.1126.10		28
7.4	even	3		161.2.g.a.68.9	yes	28
7.5	odd	6		161.2.g.a.45.10	yes	28
7.6	odd	2	inner	1127.2.c.c.1126.9		28
23.22	odd	2	inner	1127.2.c.c.1126.12		28
161.68	even	6		161.2.g.a.45.9	✓	28
161.137	odd	6		161.2.g.a.68.10	yes	28
161.160	even	2	inner	1127.2.c.c.1126.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.9	✓	28	161.68	even	6
161.2.g.a.45.10	yes	28	7.5	odd	6
161.2.g.a.68.9	yes	28	7.4	even	3
161.2.g.a.68.10	yes	28	161.137	odd	6
1127.2.c.c.1126.9		28	7.6	odd	2	inner
1127.2.c.c.1126.10		28	1.1	even	1	trivial
1127.2.c.c.1126.11		28	161.160	even	2	inner
1127.2.c.c.1126.12		28	23.22	odd	2	inner

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:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1127.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.584306 q^{2} +0.589587i q^{3} -1.65859 q^{4} +3.53325 q^{5} -0.344500i q^{6} +2.13773 q^{8} +2.65239 q^{9} -2.06450 q^{10} -0.280969i q^{11} -0.977882i q^{12} -6.20533i q^{13} +2.08316i q^{15} +2.06808 q^{16} +3.79570 q^{17} -1.54981 q^{18} -3.85425 q^{19} -5.86020 q^{20} +0.164172i q^{22} +(-2.06808 - 4.32701i) q^{23} +1.26038i q^{24} +7.48386 q^{25} +3.62581i q^{26} +3.33258i q^{27} -2.64066 q^{29} -1.21720i q^{30} -5.30430i q^{31} -5.48386 q^{32} +0.165656 q^{33} -2.21785 q^{34} -4.39921 q^{36} -0.745680i q^{37} +2.25206 q^{38} +3.65859 q^{39} +7.55315 q^{40} +4.20999i q^{41} -7.90283i q^{43} +0.466011i q^{44} +9.37155 q^{45} +(1.20839 + 2.52830i) q^{46} +6.24816i q^{47} +1.21931i q^{48} -4.37287 q^{50} +2.23790i q^{51} +10.2921i q^{52} +1.32805i q^{53} -1.94725i q^{54} -0.992733i q^{55} -2.27242i q^{57} +1.54295 q^{58} +3.59592i q^{59} -3.45510i q^{60} +10.3536 q^{61} +3.09934i q^{62} -0.931905 q^{64} -21.9250i q^{65} -0.0967936 q^{66} -11.1972i q^{67} -6.29550 q^{68} +(2.55115 - 1.21931i) q^{69} +5.77682 q^{71} +5.67010 q^{72} +7.45389i q^{73} +0.435706i q^{74} +4.41239i q^{75} +6.39260 q^{76} -2.13773 q^{78} -7.14772i q^{79} +7.30705 q^{80} +5.99231 q^{81} -2.45992i q^{82} -10.3906 q^{83} +13.4112 q^{85} +4.61768i q^{86} -1.55690i q^{87} -0.600637i q^{88} +5.58545 q^{89} -5.47585 q^{90} +(3.43009 + 7.17672i) q^{92} +3.12735 q^{93} -3.65084i q^{94} -13.6180 q^{95} -3.23322i q^{96} +10.9371 q^{97} -0.745238i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 8 q^{2} + 24 q^{4} + 12 q^{8} - 8 q^{9} - 44 q^{18} + 44 q^{25} - 44 q^{29} + 12 q^{32} + 32 q^{39} - 36 q^{46} + 84 q^{50} - 28 q^{58} - 68 q^{64} + 16 q^{71} + 8 q^{72} - 12 q^{78} - 44 q^{81}+ \cdots - 112 q^{95}+O(q^{100}) \) 28 * q + 8 * q^2 + 24 * q^4 + 12 * q^8 - 8 * q^9 - 44 * q^18 + 44 * q^25 - 44 * q^29 + 12 * q^32 + 32 * q^39 - 36 * q^46 + 84 * q^50 - 28 * q^58 - 68 * q^64 + 16 * q^71 + 8 * q^72 - 12 * q^78 - 44 * q^81 - 52 * q^85 - 28 * q^92 + 20 * q^93 - 112 * q^95

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