LMFDB - Embedded newform 867.2.e.k.616.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			616.9
Character	$\chi$	$=$	867.616
Dual form			867.2.e.k.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.44395i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.97290 q^{4} +(2.03186 - 2.03186i) q^{5} +(-1.72814 - 1.72814i) q^{6} +(-1.10487 - 1.10487i) q^{7} -4.82168i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+2.44395i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.97290 q^{4} +(2.03186 - 2.03186i) q^{5} +(-1.72814 - 1.72814i) q^{6} +(-1.10487 - 1.10487i) q^{7} -4.82168i q^{8} -1.00000i q^{9} +(4.96577 + 4.96577i) q^{10} +(4.48482 + 4.48482i) q^{11} +(2.80927 - 2.80927i) q^{12} -0.803928 q^{13} +(2.70024 - 2.70024i) q^{14} +2.87349i q^{15} +3.83815 q^{16} +2.44395 q^{18} +3.25173i q^{19} +(-8.07238 + 8.07238i) q^{20} +1.56252 q^{21} +(-10.9607 + 10.9607i) q^{22} +(4.36560 + 4.36560i) q^{23} +(3.40944 + 3.40944i) q^{24} -3.25692i q^{25} -1.96476i q^{26} +(0.707107 + 0.707107i) q^{27} +(4.38953 + 4.38953i) q^{28} +(-1.08113 + 1.08113i) q^{29} -7.02266 q^{30} +(-1.53664 + 1.53664i) q^{31} -0.263112i q^{32} -6.34249 q^{33} -4.48987 q^{35} +3.97290i q^{36} +(-0.449887 + 0.449887i) q^{37} -7.94707 q^{38} +(0.568463 - 0.568463i) q^{39} +(-9.79698 - 9.79698i) q^{40} +(3.97096 + 3.97096i) q^{41} +3.81872i q^{42} +11.0241i q^{43} +(-17.8177 - 17.8177i) q^{44} +(-2.03186 - 2.03186i) q^{45} +(-10.6693 + 10.6693i) q^{46} -7.46399 q^{47} +(-2.71398 + 2.71398i) q^{48} -4.55854i q^{49} +7.95975 q^{50} +3.19393 q^{52} +1.34692i q^{53} +(-1.72814 + 1.72814i) q^{54} +18.2250 q^{55} +(-5.32731 + 5.32731i) q^{56} +(-2.29932 - 2.29932i) q^{57} +(-2.64223 - 2.64223i) q^{58} -4.03412i q^{59} -11.4161i q^{60} +(5.91720 + 5.91720i) q^{61} +(-3.75547 - 3.75547i) q^{62} +(-1.10487 + 1.10487i) q^{63} +8.31932 q^{64} +(-1.63347 + 1.63347i) q^{65} -15.5007i q^{66} +7.75709 q^{67} -6.17389 q^{69} -10.9730i q^{70} +(3.19435 - 3.19435i) q^{71} -4.82168 q^{72} +(5.85550 - 5.85550i) q^{73} +(-1.09950 - 1.09950i) q^{74} +(2.30299 + 2.30299i) q^{75} -12.9188i q^{76} -9.91025i q^{77} +(1.38930 + 1.38930i) q^{78} +(-1.06575 - 1.06575i) q^{79} +(7.79858 - 7.79858i) q^{80} -1.00000 q^{81} +(-9.70484 + 9.70484i) q^{82} +7.52521i q^{83} -6.20773 q^{84} -26.9424 q^{86} -1.52895i q^{87} +(21.6243 - 21.6243i) q^{88} +6.12748 q^{89} +(4.96577 - 4.96577i) q^{90} +(0.888234 + 0.888234i) q^{91} +(-17.3441 - 17.3441i) q^{92} -2.17313i q^{93} -18.2416i q^{94} +(6.60707 + 6.60707i) q^{95} +(0.186048 + 0.186048i) q^{96} +(3.42351 - 3.42351i) q^{97} +11.1408 q^{98} +(4.48482 - 4.48482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 36 q^{4}+O(q^{10}) $ 24 * q - 36 * q^4	$ 24 q - 36 q^{4} - 36 q^{13} + 60 q^{16} + 12 q^{18} - 12 q^{21} - 48 q^{30} - 36 q^{33} + 24 q^{38} - 96 q^{47} + 48 q^{50} - 72 q^{52} + 96 q^{55} - 96 q^{64} - 24 q^{67} - 36 q^{69} - 48 q^{72} - 24 q^{81} - 60 q^{84} + 24 q^{86} + 228 q^{98}+O(q^{100}) $ 24 * q - 36 * q^4 - 36 * q^13 + 60 * q^16 + 12 * q^18 - 12 * q^21 - 48 * q^30 - 36 * q^33 + 24 * q^38 - 96 * q^47 + 48 * q^50 - 72 * q^52 + 96 * q^55 - 96 * q^64 - 24 * q^67 - 36 * q^69 - 48 * q^72 - 24 * q^81 - 60 * q^84 + 24 * q^86 + 228 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.44395i			1.72814i	0.503376	+	0.864068i	$0.332091\pi$
$2$			2.44395i			1.72814i	−0.503376	+	0.864068i	$0.667909\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−3.97290			−1.98645
$5$	2.03186	−	2.03186i	0.908676	−	0.908676i	−0.0874895	−	0.996165i	$-0.527884\pi$
$5$	2.03186	−	2.03186i	0.908676	−	0.908676i	0.996165	+	0.0874895i	$0.0278844\pi$
$6$	−1.72814	−	1.72814i	−0.705508	−	0.705508i
$7$	−1.10487	−	1.10487i	−0.417600	−	0.417600i	0.466775	−	0.884376i	$-0.345416\pi$
$7$	−1.10487	−	1.10487i	−0.417600	−	0.417600i	−0.884376	+	0.466775i	$0.845416\pi$
$8$		−	4.82168i		−	1.70472i
$9$		−	1.00000i		−	0.333333i
$10$	4.96577	+	4.96577i	1.57031	+	1.57031i
$11$	4.48482	+	4.48482i	1.35222	+	1.35222i	0.883170	+	0.469052i	$0.155404\pi$
$11$	4.48482	+	4.48482i	1.35222	+	1.35222i	0.469052	+	0.883170i	$0.344596\pi$
$12$	2.80927	−	2.80927i	0.810965	−	0.810965i
$13$	−0.803928			−0.222970			−0.111485	−	0.993766i	$-0.535561\pi$
$13$	−0.803928			−0.222970			−0.111485	+	0.993766i	$0.535561\pi$
$14$	2.70024	−	2.70024i	0.721670	−	0.721670i
$15$			2.87349i			0.741931i
$16$	3.83815			0.959536
$17$		0			0
$17$		0			0
$18$	2.44395			0.576045
$19$			3.25173i			0.745998i	0.927832	+	0.372999i	$0.121671\pi$
$19$			3.25173i			0.745998i	−0.927832	+	0.372999i	$0.878329\pi$
$20$	−8.07238	+	8.07238i	−1.80504	+	1.80504i
$21$	1.56252			0.340969
$22$	−10.9607	+	10.9607i	−2.33682	+	2.33682i
$23$	4.36560	+	4.36560i	0.910290	+	0.910290i	0.996295	−	0.0860050i	$-0.0274101\pi$
$23$	4.36560	+	4.36560i	0.910290	+	0.910290i	−0.0860050	+	0.996295i	$0.527410\pi$
$24$	3.40944	+	3.40944i	0.695949	+	0.695949i
$25$		−	3.25692i		−	0.651384i
$26$		−	1.96476i		−	0.385321i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	4.38953	+	4.38953i	0.829543	+	0.829543i
$29$	−1.08113	+	1.08113i	−0.200761	+	0.200761i	−0.800326	−	0.599565i	$-0.795340\pi$
$29$	−1.08113	+	1.08113i	−0.200761	+	0.200761i	0.599565	+	0.800326i	$0.295340\pi$
$30$	−7.02266			−1.28216
$31$	−1.53664	+	1.53664i	−0.275988	+	0.275988i	−0.831505	−	0.555517i	$-0.812520\pi$
$31$	−1.53664	+	1.53664i	−0.275988	+	0.275988i	0.555517	+	0.831505i	$0.312520\pi$
$32$		−	0.263112i		−	0.0465121i
$33$	−6.34249			−1.10409
$34$		0			0
$35$	−4.48987			−0.758927
$36$			3.97290i			0.662150i
$37$	−0.449887	+	0.449887i	−0.0739609	+	0.0739609i	−0.743120	−	0.669159i	$-0.766655\pi$
$37$	−0.449887	+	0.449887i	−0.0739609	+	0.0739609i	0.669159	+	0.743120i	$0.266655\pi$
$38$	−7.94707			−1.28919
$39$	0.568463	−	0.568463i	0.0910269	−	0.0910269i
$40$	−9.79698	−	9.79698i	−1.54904	−	1.54904i
$41$	3.97096	+	3.97096i	0.620160	+	0.620160i	0.945572	−	0.325412i	$-0.105503\pi$
$41$	3.97096	+	3.97096i	0.620160	+	0.620160i	−0.325412	+	0.945572i	$0.605503\pi$
$42$			3.81872i			0.589241i
$43$			11.0241i			1.68116i	0.541685	+	0.840582i	$0.317787\pi$
$43$			11.0241i			1.68116i	−0.541685	+	0.840582i	$0.682213\pi$
$44$	−17.8177	−	17.8177i	−2.68612	−	2.68612i
$45$	−2.03186	−	2.03186i	−0.302892	−	0.302892i
$46$	−10.6693	+	10.6693i	−1.57310	+	1.57310i
$47$	−7.46399			−1.08874			−0.544368	−	0.838847i	$-0.683230\pi$
$47$	−7.46399			−1.08874			−0.544368	+	0.838847i	$0.683230\pi$
$48$	−2.71398	+	2.71398i	−0.391729	+	0.391729i
$49$		−	4.55854i		−	0.651220i
$50$	7.95975			1.12568
$51$		0			0
$52$	3.19393			0.442918
$53$			1.34692i			0.185014i	0.995712	+	0.0925071i	$0.0294881\pi$
$53$			1.34692i			0.185014i	−0.995712	+	0.0925071i	$0.970512\pi$
$54$	−1.72814	+	1.72814i	−0.235169	+	0.235169i
$55$	18.2250			2.45746
$56$	−5.32731	+	5.32731i	−0.711892	+	0.711892i
$57$	−2.29932	−	2.29932i	−0.304552	−	0.304552i
$58$	−2.64223	−	2.64223i	−0.346942	−	0.346942i
$59$		−	4.03412i		−	0.525198i	−0.964905	−	0.262599i	$-0.915420\pi$
$59$		−	4.03412i		−	0.525198i	0.964905	−	0.262599i	$-0.0845796\pi$
$60$		−	11.4161i		−	1.47381i
$61$	5.91720	+	5.91720i	0.757620	+	0.757620i	0.975889	−	0.218269i	$-0.0700410\pi$
$61$	5.91720	+	5.91720i	0.757620	+	0.757620i	−0.218269	+	0.975889i	$0.570041\pi$
$62$	−3.75547	−	3.75547i	−0.476945	−	0.476945i
$63$	−1.10487	+	1.10487i	−0.139200	+	0.139200i
$64$	8.31932			1.03992
$65$	−1.63347	+	1.63347i	−0.202607	+	0.202607i
$66$		−	15.5007i		−	1.90801i
$67$	7.75709			0.947680			0.473840	−	0.880611i	$-0.342868\pi$
$67$	7.75709			0.947680			0.473840	+	0.880611i	$0.342868\pi$
$68$		0			0
$69$	−6.17389			−0.743248
$70$		−	10.9730i		−	1.31153i
$71$	3.19435	−	3.19435i	0.379099	−	0.379099i	−0.491678	−	0.870777i	$-0.663616\pi$
$71$	3.19435	−	3.19435i	0.379099	−	0.379099i	0.870777	+	0.491678i	$0.163616\pi$
$72$	−4.82168			−0.568240
$73$	5.85550	−	5.85550i	0.685335	−	0.685335i	−0.275863	−	0.961197i	$-0.588963\pi$
$73$	5.85550	−	5.85550i	0.685335	−	0.685335i	0.961197	+	0.275863i	$0.0889635\pi$
$74$	−1.09950	−	1.09950i	−0.127814	−	0.127814i
$75$	2.30299	+	2.30299i	0.265926	+	0.265926i
$76$		−	12.9188i		−	1.48189i
$77$		−	9.91025i		−	1.12938i
$78$	1.38930	+	1.38930i	0.157307	+	0.157307i
$79$	−1.06575	−	1.06575i	−0.119906	−	0.119906i	0.644607	−	0.764514i	$-0.277021\pi$
$79$	−1.06575	−	1.06575i	−0.119906	−	0.119906i	−0.764514	+	0.644607i	$0.777021\pi$
$80$	7.79858	−	7.79858i	0.871907	−	0.871907i
$81$	−1.00000			−0.111111
$82$	−9.70484	+	9.70484i	−1.07172	+	1.07172i
$83$			7.52521i			0.825999i	0.910731	+	0.413000i	$0.135519\pi$
$83$			7.52521i			0.825999i	−0.910731	+	0.413000i	$0.864481\pi$
$84$	−6.20773			−0.677319
$85$		0			0
$86$	−26.9424			−2.90528
$87$		−	1.52895i		−	0.163921i
$88$	21.6243	−	21.6243i	2.30516	−	2.30516i
$89$	6.12748			0.649511			0.324756	−	0.945798i	$-0.394718\pi$
$89$	6.12748			0.649511			0.324756	+	0.945798i	$0.394718\pi$
$90$	4.96577	−	4.96577i	0.523438	−	0.523438i
$91$	0.888234	+	0.888234i	0.0931122	+	0.0931122i
$92$	−17.3441	−	17.3441i	−1.80825	−	1.80825i
$93$		−	2.17313i		−	0.225344i
$94$		−	18.2416i		−	1.88148i
$95$	6.60707	+	6.60707i	0.677871	+	0.677871i
$96$	0.186048	+	0.186048i	0.0189885	+	0.0189885i
$97$	3.42351	−	3.42351i	0.347605	−	0.347605i	−0.511612	−	0.859217i	$-0.670951\pi$
$97$	3.42351	−	3.42351i	0.347605	−	0.347605i	0.859217	+	0.511612i	$0.170951\pi$
$98$	11.1408			1.12540
$99$	4.48482	−	4.48482i	0.450741	−	0.450741i
$100$			12.9394i			1.29394i
$101$	−15.8161			−1.57376			−0.786882	−	0.617104i	$-0.788306\pi$
$101$	−15.8161			−1.57376			−0.786882	+	0.617104i	$0.788306\pi$
$102$		0			0
$103$	−7.19272			−0.708720			−0.354360	−	0.935109i	$-0.615301\pi$
$103$	−7.19272			−0.708720			−0.354360	+	0.935109i	$0.615301\pi$
$104$			3.87628i			0.380101i
$105$	3.17482	−	3.17482i	0.309831	−	0.309831i
$106$	−3.29182			−0.319730
$107$	2.60052	−	2.60052i	0.251401	−	0.251401i	−0.570144	−	0.821545i	$-0.693112\pi$
$107$	2.60052	−	2.60052i	0.251401	−	0.251401i	0.821545	+	0.570144i	$0.193112\pi$
$108$	−2.80927	−	2.80927i	−0.270322	−	0.270322i
$109$	7.27162	+	7.27162i	0.696495	+	0.696495i	0.963653	−	0.267158i	$-0.0860845\pi$
$109$	7.27162	+	7.27162i	0.696495	+	0.696495i	−0.267158	+	0.963653i	$0.586085\pi$
$110$			44.5411i			4.24683i
$111$		−	0.636236i		−	0.0603889i
$112$	−4.24064	−	4.24064i	−0.400703	−	0.400703i
$113$	−9.85021	−	9.85021i	−0.926630	−	0.926630i	0.0708569	−	0.997486i	$-0.477427\pi$
$113$	−9.85021	−	9.85021i	−0.926630	−	0.926630i	−0.997486	+	0.0708569i	$0.977427\pi$
$114$	5.61943	−	5.61943i	0.526308	−	0.526308i
$115$	17.7406			1.65432
$116$	4.29523	−	4.29523i	0.398802	−	0.398802i
$117$			0.803928i			0.0743232i
$118$	9.85920			0.907613
$119$		0			0
$120$	13.8550			1.26478
$121$			29.2271i			2.65701i
$122$	−14.4614	+	14.4614i	−1.30927	+	1.30927i
$123$	−5.61579			−0.506359
$124$	6.10491	−	6.10491i	0.548237	−	0.548237i
$125$	3.54170	+	3.54170i	0.316779	+	0.316779i
$126$	−2.70024	−	2.70024i	−0.240557	−	0.240557i
$127$		−	2.17742i		−	0.193215i	−0.995323	−	0.0966076i	$-0.969201\pi$
$127$		−	2.17742i		−	0.193215i	0.995323	−	0.0966076i	$-0.0307992\pi$
$128$			19.8058i			1.75060i
$129$	−7.79523	−	7.79523i	−0.686332	−	0.686332i
$130$	−3.99212	−	3.99212i	−0.350132	−	0.350132i
$131$	−3.11737	+	3.11737i	−0.272366	+	0.272366i	−0.830052	−	0.557686i	$-0.811689\pi$
$131$	−3.11737	+	3.11737i	−0.272366	+	0.272366i	0.557686	+	0.830052i	$0.311689\pi$
$132$	25.1981			2.19321
$133$	3.59273	−	3.59273i	0.311529	−	0.311529i
$134$			18.9580i			1.63772i
$135$	2.87349			0.247310
$136$		0			0
$137$	0.311499			0.0266131			0.0133066	−	0.999911i	$-0.495764\pi$
$137$	0.311499			0.0266131			0.0133066	+	0.999911i	$0.495764\pi$
$138$		−	15.0887i		−	1.28443i
$139$	7.64365	−	7.64365i	0.648326	−	0.648326i	−0.304263	−	0.952588i	$-0.598410\pi$
$139$	7.64365	−	7.64365i	0.648326	−	0.648326i	0.952588	+	0.304263i	$0.0984100\pi$
$140$	17.8378			1.50757
$141$	5.27784	−	5.27784i	0.444474	−	0.444474i
$142$	7.80683	+	7.80683i	0.655135	+	0.655135i
$143$	−3.60547	−	3.60547i	−0.301504	−	0.301504i
$144$		−	3.83815i		−	0.319845i
$145$			4.39341i			0.364853i
$146$	14.3106	+	14.3106i	1.18435	+	1.18435i
$147$	3.22337	+	3.22337i	0.265859	+	0.265859i
$148$	1.78736	−	1.78736i	0.146920	−	0.146920i
$149$	−17.7269			−1.45225			−0.726123	−	0.687565i	$-0.758680\pi$
$149$	−17.7269			−1.45225			−0.726123	+	0.687565i	$0.758680\pi$
$150$	−5.62840	+	5.62840i	−0.459557	+	0.459557i
$151$		−	16.1244i		−	1.31219i	−0.754680	−	0.656093i	$-0.772208\pi$
$151$		−	16.1244i		−	1.31219i	0.754680	−	0.656093i	$-0.227792\pi$
$152$	15.6788			1.27172
$153$		0			0
$154$	24.2202			1.95172
$155$			6.24447i			0.501568i
$156$	−2.25845	+	2.25845i	−0.180821	+	0.180821i
$157$	−19.6347			−1.56702			−0.783510	−	0.621380i	$-0.786572\pi$
$157$	−19.6347			−1.56702			−0.783510	+	0.621380i	$0.786572\pi$
$158$	2.60464	−	2.60464i	0.207214	−	0.207214i
$159$	−0.952419	−	0.952419i	−0.0755318	−	0.0755318i
$160$	−0.534608	−	0.534608i	−0.0422644	−	0.0422644i
$161$		−	9.64681i		−	0.760275i
$162$		−	2.44395i		−	0.192015i
$163$	−7.69165	−	7.69165i	−0.602456	−	0.602456i	0.338507	−	0.940964i	$-0.390078\pi$
$163$	−7.69165	−	7.69165i	−0.602456	−	0.602456i	−0.940964	+	0.338507i	$0.890078\pi$
$164$	−15.7762	−	15.7762i	−1.23192	−	1.23192i
$165$	−12.8871	+	12.8871i	−1.00326	+	1.00326i
$166$	−18.3913			−1.42744
$167$	7.43457	−	7.43457i	0.575304	−	0.575304i	−0.358302	−	0.933606i	$-0.616644\pi$
$167$	7.43457	−	7.43457i	0.575304	−	0.575304i	0.933606	+	0.358302i	$0.116644\pi$
$168$		−	7.53396i		−	0.581257i
$169$	−12.3537			−0.950285
$170$		0			0
$171$	3.25173			0.248666
$172$		−	43.7978i		−	3.33955i
$173$	5.47898	−	5.47898i	0.416559	−	0.416559i	−0.467457	−	0.884016i	$-0.654830\pi$
$173$	5.47898	−	5.47898i	0.416559	−	0.416559i	0.884016	+	0.467457i	$0.154830\pi$
$174$	3.73668			0.283277
$175$	−3.59846	+	3.59846i	−0.272018	+	0.272018i
$176$	17.2134	+	17.2134i	1.29751	+	1.29751i
$177$	2.85255	+	2.85255i	0.214411	+	0.214411i
$178$			14.9753i			1.12244i
$179$			11.9475i			0.893001i	0.894783	+	0.446501i	$0.147330\pi$
$179$			11.9475i			0.893001i	−0.894783	+	0.446501i	$0.852670\pi$
$180$	8.07238	+	8.07238i	0.601680	+	0.601680i
$181$	1.23965	+	1.23965i	0.0921422	+	0.0921422i	0.751675	−	0.659533i	$-0.229246\pi$
$181$	1.23965	+	1.23965i	0.0921422	+	0.0921422i	−0.659533	+	0.751675i	$0.729246\pi$
$182$	−2.17080	+	2.17080i	−0.160910	+	0.160910i
$183$	−8.36818			−0.618594
$184$	21.0495	−	21.0495i	1.55179	−	1.55179i
$185$			1.82822i			0.134413i
$186$	5.31104			0.389424
$187$		0			0
$188$	29.6537			2.16272
$189$		−	1.56252i		−	0.113656i
$190$	−16.1474	+	16.1474i	−1.17145	+	1.17145i
$191$	22.3232			1.61525			0.807627	−	0.589694i	$-0.200752\pi$
$191$	22.3232			1.61525			0.807627	+	0.589694i	$0.200752\pi$
$192$	−5.88265	+	5.88265i	−0.424544	+	0.424544i
$193$	18.4963	+	18.4963i	1.33139	+	1.33139i	0.904128	+	0.427262i	$0.140522\pi$
$193$	18.4963	+	18.4963i	1.33139	+	1.33139i	0.427262	+	0.904128i	$0.359478\pi$
$194$	8.36690	+	8.36690i	0.600708	+	0.600708i
$195$		−	2.31008i		−	0.165428i
$196$			18.1106i			1.29362i
$197$	−12.5837	−	12.5837i	−0.896551	−	0.896551i	0.0985783	−	0.995129i	$-0.468571\pi$
$197$	−12.5837	−	12.5837i	−0.896551	−	0.896551i	−0.995129	+	0.0985783i	$0.968571\pi$
$198$	10.9607	+	10.9607i	0.778941	+	0.778941i
$199$	16.0188	−	16.0188i	1.13554	−	1.13554i	0.146305	−	0.989240i	$-0.453262\pi$
$199$	16.0188	−	16.0188i	1.13554	−	1.13554i	0.989240	−	0.146305i	$-0.0467380\pi$
$200$	−15.7038			−1.11043
$201$	−5.48509	+	5.48509i	−0.386889	+	0.386889i
$202$		−	38.6538i		−	2.71968i
$203$	2.38901			0.167676
$204$		0			0
$205$	16.1369			1.12705
$206$		−	17.5787i		−	1.22476i
$207$	4.36560	−	4.36560i	0.303430	−	0.303430i
$208$	−3.08559			−0.213947
$209$	−14.5834	+	14.5834i	−1.00876	+	1.00876i
$210$	7.75911	+	7.75911i	0.535429	+	0.535429i
$211$	16.0694	+	16.0694i	1.10626	+	1.10626i	0.993638	+	0.112623i	$0.0359253\pi$
$211$	16.0694	+	16.0694i	1.10626	+	1.10626i	0.112623	+	0.993638i	$0.464075\pi$
$212$		−	5.35120i		−	0.367522i
$213$			4.51749i			0.309533i
$214$	6.35554	+	6.35554i	0.434456	+	0.434456i
$215$	22.3995	+	22.3995i	1.52763	+	1.52763i
$216$	3.40944	−	3.40944i	0.231983	−	0.231983i
$217$	3.39556			0.230506
$218$	−17.7715	+	17.7715i	−1.20364	+	1.20364i
$219$			8.28093i			0.559573i
$220$	−72.4063			−4.88163
$221$		0			0
$222$	1.55493			0.104360
$223$			0.594738i			0.0398266i	0.999802	+	0.0199133i	$0.00633902\pi$
$223$			0.594738i			0.0398266i	−0.999802	+	0.0199133i	$0.993661\pi$
$224$	−0.290704	+	0.290704i	−0.0194235	+	0.0194235i
$225$	−3.25692			−0.217128
$226$	24.0734	−	24.0734i	1.60134	−	1.60134i
$227$	−14.1725	−	14.1725i	−0.940661	−	0.940661i	0.0576740	−	0.998335i	$-0.481632\pi$
$227$	−14.1725	−	14.1725i	−0.940661	−	0.940661i	−0.998335	+	0.0576740i	$0.981632\pi$
$228$	9.13498	+	9.13498i	0.604979	+	0.604979i
$229$		−	1.93974i		−	0.128182i	−0.997944	−	0.0640909i	$-0.979585\pi$
$229$		−	1.93974i		−	0.128182i	0.997944	−	0.0640909i	$-0.0204148\pi$
$230$			43.3571i			2.85888i
$231$	7.00760	+	7.00760i	0.461067	+	0.461067i
$232$	5.21286	+	5.21286i	0.342241	+	0.342241i
$233$	5.96993	−	5.96993i	0.391103	−	0.391103i	−0.483978	−	0.875080i	$-0.660808\pi$
$233$	5.96993	−	5.96993i	0.391103	−	0.391103i	0.875080	+	0.483978i	$0.160808\pi$
$234$	−1.96476			−0.128440
$235$	−15.1658	+	15.1658i	−0.989308	+	0.989308i
$236$			16.0272i			1.04328i
$237$	1.50720			0.0979031
$238$		0			0
$239$	15.5030			1.00281			0.501403	−	0.865214i	$-0.332817\pi$
$239$	15.5030			1.00281			0.501403	+	0.865214i	$0.332817\pi$
$240$			11.0289i			0.711909i
$241$	−21.0659	+	21.0659i	−1.35698	+	1.35698i	−0.479357	+	0.877620i	$0.659130\pi$
$241$	−21.0659	+	21.0659i	−1.35698	+	1.35698i	−0.877620	+	0.479357i	$0.840870\pi$
$242$	−71.4297			−4.59168
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−23.5085	−	23.5085i	−1.50497	−	1.50497i
$245$	−9.26232	−	9.26232i	−0.591748	−	0.591748i
$246$		−	13.7247i		−	0.875056i
$247$		−	2.61416i		−	0.166335i
$248$	7.40917	+	7.40917i	0.470483	+	0.470483i
$249$	−5.32113	−	5.32113i	−0.337213	−	0.337213i
$250$	−8.65574	+	8.65574i	−0.547437	+	0.547437i
$251$	4.59133			0.289802			0.144901	−	0.989446i	$-0.453714\pi$
$251$	4.59133			0.289802			0.144901	+	0.989446i	$0.453714\pi$
$252$	4.38953	−	4.38953i	0.276514	−	0.276514i
$253$			39.1578i			2.46183i
$254$	5.32152			0.333902
$255$		0			0
$256$	−31.7658			−1.98536
$257$		−	29.0731i		−	1.81353i	−0.421637	−	0.906765i	$-0.638544\pi$
$257$		−	29.0731i		−	1.81353i	0.421637	−	0.906765i	$-0.361456\pi$
$258$	19.0512	−	19.0512i	1.18607	−	1.18607i
$259$	0.994130			0.0617722
$260$	6.48962	−	6.48962i	0.402469	−	0.402469i
$261$	1.08113	+	1.08113i	0.0669203	+	0.0669203i
$262$	−7.61871	−	7.61871i	−0.470685	−	0.470685i
$263$			1.07458i			0.0662617i	0.999451	+	0.0331308i	$0.0105478\pi$
$263$			1.07458i			0.0662617i	−0.999451	+	0.0331308i	$0.989452\pi$
$264$			30.5814i			1.88216i
$265$	2.73676	+	2.73676i	0.168118	+	0.168118i
$266$	8.78046	+	8.78046i	0.538365	+	0.538365i
$267$	−4.33278	+	4.33278i	−0.265162	+	0.265162i
$268$	−30.8182			−1.88252
$269$	17.9032	−	17.9032i	1.09157	−	1.09157i	0.0962141	−	0.995361i	$-0.469327\pi$
$269$	17.9032	−	17.9032i	1.09157	−	1.09157i	0.995361	−	0.0962141i	$-0.0306734\pi$
$270$			7.02266i			0.427386i
$271$	19.4812			1.18340			0.591699	−	0.806159i	$-0.298458\pi$
$271$	19.4812			1.18340			0.591699	+	0.806159i	$0.298458\pi$
$272$		0			0
$273$	−1.25615			−0.0760258
$274$			0.761288i			0.0459911i
$275$	14.6067	−	14.6067i	0.880816	−	0.880816i
$276$	24.5282			1.47643
$277$	−6.71973	+	6.71973i	−0.403749	+	0.403749i	−0.879552	−	0.475803i	$-0.842158\pi$
$277$	−6.71973	+	6.71973i	−0.403749	+	0.403749i	0.475803	+	0.879552i	$0.342158\pi$
$278$	18.6807	+	18.6807i	1.12039	+	1.12039i
$279$	1.53664	+	1.53664i	0.0919961	+	0.0919961i
$280$			21.6487i			1.29376i
$281$		−	14.4217i		−	0.860329i	−0.902751	−	0.430164i	$-0.858456\pi$
$281$		−	14.4217i		−	0.860329i	0.902751	−	0.430164i	$-0.141544\pi$
$282$	12.8988	+	12.8988i	0.768112	+	0.768112i
$283$	−13.7256	−	13.7256i	−0.815900	−	0.815900i	0.169611	−	0.985511i	$-0.445749\pi$
$283$	−13.7256	−	13.7256i	−0.815900	−	0.815900i	−0.985511	+	0.169611i	$0.945749\pi$
$284$	−12.6908	+	12.6908i	−0.753062	+	0.753062i
$285$	−9.34380			−0.553479
$286$	8.81159	−	8.81159i	0.521040	−	0.521040i
$287$		−	8.77477i		−	0.517958i
$288$	−0.263112			−0.0155040
$289$		0			0
$290$	−10.7373			−0.630516
$291$			4.84158i			0.283818i
$292$	−23.2633	+	23.2633i	−1.36138	+	1.36138i
$293$	1.07338			0.0627076			0.0313538	−	0.999508i	$-0.490018\pi$
$293$	1.07338			0.0627076			0.0313538	+	0.999508i	$0.490018\pi$
$294$	−7.87777	+	7.87777i	−0.459441	+	0.459441i
$295$	−8.19677	−	8.19677i	−0.477235	−	0.477235i
$296$	2.16921	+	2.16921i	0.126083	+	0.126083i
$297$			6.34249i			0.368028i
$298$		−	43.3238i		−	2.50968i
$299$	−3.50962	−	3.50962i	−0.202967	−	0.202967i
$300$	−9.14955	−	9.14955i	−0.528250	−	0.528250i
$301$	12.1802	−	12.1802i	0.702054	−	0.702054i
$302$	39.4073			2.26764
$303$	11.1837	−	11.1837i	0.642486	−	0.642486i
$304$			12.4806i			0.715812i
$305$	24.0459			1.37686
$306$		0			0
$307$	14.5796			0.832104			0.416052	−	0.909341i	$-0.363413\pi$
$307$	14.5796			0.832104			0.416052	+	0.909341i	$0.363413\pi$
$308$			39.3724i			2.24345i
$309$	5.08602	−	5.08602i	0.289334	−	0.289334i
$310$	−15.2612			−0.866777
$311$	10.1434	−	10.1434i	0.575180	−	0.575180i	−0.358391	−	0.933571i	$-0.616675\pi$
$311$	10.1434	−	10.1434i	0.575180	−	0.575180i	0.933571	+	0.358391i	$0.116675\pi$
$312$	−2.74094	−	2.74094i	−0.155175	−	0.155175i
$313$	−8.00336	−	8.00336i	−0.452377	−	0.452377i	0.443766	−	0.896143i	$-0.353642\pi$
$313$	−8.00336	−	8.00336i	−0.452377	−	0.452377i	−0.896143	+	0.443766i	$0.853642\pi$
$314$		−	47.9863i		−	2.70802i
$315$			4.48987i			0.252976i
$316$	4.23412	+	4.23412i	0.238188	+	0.238188i
$317$	−8.31718	−	8.31718i	−0.467139	−	0.467139i	0.433847	−	0.900986i	$-0.357156\pi$
$317$	−8.31718	−	8.31718i	−0.467139	−	0.467139i	−0.900986	+	0.433847i	$0.857156\pi$
$318$	2.32767	−	2.32767i	0.130529	−	0.130529i
$319$	−9.69734			−0.542947
$320$	16.9037	−	16.9037i	0.944946	−	0.944946i
$321$			3.67769i			0.205268i
$322$	23.5763			1.31386
$323$		0			0
$324$	3.97290			0.220717
$325$			2.61833i			0.145239i
$326$	18.7980	−	18.7980i	1.04113	−	1.04113i
$327$	−10.2836			−0.568686
$328$	19.1467	−	19.1467i	1.05720	−	1.05720i
$329$	8.24672	+	8.24672i	0.454656	+	0.454656i
$330$	−31.4953	−	31.4953i	−1.73376	−	1.73376i
$331$			20.2084i			1.11075i	0.831600	+	0.555376i	$0.187426\pi$
$331$			20.2084i			1.11075i	−0.831600	+	0.555376i	$0.812574\pi$
$332$		−	29.8969i		−	1.64081i
$333$	0.449887	+	0.449887i	0.0246536	+	0.0246536i
$334$	18.1697	+	18.1697i	0.994203	+	0.994203i
$335$	15.7613	−	15.7613i	0.861134	−	0.861134i
$336$	5.99717			0.327172
$337$	−4.53115	+	4.53115i	−0.246827	+	0.246827i	−0.819667	−	0.572840i	$-0.805842\pi$
$337$	−4.53115	+	4.53115i	−0.246827	+	0.246827i	0.572840	+	0.819667i	$0.305842\pi$
$338$		−	30.1919i		−	1.64222i
$339$	13.9303			0.756590
$340$		0			0
$341$	−13.7831			−0.746395
$342$			7.94707i			0.429729i
$343$	−12.7706	+	12.7706i	−0.689550	+	0.689550i
$344$	53.1548			2.86591
$345$	−12.5445	+	12.5445i	−0.675372	+	0.675372i
$346$	13.3904	+	13.3904i	0.719871	+	0.719871i
$347$	−8.29369	−	8.29369i	−0.445229	−	0.445229i	0.448536	−	0.893765i	$-0.351946\pi$
$347$	−8.29369	−	8.29369i	−0.445229	−	0.445229i	−0.893765	+	0.448536i	$0.851946\pi$
$348$			6.07437i			0.325620i
$349$		−	25.7808i		−	1.38001i	−0.723803	−	0.690007i	$-0.757607\pi$
$349$		−	25.7808i		−	1.38001i	0.723803	−	0.690007i	$-0.242393\pi$
$350$	−8.79447	−	8.79447i	−0.470084	−	0.470084i
$351$	−0.568463	−	0.568463i	−0.0303423	−	0.0303423i
$352$	1.18001	−	1.18001i	0.0628947	−	0.0628947i
$353$	3.96309			0.210934			0.105467	−	0.994423i	$-0.466366\pi$
$353$	3.96309			0.210934			0.105467	+	0.994423i	$0.466366\pi$
$354$	−6.97151	+	6.97151i	−0.370531	+	0.370531i
$355$		−	12.9809i		−	0.688957i
$356$	−24.3439			−1.29022
$357$		0			0
$358$	−29.1992			−1.54323
$359$		−	11.2422i		−	0.593340i	−0.954980	−	0.296670i	$-0.904124\pi$
$359$		−	11.2422i		−	0.593340i	0.954980	−	0.296670i	$-0.0958762\pi$
$360$	−9.79698	+	9.79698i	−0.516346	+	0.516346i
$361$	8.42625			0.443487
$362$	−3.02964	+	3.02964i	−0.159234	+	0.159234i
$363$	−20.6667	−	20.6667i	−1.08472	−	1.08472i
$364$	−3.52886	−	3.52886i	−0.184963	−	0.184963i
$365$		−	23.7951i		−	1.24549i
$366$		−	20.4514i		−	1.06901i
$367$	−10.9270	−	10.9270i	−0.570387	−	0.570387i	0.361850	−	0.932236i	$-0.382145\pi$
$367$	−10.9270	−	10.9270i	−0.570387	−	0.570387i	−0.932236	+	0.361850i	$0.882145\pi$
$368$	16.7558	+	16.7558i	0.873456	+	0.873456i
$369$	3.97096	−	3.97096i	0.206720	−	0.206720i
$370$	−4.46807			−0.232284
$371$	1.48817	−	1.48817i	0.0772620	−	0.0772620i
$372$			8.63365i			0.447634i
$373$	−5.14892			−0.266601			−0.133300	−	0.991076i	$-0.542558\pi$
$373$	−5.14892			−0.266601			−0.133300	+	0.991076i	$0.542558\pi$
$374$		0			0
$375$	−5.00872			−0.258649
$376$			35.9890i			1.85599i
$377$	0.869151	−	0.869151i	0.0447636	−	0.0447636i
$378$	3.81872			0.196414
$379$	8.37697	−	8.37697i	0.430296	−	0.430296i	−0.458433	−	0.888729i	$-0.651589\pi$
$379$	8.37697	−	8.37697i	0.430296	−	0.430296i	0.888729	+	0.458433i	$0.151589\pi$
$380$	−26.2492	−	26.2492i	−1.34656	−	1.34656i
$381$	1.53967	+	1.53967i	0.0788797	+	0.0788797i
$382$			54.5569i			2.79138i
$383$		−	30.7346i		−	1.57047i	−0.619200	−	0.785234i	$-0.712543\pi$
$383$		−	30.7346i		−	1.57047i	0.619200	−	0.785234i	$-0.287457\pi$
$384$	−14.0048	−	14.0048i	−0.714680	−	0.714680i
$385$	−20.1362	−	20.1362i	−1.02624	−	1.02624i
$386$	−45.2040	+	45.2040i	−2.30082	+	2.30082i
$387$	11.0241			0.560388
$388$	−13.6013	+	13.6013i	−0.690500	+	0.690500i
$389$			19.3503i			0.981099i	0.871413	+	0.490549i	$0.163204\pi$
$389$			19.3503i			0.981099i	−0.871413	+	0.490549i	$0.836796\pi$
$390$	5.64571			0.285882
$391$		0			0
$392$	−21.9798			−1.11015
$393$		−	4.40863i		−	0.222386i
$394$	30.7539	−	30.7539i	1.54936	−	1.54936i
$395$	−4.33091			−0.217912
$396$	−17.8177	+	17.8177i	−0.895375	+	0.895375i
$397$	−9.57603	−	9.57603i	−0.480607	−	0.480607i	0.424718	−	0.905326i	$-0.360373\pi$
$397$	−9.57603	−	9.57603i	−0.480607	−	0.480607i	−0.905326	+	0.424718i	$0.860373\pi$
$398$	39.1492	+	39.1492i	1.96237	+	1.96237i
$399$			5.08089i			0.254363i
$400$		−	12.5005i		−	0.625026i
$401$	−6.12006	−	6.12006i	−0.305621	−	0.305621i	0.537587	−	0.843208i	$-0.319336\pi$
$401$	−6.12006	−	6.12006i	−0.305621	−	0.305621i	−0.843208	+	0.537587i	$0.819336\pi$
$402$	−13.4053	−	13.4053i	−0.668596	−	0.668596i
$403$	1.23535	−	1.23535i	0.0615370	−	0.0615370i
$404$	62.8359			3.12620
$405$	−2.03186	+	2.03186i	−0.100964	+	0.100964i
$406$			5.83863i			0.289766i
$407$	−4.03532			−0.200023
$408$		0			0
$409$	20.2269			1.00015			0.500077	−	0.865981i	$-0.333305\pi$
$409$	20.2269			1.00015			0.500077	+	0.865981i	$0.333305\pi$
$410$			39.4378i			1.94769i
$411$	−0.220263	+	0.220263i	−0.0108648	+	0.0108648i
$412$	28.5760			1.40784
$413$	−4.45717	+	4.45717i	−0.219323	+	0.219323i
$414$	10.6693	+	10.6693i	0.524368	+	0.524368i
$415$	15.2902	+	15.2902i	0.750566	+	0.750566i
$416$			0.211523i			0.0103708i
$417$			10.8097i			0.529356i
$418$	−35.6412	−	35.6412i	−1.74327	−	1.74327i
$419$	19.7048	+	19.7048i	0.962640	+	0.962640i	0.999327	−	0.0366865i	$-0.0116803\pi$
$419$	19.7048	+	19.7048i	0.962640	+	0.962640i	−0.0366865	+	0.999327i	$0.511680\pi$
$420$	−12.6132	+	12.6132i	−0.615463	+	0.615463i
$421$	30.5071			1.48682			0.743411	−	0.668834i	$-0.233206\pi$
$421$	30.5071			1.48682			0.743411	+	0.668834i	$0.233206\pi$
$422$	−39.2728	+	39.2728i	−1.91177	+	1.91177i
$423$			7.46399i			0.362912i
$424$	6.49443			0.315398
$425$		0			0
$426$	−11.0405			−0.534915
$427$		−	13.0754i		−	0.632765i
$428$	−10.3316	+	10.3316i	−0.499397	+	0.499397i
$429$	5.09890			0.246177
$430$	−54.7433	+	54.7433i	−2.63996	+	2.63996i
$431$	8.36977	+	8.36977i	0.403157	+	0.403157i	0.879344	−	0.476187i	$-0.157981\pi$
$431$	8.36977	+	8.36977i	0.403157	+	0.403157i	−0.476187	+	0.879344i	$0.657981\pi$
$432$	2.71398	+	2.71398i	0.130576	+	0.130576i
$433$		−	24.9436i		−	1.19871i	−0.800483	−	0.599355i	$-0.795424\pi$
$433$		−	24.9436i		−	1.19871i	0.800483	−	0.599355i	$-0.204576\pi$
$434$			8.29859i			0.398345i
$435$	−3.10661	−	3.10661i	−0.148951	−	0.148951i
$436$	−28.8894	−	28.8894i	−1.38355	−	1.38355i
$437$	−14.1957	+	14.1957i	−0.679075	+	0.679075i
$438$	−20.2382			−0.967018
$439$	−10.1007	+	10.1007i	−0.482079	+	0.482079i	−0.905795	−	0.423716i	$-0.860726\pi$
$439$	−10.1007	+	10.1007i	−0.482079	+	0.482079i	0.423716	+	0.905795i	$0.360726\pi$
$440$		−	87.8753i		−	4.18929i
$441$	−4.55854			−0.217073
$442$		0			0
$443$	3.36806			0.160021			0.0800107	−	0.996794i	$-0.474505\pi$
$443$	3.36806			0.160021			0.0800107	+	0.996794i	$0.474505\pi$
$444$			2.52770i			0.119959i
$445$	12.4502	−	12.4502i	0.590195	−	0.590195i
$446$	−1.45351			−0.0688257
$447$	12.5348	−	12.5348i	0.592877	−	0.592877i
$448$	−9.19175	−	9.19175i	−0.434269	−	0.434269i
$449$	−2.78325	−	2.78325i	−0.131350	−	0.131350i	0.638376	−	0.769725i	$-0.279607\pi$
$449$	−2.78325	−	2.78325i	−0.131350	−	0.131350i	−0.769725	+	0.638376i	$0.779607\pi$
$450$		−	7.95975i		−	0.375226i
$451$			35.6181i			1.67719i
$452$	39.1339	+	39.1339i	1.84070	+	1.84070i
$453$	11.4017	+	11.4017i	0.535698	+	0.535698i
$454$	34.6369	−	34.6369i	1.62559	−	1.62559i
$455$	3.60953			0.169218
$456$	−11.0866	+	11.0866i	−0.519177	+	0.519177i
$457$		−	14.8175i		−	0.693132i	−0.938026	−	0.346566i	$-0.887348\pi$
$457$		−	14.8175i		−	0.693132i	0.938026	−	0.346566i	$-0.112652\pi$
$458$	4.74064			0.221515
$459$		0			0
$460$	−70.4815			−3.28622
$461$		−	33.2839i		−	1.55019i	−0.631847	−	0.775093i	$-0.717703\pi$
$461$		−	33.2839i		−	1.55019i	0.631847	−	0.775093i	$-0.282297\pi$
$462$	−17.1262	+	17.1262i	−0.796785	+	0.796785i
$463$	−19.1509			−0.890018			−0.445009	−	0.895526i	$-0.646799\pi$
$463$	−19.1509			−0.890018			−0.445009	+	0.895526i	$0.646799\pi$
$464$	−4.14954	+	4.14954i	−0.192637	+	0.192637i
$465$	−4.41551	−	4.41551i	−0.204764	−	0.204764i
$466$	14.5902	+	14.5902i	0.675879	+	0.675879i
$467$			37.8301i			1.75057i	0.483607	+	0.875285i	$0.339326\pi$
$467$			37.8301i			1.75057i	−0.483607	+	0.875285i	$0.660674\pi$
$468$		−	3.19393i		−	0.147639i
$469$	−8.57056	−	8.57056i	−0.395752	−	0.395752i
$470$	−37.0645	−	37.0645i	−1.70966	−	1.70966i
$471$	13.8838	−	13.8838i	0.639733	−	0.639733i
$472$	−19.4512			−0.895315
$473$	−49.4412	+	49.4412i	−2.27331	+	2.27331i
$474$			3.68352i			0.169190i
$475$	10.5906			0.485931
$476$		0			0
$477$	1.34692			0.0616714
$478$			37.8886i			1.73298i
$479$	−0.303694	+	0.303694i	−0.0138761	+	0.0138761i	−0.714011	−	0.700135i	$-0.753123\pi$
$479$	−0.303694	+	0.303694i	−0.0138761	+	0.0138761i	0.700135	+	0.714011i	$0.253123\pi$
$480$	0.756049			0.0345088
$481$	0.361677	−	0.361677i	0.0164910	−	0.0164910i
$482$	−51.4842	−	51.4842i	−2.34504	−	2.34504i
$483$	6.82132	+	6.82132i	0.310381	+	0.310381i
$484$		−	116.117i		−	5.27803i
$485$		−	13.9122i		−	0.631721i
$486$	1.72814	+	1.72814i	0.0783898	+	0.0783898i
$487$	0.138329	+	0.138329i	0.00626826	+	0.00626826i	0.710234	−	0.703966i	$-0.248589\pi$
$487$	0.138329	+	0.138329i	0.00626826	+	0.00626826i	−0.703966	+	0.710234i	$0.748589\pi$
$488$	28.5308	−	28.5308i	1.29153	−	1.29153i
$489$	10.8776			0.491903
$490$	22.6367	−	22.6367i	1.02262	−	1.02262i
$491$		−	9.32805i		−	0.420969i	−0.977597	−	0.210485i	$-0.932496\pi$
$491$		−	9.32805i		−	0.420969i	0.977597	−	0.210485i	$-0.0675042\pi$
$492$	22.3110			1.00586
$493$		0			0
$494$	6.38888			0.287449
$495$		−	18.2250i		−	0.819155i
$496$	−5.89784	+	5.89784i	−0.264821	+	0.264821i
$497$	−7.05866			−0.316624
$498$	13.0046	−	13.0046i	0.582749	−	0.582749i
$499$	−5.80808	−	5.80808i	−0.260005	−	0.260005i	0.565051	−	0.825056i	$-0.308857\pi$
$499$	−5.80808	−	5.80808i	−0.260005	−	0.260005i	−0.825056	+	0.565051i	$0.808857\pi$
$500$	−14.0708	−	14.0708i	−0.629266	−	0.629266i
$501$			10.5141i			0.469734i
$502$			11.2210i			0.500818i
$503$	−21.1656	−	21.1656i	−0.943727	−	0.943727i	0.0547716	−	0.998499i	$-0.482557\pi$
$503$	−21.1656	−	21.1656i	−0.943727	−	0.943727i	−0.998499	+	0.0547716i	$0.982557\pi$
$504$	5.32731	+	5.32731i	0.237297	+	0.237297i
$505$	−32.1362	+	32.1362i	−1.43004	+	1.43004i
$506$	−95.6998			−4.25437
$507$	8.73538	−	8.73538i	0.387952	−	0.387952i
$508$			8.65069i			0.383812i
$509$	2.71603			0.120386			0.0601929	−	0.998187i	$-0.480828\pi$
$509$	2.71603			0.120386			0.0601929	+	0.998187i	$0.480828\pi$
$510$		0			0
$511$	−12.9391			−0.572392
$512$		−	38.0225i		−	1.68037i
$513$	−2.29932	+	2.29932i	−0.101517	+	0.101517i
$514$	71.0532			3.13402
$515$	−14.6146	+	14.6146i	−0.643997	+	0.643997i
$516$	30.9697	+	30.9697i	1.36336	+	1.36336i
$517$	−33.4746	−	33.4746i	−1.47221	−	1.47221i
$518$			2.42961i			0.106751i
$519$			7.74845i			0.340119i
$520$	7.87607	+	7.87607i	0.345388	+	0.345388i
$521$	1.46717	+	1.46717i	0.0642779	+	0.0642779i	0.738515	−	0.674237i	$-0.235527\pi$
$521$	1.46717	+	1.46717i	0.0642779	+	0.0642779i	−0.674237	+	0.738515i	$0.735527\pi$
$522$	−2.64223	+	2.64223i	−0.115647	+	0.115647i
$523$	−17.2333			−0.753558			−0.376779	−	0.926303i	$-0.622968\pi$
$523$	−17.2333			−0.753558			−0.376779	+	0.926303i	$0.622968\pi$
$524$	12.3850	−	12.3850i	0.541042	−	0.541042i
$525$		−	5.08899i		−	0.222102i
$526$	−2.62623			−0.114509
$527$		0			0
$528$	−24.3434			−1.05941
$529$			15.1169i			0.657255i
$530$	−6.68852	+	6.68852i	−0.290531	+	0.290531i
$531$	−4.03412			−0.175066
$532$	−14.2736	+	14.2736i	−0.618837	+	0.618837i
$533$	−3.19237	−	3.19237i	−0.138277	−	0.138277i
$534$	−10.5891	−	10.5891i	−0.458235	−	0.458235i
$535$		−	10.5678i		−	0.456885i
$536$		−	37.4022i		−	1.61553i
$537$	−8.44819	−	8.44819i	−0.364566	−	0.364566i
$538$	43.7545	+	43.7545i	1.88639	+	1.88639i
$539$	20.4442	−	20.4442i	0.880594	−	0.880594i
$540$	−11.4161			−0.491270
$541$	2.50022	−	2.50022i	0.107493	−	0.107493i	−0.651315	−	0.758808i	$-0.725782\pi$
$541$	2.50022	−	2.50022i	0.107493	−	0.107493i	0.758808	+	0.651315i	$0.225782\pi$
$542$			47.6111i			2.04507i
$543$	−1.75313			−0.0752338
$544$		0			0
$545$	29.5498			1.26578
$546$		−	3.06997i		−	0.131383i
$547$	−13.8383	+	13.8383i	−0.591683	+	0.591683i	−0.938086	−	0.346403i	$-0.887403\pi$
$547$	−13.8383	+	13.8383i	−0.591683	+	0.591683i	0.346403	+	0.938086i	$0.387403\pi$
$548$	−1.23755			−0.0528657
$549$	5.91720	−	5.91720i	0.252540	−	0.252540i
$550$	35.6980	+	35.6980i	1.52217	+	1.52217i
$551$	−3.51555	−	3.51555i	−0.149767	−	0.149767i
$552$			29.7685i			1.26703i
$553$			2.35502i			0.100146i
$554$	−16.4227	−	16.4227i	−0.697733	−	0.697733i
$555$	−1.29274	−	1.29274i	−0.0548739	−	0.0548739i
$556$	−30.3675	+	30.3675i	−1.28787	+	1.28787i
$557$	−15.0835			−0.639110			−0.319555	−	0.947568i	$-0.603533\pi$
$557$	−15.0835			−0.639110			−0.319555	+	0.947568i	$0.603533\pi$
$558$	−3.75547	+	3.75547i	−0.158982	+	0.158982i
$559$		−	8.86260i		−	0.374848i
$560$	−17.2328			−0.728218
$561$		0			0
$562$	35.2460			1.48676
$563$			38.6507i			1.62893i	0.580212	+	0.814466i	$0.302970\pi$
$563$			38.6507i			1.62893i	−0.580212	+	0.814466i	$0.697030\pi$
$564$	−20.9683	+	20.9683i	−0.882926	+	0.882926i
$565$	−40.0285			−1.68401
$566$	33.5446	−	33.5446i	1.40999	−	1.40999i
$567$	1.10487	+	1.10487i	0.0464001	+	0.0464001i
$568$	−15.4021	−	15.4021i	−0.646258	−	0.646258i
$569$			3.19348i			0.133878i	0.997757	+	0.0669389i	$0.0213233\pi$
$569$			3.19348i			0.133878i	−0.997757	+	0.0669389i	$0.978677\pi$
$570$		−	22.8358i		−	0.956487i
$571$	3.76282	+	3.76282i	0.157469	+	0.157469i	0.781444	−	0.623975i	$-0.214483\pi$
$571$	3.76282	+	3.76282i	0.157469	+	0.157469i	−0.623975	+	0.781444i	$0.714483\pi$
$572$	14.3242	+	14.3242i	0.598924	+	0.598924i
$573$	−15.7849	+	15.7849i	−0.659424	+	0.659424i
$574$	21.4451			0.895102
$575$	14.2184	−	14.2184i	0.592948	−	0.592948i
$576$		−	8.31932i		−	0.346638i
$577$	−10.4307			−0.434236			−0.217118	−	0.976145i	$-0.569666\pi$
$577$	−10.4307			−0.434236			−0.217118	+	0.976145i	$0.569666\pi$
$578$		0			0
$579$	−26.1577			−1.08708
$580$		−	17.4546i		−	0.724763i
$581$	8.31436	−	8.31436i	0.344938	−	0.344938i
$582$	−11.8326			−0.490476
$583$	−6.04071	+	6.04071i	−0.250180	+	0.250180i
$584$	−28.2333	−	28.2333i	−1.16830	−	1.16830i
$585$	1.63347	+	1.63347i	0.0675357	+	0.0675357i
$586$			2.62329i			0.108367i
$587$			18.7387i			0.773427i	0.922200	+	0.386714i	$0.126390\pi$
$587$			18.7387i			0.773427i	−0.922200	+	0.386714i	$0.873610\pi$
$588$	−12.8061	−	12.8061i	−0.528116	−	0.528116i
$589$	−4.99673	−	4.99673i	−0.205887	−	0.205887i
$590$	20.0325	−	20.0325i	0.824726	−	0.824726i
$591$	17.7960			0.732031
$592$	−1.72673	+	1.72673i	−0.0709682	+	0.0709682i
$593$		−	7.29409i		−	0.299533i	−0.988721	−	0.149766i	$-0.952148\pi$
$593$		−	7.29409i		−	0.299533i	0.988721	−	0.149766i	$-0.0478521\pi$
$594$	−15.5007			−0.636003
$595$		0			0
$596$	70.4273			2.88482
$597$			22.6540i			0.927168i
$598$	8.57736	−	8.57736i	0.350754	−	0.350754i
$599$	−31.8625			−1.30187			−0.650933	−	0.759135i	$-0.725622\pi$
$599$	−31.8625			−1.30187			−0.650933	+	0.759135i	$0.725622\pi$
$600$	11.1043	−	11.1043i	0.453330	−	0.453330i
$601$	0.370640	+	0.370640i	0.0151187	+	0.0151187i	0.714626	−	0.699507i	$-0.246597\pi$
$601$	0.370640	+	0.370640i	0.0151187	+	0.0151187i	−0.699507	+	0.714626i	$0.746597\pi$
$602$	29.7678	+	29.7678i	1.21324	+	1.21324i
$603$		−	7.75709i		−	0.315893i
$604$			64.0607i			2.60659i
$605$	59.3855	+	59.3855i	2.41436	+	2.41436i
$606$	27.3324	+	27.3324i	1.11030	+	1.11030i
$607$	−0.671134	+	0.671134i	−0.0272405	+	0.0272405i	−0.720596	−	0.693355i	$-0.756132\pi$
$607$	−0.671134	+	0.671134i	−0.0272405	+	0.0272405i	0.693355	+	0.720596i	$0.256132\pi$
$608$	0.855570			0.0346980
$609$	−1.68929	+	1.68929i	−0.0684533	+	0.0684533i
$610$			58.7669i			2.37940i
$611$	6.00051			0.242755
$612$		0			0
$613$	3.89703			0.157399			0.0786997	−	0.996898i	$-0.474923\pi$
$613$	3.89703			0.157399			0.0786997	+	0.996898i	$0.474923\pi$
$614$			35.6319i			1.43799i
$615$	−11.4105	+	11.4105i	−0.460116	+	0.460116i
$616$	−47.7840			−1.92527
$617$	−13.6831	+	13.6831i	−0.550862	+	0.550862i	−0.926690	−	0.375827i	$-0.877359\pi$
$617$	−13.6831	+	13.6831i	−0.550862	+	0.550862i	0.375827	+	0.926690i	$0.377359\pi$
$618$	12.4300	+	12.4300i	0.500008	+	0.500008i
$619$	−13.9123	−	13.9123i	−0.559182	−	0.559182i	0.369893	−	0.929074i	$-0.379394\pi$
$619$	−13.9123	−	13.9123i	−0.559182	−	0.559182i	−0.929074	+	0.369893i	$0.879394\pi$
$620$		−	24.8087i		−	0.996340i
$621$			6.17389i			0.247749i
$622$	24.7900	+	24.7900i	0.993989	+	0.993989i
$623$	−6.77005	−	6.77005i	−0.271236	−	0.271236i
$624$	2.18184	−	2.18184i	0.0873436	−	0.0873436i
$625$	30.6771			1.22708
$626$	19.5598	−	19.5598i	0.781768	−	0.781768i
$627$		−	20.6241i		−	0.823646i
$628$	78.0067			3.11281
$629$		0			0
$630$	−10.9730			−0.437176
$631$		−	2.77834i		−	0.110604i	−0.998470	−	0.0553019i	$-0.982388\pi$
$631$		−	2.77834i		−	0.110604i	0.998470	−	0.0553019i	$-0.0176121\pi$
$632$	−5.13870	+	5.13870i	−0.204407	+	0.204407i
$633$	−22.7255			−0.903258
$634$	20.3268	−	20.3268i	0.807280	−	0.807280i
$635$	−4.42422	−	4.42422i	−0.175570	−	0.175570i
$636$	3.78387	+	3.78387i	0.150040	+	0.150040i
$637$			3.66474i			0.145202i
$638$		−	23.6998i		−	0.938286i
$639$	−3.19435	−	3.19435i	−0.126366	−	0.126366i
$640$	40.2426	+	40.2426i	1.59073	+	1.59073i
$641$	15.2145	−	15.2145i	0.600938	−	0.600938i	−0.339623	−	0.940562i	$-0.610300\pi$
$641$	15.2145	−	15.2145i	0.600938	−	0.600938i	0.940562	+	0.339623i	$0.110300\pi$
$642$	−8.98809			−0.354732
$643$	31.4208	−	31.4208i	1.23912	−	1.23912i	0.278754	−	0.960362i	$-0.410078\pi$
$643$	31.4208	−	31.4208i	1.23912	−	1.23912i	0.960362	−	0.278754i	$-0.0899215\pi$
$644$			38.3258i			1.51025i
$645$	−31.6777			−1.24731
$646$		0			0
$647$	−43.8840			−1.72526			−0.862629	−	0.505838i	$-0.831183\pi$
$647$	−43.8840			−1.72526			−0.862629	+	0.505838i	$0.831183\pi$
$648$			4.82168i			0.189413i
$649$	18.0923	−	18.0923i	0.710184	−	0.710184i
$650$	−6.39907			−0.250992
$651$	−2.40102	+	2.40102i	−0.0941036	+	0.0941036i
$652$	30.5582	+	30.5582i	1.19675	+	1.19675i
$653$	6.04458	+	6.04458i	0.236543	+	0.236543i	0.815417	−	0.578874i	$-0.196508\pi$
$653$	6.04458	+	6.04458i	0.236543	+	0.236543i	−0.578874	+	0.815417i	$0.696508\pi$
$654$		−	25.1327i		−	0.982766i
$655$			12.6681i			0.494985i
$656$	15.2411	+	15.2411i	0.595066	+	0.595066i
$657$	−5.85550	−	5.85550i	−0.228445	−	0.228445i
$658$	−20.1546	+	20.1546i	−0.785708	+	0.785708i
$659$	−36.1408			−1.40785			−0.703924	−	0.710276i	$-0.748570\pi$
$659$	−36.1408			−1.40785			−0.703924	+	0.710276i	$0.748570\pi$
$660$	51.1990	−	51.1990i	1.99292	−	1.99292i
$661$			46.4203i			1.80554i	0.430122	+	0.902771i	$0.358471\pi$
$661$			46.4203i			1.80554i	−0.430122	+	0.902771i	$0.641529\pi$
$662$	−49.3882			−1.91953
$663$		0			0
$664$	36.2841			1.40810
$665$		−	14.5999i		−	0.566158i
$666$	−1.09950	+	1.09950i	−0.0426048	+	0.0426048i
$667$	−9.43956			−0.365501
$668$	−29.5368	+	29.5368i	−1.14281	+	1.14281i
$669$	−0.420543	−	0.420543i	−0.0162591	−	0.0162591i
$670$	38.5200	+	38.5200i	1.48816	+	1.48816i
$671$			53.0751i			2.04894i
$672$		−	0.411118i		−	0.0158592i
$673$	31.9122	+	31.9122i	1.23012	+	1.23012i	0.963915	+	0.266209i	$0.0857712\pi$
$673$	31.9122	+	31.9122i	1.23012	+	1.23012i	0.266209	+	0.963915i	$0.414229\pi$
$674$	−11.0739	−	11.0739i	−0.426551	−	0.426551i
$675$	2.30299	−	2.30299i	0.0886421	−	0.0886421i
$676$	49.0800			1.88769
$677$	25.6225	−	25.6225i	0.984751	−	0.984751i	−0.0151343	−	0.999885i	$-0.504818\pi$
$677$	25.6225	−	25.6225i	0.984751	−	0.984751i	0.999885	+	0.0151343i	$0.00481757\pi$
$678$			34.0450i			1.30749i
$679$	−7.56505			−0.290320
$680$		0			0
$681$	20.0429			0.768047
$682$		−	33.6852i		−	1.28987i
$683$	−17.2036	+	17.2036i	−0.658279	+	0.658279i	−0.954973	−	0.296694i	$-0.904116\pi$
$683$	−17.2036	+	17.2036i	−0.658279	+	0.658279i	0.296694	+	0.954973i	$0.404116\pi$
$684$	−12.9188			−0.493963
$685$	0.632922	−	0.632922i	0.0241827	−	0.0241827i
$686$	−31.2108	−	31.2108i	−1.19164	−	1.19164i
$687$	1.37160	+	1.37160i	0.0523300	+	0.0523300i
$688$			42.3122i			1.61314i
$689$		−	1.08283i		−	0.0412525i
$690$	−30.6581	−	30.6581i	−1.16713	−	1.16713i
$691$	15.1241	+	15.1241i	0.575349	+	0.575349i	0.933618	−	0.358269i	$-0.116633\pi$
$691$	15.1241	+	15.1241i	0.575349	+	0.575349i	−0.358269	+	0.933618i	$0.616633\pi$
$692$	−21.7675	+	21.7675i	−0.827474	+	0.827474i
$693$	−9.91025			−0.376459
$694$	20.2694	−	20.2694i	0.769415	−	0.769415i
$695$		−	31.0617i		−	1.17824i
$696$	−7.37210			−0.279439
$697$		0			0
$698$	63.0070			2.38485
$699$			8.44275i			0.319334i
$700$	14.2963	−	14.2963i	0.540351	−	0.540351i
$701$	15.3315			0.579063			0.289532	−	0.957168i	$-0.406500\pi$
$701$	15.3315			0.579063			0.289532	+	0.957168i	$0.406500\pi$
$702$	1.38930	−	1.38930i	0.0524356	−	0.0524356i
$703$	−1.46291	−	1.46291i	−0.0551747	−	0.0551747i
$704$	37.3106	+	37.3106i	1.40620	+	1.40620i
$705$		−	21.4477i		−	0.807766i
$706$			9.68560i			0.364522i
$707$	17.4747	+	17.4747i	0.657204	+	0.657204i
$708$	−11.3329	−	11.3329i	−0.425917	−	0.425917i
$709$	−27.2246	+	27.2246i	−1.02244	+	1.02244i	−0.0226975	+	0.999742i	$0.507225\pi$
$709$	−27.2246	+	27.2246i	−1.02244	+	1.02244i	−0.999742	+	0.0226975i	$0.992775\pi$
$710$	31.7248			1.19061
$711$	−1.06575	+	1.06575i	−0.0399688	+	0.0399688i
$712$		−	29.5447i		−	1.10723i
$713$	−13.4167			−0.502459
$714$		0			0
$715$	−14.6516			−0.547940
$716$		−	47.4664i		−	1.77390i
$717$	−10.9623	+	10.9623i	−0.409394	+	0.409394i
$718$	27.4754			1.02537
$719$	10.7701	−	10.7701i	0.401656	−	0.401656i	−0.477160	−	0.878816i	$-0.658334\pi$
$719$	10.7701	−	10.7701i	0.401656	−	0.401656i	0.878816	+	0.477160i	$0.158334\pi$
$720$	−7.79858	−	7.79858i	−0.290636	−	0.290636i
$721$	7.94700	+	7.94700i	0.295962	+	0.295962i
$722$			20.5933i			0.766405i
$723$		−	29.7917i		−	1.10797i
$724$	−4.92499	−	4.92499i	−0.183036	−	0.183036i
$725$	3.52116	+	3.52116i	0.130772	+	0.130772i
$726$	50.5084	−	50.5084i	1.87454	−	1.87454i
$727$	−11.2839			−0.418495			−0.209248	−	0.977863i	$-0.567101\pi$
$727$	−11.2839			−0.418495			−0.209248	+	0.977863i	$0.567101\pi$
$728$	4.28278	−	4.28278i	0.158730	−	0.158730i
$729$			1.00000i			0.0370370i
$730$	58.1542			2.15238
$731$		0			0
$732$	33.2460			1.22881
$733$		−	26.5213i		−	0.979585i	−0.871839	−	0.489793i	$-0.837073\pi$
$733$		−	26.5213i		−	0.979585i	0.871839	−	0.489793i	$-0.162927\pi$
$734$	26.7052	−	26.7052i	0.985705	−	0.985705i
$735$	13.0989			0.483160
$736$	1.14864	−	1.14864i	0.0423395	−	0.0423395i
$737$	34.7891	+	34.7891i	1.28147	+	1.28147i
$738$	9.70484	+	9.70484i	0.357240	+	0.357240i
$739$		−	0.861682i		−	0.0316975i	−0.999874	−	0.0158487i	$-0.994955\pi$
$739$		−	0.861682i		−	0.0316975i	0.999874	−	0.0158487i	$-0.00504502\pi$
$740$		−	7.26332i		−	0.267005i
$741$	1.84849	+	1.84849i	0.0679059	+	0.0679059i
$742$	3.63702	+	3.63702i	0.133519	+	0.133519i
$743$	3.06667	−	3.06667i	0.112505	−	0.112505i	−0.648613	−	0.761118i	$-0.724651\pi$
$743$	3.06667	−	3.06667i	0.112505	−	0.112505i	0.761118	+	0.648613i	$0.224651\pi$
$744$	−10.4782			−0.384148
$745$	−36.0186	+	36.0186i	−1.31962	+	1.31962i
$746$		−	12.5837i		−	0.460722i
$747$	7.52521			0.275333
$748$		0			0
$749$	−5.74645			−0.209971
$750$		−	12.2411i		−	0.446981i
$751$	−24.1088	+	24.1088i	−0.879741	+	0.879741i	−0.993508	−	0.113766i	$-0.963709\pi$
$751$	−24.1088	+	24.1088i	−0.879741	+	0.879741i	0.113766	+	0.993508i	$0.463709\pi$
$752$	−28.6479			−1.04468
$753$	−3.24656	+	3.24656i	−0.118311	+	0.118311i
$754$	2.12416	+	2.12416i	0.0773575	+	0.0773575i
$755$	−32.7626	−	32.7626i	−1.19235	−	1.19235i
$756$			6.20773i			0.225773i
$757$		−	35.7904i		−	1.30082i	−0.759581	−	0.650412i	$-0.774596\pi$
$757$		−	35.7904i		−	1.30082i	0.759581	−	0.650412i	$-0.225404\pi$
$758$	20.4729	+	20.4729i	0.743610	+	0.743610i
$759$	−27.6887	−	27.6887i	−1.00504	−	1.00504i
$760$	31.8571	−	31.8571i	1.15558	−	1.15558i
$761$	−24.8283			−0.900025			−0.450013	−	0.893022i	$-0.648580\pi$
$761$	−24.8283			−0.900025			−0.450013	+	0.893022i	$0.648580\pi$
$762$	−3.76288	+	3.76288i	−0.136315	+	0.136315i
$763$		−	16.0683i		−	0.581713i
$764$	−88.6880			−3.20862
$765$		0			0
$766$	75.1140			2.71398
$767$			3.24314i			0.117103i
$768$	22.4618	−	22.4618i	0.810521	−	0.810521i
$769$	47.0234			1.69571			0.847854	−	0.530230i	$-0.177894\pi$
$769$	47.0234			1.69571			0.847854	+	0.530230i	$0.177894\pi$
$770$	49.2120	−	49.2120i	1.77348	−	1.77348i
$771$	20.5578	+	20.5578i	0.740370	+	0.740370i
$772$	−73.4838	−	73.4838i	−2.64474	−	2.64474i
$773$		−	41.7490i		−	1.50161i	−0.660525	−	0.750804i	$-0.729666\pi$
$773$		−	41.7490i		−	1.50161i	0.660525	−	0.750804i	$-0.270334\pi$
$774$			26.9424i			0.968426i
$775$	5.00471	+	5.00471i	0.179774	+	0.179774i
$776$	−16.5071	−	16.5071i	−0.592569	−	0.592569i
$777$	−0.702956	+	0.702956i	−0.0252184	+	0.0252184i
$778$	−47.2912			−1.69547
$779$	−12.9125	+	12.9125i	−0.462638	+	0.462638i
$780$			9.17770i			0.328614i
$781$	28.6521			1.02525
$782$		0			0
$783$	−1.52895			−0.0546402
$784$		−	17.4963i		−	0.624869i
$785$	−39.8950	+	39.8950i	−1.42391	+	1.42391i
$786$	10.7745			0.384313
$787$	1.68336	−	1.68336i	0.0600054	−	0.0600054i	−0.676467	−	0.736473i	$-0.736490\pi$
$787$	1.68336	−	1.68336i	0.0600054	−	0.0600054i	0.736473	+	0.676467i	$0.236490\pi$
$788$	49.9938	+	49.9938i	1.78095	+	1.78095i
$789$	−0.759845	−	0.759845i	−0.0270512	−	0.0270512i
$790$		−	10.5845i		−	0.376581i
$791$			21.7663i			0.773922i
$792$	−21.6243	−	21.6243i	−0.768387	−	0.768387i
$793$	−4.75700	−	4.75700i	−0.168926	−	0.168926i
$794$	23.4034	−	23.4034i	0.830554	−	0.830554i
$795$	−3.87037			−0.137268
$796$	−63.6412	+	63.6412i	−2.25570	+	2.25570i
$797$		−	38.4308i		−	1.36129i	−0.732614	−	0.680645i	$-0.761700\pi$
$797$		−	38.4308i		−	1.36129i	0.732614	−	0.680645i	$-0.238300\pi$
$798$	−12.4174			−0.439573
$799$		0			0
$800$	−0.856935			−0.0302972
$801$		−	6.12748i		−	0.216504i
$802$	14.9571	−	14.9571i	0.528155	−	0.528155i
$803$	52.5217			1.85345
$804$	21.7917	−	21.7917i	0.768535	−	0.768535i
$805$	−19.6010	−	19.6010i	−0.690843	−	0.690843i
$806$	3.01913	+	3.01913i	0.106344	+	0.106344i
$807$			25.3189i			0.891267i
$808$			76.2602i			2.68283i
$809$	−10.3101	−	10.3101i	−0.362484	−	0.362484i	0.502243	−	0.864727i	$-0.332508\pi$
$809$	−10.3101	−	10.3101i	−0.362484	−	0.362484i	−0.864727	+	0.502243i	$0.832508\pi$
$810$	−4.96577	−	4.96577i	−0.174479	−	0.174479i
$811$	0.196697	−	0.196697i	0.00690697	−	0.00690697i	−0.703645	−	0.710552i	$-0.748445\pi$
$811$	0.196697	−	0.196697i	0.00690697	−	0.00690697i	0.710552	+	0.703645i	$0.248445\pi$
$812$	−9.49131			−0.333080
$813$	−13.7753	+	13.7753i	−0.483120	+	0.483120i
$814$		−	9.86213i		−	0.345667i
$815$	−31.2567			−1.09487
$816$		0			0
$817$	−35.8475			−1.25414
$818$			49.4335i			1.72840i
$819$	0.888234	−	0.888234i	0.0310374	−	0.0310374i
$820$	−64.1103			−2.23883
$821$	8.80316	−	8.80316i	0.307232	−	0.307232i	−0.536603	−	0.843835i	$-0.680293\pi$
$821$	8.80316	−	8.80316i	0.307232	−	0.307232i	0.843835	+	0.536603i	$0.180293\pi$
$822$	−0.538312	−	0.538312i	−0.0187758	−	0.0187758i
$823$	14.8015	+	14.8015i	0.515947	+	0.515947i	0.916342	−	0.400396i	$-0.131127\pi$
$823$	14.8015	+	14.8015i	0.515947	+	0.515947i	−0.400396	+	0.916342i	$0.631127\pi$
$824$			34.6810i			1.20817i
$825$			20.6570i			0.719183i
$826$	−10.8931	−	10.8931i	−0.379020	−	0.379020i
$827$	21.8744	+	21.8744i	0.760648	+	0.760648i	0.976439	−	0.215792i	$-0.0692332\pi$
$827$	21.8744	+	21.8744i	0.760648	+	0.760648i	−0.215792	+	0.976439i	$0.569233\pi$
$828$	−17.3441	+	17.3441i	−0.602749	+	0.602749i
$829$	−5.04799			−0.175324			−0.0876620	−	0.996150i	$-0.527940\pi$
$829$	−5.04799			−0.175324			−0.0876620	+	0.996150i	$0.527940\pi$
$830$	−37.3685	+	37.3685i	−1.29708	+	1.29708i
$831$		−	9.50313i		−	0.329660i
$832$	−6.68814			−0.231869
$833$		0			0
$834$	−26.4185			−0.914798
$835$		−	30.2120i		−	1.04553i
$836$	57.9385	−	57.9385i	2.00384	−	2.00384i
$837$	−2.17313			−0.0751145
$838$	−48.1575	+	48.1575i	−1.66357	+	1.66357i
$839$	−7.75414	−	7.75414i	−0.267703	−	0.267703i	0.560471	−	0.828174i	$-0.310620\pi$
$839$	−7.75414	−	7.75414i	−0.267703	−	0.267703i	−0.828174	+	0.560471i	$0.810620\pi$
$840$	−15.3080	−	15.3080i	−0.528175	−	0.528175i
$841$			26.6623i			0.919390i
$842$			74.5578i			2.56943i
$843$	10.1977	+	10.1977i	0.351228	+	0.351228i
$844$	−63.8420	−	63.8420i	−2.19753	−	2.19753i
$845$	−25.1010	+	25.1010i	−0.863501	+	0.863501i
$846$	−18.2416			−0.627161
$847$	32.2921	−	32.2921i	1.10957	−	1.10957i
$848$			5.16969i			0.177528i
$849$	19.4109			0.666180
$850$		0			0
$851$	−3.92805			−0.134652
$852$		−	17.9475i		−	0.614873i
$853$	18.8308	−	18.8308i	0.644753	−	0.644753i	−0.306967	−	0.951720i	$-0.599314\pi$
$853$	18.8308	−	18.8308i	0.644753	−	0.644753i	0.951720	+	0.306967i	$0.0993141\pi$
$854$	31.9557			1.09350
$855$	6.60707	−	6.60707i	0.225957	−	0.225957i
$856$	−12.5389	−	12.5389i	−0.428569	−	0.428569i
$857$	0.943438	+	0.943438i	0.0322272	+	0.0322272i	0.723037	−	0.690810i	$-0.242746\pi$
$857$	0.943438	+	0.943438i	0.0322272	+	0.0322272i	−0.690810	+	0.723037i	$0.742746\pi$
$858$			12.4615i			0.425428i
$859$			24.4857i			0.835441i	0.908575	+	0.417721i	$0.137171\pi$
$859$			24.4857i			0.835441i	−0.908575	+	0.417721i	$0.862829\pi$
$860$	−88.9910	−	88.9910i	−3.03457	−	3.03457i
$861$	6.20470	+	6.20470i	0.211456	+	0.211456i
$862$	−20.4553	+	20.4553i	−0.696711	+	0.696711i
$863$	39.3336			1.33893			0.669465	−	0.742843i	$-0.266523\pi$
$863$	39.3336			1.33893			0.669465	+	0.742843i	$0.266523\pi$
$864$	0.186048	−	0.186048i	0.00632950	−	0.00632950i
$865$		−	22.2651i		−	0.757035i
$866$	60.9609			2.07153
$867$		0			0
$868$	−13.4902			−0.457888
$869$		−	9.55939i		−	0.324280i
$870$	7.59241	−	7.59241i	0.257407	−	0.257407i
$871$	−6.23614			−0.211304
$872$	35.0614	−	35.0614i	1.18733	−	1.18733i
$873$	−3.42351	−	3.42351i	−0.115868	−	0.115868i
$874$	−34.6937	−	34.6937i	−1.17353	−	1.17353i
$875$		−	7.82621i		−	0.264574i
$876$		−	32.8993i		−	1.11156i
$877$	−2.73454	−	2.73454i	−0.0923388	−	0.0923388i	0.659428	−	0.751767i	$-0.270798\pi$
$877$	−2.73454	−	2.73454i	−0.0923388	−	0.0923388i	−0.751767	+	0.659428i	$0.770798\pi$
$878$	−24.6856	−	24.6856i	−0.833098	−	0.833098i
$879$	−0.758995	+	0.758995i	−0.0256003	+	0.0256003i
$880$	69.9504			2.35803
$881$	11.5575	−	11.5575i	0.389383	−	0.389383i	−0.485084	−	0.874467i	$-0.661211\pi$
$881$	11.5575	−	11.5575i	0.389383	−	0.389383i	0.874467	+	0.485084i	$0.161211\pi$
$882$		−	11.1408i		−	0.375132i
$883$	−33.5409			−1.12874			−0.564370	−	0.825522i	$-0.690881\pi$
$883$	−33.5409			−1.12874			−0.564370	+	0.825522i	$0.690881\pi$
$884$		0			0
$885$	11.5920			0.389660
$886$			8.23138i			0.276539i
$887$	17.8096	−	17.8096i	0.597988	−	0.597988i	−0.341789	−	0.939777i	$-0.611033\pi$
$887$	17.8096	−	17.8096i	0.597988	−	0.597988i	0.939777	+	0.341789i	$0.111033\pi$
$888$	−3.06772			−0.102946
$889$	−2.40576	+	2.40576i	−0.0806867	+	0.0806867i
$890$	30.4276	+	30.4276i	1.01994	+	1.01994i
$891$	−4.48482	−	4.48482i	−0.150247	−	0.150247i
$892$		−	2.36283i		−	0.0791135i
$893$		−	24.2709i		−	0.812195i
$894$	30.6345	+	30.6345i	1.02457	+	1.02457i
$895$	24.2758	+	24.2758i	0.811449	+	0.811449i
$896$	21.8828	−	21.8828i	0.731052	−	0.731052i
$897$	4.96336			0.165722
$898$	6.80212	−	6.80212i	0.226990	−	0.226990i
$899$		−	3.32261i		−	0.110815i
$900$	12.9394			0.431314
$901$		0			0
$902$	−87.0488			−2.89841
$903$			17.2254i			0.573225i
$904$	−47.4945	+	47.4945i	−1.57964	+	1.57964i
$905$	5.03758			0.167455
$906$	−27.8652	+	27.8652i	−0.925758	+	0.925758i
$907$	31.8673	+	31.8673i	1.05814	+	1.05814i	0.998202	+	0.0599326i	$0.0190886\pi$
$907$	31.8673	+	31.8673i	1.05814	+	1.05814i	0.0599326	+	0.998202i	$0.480911\pi$
$908$	56.3059	+	56.3059i	1.86858	+	1.86858i
$909$			15.8161i			0.524588i
$910$			8.82153i			0.292431i
$911$	−31.8427	−	31.8427i	−1.05500	−	1.05500i	−0.998397	−	0.0565992i	$-0.981974\pi$
$911$	−31.8427	−	31.8427i	−1.05500	−	1.05500i	−0.0565992	−	0.998397i	$-0.518026\pi$
$912$	−8.82513	−	8.82513i	−0.292229	−	0.292229i
$913$	−33.7492	+	33.7492i	−1.11694	+	1.11694i
$914$	36.2132			1.19783
$915$	−17.0030	+	17.0030i	−0.562101	+	0.562101i
$916$			7.70640i			0.254627i
$917$	6.88856			0.227480
$918$		0			0
$919$	−56.5601			−1.86574			−0.932872	−	0.360208i	$-0.882706\pi$
$919$	−56.5601			−1.86574			−0.932872	+	0.360208i	$0.882706\pi$
$920$		−	85.5393i		−	2.82015i
$921$	−10.3094	+	10.3094i	−0.339705	+	0.339705i
$922$	81.3443			2.67893
$923$	−2.56803	+	2.56803i	−0.0845276	+	0.0845276i
$924$	−27.8405	−	27.8405i	−0.915886	−	0.915886i
$925$	1.46524	+	1.46524i	0.0481770	+	0.0481770i
$926$		−	46.8039i		−	1.53807i
$927$			7.19272i			0.236240i
$928$	0.284459	+	0.284459i	0.00933782	+	0.00933782i
$929$	−23.7730	−	23.7730i	−0.779968	−	0.779968i	0.199857	−	0.979825i	$-0.435952\pi$
$929$	−23.7730	−	23.7730i	−0.779968	−	0.779968i	−0.979825	+	0.199857i	$0.935952\pi$
$930$	10.7913	−	10.7913i	0.353860	−	0.353860i
$931$	14.8231			0.485809
$932$	−23.7179	+	23.7179i	−0.776907	+	0.776907i
$933$			14.3449i			0.469633i
$934$	−92.4550			−3.02522
$935$		0			0
$936$	3.87628			0.126700
$937$		−	2.08118i		−	0.0679891i	−0.999422	−	0.0339946i	$-0.989177\pi$
$937$		−	2.08118i		−	0.0679891i	0.999422	−	0.0339946i	$-0.0108229\pi$
$938$	20.9460	−	20.9460i	0.683912	−	0.683912i
$939$	11.3185			0.369364
$940$	60.2522	−	60.2522i	1.96521	−	1.96521i
$941$	4.07691	+	4.07691i	0.132903	+	0.132903i	0.770429	−	0.637526i	$-0.220042\pi$
$941$	4.07691	+	4.07691i	0.132903	+	0.132903i	−0.637526	+	0.770429i	$0.720042\pi$
$942$	33.9314	+	33.9314i	1.10554	+	1.10554i
$943$			34.6712i			1.12905i
$944$		−	15.4835i		−	0.503946i
$945$	−3.17482	−	3.17482i	−0.103277	−	0.103277i
$946$	−120.832	−	120.832i	−3.92858	−	3.92858i
$947$	−17.3421	+	17.3421i	−0.563544	+	0.563544i	−0.930312	−	0.366768i	$-0.880464\pi$
$947$	−17.3421	+	17.3421i	−0.563544	+	0.563544i	0.366768	+	0.930312i	$0.380464\pi$
$948$	−5.98795			−0.194480
$949$	−4.70740	+	4.70740i	−0.152809	+	0.152809i
$950$			25.8830i			0.839755i
$951$	11.7623			0.381418
$952$		0			0
$953$	13.3063			0.431033			0.215517	−	0.976500i	$-0.430856\pi$
$953$	13.3063			0.431033			0.215517	+	0.976500i	$0.430856\pi$
$954$			3.29182i			0.106577i
$955$	45.3577	−	45.3577i	1.46774	−	1.46774i
$956$	−61.5919			−1.99202
$957$	6.85706	−	6.85706i	0.221657	−	0.221657i
$958$	−0.742214	−	0.742214i	−0.0239798	−	0.0239798i
$959$	−0.344165	−	0.344165i	−0.0111137	−	0.0111137i
$960$			23.9055i			0.771545i
$961$			26.2775i			0.847661i
$962$	0.883920	+	0.883920i	0.0284987	+	0.0284987i
$963$	−2.60052	−	2.60052i	−0.0838005	−	0.0838005i
$964$	83.6929	−	83.6929i	2.69557	−	2.69557i
$965$	75.1637			2.41960
$966$	−16.6710	+	16.6710i	−0.536380	+	0.536380i
$967$		−	18.0996i		−	0.582044i	−0.956716	−	0.291022i	$-0.906005\pi$
$967$		−	18.0996i		−	0.582044i	0.956716	−	0.291022i	$-0.0939953\pi$
$968$	140.924			4.52946
$969$		0			0
$970$	34.0008			1.09170
$971$			2.40360i			0.0771352i	0.999256	+	0.0385676i	$0.0122795\pi$
$971$			2.40360i			0.0771352i	−0.999256	+	0.0385676i	$0.987721\pi$
$972$	−2.80927	+	2.80927i	−0.0901072	+	0.0901072i
$973$	−16.8904			−0.541482
$974$	−0.338068	+	0.338068i	−0.0108324	+	0.0108324i
$975$	−1.85144	−	1.85144i	−0.0592935	−	0.0592935i
$976$	22.7111	+	22.7111i	0.726964	+	0.726964i
$977$		−	41.4410i		−	1.32581i	−0.748701	−	0.662907i	$-0.769322\pi$
$977$		−	41.4410i		−	1.32581i	0.748701	−	0.662907i	$-0.230678\pi$
$978$			26.5844i			0.850076i
$979$	27.4806	+	27.4806i	0.878284	+	0.878284i
$980$	36.7983	+	36.7983i	1.17548	+	1.17548i
$981$	7.27162	−	7.27162i	0.232165	−	0.232165i
$982$	22.7973			0.727491
$983$	−26.7967	+	26.7967i	−0.854682	+	0.854682i	−0.990706	−	0.136023i	$-0.956568\pi$
$983$	−26.7967	+	26.7967i	−0.854682	+	0.854682i	0.136023	+	0.990706i	$0.456568\pi$
$984$			27.0775i			0.863200i
$985$	−51.1366			−1.62935
$986$		0			0
$987$	−11.6626			−0.371225
$988$			10.3858i			0.330416i
$989$	−48.1269	+	48.1269i	−1.53035	+	1.53035i
$990$	44.5411			1.41561
$991$	−17.9220	+	17.9220i	−0.569311	+	0.569311i	−0.931935	−	0.362625i	$-0.881881\pi$
$991$	−17.9220	+	17.9220i	−0.569311	+	0.569311i	0.362625	+	0.931935i	$0.381881\pi$
$992$	0.404308	+	0.404308i	0.0128368	+	0.0128368i
$993$	−14.2895	−	14.2895i	−0.453462	−	0.453462i
$994$		−	17.2510i		−	0.547169i
$995$		−	65.0960i		−	2.06368i
$996$	21.1403	+	21.1403i	0.669857	+	0.669857i
$997$	23.8995	+	23.8995i	0.756906	+	0.756906i	0.975758	−	0.218852i	$-0.0702313\pi$
$997$	23.8995	+	23.8995i	0.756906	+	0.756906i	−0.218852	+	0.975758i	$0.570231\pi$
$998$	14.1947	−	14.1947i	0.449324	−	0.449324i
$999$	−0.636236			−0.0201296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.k.616.9		24
17.2	even	8		867.2.d.g.577.4		12
17.3	odd	16		867.2.h.m.733.9		48
17.4	even	4	inner	867.2.e.k.829.4		24
17.5	odd	16		867.2.h.m.712.3		48
17.6	odd	16		867.2.h.m.688.3		48
17.7	odd	16		867.2.h.m.757.10		48
17.8	even	8		867.2.a.p.1.5	yes	6
17.9	even	8		867.2.a.o.1.5	✓	6
17.10	odd	16		867.2.h.m.757.9		48
17.11	odd	16		867.2.h.m.688.4		48
17.12	odd	16		867.2.h.m.712.4		48
17.13	even	4	inner	867.2.e.k.829.3		24
17.14	odd	16		867.2.h.m.733.10		48
17.15	even	8		867.2.d.g.577.3		12
17.16	even	2	inner	867.2.e.k.616.10		24
51.8	odd	8		2601.2.a.bi.1.2		6
51.26	odd	8		2601.2.a.bh.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.5	✓	6	17.9	even	8
867.2.a.p.1.5	yes	6	17.8	even	8
867.2.d.g.577.3		12	17.15	even	8
867.2.d.g.577.4		12	17.2	even	8
867.2.e.k.616.9		24	1.1	even	1	trivial
867.2.e.k.616.10		24	17.16	even	2	inner
867.2.e.k.829.3		24	17.13	even	4	inner
867.2.e.k.829.4		24	17.4	even	4	inner
867.2.h.m.688.3		48	17.6	odd	16
867.2.h.m.688.4		48	17.11	odd	16
867.2.h.m.712.3		48	17.5	odd	16
867.2.h.m.712.4		48	17.12	odd	16
867.2.h.m.733.9		48	17.3	odd	16
867.2.h.m.733.10		48	17.14	odd	16
867.2.h.m.757.9		48	17.10	odd	16
867.2.h.m.757.10		48	17.7	odd	16
2601.2.a.bh.1.2		6	51.26	odd	8
2601.2.a.bi.1.2		6	51.8	odd	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.44395i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.97290 q^{4} +(2.03186 - 2.03186i) q^{5} +(-1.72814 - 1.72814i) q^{6} +(-1.10487 - 1.10487i) q^{7} -4.82168i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+2.44395i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.97290 q^{4} +(2.03186 - 2.03186i) q^{5} +(-1.72814 - 1.72814i) q^{6} +(-1.10487 - 1.10487i) q^{7} -4.82168i q^{8} -1.00000i q^{9} +(4.96577 + 4.96577i) q^{10} +(4.48482 + 4.48482i) q^{11} +(2.80927 - 2.80927i) q^{12} -0.803928 q^{13} +(2.70024 - 2.70024i) q^{14} +2.87349i q^{15} +3.83815 q^{16} +2.44395 q^{18} +3.25173i q^{19} +(-8.07238 + 8.07238i) q^{20} +1.56252 q^{21} +(-10.9607 + 10.9607i) q^{22} +(4.36560 + 4.36560i) q^{23} +(3.40944 + 3.40944i) q^{24} -3.25692i q^{25} -1.96476i q^{26} +(0.707107 + 0.707107i) q^{27} +(4.38953 + 4.38953i) q^{28} +(-1.08113 + 1.08113i) q^{29} -7.02266 q^{30} +(-1.53664 + 1.53664i) q^{31} -0.263112i q^{32} -6.34249 q^{33} -4.48987 q^{35} +3.97290i q^{36} +(-0.449887 + 0.449887i) q^{37} -7.94707 q^{38} +(0.568463 - 0.568463i) q^{39} +(-9.79698 - 9.79698i) q^{40} +(3.97096 + 3.97096i) q^{41} +3.81872i q^{42} +11.0241i q^{43} +(-17.8177 - 17.8177i) q^{44} +(-2.03186 - 2.03186i) q^{45} +(-10.6693 + 10.6693i) q^{46} -7.46399 q^{47} +(-2.71398 + 2.71398i) q^{48} -4.55854i q^{49} +7.95975 q^{50} +3.19393 q^{52} +1.34692i q^{53} +(-1.72814 + 1.72814i) q^{54} +18.2250 q^{55} +(-5.32731 + 5.32731i) q^{56} +(-2.29932 - 2.29932i) q^{57} +(-2.64223 - 2.64223i) q^{58} -4.03412i q^{59} -11.4161i q^{60} +(5.91720 + 5.91720i) q^{61} +(-3.75547 - 3.75547i) q^{62} +(-1.10487 + 1.10487i) q^{63} +8.31932 q^{64} +(-1.63347 + 1.63347i) q^{65} -15.5007i q^{66} +7.75709 q^{67} -6.17389 q^{69} -10.9730i q^{70} +(3.19435 - 3.19435i) q^{71} -4.82168 q^{72} +(5.85550 - 5.85550i) q^{73} +(-1.09950 - 1.09950i) q^{74} +(2.30299 + 2.30299i) q^{75} -12.9188i q^{76} -9.91025i q^{77} +(1.38930 + 1.38930i) q^{78} +(-1.06575 - 1.06575i) q^{79} +(7.79858 - 7.79858i) q^{80} -1.00000 q^{81} +(-9.70484 + 9.70484i) q^{82} +7.52521i q^{83} -6.20773 q^{84} -26.9424 q^{86} -1.52895i q^{87} +(21.6243 - 21.6243i) q^{88} +6.12748 q^{89} +(4.96577 - 4.96577i) q^{90} +(0.888234 + 0.888234i) q^{91} +(-17.3441 - 17.3441i) q^{92} -2.17313i q^{93} -18.2416i q^{94} +(6.60707 + 6.60707i) q^{95} +(0.186048 + 0.186048i) q^{96} +(3.42351 - 3.42351i) q^{97} +11.1408 q^{98} +(4.48482 - 4.48482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 36 q^{4}+O(q^{10}) \) 24 * q - 36 * q^4	\( 24 q - 36 q^{4} - 36 q^{13} + 60 q^{16} + 12 q^{18} - 12 q^{21} - 48 q^{30} - 36 q^{33} + 24 q^{38} - 96 q^{47} + 48 q^{50} - 72 q^{52} + 96 q^{55} - 96 q^{64} - 24 q^{67} - 36 q^{69} - 48 q^{72} - 24 q^{81} - 60 q^{84} + 24 q^{86} + 228 q^{98}+O(q^{100}) \) 24 * q - 36 * q^4 - 36 * q^13 + 60 * q^16 + 12 * q^18 - 12 * q^21 - 48 * q^30 - 36 * q^33 + 24 * q^38 - 96 * q^47 + 48 * q^50 - 72 * q^52 + 96 * q^55 - 96 * q^64 - 24 * q^67 - 36 * q^69 - 48 * q^72 - 24 * q^81 - 60 * q^84 + 24 * q^86 + 228 * q^98

Introduction

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