LMFDB - Embedded newform 495.2.bj.b.28.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

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

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

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			28.7
Character	$\chi$	$=$	495.28
Dual form			495.2.bj.b.442.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.188252 - 0.369466i) q^{2} +(1.07450 + 1.47893i) q^{4} +(-2.23606 - 0.00601689i) q^{5} +(4.21724 + 0.667945i) q^{7} +(1.56780 - 0.248316i) q^{8} +O(q^{10})$	\(q+(0.188252 - 0.369466i) q^{2} +(1.07450 + 1.47893i) q^{4} +(-2.23606 - 0.00601689i) q^{5} +(4.21724 + 0.667945i) q^{7} +(1.56780 - 0.248316i) q^{8} +(-0.423167 + 0.825016i) q^{10} +(-0.957217 + 3.17549i) q^{11} +(-1.20175 - 0.612321i) q^{13} +(1.04069 - 1.43239i) q^{14} +(-0.926402 + 2.85117i) q^{16} +(-1.39103 + 0.708765i) q^{17} +(-3.55370 - 2.58191i) q^{19} +(-2.39376 - 3.31344i) q^{20} +(0.993038 + 0.951453i) q^{22} +(6.71925 + 6.71925i) q^{23} +(4.99993 + 0.0269083i) q^{25} +(-0.452464 + 0.328734i) q^{26} +(3.54360 + 6.95470i) q^{28} +(5.75065 - 4.17809i) q^{29} +(1.83366 + 5.64343i) q^{31} +(3.12386 + 3.12386i) q^{32} +0.647365i q^{34} +(-9.42598 - 1.51894i) q^{35} +(0.411271 - 2.59666i) q^{37} +(-1.62292 + 0.826921i) q^{38} +(-3.50720 + 0.545816i) q^{40} +(3.97520 - 5.47140i) q^{41} +(-2.05603 + 2.05603i) q^{43} +(-5.72486 + 1.99642i) q^{44} +(3.74745 - 1.21762i) q^{46} +(-6.52357 + 1.03323i) q^{47} +(10.6816 + 3.47065i) q^{49} +(0.951190 - 1.84224i) q^{50} +(-0.385704 - 2.43524i) q^{52} +(0.813603 - 1.59679i) q^{53} +(2.15950 - 7.09483i) q^{55} +6.77767 q^{56} +(-0.461090 - 2.91121i) q^{58} +(-5.40351 - 7.43729i) q^{59} +(-9.79737 - 3.18336i) q^{61} +(2.43025 + 0.384913i) q^{62} +(-3.96011 + 1.28672i) q^{64} +(2.68350 + 1.37642i) q^{65} +(-4.87141 + 4.87141i) q^{67} +(-2.54288 - 1.29566i) q^{68} +(-2.33566 + 3.19664i) q^{70} +(3.98173 - 12.2545i) q^{71} +(1.45483 - 9.18545i) q^{73} +(-0.881957 - 0.640779i) q^{74} -8.02995i q^{76} +(-6.15787 + 12.7524i) q^{77} +(-2.52771 - 7.77950i) q^{79} +(2.08865 - 6.36982i) q^{80} +(-1.27316 - 2.49871i) q^{82} +(4.08172 + 8.01082i) q^{83} +(3.11469 - 1.57647i) q^{85} +(0.372581 + 1.14669i) q^{86} +(-0.712205 + 5.21624i) q^{88} -0.813663i q^{89} +(-4.65906 - 3.38501i) q^{91} +(-2.71742 + 17.1571i) q^{92} +(-0.846333 + 2.60475i) q^{94} +(7.93075 + 5.79470i) q^{95} +(-9.74154 - 4.96356i) q^{97} +(3.29312 - 3.29312i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 20 q^{7}+O(q^{10}) $ 96 * q + 20 * q^7	$ 96 q + 20 q^{7} + 40 q^{16} + 8 q^{22} - 16 q^{25} - 60 q^{28} + 16 q^{31} - 40 q^{37} + 280 q^{46} + 40 q^{52} + 24 q^{55} - 68 q^{58} + 40 q^{61} + 16 q^{67} + 52 q^{70} - 60 q^{73} - 112 q^{82} + 80 q^{85} + 24 q^{88} - 56 q^{91} - 112 q^{97}+O(q^{100}) $ 96 * q + 20 * q^7 + 40 * q^16 + 8 * q^22 - 16 * q^25 - 60 * q^28 + 16 * q^31 - 40 * q^37 + 280 * q^46 + 40 * q^52 + 24 * q^55 - 68 * q^58 + 40 * q^61 + 16 * q^67 + 52 * q^70 - 60 * q^73 - 112 * q^82 + 80 * q^85 + 24 * q^88 - 56 * q^91 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.188252	−	0.369466i	0.133115	−	0.261252i	−0.814822	−	0.579711i	$-0.803165\pi$
$2$	0.188252	−	0.369466i	0.133115	−	0.261252i	0.947937	+	0.318459i	$0.103165\pi$
$3$		0			0
$3$		0			0
$4$	1.07450	+	1.47893i	0.537252	+	0.739464i
$5$	−2.23606	−	0.00601689i	−0.999996	−	0.00269084i
$5$	−2.23606	−	0.00601689i	−0.999996	−	0.00269084i
$6$		0			0
$7$	4.21724	+	0.667945i	1.59397	+	0.252460i	0.889383	−	0.457162i	$-0.151134\pi$
$7$	4.21724	+	0.667945i	1.59397	+	0.252460i	0.704583	+	0.709621i	$0.251134\pi$
$8$	1.56780	−	0.248316i	0.554303	−	0.0877929i
$9$		0			0
$10$	−0.423167	+	0.825016i	−0.133817	+	0.260893i
$11$	−0.957217	+	3.17549i	−0.288612	+	0.957446i
$11$	−0.957217	+	3.17549i	−0.288612	+	0.957446i
$12$		0			0
$13$	−1.20175	−	0.612321i	−0.333305	−	0.169827i	0.279326	−	0.960196i	$-0.409889\pi$
$13$	−1.20175	−	0.612321i	−0.333305	−	0.169827i	−0.612631	+	0.790369i	$0.709889\pi$
$14$	1.04069	−	1.43239i	0.278136	−	0.382821i
$15$		0			0
$16$	−0.926402	+	2.85117i	−0.231600	+	0.712793i
$17$	−1.39103	+	0.708765i	−0.337374	+	0.171901i	−0.614467	−	0.788942i	$-0.710629\pi$
$17$	−1.39103	+	0.708765i	−0.337374	+	0.171901i	0.277093	+	0.960843i	$0.410629\pi$
$18$		0			0
$19$	−3.55370	−	2.58191i	−0.815275	−	0.592332i	0.100080	−	0.994979i	$-0.468090\pi$
$19$	−3.55370	−	2.58191i	−0.815275	−	0.592332i	−0.915355	+	0.402648i	$0.868090\pi$
$20$	−2.39376	−	3.31344i	−0.535260	−	0.740907i
$21$		0			0
$22$	0.993038	+	0.951453i	0.211716	+	0.202850i
$23$	6.71925	+	6.71925i	1.40106	+	1.40106i	0.796748	+	0.604312i	$0.206552\pi$
$23$	6.71925	+	6.71925i	1.40106	+	1.40106i	0.604312	+	0.796748i	$0.293448\pi$
$24$		0			0
$25$	4.99993	+	0.0269083i	0.999986	+	0.00538165i
$26$	−0.452464	+	0.328734i	−0.0887355	+	0.0644701i
$27$		0			0
$28$	3.54360	+	6.95470i	0.669677	+	1.31432i
$29$	5.75065	−	4.17809i	1.06787	−	0.775852i	0.0923407	−	0.995727i	$-0.470565\pi$
$29$	5.75065	−	4.17809i	1.06787	−	0.775852i	0.975528	+	0.219876i	$0.0705651\pi$
$30$		0			0
$31$	1.83366	+	5.64343i	0.329335	+	1.01359i	0.969446	+	0.245307i	$0.0788886\pi$
$31$	1.83366	+	5.64343i	0.329335	+	1.01359i	−0.640110	+	0.768283i	$0.721111\pi$
$32$	3.12386	+	3.12386i	0.552226	+	0.552226i
$33$		0			0
$34$			0.647365i			0.111022i
$35$	−9.42598	−	1.51894i	−1.59328	−	0.256748i
$36$		0			0
$37$	0.411271	−	2.59666i	0.0676125	−	0.426889i	−0.930543	−	0.366182i	$-0.880665\pi$
$37$	0.411271	−	2.59666i	0.0676125	−	0.426889i	0.998156	−	0.0607065i	$-0.0193354\pi$
$38$	−1.62292	+	0.826921i	−0.263273	+	0.134144i
$39$		0			0
$40$	−3.50720	+	0.545816i	−0.554537	+	0.0863011i
$41$	3.97520	−	5.47140i	0.620823	−	0.854489i	−0.376590	−	0.926380i	$-0.622903\pi$
$41$	3.97520	−	5.47140i	0.620823	−	0.854489i	0.997412	+	0.0718911i	$0.0229034\pi$
$42$		0			0
$43$	−2.05603	+	2.05603i	−0.313542	+	0.313542i	−0.846280	−	0.532738i	$-0.821163\pi$
$43$	−2.05603	+	2.05603i	−0.313542	+	0.313542i	0.532738	+	0.846280i	$0.321163\pi$
$44$	−5.72486	+	1.99642i	−0.863054	+	0.300972i
$45$		0			0
$46$	3.74745	−	1.21762i	0.552531	−	0.179528i
$47$	−6.52357	+	1.03323i	−0.951560	+	0.150712i	−0.612868	−	0.790185i	$-0.709984\pi$
$47$	−6.52357	+	1.03323i	−0.951560	+	0.150712i	−0.338692	+	0.940897i	$0.609984\pi$
$48$		0			0
$49$	10.6816	+	3.47065i	1.52594	+	0.495807i
$50$	0.951190	−	1.84224i	0.134519	−	0.260532i
$51$		0			0
$52$	−0.385704	−	2.43524i	−0.0534875	−	0.337707i
$53$	0.813603	−	1.59679i	0.111757	−	0.219335i	−0.828353	−	0.560206i	$-0.810722\pi$
$53$	0.813603	−	1.59679i	0.111757	−	0.219335i	0.940110	+	0.340871i	$0.110722\pi$
$54$		0			0
$55$	2.15950	−	7.09483i	0.291187	−	0.956666i
$56$	6.77767			0.905704
$57$		0			0
$58$	−0.461090	−	2.91121i	−0.0605441	−	0.382260i
$59$	−5.40351	−	7.43729i	−0.703477	−	0.968253i	−0.999913	−	0.0132005i	$-0.995798\pi$
$59$	−5.40351	−	7.43729i	−0.703477	−	0.968253i	0.296436	−	0.955053i	$-0.404202\pi$
$60$		0			0
$61$	−9.79737	−	3.18336i	−1.25442	−	0.407587i	−0.394920	−	0.918716i	$-0.629228\pi$
$61$	−9.79737	−	3.18336i	−1.25442	−	0.407587i	−0.859504	+	0.511128i	$0.829228\pi$
$62$	2.43025	+	0.384913i	0.308642	+	0.0488840i
$63$		0			0
$64$	−3.96011	+	1.28672i	−0.495013	+	0.160840i
$65$	2.68350	+	1.37642i	0.332847	+	0.170724i
$66$		0			0
$67$	−4.87141	+	4.87141i	−0.595138	+	0.595138i	−0.939015	−	0.343877i	$-0.888260\pi$
$67$	−4.87141	+	4.87141i	−0.595138	+	0.595138i	0.343877	+	0.939015i	$0.388260\pi$
$68$	−2.54288	−	1.29566i	−0.308369	−	0.157122i
$69$		0			0
$70$	−2.33566	+	3.19664i	−0.279165	+	0.382071i
$71$	3.98173	−	12.2545i	0.472545	−	1.45434i	−0.376696	−	0.926337i	$-0.622940\pi$
$71$	3.98173	−	12.2545i	0.472545	−	1.45434i	0.849241	−	0.528006i	$-0.177060\pi$
$72$		0			0
$73$	1.45483	−	9.18545i	0.170275	−	1.07508i	−0.743464	−	0.668775i	$-0.766819\pi$
$73$	1.45483	−	9.18545i	0.170275	−	1.07508i	0.913740	−	0.406300i	$-0.133181\pi$
$74$	−0.881957	−	0.640779i	−0.102525	−	0.0744890i
$75$		0			0
$76$		−	8.02995i		−	0.921098i
$77$	−6.15787	+	12.7524i	−0.701754	+	1.45327i
$78$		0			0
$79$	−2.52771	−	7.77950i	−0.284390	−	0.875262i	−0.986581	−	0.163274i	$-0.947795\pi$
$79$	−2.52771	−	7.77950i	−0.284390	−	0.875262i	0.702191	−	0.711989i	$-0.252205\pi$
$80$	2.08865	−	6.36982i	0.233518	−	0.712167i
$81$		0			0
$82$	−1.27316	−	2.49871i	−0.140596	−	0.275936i
$83$	4.08172	+	8.01082i	0.448026	+	0.879301i	0.998997	+	0.0447767i	$0.0142576\pi$
$83$	4.08172	+	8.01082i	0.448026	+	0.879301i	−0.550971	+	0.834525i	$0.685742\pi$
$84$		0			0
$85$	3.11469	−	1.57647i	0.337835	−	0.170992i
$86$	0.372581	+	1.14669i	0.0401764	+	0.123650i
$87$		0			0
$88$	−0.712205	+	5.21624i	−0.0759213	+	0.556053i
$89$		−	0.813663i		−	0.0862481i	−0.999070	−	0.0431240i	$-0.986269\pi$
$89$		−	0.813663i		−	0.0862481i	0.999070	−	0.0431240i	$-0.0137311\pi$
$90$		0			0
$91$	−4.65906	−	3.38501i	−0.488402	−	0.354845i
$92$	−2.71742	+	17.1571i	−0.283311	+	1.78876i
$93$		0			0
$94$	−0.846333	+	2.60475i	−0.0872926	+	0.268659i
$95$	7.93075	+	5.79470i	0.813678	+	0.594523i
$96$		0			0
$97$	−9.74154	−	4.96356i	−0.989104	−	0.503973i	−0.116914	−	0.993142i	$-0.537300\pi$
$97$	−9.74154	−	4.96356i	−0.989104	−	0.503973i	−0.872189	+	0.489169i	$0.837300\pi$
$98$	3.29312	−	3.29312i	0.332655	−	0.332655i
$99$		0			0
$100$	5.33265	+	7.42345i	0.533265	+	0.742345i
$101$	3.15319	−	1.02453i	0.313754	−	0.101945i	−0.147907	−	0.989001i	$-0.547254\pi$
$101$	3.15319	−	1.02453i	0.313754	−	0.101945i	0.461661	+	0.887056i	$0.347254\pi$
$102$		0			0
$103$	10.4338	+	1.65256i	1.02808	+	0.162831i	0.647617	−	0.761966i	$-0.275766\pi$
$103$	10.4338	+	1.65256i	1.02808	+	0.162831i	0.380460	+	0.924797i	$0.375766\pi$
$104$	−2.03615	−	0.661587i	−0.199661	−	0.0648739i
$105$		0			0
$106$	−0.436796	−	0.601197i	−0.0424253	−	0.0583935i
$107$	0.256744	+	1.62102i	0.0248204	+	0.156710i	0.996986	−	0.0775865i	$-0.0247214\pi$
$107$	0.256744	+	1.62102i	0.0248204	+	0.156710i	−0.972165	+	0.234296i	$0.924721\pi$
$108$		0			0
$109$	−3.19904			−0.306412			−0.153206	−	0.988194i	$-0.548960\pi$
$109$	−3.19904			−0.306412			−0.153206	+	0.988194i	$0.548960\pi$
$110$	−2.21477	−	2.13348i	−0.211170	−	0.203419i
$111$		0			0
$112$	−5.81128	+	11.4053i	−0.549115	+	1.07770i
$113$	−0.879461	−	5.55270i	−0.0827327	−	0.522354i	−0.993897	−	0.110311i	$-0.964815\pi$
$113$	−0.879461	−	5.55270i	−0.0827327	−	0.522354i	0.911164	−	0.412043i	$-0.135185\pi$
$114$		0			0
$115$	−14.9842	−	15.0651i	−1.39728	−	1.40482i
$116$	12.3582	+	4.01542i	1.14743	+	0.372822i
$117$		0			0
$118$	−3.76505	+	0.596326i	−0.346601	+	0.0548962i
$119$	−6.33972	+	2.05990i	−0.581161	+	0.188831i
$120$		0			0
$121$	−9.16747	−	6.07927i	−0.833406	−	0.552661i
$122$	−3.02052	+	3.02052i	−0.273465	+	0.273465i
$123$		0			0
$124$	−6.37595	+	8.77574i	−0.572577	+	0.788085i
$125$	−11.1800	−	0.0902525i	−0.999967	−	0.00807243i
$126$		0			0
$127$	12.7827	−	6.51310i	1.13428	−	0.577944i	0.216993	−	0.976173i	$-0.430375\pi$
$127$	12.7827	−	6.51310i	1.13428	−	0.577944i	0.917286	+	0.398229i	$0.130375\pi$
$128$	−1.65230	+	10.4322i	−0.146044	+	0.922084i
$129$		0			0
$130$	1.01371	−	0.732347i	0.0889086	−	0.0642311i
$131$		−	7.76725i		−	0.678627i	−0.940673	−	0.339314i	$-0.889805\pi$
$131$		−	7.76725i		−	0.678627i	0.940673	−	0.339314i	$-0.110195\pi$
$132$		0			0
$133$	−13.2622	−	13.2622i	−1.14998	−	1.14998i
$134$	0.882767	+	2.71688i	0.0762595	+	0.234703i
$135$		0			0
$136$	−2.00486	+	1.45662i	−0.171916	+	0.124904i
$137$	−6.08028	−	11.9332i	−0.519474	−	1.01952i	−0.990514	−	0.137413i	$-0.956121\pi$
$137$	−6.08028	−	11.9332i	−0.519474	−	1.01952i	0.471040	−	0.882112i	$-0.343879\pi$
$138$		0			0
$139$	−0.439152	+	0.319063i	−0.0372484	+	0.0270626i	−0.606254	−	0.795271i	$-0.707328\pi$
$139$	−0.439152	+	0.319063i	−0.0372484	+	0.0270626i	0.569005	+	0.822334i	$0.307328\pi$
$140$	−7.88185	−	15.5725i	−0.666138	−	1.31611i
$141$		0			0
$142$	−3.77806	−	3.77806i	−0.317047	−	0.317047i
$143$	3.09475	−	3.23001i	0.258796	−	0.270107i
$144$		0			0
$145$	−12.8839	+	9.30786i	−1.06995	+	0.772976i
$146$	−3.11984	−	2.26669i	−0.258200	−	0.187593i
$147$		0			0
$148$	4.28219	−	2.18189i	0.351994	−	0.179350i
$149$	2.93200	−	9.02377i	0.240199	−	0.739256i	−0.756190	−	0.654352i	$-0.772942\pi$
$149$	2.93200	−	9.02377i	0.240199	−	0.739256i	0.996389	−	0.0849041i	$-0.0270584\pi$
$150$		0			0
$151$	7.25136	−	9.98064i	0.590107	−	0.812213i	−0.404651	−	0.914471i	$-0.632607\pi$
$151$	7.25136	−	9.98064i	0.590107	−	0.812213i	0.994758	+	0.102258i	$0.0326068\pi$
$152$	−6.21264	−	3.16550i	−0.503912	−	0.256756i
$153$		0			0
$154$	3.55236	+	4.67580i	0.286257	+	0.376787i
$155$	−4.06622	−	12.6301i	−0.326607	−	1.01447i
$156$		0			0
$157$	6.64941	−	1.05316i	0.530681	−	0.0840516i	0.114657	−	0.993405i	$-0.463423\pi$
$157$	6.64941	−	1.05316i	0.530681	−	0.0840516i	0.416024	+	0.909354i	$0.363423\pi$
$158$	−3.35011	−	0.530606i	−0.266521	−	0.0422127i
$159$		0			0
$160$	−6.96635	−	7.00394i	−0.550738	−	0.553710i
$161$	23.8486	+	32.8248i	1.87953	+	2.58695i
$162$		0			0
$163$	3.10941	−	6.10256i	0.243548	−	0.477989i	−0.736582	−	0.676349i	$-0.763561\pi$
$163$	3.10941	−	6.10256i	0.243548	−	0.477989i	0.980129	+	0.198359i	$0.0635613\pi$
$164$	12.3632			0.965402
$165$		0			0
$166$	3.72812			0.289358
$167$	−9.81178	+	19.2567i	−0.759258	+	1.49013i	0.109014	+	0.994040i	$0.465231\pi$
$167$	−9.81178	+	19.2567i	−0.759258	+	1.49013i	−0.868272	+	0.496088i	$0.834769\pi$
$168$		0			0
$169$	−6.57195	−	9.04551i	−0.505534	−	0.695808i
$170$	0.00389513	−	1.44755i	0.000298742	−	0.111022i
$171$		0			0
$172$	−5.24993	−	0.831508i	−0.400304	−	0.0634019i
$173$	13.3418	−	2.11313i	1.01436	−	0.160659i	0.372945	−	0.927854i	$-0.378348\pi$
$173$	13.3418	−	2.11313i	1.01436	−	0.160659i	0.641414	+	0.767195i	$0.278348\pi$
$174$		0			0
$175$	21.0679	+	3.45316i	1.59258	+	0.261034i
$176$	−8.16710	−	5.67097i	−0.615618	−	0.427465i
$177$		0			0
$178$	−0.300621	−	0.153174i	−0.0225325	−	0.0114809i
$179$	−9.00002	+	12.3875i	−0.672693	+	0.925883i	−0.999818	−	0.0190986i	$-0.993920\pi$
$179$	−9.00002	+	12.3875i	−0.672693	+	0.925883i	0.327124	+	0.944981i	$0.393920\pi$
$180$		0			0
$181$	−4.35729	+	13.4104i	−0.323875	+	0.996785i	0.648071	+	0.761580i	$0.275576\pi$
$181$	−4.35729	+	13.4104i	−0.323875	+	0.996785i	−0.971946	+	0.235205i	$0.924424\pi$
$182$	−2.12772	+	1.08413i	−0.157717	+	0.0803611i
$183$		0			0
$184$	12.2030	+	8.86597i	0.899614	+	0.653608i
$185$	−0.935251	+	5.80382i	−0.0687610	+	0.426705i
$186$		0			0
$187$	−0.919158	−	5.09564i	−0.0672155	−	0.372630i
$188$	−8.53767	−	8.53767i	−0.622674	−	0.622674i
$189$		0			0
$190$	3.63393	−	1.83928i	0.263633	−	0.133435i
$191$	−15.8618	+	11.5242i	−1.14772	+	0.833865i	−0.988176	−	0.153327i	$-0.951001\pi$
$191$	−15.8618	+	11.5242i	−1.14772	+	0.833865i	−0.159541	+	0.987191i	$0.551001\pi$
$192$		0			0
$193$	7.73722	+	15.1852i	0.556937	+	1.09305i	0.982175	+	0.187969i	$0.0601906\pi$
$193$	7.73722	+	15.1852i	0.556937	+	1.09305i	−0.425237	+	0.905082i	$0.639809\pi$
$194$	−3.66774	+	2.66477i	−0.263328	+	0.191319i
$195$		0			0
$196$	6.34454	+	19.5265i	0.453181	+	1.39475i
$197$	−6.66756	−	6.66756i	−0.475044	−	0.475044i	0.428499	−	0.903542i	$-0.359043\pi$
$197$	−6.66756	−	6.66756i	−0.475044	−	0.475044i	−0.903542	+	0.428499i	$0.859043\pi$
$198$		0			0
$199$		−	6.90969i		−	0.489815i	−0.969546	−	0.244908i	$-0.921242\pi$
$199$		−	6.90969i		−	0.489815i	0.969546	−	0.244908i	$-0.0787576\pi$
$200$	7.84559	−	1.19937i	0.554767	−	0.0848086i
$201$		0			0
$202$	0.215065	−	1.35787i	0.0151319	−	0.0955392i
$203$	27.0426	−	13.7789i	1.89802	−	0.967089i
$204$		0			0
$205$	−8.92171	+	12.2105i	−0.623120	+	0.852815i
$206$	2.57476	−	3.54385i	0.179392	−	0.246912i
$207$		0			0
$208$	2.85913	−	2.85913i	0.198245	−	0.198245i
$209$	11.6005	−	8.81329i	0.802424	−	0.609628i
$210$		0			0
$211$	27.5871	−	8.96358i	1.89917	−	0.617078i	0.932405	−	0.361416i	$-0.117707\pi$
$211$	27.5871	−	8.96358i	1.89917	−	0.617078i	0.966766	−	0.255662i	$-0.0822934\pi$
$212$	3.23575	−	0.512493i	0.222232	−	0.0351981i
$213$		0			0
$214$	0.647244	+	0.210302i	0.0442447	+	0.0143760i
$215$	4.60978	−	4.58503i	0.314384	−	0.312697i
$216$		0			0
$217$	3.96349	+	25.0245i	0.269059	+	1.69877i
$218$	−0.602227	+	1.18194i	−0.0407879	+	0.0800508i
$219$		0			0
$220$	12.8131	−	4.42967i	0.863861	−	0.298648i
$221$	2.10566			0.141642
$222$		0			0
$223$	1.34586	+	8.49745i	0.0901257	+	0.569031i	0.990885	+	0.134712i	$0.0430110\pi$
$223$	1.34586	+	8.49745i	0.0901257	+	0.569031i	−0.900759	+	0.434319i	$0.856989\pi$
$224$	11.0875	+	15.2606i	0.740815	+	1.01964i
$225$		0			0
$226$	−2.21709	−	0.720378i	−0.147479	−	0.0479188i
$227$	21.6440	+	3.42808i	1.43657	+	0.227530i	0.825657	−	0.564172i	$-0.190804\pi$
$227$	21.6440	+	3.42808i	1.43657	+	0.227530i	0.610908	+	0.791701i	$0.290804\pi$
$228$		0			0
$229$	9.35060	−	3.03819i	0.617905	−	0.200769i	0.0166949	−	0.999861i	$-0.494686\pi$
$229$	9.35060	−	3.03819i	0.617905	−	0.200769i	0.601210	+	0.799091i	$0.294686\pi$
$230$	−8.38685	+	2.70012i	−0.553012	+	0.178041i
$231$		0			0
$232$	7.97841	−	7.97841i	0.523808	−	0.523808i
$233$	1.60956	+	0.820113i	0.105446	+	0.0537274i	0.505918	−	0.862582i	$-0.331154\pi$
$233$	1.60956	+	0.820113i	0.105446	+	0.0537274i	−0.400472	+	0.916309i	$0.631154\pi$
$234$		0			0
$235$	14.5933	−	2.27112i	0.951962	−	0.148151i
$236$	5.19313	−	15.9828i	0.338044	−	1.04039i
$237$		0			0
$238$	−0.432404	+	2.73009i	−0.0280286	+	0.176966i
$239$	−12.4793	−	9.06676i	−0.807220	−	0.586480i	0.105803	−	0.994387i	$-0.466259\pi$
$239$	−12.4793	−	9.06676i	−0.807220	−	0.586480i	−0.913023	+	0.407907i	$0.866259\pi$
$240$		0			0
$241$			21.4351i			1.38075i	0.723450	+	0.690377i	$0.242555\pi$
$241$			21.4351i			1.38075i	−0.723450	+	0.690377i	$0.757445\pi$
$242$	−3.97188	+	2.24263i	−0.255322	+	0.144162i
$243$		0			0
$244$	−5.81936	−	17.9101i	−0.372546	−	1.14658i
$245$	−23.8637	−	7.82485i	−1.52460	−	0.499911i
$246$		0			0
$247$	2.68969	+	5.27881i	0.171141	+	0.335883i
$248$	4.27618	+	8.39247i	0.271537	+	0.532922i
$249$		0			0
$250$	−2.13800	+	4.11363i	−0.135219	+	0.260169i
$251$	−4.20324	−	12.9363i	−0.265306	−	0.816529i	−0.991623	−	0.129168i	$-0.958769\pi$
$251$	−4.20324	−	12.9363i	−0.265306	−	0.816529i	0.726316	−	0.687361i	$-0.241231\pi$
$252$		0			0
$253$	−27.7687	+	14.9051i	−1.74580	+	0.937077i
$254$		−	5.94888i		−	0.373266i
$255$		0			0
$256$	−3.19404	−	2.32061i	−0.199628	−	0.145038i
$257$	−0.968637	+	6.11573i	−0.0604219	+	0.381489i	0.938884	+	0.344234i	$0.111861\pi$
$257$	−0.968637	+	6.11573i	−0.0604219	+	0.381489i	−0.999306	+	0.0372548i	$0.988139\pi$
$258$		0			0
$259$	3.46886	−	10.6760i	0.215544	−	0.663377i
$260$	0.847805	+	5.44766i	0.0525786	+	0.337850i
$261$		0			0
$262$	−2.86974	−	1.46220i	−0.177293	−	0.0903352i
$263$	−16.8707	+	16.8707i	−1.04029	+	1.04029i	−0.0411359	+	0.999154i	$0.513098\pi$
$263$	−16.8707	+	16.8707i	−1.04029	+	1.04029i	−0.999154	+	0.0411359i	$0.986902\pi$
$264$		0			0
$265$	−1.82887	+	3.56561i	−0.112347	+	0.219034i
$266$	−7.39659	+	2.40330i	−0.453514	+	0.147356i
$267$		0			0
$268$	−12.4388	−	1.97012i	−0.759822	−	0.120344i
$269$	−10.4596	−	3.39852i	−0.637732	−	0.207212i	−0.0277348	−	0.999615i	$-0.508829\pi$
$269$	−10.4596	−	3.39852i	−0.637732	−	0.207212i	−0.609997	+	0.792404i	$0.708829\pi$
$270$		0			0
$271$	2.90481	+	3.99813i	0.176455	+	0.242869i	0.888079	−	0.459691i	$-0.152040\pi$
$271$	2.90481	+	3.99813i	0.176455	+	0.242869i	−0.711624	+	0.702561i	$0.752040\pi$
$272$	−0.732158	−	4.62266i	−0.0443936	−	0.280290i
$273$		0			0
$274$	−5.55355			−0.335502
$275$	−4.87146	+	15.8515i	−0.293760	+	0.955879i
$276$		0			0
$277$	−5.48913	+	10.7730i	−0.329810	+	0.647288i	−0.995054	−	0.0993378i	$-0.968328\pi$
$277$	−5.48913	+	10.7730i	−0.329810	+	0.647288i	0.665244	+	0.746626i	$0.268328\pi$
$278$	0.0352114	+	0.222316i	0.00211184	+	0.0133336i
$279$		0			0
$280$	−15.1553	−	0.0407805i	−0.905701	−	0.00243710i
$281$	−1.55054	−	0.503800i	−0.0924972	−	0.0300542i	0.262403	−	0.964958i	$-0.415485\pi$
$281$	−1.55054	−	0.503800i	−0.0924972	−	0.0300542i	−0.354900	+	0.934904i	$0.615485\pi$
$282$		0			0
$283$	2.20619	−	0.349426i	0.131144	−	0.0207712i	−0.0905173	−	0.995895i	$-0.528852\pi$
$283$	2.20619	−	0.349426i	0.131144	−	0.0207712i	0.221661	+	0.975124i	$0.428852\pi$
$284$	22.4019	−	7.27883i	1.32931	−	0.431919i
$285$		0			0
$286$	−0.610786	−	1.75146i	−0.0361165	−	0.103566i
$287$	20.4190	−	20.4190i	1.20529	−	1.20529i
$288$		0			0
$289$	−8.55973	+	11.7815i	−0.503514	+	0.693027i
$290$	1.01351	+	6.51241i	0.0595152	+	0.382422i
$291$		0			0
$292$	15.1478	−	7.71821i	0.886460	−	0.451674i
$293$	−1.20277	+	7.59399i	−0.0702665	+	0.443646i	0.927323	+	0.374261i	$0.122104\pi$
$293$	−1.20277	+	7.59399i	−0.0702665	+	0.443646i	−0.997590	+	0.0693846i	$0.977896\pi$
$294$		0			0
$295$	12.0378	+	16.6627i	0.700869	+	0.970143i
$296$		−	4.17319i		−	0.242562i
$297$		0			0
$298$	−2.78202	−	2.78202i	−0.161158	−	0.161158i
$299$	−3.96050	−	12.1892i	−0.229042	−	0.704918i
$300$		0			0
$301$	−10.0441	+	7.29745i	−0.578931	+	0.420618i
$302$	−2.32242	−	4.55801i	−0.133640	−	0.262284i
$303$		0			0
$304$	10.6536	−	7.74032i	0.611028	−	0.443938i
$305$	21.8883	+	7.17713i	1.25332	+	0.410961i
$306$		0			0
$307$	−7.10851	−	7.10851i	−0.405704	−	0.405704i	0.474534	−	0.880237i	$-0.342617\pi$
$307$	−7.10851	−	7.10851i	−0.405704	−	0.405704i	−0.880237	+	0.474534i	$0.842617\pi$
$308$	−25.4766	+	4.59550i	−1.45166	+	0.261853i
$309$		0			0
$310$	−5.43186	−	0.875312i	−0.308509	−	0.0497144i
$311$	1.82021	+	1.32246i	0.103215	+	0.0749899i	0.638195	−	0.769874i	$-0.279681\pi$
$311$	1.82021	+	1.32246i	0.103215	+	0.0749899i	−0.534981	+	0.844864i	$0.679681\pi$
$312$		0			0
$313$	10.4257	−	5.31217i	0.589296	−	0.300262i	−0.133800	−	0.991008i	$-0.542718\pi$
$313$	10.4257	−	5.31217i	0.589296	−	0.300262i	0.723097	+	0.690747i	$0.242718\pi$
$314$	0.862659	−	2.65499i	0.0486827	−	0.149830i
$315$		0			0
$316$	8.78929	−	12.0974i	0.494436	−	0.680533i
$317$	−8.36454	−	4.26194i	−0.469799	−	0.239375i	0.203030	−	0.979173i	$-0.434921\pi$
$317$	−8.36454	−	4.26194i	−0.469799	−	0.239375i	−0.672829	+	0.739798i	$0.734921\pi$
$318$		0			0
$319$	7.76287	+	22.2605i	0.434637	+	1.24635i
$320$	8.86278	−	2.85335i	0.495444	−	0.159507i
$321$		0			0
$322$	16.6172	−	2.63190i	0.926040	−	0.146670i
$323$	6.77327	+	1.07278i	0.376875	+	0.0596911i
$324$		0			0
$325$	−5.99217	−	3.09390i	−0.332386	−	0.171619i
$326$	−1.66933	−	2.29764i	−0.0924559	−	0.127255i
$327$		0			0
$328$	4.87371	−	9.56519i	0.269106	−	0.528149i
$329$	−28.2016			−1.55480
$330$		0			0
$331$	18.7637			1.03134			0.515672	−	0.856786i	$-0.327542\pi$
$331$	18.7637			1.03134			0.515672	+	0.856786i	$0.327542\pi$
$332$	−7.46160	+	14.6442i	−0.409509	+	0.803706i
$333$		0			0
$334$	5.26761	+	7.25024i	0.288231	+	0.396716i
$335$	10.9221	−	10.8635i	0.596737	−	0.593534i
$336$		0			0
$337$	11.4727	+	1.81710i	0.624960	+	0.0989840i	0.460879	−	0.887463i	$-0.347534\pi$
$337$	11.4727	+	1.81710i	0.624960	+	0.0989840i	0.164081	+	0.986447i	$0.447534\pi$
$338$	−4.57920	+	0.725273i	−0.249075	+	0.0394497i
$339$		0			0
$340$	5.67823	+	2.91248i	0.307945	+	0.157951i
$341$	−19.6759	+	0.420786i	−1.06551	+	0.0227868i
$342$		0			0
$343$	16.0975	+	8.20209i	0.869184	+	0.442871i
$344$	−2.71291	+	3.73400i	−0.146270	+	0.201324i
$345$		0			0
$346$	1.73090	−	5.32715i	0.0930535	−	0.286389i
$347$	25.6913	−	13.0904i	1.37918	−	0.702729i	0.402102	−	0.915595i	$-0.368280\pi$
$347$	25.6913	−	13.0904i	1.37918	−	0.702729i	0.977081	+	0.212866i	$0.0682797\pi$
$348$		0			0
$349$	−9.35405	−	6.79612i	−0.500711	−	0.363788i	0.308578	−	0.951199i	$-0.400147\pi$
$349$	−9.35405	−	6.79612i	−0.500711	−	0.363788i	−0.809288	+	0.587411i	$0.800147\pi$
$350$	5.24191	−	7.13382i	0.280192	−	0.381319i
$351$		0			0
$352$	−12.9100	+	6.92958i	−0.688106	+	0.369348i
$353$	18.5340	+	18.5340i	0.986466	+	0.986466i	0.999910	−	0.0134434i	$-0.00427928\pi$
$353$	18.5340	+	18.5340i	0.986466	+	0.986466i	−0.0134434	+	0.999910i	$0.504279\pi$
$354$		0			0
$355$	−8.97712	+	27.3779i	−0.476456	+	1.45307i
$356$	1.20335	−	0.874284i	0.0637773	−	0.0463370i
$357$		0			0
$358$	2.88247	+	5.65717i	0.152344	+	0.298991i
$359$	6.57985	−	4.78054i	0.347271	−	0.252307i	−0.400452	−	0.916318i	$-0.631147\pi$
$359$	6.57985	−	4.78054i	0.347271	−	0.252307i	0.747723	+	0.664010i	$0.231147\pi$
$360$		0			0
$361$	0.0911815	+	0.280628i	0.00479903	+	0.0147699i
$362$	4.13441	+	4.13441i	0.217300	+	0.217300i
$363$		0			0
$364$		−	10.5276i		−	0.551797i
$365$	−3.30836	+	20.5305i	−0.173167	+	1.07461i
$366$		0			0
$367$	2.77066	−	17.4933i	0.144628	−	0.913142i	−0.803512	−	0.595288i	$-0.797038\pi$
$367$	2.77066	−	17.4933i	0.144628	−	0.913142i	0.948140	−	0.317854i	$-0.102962\pi$
$368$	−25.3824	+	12.9330i	−1.32315	+	0.674179i
$369$		0			0
$370$	1.96825	+	1.43813i	0.102325	+	0.0747647i
$371$	4.49772	−	6.19058i	0.233510	−	0.321399i
$372$		0			0
$373$	5.76140	−	5.76140i	0.298314	−	0.298314i	−0.542039	−	0.840353i	$-0.682348\pi$
$373$	5.76140	−	5.76140i	0.298314	−	0.298314i	0.840353	+	0.542039i	$0.182348\pi$
$374$	−2.05570	−	0.619669i	−0.106298	−	0.0320423i
$375$		0			0
$376$	−9.97111	+	3.23981i	−0.514221	+	0.167080i
$377$	−9.46916	+	1.49977i	−0.487687	+	0.0772420i
$378$		0			0
$379$	4.54268	+	1.47601i	0.233342	+	0.0758173i	0.423354	−	0.905964i	$-0.360853\pi$
$379$	4.54268	+	1.47601i	0.233342	+	0.0758173i	−0.190012	+	0.981782i	$0.560853\pi$
$380$	−0.0483153	+	17.9554i	−0.00247852	+	0.921095i
$381$		0			0
$382$	1.27180	+	8.02985i	0.0650711	+	0.410843i
$383$	7.42946	−	14.5811i	0.379628	−	0.745062i	−0.619577	−	0.784936i	$-0.712696\pi$
$383$	7.42946	−	14.5811i	0.379628	−	0.745062i	0.999205	+	0.0398744i	$0.0126958\pi$
$384$		0			0
$385$	13.8461	−	28.4782i	0.705662	−	1.45138i
$386$	7.06695			0.359698
$387$		0			0
$388$	−3.12657	−	19.7404i	−0.158728	−	1.00217i
$389$	6.92220	+	9.52759i	0.350970	+	0.483068i	0.947605	−	0.319444i	$-0.103496\pi$
$389$	6.92220	+	9.52759i	0.350970	+	0.483068i	−0.596636	+	0.802512i	$0.703496\pi$
$390$		0			0
$391$	−14.1090	−	4.58430i	−0.713525	−	0.231838i
$392$	17.6084	+	2.78890i	0.889360	+	0.140861i
$393$		0			0
$394$	−3.71862	+	1.20825i	−0.187341	+	0.0608709i
$395$	5.60531	+	17.4106i	0.282034	+	0.876025i
$396$		0			0
$397$	−7.56767	+	7.56767i	−0.379810	+	0.379810i	−0.871034	−	0.491223i	$-0.836550\pi$
$397$	−7.56767	+	7.56767i	−0.379810	+	0.379810i	0.491223	+	0.871034i	$0.336550\pi$
$398$	−2.55290	−	1.30077i	−0.127965	−	0.0652015i
$399$		0			0
$400$	−4.70866	+	14.2307i	−0.235433	+	0.711536i
$401$	−0.853124	+	2.62565i	−0.0426030	+	0.131118i	−0.970096	−	0.242723i	$-0.921959\pi$
$401$	−0.853124	+	2.62565i	−0.0426030	+	0.131118i	0.927493	+	0.373841i	$0.121959\pi$
$402$		0			0
$403$	1.25199	−	7.90476i	0.0623661	−	0.393764i
$404$	4.90332	+	3.56247i	0.243949	+	0.177240i
$405$		0			0
$406$		−	12.5852i		−	0.624595i
$407$	7.85200	+	3.79156i	0.389209	+	0.187941i
$408$		0			0
$409$	−2.15955	−	6.64640i	−0.106783	−	0.328643i	0.883362	−	0.468691i	$-0.155274\pi$
$409$	−2.15955	−	6.64640i	−0.106783	−	0.328643i	−0.990145	+	0.140048i	$0.955274\pi$
$410$	2.83182	+	5.59492i	0.139853	+	0.276313i
$411$		0			0
$412$	8.76719	+	17.2066i	0.431929	+	0.847708i
$413$	−17.8202	−	34.9741i	−0.876874	−	1.72096i
$414$		0			0
$415$	−9.07876	−	17.9372i	−0.445659	−	0.880504i
$416$	−1.84129	−	5.66690i	−0.0902766	−	0.277843i
$417$		0			0
$418$	−1.07239	−	5.94512i	−0.0524522	−	0.290785i
$419$			28.4453i			1.38964i	0.719181	+	0.694822i	$0.244517\pi$
$419$			28.4453i			1.38964i	−0.719181	+	0.694822i	$0.755483\pi$
$420$		0			0
$421$	−25.6368	−	18.6262i	−1.24946	−	0.907785i	−0.251269	−	0.967917i	$-0.580848\pi$
$421$	−25.6368	−	18.6262i	−1.24946	−	0.907785i	−0.998190	+	0.0601321i	$0.980848\pi$
$422$	1.88159	−	11.8799i	0.0915944	−	0.578304i
$423$		0			0
$424$	0.879063	−	2.70548i	0.0426911	−	0.131390i
$425$	−6.97412	+	3.50634i	−0.338294	+	0.170083i
$426$		0			0
$427$	−39.1915	−	19.9691i	−1.89661	−	0.966372i
$428$	−2.12150	+	2.12150i	−0.102546	+	0.102546i
$429$		0			0
$430$	−0.826214	−	2.56630i	−0.0398436	−	0.123758i
$431$	−29.6036	+	9.61878i	−1.42595	+	0.463320i	−0.917488	−	0.397763i	$-0.869787\pi$
$431$	−29.6036	+	9.61878i	−1.42595	+	0.463320i	−0.508465	+	0.861083i	$0.669787\pi$
$432$		0			0
$433$	−3.35216	−	0.530931i	−0.161095	−	0.0255149i	0.0753660	−	0.997156i	$-0.475987\pi$
$433$	−3.35216	−	0.530931i	−0.161095	−	0.0255149i	−0.236461	+	0.971641i	$0.575987\pi$
$434$	9.99183	+	3.24654i	0.479623	+	0.155839i
$435$		0			0
$436$	−3.43738	−	4.73115i	−0.164621	−	0.226581i
$437$	−6.52967	−	41.2267i	−0.312356	−	1.97214i
$438$		0			0
$439$	−15.1033			−0.720843			−0.360421	−	0.932790i	$-0.617367\pi$
$439$	−15.1033			−0.720843			−0.360421	+	0.932790i	$0.617367\pi$
$440$	1.62392	−	11.6595i	0.0774173	−	0.555847i
$441$		0			0
$442$	0.396395	−	0.777969i	0.0188546	−	0.0370042i
$443$	−0.0869392	−	0.548913i	−0.00413061	−	0.0260796i	0.985537	−	0.169461i	$-0.0542026\pi$
$443$	−0.0869392	−	0.548913i	−0.00413061	−	0.0260796i	−0.989668	+	0.143381i	$0.954203\pi$
$444$		0			0
$445$	−0.00489572	+	1.81940i	−0.000232079	+	0.0862477i
$446$	3.39288	+	1.10241i	0.160658	+	0.0522008i
$447$		0			0
$448$	−17.5602	+	2.78126i	−0.829640	+	0.131402i
$449$	−13.5982	+	4.41833i	−0.641740	+	0.208514i	−0.611769	−	0.791037i	$-0.709542\pi$
$449$	−13.5982	+	4.41833i	−0.641740	+	0.208514i	−0.0299714	+	0.999551i	$0.509542\pi$
$450$		0			0
$451$	13.5692	+	17.8605i	0.638950	+	0.841020i
$452$	7.26705	−	7.26705i	0.341813	−	0.341813i
$453$		0			0
$454$	5.34110	−	7.35140i	0.250670	−	0.345018i
$455$	10.3976	+	7.59711i	0.487446	+	0.356158i
$456$		0			0
$457$	−32.3237	+	16.4697i	−1.51204	+	0.770422i	−0.996269	−	0.0863064i	$-0.972494\pi$
$457$	−32.3237	+	16.4697i	−1.51204	+	0.770422i	−0.515769	+	0.856728i	$0.672494\pi$
$458$	0.637763	−	4.02668i	0.0298007	−	0.188154i
$459$		0			0
$460$	6.17956	−	38.3480i	0.288123	−	1.78799i
$461$			22.5017i			1.04801i	0.851715	+	0.524005i	$0.175563\pi$
$461$			22.5017i			1.04801i	−0.851715	+	0.524005i	$0.824437\pi$
$462$		0			0
$463$	−2.91766	−	2.91766i	−0.135595	−	0.135595i	0.636051	−	0.771647i	$-0.280567\pi$
$463$	−2.91766	−	2.91766i	−0.135595	−	0.135595i	−0.771647	+	0.636051i	$0.780567\pi$
$464$	6.58504	+	20.2667i	0.305703	+	0.940857i
$465$		0			0
$466$	0.606008	−	0.440290i	0.0280728	−	0.0203961i
$467$	0.256875	+	0.504145i	0.0118867	+	0.0233291i	0.896874	−	0.442287i	$-0.145833\pi$
$467$	0.256875	+	0.504145i	0.0118867	+	0.0233291i	−0.884987	+	0.465616i	$0.845833\pi$
$468$		0			0
$469$	−23.7978	+	17.2901i	−1.09888	+	0.798382i
$470$	1.90812	−	5.81927i	0.0880152	−	0.268423i
$471$		0			0
$472$	−10.3184	−	10.3184i	−0.474945	−	0.474945i
$473$	−4.56083	−	8.49697i	−0.209707	−	0.390691i
$474$		0			0
$475$	−17.6988	−	13.0050i	−0.812075	−	0.596711i
$476$	−9.85850	−	7.16262i	−0.451864	−	0.328298i
$477$		0			0
$478$	−5.69913	+	2.90385i	−0.260672	+	0.132819i
$479$	3.19471	−	9.83230i	0.145970	−	0.449249i	−0.851165	−	0.524899i	$-0.824103\pi$
$479$	3.19471	−	9.83230i	0.145970	−	0.449249i	0.997134	+	0.0756498i	$0.0241031\pi$
$480$		0			0
$481$	−2.08424	+	2.86870i	−0.0950330	+	0.130802i
$482$	7.91953	+	4.03520i	0.360725	+	0.183798i
$483$		0			0
$484$	−0.859688	−	20.0902i	−0.0390767	−	0.913192i
$485$	21.7528	+	11.1574i	0.987744	+	0.506633i
$486$		0			0
$487$	13.3474	−	2.11402i	0.604828	−	0.0957954i	0.153493	−	0.988150i	$-0.450948\pi$
$487$	13.3474	−	2.11402i	0.604828	−	0.0957954i	0.451336	+	0.892354i	$0.350948\pi$
$488$	−16.1508	−	2.55804i	−0.731114	−	0.115797i
$489$		0			0
$490$	−7.38342	+	7.34379i	−0.333549	+	0.331759i
$491$	−4.83999	−	6.66168i	−0.218426	−	0.300637i	0.685716	−	0.727869i	$-0.259489\pi$
$491$	−4.83999	−	6.66168i	−0.218426	−	0.300637i	−0.904142	+	0.427231i	$0.859489\pi$
$492$		0			0
$493$	−5.03804	+	9.88770i	−0.226902	+	0.445320i
$494$	2.45668			0.110531
$495$		0			0
$496$	−17.7891			−0.798754
$497$	24.9772	−	49.0206i	1.12038	−	2.19887i
$498$		0			0
$499$	9.11354	+	12.5437i	0.407978	+	0.561534i	0.962724	−	0.270486i	$-0.0871845\pi$
$499$	9.11354	+	12.5437i	0.407978	+	0.561534i	−0.554746	+	0.832020i	$0.687184\pi$
$500$	−11.8795	−	16.6314i	−0.531265	−	0.743777i
$501$		0			0
$502$	−5.57078	−	0.882325i	−0.248636	−	0.0393801i
$503$	23.1602	−	3.66821i	1.03266	−	0.163557i	0.382974	−	0.923759i	$-0.374900\pi$
$503$	23.1602	−	3.66821i	1.03266	−	0.163557i	0.649687	+	0.760202i	$0.274900\pi$
$504$		0			0
$505$	−7.05688	+	2.27194i	−0.314027	+	0.101100i
$506$	0.279418	+	13.0655i	0.0124216	+	0.580833i
$507$		0			0
$508$	23.3675	+	11.9063i	1.03676	+	0.528257i
$509$	11.9106	−	16.3935i	0.527928	−	0.726631i	−0.458885	−	0.888496i	$-0.651751\pi$
$509$	11.9106	−	16.3935i	0.527928	−	0.726631i	0.986813	+	0.161865i	$0.0517508\pi$
$510$		0			0
$511$	12.2708	−	37.7655i	0.542826	−	1.67065i
$512$	−20.2807	+	10.3335i	−0.896289	+	0.456682i
$513$		0			0
$514$	2.07721	+	1.50918i	0.0916217	+	0.0665671i
$515$	−23.3208	−	3.75800i	−1.02764	−	0.165597i
$516$		0			0
$517$	2.96345	−	21.7045i	0.130333	−	0.954565i
$518$	−3.29142	−	3.29142i	−0.144617	−	0.144617i
$519$		0			0
$520$	4.54898	+	1.49160i	0.199486	+	0.0654109i
$521$	−25.3896	+	18.4467i	−1.11234	+	0.808163i	−0.983031	−	0.183441i	$-0.941276\pi$
$521$	−25.3896	+	18.4467i	−1.11234	+	0.808163i	−0.129310	+	0.991604i	$0.541276\pi$
$522$		0			0
$523$	7.96324	+	15.6287i	0.348208	+	0.683397i	0.996986	−	0.0775807i	$-0.0247195\pi$
$523$	7.96324	+	15.6287i	0.348208	+	0.683397i	−0.648778	+	0.760978i	$0.724720\pi$
$524$	11.4872	−	8.34594i	0.501821	−	0.364594i
$525$		0			0
$526$	3.05720	+	9.40908i	0.133300	+	0.410255i
$527$	−6.55054	−	6.55054i	−0.285346	−	0.285346i
$528$		0			0
$529$			67.2966i			2.92594i
$530$	0.973084	+	1.34694i	0.0422681	+	0.0585074i
$531$		0			0
$532$	5.36356	−	33.8642i	0.232540	−	1.46820i
$533$	−8.12744	+	4.14114i	−0.352039	+	0.179373i
$534$		0			0
$535$	−0.564342	−	3.62624i	−0.0243986	−	0.156776i
$536$	−6.42778	+	8.84708i	−0.277638	+	0.382135i
$537$		0			0
$538$	−3.22468	+	3.22468i	−0.139026	+	0.139026i
$539$	−21.2456	+	30.5970i	−0.915112	+	1.31791i
$540$		0			0
$541$	12.2433	−	3.97808i	0.526379	−	0.171031i	−0.0337593	−	0.999430i	$-0.510748\pi$
$541$	12.2433	−	3.97808i	0.526379	−	0.171031i	0.560138	+	0.828399i	$0.310748\pi$
$542$	2.02401	−	0.320572i	0.0869388	−	0.0137697i
$543$		0			0
$544$	−6.55947	−	2.13130i	−0.281235	−	0.0913788i
$545$	7.15324	+	0.0192483i	0.306411	+	0.000824505i
$546$		0			0
$547$	−0.351499	−	2.21928i	−0.0150290	−	0.0948894i	0.979034	−	0.203699i	$-0.0652963\pi$
$547$	−0.351499	−	2.21928i	−0.0150290	−	0.0948894i	−0.994063	+	0.108809i	$0.965296\pi$
$548$	11.1151	−	21.8146i	0.474813	−	0.931874i
$549$		0			0
$550$	4.93952	+	4.78392i	0.210622	+	0.203987i
$551$	−31.2236			−1.33017
$552$		0			0
$553$	−5.46369	−	34.4964i	−0.232340	−	1.46694i
$554$	2.94693	+	4.05610i	0.125203	+	0.172327i
$555$		0			0
$556$	−0.943742	−	0.306640i	−0.0400236	−	0.0130044i
$557$	−20.8449	−	3.30150i	−0.883226	−	0.139889i	−0.301686	−	0.953407i	$-0.597549\pi$
$557$	−20.8449	−	3.30150i	−0.883226	−	0.139889i	−0.581540	+	0.813518i	$0.697549\pi$
$558$		0			0
$559$	3.72978	−	1.21188i	0.157753	−	0.0512570i
$560$	13.0630	−	25.4679i	0.552013	−	1.07622i
$561$		0			0
$562$	−0.478029	+	0.478029i	−0.0201644	+	0.0201644i
$563$	−26.8965	−	13.7044i	−1.13355	−	0.577574i	−0.216477	−	0.976288i	$-0.569457\pi$
$563$	−26.8965	−	13.7044i	−1.13355	−	0.577574i	−0.917075	+	0.398714i	$0.869457\pi$
$564$		0			0
$565$	1.93312	+	12.4215i	0.0813268	+	0.522574i
$566$	0.286219	−	0.880892i	0.0120307	−	0.0370266i
$567$		0			0
$568$	3.19959	−	20.2014i	0.134252	−	0.847632i
$569$	21.4558	+	15.5886i	0.899474	+	0.653506i	0.938331	−	0.345739i	$-0.112372\pi$
$569$	21.4558	+	15.5886i	0.899474	+	0.653506i	−0.0388569	+	0.999245i	$0.512372\pi$
$570$		0			0
$571$			20.1080i			0.841494i	0.907178	+	0.420747i	$0.138232\pi$
$571$			20.1080i			0.841494i	−0.907178	+	0.420747i	$0.861768\pi$
$572$	8.10228	+	1.10625i	0.338773	+	0.0462548i
$573$		0			0
$574$	−3.70020	−	11.3880i	−0.154443	−	0.475328i
$575$	33.4149	+	33.7766i	1.39350	+	1.40858i
$576$		0			0
$577$	12.7015	+	24.9282i	0.528772	+	1.03777i	0.988713	+	0.149824i	$0.0478707\pi$
$577$	12.7015	+	24.9282i	0.528772	+	1.03777i	−0.459941	+	0.887950i	$0.652129\pi$
$578$	2.74146	+	5.38042i	0.114030	+	0.223796i
$579$		0			0
$580$	−27.6095	−	9.05308i	−1.14642	−	0.375909i
$581$	11.8628	+	36.5099i	0.492151	+	1.51469i
$582$		0			0
$583$	4.29178	+	4.11206i	0.177747	+	0.170304i
$584$		−	14.7623i		−	0.610866i
$585$		0			0
$586$	2.57930	+	1.87397i	0.106550	+	0.0774130i
$587$	0.789709	−	4.98603i	0.0325948	−	0.205795i	−0.966016	−	0.258481i	$-0.916778\pi$
$587$	0.789709	−	4.98603i	0.0325948	−	0.205795i	0.998611	+	0.0526855i	$0.0167781\pi$
$588$		0			0
$589$	8.05457	−	24.7894i	0.331883	−	1.02143i
$590$	8.42247	−	1.31077i	0.346748	−	0.0539634i
$591$		0			0
$592$	7.02253	+	3.57816i	0.288624	+	0.147061i
$593$	24.2550	−	24.2550i	0.996034	−	0.996034i	−0.00395803	−	0.999992i	$-0.501260\pi$
$593$	24.2550	−	24.2550i	0.996034	−	0.996034i	0.999992	+	0.00395803i	$0.00125988\pi$
$594$		0			0
$595$	14.1884	−	4.56791i	0.581667	−	0.187266i
$596$	16.4959	−	5.35986i	0.675700	−	0.219548i
$597$		0			0
$598$	−5.24906	−	0.831370i	−0.214650	−	0.0339972i
$599$	17.0833	+	5.55069i	0.698004	+	0.226795i	0.636460	−	0.771309i	$-0.280398\pi$
$599$	17.0833	+	5.55069i	0.698004	+	0.226795i	0.0615431	+	0.998104i	$0.480398\pi$
$600$		0			0
$601$	−17.8526	−	24.5720i	−0.728221	−	1.00231i	−0.999211	−	0.0397283i	$-0.987351\pi$
$601$	−17.8526	−	24.5720i	−0.728221	−	1.00231i	0.270989	−	0.962582i	$-0.412649\pi$
$602$	0.805339	+	5.08471i	0.0328232	+	0.207237i
$603$		0			0
$604$	22.5523			0.917639
$605$	20.4624	+	13.6488i	0.831916	+	0.554901i
$606$		0			0
$607$	−19.1291	+	37.5430i	−0.776427	+	1.52382i	0.0737209	+	0.997279i	$0.476513\pi$
$607$	−19.1291	+	37.5430i	−0.776427	+	1.52382i	−0.850148	+	0.526544i	$0.823487\pi$
$608$	−3.03573	−	19.1668i	−0.123115	−	0.777317i
$609$		0			0
$610$	6.77224	−	6.73589i	0.274200	−	0.272728i
$611$	8.47235	+	2.75283i	0.342755	+	0.111368i
$612$		0			0
$613$	16.2519	−	2.57404i	0.656407	−	0.103965i	0.180658	−	0.983546i	$-0.442177\pi$
$613$	16.2519	−	2.57404i	0.656407	−	0.103965i	0.475749	+	0.879581i	$0.342177\pi$
$614$	−3.96455	+	1.28816i	−0.159996	+	0.0519859i
$615$		0			0
$616$	−6.48770	+	21.5224i	−0.261397	+	0.867163i
$617$	−5.67194	+	5.67194i	−0.228344	+	0.228344i	−0.812000	−	0.583657i	$-0.801621\pi$
$617$	−5.67194	+	5.67194i	−0.228344	+	0.228344i	0.583657	+	0.812000i	$0.301621\pi$
$618$		0			0
$619$	7.39580	−	10.1794i	0.297262	−	0.409146i	−0.634094	−	0.773256i	$-0.718627\pi$
$619$	7.39580	−	10.1794i	0.297262	−	0.409146i	0.931356	+	0.364110i	$0.118627\pi$
$620$	14.3098	−	19.5847i	0.574696	−	0.786541i
$621$		0			0
$622$	0.831264	−	0.423550i	0.0333306	−	0.0169828i
$623$	0.543482	−	3.43141i	0.0217741	−	0.137477i
$624$		0			0
$625$	24.9986	+	0.269079i	0.999942	+	0.0107631i
$626$		−	4.85198i		−	0.193924i
$627$		0			0
$628$	8.70237	+	8.70237i	0.347262	+	0.347262i
$629$	1.26833	+	3.90353i	0.0505718	+	0.155644i
$630$		0			0
$631$	−23.4246	+	17.0190i	−0.932518	+	0.677514i	−0.946608	−	0.322387i	$-0.895515\pi$
$631$	−23.4246	+	17.0190i	−0.932518	+	0.677514i	0.0140901	+	0.999901i	$0.495515\pi$
$632$	−5.89474	−	11.5691i	−0.234480	−	0.460193i
$633$		0			0
$634$	−3.14929	+	2.28809i	−0.125074	+	0.0908717i
$635$	−28.6220	+	14.4868i	−1.13583	+	0.574890i
$636$		0			0
$637$	−10.7114	−	10.7114i	−0.424401	−	0.424401i
$638$	9.68587	+	1.32247i	0.383467	+	0.0523571i
$639$		0			0
$640$	3.75740	−	23.3171i	0.148524	−	0.921688i
$641$	−26.7409	−	19.4284i	−1.05620	−	0.767375i	−0.0828197	−	0.996565i	$-0.526393\pi$
$641$	−26.7409	−	19.4284i	−1.05620	−	0.767375i	−0.973382	+	0.229189i	$0.926393\pi$
$642$		0			0
$643$	−27.0024	+	13.7584i	−1.06487	+	0.542578i	−0.896453	−	0.443138i	$-0.853865\pi$
$643$	−27.0024	+	13.7584i	−1.06487	+	0.542578i	−0.168416	+	0.985716i	$0.553865\pi$
$644$	−22.9201	+	70.5407i	−0.903177	+	2.77969i
$645$		0			0
$646$	1.67144	−	2.30054i	0.0657620	−	0.0905136i
$647$	−16.7131	−	8.51573i	−0.657058	−	0.334788i	0.0934739	−	0.995622i	$-0.470203\pi$
$647$	−16.7131	−	8.51573i	−0.657058	−	0.334788i	−0.750532	+	0.660834i	$0.770203\pi$
$648$		0			0
$649$	28.7894	−	10.0397i	1.13008	−	0.394092i
$650$	−2.27113	+	1.63147i	−0.0890811	+	0.0639916i
$651$		0			0
$652$	12.3663	−	1.95863i	0.484302	−	0.0767059i
$653$	−16.1009	−	2.55013i	−0.630076	−	0.0997942i	−0.166775	−	0.985995i	$-0.553335\pi$
$653$	−16.1009	−	2.55013i	−0.630076	−	0.0997942i	−0.463301	+	0.886201i	$0.653335\pi$
$654$		0			0
$655$	−0.0467347	+	17.3680i	−0.00182608	+	0.678625i
$656$	11.9173	+	16.4027i	0.465291	+	0.640418i
$657$		0			0
$658$	−5.30902	+	10.4195i	−0.206967	+	0.406196i
$659$	6.37901			0.248491			0.124245	−	0.992252i	$-0.460349\pi$
$659$	6.37901			0.248491			0.124245	+	0.992252i	$0.460349\pi$
$660$		0			0
$661$	−25.4204			−0.988739			−0.494370	−	0.869252i	$-0.664601\pi$
$661$	−25.4204			−0.988739			−0.494370	+	0.869252i	$0.664601\pi$
$662$	3.53230	−	6.93254i	0.137287	−	0.269441i
$663$		0			0
$664$	8.38855	+	11.5458i	0.325539	+	0.448066i
$665$	29.5753	+	29.7349i	1.14688	+	1.15307i
$666$		0			0
$667$	66.7136	+	10.5664i	2.58316	+	0.409133i
$668$	−39.0221	+	6.18049i	−1.50981	+	0.239130i
$669$		0			0
$670$	−1.95757	−	6.08041i	−0.0756277	−	0.234907i
$671$	19.4869	−	28.0643i	0.752285	−	1.08341i
$672$		0			0
$673$	37.3011	+	19.0059i	1.43785	+	0.732622i	0.987112	−	0.160033i	$-0.0511602\pi$
$673$	37.3011	+	19.0059i	1.43785	+	0.732622i	0.450740	+	0.892655i	$0.351160\pi$
$674$	2.83113	−	3.89672i	0.109051	−	0.150096i
$675$		0			0
$676$	6.31607	−	19.4389i	0.242926	−	0.747649i
$677$	23.7266	−	12.0893i	0.911889	−	0.464631i	0.0658972	−	0.997826i	$-0.479009\pi$
$677$	23.7266	−	12.0893i	0.911889	−	0.464631i	0.845992	+	0.533196i	$0.179009\pi$
$678$		0			0
$679$	−37.7670	−	27.4393i	−1.44937	−	1.05303i
$680$	4.49176	−	3.24503i	0.172251	−	0.124441i
$681$		0			0
$682$	−3.54856	+	7.34878i	−0.135881	+	0.281399i
$683$	−18.1728	−	18.1728i	−0.695363	−	0.695363i	0.268044	−	0.963407i	$-0.413623\pi$
$683$	−18.1728	−	18.1728i	−0.695363	−	0.695363i	−0.963407	+	0.268044i	$0.913623\pi$
$684$		0			0
$685$	13.5241	+	26.7200i	0.516728	+	1.02092i
$686$	6.06079	−	4.40342i	0.231402	−	0.168123i
$687$		0			0
$688$	−3.95738	−	7.76680i	−0.150874	−	0.296107i
$689$	−1.95549	+	1.42075i	−0.0744982	+	0.0541261i
$690$		0			0
$691$	−3.50457	−	10.7860i	−0.133320	−	0.410317i	0.862005	−	0.506900i	$-0.169209\pi$
$691$	−3.50457	−	10.7860i	−0.133320	−	0.410317i	−0.995325	+	0.0965830i	$0.969209\pi$
$692$	17.4610	+	17.4610i	0.663768	+	0.663768i
$693$		0			0
$694$		−	11.9564i		−	0.453858i
$695$	0.983891	−	0.710801i	0.0373211	−	0.0269622i
$696$		0			0
$697$	−1.65169	+	10.4284i	−0.0625622	+	0.395002i
$698$	−4.27186	+	2.17662i	−0.161692	+	0.0823863i
$699$		0			0
$700$	17.5306	+	34.8684i	0.662594	+	1.31790i
$701$	−10.6120	+	14.6062i	−0.400811	+	0.551669i	−0.960947	−	0.276731i	$-0.910749\pi$
$701$	−10.6120	+	14.6062i	−0.400811	+	0.551669i	0.560136	+	0.828401i	$0.310749\pi$
$702$		0			0
$703$	−8.16590	+	8.16590i	−0.307983	+	0.307983i
$704$	−0.295274	−	13.8069i	−0.0111286	−	0.520369i
$705$		0			0
$706$	10.3368	−	3.35862i	0.389029	−	0.126403i
$707$	13.9821	−	2.21454i	0.525850	−	0.0832865i
$708$		0			0
$709$	−17.9680	−	5.83817i	−0.674804	−	0.219257i	−0.0484847	−	0.998824i	$-0.515439\pi$
$709$	−17.9680	−	5.83817i	−0.674804	−	0.219257i	−0.626319	+	0.779567i	$0.715439\pi$
$710$	8.42523	+	8.47069i	0.316193	+	0.317899i
$711$		0			0
$712$	−0.202045	−	1.27566i	−0.00757197	−	0.0478075i
$713$	−25.5988	+	50.2404i	−0.958681	+	1.88152i
$714$		0			0
$715$	−6.93949	+	7.20388i	−0.259522	+	0.269410i
$716$	−27.9907			−1.04606
$717$		0			0
$718$	−0.527576	−	3.33098i	−0.0196889	−	0.124311i
$719$	−23.6271	−	32.5199i	−0.881142	−	1.21279i	−0.976103	−	0.217307i	$-0.930273\pi$
$719$	−23.6271	−	32.5199i	−0.881142	−	1.21279i	0.0949609	−	0.995481i	$-0.469727\pi$
$720$		0			0
$721$	42.8982	+	13.9385i	1.59761	+	0.519096i
$722$	0.120848	+	0.0191404i	0.00449748	+	0.000712332i
$723$		0			0
$724$	−24.5149	+	7.96537i	−0.911089	+	0.296031i
$725$	28.8653	−	20.7354i	1.07203	−	0.770094i
$726$		0			0
$727$	37.5684	−	37.5684i	1.39333	−	1.39333i	0.575611	−	0.817724i	$-0.304764\pi$
$727$	37.5684	−	37.5684i	1.39333	−	1.39333i	0.817724	−	0.575611i	$-0.195236\pi$
$728$	−8.14505	−	4.15011i	−0.301876	−	0.153813i
$729$		0			0
$730$	6.96250	+	5.08724i	0.257694	+	0.188287i
$731$	1.40276	−	4.31724i	0.0518828	−	0.159679i
$732$		0			0
$733$	−4.88285	+	30.8291i	−0.180352	+	1.13870i	0.716899	+	0.697178i	$0.245561\pi$
$733$	−4.88285	+	30.8291i	−0.180352	+	1.13870i	−0.897251	+	0.441521i	$0.854439\pi$
$734$	−5.94159	−	4.31682i	−0.219308	−	0.159337i
$735$		0			0
$736$			41.9800i			1.54740i
$737$	−10.8061	−	20.1321i	−0.398049	−	0.741576i
$738$		0			0
$739$	8.56103	+	26.3481i	0.314923	+	0.969232i	0.975786	+	0.218726i	$0.0701902\pi$
$739$	8.56103	+	26.3481i	0.314923	+	0.969232i	−0.660864	+	0.750506i	$0.729810\pi$
$740$	−9.58836	+	4.85306i	−0.352475	+	0.178402i
$741$		0			0
$742$	−1.44050	−	2.82715i	−0.0528826	−	0.103788i
$743$	−0.124664	−	0.244667i	−0.00457347	−	0.00897595i	0.888708	−	0.458473i	$-0.151603\pi$
$743$	−0.124664	−	0.244667i	−0.00457347	−	0.00897595i	−0.893282	+	0.449497i	$0.851603\pi$
$744$		0			0
$745$	−6.61042	+	20.1600i	−0.242187	+	0.738607i
$746$	−1.04404	−	3.21324i	−0.0382252	−	0.117645i
$747$		0			0
$748$	6.54845	−	6.83466i	0.239435	−	0.249900i
$749$			7.00771i			0.256056i
$750$		0			0
$751$	12.4769	+	9.06503i	0.455290	+	0.330787i	0.791681	−	0.610935i	$-0.209206\pi$
$751$	12.4769	+	9.06503i	0.455290	+	0.330787i	−0.336391	+	0.941722i	$0.609206\pi$
$752$	3.09752	−	19.5570i	0.112955	−	0.713170i
$753$		0			0
$754$	−1.22848	+	3.78087i	−0.0447386	+	0.137691i
$755$	−16.2745	+	22.2737i	−0.592291	+	0.810622i
$756$		0			0
$757$	−21.5928	−	11.0021i	−0.784802	−	0.399877i	0.0151920	−	0.999885i	$-0.495164\pi$
$757$	−21.5928	−	11.0021i	−0.784802	−	0.399877i	−0.799994	+	0.600008i	$0.795164\pi$
$758$	1.40050	−	1.40050i	0.0508686	−	0.0508686i
$759$		0			0
$760$	13.8728	+	7.11562i	0.503219	+	0.258111i
$761$	36.0172	−	11.7027i	1.30562	−	0.424222i	0.428088	−	0.903737i	$-0.359187\pi$
$761$	36.0172	−	11.7027i	1.30562	−	0.424222i	0.877534	+	0.479514i	$0.159187\pi$
$762$		0			0
$763$	−13.4911	−	2.13678i	−0.488411	−	0.0773567i
$764$	−34.0870	−	11.0756i	−1.23323	−	0.400699i
$765$		0			0
$766$	−3.98862	−	5.48987i	−0.144115	−	0.198357i
$767$	1.93964	+	12.2464i	0.0700365	+	0.442193i
$768$		0			0
$769$	28.2333			1.01812			0.509059	−	0.860732i	$-0.329994\pi$
$769$	28.2333			1.01812			0.509059	+	0.860732i	$0.329994\pi$
$770$	−7.91515	−	10.4767i	−0.285242	−	0.377556i
$771$		0			0
$772$	−14.1441	+	27.7593i	−0.509056	+	0.999079i
$773$	4.43973	+	28.0313i	0.159686	+	1.00822i	0.929197	+	0.369584i	$0.120500\pi$
$773$	4.43973	+	28.0313i	0.159686	+	1.00822i	−0.769511	+	0.638633i	$0.779500\pi$
$774$		0			0
$775$	9.01632	+	28.2661i	0.323876	+	1.01535i
$776$	−16.5054	−	5.36292i	−0.592508	−	0.192518i
$777$		0			0
$778$	4.82325	−	0.763927i	0.172922	−	0.0273881i
$779$	−28.2534	+	9.18008i	−1.01228	+	0.328910i
$780$		0			0
$781$	35.1027	+	24.3742i	1.25607	+	0.872176i
$782$	−4.34981	+	4.34981i	−0.155549	+	0.155549i
$783$		0			0
$784$	−19.7908	+	27.2397i	−0.706816	+	0.972848i
$785$	−14.8748	+	2.31493i	−0.530905	+	0.0826233i
$786$		0			0
$787$	27.6367	−	14.0816i	0.985142	−	0.501955i	0.114262	−	0.993451i	$-0.463550\pi$
$787$	27.6367	−	14.0816i	0.985142	−	0.501955i	0.870880	+	0.491496i	$0.163550\pi$
$788$	2.69652	−	17.0252i	0.0960595	−	0.606496i
$789$		0			0
$790$	7.48786	+	1.20662i	0.266406	+	0.0429297i
$791$		−	24.0045i		−	0.853501i
$792$		0			0
$793$	9.82473	+	9.82473i	0.348886	+	0.348886i
$794$	1.37137	+	4.22063i	0.0486680	+	0.149785i
$795$		0			0
$796$	10.2189	−	7.42450i	0.362201	−	0.263154i
$797$	7.43271	+	14.5875i	0.263280	+	0.516716i	0.984367	−	0.176128i	$-0.0563573\pi$
$797$	7.43271	+	14.5875i	0.263280	+	0.516716i	−0.721087	+	0.692844i	$0.756357\pi$
$798$		0			0
$799$	8.34215	−	6.06093i	0.295124	−	0.214420i
$800$	15.5350	+	15.7031i	0.549246	+	0.555190i
$801$		0			0
$802$	0.809485	+	0.809485i	0.0285839	+	0.0285839i
$803$	27.7757	+	13.4123i	0.980184	+	0.473309i
$804$		0			0
$805$	−53.1294	−	73.5416i	−1.87256	−	2.59200i
$806$	−2.68485	−	1.95066i	−0.0945699	−	0.0687091i
$807$		0			0
$808$	4.68917	−	2.38925i	0.164965	−	0.0840537i
$809$	14.2957	−	43.9977i	0.502611	−	1.54688i	−0.302140	−	0.953264i	$-0.597701\pi$
$809$	14.2957	−	43.9977i	0.502611	−	1.54688i	0.804750	−	0.593613i	$-0.202299\pi$
$810$		0			0
$811$	−25.9950	+	35.7790i	−0.912808	+	1.25637i	0.0533912	+	0.998574i	$0.482997\pi$
$811$	−25.9950	+	35.7790i	−0.912808	+	1.25637i	−0.966199	+	0.257798i	$0.917003\pi$
$812$	49.4354	+	25.1886i	1.73484	+	0.883946i
$813$		0			0
$814$	2.87901	−	2.18728i	0.100909	−	0.0766641i
$815$	−6.98954	+	13.6270i	−0.244833	+	0.477332i
$816$		0			0
$817$	12.6150	−	1.99802i	0.441343	−	0.0699019i
$818$	−2.86216	−	0.453322i	−0.100073	−	0.0158500i
$819$		0			0
$820$	−27.6448	−	0.0743879i	−0.965399	−	0.00259774i
$821$	−21.9391	−	30.1966i	−0.765680	−	1.05387i	−0.996720	−	0.0809244i	$-0.974213\pi$
$821$	−21.9391	−	30.1966i	−0.765680	−	1.05387i	0.231040	−	0.972944i	$-0.425787\pi$
$822$		0			0
$823$	−12.7247	+	24.9737i	−0.443556	+	0.870528i	0.555678	+	0.831398i	$0.312459\pi$
$823$	−12.7247	+	24.9737i	−0.443556	+	0.870528i	−0.999234	+	0.0391306i	$0.987541\pi$
$824$	16.7686			0.584161
$825$		0			0
$826$	−16.2764			−0.566330
$827$	−3.76842	+	7.39593i	−0.131041	+	0.257182i	−0.947199	−	0.320647i	$-0.896100\pi$
$827$	−3.76842	+	7.39593i	−0.131041	+	0.257182i	0.816158	+	0.577829i	$0.196100\pi$
$828$		0			0
$829$	−22.6760	−	31.2109i	−0.787571	−	1.08400i	−0.994406	−	0.105622i	$-0.966317\pi$
$829$	−22.6760	−	31.2109i	−0.787571	−	1.08400i	0.206836	−	0.978376i	$-0.433683\pi$
$830$	−8.33630	−	0.0224317i	−0.289357	−	0.000778615i
$831$		0			0
$832$	5.54693	+	0.878548i	0.192305	+	0.0304582i
$833$	−17.3182	+	2.74294i	−0.600041	+	0.0950372i
$834$		0			0
$835$	22.0556	−	43.0001i	0.763265	−	1.48808i
$836$	25.4990	+	7.68640i	0.881902	+	0.265840i
$837$		0			0
$838$	10.5096	+	5.35490i	0.363048	+	0.184982i
$839$	12.3085	−	16.9412i	0.424936	−	0.584874i	−0.541846	−	0.840478i	$-0.682274\pi$
$839$	12.3085	−	16.9412i	0.424936	−	0.584874i	0.966782	+	0.255604i	$0.0822743\pi$
$840$		0			0
$841$	6.65202	−	20.4728i	0.229380	−	0.705959i
$842$	−11.7079	+	5.96549i	−0.403482	+	0.205584i
$843$		0			0
$844$	42.8989	+	31.1679i	1.47664	+	1.07284i
$845$	14.6408	+	20.2658i	0.503660	+	0.697166i
$846$		0			0
$847$	−34.6008	−	31.7611i	−1.18890	−	1.09132i
$848$	3.79899	+	3.79899i	0.130458	+	0.130458i
$849$		0			0
$850$	−0.0174195	+	3.23678i	−0.000597483	+	0.111021i
$851$	20.2111	−	14.6842i	0.692826	−	0.503368i
$852$		0			0
$853$	−24.1367	−	47.3710i	−0.826425	−	1.62195i	−0.782281	−	0.622926i	$-0.785944\pi$
$853$	−24.1367	−	47.3710i	−0.826425	−	1.62195i	−0.0441444	−	0.999025i	$-0.514056\pi$
$854$	−14.7558	+	10.7207i	−0.504933	+	0.366855i
$855$		0			0
$856$	0.805049	+	2.47769i	0.0275160	+	0.0846856i
$857$	13.0692	+	13.0692i	0.446435	+	0.446435i	0.894168	−	0.447733i	$-0.147768\pi$
$857$	13.0692	+	13.0692i	0.446435	+	0.446435i	−0.447733	+	0.894168i	$0.647768\pi$
$858$		0			0
$859$			3.08514i			0.105264i	0.998614	+	0.0526318i	$0.0167610\pi$
$859$			3.08514i			0.105264i	−0.998614	+	0.0526318i	$0.983239\pi$
$860$	11.7342	+	1.89089i	0.400132	+	0.0644788i
$861$		0			0
$862$	−2.01913	+	12.7483i	−0.0687718	+	0.434208i
$863$	16.1674	−	8.23771i	0.550345	−	0.280415i	−0.156625	−	0.987658i	$-0.550061\pi$
$863$	16.1674	−	8.23771i	0.550345	−	0.280415i	0.706970	+	0.707243i	$0.250061\pi$
$864$		0			0
$865$	−29.8458	+	4.64482i	−1.01479	+	0.157929i
$866$	−0.827214	+	1.13856i	−0.0281099	+	0.0386899i
$867$		0			0
$868$	−32.7506	+	32.7506i	−1.11163	+	1.11163i
$869$	27.1233	−	0.580056i	0.920095	−	0.0196771i
$870$		0			0
$871$	8.83708	−	2.87134i	0.299433	−	0.0972917i
$872$	−5.01547	+	0.794372i	−0.169845	+	0.0269008i
$873$		0			0
$874$	−16.4611	−	5.34854i	−0.556805	−	0.180917i
$875$	−47.0883	−	7.84823i	−1.59188	−	0.265318i
$876$		0			0
$877$	0.335519	+	2.11838i	0.0113297	+	0.0715327i	0.992705	−	0.120566i	$-0.0384708\pi$
$877$	0.335519	+	2.11838i	0.0113297	+	0.0715327i	−0.981376	+	0.192098i	$0.938471\pi$
$878$	−2.84324	+	5.58017i	−0.0959546	+	0.188322i
$879$		0			0
$880$	18.2280	+	12.7298i	0.614466	+	0.429120i
$881$	−18.9390			−0.638069			−0.319035	−	0.947743i	$-0.603359\pi$
$881$	−18.9390			−0.638069			−0.319035	+	0.947743i	$0.603359\pi$
$882$		0			0
$883$	−5.87260	−	37.0781i	−0.197629	−	1.24778i	−0.864510	−	0.502615i	$-0.832371\pi$
$883$	−5.87260	−	37.0781i	−0.197629	−	1.24778i	0.666882	−	0.745164i	$-0.267629\pi$
$884$	2.26254	+	3.11412i	0.0760974	+	0.104739i
$885$		0			0
$886$	−0.219171	−	0.0712131i	−0.00736320	−	0.00239245i
$887$	−21.2990	−	3.37342i	−0.715149	−	0.113268i	−0.211752	−	0.977324i	$-0.567917\pi$
$887$	−21.2990	−	3.37342i	−0.715149	−	0.113268i	−0.503397	+	0.864055i	$0.667917\pi$
$888$		0			0
$889$	58.2580	−	18.9292i	1.95391	−	0.634864i
$890$	0.671285	+	0.344315i	0.0225015	+	0.0115415i
$891$		0			0
$892$	−11.1210	+	11.1210i	−0.372358	+	0.372358i
$893$	25.8505	+	13.1715i	0.865054	+	0.440767i
$894$		0			0
$895$	20.1991	−	27.6450i	0.675182	−	0.924069i
$896$	−13.9363	+	42.8914i	−0.465578	+	1.43290i
$897$		0			0
$898$	−0.927475	+	5.85585i	−0.0309502	+	0.195412i
$899$	34.1235	+	24.7922i	1.13808	+	0.826865i
$900$		0			0
$901$			2.79783i			0.0932092i
$902$	9.15331	−	1.65109i	0.304772	−	0.0549751i
$903$		0			0
$904$	−2.75765	−	8.48716i	−0.0917179	−	0.282279i
$905$	9.82386	−	29.9602i	0.326556	−	0.995910i
$906$		0			0
$907$	20.4889	+	40.2116i	0.680321	+	1.33521i	0.930245	+	0.366940i	$0.119595\pi$
$907$	20.4889	+	40.2116i	0.680321	+	1.33521i	−0.249923	+	0.968266i	$0.580405\pi$
$908$	18.1867	+	35.6935i	0.603548	+	1.18453i
$909$		0			0
$910$	4.76424	−	2.41138i	0.157933	−	0.0799364i
$911$	3.83699	+	11.8090i	0.127125	+	0.391251i	0.994282	−	0.106784i	$-0.0340553\pi$
$911$	3.83699	+	11.8090i	0.127125	+	0.391251i	−0.867157	+	0.498034i	$0.834055\pi$
$912$		0			0
$913$	−29.3454	+	5.29335i	−0.971189	+	0.175184i
$914$			15.0430i			0.497577i
$915$		0			0
$916$	14.5405	+	10.5643i	0.480432	+	0.349055i
$917$	5.18809	−	32.7563i	0.171326	−	1.08171i
$918$		0			0
$919$	−1.68023	+	5.17123i	−0.0554258	+	0.170583i	−0.974937	−	0.222480i	$-0.928585\pi$
$919$	−1.68023	+	5.17123i	−0.0554258	+	0.170583i	0.919511	+	0.393063i	$0.128585\pi$
$920$	−27.2332	−	19.8983i	−0.897852	−	0.656027i
$921$		0			0
$922$	8.31363	+	4.23600i	0.273795	+	0.139505i
$923$	−12.2887	+	12.2887i	−0.404488	+	0.404488i
$924$		0			0
$925$	2.12620	−	12.9721i	0.0699089	−	0.426519i
$926$	−1.62723	+	0.528720i	−0.0534742	+	0.0173748i
$927$		0			0
$928$	31.0160	+	4.91246i	1.01815	+	0.161259i
$929$	−2.05900	−	0.669009i	−0.0675535	−	0.0219495i	0.275045	−	0.961431i	$-0.411307\pi$
$929$	−2.05900	−	0.669009i	−0.0675535	−	0.0219495i	−0.342599	+	0.939482i	$0.611307\pi$
$930$		0			0
$931$	−28.9981	−	39.9125i	−0.950376	−	1.30808i
$932$	0.516593	+	3.26164i	0.0169216	+	0.106839i
$933$		0			0
$934$	0.234622			0.00767706
$935$	2.02463	+	11.3997i	0.0662126	+	0.372810i
$936$		0			0
$937$	−4.50627	+	8.84405i	−0.147213	+	0.288923i	−0.952824	−	0.303522i	$-0.901837\pi$
$937$	−4.50627	+	8.84405i	−0.147213	+	0.288923i	0.805611	+	0.592445i	$0.201837\pi$
$938$	1.90812	+	12.0474i	0.0623022	+	0.393360i
$939$		0			0
$940$	19.0394	+	19.1421i	0.620996	+	0.624347i
$941$	−25.5982	−	8.31736i	−0.834477	−	0.271138i	−0.139547	−	0.990215i	$-0.544565\pi$
$941$	−25.5982	−	8.31736i	−0.834477	−	0.271138i	−0.694930	+	0.719077i	$0.744565\pi$
$942$		0			0
$943$	63.4741	−	10.0533i	2.06700	−	0.327381i
$944$	26.2108	−	8.51641i	0.853090	−	0.277186i
$945$		0			0
$946$	−3.99793	+	0.0854994i	−0.129984	+	0.00277982i
$947$	−18.3626	+	18.3626i	−0.596705	+	0.596705i	−0.939434	−	0.342729i	$-0.888649\pi$
$947$	−18.3626	+	18.3626i	−0.596705	+	0.596705i	0.342729	+	0.939434i	$0.388649\pi$
$948$		0			0
$949$	−7.37278	+	10.1478i	−0.239331	+	0.329410i
$950$	−8.13675	+	4.09087i	−0.263991	+	0.132725i
$951$		0			0
$952$	−9.42794	+	4.80377i	−0.305561	+	0.155691i
$953$	7.03547	−	44.4202i	0.227901	−	1.43891i	−0.562742	−	0.826633i	$-0.690253\pi$
$953$	7.03547	−	44.4202i	0.227901	−	1.43891i	0.790643	−	0.612278i	$-0.209747\pi$
$954$		0			0
$955$	35.5372	−	25.6734i	1.14996	−	0.830773i
$956$		−	28.1983i		−	0.911998i
$957$		0			0
$958$	−3.03129	−	3.03129i	−0.0979366	−	0.0979366i
$959$	−17.6713	−	54.3866i	−0.570635	−	1.75623i
$960$		0			0
$961$	−3.40644	+	2.47492i	−0.109885	+	0.0798362i
$962$	0.667527	+	1.31010i	0.0215219	+	0.0422392i
$963$		0			0
$964$	−31.7009	+	23.0321i	−1.02102	+	0.741813i
$965$	−17.2095	−	34.0015i	−0.553994	−	1.09455i
$966$		0			0
$967$	−24.6932	−	24.6932i	−0.794078	−	0.794078i	0.188076	−	0.982154i	$-0.439775\pi$
$967$	−24.6932	−	24.6932i	−0.794078	−	0.794078i	−0.982154	+	0.188076i	$0.939775\pi$
$968$	−15.8824	−	7.25467i	−0.510479	−	0.233174i
$969$		0			0
$970$	8.21731	−	5.93651i	0.263842	−	0.190610i
$971$	46.5504	+	33.8208i	1.49387	+	1.08536i	0.972744	+	0.231883i	$0.0744887\pi$
$971$	46.5504	+	33.8208i	1.49387	+	1.08536i	0.521128	+	0.853478i	$0.325511\pi$
$972$		0			0
$973$	−2.06513	+	1.05223i	−0.0662049	+	0.0337331i
$974$	1.73162	−	5.32938i	0.0554847	−	0.170764i
$975$		0			0
$976$	18.1526	−	24.9849i	0.581051	−	0.799747i
$977$	−43.8801	−	22.3580i	−1.40385	−	0.715297i	−0.422291	−	0.906460i	$-0.638774\pi$
$977$	−43.8801	−	22.3580i	−1.40385	−	0.715297i	−0.981558	+	0.191163i	$0.938774\pi$
$978$		0			0
$979$	2.58378	+	0.778852i	0.0825779	+	0.0248922i
$980$	−14.0693	−	43.7006i	−0.449427	−	1.39596i
$981$		0			0
$982$	−3.37241	+	0.534137i	−0.107618	+	0.0170450i
$983$	38.5842	+	6.11114i	1.23064	+	0.194915i	0.737690	−	0.675140i	$-0.235917\pi$
$983$	38.5842	+	6.11114i	1.23064	+	0.194915i	0.492955	+	0.870055i	$0.335917\pi$
$984$		0			0
$985$	14.8689	+	14.9492i	0.473764	+	0.476320i
$986$	2.70475	+	3.72277i	0.0861368	+	0.118557i
$987$		0			0
$988$	−4.91690	+	9.64997i	−0.156428	+	0.307006i
$989$	−27.6299			−0.878581
$990$		0			0
$991$	−25.5896			−0.812881			−0.406440	−	0.913677i	$-0.633230\pi$
$991$	−25.5896			−0.812881			−0.406440	+	0.913677i	$0.633230\pi$
$992$	−11.9012	+	23.3574i	−0.377863	+	0.741598i
$993$		0			0
$994$	−13.4094	−	18.4565i	−0.425321	−	0.585405i
$995$	−0.0415749	+	15.4505i	−0.00131801	+	0.489813i
$996$		0			0
$997$	9.70915	+	1.53778i	0.307492	+	0.0487019i	0.308274	−	0.951298i	$-0.400249\pi$
$997$	9.70915	+	1.53778i	0.307492	+	0.0487019i	−0.000781604		1.00000i	$0.500249\pi$
$998$	6.35012	−	1.00576i	0.201010	−	0.0318368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.b.28.7	yes	96
3.2	odd	2	inner	495.2.bj.b.28.6	✓	96
5.2	odd	4	inner	495.2.bj.b.127.7	yes	96
11.2	odd	10	inner	495.2.bj.b.343.7	yes	96
15.2	even	4	inner	495.2.bj.b.127.6	yes	96
33.2	even	10	inner	495.2.bj.b.343.6	yes	96
55.2	even	20	inner	495.2.bj.b.442.7	yes	96
165.2	odd	20	inner	495.2.bj.b.442.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.bj.b.28.6	✓	96	3.2	odd	2	inner
495.2.bj.b.28.7	yes	96	1.1	even	1	trivial
495.2.bj.b.127.6	yes	96	15.2	even	4	inner
495.2.bj.b.127.7	yes	96	5.2	odd	4	inner
495.2.bj.b.343.6	yes	96	33.2	even	10	inner
495.2.bj.b.343.7	yes	96	11.2	odd	10	inner
495.2.bj.b.442.6	yes	96	165.2	odd	20	inner
495.2.bj.b.442.7	yes	96	55.2	even	20	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.188252 - 0.369466i) q^{2} +(1.07450 + 1.47893i) q^{4} +(-2.23606 - 0.00601689i) q^{5} +(4.21724 + 0.667945i) q^{7} +(1.56780 - 0.248316i) q^{8} +O(q^{10})\)	\(q+(0.188252 - 0.369466i) q^{2} +(1.07450 + 1.47893i) q^{4} +(-2.23606 - 0.00601689i) q^{5} +(4.21724 + 0.667945i) q^{7} +(1.56780 - 0.248316i) q^{8} +(-0.423167 + 0.825016i) q^{10} +(-0.957217 + 3.17549i) q^{11} +(-1.20175 - 0.612321i) q^{13} +(1.04069 - 1.43239i) q^{14} +(-0.926402 + 2.85117i) q^{16} +(-1.39103 + 0.708765i) q^{17} +(-3.55370 - 2.58191i) q^{19} +(-2.39376 - 3.31344i) q^{20} +(0.993038 + 0.951453i) q^{22} +(6.71925 + 6.71925i) q^{23} +(4.99993 + 0.0269083i) q^{25} +(-0.452464 + 0.328734i) q^{26} +(3.54360 + 6.95470i) q^{28} +(5.75065 - 4.17809i) q^{29} +(1.83366 + 5.64343i) q^{31} +(3.12386 + 3.12386i) q^{32} +0.647365i q^{34} +(-9.42598 - 1.51894i) q^{35} +(0.411271 - 2.59666i) q^{37} +(-1.62292 + 0.826921i) q^{38} +(-3.50720 + 0.545816i) q^{40} +(3.97520 - 5.47140i) q^{41} +(-2.05603 + 2.05603i) q^{43} +(-5.72486 + 1.99642i) q^{44} +(3.74745 - 1.21762i) q^{46} +(-6.52357 + 1.03323i) q^{47} +(10.6816 + 3.47065i) q^{49} +(0.951190 - 1.84224i) q^{50} +(-0.385704 - 2.43524i) q^{52} +(0.813603 - 1.59679i) q^{53} +(2.15950 - 7.09483i) q^{55} +6.77767 q^{56} +(-0.461090 - 2.91121i) q^{58} +(-5.40351 - 7.43729i) q^{59} +(-9.79737 - 3.18336i) q^{61} +(2.43025 + 0.384913i) q^{62} +(-3.96011 + 1.28672i) q^{64} +(2.68350 + 1.37642i) q^{65} +(-4.87141 + 4.87141i) q^{67} +(-2.54288 - 1.29566i) q^{68} +(-2.33566 + 3.19664i) q^{70} +(3.98173 - 12.2545i) q^{71} +(1.45483 - 9.18545i) q^{73} +(-0.881957 - 0.640779i) q^{74} -8.02995i q^{76} +(-6.15787 + 12.7524i) q^{77} +(-2.52771 - 7.77950i) q^{79} +(2.08865 - 6.36982i) q^{80} +(-1.27316 - 2.49871i) q^{82} +(4.08172 + 8.01082i) q^{83} +(3.11469 - 1.57647i) q^{85} +(0.372581 + 1.14669i) q^{86} +(-0.712205 + 5.21624i) q^{88} -0.813663i q^{89} +(-4.65906 - 3.38501i) q^{91} +(-2.71742 + 17.1571i) q^{92} +(-0.846333 + 2.60475i) q^{94} +(7.93075 + 5.79470i) q^{95} +(-9.74154 - 4.96356i) q^{97} +(3.29312 - 3.29312i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 20 q^{7}+O(q^{10}) \) 96 * q + 20 * q^7	\( 96 q + 20 q^{7} + 40 q^{16} + 8 q^{22} - 16 q^{25} - 60 q^{28} + 16 q^{31} - 40 q^{37} + 280 q^{46} + 40 q^{52} + 24 q^{55} - 68 q^{58} + 40 q^{61} + 16 q^{67} + 52 q^{70} - 60 q^{73} - 112 q^{82} + 80 q^{85} + 24 q^{88} - 56 q^{91} - 112 q^{97}+O(q^{100}) \) 96 * q + 20 * q^7 + 40 * q^16 + 8 * q^22 - 16 * q^25 - 60 * q^28 + 16 * q^31 - 40 * q^37 + 280 * q^46 + 40 * q^52 + 24 * q^55 - 68 * q^58 + 40 * q^61 + 16 * q^67 + 52 * q^70 - 60 * q^73 - 112 * q^82 + 80 * q^85 + 24 * q^88 - 56 * q^91 - 112 * q^97

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