LMFDB - Embedded newform 639.2.z.a.305.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			305.19
Character	$\chi$	$=$	639.305
Dual form			639.2.z.a.44.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34937 - 0.890708i) q^{2} +(0.241376 - 0.564726i) q^{4} +(0.0720395 + 0.0991538i) q^{5} +(0.477225 + 1.27156i) q^{7} +(0.400091 + 2.20468i) q^{8} +O(q^{10})$	\(q+(1.34937 - 0.890708i) q^{2} +(0.241376 - 0.564726i) q^{4} +(0.0720395 + 0.0991538i) q^{5} +(0.477225 + 1.27156i) q^{7} +(0.400091 + 2.20468i) q^{8} +(0.185525 + 0.0696286i) q^{10} +(0.263401 + 1.94451i) q^{11} +(3.81713 + 0.517065i) q^{13} +(1.77654 + 1.29073i) q^{14} +(3.35243 + 3.50636i) q^{16} +(-0.0384264 - 0.118264i) q^{17} +(1.18145 + 0.705881i) q^{19} +(0.0733833 - 0.0167493i) q^{20} +(2.08741 + 2.38924i) q^{22} +(-1.85669 - 2.32822i) q^{23} +(1.54044 - 4.74100i) q^{25} +(5.61125 - 2.70224i) q^{26} +(0.833275 + 0.0374224i) q^{28} +(0.924038 - 1.05765i) q^{29} +(2.37118 + 2.26708i) q^{31} +(3.27777 + 0.748130i) q^{32} +(-0.157190 - 0.125355i) q^{34} +(-0.0917012 + 0.138921i) q^{35} +(-1.95021 + 2.44549i) q^{37} +(2.22294 - 0.0998321i) q^{38} +(-0.189780 + 0.198495i) q^{40} +(-8.04164 - 3.87265i) q^{41} +(-0.171246 + 3.81309i) q^{43} +(1.16169 + 0.320607i) q^{44} +(-4.57912 - 1.48785i) q^{46} +(1.54547 - 0.139094i) q^{47} +(3.88238 - 3.39193i) q^{49} +(-2.14422 - 7.76942i) q^{50} +(1.21336 - 2.03083i) q^{52} +(-3.44696 - 8.06456i) q^{53} +(-0.173830 + 0.166198i) q^{55} +(-2.61246 + 1.56087i) q^{56} +(0.304810 - 2.25020i) q^{58} +(0.00866266 - 0.0160979i) q^{59} +(-2.87229 + 7.65319i) q^{61} +(5.21890 + 0.947090i) q^{62} +(-3.99430 + 1.49908i) q^{64} +(0.223715 + 0.415732i) q^{65} +(6.97315 + 2.98047i) q^{67} +(-0.0760621 - 0.00684571i) q^{68} +0.269135i q^{70} +(2.72868 - 7.97210i) q^{71} +(-0.962973 - 1.45884i) q^{73} +(-0.453332 + 5.03693i) q^{74} +(0.683801 - 0.496811i) q^{76} +(-2.34686 + 1.26290i) q^{77} +(-7.79889 + 1.41529i) q^{79} +(-0.106162 + 0.585003i) q^{80} +(-14.3005 + 1.93714i) q^{82} +(-9.57903 - 5.15470i) q^{83} +(0.00895814 - 0.0123298i) q^{85} +(3.16528 + 5.29778i) q^{86} +(-4.18163 + 1.35870i) q^{88} +(0.893615 - 0.381949i) q^{89} +(1.16415 + 5.10047i) q^{91} +(-1.76297 + 0.486548i) q^{92} +(1.96151 - 1.56425i) q^{94} +(0.0151199 + 0.167996i) q^{95} +(-1.89703 - 3.93922i) q^{97} +(2.21752 - 8.03502i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{27}{70}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.34937	−	0.890708i	0.954145	−	0.629826i	0.0250580	−	0.999686i	$-0.492023\pi$
$2$	1.34937	−	0.890708i	0.954145	−	0.629826i	0.929087	+	0.369860i	$0.120594\pi$
$3$		0			0
$3$		0			0
$4$	0.241376	−	0.564726i	0.120688	−	0.282363i
$5$	0.0720395	+	0.0991538i	0.0322170	+	0.0443429i	0.824822	−	0.565393i	$-0.191275\pi$
$5$	0.0720395	+	0.0991538i	0.0322170	+	0.0443429i	−0.792605	+	0.609736i	$0.791275\pi$
$6$		0			0
$7$	0.477225	+	1.27156i	0.180374	+	0.480605i	0.995057	−	0.0993010i	$-0.0316607\pi$
$7$	0.477225	+	1.27156i	0.180374	+	0.480605i	−0.814683	+	0.579906i	$0.803089\pi$
$8$	0.400091	+	2.20468i	0.141453	+	0.779473i
$9$		0			0
$10$	0.185525	+	0.0696286i	0.0586681	+	0.0220185i
$11$	0.263401	+	1.94451i	0.0794185	+	0.586291i	0.986307	+	0.164920i	$0.0527366\pi$
$11$	0.263401	+	1.94451i	0.0794185	+	0.586291i	−0.906888	+	0.421371i	$0.861549\pi$
$12$		0			0
$13$	3.81713	+	0.517065i	1.05868	+	0.143408i	0.642818	−	0.766019i	$-0.277765\pi$
$13$	3.81713	+	0.517065i	1.05868	+	0.143408i	0.415863	+	0.909427i	$0.363480\pi$
$14$	1.77654	+	1.29073i	0.474801	+	0.344963i
$15$		0			0
$16$	3.35243	+	3.50636i	0.838107	+	0.876591i
$17$	−0.0384264	−	0.118264i	−0.00931976	−	0.0286833i	0.946288	−	0.323324i	$-0.104800\pi$
$17$	−0.0384264	−	0.118264i	−0.00931976	−	0.0286833i	−0.955608	+	0.294640i	$0.904800\pi$
$18$		0			0
$19$	1.18145	+	0.705881i	0.271042	+	0.161940i	0.641989	−	0.766714i	$-0.278110\pi$
$19$	1.18145	+	0.705881i	0.271042	+	0.161940i	−0.370947	+	0.928654i	$0.620967\pi$
$20$	0.0733833	−	0.0167493i	0.0164090	−	0.00374525i
$21$		0			0
$22$	2.08741	+	2.38924i	0.445038	+	0.509387i
$23$	−1.85669	−	2.32822i	−0.387147	−	0.485467i	0.549623	−	0.835413i	$-0.314771\pi$
$23$	−1.85669	−	2.32822i	−0.387147	−	0.485467i	−0.936770	+	0.349946i	$0.886200\pi$
$24$		0			0
$25$	1.54044	−	4.74100i	0.308089	−	0.948199i
$26$	5.61125	−	2.70224i	1.10046	−	0.529952i
$27$		0			0
$28$	0.833275	+	0.0374224i	0.157474	+	0.00707217i
$29$	0.924038	−	1.05765i	0.171589	−	0.196400i	−0.660847	−	0.750521i	$-0.729803\pi$
$29$	0.924038	−	1.05765i	0.171589	−	0.196400i	0.832436	+	0.554121i	$0.186946\pi$
$30$		0			0
$31$	2.37118	+	2.26708i	0.425877	+	0.407180i	0.873331	−	0.487127i	$-0.161955\pi$
$31$	2.37118	+	2.26708i	0.425877	+	0.407180i	−0.447454	+	0.894307i	$0.647669\pi$
$32$	3.27777	+	0.748130i	0.579434	+	0.132252i
$33$		0			0
$34$	−0.157190	−	0.125355i	−0.0269579	−	0.0214982i
$35$	−0.0917012	+	0.138921i	−0.0155003	+	0.0234820i
$36$		0			0
$37$	−1.95021	+	2.44549i	−0.320613	+	0.402036i	−0.915854	−	0.401511i	$-0.868485\pi$
$37$	−1.95021	+	2.44549i	−0.320613	+	0.402036i	0.595241	+	0.803547i	$0.297057\pi$
$38$	2.22294	−	0.0998321i	0.360608	−	0.0161949i
$39$		0			0
$40$	−0.189780	+	0.198495i	−0.0300069	+	0.0313848i
$41$	−8.04164	−	3.87265i	−1.25589	−	0.604806i	−0.316807	−	0.948490i	$-0.602611\pi$
$41$	−8.04164	−	3.87265i	−1.25589	−	0.604806i	−0.939085	+	0.343684i	$0.888325\pi$
$42$		0			0
$43$	−0.171246	+	3.81309i	−0.0261148	+	0.581491i	0.942691	+	0.333668i	$0.108286\pi$
$43$	−0.171246	+	3.81309i	−0.0261148	+	0.581491i	−0.968805	+	0.247823i	$0.920285\pi$
$44$	1.16169	+	0.320607i	0.175132	+	0.0483333i
$45$		0			0
$46$	−4.57912	−	1.48785i	−0.675154	−	0.219371i
$47$	1.54547	−	0.139094i	0.225429	−	0.0202890i	0.0236513	−	0.999720i	$-0.492471\pi$
$47$	1.54547	−	0.139094i	0.225429	−	0.0202890i	0.201778	+	0.979431i	$0.435328\pi$
$48$		0			0
$49$	3.88238	−	3.39193i	0.554625	−	0.484561i
$50$	−2.14422	−	7.76942i	−0.303239	−	1.09876i
$51$		0			0
$52$	1.21336	−	2.03083i	0.168263	−	0.281625i
$53$	−3.44696	−	8.06456i	−0.473476	−	1.10775i	−0.970736	−	0.240151i	$-0.922803\pi$
$53$	−3.44696	−	8.06456i	−0.473476	−	1.10775i	0.497259	−	0.867602i	$-0.334340\pi$
$54$		0			0
$55$	−0.173830	+	0.166198i	−0.0234392	+	0.0224102i
$56$	−2.61246	+	1.56087i	−0.349104	+	0.208580i
$57$		0			0
$58$	0.304810	−	2.25020i	0.0400235	−	0.295466i
$59$	0.00866266	−	0.0160979i	0.00112778	−	0.00209577i	−0.880031	−	0.474916i	$-0.842478\pi$
$59$	0.00866266	−	0.0160979i	0.00112778	−	0.00209577i	0.881159	+	0.472820i	$0.156764\pi$
$60$		0			0
$61$	−2.87229	+	7.65319i	−0.367759	+	0.979891i	0.613923	+	0.789366i	$0.289590\pi$
$61$	−2.87229	+	7.65319i	−0.367759	+	0.979891i	−0.981682	+	0.190525i	$0.938981\pi$
$62$	5.21890	+	0.947090i	0.662801	+	0.120281i
$63$		0			0
$64$	−3.99430	+	1.49908i	−0.499287	+	0.187386i
$65$	0.223715	+	0.415732i	0.0277484	+	0.0515652i
$66$		0			0
$67$	6.97315	+	2.98047i	0.851906	+	0.364122i	0.774267	−	0.632860i	$-0.218119\pi$
$67$	6.97315	+	2.98047i	0.851906	+	0.364122i	0.0776390	+	0.996982i	$0.475262\pi$
$68$	−0.0760621	−	0.00684571i	−0.00922388	−	0.000830165i
$69$		0			0
$70$			0.269135i			0.0321677i
$71$	2.72868	−	7.97210i	0.323835	−	0.946114i
$71$	2.72868	−	7.97210i	0.323835	−	0.946114i
$72$		0			0
$73$	−0.962973	−	1.45884i	−0.112707	−	0.170744i	0.773842	−	0.633379i	$-0.218333\pi$
$73$	−0.962973	−	1.45884i	−0.112707	−	0.170744i	−0.886549	+	0.462635i	$0.846904\pi$
$74$	−0.453332	+	5.03693i	−0.0526988	+	0.585531i
$75$		0			0
$76$	0.683801	−	0.496811i	0.0784374	−	0.0569881i
$77$	−2.34686	+	1.26290i	−0.267449	+	0.143921i
$78$		0			0
$79$	−7.79889	+	1.41529i	−0.877444	+	0.159233i	−0.598546	−	0.801088i	$-0.704255\pi$
$79$	−7.79889	+	1.41529i	−0.877444	+	0.159233i	−0.278898	+	0.960321i	$0.589969\pi$
$80$	−0.106162	+	0.585003i	−0.0118693	+	0.0654053i
$81$		0			0
$82$	−14.3005	+	1.93714i	−1.57923	+	0.213921i
$83$	−9.57903	−	5.15470i	−1.05144	−	0.565801i	−0.145561	−	0.989349i	$-0.546499\pi$
$83$	−9.57903	−	5.15470i	−1.05144	−	0.565801i	−0.905874	+	0.423548i	$0.860785\pi$
$84$		0			0
$85$	0.00895814	−	0.0123298i	0.000971646	−	0.00133736i
$86$	3.16528	+	5.29778i	0.341321	+	0.571274i
$87$		0			0
$88$	−4.18163	+	1.35870i	−0.445764	+	0.144837i
$89$	0.893615	−	0.381949i	0.0947230	−	0.0404865i	−0.345142	−	0.938551i	$-0.612169\pi$
$89$	0.893615	−	0.381949i	0.0947230	−	0.0404865i	0.439865	+	0.898064i	$0.355026\pi$
$90$		0			0
$91$	1.16415	+	5.10047i	0.122036	+	0.534674i
$92$	−1.76297	+	0.486548i	−0.183802	+	0.0507261i
$93$		0			0
$94$	1.96151	−	1.56425i	0.202314	−	0.161340i
$95$	0.0151199	+	0.167996i	0.00155127	+	0.0172360i
$96$		0			0
$97$	−1.89703	−	3.93922i	−0.192614	−	0.399967i	0.782187	−	0.623044i	$-0.214104\pi$
$97$	−1.89703	−	3.93922i	−0.192614	−	0.399967i	−0.974801	+	0.223077i	$0.928390\pi$
$98$	2.21752	−	8.03502i	0.224004	−	0.811659i
$99$		0			0
$100$	−2.30554	−	2.01429i	−0.230554	−	0.201429i
$101$	−3.38615	+	7.03141i	−0.336934	+	0.699651i	−0.998748	−	0.0500168i	$-0.984073\pi$
$101$	−3.38615	+	7.03141i	−0.336934	+	0.699651i	0.661814	+	0.749668i	$0.269787\pi$
$102$		0			0
$103$	0.492581	−	2.15814i	0.0485354	−	0.212648i	−0.944845	−	0.327517i	$-0.893788\pi$
$103$	0.492581	−	2.15814i	0.0485354	−	0.212648i	0.993381	+	0.114870i	$0.0366451\pi$
$104$	0.387234	+	8.62243i	0.0379714	+	0.845498i
$105$		0			0
$106$	−11.8344	−	7.81181i	−1.14946	−	0.758750i
$107$	−3.71233	−	2.45049i	−0.358885	−	0.236898i	0.358570	−	0.933503i	$-0.383264\pi$
$107$	−3.71233	−	2.45049i	−0.358885	−	0.236898i	−0.717455	+	0.696605i	$0.754693\pi$
$108$		0			0
$109$	−0.691135	−	15.3893i	−0.0661987	−	1.47403i	−0.707485	−	0.706728i	$-0.750170\pi$
$109$	−0.691135	−	15.3893i	−0.0661987	−	1.47403i	0.641286	−	0.767302i	$-0.278401\pi$
$110$	−0.0865258	+	0.379094i	−0.00824991	+	0.0361452i
$111$		0			0
$112$	−2.85869	+	5.93614i	−0.270121	+	0.560913i
$113$	−2.29435	−	2.00451i	−0.215834	−	0.188569i	0.543231	−	0.839583i	$-0.317201\pi$
$113$	−2.29435	−	2.00451i	−0.215834	−	0.188569i	−0.759065	+	0.651015i	$0.774344\pi$
$114$		0			0
$115$	0.0970966	−	0.351822i	0.00905431	−	0.0328075i
$116$	−0.374240	−	0.777118i	−0.0347473	−	0.0721536i
$117$		0			0
$118$	−0.00264946	−	0.0294379i	−0.000243902	−	0.00270998i
$119$	0.132042	−	0.105300i	0.0121043	−	0.00965285i
$120$		0			0
$121$	6.89187	−	1.90203i	0.626533	−	0.172912i
$122$	2.94099	+	12.8853i	0.266265	+	1.16658i
$123$		0			0
$124$	1.85263	−	0.791850i	0.166371	−	0.0711102i
$125$	1.16387	−	0.378165i	0.104100	−	0.0338241i
$126$		0			0
$127$	1.25868	+	2.10668i	0.111690	+	0.186937i	0.909190	−	0.416381i	$-0.136702\pi$
$127$	1.25868	+	2.10668i	0.111690	+	0.186937i	−0.797500	+	0.603319i	$0.793845\pi$
$128$	−8.00686	+	11.0205i	−0.707713	+	0.974084i
$129$		0			0
$130$	0.672169	+	0.361710i	0.0589531	+	0.0317240i
$131$	−4.23177	+	0.573233i	−0.369732	+	0.0500836i	−0.316743	−	0.948512i	$-0.602589\pi$
$131$	−4.23177	+	0.573233i	−0.369732	+	0.0500836i	−0.0529892	+	0.998595i	$0.516875\pi$
$132$		0			0
$133$	−0.333755	+	1.83914i	−0.0289403	+	0.159474i
$134$	12.0641	−	2.18930i	1.04218	−	0.189127i
$135$		0			0
$136$	0.245361	−	0.132034i	0.0210395	−	0.0113219i
$137$	−3.15800	+	2.29442i	−0.269806	+	0.196026i	−0.714459	−	0.699677i	$-0.753327\pi$
$137$	−3.15800	+	2.29442i	−0.269806	+	0.196026i	0.444653	+	0.895703i	$0.353327\pi$
$138$		0			0
$139$	1.39304	−	15.4780i	0.118156	−	1.31283i	−0.689979	−	0.723829i	$-0.742380\pi$
$139$	1.39304	−	15.4780i	0.118156	−	1.31283i	0.808136	−	0.588996i	$-0.200477\pi$
$140$	0.0563181	+	0.0853183i	0.00475975	+	0.00721071i
$141$		0			0
$142$	−3.41882	−	13.1877i	−0.286901	−	1.10669i
$143$			7.55863i			0.632084i
$144$		0			0
$145$	0.171437	+	0.0154296i	0.0142371	+	0.00128136i
$146$	−2.59880	−	1.11078i	−0.215079	−	0.0919290i
$147$		0			0
$148$	0.910299	+	1.69162i	0.0748261	+	0.139050i
$149$	2.53291	−	0.950617i	0.207504	−	0.0778776i	−0.245459	−	0.969407i	$-0.578939\pi$
$149$	2.53291	−	0.950617i	0.207504	−	0.0778776i	0.452963	+	0.891529i	$0.350367\pi$
$150$		0			0
$151$	−3.28431	−	0.596014i	−0.267273	−	0.0485029i	0.0432658	−	0.999064i	$-0.486224\pi$
$151$	−3.28431	−	0.596014i	−0.267273	−	0.0485029i	−0.310539	+	0.950561i	$0.600509\pi$
$152$	−1.08356	+	2.88713i	−0.0878881	+	0.234177i
$153$		0			0
$154$	−2.04189	+	3.79448i	−0.164541	+	0.305768i
$155$	−0.0539712	+	0.398431i	−0.00433507	+	0.0320028i
$156$		0			0
$157$	17.0979	−	10.2155i	1.36456	−	0.815288i	0.371006	−	0.928631i	$-0.379013\pi$
$157$	17.0979	−	10.2155i	1.36456	−	0.815288i	0.993556	+	0.113343i	$0.0361558\pi$
$158$	−9.26295	+	8.85628i	−0.736920	+	0.704568i
$159$		0			0
$160$	0.161949	+	0.378899i	0.0128032	+	0.0299546i
$161$	2.07441	−	3.47198i	0.163487	−	0.273630i
$162$		0			0
$163$	0.959841	+	3.47791i	0.0751806	+	0.272411i	0.991882	−	0.127162i	$-0.0405870\pi$
$163$	0.959841	+	3.47791i	0.0751806	+	0.272411i	−0.916701	+	0.399573i	$0.869158\pi$
$164$	−4.12804	+	3.60656i	−0.322346	+	0.281625i
$165$		0			0
$166$	−17.5169	+	1.57655i	−1.35958	+	0.122364i
$167$	5.88615	+	1.91253i	0.455484	+	0.147996i	0.527768	−	0.849388i	$-0.323029\pi$
$167$	5.88615	+	1.91253i	0.455484	+	0.147996i	−0.0722845	+	0.997384i	$0.523029\pi$
$168$		0			0
$169$	1.77159	+	0.488928i	0.136276	+	0.0376098i
$170$	0.00110553	−	0.0246165i	8.47902e−5	−	0.00188800i
$171$		0			0
$172$	2.11202	+	1.01709i	0.161040	+	0.0775527i
$173$	−13.4013	+	14.0166i	−1.01888	+	1.06566i	−0.0210528	+	0.999778i	$0.506702\pi$
$173$	−13.4013	+	14.0166i	−1.01888	+	1.06566i	−0.997827	+	0.0658865i	$0.979012\pi$
$174$		0			0
$175$	6.76361	−	0.303754i	0.511281	−	0.0229616i
$176$	−5.93511	+	7.44240i	−0.447376	+	0.560992i
$177$		0			0
$178$	0.865607	−	1.31134i	0.0648800	−	0.0982890i
$179$	12.4457	+	9.92508i	0.930232	+	0.741835i	0.966274	−	0.257515i	$-0.0829038\pi$
$179$	12.4457	+	9.92508i	0.930232	+	0.741835i	−0.0360426	+	0.999350i	$0.511475\pi$
$180$		0			0
$181$	−11.3678	−	2.59461i	−0.844958	−	0.192856i	−0.221937	−	0.975061i	$-0.571238\pi$
$181$	−11.3678	−	2.59461i	−0.844958	−	0.192856i	−0.623021	+	0.782205i	$0.714095\pi$
$182$	6.11389	+	5.84548i	0.453192	+	0.433296i
$183$		0			0
$184$	4.39013	−	5.02491i	0.323645	−	0.370442i
$185$	−0.382972	−	0.0171993i	−0.0281567	−	0.00126452i
$186$		0			0
$187$	0.219844	−	0.105871i	0.0160766	−	0.00774208i
$188$	0.294487	−	0.906339i	0.0214777	−	0.0661016i
$189$		0			0
$190$	0.170038	+	0.213221i	0.0123358	+	0.0154687i
$191$	8.85608	+	10.1366i	0.640804	+	0.733459i	0.978145	−	0.207923i	$-0.0666705\pi$
$191$	8.85608	+	10.1366i	0.640804	+	0.733459i	−0.337341	+	0.941382i	$0.609528\pi$
$192$		0			0
$193$	1.46536	−	0.334458i	0.105479	−	0.0240748i	−0.169456	−	0.985538i	$-0.554201\pi$
$193$	1.46536	−	0.334458i	0.105479	−	0.0240748i	0.274934	+	0.961463i	$0.411344\pi$
$194$	−6.06848	−	3.62575i	−0.435692	−	0.260314i
$195$		0			0
$196$	−0.978401	−	3.01121i	−0.0698858	−	0.215086i
$197$	−6.02619	−	6.30290i	−0.429348	−	0.449063i	0.472361	−	0.881405i	$-0.343402\pi$
$197$	−6.02619	−	6.30290i	−0.429348	−	0.449063i	−0.901710	+	0.432342i	$0.857687\pi$
$198$		0			0
$199$	−15.1791	−	11.0282i	−1.07602	−	0.781772i	−0.0990323	−	0.995084i	$-0.531575\pi$
$199$	−15.1791	−	11.0282i	−1.07602	−	0.781772i	−0.976984	+	0.213313i	$0.931575\pi$
$200$	11.0687	+	1.49936i	0.782676	+	0.106021i
$201$		0			0
$202$	1.69378	+	12.5040i	0.119174	+	0.879779i
$203$	1.78584	+	0.670235i	0.125341	+	0.0470413i
$204$		0			0
$205$	−0.195327	−	1.07634i	−0.0136423	−	0.0751750i
$206$	−1.25760	−	3.35086i	−0.0876211	−	0.233466i
$207$		0			0
$208$	10.9836	+	15.1177i	0.761577	+	1.04822i
$209$	−1.06140	+	2.48326i	−0.0734183	+	0.171771i
$210$		0			0
$211$	11.1710	−	7.37393i	0.769046	−	0.507643i	−0.104417	−	0.994534i	$-0.533298\pi$
$211$	11.1710	−	7.37393i	0.769046	−	0.507643i	0.873463	+	0.486891i	$0.161869\pi$
$212$	−5.38628			−0.369931
$213$		0			0
$214$	−7.19197			−0.491633
$215$	−0.390419	+	0.257713i	−0.0266264	+	0.0175759i
$216$		0			0
$217$	−1.75115	+	4.09701i	−0.118876	+	0.278123i
$218$	−14.6400	−	20.1502i	−0.991545	−	1.36474i
$219$		0			0
$220$	0.0518983	+	0.138283i	0.00349898	+	0.00932301i
$221$	−0.0855281	−	0.471299i	−0.00575324	−	0.0317030i
$222$		0			0
$223$	14.9844	+	5.62375i	1.00343	+	0.376594i	0.798378	−	0.602157i	$-0.205692\pi$
$223$	14.9844	+	5.62375i	1.00343	+	0.376594i	0.205053	+	0.978751i	$0.434263\pi$
$224$	0.612941	+	4.52491i	0.0409539	+	0.302334i
$225$		0			0
$226$	−4.88136	−	0.661225i	−0.324703	−	0.0439840i
$227$	2.96735	+	2.15591i	0.196950	+	0.143093i	0.681890	−	0.731455i	$-0.261158\pi$
$227$	2.96735	+	2.15591i	0.196950	+	0.143093i	−0.484940	+	0.874548i	$0.661158\pi$
$228$		0			0
$229$	−5.39283	−	5.64046i	−0.356368	−	0.372732i	0.520171	−	0.854062i	$-0.325868\pi$
$229$	−5.39283	−	5.64046i	−0.356368	−	0.372732i	−0.876539	+	0.481330i	$0.840154\pi$
$230$	−0.182352	−	0.561221i	−0.0120239	−	0.0370058i
$231$		0			0
$232$	2.70147	+	1.61405i	0.177360	+	0.105968i
$233$	18.7793	−	4.28626i	1.23028	−	0.280802i	0.442502	−	0.896767i	$-0.354091\pi$
$233$	18.7793	−	4.28626i	1.23028	−	0.280802i	0.787773	+	0.615965i	$0.211234\pi$
$234$		0			0
$235$	0.125126	+	0.143219i	0.00816234	+	0.00934255i
$236$	−0.00699996	−	0.00877768i	−0.000455659	−	0.000571378i
$237$		0			0
$238$	0.0843815	−	0.259699i	0.00546964	−	0.0168338i
$239$	16.0662	−	7.73708i	1.03924	−	0.500470i	0.165164	−	0.986266i	$-0.447185\pi$
$239$	16.0662	−	7.73708i	1.03924	−	0.500470i	0.874072	+	0.485796i	$0.161470\pi$
$240$		0			0
$241$	−14.6712	−	0.658884i	−0.945055	−	0.0424425i	−0.432999	−	0.901395i	$-0.642545\pi$
$241$	−14.6712	−	0.658884i	−0.945055	−	0.0424425i	−0.512056	+	0.858952i	$0.671116\pi$
$242$	7.60549	−	8.70518i	0.488899	−	0.559590i
$243$		0			0
$244$	3.62866	+	3.46935i	0.232301	+	0.222103i
$245$	0.616007	+	0.140600i	0.0393553	+	0.00898258i
$246$		0			0
$247$	4.14474	+	3.30532i	0.263724	+	0.210313i
$248$	−4.04951	+	6.13474i	−0.257144	+	0.389556i
$249$		0			0
$250$	1.23365	−	1.54695i	0.0780232	−	0.0978379i
$251$	7.57456	−	0.340174i	0.478102	−	0.0214716i	0.195489	−	0.980706i	$-0.437370\pi$
$251$	7.57456	−	0.340174i	0.478102	−	0.0214716i	0.282612	+	0.959234i	$0.408799\pi$
$252$		0			0
$253$	4.03818	−	4.22361i	0.253878	−	0.265536i
$254$	3.57486	+	1.72156i	0.224306	+	0.108020i
$255$		0			0
$256$	−0.605314	+	13.4784i	−0.0378322	+	0.842398i
$257$	−19.1003	−	5.27136i	−1.19145	−	0.328818i	−0.386570	−	0.922260i	$-0.626340\pi$
$257$	−19.1003	−	5.27136i	−1.19145	−	0.328818i	−0.804877	+	0.593442i	$0.797769\pi$
$258$		0			0
$259$	−4.04028	−	1.31277i	−0.251051	−	0.0815714i
$260$	0.288774	−	0.0259901i	0.0179090	−	0.00161184i
$261$		0			0
$262$	−5.19963	+	4.54278i	−0.321234	+	0.280654i
$263$	−5.28921	−	19.1650i	−0.326146	−	1.18177i	−0.924705	−	0.380686i	$-0.875688\pi$
$263$	−5.28921	−	19.1650i	−0.326146	−	1.18177i	0.598558	−	0.801079i	$-0.295741\pi$
$264$		0			0
$265$	0.551315	−	0.922746i	0.0338670	−	0.0566839i
$266$	1.18778	+	2.77896i	0.0728276	+	0.170389i
$267$		0			0
$268$	3.36630	−	3.21851i	0.205629	−	0.196602i
$269$	16.1241	−	9.63368i	0.983101	−	0.587376i	0.0710590	−	0.997472i	$-0.477362\pi$
$269$	16.1241	−	9.63368i	0.983101	−	0.587376i	0.912042	+	0.410097i	$0.134505\pi$
$270$		0			0
$271$	−3.10436	+	22.9173i	−0.188576	+	1.39213i	0.611032	+	0.791606i	$0.290754\pi$
$271$	−3.10436	+	22.9173i	−0.188576	+	1.39213i	−0.799609	+	0.600521i	$0.794960\pi$
$272$	0.285856	−	0.531209i	0.0173325	−	0.0322093i
$273$		0			0
$274$	−2.21764	+	5.90887i	−0.133972	+	0.356968i
$275$	9.62465	+	1.74662i	0.580388	+	0.105325i
$276$		0			0
$277$	9.80903	−	3.68139i	0.589368	−	0.221193i	−0.0388317	−	0.999246i	$-0.512364\pi$
$277$	9.80903	−	3.68139i	0.589368	−	0.221193i	0.628199	+	0.778052i	$0.283792\pi$
$278$	−11.9066	−	22.1263i	−0.714113	−	1.32704i
$279$		0			0
$280$	−0.342966	−	0.146591i	−0.0204961	−	0.00876047i
$281$	−18.0037	−	1.62036i	−1.07401	−	0.0966627i	−0.461511	−	0.887134i	$-0.652693\pi$
$281$	−18.0037	−	1.62036i	−1.07401	−	0.0966627i	−0.612499	+	0.790472i	$0.709836\pi$
$282$		0			0
$283$			4.71181i			0.280088i	0.990145	+	0.140044i	$0.0447244\pi$
$283$			4.71181i			0.280088i	−0.990145	+	0.140044i	$0.955276\pi$
$284$	−3.84341	−	3.46523i	−0.228065	−	0.205623i
$285$		0			0
$286$	6.73253	+	10.1993i	0.398103	+	0.603100i
$287$	1.08664	−	12.0736i	0.0641423	−	0.712680i
$288$		0			0
$289$	13.7408	−	9.98326i	0.808281	−	0.587251i
$290$	0.245074	−	0.131880i	0.0143913	−	0.00774426i
$291$		0			0
$292$	−1.05628	+	0.191687i	−0.0618143	+	0.0112176i
$293$	0.0931304	−	0.513191i	0.00544074	−	0.0299809i	−0.981095	−	0.193527i	$-0.938007\pi$
$293$	0.0931304	−	0.513191i	0.00544074	−	0.0299809i	0.986536	+	0.163546i	$0.0522931\pi$
$294$		0			0
$295$	0.00222022		0.000300750i	0.000129266		1.75103e-5i
$296$	−6.17179	−	3.32118i	−0.358728	−	0.193040i
$297$		0			0
$298$	2.57110	−	3.53881i	0.148940	−	0.204998i
$299$	−5.88339	−	9.84714i	−0.340245	−	0.569475i
$300$		0			0
$301$	−4.93030	+	1.60195i	−0.284178	+	0.0923350i
$302$	−4.96260	+	2.12112i	−0.285566	+	0.122057i
$303$		0			0
$304$	1.48563	+	6.50899i	0.0852070	+	0.373316i
$305$	−0.965762	+	0.266533i	−0.0552994	+	0.0152617i
$306$		0			0
$307$	−7.67619	+	6.12155i	−0.438103	+	0.349376i	−0.817569	−	0.575830i	$-0.804679\pi$
$307$	−7.67619	+	6.12155i	−0.438103	+	0.349376i	0.379466	+	0.925206i	$0.376108\pi$
$308$	0.146717	+	1.63016i	0.00836001	+	0.0928873i
$309$		0			0
$310$	0.282059	+	0.585702i	0.0160199	+	0.0332656i
$311$	−0.472961	+	1.71374i	−0.0268191	+	0.0971770i	−0.976147	−	0.217110i	$-0.930337\pi$
$311$	−0.472961	+	1.71374i	−0.0268191	+	0.0971770i	0.949328	+	0.314287i	$0.101765\pi$
$312$		0			0
$313$	−0.718003	−	0.627300i	−0.0405839	−	0.0354571i	0.637408	−	0.770527i	$-0.280007\pi$
$313$	−0.718003	−	0.627300i	−0.0405839	−	0.0354571i	−0.677992	+	0.735069i	$0.737150\pi$
$314$	13.9723	−	29.0137i	0.788501	−	1.63734i
$315$		0			0
$316$	−1.08321	+	4.74586i	−0.0609354	+	0.266975i
$317$	−0.270941	−	6.03297i	−0.0152176	−	0.338845i	−0.992131	−	0.125208i	$-0.960040\pi$
$317$	−0.270941	−	6.03297i	−0.0152176	−	0.338845i	0.976913	−	0.213638i	$-0.0685312\pi$
$318$		0			0
$319$	2.29999	+	1.51821i	0.128775	+	0.0850035i
$320$	−0.436387	−	0.288056i	−0.0243948	−	0.0161028i
$321$		0			0
$322$	−0.293382	−	6.53267i	−0.0163496	−	0.364051i
$323$	0.0380818	−	0.166847i	0.00211893	−	0.00928362i
$324$		0			0
$325$	8.33147	−	17.3005i	0.462147	−	0.959658i
$326$	4.39298	+	3.83803i	0.243304	+	0.212569i
$327$		0			0
$328$	5.32057	−	19.2787i	0.293779	−	1.06449i
$329$	0.914402	+	1.89878i	0.0504126	+	0.104683i
$330$		0			0
$331$	2.53644	+	28.1822i	0.139415	+	1.54903i	0.695878	+	0.718160i	$0.255015\pi$
$331$	2.53644	+	28.1822i	0.139415	+	1.54903i	−0.556462	+	0.830873i	$0.687842\pi$
$332$	−5.22314	+	4.16531i	−0.286657	+	0.228601i
$333$		0			0
$334$	9.64607	−	2.66214i	0.527809	−	0.145666i
$335$	0.206817	+	0.906126i	0.0112996	+	0.0495069i
$336$		0			0
$337$	−20.2363	+	8.64943i	−1.10234	+	0.471164i	−0.865767	−	0.500448i	$-0.833169\pi$
$337$	−20.2363	+	8.64943i	−1.10234	+	0.471164i	−0.236578	+	0.971613i	$0.576026\pi$
$338$	2.82601	−	0.918228i	0.153715	−	0.0499450i
$339$		0			0
$340$	−0.00480070	−	0.00803501i	−0.000260354	−	0.000435760i
$341$	−3.78378	+	5.20793i	−0.204903	+	0.282025i
$342$		0			0
$343$	14.5378	+	7.82311i	0.784966	+	0.422408i
$344$	−8.47516	+	1.14804i	−0.456950	+	0.0618981i
$345$		0			0
$346$	−5.59848	+	30.8502i	−0.300976	+	1.65852i
$347$	19.5301	−	3.54419i	1.04843	−	0.190262i	0.373111	−	0.927787i	$-0.378291\pi$
$347$	19.5301	−	3.54419i	1.04843	−	0.190262i	0.675320	+	0.737525i	$0.264005\pi$
$348$		0			0
$349$	−6.82002	+	3.67001i	−0.365067	+	0.196451i	−0.646110	−	0.763244i	$-0.723605\pi$
$349$	−6.82002	+	3.67001i	−0.365067	+	0.196451i	0.281043	+	0.959695i	$0.409320\pi$
$350$	8.85602	−	6.43428i	0.473374	−	0.343926i
$351$		0			0
$352$	−0.591374	+	6.57071i	−0.0315204	+	0.350220i
$353$	3.58519	+	5.43134i	0.190821	+	0.289081i	0.917372	−	0.398032i	$-0.130307\pi$
$353$	3.58519	+	5.43134i	0.190821	+	0.289081i	−0.726551	+	0.687112i	$0.758878\pi$
$354$		0			0
$355$	0.987037	−	0.303746i	0.0523865	−	0.0161212i
$356$		−	0.596841i		−	0.0316325i
$357$		0			0
$358$	25.6341	+	2.30711i	1.35480	+	0.121934i
$359$	17.8481	+	7.62863i	0.941985	+	0.402624i	0.808546	−	0.588433i	$-0.200255\pi$
$359$	17.8481	+	7.62863i	0.941985	+	0.402624i	0.133439	+	0.991057i	$0.457398\pi$
$360$		0			0
$361$	−8.10596	−	15.0634i	−0.426629	−	0.792810i
$362$	−17.6503	+	6.62427i	−0.927679	+	0.348164i
$363$		0			0
$364$	3.16137	+	0.573703i	0.165701	+	0.0300702i
$365$	0.0752777	−	0.200577i	0.00394021	−	0.0104987i
$366$		0			0
$367$	−8.79281	+	16.3398i	−0.458981	+	0.852930i	0.540949	+	0.841056i	$0.318065\pi$
$367$	−8.79281	+	16.3398i	−0.458981	+	0.852930i	−0.999930	+	0.0118739i	$0.996220\pi$
$368$	1.93915	−	14.3154i	0.101085	−	0.746243i
$369$		0			0
$370$	−0.532089	+	0.317908i	−0.0276620	+	0.0165273i
$371$	8.60961	−	8.23163i	0.446989	−	0.427365i
$372$		0			0
$373$	−7.74367	−	18.1172i	−0.400952	−	0.938074i	−0.991384	−	0.130987i	$-0.958186\pi$
$373$	−7.74367	−	18.1172i	−0.400952	−	0.938074i	0.590432	−	0.807087i	$-0.298957\pi$
$374$	0.202349	−	0.338676i	0.0104632	−	0.0175125i
$375$		0			0
$376$	0.924986	+	3.35161i	0.0477025	+	0.172846i
$377$	4.07404	−	3.55938i	0.209824	−	0.183318i
$378$		0			0
$379$	1.61232	−	0.145112i	0.0828194	−	0.00745388i	−0.0481521	−	0.998840i	$-0.515333\pi$
$379$	1.61232	−	0.145112i	0.0828194	−	0.00745388i	0.130971	+	0.991386i	$0.458190\pi$
$380$	0.0985214	+	0.0320115i	0.00505404	+	0.00164216i
$381$		0			0
$382$	20.9789	+	5.78980i	1.07337	+	0.296232i
$383$	0.943901	−	21.0176i	0.0482311	−	1.07395i	−0.818289	−	0.574807i	$-0.805077\pi$
$383$	0.943901	−	21.0176i	0.0482311	−	1.07395i	0.866520	−	0.499142i	$-0.166351\pi$
$384$		0			0
$385$	−0.294288	−	0.141721i	−0.0149983	−	0.00722279i
$386$	1.67940	−	1.75651i	0.0854791	−	0.0894041i
$387$		0			0
$388$	−2.68248	+	0.120470i	−0.136182	+	0.00611595i
$389$	9.19482	−	11.5299i	0.466196	−	0.584591i	−0.492039	−	0.870573i	$-0.663748\pi$
$389$	9.19482	−	11.5299i	0.466196	−	0.584591i	0.958235	+	0.285982i	$0.0923198\pi$
$390$		0			0
$391$	−0.203999	+	0.309045i	−0.0103167	+	0.0156291i
$392$	9.03143	+	7.20232i	0.456156	+	0.363772i
$393$		0			0
$394$	−13.7456	−	3.13734i	−0.692492	−	0.158057i
$395$	−0.702160	−	0.671333i	−0.0353295	−	0.0337784i
$396$		0			0
$397$	3.56513	−	4.08062i	0.178929	−	0.204800i	−0.656613	−	0.754228i	$-0.728011\pi$
$397$	3.56513	−	4.08062i	0.178929	−	0.204800i	0.835541	+	0.549428i	$0.185154\pi$
$398$	−30.3051	−	1.36100i	−1.51906	−	0.0682209i
$399$		0			0
$400$	21.7879	−	10.4925i	1.08939	−	0.524624i
$401$	−11.6396	+	35.8231i	−0.581256	+	1.78892i	0.0325564	+	0.999470i	$0.489635\pi$
$401$	−11.6396	+	35.8231i	−0.581256	+	1.78892i	−0.613812	+	0.789452i	$0.710365\pi$
$402$		0			0
$403$	7.87887	+	9.87979i	0.392475	+	0.492148i
$404$	3.15349	+	3.60946i	0.156892	+	0.179577i
$405$		0			0
$406$	3.00673	−	0.686266i	0.149221	−	0.0340588i
$407$	−5.26896	−	3.14806i	−0.261173	−	0.156043i
$408$		0			0
$409$	−7.38529	−	22.7296i	−0.365179	−	1.12391i	−0.949869	−	0.312649i	$-0.898784\pi$
$409$	−7.38529	−	22.7296i	−0.365179	−	1.12391i	0.584689	−	0.811257i	$-0.301216\pi$
$410$	−1.22228	−	1.27840i	−0.0603639	−	0.0631357i
$411$		0			0
$412$	−1.09986	−	0.799095i	−0.0541862	−	0.0393686i
$413$	0.0246035	+	0.00333277i	0.00121066	+	0.000163995i
$414$		0			0
$415$	−0.178960	−	1.32114i	−0.00878482	−	0.0648522i
$416$	12.1248	+	4.55053i	0.594469	+	0.223108i
$417$		0			0
$418$	0.779648	+	4.29622i	0.0381338	+	0.210135i
$419$	−9.05009	−	24.1139i	−0.442126	−	1.17804i	−0.948793	−	0.315899i	$-0.897694\pi$
$419$	−9.05009	−	24.1139i	−0.442126	−	1.17804i	0.506667	−	0.862142i	$-0.330877\pi$
$420$		0			0
$421$	17.8122	+	24.5163i	0.868111	+	1.19485i	0.979574	+	0.201084i	$0.0644464\pi$
$421$	17.8122	+	24.5163i	0.868111	+	1.19485i	−0.111463	+	0.993769i	$0.535554\pi$
$422$	8.50578	−	19.9003i	0.414055	−	0.968730i
$423$		0			0
$424$	16.4007	−	10.8260i	0.796489	−	0.525757i
$425$	−0.619884			−0.0300688
$426$		0			0
$427$	−11.1022			−0.537275
$428$	−2.27992	+	1.50496i	−0.110204	+	0.0727452i
$429$		0			0
$430$	−0.297270	+	0.695499i	−0.0143357	+	0.0335399i
$431$	14.8993	+	20.5072i	0.717676	+	0.987797i	0.999598	+	0.0283593i	$0.00902825\pi$
$431$	14.8993	+	20.5072i	0.717676	+	0.987797i	−0.281921	+	0.959437i	$0.590972\pi$
$432$		0			0
$433$	−2.04574	−	5.45086i	−0.0983121	−	0.261952i	0.877872	−	0.478895i	$-0.158963\pi$
$433$	−2.04574	−	5.45086i	−0.0983121	−	0.261952i	−0.976184	+	0.216944i	$0.930391\pi$
$434$	1.28630	+	7.08812i	0.0617446	+	0.340241i
$435$		0			0
$436$	−8.85758	−	3.32430i	−0.424201	−	0.159205i
$437$	−0.550136	−	4.06127i	−0.0263166	−	0.194277i
$438$		0			0
$439$	4.64674	+	0.629444i	0.221777	+	0.0300417i	0.244279	−	0.969705i	$-0.421449\pi$
$439$	4.64674	+	0.629444i	0.221777	+	0.0300417i	−0.0225017	+	0.999747i	$0.507163\pi$
$440$	−0.435963	−	0.316745i	−0.0207837	−	0.0151002i
$441$		0			0
$442$	−0.535198	−	0.559773i	−0.0254568	−	0.0266257i
$443$	11.4985	+	35.3888i	0.546312	+	1.68137i	0.717851	+	0.696197i	$0.245126\pi$
$443$	11.4985	+	35.3888i	0.546312	+	1.68137i	−0.171539	+	0.985177i	$0.554874\pi$
$444$		0			0
$445$	0.102247	+	0.0610899i	0.00484698	+	0.00289594i
$446$	25.2286	−	5.75826i	1.19461	−	0.272661i
$447$		0			0
$448$	−3.81236	−	4.36359i	−0.180117	−	0.206160i
$449$	18.4743	+	23.1661i	0.871858	+	1.09328i	0.994899	+	0.100874i	$0.0321639\pi$
$449$	18.4743	+	23.1661i	0.871858	+	1.09328i	−0.123041	+	0.992402i	$0.539265\pi$
$450$		0			0
$451$	5.41221	−	16.6571i	0.254851	−	0.784351i
$452$	−1.68580	+	0.811840i	−0.0792935	+	0.0381857i
$453$		0			0
$454$	5.92433	+	0.266062i	0.278042	+	0.0124869i
$455$	−0.421866	+	0.482865i	−0.0197774	+	0.0226371i
$456$		0			0
$457$	−11.6899	−	11.1766i	−0.546828	−	0.522821i	0.366298	−	0.930497i	$-0.380625\pi$
$457$	−11.6899	−	11.1766i	−0.546828	−	0.522821i	−0.913127	+	0.407676i	$0.866339\pi$
$458$	−12.3009	−	2.80760i	−0.574783	−	0.131191i
$459$		0			0
$460$	−0.175246	−	0.139754i	−0.00817090	−	0.00651607i
$461$	−14.8709	+	22.5285i	−0.692607	+	1.04926i	0.302756	+	0.953068i	$0.402093\pi$
$461$	−14.8709	+	22.5285i	−0.692607	+	1.04926i	−0.995363	+	0.0961871i	$0.969335\pi$
$462$		0			0
$463$	−20.4075	+	25.5902i	−0.948416	+	1.18928i	0.0334003	+	0.999442i	$0.489366\pi$
$463$	−20.4075	+	25.5902i	−0.948416	+	1.18928i	−0.981816	+	0.189834i	$0.939205\pi$
$464$	6.80626	−	0.305669i	0.315973	−	0.0141903i
$465$		0			0
$466$	21.5224	−	22.5106i	0.997005	−	1.04279i
$467$	−4.23226	−	2.03815i	−0.195846	−	0.0943142i	0.333391	−	0.942789i	$-0.391807\pi$
$467$	−4.23226	−	2.03815i	−0.195846	−	0.0943142i	−0.529236	+	0.848475i	$0.677521\pi$
$468$		0			0
$469$	−0.462086	+	10.2891i	−0.0213371	+	0.475108i
$470$	0.296407	+	0.0818032i	0.0136722	+	0.00377330i
$471$		0			0
$472$	0.0389566	+	0.0126578i	0.00179312	+	0.000582622i
$473$	−7.45968	+	0.671384i	−0.342997	+	0.0308703i
$474$		0			0
$475$	5.16653	−	4.51386i	0.237057	−	0.207110i
$476$	−0.0275940	−	0.0999846i	−0.00126477	−	0.00458279i
$477$		0			0
$478$	14.7877	−	24.7504i	0.676374	−	1.13206i
$479$	16.7303	+	39.1425i	0.764427	+	1.78847i	0.596405	+	0.802684i	$0.296595\pi$
$479$	16.7303	+	39.1425i	0.764427	+	1.78847i	0.168022	+	0.985783i	$0.446262\pi$
$480$		0			0
$481$	−8.70869	+	8.32636i	−0.397082	+	0.379649i
$482$	−20.3837	+	12.1787i	−0.928451	+	0.554724i
$483$		0			0
$484$	0.589400	−	4.35112i	0.0267909	−	0.197778i
$485$	0.253928	−	0.471877i	0.0115303	−	0.0214268i
$486$		0			0
$487$	−3.25884	+	8.68316i	−0.147672	+	0.393471i	−0.989167	−	0.146794i	$-0.953105\pi$
$487$	−3.25884	+	8.68316i	−0.147672	+	0.393471i	0.841495	+	0.540265i	$0.181676\pi$
$488$	−18.0220	−	3.27052i	−0.815819	−	0.148049i
$489$		0			0
$490$	0.956452	−	0.358962i	0.0432081	−	0.0162163i
$491$	−4.55749	−	8.46924i	−0.205677	−	0.382211i	0.756770	−	0.653681i	$-0.226776\pi$
$491$	−4.55749	−	8.46924i	−0.205677	−	0.382211i	−0.962447	+	0.271469i	$0.912490\pi$
$492$		0			0
$493$	−0.160589	−	0.0686391i	−0.00723257	−	0.00309135i
$494$	8.53685	+	0.768330i	0.384091	+	0.0345688i
$495$		0			0
$496$			15.9144i			0.714580i
$497$	11.4392	−	0.334797i	0.513118	−	0.0150177i
$498$		0			0
$499$	19.8697	+	30.1014i	0.889492	+	1.34752i	0.937248	+	0.348663i	$0.113364\pi$
$499$	19.8697	+	30.1014i	0.889492	+	1.34752i	−0.0477566	+	0.998859i	$0.515207\pi$
$500$	0.0673706	−	0.748549i	0.00301291	−	0.0334761i
$501$		0			0
$502$	9.91785	−	7.20574i	0.442655	−	0.321608i
$503$	−19.5990	+	10.5467i	−0.873878	+	0.470254i	−0.848359	−	0.529421i	$-0.822409\pi$
$503$	−19.5990	+	10.5467i	−0.873878	+	0.470254i	−0.0255183	+	0.999674i	$0.508124\pi$
$504$		0			0
$505$	−0.941127	+	0.170789i	−0.0418796	+	0.00760003i
$506$	1.68698	−	9.29603i	0.0749954	−	0.413259i
$507$		0			0
$508$	1.49351	−	0.202310i	0.0662638	−	0.00897605i
$509$	−3.00844	−	1.61891i	−0.133347	−	0.0717570i	0.405835	−	0.913946i	$-0.366981\pi$
$509$	−3.00844	−	1.61891i	−0.133347	−	0.0717570i	−0.539182	+	0.842189i	$0.681266\pi$
$510$		0			0
$511$	1.39545	−	1.92067i	0.0617311	−	0.0849656i
$512$	−2.78501	−	4.66132i	−0.123081	−	0.206003i
$513$		0			0
$514$	−30.4686	+	9.89984i	−1.34391	+	0.436663i
$515$	0.249473	−	0.106630i	0.0109931	−	0.00469867i
$516$		0			0
$517$	0.677548	+	2.96853i	0.0297985	+	0.130556i
$518$	−6.62111	+	1.82731i	−0.290915	+	0.0802874i
$519$		0			0
$520$	−0.827050	+	0.659551i	−0.0362686	+	0.0289232i
$521$	3.22210	+	35.8005i	0.141163	+	1.56845i	0.684551	+	0.728965i	$0.259998\pi$
$521$	3.22210	+	35.8005i	0.141163	+	1.56845i	−0.543388	+	0.839482i	$0.682859\pi$
$522$		0			0
$523$	5.27997	+	10.9640i	0.230877	+	0.479421i	0.983934	−	0.178535i	$-0.0571356\pi$
$523$	5.27997	+	10.9640i	0.230877	+	0.479421i	−0.753057	+	0.657956i	$0.771421\pi$
$524$	−0.697727	+	2.52816i	−0.0304804	+	0.110443i
$525$		0			0
$526$	−24.2075	−	21.1495i	−1.05550	−	0.922160i
$527$	0.176999	−	0.367542i	0.00771019	−	0.0160104i
$528$		0			0
$529$	3.14469	−	13.7778i	0.136726	−	0.599034i
$530$	−0.0779721	−	1.73618i	−0.00338689	−	0.0754150i
$531$		0			0
$532$	0.958053	+	0.632405i	0.0415368	+	0.0274182i
$533$	−28.6935	−	18.9404i	−1.24286	−	0.820402i
$534$		0			0
$535$	−0.0244591	−	0.544624i	−0.00105746	−	0.0235462i
$536$	−3.78109	+	16.5660i	−0.163318	+	0.715544i
$537$		0			0
$538$	13.1764	−	27.3612i	0.568077	−	1.17962i
$539$	7.61825	+	6.65587i	0.328141	+	0.286688i
$540$		0			0
$541$	4.91833	−	17.8212i	0.211456	−	0.766192i	−0.778841	−	0.627222i	$-0.784192\pi$
$541$	4.91833	−	17.8212i	0.211456	−	0.766192i	0.990296	−	0.138971i	$-0.0443794\pi$
$542$	16.2237	+	33.6889i	0.696868	+	1.44706i
$543$		0			0
$544$	−0.0374759	−	0.416391i	−0.00160676	−	0.0178526i
$545$	1.47612	−	1.17717i	0.0632301	−	0.0504243i
$546$		0			0
$547$	9.09893	−	2.51114i	0.389042	−	0.107369i	−0.0660430	−	0.997817i	$-0.521037\pi$
$547$	9.09893	−	2.51114i	0.389042	−	0.107369i	0.455085	+	0.890448i	$0.349609\pi$
$548$	0.533456	+	2.33722i	0.0227881	+	0.0998412i
$549$		0			0
$550$	14.5429	−	6.21593i	0.620111	−	0.265048i
$551$	1.83827	−	0.597291i	0.0783130	−	0.0254454i
$552$		0			0
$553$	−5.52146	−	9.24136i	−0.234796	−	0.392983i
$554$	9.95693	−	13.7045i	0.423029	−	0.582250i
$555$		0			0
$556$	−8.40458	−	4.52270i	−0.356433	−	0.191805i
$557$	13.3198	−	1.80429i	0.564378	−	0.0764503i	0.153514	−	0.988147i	$-0.450941\pi$
$557$	13.3198	−	1.80429i	0.564378	−	0.0764503i	0.410865	+	0.911696i	$0.365227\pi$
$558$		0			0
$559$	−2.62528	+	14.4665i	−0.111038	+	0.611868i
$560$	−0.794530	+	0.144186i	−0.0335750	+	0.00609297i
$561$		0			0
$562$	−25.7368	+	13.8496i	−1.08564	+	0.584209i
$563$	−13.2351	+	9.61583i	−0.557791	+	0.405259i	−0.830650	−	0.556795i	$-0.812031\pi$
$563$	−13.2351	+	9.61583i	−0.557791	+	0.405259i	0.272859	+	0.962054i	$0.412031\pi$
$564$		0			0
$565$	0.0334714	−	0.371898i	0.00140815	−	0.0156459i
$566$	4.19685	+	6.35795i	0.176407	+	0.267245i
$567$		0			0
$568$	18.6677	+	2.82631i	0.783277	+	0.118589i
$569$			11.8427i			0.496473i	0.968699	+	0.248237i	$0.0798510\pi$
$569$			11.8427i			0.496473i	−0.968699	+	0.248237i	$0.920149\pi$
$570$		0			0
$571$	−32.3381	−	2.91048i	−1.35331	−	0.121800i	−0.610878	−	0.791725i	$-0.709183\pi$
$571$	−32.3381	−	2.91048i	−1.35331	−	0.121800i	−0.742428	+	0.669925i	$0.766326\pi$
$572$	4.26855	+	1.82447i	0.178477	+	0.0762848i
$573$		0			0
$574$	−9.28775	−	17.2595i	−0.387663	−	0.720399i
$575$	−13.8982	+	5.21608i	−0.579595	+	0.217526i
$576$		0			0
$577$	−35.4767	−	6.43807i	−1.47691	−	0.268020i	−0.620457	−	0.784240i	$-0.713053\pi$
$577$	−35.4767	−	6.43807i	−1.47691	−	0.268020i	−0.856456	+	0.516220i	$0.827339\pi$
$578$	9.64916	−	25.7101i	0.401352	−	1.06940i
$579$		0			0
$580$	0.0500942	−	0.0930906i	0.00208005	−	0.00386538i
$581$	1.98316	−	14.6403i	0.0822753	−	0.607381i
$582$		0			0
$583$	14.7737	−	8.82685i	0.611863	−	0.365571i
$584$	2.83100	−	2.70672i	0.117148	−	0.112005i
$585$		0			0
$586$	−0.331437	−	0.775434i	−0.0136915	−	0.0320329i
$587$	5.98633	−	10.0194i	0.247082	−	0.413546i	−0.709633	−	0.704571i	$-0.751139\pi$
$587$	5.98633	−	10.0194i	0.247082	−	0.413546i	0.956715	+	0.291025i	$0.0939964\pi$
$588$		0			0
$589$	1.20113	+	4.35220i	0.0494918	+	0.179329i
$590$	0.00272801	−	0.00238339i	0.000112311	−	9.81227e-5i
$591$		0			0
$592$	−15.1127	+	1.36017i	−0.621129	+	0.0559026i
$593$	−42.0603	−	13.6662i	−1.72721	−	0.561204i	−0.734166	−	0.678970i	$-0.762427\pi$
$593$	−42.0603	−	13.6662i	−1.72721	−	0.561204i	−0.993041	+	0.117766i	$0.962427\pi$
$594$		0			0
$595$	0.0199532	+	0.00550672i	0.000818000	+	0.000225754i
$596$	0.0745443	−	1.65986i	0.00305345	−	0.0679904i
$597$		0			0
$598$	−16.7098	−	8.04700i	−0.683313	−	0.329066i
$599$	−11.6052	+	12.1381i	−0.474176	+	0.495950i	−0.916014	−	0.401145i	$-0.868612\pi$
$599$	−11.6052	+	12.1381i	−0.474176	+	0.495950i	0.441838	+	0.897095i	$0.354327\pi$
$600$		0			0
$601$	−34.5086	+	1.54978i	−1.40764	+	0.0632170i	−0.735658	−	0.677354i	$-0.763127\pi$
$601$	−34.5086	+	1.54978i	−1.40764	+	0.0632170i	−0.671978	+	0.740571i	$0.734555\pi$
$602$	−5.22590	+	6.55308i	−0.212992	+	0.267083i
$603$		0			0
$604$	−1.12934	+	1.71087i	−0.0459520	+	0.0696143i
$605$	0.685080	+	0.546333i	0.0278525	+	0.0222116i
$606$		0			0
$607$	−36.6389	−	8.36258i	−1.48713	−	0.339427i	−0.599643	−	0.800268i	$-0.704691\pi$
$607$	−36.6389	−	8.36258i	−1.48713	−	0.339427i	−0.887483	+	0.460841i	$0.847548\pi$
$608$	3.34442	+	3.19759i	0.135634	+	0.129679i
$609$		0			0
$610$	−1.06576	+	1.21986i	−0.0431514	+	0.0493908i
$611$	5.97116	+	0.268165i	0.241567	+	0.0108488i
$612$		0			0
$613$	41.5358	−	20.0026i	1.67761	−	0.807896i	0.680438	−	0.732806i	$-0.261790\pi$
$613$	41.5358	−	20.0026i	1.67761	−	0.807896i	0.997177	−	0.0750905i	$-0.0239246\pi$
$614$	−4.90546	+	15.0975i	−0.197968	+	0.609284i
$615$		0			0
$616$	−3.72324	−	4.66880i	−0.150014	−	0.188111i
$617$	−7.01772	−	8.03243i	−0.282523	−	0.323373i	0.594248	−	0.804282i	$-0.297450\pi$
$617$	−7.01772	−	8.03243i	−0.282523	−	0.323373i	−0.876771	+	0.480908i	$0.840307\pi$
$618$		0			0
$619$	−44.0783	+	10.0606i	−1.77166	+	0.404369i	−0.978763	−	0.204993i	$-0.934283\pi$
$619$	−44.0783	+	10.0606i	−1.77166	+	0.404369i	−0.792892	+	0.609362i	$0.791426\pi$
$620$	0.211977	+	0.126650i	0.00851321	+	0.00508641i
$621$		0			0
$622$	0.888241	+	2.73372i	0.0356152	+	0.109612i
$623$	0.912127	+	0.954010i	0.0365436	+	0.0382216i
$624$		0			0
$625$	−20.0433	−	14.5623i	−0.801733	−	0.582493i
$626$	−1.52759	−	0.206926i	−0.0610547	−	0.00827043i
$627$		0			0
$628$	−1.64196	−	12.1214i	−0.0655212	−	0.483697i
$629$	0.364154	+	0.136669i	0.0145198	+	0.00544936i
$630$		0			0
$631$	1.15304	+	6.35378i	0.0459019	+	0.252940i	0.998719	−	0.0506057i	$-0.0161152\pi$
$631$	1.15304	+	6.35378i	0.0459019	+	0.252940i	−0.952817	+	0.303546i	$0.901829\pi$
$632$	−6.24053	−	16.6278i	−0.248235	−	0.661420i
$633$		0			0
$634$	−5.73921	−	7.89935i	−0.227933	−	0.313723i
$635$	−0.118210	+	0.276567i	−0.00469104	+	0.0109752i
$636$		0			0
$637$	16.5734	−	10.9400i	0.656661	−	0.433458i
$638$	4.45581			0.176407
$639$		0			0
$640$	−1.66954			−0.0659942
$641$	−6.36695	+	4.20279i	−0.251479	+	0.166000i	−0.670348	−	0.742047i	$-0.733855\pi$
$641$	−6.36695	+	4.20279i	−0.251479	+	0.166000i	0.418869	+	0.908047i	$0.362427\pi$
$642$		0			0
$643$	1.07508	−	2.51528i	0.0423972	−	0.0991931i	−0.896991	−	0.442049i	$-0.854252\pi$
$643$	1.07508	−	2.51528i	0.0423972	−	0.0991931i	0.939388	+	0.342856i	$0.111394\pi$
$644$	−1.46001	−	2.00953i	−0.0575323	−	0.0791864i
$645$		0			0
$646$	−0.0972259	−	0.259057i	−0.00382530	−	0.0101925i
$647$	3.46271	+	19.0811i	0.136133	+	0.750156i	0.977701	+	0.210004i	$0.0673476\pi$
$647$	3.46271	+	19.0811i	0.136133	+	0.750156i	−0.841567	+	0.540152i	$0.818367\pi$
$648$		0			0
$649$	0.0335843	+	0.0126044i	0.00131830	+	0.000494765i
$650$	−4.16748	−	30.7656i	−0.163462	−	1.20673i
$651$		0			0
$652$	2.19575	+	0.297434i	0.0859921	+	0.0116484i
$653$	−17.2227	−	12.5130i	−0.673978	−	0.489673i	0.197377	−	0.980328i	$-0.436758\pi$
$653$	−17.2227	−	12.5130i	−0.673978	−	0.489673i	−0.871354	+	0.490654i	$0.836758\pi$
$654$		0			0
$655$	−0.361693	−	0.378301i	−0.0141325	−	0.0147815i
$656$	−13.3801	−	41.1797i	−0.522405	−	1.60780i
$657$		0			0
$658$	2.92512	+	1.74768i	0.114033	+	0.0681315i
$659$	32.2782	−	7.36728i	1.25738	−	0.286988i	0.458616	−	0.888635i	$-0.348345\pi$
$659$	32.2782	−	7.36728i	1.25738	−	0.286988i	0.798763	+	0.601646i	$0.205488\pi$
$660$		0			0
$661$	3.69605	+	4.23047i	0.143760	+	0.164546i	0.820444	−	0.571727i	$-0.193727\pi$
$661$	3.69605	+	4.23047i	0.143760	+	0.164546i	−0.676684	+	0.736274i	$0.736584\pi$
$662$	28.5247	+	35.7688i	1.10864	+	1.39020i
$663$		0			0
$664$	7.53198	−	23.1811i	0.292298	−	0.899600i
$665$	−0.206402	+	0.0993979i	−0.00800392	+	0.00385448i
$666$		0			0
$667$	−4.17808	−	0.187638i	−0.161776	−	0.00726537i
$668$	2.50083	−	2.86242i	0.0967598	−	0.110751i
$669$		0			0
$670$	1.08617	+	1.03848i	0.0419622	+	0.0401200i
$671$	−15.6382	−	3.56933i	−0.603708	−	0.137792i
$672$		0			0
$673$	6.41636	+	5.11688i	0.247333	+	0.197241i	0.739307	−	0.673368i	$-0.235153\pi$
$673$	6.41636	+	5.11688i	0.247333	+	0.197241i	−0.491974	+	0.870610i	$0.663725\pi$
$674$	−19.6021	+	29.6959i	−0.755045	+	1.14384i
$675$		0			0
$676$	0.703729	−	0.882448i	0.0270665	−	0.0339403i
$677$	−19.3241	+	0.867846i	−0.742685	+	0.0333540i	−0.412993	−	0.910734i	$-0.635517\pi$
$677$	−19.3241	+	0.867846i	−0.742685	+	0.0333540i	−0.329693	+	0.944088i	$0.606945\pi$
$678$		0			0
$679$	4.10365	−	4.29209i	0.157484	−	0.164715i
$680$	0.0307674	+	0.0148168i	0.00117988	+	0.000568198i
$681$		0			0
$682$	−0.466959	+	10.3976i	−0.0178808	+	0.398146i
$683$	−22.7424	−	6.27649i	−0.870212	−	0.240163i	−0.197712	−	0.980260i	$-0.563351\pi$
$683$	−22.7424	−	6.27649i	−0.870212	−	0.240163i	−0.672500	+	0.740097i	$0.734780\pi$
$684$		0			0
$685$	−0.455001	−	0.147839i	−0.0173847	−	0.00564864i
$686$	26.5849	−	2.39268i	1.01502	−	0.0913530i
$687$		0			0
$688$	−13.9442	+	12.1827i	−0.531616	+	0.464459i
$689$	−8.98758	−	32.5658i	−0.342400	−	1.24066i
$690$		0			0
$691$	−18.5074	+	30.9762i	−0.704055	+	1.17839i	0.272299	+	0.962213i	$0.412216\pi$
$691$	−18.5074	+	30.9762i	−0.704055	+	1.17839i	−0.976354	+	0.216177i	$0.930641\pi$
$692$	4.68082	+	10.9513i	0.177938	+	0.416307i
$693$		0			0
$694$	23.1964	−	22.1780i	0.880523	−	0.841866i
$695$	1.63506	−	0.976900i	0.0620212	−	0.0370559i
$696$		0			0
$697$	−0.148985	+	1.09985i	−0.00564320	+	0.0416598i
$698$	−5.93379	+	11.0268i	−0.224597	+	0.417372i
$699$		0			0
$700$	1.46103	−	3.89290i	0.0552218	−	0.147138i
$701$	−19.8306	−	3.59872i	−0.748990	−	0.135922i	−0.209377	−	0.977835i	$-0.567144\pi$
$701$	−19.8306	−	3.59872i	−0.748990	−	0.135922i	−0.539613	+	0.841913i	$0.681429\pi$
$702$		0			0
$703$	−4.03030	+	1.51260i	−0.152005	+	0.0570486i
$704$	−3.96708	−	7.37207i	−0.149515	−	0.277845i
$705$		0			0
$706$	9.67548	+	4.13550i	0.364141	+	0.155641i
$707$	−10.5568	−	0.950131i	−0.397030	−	0.0357334i
$708$		0			0
$709$			34.0577i			1.27906i	0.768765	+	0.639531i	$0.220871\pi$
$709$			34.0577i			1.27906i	−0.768765	+	0.639531i	$0.779129\pi$
$710$	1.06132	−	1.28903i	0.0398308	−	0.0483763i
$711$		0			0
$712$	1.19960	+	1.81732i	0.0449570	+	0.0681070i
$713$	0.875707	−	9.72990i	0.0327955	−	0.364388i
$714$		0			0
$715$	−0.749467	+	0.544519i	−0.0280285	+	0.0203639i
$716$	8.60903	−	4.63271i	0.321734	−	0.173133i
$717$		0			0
$718$	30.8785	−	5.60361i	1.15237	−	0.209125i
$719$	6.59187	−	36.3242i	0.245835	−	1.35466i	−0.590762	−	0.806846i	$-0.701173\pi$
$719$	6.59187	−	36.3242i	0.245835	−	1.35466i	0.836597	−	0.547818i	$-0.184542\pi$
$720$		0			0
$721$	2.97928	−	0.403570i	0.110954	−	0.0150297i
$722$	−24.3550	−	13.1060i	−0.906399	−	0.487754i
$723$		0			0
$724$	−4.20914	+	5.79339i	−0.156432	+	0.215310i
$725$	−3.59087	−	6.01010i	−0.133362	−	0.223210i
$726$		0			0
$727$	−44.5769	+	14.4839i	−1.65327	+	0.537178i	−0.979444	−	0.201716i	$-0.935348\pi$
$727$	−44.5769	+	14.4839i	−1.65327	+	0.537178i	−0.673821	+	0.738894i	$0.735348\pi$
$728$	−10.7791	+	4.60723i	−0.399502	+	0.170755i
$729$		0			0
$730$	−0.0770782	−	0.337702i	−0.00285279	−	0.0124989i
$731$	0.457532	−	0.126271i	0.0169224	−	0.00467030i
$732$		0			0
$733$	−30.9236	+	24.6607i	−1.14219	+	0.910866i	−0.996912	−	0.0785254i	$-0.974979\pi$
$733$	−30.9236	+	24.6607i	−1.14219	+	0.910866i	−0.145277	+	0.989391i	$0.546407\pi$
$734$	2.68926	+	29.8802i	0.0992625	+	1.10290i
$735$		0			0
$736$	−4.34400	−	9.02041i	−0.160122	−	0.332497i
$737$	−3.95880	+	14.3444i	−0.145824	+	0.528382i
$738$		0			0
$739$	1.50752	+	1.31708i	0.0554550	+	0.0484496i	0.685220	−	0.728336i	$-0.259706\pi$
$739$	1.50752	+	1.31708i	0.0554550	+	0.0484496i	−0.629765	+	0.776786i	$0.716849\pi$
$740$	−0.102153	+	0.212123i	−0.00375522	+	0.00779779i
$741$		0			0
$742$	4.28553	−	18.7761i	0.157327	−	0.689294i
$743$	−0.155268	−	3.45732i	−0.00569624	−	0.126837i	−0.999826	−	0.0186440i	$-0.994065\pi$
$743$	−0.155268	−	3.45732i	−0.00569624	−	0.126837i	0.994130	−	0.108193i	$-0.0345063\pi$
$744$		0			0
$745$	0.276727	+	0.182666i	0.0101385	+	0.00669236i
$746$	−26.5862	−	17.5494i	−0.973390	−	0.642529i
$747$		0			0
$748$	−0.00672332	−	0.149706i	−0.000245829	−	0.00547381i
$749$	1.34433	−	5.88990i	0.0491208	−	0.215212i
$750$		0			0
$751$	−8.15165	+	16.9271i	−0.297458	+	0.617678i	−0.995112	−	0.0987573i	$-0.968513\pi$
$751$	−8.15165	+	16.9271i	−0.297458	+	0.617678i	0.697653	+	0.716435i	$0.254228\pi$
$752$	5.66878	+	4.95266i	0.206719	+	0.180605i
$753$		0			0
$754$	2.32700	−	8.43169i	0.0847443	−	0.307064i
$755$	−0.177503	−	0.368588i	−0.00645998	−	0.0134143i
$756$		0			0
$757$	3.45705	+	38.4109i	0.125648	+	1.39607i	0.773256	+	0.634094i	$0.218627\pi$
$757$	3.45705	+	38.4109i	0.125648	+	1.39607i	−0.647607	+	0.761974i	$0.724230\pi$
$758$	2.04636	−	1.63192i	0.0743271	−	0.0592739i
$759$		0			0
$760$	−0.364329	+	0.100548i	−0.0132156	+	0.00364727i
$761$	8.77212	+	38.4332i	0.317989	+	1.39320i	0.841074	+	0.540921i	$0.181924\pi$
$761$	8.77212	+	38.4332i	0.317989	+	1.39320i	−0.523085	+	0.852281i	$0.675219\pi$
$762$		0			0
$763$	19.2386	−	8.22299i	0.696486	−	0.297692i
$764$	7.86205	−	2.55453i	0.284439	−	0.0924198i
$765$		0			0
$766$	−17.4469	−	29.2011i	−0.630381	−	1.05508i
$767$	0.0413901	−	0.0569687i	0.00149451	−	0.00205702i
$768$		0			0
$769$	−21.4555	−	11.5457i	−0.773707	−	0.416349i	0.0388401	−	0.999245i	$-0.487634\pi$
$769$	−21.4555	−	11.5457i	−0.773707	−	0.416349i	−0.812547	+	0.582896i	$0.801919\pi$
$770$	−0.523334	+	0.0708904i	−0.0188596	+	0.00255471i
$771$		0			0
$772$	0.164824	−	0.908256i	0.00593215	−	0.0326888i
$773$	35.4292	−	6.42945i	1.27430	−	0.231251i	0.501086	−	0.865398i	$-0.332934\pi$
$773$	35.4292	−	6.42945i	1.27430	−	0.231251i	0.773213	+	0.634147i	$0.218648\pi$
$774$		0			0
$775$	14.4009	−	7.74945i	0.517295	−	0.278369i
$776$	7.92575	−	5.75839i	0.284518	−	0.206714i
$777$		0			0
$778$	2.13736	−	23.7480i	0.0766280	−	0.851407i
$779$	−6.76713	−	10.2518i	−0.242457	−	0.367307i
$780$		0			0
$781$	16.2205	+	3.20608i	0.580416	+	0.114722i
$782$			0.598718i			0.0214101i
$783$		0			0
$784$	24.9087	+	2.24183i	0.889597	+	0.0800652i
$785$	2.24463	+	0.959402i	0.0801144	+	0.0342425i
$786$		0			0
$787$	−24.3252	−	45.2038i	−0.867099	−	1.61134i	−0.788999	−	0.614394i	$-0.789400\pi$
$787$	−24.3252	−	45.2038i	−0.867099	−	1.61134i	−0.0780997	−	0.996946i	$-0.524885\pi$
$788$	−5.01399	+	1.88178i	−0.178616	+	0.0670357i
$789$		0			0
$790$	−1.54543	−	0.280455i	−0.0549840	−	0.00997813i
$791$	1.45394	−	3.87401i	0.0516962	−	0.137744i
$792$		0			0
$793$	−14.9211	+	27.7281i	−0.529864	+	0.984652i
$794$	1.17602	−	8.68174i	0.0417354	−	0.308103i
$795$		0			0
$796$	−9.89180	+	5.91007i	−0.350605	+	0.209477i
$797$	11.7313	−	11.2162i	0.415543	−	0.397300i	−0.454124	−	0.890938i	$-0.650048\pi$
$797$	11.7313	−	11.2162i	0.415543	−	0.397300i	0.869667	+	0.493639i	$0.164333\pi$
$798$		0			0
$799$	−0.0758366	−	0.177428i	−0.00268290	−	0.00627697i
$800$	8.59610	−	14.3875i	0.303918	−	0.508673i
$801$		0			0
$802$	16.2018	+	58.7060i	0.572107	+	2.07298i
$803$	2.58308	−	2.25677i	0.0911548	−	0.0796396i
$804$		0			0
$805$	0.493700	−	0.0444338i	0.0174006	−	0.00156609i
$806$	19.4315	+	6.31367i	0.684445	+	0.222390i
$807$		0			0
$808$	−16.8568	−	4.65218i	−0.593020	−	0.163663i
$809$	−0.484829	+	10.7956i	−0.0170457	+	0.379551i	0.972279	+	0.233824i	$0.0751238\pi$
$809$	−0.484829	+	10.7956i	−0.0170457	+	0.379551i	−0.989325	+	0.145728i	$0.953448\pi$
$810$		0			0
$811$	2.55893	+	1.23232i	0.0898563	+	0.0432725i	0.478272	−	0.878212i	$-0.341263\pi$
$811$	2.55893	+	1.23232i	0.0898563	+	0.0432725i	−0.388416	+	0.921484i	$0.626978\pi$
$812$	0.809557	−	0.846730i	0.0284099	−	0.0297144i
$813$		0			0
$814$	−9.91375	+	0.445227i	−0.347477	+	0.0156052i
$815$	−0.275701	+	0.345718i	−0.00965739	+	0.0121100i
$816$		0			0
$817$	−2.89390	+	4.38408i	−0.101245	+	0.153379i
$818$	−30.2109	−	24.0924i	−1.05630	−	0.842371i
$819$		0			0
$820$	−0.654986	−	0.149496i	−0.0228731	−	0.00522064i
$821$	28.6632	+	27.4048i	1.00035	+	0.956434i	0.999051	−	0.0435649i	$-0.0138715\pi$
$821$	28.6632	+	27.4048i	1.00035	+	0.956434i	0.00130124	+	0.999999i	$0.499586\pi$
$822$		0			0
$823$	22.9955	−	26.3204i	0.801572	−	0.917473i	−0.196439	−	0.980516i	$-0.562938\pi$
$823$	22.9955	−	26.3204i	0.801572	−	0.917473i	0.998011	+	0.0630430i	$0.0200805\pi$
$824$	4.95508	+	0.222533i	0.172619	+	0.00775231i
$825$		0			0
$826$	0.0361677	−	0.0174174i	0.00125843	−	0.000606030i
$827$	−12.0486	+	37.0817i	−0.418969	+	1.28946i	0.489682	+	0.871901i	$0.337113\pi$
$827$	−12.0486	+	37.0817i	−0.418969	+	1.28946i	−0.908652	+	0.417555i	$0.862887\pi$
$828$		0			0
$829$	15.0366	+	18.8552i	0.522241	+	0.654870i	0.971083	−	0.238742i	$-0.0767349\pi$
$829$	15.0366	+	18.8552i	0.522241	+	0.654870i	−0.448842	+	0.893611i	$0.648163\pi$
$830$	−1.41823	−	1.62330i	−0.0492276	−	0.0563455i
$831$		0			0
$832$	−16.0219	+	3.65688i	−0.555458	+	0.126780i
$833$	−0.550329	−	0.328807i	−0.0190678	−	0.0113925i
$834$		0			0
$835$	0.234401	+	0.721411i	0.00811177	+	0.0249655i
$836$	1.14617	+	1.19880i	0.0396410	+	0.0414612i
$837$		0			0
$838$	−33.6903	−	24.4775i	−1.16381	−	0.845560i
$839$	41.9098	+	5.67707i	1.44689	+	0.195994i	0.815178	−	0.579210i	$-0.196639\pi$
$839$	41.9098	+	5.67707i	1.44689	+	0.195994i	0.631710	+	0.775205i	$0.282353\pi$
$840$		0			0
$841$	3.62799	+	26.7829i	0.125103	+	0.923549i
$842$	45.8720	+	17.2160i	1.58085	+	0.593304i
$843$		0			0
$844$	−1.46784	−	8.08846i	−0.0505251	−	0.278416i
$845$	0.0791453	+	0.210882i	0.00272268	+	0.00725456i
$846$		0			0
$847$	5.70752	+	7.85573i	0.196113	+	0.269926i
$848$	16.7216	−	39.1222i	0.574223	−	1.34346i
$849$		0			0
$850$	−0.836450	+	0.552136i	−0.0286900	+	0.0189381i
$851$	9.31458			0.319300
$852$		0			0
$853$	8.56514			0.293265			0.146632	−	0.989191i	$-0.453157\pi$
$853$	8.56514			0.293265			0.146632	+	0.989191i	$0.453157\pi$
$854$	−14.9810	+	9.88885i	−0.512638	+	0.338390i
$855$		0			0
$856$	3.91728	−	9.16493i	0.133890	−	0.313251i
$857$	−2.69830	−	3.71389i	−0.0921721	−	0.126864i	0.760440	−	0.649408i	$-0.224983\pi$
$857$	−2.69830	−	3.71389i	−0.0921721	−	0.126864i	−0.852612	+	0.522544i	$0.824983\pi$
$858$		0			0
$859$	16.6183	+	44.2792i	0.567008	+	1.51079i	0.836601	+	0.547813i	$0.184539\pi$
$859$	16.6183	+	44.2792i	0.567008	+	1.51079i	−0.269593	+	0.962974i	$0.586889\pi$
$860$	0.0512999	+	0.282686i	0.00174931	+	0.00963950i
$861$		0			0
$862$	38.3706	+	14.4007i	1.30691	+	0.490491i
$863$	−2.58477	−	19.0815i	−0.0879865	−	0.649543i	−0.980212	−	0.197952i	$-0.936571\pi$
$863$	−2.58477	−	19.0815i	−0.0879865	−	0.649543i	0.892225	−	0.451591i	$-0.149143\pi$
$864$		0			0
$865$	−2.35522	−	0.319037i	−0.0800800	−	0.0108476i
$866$	−7.61558	−	5.53304i	−0.258788	−	0.188020i
$867$		0			0
$868$	1.89101	+	1.97784i	0.0641849	+	0.0671321i
$869$	−4.80628	−	14.7922i	−0.163042	−	0.501791i
$870$		0			0
$871$	25.0763	+	14.9824i	0.849678	+	0.507659i
$872$	33.6520	−	7.68086i	1.13960	−	0.260107i
$873$		0			0
$874$	−4.35974	−	4.99012i	−0.147470	−	0.168793i
$875$	1.03629	+	1.29947i	0.0350330	+	0.0439299i
$876$		0			0
$877$	16.1406	−	49.6757i	0.545030	−	1.67743i	−0.175889	−	0.984410i	$-0.556280\pi$
$877$	16.1406	−	49.6757i	0.545030	−	1.67743i	0.720919	−	0.693019i	$-0.243720\pi$
$878$	6.83081	−	3.28954i	0.230529	−	0.111017i
$879$		0			0
$880$	−1.16550	−	0.0523429i	−0.0392892	−	0.00176448i
$881$	−1.91962	+	2.19718i	−0.0646736	+	0.0740249i	−0.784498	−	0.620131i	$-0.787079\pi$
$881$	−1.91962	+	2.19718i	−0.0646736	+	0.0740249i	0.719825	+	0.694156i	$0.244222\pi$
$882$		0			0
$883$	−2.56009	−	2.44770i	−0.0861539	−	0.0823716i	0.646757	−	0.762696i	$-0.276125\pi$
$883$	−2.56009	−	2.44770i	−0.0861539	−	0.0823716i	−0.732911	+	0.680324i	$0.761839\pi$
$884$	−0.286799	−	0.0654600i	−0.00964610	−	0.00220166i
$885$		0			0
$886$	47.0368	+	37.5106i	1.58023	+	1.26019i
$887$	−14.4977	+	21.9631i	−0.486787	+	0.737450i	−0.992095	−	0.125489i	$-0.959950\pi$
$887$	−14.4977	+	21.9631i	−0.486787	+	0.737450i	0.505308	+	0.862939i	$0.331379\pi$
$888$		0			0
$889$	−2.07810	+	2.60585i	−0.0696971	+	0.0873974i
$890$	0.192382	−	0.00863989i	0.00644867	−	0.000289610i
$891$		0			0
$892$	6.79275	−	7.10466i	0.227438	−	0.237882i
$893$	1.92407	+	0.926582i	0.0643865	+	0.0310069i
$894$		0			0
$895$	−0.0875311	+	1.94903i	−0.00292584	+	0.0651489i
$896$	−17.8343	−	4.92196i	−0.595803	−	0.164431i
$897$		0			0
$898$	45.5629	+	14.8043i	1.52045	+	0.494025i
$899$	4.58883	−	0.413002i	0.153046	−	0.0137744i
$900$		0			0
$901$	−0.821295	+	0.717544i	−0.0273613	+	0.0239049i
$902$	−7.53354	−	27.2972i	−0.250840	−	0.908897i
$903$		0			0
$904$	3.50137	−	5.86030i	0.116454	−	0.194911i
$905$	−0.561661	−	1.31407i	−0.0186702	−	0.0436812i
$906$		0			0
$907$	36.2011	−	34.6118i	1.20204	−	1.14927i	0.217137	−	0.976141i	$-0.430328\pi$
$907$	36.2011	−	34.6118i	1.20204	−	1.14927i	0.984900	−	0.173124i	$-0.0553862\pi$
$908$	1.93374	−	1.15536i	0.0641735	−	0.0383419i
$909$		0			0
$910$	−0.139160	+	1.02732i	−0.00461311	+	0.0340554i
$911$	−10.1454	+	18.8533i	−0.336132	+	0.624637i	−0.991416	−	0.130745i	$-0.958263\pi$
$911$	−10.1454	+	18.8533i	−0.336132	+	0.624637i	0.655284	+	0.755382i	$0.272549\pi$
$912$		0			0
$913$	7.50021	−	19.9842i	0.248221	−	0.661382i
$914$	−25.7290	−	4.66913i	−0.851040	−	0.154441i
$915$		0			0
$916$	−4.48701	+	1.68400i	−0.148255	+	0.0556410i
$917$	−2.74841	−	5.10740i	−0.0907605	−	0.168661i
$918$		0			0
$919$	31.3505	+	13.3999i	1.03416	+	0.442021i	0.842076	−	0.539358i	$-0.181333\pi$
$919$	31.3505	+	13.3999i	1.03416	+	0.442021i	0.192082	+	0.981379i	$0.438476\pi$
$920$	0.814503	+	0.0733066i	0.0268534	+	0.00241685i
$921$		0			0
$922$			43.6448i			1.43736i
$923$	14.5378	−	29.0196i	0.478518	−	0.955192i
$924$		0			0
$925$	8.58987	+	13.0131i	0.282433	+	0.427868i
$926$	−4.74377	+	52.7076i	−0.155890	+	1.73208i
$927$		0			0
$928$	3.82004	−	2.77542i	0.125399	−	0.0911077i
$929$	−11.6368	+	6.26203i	−0.381791	+	0.205450i	−0.653496	−	0.756930i	$-0.726698\pi$
$929$	−11.6368	+	6.26203i	−0.381791	+	0.205450i	0.271705	+	0.962381i	$0.412413\pi$
$930$		0			0
$931$	6.98111	−	1.26689i	0.228797	−	0.0415205i
$932$	2.11231	−	11.6398i	0.0691910	−	0.381274i
$933$		0			0
$934$	−7.52626	+	1.01950i	−0.246267	+	0.0333591i
$935$	0.0263350	+	0.0141715i	0.000861246	+	0.000463456i
$936$		0			0
$937$	23.0237	−	31.6894i	0.752150	−	1.03525i	−0.245676	−	0.969352i	$-0.579010\pi$
$937$	23.0237	−	31.6894i	0.752150	−	1.03525i	0.997827	−	0.0658942i	$-0.0209900\pi$
$938$	8.54110	+	14.2954i	0.278877	+	0.466761i
$939$		0			0
$940$	0.111082	−	0.0360926i	0.00362309	−	0.00117721i
$941$	17.8072	−	7.61115i	0.580497	−	0.248116i	−0.0826834	−	0.996576i	$-0.526349\pi$
$941$	17.8072	−	7.61115i	0.580497	−	0.248116i	0.663180	+	0.748460i	$0.269206\pi$
$942$		0			0
$943$	5.91447	+	25.9130i	0.192602	+	0.843843i
$944$	0.0854861	−	0.0235927i	0.00278234	−	0.000767876i
$945$		0			0
$946$	−9.46783	+	7.55034i	−0.307826	+	0.245483i
$947$	1.78422	+	19.8243i	0.0579793	+	0.644203i	0.971441	+	0.237279i	$0.0762556\pi$
$947$	1.78422	+	19.8243i	0.0579793	+	0.644203i	−0.913462	+	0.406924i	$0.866602\pi$
$948$		0			0
$949$	−2.92147	−	6.06650i	−0.0948350	−	0.196927i
$950$	2.95100	−	10.6927i	0.0957431	−	0.346917i
$951$		0			0
$952$	0.284982	+	0.248981i	0.00923632	+	0.00806953i
$953$	−11.4191	+	23.7119i	−0.369900	+	0.768105i	−0.999964	−	0.00843769i	$-0.997314\pi$
$953$	−11.4191	+	23.7119i	−0.369900	+	0.768105i	0.630064	+	0.776543i	$0.283028\pi$
$954$		0			0
$955$	−0.367096	+	1.60835i	−0.0118789	+	0.0520450i
$956$	−0.491341	−	10.9405i	−0.0158911	−	0.353843i
$957$		0			0
$958$	57.4399	+	37.9157i	1.85580	+	1.22500i
$959$	−4.42457	−	2.92064i	−0.142877	−	0.0943123i
$960$		0			0
$961$	−0.907967	−	20.2175i	−0.0292893	−	0.652176i
$962$	−4.33485	+	18.9922i	−0.139761	+	0.612333i
$963$		0			0
$964$	−3.91336	+	8.12617i	−0.126041	+	0.261726i
$965$	0.138726	+	0.121202i	0.00446576	+	0.00390162i
$966$		0			0
$967$	3.44243	−	12.4734i	0.110701	−	0.401117i	−0.887518	−	0.460773i	$-0.847572\pi$
$967$	3.44243	−	12.4734i	0.110701	−	0.401117i	0.998219	+	0.0596568i	$0.0190006\pi$
$968$	6.95075	+	14.4334i	0.223406	+	0.463907i
$969$		0			0
$970$	−0.0776634	−	0.862911i	−0.00249362	−	0.0277064i
$971$	−23.9121	+	19.0693i	−0.767376	+	0.611962i	−0.926933	−	0.375227i	$-0.877565\pi$
$971$	−23.9121	+	19.0693i	−0.767376	+	0.611962i	0.159557	+	0.987189i	$0.448993\pi$
$972$		0			0
$973$	20.3460	−	5.61514i	0.652263	−	0.180013i
$974$	3.33679	+	14.6194i	0.106918	+	0.468437i
$975$		0			0
$976$	−36.4640	+	15.5855i	−1.16718	+	0.498879i
$977$	−6.33672	+	2.05892i	−0.202730	+	0.0658708i	−0.408622	−	0.912704i	$-0.633990\pi$
$977$	−6.33672	+	2.05892i	−0.202730	+	0.0658708i	0.205892	+	0.978575i	$0.433990\pi$
$978$		0			0
$979$	0.978082	+	1.63703i	0.0312596	+	0.0523198i
$980$	0.228089	−	0.313938i	0.00728605	−	0.0100284i
$981$		0			0
$982$	−13.6933	−	7.36870i	−0.436972	−	0.235145i
$983$	40.6416	−	5.50527i	1.29626	−	0.175591i	0.546592	−	0.837399i	$-0.315925\pi$
$983$	40.6416	−	5.50527i	1.29626	−	0.175591i	0.749673	+	0.661808i	$0.230211\pi$
$984$		0			0
$985$	0.190833	−	1.05158i	0.00608045	−	0.0335061i
$986$	−0.277831	+	0.0504188i	−0.00884793	+	0.00160566i
$987$		0			0
$988$	2.86704	−	1.54282i	0.0912127	−	0.0490837i
$989$	9.19566	−	6.68103i	0.292405	−	0.212445i
$990$		0			0
$991$	4.14983	−	46.1083i	0.131824	−	1.46468i	−0.609102	−	0.793092i	$-0.708470\pi$
$991$	4.14983	−	46.1083i	0.131824	−	1.46468i	0.740925	−	0.671588i	$-0.234387\pi$
$992$	6.07612	+	9.20493i	0.192917	+	0.292257i
$993$		0			0
$994$	15.1375	−	10.6408i	0.480131	−	0.337504i
$995$		−	2.29953i		−	0.0729001i
$996$		0			0
$997$	−1.36349	−	0.122716i	−0.0431821	−	0.00388646i	0.0680272	−	0.997683i	$-0.478330\pi$
$997$	−1.36349	−	0.122716i	−0.0431821	−	0.00388646i	−0.111209	+	0.993797i	$0.535472\pi$
$998$	53.6231	+	22.9196i	1.69741	+	0.725507i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.305.19	yes	576
3.2	odd	2	inner	639.2.z.a.305.6	yes	576
71.44	odd	70	inner	639.2.z.a.44.6	✓	576
213.44	even	70	inner	639.2.z.a.44.19	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.44.6	✓	576	71.44	odd	70	inner
639.2.z.a.44.19	yes	576	213.44	even	70	inner
639.2.z.a.305.6	yes	576	3.2	odd	2	inner
639.2.z.a.305.19	yes	576	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34937 - 0.890708i) q^{2} +(0.241376 - 0.564726i) q^{4} +(0.0720395 + 0.0991538i) q^{5} +(0.477225 + 1.27156i) q^{7} +(0.400091 + 2.20468i) q^{8} +O(q^{10})\)	\(q+(1.34937 - 0.890708i) q^{2} +(0.241376 - 0.564726i) q^{4} +(0.0720395 + 0.0991538i) q^{5} +(0.477225 + 1.27156i) q^{7} +(0.400091 + 2.20468i) q^{8} +(0.185525 + 0.0696286i) q^{10} +(0.263401 + 1.94451i) q^{11} +(3.81713 + 0.517065i) q^{13} +(1.77654 + 1.29073i) q^{14} +(3.35243 + 3.50636i) q^{16} +(-0.0384264 - 0.118264i) q^{17} +(1.18145 + 0.705881i) q^{19} +(0.0733833 - 0.0167493i) q^{20} +(2.08741 + 2.38924i) q^{22} +(-1.85669 - 2.32822i) q^{23} +(1.54044 - 4.74100i) q^{25} +(5.61125 - 2.70224i) q^{26} +(0.833275 + 0.0374224i) q^{28} +(0.924038 - 1.05765i) q^{29} +(2.37118 + 2.26708i) q^{31} +(3.27777 + 0.748130i) q^{32} +(-0.157190 - 0.125355i) q^{34} +(-0.0917012 + 0.138921i) q^{35} +(-1.95021 + 2.44549i) q^{37} +(2.22294 - 0.0998321i) q^{38} +(-0.189780 + 0.198495i) q^{40} +(-8.04164 - 3.87265i) q^{41} +(-0.171246 + 3.81309i) q^{43} +(1.16169 + 0.320607i) q^{44} +(-4.57912 - 1.48785i) q^{46} +(1.54547 - 0.139094i) q^{47} +(3.88238 - 3.39193i) q^{49} +(-2.14422 - 7.76942i) q^{50} +(1.21336 - 2.03083i) q^{52} +(-3.44696 - 8.06456i) q^{53} +(-0.173830 + 0.166198i) q^{55} +(-2.61246 + 1.56087i) q^{56} +(0.304810 - 2.25020i) q^{58} +(0.00866266 - 0.0160979i) q^{59} +(-2.87229 + 7.65319i) q^{61} +(5.21890 + 0.947090i) q^{62} +(-3.99430 + 1.49908i) q^{64} +(0.223715 + 0.415732i) q^{65} +(6.97315 + 2.98047i) q^{67} +(-0.0760621 - 0.00684571i) q^{68} +0.269135i q^{70} +(2.72868 - 7.97210i) q^{71} +(-0.962973 - 1.45884i) q^{73} +(-0.453332 + 5.03693i) q^{74} +(0.683801 - 0.496811i) q^{76} +(-2.34686 + 1.26290i) q^{77} +(-7.79889 + 1.41529i) q^{79} +(-0.106162 + 0.585003i) q^{80} +(-14.3005 + 1.93714i) q^{82} +(-9.57903 - 5.15470i) q^{83} +(0.00895814 - 0.0123298i) q^{85} +(3.16528 + 5.29778i) q^{86} +(-4.18163 + 1.35870i) q^{88} +(0.893615 - 0.381949i) q^{89} +(1.16415 + 5.10047i) q^{91} +(-1.76297 + 0.486548i) q^{92} +(1.96151 - 1.56425i) q^{94} +(0.0151199 + 0.167996i) q^{95} +(-1.89703 - 3.93922i) q^{97} +(2.21752 - 8.03502i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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