LMFDB - Embedded newform 624.2.cn.f.305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.2
Character	$\chi$	$=$	624.305
Dual form			624.2.cn.f.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55432 - 0.764251i) q^{3} +(-0.504580 - 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.83184 + 2.37579i) q^{9} +O(q^{10})$	\(q+(-1.55432 - 0.764251i) q^{3} +(-0.504580 - 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.83184 + 2.37579i) q^{9} +(-0.296516 - 1.10661i) q^{11} +(3.23695 + 1.58812i) q^{13} +(0.398654 + 1.16991i) q^{15} +(-1.51919 - 2.63131i) q^{17} +(-4.59867 - 1.23221i) q^{19} +(-3.68744 + 4.21464i) q^{21} +(-2.43079 + 4.21025i) q^{23} -4.49080i q^{25} +(-1.03158 - 5.09273i) q^{27} +(-8.98018 - 5.18471i) q^{29} +(1.93142 - 1.93142i) q^{31} +(-0.384848 + 1.94665i) q^{33} +(-1.99805 + 1.15357i) q^{35} +(-7.49362 + 2.00791i) q^{37} +(-3.81755 - 4.94230i) q^{39} +(6.55081 - 1.75528i) q^{41} +(-1.98070 + 1.14356i) q^{43} +(0.274463 - 2.12308i) q^{45} +(1.27830 - 1.27830i) q^{47} +(-2.99079 - 1.72673i) q^{49} +(0.350327 + 5.25094i) q^{51} -2.42966i q^{53} +(-0.408758 + 0.707990i) q^{55} +(6.20611 + 5.42979i) q^{57} +(-5.61424 - 1.50433i) q^{59} +(-5.23702 - 9.07078i) q^{61} +(8.95251 - 3.73279i) q^{63} +(-0.831967 - 2.43463i) q^{65} +(1.57758 + 5.88762i) q^{67} +(6.99591 - 4.68635i) q^{69} +(1.02693 - 3.83254i) q^{71} +(-4.06395 - 4.06395i) q^{73} +(-3.43210 + 6.98015i) q^{75} -3.70409 q^{77} -6.77768 q^{79} +(-2.28872 + 8.70412i) q^{81} +(11.9425 + 11.9425i) q^{83} +(-0.561154 + 2.09426i) q^{85} +(9.99568 + 14.9218i) q^{87} +(2.07215 + 7.73338i) q^{89} +(7.66844 - 8.78010i) q^{91} +(-4.47815 + 1.52597i) q^{93} +(1.69865 + 2.94215i) q^{95} +(-0.989115 - 0.265032i) q^{97} +(2.08590 - 2.73160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^7	$ 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.55432	−	0.764251i	−0.897389	−	0.441240i
$3$	−1.55432	−	0.764251i	−0.897389	−	0.441240i
$4$		0			0
$5$	−0.504580	−	0.504580i	−0.225655	−	0.225655i	0.585220	−	0.810875i	$-0.301008\pi$
$5$	−0.504580	−	0.504580i	−0.225655	−	0.225655i	−0.810875	+	0.585220i	$0.801008\pi$
$6$		0			0
$7$	0.836809	−	3.12301i	0.316284	−	1.18039i	−0.606504	−	0.795080i	$-0.707429\pi$
$7$	0.836809	−	3.12301i	0.316284	−	1.18039i	0.922788	−	0.385308i	$-0.125905\pi$
$8$		0			0
$9$	1.83184	+	2.37579i	0.610614	+	0.791929i
$10$		0			0
$11$	−0.296516	−	1.10661i	−0.0894029	−	0.333656i	0.906709	−	0.421758i	$-0.138587\pi$
$11$	−0.296516	−	1.10661i	−0.0894029	−	0.333656i	−0.996112	+	0.0881015i	$0.971920\pi$
$12$		0			0
$13$	3.23695	+	1.58812i	0.897769	+	0.440466i
$13$	3.23695	+	1.58812i	0.897769	+	0.440466i
$14$		0			0
$15$	0.398654	+	1.16991i	0.102932	+	0.302068i
$16$		0			0
$17$	−1.51919	−	2.63131i	−0.368457	−	0.638186i	0.620868	−	0.783916i	$-0.286780\pi$
$17$	−1.51919	−	2.63131i	−0.368457	−	0.638186i	−0.989325	+	0.145729i	$0.953447\pi$
$18$		0			0
$19$	−4.59867	−	1.23221i	−1.05501	−	0.282689i	−0.310688	−	0.950512i	$-0.600560\pi$
$19$	−4.59867	−	1.23221i	−1.05501	−	0.282689i	−0.744320	+	0.667823i	$0.767226\pi$
$20$		0			0
$21$	−3.68744	+	4.21464i	−0.804665	+	0.919710i
$22$		0			0
$23$	−2.43079	+	4.21025i	−0.506854	+	0.877897i	0.493114	+	0.869964i	$0.335858\pi$
$23$	−2.43079	+	4.21025i	−0.506854	+	0.877897i	−0.999969	+	0.00793257i	$0.997475\pi$
$24$		0			0
$25$		−	4.49080i		−	0.898160i
$26$		0			0
$27$	−1.03158	−	5.09273i	−0.198527	−	0.980095i
$28$		0			0
$29$	−8.98018	−	5.18471i	−1.66758	−	0.962776i	−0.968939	−	0.247301i	$-0.920456\pi$
$29$	−8.98018	−	5.18471i	−1.66758	−	0.962776i	−0.698638	−	0.715475i	$-0.746210\pi$
$30$		0			0
$31$	1.93142	−	1.93142i	0.346894	−	0.346894i	−0.512057	−	0.858951i	$-0.671116\pi$
$31$	1.93142	−	1.93142i	0.346894	−	0.346894i	0.858951	+	0.512057i	$0.171116\pi$
$32$		0			0
$33$	−0.384848	+	1.94665i	−0.0669934	+	0.338867i
$34$		0			0
$35$	−1.99805	+	1.15357i	−0.337731	+	0.194989i
$36$		0			0
$37$	−7.49362	+	2.00791i	−1.23194	+	0.330098i	−0.815336	−	0.578988i	$-0.803448\pi$
$37$	−7.49362	+	2.00791i	−1.23194	+	0.330098i	−0.416608	+	0.909086i	$0.636781\pi$
$38$		0			0
$39$	−3.81755	−	4.94230i	−0.611297	−	0.791401i
$40$		0			0
$41$	6.55081	−	1.75528i	1.02306	−	0.274129i	0.291986	−	0.956423i	$-0.405684\pi$
$41$	6.55081	−	1.75528i	1.02306	−	0.274129i	0.731079	+	0.682293i	$0.239017\pi$
$42$		0			0
$43$	−1.98070	+	1.14356i	−0.302054	+	0.174391i	−0.643365	−	0.765559i	$-0.722462\pi$
$43$	−1.98070	+	1.14356i	−0.302054	+	0.174391i	0.341311	+	0.939950i	$0.389129\pi$
$44$		0			0
$45$	0.274463	−	2.12308i	0.0409146	−	0.316491i
$46$		0			0
$47$	1.27830	−	1.27830i	0.186459	−	0.186459i	−0.607704	−	0.794163i	$-0.707909\pi$
$47$	1.27830	−	1.27830i	0.186459	−	0.186459i	0.794163	+	0.607704i	$0.207909\pi$
$48$		0			0
$49$	−2.99079	−	1.72673i	−0.427256	−	0.246676i
$50$		0			0
$51$	0.350327	+	5.25094i	0.0490556	+	0.735279i
$52$		0			0
$53$		−	2.42966i		−	0.333740i	−0.985979	−	0.166870i	$-0.946634\pi$
$53$		−	2.42966i		−	0.333740i	0.985979	−	0.166870i	$-0.0533660\pi$
$54$		0			0
$55$	−0.408758	+	0.707990i	−0.0551169	+	0.0954653i
$56$		0			0
$57$	6.20611	+	5.42979i	0.822019	+	0.719194i
$58$		0			0
$59$	−5.61424	−	1.50433i	−0.730911	−	0.195847i	−0.125876	−	0.992046i	$-0.540174\pi$
$59$	−5.61424	−	1.50433i	−0.730911	−	0.195847i	−0.605035	+	0.796199i	$0.706841\pi$
$60$		0			0
$61$	−5.23702	−	9.07078i	−0.670531	−	1.16139i	−0.977754	−	0.209756i	$-0.932733\pi$
$61$	−5.23702	−	9.07078i	−0.670531	−	1.16139i	0.307223	−	0.951638i	$-0.400600\pi$
$62$		0			0
$63$	8.95251	−	3.73279i	1.12791	−	0.470287i
$64$		0			0
$65$	−0.831967	−	2.43463i	−0.103193	−	0.301979i
$66$		0			0
$67$	1.57758	+	5.88762i	0.192732	+	0.719287i	0.992842	+	0.119433i	$0.0381078\pi$
$67$	1.57758	+	5.88762i	0.192732	+	0.719287i	−0.800110	+	0.599853i	$0.795226\pi$
$68$		0			0
$69$	6.99591	−	4.68635i	0.842209	−	0.564171i
$70$		0			0
$71$	1.02693	−	3.83254i	0.121874	−	0.454839i	−0.877835	−	0.478963i	$-0.841013\pi$
$71$	1.02693	−	3.83254i	0.121874	−	0.454839i	0.999709	+	0.0241235i	$0.00767950\pi$
$72$		0			0
$73$	−4.06395	−	4.06395i	−0.475650	−	0.475650i	0.428088	−	0.903737i	$-0.359187\pi$
$73$	−4.06395	−	4.06395i	−0.475650	−	0.475650i	−0.903737	+	0.428088i	$0.859187\pi$
$74$		0			0
$75$	−3.43210	+	6.98015i	−0.396304	+	0.805999i
$76$		0			0
$77$	−3.70409			−0.422121
$78$		0			0
$79$	−6.77768			−0.762549			−0.381274	−	0.924462i	$-0.624515\pi$
$79$	−6.77768			−0.762549			−0.381274	+	0.924462i	$0.624515\pi$
$80$		0			0
$81$	−2.28872	+	8.70412i	−0.254302	+	0.967125i
$82$		0			0
$83$	11.9425	+	11.9425i	1.31086	+	1.31086i	0.920783	+	0.390075i	$0.127551\pi$
$83$	11.9425	+	11.9425i	1.31086	+	1.31086i	0.390075	+	0.920783i	$0.372449\pi$
$84$		0			0
$85$	−0.561154	+	2.09426i	−0.0608657	+	0.227154i
$86$		0			0
$87$	9.99568	+	14.9218i	1.07165	+	1.59979i
$88$		0			0
$89$	2.07215	+	7.73338i	0.219648	+	0.819737i	0.984478	+	0.175505i	$0.0561559\pi$
$89$	2.07215	+	7.73338i	0.219648	+	0.819737i	−0.764831	+	0.644231i	$0.777177\pi$
$90$		0			0
$91$	7.66844	−	8.78010i	0.803871	−	0.920404i
$92$		0			0
$93$	−4.47815	+	1.52597i	−0.464363	+	0.158235i
$94$		0			0
$95$	1.69865	+	2.94215i	0.174278	+	0.301858i
$96$		0			0
$97$	−0.989115	−	0.265032i	−0.100429	−	0.0269100i	0.208254	−	0.978075i	$-0.433222\pi$
$97$	−0.989115	−	0.265032i	−0.100429	−	0.0269100i	−0.308684	+	0.951165i	$0.599888\pi$
$98$		0			0
$99$	2.08590	−	2.73160i	0.209641	−	0.274536i
$100$		0			0
$101$	−3.77328	+	6.53550i	−0.375455	+	0.650307i	−0.990395	−	0.138267i	$-0.955847\pi$
$101$	−3.77328	+	6.53550i	−0.375455	+	0.650307i	0.614940	+	0.788574i	$0.289180\pi$
$102$		0			0
$103$		−	6.31264i		−	0.622003i	−0.950409	−	0.311001i	$-0.899336\pi$
$103$		−	6.31264i		−	0.622003i	0.950409	−	0.311001i	$-0.100664\pi$
$104$		0			0
$105$	3.98723	−	0.266016i	0.389114	−	0.0259605i
$106$		0			0
$107$	7.26480	+	4.19434i	0.702315	+	0.405482i	0.808209	−	0.588896i	$-0.200437\pi$
$107$	7.26480	+	4.19434i	0.702315	+	0.405482i	−0.105894	+	0.994377i	$0.533770\pi$
$108$		0			0
$109$	10.3472	−	10.3472i	0.991084	−	0.991084i	−0.00887687	−	0.999961i	$-0.502826\pi$
$109$	10.3472	−	10.3472i	0.991084	−	0.991084i	0.999961	+	0.00887687i	$0.00282563\pi$
$110$		0			0
$111$	13.1821	+	2.60607i	1.25119	+	0.247357i
$112$		0			0
$113$	13.0474	−	7.53294i	1.22740	−	0.708639i	0.260914	−	0.965362i	$-0.415976\pi$
$113$	13.0474	−	7.53294i	1.22740	−	0.708639i	0.966485	+	0.256723i	$0.0826428\pi$
$114$		0			0
$115$	3.35093	−	0.897879i	0.312476	−	0.0837277i
$116$		0			0
$117$	2.15655	+	10.5995i	0.199373	+	0.979924i
$118$		0			0
$119$	−9.48889	+	2.54254i	−0.869845	+	0.233074i
$120$		0			0
$121$	8.38961	−	4.84374i	0.762692	−	0.440340i
$122$		0			0
$123$	−11.5236	−	2.27818i	−1.03904	−	0.205417i
$124$		0			0
$125$	−4.78886	+	4.78886i	−0.428329	+	0.428329i
$126$		0			0
$127$	−7.12606	−	4.11423i	−0.632336	−	0.365079i	0.149320	−	0.988789i	$-0.452291\pi$
$127$	−7.12606	−	4.11423i	−0.632336	−	0.365079i	−0.781656	+	0.623710i	$0.785625\pi$
$128$		0			0
$129$	3.95261	−	0.263706i	0.348008	−	0.0232181i
$130$		0			0
$131$		−	13.4099i		−	1.17163i	−0.810446	−	0.585814i	$-0.800775\pi$
$131$		−	13.4099i		−	1.17163i	0.810446	−	0.585814i	$-0.199225\pi$
$132$		0			0
$133$	−7.69642	+	13.3306i	−0.667365	+	1.15591i
$134$		0			0
$135$	−2.04917	+	3.09020i	−0.176365	+	0.265962i
$136$		0			0
$137$	13.2257	+	3.54382i	1.12995	+	0.302769i	0.774904	−	0.632079i	$-0.217798\pi$
$137$	13.2257	+	3.54382i	1.12995	+	0.302769i	0.355047	+	0.934849i	$0.384465\pi$
$138$		0			0
$139$	9.49420	+	16.4444i	0.805288	+	1.39480i	0.916097	+	0.400957i	$0.131322\pi$
$139$	9.49420	+	16.4444i	0.805288	+	1.39480i	−0.110809	+	0.993842i	$0.535344\pi$
$140$		0			0
$141$	−2.96383	+	1.00995i	−0.249599	+	0.0850529i
$142$		0			0
$143$	0.797626	−	4.05296i	0.0667009	−	0.338925i
$144$		0			0
$145$	1.91512	+	7.14731i	0.159042	+	0.593552i
$146$		0			0
$147$	3.32900	+	4.96962i	0.274571	+	0.409887i
$148$		0			0
$149$	1.55037	−	5.78607i	0.127012	−	0.474014i	−0.872892	−	0.487914i	$-0.837758\pi$
$149$	1.55037	−	5.78607i	0.127012	−	0.474014i	0.999903	+	0.0139002i	$0.00442471\pi$
$150$		0			0
$151$	−10.9825	−	10.9825i	−0.893741	−	0.893741i	0.101132	−	0.994873i	$-0.467753\pi$
$151$	−10.9825	−	10.9825i	−0.893741	−	0.893741i	−0.994873	+	0.101132i	$0.967753\pi$
$152$		0			0
$153$	3.46852	−	8.42940i	0.280413	−	0.681477i
$154$		0			0
$155$	−1.94912			−0.156557
$156$		0			0
$157$	10.2214			0.815760			0.407880	−	0.913036i	$-0.366268\pi$
$157$	10.2214			0.815760			0.407880	+	0.913036i	$0.366268\pi$
$158$		0			0
$159$	−1.85687	+	3.77648i	−0.147260	+	0.299495i
$160$		0			0
$161$	11.1146	+	11.1146i	0.875950	+	0.875950i
$162$		0			0
$163$	5.56650	−	20.7745i	0.436002	−	1.62718i	−0.302655	−	0.953100i	$-0.597873\pi$
$163$	5.56650	−	20.7745i	0.436002	−	1.62718i	0.738657	−	0.674082i	$-0.235460\pi$
$164$		0			0
$165$	1.17642	−	0.788051i	0.0915845	−	0.0613497i
$166$		0			0
$167$	2.83710	+	10.5882i	0.219542	+	0.819341i	0.984518	+	0.175283i	$0.0560839\pi$
$167$	2.83710	+	10.5882i	0.219542	+	0.819341i	−0.764976	+	0.644058i	$0.777249\pi$
$168$		0			0
$169$	7.95574	+	10.2814i	0.611980	+	0.790873i
$170$		0			0
$171$	−5.49657	−	13.1827i	−0.420333	−	1.00810i
$172$		0			0
$173$	10.1274	+	17.5412i	0.769975	+	1.33364i	0.937576	+	0.347781i	$0.113065\pi$
$173$	10.1274	+	17.5412i	0.769975	+	1.33364i	−0.167601	+	0.985855i	$0.553602\pi$
$174$		0			0
$175$	−14.0248	−	3.75794i	−1.06018	−	0.284074i
$176$		0			0
$177$	7.57665	+	6.62890i	0.569496	+	0.498259i
$178$		0			0
$179$	10.5903	−	18.3430i	0.791557	−	1.37102i	−0.133445	−	0.991056i	$-0.542604\pi$
$179$	10.5903	−	18.3430i	0.791557	−	1.37102i	0.925003	−	0.379961i	$-0.124063\pi$
$180$		0			0
$181$		−	14.0377i		−	1.04342i	−0.853124	−	0.521709i	$-0.825295\pi$
$181$		−	14.0377i		−	1.04342i	0.853124	−	0.521709i	$-0.174705\pi$
$182$		0			0
$183$	1.20767	+	18.1013i	0.0892732	+	1.33809i
$184$		0			0
$185$	4.79428	+	2.76798i	0.352483	+	0.203506i
$186$		0			0
$187$	−2.46138	+	2.46138i	−0.179994	+	0.179994i
$188$		0			0
$189$	−16.7679	−	1.04001i	−1.21968	−	0.0756496i
$190$		0			0
$191$	18.7332	−	10.8156i	1.35549	−	0.782592i	0.366477	−	0.930427i	$-0.380564\pi$
$191$	18.7332	−	10.8156i	1.35549	−	0.782592i	0.989012	+	0.147835i	$0.0472305\pi$
$192$		0			0
$193$	−20.6023	+	5.52036i	−1.48298	+	0.397364i	−0.907361	−	0.420352i	$-0.861907\pi$
$193$	−20.6023	+	5.52036i	−1.48298	+	0.397364i	−0.575622	+	0.817716i	$0.695240\pi$
$194$		0			0
$195$	−0.567526	+	4.42004i	−0.0406414	+	0.316526i
$196$		0			0
$197$	−24.7548	+	6.63302i	−1.76371	+	0.472583i	−0.987463	−	0.157851i	$-0.949543\pi$
$197$	−24.7548	+	6.63302i	−1.76371	+	0.472583i	−0.776242	+	0.630435i	$0.782877\pi$
$198$		0			0
$199$	−13.6540	+	7.88312i	−0.967904	+	0.558820i	−0.898597	−	0.438776i	$-0.855412\pi$
$199$	−13.6540	+	7.88312i	−0.967904	+	0.558820i	−0.0693073	+	0.997595i	$0.522079\pi$
$200$		0			0
$201$	2.04754	−	10.3569i	0.144423	−	0.730521i
$202$		0			0
$203$	−23.7066	+	23.7066i	−1.66388	+	1.66388i
$204$		0			0
$205$	−4.19109	−	2.41973i	−0.292718	−	0.169001i
$206$		0			0
$207$	−14.4555	+	1.93747i	−1.00472	+	0.134664i
$208$		0			0
$209$			5.45432i			0.377283i
$210$		0			0
$211$	5.20303	−	9.01192i	0.358192	−	0.620406i	−0.629467	−	0.777027i	$-0.716727\pi$
$211$	5.20303	−	9.01192i	0.358192	−	0.620406i	0.987659	+	0.156621i	$0.0500601\pi$
$212$		0			0
$213$	−4.52520	+	5.17218i	−0.310062	+	0.354392i
$214$		0			0
$215$	1.57644	+	0.422405i	0.107512	+	0.0288078i
$216$		0			0
$217$	−4.41563	−	7.64810i	−0.299753	−	0.519187i
$218$		0			0
$219$	3.21082	+	9.42258i	0.216967	+	0.636719i
$220$		0			0
$221$	−0.738700	−	10.9301i	−0.0496903	−	0.735237i
$222$		0			0
$223$	5.88651	+	21.9688i	0.394190	+	1.47114i	0.823156	+	0.567816i	$0.192211\pi$
$223$	5.88651	+	21.9688i	0.394190	+	1.47114i	−0.428966	+	0.903321i	$0.641122\pi$
$224$		0			0
$225$	10.6692	−	8.22643i	0.711278	−	0.548429i
$226$		0			0
$227$	5.14469	−	19.2003i	0.341465	−	1.27437i	−0.555222	−	0.831702i	$-0.687367\pi$
$227$	5.14469	−	19.2003i	0.341465	−	1.27437i	0.896688	−	0.442664i	$-0.145967\pi$
$228$		0			0
$229$	1.16288	+	1.16288i	0.0768456	+	0.0768456i	0.744485	−	0.667639i	$-0.232695\pi$
$229$	1.16288	+	1.16288i	0.0768456	+	0.0768456i	−0.667639	+	0.744485i	$0.732695\pi$
$230$		0			0
$231$	5.75736	+	2.83086i	0.378806	+	0.186257i
$232$		0			0
$233$	−23.8148			−1.56016			−0.780080	−	0.625680i	$-0.784822\pi$
$233$	−23.8148			−1.56016			−0.780080	+	0.625680i	$0.784822\pi$
$234$		0			0
$235$	−1.29001			−0.0841507
$236$		0			0
$237$	10.5347	+	5.17985i	0.684303	+	0.336467i
$238$		0			0
$239$	3.10170	+	3.10170i	0.200632	+	0.200632i	0.800271	−	0.599639i	$-0.204689\pi$
$239$	3.10170	+	3.10170i	0.200632	+	0.200632i	−0.599639	+	0.800271i	$0.704689\pi$
$240$		0			0
$241$	−2.25233	+	8.40583i	−0.145086	+	0.541467i	0.854666	+	0.519178i	$0.173762\pi$
$241$	−2.25233	+	8.40583i	−0.145086	+	0.541467i	−0.999752	+	0.0222886i	$0.992905\pi$
$242$		0			0
$243$	10.2095	−	11.7799i	0.654942	−	0.755679i
$244$		0			0
$245$	0.637817	+	2.38037i	0.0407487	+	0.152076i
$246$		0			0
$247$	−12.9288	−	11.2919i	−0.822640	−	0.718484i
$248$		0			0
$249$	−9.43543	−	27.6895i	−0.597946	−	1.75475i
$250$		0			0
$251$	−4.34184	−	7.52029i	−0.274055	−	0.474677i	0.695842	−	0.718195i	$-0.255032\pi$
$251$	−4.34184	−	7.52029i	−0.274055	−	0.474677i	−0.969896	+	0.243519i	$0.921698\pi$
$252$		0			0
$253$	5.37988	+	1.44153i	0.338230	+	0.0906284i
$254$		0			0
$255$	2.47275	−	2.82629i	0.154850	−	0.176989i
$256$		0			0
$257$	2.99467	−	5.18692i	0.186802	−	0.323551i	−0.757380	−	0.652974i	$-0.773521\pi$
$257$	2.99467	−	5.18692i	0.186802	−	0.323551i	0.944182	+	0.329423i	$0.106854\pi$
$258$		0			0
$259$			25.0829i			1.55858i
$260$		0			0
$261$	−4.13250	−	30.8325i	−0.255796	−	1.90849i
$262$		0			0
$263$	−16.5914	−	9.57907i	−1.02307	−	0.590670i	−0.108079	−	0.994142i	$-0.534470\pi$
$263$	−16.5914	−	9.57907i	−1.02307	−	0.590670i	−0.914992	+	0.403472i	$0.867803\pi$
$264$		0			0
$265$	−1.22596	+	1.22596i	−0.0753101	+	0.0753101i
$266$		0			0
$267$	2.68945	−	13.6038i	0.164591	−	0.832540i
$268$		0			0
$269$	22.0370	−	12.7231i	1.34362	−	0.775741i	0.356285	−	0.934377i	$-0.384043\pi$
$269$	22.0370	−	12.7231i	1.34362	−	0.775741i	0.987337	+	0.158637i	$0.0507098\pi$
$270$		0			0
$271$	22.0299	−	5.90289i	1.33822	−	0.358575i	0.482447	−	0.875925i	$-0.339748\pi$
$271$	22.0299	−	5.90289i	1.33822	−	0.358575i	0.855774	+	0.517350i	$0.173081\pi$
$272$		0			0
$273$	−18.6294	+	7.78650i	−1.12750	+	0.471260i
$274$		0			0
$275$	−4.96957	+	1.33159i	−0.299677	+	0.0802981i
$276$		0			0
$277$	−11.4444	+	6.60744i	−0.687628	+	0.397002i	−0.802723	−	0.596352i	$-0.796616\pi$
$277$	−11.4444	+	6.60744i	−0.687628	+	0.397002i	0.115095	+	0.993355i	$0.463283\pi$
$278$		0			0
$279$	8.12671	+	1.05059i	0.486534	+	0.0628971i
$280$		0			0
$281$	1.24623	−	1.24623i	0.0743436	−	0.0743436i	−0.668957	−	0.743301i	$-0.733259\pi$
$281$	1.24623	−	1.24623i	0.0743436	−	0.0743436i	0.743301	+	0.668957i	$0.233259\pi$
$282$		0			0
$283$	20.1262	+	11.6199i	1.19638	+	0.690728i	0.959745	−	0.280871i	$-0.0906233\pi$
$283$	20.1262	+	11.6199i	1.19638	+	0.690728i	0.236631	+	0.971600i	$0.423957\pi$
$284$		0			0
$285$	−0.391711	−	5.87124i	−0.0232030	−	0.347782i
$286$		0			0
$287$		−	21.9271i		−	1.29432i
$288$		0			0
$289$	3.88414	−	6.72753i	0.228479	−	0.395737i
$290$		0			0
$291$	1.33485	+	1.16788i	0.0782504	+	0.0684622i
$292$		0			0
$293$	2.69061	+	0.720947i	0.157187	+	0.0421182i	0.336555	−	0.941664i	$-0.390738\pi$
$293$	2.69061	+	0.720947i	0.157187	+	0.0421182i	−0.179367	+	0.983782i	$0.557405\pi$
$294$		0			0
$295$	2.07378	+	3.59188i	0.120740	+	0.209128i
$296$		0			0
$297$	−5.32979	+	2.65163i	−0.309266	+	0.153863i
$298$		0			0
$299$	−14.5547	+	9.76799i	−0.841722	+	0.564897i
$300$		0			0
$301$	1.91388	+	7.14269i	0.110314	+	0.411698i
$302$		0			0
$303$	10.8597	−	7.27456i	0.623871	−	0.417912i
$304$		0			0
$305$	−1.93444	+	7.21942i	−0.110766	+	0.413383i
$306$		0			0
$307$	15.5744	+	15.5744i	0.888881	+	0.888881i	0.994416	−	0.105535i	$-0.0336555\pi$
$307$	15.5744	+	15.5744i	0.888881	+	0.888881i	−0.105535	+	0.994416i	$0.533656\pi$
$308$		0			0
$309$	−4.82444	+	9.81188i	−0.274453	+	0.558179i
$310$		0			0
$311$	−16.8640			−0.956272			−0.478136	−	0.878286i	$-0.658687\pi$
$311$	−16.8640			−0.956272			−0.478136	+	0.878286i	$0.658687\pi$
$312$		0			0
$313$	14.7731			0.835026			0.417513	−	0.908671i	$-0.362902\pi$
$313$	14.7731			0.835026			0.417513	+	0.908671i	$0.362902\pi$
$314$		0			0
$315$	−6.40074	−	2.63377i	−0.360641	−	0.148396i
$316$		0			0
$317$	−3.02944	−	3.02944i	−0.170150	−	0.170150i	0.616895	−	0.787045i	$-0.288390\pi$
$317$	−3.02944	−	3.02944i	−0.170150	−	0.170150i	−0.787045	+	0.616895i	$0.788390\pi$
$318$		0			0
$319$	−3.07470	+	11.4749i	−0.172150	+	0.642472i
$320$		0			0
$321$	−8.08633	−	12.0715i	−0.451335	−	0.673765i
$322$		0			0
$323$	3.74392	+	13.9725i	0.208317	+	0.777450i
$324$		0			0
$325$	7.13193	−	14.5365i	0.395609	−	0.806340i
$326$		0			0
$327$	−23.9908	+	8.17505i	−1.32669	+	0.452081i
$328$		0			0
$329$	−2.92245	−	5.06183i	−0.161120	−	0.279068i
$330$		0			0
$331$	0.735585	+	0.197099i	0.0404314	+	0.0108336i	0.278978	−	0.960297i	$-0.410004\pi$
$331$	0.735585	+	0.197099i	0.0404314	+	0.0108336i	−0.238547	+	0.971131i	$0.576671\pi$
$332$		0			0
$333$	−18.4975	−	14.1251i	−1.01366	−	0.774049i
$334$		0			0
$335$	2.17476	−	3.76679i	0.118820	−	0.205802i
$336$		0			0
$337$			6.15955i			0.335532i	0.985827	+	0.167766i	$0.0536554\pi$
$337$			6.15955i			0.335532i	−0.985827	+	0.167766i	$0.946345\pi$
$338$		0			0
$339$	−26.0370	+	1.73711i	−1.41413	+	0.0943468i
$340$		0			0
$341$	−2.71004	−	1.56464i	−0.146757	−	0.0847300i
$342$		0			0
$343$	8.10810	−	8.10810i	0.437796	−	0.437796i
$344$		0			0
$345$	−5.89463	−	1.16536i	−0.317356	−	0.0627407i
$346$		0			0
$347$	5.68995	−	3.28509i	0.305452	−	0.176353i	−0.339437	−	0.940629i	$-0.610237\pi$
$347$	5.68995	−	3.28509i	0.305452	−	0.176353i	0.644890	+	0.764276i	$0.276903\pi$
$348$		0			0
$349$	1.81261	−	0.485688i	0.0970270	−	0.0259983i	−0.209979	−	0.977706i	$-0.567340\pi$
$349$	1.81261	−	0.485688i	0.0970270	−	0.0259983i	0.307006	+	0.951708i	$0.400673\pi$
$350$		0			0
$351$	4.74870	−	18.1232i	0.253467	−	0.967344i
$352$		0			0
$353$	−26.6737	+	7.14721i	−1.41970	+	0.380407i	−0.885377	−	0.464873i	$-0.846100\pi$
$353$	−26.6737	+	7.14721i	−1.41970	+	0.380407i	−0.534323	+	0.845281i	$0.679433\pi$
$354$		0			0
$355$	−2.45199	+	1.41566i	−0.130138	+	0.0751353i
$356$		0			0
$357$	16.6919	+	3.29996i	0.883431	+	0.174652i
$358$		0			0
$359$	−10.1971	+	10.1971i	−0.538182	+	0.538182i	−0.922995	−	0.384813i	$-0.874266\pi$
$359$	−10.1971	+	10.1971i	−0.538182	+	0.538182i	0.384813	+	0.922995i	$0.374266\pi$
$360$		0			0
$361$	3.17498	+	1.83307i	0.167104	+	0.0964775i
$362$		0			0
$363$	−16.7420	+	1.11698i	−0.878727	+	0.0586260i
$364$		0			0
$365$			4.10118i			0.214665i
$366$		0			0
$367$	2.25960	−	3.91375i	0.117950	−	0.204296i	−0.801005	−	0.598658i	$-0.795701\pi$
$367$	2.25960	−	3.91375i	0.117950	−	0.204296i	0.918955	+	0.394362i	$0.129034\pi$
$368$		0			0
$369$	16.1702	+	12.3479i	0.841788	+	0.642807i
$370$		0			0
$371$	−7.58788	−	2.03316i	−0.393943	−	0.105557i
$372$		0			0
$373$	2.40745	+	4.16983i	0.124653	+	0.215905i	0.921597	−	0.388147i	$-0.126885\pi$
$373$	2.40745	+	4.16983i	0.124653	+	0.215905i	−0.796944	+	0.604053i	$0.793552\pi$
$374$		0			0
$375$	11.1033	−	3.78355i	0.573374	−	0.195382i
$376$		0			0
$377$	−20.8345	−	31.0443i	−1.07303	−	1.59886i
$378$		0			0
$379$	0.736874	+	2.75005i	0.0378507	+	0.141261i	0.982265	−	0.187496i	$-0.0600371\pi$
$379$	0.736874	+	2.75005i	0.0378507	+	0.141261i	−0.944415	+	0.328757i	$0.893370\pi$
$380$		0			0
$381$	7.93190	+	11.8409i	0.406363	+	0.606630i
$382$		0			0
$383$	−1.67036	+	6.23387i	−0.0853514	+	0.318536i	−0.995381	−	0.0960085i	$-0.969392\pi$
$383$	−1.67036	+	6.23387i	−0.0853514	+	0.318536i	0.910029	+	0.414544i	$0.136059\pi$
$384$		0			0
$385$	1.86901	+	1.86901i	0.0952536	+	0.0952536i
$386$		0			0
$387$	−6.34518	−	2.61090i	−0.322543	−	0.132720i
$388$		0			0
$389$	−5.45516			−0.276588			−0.138294	−	0.990391i	$-0.544162\pi$
$389$	−5.45516			−0.276588			−0.138294	+	0.990391i	$0.544162\pi$
$390$		0			0
$391$	14.7713			0.747016
$392$		0			0
$393$	−10.2485	+	20.8433i	−0.516970	+	1.05141i
$394$		0			0
$395$	3.41988	+	3.41988i	0.172073	+	0.172073i
$396$		0			0
$397$	−0.437429	+	1.63251i	−0.0219539	+	0.0819331i	−0.976034	−	0.217620i	$-0.930171\pi$
$397$	−0.437429	+	1.63251i	−0.0219539	+	0.0819331i	0.954080	+	0.299553i	$0.0968374\pi$
$398$		0			0
$399$	22.1507	−	14.8381i	1.10892	−	0.742832i
$400$		0			0
$401$	−5.16790	−	19.2869i	−0.258073	−	0.963141i	−0.966355	−	0.257212i	$-0.917196\pi$
$401$	−5.16790	−	19.2869i	−0.258073	−	0.963141i	0.708282	−	0.705929i	$-0.249470\pi$
$402$		0			0
$403$	9.31927	−	3.18460i	0.464226	−	0.158636i
$404$		0			0
$405$	5.54676	−	3.23708i	0.275621	−	0.160852i
$406$		0			0
$407$	4.44396	+	7.69716i	0.220279	+	0.381534i
$408$		0			0
$409$	8.48733	+	2.27417i	0.419671	+	0.112451i	0.462474	−	0.886633i	$-0.346962\pi$
$409$	8.48733	+	2.27417i	0.419671	+	0.112451i	−0.0428024	+	0.999084i	$0.513629\pi$
$410$		0			0
$411$	−17.8487	−	15.6160i	−0.880411	−	0.770281i
$412$		0			0
$413$	−9.39609	+	16.2745i	−0.462351	+	0.800816i
$414$		0			0
$415$		−	12.0519i		−	0.591603i
$416$		0			0
$417$	−2.18938	−	32.8159i	−0.107214	−	1.60700i
$418$		0			0
$419$	7.34045	+	4.23801i	0.358604	+	0.207040i	0.668468	−	0.743741i	$-0.266950\pi$
$419$	7.34045	+	4.23801i	0.358604	+	0.207040i	−0.309864	+	0.950781i	$0.600284\pi$
$420$		0			0
$421$	−15.5203	+	15.5203i	−0.756412	+	0.756412i	−0.975667	−	0.219255i	$-0.929637\pi$
$421$	−15.5203	+	15.5203i	−0.756412	+	0.756412i	0.219255	+	0.975667i	$0.429637\pi$
$422$		0			0
$423$	5.37860	+	0.695323i	0.261517	+	0.0338078i
$424$		0			0
$425$	−11.8167	+	6.82236i	−0.573193	+	0.330933i
$426$		0			0
$427$	−32.7105	+	8.76477i	−1.58297	+	0.424157i
$428$		0			0
$429$	−4.33724	+	5.69002i	−0.209404	+	0.274717i
$430$		0			0
$431$	26.3726	−	7.06652i	1.27032	−	0.340382i	0.440169	−	0.897915i	$-0.354919\pi$
$431$	26.3726	−	7.06652i	1.27032	−	0.340382i	0.830155	+	0.557533i	$0.188252\pi$
$432$		0			0
$433$	9.03766	−	5.21790i	0.434322	−	0.250756i	−0.266864	−	0.963734i	$-0.585987\pi$
$433$	9.03766	−	5.21790i	0.434322	−	0.250756i	0.701186	+	0.712978i	$0.252654\pi$
$434$		0			0
$435$	2.48563	−	12.5729i	0.119177	−	0.602823i
$436$		0			0
$437$	16.3663	−	16.3663i	0.782907	−	0.782907i
$438$		0			0
$439$	−22.1085	−	12.7643i	−1.05518	−	0.609208i	−0.131084	−	0.991371i	$-0.541846\pi$
$439$	−22.1085	−	12.7643i	−1.05518	−	0.609208i	−0.924095	+	0.382163i	$0.875179\pi$
$440$		0			0
$441$	−1.37630	−	10.2686i	−0.0655383	−	0.488980i
$442$		0			0
$443$		−	27.6082i		−	1.31170i	−0.754889	−	0.655852i	$-0.772309\pi$
$443$		−	27.6082i		−	1.31170i	0.754889	−	0.655852i	$-0.227691\pi$
$444$		0			0
$445$	2.85654	−	4.94767i	0.135413	−	0.234542i
$446$		0			0
$447$	−6.83179	+	7.80855i	−0.323133	+	0.369332i
$448$		0			0
$449$	26.6058	+	7.12899i	1.25560	+	0.336438i	0.824499	−	0.565864i	$-0.191457\pi$
$449$	26.6058	+	7.12899i	1.25560	+	0.336438i	0.431105	+	0.902302i	$0.358124\pi$
$450$		0			0
$451$	−3.88484	−	6.72874i	−0.182930	−	0.316844i
$452$		0			0
$453$	8.67694	+	25.4637i	0.407678	+	1.19639i
$454$		0			0
$455$	−8.29960	+	0.560921i	−0.389091	+	0.0262964i
$456$		0			0
$457$	5.68707	+	21.2244i	0.266030	+	0.992838i	0.961617	+	0.274396i	$0.0884778\pi$
$457$	5.68707	+	21.2244i	0.266030	+	0.992838i	−0.695587	+	0.718442i	$0.744856\pi$
$458$		0			0
$459$	−11.8334	+	10.4512i	−0.552335	+	0.487820i
$460$		0			0
$461$	5.98430	−	22.3337i	0.278717	−	1.04019i	−0.674593	−	0.738190i	$-0.735681\pi$
$461$	5.98430	−	22.3337i	0.278717	−	1.04019i	0.953310	−	0.301995i	$-0.0976526\pi$
$462$		0			0
$463$	−8.48586	−	8.48586i	−0.394371	−	0.394371i	0.481871	−	0.876242i	$-0.339957\pi$
$463$	−8.48586	−	8.48586i	−0.394371	−	0.394371i	−0.876242	+	0.481871i	$0.839957\pi$
$464$		0			0
$465$	3.02955	+	1.48961i	0.140492	+	0.0690791i
$466$		0			0
$467$	26.9837			1.24866			0.624329	−	0.781162i	$-0.285373\pi$
$467$	26.9837			1.24866			0.624329	+	0.781162i	$0.285373\pi$
$468$		0			0
$469$	19.7072			0.909996
$470$		0			0
$471$	−15.8874	−	7.81175i	−0.732054	−	0.359946i
$472$		0			0
$473$	1.85278	+	1.85278i	0.0851911	+	0.0851911i
$474$		0			0
$475$	−5.53361	+	20.6517i	−0.253900	+	0.947566i
$476$		0			0
$477$	5.77236	−	4.45076i	0.264298	−	0.203786i
$478$		0			0
$479$	5.46091	+	20.3804i	0.249515	+	0.931203i	0.971060	+	0.238836i	$0.0767657\pi$
$479$	5.46091	+	20.3804i	0.249515	+	0.931203i	−0.721545	+	0.692368i	$0.756568\pi$
$480$		0			0
$481$	−27.4453	−	5.40127i	−1.25140	−	0.246277i
$482$		0			0
$483$	−8.78130	−	25.7699i	−0.399563	−	1.17257i
$484$		0			0
$485$	0.365357	+	0.632817i	0.0165900	+	0.0287347i
$486$		0			0
$487$	15.7355	+	4.21633i	0.713046	+	0.191060i	0.597067	−	0.802192i	$-0.296333\pi$
$487$	15.7355	+	4.21633i	0.713046	+	0.191060i	0.115979	+	0.993252i	$0.462999\pi$
$488$		0			0
$489$	−24.5290	+	28.0360i	−1.10924	+	1.26783i
$490$		0			0
$491$	−16.2519	+	28.1492i	−0.733440	+	1.27036i	0.221965	+	0.975055i	$0.428753\pi$
$491$	−16.2519	+	28.1492i	−0.733440	+	1.27036i	−0.955404	+	0.295300i	$0.904580\pi$
$492$		0			0
$493$			31.5062i			1.41897i
$494$		0			0
$495$	−2.43081	+	0.325803i	−0.109257	+	0.0146438i
$496$		0			0
$497$	−11.1097	−	6.41422i	−0.498340	−	0.287717i
$498$		0			0
$499$	−10.3481	+	10.3481i	−0.463245	+	0.463245i	−0.899718	−	0.436472i	$-0.856228\pi$
$499$	−10.3481	+	10.3481i	−0.463245	+	0.463245i	0.436472	+	0.899718i	$0.356228\pi$
$500$		0			0
$501$	3.68228	−	18.6258i	0.164512	−	0.832138i
$502$		0			0
$503$	−19.4725	+	11.2424i	−0.868235	+	0.501276i	−0.866761	−	0.498723i	$-0.833803\pi$
$503$	−19.4725	+	11.2424i	−0.868235	+	0.501276i	−0.00147394	+	0.999999i	$0.500469\pi$
$504$		0			0
$505$	5.20160	−	1.39376i	0.231468	−	0.0620217i
$506$		0			0
$507$	−4.50826	−	22.0607i	−0.200219	−	0.979751i
$508$		0			0
$509$	27.6271	−	7.40267i	1.22455	−	0.328117i	0.412095	−	0.911141i	$-0.364797\pi$
$509$	27.6271	−	7.40267i	1.22455	−	0.328117i	0.812455	+	0.583023i	$0.198130\pi$
$510$		0			0
$511$	−16.0925	+	9.29103i	−0.711892	+	0.411011i
$512$		0			0
$513$	−1.53143	+	24.6909i	−0.0676141	+	1.09013i
$514$		0			0
$515$	−3.18523	+	3.18523i	−0.140358	+	0.140358i
$516$		0			0
$517$	−1.79362	−	1.03554i	−0.0788831	−	0.0455432i
$518$		0			0
$519$	−2.33541	−	35.0047i	−0.102513	−	1.53653i
$520$		0			0
$521$			7.17424i			0.314309i	0.987574	+	0.157155i	$0.0502321\pi$
$521$			7.17424i			0.314309i	−0.987574	+	0.157155i	$0.949768\pi$
$522$		0			0
$523$	11.5992	−	20.0904i	0.507199	−	0.878494i	−0.492767	−	0.870161i	$-0.664014\pi$
$523$	11.5992	−	20.0904i	0.507199	−	0.878494i	0.999965	−	0.00833218i	$-0.00265225\pi$
$524$		0			0
$525$	18.9271	+	16.5595i	0.826047	+	0.722718i
$526$		0			0
$527$	−8.01637	−	2.14798i	−0.349199	−	0.0935675i
$528$		0			0
$529$	−0.317449	−	0.549837i	−0.0138021	−	0.0239060i
$530$		0			0
$531$	−6.71042	−	16.0939i	−0.291208	−	0.698417i
$532$		0			0
$533$	23.9923	+	4.72171i	1.03922	+	0.204520i
$534$		0			0
$535$	−1.54930	−	5.78205i	−0.0669819	−	0.249980i
$536$		0			0
$537$	−30.4794	+	20.4172i	−1.31528	+	0.881069i
$538$		0			0
$539$	−1.02401	+	3.82165i	−0.0441071	+	0.164610i
$540$		0			0
$541$	30.2641	+	30.2641i	1.30115	+	1.30115i	0.927615	+	0.373539i	$0.121856\pi$
$541$	30.2641	+	30.2641i	1.30115	+	1.30115i	0.373539	+	0.927615i	$0.378144\pi$
$542$		0			0
$543$	−10.7284	+	21.8192i	−0.460398	+	0.936351i
$544$		0			0
$545$	−10.4420			−0.447286
$546$		0			0
$547$	29.5412			1.26309			0.631545	−	0.775339i	$-0.282421\pi$
$547$	29.5412			1.26309			0.631545	+	0.775339i	$0.282421\pi$
$548$		0			0
$549$	11.9568	−	29.0582i	0.510306	−	1.24018i
$550$		0			0
$551$	34.9083	+	34.9083i	1.48714	+	1.48714i
$552$		0			0
$553$	−5.67163	+	21.1668i	−0.241182	+	0.900104i
$554$		0			0
$555$	−5.33643	−	7.96637i	−0.226519	−	0.338153i
$556$		0			0
$557$	6.70422	+	25.0205i	0.284067	+	1.06015i	0.949518	+	0.313712i	$0.101572\pi$
$557$	6.70422	+	25.0205i	0.284067	+	1.06015i	−0.665451	+	0.746441i	$0.731761\pi$
$558$		0			0
$559$	−8.22754	+	0.556051i	−0.347988	+	0.0235185i
$560$		0			0
$561$	5.70688	−	1.94466i	0.240945	−	0.0821038i
$562$		0			0
$563$	2.40232	+	4.16095i	0.101246	+	0.175363i	0.912198	−	0.409749i	$-0.134384\pi$
$563$	2.40232	+	4.16095i	0.101246	+	0.175363i	−0.810952	+	0.585112i	$0.801050\pi$
$564$		0			0
$565$	−10.3844	−	2.78250i	−0.436876	−	0.117061i
$566$		0			0
$567$	25.2679	+	14.4314i	1.06115	+	0.606061i
$568$		0			0
$569$	1.00204	−	1.73559i	0.0420078	−	0.0727597i	−0.844257	−	0.535938i	$-0.819958\pi$
$569$	1.00204	−	1.73559i	0.0420078	−	0.0727597i	0.886265	+	0.463179i	$0.153291\pi$
$570$		0			0
$571$			16.7105i			0.699311i	0.936878	+	0.349656i	$0.113701\pi$
$571$			16.7105i			0.699311i	−0.936878	+	0.349656i	$0.886299\pi$
$572$		0			0
$573$	−37.3834	+	2.49411i	−1.56171	+	0.104193i
$574$		0			0
$575$	18.9074	+	10.9162i	0.788492	+	0.455236i
$576$		0			0
$577$	14.2655	−	14.2655i	0.593883	−	0.593883i	−0.344795	−	0.938678i	$-0.612052\pi$
$577$	14.2655	−	14.2655i	0.593883	−	0.593883i	0.938678	+	0.344795i	$0.112052\pi$
$578$		0			0
$579$	36.2415	+	7.16487i	1.50615	+	0.297762i
$580$		0			0
$581$	47.2901	−	27.3030i	1.96193	−	1.13272i
$582$		0			0
$583$	−2.68870	+	0.720434i	−0.111354	+	0.0298373i
$584$		0			0
$585$	4.26014	−	6.43644i	0.176135	−	0.266114i
$586$		0			0
$587$	−1.79654	+	0.481380i	−0.0741509	+	0.0198687i	−0.295704	−	0.955280i	$-0.595554\pi$
$587$	−1.79654	+	0.481380i	−0.0741509	+	0.0198687i	0.221553	+	0.975148i	$0.428887\pi$
$588$		0			0
$589$	−11.2619	+	6.50207i	−0.464039	+	0.267913i
$590$		0			0
$591$	43.5462	+	8.60900i	1.79125	+	0.354127i
$592$		0			0
$593$	−32.1956	+	32.1956i	−1.32212	+	1.32212i	−0.410057	+	0.912060i	$0.634491\pi$
$593$	−32.1956	+	32.1956i	−1.32212	+	1.32212i	−0.912060	+	0.410057i	$0.865509\pi$
$594$		0			0
$595$	6.07081	+	3.50499i	0.248879	+	0.143690i
$596$		0			0
$597$	27.2474	−	1.81786i	1.11516	−	0.0744001i
$598$		0			0
$599$		−	14.7278i		−	0.601762i	−0.953662	−	0.300881i	$-0.902719\pi$
$599$		−	14.7278i		−	0.601762i	0.953662	−	0.300881i	$-0.0972807\pi$
$600$		0			0
$601$	23.2965	−	40.3507i	0.950282	−	1.64594i	0.205470	−	0.978663i	$-0.434128\pi$
$601$	23.2965	−	40.3507i	0.950282	−	1.64594i	0.744812	−	0.667274i	$-0.232539\pi$
$602$		0			0
$603$	−11.0978	+	14.5332i	−0.451939	+	0.591837i
$604$		0			0
$605$	−6.67728	−	1.78917i	−0.271470	−	0.0727402i
$606$		0			0
$607$	−5.31772	−	9.21056i	−0.215840	−	0.373845i	0.737692	−	0.675137i	$-0.235915\pi$
$607$	−5.31772	−	9.21056i	−0.215840	−	0.373845i	−0.953532	+	0.301292i	$0.902582\pi$
$608$		0			0
$609$	54.9655	−	18.7299i	2.22732	−	0.758975i
$610$		0			0
$611$	6.16788	−	2.10770i	0.249526	−	0.0852684i
$612$		0			0
$613$	−4.55636	−	17.0046i	−0.184030	−	0.686808i	−0.994836	−	0.101494i	$-0.967638\pi$
$613$	−4.55636	−	17.0046i	−0.184030	−	0.686808i	0.810806	−	0.585314i	$-0.199029\pi$
$614$		0			0
$615$	4.66503	+	6.96408i	0.188112	+	0.280819i
$616$		0			0
$617$	−1.61026	+	6.00956i	−0.0648265	+	0.241936i	−0.990734	−	0.135813i	$-0.956635\pi$
$617$	−1.61026	+	6.00956i	−0.0648265	+	0.241936i	0.925908	+	0.377749i	$0.123302\pi$
$618$		0			0
$619$	20.3122	+	20.3122i	0.816415	+	0.816415i	0.985587	−	0.169172i	$-0.0541093\pi$
$619$	20.3122	+	20.3122i	0.816415	+	0.816415i	−0.169172	+	0.985587i	$0.554109\pi$
$620$		0			0
$621$	23.9492	+	8.03614i	0.961047	+	0.322479i
$622$		0			0
$623$	25.8854			1.03708
$624$		0			0
$625$	−17.6213			−0.704851
$626$		0			0
$627$	4.16847	−	8.47777i	0.166473	−	0.338570i
$628$		0			0
$629$	16.6676	+	16.6676i	0.664583	+	0.664583i
$630$		0			0
$631$	−7.88943	+	29.4438i	−0.314073	+	1.17214i	0.610776	+	0.791804i	$0.290858\pi$
$631$	−7.88943	+	29.4438i	−0.314073	+	1.17214i	−0.924849	+	0.380334i	$0.875809\pi$
$632$		0			0
$633$	−14.9746	+	10.0310i	−0.595186	+	0.398697i
$634$		0			0
$635$	1.51971	+	5.67162i	0.0603077	+	0.225072i
$636$		0			0
$637$	−6.93879	−	10.3391i	−0.274925	−	0.409650i
$638$		0			0
$639$	10.9865	−	4.58085i	0.434618	−	0.181216i
$640$		0			0
$641$	−15.6856	−	27.1682i	−0.619543	−	1.07308i	−0.989569	−	0.144058i	$-0.953985\pi$
$641$	−15.6856	−	27.1682i	−0.619543	−	1.07308i	0.370026	−	0.929021i	$-0.379349\pi$
$642$		0			0
$643$	4.97838	+	1.33395i	0.196328	+	0.0526060i	0.355643	−	0.934622i	$-0.384262\pi$
$643$	4.97838	+	1.33395i	0.196328	+	0.0526060i	−0.159315	+	0.987228i	$0.550929\pi$
$644$		0			0
$645$	−2.12747	−	1.86135i	−0.0837690	−	0.0732905i
$646$		0			0
$647$	4.80729	−	8.32648i	0.188994	−	0.327348i	−0.755921	−	0.654663i	$-0.772811\pi$
$647$	4.80729	−	8.32648i	0.188994	−	0.327348i	0.944915	+	0.327315i	$0.106144\pi$
$648$		0			0
$649$			6.65884i			0.261382i
$650$		0			0
$651$	1.01825	+	15.2623i	0.0399085	+	0.598176i
$652$		0			0
$653$	−16.4158	−	9.47768i	−0.642401	−	0.370890i	0.143138	−	0.989703i	$-0.454281\pi$
$653$	−16.4158	−	9.47768i	−0.642401	−	0.370890i	−0.785539	+	0.618813i	$0.787614\pi$
$654$		0			0
$655$	−6.76636	+	6.76636i	−0.264384	+	0.264384i
$656$		0			0
$657$	2.21057	−	17.0996i	0.0862424	−	0.667119i
$658$		0			0
$659$	23.6778	−	13.6704i	0.922357	−	0.532523i	0.0379709	−	0.999279i	$-0.487911\pi$
$659$	23.6778	−	13.6704i	0.922357	−	0.532523i	0.884386	+	0.466756i	$0.154577\pi$
$660$		0			0
$661$	−9.46548	+	2.53627i	−0.368165	+	0.0986494i	−0.438158	−	0.898898i	$-0.644369\pi$
$661$	−9.46548	+	2.53627i	−0.368165	+	0.0986494i	0.0699932	+	0.997547i	$0.477702\pi$
$662$		0			0
$663$	−7.20515	+	17.5534i	−0.279825	+	0.681719i
$664$		0			0
$665$	10.6098	−	2.84289i	0.411431	−	0.110243i
$666$		0			0
$667$	43.6578	−	25.2058i	1.69044	−	0.975974i
$668$		0			0
$669$	7.64010	−	38.6453i	0.295383	−	1.49411i
$670$		0			0
$671$	−8.48497	+	8.48497i	−0.327559	+	0.327559i
$672$		0			0
$673$	−6.65548	−	3.84254i	−0.256550	−	0.148119i	0.366210	−	0.930532i	$-0.380655\pi$
$673$	−6.65548	−	3.84254i	−0.256550	−	0.148119i	−0.622760	+	0.782413i	$0.713989\pi$
$674$		0			0
$675$	−22.8704	+	4.63260i	−0.880282	+	0.178309i
$676$		0			0
$677$			11.5419i			0.443593i	0.975093	+	0.221797i	$0.0711921\pi$
$677$			11.5419i			0.443593i	−0.975093	+	0.221797i	$0.928808\pi$
$678$		0			0
$679$	−1.65540	+	2.86724i	−0.0635284	+	0.110034i
$680$		0			0
$681$	−22.6703	+	25.9116i	−0.868729	+	0.992933i
$682$		0			0
$683$	−19.8376	−	5.31546i	−0.759063	−	0.203390i	−0.141529	−	0.989934i	$-0.545202\pi$
$683$	−19.8376	−	5.31546i	−0.759063	−	0.203390i	−0.617535	+	0.786544i	$0.711868\pi$
$684$		0			0
$685$	−4.88529	−	8.46157i	−0.186657	−	0.323300i
$686$		0			0
$687$	−0.918763	−	2.69623i	−0.0350530	−	0.102868i
$688$		0			0
$689$	3.85860	−	7.86471i	0.147001	−	0.299622i
$690$		0			0
$691$	−0.529217	−	1.97507i	−0.0201324	−	0.0751350i	0.955129	−	0.296191i	$-0.0957164\pi$
$691$	−0.529217	−	1.97507i	−0.0201324	−	0.0751350i	−0.975261	+	0.221056i	$0.929050\pi$
$692$		0			0
$693$	−6.78531	−	8.80013i	−0.257753	−	0.334289i
$694$		0			0
$695$	3.50695	−	13.0881i	0.133026	−	0.496460i
$696$		0			0
$697$	−14.5706	−	14.5706i	−0.551901	−	0.551901i
$698$		0			0
$699$	37.0159	+	18.2005i	1.40007	+	0.688406i
$700$		0			0
$701$	−13.4888			−0.509464			−0.254732	−	0.967012i	$-0.581987\pi$
$701$	−13.4888			−0.509464			−0.254732	+	0.967012i	$0.581987\pi$
$702$		0			0
$703$	36.9349			1.39303
$704$		0			0
$705$	2.00509	+	0.985888i	0.0755159	+	0.0371307i
$706$		0			0
$707$	17.2530	+	17.2530i	0.648864	+	0.648864i
$708$		0			0
$709$	−3.48407	+	13.0027i	−0.130847	+	0.488328i	−0.999980	−	0.00624974i	$-0.998011\pi$
$709$	−3.48407	+	13.0027i	−0.130847	+	0.488328i	0.869133	+	0.494578i	$0.164677\pi$
$710$		0			0
$711$	−12.4156	−	16.1023i	−0.465623	−	0.603884i
$712$		0			0
$713$	3.43689	+	12.8267i	0.128713	+	0.480362i
$714$		0			0
$715$	−2.44751	+	1.64257i	−0.0915315	+	0.0614287i
$716$		0			0
$717$	−2.45057	−	7.19152i	−0.0915181	−	0.268572i
$718$		0			0
$719$	−9.18916	−	15.9161i	−0.342698	−	0.593570i	0.642235	−	0.766508i	$-0.278007\pi$
$719$	−9.18916	−	15.9161i	−0.342698	−	0.593570i	−0.984933	+	0.172938i	$0.944674\pi$
$720$		0			0
$721$	−19.7145	−	5.28248i	−0.734205	−	0.196730i
$722$		0			0
$723$	9.92502	−	11.3440i	0.369115	−	0.421889i
$724$		0			0
$725$	−23.2835	+	40.3282i	−0.864727	+	1.49775i
$726$		0			0
$727$			14.3838i			0.533466i	0.963770	+	0.266733i	$0.0859442\pi$
$727$			14.3838i			0.533466i	−0.963770	+	0.266733i	$0.914056\pi$
$728$		0			0
$729$	−24.8717	+	10.5071i	−0.921174	+	0.389151i
$730$		0			0
$731$	6.01811	+	3.47456i	0.222588	+	0.128511i
$732$		0			0
$733$	3.75917	−	3.75917i	0.138848	−	0.138848i	−0.634266	−	0.773114i	$-0.718698\pi$
$733$	3.75917	−	3.75917i	0.138848	−	0.138848i	0.773114	+	0.634266i	$0.218698\pi$
$734$		0			0
$735$	0.827823	−	4.18731i	0.0305347	−	0.154451i
$736$		0			0
$737$	6.04753	−	3.49154i	0.222764	−	0.128613i
$738$		0			0
$739$	−37.0517	+	9.92797i	−1.36297	+	0.365206i	−0.864905	−	0.501935i	$-0.832622\pi$
$739$	−37.0517	+	9.92797i	−1.36297	+	0.365206i	−0.498063	+	0.867141i	$0.665955\pi$
$740$		0			0
$741$	11.4657	+	27.4320i	0.421203	+	1.00774i
$742$		0			0
$743$	−32.0441	+	8.58618i	−1.17558	+	0.314996i	−0.793173	−	0.608996i	$-0.791572\pi$
$743$	−32.0441	+	8.58618i	−1.17558	+	0.314996i	−0.382410	+	0.923993i	$0.624906\pi$
$744$		0			0
$745$	−3.70182	+	2.13725i	−0.135624	+	0.0783027i
$746$		0			0
$747$	−6.49605	+	50.2495i	−0.237678	+	1.83853i
$748$		0			0
$749$	19.1782	−	19.1782i	0.700757	−	0.700757i
$750$		0			0
$751$	−19.2045	−	11.0877i	−0.700782	−	0.404597i	0.106857	−	0.994274i	$-0.465921\pi$
$751$	−19.2045	−	11.0877i	−0.700782	−	0.404597i	−0.807639	+	0.589678i	$0.799255\pi$
$752$		0			0
$753$	1.00124	+	15.0072i	0.0364871	+	0.546893i
$754$		0			0
$755$			11.0831i			0.403354i
$756$		0			0
$757$	10.5455	−	18.2654i	0.383284	−	0.663868i	−0.608245	−	0.793749i	$-0.708126\pi$
$757$	10.5455	−	18.2654i	0.383284	−	0.663868i	0.991530	+	0.129881i	$0.0414597\pi$
$758$		0			0
$759$	−7.26037	−	6.35218i	−0.263535	−	0.230570i
$760$		0			0
$761$	31.8738	+	8.54057i	1.15543	+	0.309595i	0.785137	−	0.619322i	$-0.212592\pi$
$761$	31.8738	+	8.54057i	1.15543	+	0.309595i	0.370288	+	0.928917i	$0.379259\pi$
$762$		0			0
$763$	−23.6559	−	40.9732i	−0.856400	−	1.48333i
$764$		0			0
$765$	−6.00345	+	2.50316i	−0.217055	+	0.0905020i
$766$		0			0
$767$	−15.7840	−	13.7855i	−0.569926	−	0.497767i
$768$		0			0
$769$	−1.87152	−	6.98462i	−0.0674889	−	0.251872i	0.923937	−	0.382546i	$-0.124953\pi$
$769$	−1.87152	−	6.98462i	−0.0674889	−	0.251872i	−0.991425	+	0.130674i	$0.958286\pi$
$770$		0			0
$771$	−8.61880	+	5.77347i	−0.310398	+	0.207927i
$772$		0			0
$773$	2.16927	−	8.09584i	0.0780234	−	0.291187i	−0.915878	−	0.401456i	$-0.868504\pi$
$773$	2.16927	−	8.09584i	0.0780234	−	0.291187i	0.993902	+	0.110268i	$0.0351710\pi$
$774$		0			0
$775$	−8.67364	−	8.67364i	−0.311566	−	0.311566i
$776$		0			0
$777$	19.1697	−	38.9870i	0.687707	−	1.39865i
$778$		0			0
$779$	−32.2879			−1.15684
$780$		0			0
$781$	−4.54564			−0.162656
$782$		0			0
$783$	−17.1405	+	51.0820i	−0.612553	+	1.82552i
$784$		0			0
$785$	−5.15753	−	5.15753i	−0.184080	−	0.184080i
$786$		0			0
$787$	−8.20017	+	30.6035i	−0.292305	+	1.09090i	0.651030	+	0.759052i	$0.274337\pi$
$787$	−8.20017	+	30.6035i	−0.292305	+	1.09090i	−0.943335	+	0.331843i	$0.892329\pi$
$788$		0			0
$789$	18.4676	+	27.5690i	0.657465	+	0.981482i
$790$		0			0
$791$	−12.6073	−	47.0509i	−0.448263	−	1.67294i
$792$		0			0
$793$	−2.54648	−	37.6787i	−0.0904282	−	1.33801i
$794$		0			0
$795$	2.84248	−	0.968596i	0.100812	−	0.0343526i
$796$		0			0
$797$	19.0468	+	32.9900i	0.674673	+	1.16857i	0.976564	+	0.215225i	$0.0690486\pi$
$797$	19.0468	+	32.9900i	0.674673	+	1.16857i	−0.301892	+	0.953342i	$0.597618\pi$
$798$		0			0
$799$	−5.30557	−	1.42162i	−0.187698	−	0.0502934i
$800$		0			0
$801$	−14.5770	+	19.0893i	−0.515053	+	0.674488i
$802$		0			0
$803$	−3.29219	+	5.70225i	−0.116179	+	0.201228i
$804$		0			0
$805$		−	11.2164i		−	0.395325i
$806$		0			0
$807$	−43.9763	+	2.93397i	−1.54804	+	0.103281i
$808$		0			0
$809$	−22.2820	−	12.8645i	−0.783395	−	0.452293i	0.0542373	−	0.998528i	$-0.482727\pi$
$809$	−22.2820	−	12.8645i	−0.783395	−	0.452293i	−0.837632	+	0.546235i	$0.816061\pi$
$810$		0			0
$811$	33.3327	−	33.3327i	1.17047	−	1.17047i	0.188370	−	0.982098i	$-0.439679\pi$
$811$	33.3327	−	33.3327i	1.17047	−	1.17047i	0.982098	−	0.188370i	$-0.0603205\pi$
$812$		0			0
$813$	−38.7529	−	7.66136i	−1.35912	−	0.268696i
$814$		0			0
$815$	−13.2911	+	7.67363i	−0.465568	+	0.268796i
$816$		0			0
$817$	10.5177	−	2.81821i	0.367968	−	0.0985966i
$818$		0			0
$819$	34.9070	+	2.13482i	1.21975	+	0.0745967i
$820$		0			0
$821$	−14.7208	+	3.94443i	−0.513759	+	0.137661i	−0.506378	−	0.862311i	$-0.669016\pi$
$821$	−14.7208	+	3.94443i	−0.513759	+	0.137661i	−0.00738091	+	0.999973i	$0.502349\pi$
$822$		0			0
$823$	9.16080	−	5.28899i	0.319325	−	0.184363i	−0.331766	−	0.943362i	$-0.607645\pi$
$823$	9.16080	−	5.28899i	0.319325	−	0.184363i	0.651092	+	0.758999i	$0.274311\pi$
$824$		0			0
$825$	8.74199	+	1.72827i	0.304357	+	0.0601708i
$826$		0			0
$827$	18.9244	−	18.9244i	0.658067	−	0.658067i	−0.296855	−	0.954922i	$-0.595938\pi$
$827$	18.9244	−	18.9244i	0.658067	−	0.658067i	0.954922	+	0.296855i	$0.0959379\pi$
$828$		0			0
$829$	−21.9686	−	12.6836i	−0.763000	−	0.440518i	0.0673717	−	0.997728i	$-0.478539\pi$
$829$	−21.9686	−	12.6836i	−0.763000	−	0.440518i	−0.830372	+	0.557210i	$0.811872\pi$
$830$		0			0
$831$	22.8381	−	1.52369i	0.792244	−	0.0528561i
$832$		0			0
$833$			10.4929i			0.363558i
$834$		0			0
$835$	3.91105	−	6.77414i	0.135348	−	0.234429i
$836$		0			0
$837$	−11.8286	−	7.84380i	−0.408857	−	0.271121i
$838$		0			0
$839$	−38.4597	−	10.3053i	−1.32778	−	0.355777i	−0.475891	−	0.879504i	$-0.657874\pi$
$839$	−38.4597	−	10.3053i	−1.32778	−	0.355777i	−0.851886	+	0.523727i	$0.824541\pi$
$840$		0			0
$841$	39.2624	+	68.0045i	1.35388	+	2.34498i
$842$		0			0
$843$	−2.88947	+	0.984608i	−0.0995185	+	0.0339117i
$844$		0			0
$845$	1.17346	−	9.20207i	0.0403681	−	0.316561i
$846$		0			0
$847$	−8.10658	−	30.2542i	−0.278545	−	1.03955i
$848$		0			0
$849$	−22.4021	−	33.4424i	−0.768838	−	1.14774i
$850$		0			0
$851$	9.76160	−	36.4308i	0.334623	−	1.24883i
$852$		0			0
$853$	−11.4412	−	11.4412i	−0.391738	−	0.391738i	0.483569	−	0.875306i	$-0.339340\pi$
$853$	−11.4412	−	11.4412i	−0.391738	−	0.391738i	−0.875306	+	0.483569i	$0.839340\pi$
$854$		0			0
$855$	−3.87825	+	9.42517i	−0.132633	+	0.322334i
$856$		0			0
$857$	−9.00658			−0.307659			−0.153830	−	0.988097i	$-0.549161\pi$
$857$	−9.00658			−0.307659			−0.153830	+	0.988097i	$0.549161\pi$
$858$		0			0
$859$	−9.85659			−0.336302			−0.168151	−	0.985761i	$-0.553780\pi$
$859$	−9.85659			−0.336302			−0.168151	+	0.985761i	$0.553780\pi$
$860$		0			0
$861$	−16.7578	+	34.0818i	−0.571105	+	1.16151i
$862$		0			0
$863$	−5.16629	−	5.16629i	−0.175862	−	0.175862i	0.613687	−	0.789549i	$-0.289686\pi$
$863$	−5.16629	−	5.16629i	−0.175862	−	0.175862i	−0.789549	+	0.613687i	$0.789686\pi$
$864$		0			0
$865$	3.74085	−	13.9611i	0.127193	−	0.474690i
$866$		0			0
$867$	−11.1787	+	7.48830i	−0.379650	+	0.254316i
$868$		0			0
$869$	2.00969	+	7.50027i	0.0681741	+	0.254429i
$870$		0			0
$871$	−4.24369	+	21.5633i	−0.143792	+	0.730646i
$872$		0			0
$873$	−1.18224	−	2.83542i	−0.0400128	−	0.0959645i
$874$		0			0
$875$	10.9483	+	18.9631i	0.370121	+	0.641068i
$876$		0			0
$877$	−10.7822	−	2.88909i	−0.364090	−	0.0975575i	0.0721361	−	0.997395i	$-0.477018\pi$
$877$	−10.7822	−	2.88909i	−0.364090	−	0.0975575i	−0.436226	+	0.899837i	$0.643685\pi$
$878$		0			0
$879$	−3.63110	−	3.17689i	−0.122474	−	0.107154i
$880$		0			0
$881$	16.9734	−	29.3987i	0.571848	−	0.990469i	−0.424529	−	0.905414i	$-0.639560\pi$
$881$	16.9734	−	29.3987i	0.571848	−	0.990469i	0.996376	−	0.0850545i	$-0.0271064\pi$
$882$		0			0
$883$		−	38.3063i		−	1.28911i	−0.764558	−	0.644555i	$-0.777043\pi$
$883$		−	38.3063i		−	1.28911i	0.764558	−	0.644555i	$-0.222957\pi$
$884$		0			0
$885$	−0.478216	−	7.16783i	−0.0160751	−	0.240944i
$886$		0			0
$887$	33.5942	+	19.3956i	1.12798	+	0.651242i	0.943427	−	0.331580i	$-0.107582\pi$
$887$	33.5942	+	19.3956i	1.12798	+	0.651242i	0.184557	+	0.982822i	$0.440915\pi$
$888$		0			0
$889$	−18.8120	+	18.8120i	−0.630933	+	0.630933i
$890$		0			0
$891$	10.3107	−	0.0481897i	0.345422	−	0.00161442i
$892$		0			0
$893$	−7.45361	+	4.30334i	−0.249425	+	0.144006i
$894$		0			0
$895$	−14.5991	+	3.91183i	−0.487995	+	0.130758i
$896$		0			0
$897$	30.0879	−	4.05915i	1.00461	−	0.135531i
$898$		0			0
$899$	−27.3584	+	7.33066i	−0.912454	+	0.244491i
$900$		0			0
$901$	−6.39320	+	3.69111i	−0.212988	+	0.122969i
$902$		0			0
$903$	2.48402	−	12.5647i	0.0826631	−	0.418128i
$904$		0			0
$905$	−7.08316	+	7.08316i	−0.235452	+	0.235452i
$906$		0			0
$907$	−46.6252	−	26.9191i	−1.54816	−	0.893833i	−0.998282	−	0.0585904i	$-0.981339\pi$
$907$	−46.6252	−	26.9191i	−1.54816	−	0.893833i	−0.549882	−	0.835242i	$-0.685327\pi$
$908$		0			0
$909$	−22.4390	+	3.00751i	−0.744255	+	0.0997529i
$910$		0			0
$911$		−	25.8976i		−	0.858026i	−0.903298	−	0.429013i	$-0.858861\pi$
$911$		−	25.8976i		−	0.858026i	0.903298	−	0.429013i	$-0.141139\pi$
$912$		0			0
$913$	9.67457	−	16.7568i	0.320181	−	0.554570i
$914$		0			0
$915$	8.52419	−	9.74292i	0.281801	−	0.322091i
$916$		0			0
$917$	−41.8793	−	11.2215i	−1.38298	−	0.370567i
$918$		0			0
$919$	−17.0250	−	29.4881i	−0.561602	−	0.972723i	−0.997357	−	0.0726574i	$-0.976852\pi$
$919$	−17.0250	−	29.4881i	−0.561602	−	0.972723i	0.435755	−	0.900065i	$-0.356481\pi$
$920$		0			0
$921$	−12.3049	−	36.1105i	−0.405461	−	1.18988i
$922$		0			0
$923$	9.41066	−	10.7749i	0.309756	−	0.354660i
$924$		0			0
$925$	9.01712	+	33.6524i	0.296481	+	1.10648i
$926$		0			0
$927$	14.9975	−	11.5638i	0.492582	−	0.379804i
$928$		0			0
$929$	−7.98031	+	29.7829i	−0.261826	+	0.977146i	0.702339	+	0.711842i	$0.252139\pi$
$929$	−7.98031	+	29.7829i	−0.261826	+	0.977146i	−0.964165	+	0.265304i	$0.914528\pi$
$930$		0			0
$931$	11.6260	+	11.6260i	0.381026	+	0.381026i
$932$		0			0
$933$	26.2122	+	12.8884i	0.858148	+	0.421946i
$934$		0			0
$935$	2.48392			0.0812329
$936$		0			0
$937$	23.2796			0.760511			0.380255	−	0.924881i	$-0.375836\pi$
$937$	23.2796			0.760511			0.380255	+	0.924881i	$0.375836\pi$
$938$		0			0
$939$	−22.9622	−	11.2904i	−0.749343	−	0.368447i
$940$		0			0
$941$	−37.3219	−	37.3219i	−1.21666	−	1.21666i	−0.968794	−	0.247867i	$-0.920271\pi$
$941$	−37.3219	−	37.3219i	−1.21666	−	1.21666i	−0.247867	−	0.968794i	$-0.579729\pi$
$942$		0			0
$943$	−8.53345	+	31.8473i	−0.277887	+	1.03709i
$944$		0			0
$945$	7.93597	+	8.98550i	0.258157	+	0.292298i
$946$		0			0
$947$	−11.2676	−	42.0512i	−0.366147	−	1.36648i	−0.865859	−	0.500289i	$-0.833227\pi$
$947$	−11.2676	−	42.0512i	−0.366147	−	1.36648i	0.499711	−	0.866192i	$-0.333439\pi$
$948$		0			0
$949$	−6.70078	−	19.6089i	−0.217516	−	0.636531i
$950$		0			0
$951$	2.39348	+	7.02399i	0.0776139	+	0.227768i
$952$		0			0
$953$	16.4099	+	28.4228i	0.531570	+	0.920706i	0.999321	+	0.0368460i	$0.0117311\pi$
$953$	16.4099	+	28.4228i	0.531570	+	0.920706i	−0.467751	+	0.883860i	$0.654936\pi$
$954$		0			0
$955$	−14.9098	−	3.99506i	−0.482468	−	0.129277i
$956$		0			0
$957$	13.5488	−	15.4859i	0.437970	−	0.500588i
$958$		0			0
$959$	22.1348	−	38.3386i	0.714771	−	1.23802i
$960$		0			0
$961$			23.5392i			0.759329i
$962$		0			0
$963$	3.34312	+	24.9430i	0.107731	+	0.803776i
$964$		0			0
$965$	13.1809	+	7.61002i	0.424310	+	0.244975i
$966$		0			0
$967$	16.9803	−	16.9803i	0.546048	−	0.546048i	−0.379247	−	0.925295i	$-0.623817\pi$
$967$	16.9803	−	16.9803i	0.546048	−	0.546048i	0.925295	+	0.379247i	$0.123817\pi$
$968$		0			0
$969$	4.85923	−	24.5791i	0.156101	−	0.789593i
$970$		0			0
$971$	−14.0133	+	8.09059i	−0.449708	+	0.259639i	−0.707707	−	0.706506i	$-0.750270\pi$
$971$	−14.0133	+	8.09059i	−0.449708	+	0.259639i	0.257999	+	0.966145i	$0.416937\pi$
$972$		0			0
$973$	59.3011	−	15.8897i	1.90110	−	0.509399i
$974$		0			0
$975$	−22.1949	+	17.1438i	−0.710805	+	0.549042i
$976$		0			0
$977$	−25.2983	+	6.77867i	−0.809366	+	0.216869i	−0.639692	−	0.768631i	$-0.720938\pi$
$977$	−25.2983	+	6.77867i	−0.809366	+	0.216869i	−0.169674	+	0.985500i	$0.554271\pi$
$978$		0			0
$979$	7.94343	−	4.58614i	0.253873	−	0.146574i
$980$		0			0
$981$	43.5372	+	5.62831i	1.39004	+	0.179698i
$982$		0			0
$983$	−22.1588	+	22.1588i	−0.706756	+	0.706756i	−0.965852	−	0.259096i	$-0.916575\pi$
$983$	−22.1588	+	22.1588i	−0.706756	+	0.706756i	0.259096	+	0.965852i	$0.416575\pi$
$984$		0			0
$985$	15.8376	+	9.14387i	0.504629	+	0.291348i
$986$		0			0
$987$	0.673923	+	10.1012i	0.0214512	+	0.321525i
$988$		0			0
$989$		−	11.1190i		−	0.353563i
$990$		0			0
$991$	3.86918	−	6.70161i	0.122908	−	0.212884i	−0.798005	−	0.602651i	$-0.794111\pi$
$991$	3.86918	−	6.70161i	0.122908	−	0.212884i	0.920913	+	0.389767i	$0.127445\pi$
$992$		0			0
$993$	−0.992703	−	0.868528i	−0.0315025	−	0.0275619i
$994$		0			0
$995$	10.8672	+	2.91185i	0.344513	+	0.0923119i
$996$		0			0
$997$	3.13628	+	5.43219i	0.0993269	+	0.172039i	0.911406	−	0.411508i	$-0.134998\pi$
$997$	3.13628	+	5.43219i	0.0993269	+	0.172039i	−0.812079	+	0.583547i	$0.801664\pi$
$998$		0			0
$999$	17.9560	+	36.0916i	0.568102	+	1.14189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.305.2		56
3.2	odd	2	inner	624.2.cn.f.305.13		56
4.3	odd	2		312.2.bp.a.305.13	yes	56
12.11	even	2		312.2.bp.a.305.2	yes	56
13.11	odd	12	inner	624.2.cn.f.401.13		56
39.11	even	12	inner	624.2.cn.f.401.2		56
52.11	even	12		312.2.bp.a.89.2	✓	56
156.11	odd	12		312.2.bp.a.89.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.2	✓	56	52.11	even	12
312.2.bp.a.89.13	yes	56	156.11	odd	12
312.2.bp.a.305.2	yes	56	12.11	even	2
312.2.bp.a.305.13	yes	56	4.3	odd	2
624.2.cn.f.305.2		56	1.1	even	1	trivial
624.2.cn.f.305.13		56	3.2	odd	2	inner
624.2.cn.f.401.2		56	39.11	even	12	inner
624.2.cn.f.401.13		56	13.11	odd	12	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.55432 - 0.764251i) q^{3} +(-0.504580 - 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.83184 + 2.37579i) q^{9} +O(q^{10})\)	\(q+(-1.55432 - 0.764251i) q^{3} +(-0.504580 - 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.83184 + 2.37579i) q^{9} +(-0.296516 - 1.10661i) q^{11} +(3.23695 + 1.58812i) q^{13} +(0.398654 + 1.16991i) q^{15} +(-1.51919 - 2.63131i) q^{17} +(-4.59867 - 1.23221i) q^{19} +(-3.68744 + 4.21464i) q^{21} +(-2.43079 + 4.21025i) q^{23} -4.49080i q^{25} +(-1.03158 - 5.09273i) q^{27} +(-8.98018 - 5.18471i) q^{29} +(1.93142 - 1.93142i) q^{31} +(-0.384848 + 1.94665i) q^{33} +(-1.99805 + 1.15357i) q^{35} +(-7.49362 + 2.00791i) q^{37} +(-3.81755 - 4.94230i) q^{39} +(6.55081 - 1.75528i) q^{41} +(-1.98070 + 1.14356i) q^{43} +(0.274463 - 2.12308i) q^{45} +(1.27830 - 1.27830i) q^{47} +(-2.99079 - 1.72673i) q^{49} +(0.350327 + 5.25094i) q^{51} -2.42966i q^{53} +(-0.408758 + 0.707990i) q^{55} +(6.20611 + 5.42979i) q^{57} +(-5.61424 - 1.50433i) q^{59} +(-5.23702 - 9.07078i) q^{61} +(8.95251 - 3.73279i) q^{63} +(-0.831967 - 2.43463i) q^{65} +(1.57758 + 5.88762i) q^{67} +(6.99591 - 4.68635i) q^{69} +(1.02693 - 3.83254i) q^{71} +(-4.06395 - 4.06395i) q^{73} +(-3.43210 + 6.98015i) q^{75} -3.70409 q^{77} -6.77768 q^{79} +(-2.28872 + 8.70412i) q^{81} +(11.9425 + 11.9425i) q^{83} +(-0.561154 + 2.09426i) q^{85} +(9.99568 + 14.9218i) q^{87} +(2.07215 + 7.73338i) q^{89} +(7.66844 - 8.78010i) q^{91} +(-4.47815 + 1.52597i) q^{93} +(1.69865 + 2.94215i) q^{95} +(-0.989115 - 0.265032i) q^{97} +(2.08590 - 2.73160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^7	\( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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