LMFDB - Embedded newform 312.2.bp.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(41,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 1]))

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

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

chi := DirichletCharacter("312.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bp (of order $12$, degree $4$, 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.2
Character	$\chi$	$=$	312.89
Dual form			312.2.bp.a.305.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43902 + 0.963958i) q^{3} +(0.504580 - 0.504580i) q^{5} +(-0.836809 - 3.12301i) q^{7} +(1.14157 - 2.77431i) q^{9} +O(q^{10})$	\(q+(-1.43902 + 0.963958i) q^{3} +(0.504580 - 0.504580i) q^{5} +(-0.836809 - 3.12301i) q^{7} +(1.14157 - 2.77431i) q^{9} +(-0.296516 + 1.10661i) q^{11} +(3.23695 - 1.58812i) q^{13} +(-0.239708 + 1.21249i) q^{15} +(1.51919 - 2.63131i) q^{17} +(4.59867 - 1.23221i) q^{19} +(4.21464 + 3.68744i) q^{21} +(-2.43079 - 4.21025i) q^{23} +4.49080i q^{25} +(1.03158 + 5.09273i) q^{27} +(8.98018 - 5.18471i) q^{29} +(-1.93142 - 1.93142i) q^{31} +(-0.640035 - 1.87827i) q^{33} +(-1.99805 - 1.15357i) q^{35} +(-7.49362 - 2.00791i) q^{37} +(-3.12717 + 5.40563i) q^{39} +(-6.55081 - 1.75528i) q^{41} +(1.98070 + 1.14356i) q^{43} +(-0.823849 - 1.97588i) q^{45} +(1.27830 + 1.27830i) q^{47} +(-2.99079 + 1.72673i) q^{49} +(0.350327 + 5.25094i) q^{51} -2.42966i q^{53} +(0.408758 + 0.707990i) q^{55} +(-5.42979 + 6.20611i) q^{57} +(-5.61424 + 1.50433i) q^{59} +(-5.23702 + 9.07078i) q^{61} +(-9.61950 - 1.24357i) q^{63} +(0.831967 - 2.43463i) q^{65} +(-1.57758 + 5.88762i) q^{67} +(7.55646 + 3.71546i) q^{69} +(1.02693 + 3.83254i) q^{71} +(-4.06395 + 4.06395i) q^{73} +(-4.32894 - 6.46236i) q^{75} +3.70409 q^{77} +6.77768 q^{79} +(-6.39363 - 6.33415i) q^{81} +(11.9425 - 11.9425i) q^{83} +(-0.561154 - 2.09426i) q^{85} +(-7.92484 + 16.1174i) q^{87} +(-2.07215 + 7.73338i) q^{89} +(-7.66844 - 8.78010i) q^{91} +(4.64117 + 0.917551i) q^{93} +(1.69865 - 2.94215i) q^{95} +(-0.989115 + 0.265032i) q^{97} +(2.73160 + 2.08590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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
$3$	−1.43902	+	0.963958i	−0.830820	+	0.556541i
$3$	−1.43902	+	0.963958i	−0.830820	+	0.556541i
$4$		0			0
$5$	0.504580	−	0.504580i	0.225655	−	0.225655i	−0.585220	−	0.810875i	$-0.698992\pi$
$5$	0.504580	−	0.504580i	0.225655	−	0.225655i	0.810875	+	0.585220i	$0.198992\pi$
$6$		0			0
$7$	−0.836809	−	3.12301i	−0.316284	−	1.18039i	−0.922788	−	0.385308i	$-0.874095\pi$
$7$	−0.836809	−	3.12301i	−0.316284	−	1.18039i	0.606504	−	0.795080i	$-0.292571\pi$
$8$		0			0
$9$	1.14157	−	2.77431i	0.380523	−	0.924771i
$10$		0			0
$11$	−0.296516	+	1.10661i	−0.0894029	+	0.333656i	−0.996112	−	0.0881015i	$-0.971920\pi$
$11$	−0.296516	+	1.10661i	−0.0894029	+	0.333656i	0.906709	+	0.421758i	$0.138587\pi$
$12$		0			0
$13$	3.23695	−	1.58812i	0.897769	−	0.440466i
$13$	3.23695	−	1.58812i	0.897769	−	0.440466i
$14$		0			0
$15$	−0.239708	+	1.21249i	−0.0618923	+	0.313065i
$16$		0			0
$17$	1.51919	−	2.63131i	0.368457	−	0.638186i	−0.620868	−	0.783916i	$-0.713220\pi$
$17$	1.51919	−	2.63131i	0.368457	−	0.638186i	0.989325	+	0.145729i	$0.0465529\pi$
$18$		0			0
$19$	4.59867	−	1.23221i	1.05501	−	0.282689i	0.310688	−	0.950512i	$-0.399440\pi$
$19$	4.59867	−	1.23221i	1.05501	−	0.282689i	0.744320	+	0.667823i	$0.232774\pi$
$20$		0			0
$21$	4.21464	+	3.68744i	0.919710	+	0.804665i
$22$		0			0
$23$	−2.43079	−	4.21025i	−0.506854	−	0.877897i	−0.999969	−	0.00793257i	$-0.997475\pi$
$23$	−2.43079	−	4.21025i	−0.506854	−	0.877897i	0.493114	−	0.869964i	$-0.335858\pi$
$24$		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	0.698638	−	0.715475i	$-0.253790\pi$
$29$	8.98018	−	5.18471i	1.66758	−	0.962776i	0.968939	−	0.247301i	$-0.0795437\pi$
$30$		0			0
$31$	−1.93142	−	1.93142i	−0.346894	−	0.346894i	0.512057	−	0.858951i	$-0.328884\pi$
$31$	−1.93142	−	1.93142i	−0.346894	−	0.346894i	−0.858951	+	0.512057i	$0.828884\pi$
$32$		0			0
$33$	−0.640035	−	1.87827i	−0.111416	−	0.326965i
$34$		0			0
$35$	−1.99805	−	1.15357i	−0.337731	−	0.194989i
$36$		0			0
$37$	−7.49362	−	2.00791i	−1.23194	−	0.330098i	−0.416608	−	0.909086i	$-0.636781\pi$
$37$	−7.49362	−	2.00791i	−1.23194	−	0.330098i	−0.815336	+	0.578988i	$0.803448\pi$
$38$		0			0
$39$	−3.12717	+	5.40563i	−0.500747	+	0.865593i
$40$		0			0
$41$	−6.55081	−	1.75528i	−1.02306	−	0.274129i	−0.291986	−	0.956423i	$-0.594316\pi$
$41$	−6.55081	−	1.75528i	−1.02306	−	0.274129i	−0.731079	+	0.682293i	$0.760983\pi$
$42$		0			0
$43$	1.98070	+	1.14356i	0.302054	+	0.174391i	0.643365	−	0.765559i	$-0.277538\pi$
$43$	1.98070	+	1.14356i	0.302054	+	0.174391i	−0.341311	+	0.939950i	$0.610871\pi$
$44$		0			0
$45$	−0.823849	−	1.97588i	−0.122812	−	0.294546i
$46$		0			0
$47$	1.27830	+	1.27830i	0.186459	+	0.186459i	0.794163	−	0.607704i	$-0.207909\pi$
$47$	1.27830	+	1.27830i	0.186459	+	0.186459i	−0.607704	+	0.794163i	$0.707909\pi$
$48$		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
$57$	−5.42979	+	6.20611i	−0.719194	+	0.822019i
$58$		0			0
$59$	−5.61424	+	1.50433i	−0.730911	+	0.195847i	−0.605035	−	0.796199i	$-0.706841\pi$
$59$	−5.61424	+	1.50433i	−0.730911	+	0.195847i	−0.125876	+	0.992046i	$0.540174\pi$
$60$		0			0
$61$	−5.23702	+	9.07078i	−0.670531	+	1.16139i	0.307223	+	0.951638i	$0.400600\pi$
$61$	−5.23702	+	9.07078i	−0.670531	+	1.16139i	−0.977754	+	0.209756i	$0.932733\pi$
$62$		0			0
$63$	−9.61950	−	1.24357i	−1.21194	−	0.156675i
$64$		0			0
$65$	0.831967	−	2.43463i	0.103193	−	0.301979i
$66$		0			0
$67$	−1.57758	+	5.88762i	−0.192732	+	0.719287i	0.800110	+	0.599853i	$0.204774\pi$
$67$	−1.57758	+	5.88762i	−0.192732	+	0.719287i	−0.992842	+	0.119433i	$0.961892\pi$
$68$		0			0
$69$	7.55646	+	3.71546i	0.909690	+	0.447289i
$70$		0			0
$71$	1.02693	+	3.83254i	0.121874	+	0.454839i	0.999709	−	0.0241235i	$-0.00767950\pi$
$71$	1.02693	+	3.83254i	0.121874	+	0.454839i	−0.877835	+	0.478963i	$0.841013\pi$
$72$		0			0
$73$	−4.06395	+	4.06395i	−0.475650	+	0.475650i	−0.903737	−	0.428088i	$-0.859187\pi$
$73$	−4.06395	+	4.06395i	−0.475650	+	0.475650i	0.428088	+	0.903737i	$0.359187\pi$
$74$		0			0
$75$	−4.32894	−	6.46236i	−0.499863	−	0.746209i
$76$		0			0
$77$	3.70409			0.422121
$78$		0			0
$79$	6.77768			0.762549			0.381274	−	0.924462i	$-0.375485\pi$
$79$	6.77768			0.762549			0.381274	+	0.924462i	$0.375485\pi$
$80$		0			0
$81$	−6.39363	−	6.33415i	−0.710404	−	0.703794i
$82$		0			0
$83$	11.9425	−	11.9425i	1.31086	−	1.31086i	0.390075	−	0.920783i	$-0.372449\pi$
$83$	11.9425	−	11.9425i	1.31086	−	1.31086i	0.920783	−	0.390075i	$-0.127551\pi$
$84$		0			0
$85$	−0.561154	−	2.09426i	−0.0608657	−	0.227154i
$86$		0			0
$87$	−7.92484	+	16.1174i	−0.849632	+	1.72797i
$88$		0			0
$89$	−2.07215	+	7.73338i	−0.219648	+	0.819737i	0.764831	+	0.644231i	$0.222823\pi$
$89$	−2.07215	+	7.73338i	−0.219648	+	0.819737i	−0.984478	+	0.175505i	$0.943844\pi$
$90$		0			0
$91$	−7.66844	−	8.78010i	−0.803871	−	0.920404i
$92$		0			0
$93$	4.64117	+	0.917551i	0.481267	+	0.0951456i
$94$		0			0
$95$	1.69865	−	2.94215i	0.174278	−	0.301858i
$96$		0			0
$97$	−0.989115	+	0.265032i	−0.100429	+	0.0269100i	−0.308684	−	0.951165i	$-0.599888\pi$
$97$	−0.989115	+	0.265032i	−0.100429	+	0.0269100i	0.208254	+	0.978075i	$0.433222\pi$
$98$		0			0
$99$	2.73160	+	2.08590i	0.274536	+	0.209641i
$100$		0			0
$101$	3.77328	+	6.53550i	0.375455	+	0.650307i	0.990395	−	0.138267i	$-0.0441532\pi$
$101$	3.77328	+	6.53550i	0.375455	+	0.650307i	−0.614940	+	0.788574i	$0.710820\pi$
$102$		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	−0.105894	−	0.994377i	$-0.533770\pi$
$107$	7.26480	−	4.19434i	0.702315	−	0.405482i	0.808209	+	0.588896i	$0.200437\pi$
$108$		0			0
$109$	10.3472	+	10.3472i	0.991084	+	0.991084i	0.999961	−	0.00887687i	$-0.00282563\pi$
$109$	10.3472	+	10.3472i	0.991084	+	0.991084i	−0.00887687	+	0.999961i	$0.502826\pi$
$110$		0			0
$111$	12.7190	−	4.33411i	1.20724	−	0.411375i
$112$		0			0
$113$	−13.0474	−	7.53294i	−1.22740	−	0.708639i	−0.260914	−	0.965362i	$-0.584024\pi$
$113$	−13.0474	−	7.53294i	−1.22740	−	0.708639i	−0.966485	+	0.256723i	$0.917357\pi$
$114$		0			0
$115$	−3.35093	−	0.897879i	−0.312476	−	0.0837277i
$116$		0			0
$117$	−0.710737	−	10.7933i	−0.0657077	−	0.997839i
$118$		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
$123$	11.1188	−	3.78881i	1.00255	−	0.341626i
$124$		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	$-0.547709\pi$
$127$	7.12606	−	4.11423i	0.632336	−	0.365079i	0.781656	+	0.623710i	$0.214375\pi$
$128$		0			0
$129$	−3.95261	+	0.263706i	−0.348008	+	0.0232181i
$130$		0			0
$131$			13.4099i			1.17163i	0.810446	+	0.585814i	$0.199225\pi$
$131$			13.4099i			1.17163i	−0.810446	+	0.585814i	$0.800775\pi$
$132$		0			0
$133$	−7.69642	−	13.3306i	−0.667365	−	1.15591i
$134$		0			0
$135$	3.09020	+	2.04917i	0.265962	+	0.176365i
$136$		0			0
$137$	−13.2257	+	3.54382i	−1.12995	+	0.302769i	−0.774904	−	0.632079i	$-0.782202\pi$
$137$	−13.2257	+	3.54382i	−1.12995	+	0.302769i	−0.355047	+	0.934849i	$0.615535\pi$
$138$		0			0
$139$	−9.49420	+	16.4444i	−0.805288	+	1.39480i	0.110809	+	0.993842i	$0.464656\pi$
$139$	−9.49420	+	16.4444i	−0.805288	+	1.39480i	−0.916097	+	0.400957i	$0.868678\pi$
$140$		0			0
$141$	−3.07172	−	0.607274i	−0.258686	−	0.0511417i
$142$		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
$147$	2.63932	−	5.36780i	0.217687	−	0.442729i
$148$		0			0
$149$	−1.55037	−	5.78607i	−0.127012	−	0.474014i	0.872892	−	0.487914i	$-0.162242\pi$
$149$	−1.55037	−	5.78607i	−0.127012	−	0.474014i	−0.999903	+	0.0139002i	$0.995575\pi$
$150$		0			0
$151$	10.9825	−	10.9825i	0.893741	−	0.893741i	−0.101132	−	0.994873i	$-0.532247\pi$
$151$	10.9825	−	10.9825i	0.893741	−	0.893741i	0.994873	+	0.101132i	$0.0322466\pi$
$152$		0			0
$153$	−5.56582	−	7.21853i	−0.449970	−	0.583583i
$154$		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
$159$	2.34209	+	3.49634i	0.185740	+	0.277278i
$160$		0			0
$161$	−11.1146	+	11.1146i	−0.875950	+	0.875950i
$162$		0			0
$163$	−5.56650	−	20.7745i	−0.436002	−	1.62718i	−0.738657	−	0.674082i	$-0.764540\pi$
$163$	−5.56650	−	20.7745i	−0.436002	−	1.62718i	0.302655	−	0.953100i	$-0.402127\pi$
$164$		0			0
$165$	−1.27068	−	0.624788i	−0.0989227	−	0.0486396i
$166$		0			0
$167$	2.83710	−	10.5882i	0.219542	−	0.819341i	−0.764976	−	0.644058i	$-0.777249\pi$
$167$	2.83710	−	10.5882i	0.219542	−	0.819341i	0.984518	−	0.175283i	$-0.0560839\pi$
$168$		0			0
$169$	7.95574	−	10.2814i	0.611980	−	0.790873i
$170$		0			0
$171$	1.83117	−	14.1648i	0.140033	−	1.08321i
$172$		0			0
$173$	−10.1274	+	17.5412i	−0.769975	+	1.33364i	0.167601	+	0.985855i	$0.446398\pi$
$173$	−10.1274	+	17.5412i	−0.769975	+	1.33364i	−0.937576	+	0.347781i	$0.886935\pi$
$174$		0			0
$175$	14.0248	−	3.75794i	1.06018	−	0.284074i
$176$		0			0
$177$	6.62890	−	7.57665i	0.498259	−	0.569496i
$178$		0			0
$179$	10.5903	+	18.3430i	0.791557	+	1.37102i	0.925003	+	0.379961i	$0.124063\pi$
$179$	10.5903	+	18.3430i	0.791557	+	1.37102i	−0.133445	+	0.991056i	$0.542604\pi$
$180$		0			0
$181$			14.0377i			1.04342i	0.853124	+	0.521709i	$0.174705\pi$
$181$			14.0377i			1.04342i	−0.853124	+	0.521709i	$0.825295\pi$
$182$		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
$189$	15.0414	−	7.48327i	1.09410	−	0.544328i
$190$		0			0
$191$	18.7332	+	10.8156i	1.35549	+	0.782592i	0.989012	−	0.147835i	$-0.0472305\pi$
$191$	18.7332	+	10.8156i	1.35549	+	0.782592i	0.366477	+	0.930427i	$0.380564\pi$
$192$		0			0
$193$	−20.6023	−	5.52036i	−1.48298	−	0.397364i	−0.575622	−	0.817716i	$-0.695240\pi$
$193$	−20.6023	−	5.52036i	−1.48298	−	0.397364i	−0.907361	+	0.420352i	$0.861907\pi$
$194$		0			0
$195$	1.14967	+	4.30548i	0.0823293	+	0.308321i
$196$		0			0
$197$	24.7548	+	6.63302i	1.76371	+	0.472583i	0.987463	−	0.157851i	$-0.0504567\pi$
$197$	24.7548	+	6.63302i	1.76371	+	0.472583i	0.776242	+	0.630435i	$0.217123\pi$
$198$		0			0
$199$	13.6540	+	7.88312i	0.967904	+	0.558820i	0.898597	−	0.438776i	$-0.144588\pi$
$199$	13.6540	+	7.88312i	0.967904	+	0.558820i	0.0693073	+	0.997595i	$0.477921\pi$
$200$		0			0
$201$	−3.40524	−	9.99313i	−0.240187	−	0.704861i
$202$		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	$-0.283273\pi$
$211$	−5.20303	−	9.01192i	−0.358192	−	0.620406i	−0.987659	+	0.156621i	$0.949940\pi$
$212$		0			0
$213$	−5.17218	−	4.52520i	−0.354392	−	0.310062i
$214$		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
$219$	1.93064	−	9.76560i	0.130461	−	0.659898i
$220$		0			0
$221$	0.738700	−	10.9301i	0.0496903	−	0.735237i
$222$		0			0
$223$	−5.88651	+	21.9688i	−0.394190	+	1.47114i	0.428966	+	0.903321i	$0.358878\pi$
$223$	−5.88651	+	21.9688i	−0.394190	+	1.47114i	−0.823156	+	0.567816i	$0.807789\pi$
$224$		0			0
$225$	12.4589	+	5.12656i	0.830592	+	0.341771i
$226$		0			0
$227$	5.14469	+	19.2003i	0.341465	+	1.27437i	0.896688	+	0.442664i	$0.145967\pi$
$227$	5.14469	+	19.2003i	0.341465	+	1.27437i	−0.555222	+	0.831702i	$0.687367\pi$
$228$		0			0
$229$	1.16288	−	1.16288i	0.0768456	−	0.0768456i	−0.667639	−	0.744485i	$-0.732695\pi$
$229$	1.16288	−	1.16288i	0.0768456	−	0.0768456i	0.744485	+	0.667639i	$0.232695\pi$
$230$		0			0
$231$	−5.33027	+	3.57059i	−0.350706	+	0.234928i
$232$		0			0
$233$	23.8148			1.56016			0.780080	−	0.625680i	$-0.215178\pi$
$233$	23.8148			1.56016			0.780080	+	0.625680i	$0.215178\pi$
$234$		0			0
$235$	1.29001			0.0841507
$236$		0			0
$237$	−9.75323	+	6.53340i	−0.633541	+	0.424390i
$238$		0			0
$239$	3.10170	−	3.10170i	0.200632	−	0.200632i	−0.599639	−	0.800271i	$-0.704689\pi$
$239$	3.10170	−	3.10170i	0.200632	−	0.200632i	0.800271	+	0.599639i	$0.204689\pi$
$240$		0			0
$241$	−2.25233	−	8.40583i	−0.145086	−	0.541467i	−0.999752	−	0.0222886i	$-0.992905\pi$
$241$	−2.25233	−	8.40583i	−0.145086	−	0.541467i	0.854666	−	0.519178i	$-0.173762\pi$
$242$		0			0
$243$	15.3064	+	2.95179i	0.981908	+	0.189357i
$244$		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
$249$	−5.67345	+	28.6976i	−0.359540	+	1.81863i
$250$		0			0
$251$	−4.34184	+	7.52029i	−0.274055	+	0.474677i	−0.969896	−	0.243519i	$-0.921698\pi$
$251$	−4.34184	+	7.52029i	−0.274055	+	0.474677i	0.695842	+	0.718195i	$0.255032\pi$
$252$		0			0
$253$	5.37988	−	1.44153i	0.338230	−	0.0906284i
$254$		0			0
$255$	2.82629	+	2.47275i	0.176989	+	0.154850i
$256$		0			0
$257$	−2.99467	−	5.18692i	−0.186802	−	0.323551i	0.757380	−	0.652974i	$-0.226479\pi$
$257$	−2.99467	−	5.18692i	−0.186802	−	0.323551i	−0.944182	+	0.329423i	$0.893146\pi$
$258$		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	−0.914992	−	0.403472i	$-0.867803\pi$
$263$	−16.5914	+	9.57907i	−1.02307	+	0.590670i	−0.108079	+	0.994142i	$0.534470\pi$
$264$		0			0
$265$	−1.22596	−	1.22596i	−0.0753101	−	0.0753101i
$266$		0			0
$267$	−4.47278	−	13.1260i	−0.273730	−	0.803297i
$268$		0			0
$269$	−22.0370	−	12.7231i	−1.34362	−	0.775741i	−0.356285	−	0.934377i	$-0.615957\pi$
$269$	−22.0370	−	12.7231i	−1.34362	−	0.775741i	−0.987337	+	0.158637i	$0.949290\pi$
$270$		0			0
$271$	−22.0299	−	5.90289i	−1.33822	−	0.358575i	−0.482447	−	0.875925i	$-0.660252\pi$
$271$	−22.0299	−	5.90289i	−1.33822	−	0.358575i	−0.855774	+	0.517350i	$0.826919\pi$
$272$		0			0
$273$	19.4987	+	5.24271i	1.18011	+	0.317303i
$274$		0			0
$275$	−4.96957	−	1.33159i	−0.299677	−	0.0802981i
$276$		0			0
$277$	−11.4444	−	6.60744i	−0.687628	−	0.397002i	0.115095	−	0.993355i	$-0.463283\pi$
$277$	−11.4444	−	6.60744i	−0.687628	−	0.397002i	−0.802723	+	0.596352i	$0.796616\pi$
$278$		0			0
$279$	−7.56323	+	3.15352i	−0.452799	+	0.188796i
$280$		0			0
$281$	−1.24623	−	1.24623i	−0.0743436	−	0.0743436i	0.668957	−	0.743301i	$-0.266741\pi$
$281$	−1.24623	−	1.24623i	−0.0743436	−	0.0743436i	−0.743301	+	0.668957i	$0.766741\pi$
$282$		0			0
$283$	−20.1262	+	11.6199i	−1.19638	+	0.690728i	−0.959745	−	0.280871i	$-0.909377\pi$
$283$	−20.1262	+	11.6199i	−1.19638	+	0.690728i	−0.236631	+	0.971600i	$0.576043\pi$
$284$		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
$291$	1.16788	−	1.33485i	0.0684622	−	0.0782504i
$292$		0			0
$293$	−2.69061	+	0.720947i	−0.157187	+	0.0421182i	−0.336555	−	0.941664i	$-0.609262\pi$
$293$	−2.69061	+	0.720947i	−0.157187	+	0.0421182i	0.179367	+	0.983782i	$0.442595\pi$
$294$		0			0
$295$	−2.07378	+	3.59188i	−0.120740	+	0.209128i
$296$		0			0
$297$	−5.94155	−	0.368518i	−0.344764	−	0.0213836i
$298$		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
$303$	−11.7298	−	5.76746i	−0.673858	−	0.331332i
$304$		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	$-0.966344\pi$
$307$	−15.5744	+	15.5744i	−0.888881	+	0.888881i	0.105535	+	0.994416i	$0.466344\pi$
$308$		0			0
$309$	6.08512	+	9.08403i	0.346170	+	0.516772i
$310$		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
$315$	−5.48128	+	4.22632i	−0.308835	+	0.238126i
$316$		0			0
$317$	3.02944	−	3.02944i	0.170150	−	0.170150i	−0.616895	−	0.787045i	$-0.711610\pi$
$317$	3.02944	−	3.02944i	0.170150	−	0.170150i	0.787045	+	0.616895i	$0.211610\pi$
$318$		0			0
$319$	3.07470	+	11.4749i	0.172150	+	0.642472i
$320$		0			0
$321$	−6.41105	+	13.0387i	−0.357830	+	0.727750i
$322$		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
$327$	−24.8642	−	4.91559i	−1.37499	−	0.271833i
$328$		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	$-0.589996\pi$
$331$	−0.735585	+	0.197099i	−0.0404314	+	0.0108336i	0.238547	+	0.971131i	$0.423329\pi$
$332$		0			0
$333$	−14.1251	+	18.4975i	−0.774049	+	1.01366i
$334$		0			0
$335$	2.17476	+	3.76679i	0.118820	+	0.205802i
$336$		0			0
$337$		−	6.15955i		−	0.335532i	−0.985827	−	0.167766i	$-0.946345\pi$
$337$		−	6.15955i		−	0.335532i	0.985827	−	0.167766i	$-0.0536554\pi$
$338$		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
$345$	5.68758	−	1.93809i	0.306209	−	0.104343i
$346$		0			0
$347$	5.68995	+	3.28509i	0.305452	+	0.176353i	0.644890	−	0.764276i	$-0.276903\pi$
$347$	5.68995	+	3.28509i	0.305452	+	0.176353i	−0.339437	+	0.940629i	$0.610237\pi$
$348$		0			0
$349$	1.81261	+	0.485688i	0.0970270	+	0.0259983i	0.307006	−	0.951708i	$-0.400673\pi$
$349$	1.81261	+	0.485688i	0.0970270	+	0.0259983i	−0.209979	+	0.977706i	$0.567340\pi$
$350$		0			0
$351$	11.4270	+	14.8466i	0.609930	+	0.792455i
$352$		0			0
$353$	26.6737	+	7.14721i	1.41970	+	0.380407i	0.885377	−	0.464873i	$-0.153900\pi$
$353$	26.6737	+	7.14721i	1.41970	+	0.380407i	0.534323	+	0.845281i	$0.320567\pi$
$354$		0			0
$355$	2.45199	+	1.41566i	0.130138	+	0.0751353i
$356$		0			0
$357$	16.1056	−	5.48812i	0.852400	−	0.290462i
$358$		0			0
$359$	−10.1971	−	10.1971i	−0.538182	−	0.538182i	0.384813	−	0.922995i	$-0.374266\pi$
$359$	−10.1971	−	10.1971i	−0.538182	−	0.538182i	−0.922995	+	0.384813i	$0.874266\pi$
$360$		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	$-0.204299\pi$
$367$	−2.25960	−	3.91375i	−0.117950	−	0.204296i	−0.918955	+	0.394362i	$0.870966\pi$
$368$		0			0
$369$	−12.3479	+	16.1702i	−0.642807	+	0.841788i
$370$		0			0
$371$	−7.58788	+	2.03316i	−0.393943	+	0.105557i
$372$		0			0
$373$	2.40745	−	4.16983i	0.124653	−	0.215905i	−0.796944	−	0.604053i	$-0.793552\pi$
$373$	2.40745	−	4.16983i	0.124653	−	0.215905i	0.921597	+	0.388147i	$0.126885\pi$
$374$		0			0
$375$	−11.5075	−	2.27502i	−0.594247	−	0.117481i
$376$		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	$-0.939963\pi$
$379$	−0.736874	+	2.75005i	−0.0378507	+	0.141261i	0.944415	+	0.328757i	$0.106630\pi$
$380$		0			0
$381$	−6.28861	+	12.7897i	−0.322175	+	0.655236i
$382$		0			0
$383$	−1.67036	−	6.23387i	−0.0853514	−	0.318536i	0.910029	−	0.414544i	$-0.136059\pi$
$383$	−1.67036	−	6.23387i	−0.0853514	−	0.318536i	−0.995381	+	0.0960085i	$0.969392\pi$
$384$		0			0
$385$	1.86901	−	1.86901i	0.0952536	−	0.0952536i
$386$		0			0
$387$	5.43370	−	4.18963i	0.276210	−	0.212971i
$388$		0			0
$389$	5.45516			0.276588			0.138294	−	0.990391i	$-0.455838\pi$
$389$	5.45516			0.276588			0.138294	+	0.990391i	$0.455838\pi$
$390$		0			0
$391$	−14.7713			−0.747016
$392$		0			0
$393$	−12.9266	−	19.2971i	−0.652059	−	0.973412i
$394$		0			0
$395$	3.41988	−	3.41988i	0.172073	−	0.172073i
$396$		0			0
$397$	−0.437429	−	1.63251i	−0.0219539	−	0.0819331i	0.954080	−	0.299553i	$-0.0968374\pi$
$397$	−0.437429	−	1.63251i	−0.0219539	−	0.0819331i	−0.976034	+	0.217620i	$0.930171\pi$
$398$		0			0
$399$	23.9255	+	11.7640i	1.19777	+	0.588937i
$400$		0			0
$401$	5.16790	−	19.2869i	0.258073	−	0.963141i	−0.708282	−	0.705929i	$-0.750530\pi$
$401$	5.16790	−	19.2869i	0.258073	−	0.963141i	0.966355	−	0.257212i	$-0.0828037\pi$
$402$		0			0
$403$	−9.31927	−	3.18460i	−0.464226	−	0.158636i
$404$		0			0
$405$	−6.42218	+	0.0300156i	−0.319121	+	0.00149149i
$406$		0			0
$407$	4.44396	−	7.69716i	0.220279	−	0.381534i
$408$		0			0
$409$	8.48733	−	2.27417i	0.419671	−	0.112451i	−0.0428024	−	0.999084i	$-0.513629\pi$
$409$	8.48733	−	2.27417i	0.419671	−	0.112451i	0.462474	+	0.886633i	$0.346962\pi$
$410$		0			0
$411$	15.6160	−	17.8487i	0.770281	−	0.880411i
$412$		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	−0.309864	−	0.950781i	$-0.600284\pi$
$419$	7.34045	−	4.23801i	0.358604	−	0.207040i	0.668468	+	0.743741i	$0.266950\pi$
$420$		0			0
$421$	−15.5203	−	15.5203i	−0.756412	−	0.756412i	0.219255	−	0.975667i	$-0.429637\pi$
$421$	−15.5203	−	15.5203i	−0.756412	−	0.756412i	−0.975667	+	0.219255i	$0.929637\pi$
$422$		0			0
$423$	5.00567	−	2.08713i	0.243384	−	0.101480i
$424$		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
$429$	−5.05468	−	5.06342i	−0.244042	−	0.244464i
$430$		0			0
$431$	26.3726	+	7.06652i	1.27032	+	0.340382i	0.830155	−	0.557533i	$-0.188252\pi$
$431$	26.3726	+	7.06652i	1.27032	+	0.340382i	0.440169	+	0.897915i	$0.354919\pi$
$432$		0			0
$433$	9.03766	+	5.21790i	0.434322	+	0.250756i	0.701186	−	0.712978i	$-0.252654\pi$
$433$	9.03766	+	5.21790i	0.434322	+	0.250756i	−0.266864	+	0.963734i	$0.585987\pi$
$434$		0			0
$435$	4.13381	+	12.1312i	0.198201	+	0.581648i
$436$		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	$-0.458154\pi$
$439$	22.1085	−	12.7643i	1.05518	−	0.609208i	0.924095	+	0.382163i	$0.124821\pi$
$440$		0			0
$441$	1.37630	+	10.2686i	0.0655383	+	0.488980i
$442$		0			0
$443$			27.6082i			1.31170i	0.754889	+	0.655852i	$0.227691\pi$
$443$			27.6082i			1.31170i	−0.754889	+	0.655852i	$0.772309\pi$
$444$		0			0
$445$	2.85654	+	4.94767i	0.135413	+	0.234542i
$446$		0			0
$447$	7.80855	+	6.83179i	0.369332	+	0.323133i
$448$		0			0
$449$	−26.6058	+	7.12899i	−1.25560	+	0.336438i	−0.824499	−	0.565864i	$-0.808543\pi$
$449$	−26.6058	+	7.12899i	−1.25560	+	0.336438i	−0.431105	+	0.902302i	$0.641876\pi$
$450$		0			0
$451$	3.88484	−	6.72874i	0.182930	−	0.316844i
$452$		0			0
$453$	−5.21738	+	26.3907i	−0.245134	+	1.23994i
$454$		0			0
$455$	−8.29960	−	0.560921i	−0.389091	−	0.0262964i
$456$		0			0
$457$	5.68707	−	21.2244i	0.266030	−	0.992838i	−0.695587	−	0.718442i	$-0.744856\pi$
$457$	5.68707	−	21.2244i	0.266030	−	0.992838i	0.961617	−	0.274396i	$-0.0884778\pi$
$458$		0			0
$459$	14.9677	+	5.02240i	0.698632	+	0.234426i
$460$		0			0
$461$	−5.98430	−	22.3337i	−0.278717	−	1.04019i	−0.953310	−	0.301995i	$-0.902347\pi$
$461$	−5.98430	−	22.3337i	−0.278717	−	1.04019i	0.674593	−	0.738190i	$-0.264319\pi$
$462$		0			0
$463$	8.48586	−	8.48586i	0.394371	−	0.394371i	−0.481871	−	0.876242i	$-0.660043\pi$
$463$	8.48586	−	8.48586i	0.394371	−	0.394371i	0.876242	+	0.481871i	$0.160043\pi$
$464$		0			0
$465$	2.80482	−	1.87886i	0.130070	−	0.0871303i
$466$		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
$471$	−14.7089	+	9.85304i	−0.677750	+	0.454004i
$472$		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
$477$	−6.74065	−	2.77363i	−0.308633	−	0.126996i
$478$		0			0
$479$	5.46091	−	20.3804i	0.249515	−	0.931203i	−0.721545	−	0.692368i	$-0.756568\pi$
$479$	5.46091	−	20.3804i	0.249515	−	0.931203i	0.971060	−	0.238836i	$-0.0767657\pi$
$480$		0			0
$481$	−27.4453	+	5.40127i	−1.25140	+	0.246277i
$482$		0			0
$483$	5.28013	−	26.7081i	0.240254	−	1.21526i
$484$		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	$-0.703667\pi$
$487$	−15.7355	+	4.21633i	−0.713046	+	0.191060i	−0.115979	+	0.993252i	$0.537001\pi$
$488$		0			0
$489$	28.0360	+	24.5290i	1.26783	+	1.10924i
$490$		0			0
$491$	−16.2519	−	28.1492i	−0.733440	−	1.27036i	−0.955404	−	0.295300i	$-0.904580\pi$
$491$	−16.2519	−	28.1492i	−0.733440	−	1.27036i	0.221965	−	0.975055i	$-0.428753\pi$
$492$		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	$-0.143772\pi$
$499$	10.3481	+	10.3481i	0.463245	+	0.463245i	−0.436472	+	0.899718i	$0.643772\pi$
$500$		0			0
$501$	6.12394	+	17.9715i	0.273597	+	0.802909i
$502$		0			0
$503$	−19.4725	−	11.2424i	−0.868235	−	0.501276i	−0.00147394	−	0.999999i	$-0.500469\pi$
$503$	−19.4725	−	11.2424i	−0.868235	−	0.501276i	−0.866761	+	0.498723i	$0.833803\pi$
$504$		0			0
$505$	5.20160	+	1.39376i	0.231468	+	0.0620217i
$506$		0			0
$507$	−1.53770	+	22.4641i	−0.0682915	+	0.997665i
$508$		0			0
$509$	−27.6271	−	7.40267i	−1.22455	−	0.328117i	−0.412095	−	0.911141i	$-0.635203\pi$
$509$	−27.6271	−	7.40267i	−1.22455	−	0.328117i	−0.812455	+	0.583023i	$0.801870\pi$
$510$		0			0
$511$	16.0925	+	9.29103i	0.711892	+	0.411011i
$512$		0			0
$513$	11.0192	+	22.1487i	0.486509	+	0.977887i
$514$		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	−0.999965	−	0.00833218i	$-0.997348\pi$
$523$	−11.5992	−	20.0904i	−0.507199	−	0.878494i	0.492767	−	0.870161i	$-0.335986\pi$
$524$		0			0
$525$	−16.5595	+	18.9271i	−0.722718	+	0.826047i
$526$		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
$531$	−2.23556	+	17.2930i	−0.0970151	+	0.750450i
$532$		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
$537$	−32.9215	−	16.1873i	−1.42067	−	0.698534i
$538$		0			0
$539$	−1.02401	−	3.82165i	−0.0441071	−	0.164610i
$540$		0			0
$541$	30.2641	−	30.2641i	1.30115	−	1.30115i	0.373539	−	0.927615i	$-0.378144\pi$
$541$	30.2641	−	30.2641i	1.30115	−	1.30115i	0.927615	−	0.373539i	$-0.121856\pi$
$542$		0			0
$543$	−13.5318	−	20.2006i	−0.580705	−	0.866892i
$544$		0			0
$545$	10.4420			0.447286
$546$		0			0
$547$	−29.5412			−1.26309			−0.631545	−	0.775339i	$-0.717579\pi$
$547$	−29.5412			−1.26309			−0.631545	+	0.775339i	$0.717579\pi$
$548$		0			0
$549$	19.1868	+	24.8841i	0.818871	+	1.06203i
$550$		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
$555$	4.23086	−	8.60467i	0.179590	−	0.365248i
$556$		0			0
$557$	−6.70422	+	25.0205i	−0.284067	+	1.06015i	0.665451	+	0.746441i	$0.268239\pi$
$557$	−6.70422	+	25.0205i	−0.284067	+	1.06015i	−0.949518	+	0.313712i	$0.898428\pi$
$558$		0			0
$559$	8.22754	+	0.556051i	0.347988	+	0.0235185i
$560$		0			0
$561$	−5.91464	−	1.16931i	−0.249716	−	0.0493684i
$562$		0			0
$563$	2.40232	−	4.16095i	0.101246	−	0.175363i	−0.810952	−	0.585112i	$-0.801050\pi$
$563$	2.40232	−	4.16095i	0.101246	−	0.175363i	0.912198	+	0.409749i	$0.134384\pi$
$564$		0			0
$565$	−10.3844	+	2.78250i	−0.436876	+	0.117061i
$566$		0			0
$567$	−14.4314	+	25.2679i	−0.606061	+	1.06115i
$568$		0			0
$569$	−1.00204	−	1.73559i	−0.0420078	−	0.0727597i	0.844257	−	0.535938i	$-0.180042\pi$
$569$	−1.00204	−	1.73559i	−0.0420078	−	0.0727597i	−0.886265	+	0.463179i	$0.846709\pi$
$570$		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	0.938678	−	0.344795i	$-0.112052\pi$
$577$	14.2655	+	14.2655i	0.593883	+	0.593883i	−0.344795	+	0.938678i	$0.612052\pi$
$578$		0			0
$579$	34.9685	−	11.9158i	1.45324	−	0.495203i
$580$		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
$585$	−5.80469	−	5.08745i	−0.239994	−	0.210340i
$586$		0			0
$587$	−1.79654	−	0.481380i	−0.0741509	−	0.0198687i	0.221553	−	0.975148i	$-0.428887\pi$
$587$	−1.79654	−	0.481380i	−0.0741509	−	0.0198687i	−0.295704	+	0.955280i	$0.595554\pi$
$588$		0			0
$589$	−11.2619	−	6.50207i	−0.464039	−	0.267913i
$590$		0			0
$591$	−42.0166	+	14.3175i	−1.72833	+	0.588943i
$592$		0			0
$593$	32.1956	+	32.1956i	1.32212	+	1.32212i	0.912060	+	0.410057i	$0.134491\pi$
$593$	32.1956	+	32.1956i	1.32212	+	1.32212i	0.410057	+	0.912060i	$0.365509\pi$
$594$		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	$0.0972807\pi$
$599$			14.7278i			0.601762i	−0.953662	+	0.300881i	$0.902719\pi$
$600$		0			0
$601$	23.2965	+	40.3507i	0.950282	+	1.64594i	0.744812	+	0.667274i	$0.232539\pi$
$601$	23.2965	+	40.3507i	0.950282	+	1.64594i	0.205470	+	0.978663i	$0.434128\pi$
$602$		0			0
$603$	14.5332	+	11.0978i	0.591837	+	0.451939i
$604$		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	$-0.764085\pi$
$607$	5.31772	−	9.21056i	0.215840	−	0.373845i	0.953532	+	0.301292i	$0.0974178\pi$
$608$		0			0
$609$	56.9665	+	11.2622i	2.30840	+	0.456366i
$610$		0			0
$611$	6.16788	+	2.10770i	0.249526	+	0.0852684i
$612$		0			0
$613$	−4.55636	+	17.0046i	−0.184030	+	0.686808i	0.810806	+	0.585314i	$0.199029\pi$
$613$	−4.55636	+	17.0046i	−0.184030	+	0.686808i	−0.994836	+	0.101494i	$0.967638\pi$
$614$		0			0
$615$	3.69855	−	7.52207i	0.149140	−	0.303319i
$616$		0			0
$617$	1.61026	+	6.00956i	0.0648265	+	0.241936i	0.990734	−	0.135813i	$-0.0433648\pi$
$617$	1.61026	+	6.00956i	0.0648265	+	0.241936i	−0.925908	+	0.377749i	$0.876698\pi$
$618$		0			0
$619$	−20.3122	+	20.3122i	−0.816415	+	0.816415i	−0.985587	−	0.169172i	$-0.945891\pi$
$619$	−20.3122	+	20.3122i	−0.816415	+	0.816415i	0.169172	+	0.985587i	$0.445891\pi$
$620$		0			0
$621$	18.9341	−	16.7225i	0.759799	−	0.671052i
$622$		0			0
$623$	25.8854			1.03708
$624$		0			0
$625$	−17.6213			−0.704851
$626$		0			0
$627$	−5.25773	−	7.84889i	−0.209974	−	0.313454i
$628$		0			0
$629$	−16.6676	+	16.6676i	−0.664583	+	0.664583i
$630$		0			0
$631$	7.88943	+	29.4438i	0.314073	+	1.17214i	0.924849	+	0.380334i	$0.124191\pi$
$631$	7.88943	+	29.4438i	0.314073	+	1.17214i	−0.610776	+	0.791804i	$0.709142\pi$
$632$		0			0
$633$	16.1744	+	7.95285i	0.642875	+	0.316097i
$634$		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
$639$	11.8050	+	1.52610i	0.466998	+	0.0603716i
$640$		0			0
$641$	15.6856	−	27.1682i	0.619543	−	1.07308i	−0.370026	−	0.929021i	$-0.620651\pi$
$641$	15.6856	−	27.1682i	0.619543	−	1.07308i	0.989569	−	0.144058i	$-0.0460153\pi$
$642$		0			0
$643$	−4.97838	+	1.33395i	−0.196328	+	0.0526060i	−0.355643	−	0.934622i	$-0.615738\pi$
$643$	−4.97838	+	1.33395i	−0.196328	+	0.0526060i	0.159315	+	0.987228i	$0.449071\pi$
$644$		0			0
$645$	−1.86135	+	2.12747i	−0.0732905	+	0.0837690i
$646$		0			0
$647$	4.80729	+	8.32648i	0.188994	+	0.327348i	0.944915	−	0.327315i	$-0.106144\pi$
$647$	4.80729	+	8.32648i	0.188994	+	0.327348i	−0.755921	+	0.654663i	$0.772811\pi$
$648$		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	$-0.545719\pi$
$653$	16.4158	−	9.47768i	0.642401	−	0.370890i	0.785539	+	0.618813i	$0.212386\pi$
$654$		0			0
$655$	6.76636	+	6.76636i	0.264384	+	0.264384i
$656$		0			0
$657$	6.63539	+	15.9140i	0.258871	+	0.620863i
$658$		0			0
$659$	23.6778	+	13.6704i	0.922357	+	0.532523i	0.884386	−	0.466756i	$-0.154577\pi$
$659$	23.6778	+	13.6704i	0.922357	+	0.532523i	0.0379709	+	0.999279i	$0.487911\pi$
$660$		0			0
$661$	−9.46548	−	2.53627i	−0.368165	−	0.0986494i	0.0699932	−	0.997547i	$-0.477702\pi$
$661$	−9.46548	−	2.53627i	−0.368165	−	0.0986494i	−0.438158	+	0.898898i	$0.644369\pi$
$662$		0			0
$663$	9.47313	+	16.4407i	0.367906	+	0.638504i
$664$		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
$669$	−12.7061	−	37.2879i	−0.491248	−	1.44163i
$670$		0			0
$671$	−8.48497	−	8.48497i	−0.327559	−	0.327559i
$672$		0			0
$673$	−6.65548	+	3.84254i	−0.256550	+	0.148119i	−0.622760	−	0.782413i	$-0.713989\pi$
$673$	−6.65548	+	3.84254i	−0.256550	+	0.148119i	0.366210	+	0.930532i	$0.380655\pi$
$674$		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
$681$	−25.9116	−	22.6703i	−0.992933	−	0.868729i
$682$		0			0
$683$	−19.8376	+	5.31546i	−0.759063	+	0.203390i	−0.617535	−	0.786544i	$-0.711868\pi$
$683$	−19.8376	+	5.31546i	−0.759063	+	0.203390i	−0.141529	+	0.989934i	$0.545202\pi$
$684$		0			0
$685$	−4.88529	+	8.46157i	−0.186657	+	0.323300i
$686$		0			0
$687$	−0.552445	+	2.79439i	−0.0210771	+	0.106613i
$688$		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	$-0.904284\pi$
$691$	0.529217	−	1.97507i	0.0201324	−	0.0751350i	0.975261	+	0.221056i	$0.0709503\pi$
$692$		0			0
$693$	4.22848	−	10.2763i	0.160627	−	0.390365i
$694$		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
$699$	−34.2700	+	22.9565i	−1.29621	+	0.868294i
$700$		0			0
$701$	13.4888			0.509464			0.254732	−	0.967012i	$-0.418013\pi$
$701$	13.4888			0.509464			0.254732	+	0.967012i	$0.418013\pi$
$702$		0			0
$703$	−36.9349			−1.39303
$704$		0			0
$705$	−1.85635	+	1.24351i	−0.0699141	+	0.0468334i
$706$		0			0
$707$	17.2530	−	17.2530i	0.648864	−	0.648864i
$708$		0			0
$709$	−3.48407	−	13.0027i	−0.130847	−	0.488328i	0.869133	−	0.494578i	$-0.164677\pi$
$709$	−3.48407	−	13.0027i	−0.130847	−	0.488328i	−0.999980	+	0.00624974i	$0.998011\pi$
$710$		0			0
$711$	7.73720	−	18.8034i	0.290168	−	0.705183i
$712$		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
$717$	−1.47351	+	7.45333i	−0.0550291	+	0.278350i
$718$		0			0
$719$	−9.18916	+	15.9161i	−0.342698	+	0.593570i	−0.984933	−	0.172938i	$-0.944674\pi$
$719$	−9.18916	+	15.9161i	−0.342698	+	0.593570i	0.642235	+	0.766508i	$0.278007\pi$
$720$		0			0
$721$	−19.7145	+	5.28248i	−0.734205	+	0.196730i
$722$		0			0
$723$	11.3440	+	9.92502i	0.421889	+	0.369115i
$724$		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	0.773114	−	0.634266i	$-0.218698\pi$
$733$	3.75917	+	3.75917i	0.138848	+	0.138848i	−0.634266	+	0.773114i	$0.718698\pi$
$734$		0			0
$735$	−1.37674	−	4.04023i	−0.0507818	−	0.149026i
$736$		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	$-0.167378\pi$
$739$	37.0517	+	9.92797i	1.36297	+	0.365206i	0.498063	+	0.867141i	$0.334045\pi$
$740$		0			0
$741$	−7.71994	+	28.7121i	−0.283599	+	1.05476i
$742$		0			0
$743$	−32.0441	−	8.58618i	−1.17558	−	0.314996i	−0.382410	−	0.923993i	$-0.624906\pi$
$743$	−32.0441	−	8.58618i	−1.17558	−	0.314996i	−0.793173	+	0.608996i	$0.791572\pi$
$744$		0			0
$745$	−3.70182	−	2.13725i	−0.135624	−	0.0783027i
$746$		0			0
$747$	−19.4990	−	46.7654i	−0.713432	−	1.71106i
$748$		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	$-0.534079\pi$
$751$	19.2045	−	11.0877i	0.700782	−	0.404597i	0.807639	+	0.589678i	$0.200745\pi$
$752$		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	0.991530	−	0.129881i	$-0.0414597\pi$
$757$	10.5455	+	18.2654i	0.383284	+	0.663868i	−0.608245	+	0.793749i	$0.708126\pi$
$758$		0			0
$759$	−6.35218	+	7.26037i	−0.230570	+	0.263535i
$760$		0			0
$761$	−31.8738	+	8.54057i	−1.15543	+	0.309595i	−0.785137	−	0.619322i	$-0.787408\pi$
$761$	−31.8738	+	8.54057i	−1.15543	+	0.309595i	−0.370288	+	0.928917i	$0.620741\pi$
$762$		0			0
$763$	23.6559	−	40.9732i	0.856400	−	1.48333i
$764$		0			0
$765$	−6.45072	−	0.833922i	−0.233226	−	0.0301505i
$766$		0			0
$767$	−15.7840	+	13.7855i	−0.569926	+	0.497767i
$768$		0			0
$769$	−1.87152	+	6.98462i	−0.0674889	+	0.251872i	−0.991425	−	0.130674i	$-0.958286\pi$
$769$	−1.87152	+	6.98462i	−0.0674889	+	0.251872i	0.923937	+	0.382546i	$0.124953\pi$
$770$		0			0
$771$	9.30937	+	4.57736i	0.335269	+	0.164850i
$772$		0			0
$773$	−2.16927	−	8.09584i	−0.0780234	−	0.291187i	0.915878	−	0.401456i	$-0.131496\pi$
$773$	−2.16927	−	8.09584i	−0.0780234	−	0.291187i	−0.993902	+	0.110268i	$0.964829\pi$
$774$		0			0
$775$	8.67364	−	8.67364i	0.311566	−	0.311566i
$776$		0			0
$777$	−24.1789	−	36.0949i	−0.867413	−	1.29490i
$778$		0			0
$779$	−32.2879			−1.15684
$780$		0			0
$781$	−4.54564			−0.162656
$782$		0			0
$783$	35.6680	+	40.3852i	1.27467	+	1.44325i
$784$		0			0
$785$	5.15753	−	5.15753i	0.184080	−	0.184080i
$786$		0			0
$787$	8.20017	+	30.6035i	0.292305	+	1.09090i	0.943335	+	0.331843i	$0.107671\pi$
$787$	8.20017	+	30.6035i	0.292305	+	1.09090i	−0.651030	+	0.759052i	$0.725663\pi$
$788$		0			0
$789$	14.6416	−	29.7779i	0.521255	−	1.06012i
$790$		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
$795$	2.94596	+	0.582409i	0.104482	+	0.0206559i
$796$		0			0
$797$	−19.0468	+	32.9900i	−0.674673	+	1.16857i	0.301892	+	0.953342i	$0.402382\pi$
$797$	−19.0468	+	32.9900i	−0.674673	+	1.16857i	−0.976564	+	0.215225i	$0.930951\pi$
$798$		0			0
$799$	5.30557	−	1.42162i	0.187698	−	0.0502934i
$800$		0			0
$801$	19.0893	+	14.5770i	0.674488	+	0.515053i
$802$		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	$-0.517273\pi$
$809$	22.2820	−	12.8645i	0.783395	−	0.452293i	0.837632	+	0.546235i	$0.183939\pi$
$810$		0			0
$811$	−33.3327	−	33.3327i	−1.17047	−	1.17047i	−0.982098	−	0.188370i	$-0.939679\pi$
$811$	−33.3327	−	33.3327i	−1.17047	−	1.17047i	−0.188370	−	0.982098i	$-0.560321\pi$
$812$		0			0
$813$	37.3916	−	12.7415i	1.31138	−	0.446864i
$814$		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
$819$	−33.1128	+	11.2516i	−1.15706	+	0.393161i
$820$		0			0
$821$	14.7208	+	3.94443i	0.513759	+	0.137661i	0.506378	−	0.862311i	$-0.330984\pi$
$821$	14.7208	+	3.94443i	0.513759	+	0.137661i	0.00738091	+	0.999973i	$0.497651\pi$
$822$		0			0
$823$	−9.16080	−	5.28899i	−0.319325	−	0.184363i	0.331766	−	0.943362i	$-0.392355\pi$
$823$	−9.16080	−	5.28899i	−0.319325	−	0.184363i	−0.651092	+	0.758999i	$0.725689\pi$
$824$		0			0
$825$	8.43493	−	2.87427i	0.293666	−	0.100069i
$826$		0			0
$827$	18.9244	+	18.9244i	0.658067	+	0.658067i	0.954922	−	0.296855i	$-0.0959379\pi$
$827$	18.9244	+	18.9244i	0.658067	+	0.658067i	−0.296855	+	0.954922i	$0.595938\pi$
$828$		0			0
$829$	−21.9686	+	12.6836i	−0.763000	+	0.440518i	−0.830372	−	0.557210i	$-0.811872\pi$
$829$	−21.9686	+	12.6836i	−0.763000	+	0.440518i	0.0673717	+	0.997728i	$0.478539\pi$
$830$		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
$837$	7.84380	−	11.8286i	0.271121	−	0.408857i
$838$		0			0
$839$	−38.4597	+	10.3053i	−1.32778	+	0.355777i	−0.851886	−	0.523727i	$-0.824541\pi$
$839$	−38.4597	+	10.3053i	−1.32778	+	0.355777i	−0.475891	+	0.879504i	$0.657874\pi$
$840$		0			0
$841$	39.2624	−	68.0045i	1.35388	−	2.34498i
$842$		0			0
$843$	2.99465	+	0.592037i	0.103141	+	0.0203908i
$844$		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
$849$	17.7610	−	36.1220i	0.609555	−	1.23970i
$850$		0			0
$851$	9.76160	+	36.4308i	0.334623	+	1.24883i
$852$		0			0
$853$	−11.4412	+	11.4412i	−0.391738	+	0.391738i	−0.875306	−	0.483569i	$-0.839340\pi$
$853$	−11.4412	+	11.4412i	−0.391738	+	0.391738i	0.483569	+	0.875306i	$0.339340\pi$
$854$		0			0
$855$	−6.22331	−	8.07125i	−0.212833	−	0.276031i
$856$		0			0
$857$	9.00658			0.307659			0.153830	−	0.988097i	$-0.450839\pi$
$857$	9.00658			0.307659			0.153830	+	0.988097i	$0.450839\pi$
$858$		0			0
$859$	9.85659			0.336302			0.168151	−	0.985761i	$-0.446220\pi$
$859$	9.85659			0.336302			0.168151	+	0.985761i	$0.446220\pi$
$860$		0			0
$861$	−21.1368	−	31.5536i	−0.720341	−	1.07534i
$862$		0			0
$863$	−5.16629	+	5.16629i	−0.175862	+	0.175862i	−0.789549	−	0.613687i	$-0.789686\pi$
$863$	−5.16629	+	5.16629i	−0.175862	+	0.175862i	0.613687	+	0.789549i	$0.289686\pi$
$864$		0			0
$865$	3.74085	+	13.9611i	0.127193	+	0.474690i
$866$		0			0
$867$	−12.0744	−	5.93692i	−0.410069	−	0.201628i
$868$		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
$873$	−0.393861	+	3.04667i	−0.0133302	+	0.103114i
$874$		0			0
$875$	10.9483	−	18.9631i	0.370121	−	0.641068i
$876$		0			0
$877$	−10.7822	+	2.88909i	−0.364090	+	0.0975575i	−0.436226	−	0.899837i	$-0.643685\pi$
$877$	−10.7822	+	2.88909i	−0.364090	+	0.0975575i	0.0721361	+	0.997395i	$0.477018\pi$
$878$		0			0
$879$	3.17689	−	3.63110i	0.107154	−	0.122474i
$880$		0			0
$881$	−16.9734	−	29.3987i	−0.571848	−	0.990469i	−0.996376	−	0.0850545i	$-0.972894\pi$
$881$	−16.9734	−	29.3987i	−0.571848	−	0.990469i	0.424529	−	0.905414i	$-0.360440\pi$
$882$		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	0.184557	−	0.982822i	$-0.440915\pi$
$887$	33.5942	−	19.3956i	1.12798	−	0.651242i	0.943427	+	0.331580i	$0.107582\pi$
$888$		0			0
$889$	−18.8120	−	18.8120i	−0.630933	−	0.630933i
$890$		0			0
$891$	8.90526	−	5.19710i	0.298337	−	0.174109i
$892$		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
$897$	30.3605	+	0.0262078i	1.01371	+	0.000875054i
$898$		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
$903$	4.13114	+	12.1234i	0.137476	+	0.403441i
$904$		0			0
$905$	7.08316	+	7.08316i	0.235452	+	0.235452i
$906$		0			0
$907$	46.6252	−	26.9191i	1.54816	−	0.893833i	0.549882	−	0.835242i	$-0.314673\pi$
$907$	46.6252	−	26.9191i	1.54816	−	0.893833i	0.998282	−	0.0585904i	$-0.0186606\pi$
$908$		0			0
$909$	22.4390	−	3.00751i	0.744255	−	0.0997529i
$910$		0			0
$911$			25.8976i			0.858026i	0.903298	+	0.429013i	$0.141139\pi$
$911$			25.8976i			0.858026i	−0.903298	+	0.429013i	$0.858861\pi$
$912$		0			0
$913$	9.67457	+	16.7568i	0.320181	+	0.554570i
$914$		0			0
$915$	−9.74292	−	8.52419i	−0.322091	−	0.281801i
$916$		0			0
$917$	41.8793	−	11.2215i	1.38298	−	0.370567i
$918$		0			0
$919$	17.0250	−	29.4881i	0.561602	−	0.972723i	−0.435755	−	0.900065i	$-0.643519\pi$
$919$	17.0250	−	29.4881i	0.561602	−	0.972723i	0.997357	−	0.0726574i	$-0.0231480\pi$
$920$		0			0
$921$	7.39886	−	37.4251i	0.243801	−	1.23320i
$922$		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
$927$	−17.5132	−	7.20632i	−0.575210	−	0.236687i
$928$		0			0
$929$	7.98031	+	29.7829i	0.261826	+	0.977146i	0.964165	+	0.265304i	$0.0854723\pi$
$929$	7.98031	+	29.7829i	0.261826	+	0.977146i	−0.702339	+	0.711842i	$0.747861\pi$
$930$		0			0
$931$	−11.6260	+	11.6260i	−0.381026	+	0.381026i
$932$		0			0
$933$	24.2677	−	16.2562i	0.794490	−	0.532205i
$934$		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
$939$	−21.2589	+	14.2407i	−0.693756	+	0.464727i
$940$		0			0
$941$	37.3219	−	37.3219i	1.21666	−	1.21666i	0.247867	−	0.968794i	$-0.420271\pi$
$941$	37.3219	−	37.3219i	1.21666	−	1.21666i	0.968794	−	0.247867i	$-0.0797294\pi$
$942$		0			0
$943$	8.53345	+	31.8473i	0.277887	+	1.03709i
$944$		0			0
$945$	3.81369	−	11.3655i	0.124059	−	0.369720i
$946$		0			0
$947$	−11.2676	+	42.0512i	−0.366147	+	1.36648i	0.499711	+	0.866192i	$0.333439\pi$
$947$	−11.2676	+	42.0512i	−0.366147	+	1.36648i	−0.865859	+	0.500289i	$0.833227\pi$
$948$		0			0
$949$	−6.70078	+	19.6089i	−0.217516	+	0.636531i
$950$		0			0
$951$	−1.43918	+	7.27969i	−0.0466686	+	0.236060i
$952$		0			0
$953$	−16.4099	+	28.4228i	−0.531570	+	0.920706i	0.467751	+	0.883860i	$0.345064\pi$
$953$	−16.4099	+	28.4228i	−0.531570	+	0.920706i	−0.999321	+	0.0368460i	$0.988269\pi$
$954$		0			0
$955$	14.9098	−	3.99506i	0.482468	−	0.129277i
$956$		0			0
$957$	−15.4859	−	13.5488i	−0.500588	−	0.437970i
$958$		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	$-0.376183\pi$
$967$	−16.9803	−	16.9803i	−0.546048	−	0.546048i	−0.925295	+	0.379247i	$0.876183\pi$
$968$		0			0
$969$	8.08131	+	23.7157i	0.259609	+	0.761858i
$970$		0			0
$971$	−14.0133	−	8.09059i	−0.449708	−	0.259639i	0.257999	−	0.966145i	$-0.416937\pi$
$971$	−14.0133	−	8.09059i	−0.449708	−	0.259639i	−0.707707	+	0.706506i	$0.750270\pi$
$972$		0			0
$973$	59.3011	+	15.8897i	1.90110	+	0.509399i
$974$		0			0
$975$	−24.2756	−	14.0435i	−0.777441	−	0.449751i
$976$		0			0
$977$	25.2983	+	6.77867i	0.809366	+	0.216869i	0.639692	−	0.768631i	$-0.279062\pi$
$977$	25.2983	+	6.77867i	0.809366	+	0.216869i	0.169674	+	0.985500i	$0.445729\pi$
$978$		0			0
$979$	−7.94343	−	4.58614i	−0.253873	−	0.146574i
$980$		0			0
$981$	40.5185	−	16.8944i	1.29366	−	0.539395i
$982$		0			0
$983$	−22.1588	−	22.1588i	−0.706756	−	0.706756i	0.259096	−	0.965852i	$-0.416575\pi$
$983$	−22.1588	−	22.1588i	−0.706756	−	0.706756i	−0.965852	+	0.259096i	$0.916575\pi$
$984$		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	$-0.205889\pi$
$991$	−3.86918	−	6.70161i	−0.122908	−	0.212884i	−0.920913	+	0.389767i	$0.872555\pi$
$992$		0			0
$993$	0.868528	−	0.992703i	0.0275619	−	0.0315025i
$994$		0			0
$995$	10.8672	−	2.91185i	0.344513	−	0.0923119i
$996$		0			0
$997$	3.13628	−	5.43219i	0.0993269	−	0.172039i	−0.812079	−	0.583547i	$-0.801664\pi$
$997$	3.13628	−	5.43219i	0.0993269	−	0.172039i	0.911406	+	0.411508i	$0.134998\pi$
$998$		0			0
$999$	2.49549	−	40.2343i	0.0789537	−	1.27296i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.2	✓	56	1.1	even	1	trivial
312.2.bp.a.89.13	yes	56	3.2	odd	2	inner
312.2.bp.a.305.2	yes	56	39.32	even	12	inner
312.2.bp.a.305.13	yes	56	13.6	odd	12	inner
624.2.cn.f.305.2		56	52.19	even	12
624.2.cn.f.305.13		56	156.71	odd	12
624.2.cn.f.401.2		56	12.11	even	2
624.2.cn.f.401.13		56	4.3	odd	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43902 + 0.963958i) q^{3} +(0.504580 - 0.504580i) q^{5} +(-0.836809 - 3.12301i) q^{7} +(1.14157 - 2.77431i) q^{9} +O(q^{10})\)	\(q+(-1.43902 + 0.963958i) q^{3} +(0.504580 - 0.504580i) q^{5} +(-0.836809 - 3.12301i) q^{7} +(1.14157 - 2.77431i) q^{9} +(-0.296516 + 1.10661i) q^{11} +(3.23695 - 1.58812i) q^{13} +(-0.239708 + 1.21249i) q^{15} +(1.51919 - 2.63131i) q^{17} +(4.59867 - 1.23221i) q^{19} +(4.21464 + 3.68744i) q^{21} +(-2.43079 - 4.21025i) q^{23} +4.49080i q^{25} +(1.03158 + 5.09273i) q^{27} +(8.98018 - 5.18471i) q^{29} +(-1.93142 - 1.93142i) q^{31} +(-0.640035 - 1.87827i) q^{33} +(-1.99805 - 1.15357i) q^{35} +(-7.49362 - 2.00791i) q^{37} +(-3.12717 + 5.40563i) q^{39} +(-6.55081 - 1.75528i) q^{41} +(1.98070 + 1.14356i) q^{43} +(-0.823849 - 1.97588i) q^{45} +(1.27830 + 1.27830i) q^{47} +(-2.99079 + 1.72673i) q^{49} +(0.350327 + 5.25094i) q^{51} -2.42966i q^{53} +(0.408758 + 0.707990i) q^{55} +(-5.42979 + 6.20611i) q^{57} +(-5.61424 + 1.50433i) q^{59} +(-5.23702 + 9.07078i) q^{61} +(-9.61950 - 1.24357i) q^{63} +(0.831967 - 2.43463i) q^{65} +(-1.57758 + 5.88762i) q^{67} +(7.55646 + 3.71546i) q^{69} +(1.02693 + 3.83254i) q^{71} +(-4.06395 + 4.06395i) q^{73} +(-4.32894 - 6.46236i) q^{75} +3.70409 q^{77} +6.77768 q^{79} +(-6.39363 - 6.33415i) q^{81} +(11.9425 - 11.9425i) q^{83} +(-0.561154 - 2.09426i) q^{85} +(-7.92484 + 16.1174i) q^{87} +(-2.07215 + 7.73338i) q^{89} +(-7.66844 - 8.78010i) q^{91} +(4.64117 + 0.917551i) q^{93} +(1.69865 - 2.94215i) q^{95} +(-0.989115 + 0.265032i) q^{97} +(2.73160 + 2.08590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 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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