LMFDB - Embedded newform 920.2.bv.a.217.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.19
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.163164 - 0.0354943i) q^{3} +(0.114282 - 2.23315i) q^{5} +(-0.745341 + 0.406987i) q^{7} +(-2.70353 + 1.23466i) q^{9} +O(q^{10})$	\(q+(0.163164 - 0.0354943i) q^{3} +(0.114282 - 2.23315i) q^{5} +(-0.745341 + 0.406987i) q^{7} +(-2.70353 + 1.23466i) q^{9} +(-0.0692436 - 0.0600000i) q^{11} +(-0.434356 + 0.795465i) q^{13} +(-0.0606172 - 0.368426i) q^{15} +(-3.67172 - 2.74862i) q^{17} +(0.814632 - 5.66589i) q^{19} +(-0.107167 + 0.0928611i) q^{21} +(1.77835 - 4.45393i) q^{23} +(-4.97388 - 0.510415i) q^{25} +(-0.798322 + 0.597616i) q^{27} +(-2.33987 + 0.336423i) q^{29} +(-2.90973 + 1.86997i) q^{31} +(-0.0134278 - 0.00733211i) q^{33} +(0.823682 + 1.71097i) q^{35} +(-6.29709 - 2.34869i) q^{37} +(-0.0426371 + 0.145209i) q^{39} +(-0.746518 + 1.63465i) q^{41} +(1.20926 + 5.55888i) q^{43} +(2.44822 + 6.17848i) q^{45} +(-8.68174 - 8.68174i) q^{47} +(-3.39459 + 5.28209i) q^{49} +(-0.696655 - 0.318152i) q^{51} +(4.76735 + 8.73075i) q^{53} +(-0.141902 + 0.147774i) q^{55} +(-0.0681875 - 0.953386i) q^{57} +(-3.10212 - 10.5649i) q^{59} +(-0.407302 - 0.633775i) q^{61} +(1.51256 - 2.02055i) q^{63} +(1.72675 + 1.06089i) q^{65} +(-0.632362 - 0.0452274i) q^{67} +(0.132075 - 0.789844i) q^{69} +(5.25795 + 6.06800i) q^{71} +(-9.81179 - 13.1070i) q^{73} +(-0.829677 + 0.0932626i) q^{75} +(0.0760293 + 0.0165392i) q^{77} +(6.70270 - 1.96809i) q^{79} +(5.72992 - 6.61268i) q^{81} +(4.03584 - 10.8205i) q^{83} +(-6.55767 + 7.88537i) q^{85} +(-0.369843 + 0.137944i) q^{87} +(2.88491 + 1.85402i) q^{89} -0.769669i q^{91} +(-0.408392 + 0.408392i) q^{93} +(-12.5597 - 2.46670i) q^{95} +(3.44620 + 9.23962i) q^{97} +(0.261282 + 0.0767194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.163164	−	0.0354943i	0.0942031	−	0.0204926i	−0.165217	−	0.986257i	$-0.552832\pi$
$3$	0.163164	−	0.0354943i	0.0942031	−	0.0204926i	0.259420	+	0.965765i	$0.416469\pi$
$4$		0			0
$5$	0.114282	−	2.23315i	0.0511083	−	0.998693i
$5$	0.114282	−	2.23315i	0.0511083	−	0.998693i
$6$		0			0
$7$	−0.745341	+	0.406987i	−0.281712	+	0.153827i	−0.613893	−	0.789389i	$-0.710397\pi$
$7$	−0.745341	+	0.406987i	−0.281712	+	0.153827i	0.332181	+	0.943216i	$0.392216\pi$
$8$		0			0
$9$	−2.70353	+	1.23466i	−0.901178	+	0.411554i
$10$		0			0
$11$	−0.0692436	−	0.0600000i	−0.0208777	−	0.0180907i	0.644359	−	0.764723i	$-0.277124\pi$
$11$	−0.0692436	−	0.0600000i	−0.0208777	−	0.0180907i	−0.665237	+	0.746632i	$0.731670\pi$
$12$		0			0
$13$	−0.434356	+	0.795465i	−0.120469	+	0.220622i	−0.930954	−	0.365138i	$-0.881022\pi$
$13$	−0.434356	+	0.795465i	−0.120469	+	0.220622i	0.810485	+	0.585760i	$0.199204\pi$
$14$		0			0
$15$	−0.0606172	−	0.368426i	−0.0156513	−	0.0951273i
$16$		0			0
$17$	−3.67172	−	2.74862i	−0.890523	−	0.666638i	0.0527667	−	0.998607i	$-0.483196\pi$
$17$	−3.67172	−	2.74862i	−0.890523	−	0.666638i	−0.943290	+	0.331969i	$0.892287\pi$
$18$		0			0
$19$	0.814632	−	5.66589i	0.186889	−	1.29984i	−0.653113	−	0.757261i	$-0.726537\pi$
$19$	0.814632	−	5.66589i	0.186889	−	1.29984i	0.840002	−	0.542583i	$-0.182554\pi$
$20$		0			0
$21$	−0.107167	+	0.0928611i	−0.0233858	+	0.0202639i
$22$		0			0
$23$	1.77835	−	4.45393i	0.370812	−	0.928708i
$23$	1.77835	−	4.45393i	0.370812	−	0.928708i
$24$		0			0
$25$	−4.97388	−	0.510415i	−0.994776	−	0.102083i
$26$		0			0
$27$	−0.798322	+	0.597616i	−0.153637	+	0.115011i
$28$		0			0
$29$	−2.33987	+	0.336423i	−0.434503	+	0.0624721i	−0.356096	−	0.934449i	$-0.615892\pi$
$29$	−2.33987	+	0.336423i	−0.434503	+	0.0624721i	−0.0784070	+	0.996921i	$0.524983\pi$
$30$		0			0
$31$	−2.90973	+	1.86997i	−0.522603	+	0.335857i	−0.775201	−	0.631715i	$-0.782351\pi$
$31$	−2.90973	+	1.86997i	−0.522603	+	0.335857i	0.252598	+	0.967571i	$0.418715\pi$
$32$		0			0
$33$	−0.0134278	−	0.00733211i	−0.00233747	−	0.00127636i
$34$		0			0
$35$	0.823682	+	1.71097i	0.139228	+	0.289206i
$36$		0			0
$37$	−6.29709	−	2.34869i	−1.03524	−	0.386123i	−0.226323	−	0.974052i	$-0.572671\pi$
$37$	−6.29709	−	2.34869i	−1.03524	−	0.386123i	−0.808912	+	0.587929i	$0.799943\pi$
$38$		0			0
$39$	−0.0426371	+	0.145209i	−0.00682740	+	0.0232520i
$40$		0			0
$41$	−0.746518	+	1.63465i	−0.116587	+	0.255289i	−0.958925	−	0.283660i	$-0.908451\pi$
$41$	−0.746518	+	1.63465i	−0.116587	+	0.255289i	0.842338	+	0.538949i	$0.181179\pi$
$42$		0			0
$43$	1.20926	+	5.55888i	0.184410	+	0.847721i	0.972636	+	0.232334i	$0.0746364\pi$
$43$	1.20926	+	5.55888i	0.184410	+	0.847721i	−0.788226	+	0.615386i	$0.789000\pi$
$44$		0			0
$45$	2.44822	+	6.17848i	0.364959	+	0.921034i
$46$		0			0
$47$	−8.68174	−	8.68174i	−1.26636	−	1.26636i	−0.947954	−	0.318407i	$-0.896852\pi$
$47$	−8.68174	−	8.68174i	−1.26636	−	1.26636i	−0.318407	−	0.947954i	$-0.603148\pi$
$48$		0			0
$49$	−3.39459	+	5.28209i	−0.484942	+	0.754584i
$50$		0			0
$51$	−0.696655	−	0.318152i	−0.0975512	−	0.0445501i
$52$		0			0
$53$	4.76735	+	8.73075i	0.654846	+	1.19926i	0.968332	+	0.249668i	$0.0803214\pi$
$53$	4.76735	+	8.73075i	0.654846	+	1.19926i	−0.313486	+	0.949593i	$0.601497\pi$
$54$		0			0
$55$	−0.141902	+	0.147774i	−0.0191341	+	0.0199259i
$56$		0			0
$57$	−0.0681875	−	0.953386i	−0.00903166	−	0.126279i
$58$		0			0
$59$	−3.10212	−	10.5649i	−0.403862	−	1.37543i	−0.871018	−	0.491252i	$-0.836540\pi$
$59$	−3.10212	−	10.5649i	−0.403862	−	1.37543i	0.467156	−	0.884175i	$-0.345279\pi$
$60$		0			0
$61$	−0.407302	−	0.633775i	−0.0521497	−	0.0811465i	0.814200	−	0.580585i	$-0.197176\pi$
$61$	−0.407302	−	0.633775i	−0.0521497	−	0.0811465i	−0.866349	+	0.499438i	$0.833540\pi$
$62$		0			0
$63$	1.51256	−	2.02055i	0.190565	−	0.254565i
$64$		0			0
$65$	1.72675	+	1.06089i	0.214177	+	0.131587i
$66$		0			0
$67$	−0.632362	−	0.0452274i	−0.0772553	−	0.00552541i	0.0326580	−	0.999467i	$-0.489603\pi$
$67$	−0.632362	−	0.0452274i	−0.0772553	−	0.00552541i	−0.109913	+	0.993941i	$0.535057\pi$
$68$		0			0
$69$	0.132075	−	0.789844i	0.0159000	−	0.0950860i
$70$		0			0
$71$	5.25795	+	6.06800i	0.624004	+	0.720139i	0.976462	−	0.215688i	$-0.0691995\pi$
$71$	5.25795	+	6.06800i	0.624004	+	0.720139i	−0.352458	+	0.935828i	$0.614654\pi$
$72$		0			0
$73$	−9.81179	−	13.1070i	−1.14838	−	1.53406i	−0.803389	−	0.595455i	$-0.796972\pi$
$73$	−9.81179	−	13.1070i	−1.14838	−	1.53406i	−0.344994	−	0.938605i	$-0.612119\pi$
$74$		0			0
$75$	−0.829677	+	0.0932626i	−0.0958029	+	0.0107690i
$76$		0			0
$77$	0.0760293	+	0.0165392i	0.00866434	+	0.00188481i
$78$		0			0
$79$	6.70270	−	1.96809i	0.754113	−	0.221428i	0.117990	−	0.993015i	$-0.462355\pi$
$79$	6.70270	−	1.96809i	0.754113	−	0.221428i	0.636123	+	0.771587i	$0.280537\pi$
$80$		0			0
$81$	5.72992	−	6.61268i	0.636658	−	0.734743i
$82$		0			0
$83$	4.03584	−	10.8205i	0.442991	−	1.18770i	−0.503221	−	0.864158i	$-0.667852\pi$
$83$	4.03584	−	10.8205i	0.442991	−	1.18770i	0.946212	−	0.323547i	$-0.104875\pi$
$84$		0			0
$85$	−6.55767	+	7.88537i	−0.711279	+	0.855289i
$86$		0			0
$87$	−0.369843	+	0.137944i	−0.0396513	+	0.0147892i
$88$		0			0
$89$	2.88491	+	1.85402i	0.305800	+	0.196525i	0.684536	−	0.728979i	$-0.260005\pi$
$89$	2.88491	+	1.85402i	0.305800	+	0.196525i	−0.378736	+	0.925505i	$0.623641\pi$
$90$		0			0
$91$		−	0.769669i		−	0.0806833i
$92$		0			0
$93$	−0.408392	+	0.408392i	−0.0423483	+	0.0423483i
$94$		0			0
$95$	−12.5597	−	2.46670i	−1.28859	−	0.253078i
$96$		0			0
$97$	3.44620	+	9.23962i	0.349909	+	0.938141i	0.986032	+	0.166554i	$0.0532641\pi$
$97$	3.44620	+	9.23962i	0.349909	+	0.938141i	−0.636124	+	0.771587i	$0.719463\pi$
$98$		0			0
$99$	0.261282	+	0.0767194i	0.0262598	+	0.00771059i
$100$		0			0
$101$	1.86270	+	4.07875i	0.185346	+	0.405851i	0.979381	−	0.202021i	$-0.0647508\pi$
$101$	1.86270	+	4.07875i	0.185346	+	0.405851i	−0.794035	+	0.607872i	$0.792024\pi$
$102$		0			0
$103$	5.84201	−	0.417829i	0.575631	−	0.0411699i	0.219511	−	0.975610i	$-0.429554\pi$
$103$	5.84201	−	0.417829i	0.575631	−	0.0411699i	0.356120	+	0.934440i	$0.384099\pi$
$104$		0			0
$105$	0.195125	+	0.249933i	0.0190423	+	0.0243909i
$106$		0			0
$107$	2.15526	−	9.90756i	0.208357	−	0.957800i	−0.747567	−	0.664186i	$-0.768778\pi$
$107$	2.15526	−	9.90756i	0.208357	−	0.957800i	0.955924	−	0.293614i	$-0.0948581\pi$
$108$		0			0
$109$	1.59060	+	11.0629i	0.152352	+	1.05963i	0.912263	+	0.409605i	$0.134334\pi$
$109$	1.59060	+	11.0629i	0.152352	+	1.05963i	−0.759911	+	0.650027i	$0.774757\pi$
$110$		0			0
$111$	−1.11083	−	0.159713i	−0.105435	−	0.0151593i
$112$		0			0
$113$	0.842906	−	11.7854i	0.0792940	−	1.10867i	−0.789582	−	0.613645i	$-0.789703\pi$
$113$	0.842906	−	11.7854i	0.0792940	−	1.10867i	0.868876	−	0.495030i	$-0.164843\pi$
$114$		0			0
$115$	−9.74303	−	4.48032i	−0.908543	−	0.417792i
$116$		0			0
$117$	0.192167	−	2.68685i	0.0177659	−	0.248399i
$118$		0			0
$119$	3.85533	+	0.554313i	0.353418	+	0.0508138i
$120$		0			0
$121$	−1.56427	−	10.8797i	−0.142206	−	0.989066i
$122$		0			0
$123$	−0.0637847	+	0.293213i	−0.00575127	+	0.0264382i
$124$		0			0
$125$	−1.70825	+	11.0491i	−0.152791	+	0.988259i
$126$		0			0
$127$	−3.67718	+	0.262997i	−0.326297	+	0.0233372i	−0.233527	−	0.972350i	$-0.575027\pi$
$127$	−3.67718	+	0.262997i	−0.326297	+	0.0233372i	−0.0927700	+	0.995688i	$0.529572\pi$
$128$		0			0
$129$	0.394616	+	0.864090i	0.0347440	+	0.0760788i
$130$		0			0
$131$	12.2241	+	3.58931i	1.06802	+	0.313600i	0.768077	−	0.640357i	$-0.221214\pi$
$131$	12.2241	+	3.58931i	1.06802	+	0.313600i	0.299945	+	0.953957i	$0.403032\pi$
$132$		0			0
$133$	1.69876	+	4.55456i	0.147301	+	0.394930i
$134$		0			0
$135$	1.24333	+	1.85106i	0.107009	+	0.159314i
$136$		0			0
$137$	7.42311	−	7.42311i	0.634199	−	0.634199i	−0.314919	−	0.949118i	$-0.601977\pi$
$137$	7.42311	−	7.42311i	0.634199	−	0.634199i	0.949118	+	0.314919i	$0.101977\pi$
$138$		0			0
$139$			8.56172i			0.726195i	0.931751	+	0.363098i	$0.118281\pi$
$139$			8.56172i			0.726195i	−0.931751	+	0.363098i	$0.881719\pi$
$140$		0			0
$141$	−1.72470	−	1.10840i	−0.145246	−	0.0933440i
$142$		0			0
$143$	0.0778043	−	0.0290195i	0.00650632	−	0.00242673i
$144$		0			0
$145$	0.483877	+	5.26372i	0.0401838	+	0.437128i
$146$		0			0
$147$	−0.366393	+	0.982338i	−0.0302196	+	0.0810218i
$148$		0			0
$149$	−11.4136	+	13.1721i	−0.935042	+	1.07910i	0.0616717	+	0.998096i	$0.480357\pi$
$149$	−11.4136	+	13.1721i	−0.935042	+	1.07910i	−0.996714	+	0.0809999i	$0.974189\pi$
$150$		0			0
$151$	19.8577	−	5.83074i	1.61600	−	0.474499i	0.656058	−	0.754711i	$-0.272223\pi$
$151$	19.8577	−	5.83074i	1.61600	−	0.474499i	0.959938	+	0.280212i	$0.0904047\pi$
$152$		0			0
$153$	13.3202	+	2.89764i	1.07688	+	0.234260i
$154$		0			0
$155$	3.84339	+	6.71156i	0.308709	+	0.539086i
$156$		0			0
$157$	−7.25309	−	9.68899i	−0.578859	−	0.773266i	0.411556	−	0.911384i	$-0.364985\pi$
$157$	−7.25309	−	9.68899i	−0.578859	−	0.773266i	−0.990416	+	0.138119i	$0.955894\pi$
$158$		0			0
$159$	1.08775	+	1.25533i	0.0862645	+	0.0995545i
$160$		0			0
$161$	0.487210	+	4.04346i	0.0383975	+	0.318669i
$162$		0			0
$163$	−5.49375	−	0.392921i	−0.430304	−	0.0307759i	−0.145492	−	0.989359i	$-0.546477\pi$
$163$	−5.49375	−	0.392921i	−0.430304	−	0.0307759i	−0.284812	+	0.958583i	$0.591931\pi$
$164$		0			0
$165$	−0.0179082	+	0.0291482i	−0.00139415	+	0.00226919i
$166$		0			0
$167$	0.682179	−	0.911285i	0.0527886	−	0.0705173i	−0.773370	−	0.633955i	$-0.781431\pi$
$167$	0.682179	−	0.911285i	0.0527886	−	0.0705173i	0.826159	+	0.563437i	$0.190521\pi$
$168$		0			0
$169$	6.58423	+	10.2453i	0.506479	+	0.788097i
$170$		0			0
$171$	4.79307	+	16.3237i	0.366536	+	1.24831i
$172$		0			0
$173$	0.292354	+	4.08764i	0.0222272	+	0.310777i	0.996388	+	0.0849205i	$0.0270636\pi$
$173$	0.292354	+	4.08764i	0.0222272	+	0.310777i	−0.974161	+	0.225857i	$0.927482\pi$
$174$		0			0
$175$	3.91497	−	1.64387i	0.295944	−	0.124265i
$176$		0			0
$177$	−0.881148	−	1.61370i	−0.0662311	−	0.121293i
$178$		0			0
$179$	22.2926	+	10.1807i	1.66622	+	0.760939i	0.999883	+	0.0152914i	$0.00486760\pi$
$179$	22.2926	+	10.1807i	1.66622	+	0.760939i	0.666341	+	0.745647i	$0.267860\pi$
$180$		0			0
$181$	0.196692	−	0.306059i	0.0146200	−	0.0227492i	−0.833867	−	0.551966i	$-0.813878\pi$
$181$	0.196692	−	0.306059i	0.0146200	−	0.0227492i	0.848487	+	0.529217i	$0.177514\pi$
$182$		0			0
$183$	−0.0889526	−	0.0889526i	−0.00657557	−	0.00657557i
$184$		0			0
$185$	−5.96462	+	13.7939i	−0.438528	+	1.01415i
$186$		0			0
$187$	0.0893265	+	0.410627i	0.00653220	+	0.0300281i
$188$		0			0
$189$	0.351800	−	0.770334i	0.0255897	−	0.0560335i
$190$		0			0
$191$	0.388443	−	1.32292i	0.0281068	−	0.0957229i	−0.944245	−	0.329243i	$-0.893206\pi$
$191$	0.388443	−	1.32292i	0.0281068	−	0.0957229i	0.972352	+	0.233520i	$0.0750246\pi$
$192$		0			0
$193$	−3.65405	−	1.36289i	−0.263024	−	0.0981028i	0.214493	−	0.976726i	$-0.431190\pi$
$193$	−3.65405	−	1.36289i	−0.263024	−	0.0981028i	−0.477517	+	0.878623i	$0.658463\pi$
$194$		0			0
$195$	0.319400	+	0.111810i	0.0228727	+	0.00800685i
$196$		0			0
$197$	−10.4063	−	5.68227i	−0.741418	−	0.404845i	0.0636924	−	0.997970i	$-0.479712\pi$
$197$	−10.4063	−	5.68227i	−0.741418	−	0.404845i	−0.805111	+	0.593125i	$0.797894\pi$
$198$		0			0
$199$	−2.51851	+	1.61855i	−0.178533	+	0.114736i	−0.626855	−	0.779136i	$-0.715658\pi$
$199$	−2.51851	+	1.61855i	−0.178533	+	0.114736i	0.448322	+	0.893872i	$0.352022\pi$
$200$		0			0
$201$	−0.104784	+	0.0150657i	−0.00739092	+	0.00106265i
$202$		0			0
$203$	1.60708	−	1.20305i	0.112795	−	0.0844373i
$204$		0			0
$205$	3.56509	+	1.85389i	0.248997	+	0.129482i
$206$		0			0
$207$	0.691257	+	14.2370i	0.0480457	+	0.989540i
$208$		0			0
$209$	−0.396361	+	0.343449i	−0.0274169	+	0.0237569i
$210$		0			0
$211$	2.33356	−	16.2302i	0.160649	−	1.11734i	−0.736766	−	0.676148i	$-0.763648\pi$
$211$	2.33356	−	16.2302i	0.160649	−	1.11734i	0.897415	−	0.441188i	$-0.145443\pi$
$212$		0			0
$213$	1.07329	+	0.803455i	0.0735407	+	0.0550519i
$214$		0			0
$215$	12.5520	−	2.06518i	0.856038	−	0.140844i
$216$		0			0
$217$	1.40769	−	2.57799i	0.0955601	−	0.175005i
$218$		0			0
$219$	−2.06616	−	1.79034i	−0.139618	−	0.120980i
$220$		0			0
$221$	3.78126	−	1.72685i	0.254355	−	0.116160i
$222$		0			0
$223$	−7.06855	+	3.85972i	−0.473345	+	0.258466i	−0.698168	−	0.715934i	$-0.746001\pi$
$223$	−7.06855	+	3.85972i	−0.473345	+	0.258466i	0.224823	+	0.974400i	$0.427820\pi$
$224$		0			0
$225$	14.0772	−	4.76114i	0.938483	−	0.317409i
$226$		0			0
$227$	−3.34710	+	0.728117i	−0.222155	+	0.0483268i	−0.322265	−	0.946650i	$-0.604444\pi$
$227$	−3.34710	+	0.728117i	−0.222155	+	0.0483268i	0.100110	+	0.994976i	$0.468081\pi$
$228$		0			0
$229$	−24.6284			−1.62749			−0.813747	−	0.581220i	$-0.802576\pi$
$229$	−24.6284			−1.62749			−0.813747	+	0.581220i	$0.802576\pi$
$230$		0			0
$231$	0.0129923			0.000854832
$232$		0			0
$233$	22.7490	−	4.94874i	1.49034	−	0.324203i	0.607664	−	0.794194i	$-0.292107\pi$
$233$	22.7490	−	4.94874i	1.49034	−	0.324203i	0.882671	+	0.469992i	$0.155743\pi$
$234$		0			0
$235$	−20.3797	+	18.3954i	−1.32943	+	1.19998i
$236$		0			0
$237$	1.02379	−	0.559030i	0.0665021	−	0.0363129i
$238$		0			0
$239$	−4.03563	+	1.84301i	−0.261043	+	0.119214i	−0.541638	−	0.840612i	$-0.682196\pi$
$239$	−4.03563	+	1.84301i	−0.261043	+	0.119214i	0.280595	+	0.959826i	$0.409468\pi$
$240$		0			0
$241$	−8.88985	−	7.70310i	−0.572645	−	0.496200i	0.319721	−	0.947512i	$-0.396411\pi$
$241$	−8.88985	−	7.70310i	−0.572645	−	0.496200i	−0.892366	+	0.451312i	$0.850956\pi$
$242$		0			0
$243$	2.13397	−	3.90807i	0.136894	−	0.250703i
$244$		0			0
$245$	11.4077	+	8.18426i	0.728813	+	0.522873i
$246$		0			0
$247$	4.15317	+	3.10903i	0.264260	+	0.197823i
$248$		0			0
$249$	0.274440	−	1.90877i	0.0173919	−	0.120963i
$250$		0			0
$251$	14.8893	−	12.9016i	0.939804	−	0.814345i	−0.0429851	−	0.999076i	$-0.513687\pi$
$251$	14.8893	−	12.9016i	0.939804	−	0.814345i	0.982789	+	0.184731i	$0.0591414\pi$
$252$		0			0
$253$	−0.390375	+	0.201705i	−0.0245427	+	0.0126811i
$254$		0			0
$255$	−0.790094	+	1.51937i	−0.0494776	+	0.0951468i
$256$		0			0
$257$	15.3010	−	11.4542i	0.954449	−	0.714492i	−0.00392941	−	0.999992i	$-0.501251\pi$
$257$	15.3010	−	11.4542i	0.954449	−	0.714492i	0.958379	+	0.285501i	$0.0921599\pi$
$258$		0			0
$259$	5.64937	−	0.812256i	0.351035	−	0.0504711i
$260$		0			0
$261$	5.91055	−	3.79848i	0.365854	−	0.235120i
$262$		0			0
$263$	4.75811	+	2.59812i	0.293398	+	0.160207i	0.619206	−	0.785229i	$-0.287455\pi$
$263$	4.75811	+	2.59812i	0.293398	+	0.160207i	−0.325808	+	0.945436i	$0.605636\pi$
$264$		0			0
$265$	20.0419	−	9.64842i	1.23116	−	0.592698i
$266$		0			0
$267$	0.536521	+	0.200112i	0.0328346	+	0.0122467i
$268$		0			0
$269$	0.491433	−	1.67367i	0.0299632	−	0.102045i	−0.943154	−	0.332357i	$-0.892156\pi$
$269$	0.491433	−	1.67367i	0.0299632	−	0.102045i	0.973117	+	0.230311i	$0.0739745\pi$
$270$		0			0
$271$	−1.93577	+	4.23875i	−0.117590	+	0.257485i	−0.959270	−	0.282491i	$-0.908839\pi$
$271$	−1.93577	+	4.23875i	−0.117590	+	0.257485i	0.841680	+	0.539976i	$0.181567\pi$
$272$		0			0
$273$	−0.0273188	−	0.125583i	−0.00165341	−	0.00760061i
$274$		0			0
$275$	0.313785	+	0.333776i	0.0189219	+	0.0201274i
$276$		0			0
$277$	−5.22180	−	5.22180i	−0.313748	−	0.313748i	0.532612	−	0.846360i	$-0.321211\pi$
$277$	−5.22180	−	5.22180i	−0.313748	−	0.313748i	−0.846360	+	0.532612i	$0.821211\pi$
$278$		0			0
$279$	5.55778	−	8.64807i	0.332735	−	0.517746i
$280$		0			0
$281$	25.1433	+	11.4825i	1.49992	+	0.684991i	0.985049	−	0.172276i	$-0.0551122\pi$
$281$	25.1433	+	11.4825i	1.49992	+	0.684991i	0.514872	+	0.857267i	$0.327839\pi$
$282$		0			0
$283$	−1.38500	−	2.53644i	−0.0823297	−	0.150776i	0.833270	−	0.552866i	$-0.186466\pi$
$283$	−1.38500	−	2.53644i	−0.0823297	−	0.150776i	−0.915600	+	0.402090i	$0.868284\pi$
$284$		0			0
$285$	−2.13684	+	0.0433182i	−0.126576	+	0.00256595i
$286$		0			0
$287$	−0.108869	−	1.52219i	−0.00642635	−	0.0898521i
$288$		0			0
$289$	1.13720	+	3.87294i	0.0668939	+	0.227820i
$290$		0			0
$291$	0.890251	+	1.38526i	0.0521874	+	0.0812052i
$292$		0			0
$293$	−4.08919	+	5.46252i	−0.238893	+	0.319124i	−0.903925	−	0.427691i	$-0.859327\pi$
$293$	−4.08919	+	5.46252i	−0.238893	+	0.319124i	0.665032	+	0.746815i	$0.268418\pi$
$294$		0			0
$295$	−23.9474	+	5.72012i	−1.39427	+	0.333038i
$296$		0			0
$297$	0.0911356	+	0.00651815i	0.00528823	+	0.000378221i
$298$		0			0
$299$	2.77050	+	3.34921i	0.160222	+	0.193690i
$300$		0			0
$301$	−3.16370	−	3.65110i	−0.182353	−	0.210446i
$302$		0			0
$303$	0.448699	+	0.599392i	0.0257771	+	0.0344342i
$304$		0			0
$305$	−1.46186	+	0.837136i	−0.0837058	+	0.0479343i
$306$		0			0
$307$	−23.2080	−	5.04860i	−1.32455	−	0.288139i	−0.505982	−	0.862544i	$-0.668870\pi$
$307$	−23.2080	−	5.04860i	−1.32455	−	0.288139i	−0.818571	+	0.574405i	$0.805233\pi$
$308$		0			0
$309$	0.938379	−	0.275533i	0.0533825	−	0.0156745i
$310$		0			0
$311$	−0.820225	+	0.946590i	−0.0465107	+	0.0536762i	−0.778528	−	0.627610i	$-0.784033\pi$
$311$	−0.820225	+	0.946590i	−0.0465107	+	0.0536762i	0.732018	+	0.681286i	$0.238579\pi$
$312$		0			0
$313$	2.05936	−	5.52135i	0.116402	−	0.312085i	−0.865663	−	0.500626i	$-0.833103\pi$
$313$	2.05936	−	5.52135i	0.116402	−	0.312085i	0.982065	+	0.188541i	$0.0603758\pi$
$314$		0			0
$315$	−4.33932	−	3.60868i	−0.244493	−	0.203326i
$316$		0			0
$317$	−13.6176	+	5.07910i	−0.764841	+	0.285271i	−0.701451	−	0.712718i	$-0.747464\pi$
$317$	−13.6176	+	5.07910i	−0.764841	+	0.285271i	−0.0633900	+	0.997989i	$0.520191\pi$
$318$		0			0
$319$	0.182207	+	0.117097i	0.0102016	+	0.00655617i
$320$		0			0
$321$		−	1.69306i		−	0.0944975i
$322$		0			0
$323$	−18.5645	+	18.5645i	−1.03295	+	1.03295i
$324$		0			0
$325$	2.56645	−	3.73484i	0.142361	−	0.207172i
$326$		0			0
$327$	0.652199	+	1.74861i	0.0360667	+	0.0966985i
$328$		0			0
$329$	10.0042	+	2.93750i	0.551549	+	0.161950i
$330$		0			0
$331$	9.33461	+	20.4399i	0.513077	+	1.12348i	0.971995	+	0.235002i	$0.0755098\pi$
$331$	9.33461	+	20.4399i	0.513077	+	1.12348i	−0.458918	+	0.888478i	$0.651763\pi$
$332$		0			0
$333$	19.9242	−	1.42501i	1.09184	−	0.0780901i
$334$		0			0
$335$	−0.173267	+	1.40699i	−0.00946658	+	0.0768720i
$336$		0			0
$337$	5.98385	−	27.5073i	0.325961	−	1.49842i	−0.464317	−	0.885669i	$-0.653700\pi$
$337$	5.98385	−	27.5073i	0.325961	−	1.49842i	0.790278	−	0.612749i	$-0.209936\pi$
$338$		0			0
$339$	−0.280781	−	1.95287i	−0.0152499	−	0.106065i
$340$		0			0
$341$	0.313679	+	0.0451002i	0.0169867	+	0.00244231i
$342$		0			0
$343$	0.804465	−	11.2479i	0.0434370	−	0.607329i
$344$		0			0
$345$	−1.74874	−	0.385208i	−0.0941491	−	0.0207389i
$346$		0			0
$347$	−1.90941	+	26.6970i	−0.102502	+	1.43317i	0.642591	+	0.766210i	$0.277860\pi$
$347$	−1.90941	+	26.6970i	−0.102502	+	1.43317i	−0.745093	+	0.666961i	$0.767595\pi$
$348$		0			0
$349$	−11.3295	−	1.62894i	−0.606455	−	0.0871950i	−0.167755	−	0.985829i	$-0.553652\pi$
$349$	−11.3295	−	1.62894i	−0.606455	−	0.0871950i	−0.438700	+	0.898634i	$0.644561\pi$
$350$		0			0
$351$	−0.128626	−	0.894615i	−0.00686556	−	0.0477510i
$352$		0			0
$353$	5.77698	−	26.5563i	0.307477	−	1.41345i	−0.521061	−	0.853519i	$-0.674464\pi$
$353$	5.77698	−	26.5563i	0.307477	−	1.41345i	0.828539	−	0.559932i	$-0.189173\pi$
$354$		0			0
$355$	14.1516	−	11.0483i	0.751090	−	0.586384i
$356$		0			0
$357$	0.648728	−	0.0463980i	0.0343344	−	0.00245564i
$358$		0			0
$359$	3.00822	+	6.58709i	0.158768	+	0.347654i	0.972253	−	0.233933i	$-0.0751596\pi$
$359$	3.00822	+	6.58709i	0.158768	+	0.347654i	−0.813485	+	0.581586i	$0.802432\pi$
$360$		0			0
$361$	−13.2083	−	3.87831i	−0.695174	−	0.204121i
$362$		0			0
$363$	−0.641401	−	1.71966i	−0.0336648	−	0.0902589i
$364$		0			0
$365$	−30.3912	+	20.4133i	−1.59075	+	1.06848i
$366$		0			0
$367$	−5.62419	+	5.62419i	−0.293580	+	0.293580i	−0.838493	−	0.544913i	$-0.816563\pi$
$367$	−5.62419	+	5.62419i	−0.293580	+	0.293580i	0.544913	+	0.838493i	$0.316563\pi$
$368$		0			0
$369$		−	5.34102i		−	0.278042i
$370$		0			0
$371$	−7.10660	−	4.56713i	−0.368956	−	0.237114i
$372$		0			0
$373$	12.3837	−	4.61888i	0.641203	−	0.239156i	−0.00776741	−	0.999970i	$-0.502472\pi$
$373$	12.3837	−	4.61888i	0.641203	−	0.239156i	0.648971	+	0.760813i	$0.275200\pi$
$374$		0			0
$375$	0.113452	+	1.86345i	0.00585864	+	0.0962281i
$376$		0			0
$377$	0.748726	−	2.00741i	0.0385613	−	0.103387i
$378$		0			0
$379$	−20.9002	+	24.1201i	−1.07357	+	1.23897i	−0.103893	+	0.994589i	$0.533130\pi$
$379$	−20.9002	+	24.1201i	−1.07357	+	1.23897i	−0.969680	+	0.244380i	$0.921416\pi$
$380$		0			0
$381$	−0.590650	+	0.173431i	−0.0302599	+	0.00888512i
$382$		0			0
$383$	−26.0394	−	5.66452i	−1.33055	−	0.289443i	−0.509584	−	0.860421i	$-0.670201\pi$
$383$	−26.0394	−	5.66452i	−1.33055	−	0.289443i	−0.820966	+	0.570978i	$0.806564\pi$
$384$		0			0
$385$	0.0456231	−	0.167894i	0.00232517	−	0.00855669i
$386$		0			0
$387$	−10.1326	−	13.5356i	−0.515070	−	0.688052i
$388$		0			0
$389$	11.7483	+	13.5582i	0.595662	+	0.687430i	0.970896	−	0.239500i	$-0.0769834\pi$
$389$	11.7483	+	13.5582i	0.595662	+	0.687430i	−0.375235	+	0.926930i	$0.622438\pi$
$390$		0			0
$391$	−18.7718	+	11.4656i	−0.949329	+	0.579839i
$392$		0			0
$393$	2.12193	+	0.151764i	0.107037	+	0.00765547i
$394$		0			0
$395$	−3.62904	−	15.1930i	−0.182597	−	0.764444i
$396$		0			0
$397$	11.8039	−	15.7681i	0.592419	−	0.791379i	−0.399705	−	0.916644i	$-0.630887\pi$
$397$	11.8039	−	15.7681i	0.592419	−	0.791379i	0.992123	+	0.125265i	$0.0399782\pi$
$398$		0			0
$399$	0.438839	+	0.682846i	0.0219694	+	0.0341851i
$400$		0			0
$401$	6.25817	+	21.3134i	0.312518	+	1.06434i	0.954646	+	0.297742i	$0.0962334\pi$
$401$	6.25817	+	21.3134i	0.312518	+	1.06434i	−0.642128	+	0.766597i	$0.721948\pi$
$402$		0			0
$403$	−0.223635	−	3.12682i	−0.0111400	−	0.155758i
$404$		0			0
$405$	−14.1123	−	13.5515i	−0.701244	−	0.673378i
$406$		0			0
$407$	0.295112	+	0.540458i	0.0146282	+	0.0267895i
$408$		0			0
$409$	−21.7429	−	9.92964i	−1.07512	−	0.490989i	−0.202443	−	0.979294i	$-0.564888\pi$
$409$	−21.7429	−	9.92964i	−1.07512	−	0.490989i	−0.872673	+	0.488305i	$0.837615\pi$
$410$		0			0
$411$	0.947710	−	1.47467i	0.0467471	−	0.0727399i
$412$		0			0
$413$	6.61189	+	6.61189i	0.325350	+	0.325350i
$414$		0			0
$415$	−23.7025	−	10.2492i	−1.16351	−	0.503114i
$416$		0			0
$417$	0.303892	+	1.39697i	0.0148816	+	0.0684098i
$418$		0			0
$419$	12.6549	−	27.7103i	0.618231	−	1.35374i	−0.298567	−	0.954389i	$-0.596509\pi$
$419$	12.6549	−	27.7103i	0.618231	−	1.35374i	0.916799	−	0.399349i	$-0.130764\pi$
$420$		0			0
$421$	−3.98031	+	13.5557i	−0.193988	+	0.660663i	0.803843	+	0.594841i	$0.202785\pi$
$421$	−3.98031	+	13.5557i	−0.193988	+	0.660663i	−0.997831	+	0.0658220i	$0.979033\pi$
$422$		0			0
$423$	34.1904	+	12.7523i	1.66239	+	0.620040i
$424$		0			0
$425$	16.8598	+	15.5454i	0.817819	+	0.754062i
$426$		0			0
$427$	0.561517	+	0.306611i	0.0271737	+	0.0148380i
$428$		0			0
$429$	0.0116649	−	0.00749655i	0.000563185	−	0.000361937i
$430$		0			0
$431$	18.0042	−	2.58861i	0.867230	−	0.124689i	0.305683	−	0.952133i	$-0.401115\pi$
$431$	18.0042	−	2.58861i	0.867230	−	0.124689i	0.561547	+	0.827445i	$0.310206\pi$
$432$		0			0
$433$	−14.0360	+	10.5072i	−0.674529	+	0.504946i	−0.880763	−	0.473557i	$-0.842970\pi$
$433$	−14.0360	+	10.5072i	−0.674529	+	0.504946i	0.206235	+	0.978503i	$0.433879\pi$
$434$		0			0
$435$	0.265783	+	0.841677i	0.0127433	+	0.0403553i
$436$		0			0
$437$	−23.7867	−	13.7043i	−1.13787	−	0.655564i
$438$		0			0
$439$	−0.746372	+	0.646735i	−0.0356224	+	0.0308670i	−0.672490	−	0.740106i	$-0.734775\pi$
$439$	−0.746372	+	0.646735i	−0.0356224	+	0.0308670i	0.636868	+	0.770973i	$0.280230\pi$
$440$		0			0
$441$	2.65580	−	18.4715i	0.126467	−	0.879594i
$442$		0			0
$443$	−22.6199	−	16.9330i	−1.07470	−	0.804513i	−0.0931410	−	0.995653i	$-0.529691\pi$
$443$	−22.6199	−	16.9330i	−1.07470	−	0.804513i	−0.981563	+	0.191140i	$0.938782\pi$
$444$		0			0
$445$	4.46998	−	6.23054i	0.211898	−	0.295356i
$446$		0			0
$447$	−1.39477	+	2.55433i	−0.0659703	+	0.120816i
$448$		0			0
$449$	−2.20435	−	1.91008i	−0.104030	−	0.0901423i	0.601293	−	0.799029i	$-0.294652\pi$
$449$	−2.20435	−	1.91008i	−0.104030	−	0.0901423i	−0.705323	+	0.708886i	$0.749198\pi$
$450$		0			0
$451$	0.149770	−	0.0683978i	0.00705241	−	0.00322073i
$452$		0			0
$453$	3.03311	−	1.65620i	0.142508	−	0.0778153i
$454$		0			0
$455$	−1.71878	−	0.0879591i	−0.0805778	−	0.00412358i
$456$		0			0
$457$	−23.5606	+	5.12529i	−1.10212	+	0.239751i	−0.726597	−	0.687064i	$-0.758899\pi$
$457$	−23.5606	+	5.12529i	−1.10212	+	0.239751i	−0.375519	+	0.926815i	$0.622536\pi$
$458$		0			0
$459$	4.57383			0.213488
$460$		0			0
$461$	−29.9157			−1.39331			−0.696657	−	0.717405i	$-0.745330\pi$
$461$	−29.9157			−1.39331			−0.696657	+	0.717405i	$0.745330\pi$
$462$		0			0
$463$	−27.4983	+	5.98189i	−1.27795	+	0.278002i	−0.799796	−	0.600271i	$-0.795059\pi$
$463$	−27.4983	+	5.98189i	−1.27795	+	0.278002i	−0.478159	+	0.878273i	$0.658696\pi$
$464$		0			0
$465$	0.865327	+	0.958670i	0.0401286	+	0.0444573i
$466$		0			0
$467$	−12.9738	+	7.08423i	−0.600356	+	0.327819i	−0.750526	−	0.660841i	$-0.770200\pi$
$467$	−12.9738	+	7.08423i	−0.600356	+	0.327819i	0.150170	+	0.988660i	$0.452018\pi$
$468$		0			0
$469$	0.489732	−	0.223653i	0.0226137	−	0.0103273i
$470$		0			0
$471$	−1.52735	−	1.32346i	−0.0703766	−	0.0609816i
$472$		0			0
$473$	0.249799	−	0.457472i	0.0114858	−	0.0210346i
$474$		0			0
$475$	−6.94383	+	27.7656i	−0.318605	+	1.27398i
$476$		0			0
$477$	−23.6682	−	17.7178i	−1.08369	−	0.811242i
$478$		0			0
$479$	−0.810989	+	5.64055i	−0.0370550	+	0.257723i	−0.999925	−	0.0122420i	$-0.996103\pi$
$479$	−0.810989	+	5.64055i	−0.0370550	+	0.257723i	0.962870	+	0.269965i	$0.0870123\pi$
$480$		0			0
$481$	4.60349	−	3.98894i	0.209901	−	0.181880i
$482$		0			0
$483$	0.223015	+	0.642456i	0.0101475	+	0.0292327i
$484$		0			0
$485$	21.0273	−	6.63995i	0.954799	−	0.301505i
$486$		0			0
$487$	17.3207	−	12.9661i	0.784875	−	0.587550i	−0.129894	−	0.991528i	$-0.541464\pi$
$487$	17.3207	−	12.9661i	0.784875	−	0.587550i	0.914769	+	0.403978i	$0.132373\pi$
$488$		0			0
$489$	−0.910332	+	0.130886i	−0.0411666	+	0.00591887i
$490$		0			0
$491$	−29.5758	+	19.0072i	−1.33474	+	0.857784i	−0.996526	−	0.0832859i	$-0.973459\pi$
$491$	−29.5758	+	19.0072i	−1.33474	+	0.857784i	−0.338212	+	0.941070i	$0.609822\pi$
$492$		0			0
$493$	9.51605	+	5.19616i	0.428581	+	0.234023i
$494$		0			0
$495$	0.201185	−	0.574714i	0.00904261	−	0.0258315i
$496$		0			0
$497$	−6.38856	−	2.38281i	−0.286566	−	0.106884i
$498$		0			0
$499$	4.12121	−	14.0356i	0.184491	−	0.628318i	−0.814359	−	0.580362i	$-0.802911\pi$
$499$	4.12121	−	14.0356i	0.184491	−	0.628318i	0.998849	−	0.0479562i	$-0.0152708\pi$
$500$		0			0
$501$	0.0789621	−	0.172903i	0.00352776	−	0.00772473i
$502$		0			0
$503$	−2.59546	−	11.9311i	−0.115726	−	0.531983i	−0.998110	−	0.0614534i	$-0.980426\pi$
$503$	−2.59546	−	11.9311i	−0.115726	−	0.531983i	0.882384	−	0.470530i	$-0.155937\pi$
$504$		0			0
$505$	9.32132	−	3.69356i	0.414793	−	0.164361i
$506$		0			0
$507$	1.43796	+	1.43796i	0.0638621	+	0.0638621i
$508$		0			0
$509$	10.2564	−	15.9593i	0.454609	−	0.707385i	−0.535984	−	0.844228i	$-0.680059\pi$
$509$	10.2564	−	15.9593i	0.454609	−	0.707385i	0.990593	+	0.136843i	$0.0436957\pi$
$510$		0			0
$511$	12.6475	+	5.77592i	0.559492	+	0.255512i
$512$		0			0
$513$	2.73569	+	5.01004i	0.120784	+	0.221199i
$514$		0			0
$515$	−0.265438	−	13.0938i	−0.0116966	−	0.576983i
$516$		0			0
$517$	0.0802512	+	1.12206i	0.00352944	+	0.0493481i
$518$		0			0
$519$	0.192789	+	0.656580i	0.00846251	+	0.0288207i
$520$		0			0
$521$	−20.9052	−	32.5291i	−0.915873	−	1.42513i	−0.905107	−	0.425184i	$-0.860209\pi$
$521$	−20.9052	−	32.5291i	−0.915873	−	1.42513i	−0.0107660	−	0.999942i	$-0.503427\pi$
$522$		0			0
$523$	12.3938	−	16.5562i	0.541944	−	0.723952i	−0.443059	−	0.896493i	$-0.646107\pi$
$523$	12.3938	−	16.5562i	0.541944	−	0.723952i	0.985002	+	0.172541i	$0.0551976\pi$
$524$		0			0
$525$	0.580435	−	0.407180i	0.0253323	−	0.0177708i
$526$		0			0
$527$	15.8236	+	1.13172i	0.689285	+	0.0492987i
$528$		0			0
$529$	−16.6749	−	15.8413i	−0.724996	−	0.688753i
$530$		0			0
$531$	21.4307	+	24.7324i	0.930014	+	1.07329i
$532$		0			0
$533$	−0.976049	−	1.30385i	−0.0422774	−	0.0564759i
$534$		0			0
$535$	−21.8787	−	5.94526i	−0.945900	−	0.257036i
$536$		0			0
$537$	3.99871	+	0.869866i	0.172557	+	0.0375375i
$538$		0			0
$539$	0.551979	−	0.162076i	0.0237754	−	0.00698109i
$540$		0			0
$541$	19.2745	−	22.2440i	0.828676	−	0.956343i	−0.170905	−	0.985288i	$-0.554669\pi$
$541$	19.2745	−	22.2440i	0.828676	−	0.956343i	0.999581	+	0.0289442i	$0.00921450\pi$
$542$		0			0
$543$	0.0212298	−	0.0569193i	0.000911059	−	0.00244264i
$544$		0			0
$545$	24.8868	−	2.28776i	1.06603	−	0.0979970i
$546$		0			0
$547$	3.06276	−	1.14235i	0.130954	−	0.0488435i	−0.283133	−	0.959081i	$-0.591374\pi$
$547$	3.06276	−	1.14235i	0.130954	−	0.0488435i	0.414087	+	0.910237i	$0.364101\pi$
$548$		0			0
$549$	1.88365	+	1.21055i	0.0803923	+	0.0516650i
$550$		0			0
$551$			13.5315i			0.576462i
$552$		0			0
$553$	−4.19481	+	4.19481i	−0.178381	+	0.178381i
$554$		0			0
$555$	−0.483609	+	2.46239i	−0.0205281	+	0.104522i
$556$		0			0
$557$	7.52370	+	20.1718i	0.318789	+	0.854707i	0.993207	+	0.116357i	$0.0371218\pi$
$557$	7.52370	+	20.1718i	0.318789	+	0.854707i	−0.674418	+	0.738350i	$0.735605\pi$
$558$		0			0
$559$	−4.94714	−	1.45261i	−0.209242	−	0.0614389i
$560$		0			0
$561$	0.0291498	+	0.0638292i	0.00123071	+	0.00269487i
$562$		0			0
$563$	2.07292	−	0.148258i	0.0873633	−	0.00624834i	−0.0275891	−	0.999619i	$-0.508783\pi$
$563$	2.07292	−	0.148258i	0.0873633	−	0.00624834i	0.114952	+	0.993371i	$0.463328\pi$
$564$		0			0
$565$	−26.2221	−	3.22918i	−1.10317	−	0.135853i
$566$		0			0
$567$	−1.57947	+	7.26070i	−0.0663315	+	0.304921i
$568$		0			0
$569$	−3.95843	−	27.5315i	−0.165946	−	1.15418i	−0.887158	−	0.461466i	$-0.847323\pi$
$569$	−3.95843	−	27.5315i	−0.165946	−	1.15418i	0.721211	−	0.692715i	$-0.243586\pi$
$570$		0			0
$571$	−32.0150	−	4.60306i	−1.33978	−	0.192632i	−0.565122	−	0.825007i	$-0.691171\pi$
$571$	−32.0150	−	4.60306i	−1.33978	−	0.192632i	−0.774662	+	0.632375i	$0.782080\pi$
$572$		0			0
$573$	0.0164242	−	0.229641i	0.000686131	−	0.00959337i
$574$		0			0
$575$	−11.1187	+	21.2456i	−0.463680	+	0.886003i
$576$		0			0
$577$	1.59773	−	22.3392i	0.0665144	−	0.929993i	−0.849176	−	0.528109i	$-0.822901\pi$
$577$	1.59773	−	22.3392i	0.0665144	−	0.929993i	0.915691	−	0.401884i	$-0.131644\pi$
$578$		0			0
$579$	−0.644585	−	0.0926773i	−0.0267880	−	0.00385154i
$580$		0			0
$581$	1.39573	+	9.70749i	0.0579045	+	0.402735i
$582$		0			0
$583$	0.193736	−	0.890590i	0.00802372	−	0.0368844i
$584$		0			0
$585$	−5.97816	−	0.736195i	−0.247167	−	0.0304379i
$586$		0			0
$587$	26.2415	−	1.87683i	1.08310	−	0.0774650i	0.481642	−	0.876368i	$-0.340040\pi$
$587$	26.2415	−	1.87683i	1.08310	−	0.0774650i	0.601460	+	0.798903i	$0.294586\pi$
$588$		0			0
$589$	8.22469	+	18.0096i	0.338892	+	0.742071i
$590$		0			0
$591$	−1.89963	−	0.557781i	−0.0781402	−	0.0229440i
$592$		0			0
$593$	−4.71902	−	12.6522i	−0.193787	−	0.519562i	0.803322	−	0.595544i	$-0.203064\pi$
$593$	−4.71902	−	12.6522i	−0.193787	−	0.519562i	−0.997109	+	0.0759820i	$0.975791\pi$
$594$		0			0
$595$	1.67846	−	8.54617i	0.0688100	−	0.350359i
$596$		0			0
$597$	−0.353483	+	0.353483i	−0.0144671	+	0.0144671i
$598$		0			0
$599$		−	47.9772i		−	1.96030i	−0.198266	−	0.980148i	$-0.563531\pi$
$599$		−	47.9772i		−	1.96030i	0.198266	−	0.980148i	$-0.436469\pi$
$600$		0			0
$601$	−25.2136	−	16.2038i	−1.02848	−	0.660966i	−0.0863706	−	0.996263i	$-0.527527\pi$
$601$	−25.2136	−	16.2038i	−1.02848	−	0.660966i	−0.942112	+	0.335297i	$0.891163\pi$
$602$		0			0
$603$	1.76545	−	0.658480i	0.0718948	−	0.0268154i
$604$		0			0
$605$	−24.4748	+	2.24989i	−0.995041	+	0.0914709i
$606$		0			0
$607$	−14.3801	+	38.5546i	−0.583671	+	1.56488i	0.223588	+	0.974684i	$0.428223\pi$
$607$	−14.3801	+	38.5546i	−0.583671	+	1.56488i	−0.807259	+	0.590198i	$0.799050\pi$
$608$		0			0
$609$	0.219517	−	0.253336i	0.00889529	−	0.0102657i
$610$		0			0
$611$	10.6770	−	3.13504i	0.431944	−	0.126830i
$612$		0			0
$613$	−13.7816	−	2.99800i	−0.556633	−	0.121088i	−0.0745558	−	0.997217i	$-0.523754\pi$
$613$	−13.7816	−	2.99800i	−0.556633	−	0.121088i	−0.482077	+	0.876129i	$0.660118\pi$
$614$		0			0
$615$	0.647499	+	0.175949i	0.0261097	+	0.00709496i
$616$		0			0
$617$	1.90451	+	2.54413i	0.0766726	+	0.102423i	0.837238	−	0.546839i	$-0.184169\pi$
$617$	1.90451	+	2.54413i	0.0766726	+	0.102423i	−0.760565	+	0.649262i	$0.775078\pi$
$618$		0			0
$619$	12.8593	+	14.8405i	0.516861	+	0.596489i	0.952842	−	0.303467i	$-0.0981441\pi$
$619$	12.8593	+	14.8405i	0.516861	+	0.596489i	−0.435981	+	0.899956i	$0.643599\pi$
$620$		0			0
$621$	1.24204	+	4.61844i	0.0498413	+	0.185332i
$622$		0			0
$623$	−2.90480	−	0.207755i	−0.116378	−	0.00832354i
$624$		0			0
$625$	24.4790	+	5.07749i	0.979158	+	0.203099i
$626$		0			0
$627$	−0.0524816	+	0.0701072i	−0.00209591	+	0.00279981i
$628$		0			0
$629$	16.6655	+	25.9321i	0.664498	+	1.03398i
$630$		0			0
$631$	−6.67141	−	22.7207i	−0.265585	−	0.904498i	−0.979018	−	0.203775i	$-0.934679\pi$
$631$	−6.67141	−	22.7207i	−0.265585	−	0.904498i	0.713433	−	0.700723i	$-0.247139\pi$
$632$		0			0
$633$	−0.195327	−	2.73103i	−0.00776354	−	0.108549i
$634$		0			0
$635$	0.167077	+	8.24173i	0.00663024	+	0.327063i
$636$		0			0
$637$	−2.72725	−	4.99459i	−0.108058	−	0.197893i
$638$		0			0
$639$	−21.7070	−	9.91325i	−0.858715	−	0.392162i
$640$		0			0
$641$	−10.7799	+	16.7738i	−0.425779	+	0.662525i	−0.986176	−	0.165699i	$-0.947012\pi$
$641$	−10.7799	+	16.7738i	−0.425779	+	0.662525i	0.560397	+	0.828224i	$0.310648\pi$
$642$		0			0
$643$	22.6162	+	22.6162i	0.891898	+	0.891898i	0.994702	−	0.102804i	$-0.0327814\pi$
$643$	22.6162	+	22.6162i	0.891898	+	0.891898i	−0.102804	+	0.994702i	$0.532781\pi$
$644$		0			0
$645$	1.97474	−	0.782487i	0.0777551	−	0.0308104i
$646$		0			0
$647$	−4.89774	−	22.5145i	−0.192550	−	0.885137i	−0.967452	−	0.253056i	$-0.918564\pi$
$647$	−4.89774	−	22.5145i	−0.192550	−	0.885137i	0.774902	−	0.632082i	$-0.217799\pi$
$648$		0			0
$649$	−0.419089	+	0.917676i	−0.0164507	+	0.0360219i
$650$		0			0
$651$	0.138181	−	0.470601i	0.00541574	−	0.0184443i
$652$		0			0
$653$	−6.76287	−	2.52242i	−0.264652	−	0.0987100i	0.213636	−	0.976913i	$-0.431469\pi$
$653$	−6.76287	−	2.52242i	−0.264652	−	0.0987100i	−0.478287	+	0.878203i	$0.658742\pi$
$654$		0			0
$655$	9.41244	−	26.8879i	0.367775	−	1.05060i
$656$		0			0
$657$	42.7092	+	23.3210i	1.66625	+	0.909839i
$658$		0			0
$659$	−5.44503	+	3.49931i	−0.212108	+	0.136314i	−0.642382	−	0.766385i	$-0.722054\pi$
$659$	−5.44503	+	3.49931i	−0.212108	+	0.136314i	0.430273	+	0.902699i	$0.358417\pi$
$660$		0			0
$661$	6.67813	−	0.960171i	0.259749	−	0.0373463i	−0.0112098	−	0.999937i	$-0.503568\pi$
$661$	6.67813	−	0.960171i	0.259749	−	0.0373463i	0.270959	+	0.962591i	$0.412659\pi$
$662$		0			0
$663$	0.555675	−	0.415973i	0.0215806	−	0.0161551i
$664$		0			0
$665$	10.3651	−	3.27308i	0.401943	−	0.126925i
$666$		0			0
$667$	−2.66272	+	11.0199i	−0.103101	+	0.426692i
$668$		0			0
$669$	−1.01634	+	0.880662i	−0.0392939	+	0.0340484i
$670$		0			0
$671$	−0.00982336	+	0.0683230i	−0.000379227	+	0.00263758i
$672$		0			0
$673$	−0.646935	−	0.484290i	−0.0249375	−	0.0186680i	0.586736	−	0.809778i	$-0.300413\pi$
$673$	−0.646935	−	0.484290i	−0.0249375	−	0.0186680i	−0.611674	+	0.791110i	$0.709503\pi$
$674$		0			0
$675$	4.27579	−	2.56499i	0.164575	−	0.0987267i
$676$		0			0
$677$	−13.8271	+	25.3225i	−0.531419	+	0.973221i	0.464722	+	0.885457i	$0.346154\pi$
$677$	−13.8271	+	25.3225i	−0.531419	+	0.973221i	−0.996141	+	0.0877648i	$0.972028\pi$
$678$		0			0
$679$	−6.32900	−	5.48411i	−0.242885	−	0.210461i
$680$		0			0
$681$	−0.520284	+	0.237606i	−0.0199373	+	0.00910507i
$682$		0			0
$683$	−2.59707	+	1.41811i	−0.0993741	+	0.0542624i	−0.528167	−	0.849140i	$-0.677121\pi$
$683$	−2.59707	+	1.41811i	−0.0993741	+	0.0542624i	0.428793	+	0.903403i	$0.358939\pi$
$684$		0			0
$685$	−15.7286	−	17.4252i	−0.600957	−	0.665783i
$686$		0			0
$687$	−4.01849	+	0.874168i	−0.153315	+	0.0333516i
$688$		0			0
$689$	−9.01573			−0.343472
$690$		0			0
$691$	−9.81898			−0.373532			−0.186766	−	0.982404i	$-0.559801\pi$
$691$	−9.81898			−0.373532			−0.186766	+	0.982404i	$0.559801\pi$
$692$		0			0
$693$	−0.225968	+	0.0491563i	−0.00858381	+	0.00186729i
$694$		0			0
$695$	19.1196	+	0.978447i	0.725246	+	0.0371146i
$696$		0			0
$697$	7.23403	−	3.95008i	0.274008	−	0.149620i
$698$		0			0
$699$	3.53617	−	1.61492i	0.133750	−	0.0610817i
$700$		0			0
$701$	13.6693	+	11.8446i	0.516284	+	0.447363i	0.873617	−	0.486614i	$-0.161768\pi$
$701$	13.6693	+	11.8446i	0.516284	+	0.447363i	−0.357333	+	0.933977i	$0.616314\pi$
$702$		0			0
$703$	−18.4373	+	33.7653i	−0.695374	+	1.27348i
$704$		0			0
$705$	−2.67232	+	3.72484i	−0.100645	+	0.140286i
$706$		0			0
$707$	−3.04835	−	2.28196i	−0.114645	−	0.0858221i
$708$		0			0
$709$	0.637059	−	4.43084i	0.0239252	−	0.166404i	−0.974356	−	0.225013i	$-0.927758\pi$
$709$	0.637059	−	4.43084i	0.0239252	−	0.166404i	0.998281	+	0.0586093i	$0.0186666\pi$
$710$		0			0
$711$	−15.6911	+	13.5964i	−0.588460	+	0.509904i
$712$		0			0
$713$	3.15418	+	16.2852i	0.118125	+	0.609886i
$714$		0			0
$715$	−0.0559131	−	0.177065i	−0.00209103	−	0.00662184i
$716$		0			0
$717$	−0.593055	+	0.443955i	−0.0221480	+	0.0165798i
$718$		0			0
$719$	39.2973	−	5.65010i	1.46554	−	0.210713i	0.637098	−	0.770783i	$-0.280135\pi$
$719$	39.2973	−	5.65010i	1.46554	−	0.210713i	0.828446	+	0.560070i	$0.189226\pi$
$720$		0			0
$721$	−4.18424	+	2.68905i	−0.155829	+	0.100145i
$722$		0			0
$723$	−1.72392	−	0.941333i	−0.0641134	−	0.0350086i
$724$		0			0
$725$	11.8100	−	0.479020i	0.438611	−	0.0177904i
$726$		0			0
$727$	11.2140	+	4.18262i	0.415906	+	0.155125i	0.548701	−	0.836019i	$-0.315123\pi$
$727$	11.2140	+	4.18262i	0.415906	+	0.155125i	−0.132795	+	0.991143i	$0.542395\pi$
$728$		0			0
$729$	−7.18587	+	24.4728i	−0.266143	+	0.906401i
$730$		0			0
$731$	10.8392	−	23.7344i	0.400901	−	0.877850i
$732$		0			0
$733$	7.07852	+	32.5394i	0.261451	+	1.20187i	0.901240	+	0.433321i	$0.142658\pi$
$733$	7.07852	+	32.5394i	0.261451	+	1.20187i	−0.639789	+	0.768551i	$0.720978\pi$
$734$		0			0
$735$	2.15183	+	0.930472i	0.0793715	+	0.0343210i
$736$		0			0
$737$	0.0410734	+	0.0410734i	0.00151296	+	0.00151296i
$738$		0			0
$739$	11.0555	−	17.2027i	0.406683	−	0.632810i	−0.576143	−	0.817349i	$-0.695443\pi$
$739$	11.0555	−	17.2027i	0.406683	−	0.632810i	0.982825	+	0.184539i	$0.0590791\pi$
$740$		0			0
$741$	0.788003	+	0.359869i	0.0289480	+	0.0132201i
$742$		0			0
$743$	10.6272	+	19.4623i	0.389874	+	0.714001i	0.996729	−	0.0808112i	$-0.0257511\pi$
$743$	10.6272	+	19.4623i	0.389874	+	0.714001i	−0.606855	+	0.794812i	$0.707569\pi$
$744$		0			0
$745$	28.1107	+	26.9937i	1.02990	+	0.988971i
$746$		0			0
$747$	2.44864	+	34.2365i	0.0895911	+	1.25265i
$748$		0			0
$749$	2.42585	+	8.26167i	0.0886385	+	0.301875i
$750$		0			0
$751$	−9.17580	−	14.2778i	−0.334830	−	0.521005i	0.632489	−	0.774570i	$-0.282033\pi$
$751$	−9.17580	−	14.2778i	−0.334830	−	0.521005i	−0.967319	+	0.253564i	$0.918397\pi$
$752$		0			0
$753$	1.97147	−	2.63358i	0.0718443	−	0.0959728i
$754$		0			0
$755$	−10.7515	−	45.0115i	−0.391288	−	1.63813i
$756$		0			0
$757$	18.5473	+	1.32653i	0.674113	+	0.0482135i	0.404199	−	0.914671i	$-0.367550\pi$
$757$	18.5473	+	1.32653i	0.674113	+	0.0482135i	0.269914	+	0.962884i	$0.413005\pi$
$758$		0			0
$759$	−0.0565360	+	0.0467672i	−0.00205213	+	0.00169754i
$760$		0			0
$761$	7.81144	+	9.01488i	0.283165	+	0.326789i	0.879457	−	0.475978i	$-0.157906\pi$
$761$	7.81144	+	9.01488i	0.283165	+	0.326789i	−0.596293	+	0.802767i	$0.703360\pi$
$762$		0			0
$763$	−5.68799	−	7.59827i	−0.205919	−	0.275076i
$764$		0			0
$765$	7.99311	−	29.4149i	0.288992	−	1.06350i
$766$		0			0
$767$	9.75139	+	2.12129i	0.352102	+	0.0765952i
$768$		0			0
$769$	−33.3452	+	9.79104i	−1.20246	+	0.353074i	−0.820793	−	0.571226i	$-0.806468\pi$
$769$	−33.3452	+	9.79104i	−1.20246	+	0.353074i	−0.381667	+	0.924300i	$0.624650\pi$
$770$		0			0
$771$	2.09002	−	2.41201i	0.0752702	−	0.0868665i
$772$		0			0
$773$	−12.3513	+	33.1151i	−0.444245	+	1.19107i	0.501213	+	0.865324i	$0.332887\pi$
$773$	−12.3513	+	33.1151i	−0.444245	+	1.19107i	−0.945458	+	0.325743i	$0.894386\pi$
$774$		0			0
$775$	15.4271	−	7.81584i	0.554159	−	0.280753i
$776$		0			0
$777$	0.892946	−	0.333051i	0.0320342	−	0.0119482i
$778$		0			0
$779$	8.65359	+	5.56132i	0.310047	+	0.199255i
$780$		0			0
$781$		−	0.735648i		−	0.0263235i
$782$		0			0
$783$	1.66692	−	1.66692i	0.0595708	−	0.0595708i
$784$		0			0
$785$	−22.4658	+	15.0899i	−0.801840	+	0.538583i
$786$		0			0
$787$	15.8242	+	42.4264i	0.564073	+	1.51234i	0.835284	+	0.549819i	$0.185303\pi$
$787$	15.8242	+	42.4264i	0.564073	+	1.51234i	−0.271211	+	0.962520i	$0.587424\pi$
$788$		0			0
$789$	0.868573	+	0.255036i	0.0309220	+	0.00907952i
$790$		0			0
$791$	4.16824	+	9.12717i	0.148205	+	0.324525i
$792$		0			0
$793$	0.681060	−	0.0487103i	0.0241851	−	0.00172975i
$794$		0			0
$795$	2.92765	−	2.28565i	0.103833	−	0.0810637i
$796$		0			0
$797$	0.00540468	−	0.0248449i	0.000191444	−	0.000880053i	−0.977051	−	0.213005i	$-0.931675\pi$
$797$	0.00540468	−	0.0248449i	0.000191444	−	0.000880053i	0.977242	+	0.212125i	$0.0680385\pi$
$798$		0			0
$799$	8.01416	+	55.7397i	0.283521	+	1.97193i
$800$		0			0
$801$	−10.0885	−	1.45051i	−0.356461	−	0.0512513i
$802$		0			0
$803$	−0.107016	+	1.49628i	−0.00377652	+	0.0528027i
$804$		0			0
$805$	9.08531	−	0.625918i	0.320215	−	0.0220607i
$806$		0			0
$807$	0.0207788	−	0.290526i	0.000731449	−	0.0102270i
$808$		0			0
$809$	−26.5559	−	3.81816i	−0.933656	−	0.134239i	−0.341335	−	0.939942i	$-0.610879\pi$
$809$	−26.5559	−	3.81816i	−0.933656	−	0.134239i	−0.592321	+	0.805702i	$0.701788\pi$
$810$		0			0
$811$	−6.25844	−	43.5284i	−0.219764	−	1.52849i	−0.738910	−	0.673804i	$-0.764659\pi$
$811$	−6.25844	−	43.5284i	−0.219764	−	1.52849i	0.519146	−	0.854686i	$-0.326250\pi$
$812$		0			0
$813$	−0.165398	+	0.760321i	−0.00580075	+	0.0266656i
$814$		0			0
$815$	−1.50528	+	12.2234i	−0.0527278	+	0.428169i
$816$		0			0
$817$	32.4811	−	2.32309i	1.13637	−	0.0812747i
$818$		0			0
$819$	0.950282	+	2.08083i	0.0332055	+	0.0727100i
$820$		0			0
$821$	26.0666	+	7.65386i	0.909732	+	0.267121i	0.702928	−	0.711261i	$-0.251876\pi$
$821$	26.0666	+	7.65386i	0.909732	+	0.267121i	0.206804	+	0.978382i	$0.433694\pi$
$822$		0			0
$823$	4.37973	+	11.7425i	0.152668	+	0.409319i	0.990659	−	0.136366i	$-0.0435424\pi$
$823$	4.37973	+	11.7425i	0.152668	+	0.409319i	−0.837991	+	0.545685i	$0.816270\pi$
$824$		0			0
$825$	0.0630456	+	0.0433228i	0.00219497	+	0.00150830i
$826$		0			0
$827$	26.1511	−	26.1511i	0.909364	−	0.909364i	−0.0868572	−	0.996221i	$-0.527682\pi$
$827$	26.1511	−	26.1511i	0.909364	−	0.909364i	0.996221	+	0.0868572i	$0.0276824\pi$
$828$		0			0
$829$			35.4358i			1.23074i	0.788240	+	0.615368i	$0.210993\pi$
$829$			35.4358i			1.23074i	−0.788240	+	0.615368i	$0.789007\pi$
$830$		0			0
$831$	−1.03736	−	0.666668i	−0.0359855	−	0.0231265i
$832$		0			0
$833$	26.9824	−	10.0639i	0.934886	−	0.348694i
$834$		0			0
$835$	−1.95707	−	1.62755i	−0.0677273	−	0.0563237i
$836$		0			0
$837$	1.20538	−	3.23174i	0.0416639	−	0.111705i
$838$		0			0
$839$	27.5879	−	31.8382i	0.952441	−	1.09918i	−0.0425383	−	0.999095i	$-0.513544\pi$
$839$	27.5879	−	31.8382i	0.952441	−	1.09918i	0.994979	−	0.100081i	$-0.0319101\pi$
$840$		0			0
$841$	−22.4635	+	6.59587i	−0.774603	+	0.227444i
$842$		0			0
$843$	4.51005	+	0.981101i	0.155334	+	0.0337909i
$844$		0			0
$845$	23.6316	−	13.5327i	0.812953	−	0.465539i
$846$		0			0
$847$	5.59382	+	7.47246i	0.192206	+	0.256757i
$848$		0			0
$849$	−0.316012	−	0.364697i	−0.0108455	−	0.0125164i
$850$		0			0
$851$	−21.6594	+	23.8700i	−0.742474	+	0.818252i
$852$		0			0
$853$	−10.9530	−	0.783376i	−0.375025	−	0.0268223i	−0.117445	−	0.993079i	$-0.537470\pi$
$853$	−10.9530	−	0.783376i	−0.375025	−	0.0268223i	−0.257580	+	0.966257i	$0.582925\pi$
$854$		0			0
$855$	37.0010	−	8.83813i	1.26541	−	0.302258i
$856$		0			0
$857$	13.3410	−	17.8215i	0.455721	−	0.608772i	−0.512555	−	0.858654i	$-0.671301\pi$
$857$	13.3410	−	17.8215i	0.455721	−	0.608772i	0.968276	+	0.249882i	$0.0803920\pi$
$858$		0			0
$859$	−28.7778	−	44.7792i	−0.981887	−	1.52785i	−0.843263	−	0.537501i	$-0.819369\pi$
$859$	−28.7778	−	44.7792i	−0.981887	−	1.52785i	−0.138624	−	0.990345i	$-0.544268\pi$
$860$		0			0
$861$	−0.0717927	−	0.244503i	−0.00244669	−	0.00833265i
$862$		0			0
$863$	−3.34811	−	46.8126i	−0.113971	−	1.59352i	−0.657055	−	0.753843i	$-0.728198\pi$
$863$	−3.34811	−	46.8126i	−0.113971	−	1.59352i	0.543084	−	0.839678i	$-0.317256\pi$
$864$		0			0
$865$	9.16170	−	0.185726i	0.311507	−	0.00631488i
$866$		0			0
$867$	0.323017	+	0.591562i	0.0109702	+	0.0200905i
$868$		0			0
$869$	−0.582205	−	0.265884i	−0.0197499	−	0.00901950i
$870$		0			0
$871$	0.310647	−	0.483377i	0.0105259	−	0.0163786i
$872$		0			0
$873$	−20.7247	−	20.7247i	−0.701426	−	0.701426i
$874$		0			0
$875$	−3.22359	−	8.93055i	−0.108977	−	0.301908i
$876$		0			0
$877$	8.41144	+	38.6667i	0.284034	+	1.30568i	0.869075	+	0.494680i	$0.164715\pi$
$877$	8.41144	+	38.6667i	0.284034	+	1.30568i	−0.585041	+	0.811003i	$0.698922\pi$
$878$		0			0
$879$	−0.473322	+	1.03643i	−0.0159648	+	0.0349580i
$880$		0			0
$881$	3.34802	−	11.4023i	0.112798	−	0.384154i	−0.883672	−	0.468107i	$-0.844936\pi$
$881$	3.34802	−	11.4023i	0.112798	−	0.384154i	0.996470	+	0.0839527i	$0.0267545\pi$
$882$		0			0
$883$	−11.0578	−	4.12436i	−0.372125	−	0.138796i	0.156442	−	0.987687i	$-0.449998\pi$
$883$	−11.0578	−	4.12436i	−0.372125	−	0.138796i	−0.528567	+	0.848892i	$0.677270\pi$
$884$		0			0
$885$	−3.70433	+	1.78331i	−0.124520	+	0.0599455i
$886$		0			0
$887$	2.77059	+	1.51286i	0.0930274	+	0.0507968i	0.525089	−	0.851047i	$-0.324032\pi$
$887$	2.77059	+	1.51286i	0.0930274	+	0.0507968i	−0.432062	+	0.901844i	$0.642214\pi$
$888$		0			0
$889$	2.63371	−	1.69259i	0.0883319	−	0.0567675i
$890$		0			0
$891$	−0.793522	+	0.114091i	−0.0265840	+	0.00382220i
$892$		0			0
$893$	−56.2622	+	42.1173i	−1.88274	+	1.40940i
$894$		0			0
$895$	25.2825	−	48.6191i	0.845102	−	1.62516i
$896$		0			0
$897$	0.570925	+	0.448135i	0.0190626	+	0.0149628i
$898$		0			0
$899$	6.17930	−	5.35439i	0.206091	−	0.178579i
$900$		0			0
$901$	6.49310	−	45.1605i	0.216317	−	1.50451i
$902$		0			0
$903$	−0.645797	−	0.483437i	−0.0214908	−	0.0160878i
$904$		0			0
$905$	−0.660995	−	0.474219i	−0.0219722	−	0.0157636i
$906$		0			0
$907$	−7.75825	+	14.2082i	−0.257608	+	0.471775i	−0.974190	−	0.225728i	$-0.927524\pi$
$907$	−7.75825	+	14.2082i	−0.257608	+	0.471775i	0.716582	+	0.697503i	$0.245706\pi$
$908$		0			0
$909$	−10.0718	−	8.72723i	−0.334059	−	0.289464i
$910$		0			0
$911$	42.6692	−	19.4864i	1.41369	−	0.645612i	0.445378	−	0.895343i	$-0.353069\pi$
$911$	42.6692	−	19.4864i	1.41369	−	0.645612i	0.968315	+	0.249731i	$0.0803421\pi$
$912$		0			0
$913$	−0.928686	+	0.507101i	−0.0307350	+	0.0167826i
$914$		0			0
$915$	−0.208810	+	0.188478i	−0.00690304	+	0.00623091i
$916$		0			0
$917$	−10.5719	+	2.29978i	−0.349115	+	0.0759453i
$918$		0			0
$919$	−12.2609			−0.404450			−0.202225	−	0.979339i	$-0.564817\pi$
$919$	−12.2609			−0.404450			−0.202225	+	0.979339i	$0.564817\pi$
$920$		0			0
$921$	−3.96592			−0.130682
$922$		0			0
$923$	−7.11071	+	1.54684i	−0.234052	+	0.0509148i
$924$		0			0
$925$	30.1222	+	14.8963i	0.990411	+	0.489786i
$926$		0			0
$927$	−15.2782	+	8.34253i	−0.501802	+	0.274005i
$928$		0			0
$929$	10.3936	−	4.74662i	0.341004	−	0.155731i	−0.237550	−	0.971375i	$-0.576344\pi$
$929$	10.3936	−	4.74662i	0.341004	−	0.155731i	0.578554	+	0.815644i	$0.303617\pi$
$930$		0			0
$931$	27.1624	+	23.5363i	0.890211	+	0.771372i
$932$		0			0
$933$	−0.100233	+	0.183563i	−0.00328148	+	0.00600959i
$934$		0			0
$935$	0.927199	−	0.152552i	0.0303227	−	0.00498898i
$936$		0			0
$937$	42.7806	+	32.0252i	1.39758	+	1.04622i	0.991180	+	0.132522i	$0.0423076\pi$
$937$	42.7806	+	32.0252i	1.39758	+	1.04622i	0.406402	+	0.913694i	$0.366783\pi$
$938$		0			0
$939$	0.140038	−	0.973984i	0.00456996	−	0.0317848i
$940$		0			0
$941$	11.8009	−	10.2256i	0.384699	−	0.333344i	−0.440946	−	0.897534i	$-0.645357\pi$
$941$	11.8009	−	10.2256i	0.384699	−	0.333344i	0.825645	+	0.564190i	$0.190811\pi$
$942$		0			0
$943$	5.95302	+	6.23192i	0.193857	+	0.202939i
$944$		0			0
$945$	−1.68006	−	0.873655i	−0.0546525	−	0.0284200i
$946$		0			0
$947$	41.4138	−	31.0020i	1.34577	−	1.00743i	0.348221	−	0.937412i	$-0.386786\pi$
$947$	41.4138	−	31.0020i	1.34577	−	1.00743i	0.997546	−	0.0700161i	$-0.0223051\pi$
$948$		0			0
$949$	14.6880	−	2.11181i	0.476792	−	0.0685523i
$950$		0			0
$951$	−2.04163	+	1.31208i	−0.0662044	+	0.0425470i
$952$		0			0
$953$	−27.9856	−	15.2813i	−0.906541	−	0.495009i	−0.0428793	−	0.999080i	$-0.513653\pi$
$953$	−27.9856	−	15.2813i	−0.906541	−	0.495009i	−0.863662	+	0.504071i	$0.831835\pi$
$954$		0			0
$955$	−2.90987	−	1.01864i	−0.0941613	−	0.0329623i
$956$		0			0
$957$	0.0338859	+	0.0126388i	0.00109538	+	0.000408554i
$958$		0			0
$959$	−2.51164	+	8.55385i	−0.0811050	+	0.276218i
$960$		0			0
$961$	−7.90811	+	17.3164i	−0.255100	+	0.558592i
$962$		0			0
$963$	6.40568	+	29.4464i	0.206420	+	0.948898i
$964$		0			0
$965$	−3.46112	+	8.00426i	−0.111417	+	0.257666i
$966$		0			0
$967$	−32.7192	−	32.7192i	−1.05218	−	1.05218i	−0.998562	−	0.0536154i	$-0.982926\pi$
$967$	−32.7192	−	32.7192i	−1.05218	−	1.05218i	−0.0536154	−	0.998562i	$-0.517074\pi$
$968$		0			0
$969$	−2.37013	+	3.68799i	−0.0761395	+	0.118475i
$970$		0			0
$971$	9.07362	+	4.14379i	0.291186	+	0.132980i	0.555653	−	0.831415i	$-0.312468\pi$
$971$	9.07362	+	4.14379i	0.291186	+	0.132980i	−0.264466	+	0.964395i	$0.585196\pi$
$972$		0			0
$973$	−3.48451	−	6.38139i	−0.111708	−	0.204578i
$974$		0			0
$975$	0.286189	−	0.700488i	0.00916537	−	0.0224336i
$976$		0			0
$977$	2.20513	+	30.8318i	0.0705485	+	0.986397i	0.902261	+	0.431190i	$0.141906\pi$
$977$	2.20513	+	30.8318i	0.0705485	+	0.986397i	−0.831713	+	0.555206i	$0.812639\pi$
$978$		0			0
$979$	−0.0885205	−	0.301473i	−0.00282913	−	0.00963513i
$980$		0			0
$981$	−17.9592	−	27.9450i	−0.573393	−	0.892216i
$982$		0			0
$983$	−15.4786	+	20.6770i	−0.493691	+	0.659494i	−0.976320	−	0.216331i	$-0.930591\pi$
$983$	−15.4786	+	20.6770i	−0.493691	+	0.659494i	0.482629	+	0.875825i	$0.339682\pi$
$984$		0			0
$985$	−13.8786	+	22.5894i	−0.442209	+	0.719758i
$986$		0			0
$987$	1.73659	+	0.124204i	0.0552764	+	0.00395345i
$988$		0			0
$989$	26.9093	+	4.49969i	0.855667	+	0.143082i
$990$		0			0
$991$	36.4878	+	42.1091i	1.15907	+	1.33764i	0.931441	+	0.363893i	$0.118553\pi$
$991$	36.4878	+	42.1091i	1.15907	+	1.33764i	0.227631	+	0.973747i	$0.426902\pi$
$992$		0			0
$993$	2.24858	+	3.00375i	0.0713564	+	0.0953210i
$994$		0			0
$995$	3.32664	+	5.80918i	0.105461	+	0.184163i
$996$		0			0
$997$	45.4421	+	9.88532i	1.43916	+	0.313071i	0.863390	−	0.504537i	$-0.168337\pi$
$997$	45.4421	+	9.88532i	1.43916	+	0.313071i	0.575775	+	0.817608i	$0.304701\pi$
$998$		0			0
$999$	6.43072	−	1.88823i	0.203459	−	0.0597410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.19	yes	720
5.3	odd	4	inner	920.2.bv.a.33.19	✓	720
23.7	odd	22	inner	920.2.bv.a.697.19	yes	720
115.53	even	44	inner	920.2.bv.a.513.19	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.19	✓	720	5.3	odd	4	inner
920.2.bv.a.217.19	yes	720	1.1	even	1	trivial
920.2.bv.a.513.19	yes	720	115.53	even	44	inner
920.2.bv.a.697.19	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.163164 - 0.0354943i) q^{3} +(0.114282 - 2.23315i) q^{5} +(-0.745341 + 0.406987i) q^{7} +(-2.70353 + 1.23466i) q^{9} +O(q^{10})\)	\(q+(0.163164 - 0.0354943i) q^{3} +(0.114282 - 2.23315i) q^{5} +(-0.745341 + 0.406987i) q^{7} +(-2.70353 + 1.23466i) q^{9} +(-0.0692436 - 0.0600000i) q^{11} +(-0.434356 + 0.795465i) q^{13} +(-0.0606172 - 0.368426i) q^{15} +(-3.67172 - 2.74862i) q^{17} +(0.814632 - 5.66589i) q^{19} +(-0.107167 + 0.0928611i) q^{21} +(1.77835 - 4.45393i) q^{23} +(-4.97388 - 0.510415i) q^{25} +(-0.798322 + 0.597616i) q^{27} +(-2.33987 + 0.336423i) q^{29} +(-2.90973 + 1.86997i) q^{31} +(-0.0134278 - 0.00733211i) q^{33} +(0.823682 + 1.71097i) q^{35} +(-6.29709 - 2.34869i) q^{37} +(-0.0426371 + 0.145209i) q^{39} +(-0.746518 + 1.63465i) q^{41} +(1.20926 + 5.55888i) q^{43} +(2.44822 + 6.17848i) q^{45} +(-8.68174 - 8.68174i) q^{47} +(-3.39459 + 5.28209i) q^{49} +(-0.696655 - 0.318152i) q^{51} +(4.76735 + 8.73075i) q^{53} +(-0.141902 + 0.147774i) q^{55} +(-0.0681875 - 0.953386i) q^{57} +(-3.10212 - 10.5649i) q^{59} +(-0.407302 - 0.633775i) q^{61} +(1.51256 - 2.02055i) q^{63} +(1.72675 + 1.06089i) q^{65} +(-0.632362 - 0.0452274i) q^{67} +(0.132075 - 0.789844i) q^{69} +(5.25795 + 6.06800i) q^{71} +(-9.81179 - 13.1070i) q^{73} +(-0.829677 + 0.0932626i) q^{75} +(0.0760293 + 0.0165392i) q^{77} +(6.70270 - 1.96809i) q^{79} +(5.72992 - 6.61268i) q^{81} +(4.03584 - 10.8205i) q^{83} +(-6.55767 + 7.88537i) q^{85} +(-0.369843 + 0.137944i) q^{87} +(2.88491 + 1.85402i) q^{89} -0.769669i q^{91} +(-0.408392 + 0.408392i) q^{93} +(-12.5597 - 2.46670i) q^{95} +(3.44620 + 9.23962i) q^{97} +(0.261282 + 0.0767194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more