LMFDB - Embedded newform 920.2.bv.a.753.29

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			753.29
Character	$\chi$	$=$	920.753
Dual form			920.2.bv.a.617.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939627 + 1.72080i) q^{3} +(1.36626 - 1.77012i) q^{5} +(2.23600 - 1.67385i) q^{7} +(-0.456326 + 0.710057i) q^{9} +O(q^{10})$	\(q+(0.939627 + 1.72080i) q^{3} +(1.36626 - 1.77012i) q^{5} +(2.23600 - 1.67385i) q^{7} +(-0.456326 + 0.710057i) q^{9} +(-0.591468 + 0.270114i) q^{11} +(-3.29441 + 4.40081i) q^{13} +(4.32980 + 0.687798i) q^{15} +(4.09681 - 0.293010i) q^{17} +(2.14676 + 2.47750i) q^{19} +(4.98136 + 2.27491i) q^{21} +(-0.785024 - 4.73115i) q^{23} +(-1.26668 - 4.83689i) q^{25} +(4.21624 + 0.301552i) q^{27} +(-2.25352 - 1.95268i) q^{29} +(9.90163 - 2.90738i) q^{31} +(-1.02057 - 0.763990i) q^{33} +(0.0920327 - 6.24490i) q^{35} +(0.319017 + 1.46650i) q^{37} +(-10.6684 - 1.53389i) q^{39} +(-9.11200 + 5.85593i) q^{41} +(0.552474 - 0.301674i) q^{43} +(0.633430 + 1.77788i) q^{45} +(8.15536 - 8.15536i) q^{47} +(0.225797 - 0.768995i) q^{49} +(4.35369 + 6.77447i) q^{51} +(5.55216 + 7.41682i) q^{53} +(-0.329962 + 1.41602i) q^{55} +(-2.24612 + 6.02207i) q^{57} +(-7.78341 + 1.11909i) q^{59} +(-0.423373 - 1.44188i) q^{61} +(0.168183 + 2.35151i) q^{63} +(3.28897 + 11.8442i) q^{65} +(-8.75398 + 3.26507i) q^{67} +(7.40372 - 5.79638i) q^{69} +(-0.818740 + 1.79279i) q^{71} +(0.0272145 - 0.380508i) q^{73} +(7.13311 - 6.72457i) q^{75} +(-0.870391 + 1.59400i) q^{77} +(1.44106 + 10.0228i) q^{79} +(4.49468 + 9.84197i) q^{81} +(-1.86367 + 0.405417i) q^{83} +(5.07864 - 7.65219i) q^{85} +(1.24271 - 5.71264i) q^{87} +(9.98888 + 2.93300i) q^{89} +15.3545i q^{91} +(14.3069 + 14.3069i) q^{93} +(7.31851 - 0.415138i) q^{95} +(-17.5729 - 3.82275i) q^{97} +(0.0781056 - 0.543236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.939627	+	1.72080i	0.542494	+	0.993504i	0.994820	+	0.101651i	$0.0324125\pi$
$3$	0.939627	+	1.72080i	0.542494	+	0.993504i	−0.452326	+	0.891853i	$0.649406\pi$
$4$		0			0
$5$	1.36626	−	1.77012i	0.611009	−	0.791624i
$5$	1.36626	−	1.77012i	0.611009	−	0.791624i
$6$		0			0
$7$	2.23600	−	1.67385i	0.845128	−	0.632655i	−0.0864256	−	0.996258i	$-0.527544\pi$
$7$	2.23600	−	1.67385i	0.845128	−	0.632655i	0.931554	+	0.363603i	$0.118454\pi$
$8$		0			0
$9$	−0.456326	+	0.710057i	−0.152109	+	0.236686i
$10$		0			0
$11$	−0.591468	+	0.270114i	−0.178334	+	0.0814425i	−0.502581	−	0.864530i	$-0.667616\pi$
$11$	−0.591468	+	0.270114i	−0.178334	+	0.0814425i	0.324247	+	0.945972i	$0.394889\pi$
$12$		0			0
$13$	−3.29441	+	4.40081i	−0.913704	+	1.22057i	0.0612418	+	0.998123i	$0.480494\pi$
$13$	−3.29441	+	4.40081i	−0.913704	+	1.22057i	−0.974946	+	0.222443i	$0.928597\pi$
$14$		0			0
$15$	4.32980	+	0.687798i	1.11795	+	0.177589i
$16$		0			0
$17$	4.09681	−	0.293010i	0.993623	−	0.0710653i	0.434951	−	0.900454i	$-0.356766\pi$
$17$	4.09681	−	0.293010i	0.993623	−	0.0710653i	0.558672	+	0.829389i	$0.311311\pi$
$18$		0			0
$19$	2.14676	+	2.47750i	0.492501	+	0.568377i	0.946532	−	0.322609i	$-0.104560\pi$
$19$	2.14676	+	2.47750i	0.492501	+	0.568377i	−0.454031	+	0.890986i	$0.650015\pi$
$20$		0			0
$21$	4.98136	+	2.27491i	1.08702	+	0.496426i
$22$		0			0
$23$	−0.785024	−	4.73115i	−0.163689	−	0.986512i
$23$	−0.785024	−	4.73115i	−0.163689	−	0.986512i
$24$		0			0
$25$	−1.26668	−	4.83689i	−0.253336	−	0.967378i
$26$		0			0
$27$	4.21624	+	0.301552i	0.811417	+	0.0580337i
$28$		0			0
$29$	−2.25352	−	1.95268i	−0.418467	−	0.362604i	0.420029	−	0.907510i	$-0.362020\pi$
$29$	−2.25352	−	1.95268i	−0.418467	−	0.362604i	−0.838497	+	0.544906i	$0.816565\pi$
$30$		0			0
$31$	9.90163	−	2.90738i	1.77839	−	0.522181i	0.783340	−	0.621594i	$-0.213515\pi$
$31$	9.90163	−	2.90738i	1.77839	−	0.522181i	0.995046	+	0.0994125i	$0.0316963\pi$
$32$		0			0
$33$	−1.02057	−	0.763990i	−0.177659	−	0.132994i
$34$		0			0
$35$	0.0920327	−	6.24490i	0.0155564	−	1.05558i
$36$		0			0
$37$	0.319017	+	1.46650i	0.0524461	+	0.241091i	0.995906	−	0.0903961i	$-0.0288133\pi$
$37$	0.319017	+	1.46650i	0.0524461	+	0.241091i	−0.943460	+	0.331487i	$0.892450\pi$
$38$		0			0
$39$	−10.6684	−	1.53389i	−1.70832	−	0.245619i
$40$		0			0
$41$	−9.11200	+	5.85593i	−1.42306	+	0.914542i	−0.423091	+	0.906087i	$0.639055\pi$
$41$	−9.11200	+	5.85593i	−1.42306	+	0.914542i	−0.999964	+	0.00845469i	$0.997309\pi$
$42$		0			0
$43$	0.552474	−	0.301674i	0.0842515	−	0.0460048i	−0.436571	−	0.899670i	$-0.643807\pi$
$43$	0.552474	−	0.301674i	0.0842515	−	0.0460048i	0.520822	+	0.853665i	$0.325625\pi$
$44$		0			0
$45$	0.633430	+	1.77788i	0.0944262	+	0.265030i
$46$		0			0
$47$	8.15536	−	8.15536i	1.18958	−	1.18958i	0.212398	−	0.977183i	$-0.431873\pi$
$47$	8.15536	−	8.15536i	1.18958	−	1.18958i	0.977183	−	0.212398i	$-0.0681274\pi$
$48$		0			0
$49$	0.225797	−	0.768995i	0.0322568	−	0.109856i
$50$		0			0
$51$	4.35369	+	6.77447i	0.609638	+	0.948615i
$52$		0			0
$53$	5.55216	+	7.41682i	0.762648	+	1.01878i	0.998891	+	0.0470844i	$0.0149930\pi$
$53$	5.55216	+	7.41682i	0.762648	+	1.01878i	−0.236243	+	0.971694i	$0.575916\pi$
$54$		0			0
$55$	−0.329962	+	1.41602i	−0.0444920	+	0.190936i
$56$		0			0
$57$	−2.24612	+	6.02207i	−0.297505	+	0.797642i
$58$		0			0
$59$	−7.78341	+	1.11909i	−1.01331	+	0.145693i	−0.628915	−	0.777474i	$-0.716501\pi$
$59$	−7.78341	+	1.11909i	−1.01331	+	0.145693i	−0.384399	+	0.923167i	$0.625591\pi$
$60$		0			0
$61$	−0.423373	−	1.44188i	−0.0542074	−	0.184613i	0.927939	−	0.372733i	$-0.121579\pi$
$61$	−0.423373	−	1.44188i	−0.0542074	−	0.184613i	−0.982146	+	0.188119i	$0.939761\pi$
$62$		0			0
$63$	0.168183	+	2.35151i	0.0211891	+	0.296262i
$64$		0			0
$65$	3.28897	+	11.8442i	0.407947	+	1.46909i
$66$		0			0
$67$	−8.75398	+	3.26507i	−1.06947	+	0.398891i	−0.821696	−	0.569927i	$-0.806972\pi$
$67$	−8.75398	+	3.26507i	−1.06947	+	0.398891i	−0.247773	+	0.968818i	$0.579699\pi$
$68$		0			0
$69$	7.40372	−	5.79638i	0.891303	−	0.697802i
$70$		0			0
$71$	−0.818740	+	1.79279i	−0.0971665	+	0.212765i	−0.951973	−	0.306182i	$-0.900948\pi$
$71$	−0.818740	+	1.79279i	−0.0971665	+	0.212765i	0.854807	+	0.518947i	$0.173676\pi$
$72$		0			0
$73$	0.0272145	−	0.380508i	0.00318521	−	0.0445351i	−0.995611	−	0.0935890i	$-0.970166\pi$
$73$	0.0272145	−	0.380508i	0.00318521	−	0.0445351i	0.998796	+	0.0490539i	$0.0156206\pi$
$74$		0			0
$75$	7.13311	−	6.72457i	0.823661	−	0.776487i
$76$		0			0
$77$	−0.870391	+	1.59400i	−0.0991903	+	0.181653i
$78$		0			0
$79$	1.44106	+	10.0228i	0.162131	+	1.12765i	0.894606	+	0.446855i	$0.147456\pi$
$79$	1.44106	+	10.0228i	0.162131	+	1.12765i	−0.732475	+	0.680794i	$0.761635\pi$
$80$		0			0
$81$	4.49468	+	9.84197i	0.499408	+	1.09355i
$82$		0			0
$83$	−1.86367	+	0.405417i	−0.204564	+	0.0445003i	−0.313680	−	0.949529i	$-0.601562\pi$
$83$	−1.86367	+	0.405417i	−0.204564	+	0.0445003i	0.109115	+	0.994029i	$0.465198\pi$
$84$		0			0
$85$	5.07864	−	7.65219i	0.550856	−	0.829997i
$86$		0			0
$87$	1.24271	−	5.71264i	0.133232	−	0.612459i
$88$		0			0
$89$	9.98888	+	2.93300i	1.05882	+	0.310898i	0.764376	−	0.644771i	$-0.223047\pi$
$89$	9.98888	+	2.93300i	1.05882	+	0.310898i	0.294444	+	0.955669i	$0.404866\pi$
$90$		0			0
$91$			15.3545i			1.60959i
$92$		0			0
$93$	14.3069	+	14.3069i	1.48355	+	1.48355i
$94$		0			0
$95$	7.31851	−	0.415138i	0.750863	−	0.0425922i
$96$		0			0
$97$	−17.5729	−	3.82275i	−1.78426	−	0.388141i	−0.805407	−	0.592722i	$-0.798053\pi$
$97$	−17.5729	−	3.82275i	−1.78426	−	0.388141i	−0.978850	+	0.204581i	$0.934417\pi$
$98$		0			0
$99$	0.0781056	−	0.543236i	0.00784991	−	0.0545973i
$100$		0			0
$101$	−9.47526	−	6.08938i	−0.942824	−	0.605916i	−0.0236296	−	0.999721i	$-0.507522\pi$
$101$	−9.47526	−	6.08938i	−0.942824	−	0.605916i	−0.919194	+	0.393805i	$0.871159\pi$
$102$		0			0
$103$	−12.5284	−	4.67284i	−1.23446	−	0.460429i	−0.354309	−	0.935128i	$-0.615284\pi$
$103$	−12.5284	−	4.67284i	−1.23446	−	0.460429i	−0.880148	+	0.474700i	$0.842557\pi$
$104$		0			0
$105$	10.8327	−	5.70951i	1.05716	−	0.557191i
$106$		0			0
$107$	−12.2014	−	6.66246i	−1.17955	−	0.644084i	−0.234855	−	0.972030i	$-0.575462\pi$
$107$	−12.2014	−	6.66246i	−1.17955	−	0.644084i	−0.944696	+	0.327946i	$0.893644\pi$
$108$		0			0
$109$	−5.06994	+	5.85102i	−0.485612	+	0.560426i	−0.944688	−	0.327971i	$-0.893635\pi$
$109$	−5.06994	+	5.85102i	−0.485612	+	0.560426i	0.459076	+	0.888397i	$0.348181\pi$
$110$		0			0
$111$	−2.22379	+	1.92693i	−0.211073	+	0.182896i
$112$		0			0
$113$	−3.23307	−	8.66820i	−0.304142	−	0.815436i	−0.995659	−	0.0930760i	$-0.970330\pi$
$113$	−3.23307	−	8.66820i	−0.304142	−	0.815436i	0.691517	−	0.722360i	$-0.256943\pi$
$114$		0			0
$115$	−9.44726	−	5.07437i	−0.880962	−	0.473188i
$116$		0			0
$117$	−1.62150	−	4.34742i	−0.149908	−	0.401919i
$118$		0			0
$119$	8.67002	−	7.51261i	0.794779	−	0.688680i
$120$		0			0
$121$	−6.92660	+	7.99372i	−0.629691	+	0.726702i
$122$		0			0
$123$	−18.6387	−	10.1775i	−1.68060	−	0.917677i
$124$		0			0
$125$	−10.2925	−	4.36626i	−0.920590	−	0.390530i
$126$		0			0
$127$	−0.0568860	−	0.0212174i	−0.00504781	−	0.00188274i	0.346939	−	0.937888i	$-0.387221\pi$
$127$	−0.0568860	−	0.0212174i	−0.00504781	−	0.00188274i	−0.351987	+	0.936005i	$0.614494\pi$
$128$		0			0
$129$	1.03824	+	0.667236i	0.0914119	+	0.0587468i
$130$		0			0
$131$	0.666539	−	4.63588i	0.0582358	−	0.405039i	−0.939764	−	0.341824i	$-0.888955\pi$
$131$	0.666539	−	4.63588i	0.0582358	−	0.405039i	0.998000	−	0.0632151i	$-0.0201354\pi$
$132$		0			0
$133$	8.94711	+	1.94632i	0.775813	+	0.168768i
$134$		0			0
$135$	6.29426	−	7.05128i	0.541724	−	0.606877i
$136$		0			0
$137$	12.1882	+	12.1882i	1.04131	+	1.04131i	0.999109	+	0.0422016i	$0.0134372\pi$
$137$	12.1882	+	12.1882i	1.04131	+	1.04131i	0.0422016	+	0.999109i	$0.486563\pi$
$138$		0			0
$139$		−	12.1966i		−	1.03451i	−0.855833	−	0.517253i	$-0.826955\pi$
$139$		−	12.1966i		−	1.03451i	0.855833	−	0.517253i	$-0.173045\pi$
$140$		0			0
$141$	21.6967	+	6.37073i	1.82719	+	0.536513i
$142$		0			0
$143$	0.759813	−	3.49280i	0.0635388	−	0.292083i
$144$		0			0
$145$	−6.53538	+	1.32114i	−0.542733	+	0.109714i
$146$		0			0
$147$	1.53545	−	0.334017i	0.126642	−	0.0275493i
$148$		0			0
$149$	−1.33443	−	2.92199i	−0.109321	−	0.239379i	0.847063	−	0.531493i	$-0.178369\pi$
$149$	−1.33443	−	2.92199i	−0.109321	−	0.239379i	−0.956384	+	0.292114i	$0.905641\pi$
$150$		0			0
$151$	−0.117377	−	0.816377i	−0.00955203	−	0.0664358i	0.984488	−	0.175453i	$-0.0561389\pi$
$151$	−0.117377	−	0.816377i	−0.00955203	−	0.0664358i	−0.994040	+	0.109017i	$0.965230\pi$
$152$		0			0
$153$	−1.66143	+	3.04268i	−0.134319	+	0.245986i
$154$		0			0
$155$	8.38176	−	21.4994i	0.673239	−	1.72687i
$156$		0			0
$157$	−0.0869436	+	1.21563i	−0.00693886	+	0.0970179i	−0.999741	−	0.0227458i	$-0.992759\pi$
$157$	−0.0869436	+	1.21563i	−0.00693886	+	0.0970179i	0.992802	+	0.119764i	$0.0382137\pi$
$158$		0			0
$159$	−7.54589	+	16.5232i	−0.598428	+	1.31037i
$160$		0			0
$161$	−9.67453	−	9.26483i	−0.762460	−	0.730171i
$162$		0			0
$163$	−5.01846	+	1.87179i	−0.393076	+	0.146610i	−0.538228	−	0.842800i	$-0.680906\pi$
$163$	−5.01846	+	1.87179i	−0.393076	+	0.146610i	0.145151	+	0.989409i	$0.453633\pi$
$164$		0			0
$165$	−2.74672	+	0.762730i	−0.213832	+	0.0593785i
$166$		0			0
$167$	−0.815598	−	11.4035i	−0.0631129	−	0.882433i	−0.926117	−	0.377236i	$-0.876874\pi$
$167$	−0.815598	−	11.4035i	−0.0631129	−	0.882433i	0.863004	−	0.505197i	$-0.168580\pi$
$168$		0			0
$169$	−4.85151	−	16.5227i	−0.373193	−	1.27098i
$170$		0			0
$171$	−2.73879	+	0.393778i	−0.209440	+	0.0301130i
$172$		0			0
$173$	1.08652	−	2.91308i	0.0826069	−	0.221478i	−0.889079	−	0.457754i	$-0.848654\pi$
$173$	1.08652	−	2.91308i	0.0826069	−	0.221478i	0.971686	+	0.236276i	$0.0759269\pi$
$174$		0			0
$175$	−10.9285	−	8.69506i	−0.826118	−	0.657285i
$176$		0			0
$177$	−9.23923	−	12.3422i	−0.694463	−	0.927694i
$178$		0			0
$179$	13.1536	+	20.4674i	0.983147	+	1.52981i	0.841760	+	0.539852i	$0.181520\pi$
$179$	13.1536	+	20.4674i	0.983147	+	1.52981i	0.141387	+	0.989954i	$0.454844\pi$
$180$		0			0
$181$	−3.14593	+	10.7141i	−0.233835	+	0.796370i	0.756052	+	0.654512i	$0.227126\pi$
$181$	−3.14593	+	10.7141i	−0.233835	+	0.796370i	−0.989887	+	0.141858i	$0.954692\pi$
$182$		0			0
$183$	2.08337	−	2.08337i	0.154007	−	0.154007i
$184$		0			0
$185$	3.03174	+	1.43892i	0.222898	+	0.105791i
$186$		0			0
$187$	−2.34399	+	1.27991i	−0.171409	+	0.0935965i
$188$		0			0
$189$	9.93227	−	6.38308i	0.722466	−	0.464301i
$190$		0			0
$191$	21.6531	+	3.11325i	1.56677	+	0.225267i	0.870372	−	0.492394i	$-0.163878\pi$
$191$	21.6531	+	3.11325i	1.56677	+	0.225267i	0.696393	+	0.717661i	$0.254787\pi$
$192$		0			0
$193$	−0.644096	−	2.96086i	−0.0463631	−	0.213128i	0.948137	−	0.317861i	$-0.102965\pi$
$193$	−0.644096	−	2.96086i	−0.0463631	−	0.213128i	−0.994500	+	0.104734i	$0.966601\pi$
$194$		0			0
$195$	−17.2910	+	16.7887i	−1.23823	+	1.20227i
$196$		0			0
$197$	−15.9962	−	11.9746i	−1.13968	−	0.853157i	−0.148933	−	0.988847i	$-0.547584\pi$
$197$	−15.9962	−	11.9746i	−1.13968	−	0.853157i	−0.990751	+	0.135690i	$0.956675\pi$
$198$		0			0
$199$	−0.516240	+	0.151582i	−0.0365953	+	0.0107454i	−0.299979	−	0.953946i	$-0.596980\pi$
$199$	−0.516240	+	0.151582i	−0.0365953	+	0.0107454i	0.263384	+	0.964691i	$0.415161\pi$
$200$		0			0
$201$	−13.8440	−	11.9959i	−0.976480	−	0.846125i
$202$		0			0
$203$	−8.30736	−	0.594154i	−0.583062	−	0.0417014i
$204$		0			0
$205$	−2.08362	+	24.1301i	−0.145527	+	1.68532i
$206$		0			0
$207$	3.71761	+	1.60153i	0.258392	+	0.111314i
$208$		0			0
$209$	−1.93895	−	0.885488i	−0.134120	−	0.0612505i
$210$		0			0
$211$	1.60274	+	1.84966i	0.110337	+	0.127336i	0.808231	−	0.588865i	$-0.200425\pi$
$211$	1.60274	+	1.84966i	0.110337	+	0.127336i	−0.697894	+	0.716201i	$0.745880\pi$
$212$		0			0
$213$	−3.85434	+	0.275668i	−0.264095	+	0.0188885i
$214$		0			0
$215$	0.220822	−	1.39011i	0.0150599	−	0.0948048i
$216$		0			0
$217$	17.2735	−	23.0747i	1.17260	−	1.56642i
$218$		0			0
$219$	0.680349	−	0.310705i	0.0459737	−	0.0209955i
$220$		0			0
$221$	−12.2071	+	18.9946i	−0.821137	+	1.27771i
$222$		0			0
$223$	7.69308	−	5.75897i	0.515167	−	0.385649i	−0.309825	−	0.950794i	$-0.600271\pi$
$223$	7.69308	−	5.75897i	0.515167	−	0.385649i	0.824992	+	0.565145i	$0.191180\pi$
$224$		0			0
$225$	4.01249	+	1.30779i	0.267499	+	0.0871857i
$226$		0			0
$227$	−12.0883	−	22.1380i	−0.802326	−	1.46935i	−0.881343	−	0.472478i	$-0.843360\pi$
$227$	−12.0883	−	22.1380i	−0.802326	−	1.46935i	0.0790161	−	0.996873i	$-0.474822\pi$
$228$		0			0
$229$	12.3048			0.813126			0.406563	−	0.913623i	$-0.366727\pi$
$229$	12.3048			0.813126			0.406563	+	0.913623i	$0.366727\pi$
$230$		0			0
$231$	−3.56080			−0.234283
$232$		0			0
$233$	−1.54469	−	2.82889i	−0.101196	−	0.185327i	0.822176	−	0.569234i	$-0.192760\pi$
$233$	−1.54469	−	2.82889i	−0.101196	−	0.185327i	−0.923372	+	0.383907i	$0.874578\pi$
$234$		0			0
$235$	−3.29367	−	25.5783i	−0.214856	−	1.66855i
$236$		0			0
$237$	−15.8931	+	11.8974i	−1.03237	+	0.772821i
$238$		0			0
$239$	−5.49305	+	8.54735i	−0.355316	+	0.552882i	−0.972194	−	0.234176i	$-0.924761\pi$
$239$	−5.49305	+	8.54735i	−0.355316	+	0.552882i	0.616878	+	0.787059i	$0.288397\pi$
$240$		0			0
$241$	−10.9559	+	5.00338i	−0.705730	+	0.322296i	−0.735750	−	0.677253i	$-0.763170\pi$
$241$	−10.9559	+	5.00338i	−0.705730	+	0.322296i	0.0300200	+	0.999549i	$0.490443\pi$
$242$		0			0
$243$	−5.11326	+	6.83052i	−0.328016	+	0.438178i
$244$		0			0
$245$	−1.05272	−	1.45034i	−0.0672558	−	0.0926585i
$246$		0			0
$247$	−17.9753	+	1.28562i	−1.14374	+	0.0818020i
$248$		0			0
$249$	−2.44880	−	2.82606i	−0.155186	−	0.179094i
$250$		0			0
$251$	−0.730548	−	0.333630i	−0.0461118	−	0.0210586i	0.392226	−	0.919869i	$-0.371705\pi$
$251$	−0.730548	−	0.333630i	−0.0461118	−	0.0210586i	−0.438337	+	0.898810i	$0.644433\pi$
$252$		0			0
$253$	1.74227	+	2.58627i	0.109535	+	0.162598i
$254$		0			0
$255$	17.9399	+	1.54911i	1.12344	+	0.0970087i
$256$		0			0
$257$	−24.6752	−	1.76481i	−1.53920	−	0.110086i	−0.724217	−	0.689572i	$-0.757799\pi$
$257$	−24.6752	−	1.76481i	−1.53920	−	0.110086i	−0.814982	+	0.579486i	$0.803253\pi$
$258$		0			0
$259$	3.16802	+	2.74510i	0.196851	+	0.170572i
$260$		0			0
$261$	2.41486	−	0.709066i	0.149476	−	0.0438901i
$262$		0			0
$263$	−0.675468	−	0.505649i	−0.0416511	−	0.0311796i	0.578249	−	0.815860i	$-0.303736\pi$
$263$	−0.675468	−	0.505649i	−0.0416511	−	0.0311796i	−0.619900	+	0.784680i	$0.712827\pi$
$264$		0			0
$265$	20.7144	+	0.305273i	1.27247	+	0.0187528i
$266$		0			0
$267$	4.33872	+	19.9448i	0.265526	+	1.22060i
$268$		0			0
$269$	23.2696	+	3.34566i	1.41877	+	0.203988i	0.808636	−	0.588309i	$-0.200206\pi$
$269$	23.2696	+	3.34566i	1.41877	+	0.203988i	0.610135	+	0.792298i	$0.291115\pi$
$270$		0			0
$271$	−10.5037	+	6.75032i	−0.638055	+	0.410053i	−0.819284	−	0.573388i	$-0.805629\pi$
$271$	−10.5037	+	6.75032i	−0.638055	+	0.410053i	0.181229	+	0.983441i	$0.441992\pi$
$272$		0			0
$273$	−26.4221	+	14.4275i	−1.59914	+	0.873195i
$274$		0			0
$275$	2.05571	+	2.51872i	0.123964	+	0.151884i
$276$		0			0
$277$	−21.0422	+	21.0422i	−1.26430	+	1.26430i	−0.315313	+	0.948988i	$0.602109\pi$
$277$	−21.0422	+	21.0422i	−1.26430	+	1.26430i	−0.948988	+	0.315313i	$0.897891\pi$
$278$		0			0
$279$	−2.45397	+	8.35744i	−0.146915	+	0.500347i
$280$		0			0
$281$	−15.3191	−	23.8370i	−0.913861	−	1.42200i	−0.906586	−	0.422022i	$-0.861321\pi$
$281$	−15.3191	−	23.8370i	−0.913861	−	1.42200i	−0.00727540	−	0.999974i	$-0.502316\pi$
$282$		0			0
$283$	18.0948	+	24.1719i	1.07563	+	1.43687i	0.890968	+	0.454067i	$0.150027\pi$
$283$	18.0948	+	24.1719i	1.07563	+	1.43687i	0.184659	+	0.982803i	$0.440882\pi$
$284$		0			0
$285$	7.59104	+	12.2036i	0.449654	+	0.722879i
$286$		0			0
$287$	−10.5725	+	28.3459i	−0.624074	+	1.67321i
$288$		0			0
$289$	−0.128949	+	0.0185401i	−0.00758526	+	0.00109060i
$290$		0			0
$291$	−9.93378	−	33.8314i	−0.582329	−	1.98323i
$292$		0			0
$293$	1.13919	+	15.9279i	0.0665519	+	0.930518i	0.915571	+	0.402156i	$0.131739\pi$
$293$	1.13919	+	15.9279i	0.0665519	+	0.930518i	−0.849019	+	0.528362i	$0.822806\pi$
$294$		0			0
$295$	−8.65323	+	15.3066i	−0.503810	+	0.891183i
$296$		0			0
$297$	−2.57523	+	0.960510i	−0.149430	+	0.0557344i
$298$		0			0
$299$	23.4071	+	12.1316i	1.35367	+	0.701587i
$300$		0			0
$301$	0.730376	−	1.59930i	0.0420982	−	0.0921821i
$302$		0			0
$303$	1.57539	−	22.0268i	0.0905035	−	1.26540i
$304$		0			0
$305$	−3.13074	−	1.22055i	−0.179266	−	0.0698887i
$306$		0			0
$307$	2.29175	−	4.19703i	0.130797	−	0.239537i	−0.804070	−	0.594534i	$-0.797336\pi$
$307$	2.29175	−	4.19703i	0.130797	−	0.239537i	0.934867	+	0.354997i	$0.115518\pi$
$308$		0			0
$309$	−3.73098	−	25.9495i	−0.212248	−	1.47622i
$310$		0			0
$311$	2.95884	+	6.47896i	0.167780	+	0.367388i	0.974781	−	0.223162i	$-0.0716380\pi$
$311$	2.95884	+	6.47896i	0.167780	+	0.367388i	−0.807001	+	0.590550i	$0.798911\pi$
$312$		0			0
$313$	−23.1849	+	5.04357i	−1.31049	+	0.285079i	−0.812935	−	0.582354i	$-0.802132\pi$
$313$	−23.1849	+	5.04357i	−1.31049	+	0.285079i	−0.497553	+	0.867434i	$0.665768\pi$
$314$		0			0
$315$	4.39224	+	2.91506i	0.247475	+	0.164245i
$316$		0			0
$317$	5.42926	−	24.9579i	0.304938	−	1.40178i	−0.528393	−	0.849000i	$-0.677205\pi$
$317$	5.42926	−	24.9579i	0.304938	−	1.40178i	0.833330	−	0.552775i	$-0.186431\pi$
$318$		0			0
$319$	1.86033	+	0.546242i	0.104158	+	0.0305837i
$320$		0			0
$321$		−	27.2563i		−	1.52130i
$322$		0			0
$323$	9.52081	+	9.52081i	0.529752	+	0.529752i
$324$		0			0
$325$	25.4592	+	10.3603i	1.41222	+	0.574685i
$326$		0			0
$327$	−14.8323	−	3.22656i	−0.820227	−	0.178429i
$328$		0			0
$329$	4.58454	−	31.8862i	0.252754	−	1.75794i
$330$		0			0
$331$	16.3074	+	10.4801i	0.896335	+	0.576040i	0.905701	−	0.423917i	$-0.139345\pi$
$331$	16.3074	+	10.4801i	0.896335	+	0.576040i	−0.00936615	+	0.999956i	$0.502981\pi$
$332$		0			0
$333$	−1.18687	−	0.442681i	−0.0650403	−	0.0242588i
$334$		0			0
$335$	−6.18062	+	19.9566i	−0.337684	+	1.09034i
$336$		0			0
$337$	−20.4332	−	11.1573i	−1.11307	−	0.607780i	−0.185951	−	0.982559i	$-0.559537\pi$
$337$	−20.4332	−	11.1573i	−1.11307	−	0.607780i	−0.927114	+	0.374779i	$0.877718\pi$
$338$		0			0
$339$	11.8784	−	13.7083i	0.645143	−	0.744535i
$340$		0			0
$341$	−5.07117	+	4.39420i	−0.274619	+	0.237959i
$342$		0			0
$343$	6.05034	+	16.2216i	0.326688	+	0.875884i
$344$		0			0
$345$	−0.144924	−	21.0249i	−0.00780246	−	1.13194i
$346$		0			0
$347$	1.39464	+	3.73917i	0.0748680	+	0.200729i	0.968993	−	0.247089i	$-0.0794740\pi$
$347$	1.39464	+	3.73917i	0.0748680	+	0.200729i	−0.894125	+	0.447818i	$0.852201\pi$
$348$		0			0
$349$	−20.9749	+	18.1748i	−1.12276	+	0.972877i	−0.999809	−	0.0195355i	$-0.993781\pi$
$349$	−20.9749	+	18.1748i	−1.12276	+	0.972877i	−0.122951	+	0.992413i	$0.539236\pi$
$350$		0			0
$351$	−15.2171	+	17.5615i	−0.812228	+	0.937362i
$352$		0			0
$353$	12.4680	+	6.80802i	0.663602	+	0.362354i	0.775484	−	0.631367i	$-0.217506\pi$
$353$	12.4680	+	6.80802i	0.663602	+	0.362354i	−0.111882	+	0.993722i	$0.535688\pi$
$354$		0			0
$355$	2.05485	+	3.89869i	0.109060	+	0.206921i
$356$		0			0
$357$	21.0743	+	7.86030i	1.11537	+	0.416011i
$358$		0			0
$359$	−0.626924	−	0.402899i	−0.0330878	−	0.0212642i	0.523992	−	0.851723i	$-0.324442\pi$
$359$	−0.626924	−	0.402899i	−0.0330878	−	0.0212642i	−0.557080	+	0.830459i	$0.688078\pi$
$360$		0			0
$361$	1.17458	−	8.16942i	0.0618203	−	0.429969i
$362$		0			0
$363$	−20.2640	−	4.40816i	−1.06358	−	0.231369i
$364$		0			0
$365$	−0.636364	−	0.568045i	−0.0333088	−	0.0297328i
$366$		0			0
$367$	0.821830	+	0.821830i	0.0428992	+	0.0428992i	0.728231	−	0.685332i	$-0.240343\pi$
$367$	0.821830	+	0.821830i	0.0428992	+	0.0428992i	−0.685332	+	0.728231i	$0.740343\pi$
$368$		0			0
$369$		−	9.14225i		−	0.475927i
$370$		0			0
$371$	24.8293	+	7.29053i	1.28907	+	0.378505i
$372$		0			0
$373$	−0.873747	+	4.01655i	−0.0452409	+	0.207969i	−0.994219	−	0.107374i	$-0.965756\pi$
$373$	−0.873747	+	4.01655i	−0.0452409	+	0.207969i	0.948978	+	0.315343i	$0.102120\pi$
$374$		0			0
$375$	−2.15766	−	21.8140i	−0.111421	−	1.12647i
$376$		0			0
$377$	16.0174	−	3.48437i	0.824938	−	0.179454i
$378$		0			0
$379$	−3.62276	−	7.93273i	−0.186089	−	0.407477i	0.793478	−	0.608599i	$-0.208268\pi$
$379$	−3.62276	−	7.93273i	−0.186089	−	0.407477i	−0.979566	+	0.201122i	$0.935541\pi$
$380$		0			0
$381$	−0.0169408	−	0.117826i	−0.000867902	−	0.00603639i
$382$		0			0
$383$	7.24485	−	13.2679i	0.370194	−	0.677960i	−0.624479	−	0.781042i	$-0.714688\pi$
$383$	7.24485	−	13.2679i	0.370194	−	0.677960i	0.994673	+	0.103082i	$0.0328703\pi$
$384$		0			0
$385$	1.63240	+	3.71852i	0.0831950	+	0.189513i
$386$		0			0
$387$	−0.0379028	+	0.529950i	−0.00192671	+	0.0269389i
$388$		0			0
$389$	11.0478	−	24.1914i	0.560147	−	1.22655i	−0.391733	−	0.920079i	$-0.628124\pi$
$389$	11.0478	−	24.1914i	0.560147	−	1.22655i	0.951880	−	0.306472i	$-0.0991486\pi$
$390$		0			0
$391$	−4.60237	−	19.1526i	−0.232752	−	0.968588i
$392$		0			0
$393$	8.60371	−	3.20902i	0.434000	−	0.161874i
$394$		0			0
$395$	19.7104	+	11.1428i	0.991737	+	0.560657i
$396$		0			0
$397$	−2.18770	−	30.5881i	−0.109798	−	1.53517i	−0.691862	−	0.722030i	$-0.743209\pi$
$397$	−2.18770	−	30.5881i	−0.109798	−	1.53517i	0.582064	−	0.813143i	$-0.302245\pi$
$398$		0			0
$399$	5.05772	+	17.2250i	0.253202	+	0.862328i
$400$		0			0
$401$	7.46212	−	1.07289i	0.372640	−	0.0535776i	0.0465494	−	0.998916i	$-0.485178\pi$
$401$	7.46212	−	1.07289i	0.372640	−	0.0535776i	0.326091	+	0.945338i	$0.394268\pi$
$402$		0			0
$403$	−19.8252	+	53.1533i	−0.987562	+	2.64776i
$404$		0			0
$405$	23.5624	+	5.49053i	1.17082	+	0.272827i
$406$		0			0
$407$	−0.584811	−	0.781216i	−0.0289880	−	0.0387234i
$408$		0			0
$409$	7.59098	+	11.8118i	0.375350	+	0.584056i	0.976616	−	0.214993i	$-0.0689730\pi$
$409$	7.59098	+	11.8118i	0.375350	+	0.584056i	−0.601266	+	0.799049i	$0.705337\pi$
$410$		0			0
$411$	−9.52110	+	32.4259i	−0.469641	+	1.59945i
$412$		0			0
$413$	−15.5305	+	15.5305i	−0.764207	+	0.764207i
$414$		0			0
$415$	−1.82862	+	3.85283i	−0.0897633	+	0.189128i
$416$		0			0
$417$	20.9880	−	11.4603i	1.02778	−	0.561213i
$418$		0			0
$419$	−11.8543	+	7.61828i	−0.579119	+	0.372177i	−0.797165	−	0.603761i	$-0.793668\pi$
$419$	−11.8543	+	7.61828i	−0.579119	+	0.372177i	0.218046	+	0.975938i	$0.430032\pi$
$420$		0			0
$421$	17.1623	+	2.46756i	0.836438	+	0.120262i	0.547207	−	0.836998i	$-0.315691\pi$
$421$	17.1623	+	2.46756i	0.836438	+	0.120262i	0.289231	+	0.957259i	$0.406600\pi$
$422$		0			0
$423$	2.06927	+	9.51228i	0.100611	+	0.462503i
$424$		0			0
$425$	−6.60660	−	19.4447i	−0.320467	−	0.943206i
$426$		0			0
$427$	−3.36015	−	2.51537i	−0.162609	−	0.121727i
$428$		0			0
$429$	6.72435	−	1.97445i	0.324655	−	0.0953273i
$430$		0			0
$431$	15.5143	+	13.4432i	0.747299	+	0.647538i	0.942874	−	0.333151i	$-0.108112\pi$
$431$	15.5143	+	13.4432i	0.747299	+	0.647538i	−0.195575	+	0.980689i	$0.562657\pi$
$432$		0			0
$433$	−14.4388	−	1.03268i	−0.693885	−	0.0496276i	−0.280058	−	0.959983i	$-0.590354\pi$
$433$	−14.4388	−	1.03268i	−0.693885	−	0.0496276i	−0.413827	+	0.910356i	$0.635808\pi$
$434$		0			0
$435$	−8.41422	−	10.0047i	−0.403431	−	0.479688i
$436$		0			0
$437$	10.0361	−	12.1015i	0.480093	−	0.578895i
$438$		0			0
$439$	1.64131	+	0.749562i	0.0783356	+	0.0357747i	0.454198	−	0.890901i	$-0.349926\pi$
$439$	1.64131	+	0.749562i	0.0783356	+	0.0357747i	−0.375862	+	0.926676i	$0.622653\pi$
$440$		0			0
$441$	0.442994	+	0.511242i	0.0210949	+	0.0243448i
$442$		0			0
$443$	23.4593	−	1.67784i	1.11459	−	0.0797168i	0.498127	−	0.867104i	$-0.334021\pi$
$443$	23.4593	−	1.67784i	1.11459	−	0.0797168i	0.616459	+	0.787387i	$0.288567\pi$
$444$		0			0
$445$	18.8392	−	13.6743i	0.893062	−	0.648225i
$446$		0			0
$447$	3.77429	−	5.04186i	0.178518	−	0.238472i
$448$		0			0
$449$	15.5857	−	7.11774i	0.735534	−	0.335907i	−0.0121822	−	0.999926i	$-0.503878\pi$
$449$	15.5857	−	7.11774i	0.735534	−	0.335907i	0.747716	+	0.664019i	$0.231151\pi$
$450$		0			0
$451$	3.80768	−	5.92487i	0.179297	−	0.278991i
$452$		0			0
$453$	1.29453	−	0.969073i	0.0608223	−	0.0455310i
$454$		0			0
$455$	27.1795	+	20.9783i	1.27419	+	0.983477i
$456$		0			0
$457$	3.86774	+	7.08324i	0.180925	+	0.331340i	0.952364	−	0.304964i	$-0.0986444\pi$
$457$	3.86774	+	7.08324i	0.180925	+	0.331340i	−0.771439	+	0.636304i	$0.780463\pi$
$458$		0			0
$459$	17.3615			0.810366
$460$		0			0
$461$	22.1451			1.03140			0.515700	−	0.856770i	$-0.327532\pi$
$461$	22.1451			1.03140			0.515700	+	0.856770i	$0.327532\pi$
$462$		0			0
$463$	−15.2293	−	27.8903i	−0.707765	−	1.29617i	−0.945747	−	0.324905i	$-0.894668\pi$
$463$	−15.2293	−	27.8903i	−0.707765	−	1.29617i	0.237982	−	0.971270i	$-0.423514\pi$
$464$		0			0
$465$	44.8718	−	5.77806i	2.08088	−	0.267951i
$466$		0			0
$467$	17.1273	−	12.8214i	0.792559	−	0.593302i	−0.124424	−	0.992229i	$-0.539708\pi$
$467$	17.1273	−	12.8214i	0.792559	−	0.593302i	0.916983	+	0.398927i	$0.130617\pi$
$468$		0			0
$469$	−14.1087	+	21.9535i	−0.651478	+	1.01372i
$470$		0			0
$471$	−2.17355	+	0.992627i	−0.100152	+	0.0457378i
$472$		0			0
$473$	−0.245284	+	0.327661i	−0.0112782	+	0.0150659i
$474$		0			0
$475$	9.26412	−	13.5219i	0.425067	−	0.620425i
$476$		0			0
$477$	−7.79996	+	0.557864i	−0.357136	+	0.0255429i
$478$		0			0
$479$	−7.76101	−	8.95668i	−0.354610	−	0.409241i	0.550217	−	0.835022i	$-0.314545\pi$
$479$	−7.76101	−	8.95668i	−0.354610	−	0.409241i	−0.904827	+	0.425780i	$0.860000\pi$
$480$		0			0
$481$	−7.50476	−	3.42731i	−0.342187	−	0.156272i
$482$		0			0
$483$	6.85245	−	25.3534i	0.311797	−	1.15362i
$484$		0			0
$485$	−30.7758	+	25.8833i	−1.39746	+	1.17530i
$486$		0			0
$487$	26.0482	+	1.86300i	1.18035	+	0.0844207i	0.647689	−	0.761905i	$-0.275736\pi$
$487$	26.0482	+	1.86300i	1.18035	+	0.0844207i	0.532666	+	0.846326i	$0.321190\pi$
$488$		0			0
$489$	−7.93646	−	6.87698i	−0.358899	−	0.310988i
$490$		0			0
$491$	−1.35724	+	0.398520i	−0.0612512	+	0.0179850i	−0.312215	−	0.950012i	$-0.601071\pi$
$491$	−1.35724	+	0.398520i	−0.0612512	+	0.0179850i	0.250963	+	0.967997i	$0.419253\pi$
$492$		0			0
$493$	−9.80439	−	7.33947i	−0.441567	−	0.330553i
$494$		0			0
$495$	−0.854883	−	0.880457i	−0.0384241	−	0.0395736i
$496$		0			0
$497$	1.17016	+	5.37912i	0.0524887	+	0.241287i
$498$		0			0
$499$	−20.8213	−	2.99365i	−0.932089	−	0.134014i	−0.340492	−	0.940248i	$-0.610594\pi$
$499$	−20.8213	−	2.99365i	−0.932089	−	0.134014i	−0.591598	+	0.806233i	$0.701503\pi$
$500$		0			0
$501$	18.8569	−	12.1186i	0.842462	−	0.541417i
$502$		0			0
$503$	6.92381	−	3.78068i	0.308717	−	0.168572i	−0.317420	−	0.948285i	$-0.602817\pi$
$503$	6.92381	−	3.78068i	0.308717	−	0.168572i	0.626138	+	0.779713i	$0.284635\pi$
$504$		0			0
$505$	−23.7246	+	8.45272i	−1.05573	+	0.376141i
$506$		0			0
$507$	23.8737	−	23.8737i	1.06027	−	1.06027i
$508$		0			0
$509$	1.13181	−	3.85460i	0.0501667	−	0.170852i	−0.930599	−	0.366040i	$-0.880713\pi$
$509$	1.13181	−	3.85460i	0.0501667	−	0.170852i	0.980766	+	0.195188i	$0.0625316\pi$
$510$		0			0
$511$	−0.576061	−	0.896369i	−0.0254834	−	0.0396530i
$512$		0			0
$513$	8.30418	+	11.0931i	0.366639	+	0.489772i
$514$		0			0
$515$	−25.3885	+	15.7925i	−1.11875	+	0.695899i
$516$		0			0
$517$	−2.62075	+	7.02651i	−0.115261	+	0.309026i
$518$		0			0
$519$	6.03376	−	0.867523i	0.264852	−	0.0380800i
$520$		0			0
$521$	2.05042	+	6.98308i	0.0898304	+	0.305934i	0.992136	−	0.125162i	$-0.0399451\pi$
$521$	2.05042	+	6.98308i	0.0898304	+	0.305934i	−0.902306	+	0.431096i	$0.858127\pi$
$522$		0			0
$523$	−0.655244	−	9.16151i	−0.0286518	−	0.400605i	−0.991459	−	0.130416i	$-0.958369\pi$
$523$	−0.655244	−	9.16151i	−0.0286518	−	0.400605i	0.962807	−	0.270188i	$-0.0870860\pi$
$524$		0			0
$525$	4.69372	−	26.9759i	0.204851	−	1.17732i
$526$		0			0
$527$	39.7132	−	14.8123i	1.72994	−	0.645233i
$528$		0			0
$529$	−21.7675	+	7.42812i	−0.946412	+	0.322962i
$530$		0			0
$531$	2.75716	−	6.03734i	0.119651	−	0.261998i
$532$		0			0
$533$	4.24780	−	59.3920i	0.183993	−	2.57255i
$534$		0			0
$535$	−28.4636	+	12.4953i	−1.23059	+	0.540220i
$536$		0			0
$537$	−22.8608	+	41.8665i	−0.986517	+	1.80667i
$538$		0			0
$539$	0.0741647	+	0.515827i	0.00319450	+	0.0222182i
$540$		0			0
$541$	19.0962	+	41.8148i	0.821009	+	1.79776i	0.549955	+	0.835194i	$0.314645\pi$
$541$	19.0962	+	41.8148i	0.821009	+	1.79776i	0.271054	+	0.962564i	$0.412628\pi$
$542$		0			0
$543$	−21.3927	+	4.65370i	−0.918050	+	0.199710i
$544$		0			0
$545$	3.43019	+	16.9684i	0.146933	+	0.726847i
$546$		0			0
$547$	−0.700047	+	3.21806i	−0.0299318	+	0.137594i	−0.989688	−	0.143241i	$-0.954248\pi$
$547$	−0.700047	+	3.21806i	−0.0299318	+	0.137594i	0.959756	+	0.280835i	$0.0906114\pi$
$548$		0			0
$549$	1.21701	+	0.357347i	0.0519408	+	0.0152512i
$550$		0			0
$551$		−	9.77502i		−	0.416430i
$552$		0			0
$553$	19.9988	+	19.9988i	0.850435	+	0.850435i
$554$		0			0
$555$	0.372626	+	6.56907i	0.0158171	+	0.278841i
$556$		0			0
$557$	−27.1899	−	5.91480i	−1.15207	−	0.250618i	−0.404334	−	0.914611i	$-0.632497\pi$
$557$	−27.1899	−	5.91480i	−1.15207	−	0.250618i	−0.747739	+	0.663993i	$0.768860\pi$
$558$		0			0
$559$	−0.492465	+	3.42517i	−0.0208291	+	0.144869i
$560$		0			0
$561$	−4.40495	−	2.83089i	−0.185977	−	0.119520i
$562$		0			0
$563$	34.8007	+	12.9800i	1.46667	+	0.547041i	0.950849	−	0.309654i	$-0.100213\pi$
$563$	34.8007	+	12.9800i	1.46667	+	0.547041i	0.515824	+	0.856695i	$0.327486\pi$
$564$		0			0
$565$	−19.7610	−	6.12006i	−0.831352	−	0.257473i
$566$		0			0
$567$	26.5241	+	14.4832i	1.11391	+	0.608238i
$568$		0			0
$569$	12.7846	−	14.7542i	0.535959	−	0.618530i	−0.421595	−	0.906784i	$-0.638530\pi$
$569$	12.7846	−	14.7542i	0.535959	−	0.618530i	0.957554	+	0.288255i	$0.0930750\pi$
$570$		0			0
$571$	6.25293	−	5.41819i	0.261677	−	0.226744i	−0.514134	−	0.857710i	$-0.671887\pi$
$571$	6.25293	−	5.41819i	0.261677	−	0.226744i	0.775811	+	0.630966i	$0.217341\pi$
$572$		0			0
$573$	14.9886	+	40.1860i	0.626157	+	1.67879i
$574$		0			0
$575$	−21.8897	+	9.78992i	−0.912862	+	0.408268i
$576$		0			0
$577$	7.34021	+	19.6799i	0.305577	+	0.819283i	0.995444	+	0.0953471i	$0.0303961\pi$
$577$	7.34021	+	19.6799i	0.305577	+	0.819283i	−0.689867	+	0.723936i	$0.742331\pi$
$578$		0			0
$579$	4.48984	−	3.89047i	0.186591	−	0.161682i
$580$		0			0
$581$	−3.48856	+	4.02601i	−0.144730	+	0.167027i
$582$		0			0
$583$	−5.28731	−	2.88709i	−0.218978	−	0.119571i
$584$		0			0
$585$	−9.91087	−	3.06944i	−0.409764	−	0.126906i
$586$		0			0
$587$	−29.8127	−	11.1196i	−1.23050	−	0.458953i	−0.351688	−	0.936117i	$-0.614392\pi$
$587$	−29.8127	−	11.1196i	−1.23050	−	0.458953i	−0.878814	+	0.477164i	$0.841665\pi$
$588$		0			0
$589$	28.4595	+	18.2898i	1.17265	+	0.753618i
$590$		0			0
$591$	5.57543	−	38.7780i	0.229343	−	1.59511i
$592$		0			0
$593$	28.8473	+	6.27535i	1.18462	+	0.257698i	0.761371	−	0.648317i	$-0.224527\pi$
$593$	28.8473	+	6.27535i	1.18462	+	0.257698i	0.423247	+	0.906014i	$0.360890\pi$
$594$		0			0
$595$	−1.45278	−	25.6112i	−0.0595581	−	1.04996i
$596$		0			0
$597$	−0.745915	−	0.745915i	−0.0305283	−	0.0305283i
$598$		0			0
$599$			15.9705i			0.652537i	0.945277	+	0.326269i	$0.105791\pi$
$599$			15.9705i			0.652537i	−0.945277	+	0.326269i	$0.894209\pi$
$600$		0			0
$601$	−5.11686	−	1.50245i	−0.208721	−	0.0612861i	0.175701	−	0.984444i	$-0.443781\pi$
$601$	−5.11686	−	1.50245i	−0.208721	−	0.0612861i	−0.384422	+	0.923158i	$0.625599\pi$
$602$		0			0
$603$	1.67629	−	7.70576i	0.0682636	−	0.313803i
$604$		0			0
$605$	4.68636	+	23.1824i	0.190527	+	0.942499i
$606$		0			0
$607$	23.3291	−	5.07493i	0.946898	−	0.205985i	0.287501	−	0.957780i	$-0.407175\pi$
$607$	23.3291	−	5.07493i	0.946898	−	0.205985i	0.659397	+	0.751795i	$0.270812\pi$
$608$		0			0
$609$	−6.78340	−	14.8536i	−0.274877	−	0.601897i
$610$		0			0
$611$	9.02313	+	62.7573i	0.365037	+	2.53889i
$612$		0			0
$613$	20.5819	−	37.6929i	0.831294	−	1.52240i	−0.0212671	−	0.999774i	$-0.506770\pi$
$613$	20.5819	−	37.6929i	0.831294	−	1.52240i	0.852561	−	0.522627i	$-0.175048\pi$
$614$		0			0
$615$	−43.4808	+	19.0878i	−1.75332	+	0.769693i
$616$		0			0
$617$	−0.663163	+	9.27223i	−0.0266979	+	0.373286i	0.966485	+	0.256722i	$0.0826425\pi$
$617$	−0.663163	+	9.27223i	−0.0266979	+	0.373286i	−0.993183	+	0.116564i	$0.962812\pi$
$618$		0			0
$619$	−11.9756	+	26.2229i	−0.481341	+	1.05399i	0.500752	+	0.865591i	$0.333057\pi$
$619$	−11.9756	+	26.2229i	−0.481341	+	1.05399i	−0.982093	+	0.188398i	$0.939670\pi$
$620$		0			0
$621$	−1.88317	−	20.1844i	−0.0755689	−	0.809972i
$622$		0			0
$623$	27.2445	−	10.1617i	1.09153	−	0.407119i
$624$		0			0
$625$	−21.7910	+	12.2536i	−0.871642	+	0.490143i
$626$		0			0
$627$	−0.298142	−	4.16857i	−0.0119066	−	0.166477i
$628$		0			0
$629$	1.73665	+	5.91449i	0.0692449	+	0.235826i
$630$		0			0
$631$	−44.3584	+	6.37777i	−1.76588	+	0.253895i	−0.947265	−	0.320450i	$-0.896166\pi$
$631$	−44.3584	+	6.37777i	−1.76588	+	0.253895i	−0.818613	+	0.574345i	$0.805257\pi$
$632$		0			0
$633$	−1.67691	+	4.49597i	−0.0666513	+	0.178699i
$634$		0			0
$635$	−0.115278	+	0.0717068i	−0.00457468	+	0.00284560i
$636$		0			0
$637$	2.64034	+	3.52708i	0.104614	+	0.139748i
$638$		0			0
$639$	−0.899371	−	1.39945i	−0.0355786	−	0.0553614i
$640$		0			0
$641$	−11.9012	+	40.5316i	−0.470067	+	1.60090i	0.294027	+	0.955797i	$0.405004\pi$
$641$	−11.9012	+	40.5316i	−0.470067	+	1.60090i	−0.764094	+	0.645105i	$0.776814\pi$
$642$		0			0
$643$	−14.9440	+	14.9440i	−0.589333	+	0.589333i	−0.937451	−	0.348118i	$-0.886821\pi$
$643$	−14.9440	+	14.9440i	−0.589333	+	0.589333i	0.348118	+	0.937451i	$0.386821\pi$
$644$		0			0
$645$	2.59959	−	0.926196i	0.102359	−	0.0364689i
$646$		0			0
$647$	−1.71326	+	0.935512i	−0.0673553	+	0.0367788i	−0.512574	−	0.858643i	$-0.671308\pi$
$647$	−1.71326	+	0.935512i	−0.0673553	+	0.0367788i	0.445218	+	0.895422i	$0.353126\pi$
$648$		0			0
$649$	4.30136	−	2.76431i	0.168843	−	0.108509i
$650$		0			0
$651$	55.9377	+	8.04262i	2.19237	+	0.315215i
$652$		0			0
$653$	−1.63427	−	7.51262i	−0.0639539	−	0.293991i	0.934050	−	0.357142i	$-0.116249\pi$
$653$	−1.63427	−	7.51262i	−0.0639539	−	0.293991i	−0.998004	+	0.0631506i	$0.979885\pi$
$654$		0			0
$655$	−7.29542	−	7.51366i	−0.285056	−	0.293583i
$656$		0			0
$657$	0.257764	+	0.192960i	0.0100563	+	0.00752807i
$658$		0			0
$659$	32.1664	−	9.44489i	1.25302	−	0.367921i	0.413130	−	0.910672i	$-0.364436\pi$
$659$	32.1664	−	9.44489i	1.25302	−	0.367921i	0.839893	+	0.542751i	$0.182617\pi$
$660$		0			0
$661$	22.6283	+	19.6075i	0.880138	+	0.762644i	0.972456	−	0.233085i	$-0.0748821\pi$
$661$	22.6283	+	19.6075i	0.880138	+	0.762644i	−0.0923178	+	0.995730i	$0.529428\pi$
$662$		0			0
$663$	−44.1560	−	3.15810i	−1.71488	−	0.122650i
$664$		0			0
$665$	15.6693	−	13.1783i	0.607629	−	0.511033i
$666$		0			0
$667$	−7.46936	+	12.1946i	−0.289215	+	0.472177i
$668$		0			0
$669$	17.1387	+	7.82696i	0.662619	+	0.302608i
$670$		0			0
$671$	0.639883	+	0.738465i	0.0247024	+	0.0285081i
$672$		0			0
$673$	−14.1647	+	1.01308i	−0.546011	+	0.0390514i	−0.341620	−	0.939838i	$-0.610976\pi$
$673$	−14.1647	+	1.01308i	−0.546011	+	0.0390514i	−0.204390	+	0.978889i	$0.565521\pi$
$674$		0			0
$675$	−3.88205	−	20.7755i	−0.149420	−	0.799649i
$676$		0			0
$677$	−15.2822	+	20.4147i	−0.587344	+	0.784599i	−0.991502	−	0.130090i	$-0.958474\pi$
$677$	−15.2822	+	20.4147i	−0.587344	+	0.784599i	0.404158	+	0.914689i	$0.367564\pi$
$678$		0			0
$679$	−45.6917	+	20.8667i	−1.75349	+	0.800790i
$680$		0			0
$681$	26.7366	−	41.6029i	1.02455	−	1.59423i
$682$		0			0
$683$	17.3311	−	12.9739i	0.663155	−	0.496432i	−0.213879	−	0.976860i	$-0.568610\pi$
$683$	17.3311	−	12.9739i	0.663155	−	0.496432i	0.877034	+	0.480429i	$0.159519\pi$
$684$		0			0
$685$	38.2269	−	4.92241i	1.46058	−	0.188076i
$686$		0			0
$687$	11.5619	+	21.1741i	0.441116	+	0.807843i
$688$		0			0
$689$	−50.9311			−1.94032
$690$		0			0
$691$	−9.64997			−0.367102			−0.183551	−	0.983010i	$-0.558759\pi$
$691$	−9.64997			−0.367102			−0.183551	+	0.983010i	$0.558759\pi$
$692$		0			0
$693$	−0.734651	−	1.34541i	−0.0279071	−	0.0511080i
$694$		0			0
$695$	−21.5896	−	16.6637i	−0.818939	−	0.632092i
$696$		0			0
$697$	−35.6143	+	26.6605i	−1.34899	+	1.00984i
$698$		0			0
$699$	3.41652	−	5.31621i	0.129225	−	0.201078i
$700$		0			0
$701$	−29.1001	+	13.2895i	−1.09909	+	0.501939i	−0.880581	−	0.473895i	$-0.842848\pi$
$701$	−29.1001	+	13.2895i	−1.09909	+	0.501939i	−0.218512	+	0.975834i	$0.570120\pi$
$702$		0			0
$703$	−2.94839	+	3.93859i	−0.111201	+	0.148547i
$704$		0			0
$705$	40.9203	−	29.7018i	1.54115	−	1.11864i
$706$		0			0
$707$	−31.3794	+	2.24430i	−1.18014	+	0.0844055i
$708$		0			0
$709$	−3.98547	−	4.59948i	−0.149678	−	0.172737i	0.675959	−	0.736939i	$-0.263729\pi$
$709$	−3.98547	−	4.59948i	−0.149678	−	0.172737i	−0.825637	+	0.564202i	$0.809184\pi$
$710$		0			0
$711$	−7.77433	−	3.55042i	−0.291560	−	0.133151i
$712$		0			0
$713$	−21.5283	−	44.5637i	−0.806240	−	1.66892i
$714$		0			0
$715$	−5.14460	−	6.11704i	−0.192397	−	0.228764i
$716$		0			0
$717$	−19.8697	−	1.42111i	−0.742047	−	0.0530723i
$718$		0			0
$719$	−23.6967	−	20.5333i	−0.883738	−	0.765763i	0.0893979	−	0.995996i	$-0.471506\pi$
$719$	−23.6967	−	20.5333i	−0.883738	−	0.765763i	−0.973136	+	0.230233i	$0.926051\pi$
$720$		0			0
$721$	−35.8351	+	10.5221i	−1.33457	+	0.391864i
$722$		0			0
$723$	−18.9043	−	14.1515i	−0.703057	−	0.526302i
$724$		0			0
$725$	−6.59044	+	13.3734i	−0.244763	+	0.496677i
$726$		0			0
$727$	−2.35810	−	10.8400i	−0.0874572	−	0.402034i	0.912518	−	0.409036i	$-0.134135\pi$
$727$	−2.35810	−	10.8400i	−0.0874572	−	0.402034i	−0.999975	+	0.00700162i	$0.997771\pi$
$728$		0			0
$729$	15.5703	+	2.23867i	0.576677	+	0.0829137i
$730$		0			0
$731$	2.17499	−	1.39778i	0.0804449	−	0.0516988i
$732$		0			0
$733$	−2.81312	+	1.53608i	−0.103905	+	0.0567363i	−0.530361	−	0.847772i	$-0.677944\pi$
$733$	−2.81312	+	1.53608i	−0.103905	+	0.0567363i	0.426456	+	0.904508i	$0.359762\pi$
$734$		0			0
$735$	1.50657	−	3.17429i	0.0555707	−	0.117086i
$736$		0			0
$737$	4.29576	−	4.29576i	0.158236	−	0.158236i
$738$		0			0
$739$	−5.70345	+	19.4242i	−0.209805	+	0.714529i	0.785597	+	0.618739i	$0.212356\pi$
$739$	−5.70345	+	19.4242i	−0.209805	+	0.714529i	−0.995402	+	0.0957905i	$0.969462\pi$
$740$		0			0
$741$	−19.1024	−	29.7239i	−0.701743	−	1.09193i
$742$		0			0
$743$	12.9297	+	17.2721i	0.474346	+	0.633653i	0.972352	−	0.233521i	$-0.0750249\pi$
$743$	12.9297	+	17.2721i	0.474346	+	0.633653i	−0.498005	+	0.867174i	$0.665934\pi$
$744$		0			0
$745$	−6.99546	−	1.63009i	−0.256294	−	0.0597218i
$746$		0			0
$747$	0.562573	−	1.50832i	0.0205835	−	0.0551864i
$748$		0			0
$749$	−38.4342	+	5.52601i	−1.40436	+	0.201916i
$750$		0			0
$751$	3.08873	+	10.5192i	0.112709	+	0.383853i	0.996456	−	0.0841125i	$-0.0268055\pi$
$751$	3.08873	+	10.5192i	0.112709	+	0.383853i	−0.883747	+	0.467965i	$0.844987\pi$
$752$		0			0
$753$	−0.112333	−	1.57061i	−0.00409363	−	0.0572364i
$754$		0			0
$755$	−1.60546	−	0.907609i	−0.0584286	−	0.0330313i
$756$		0			0
$757$	39.2393	−	14.6355i	1.42618	−	0.531936i	0.486403	−	0.873734i	$-0.338309\pi$
$757$	39.2393	−	14.6355i	1.42618	−	0.531936i	0.939773	+	0.341798i	$0.111036\pi$
$758$		0			0
$759$	−2.81338	+	5.42822i	−0.102119	+	0.197032i
$760$		0			0
$761$	14.1688	−	31.0253i	0.513618	−	1.12467i	−0.458181	−	0.888859i	$-0.651499\pi$
$761$	14.1688	−	31.0253i	0.513618	−	1.12467i	0.971800	−	0.235808i	$-0.0757738\pi$
$762$		0			0
$763$	−1.54266	+	21.5692i	−0.0558480	+	0.780857i
$764$		0			0
$765$	3.11598	+	7.09802i	0.112659	+	0.256629i
$766$		0			0
$767$	20.7168	−	37.9401i	0.748042	−	1.36994i
$768$		0			0
$769$	−1.16285	−	8.08782i	−0.0419335	−	0.291654i	−0.999987	−	0.00506518i	$-0.998388\pi$
$769$	−1.16285	−	8.08782i	−0.0419335	−	0.291654i	0.958054	−	0.286589i	$-0.0925214\pi$
$770$		0			0
$771$	−20.1486	−	44.1194i	−0.725636	−	1.58892i
$772$		0			0
$773$	1.65432	−	0.359876i	0.0595018	−	0.0129438i	−0.182716	−	0.983166i	$-0.558489\pi$
$773$	1.65432	−	0.359876i	0.0595018	−	0.0129438i	0.242218	+	0.970222i	$0.422125\pi$
$774$		0			0
$775$	−26.6049	−	44.2104i	−0.955676	−	1.58809i
$776$		0			0
$777$	−1.74701	+	8.03090i	−0.0626738	+	0.288107i
$778$		0			0
$779$	−34.0693	−	10.0037i	−1.22066	−	0.358418i
$780$		0			0
$781$		−	1.28153i		−	0.0458568i
$782$		0			0
$783$	−8.91254	−	8.91254i	−0.318508	−	0.318508i
$784$		0			0
$785$	2.03303	+	1.81477i	0.0725619	+	0.0647718i
$786$		0			0
$787$	27.8824	+	6.06544i	0.993899	+	0.216209i	0.679972	−	0.733238i	$-0.261992\pi$
$787$	27.8824	+	6.06544i	0.993899	+	0.216209i	0.313927	+	0.949447i	$0.398355\pi$
$788$		0			0
$789$	0.235432	−	1.63746i	0.00838160	−	0.0582953i
$790$		0			0
$791$	−21.7384	−	13.9704i	−0.772929	−	0.496731i
$792$		0			0
$793$	7.74020	+	2.88694i	0.274862	+	0.102518i
$794$		0			0
$795$	18.9385	+	35.9321i	0.671678	+	1.27438i
$796$		0			0
$797$	19.8423	+	10.8347i	0.702850	+	0.383785i	0.790580	−	0.612359i	$-0.209779\pi$
$797$	19.8423	+	10.8347i	0.702850	+	0.383785i	−0.0877294	+	0.996144i	$0.527961\pi$
$798$		0			0
$799$	31.0214	−	35.8006i	1.09746	−	1.26653i
$800$		0			0
$801$	−6.64079	+	5.75428i	−0.234641	+	0.203317i
$802$		0			0
$803$	0.0866842	+	0.232409i	0.00305902	+	0.00820154i
$804$		0			0
$805$	−29.6178	+	4.46698i	−1.04389	+	0.157440i
$806$		0			0
$807$	16.1075	+	43.1859i	0.567011	+	1.52022i
$808$		0			0
$809$	0.932988	−	0.808439i	0.0328021	−	0.0284232i	−0.638305	−	0.769783i	$-0.720364\pi$
$809$	0.932988	−	0.808439i	0.0328021	−	0.0284232i	0.671108	+	0.741360i	$0.265819\pi$
$810$		0			0
$811$	−0.450105	+	0.519449i	−0.0158053	+	0.0182403i	−0.763597	−	0.645693i	$-0.776569\pi$
$811$	−0.450105	+	0.519449i	−0.0158053	+	0.0182403i	0.747792	+	0.663933i	$0.231114\pi$
$812$		0			0
$813$	−21.4855	−	11.7320i	−0.753530	−	0.411458i
$814$		0			0
$815$	−3.54321	+	11.4407i	−0.124113	+	0.400749i
$816$		0			0
$817$	1.93343	+	0.721130i	0.0676420	+	0.0252292i
$818$		0			0
$819$	−10.9026	−	7.00668i	−0.380968	−	0.244833i
$820$		0			0
$821$	−1.20863	+	8.40619i	−0.0421814	+	0.293378i	0.957801	+	0.287432i	$0.0928017\pi$
$821$	−1.20863	+	8.40619i	−0.0421814	+	0.293378i	−0.999982	+	0.00594566i	$0.998107\pi$
$822$		0			0
$823$	34.0950	+	7.41691i	1.18848	+	0.258537i	0.762979	−	0.646423i	$-0.223736\pi$
$823$	34.0950	+	7.41691i	1.18848	+	0.258537i	0.425497	+	0.904960i	$0.360099\pi$
$824$		0			0
$825$	−2.40260	+	5.90412i	−0.0836479	+	0.205555i
$826$		0			0
$827$	25.7472	+	25.7472i	0.895320	+	0.895320i	0.995018	−	0.0996982i	$-0.0317877\pi$
$827$	25.7472	+	25.7472i	0.895320	+	0.895320i	−0.0996982	+	0.995018i	$0.531788\pi$
$828$		0			0
$829$		−	14.6148i		−	0.507594i	−0.967258	−	0.253797i	$-0.918321\pi$
$829$		−	14.6148i		−	0.507594i	0.967258	−	0.253797i	$-0.0816795\pi$
$830$		0			0
$831$	−55.9811	−	16.4375i	−1.94196	−	0.570212i
$832$		0			0
$833$	0.699726	−	3.21659i	0.0242441	−	0.111448i
$834$		0			0
$835$	−21.3000	−	14.1365i	−0.737117	−	0.489213i
$836$		0			0
$837$	42.6244	−	9.27238i	1.47332	−	0.320500i
$838$		0			0
$839$	0.723610	+	1.58448i	0.0249818	+	0.0547025i	0.921712	−	0.387876i	$-0.126791\pi$
$839$	0.723610	+	1.58448i	0.0249818	+	0.0547025i	−0.896730	+	0.442578i	$0.854064\pi$
$840$		0			0
$841$	−2.86177	−	19.9040i	−0.0986816	−	0.686345i
$842$		0			0
$843$	26.6244	−	48.7590i	0.916993	−	1.67935i
$844$		0			0
$845$	−35.8757	−	13.9865i	−1.23416	−	0.481151i
$846$		0			0
$847$	−2.10759	+	29.4680i	−0.0724178	+	1.01253i
$848$		0			0
$849$	−24.5925	+	53.8501i	−0.844014	+	1.84813i
$850$		0			0
$851$	6.68778	−	2.66055i	0.229254	−	0.0912026i
$852$		0			0
$853$	48.4023	−	18.0531i	1.65726	−	0.618128i	0.665522	−	0.746378i	$-0.268209\pi$
$853$	48.4023	−	18.0531i	1.65726	−	0.618128i	0.991742	+	0.128250i	$0.0409361\pi$
$854$		0			0
$855$	−3.04485	+	5.38600i	−0.104132	+	0.184197i
$856$		0			0
$857$	2.01282	+	28.1429i	0.0687566	+	0.961343i	0.908372	+	0.418162i	$0.137326\pi$
$857$	2.01282	+	28.1429i	0.0687566	+	0.961343i	−0.839616	+	0.543181i	$0.817220\pi$
$858$		0			0
$859$	3.09221	+	10.5311i	0.105505	+	0.359317i	0.995275	−	0.0970914i	$-0.0309539\pi$
$859$	3.09221	+	10.5311i	0.105505	+	0.359317i	−0.889771	+	0.456408i	$0.849136\pi$
$860$		0			0
$861$	−58.7119	+	8.44149i	−2.00089	+	0.287685i
$862$		0			0
$863$	6.19361	−	16.6057i	0.210833	−	0.565265i	−0.787889	−	0.615818i	$-0.788826\pi$
$863$	6.19361	−	16.6057i	0.210833	−	0.565265i	0.998721	+	0.0505532i	$0.0160984\pi$
$864$		0			0
$865$	−3.67205	−	5.90330i	−0.124853	−	0.200718i
$866$		0			0
$867$	−0.153068	−	0.204475i	−0.00519847	−	0.00694434i
$868$		0			0
$869$	−3.55963	−	5.53889i	−0.120752	−	0.187894i
$870$		0			0
$871$	14.4702	−	49.2811i	0.490305	−	1.66983i
$872$		0			0
$873$	10.7333	−	10.7333i	0.363268	−	0.363268i
$874$		0			0
$875$	−30.3225	+	7.46514i	−1.02509	+	0.252368i
$876$		0			0
$877$	−30.2256	+	16.5044i	−1.02065	+	0.557315i	−0.900233	−	0.435409i	$-0.856604\pi$
$877$	−30.2256	+	16.5044i	−1.02065	+	0.557315i	−0.120413	+	0.992724i	$0.538422\pi$
$878$		0			0
$879$	−26.3383	+	16.9266i	−0.888369	+	0.570920i
$880$		0			0
$881$	−7.36709	−	1.05923i	−0.248204	−	0.0356863i	0.0170900	−	0.999854i	$-0.494560\pi$
$881$	−7.36709	−	1.05923i	−0.248204	−	0.0356863i	−0.265294	+	0.964168i	$0.585469\pi$
$882$		0			0
$883$	−3.12788	−	14.3787i	−0.105262	−	0.483880i	−0.999352	−	0.0359935i	$-0.988540\pi$
$883$	−3.12788	−	14.3787i	−0.105262	−	0.483880i	0.894090	−	0.447887i	$-0.147823\pi$
$884$		0			0
$885$	−34.4703	−	0.507998i	−1.15871	−	0.0170762i
$886$		0			0
$887$	7.22488	+	5.40848i	0.242588	+	0.181599i	0.713653	−	0.700499i	$-0.247039\pi$
$887$	7.22488	+	5.40848i	0.242588	+	0.181599i	−0.471065	+	0.882098i	$0.656130\pi$
$888$		0			0
$889$	−0.162712	+	0.0477764i	−0.00545717	+	0.00160237i
$890$		0			0
$891$	−5.31691	−	4.60713i	−0.178123	−	0.154345i
$892$		0			0
$893$	37.7125	+	2.69725i	1.26200	+	0.0902600i
$894$		0			0
$895$	54.2011	+	4.68025i	1.81174	+	0.156443i
$896$		0			0
$897$	1.11792	+	51.6780i	0.0373263	+	1.72548i
$898$		0			0
$899$	−27.9907	−	12.7829i	−0.933542	−	0.426334i
$900$		0			0
$901$	24.9194	+	28.7585i	0.830184	+	0.958084i
$902$		0			0
$903$	3.43835	−	0.245916i	0.114421	−	0.00818357i
$904$		0			0
$905$	14.6671	+	20.2069i	0.487549	+	0.671698i
$906$		0			0
$907$	−1.90526	+	2.54512i	−0.0632630	+	0.0845095i	−0.831057	−	0.556188i	$-0.812264\pi$
$907$	−1.90526	+	2.54512i	−0.0632630	+	0.0845095i	0.767794	+	0.640697i	$0.221355\pi$
$908$		0			0
$909$	8.64762	−	3.94923i	0.286823	−	0.130988i
$910$		0			0
$911$	−4.26176	+	6.63142i	−0.141198	+	0.219709i	−0.904649	−	0.426157i	$-0.859867\pi$
$911$	−4.26176	+	6.63142i	−0.141198	+	0.219709i	0.763451	+	0.645866i	$0.223503\pi$
$912$		0			0
$913$	0.992792	−	0.743195i	0.0328566	−	0.0245962i
$914$		0			0
$915$	−0.841402	−	6.53424i	−0.0278159	−	0.216015i
$916$		0			0
$917$	−6.26938	−	11.4815i	−0.207033	−	0.379153i
$918$		0			0
$919$	−39.3490			−1.29801			−0.649003	−	0.760786i	$-0.724814\pi$
$919$	−39.3490			−1.29801			−0.649003	+	0.760786i	$0.724814\pi$
$920$		0			0
$921$	9.37563			0.308937
$922$		0			0
$923$	−5.19247	−	9.50930i	−0.170912	−	0.313002i
$924$		0			0
$925$	6.68920	−	3.40064i	0.219940	−	0.111812i
$926$		0			0
$927$	9.03501	−	6.76352i	0.296749	−	0.222143i
$928$		0			0
$929$	−16.6961	+	25.9796i	−0.547781	+	0.852363i	−0.999202	−	0.0399478i	$-0.987281\pi$
$929$	−16.6961	+	25.9796i	−0.547781	+	0.852363i	0.451421	+	0.892311i	$0.350917\pi$
$930$		0			0
$931$	2.38992	−	1.09144i	0.0783263	−	0.0357704i
$932$		0			0
$933$	−8.36877	+	11.1794i	−0.273981	+	0.365996i
$934$		0			0
$935$	−0.936884	+	5.89784i	−0.0306394	+	0.192880i
$936$		0			0
$937$	28.7226	−	2.05428i	0.938327	−	0.0671104i	0.406208	−	0.913780i	$-0.366851\pi$
$937$	28.7226	−	2.05428i	0.938327	−	0.0671104i	0.532118	+	0.846670i	$0.321396\pi$
$938$		0			0
$939$	−30.4641	−	35.1575i	−0.994159	−	1.14732i
$940$		0			0
$941$	−33.0180	−	15.0788i	−1.07635	−	0.491555i	−0.203270	−	0.979123i	$-0.565157\pi$
$941$	−33.0180	−	15.0788i	−1.07635	−	0.491555i	−0.873085	+	0.487568i	$0.837884\pi$
$942$		0			0
$943$	34.8584	+	38.5131i	1.13514	+	1.25416i
$944$		0			0
$945$	2.27119	−	26.3023i	0.0738819	−	0.855613i
$946$		0			0
$947$	−18.5751	−	1.32851i	−0.603608	−	0.0431709i	−0.233809	−	0.972283i	$-0.575119\pi$
$947$	−18.5751	−	1.32851i	−0.603608	−	0.0431709i	−0.369799	+	0.929112i	$0.620574\pi$
$948$		0			0
$949$	1.58489	+	1.37331i	0.0514477	+	0.0445797i
$950$		0			0
$951$	48.0490	−	14.1085i	1.55810	−	0.457498i
$952$		0			0
$953$	−48.2089	−	36.0887i	−1.56164	−	1.16903i	−0.913021	−	0.407912i	$-0.866257\pi$
$953$	−48.2089	−	36.0887i	−1.56164	−	1.16903i	−0.648617	−	0.761115i	$-0.724652\pi$
$954$		0			0
$955$	35.0946	−	34.0752i	1.13563	−	1.10265i
$956$		0			0
$957$	0.808044	+	3.71452i	0.0261203	+	0.120073i
$958$		0			0
$959$	47.6541	+	6.85163i	1.53883	+	0.221251i
$960$		0			0
$961$	63.5106	−	40.8158i	2.04873	−	1.31664i
$962$		0			0
$963$	10.2985	−	5.62343i	0.331866	−	0.181212i
$964$		0			0
$965$	−6.12110	−	2.90517i	−0.197045	−	0.0935208i
$966$		0			0
$967$	27.9786	−	27.9786i	0.899730	−	0.899730i	−0.0956822	−	0.995412i	$-0.530503\pi$
$967$	27.9786	−	27.9786i	0.899730	−	0.899730i	0.995412	+	0.0956822i	$0.0305033\pi$
$968$		0			0
$969$	−7.43739	+	25.3294i	−0.238923	+	0.813698i
$970$		0			0
$971$	5.45126	+	8.48233i	0.174939	+	0.272211i	0.917640	−	0.397413i	$-0.130092\pi$
$971$	5.45126	+	8.48233i	0.174939	+	0.272211i	−0.742701	+	0.669624i	$0.766455\pi$
$972$		0			0
$973$	−20.4153	−	27.2717i	−0.654485	−	0.874290i
$974$		0			0
$975$	6.09422	+	53.5450i	0.195171	+	1.71481i
$976$		0			0
$977$	12.5322	−	33.6002i	0.400941	−	1.07496i	−0.566985	−	0.823728i	$-0.691890\pi$
$977$	12.5322	−	33.6002i	0.400941	−	1.07496i	0.967926	−	0.251236i	$-0.0808370\pi$
$978$		0			0
$979$	−6.70035	+	0.963365i	−0.214144	+	0.0307893i
$980$		0			0
$981$	−1.84101	−	6.26992i	−0.0587791	−	0.200183i
$982$		0			0
$983$	2.71007	+	37.8918i	0.0864379	+	1.20856i	0.836791	+	0.547523i	$0.184429\pi$
$983$	2.71007	+	37.8918i	0.0864379	+	1.20856i	−0.750353	+	0.661037i	$0.770116\pi$
$984$		0			0
$985$	−43.0516	+	11.9549i	−1.37174	+	0.380914i
$986$		0			0
$987$	59.1775	−	22.0721i	1.88364	−	0.702562i
$988$		0			0
$989$	−1.86097	−	2.37701i	−0.0591753	−	0.0755846i
$990$		0			0
$991$	−7.43457	+	16.2794i	−0.236167	+	0.517134i	−0.990192	−	0.139712i	$-0.955382\pi$
$991$	−7.43457	+	16.2794i	−0.236167	+	0.517134i	0.754025	+	0.656845i	$0.228110\pi$
$992$		0			0
$993$	−2.71131	+	37.9091i	−0.0860410	+	1.20301i
$994$		0			0
$995$	−0.436999	+	1.12091i	−0.0138538	+	0.0355352i
$996$		0			0
$997$	−15.4270	+	28.2524i	−0.488576	+	0.894761i	0.510809	+	0.859695i	$0.329346\pi$
$997$	−15.4270	+	28.2524i	−0.488576	+	0.894761i	−0.999385	+	0.0350665i	$0.988836\pi$
$998$		0			0
$999$	0.902829	+	6.27932i	0.0285643	+	0.198669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.753.29	yes	720
5.2	odd	4	inner	920.2.bv.a.17.29	✓	720
23.19	odd	22	inner	920.2.bv.a.433.29	yes	720
115.42	even	44	inner	920.2.bv.a.617.29	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.29	✓	720	5.2	odd	4	inner
920.2.bv.a.433.29	yes	720	23.19	odd	22	inner
920.2.bv.a.617.29	yes	720	115.42	even	44	inner
920.2.bv.a.753.29	yes	720	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939627 + 1.72080i) q^{3} +(1.36626 - 1.77012i) q^{5} +(2.23600 - 1.67385i) q^{7} +(-0.456326 + 0.710057i) q^{9} +O(q^{10})\)	\(q+(0.939627 + 1.72080i) q^{3} +(1.36626 - 1.77012i) q^{5} +(2.23600 - 1.67385i) q^{7} +(-0.456326 + 0.710057i) q^{9} +(-0.591468 + 0.270114i) q^{11} +(-3.29441 + 4.40081i) q^{13} +(4.32980 + 0.687798i) q^{15} +(4.09681 - 0.293010i) q^{17} +(2.14676 + 2.47750i) q^{19} +(4.98136 + 2.27491i) q^{21} +(-0.785024 - 4.73115i) q^{23} +(-1.26668 - 4.83689i) q^{25} +(4.21624 + 0.301552i) q^{27} +(-2.25352 - 1.95268i) q^{29} +(9.90163 - 2.90738i) q^{31} +(-1.02057 - 0.763990i) q^{33} +(0.0920327 - 6.24490i) q^{35} +(0.319017 + 1.46650i) q^{37} +(-10.6684 - 1.53389i) q^{39} +(-9.11200 + 5.85593i) q^{41} +(0.552474 - 0.301674i) q^{43} +(0.633430 + 1.77788i) q^{45} +(8.15536 - 8.15536i) q^{47} +(0.225797 - 0.768995i) q^{49} +(4.35369 + 6.77447i) q^{51} +(5.55216 + 7.41682i) q^{53} +(-0.329962 + 1.41602i) q^{55} +(-2.24612 + 6.02207i) q^{57} +(-7.78341 + 1.11909i) q^{59} +(-0.423373 - 1.44188i) q^{61} +(0.168183 + 2.35151i) q^{63} +(3.28897 + 11.8442i) q^{65} +(-8.75398 + 3.26507i) q^{67} +(7.40372 - 5.79638i) q^{69} +(-0.818740 + 1.79279i) q^{71} +(0.0272145 - 0.380508i) q^{73} +(7.13311 - 6.72457i) q^{75} +(-0.870391 + 1.59400i) q^{77} +(1.44106 + 10.0228i) q^{79} +(4.49468 + 9.84197i) q^{81} +(-1.86367 + 0.405417i) q^{83} +(5.07864 - 7.65219i) q^{85} +(1.24271 - 5.71264i) q^{87} +(9.98888 + 2.93300i) q^{89} +15.3545i q^{91} +(14.3069 + 14.3069i) q^{93} +(7.31851 - 0.415138i) q^{95} +(-17.5729 - 3.82275i) q^{97} +(0.0781056 - 0.543236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 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

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