LMFDB - Embedded newform 1080.2.bm.a.251.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(251,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("1080.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.20
Character	$\chi$	$=$	1080.251
Dual form			1080.2.bm.a.611.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17035 - 0.793896i) q^{2} +(0.739459 - 1.85828i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.97204 + 2.29326i) q^{7} +(-0.609850 - 2.76190i) q^{8} +O(q^{10})$	\(q+(1.17035 - 0.793896i) q^{2} +(0.739459 - 1.85828i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.97204 + 2.29326i) q^{7} +(-0.609850 - 2.76190i) q^{8} +(-1.27271 - 0.616609i) q^{10} +(4.08838 + 2.36043i) q^{11} +(-1.87107 + 1.08026i) q^{13} +(6.46930 - 0.469460i) q^{14} +(-2.90640 - 2.74824i) q^{16} +1.23675i q^{17} +4.35920 q^{19} +(-1.97905 + 0.288749i) q^{20} +(6.65878 - 0.483211i) q^{22} +(0.117833 + 0.204092i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.33220 + 2.74973i) q^{26} +(7.19867 - 5.68538i) q^{28} +(2.84210 - 4.92266i) q^{29} +(-4.06804 + 2.34868i) q^{31} +(-5.58334 - 0.909039i) q^{32} +(0.981854 + 1.44744i) q^{34} -4.58651i q^{35} -9.91926i q^{37} +(5.10181 - 3.46075i) q^{38} +(-2.08695 + 1.90910i) q^{40} +(-6.34052 + 3.66070i) q^{41} +(-2.62545 + 4.54741i) q^{43} +(7.40952 - 5.85191i) q^{44} +(0.299934 + 0.145313i) q^{46} +(1.05958 - 1.83524i) q^{47} +(7.01804 + 12.1556i) q^{49} +(0.102357 + 1.41050i) q^{50} +(0.623850 + 4.27578i) q^{52} -7.92028 q^{53} -4.72085i q^{55} +(3.91139 - 12.3689i) q^{56} +(-0.581815 - 8.01758i) q^{58} +(10.1979 - 5.88778i) q^{59} +(-6.27586 - 3.62337i) q^{61} +(-2.89644 + 5.97839i) q^{62} +(-7.25617 + 3.36869i) q^{64} +(1.87107 + 1.08026i) q^{65} +(-7.51856 - 13.0225i) q^{67} +(2.29823 + 0.914529i) q^{68} +(-3.64121 - 5.36784i) q^{70} +0.851441 q^{71} +10.6769 q^{73} +(-7.87486 - 11.6090i) q^{74} +(3.22345 - 8.10061i) q^{76} +(10.8261 + 18.7514i) q^{77} +(-10.0179 - 5.78381i) q^{79} +(-0.926848 + 3.89114i) q^{80} +(-4.51444 + 9.31802i) q^{82} +(2.35035 + 1.35698i) q^{83} +(1.07106 - 0.618377i) q^{85} +(0.537464 + 7.40641i) q^{86} +(4.02596 - 12.7312i) q^{88} +12.9321i q^{89} -9.90928 q^{91} +(0.466393 - 0.0680482i) q^{92} +(-0.216910 - 2.98908i) q^{94} +(-2.17960 - 3.77518i) q^{95} +(-0.816409 + 1.41406i) q^{97} +(17.8639 + 8.65477i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 - 6 * q^8	$ 48 q - 24 q^{5} - 6 q^{8} - 15 q^{14} - 12 q^{16} - 21 q^{22} - 24 q^{25} - 27 q^{34} + 27 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 24 q^{49} + 54 q^{52} - 21 q^{56} + 33 q^{58} + 36 q^{59} - 12 q^{61} + 42 q^{62} - 12 q^{64} - 51 q^{68} + 15 q^{70} - 54 q^{74} - 51 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} - 57 q^{88} + 9 q^{92} - 75 q^{94} + 42 q^{98}+O(q^{100}) $ 48 * q - 24 * q^5 - 6 * q^8 - 15 * q^14 - 12 * q^16 - 21 * q^22 - 24 * q^25 - 27 * q^34 + 27 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 24 * q^49 + 54 * q^52 - 21 * q^56 + 33 * q^58 + 36 * q^59 - 12 * q^61 + 42 * q^62 - 12 * q^64 - 51 * q^68 + 15 * q^70 - 54 * q^74 - 51 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 - 57 * q^88 + 9 * q^92 - 75 * q^94 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.17035	−	0.793896i	0.827566	−	0.561369i
$2$	1.17035	−	0.793896i	0.827566	−	0.561369i
$3$		0			0
$3$		0			0
$4$	0.739459	−	1.85828i	0.369730	−	0.929139i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	3.97204	+	2.29326i	1.50129	+	0.866769i	0.999999	+	0.00148944i	$0.000474104\pi$
$7$	3.97204	+	2.29326i	1.50129	+	0.866769i	0.501289	+	0.865280i	$0.332859\pi$
$8$	−0.609850	−	2.76190i	−0.215615	−	0.976479i
$9$		0			0
$10$	−1.27271	−	0.616609i	−0.402467	−	0.194989i
$11$	4.08838	+	2.36043i	1.23269	+	0.711695i	0.967590	−	0.252525i	$-0.0812610\pi$
$11$	4.08838	+	2.36043i	1.23269	+	0.711695i	0.265102	+	0.964220i	$0.414594\pi$
$12$		0			0
$13$	−1.87107	+	1.08026i	−0.518942	+	0.299611i	−0.736501	−	0.676436i	$-0.763524\pi$
$13$	−1.87107	+	1.08026i	−0.518942	+	0.299611i	0.217560	+	0.976047i	$0.430190\pi$
$14$	6.46930	−	0.469460i	1.72899	−	0.125468i
$15$		0			0
$16$	−2.90640	−	2.74824i	−0.726600	−	0.687061i
$17$			1.23675i			0.299957i	0.988689	+	0.149978i	$0.0479204\pi$
$17$			1.23675i			0.299957i	−0.988689	+	0.149978i	$0.952080\pi$
$18$		0			0
$19$	4.35920			1.00007			0.500034	−	0.866005i	$-0.333321\pi$
$19$	4.35920			1.00007			0.500034	+	0.866005i	$0.333321\pi$
$20$	−1.97905	+	0.288749i	−0.442528	+	0.0645662i
$21$		0			0
$22$	6.65878	−	0.483211i	1.41966	−	0.103021i
$23$	0.117833	+	0.204092i	0.0245698	+	0.0425562i	0.878049	−	0.478571i	$-0.158845\pi$
$23$	0.117833	+	0.204092i	0.0245698	+	0.0425562i	−0.853479	+	0.521127i	$0.825512\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.33220	+	2.74973i	−0.261266	+	0.539265i
$27$		0			0
$28$	7.19867	−	5.68538i	1.36042	−	1.07444i
$29$	2.84210	−	4.92266i	0.527764	−	0.914114i	−0.471712	−	0.881753i	$-0.656364\pi$
$29$	2.84210	−	4.92266i	0.527764	−	0.914114i	0.999476	−	0.0323617i	$-0.0103028\pi$
$30$		0			0
$31$	−4.06804	+	2.34868i	−0.730641	+	0.421836i	−0.818657	−	0.574283i	$-0.805281\pi$
$31$	−4.06804	+	2.34868i	−0.730641	+	0.421836i	0.0880155	+	0.996119i	$0.471947\pi$
$32$	−5.58334	−	0.909039i	−0.987004	−	0.160697i
$33$		0			0
$34$	0.981854	+	1.44744i	0.168387	+	0.248234i
$35$		−	4.58651i		−	0.775262i
$36$		0			0
$37$		−	9.91926i		−	1.63072i	−0.578957	−	0.815358i	$-0.696540\pi$
$37$		−	9.91926i		−	1.63072i	0.578957	−	0.815358i	$-0.303460\pi$
$38$	5.10181	−	3.46075i	0.827623	−	0.561408i
$39$		0			0
$40$	−2.08695	+	1.90910i	−0.329976	+	0.301854i
$41$	−6.34052	+	3.66070i	−0.990222	+	0.571705i	−0.905341	−	0.424686i	$-0.860384\pi$
$41$	−6.34052	+	3.66070i	−0.990222	+	0.571705i	−0.0848815	+	0.996391i	$0.527051\pi$
$42$		0			0
$43$	−2.62545	+	4.54741i	−0.400377	+	0.693473i	−0.993771	−	0.111439i	$-0.964454\pi$
$43$	−2.62545	+	4.54741i	−0.400377	+	0.693473i	0.593394	+	0.804912i	$0.297788\pi$
$44$	7.40952	−	5.85191i	1.11703	−	0.882208i
$45$		0			0
$46$	0.299934	+	0.145313i	0.0442229	+	0.0214253i
$47$	1.05958	−	1.83524i	0.154555	−	0.267698i	−0.778342	−	0.627841i	$-0.783939\pi$
$47$	1.05958	−	1.83524i	0.154555	−	0.267698i	0.932897	+	0.360143i	$0.117272\pi$
$48$		0			0
$49$	7.01804	+	12.1556i	1.00258	+	1.73652i
$50$	0.102357	+	1.41050i	0.0144754	+	0.199475i
$51$		0			0
$52$	0.623850	+	4.27578i	0.0865124	+	0.592944i
$53$	−7.92028			−1.08793			−0.543967	−	0.839107i	$-0.683078\pi$
$53$	−7.92028			−1.08793			−0.543967	+	0.839107i	$0.683078\pi$
$54$		0			0
$55$		−	4.72085i		−	0.636560i
$56$	3.91139	−	12.3689i	0.522682	−	1.65286i
$57$		0			0
$58$	−0.581815	−	8.01758i	−0.0763961	−	1.05276i
$59$	10.1979	−	5.88778i	1.32766	−	0.766524i	0.342722	−	0.939437i	$-0.388651\pi$
$59$	10.1979	−	5.88778i	1.32766	−	0.766524i	0.984937	+	0.172913i	$0.0553179\pi$
$60$		0			0
$61$	−6.27586	−	3.62337i	−0.803541	−	0.463925i	0.0411667	−	0.999152i	$-0.486893\pi$
$61$	−6.27586	−	3.62337i	−0.803541	−	0.463925i	−0.844708	+	0.535228i	$0.820226\pi$
$62$	−2.89644	+	5.97839i	−0.367848	+	0.759256i
$63$		0			0
$64$	−7.25617	+	3.36869i	−0.907021	+	0.421086i
$65$	1.87107	+	1.08026i	0.232078	+	0.133990i
$66$		0			0
$67$	−7.51856	−	13.0225i	−0.918538	−	1.59095i	−0.801637	−	0.597811i	$-0.796038\pi$
$67$	−7.51856	−	13.0225i	−0.918538	−	1.59095i	−0.116900	−	0.993144i	$-0.537296\pi$
$68$	2.29823	+	0.914529i	0.278702	+	0.110903i
$69$		0			0
$70$	−3.64121	−	5.36784i	−0.435208	−	0.641580i
$71$	0.851441			0.101047			0.0505237	−	0.998723i	$-0.483911\pi$
$71$	0.851441			0.101047			0.0505237	+	0.998723i	$0.483911\pi$
$72$		0			0
$73$	10.6769			1.24964			0.624819	−	0.780770i	$-0.285173\pi$
$73$	10.6769			1.24964			0.624819	+	0.780770i	$0.285173\pi$
$74$	−7.87486	−	11.6090i	−0.915434	−	1.34952i
$75$		0			0
$76$	3.22345	−	8.10061i	0.369755	−	0.929204i
$77$	10.8261	+	18.7514i	1.23375	+	2.13692i
$78$		0			0
$79$	−10.0179	−	5.78381i	−1.12710	−	0.650730i	−0.183894	−	0.982946i	$-0.558870\pi$
$79$	−10.0179	−	5.78381i	−1.12710	−	0.650730i	−0.943203	+	0.332217i	$0.892204\pi$
$80$	−0.926848	+	3.89114i	−0.103625	+	0.435042i
$81$		0			0
$82$	−4.51444	+	9.31802i	−0.498536	+	1.02900i
$83$	2.35035	+	1.35698i	0.257985	+	0.148948i	0.623415	−	0.781891i	$-0.285745\pi$
$83$	2.35035	+	1.35698i	0.257985	+	0.148948i	−0.365430	+	0.930839i	$0.619078\pi$
$84$		0			0
$85$	1.07106	−	0.618377i	0.116173	−	0.0670724i
$86$	0.537464	+	7.40641i	0.0579562	+	0.798654i
$87$		0			0
$88$	4.02596	−	12.7312i	0.429169	−	1.35715i
$89$			12.9321i			1.37080i	0.728166	+	0.685401i	$0.240373\pi$
$89$			12.9321i			1.37080i	−0.728166	+	0.685401i	$0.759627\pi$
$90$		0			0
$91$	−9.90928			−1.03877
$92$	0.466393	−	0.0680482i	0.0486248	−	0.00709451i
$93$		0			0
$94$	−0.216910	−	2.98908i	−0.0223725	−	0.308300i
$95$	−2.17960	−	3.77518i	−0.223622	−	0.387325i
$96$		0			0
$97$	−0.816409	+	1.41406i	−0.0828938	+	0.143576i	−0.904492	−	0.426491i	$-0.859750\pi$
$97$	−0.816409	+	1.41406i	−0.0828938	+	0.143576i	0.821598	+	0.570067i	$0.193083\pi$
$98$	17.8639	+	8.65477i	1.80452	+	0.874264i
$99$		0			0
$100$	1.23959	+	1.56953i	0.123959	+	0.156953i
$101$	1.28871	−	2.23211i	0.128231	−	0.222103i	−0.794760	−	0.606924i	$-0.792403\pi$
$101$	1.28871	−	2.23211i	0.128231	−	0.222103i	0.922991	+	0.384820i	$0.125737\pi$
$102$		0			0
$103$	−8.62567	+	4.98003i	−0.849913	+	0.490697i	−0.860621	−	0.509245i	$-0.829925\pi$
$103$	−8.62567	+	4.98003i	−0.849913	+	0.490697i	0.0107087	+	0.999943i	$0.496591\pi$
$104$	4.12465	+	4.50891i	0.404455	+	0.442135i
$105$		0			0
$106$	−9.26953	+	6.28788i	−0.900337	+	0.610733i
$107$			7.28403i			0.704173i	0.935967	+	0.352087i	$0.114528\pi$
$107$			7.28403i			0.704173i	−0.935967	+	0.352087i	$0.885472\pi$
$108$		0			0
$109$		−	2.56505i		−	0.245687i	−0.992426	−	0.122844i	$-0.960799\pi$
$109$		−	2.56505i		−	0.245687i	0.992426	−	0.122844i	$-0.0392014\pi$
$110$	−3.74786	−	5.52507i	−0.357345	−	0.526795i
$111$		0			0
$112$	−5.24190	−	17.5812i	−0.495313	−	1.66127i
$113$	−0.311444	+	0.179812i	−0.0292981	+	0.0169153i	−0.514578	−	0.857444i	$-0.672051\pi$
$113$	−0.311444	+	0.179812i	−0.0292981	+	0.0169153i	0.485279	+	0.874359i	$0.338718\pi$
$114$		0			0
$115$	0.117833	−	0.204092i	0.0109880	−	0.0190317i
$116$	−7.04605	−	8.92151i	−0.654210	−	0.828342i
$117$		0			0
$118$	7.26092	−	14.9869i	0.668422	−	1.37966i
$119$	−2.83619	+	4.91243i	−0.259993	+	0.450322i
$120$		0			0
$121$	5.64322	+	9.77435i	0.513020	+	0.888577i
$122$	−10.2216	+	0.741752i	−0.925416	+	0.0671550i
$123$		0			0
$124$	1.35636	+	9.29630i	0.121805	+	0.834833i
$125$	1.00000			0.0894427
$126$		0			0
$127$			9.02927i			0.801218i	0.916249	+	0.400609i	$0.131201\pi$
$127$			9.02927i			0.801218i	−0.916249	+	0.400609i	$0.868799\pi$
$128$	−5.81790	+	9.70320i	−0.514234	+	0.857650i
$129$		0			0
$130$	3.04743	−	0.221144i	0.267277	−	0.0193956i
$131$	0.986098	−	0.569324i	0.0861558	−	0.0497421i	−0.456303	−	0.889824i	$-0.650827\pi$
$131$	0.986098	−	0.569324i	0.0861558	−	0.0497421i	0.542459	+	0.840082i	$0.317493\pi$
$132$		0			0
$133$	17.3149	+	9.99676i	1.50139	+	0.866829i
$134$	−19.1379	−	9.27202i	−1.65326	−	0.800980i
$135$		0			0
$136$	3.41579	−	0.754235i	0.292902	−	0.0646751i
$137$	3.39260	+	1.95872i	0.289850	+	0.167345i	0.637874	−	0.770141i	$-0.279814\pi$
$137$	3.39260	+	1.95872i	0.289850	+	0.167345i	−0.348024	+	0.937485i	$0.613147\pi$
$138$		0			0
$139$	5.70435	+	9.88022i	0.483836	+	0.838029i	0.999828	−	0.0185646i	$-0.00590963\pi$
$139$	5.70435	+	9.88022i	0.483836	+	0.838029i	−0.515991	+	0.856594i	$0.672576\pi$
$140$	−8.52302	−	3.39154i	−0.720326	−	0.286637i
$141$		0			0
$142$	0.996487	−	0.675955i	0.0836234	−	0.0567249i
$143$	−10.1995			−0.852927
$144$		0			0
$145$	−5.68419			−0.472047
$146$	12.4958	−	8.47635i	1.03416	−	0.701508i
$147$		0			0
$148$	−18.4327	−	7.33489i	−1.51516	−	0.602924i
$149$	9.86802	+	17.0919i	0.808420	+	1.40022i	0.913958	+	0.405809i	$0.133010\pi$
$149$	9.86802	+	17.0919i	0.808420	+	1.40022i	−0.105538	+	0.994415i	$0.533656\pi$
$150$		0			0
$151$	−5.32377	−	3.07368i	−0.433243	−	0.250133i	0.267484	−	0.963562i	$-0.413808\pi$
$151$	−5.32377	−	3.07368i	−0.433243	−	0.250133i	−0.700727	+	0.713429i	$0.747141\pi$
$152$	−2.65846	−	12.0397i	−0.215630	−	0.976546i
$153$		0			0
$154$	27.5570	+	13.3510i	2.22061	+	1.07585i
$155$	4.06804	+	2.34868i	0.326753	+	0.188651i
$156$		0			0
$157$	−0.339511	+	0.196017i	−0.0270959	+	0.0156438i	−0.513487	−	0.858098i	$-0.671646\pi$
$157$	−0.339511	+	0.196017i	−0.0270959	+	0.0156438i	0.486391	+	0.873741i	$0.338313\pi$
$158$	−16.3162	+	1.18402i	−1.29805	+	0.0941958i
$159$		0			0
$160$	2.00442	+	5.28983i	0.158463	+	0.418198i
$161$			1.08088i			0.0851855i
$162$		0			0
$163$	−24.6306			−1.92922			−0.964609	−	0.263683i	$-0.915063\pi$
$163$	−24.6306			−1.92922			−0.964609	+	0.263683i	$0.915063\pi$
$164$	2.11405	+	14.4894i	0.165079	+	1.13143i
$165$		0			0
$166$	3.82805	−	0.277791i	0.297114	−	0.0215608i
$167$	−1.50486	−	2.60649i	−0.116450	−	0.201697i	0.801909	−	0.597447i	$-0.203818\pi$
$167$	−1.50486	−	2.60649i	−0.116450	−	0.201697i	−0.918358	+	0.395750i	$0.870485\pi$
$168$		0			0
$169$	−4.16606	+	7.21583i	−0.320466	+	0.555064i
$170$	0.762594	−	1.57403i	0.0584883	−	0.120723i
$171$		0			0
$172$	6.50894	+	8.24144i	0.496302	+	0.628404i
$173$	−4.98815	+	8.63974i	−0.379242	+	0.656867i	−0.990952	−	0.134215i	$-0.957149\pi$
$173$	−4.98815	+	8.63974i	−0.379242	+	0.656867i	0.611710	+	0.791082i	$0.290482\pi$
$174$		0			0
$175$	−3.97204	+	2.29326i	−0.300258	+	0.173354i
$176$	−5.39544	−	18.0962i	−0.406697	−	1.36405i
$177$		0			0
$178$	10.2668	+	15.1352i	0.769526	+	1.13443i
$179$		−	11.1600i		−	0.834136i	−0.908875	−	0.417068i	$-0.863058\pi$
$179$		−	11.1600i		−	0.834136i	0.908875	−	0.417068i	$-0.136942\pi$
$180$		0			0
$181$			4.80407i			0.357083i	0.983932	+	0.178542i	$0.0571379\pi$
$181$			4.80407i			0.357083i	−0.983932	+	0.178542i	$0.942862\pi$
$182$	−11.5974	+	7.86693i	−0.859654	+	0.583136i
$183$		0			0
$184$	0.491822	−	0.449908i	0.0362576	−	0.0331676i
$185$	−8.59033	+	4.95963i	−0.631574	+	0.364639i
$186$		0			0
$187$	−2.91927	+	5.05632i	−0.213478	+	0.369755i
$188$	−2.62688	−	3.32608i	−0.191585	−	0.242579i
$189$		0			0
$190$	−5.54800	−	2.68792i	−0.402494	−	0.195002i
$191$	0.143662	−	0.248830i	0.0103950	−	0.0180047i	−0.860781	−	0.508975i	$-0.830024\pi$
$191$	0.143662	−	0.248830i	0.0103950	−	0.0180047i	0.871176	+	0.490971i	$0.163358\pi$
$192$		0			0
$193$	1.19503	+	2.06986i	0.0860204	+	0.148992i	0.905826	−	0.423651i	$-0.139252\pi$
$193$	1.19503	+	2.06986i	0.0860204	+	0.148992i	−0.819805	+	0.572643i	$0.805918\pi$
$194$	0.167130	+	2.30310i	0.0119992	+	0.165353i
$195$		0			0
$196$	27.7781	−	4.05291i	1.98415	−	0.289493i
$197$	−10.8177			−0.770732			−0.385366	−	0.922764i	$-0.625925\pi$
$197$	−10.8177			−0.770732			−0.385366	+	0.922764i	$0.625925\pi$
$198$		0			0
$199$			5.10541i			0.361913i	0.983491	+	0.180957i	$0.0579193\pi$
$199$			5.10541i			0.361913i	−0.983491	+	0.180957i	$0.942081\pi$
$200$	2.69680	+	0.852803i	0.190693	+	0.0603023i
$201$		0			0
$202$	−0.263816	−	3.63546i	−0.0185620	−	0.255790i
$203$	22.5778	−	13.0353i	1.58465	−	0.914899i
$204$		0			0
$205$	6.34052	+	3.66070i	0.442841	+	0.255674i
$206$	−6.14147	+	12.6763i	−0.427896	+	0.883199i
$207$		0			0
$208$	8.40690	+	2.00248i	0.582914	+	0.138847i
$209$	17.8221	+	10.2896i	1.23278	+	0.711744i
$210$		0			0
$211$	0.491584	+	0.851449i	0.0338420	+	0.0586161i	0.882450	−	0.470406i	$-0.155892\pi$
$211$	0.491584	+	0.851449i	0.0338420	+	0.0586161i	−0.848608	+	0.529022i	$0.822559\pi$
$212$	−5.85672	+	14.7181i	−0.402241	+	1.01084i
$213$		0			0
$214$	5.78276	+	8.52489i	0.395301	+	0.582750i
$215$	5.25090			0.358108
$216$		0			0
$217$	−21.5445			−1.46254
$218$	−2.03638	−	3.00202i	−0.137921	−	0.203322i
$219$		0			0
$220$	−8.77266	−	3.49088i	−0.591453	−	0.235355i
$221$	−1.33602	−	2.31405i	−0.0898704	−	0.155660i
$222$		0			0
$223$	10.3531	+	5.97739i	0.693297	+	0.400275i	0.804846	−	0.593484i	$-0.202248\pi$
$223$	10.3531	+	5.97739i	0.693297	+	0.400275i	−0.111549	+	0.993759i	$0.535581\pi$
$224$	−20.0926	−	16.4148i	−1.34249	−	1.09676i
$225$		0			0
$226$	−0.221747	+	0.457698i	−0.0147504	+	0.0304456i
$227$	−17.0870	−	9.86519i	−1.13410	−	0.654775i	−0.189140	−	0.981950i	$-0.560570\pi$
$227$	−17.0870	−	9.86519i	−1.13410	−	0.654775i	−0.944964	+	0.327175i	$0.893903\pi$
$228$		0			0
$229$	−0.735791	+	0.424809i	−0.0486225	+	0.0280722i	−0.524114	−	0.851648i	$-0.675603\pi$
$229$	−0.735791	+	0.424809i	−0.0486225	+	0.0280722i	0.475492	+	0.879720i	$0.342270\pi$
$230$	−0.0241219	−	0.332407i	−0.00159055	−	0.0219183i
$231$		0			0
$232$	−15.3291	−	4.84750i	−1.00641	−	0.318254i
$233$		−	26.9773i		−	1.76734i	−0.468111	−	0.883670i	$-0.655065\pi$
$233$		−	26.9773i		−	1.76734i	0.468111	−	0.883670i	$-0.344935\pi$
$234$		0			0
$235$	−2.11916			−0.138239
$236$	−3.40018	−	23.3044i	−0.221333	−	1.51699i
$237$		0			0
$238$	0.580607	+	8.00093i	0.0376351	+	0.518623i
$239$	−6.98946	−	12.1061i	−0.452111	−	0.783079i	0.546406	−	0.837520i	$-0.315995\pi$
$239$	−6.98946	−	12.1061i	−0.452111	−	0.783079i	−0.998517	+	0.0544415i	$0.982662\pi$
$240$		0			0
$241$	7.14583	−	12.3769i	0.460303	−	0.797269i	−0.538673	−	0.842515i	$-0.681074\pi$
$241$	7.14583	−	12.3769i	0.460303	−	0.797269i	0.998976	+	0.0452465i	$0.0144073\pi$
$242$	14.3644	+	6.95932i	0.923378	+	0.447362i
$243$		0			0
$244$	−11.3740	+	8.98296i	−0.728144	+	0.575075i
$245$	7.01804	−	12.1556i	0.448366	−	0.776593i
$246$		0			0
$247$	−8.15637	+	4.70908i	−0.518977	+	0.299632i
$248$	8.96772	+	9.80316i	0.569451	+	0.622501i
$249$		0			0
$250$	1.17035	−	0.793896i	0.0740197	−	0.0502104i
$251$		−	9.70630i		−	0.612656i	−0.951926	−	0.306328i	$-0.900900\pi$
$251$		−	9.70630i		−	0.612656i	0.951926	−	0.306328i	$-0.0991004\pi$
$252$		0			0
$253$			1.11254i			0.0699449i
$254$	7.16830	+	10.5675i	0.449779	+	0.663061i
$255$		0			0
$256$	0.894327	+	15.9750i	0.0558954	+	0.998437i
$257$	−16.4543	+	9.49991i	−1.02639	+	0.592588i	−0.915949	−	0.401294i	$-0.868561\pi$
$257$	−16.4543	+	9.49991i	−1.02639	+	0.592588i	−0.110444	+	0.993882i	$0.535227\pi$
$258$		0			0
$259$	22.7474	−	39.3996i	1.41345	−	2.44817i
$260$	3.39101	−	2.67816i	0.210301	−	0.166092i
$261$		0			0
$262$	0.702100	−	1.44917i	0.0433759	−	0.0895300i
$263$	−12.6788	+	21.9603i	−0.781806	+	1.35413i	0.149083	+	0.988825i	$0.452368\pi$
$263$	−12.6788	+	21.9603i	−0.781806	+	1.35413i	−0.930889	+	0.365303i	$0.880965\pi$
$264$		0			0
$265$	3.96014	+	6.85916i	0.243269	+	0.421355i
$266$	28.2009	−	2.04647i	1.72911	−	0.125477i
$267$		0			0
$268$	−29.7591	+	4.34195i	−1.81783	+	0.265227i
$269$	10.6387			0.648652			0.324326	−	0.945945i	$-0.394862\pi$
$269$	10.6387			0.648652			0.324326	+	0.945945i	$0.394862\pi$
$270$		0			0
$271$		−	22.9127i		−	1.39185i	−0.718115	−	0.695924i	$-0.754995\pi$
$271$		−	22.9127i		−	1.39185i	0.718115	−	0.695924i	$-0.245005\pi$
$272$	3.39890	−	3.59450i	0.206089	−	0.217949i
$273$		0			0
$274$	5.52557	−	0.400976i	0.333812	−	0.0242239i
$275$	−4.08838	+	2.36043i	−0.246538	+	0.142339i
$276$		0			0
$277$	−13.2767	−	7.66533i	−0.797722	−	0.460565i	0.0449517	−	0.998989i	$-0.485687\pi$
$277$	−13.2767	−	7.66533i	−0.797722	−	0.460565i	−0.842674	+	0.538424i	$0.819020\pi$
$278$	14.5200	+	7.03470i	0.870850	+	0.421913i
$279$		0			0
$280$	−12.6675	+	2.79709i	−0.757027	+	0.167158i
$281$	9.30426	+	5.37182i	0.555046	+	0.320456i	0.751155	−	0.660126i	$-0.229497\pi$
$281$	9.30426	+	5.37182i	0.555046	+	0.320456i	−0.196109	+	0.980582i	$0.562831\pi$
$282$		0			0
$283$	8.88802	+	15.3945i	0.528338	+	0.915108i	0.999454	+	0.0330371i	$0.0105180\pi$
$283$	8.88802	+	15.3945i	0.528338	+	0.915108i	−0.471116	+	0.882071i	$0.656149\pi$
$284$	0.629606	−	1.58221i	0.0373602	−	0.0938871i
$285$		0			0
$286$	−11.9371	+	8.09736i	−0.705853	+	0.478807i
$287$	−33.5797			−1.98215
$288$		0			0
$289$	15.4704			0.910026
$290$	−6.65252	+	4.51266i	−0.390650	+	0.264992i
$291$		0			0
$292$	7.89514	−	19.8407i	0.462028	−	1.16109i
$293$	−13.9870	−	24.2262i	−0.817129	−	1.41531i	−0.907789	−	0.419428i	$-0.862231\pi$
$293$	−13.9870	−	24.2262i	−0.817129	−	1.41531i	0.0906593	−	0.995882i	$-0.471103\pi$
$294$		0			0
$295$	−10.1979	−	5.88778i	−0.593747	−	0.342800i
$296$	−27.3960	+	6.04926i	−1.59236	+	0.351606i
$297$		0			0
$298$	25.1183	+	12.1694i	1.45506	+	0.704955i
$299$	−0.440947	−	0.254581i	−0.0255006	−	0.0147228i
$300$		0			0
$301$	−20.8567	+	12.0416i	−1.20216	+	0.694069i
$302$	−8.67089	+	0.629224i	−0.498953	+	0.0362078i
$303$		0			0
$304$	−12.6696	−	11.9801i	−0.726650	−	0.687108i
$305$			7.24674i			0.414947i
$306$		0			0
$307$	15.3914			0.878434			0.439217	−	0.898381i	$-0.355256\pi$
$307$	15.3914			0.878434			0.439217	+	0.898381i	$0.355256\pi$
$308$	42.8508	−	6.25206i	2.44165	−	0.356244i
$309$		0			0
$310$	6.62566	−	0.480807i	0.376312	−	0.0273080i
$311$	9.87577	+	17.1053i	0.560004	+	0.969955i	0.997495	+	0.0707323i	$0.0225336\pi$
$311$	9.87577	+	17.1053i	0.560004	+	0.969955i	−0.437492	+	0.899222i	$0.644133\pi$
$312$		0			0
$313$	−8.85105	+	15.3305i	−0.500291	+	0.866529i	0.499709	+	0.866193i	$0.333440\pi$
$313$	−8.85105	+	15.3305i	−0.500291	+	0.866529i	−1.00000		0.000335911i	$0.999893\pi$
$314$	−0.241731	+	0.498945i	−0.0136417	+	0.0281571i
$315$		0			0
$316$	−18.1557	+	14.3391i	−1.02134	+	0.806636i
$317$	2.67910	−	4.64033i	0.150473	−	0.260627i	−0.780928	−	0.624621i	$-0.785254\pi$
$317$	2.67910	−	4.64033i	0.150473	−	0.260627i	0.931401	+	0.363994i	$0.118587\pi$
$318$		0			0
$319$	23.2391	−	13.4171i	1.30114	−	0.751214i
$320$	6.54545	+	4.59968i	0.365902	+	0.257130i
$321$		0			0
$322$	0.858108	+	1.26502i	0.0478205	+	0.0704966i
$323$			5.39126i			0.299978i
$324$		0			0
$325$		−	2.16053i		−	0.119844i
$326$	−28.8265	+	19.5541i	−1.59655	+	1.08300i
$327$		0			0
$328$	13.9772	+	15.2794i	0.771764	+	0.843663i
$329$	8.41736	−	4.85977i	0.464064	−	0.267928i
$330$		0			0
$331$	12.9222	−	22.3818i	0.710266	−	1.23022i	−0.254491	−	0.967075i	$-0.581908\pi$
$331$	12.9222	−	22.3818i	0.710266	−	1.23022i	0.964757	−	0.263142i	$-0.0847587\pi$
$332$	4.25963	−	3.36418i	0.233778	−	0.184634i
$333$		0			0
$334$	−3.83050	−	1.85582i	−0.209596	−	0.101546i
$335$	−7.51856	+	13.0225i	−0.410783	+	0.711496i
$336$		0			0
$337$	8.23294	+	14.2599i	0.448477	+	0.776784i	0.998287	−	0.0585051i	$-0.0186334\pi$
$337$	8.23294	+	14.2599i	0.448477	+	0.776784i	−0.549810	+	0.835289i	$0.685300\pi$
$338$	0.852849	+	11.7525i	0.0463889	+	0.639252i
$339$		0			0
$340$	−0.357112	−	2.44759i	−0.0193671	−	0.132739i
$341$	−22.1756			−1.20087
$342$		0			0
$343$			32.2711i			1.74247i
$344$	14.1606	+	4.47798i	0.763489	+	0.241437i
$345$		0			0
$346$	1.02114	+	14.0716i	0.0548969	+	0.756495i
$347$	−13.0391	+	7.52814i	−0.699976	+	0.404132i	−0.807339	−	0.590088i	$-0.799093\pi$
$347$	−13.0391	+	7.52814i	−0.699976	+	0.404132i	0.107362	+	0.994220i	$0.465760\pi$
$348$		0			0
$349$	7.00796	+	4.04605i	0.375128	+	0.216580i	0.675696	−	0.737180i	$-0.263843\pi$
$349$	7.00796	+	4.04605i	0.375128	+	0.216580i	−0.300569	+	0.953760i	$0.597176\pi$
$350$	−2.82808	+	5.83730i	−0.151167	+	0.312017i
$351$		0			0
$352$	−20.6811	−	16.8955i	−1.10230	−	0.900536i
$353$	−8.16936	−	4.71658i	−0.434811	−	0.251038i	0.266583	−	0.963812i	$-0.414105\pi$
$353$	−8.16936	−	4.71658i	−0.434811	−	0.251038i	−0.701394	+	0.712774i	$0.747439\pi$
$354$		0			0
$355$	−0.425720	−	0.737369i	−0.0225949	−	0.0391355i
$356$	24.0315	+	9.56277i	1.27367	+	0.506826i
$357$		0			0
$358$	−8.85986	−	13.0611i	−0.468258	−	0.690302i
$359$	28.9175			1.52621			0.763103	−	0.646277i	$-0.223675\pi$
$359$	28.9175			1.52621			0.763103	+	0.646277i	$0.223675\pi$
$360$		0			0
$361$	0.00262185			0.000137992
$362$	3.81393	+	5.62246i	0.200456	+	0.295510i
$363$		0			0
$364$	−7.32750	+	18.4142i	−0.384066	+	0.965166i
$365$	−5.33845	−	9.24648i	−0.279428	−	0.483983i
$366$		0			0
$367$	27.0895	+	15.6401i	1.41406	+	0.816407i	0.995768	−	0.0919062i	$-0.0292960\pi$
$367$	27.0895	+	15.6401i	1.41406	+	0.816407i	0.418291	+	0.908313i	$0.362629\pi$
$368$	0.218426	−	0.917007i	0.0113862	−	0.0478023i
$369$		0			0
$370$	−6.11630	+	12.6244i	−0.317971	+	0.656309i
$371$	−31.4596	−	18.1632i	−1.63330	−	0.942988i
$372$		0			0
$373$	17.8238	−	10.2906i	0.922882	−	0.532826i	0.0383285	−	0.999265i	$-0.487797\pi$
$373$	17.8238	−	10.2906i	0.922882	−	0.532826i	0.884553	+	0.466439i	$0.154463\pi$
$374$	0.597613	+	8.23528i	0.0309018	+	0.425836i
$375$		0			0
$376$	−5.71494	−	1.80722i	−0.294726	−	0.0932004i
$377$			12.2808i			0.632496i
$378$		0			0
$379$	1.15098			0.0591219			0.0295609	−	0.999563i	$-0.490589\pi$
$379$	1.15098			0.0591219			0.0295609	+	0.999563i	$0.490589\pi$
$380$	−8.62706	+	1.25871i	−0.442559	+	0.0645707i
$381$		0			0
$382$	−0.0294096	−	0.405273i	−0.00150473	−	0.0207356i
$383$	0.0240645	+	0.0416809i	0.00122964	+	0.00212979i	0.866640	−	0.498935i	$-0.166275\pi$
$383$	0.0240645	+	0.0416809i	0.00122964	+	0.00212979i	−0.865410	+	0.501065i	$0.832942\pi$
$384$		0			0
$385$	10.8261	−	18.7514i	0.551750	−	0.955659i
$386$	3.04186	+	1.47374i	0.154827	+	0.0750112i
$387$		0			0
$388$	2.02402	+	2.56276i	0.102754	+	0.130104i
$389$	10.1379	−	17.5594i	0.514012	−	0.890294i	−0.485856	−	0.874039i	$-0.661492\pi$
$389$	10.1379	−	17.5594i	0.514012	−	0.890294i	0.999868	−	0.0162556i	$-0.00517455\pi$
$390$		0			0
$391$	−0.252412	+	0.145730i	−0.0127650	+	0.00736989i
$392$	29.2926	−	26.7962i	1.47950	−	1.35341i
$393$		0			0
$394$	−12.6606	+	8.58815i	−0.637831	+	0.432665i
$395$			11.5676i			0.582030i
$396$		0			0
$397$			16.5809i			0.832169i	0.909326	+	0.416085i	$0.136598\pi$
$397$			16.5809i			0.832169i	−0.909326	+	0.416085i	$0.863402\pi$
$398$	4.05316	+	5.97514i	0.203167	+	0.299507i
$399$		0			0
$400$	3.83325	−	1.14290i	0.191662	−	0.0571448i
$401$	−18.1229	+	10.4632i	−0.905013	+	0.522510i	−0.878823	−	0.477147i	$-0.841671\pi$
$401$	−18.1229	+	10.4632i	−0.905013	+	0.522510i	−0.0261899	+	0.999657i	$0.508337\pi$
$402$		0			0
$403$	5.07439	−	8.78910i	0.252773	−	0.437816i
$404$	−3.19494	−	4.04534i	−0.158954	−	0.201263i
$405$		0			0
$406$	16.0754	−	33.1804i	0.797807	−	1.64671i
$407$	23.4137	−	40.5537i	1.16057	−	2.01017i
$408$		0			0
$409$	−8.62868	−	14.9453i	−0.426661	−	0.738998i	0.569913	−	0.821705i	$-0.306977\pi$
$409$	−8.62868	−	14.9453i	−0.426661	−	0.738998i	−0.996574	+	0.0827069i	$0.973643\pi$
$410$	10.3269	−	0.749394i	0.510007	−	0.0370099i
$411$		0			0
$412$	2.87596	+	19.7114i	0.141688	+	0.971113i
$413$	54.0088			2.65760
$414$		0			0
$415$		−	2.71396i		−	0.133223i
$416$	11.4288	−	4.33060i	0.560344	−	0.212325i
$417$		0			0
$418$	29.0270	−	2.10641i	1.41976	−	0.103028i
$419$	12.4910	−	7.21167i	0.610224	−	0.352313i	−0.162829	−	0.986654i	$-0.552062\pi$
$419$	12.4910	−	7.21167i	0.610224	−	0.352313i	0.773053	+	0.634341i	$0.218729\pi$
$420$		0			0
$421$	23.2632	+	13.4310i	1.13378	+	0.654588i	0.944883	−	0.327409i	$-0.106175\pi$
$421$	23.2632	+	13.4310i	1.13378	+	0.654588i	0.188897	+	0.981997i	$0.439509\pi$
$422$	1.25129	+	0.606230i	0.0609118	+	0.0295108i
$423$		0			0
$424$	4.83019	+	21.8750i	0.234575	+	1.06234i
$425$	−1.07106	−	0.618377i	−0.0519541	−	0.0299957i
$426$		0			0
$427$	−16.6186	−	28.7843i	−0.804231	−	1.39297i
$428$	13.5358	+	5.38624i	0.654275	+	0.260354i
$429$		0			0
$430$	6.14541	−	4.16866i	0.296358	−	0.201031i
$431$	12.6429			0.608988			0.304494	−	0.952514i	$-0.401513\pi$
$431$	12.6429			0.608988			0.304494	+	0.952514i	$0.401513\pi$
$432$		0			0
$433$	−28.3673			−1.36324			−0.681622	−	0.731705i	$-0.738725\pi$
$433$	−28.3673			−1.36324			−0.681622	+	0.731705i	$0.738725\pi$
$434$	−25.2147	+	17.1041i	−1.21035	+	0.821023i
$435$		0			0
$436$	−4.76658	−	1.89675i	−0.228278	−	0.0908378i
$437$	0.513656	+	0.889679i	0.0245715	+	0.0425591i
$438$		0			0
$439$	−1.62013	−	0.935382i	−0.0773246	−	0.0446434i	0.460839	−	0.887484i	$-0.347548\pi$
$439$	−1.62013	−	0.935382i	−0.0773246	−	0.0446434i	−0.538164	+	0.842840i	$0.680882\pi$
$440$	−13.0385	+	2.87901i	−0.621587	+	0.137252i
$441$		0			0
$442$	−3.40073	−	1.64760i	−0.161756	−	0.0783685i
$443$	−32.9508	−	19.0242i	−1.56554	−	0.903866i	−0.996679	−	0.0814332i	$-0.974050\pi$
$443$	−32.9508	−	19.0242i	−1.56554	−	0.903866i	−0.568863	−	0.822433i	$-0.692616\pi$
$444$		0			0
$445$	11.1995	−	6.46606i	0.530909	−	0.306521i
$446$	16.8623	−	1.22365i	0.798451	−	0.0579415i
$447$		0			0
$448$	−36.5470	−	3.25969i	−1.72668	−	0.154006i
$449$		−	4.53199i		−	0.213878i	−0.994266	−	0.106939i	$-0.965895\pi$
$449$		−	4.53199i		−	0.213878i	0.994266	−	0.106939i	$-0.0341049\pi$
$450$		0			0
$451$	−34.5632			−1.62752
$452$	0.103841	+	0.711713i	0.00488427	+	0.0334761i
$453$		0			0
$454$	−27.8298	+	2.01953i	−1.30612	+	0.0947815i
$455$	4.95464	+	8.58169i	0.232277	+	0.402316i
$456$		0			0
$457$	6.38333	−	11.0562i	0.298599	−	0.517189i	−0.677216	−	0.735784i	$-0.736814\pi$
$457$	6.38333	−	11.0562i	0.298599	−	0.517189i	0.975816	+	0.218595i	$0.0701472\pi$
$458$	−0.523882	+	1.08132i	−0.0244794	+	0.0505267i
$459$		0			0
$460$	−0.292128	−	0.369884i	−0.0136205	−	0.0172459i
$461$	−17.8836	+	30.9753i	−0.832923	+	1.44266i	0.0627876	+	0.998027i	$0.480001\pi$
$461$	−17.8836	+	30.9753i	−0.832923	+	1.44266i	−0.895710	+	0.444638i	$0.853332\pi$
$462$		0			0
$463$	−27.6653	+	15.9726i	−1.28572	+	0.742309i	−0.977887	−	0.209133i	$-0.932936\pi$
$463$	−27.6653	+	15.9726i	−1.28572	+	0.742309i	−0.307829	+	0.951442i	$0.599602\pi$
$464$	−21.7889	+	6.49644i	−1.01153	+	0.301590i
$465$		0			0
$466$	−21.4171	−	31.5730i	−0.992130	−	1.46259i
$467$			0.817062i			0.0378091i	0.999821	+	0.0189046i	$0.00601787\pi$
$467$			0.817062i			0.0378091i	−0.999821	+	0.0189046i	$0.993982\pi$
$468$		0			0
$469$		−	68.9679i		−	3.18464i
$470$	−2.48016	+	1.68239i	−0.114401	+	0.0776028i
$471$		0			0
$472$	−22.4807	−	24.5750i	−1.03476	−	1.13116i
$473$	−21.4676	+	12.3944i	−0.987083	+	0.569893i
$474$		0			0
$475$	−2.17960	+	3.77518i	−0.100007	+	0.173217i
$476$	7.03142	+	8.90298i	0.322285	+	0.408067i
$477$		0			0
$478$	−17.7911	−	8.61953i	−0.813748	−	0.394248i
$479$	17.3720	−	30.0891i	0.793746	−	1.37481i	−0.129887	−	0.991529i	$-0.541461\pi$
$479$	17.3720	−	30.0891i	0.793746	−	1.37481i	0.923633	−	0.383279i	$-0.125205\pi$
$480$		0			0
$481$	10.7154	+	18.5596i	0.488581	+	0.846246i
$482$	−1.46285	−	20.1584i	−0.0666308	−	0.918192i
$483$		0			0
$484$	22.3364	−	3.25895i	1.01529	−	0.148134i
$485$	1.63282			0.0741425
$486$		0			0
$487$		−	39.8130i		−	1.80410i	−0.431630	−	0.902051i	$-0.642061\pi$
$487$		−	39.8130i		−	1.80410i	0.431630	−	0.902051i	$-0.357939\pi$
$488$	−6.18004	+	19.5430i	−0.279757	+	0.884670i
$489$		0			0
$490$	−1.43669	−	19.7980i	−0.0649029	−	0.894381i
$491$	21.9098	−	12.6496i	0.988775	−	0.570870i	0.0838674	−	0.996477i	$-0.473273\pi$
$491$	21.9098	−	12.6496i	0.988775	−	0.570870i	0.904908	+	0.425607i	$0.139939\pi$
$492$		0			0
$493$	6.08812	+	3.51498i	0.274195	+	0.158307i
$494$	−5.80732	+	11.9866i	−0.261284	+	0.539303i
$495$		0			0
$496$	18.2781	+	4.35374i	0.820711	+	0.195489i
$497$	3.38195	+	1.95257i	0.151701	+	0.0875848i
$498$		0			0
$499$	5.75232	+	9.96331i	0.257509	+	0.446019i	0.965574	−	0.260128i	$-0.0837649\pi$
$499$	5.75232	+	9.96331i	0.257509	+	0.446019i	−0.708065	+	0.706147i	$0.750432\pi$
$500$	0.739459	−	1.85828i	0.0330696	−	0.0831048i
$501$		0			0
$502$	−7.70579	−	11.3598i	−0.343926	−	0.507013i
$503$	−16.2502			−0.724561			−0.362281	−	0.932069i	$-0.618002\pi$
$503$	−16.2502			−0.724561			−0.362281	+	0.932069i	$0.618002\pi$
$504$		0			0
$505$	−2.57742			−0.114694
$506$	0.883242	+	1.30207i	0.0392649	+	0.0578840i
$507$		0			0
$508$	16.7789	+	6.67678i	0.744444	+	0.296234i
$509$	−2.87628	−	4.98186i	−0.127489	−	0.220817i	0.795214	−	0.606328i	$-0.207358\pi$
$509$	−2.87628	−	4.98186i	−0.127489	−	0.220817i	−0.922703	+	0.385512i	$0.874025\pi$
$510$		0			0
$511$	42.4091	+	24.4849i	1.87607	+	1.08315i
$512$	13.7292	+	17.9864i	0.606749	+	0.794894i
$513$		0			0
$514$	−11.7155	+	24.1813i	−0.516747	+	1.06659i
$515$	8.62567	+	4.98003i	0.380093	+	0.219447i
$516$		0			0
$517$	8.66391	−	5.00211i	0.381038	−	0.219993i
$518$	−4.65669	−	64.1706i	−0.204603	−	2.81949i
$519$		0			0
$520$	1.84250	−	5.82650i	0.0807991	−	0.255509i
$521$		−	30.4544i		−	1.33423i	−0.744953	−	0.667117i	$-0.767528\pi$
$521$		−	30.4544i		−	1.33423i	0.744953	−	0.667117i	$-0.232472\pi$
$522$		0			0
$523$	18.7457			0.819694			0.409847	−	0.912154i	$-0.365582\pi$
$523$	18.7457			0.819694			0.409847	+	0.912154i	$0.365582\pi$
$524$	−0.328783	−	2.25344i	−0.0143630	−	0.0984418i
$525$		0			0
$526$	2.59551	+	35.7669i	0.113170	+	1.55951i
$527$	−2.90474	−	5.03116i	−0.126533	−	0.219161i
$528$		0			0
$529$	11.4722	−	19.8705i	0.498793	−	0.863934i
$530$	10.0802	+	4.88371i	0.437857	+	0.212135i
$531$		0			0
$532$	31.3804	−	24.7837i	1.36051	−	1.07451i
$533$	7.90903	−	13.6988i	0.342578	−	0.593363i
$534$		0			0
$535$	6.30815	−	3.64201i	0.272725	−	0.157458i
$536$	−31.3817	+	28.7073i	−1.35548	+	1.23997i
$537$		0			0
$538$	12.4510	−	8.44601i	0.536802	−	0.364133i
$539$			66.2623i			2.85412i
$540$		0			0
$541$			28.8219i			1.23915i	0.784938	+	0.619575i	$0.212695\pi$
$541$			28.8219i			1.23915i	−0.784938	+	0.619575i	$0.787305\pi$
$542$	−18.1903	−	26.8160i	−0.781341	−	1.15185i
$543$		0			0
$544$	1.12426	−	6.90521i	0.0482021	−	0.296059i
$545$	−2.22140	+	1.28253i	−0.0951543	+	0.0549373i
$546$		0			0
$547$	−8.43142	+	14.6036i	−0.360502	+	0.624407i	−0.988043	−	0.154176i	$-0.950728\pi$
$547$	−8.43142	+	14.6036i	−0.360502	+	0.624407i	0.627542	+	0.778583i	$0.284061\pi$
$548$	6.14854	−	4.85601i	0.262653	−	0.207438i
$549$		0			0
$550$	−2.91092	+	6.00828i	−0.124122	+	0.256194i
$551$	12.3893	−	21.4588i	0.527801	−	0.914177i
$552$		0			0
$553$	−26.5275	−	45.9470i	−1.12806	−	1.95387i
$554$	−21.6240	+	1.56920i	−0.918715	+	0.0666687i
$555$		0			0
$556$	22.5783	−	3.29425i	0.957535	−	0.139707i
$557$	−20.1743			−0.854811			−0.427406	−	0.904060i	$-0.640572\pi$
$557$	−20.1743			−0.854811			−0.427406	+	0.904060i	$0.640572\pi$
$558$		0			0
$559$		−	11.3447i		−	0.479830i
$560$	−12.6048	+	13.3302i	−0.532652	+	0.563305i
$561$		0			0
$562$	15.1539	−	1.09968i	0.639231	−	0.0463873i
$563$	−5.22595	+	3.01721i	−0.220248	+	0.127160i	−0.606065	−	0.795415i	$-0.707253\pi$
$563$	−5.22595	+	3.01721i	−0.220248	+	0.127160i	0.385817	+	0.922575i	$0.373920\pi$
$564$		0			0
$565$	0.311444	+	0.179812i	0.0131025	+	0.00756475i
$566$	22.6238	+	10.9609i	0.950948	+	0.460720i
$567$		0			0
$568$	−0.519251	−	2.35159i	−0.0217873	−	0.0986706i
$569$	−12.8303	−	7.40759i	−0.537875	−	0.310543i	0.206342	−	0.978480i	$-0.433844\pi$
$569$	−12.8303	−	7.40759i	−0.537875	−	0.310543i	−0.744217	+	0.667937i	$0.767177\pi$
$570$		0			0
$571$	−3.96582	−	6.86900i	−0.165964	−	0.287459i	0.771033	−	0.636795i	$-0.219740\pi$
$571$	−3.96582	−	6.86900i	−0.165964	−	0.287459i	−0.936997	+	0.349337i	$0.886407\pi$
$572$	−7.54213	+	18.9536i	−0.315352	+	0.792488i
$573$		0			0
$574$	−39.3001	+	26.6588i	−1.64036	+	1.11271i
$575$	−0.235665			−0.00982793
$576$		0			0
$577$	−9.19579			−0.382826			−0.191413	−	0.981510i	$-0.561307\pi$
$577$	−9.19579			−0.382826			−0.191413	+	0.981510i	$0.561307\pi$
$578$	18.1059	−	12.2819i	0.753106	−	0.510860i
$579$		0			0
$580$	−4.20323	+	10.5628i	−0.174530	+	0.438597i
$581$	6.22379	+	10.7799i	0.258207	+	0.447227i
$582$		0			0
$583$	−32.3811	−	18.6952i	−1.34109	−	0.774278i
$584$	−6.51132	−	29.4885i	−0.269440	−	1.22024i
$585$		0			0
$586$	−35.6028	−	17.2490i	−1.47074	−	0.712550i
$587$	−6.45327	−	3.72580i	−0.266355	−	0.153780i	0.360875	−	0.932614i	$-0.382478\pi$
$587$	−6.45327	−	3.72580i	−0.266355	−	0.153780i	−0.627230	+	0.778834i	$0.715811\pi$
$588$		0			0
$589$	−17.7334	+	10.2384i	−0.730692	+	0.421865i
$590$	−16.6095	+	1.20531i	−0.683802	+	0.0496217i
$591$		0			0
$592$	−27.2605	+	28.8293i	−1.12040	+	1.18488i
$593$		−	5.98713i		−	0.245862i	−0.992415	−	0.122931i	$-0.960771\pi$
$593$		−	5.98713i		−	0.245862i	0.992415	−	0.122931i	$-0.0392294\pi$
$594$		0			0
$595$	5.67239			0.232545
$596$	39.0585	−	5.69876i	1.59990	−	0.233430i
$597$		0			0
$598$	−0.718174	+	0.0521161i	−0.0293683	+	0.00213118i
$599$	−18.3740	−	31.8246i	−0.750740	−	1.30032i	−0.947465	−	0.319861i	$-0.896364\pi$
$599$	−18.3740	−	31.8246i	−0.750740	−	1.30032i	0.196725	−	0.980459i	$-0.436969\pi$
$600$		0			0
$601$	−5.67611	+	9.83130i	−0.231533	+	0.401027i	−0.958260	−	0.285900i	$-0.907708\pi$
$601$	−5.67611	+	9.83130i	−0.231533	+	0.401027i	0.726726	+	0.686927i	$0.241041\pi$
$602$	−14.8500	+	30.6511i	−0.605240	+	1.24924i
$603$		0			0
$604$	−9.64847	+	7.62019i	−0.392591	+	0.310061i
$605$	5.64322	−	9.77435i	0.229430	−	0.397384i
$606$		0			0
$607$	5.06707	−	2.92548i	0.205666	−	0.118741i	−0.393630	−	0.919269i	$-0.628781\pi$
$607$	5.06707	−	2.92548i	0.205666	−	0.118741i	0.599296	+	0.800528i	$0.295447\pi$
$608$	−24.3389	−	3.96268i	−0.987072	−	0.160708i
$609$		0			0
$610$	5.75315	+	8.48125i	0.232938	+	0.343396i
$611$			4.57849i			0.185226i
$612$		0			0
$613$			18.4132i			0.743703i	0.928292	+	0.371851i	$0.121277\pi$
$613$			18.4132i			0.743703i	−0.928292	+	0.371851i	$0.878723\pi$
$614$	18.0134	−	12.2192i	0.726962	−	0.493126i
$615$		0			0
$616$	45.1871	−	41.3362i	1.82064	−	1.66548i
$617$	−7.12123	+	4.11144i	−0.286690	+	0.165520i	−0.636448	−	0.771320i	$-0.719597\pi$
$617$	−7.12123	+	4.11144i	−0.286690	+	0.165520i	0.349758	+	0.936840i	$0.386264\pi$
$618$		0			0
$619$	−22.2663	+	38.5663i	−0.894957	+	1.55011i	−0.0610991	+	0.998132i	$0.519461\pi$
$619$	−22.2663	+	38.5663i	−0.894957	+	1.55011i	−0.833858	+	0.551979i	$0.813873\pi$
$620$	7.37266	−	5.82279i	0.296093	−	0.233849i
$621$		0			0
$622$	25.1380	+	12.1790i	1.00794	+	0.488332i
$623$	−29.6567	+	51.3668i	−1.18817	+	2.05797i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.81193	+	24.9689i	0.0724192	+	0.997958i
$627$		0			0
$628$	0.113199	+	0.775852i	0.00451714	+	0.0309599i
$629$	12.2677			0.489145
$630$		0			0
$631$		−	2.02785i		−	0.0807273i	−0.999185	−	0.0403637i	$-0.987148\pi$
$631$		−	2.02785i		−	0.0807273i	0.999185	−	0.0403637i	$-0.0128516\pi$
$632$	−9.86491	+	31.1956i	−0.392405	+	1.24089i
$633$		0			0
$634$	−0.548447	−	7.55775i	−0.0217816	−	0.300157i
$635$	7.81958	−	4.51464i	0.310311	−	0.179158i
$636$		0			0
$637$	−26.2625	−	15.1627i	−1.04056	−	0.600767i
$638$	16.5462	−	34.1522i	0.655071	−	1.35210i
$639$		0			0
$640$	11.3122	+	0.186847i	0.447153	+	0.00738577i
$641$	22.2376	+	12.8389i	0.878332	+	0.507105i	0.870108	−	0.492861i	$-0.164049\pi$
$641$	22.2376	+	12.8389i	0.878332	+	0.507105i	0.00822364	+	0.999966i	$0.497382\pi$
$642$		0			0
$643$	3.54072	+	6.13270i	0.139632	+	0.241850i	0.927357	−	0.374177i	$-0.122075\pi$
$643$	3.54072	+	6.13270i	0.139632	+	0.241850i	−0.787725	+	0.616027i	$0.788741\pi$
$644$	2.00858	+	0.799268i	0.0791492	+	0.0314956i
$645$		0			0
$646$	4.28010	+	6.30968i	0.168398	+	0.248251i
$647$	48.6780			1.91373			0.956865	−	0.290533i	$-0.0938325\pi$
$647$	48.6780			1.91373			0.956865	+	0.290533i	$0.0938325\pi$
$648$		0			0
$649$	55.5907			2.18213
$650$	−1.71523	−	2.52858i	−0.0672769	−	0.0991791i
$651$		0			0
$652$	−18.2133	+	45.7705i	−0.713289	+	1.79251i
$653$	1.32043	+	2.28705i	0.0516724	+	0.0894993i	0.890705	−	0.454582i	$-0.150211\pi$
$653$	1.32043	+	2.28705i	0.0516724	+	0.0894993i	−0.839032	+	0.544082i	$0.816878\pi$
$654$		0			0
$655$	−0.986098	−	0.569324i	−0.0385300	−	0.0222453i
$656$	28.4886	+	6.78582i	1.11229	+	0.264942i
$657$		0			0
$658$	5.99315	−	12.3702i	0.233637	−	0.482239i
$659$	−3.04662	−	1.75896i	−0.118679	−	0.0685195i	0.439485	−	0.898250i	$-0.355161\pi$
$659$	−3.04662	−	1.75896i	−0.118679	−	0.0685195i	−0.558165	+	0.829730i	$0.688494\pi$
$660$		0			0
$661$	3.44771	−	1.99053i	0.134100	−	0.0774228i	−0.431449	−	0.902137i	$-0.641998\pi$
$661$	3.44771	−	1.99053i	0.134100	−	0.0774228i	0.565549	+	0.824715i	$0.308664\pi$
$662$	−2.64534	−	36.4535i	−0.102814	−	1.41681i
$663$		0			0
$664$	2.31447	−	7.31899i	0.0898189	−	0.284032i
$665$		−	19.9935i		−	0.775315i
$666$		0			0
$667$	1.33957			0.0518683
$668$	−5.95637	+	0.869054i	−0.230459	+	0.0336247i
$669$		0			0
$670$	1.53915	+	21.2099i	0.0594625	+	0.819411i
$671$	−17.1054	−	29.6274i	−0.660346	−	1.14375i
$672$		0			0
$673$	8.00949	−	13.8728i	0.308743	−	0.534759i	−0.669345	−	0.742952i	$-0.733425\pi$
$673$	8.00949	−	13.8728i	0.308743	−	0.534759i	0.978088	+	0.208193i	$0.0667583\pi$
$674$	20.9563	+	10.1530i	0.807207	+	0.391079i
$675$		0			0
$676$	10.3284	+	13.0775i	0.397246	+	0.502982i
$677$	0.225619	−	0.390784i	0.00867125	−	0.0150190i	−0.861657	−	0.507491i	$-0.830573\pi$
$677$	0.225619	−	0.390784i	0.00867125	−	0.0150190i	0.870328	+	0.492472i	$0.163906\pi$
$678$		0			0
$679$	−6.48561	+	3.74447i	−0.248895	+	0.143700i
$680$	−2.36108	−	2.58104i	−0.0905433	−	0.0989785i
$681$		0			0
$682$	−25.9533	+	17.6051i	−0.993802	+	0.674134i
$683$		−	23.3047i		−	0.891728i	−0.895101	−	0.445864i	$-0.852896\pi$
$683$		−	23.3047i		−	0.891728i	0.895101	−	0.445864i	$-0.147104\pi$
$684$		0			0
$685$		−	3.91744i		−	0.149678i
$686$	25.6199	+	37.7686i	0.978172	+	1.44201i
$687$		0			0
$688$	20.1280	−	6.00122i	0.767372	−	0.228795i
$689$	14.8194	−	8.55598i	0.564574	−	0.325957i
$690$		0			0
$691$	−4.50424	+	7.80158i	−0.171349	+	0.296786i	−0.938892	−	0.344212i	$-0.888146\pi$
$691$	−4.50424	+	7.80158i	−0.171349	+	0.296786i	0.767542	+	0.640998i	$0.221479\pi$
$692$	12.3665	+	15.6581i	0.470104	+	0.595232i
$693$		0			0
$694$	−9.28383	+	19.1623i	−0.352409	+	0.727390i
$695$	5.70435	−	9.88022i	0.216378	−	0.374778i
$696$		0			0
$697$	−4.52738	−	7.84166i	−0.171487	−	0.297024i
$698$	11.4139	−	0.828280i	0.432024	−	0.0313509i
$699$		0			0
$700$	1.32435	+	9.07692i	0.0500558	+	0.343075i
$701$	−10.3925			−0.392520			−0.196260	−	0.980552i	$-0.562880\pi$
$701$	−10.3925			−0.392520			−0.196260	+	0.980552i	$0.562880\pi$
$702$		0			0
$703$		−	43.2400i		−	1.63083i
$704$	−37.6175	−	3.35517i	−1.41776	−	0.126453i
$705$		0			0
$706$	−13.3055	+	0.965547i	−0.500760	+	0.0363388i
$707$	10.2376	−	5.91068i	0.385025	−	0.222294i
$708$		0			0
$709$	−22.1577	−	12.7927i	−0.832149	−	0.480442i	0.0224386	−	0.999748i	$-0.492857\pi$
$709$	−22.1577	−	12.7927i	−0.832149	−	0.480442i	−0.854588	+	0.519307i	$0.826190\pi$
$710$	−1.08364	−	0.525006i	−0.0406682	−	0.0197031i
$711$		0			0
$712$	35.7172	−	7.88666i	1.33856	−	0.295565i
$713$	−0.958696	−	0.553503i	−0.0359035	−	0.0207289i
$714$		0			0
$715$	5.09976	+	8.83305i	0.190720	+	0.330337i
$716$	−20.7383	−	8.25234i	−0.775028	−	0.308405i
$717$		0			0
$718$	33.8437	−	22.9575i	1.26304	−	0.856765i
$719$	36.4552			1.35955			0.679774	−	0.733422i	$-0.262078\pi$
$719$	36.4552			1.35955			0.679774	+	0.733422i	$0.262078\pi$
$720$		0			0
$721$	−45.6820			−1.70129
$722$	0.00306849	−	0.00208147i	0.000114197	−	7.74644e-5i
$723$		0			0
$724$	8.92730	+	3.55241i	0.331780	+	0.132024i
$725$	2.84210	+	4.92266i	0.105553	+	0.182823i
$726$		0			0
$727$	−21.4834	−	12.4034i	−0.796774	−	0.460018i	0.0455677	−	0.998961i	$-0.485490\pi$
$727$	−21.4834	−	12.4034i	−0.796774	−	0.460018i	−0.842342	+	0.538943i	$0.818824\pi$
$728$	6.04318	+	27.3684i	0.223975	+	1.01434i
$729$		0			0
$730$	−13.5886	−	6.58348i	−0.502937	−	0.243665i
$731$	−5.62403	−	3.24703i	−0.208012	−	0.120096i
$732$		0			0
$733$	27.3108	−	15.7679i	1.00875	−	0.582400i	0.0979219	−	0.995194i	$-0.468780\pi$
$733$	27.3108	−	15.7679i	1.00875	−	0.582400i	0.910824	+	0.412794i	$0.135447\pi$
$734$	44.1209	−	3.20174i	1.62853	−	0.118178i
$735$		0			0
$736$	−0.472372	−	1.24663i	−0.0174119	−	0.0459514i
$737$		−	70.9880i		−	2.61488i
$738$		0			0
$739$	20.1619			0.741668			0.370834	−	0.928699i	$-0.379072\pi$
$739$	20.1619			0.741668			0.370834	+	0.928699i	$0.379072\pi$
$740$	2.86418	+	19.6307i	0.105289	+	0.721638i
$741$		0			0
$742$	−51.2386	+	3.71825i	−1.88103	+	0.136501i
$743$	−0.498520	−	0.863461i	−0.0182889	−	0.0316773i	0.856736	−	0.515755i	$-0.172489\pi$
$743$	−0.498520	−	0.863461i	−0.0182889	−	0.0316773i	−0.875025	+	0.484078i	$0.839155\pi$
$744$		0			0
$745$	9.86802	−	17.0919i	0.361536	−	0.626199i
$746$	12.6905	−	26.1939i	0.464633	−	0.959026i
$747$		0			0
$748$	7.23737	+	9.16375i	0.264624	+	0.335060i
$749$	−16.7041	+	28.9324i	−0.610356	+	1.05717i
$750$		0			0
$751$	37.7503	−	21.7951i	1.37753	−	0.795316i	0.385666	−	0.922639i	$-0.373972\pi$
$751$	37.7503	−	21.7951i	1.37753	−	0.795316i	0.991861	+	0.127323i	$0.0406385\pi$
$752$	−8.12325	+	2.42197i	−0.296225	+	0.0883203i
$753$		0			0
$754$	9.74971	+	14.3729i	0.355064	+	0.523432i
$755$			6.14737i			0.223726i
$756$		0			0
$757$			5.54083i			0.201385i	0.994918	+	0.100692i	$0.0321058\pi$
$757$			5.54083i			0.201385i	−0.994918	+	0.100692i	$0.967894\pi$
$758$	1.34706	−	0.913759i	0.0489272	−	0.0331892i
$759$		0			0
$760$	−9.09743	+	8.32213i	−0.329998	+	0.301875i
$761$	23.1798	−	13.3829i	0.840267	−	0.485128i	−0.0170880	−	0.999854i	$-0.505440\pi$
$761$	23.1798	−	13.3829i	0.840267	−	0.485128i	0.857355	+	0.514726i	$0.172106\pi$
$762$		0			0
$763$	5.88232	−	10.1885i	0.212954	−	0.368847i
$764$	−0.356164	−	0.450964i	−0.0128856	−	0.0163153i
$765$		0			0
$766$	0.0612542	+	0.0296767i	0.00221320	+	0.00107226i
$767$	−12.7207	+	22.0329i	−0.459318	+	0.795562i
$768$		0			0
$769$	−1.93609	−	3.35341i	−0.0698174	−	0.120927i	0.829003	−	0.559244i	$-0.188908\pi$
$769$	−1.93609	−	3.35341i	−0.0698174	−	0.120927i	−0.898821	+	0.438316i	$0.855575\pi$
$770$	−2.21625	−	30.5406i	−0.0798681	−	1.10061i
$771$		0			0
$772$	4.73005	−	0.690129i	0.170238	−	0.0248383i
$773$	−26.7361			−0.961632			−0.480816	−	0.876821i	$-0.659660\pi$
$773$	−26.7361			−0.961632			−0.480816	+	0.876821i	$0.659660\pi$
$774$		0			0
$775$		−	4.69737i		−	0.168734i
$776$	4.40338	+	1.39247i	0.158072	+	0.0499869i
$777$		0			0
$778$	−2.07536	−	28.5991i	−0.0744053	−	1.02533i
$779$	−27.6396	+	15.9577i	−0.990290	+	0.571744i
$780$		0			0
$781$	3.48101	+	2.00976i	0.124560	+	0.0719150i
$782$	−0.179717	+	0.370945i	−0.00642667	+	0.0132650i
$783$		0			0
$784$	13.0093	−	54.6163i	0.464618	−	1.95058i
$785$	0.339511	+	0.196017i	0.0121177	+	0.00699614i
$786$		0			0
$787$	4.82568	+	8.35833i	0.172017	+	0.297942i	0.939125	−	0.343576i	$-0.111638\pi$
$787$	4.82568	+	8.35833i	0.172017	+	0.297942i	−0.767108	+	0.641518i	$0.778305\pi$
$788$	−7.99927	+	20.1024i	−0.284962	+	0.716117i
$789$		0			0
$790$	9.18349	+	13.5382i	0.326734	+	0.481668i
$791$	−1.64942			−0.0586466
$792$		0			0
$793$	15.6568			0.555988
$794$	13.1635	+	19.4055i	0.467154	+	0.688675i
$795$		0			0
$796$	9.48728	+	3.77524i	0.336268	+	0.133810i
$797$	12.7189	+	22.0298i	0.450528	+	0.780337i	0.998419	−	0.0562130i	$-0.0179026\pi$
$797$	12.7189	+	22.0298i	0.450528	+	0.780337i	−0.547891	+	0.836550i	$0.684569\pi$
$798$		0			0
$799$	2.26974	+	1.31044i	0.0802978	+	0.0463600i
$800$	3.57892	−	4.38079i	0.126534	−	0.154884i
$801$		0			0
$802$	−12.9035	+	26.6334i	−0.455637	+	0.940457i
$803$	43.6512	+	25.2021i	1.54042	+	0.889361i
$804$		0			0
$805$	0.936072	−	0.540441i	0.0329922	−	0.0190481i
$806$	−1.03880	−	14.3149i	−0.0365900	−	0.504221i
$807$		0			0
$808$	−6.95079	−	2.19803i	−0.244528	−	0.0773265i
$809$		−	10.7268i		−	0.377134i	−0.982060	−	0.188567i	$-0.939616\pi$
$809$		−	10.7268i		−	0.377134i	0.982060	−	0.188567i	$-0.0603843\pi$
$810$		0			0
$811$	5.16201			0.181263			0.0906314	−	0.995885i	$-0.471111\pi$
$811$	5.16201			0.181263			0.0906314	+	0.995885i	$0.471111\pi$
$812$	−7.52787	−	51.5950i	−0.264176	−	1.81063i
$813$		0			0
$814$	−4.79309	−	66.0502i	−0.167998	−	2.31506i
$815$	12.3153	+	21.3307i	0.431386	+	0.747183i
$816$		0			0
$817$	−11.4449	+	19.8231i	−0.400405	+	0.693521i
$818$	−21.9636	−	10.6410i	−0.767940	−	0.372055i
$819$		0			0
$820$	11.4912	−	9.07551i	0.401288	−	0.316931i
$821$	9.71181	−	16.8213i	0.338944	−	0.587069i	−0.645290	−	0.763938i	$-0.723263\pi$
$821$	9.71181	−	16.8213i	0.338944	−	0.587069i	0.984234	+	0.176869i	$0.0565968\pi$
$822$		0			0
$823$	−29.5617	+	17.0675i	−1.03046	+	0.594935i	−0.917116	−	0.398621i	$-0.869489\pi$
$823$	−29.5617	+	17.0675i	−1.03046	+	0.594935i	−0.113342	+	0.993556i	$0.536155\pi$
$824$	19.0147	+	20.7862i	0.662409	+	0.724120i
$825$		0			0
$826$	63.2094	−	42.8773i	2.19934	−	1.49189i
$827$		−	21.1098i		−	0.734061i	−0.930209	−	0.367031i	$-0.880374\pi$
$827$		−	21.1098i		−	0.734061i	0.930209	−	0.367031i	$-0.119626\pi$
$828$		0			0
$829$		−	2.27907i		−	0.0791554i	−0.999216	−	0.0395777i	$-0.987399\pi$
$829$		−	2.27907i		−	0.0791554i	0.999216	−	0.0395777i	$-0.0126013\pi$
$830$	−2.15460	−	3.17629i	−0.0747872	−	0.110251i
$831$		0			0
$832$	9.93772	−	14.1416i	0.344529	−	0.490272i
$833$	−15.0335	+	8.67959i	−0.520880	+	0.300730i
$834$		0			0
$835$	−1.50486	+	2.60649i	−0.0520778	+	0.0902014i
$836$	32.2996	−	25.5096i	1.11710	−	0.882269i
$837$		0			0
$838$	8.89356	−	18.3567i	0.307223	−	0.634123i
$839$	−20.2338	+	35.0460i	−0.698548	+	1.20992i	0.270421	+	0.962742i	$0.412837\pi$
$839$	−20.2338	+	35.0460i	−0.698548	+	1.20992i	−0.968970	+	0.247179i	$0.920496\pi$
$840$		0			0
$841$	−1.65503	−	2.86660i	−0.0570700	−	0.0988481i
$842$	37.8891	−	2.74951i	1.30574	−	0.0947544i
$843$		0			0
$844$	1.94574	−	0.283889i	0.0669750	−	0.00977186i
$845$	8.33213			0.286634
$846$		0			0
$847$			51.7654i			1.77868i
$848$	23.0195	+	21.7668i	0.790493	+	0.747477i
$849$		0			0
$850$	−1.74445	+	0.126590i	−0.0598341	+	0.00434200i
$851$	2.02444	−	1.16881i	0.0693971	−	0.0400664i
$852$		0			0
$853$	−14.2703	−	8.23893i	−0.488604	−	0.282096i	0.235391	−	0.971901i	$-0.424363\pi$
$853$	−14.2703	−	8.23893i	−0.488604	−	0.282096i	−0.723995	+	0.689805i	$0.757696\pi$
$854$	−42.3014	−	20.4944i	−1.44752	−	0.701303i
$855$		0			0
$856$	20.1177	−	4.44217i	0.687610	−	0.151830i
$857$	41.2192	+	23.7979i	1.40802	+	0.812921i	0.995197	−	0.0978896i	$-0.0312092\pi$
$857$	41.2192	+	23.7979i	1.40802	+	0.812921i	0.412824	+	0.910811i	$0.364543\pi$
$858$		0			0
$859$	−15.2357	−	26.3890i	−0.519836	−	0.900382i	−0.999734	−	0.0230580i	$-0.992660\pi$
$859$	−15.2357	−	26.3890i	−0.519836	−	0.900382i	0.479898	−	0.877324i	$-0.340674\pi$
$860$	3.88282	−	9.75763i	0.132403	−	0.332732i
$861$		0			0
$862$	14.7967	−	10.0372i	0.503978	−	0.341867i
$863$	30.4421			1.03626			0.518131	−	0.855301i	$-0.326628\pi$
$863$	30.4421			1.03626			0.518131	+	0.855301i	$0.326628\pi$
$864$		0			0
$865$	9.97631			0.339205
$866$	−33.1998	+	22.5207i	−1.12817	+	0.765283i
$867$		0			0
$868$	−15.9313	+	40.0357i	−0.540743	+	1.35890i
$869$	−27.3045	−	47.2928i	−0.926242	−	1.60430i
$870$		0			0
$871$	28.1355	+	16.2440i	0.953335	+	0.550408i
$872$	−7.08441	+	1.56430i	−0.239908	+	0.0529738i
$873$		0			0
$874$	1.30747	+	0.633450i	0.0442259	+	0.0214268i
$875$	3.97204	+	2.29326i	0.134279	+	0.0775262i
$876$		0			0
$877$	−22.1778	+	12.8044i	−0.748892	+	0.432373i	−0.825293	−	0.564704i	$-0.808990\pi$
$877$	−22.1778	+	12.8044i	−0.748892	+	0.432373i	0.0764015	+	0.997077i	$0.475657\pi$
$878$	−2.63872	+	0.191485i	−0.0890526	+	0.00646231i
$879$		0			0
$880$	−12.9740	+	13.7207i	−0.437355	+	0.462524i
$881$			43.3621i			1.46091i	0.682963	+	0.730453i	$0.260691\pi$
$881$			43.3621i			1.46091i	−0.682963	+	0.730453i	$0.739309\pi$
$882$		0			0
$883$	−15.4645			−0.520421			−0.260210	−	0.965552i	$-0.583792\pi$
$883$	−15.4645			−0.520421			−0.260210	+	0.965552i	$0.583792\pi$
$884$	−5.28809	+	0.771549i	−0.177858	+	0.0259500i
$885$		0			0
$886$	−53.6674	+	3.89450i	−1.80299	+	0.130838i
$887$	−1.66974	−	2.89207i	−0.0560642	−	0.0971061i	0.836631	−	0.547767i	$-0.184522\pi$
$887$	−1.66974	−	2.89207i	−0.0560642	−	0.0971061i	−0.892695	+	0.450661i	$0.851188\pi$
$888$		0			0
$889$	−20.7064	+	35.8646i	−0.694471	+	1.20286i
$890$	7.97406	−	16.4589i	0.267291	−	0.551702i
$891$		0			0
$892$	18.7634	−	14.8190i	0.628244	−	0.496176i
$893$	4.61891	−	8.00019i	0.154566	−	0.267716i
$894$		0			0
$895$	−9.66482	+	5.57999i	−0.323059	+	0.186518i
$896$	−45.3608	+	25.1995i	−1.51540	+	0.841857i
$897$		0			0
$898$	−3.59793	−	5.30404i	−0.120064	−	0.176998i
$899$			26.7007i			0.890519i
$900$		0			0
$901$		−	9.79544i		−	0.326333i
$902$	−40.4512	+	27.4396i	−1.34688	+	0.913639i
$903$		0			0
$904$	0.686557	+	0.750517i	0.0228345	+	0.0249618i
$905$	4.16044	−	2.40203i	0.138298	−	0.0798463i
$906$		0			0
$907$	1.40422	−	2.43218i	0.0466263	−	0.0807592i	−0.841770	−	0.539836i	$-0.818486\pi$
$907$	1.40422	−	2.43218i	0.0466263	−	0.0807592i	0.888397	+	0.459077i	$0.151820\pi$
$908$	−30.9674	+	24.4575i	−1.02769	+	0.811651i
$909$		0			0
$910$	12.6116	+	6.11015i	0.418072	+	0.202549i
$911$	−15.6065	+	27.0312i	−0.517066	+	0.895585i	0.482738	+	0.875765i	$0.339642\pi$
$911$	−15.6065	+	27.0312i	−0.517066	+	0.895585i	−0.999804	+	0.0198195i	$0.993691\pi$
$912$		0			0
$913$	6.40609	+	11.0957i	0.212011	+	0.367213i
$914$	−1.30675	−	18.0074i	−0.0432235	−	0.595633i
$915$		0			0
$916$	0.245327	+	1.68143i	0.00810582	+	0.0555562i
$917$	5.22242			0.172460
$918$		0			0
$919$			41.3010i			1.36240i	0.732100	+	0.681198i	$0.238541\pi$
$919$			41.3010i			1.36240i	−0.732100	+	0.681198i	$0.761459\pi$
$920$	−0.635543	−	0.200976i	−0.0209532	−	0.00662599i
$921$		0			0
$922$	3.66101	+	50.4498i	0.120569	+	1.66148i
$923$	−1.59311	+	0.919780i	−0.0524377	+	0.0302749i
$924$		0			0
$925$	8.59033	+	4.95963i	0.282448	+	0.163072i
$926$	−19.6977	+	40.6569i	−0.647305	+	1.33607i
$927$		0			0
$928$	−20.3433	+	24.9013i	−0.667801	+	0.817424i
$929$	−2.46762	−	1.42468i	−0.0809599	−	0.0467422i	0.458974	−	0.888450i	$-0.348217\pi$
$929$	−2.46762	−	1.42468i	−0.0809599	−	0.0467422i	−0.539933	+	0.841708i	$0.681551\pi$
$930$		0			0
$931$	30.5931	+	52.9887i	1.00265	+	1.73664i
$932$	−50.1313	−	19.9486i	−1.64210	−	0.653438i
$933$		0			0
$934$	0.648662	+	0.956252i	0.0212249	+	0.0312895i
$935$	5.83853			0.190940
$936$		0			0
$937$	33.6983			1.10088			0.550438	−	0.834876i	$-0.314461\pi$
$937$	33.6983			1.10088			0.550438	+	0.834876i	$0.314461\pi$
$938$	−54.7533	−	80.7169i	−1.78776	−	2.63550i
$939$		0			0
$940$	−1.56703	+	3.93798i	−0.0511109	+	0.128443i
$941$	12.1325	+	21.0141i	0.395507	+	0.685039i	0.993166	−	0.116712i	$-0.0372355\pi$
$941$	12.1325	+	21.0141i	0.395507	+	0.685039i	−0.597659	+	0.801751i	$0.703902\pi$
$942$		0			0
$943$	−1.49424	−	0.862700i	−0.0486592	−	0.0280934i
$944$	−45.8204	−	10.9142i	−1.49133	−	0.355226i
$945$		0			0
$946$	−15.2849	+	31.5489i	−0.496956	+	1.02574i
$947$	31.5042	+	18.1890i	1.02375	+	0.591062i	0.915188	−	0.403028i	$-0.132042\pi$
$947$	31.5042	+	18.1890i	1.02375	+	0.591062i	0.108561	+	0.994090i	$0.465376\pi$
$948$		0			0
$949$	−19.9772	+	11.5339i	−0.648489	+	0.374405i
$950$	0.446193	+	6.14867i	0.0144764	+	0.199489i
$951$		0			0
$952$	15.2973	+	4.83743i	0.495788	+	0.156782i
$953$			26.2586i			0.850598i	0.905053	+	0.425299i	$0.139831\pi$
$953$			26.2586i			0.850598i	−0.905053	+	0.425299i	$0.860169\pi$
$954$		0			0
$955$	−0.287325			−0.00929760
$956$	−27.6649	+	4.03640i	−0.894748	+	0.130547i
$957$		0			0
$958$	−3.55627	−	49.0065i	−0.114898	−	1.58333i
$959$	8.98369	+	15.5602i	0.290099	+	0.502466i
$960$		0			0
$961$	−4.46738	+	7.73773i	−0.144109	+	0.249604i
$962$	27.2752	+	13.2144i	0.879389	+	0.426050i
$963$		0			0
$964$	−17.7158	−	22.4312i	−0.570586	−	0.722460i
$965$	1.19503	−	2.06986i	0.0384695	−	0.0666311i
$966$		0			0
$967$	42.3417	−	24.4460i	1.36162	−	0.786130i	0.371777	−	0.928322i	$-0.378749\pi$
$967$	42.3417	−	24.4460i	1.36162	−	0.786130i	0.989839	+	0.142192i	$0.0454152\pi$
$968$	23.5542	−	21.5469i	0.757062	−	0.692544i
$969$		0			0
$970$	1.91098	−	1.29629i	0.0613577	−	0.0416213i
$971$			23.9838i			0.769678i	0.922984	+	0.384839i	$0.125743\pi$
$971$			23.9838i			0.769678i	−0.922984	+	0.384839i	$0.874257\pi$
$972$		0			0
$973$			52.3261i			1.67750i
$974$	−31.6074	−	46.5954i	−1.01277	−	1.49301i
$975$		0			0
$976$	8.28226	+	27.7785i	0.265109	+	0.889169i
$977$	23.1131	−	13.3444i	0.739455	−	0.426924i	−0.0824164	−	0.996598i	$-0.526264\pi$
$977$	23.1131	−	13.3444i	0.739455	−	0.426924i	0.821871	+	0.569674i	$0.192930\pi$
$978$		0			0
$979$	−30.5253	+	52.8714i	−0.975593	+	1.68978i
$980$	−17.3990	−	22.0301i	−0.555789	−	0.703724i
$981$		0			0
$982$	15.5997	−	32.1986i	0.497808	−	1.02750i
$983$	−21.9816	+	38.0733i	−0.701104	+	1.21435i	0.266975	+	0.963703i	$0.413976\pi$
$983$	−21.9816	+	38.0733i	−0.701104	+	1.21435i	−0.968079	+	0.250645i	$0.919357\pi$
$984$		0			0
$985$	5.40887	+	9.36843i	0.172341	+	0.298503i
$986$	9.91578	−	0.719562i	0.315783	−	0.0229155i
$987$		0			0
$988$	2.71949	+	18.6390i	0.0865184	+	0.592985i
$989$	−1.23745			−0.0393488
$990$		0			0
$991$			43.4855i			1.38136i	0.723159	+	0.690682i	$0.242689\pi$
$991$			43.4855i			1.38136i	−0.723159	+	0.690682i	$0.757311\pi$
$992$	24.8483	−	9.41548i	0.788933	−	0.298942i
$993$		0			0
$994$	5.50822	−	0.399717i	0.174710	−	0.0126783i
$995$	4.42142	−	2.55271i	0.140168	−	0.0809262i
$996$		0			0
$997$	5.50039	+	3.17565i	0.174199	+	0.100574i	0.584564	−	0.811347i	$-0.301265\pi$
$997$	5.50039	+	3.17565i	0.174199	+	0.100574i	−0.410365	+	0.911921i	$0.634599\pi$
$998$	14.6421	+	7.09386i	0.463487	+	0.224552i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.bm.a.251.20		48
3.2	odd	2		360.2.bm.b.11.5	yes	48
4.3	odd	2		4320.2.cc.a.1871.2		48
8.3	odd	2		1080.2.bm.b.251.12		48
8.5	even	2		4320.2.cc.b.1871.23		48
9.4	even	3		360.2.bm.a.131.13	yes	48
9.5	odd	6		1080.2.bm.b.611.12		48
12.11	even	2		1440.2.cc.b.911.1		48
24.5	odd	2		1440.2.cc.a.911.1		48
24.11	even	2		360.2.bm.a.11.13	✓	48
36.23	even	6		4320.2.cc.b.3311.23		48
36.31	odd	6		1440.2.cc.a.1391.1		48
72.5	odd	6		4320.2.cc.a.3311.2		48
72.13	even	6		1440.2.cc.b.1391.1		48
72.59	even	6	inner	1080.2.bm.a.611.20		48
72.67	odd	6		360.2.bm.b.131.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.13	✓	48	24.11	even	2
360.2.bm.a.131.13	yes	48	9.4	even	3
360.2.bm.b.11.5	yes	48	3.2	odd	2
360.2.bm.b.131.5	yes	48	72.67	odd	6
1080.2.bm.a.251.20		48	1.1	even	1	trivial
1080.2.bm.a.611.20		48	72.59	even	6	inner
1080.2.bm.b.251.12		48	8.3	odd	2
1080.2.bm.b.611.12		48	9.5	odd	6
1440.2.cc.a.911.1		48	24.5	odd	2
1440.2.cc.a.1391.1		48	36.31	odd	6
1440.2.cc.b.911.1		48	12.11	even	2
1440.2.cc.b.1391.1		48	72.13	even	6
4320.2.cc.a.1871.2		48	4.3	odd	2
4320.2.cc.a.3311.2		48	72.5	odd	6
4320.2.cc.b.1871.23		48	8.5	even	2
4320.2.cc.b.3311.23		48	36.23	even	6

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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17035 - 0.793896i) q^{2} +(0.739459 - 1.85828i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.97204 + 2.29326i) q^{7} +(-0.609850 - 2.76190i) q^{8} +O(q^{10})\)	\(q+(1.17035 - 0.793896i) q^{2} +(0.739459 - 1.85828i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.97204 + 2.29326i) q^{7} +(-0.609850 - 2.76190i) q^{8} +(-1.27271 - 0.616609i) q^{10} +(4.08838 + 2.36043i) q^{11} +(-1.87107 + 1.08026i) q^{13} +(6.46930 - 0.469460i) q^{14} +(-2.90640 - 2.74824i) q^{16} +1.23675i q^{17} +4.35920 q^{19} +(-1.97905 + 0.288749i) q^{20} +(6.65878 - 0.483211i) q^{22} +(0.117833 + 0.204092i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.33220 + 2.74973i) q^{26} +(7.19867 - 5.68538i) q^{28} +(2.84210 - 4.92266i) q^{29} +(-4.06804 + 2.34868i) q^{31} +(-5.58334 - 0.909039i) q^{32} +(0.981854 + 1.44744i) q^{34} -4.58651i q^{35} -9.91926i q^{37} +(5.10181 - 3.46075i) q^{38} +(-2.08695 + 1.90910i) q^{40} +(-6.34052 + 3.66070i) q^{41} +(-2.62545 + 4.54741i) q^{43} +(7.40952 - 5.85191i) q^{44} +(0.299934 + 0.145313i) q^{46} +(1.05958 - 1.83524i) q^{47} +(7.01804 + 12.1556i) q^{49} +(0.102357 + 1.41050i) q^{50} +(0.623850 + 4.27578i) q^{52} -7.92028 q^{53} -4.72085i q^{55} +(3.91139 - 12.3689i) q^{56} +(-0.581815 - 8.01758i) q^{58} +(10.1979 - 5.88778i) q^{59} +(-6.27586 - 3.62337i) q^{61} +(-2.89644 + 5.97839i) q^{62} +(-7.25617 + 3.36869i) q^{64} +(1.87107 + 1.08026i) q^{65} +(-7.51856 - 13.0225i) q^{67} +(2.29823 + 0.914529i) q^{68} +(-3.64121 - 5.36784i) q^{70} +0.851441 q^{71} +10.6769 q^{73} +(-7.87486 - 11.6090i) q^{74} +(3.22345 - 8.10061i) q^{76} +(10.8261 + 18.7514i) q^{77} +(-10.0179 - 5.78381i) q^{79} +(-0.926848 + 3.89114i) q^{80} +(-4.51444 + 9.31802i) q^{82} +(2.35035 + 1.35698i) q^{83} +(1.07106 - 0.618377i) q^{85} +(0.537464 + 7.40641i) q^{86} +(4.02596 - 12.7312i) q^{88} +12.9321i q^{89} -9.90928 q^{91} +(0.466393 - 0.0680482i) q^{92} +(-0.216910 - 2.98908i) q^{94} +(-2.17960 - 3.77518i) q^{95} +(-0.816409 + 1.41406i) q^{97} +(17.8639 + 8.65477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 - 6 * q^8	\( 48 q - 24 q^{5} - 6 q^{8} - 15 q^{14} - 12 q^{16} - 21 q^{22} - 24 q^{25} - 27 q^{34} + 27 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 24 q^{49} + 54 q^{52} - 21 q^{56} + 33 q^{58} + 36 q^{59} - 12 q^{61} + 42 q^{62} - 12 q^{64} - 51 q^{68} + 15 q^{70} - 54 q^{74} - 51 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} - 57 q^{88} + 9 q^{92} - 75 q^{94} + 42 q^{98}+O(q^{100}) \) 48 * q - 24 * q^5 - 6 * q^8 - 15 * q^14 - 12 * q^16 - 21 * q^22 - 24 * q^25 - 27 * q^34 + 27 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 24 * q^49 + 54 * q^52 - 21 * q^56 + 33 * q^58 + 36 * q^59 - 12 * q^61 + 42 * q^62 - 12 * q^64 - 51 * q^68 + 15 * q^70 - 54 * q^74 - 51 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 - 57 * q^88 + 9 * q^92 - 75 * q^94 + 42 * q^98

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