LMFDB - Embedded newform 1080.2.bm.b.251.12

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			251.12
Character	$\chi$	$=$	1080.251
Dual form			1080.2.bm.b.611.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.102357 + 1.41050i) q^{2} +(-1.97905 - 0.288749i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(0.609850 - 2.76190i) q^{8} +O(q^{10})$	\(q+(-0.102357 + 1.41050i) q^{2} +(-1.97905 - 0.288749i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(0.609850 - 2.76190i) q^{8} +(-1.27271 + 0.616609i) q^{10} +(4.08838 + 2.36043i) q^{11} +(1.87107 - 1.08026i) q^{13} +(3.64121 - 5.36784i) q^{14} +(3.83325 + 1.14290i) q^{16} +1.23675i q^{17} +4.35920 q^{19} +(-0.739459 - 1.85828i) q^{20} +(-3.74786 + 5.52507i) q^{22} +(-0.117833 - 0.204092i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.33220 + 2.74973i) q^{26} +(7.19867 + 5.68538i) q^{28} +(-2.84210 + 4.92266i) q^{29} +(4.06804 - 2.34868i) q^{31} +(-2.00442 + 5.28983i) q^{32} +(-1.74445 - 0.126590i) q^{34} -4.58651i q^{35} +9.91926i q^{37} +(-0.446193 + 6.14867i) q^{38} +(2.69680 - 0.852803i) q^{40} +(-6.34052 + 3.66070i) q^{41} +(-2.62545 + 4.54741i) q^{43} +(-7.40952 - 5.85191i) q^{44} +(0.299934 - 0.145313i) q^{46} +(-1.05958 + 1.83524i) q^{47} +(7.01804 + 12.1556i) q^{49} +(-1.17035 - 0.793896i) q^{50} +(-4.01486 + 1.59762i) q^{52} +7.92028 q^{53} +4.72085i q^{55} +(-8.75609 + 9.57181i) q^{56} +(-6.65252 - 4.51266i) q^{58} +(10.1979 - 5.88778i) q^{59} +(6.27586 + 3.62337i) q^{61} +(2.89644 + 5.97839i) q^{62} +(-7.25617 - 3.36869i) q^{64} +(1.87107 + 1.08026i) q^{65} +(-7.51856 - 13.0225i) q^{67} +(0.357112 - 2.44759i) q^{68} +(6.46930 + 0.469460i) q^{70} -0.851441 q^{71} +10.6769 q^{73} +(-13.9912 - 1.01530i) q^{74} +(-8.62706 - 1.25871i) q^{76} +(-10.8261 - 18.7514i) q^{77} +(10.0179 + 5.78381i) q^{79} +(0.926848 + 3.89114i) q^{80} +(-4.51444 - 9.31802i) q^{82} +(2.35035 + 1.35698i) q^{83} +(-1.07106 + 0.618377i) q^{85} +(-6.14541 - 4.16866i) q^{86} +(9.01256 - 9.85218i) q^{88} +12.9321i q^{89} -9.90928 q^{91} +(0.174265 + 0.437932i) q^{92} +(-2.48016 - 1.68239i) q^{94} +(2.17960 + 3.77518i) q^{95} +(-0.816409 + 1.41406i) q^{97} +(-17.8639 + 8.65477i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 33 q^{34} + 33 q^{38} - 6 q^{40} - 12 q^{41} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 24 q^{49} - 36 q^{52} - 21 q^{56} - 51 q^{58} + 36 q^{59} + 12 q^{61} - 42 q^{62} - 12 q^{64} - 57 q^{68} - 15 q^{70} - 30 q^{74} + 57 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} + 57 q^{88} + 51 q^{92} + 57 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 + 33 * q^34 + 33 * q^38 - 6 * q^40 - 12 * q^41 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 24 * q^49 - 36 * q^52 - 21 * q^56 - 51 * q^58 + 36 * q^59 + 12 * q^61 - 42 * q^62 - 12 * q^64 - 57 * q^68 - 15 * q^70 - 30 * q^74 + 57 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 + 57 * q^88 + 51 * q^92 + 57 * 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 $

$2$	−0.102357	+	1.41050i	−0.0723771	+	0.997377i
$2$	−0.102357	+	1.41050i	−0.0723771	+	0.997377i
$3$		0			0
$3$		0			0
$4$	−1.97905	−	0.288749i	−0.989523	−	0.144375i
$5$	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	$-0.999526\pi$
$7$	−3.97204	−	2.29326i	−1.50129	−	0.866769i	−0.501289	−	0.865280i	$-0.667141\pi$
$8$	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	−0.217560	−	0.976047i	$-0.569810\pi$
$13$	1.87107	−	1.08026i	0.518942	−	0.299611i	0.736501	+	0.676436i	$0.236476\pi$
$14$	3.64121	−	5.36784i	0.973155	−	1.43462i
$15$		0			0
$16$	3.83325	+	1.14290i	0.958312	+	0.285724i
$17$			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	$0.333321\pi$
$20$	−0.739459	−	1.85828i	−0.165348	−	0.415524i
$21$		0			0
$22$	−3.74786	+	5.52507i	−0.799047	+	1.17795i
$23$	−0.117833	−	0.204092i	−0.0245698	−	0.0425562i	0.853479	−	0.521127i	$-0.174488\pi$
$23$	−0.117833	−	0.204092i	−0.0245698	−	0.0425562i	−0.878049	+	0.478571i	$0.841155\pi$
$24$		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	$0.343636\pi$
$29$	−2.84210	+	4.92266i	−0.527764	+	0.914114i	−0.999476	+	0.0323617i	$0.989697\pi$
$30$		0			0
$31$	4.06804	−	2.34868i	0.730641	−	0.421836i	−0.0880155	−	0.996119i	$-0.528053\pi$
$31$	4.06804	−	2.34868i	0.730641	−	0.421836i	0.818657	+	0.574283i	$0.194719\pi$
$32$	−2.00442	+	5.28983i	−0.354334	+	0.935119i
$33$		0			0
$34$	−1.74445	−	0.126590i	−0.299170	−	0.0217100i
$35$		−	4.58651i		−	0.775262i
$36$		0			0
$37$			9.91926i			1.63072i	0.578957	+	0.815358i	$0.303460\pi$
$37$			9.91926i			1.63072i	−0.578957	+	0.815358i	$0.696540\pi$
$38$	−0.446193	+	6.14867i	−0.0723821	+	0.997446i
$39$		0			0
$40$	2.69680	−	0.852803i	0.426401	−	0.134840i
$41$	−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	−0.932897	−	0.360143i	$-0.882728\pi$
$47$	−1.05958	+	1.83524i	−0.154555	+	0.267698i	0.778342	+	0.627841i	$0.216061\pi$
$48$		0			0
$49$	7.01804	+	12.1556i	1.00258	+	1.73652i
$50$	−1.17035	−	0.793896i	−0.165513	−	0.112274i
$51$		0			0
$52$	−4.01486	+	1.59762i	−0.556761	+	0.221550i
$53$	7.92028			1.08793			0.543967	−	0.839107i	$-0.316922\pi$
$53$	7.92028			1.08793			0.543967	+	0.839107i	$0.316922\pi$
$54$		0			0
$55$			4.72085i			0.636560i
$56$	−8.75609	+	9.57181i	−1.17008	+	1.27909i
$57$		0			0
$58$	−6.65252	−	4.51266i	−0.873519	−	0.592541i
$59$	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	0.844708	−	0.535228i	$-0.179774\pi$
$61$	6.27586	+	3.62337i	0.803541	+	0.463925i	−0.0411667	+	0.999152i	$0.513107\pi$
$62$	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	$-0.537296\pi$
$68$	0.357112	−	2.44759i	0.0433061	−	0.296814i
$69$		0			0
$70$	6.46930	+	0.469460i	0.773229	+	0.0561112i
$71$	−0.851441			−0.101047			−0.0505237	−	0.998723i	$-0.516089\pi$
$71$	−0.851441			−0.101047			−0.0505237	+	0.998723i	$0.516089\pi$
$72$		0			0
$73$	10.6769			1.24964			0.624819	−	0.780770i	$-0.285173\pi$
$73$	10.6769			1.24964			0.624819	+	0.780770i	$0.285173\pi$
$74$	−13.9912	−	1.01530i	−1.62644	−	0.118026i
$75$		0			0
$76$	−8.62706	−	1.25871i	−0.989591	−	0.144384i
$77$	−10.8261	−	18.7514i	−1.23375	−	2.13692i
$78$		0			0
$79$	10.0179	+	5.78381i	1.12710	+	0.650730i	0.943203	−	0.332217i	$-0.107796\pi$
$79$	10.0179	+	5.78381i	1.12710	+	0.650730i	0.183894	+	0.982946i	$0.441130\pi$
$80$	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
$86$	−6.14541	−	4.16866i	−0.662677	−	0.449519i
$87$		0			0
$88$	9.01256	−	9.85218i	0.960742	−	1.05025i
$89$			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
$92$	0.174265	+	0.437932i	0.0181684	+	0.0456576i
$93$		0			0
$94$	−2.48016	−	1.68239i	−0.255809	−	0.173525i
$95$	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	−0.922991	−	0.384820i	$-0.874263\pi$
$101$	−1.28871	+	2.23211i	−0.128231	+	0.222103i	0.794760	+	0.606924i	$0.207597\pi$
$102$		0			0
$103$	8.62567	−	4.98003i	0.849913	−	0.490697i	−0.0107087	−	0.999943i	$-0.503409\pi$
$103$	8.62567	−	4.98003i	0.849913	−	0.490697i	0.860621	+	0.509245i	$0.170075\pi$
$104$	−1.84250	−	5.82650i	−0.180672	−	0.571336i
$105$		0			0
$106$	−0.810693	+	11.1716i	−0.0787415	+	1.08508i
$107$			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	$0.0392014\pi$
$109$			2.56505i			0.245687i	−0.992426	+	0.122844i	$0.960799\pi$
$110$	−6.65878	−	0.483211i	−0.634890	−	0.0460723i
$111$		0			0
$112$	−12.6048	−	13.3302i	−1.19105	−	1.25959i
$113$	−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
$122$	−5.75315	+	8.48125i	−0.520866	+	0.767856i
$123$		0			0
$124$	−8.72901	+	3.47351i	−0.783889	+	0.311930i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	9.02927i		−	0.801218i	−0.916249	−	0.400609i	$-0.868799\pi$
$127$		−	9.02927i		−	0.801218i	0.916249	−	0.400609i	$-0.131201\pi$
$128$	5.49427	−	9.89005i	0.485629	−	0.874165i
$129$		0			0
$130$	−1.71523	+	2.52858i	−0.150436	+	0.221771i
$131$	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	$0.672576\pi$
$140$	−1.32435	+	9.07692i	−0.111928	+	0.767140i
$141$		0			0
$142$	0.0871506	−	1.20096i	0.00731352	−	0.100782i
$143$	10.1995			0.852927
$144$		0			0
$145$	−5.68419			−0.472047
$146$	−1.09285	+	15.0598i	−0.0904451	+	1.24636i
$147$		0			0
$148$	2.86418	−	19.6307i	0.235434	−	1.61363i
$149$	−9.86802	−	17.0919i	−0.808420	−	1.40022i	−0.913958	−	0.405809i	$-0.866990\pi$
$149$	−9.86802	−	17.0919i	−0.808420	−	1.40022i	0.105538	−	0.994415i	$-0.466344\pi$
$150$		0			0
$151$	5.32377	+	3.07368i	0.433243	+	0.250133i	0.700727	−	0.713429i	$-0.252859\pi$
$151$	5.32377	+	3.07368i	0.433243	+	0.250133i	−0.267484	+	0.963562i	$0.586192\pi$
$152$	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	−0.486391	−	0.873741i	$-0.661687\pi$
$157$	0.339511	−	0.196017i	0.0270959	−	0.0156438i	0.513487	+	0.858098i	$0.328354\pi$
$158$	−9.18349	+	13.5382i	−0.730599	+	1.07704i
$159$		0			0
$160$	−5.58334	+	0.909039i	−0.441402	+	0.0718658i
$161$			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	$0.915063\pi$
$164$	13.6052	−	5.41387i	1.06239	−	0.422752i
$165$		0			0
$166$	−2.15460	+	3.17629i	−0.167229	+	0.246528i
$167$	1.50486	+	2.60649i	0.116450	+	0.201697i	0.918358	−	0.395750i	$-0.129515\pi$
$167$	1.50486	+	2.60649i	0.116450	+	0.201697i	−0.801909	+	0.597447i	$0.796182\pi$
$168$		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	−0.611710	−	0.791082i	$-0.709518\pi$
$173$	4.98815	−	8.63974i	0.379242	−	0.656867i	0.990952	+	0.134215i	$0.0428513\pi$
$174$		0			0
$175$	3.97204	−	2.29326i	0.300258	−	0.173354i
$176$	12.9740	+	13.7207i	0.977956	+	1.03424i
$177$		0			0
$178$	−18.2408	−	1.32369i	−1.36721	−	0.0992146i
$179$		−	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	$-0.942862\pi$
$181$		−	4.80407i		−	0.357083i	0.983932	−	0.178542i	$-0.0571379\pi$
$182$	1.01428	−	13.9771i	0.0751835	−	1.03605i
$183$		0			0
$184$	−0.635543	+	0.200976i	−0.0468528	+	0.0148162i
$185$	−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	−0.871176	−	0.490971i	$-0.836642\pi$
$191$	−0.143662	+	0.248830i	−0.0103950	+	0.0180047i	0.860781	+	0.508975i	$0.169976\pi$
$192$		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	$0.805918\pi$
$194$	−1.91098	−	1.29629i	−0.137200	−	0.0930680i
$195$		0			0
$196$	−10.3791	−	26.0830i	−0.741365	−	1.86307i
$197$	10.8177			0.770732			0.385366	−	0.922764i	$-0.374075\pi$
$197$	10.8177			0.770732			0.385366	+	0.922764i	$0.374075\pi$
$198$		0			0
$199$		−	5.10541i		−	0.361913i	−0.983491	−	0.180957i	$-0.942081\pi$
$199$		−	5.10541i		−	0.361913i	0.983491	−	0.180957i	$-0.0579193\pi$
$200$	2.08695	+	1.90910i	0.147570	+	0.134993i
$201$		0			0
$202$	−3.01650	−	2.04620i	−0.212240	−	0.143970i
$203$	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	$0.822559\pi$
$212$	−15.6746	−	2.28697i	−1.07654	−	0.157070i
$213$		0			0
$214$	−10.2742	−	0.745569i	−0.702327	−	0.0509660i
$215$	−5.25090			−0.358108
$216$		0			0
$217$	−21.5445			−1.46254
$218$	−3.61801	−	0.262550i	−0.245043	−	0.0177821i
$219$		0			0
$220$	1.36314	−	9.34278i	0.0919030	−	0.629890i
$221$	1.33602	+	2.31405i	0.0898704	+	0.155660i
$222$		0			0
$223$	−10.3531	−	5.97739i	−0.693297	−	0.400275i	0.111549	−	0.993759i	$-0.464419\pi$
$223$	−10.3531	−	5.97739i	−0.693297	−	0.400275i	−0.804846	+	0.593484i	$0.797752\pi$
$224$	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	−0.475492	−	0.879720i	$-0.657730\pi$
$229$	0.735791	−	0.424809i	0.0486225	−	0.0280722i	0.524114	+	0.851648i	$0.324397\pi$
$230$	0.275812	+	0.187094i	0.0181865	+	0.0123366i
$231$		0			0
$232$	11.8626	+	10.8517i	0.778819	+	0.712447i
$233$		−	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
$236$	−21.8823	+	8.70755i	−1.42442	+	0.566813i
$237$		0			0
$238$	6.63870	+	4.50328i	0.430323	+	0.291905i
$239$	6.98946	+	12.1061i	0.452111	+	0.783079i	0.998517	−	0.0544415i	$-0.0173378\pi$
$239$	6.98946	+	12.1061i	0.452111	+	0.783079i	−0.546406	+	0.837520i	$0.684005\pi$
$240$		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
$248$	−4.00593	−	12.6679i	−0.254377	−	0.804409i
$249$		0			0
$250$	0.102357	−	1.41050i	0.00647360	−	0.0892081i
$251$		−	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
$254$	12.7358	+	0.924206i	0.799117	+	0.0579898i
$255$		0			0
$256$	13.3876	+	8.76200i	0.836724	+	0.547625i
$257$	−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	$-0.547632\pi$
$263$	12.6788	−	21.9603i	0.781806	−	1.35413i	0.930889	−	0.365303i	$-0.119035\pi$
$264$		0			0
$265$	3.96014	+	6.85916i	0.243269	+	0.421355i
$266$	15.8728	−	23.3995i	0.973222	−	1.43472i
$267$		0			0
$268$	11.1193	+	27.9431i	0.679221	+	1.70690i
$269$	−10.6387			−0.648652			−0.324326	−	0.945945i	$-0.605138\pi$
$269$	−10.6387			−0.648652			−0.324326	+	0.945945i	$0.605138\pi$
$270$		0			0
$271$			22.9127i			1.39185i	0.718115	+	0.695924i	$0.245005\pi$
$271$			22.9127i			1.39185i	−0.718115	+	0.695924i	$0.754995\pi$
$272$	−1.41348	+	4.74079i	−0.0857049	+	0.287452i
$273$		0			0
$274$	−3.11004	+	4.58480i	−0.187884	+	0.276978i
$275$	−4.08838	+	2.36043i	−0.246538	+	0.142339i
$276$		0			0
$277$	13.2767	+	7.66533i	0.797722	+	0.460565i	0.842674	−	0.538424i	$-0.180980\pi$
$277$	13.2767	+	7.66533i	0.797722	+	0.460565i	−0.0449517	+	0.998989i	$0.514313\pi$
$278$	−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	$0.656149\pi$
$284$	1.68504	+	0.245853i	0.0999887	+	0.0145887i
$285$		0			0
$286$	−1.04399	+	14.3865i	−0.0617324	+	0.850690i
$287$	33.5797			1.98215
$288$		0			0
$289$	15.4704			0.910026
$290$	0.581815	−	8.01758i	0.0341654	−	0.470809i
$291$		0			0
$292$	−21.1301	−	3.08295i	−1.23655	−	0.180416i
$293$	13.9870	+	24.2262i	0.817129	+	1.41531i	0.907789	+	0.419428i	$0.137769\pi$
$293$	13.9870	+	24.2262i	0.817129	+	1.41531i	−0.0906593	+	0.995882i	$0.528897\pi$
$294$		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
$302$	−4.88037	+	7.19460i	−0.280834	+	0.414003i
$303$		0			0
$304$	16.7099	+	4.98211i	0.958378	+	0.285744i
$305$			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	$0.355256\pi$
$308$	16.0109	+	40.2359i	0.912308	+	2.29265i
$309$		0			0
$310$	−3.72922	+	5.49758i	−0.211805	+	0.312242i
$311$	−9.87577	−	17.1053i	−0.560004	−	0.969955i	−0.997495	−	0.0707323i	$-0.977466\pi$
$311$	−9.87577	−	17.1053i	−0.560004	−	0.969955i	0.437492	−	0.899222i	$-0.355867\pi$
$312$		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	−0.931401	−	0.363994i	$-0.881413\pi$
$317$	−2.67910	+	4.64033i	−0.150473	+	0.260627i	0.780928	+	0.624621i	$0.214746\pi$
$318$		0			0
$319$	−23.2391	+	13.4171i	−1.30114	+	0.751214i
$320$	−0.710712	−	7.96837i	−0.0397300	−	0.445445i
$321$		0			0
$322$	−1.52459	−	0.110636i	−0.0849621	−	0.00616548i
$323$			5.39126i			0.299978i
$324$		0			0
$325$			2.16053i			0.119844i
$326$	2.52111	−	34.7416i	0.139631	−	1.92416i
$327$		0			0
$328$	6.24371	+	19.7443i	0.344751	+	1.09020i
$329$	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	$0.685300\pi$
$338$	−9.75154	−	6.61484i	−0.530414	−	0.359800i
$339$		0			0
$340$	2.29823	−	0.914529i	0.124639	−	0.0495973i
$341$	22.1756			1.20087
$342$		0			0
$343$		−	32.2711i		−	1.74247i
$344$	10.9584	+	10.0245i	0.590835	+	0.540483i
$345$		0			0
$346$	11.6758	+	7.92015i	0.627696	+	0.425790i
$347$	−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	0.300569	−	0.953760i	$-0.402824\pi$
$349$	−7.00796	−	4.04605i	−0.375128	−	0.216580i	−0.675696	+	0.737180i	$0.736157\pi$
$350$	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
$356$	3.73414	−	25.5933i	0.197909	−	1.35644i
$357$		0			0
$358$	15.7412	+	1.14230i	0.831948	+	0.0603723i
$359$	−28.9175			−1.52621			−0.763103	−	0.646277i	$-0.776325\pi$
$359$	−28.9175			−1.52621			−0.763103	+	0.646277i	$0.776325\pi$
$360$		0			0
$361$	0.00262185			0.000137992
$362$	6.77616	+	0.491728i	0.356147	+	0.0258447i
$363$		0			0
$364$	19.6109	+	2.86129i	1.02789	+	0.149973i
$365$	5.33845	+	9.24648i	0.279428	+	0.483983i
$366$		0			0
$367$	−27.0895	−	15.6401i	−1.41406	−	0.816407i	−0.418291	−	0.908313i	$-0.637371\pi$
$367$	−27.0895	−	15.6401i	−1.41406	−	0.816407i	−0.995768	+	0.0919062i	$0.970704\pi$
$368$	−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	−0.884553	−	0.466439i	$-0.845537\pi$
$373$	−17.8238	+	10.2906i	−0.922882	+	0.532826i	−0.0383285	+	0.999265i	$0.512203\pi$
$374$	−6.83315	−	4.63519i	−0.353334	−	0.239680i
$375$		0			0
$376$	4.42257	+	4.04567i	0.228077	+	0.208640i
$377$			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	$0.490589\pi$
$380$	−3.22345	−	8.10061i	−0.165359	−	0.415552i
$381$		0			0
$382$	−0.336272	−	0.228106i	−0.0172052	−	0.0116709i
$383$	−0.0240645	−	0.0416809i	−0.00122964	−	0.00212979i	0.865410	−	0.501065i	$-0.167058\pi$
$383$	−0.0240645	−	0.0416809i	−0.00122964	−	0.00212979i	−0.866640	+	0.498935i	$0.833725\pi$
$384$		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	$0.338508\pi$
$389$	−10.1379	+	17.5594i	−0.514012	+	0.890294i	−0.999868	+	0.0162556i	$0.994825\pi$
$390$		0			0
$391$	0.252412	−	0.145730i	0.0127650	−	0.00736989i
$392$	37.8525	−	11.9700i	1.91184	−	0.604577i
$393$		0			0
$394$	−1.10727	+	15.2585i	−0.0557833	+	0.768710i
$395$			11.5676i			0.582030i
$396$		0			0
$397$		−	16.5809i		−	0.832169i	−0.909326	−	0.416085i	$-0.863402\pi$
$397$		−	16.5809i		−	0.832169i	0.909326	−	0.416085i	$-0.136598\pi$
$398$	7.20121	+	0.522573i	0.360964	+	0.0261942i
$399$		0			0
$400$	−2.90640	+	2.74824i	−0.145320	+	0.137412i
$401$	−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	$0.973643\pi$
$410$	5.81243	−	8.56863i	0.287055	−	0.423174i
$411$		0			0
$412$	−18.5086	+	7.36506i	−0.911852	+	0.362851i
$413$	−54.0088			−2.65760
$414$		0			0
$415$			2.71396i			0.133223i
$416$	1.96400	+	12.0629i	0.0962931	+	0.591434i
$417$		0			0
$418$	−16.3377	+	24.0849i	−0.799103	+	1.17803i
$419$	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	−0.188897	−	0.981997i	$-0.560491\pi$
$421$	−23.2632	−	13.4310i	−1.13378	−	0.654588i	−0.944883	+	0.327409i	$0.893825\pi$
$422$	−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
$428$	2.10326	−	14.4154i	0.101665	−	0.696796i
$429$		0			0
$430$	0.537464	−	7.40641i	0.0259188	−	0.357169i
$431$	−12.6429			−0.608988			−0.304494	−	0.952514i	$-0.598487\pi$
$431$	−12.6429			−0.608988			−0.304494	+	0.952514i	$0.598487\pi$
$432$		0			0
$433$	−28.3673			−1.36324			−0.681622	−	0.731705i	$-0.738725\pi$
$433$	−28.3673			−1.36324			−0.681622	+	0.731705i	$0.738725\pi$
$434$	2.20522	−	30.3886i	0.105854	−	1.45870i
$435$		0			0
$436$	0.740656	−	5.07635i	0.0354710	−	0.243113i
$437$	−0.513656	−	0.889679i	−0.0245715	−	0.0425591i
$438$		0			0
$439$	1.62013	+	0.935382i	0.0773246	+	0.0446434i	0.538164	−	0.842840i	$-0.319118\pi$
$439$	1.62013	+	0.935382i	0.0773246	+	0.0446434i	−0.460839	+	0.887484i	$0.652452\pi$
$440$	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
$446$	9.49084	−	13.9913i	0.449404	−	0.662508i
$447$		0			0
$448$	21.0965	+	30.0208i	0.996715	+	1.41835i
$449$		−	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
$452$	0.668282	−	0.265927i	0.0314333	−	0.0125082i
$453$		0			0
$454$	15.6639	−	23.0915i	0.735141	−	1.08374i
$455$	−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	$-0.519999\pi$
$461$	17.8836	−	30.9753i	0.832923	−	1.44266i	0.895710	−	0.444638i	$-0.146668\pi$
$462$		0			0
$463$	27.6653	−	15.9726i	1.28572	−	0.742309i	0.307829	−	0.951442i	$-0.400398\pi$
$463$	27.6653	−	15.9726i	1.28572	−	0.742309i	0.977887	+	0.209133i	$0.0670642\pi$
$464$	−16.5205	+	15.6215i	−0.766947	+	0.725212i
$465$		0			0
$466$	38.0516	+	2.76130i	1.76270	+	0.127915i
$467$			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
$470$	0.216910	−	2.98908i	0.0100053	−	0.137876i
$471$		0			0
$472$	−10.0422	−	31.7563i	−0.462232	−	1.46170i
$473$	−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	$0.458539\pi$
$479$	−17.3720	+	30.0891i	−0.793746	+	1.37481i	−0.923633	+	0.383279i	$0.874795\pi$
$480$		0			0
$481$	10.7154	+	18.5596i	0.488581	+	0.846246i
$482$	16.7263	+	11.3461i	0.761862	+	0.516800i
$483$		0			0
$484$	−8.34587	−	20.9734i	−0.379358	−	0.953335i
$485$	−1.63282			−0.0741425
$486$		0			0
$487$			39.8130i			1.80410i	0.431630	+	0.902051i	$0.357939\pi$
$487$			39.8130i			1.80410i	−0.431630	+	0.902051i	$0.642061\pi$
$488$	13.8347	−	15.1236i	0.626268	−	0.684612i
$489$		0			0
$490$	−16.4272	−	11.1432i	−0.742105	−	0.503398i
$491$	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	$0.750432\pi$
$500$	1.97905	+	0.288749i	0.0885056	+	0.0129132i
$501$		0			0
$502$	13.6908	+	0.993504i	0.611049	+	0.0443423i
$503$	16.2502			0.724561			0.362281	−	0.932069i	$-0.381998\pi$
$503$	16.2502			0.724561			0.362281	+	0.932069i	$0.381998\pi$
$504$		0			0
$505$	−2.57742			−0.114694
$506$	1.56925	+	0.113876i	0.0697615	+	0.00506241i
$507$		0			0
$508$	−2.60719	+	17.8693i	−0.115676	+	0.792824i
$509$	2.87628	+	4.98186i	0.127489	+	0.220817i	0.922703	−	0.385512i	$-0.125975\pi$
$509$	2.87628	+	4.98186i	0.127489	+	0.220817i	−0.795214	+	0.606328i	$0.792642\pi$
$510$		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
$518$	53.2450	+	36.1181i	2.33945	+	1.58694i
$519$		0			0
$520$	4.12465	−	4.50891i	0.180878	−	0.197729i
$521$		−	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	$0.365582\pi$
$524$	−2.11592	+	0.841983i	−0.0924346	+	0.0367822i
$525$		0			0
$526$	29.6773	+	20.1312i	1.29399	+	0.877763i
$527$	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
$536$	−40.5521	+	12.8237i	−1.75158	+	0.553899i
$537$		0			0
$538$	1.08894	−	15.0059i	0.0469476	−	0.646951i
$539$			66.2623i			2.85412i
$540$		0			0
$541$		−	28.8219i		−	1.23915i	−0.784938	−	0.619575i	$-0.787305\pi$
$541$		−	28.8219i		−	1.23915i	0.784938	−	0.619575i	$-0.212695\pi$
$542$	−32.3185	−	2.34527i	−1.38820	−	0.100738i
$543$		0			0
$544$	−6.54222	−	2.47897i	−0.280495	−	0.106285i
$545$	−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
$554$	−12.1710	+	17.9423i	−0.517094	+	0.762296i
$555$		0			0
$556$	−8.43626	−	21.2005i	−0.357777	−	0.899103i
$557$	20.1743			0.854811			0.427406	−	0.904060i	$-0.359428\pi$
$557$	20.1743			0.854811			0.427406	+	0.904060i	$0.359428\pi$
$558$		0			0
$559$			11.3447i			0.479830i
$560$	5.24190	−	17.5812i	0.221511	−	0.742943i
$561$		0			0
$562$	−8.52932	+	12.5739i	−0.359788	+	0.530396i
$563$	−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	$0.886407\pi$
$572$	−20.1853	−	2.94510i	−0.843991	−	0.123141i
$573$		0			0
$574$	−3.43710	+	47.3643i	−0.143462	+	1.97695i
$575$	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	$0.561307\pi$
$578$	−1.58350	+	21.8211i	−0.0658650	+	0.907639i
$579$		0			0
$580$	11.2493	+	1.64131i	0.467101	+	0.0681515i
$581$	−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
$590$	−9.34857	+	13.7816i	−0.384875	+	0.567379i
$591$		0			0
$592$	−11.3367	+	38.0230i	−0.465934	+	1.56273i
$593$		−	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
$596$	14.5940	+	36.6751i	0.597793	+	1.50227i
$597$		0			0
$598$	0.404221	−	0.595899i	0.0165298	−	0.0243681i
$599$	18.3740	+	31.8246i	0.750740	+	1.30032i	0.947465	+	0.319861i	$0.103636\pi$
$599$	18.3740	+	31.8246i	0.750740	+	1.30032i	−0.196725	+	0.980459i	$0.563031\pi$
$600$		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	−0.599296	−	0.800528i	$-0.704553\pi$
$607$	−5.06707	+	2.92548i	−0.205666	+	0.118741i	0.393630	+	0.919269i	$0.371219\pi$
$608$	−8.73766	+	23.0594i	−0.354359	+	0.935183i
$609$		0			0
$610$	−10.2216	−	0.741752i	−0.413859	−	0.0300326i
$611$			4.57849i			0.185226i
$612$		0			0
$613$		−	18.4132i		−	0.743703i	−0.928292	−	0.371851i	$-0.878723\pi$
$613$		−	18.4132i		−	0.743703i	0.928292	−	0.371851i	$-0.121277\pi$
$614$	−1.57541	+	21.7096i	−0.0635785	+	0.876130i
$615$		0			0
$616$	−58.3918	+	18.4651i	−2.35267	+	0.743980i
$617$	−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
$626$	−20.7177	−	14.0536i	−0.828047	−	0.561696i
$627$		0			0
$628$	−0.728507	+	0.289893i	−0.0290706	+	0.0115680i
$629$	−12.2677			−0.489145
$630$		0			0
$631$			2.02785i			0.0807273i	0.999185	+	0.0403637i	$0.0128516\pi$
$631$			2.02785i			0.0807273i	−0.999185	+	0.0403637i	$0.987148\pi$
$632$	22.0837	−	24.1410i	0.878442	−	0.960279i
$633$		0			0
$634$	−6.27098	−	4.25385i	−0.249053	−	0.168942i
$635$	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	$0.788741\pi$
$644$	0.312104	−	2.13912i	0.0122986	−	0.0842930i
$645$		0			0
$646$	−7.60439	−	0.551831i	−0.299191	−	0.0217115i
$647$	−48.6780			−1.91373			−0.956865	−	0.290533i	$-0.906168\pi$
$647$	−48.6780			−1.91373			−0.956865	+	0.290533i	$0.906168\pi$
$648$		0			0
$649$	55.5907			2.18213
$650$	−3.04743	−	0.221144i	−0.119530	−	0.00867399i
$651$		0			0
$652$	48.7451	+	7.11207i	1.90901	+	0.278530i
$653$	−1.32043	−	2.28705i	−0.0516724	−	0.0894993i	0.839032	−	0.544082i	$-0.183122\pi$
$653$	−1.32043	−	2.28705i	−0.0516724	−	0.0894993i	−0.890705	+	0.454582i	$0.849789\pi$
$654$		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	−0.565549	−	0.824715i	$-0.691336\pi$
$661$	−3.44771	+	1.99053i	−0.134100	+	0.0774228i	0.431449	+	0.902137i	$0.358002\pi$
$662$	30.2470	+	20.5177i	1.17558	+	0.797443i
$663$		0			0
$664$	5.18120	−	5.66389i	0.201070	−	0.219801i
$665$		−	19.9935i		−	0.775315i
$666$		0			0
$667$	1.33957			0.0518683
$668$	−2.22556	−	5.59290i	−0.0861097	−	0.216396i
$669$		0			0
$670$	17.5988	+	11.9379i	0.679899	+	0.461201i
$671$	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	−0.870328	−	0.492472i	$-0.836094\pi$
$677$	−0.225619	+	0.390784i	−0.00867125	+	0.0150190i	0.861657	+	0.507491i	$0.169427\pi$
$678$		0			0
$679$	6.48561	−	3.74447i	0.248895	−	0.143700i
$680$	1.05471	+	3.33528i	0.0404462	+	0.127902i
$681$		0			0
$682$	−2.26982	+	31.2787i	−0.0869158	+	1.19772i
$683$		−	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
$686$	45.5185	+	3.30316i	1.73791	+	0.126115i
$687$		0			0
$688$	−15.2612	+	14.4307i	−0.581828	+	0.550167i
$689$	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
$698$	6.42428	−	9.47063i	0.243163	−	0.358468i
$699$		0			0
$700$	−8.52302	+	3.39154i	−0.322140	+	0.128188i
$701$	10.3925			0.392520			0.196260	−	0.980552i	$-0.437120\pi$
$701$	10.3925			0.392520			0.196260	+	0.980552i	$0.437120\pi$
$702$		0			0
$703$			43.2400i			1.63083i
$704$	−21.7144	−	30.9001i	−0.818392	−	1.16459i
$705$		0			0
$706$	7.48895	−	11.0401i	0.281850	−	0.415501i
$707$	10.2376	−	5.91068i	0.385025	−	0.222294i
$708$		0			0
$709$	22.1577	+	12.7927i	0.832149	+	0.480442i	0.854588	−	0.519307i	$-0.173810\pi$
$709$	22.1577	+	12.7927i	0.832149	+	0.480442i	−0.0224386	+	0.999748i	$0.507143\pi$
$710$	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
$716$	−3.22243	+	22.0861i	−0.120428	+	0.825396i
$717$		0			0
$718$	2.95989	−	40.7882i	0.110462	−	1.52220i
$719$	−36.4552			−1.35955			−0.679774	−	0.733422i	$-0.737922\pi$
$719$	−36.4552			−1.35955			−0.679774	+	0.733422i	$0.737922\pi$
$720$		0			0
$721$	−45.6820			−1.70129
$722$	−0.000268363		0.00369813i	−9.98745e−6		0.000137630i
$723$		0			0
$724$	−1.38717	+	9.50747i	−0.0515538	+	0.353342i
$725$	−2.84210	−	4.92266i	−0.105553	−	0.182823i
$726$		0			0
$727$	21.4834	+	12.4034i	0.796774	+	0.460018i	0.842342	−	0.538943i	$-0.181176\pi$
$727$	21.4834	+	12.4034i	0.796774	+	0.460018i	−0.0455677	+	0.998961i	$0.514510\pi$
$728$	−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	−0.910824	−	0.412794i	$-0.864553\pi$
$733$	−27.3108	+	15.7679i	−1.00875	+	0.582400i	−0.0979219	+	0.995194i	$0.531220\pi$
$734$	24.8332	−	36.6089i	0.916611	−	1.35126i
$735$		0			0
$736$	1.31580	−	0.214229i	0.0485010	−	0.00789659i
$737$		−	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	$0.379072\pi$
$740$	18.4327	−	7.33489i	0.677601	−	0.269636i
$741$		0			0
$742$	28.8394	−	42.5148i	1.05873	−	1.56077i
$743$	0.498520	+	0.863461i	0.0182889	+	0.0316773i	0.875025	−	0.484078i	$-0.160845\pi$
$743$	0.498520	+	0.863461i	0.0182889	+	0.0316773i	−0.856736	+	0.515755i	$0.827511\pi$
$744$		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	−0.991861	−	0.127323i	$-0.959362\pi$
$751$	−37.7503	+	21.7951i	−1.37753	+	0.795316i	−0.385666	+	0.922639i	$0.626028\pi$
$752$	−6.15912	+	5.82396i	−0.224600	+	0.212378i
$753$		0			0
$754$	−17.3222	−	1.25703i	−0.630837	−	0.0457782i
$755$			6.14737i			0.223726i
$756$		0			0
$757$		−	5.54083i		−	0.201385i	−0.994918	−	0.100692i	$-0.967894\pi$
$757$		−	5.54083i		−	0.201385i	0.994918	−	0.100692i	$-0.0321058\pi$
$758$	−0.117811	+	1.62346i	−0.00427907	+	0.0589668i
$759$		0			0
$760$	11.7559	−	3.71754i	0.426431	−	0.134849i
$761$	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	$0.855575\pi$
$770$	25.3408	+	17.1896i	0.913219	+	0.619471i
$771$		0			0
$772$	−1.76736	−	4.44141i	−0.0636085	−	0.159850i
$773$	26.7361			0.961632			0.480816	−	0.876821i	$-0.340340\pi$
$773$	26.7361			0.961632			0.480816	+	0.876821i	$0.340340\pi$
$774$		0			0
$775$			4.69737i			0.168734i
$776$	3.40761	+	3.11721i	0.122326	+	0.111901i
$777$		0			0
$778$	−23.7299	−	16.0969i	−0.850757	−	0.577101i
$779$	−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	$0.778305\pi$
$788$	−21.4088	−	3.12361i	−0.762657	−	0.111274i
$789$		0			0
$790$	−16.3162	−	1.18402i	−0.580504	−	0.0421257i
$791$	1.64942			0.0586466
$792$		0			0
$793$	15.6568			0.555988
$794$	23.3874	+	1.69716i	0.829987	+	0.0602300i
$795$		0			0
$796$	−1.47418	+	10.1038i	−0.0522510	+	0.358121i
$797$	−12.7189	−	22.0298i	−0.450528	−	0.780337i	0.547891	−	0.836550i	$-0.315431\pi$
$797$	−12.7189	−	22.0298i	−0.450528	−	0.780337i	−0.998419	+	0.0562130i	$0.982097\pi$
$798$		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
$806$	11.8777	+	8.05707i	0.418373	+	0.283798i
$807$		0			0
$808$	5.37895	+	4.92054i	0.189231	+	0.173104i
$809$		−	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	$0.471111\pi$
$812$	−48.4465	+	19.2782i	−1.70014	+	0.676531i
$813$		0			0
$814$	−54.8046	−	37.1760i	−1.92090	−	1.30302i
$815$	−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	−0.984234	−	0.176869i	$-0.943403\pi$
$821$	−9.71181	+	16.8213i	−0.338944	+	0.587069i	0.645290	+	0.763938i	$0.276737\pi$
$822$		0			0
$823$	29.5617	−	17.0675i	1.03046	−	0.594935i	0.113342	−	0.993556i	$-0.463845\pi$
$823$	29.5617	−	17.0675i	1.03046	−	0.594935i	0.917116	+	0.398621i	$0.130511\pi$
$824$	−8.49398	−	26.8603i	−0.295902	−	0.935723i
$825$		0			0
$826$	5.52816	−	76.1796i	0.192349	−	2.65063i
$827$		−	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	$0.0126013\pi$
$829$			2.27907i			0.0791554i	−0.999216	+	0.0395777i	$0.987399\pi$
$830$	−3.82805	−	0.277791i	−0.132873	−	0.00964228i
$831$		0			0
$832$	−17.2159	+	1.53551i	−0.596853	+	0.0532343i
$833$	−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	$-0.587163\pi$
$839$	20.2338	−	35.0460i	0.698548	−	1.20992i	0.968970	−	0.247179i	$-0.0795037\pi$
$840$		0			0
$841$	−1.65503	−	2.86660i	−0.0570700	−	0.0988481i
$842$	21.3257	−	31.4381i	0.734931	−	1.08343i
$843$		0			0
$844$	−0.727013	−	1.82700i	−0.0250248	−	0.0628880i
$845$	−8.33213			−0.286634
$846$		0			0
$847$		−	51.7654i		−	1.77868i
$848$	30.3604	+	9.05205i	1.04258	+	0.310849i
$849$		0			0
$850$	0.981854	−	1.44744i	0.0336773	−	0.0496468i
$851$	2.02444	−	1.16881i	0.0693971	−	0.0400664i
$852$		0			0
$853$	14.2703	+	8.23893i	0.488604	+	0.282096i	0.723995	−	0.689805i	$-0.242304\pi$
$853$	14.2703	+	8.23893i	0.488604	+	0.282096i	−0.235391	+	0.971901i	$0.575637\pi$
$854$	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	$-0.340674\pi$
$860$	10.3918	+	1.51619i	0.354356	+	0.0517017i
$861$		0			0
$862$	1.29409	−	17.8329i	0.0440768	−	0.607391i
$863$	−30.4421			−1.03626			−0.518131	−	0.855301i	$-0.673372\pi$
$863$	−30.4421			−1.03626			−0.518131	+	0.855301i	$0.673372\pi$
$864$		0			0
$865$	9.97631			0.339205
$866$	2.90358	−	40.0122i	0.0986676	−	1.35967i
$867$		0			0
$868$	42.6376	+	6.22096i	1.44721	+	0.211153i
$869$	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	−0.0764015	−	0.997077i	$-0.524343\pi$
$877$	22.1778	−	12.8044i	0.748892	−	0.432373i	0.825293	+	0.564704i	$0.191010\pi$
$878$	−1.48519	+	2.18946i	−0.0501228	+	0.0738906i
$879$		0			0
$880$	−5.39544	+	18.0962i	−0.181880	+	0.610023i
$881$			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	$0.583792\pi$
$884$	−1.97586	−	4.96539i	−0.0664555	−	0.167004i
$885$		0			0
$886$	30.2064	−	44.5301i	1.01480	−	1.49602i
$887$	1.66974	+	2.89207i	0.0560642	+	0.0971061i	0.892695	−	0.450661i	$-0.148812\pi$
$887$	1.66974	+	2.89207i	0.0560642	+	0.0971061i	−0.836631	+	0.547767i	$0.815478\pi$
$888$		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
$896$	−44.5038	+	26.6838i	−1.48677	+	0.891445i
$897$		0			0
$898$	6.39239	+	0.463879i	0.213317	+	0.0154799i
$899$			26.7007i			0.890519i
$900$		0			0
$901$			9.79544i			0.326333i
$902$	3.53778	−	48.7516i	0.117795	−	1.62325i
$903$		0			0
$904$	0.306689	+	0.969834i	0.0102003	+	0.0322562i
$905$	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	$-0.660358\pi$
$911$	15.6065	−	27.0312i	0.517066	−	0.895585i	0.999804	−	0.0198195i	$-0.00630916\pi$
$912$		0			0
$913$	6.40609	+	11.0957i	0.212011	+	0.367213i
$914$	14.9415	+	10.1354i	0.494221	+	0.335249i
$915$		0			0
$916$	−1.57883	+	0.628258i	−0.0521660	+	0.0207582i
$917$	−5.22242			−0.172460
$918$		0			0
$919$		−	41.3010i		−	1.36240i	−0.732100	−	0.681198i	$-0.761459\pi$
$919$		−	41.3010i		−	1.36240i	0.732100	−	0.681198i	$-0.238541\pi$
$920$	−0.491822	−	0.449908i	−0.0162149	−	0.0148330i
$921$		0			0
$922$	41.8603	+	28.3954i	1.37860	+	0.935154i
$923$	−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
$932$	−7.78966	+	53.3893i	−0.255159	+	1.74882i
$933$		0			0
$934$	−1.15247	−	0.0836317i	−0.0377099	−	0.00273651i
$935$	−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	$0.314461\pi$
$938$	−97.2795	−	7.05932i	−3.17629	−	0.230495i
$939$		0			0
$940$	4.19391	+	0.611904i	0.136790	+	0.0199581i
$941$	−12.1325	−	21.0141i	−0.395507	−	0.685039i	0.597659	−	0.801751i	$-0.296098\pi$
$941$	−12.1325	−	21.0141i	−0.395507	−	0.685039i	−0.993166	+	0.116712i	$0.962765\pi$
$942$		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
$950$	−5.10181	−	3.46075i	−0.165525	−	0.112282i
$951$		0			0
$952$	−11.8380	−	10.8291i	−0.383671	−	0.350974i
$953$			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
$956$	−10.3368	−	25.9767i	−0.334317	−	0.840148i
$957$		0			0
$958$	−40.6627	−	27.5831i	−1.31375	−	0.891169i
$959$	−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	−0.989839	−	0.142192i	$-0.954585\pi$
$967$	−42.3417	+	24.4460i	−1.36162	+	0.786130i	−0.371777	+	0.928322i	$0.621251\pi$
$968$	30.4373	−	9.62512i	0.978291	−	0.309363i
$969$		0			0
$970$	0.167130	−	2.30310i	0.00536621	−	0.0739480i
$971$			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
$974$	−56.1565	−	4.07513i	−1.79937	−	0.130576i
$975$		0			0
$976$	19.9158	+	21.0619i	0.637489	+	0.674175i
$977$	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	$-0.586024\pi$
$983$	21.9816	−	38.0733i	0.701104	−	1.21435i	0.968079	−	0.250645i	$-0.0806426\pi$
$984$		0			0
$985$	5.40887	+	9.36843i	0.172341	+	0.298503i
$986$	5.58105	−	8.22753i	0.177737	−	0.262018i
$987$		0			0
$988$	−17.5016	+	6.96435i	−0.556799	+	0.221565i
$989$	1.23745			0.0393488
$990$		0			0
$991$		−	43.4855i		−	1.38136i	−0.723159	−	0.690682i	$-0.757311\pi$
$991$		−	43.4855i		−	1.38136i	0.723159	−	0.690682i	$-0.242689\pi$
$992$	4.27009	+	26.2270i	0.135575	+	0.832707i
$993$		0			0
$994$	−3.10028	+	4.57040i	−0.0983348	+	0.144964i
$995$	4.42142	−	2.55271i	0.140168	−	0.0809262i
$996$		0			0
$997$	−5.50039	−	3.17565i	−0.174199	−	0.100574i	0.410365	−	0.911921i	$-0.365401\pi$
$997$	−5.50039	−	3.17565i	−0.174199	−	0.100574i	−0.584564	+	0.811347i	$0.698735\pi$
$998$	−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.b.251.12		48
3.2	odd	2		360.2.bm.a.11.13	✓	48
4.3	odd	2		4320.2.cc.b.1871.23		48
8.3	odd	2		1080.2.bm.a.251.20		48
8.5	even	2		4320.2.cc.a.1871.2		48
9.4	even	3		360.2.bm.b.131.5	yes	48
9.5	odd	6		1080.2.bm.a.611.20		48
12.11	even	2		1440.2.cc.a.911.1		48
24.5	odd	2		1440.2.cc.b.911.1		48
24.11	even	2		360.2.bm.b.11.5	yes	48
36.23	even	6		4320.2.cc.a.3311.2		48
36.31	odd	6		1440.2.cc.b.1391.1		48
72.5	odd	6		4320.2.cc.b.3311.23		48
72.13	even	6		1440.2.cc.a.1391.1		48
72.59	even	6	inner	1080.2.bm.b.611.12		48
72.67	odd	6		360.2.bm.a.131.13	yes	48

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

\(f(q)\)	\(=\)	\(q+(-0.102357 + 1.41050i) q^{2} +(-1.97905 - 0.288749i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(0.609850 - 2.76190i) q^{8} +O(q^{10})\)	\(q+(-0.102357 + 1.41050i) q^{2} +(-1.97905 - 0.288749i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(0.609850 - 2.76190i) q^{8} +(-1.27271 + 0.616609i) q^{10} +(4.08838 + 2.36043i) q^{11} +(1.87107 - 1.08026i) q^{13} +(3.64121 - 5.36784i) q^{14} +(3.83325 + 1.14290i) q^{16} +1.23675i q^{17} +4.35920 q^{19} +(-0.739459 - 1.85828i) q^{20} +(-3.74786 + 5.52507i) q^{22} +(-0.117833 - 0.204092i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.33220 + 2.74973i) q^{26} +(7.19867 + 5.68538i) q^{28} +(-2.84210 + 4.92266i) q^{29} +(4.06804 - 2.34868i) q^{31} +(-2.00442 + 5.28983i) q^{32} +(-1.74445 - 0.126590i) q^{34} -4.58651i q^{35} +9.91926i q^{37} +(-0.446193 + 6.14867i) q^{38} +(2.69680 - 0.852803i) q^{40} +(-6.34052 + 3.66070i) q^{41} +(-2.62545 + 4.54741i) q^{43} +(-7.40952 - 5.85191i) q^{44} +(0.299934 - 0.145313i) q^{46} +(-1.05958 + 1.83524i) q^{47} +(7.01804 + 12.1556i) q^{49} +(-1.17035 - 0.793896i) q^{50} +(-4.01486 + 1.59762i) q^{52} +7.92028 q^{53} +4.72085i q^{55} +(-8.75609 + 9.57181i) q^{56} +(-6.65252 - 4.51266i) q^{58} +(10.1979 - 5.88778i) q^{59} +(6.27586 + 3.62337i) q^{61} +(2.89644 + 5.97839i) q^{62} +(-7.25617 - 3.36869i) q^{64} +(1.87107 + 1.08026i) q^{65} +(-7.51856 - 13.0225i) q^{67} +(0.357112 - 2.44759i) q^{68} +(6.46930 + 0.469460i) q^{70} -0.851441 q^{71} +10.6769 q^{73} +(-13.9912 - 1.01530i) q^{74} +(-8.62706 - 1.25871i) q^{76} +(-10.8261 - 18.7514i) q^{77} +(10.0179 + 5.78381i) q^{79} +(0.926848 + 3.89114i) q^{80} +(-4.51444 - 9.31802i) q^{82} +(2.35035 + 1.35698i) q^{83} +(-1.07106 + 0.618377i) q^{85} +(-6.14541 - 4.16866i) q^{86} +(9.01256 - 9.85218i) q^{88} +12.9321i q^{89} -9.90928 q^{91} +(0.174265 + 0.437932i) q^{92} +(-2.48016 - 1.68239i) q^{94} +(2.17960 + 3.77518i) q^{95} +(-0.816409 + 1.41406i) q^{97} +(-17.8639 + 8.65477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 + 6 * q^8	\( 48 q + 24 q^{5} + 6 q^{8} - 15 q^{14} + 12 q^{16} + 21 q^{22} - 24 q^{25} + 33 q^{34} + 33 q^{38} - 6 q^{40} - 12 q^{41} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 24 q^{49} - 36 q^{52} - 21 q^{56} - 51 q^{58} + 36 q^{59} + 12 q^{61} - 42 q^{62} - 12 q^{64} - 57 q^{68} - 15 q^{70} - 30 q^{74} + 57 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} + 57 q^{88} + 51 q^{92} + 57 q^{94} - 42 q^{98}+O(q^{100}) \) 48 * q + 24 * q^5 + 6 * q^8 - 15 * q^14 + 12 * q^16 + 21 * q^22 - 24 * q^25 + 33 * q^34 + 33 * q^38 - 6 * q^40 - 12 * q^41 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 24 * q^49 - 36 * q^52 - 21 * q^56 - 51 * q^58 + 36 * q^59 + 12 * q^61 - 42 * q^62 - 12 * q^64 - 57 * q^68 - 15 * q^70 - 30 * q^74 + 57 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 + 57 * q^88 + 51 * q^92 + 57 * q^94 - 42 * q^98

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