LMFDB - Embedded newform 1456.2.cc.d.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.2
Root			$0.500000 - 1.73154i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.d.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.432757 - 0.749558i) q^{3} +3.71131i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.12544 - 1.94932i) q^{9} +O(q^{10})$	\(q+(-0.432757 - 0.749558i) q^{3} +3.71131i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.12544 - 1.94932i) q^{9} +(5.00118 - 2.88743i) q^{11} +(2.87757 + 2.17246i) q^{13} +(2.78184 - 1.60610i) q^{15} +(-0.106098 + 0.183768i) q^{17} +(-1.85081 - 1.06857i) q^{19} -0.865515i q^{21} +(-1.23970 - 2.14722i) q^{23} -8.77384 q^{25} -4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} +2.31076i q^{31} +(-4.32860 - 2.49912i) q^{33} +(-1.85566 + 3.21409i) q^{35} +(6.81859 - 3.93672i) q^{37} +(0.383091 - 3.09706i) q^{39} +(6.51354 - 3.76060i) q^{41} +(-2.28987 + 3.96617i) q^{43} +(7.23455 + 4.17687i) q^{45} +9.15570i q^{47} +(0.500000 + 0.866025i) q^{49} +0.183660 q^{51} +12.0948 q^{53} +(10.7162 + 18.5609i) q^{55} +1.84972i q^{57} +(0.200843 + 0.115957i) q^{59} +(-4.01605 + 6.95601i) q^{61} +(1.94932 - 1.12544i) q^{63} +(-8.06267 + 10.6796i) q^{65} +(11.2323 - 6.48500i) q^{67} +(-1.07298 + 1.85845i) q^{69} +(-6.37721 - 3.68188i) q^{71} -5.60414i q^{73} +(3.79695 + 6.57650i) q^{75} +5.77486 q^{77} +9.19749 q^{79} +(-1.40956 - 2.44144i) q^{81} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +(0.0426552 - 0.0738809i) q^{87} +(-10.2335 + 5.90833i) q^{89} +(1.40582 + 3.32019i) q^{91} +(1.73205 - 1.00000i) q^{93} +(3.96579 - 6.86895i) q^{95} +(12.1952 + 7.04093i) q^{97} -12.9985i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 6 * q^9	$ 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.432757	−	0.749558i	−0.249853	−	0.432757i	0.713632	−	0.700521i	$-0.247049\pi$
$3$	−0.432757	−	0.749558i	−0.249853	−	0.432757i	−0.963485	+	0.267763i	$0.913716\pi$
$4$		0			0
$5$			3.71131i			1.65975i	0.557950	+	0.829875i	$0.311588\pi$
$5$			3.71131i			1.65975i	−0.557950	+	0.829875i	$0.688412\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	1.12544	−	1.94932i	0.375147	−	0.649774i
$10$		0			0
$11$	5.00118	−	2.88743i	1.50791	−	0.870594i	0.507955	−	0.861384i	$-0.330402\pi$
$11$	5.00118	−	2.88743i	1.50791	−	0.870594i	0.999958	−	0.00920984i	$-0.00293162\pi$
$12$		0			0
$13$	2.87757	+	2.17246i	0.798095	+	0.602531i
$13$	2.87757	+	2.17246i	0.798095	+	0.602531i
$14$		0			0
$15$	2.78184	−	1.60610i	0.718269	−	0.414693i
$16$		0			0
$17$	−0.106098	+	0.183768i	−0.0257327	+	0.0445703i	−0.878605	−	0.477549i	$-0.841525\pi$
$17$	−0.106098	+	0.183768i	−0.0257327	+	0.0445703i	0.852872	+	0.522120i	$0.174859\pi$
$18$		0			0
$19$	−1.85081	−	1.06857i	−0.424606	−	0.245146i	0.272440	−	0.962173i	$-0.412169\pi$
$19$	−1.85081	−	1.06857i	−0.424606	−	0.245146i	−0.697046	+	0.717026i	$0.745503\pi$
$20$		0			0
$21$		−	0.865515i		−	0.188871i
$22$		0			0
$23$	−1.23970	−	2.14722i	−0.258495	−	0.447727i	0.707344	−	0.706870i	$-0.249893\pi$
$23$	−1.23970	−	2.14722i	−0.258495	−	0.447727i	−0.965839	+	0.259143i	$0.916560\pi$
$24$		0			0
$25$	−8.77384			−1.75477
$26$		0			0
$27$	−4.54472			−0.874632
$28$		0			0
$29$	0.0492830	+	0.0853606i	0.00915162	+	0.0158511i	0.870565	−	0.492054i	$-0.163754\pi$
$29$	0.0492830	+	0.0853606i	0.00915162	+	0.0158511i	−0.861413	+	0.507905i	$0.830420\pi$
$30$		0			0
$31$			2.31076i			0.415025i	0.978232	+	0.207513i	$0.0665368\pi$
$31$			2.31076i			0.415025i	−0.978232	+	0.207513i	$0.933463\pi$
$32$		0			0
$33$	−4.32860	−	2.49912i	−0.753512	−	0.435040i
$34$		0			0
$35$	−1.85566	+	3.21409i	−0.313663	+	0.543281i
$36$		0			0
$37$	6.81859	−	3.93672i	1.12097	−	0.647192i	0.179321	−	0.983791i	$-0.442610\pi$
$37$	6.81859	−	3.93672i	1.12097	−	0.647192i	0.941648	+	0.336599i	$0.109277\pi$
$38$		0			0
$39$	0.383091	−	3.09706i	0.0613436	−	0.495926i
$40$		0			0
$41$	6.51354	−	3.76060i	1.01724	−	0.587306i	0.103940	−	0.994584i	$-0.466855\pi$
$41$	6.51354	−	3.76060i	1.01724	−	0.587306i	0.913305	+	0.407277i	$0.133522\pi$
$42$		0			0
$43$	−2.28987	+	3.96617i	−0.349201	+	0.604835i	−0.986108	−	0.166107i	$-0.946880\pi$
$43$	−2.28987	+	3.96617i	−0.349201	+	0.604835i	0.636906	+	0.770941i	$0.280214\pi$
$44$		0			0
$45$	7.23455	+	4.17687i	1.07846	+	0.622651i
$46$		0			0
$47$			9.15570i			1.33550i	0.744388	+	0.667748i	$0.232742\pi$
$47$			9.15570i			1.33550i	−0.744388	+	0.667748i	$0.767258\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	0.183660			0.0257175
$52$		0			0
$53$	12.0948			1.66135			0.830674	−	0.556759i	$-0.187955\pi$
$53$	12.0948			1.66135			0.830674	+	0.556759i	$0.187955\pi$
$54$		0			0
$55$	10.7162	+	18.5609i	1.44497	+	2.50276i
$56$		0			0
$57$			1.84972i			0.245002i
$58$		0			0
$59$	0.200843	+	0.115957i	0.0261476	+	0.0150963i	0.513017	−	0.858379i	$-0.328528\pi$
$59$	0.200843	+	0.115957i	0.0261476	+	0.0150963i	−0.486869	+	0.873475i	$0.661861\pi$
$60$		0			0
$61$	−4.01605	+	6.95601i	−0.514203	+	0.890626i	0.485661	+	0.874147i	$0.338579\pi$
$61$	−4.01605	+	6.95601i	−0.514203	+	0.890626i	−0.999864	+	0.0164787i	$0.994754\pi$
$62$		0			0
$63$	1.94932	−	1.12544i	0.245592	−	0.141792i
$64$		0			0
$65$	−8.06267	+	10.6796i	−1.00005	+	1.32464i
$66$		0			0
$67$	11.2323	−	6.48500i	1.37225	−	0.792269i	0.381039	−	0.924559i	$-0.375567\pi$
$67$	11.2323	−	6.48500i	1.37225	−	0.792269i	0.991211	+	0.132291i	$0.0422332\pi$
$68$		0			0
$69$	−1.07298	+	1.85845i	−0.129171	+	0.223731i
$70$		0			0
$71$	−6.37721	−	3.68188i	−0.756836	−	0.436959i	0.0713229	−	0.997453i	$-0.477278\pi$
$71$	−6.37721	−	3.68188i	−0.756836	−	0.436959i	−0.828158	+	0.560494i	$0.810611\pi$
$72$		0			0
$73$		−	5.60414i		−	0.655915i	−0.944692	−	0.327958i	$-0.893640\pi$
$73$		−	5.60414i		−	0.655915i	0.944692	−	0.327958i	$-0.106360\pi$
$74$		0			0
$75$	3.79695	+	6.57650i	0.438434	+	0.759389i
$76$		0			0
$77$	5.77486			0.658107
$78$		0			0
$79$	9.19749			1.03480			0.517399	−	0.855744i	$-0.326900\pi$
$79$	9.19749			1.03480			0.517399	+	0.855744i	$0.326900\pi$
$80$		0			0
$81$	−1.40956	−	2.44144i	−0.156618	−	0.271271i
$82$		0			0
$83$			3.17186i			0.348157i	0.984732	+	0.174078i	$0.0556946\pi$
$83$			3.17186i			0.348157i	−0.984732	+	0.174078i	$0.944305\pi$
$84$		0			0
$85$	−0.682021	−	0.393765i	−0.0739755	−	0.0427098i
$86$		0			0
$87$	0.0426552	−	0.0738809i	0.00457311	−	0.00792087i
$88$		0			0
$89$	−10.2335	+	5.90833i	−1.08475	+	0.626282i	−0.932174	−	0.362010i	$-0.882091\pi$
$89$	−10.2335	+	5.90833i	−1.08475	+	0.626282i	−0.152577	+	0.988292i	$0.548757\pi$
$90$		0			0
$91$	1.40582	+	3.32019i	0.147370	+	0.348050i
$92$		0			0
$93$	1.73205	−	1.00000i	0.179605	−	0.103695i
$94$		0			0
$95$	3.96579	−	6.86895i	0.406882	−	0.704740i
$96$		0			0
$97$	12.1952	+	7.04093i	1.23824	+	0.714898i	0.968734	−	0.248101i	$-0.0798064\pi$
$97$	12.1952	+	7.04093i	1.23824	+	0.714898i	0.269506	+	0.962999i	$0.413140\pi$
$98$		0			0
$99$		−	12.9985i		−	1.30640i
$100$		0			0
$101$	−3.07622	−	5.32816i	−0.306095	−	0.530172i	0.671410	−	0.741087i	$-0.265689\pi$
$101$	−3.07622	−	5.32816i	−0.306095	−	0.530172i	−0.977505	+	0.210914i	$0.932356\pi$
$102$		0			0
$103$	−19.3491			−1.90652			−0.953260	−	0.302152i	$-0.902295\pi$
$103$	−19.3491			−1.90652			−0.953260	+	0.302152i	$0.902295\pi$
$104$		0			0
$105$	3.21220			0.313478
$106$		0			0
$107$	5.82506	+	10.0893i	0.563130	+	0.975369i	0.997221	+	0.0745005i	$0.0237362\pi$
$107$	5.82506	+	10.0893i	0.563130	+	0.975369i	−0.434091	+	0.900869i	$0.642930\pi$
$108$		0			0
$109$			5.73307i			0.549129i	0.961569	+	0.274564i	$0.0885336\pi$
$109$			5.73307i			0.549129i	−0.961569	+	0.274564i	$0.911466\pi$
$110$		0			0
$111$	−5.90159	−	3.40729i	−0.560154	−	0.323405i
$112$		0			0
$113$	−8.25971	+	14.3062i	−0.777008	+	1.34582i	0.156650	+	0.987654i	$0.449930\pi$
$113$	−8.25971	+	14.3062i	−0.777008	+	1.34582i	−0.933659	+	0.358164i	$0.883403\pi$
$114$		0			0
$115$	7.96901	−	4.60091i	0.743114	−	0.429037i
$116$		0			0
$117$	7.47336	−	3.16435i	0.690913	−	0.292544i
$118$		0			0
$119$	−0.183768	+	0.106098i	−0.0168460	+	0.00972603i
$120$		0			0
$121$	11.1745	−	19.3549i	1.01587	−	1.75953i
$122$		0			0
$123$	−5.63757	−	3.25485i	−0.508323	−	0.293480i
$124$		0			0
$125$		−	14.0059i		−	1.25273i
$126$		0			0
$127$	5.89420	+	10.2090i	0.523025	+	0.905907i	0.999641	+	0.0267947i	$0.00853005\pi$
$127$	5.89420	+	10.2090i	0.523025	+	0.905907i	−0.476616	+	0.879112i	$0.658137\pi$
$128$		0			0
$129$	3.96383			0.348996
$130$		0			0
$131$	5.12859			0.448087			0.224043	−	0.974579i	$-0.428074\pi$
$131$	5.12859			0.448087			0.224043	+	0.974579i	$0.428074\pi$
$132$		0			0
$133$	−1.06857	−	1.85081i	−0.0926566	−	0.160486i
$134$		0			0
$135$		−	16.8669i		−	1.45167i
$136$		0			0
$137$	−8.13482	−	4.69664i	−0.695005	−	0.401261i	0.110479	−	0.993878i	$-0.464761\pi$
$137$	−8.13482	−	4.69664i	−0.695005	−	0.401261i	−0.805484	+	0.592617i	$0.798095\pi$
$138$		0			0
$139$	7.57063	−	13.1127i	0.642133	−	1.11221i	−0.342823	−	0.939400i	$-0.611383\pi$
$139$	7.57063	−	13.1127i	0.642133	−	1.11221i	0.984956	−	0.172806i	$-0.0552835\pi$
$140$		0			0
$141$	6.86273	−	3.96220i	0.577946	−	0.333677i
$142$		0			0
$143$	20.6641	+	2.55605i	1.72802	+	0.213747i
$144$		0			0
$145$	−0.316800	+	0.182905i	−0.0263088	+	0.0151894i
$146$		0			0
$147$	0.432757	−	0.749558i	0.0356932	−	0.0618225i
$148$		0			0
$149$	−17.8425	−	10.3013i	−1.46171	−	0.843919i	−0.462620	−	0.886557i	$-0.653091\pi$
$149$	−17.8425	−	10.3013i	−1.46171	−	0.843919i	−0.999091	+	0.0426374i	$0.986424\pi$
$150$		0			0
$151$			11.9407i			0.971721i	0.874036	+	0.485861i	$0.161494\pi$
$151$			11.9407i			0.971721i	−0.874036	+	0.485861i	$0.838506\pi$
$152$		0			0
$153$	0.238815	+	0.413640i	0.0193071	+	0.0334408i
$154$		0			0
$155$	−8.57596			−0.688838
$156$		0			0
$157$	9.34022			0.745431			0.372715	−	0.927946i	$-0.378427\pi$
$157$	9.34022			0.745431			0.372715	+	0.927946i	$0.378427\pi$
$158$		0			0
$159$	−5.23411	−	9.06575i	−0.415092	−	0.718961i
$160$		0			0
$161$		−	2.47940i		−	0.195404i
$162$		0			0
$163$	−3.87746	−	2.23865i	−0.303706	−	0.175345i	0.340401	−	0.940280i	$-0.389437\pi$
$163$	−3.87746	−	2.23865i	−0.303706	−	0.175345i	−0.644106	+	0.764936i	$0.722771\pi$
$164$		0			0
$165$	9.27500	−	16.0648i	0.722058	−	1.25064i
$166$		0			0
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.903950	−	0.427638i	$-0.859346\pi$
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.0816295	+	0.996663i	$0.526012\pi$
$168$		0			0
$169$	3.56086	+	12.5028i	0.273912	+	0.961755i
$170$		0			0
$171$	−4.16597	+	2.40522i	−0.318580	+	0.183932i
$172$		0			0
$173$	6.88286	−	11.9215i	0.523294	−	0.906372i	−0.476339	−	0.879262i	$-0.658036\pi$
$173$	6.88286	−	11.9215i	0.523294	−	0.906372i	0.999632	−	0.0271097i	$-0.00863036\pi$
$174$		0			0
$175$	−7.59837	−	4.38692i	−0.574383	−	0.331620i
$176$		0			0
$177$		−	0.200725i		−	0.0150874i
$178$		0			0
$179$	−7.63936	−	13.2318i	−0.570992	−	0.988988i	−0.996464	−	0.0840164i	$-0.973225\pi$
$179$	−7.63936	−	13.2318i	−0.570992	−	0.988988i	0.425472	−	0.904972i	$-0.360108\pi$
$180$		0			0
$181$	−1.66748			−0.123943			−0.0619713	−	0.998078i	$-0.519739\pi$
$181$	−1.66748			−0.123943			−0.0619713	+	0.998078i	$0.519739\pi$
$182$		0			0
$183$	6.95191			0.513900
$184$		0			0
$185$	14.6104	+	25.3059i	1.07418	+	1.86053i
$186$		0			0
$187$			1.22541i			0.0896108i
$188$		0			0
$189$	−3.93584	−	2.27236i	−0.286290	−	0.165290i
$190$		0			0
$191$	0.0604880	−	0.104768i	0.00437676	−	0.00758076i	−0.863829	−	0.503786i	$-0.831940\pi$
$191$	0.0604880	−	0.104768i	0.00437676	−	0.00758076i	0.868205	+	0.496205i	$0.165273\pi$
$192$		0			0
$193$	−2.38633	+	1.37775i	−0.171772	+	0.0991725i	−0.583421	−	0.812170i	$-0.698286\pi$
$193$	−2.38633	+	1.37775i	−0.171772	+	0.0991725i	0.411649	+	0.911342i	$0.364953\pi$
$194$		0			0
$195$	11.4941	+	1.42177i	0.823113	+	0.101815i
$196$		0			0
$197$	−13.0989	+	7.56267i	−0.933260	+	0.538818i	−0.887841	−	0.460150i	$-0.847796\pi$
$197$	−13.0989	+	7.56267i	−0.933260	+	0.538818i	−0.0454187	+	0.998968i	$0.514462\pi$
$198$		0			0
$199$	−2.65320	+	4.59548i	−0.188080	+	0.325765i	−0.944610	−	0.328194i	$-0.893560\pi$
$199$	−2.65320	+	4.59548i	−0.188080	+	0.325765i	0.756530	+	0.653959i	$0.226893\pi$
$200$		0			0
$201$	−9.72176	−	5.61286i	−0.685720	−	0.395901i
$202$		0			0
$203$			0.0985660i			0.00691798i
$204$		0			0
$205$	13.9567	+	24.1738i	0.974782	+	1.68837i
$206$		0			0
$207$	−5.58084			−0.387895
$208$		0			0
$209$	−12.3417			−0.853691
$210$		0			0
$211$	8.94910	+	15.5003i	0.616081	+	1.06708i	0.990194	+	0.139701i	$0.0446141\pi$
$211$	8.94910	+	15.5003i	0.616081	+	1.06708i	−0.374112	+	0.927383i	$0.622053\pi$
$212$		0			0
$213$			6.37345i			0.436702i
$214$		0			0
$215$	−14.7197	−	8.49841i	−1.00387	−	0.579587i
$216$		0			0
$217$	−1.15538	+	2.00118i	−0.0784324	+	0.135849i
$218$		0			0
$219$	−4.20063	+	2.42524i	−0.283852	+	0.163882i
$220$		0			0
$221$	−0.704534	+	0.298312i	−0.0473921	+	0.0200666i
$222$		0			0
$223$	14.2362	−	8.21925i	0.953324	−	0.550402i	0.0592118	−	0.998245i	$-0.481141\pi$
$223$	14.2362	−	8.21925i	0.953324	−	0.550402i	0.894112	+	0.447844i	$0.147808\pi$
$224$		0			0
$225$	−9.87445	+	17.1031i	−0.658297	+	1.14020i
$226$		0			0
$227$	4.87655	+	2.81547i	0.323668	+	0.186870i	0.653026	−	0.757335i	$-0.273499\pi$
$227$	4.87655	+	2.81547i	0.323668	+	0.186870i	−0.329359	+	0.944205i	$0.606832\pi$
$228$		0			0
$229$		−	27.7225i		−	1.83196i	−0.401228	−	0.915978i	$-0.631416\pi$
$229$		−	27.7225i		−	1.83196i	0.401228	−	0.915978i	$-0.368584\pi$
$230$		0			0
$231$	−2.49912	−	4.32860i	−0.164430	−	0.284801i
$232$		0			0
$233$	−20.1104			−1.31747			−0.658737	−	0.752374i	$-0.728909\pi$
$233$	−20.1104			−1.31747			−0.658737	+	0.752374i	$0.728909\pi$
$234$		0			0
$235$	−33.9797			−2.21659
$236$		0			0
$237$	−3.98028	−	6.89405i	−0.258547	−	0.447817i
$238$		0			0
$239$			6.62968i			0.428838i	0.976742	+	0.214419i	$0.0687858\pi$
$239$			6.62968i			0.428838i	−0.976742	+	0.214419i	$0.931214\pi$
$240$		0			0
$241$	1.40025	+	0.808433i	0.0901978	+	0.0520757i	0.544420	−	0.838812i	$-0.316750\pi$
$241$	1.40025	+	0.808433i	0.0901978	+	0.0520757i	−0.454223	+	0.890888i	$0.650083\pi$
$242$		0			0
$243$	−8.03708	+	13.9206i	−0.515579	+	0.893009i
$244$		0			0
$245$	−3.21409	+	1.85566i	−0.205341	+	0.118554i
$246$		0			0
$247$	−3.00444	−	7.09570i	−0.191168	−	0.451489i
$248$		0			0
$249$	2.37749	−	1.37265i	0.150667	−	0.0869879i
$250$		0			0
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	−0.873915	−	0.486079i	$-0.838427\pi$
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	0.857914	+	0.513793i	$0.171760\pi$
$252$		0			0
$253$	−12.3999	−	7.15910i	−0.779576	−	0.450089i
$254$		0			0
$255$			0.681619i			0.0426846i
$256$		0			0
$257$	−4.82032	−	8.34903i	−0.300683	−	0.520798i	0.675608	−	0.737261i	$-0.263881\pi$
$257$	−4.82032	−	8.34903i	−0.300683	−	0.520798i	−0.976291	+	0.216463i	$0.930548\pi$
$258$		0			0
$259$	7.87343			0.489231
$260$		0			0
$261$	0.221861			0.0137328
$262$		0			0
$263$	−3.67309	−	6.36197i	−0.226492	−	0.392296i	0.730274	−	0.683155i	$-0.239392\pi$
$263$	−3.67309	−	6.36197i	−0.226492	−	0.392296i	−0.956766	+	0.290858i	$0.906059\pi$
$264$		0			0
$265$			44.8876i			2.75742i
$266$		0			0
$267$	8.85727	+	5.11375i	0.542056	+	0.312956i
$268$		0			0
$269$	−11.1770	+	19.3592i	−0.681476	+	1.18035i	0.293055	+	0.956096i	$0.405328\pi$
$269$	−11.1770	+	19.3592i	−0.681476	+	1.18035i	−0.974530	+	0.224255i	$0.928005\pi$
$270$		0			0
$271$	8.32891	−	4.80870i	0.505945	−	0.292108i	−0.225220	−	0.974308i	$-0.572310\pi$
$271$	8.32891	−	4.80870i	0.505945	−	0.292108i	0.731165	+	0.682200i	$0.238977\pi$
$272$		0			0
$273$	1.88029	−	2.49058i	0.113801	−	0.150737i
$274$		0			0
$275$	−43.8796	+	25.3339i	−2.64604	+	1.52769i
$276$		0			0
$277$	5.08945	−	8.81518i	0.305795	−	0.529653i	−0.671643	−	0.740875i	$-0.734411\pi$
$277$	5.08945	−	8.81518i	0.305795	−	0.529653i	0.977438	+	0.211222i	$0.0677444\pi$
$278$		0			0
$279$	4.50442	+	2.60063i	0.269673	+	0.155696i
$280$		0			0
$281$		−	14.1692i		−	0.845265i	−0.906301	−	0.422633i	$-0.861106\pi$
$281$		−	14.1692i		−	0.845265i	0.906301	−	0.422633i	$-0.138894\pi$
$282$		0			0
$283$	−9.46631	−	16.3961i	−0.562714	−	0.974649i	−0.997258	−	0.0739986i	$-0.976424\pi$
$283$	−9.46631	−	16.3961i	−0.562714	−	0.974649i	0.434545	−	0.900650i	$-0.356909\pi$
$284$		0			0
$285$	−6.86490			−0.406642
$286$		0			0
$287$	7.52119			0.443962
$288$		0			0
$289$	8.47749	+	14.6834i	0.498676	+	0.863732i
$290$		0			0
$291$		−	12.1881i		−	0.714477i
$292$		0			0
$293$	3.16950	+	1.82991i	0.185164	+	0.106905i	0.589717	−	0.807610i	$-0.299239\pi$
$293$	3.16950	+	1.82991i	0.185164	+	0.106905i	−0.404553	+	0.914515i	$0.632573\pi$
$294$		0			0
$295$	−0.430353	+	0.745393i	−0.0250561	+	0.0433985i
$296$		0			0
$297$	−22.7290	+	13.1226i	−1.31887	+	0.761449i
$298$		0			0
$299$	1.09742	−	8.87198i	0.0634655	−	0.513080i
$300$		0			0
$301$	−3.96617	+	2.28987i	−0.228606	+	0.131986i
$302$		0			0
$303$	−2.66251	+	4.61161i	−0.152957	+	0.264930i
$304$		0			0
$305$	−25.8159	−	14.9048i	−1.47822	−	0.853448i
$306$		0			0
$307$		−	19.6987i		−	1.12426i	−0.827048	−	0.562132i	$-0.809981\pi$
$307$		−	19.6987i		−	1.12426i	0.827048	−	0.562132i	$-0.190019\pi$
$308$		0			0
$309$	8.37345	+	14.5032i	0.476349	+	0.825061i
$310$		0			0
$311$	−16.9685			−0.962195			−0.481098	−	0.876667i	$-0.659762\pi$
$311$	−16.9685			−0.962195			−0.481098	+	0.876667i	$0.659762\pi$
$312$		0			0
$313$	−4.53794			−0.256500			−0.128250	−	0.991742i	$-0.540936\pi$
$313$	−4.53794			−0.256500			−0.128250	+	0.991742i	$0.540936\pi$
$314$		0			0
$315$	4.17687	+	7.23455i	0.235340	+	0.407620i
$316$		0			0
$317$		−	29.1866i		−	1.63928i	−0.572877	−	0.819641i	$-0.694173\pi$
$317$		−	29.1866i		−	1.63928i	0.572877	−	0.819641i	$-0.305827\pi$
$318$		0			0
$319$	0.492946	+	0.284603i	0.0275997	+	0.0159347i
$320$		0			0
$321$	5.04168	−	8.73244i	0.281399	−	0.487397i
$322$		0			0
$323$	0.392737	−	0.226747i	0.0218525	−	0.0126165i
$324$		0			0
$325$	−25.2474	−	19.0608i	−1.40047	−	1.05730i
$326$		0			0
$327$	4.29727	−	2.48103i	0.237640	−	0.137201i
$328$		0			0
$329$	−4.57785	+	7.92907i	−0.252385	+	0.437144i
$330$		0			0
$331$	−4.16161	−	2.40271i	−0.228743	−	0.132065i	0.381249	−	0.924472i	$-0.375494\pi$
$331$	−4.16161	−	2.40271i	−0.228743	−	0.132065i	−0.609992	+	0.792408i	$0.708827\pi$
$332$		0			0
$333$		−	17.7222i		−	0.971169i
$334$		0			0
$335$	24.0679	+	41.6868i	1.31497	+	2.27759i
$336$		0			0
$337$	17.7312			0.965883			0.482941	−	0.875653i	$-0.339568\pi$
$337$	17.7312			0.965883			0.482941	+	0.875653i	$0.339568\pi$
$338$		0			0
$339$	14.2978			0.776550
$340$		0			0
$341$	6.67217	+	11.5565i	0.361318	+	0.625822i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−6.89730	−	3.98216i	−0.371338	−	0.214392i
$346$		0			0
$347$	−8.35240	+	14.4668i	−0.448380	+	0.776617i	−0.998281	−	0.0586128i	$-0.981332\pi$
$347$	−8.35240	+	14.4668i	−0.448380	+	0.776617i	0.549901	+	0.835230i	$0.314666\pi$
$348$		0			0
$349$	0.0173616	−	0.0100237i	0.000929347	−	0.000536559i	−0.499535	−	0.866294i	$-0.666496\pi$
$349$	0.0173616	−	0.0100237i	0.000929347	−	0.000536559i	0.500465	+	0.865757i	$0.333163\pi$
$350$		0			0
$351$	−13.0778	−	9.87321i	−0.698039	−	0.526993i
$352$		0			0
$353$	25.8299	−	14.9129i	1.37479	−	0.793734i	0.383262	−	0.923640i	$-0.374801\pi$
$353$	25.8299	−	14.9129i	1.37479	−	0.793734i	0.991526	+	0.129905i	$0.0414674\pi$
$354$		0			0
$355$	13.6646	−	23.6678i	0.725243	−	1.25616i
$356$		0			0
$357$	0.159054	+	0.0918298i	0.00841803	+	0.00486015i
$358$		0			0
$359$		−	18.3351i		−	0.967687i	−0.875154	−	0.483844i	$-0.839240\pi$
$359$		−	18.3351i		−	0.967687i	0.875154	−	0.483844i	$-0.160760\pi$
$360$		0			0
$361$	−7.21632	−	12.4990i	−0.379806	−	0.657844i
$362$		0			0
$363$	−19.3434			−1.01527
$364$		0			0
$365$	20.7987			1.08866
$366$		0			0
$367$	0.672426	+	1.16468i	0.0351004	+	0.0607956i	0.883042	−	0.469294i	$-0.155492\pi$
$367$	0.672426	+	1.16468i	0.0351004	+	0.0607956i	−0.847942	+	0.530090i	$0.822158\pi$
$368$		0			0
$369$		−	16.9293i		−	0.881306i
$370$		0			0
$371$	10.4744	+	6.04740i	0.543804	+	0.313965i
$372$		0			0
$373$	5.53575	−	9.58821i	0.286630	−	0.496458i	−0.686373	−	0.727250i	$-0.740798\pi$
$373$	5.53575	−	9.58821i	0.286630	−	0.496458i	0.973003	+	0.230791i	$0.0741315\pi$
$374$		0			0
$375$	−10.4982	+	6.06116i	−0.542127	+	0.312997i
$376$		0			0
$377$	−0.0436269	+	0.352697i	−0.00224690	+	0.0181648i
$378$		0			0
$379$	−14.5583	+	8.40523i	−0.747808	+	0.431747i	−0.824902	−	0.565276i	$-0.808769\pi$
$379$	−14.5583	+	8.40523i	−0.747808	+	0.431747i	0.0770930	+	0.997024i	$0.475436\pi$
$380$		0			0
$381$	5.10152	−	8.83608i	0.261359	−	0.452686i
$382$		0			0
$383$	−14.3562	−	8.28855i	−0.733567	−	0.423525i	0.0861585	−	0.996281i	$-0.472541\pi$
$383$	−14.3562	−	8.28855i	−0.733567	−	0.423525i	−0.819726	+	0.572756i	$0.805874\pi$
$384$		0			0
$385$			21.4323i			1.09229i
$386$		0			0
$387$	5.15422	+	8.92738i	0.262004	+	0.453804i
$388$		0			0
$389$	−1.17013			−0.0593280			−0.0296640	−	0.999560i	$-0.509444\pi$
$389$	−1.17013			−0.0593280			−0.0296640	+	0.999560i	$0.509444\pi$
$390$		0			0
$391$	0.526121			0.0266071
$392$		0			0
$393$	−2.21944	−	3.84418i	−0.111956	−	0.193913i
$394$		0			0
$395$			34.1348i			1.71751i
$396$		0			0
$397$	22.6877	+	13.0987i	1.13866	+	0.657406i	0.946099	−	0.323878i	$-0.104987\pi$
$397$	22.6877	+	13.0987i	1.13866	+	0.657406i	0.192562	+	0.981285i	$0.438320\pi$
$398$		0			0
$399$	−0.924862	+	1.60191i	−0.0463010	+	0.0801957i
$400$		0			0
$401$	−9.84559	+	5.68436i	−0.491665	+	0.283863i	−0.725265	−	0.688470i	$-0.758283\pi$
$401$	−9.84559	+	5.68436i	−0.491665	+	0.283863i	0.233600	+	0.972333i	$0.424949\pi$
$402$		0			0
$403$	−5.02003	+	6.64939i	−0.250066	+	0.331230i
$404$		0			0
$405$	9.06094	−	5.23134i	0.450242	−	0.259947i
$406$		0			0
$407$	22.7340	−	39.3764i	1.12688	−	1.95182i
$408$		0			0
$409$	−20.2056	−	11.6657i	−0.999102	−	0.576832i	−0.0911196	−	0.995840i	$-0.529045\pi$
$409$	−20.2056	−	11.6657i	−0.999102	−	0.576832i	−0.907982	+	0.419008i	$0.862378\pi$
$410$		0			0
$411$			8.13003i			0.401025i
$412$		0			0
$413$	0.115957	+	0.200843i	0.00570587	+	0.00988286i
$414$		0			0
$415$	−11.7718			−0.577853
$416$		0			0
$417$	−13.1050			−0.641754
$418$		0			0
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	0.668802	−	0.743441i	$-0.266807\pi$
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	−0.978239	+	0.207479i	$0.933474\pi$
$420$		0			0
$421$		−	27.6625i		−	1.34819i	−0.738646	−	0.674094i	$-0.764534\pi$
$421$		−	27.6625i		−	1.34819i	0.738646	−	0.674094i	$-0.235466\pi$
$422$		0			0
$423$	17.8474	+	10.3042i	0.867771	+	0.501008i
$424$		0			0
$425$	0.930892	−	1.61235i	0.0451549	−	0.0782105i
$426$		0			0
$427$	−6.95601	+	4.01605i	−0.336625	+	0.194351i
$428$		0			0
$429$	−7.02663	−	16.5951i	−0.339249	−	0.801218i
$430$		0			0
$431$	−5.55462	+	3.20696i	−0.267557	+	0.154474i	−0.627777	−	0.778393i	$-0.716035\pi$
$431$	−5.55462	+	3.20696i	−0.267557	+	0.154474i	0.360220	+	0.932867i	$0.382702\pi$
$432$		0			0
$433$	−0.0325135	+	0.0563150i	−0.00156250	+	0.00270633i	−0.866806	−	0.498646i	$-0.833831\pi$
$433$	−0.0325135	+	0.0563150i	−0.00156250	+	0.00270633i	0.865243	+	0.501353i	$0.167164\pi$
$434$		0			0
$435$	0.274195	+	0.158307i	0.0131467	+	0.00759022i
$436$		0			0
$437$			5.29881i			0.253477i
$438$		0			0
$439$	−18.3889	−	31.8505i	−0.877655	−	1.52014i	−0.853908	−	0.520424i	$-0.825774\pi$
$439$	−18.3889	−	31.8505i	−0.877655	−	1.52014i	−0.0237469	−	0.999718i	$-0.507560\pi$
$440$		0			0
$441$	2.25088			0.107185
$442$		0			0
$443$	8.46383			0.402129			0.201064	−	0.979578i	$-0.435560\pi$
$443$	8.46383			0.402129			0.201064	+	0.979578i	$0.435560\pi$
$444$		0			0
$445$	−21.9277	−	37.9798i	−1.03947	−	1.80042i
$446$		0			0
$447$			17.8319i			0.843422i
$448$		0			0
$449$	−19.5984	−	11.3152i	−0.924907	−	0.533995i	−0.0397096	−	0.999211i	$-0.512643\pi$
$449$	−19.5984	−	11.3152i	−0.924907	−	0.533995i	−0.885197	+	0.465216i	$0.845977\pi$
$450$		0			0
$451$	21.7169	−	37.6148i	1.02261	−	1.77121i
$452$		0			0
$453$	8.95026	−	5.16743i	0.420520	−	0.242787i
$454$		0			0
$455$	−12.3223	+	5.21745i	−0.577677	+	0.244598i
$456$		0			0
$457$	−14.1310	+	8.15851i	−0.661018	+	0.381639i	−0.792665	−	0.609658i	$-0.791307\pi$
$457$	−14.1310	+	8.15851i	−0.661018	+	0.381639i	0.131647	+	0.991297i	$0.457974\pi$
$458$		0			0
$459$	0.482188	−	0.835174i	0.0225066	−	0.0389826i
$460$		0			0
$461$	16.6951	+	9.63892i	0.777568	+	0.448929i	0.835568	−	0.549387i	$-0.185139\pi$
$461$	16.6951	+	9.63892i	0.777568	+	0.448929i	−0.0579996	+	0.998317i	$0.518472\pi$
$462$		0			0
$463$		−	2.70218i		−	0.125581i	−0.998027	−	0.0627904i	$-0.980000\pi$
$463$		−	2.70218i		−	0.125581i	0.998027	−	0.0627904i	$-0.0200000\pi$
$464$		0			0
$465$	3.71131	+	6.42818i	0.172108	+	0.298100i
$466$		0			0
$467$	18.3906			0.851014			0.425507	−	0.904955i	$-0.360096\pi$
$467$	18.3906			0.851014			0.425507	+	0.904955i	$0.360096\pi$
$468$		0			0
$469$	12.9700			0.598899
$470$		0			0
$471$	−4.04205	−	7.00104i	−0.186248	−	0.322591i
$472$		0			0
$473$			26.4473i			1.21605i
$474$		0			0
$475$	16.2388	+	9.37545i	0.745085	+	0.430175i
$476$		0			0
$477$	13.6120	−	23.5767i	0.623250	−	1.07950i
$478$		0			0
$479$	−35.3951	+	20.4354i	−1.61725	+	0.933717i	−0.629617	+	0.776906i	$0.716788\pi$
$479$	−35.3951	+	20.4354i	−1.61725	+	0.933717i	−0.987629	+	0.156811i	$0.949879\pi$
$480$		0			0
$481$	28.1733	+	3.48491i	1.28459	+	0.158898i
$482$		0			0
$483$	−1.85845	+	1.07298i	−0.0845625	+	0.0488222i
$484$		0			0
$485$	−26.1311	+	45.2604i	−1.18655	+	2.05517i
$486$		0			0
$487$	−15.2674	−	8.81466i	−0.691834	−	0.399430i	0.112465	−	0.993656i	$-0.464125\pi$
$487$	−15.2674	−	8.81466i	−0.691834	−	0.399430i	−0.804299	+	0.594225i	$0.797459\pi$
$488$		0			0
$489$			3.87517i			0.175241i
$490$		0			0
$491$	9.42997	+	16.3332i	0.425569	+	0.737106i	0.996473	−	0.0839098i	$-0.0267408\pi$
$491$	9.42997	+	16.3332i	0.425569	+	0.737106i	−0.570905	+	0.821016i	$0.693407\pi$
$492$		0			0
$493$	−0.0209154			−0.000941982
$494$		0			0
$495$	48.2417			2.16830
$496$		0			0
$497$	−3.68188	−	6.37721i	−0.165155	−	0.286057i
$498$		0			0
$499$			2.10742i			0.0943410i	0.998887	+	0.0471705i	$0.0150204\pi$
$499$			2.10742i			0.0943410i	−0.998887	+	0.0471705i	$0.984980\pi$
$500$		0			0
$501$	11.0236	+	6.36449i	0.492499	+	0.284345i
$502$		0			0
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	−0.514117	−	0.857720i	$-0.671880\pi$
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	0.999866	+	0.0163784i	$0.00521363\pi$
$504$		0			0
$505$	19.7745	−	11.4168i	0.879953	−	0.508041i
$506$		0			0
$507$	7.83059	−	8.07976i	0.347769	−	0.358835i
$508$		0			0
$509$	−10.5636	+	6.09887i	−0.468221	+	0.270328i	−0.715495	−	0.698618i	$-0.753799\pi$
$509$	−10.5636	+	6.09887i	−0.468221	+	0.270328i	0.247273	+	0.968946i	$0.420465\pi$
$510$		0			0
$511$	2.80207	−	4.85333i	0.123956	−	0.214699i
$512$		0			0
$513$	8.41143	+	4.85634i	0.371374	+	0.214413i
$514$		0			0
$515$		−	71.8104i		−	3.16435i
$516$		0			0
$517$	26.4365	+	45.7893i	1.16267	+	2.01381i
$518$		0			0
$519$	−11.9144			−0.522986
$520$		0			0
$521$	−26.9765			−1.18186			−0.590932	−	0.806722i	$-0.701240\pi$
$521$	−26.9765			−1.18186			−0.590932	+	0.806722i	$0.701240\pi$
$522$		0			0
$523$	−1.87683	−	3.25076i	−0.0820679	−	0.142146i	0.822070	−	0.569386i	$-0.192819\pi$
$523$	−1.87683	−	3.25076i	−0.0820679	−	0.142146i	−0.904138	+	0.427241i	$0.859486\pi$
$524$		0			0
$525$			7.59389i			0.331425i
$526$		0			0
$527$	−0.424644	−	0.245168i	−0.0184978	−	0.0106797i
$528$		0			0
$529$	8.42629	−	14.5948i	0.366360	−	0.634555i
$530$		0			0
$531$	0.452075	−	0.261006i	0.0196184	−	0.0113267i
$532$		0			0
$533$	26.9129	+	3.32900i	1.16573	+	0.144195i
$534$		0			0
$535$	−37.4445	+	21.6186i	−1.61887	+	0.934654i
$536$		0			0
$537$	−6.61198	+	11.4523i	−0.285328	+	0.494203i
$538$		0			0
$539$	5.00118	+	2.88743i	0.215416	+	0.124371i
$540$		0			0
$541$			0.0135705i			0.000583440i	1.00000		0.000291720i	$9.28574e-5\pi$
$541$			0.0135705i			0.000583440i	−1.00000		0.000291720i	$0.999907\pi$
$542$		0			0
$543$	0.721614	+	1.24987i	0.0309674	+	0.0536371i
$544$		0			0
$545$	−21.2772			−0.911416
$546$		0			0
$547$	9.66115			0.413081			0.206540	−	0.978438i	$-0.433780\pi$
$547$	9.66115			0.413081			0.206540	+	0.978438i	$0.433780\pi$
$548$		0			0
$549$	9.03967	+	15.6572i	0.385804	+	0.668232i
$550$		0			0
$551$		−	0.210649i		−	0.00897395i
$552$		0			0
$553$	7.96526	+	4.59875i	0.338717	+	0.195559i
$554$		0			0
$555$	12.6455	−	21.9027i	0.536772	−	0.929716i
$556$		0			0
$557$	−21.6145	+	12.4791i	−0.915834	+	0.528757i	−0.882304	−	0.470680i	$-0.844008\pi$
$557$	−21.6145	+	12.4791i	−0.915834	+	0.528757i	−0.0335307	+	0.999438i	$0.510675\pi$
$558$		0			0
$559$	−15.2056	+	6.43830i	−0.643128	+	0.272311i
$560$		0			0
$561$	0.918515	−	0.530305i	0.0387797	−	0.0223895i
$562$		0			0
$563$	−7.94970	+	13.7693i	−0.335040	+	0.580306i	−0.983492	−	0.180949i	$-0.942083\pi$
$563$	−7.94970	+	13.7693i	−0.335040	+	0.580306i	0.648453	+	0.761255i	$0.275416\pi$
$564$		0			0
$565$	−53.0949	−	30.6544i	−2.23372	−	1.28964i
$566$		0			0
$567$		−	2.81913i		−	0.118392i
$568$		0			0
$569$	−8.95465	−	15.5099i	−0.375398	−	0.650209i	0.614988	−	0.788536i	$-0.289161\pi$
$569$	−8.95465	−	15.5099i	−0.375398	−	0.650209i	−0.990387	+	0.138327i	$0.955827\pi$
$570$		0			0
$571$	12.5123			0.523623			0.261812	−	0.965119i	$-0.415680\pi$
$571$	12.5123			0.523623			0.261812	+	0.965119i	$0.415680\pi$
$572$		0			0
$573$	−0.104707			−0.00437418
$574$		0			0
$575$	10.8769	+	18.8394i	0.453599	+	0.785657i
$576$		0			0
$577$		−	22.0910i		−	0.919662i	−0.888007	−	0.459831i	$-0.847910\pi$
$577$		−	22.0910i		−	0.919662i	0.888007	−	0.459831i	$-0.152090\pi$
$578$		0			0
$579$	2.06540	+	1.19246i	0.0858353	+	0.0495570i
$580$		0			0
$581$	−1.58593	+	2.74691i	−0.0657954	+	0.113961i
$582$		0			0
$583$	60.4883	−	34.9229i	2.50517	−	1.44636i
$584$		0			0
$585$	11.7439	+	27.7360i	0.485550	+	1.14674i
$586$		0			0
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	−0.0722727	−	0.997385i	$-0.523025\pi$
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	0.827624	+	0.561282i	$0.189692\pi$
$588$		0			0
$589$	2.46921	−	4.27679i	0.101742	−	0.176222i
$590$		0			0
$591$	11.3373	+	6.54560i	0.466355	+	0.269250i
$592$		0			0
$593$			8.95493i			0.367735i	0.982951	+	0.183867i	$0.0588617\pi$
$593$			8.95493i			0.367735i	−0.982951	+	0.183867i	$0.941138\pi$
$594$		0			0
$595$	−0.393765	−	0.682021i	−0.0161428	−	0.0279601i
$596$		0			0
$597$	4.59277			0.187970
$598$		0			0
$599$	−41.7996			−1.70788			−0.853942	−	0.520368i	$-0.825795\pi$
$599$	−41.7996			−1.70788			−0.853942	+	0.520368i	$0.825795\pi$
$600$		0			0
$601$	−7.64481	−	13.2412i	−0.311838	−	0.540120i	0.666922	−	0.745127i	$-0.267611\pi$
$601$	−7.64481	−	13.2412i	−0.311838	−	0.540120i	−0.978760	+	0.205008i	$0.934278\pi$
$602$		0			0
$603$		−	29.1940i		−	1.18887i
$604$		0			0
$605$	71.8319	+	41.4722i	2.92038	+	1.68608i
$606$		0			0
$607$	7.30434	−	12.6515i	0.296474	−	0.513508i	−0.678853	−	0.734275i	$-0.737522\pi$
$607$	7.30434	−	12.6515i	0.296474	−	0.513508i	0.975327	+	0.220766i	$0.0708558\pi$
$608$		0			0
$609$	0.0738809	−	0.0426552i	0.00299381	−	0.00172847i
$610$		0			0
$611$	−19.8904	+	26.3462i	−0.804678	+	1.06585i
$612$		0			0
$613$	−33.9623	+	19.6081i	−1.37172	+	0.791965i	−0.991145	−	0.132783i	$-0.957609\pi$
$613$	−33.9623	+	19.6081i	−1.37172	+	0.791965i	−0.380579	+	0.924748i	$0.624275\pi$
$614$		0			0
$615$	12.0798	−	20.9228i	0.487104	−	0.843688i
$616$		0			0
$617$	8.10486	+	4.67934i	0.326289	+	0.188383i	0.654192	−	0.756328i	$-0.273009\pi$
$617$	8.10486	+	4.67934i	0.326289	+	0.188383i	−0.327903	+	0.944711i	$0.606342\pi$
$618$		0			0
$619$			43.7075i			1.75675i	0.477970	+	0.878376i	$0.341373\pi$
$619$			43.7075i			1.75675i	−0.477970	+	0.878376i	$0.658627\pi$
$620$		0			0
$621$	5.63409	+	9.75852i	0.226088	+	0.391596i
$622$		0			0
$623$	−11.8167			−0.473424
$624$		0			0
$625$	8.11112			0.324445
$626$		0			0
$627$	5.34095	+	9.25080i	0.213297	+	0.369441i
$628$		0			0
$629$			1.67072i			0.0666159i
$630$		0			0
$631$	18.0096	+	10.3978i	0.716951	+	0.413932i	0.813629	−	0.581384i	$-0.197489\pi$
$631$	18.0096	+	10.3978i	0.716951	+	0.413932i	−0.0966785	+	0.995316i	$0.530822\pi$
$632$		0			0
$633$	7.74558	−	13.4157i	0.307859	−	0.533228i
$634$		0			0
$635$	−37.8890	+	21.8752i	−1.50358	+	0.868091i
$636$		0			0
$637$	−0.442616	+	3.57828i	−0.0175371	+	0.141777i
$638$		0			0
$639$	−14.3544	+	8.28749i	−0.567850	+	0.327848i
$640$		0			0
$641$	−3.61897	+	6.26824i	−0.142941	+	0.247581i	−0.928603	−	0.371075i	$-0.878989\pi$
$641$	−3.61897	+	6.26824i	−0.142941	+	0.247581i	0.785662	+	0.618656i	$0.212323\pi$
$642$		0			0
$643$	−34.7898	−	20.0859i	−1.37198	−	0.792111i	−0.380800	−	0.924658i	$-0.624351\pi$
$643$	−34.7898	−	20.0859i	−1.37198	−	0.792111i	−0.991177	+	0.132547i	$0.957685\pi$
$644$		0			0
$645$			14.7110i			0.579245i
$646$		0			0
$647$	−7.27561	−	12.6017i	−0.286034	−	0.495425i	0.686826	−	0.726822i	$-0.259004\pi$
$647$	−7.27561	−	12.6017i	−0.286034	−	0.495425i	−0.972859	+	0.231397i	$0.925670\pi$
$648$		0			0
$649$	1.33927			0.0525710
$650$		0			0
$651$	2.00000			0.0783862
$652$		0			0
$653$	24.8634	+	43.0646i	0.972978	+	1.68525i	0.686451	+	0.727176i	$0.259168\pi$
$653$	24.8634	+	43.0646i	0.972978	+	1.68525i	0.286527	+	0.958072i	$0.407499\pi$
$654$		0			0
$655$			19.0338i			0.743712i
$656$		0			0
$657$	−10.9243	−	6.30714i	−0.426197	−	0.246065i
$658$		0			0
$659$	−15.7988	+	27.3644i	−0.615436	+	1.06597i	0.374872	+	0.927076i	$0.377687\pi$
$659$	−15.7988	+	27.3644i	−0.615436	+	1.06597i	−0.990308	+	0.138889i	$0.955647\pi$
$660$		0			0
$661$	−21.5391	+	12.4356i	−0.837775	+	0.483689i	−0.856507	−	0.516135i	$-0.827370\pi$
$661$	−21.5391	+	12.4356i	−0.837775	+	0.483689i	0.0187325	+	0.999825i	$0.494037\pi$
$662$		0			0
$663$	0.528494	+	0.398993i	0.0205250	+	0.0154956i
$664$		0			0
$665$	6.86895	−	3.96579i	0.266367	−	0.153787i
$666$		0			0
$667$	0.122192	−	0.211643i	0.00473130	−	0.00819485i
$668$		0			0
$669$	−12.3216	−	7.11388i	−0.476381	−	0.275039i
$670$		0			0
$671$			46.3843i			1.79065i
$672$		0			0
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	0.578408	−	0.815748i	$-0.303674\pi$
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	−0.995662	+	0.0930423i	$0.970341\pi$
$674$		0			0
$675$	39.8747			1.53478
$676$		0			0
$677$	14.3935			0.553187			0.276594	−	0.960987i	$-0.410794\pi$
$677$	14.3935			0.553187			0.276594	+	0.960987i	$0.410794\pi$
$678$		0			0
$679$	7.04093	+	12.1952i	0.270206	+	0.468011i
$680$		0			0
$681$		−	4.87367i		−	0.186759i
$682$		0			0
$683$	36.6968	+	21.1869i	1.40416	+	0.810694i	0.994817	−	0.101686i	$-0.0324235\pi$
$683$	36.6968	+	21.1869i	1.40416	+	0.810694i	0.409346	+	0.912379i	$0.365757\pi$
$684$		0			0
$685$	17.4307	−	30.1909i	0.665993	−	1.15353i
$686$		0			0
$687$	−20.7796	+	11.9971i	−0.792793	+	0.457719i
$688$		0			0
$689$	34.8037	+	26.2754i	1.32591	+	1.00101i
$690$		0			0
$691$	19.8651	−	11.4691i	0.755703	−	0.436305i	−0.0720480	−	0.997401i	$-0.522953\pi$
$691$	19.8651	−	11.4691i	0.755703	−	0.436305i	0.827751	+	0.561096i	$0.189620\pi$
$692$		0			0
$693$	6.49927	−	11.2571i	0.246887	−	0.427621i
$694$		0			0
$695$	48.6654	+	28.0970i	1.84598	+	1.06578i
$696$		0			0
$697$			1.59597i			0.0604518i
$698$		0			0
$699$	8.70291	+	15.0739i	0.329174	+	0.570146i
$700$		0			0
$701$	1.70699			0.0644723			0.0322361	−	0.999480i	$-0.489737\pi$
$701$	1.70699			0.0644723			0.0322361	+	0.999480i	$0.489737\pi$
$702$		0			0
$703$	−16.8266			−0.634627
$704$		0			0
$705$	14.7050	+	25.4697i	0.553821	+	0.959245i
$706$		0			0
$707$		−	6.15243i		−	0.231386i
$708$		0			0
$709$	−15.7730	−	9.10657i	−0.592369	−	0.342005i	0.173665	−	0.984805i	$-0.444439\pi$
$709$	−15.7730	−	9.10657i	−0.592369	−	0.342005i	−0.766034	+	0.642800i	$0.777772\pi$
$710$		0			0
$711$	10.3512	−	17.9289i	0.388202	−	0.672385i
$712$		0			0
$713$	4.96172	−	2.86465i	0.185818	−	0.107282i
$714$		0			0
$715$	−9.48629	+	76.6909i	−0.354767	+	2.86808i
$716$		0			0
$717$	4.96933	−	2.86904i	0.185583	−	0.107146i
$718$		0			0
$719$	−1.79107	+	3.10222i	−0.0667956	+	0.115693i	−0.897489	−	0.441037i	$-0.854611\pi$
$719$	−1.79107	+	3.10222i	−0.0667956	+	0.115693i	0.830694	+	0.556730i	$0.187944\pi$
$720$		0			0
$721$	−16.7568	−	9.67453i	−0.624055	−	0.360298i
$722$		0			0
$723$		−	1.39942i		−	0.0520450i
$724$		0			0
$725$	−0.432401	−	0.748941i	−0.0160590	−	0.0278150i
$726$		0			0
$727$	−3.21747			−0.119329			−0.0596647	−	0.998218i	$-0.519003\pi$
$727$	−3.21747			−0.119329			−0.0596647	+	0.998218i	$0.519003\pi$
$728$		0			0
$729$	5.45503			0.202038
$730$		0			0
$731$	−0.485903	−	0.841608i	−0.0179718	−	0.0311280i
$732$		0			0
$733$			4.79233i			0.177009i	0.996076	+	0.0885043i	$0.0282087\pi$
$733$			4.79233i			0.177009i	−0.996076	+	0.0885043i	$0.971791\pi$
$734$		0			0
$735$	2.78184	+	1.60610i	0.102610	+	0.0592418i
$736$		0			0
$737$	37.4500	−	64.8653i	1.37949	−	2.38934i
$738$		0			0
$739$	−9.69853	+	5.59945i	−0.356766	+	0.205979i	−0.667661	−	0.744465i	$-0.732705\pi$
$739$	−9.69853	+	5.59945i	−0.356766	+	0.205979i	0.310895	+	0.950444i	$0.399371\pi$
$740$		0			0
$741$	−4.01845	+	5.32272i	−0.147621	+	0.195535i
$742$		0			0
$743$	33.1315	−	19.1285i	1.21548	−	0.701757i	0.251531	−	0.967849i	$-0.419066\pi$
$743$	33.1315	−	19.1285i	1.21548	−	0.701757i	0.963947	+	0.266093i	$0.0857328\pi$
$744$		0			0
$745$	38.2315	−	66.2189i	1.40069	−	2.42607i
$746$		0			0
$747$	6.18297	+	3.56974i	0.226223	+	0.130610i
$748$		0			0
$749$			11.6501i			0.425686i
$750$		0			0
$751$	0.920125	+	1.59370i	0.0335758	+	0.0581551i	0.882325	−	0.470641i	$-0.155977\pi$
$751$	0.920125	+	1.59370i	0.0335758	+	0.0581551i	−0.848749	+	0.528796i	$0.822644\pi$
$752$		0			0
$753$	0.438826			0.0159917
$754$		0			0
$755$	−44.3157			−1.61281
$756$		0			0
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	0.991786	−	0.127909i	$-0.0408266\pi$
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	−0.606666	+	0.794957i	$0.707493\pi$
$758$		0			0
$759$			12.3926i			0.449823i
$760$		0			0
$761$	−12.2381	−	7.06566i	−0.443630	−	0.256130i	0.261506	−	0.965202i	$-0.415781\pi$
$761$	−12.2381	−	7.06566i	−0.443630	−	0.256130i	−0.705136	+	0.709072i	$0.749114\pi$
$762$		0			0
$763$	−2.86654	+	4.96499i	−0.103776	+	0.179745i
$764$		0			0
$765$	−1.53515	+	0.886319i	−0.0555034	+	0.0320449i
$766$		0			0
$767$	0.326030	+	0.769999i	0.0117723	+	0.0278030i
$768$		0			0
$769$	−26.5219	+	15.3124i	−0.956405	+	0.552181i	−0.895065	−	0.445936i	$-0.852871\pi$
$769$	−26.5219	+	15.3124i	−0.956405	+	0.552181i	−0.0613401	+	0.998117i	$0.519537\pi$
$770$		0			0
$771$	−4.17206	+	7.22621i	−0.150253	+	0.260246i
$772$		0			0
$773$	−8.48254	−	4.89740i	−0.305096	−	0.176147i	0.339634	−	0.940558i	$-0.389697\pi$
$773$	−8.48254	−	4.89740i	−0.305096	−	0.176147i	−0.644730	+	0.764411i	$0.723030\pi$
$774$		0			0
$775$		−	20.2743i		−	0.728273i
$776$		0			0
$777$	−3.40729	−	5.90159i	−0.122236	−	0.211718i
$778$		0			0
$779$	−16.0738			−0.575904
$780$		0			0
$781$	−42.5248			−1.52166
$782$		0			0
$783$	−0.223977	−	0.387940i	−0.00800430	−	0.0138638i
$784$		0			0
$785$			34.6645i			1.23723i
$786$		0			0
$787$	−17.8665	−	10.3152i	−0.636873	−	0.367699i	0.146536	−	0.989205i	$-0.453188\pi$
$787$	−17.8665	−	10.3152i	−0.636873	−	0.367699i	−0.783409	+	0.621507i	$0.786521\pi$
$788$		0			0
$789$	−3.17911	+	5.50638i	−0.113179	+	0.196032i
$790$		0			0
$791$	−14.3062	+	8.25971i	−0.508671	+	0.293682i
$792$		0			0
$793$	−26.6681	+	11.2917i	−0.947013	+	0.400981i
$794$		0			0
$795$	33.6458	−	19.4254i	1.19330	−	0.688949i
$796$		0			0
$797$	3.88584	−	6.73047i	0.137643	−	0.238405i	−0.788961	−	0.614444i	$-0.789381\pi$
$797$	3.88584	−	6.73047i	0.137643	−	0.238405i	0.926604	+	0.376038i	$0.122714\pi$
$798$		0			0
$799$	−1.68252	−	0.971406i	−0.0595234	−	0.0343659i
$800$		0			0
$801$			26.5979i			0.939791i
$802$		0			0
$803$	−16.1816	−	28.0273i	−0.571036	−	0.989063i
$804$		0			0
$805$	9.20183			0.324322
$806$		0			0
$807$	19.3478			0.681074
$808$		0			0
$809$	−21.2715	−	36.8433i	−0.747866	−	1.29534i	−0.948844	−	0.315746i	$-0.897745\pi$
$809$	−21.2715	−	36.8433i	−0.747866	−	1.29534i	0.200977	−	0.979596i	$-0.435588\pi$
$810$		0			0
$811$			22.1131i			0.776494i	0.921555	+	0.388247i	$0.126919\pi$
$811$			22.1131i			0.776494i	−0.921555	+	0.388247i	$0.873081\pi$
$812$		0			0
$813$	−7.20880	−	4.16200i	−0.252824	−	0.145968i
$814$		0			0
$815$	8.30833	−	14.3905i	0.291028	−	0.504076i
$816$		0			0
$817$	8.47624	−	4.89376i	0.296546	−	0.171211i
$818$		0			0
$819$	8.05429	+	0.996277i	0.281440	+	0.0348127i
$820$		0			0
$821$	21.0920	−	12.1775i	0.736115	−	0.424996i	−0.0845401	−	0.996420i	$-0.526942\pi$
$821$	21.0920	−	12.1775i	0.736115	−	0.424996i	0.820655	+	0.571424i	$0.193609\pi$
$822$		0			0
$823$	2.37957	−	4.12153i	0.0829465	−	0.143668i	−0.821568	−	0.570111i	$-0.806900\pi$
$823$	2.37957	−	4.12153i	0.0829465	−	0.143668i	0.904514	+	0.426443i	$0.140234\pi$
$824$		0			0
$825$	37.9784	+	21.9269i	1.32224	+	0.763395i
$826$		0			0
$827$		−	7.00333i		−	0.243530i	−0.992559	−	0.121765i	$-0.961145\pi$
$827$		−	7.00333i		−	0.243530i	0.992559	−	0.121765i	$-0.0388554\pi$
$828$		0			0
$829$	−2.87619	−	4.98170i	−0.0998941	−	0.173022i	0.811747	−	0.584010i	$-0.198517\pi$
$829$	−2.87619	−	4.98170i	−0.0998941	−	0.173022i	−0.911641	+	0.410988i	$0.865184\pi$
$830$		0			0
$831$	−8.80998			−0.305615
$832$		0			0
$833$	−0.212197			−0.00735219
$834$		0			0
$835$	−27.2908	−	47.2691i	−0.944438	−	1.63582i
$836$		0			0
$837$		−	10.5018i		−	0.362994i
$838$		0			0
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.967452	−	0.253054i	$-0.0814350\pi$
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.264575	+	0.964365i	$0.414768\pi$
$840$		0			0
$841$	14.4951	−	25.1063i	0.499832	−	0.865735i
$842$		0			0
$843$	−10.6207	+	6.13184i	−0.365795	+	0.211192i
$844$		0			0
$845$	−46.4018	+	13.2155i	−1.59627	+	0.454626i
$846$		0			0
$847$	19.3549	−	11.1745i	0.665041	−	0.383961i
$848$		0			0
$849$	−8.19323	+	14.1911i	−0.281191	+	0.487037i
$850$		0			0
$851$	−16.9060	−	9.76069i	−0.579530	−	0.334592i
$852$		0			0
$853$		−	2.38939i		−	0.0818113i	−0.999163	−	0.0409056i	$-0.986976\pi$
$853$		−	2.38939i		−	0.0818113i	0.999163	−	0.0409056i	$-0.0130243\pi$
$854$		0			0
$855$	−8.92654	−	15.4612i	−0.305281	−	0.528762i
$856$		0			0
$857$	−13.8037			−0.471526			−0.235763	−	0.971811i	$-0.575759\pi$
$857$	−13.8037			−0.471526			−0.235763	+	0.971811i	$0.575759\pi$
$858$		0			0
$859$	37.7276			1.28725			0.643624	−	0.765342i	$-0.277430\pi$
$859$	37.7276			1.28725			0.643624	+	0.765342i	$0.277430\pi$
$860$		0			0
$861$	−3.25485	−	5.63757i	−0.110925	−	0.192128i
$862$		0			0
$863$		−	25.5180i		−	0.868643i	−0.900758	−	0.434322i	$-0.856988\pi$
$863$		−	25.5180i		−	0.868643i	0.900758	−	0.434322i	$-0.143012\pi$
$864$		0			0
$865$	44.2443	+	25.5444i	1.50435	+	0.868537i
$866$		0			0
$867$	7.33739	−	12.7087i	0.249191	−	0.431611i
$868$		0			0
$869$	45.9983	−	26.5571i	1.56039	−	0.900889i
$870$		0			0
$871$	46.4103	+	5.74073i	1.57255	+	0.194517i
$872$		0			0
$873$	27.4501	−	15.8483i	0.929045	−	0.536384i
$874$		0			0
$875$	7.00296	−	12.1295i	0.236743	−	0.410051i
$876$		0			0
$877$	10.7726	+	6.21955i	0.363764	+	0.210019i	0.670731	−	0.741701i	$-0.265981\pi$
$877$	10.7726	+	6.21955i	0.363764	+	0.210019i	−0.306966	+	0.951720i	$0.599314\pi$
$878$		0			0
$879$		−	3.16763i		−	0.106842i
$880$		0			0
$881$	−11.2710	−	19.5219i	−0.379728	−	0.657709i	0.611294	−	0.791404i	$-0.290649\pi$
$881$	−11.2710	−	19.5219i	−0.379728	−	0.657709i	−0.991023	+	0.133694i	$0.957316\pi$
$882$		0			0
$883$	15.1548			0.509998			0.254999	−	0.966941i	$-0.417925\pi$
$883$	15.1548			0.509998			0.254999	+	0.966941i	$0.417925\pi$
$884$		0			0
$885$	0.744954			0.0250413
$886$		0			0
$887$	20.8875	+	36.1781i	0.701332	+	1.21474i	0.967999	+	0.250954i	$0.0807443\pi$
$887$	20.8875	+	36.1781i	0.701332	+	1.21474i	−0.266667	+	0.963789i	$0.585922\pi$
$888$		0			0
$889$			11.7884i			0.395370i
$890$		0			0
$891$	−14.0990	−	8.14004i	−0.472333	−	0.272702i
$892$		0			0
$893$	9.78349	−	16.9455i	0.327392	−	0.567060i
$894$		0			0
$895$	49.1072	−	28.3521i	1.64147	−	0.947705i
$896$		0			0
$897$	−7.12498	+	3.01684i	−0.237896	+	0.100729i
$898$		0			0
$899$	−0.197248	+	0.113881i	−0.00657860	+	0.00379815i
$900$		0			0
$901$	−1.28324	+	2.22264i	−0.0427509	+	0.0740468i
$902$		0			0
$903$	3.43278	+	1.98191i	0.114236	+	0.0659540i
$904$		0			0
$905$		−	6.18853i		−	0.205714i
$906$		0			0
$907$	−2.14376	−	3.71310i	−0.0711823	−	0.123291i	0.828237	−	0.560377i	$-0.189344\pi$
$907$	−2.14376	−	3.71310i	−0.0711823	−	0.123291i	−0.899420	+	0.437086i	$0.856011\pi$
$908$		0			0
$909$	−13.8484			−0.459323
$910$		0			0
$911$	3.87618			0.128423			0.0642117	−	0.997936i	$-0.479547\pi$
$911$	3.87618			0.128423			0.0642117	+	0.997936i	$0.479547\pi$
$912$		0			0
$913$	9.15853	+	15.8630i	0.303103	+	0.524990i
$914$		0			0
$915$			25.8007i			0.852945i
$916$		0			0
$917$	4.44149	+	2.56429i	0.146671	+	0.0846805i
$918$		0			0
$919$	22.9524	−	39.7547i	0.757129	−	1.31139i	−0.187180	−	0.982326i	$-0.559935\pi$
$919$	22.9524	−	39.7547i	0.757129	−	1.31139i	0.944309	−	0.329060i	$-0.106732\pi$
$920$		0			0
$921$	−14.7653	+	8.52476i	−0.486534	+	0.280900i
$922$		0			0
$923$	−10.3522	−	24.4491i	−0.340745	−	0.804752i
$924$		0			0
$925$	−59.8253	+	34.5401i	−1.96704	+	1.13567i
$926$		0			0
$927$	−21.7762	+	37.7176i	−0.715226	+	1.23881i
$928$		0			0
$929$	8.51833	+	4.91806i	0.279477	+	0.161356i	0.633187	−	0.773999i	$-0.281746\pi$
$929$	8.51833	+	4.91806i	0.279477	+	0.161356i	−0.353709	+	0.935355i	$0.615080\pi$
$930$		0			0
$931$		−	2.13714i		−	0.0700418i
$932$		0			0
$933$	7.34325	+	12.7189i	0.240407	+	0.416397i
$934$		0			0
$935$	−4.54788			−0.148731
$936$		0			0
$937$	21.5135			0.702815			0.351407	−	0.936223i	$-0.385703\pi$
$937$	21.5135			0.702815			0.351407	+	0.936223i	$0.385703\pi$
$938$		0			0
$939$	1.96383	+	3.40145i	0.0640871	+	0.111002i
$940$		0			0
$941$			6.41845i			0.209236i	0.994513	+	0.104618i	$0.0333619\pi$
$941$			6.41845i			0.209236i	−0.994513	+	0.104618i	$0.966638\pi$
$942$		0			0
$943$	−16.1497	−	9.32402i	−0.525906	−	0.303632i
$944$		0			0
$945$	8.43344	−	14.6071i	0.274340	−	0.475170i
$946$		0			0
$947$	−6.55812	+	3.78633i	−0.213110	+	0.123039i	−0.602756	−	0.797926i	$-0.705931\pi$
$947$	−6.55812	+	3.78633i	−0.213110	+	0.123039i	0.389646	+	0.920965i	$0.372597\pi$
$948$		0			0
$949$	12.1748	−	16.1263i	0.395209	−	0.523483i
$950$		0			0
$951$	−21.8770	+	12.6307i	−0.709412	+	0.409579i
$952$		0			0
$953$	−17.9022	+	31.0075i	−0.579909	+	1.00443i	0.415580	+	0.909557i	$0.363579\pi$
$953$	−17.9022	+	31.0075i	−0.579909	+	1.00443i	−0.995489	+	0.0948754i	$0.969755\pi$
$954$		0			0
$955$	0.388828	+	0.224490i	0.0125822	+	0.00726432i
$956$		0			0
$957$		−	0.492656i		−	0.0159253i
$958$		0			0
$959$	−4.69664	−	8.13482i	−0.151662	−	0.262687i
$960$		0			0
$961$	25.6604			0.827754
$962$		0			0
$963$	26.2231			0.845027
$964$		0			0
$965$	−5.11326	−	8.85642i	−0.164602	−	0.285098i
$966$		0			0
$967$			32.3876i			1.04152i	0.853704	+	0.520758i	$0.174351\pi$
$967$			32.3876i			1.04152i	−0.853704	+	0.520758i	$0.825649\pi$
$968$		0			0
$969$	−0.339920	−	0.196253i	−0.0109198	−	0.00630455i
$970$		0			0
$971$	17.2033	−	29.7969i	0.552079	−	0.956229i	−0.446045	−	0.895010i	$-0.647168\pi$
$971$	17.2033	−	29.7969i	0.552079	−	0.956229i	0.998124	−	0.0612186i	$-0.0194987\pi$
$972$		0			0
$973$	13.1127	−	7.57063i	0.420374	−	0.242703i
$974$		0			0
$975$	−3.36118	+	27.1731i	−0.107644	+	0.870235i
$976$		0			0
$977$	20.0471	−	11.5742i	0.641364	−	0.370291i	−0.143776	−	0.989610i	$-0.545924\pi$
$977$	20.0471	−	11.5742i	0.641364	−	0.370291i	0.785140	+	0.619319i	$0.212591\pi$
$978$		0			0
$979$	−34.1198	+	59.0972i	−1.09047	+	1.88876i
$980$		0			0
$981$	11.1756	+	6.45224i	0.356810	+	0.206004i
$982$		0			0
$983$		−	47.0579i		−	1.50092i	−0.660919	−	0.750458i	$-0.729833\pi$
$983$		−	47.0579i		−	1.50092i	0.660919	−	0.750458i	$-0.270167\pi$
$984$		0			0
$985$	−28.0674	−	48.6142i	−0.894303	−	1.54898i
$986$		0			0
$987$	7.92439			0.252236
$988$		0			0
$989$	11.3550			0.361068
$990$		0			0
$991$	−5.95052	−	10.3066i	−0.189025	−	0.327400i	0.755901	−	0.654686i	$-0.227199\pi$
$991$	−5.95052	−	10.3066i	−0.189025	−	0.327400i	−0.944925	+	0.327286i	$0.893866\pi$
$992$		0			0
$993$			4.15916i			0.131987i
$994$		0			0
$995$	−17.0553	−	9.84686i	−0.540688	−	0.312167i
$996$		0			0
$997$	−6.50714	+	11.2707i	−0.206083	+	0.356946i	−0.950477	−	0.310794i	$-0.899405\pi$
$997$	−6.50714	+	11.2707i	−0.206083	+	0.356946i	0.744394	+	0.667740i	$0.232738\pi$
$998$		0			0
$999$	−30.9886	+	17.8913i	−0.980435	+	0.566055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.d.673.2		12
4.3	odd	2		182.2.m.b.127.3	yes	12
12.11	even	2		1638.2.bj.g.127.4		12
13.4	even	6	inner	1456.2.cc.d.225.2		12
28.3	even	6		1274.2.o.e.569.1		12
28.11	odd	6		1274.2.o.d.569.3		12
28.19	even	6		1274.2.v.d.361.6		12
28.23	odd	6		1274.2.v.e.361.4		12
28.27	even	2		1274.2.m.c.491.1		12
52.3	odd	6		2366.2.d.r.337.2		12
52.11	even	12		2366.2.a.bh.1.2		6
52.15	even	12		2366.2.a.bf.1.2		6
52.23	odd	6		2366.2.d.r.337.8		12
52.43	odd	6		182.2.m.b.43.3	✓	12
156.95	even	6		1638.2.bj.g.1135.6		12
364.95	odd	6		1274.2.v.e.667.4		12
364.199	even	6		1274.2.v.d.667.6		12
364.251	even	6		1274.2.m.c.589.1		12
364.303	odd	6		1274.2.o.d.459.6		12
364.355	even	6		1274.2.o.e.459.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.3	✓	12	52.43	odd	6
182.2.m.b.127.3	yes	12	4.3	odd	2
1274.2.m.c.491.1		12	28.27	even	2
1274.2.m.c.589.1		12	364.251	even	6
1274.2.o.d.459.6		12	364.303	odd	6
1274.2.o.d.569.3		12	28.11	odd	6
1274.2.o.e.459.4		12	364.355	even	6
1274.2.o.e.569.1		12	28.3	even	6
1274.2.v.d.361.6		12	28.19	even	6
1274.2.v.d.667.6		12	364.199	even	6
1274.2.v.e.361.4		12	28.23	odd	6
1274.2.v.e.667.4		12	364.95	odd	6
1456.2.cc.d.225.2		12	13.4	even	6	inner
1456.2.cc.d.673.2		12	1.1	even	1	trivial
1638.2.bj.g.127.4		12	12.11	even	2
1638.2.bj.g.1135.6		12	156.95	even	6
2366.2.a.bf.1.2		6	52.15	even	12
2366.2.a.bh.1.2		6	52.11	even	12
2366.2.d.r.337.2		12	52.3	odd	6
2366.2.d.r.337.8		12	52.23	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.432757 - 0.749558i) q^{3} +3.71131i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.12544 - 1.94932i) q^{9} +O(q^{10})\)	\(q+(-0.432757 - 0.749558i) q^{3} +3.71131i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.12544 - 1.94932i) q^{9} +(5.00118 - 2.88743i) q^{11} +(2.87757 + 2.17246i) q^{13} +(2.78184 - 1.60610i) q^{15} +(-0.106098 + 0.183768i) q^{17} +(-1.85081 - 1.06857i) q^{19} -0.865515i q^{21} +(-1.23970 - 2.14722i) q^{23} -8.77384 q^{25} -4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} +2.31076i q^{31} +(-4.32860 - 2.49912i) q^{33} +(-1.85566 + 3.21409i) q^{35} +(6.81859 - 3.93672i) q^{37} +(0.383091 - 3.09706i) q^{39} +(6.51354 - 3.76060i) q^{41} +(-2.28987 + 3.96617i) q^{43} +(7.23455 + 4.17687i) q^{45} +9.15570i q^{47} +(0.500000 + 0.866025i) q^{49} +0.183660 q^{51} +12.0948 q^{53} +(10.7162 + 18.5609i) q^{55} +1.84972i q^{57} +(0.200843 + 0.115957i) q^{59} +(-4.01605 + 6.95601i) q^{61} +(1.94932 - 1.12544i) q^{63} +(-8.06267 + 10.6796i) q^{65} +(11.2323 - 6.48500i) q^{67} +(-1.07298 + 1.85845i) q^{69} +(-6.37721 - 3.68188i) q^{71} -5.60414i q^{73} +(3.79695 + 6.57650i) q^{75} +5.77486 q^{77} +9.19749 q^{79} +(-1.40956 - 2.44144i) q^{81} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +(0.0426552 - 0.0738809i) q^{87} +(-10.2335 + 5.90833i) q^{89} +(1.40582 + 3.32019i) q^{91} +(1.73205 - 1.00000i) q^{93} +(3.96579 - 6.86895i) q^{95} +(12.1952 + 7.04093i) q^{97} -12.9985i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 6 * q^9	\( 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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