LMFDB - Embedded newform 1456.2.r.j.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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, 4, 0]))

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

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

chi := DirichletCharacter("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.j.417.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11803 + 1.93649i) q^{3} +(1.11803 - 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(1.11803 + 1.93649i) q^{3} +(1.11803 - 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +5.00000 q^{15} +(3.73607 + 6.47106i) q^{17} +(1.50000 - 2.59808i) q^{19} +(-1.11803 + 5.80948i) q^{21} +(-1.88197 + 3.25966i) q^{23} +2.23607 q^{27} -4.47214 q^{29} +(2.50000 + 4.33013i) q^{31} +(3.35410 - 5.80948i) q^{33} +(5.59017 - 1.93649i) q^{35} +(4.35410 - 7.54153i) q^{37} +(-1.11803 - 1.93649i) q^{39} +4.47214 q^{41} +8.00000 q^{43} +(2.23607 + 3.87298i) q^{45} +(0.736068 - 1.27491i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-8.35410 + 14.4697i) q^{51} +(-0.736068 - 1.27491i) q^{53} -6.70820 q^{55} +6.70820 q^{57} +(3.73607 + 6.47106i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-5.00000 + 1.73205i) q^{63} +(-1.11803 + 1.93649i) q^{65} +(-1.50000 - 2.59808i) q^{67} -8.41641 q^{69} -8.94427 q^{71} +(-5.35410 - 9.27358i) q^{73} +(1.50000 - 7.79423i) q^{77} +(5.35410 - 9.27358i) q^{79} +(5.50000 + 9.52628i) q^{81} +16.7082 q^{85} +(-5.00000 - 8.66025i) q^{87} +(1.11803 - 1.93649i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(-5.59017 + 9.68246i) q^{93} +(-3.35410 - 5.80948i) q^{95} -17.4164 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + 8 * q^7 - 4 * q^9	$ 4 q + 8 q^{7} - 4 q^{9} - 6 q^{11} - 4 q^{13} + 20 q^{15} + 6 q^{17} + 6 q^{19} - 12 q^{23} + 10 q^{31} + 4 q^{37} + 32 q^{43} - 6 q^{47} + 4 q^{49} - 20 q^{51} + 6 q^{53} + 6 q^{59} - 6 q^{61} - 20 q^{63} - 6 q^{67} + 20 q^{69} - 8 q^{73} + 6 q^{77} + 8 q^{79} + 22 q^{81} + 40 q^{85} - 20 q^{87} - 8 q^{91} - 16 q^{97} + 24 q^{99}+O(q^{100}) $ 4 * q + 8 * q^7 - 4 * q^9 - 6 * q^11 - 4 * q^13 + 20 * q^15 + 6 * q^17 + 6 * q^19 - 12 * q^23 + 10 * q^31 + 4 * q^37 + 32 * q^43 - 6 * q^47 + 4 * q^49 - 20 * q^51 + 6 * q^53 + 6 * q^59 - 6 * q^61 - 20 * q^63 - 6 * q^67 + 20 * q^69 - 8 * q^73 + 6 * q^77 + 8 * q^79 + 22 * q^81 + 40 * q^85 - 20 * q^87 - 8 * q^91 - 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.11803	+	1.93649i	0.645497	+	1.11803i	0.984186	+	0.177136i	$0.0566831\pi$
$3$	1.11803	+	1.93649i	0.645497	+	1.11803i	−0.338689	+	0.940898i	$0.609984\pi$
$4$		0			0
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	1.00000			$0$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	5.00000			1.29099
$16$		0			0
$17$	3.73607	+	6.47106i	0.906130	+	1.56946i	0.819394	+	0.573231i	$0.194310\pi$
$17$	3.73607	+	6.47106i	0.906130	+	1.56946i	0.0867359	+	0.996231i	$0.472356\pi$
$18$		0			0
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$		0			0
$21$	−1.11803	+	5.80948i	−0.243975	+	1.26773i
$22$		0			0
$23$	−1.88197	+	3.25966i	−0.392417	+	0.679686i	−0.992768	−	0.120051i	$-0.961694\pi$
$23$	−1.88197	+	3.25966i	−0.392417	+	0.679686i	0.600351	+	0.799737i	$0.295028\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.23607			0.430331
$28$		0			0
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$		0			0
$33$	3.35410	−	5.80948i	0.583874	−	1.01130i
$34$		0			0
$35$	5.59017	−	1.93649i	0.944911	−	0.327327i
$36$		0			0
$37$	4.35410	−	7.54153i	0.715810	−	1.23982i	−0.246836	−	0.969057i	$-0.579391\pi$
$37$	4.35410	−	7.54153i	0.715810	−	1.23982i	0.962646	−	0.270762i	$-0.0872757\pi$
$38$		0			0
$39$	−1.11803	−	1.93649i	−0.179029	−	0.310087i
$40$		0			0
$41$	4.47214			0.698430			0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214			0.698430			0.349215	+	0.937043i	$0.386448\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	2.23607	+	3.87298i	0.333333	+	0.577350i
$46$		0			0
$47$	0.736068	−	1.27491i	0.107367	−	0.185964i	−0.807336	−	0.590092i	$-0.799091\pi$
$47$	0.736068	−	1.27491i	0.107367	−	0.185964i	0.914703	+	0.404128i	$0.132425\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−8.35410	+	14.4697i	−1.16981	+	2.02617i
$52$		0			0
$53$	−0.736068	−	1.27491i	−0.101107	−	0.175122i	0.811034	−	0.584999i	$-0.198905\pi$
$53$	−0.736068	−	1.27491i	−0.101107	−	0.175122i	−0.912141	+	0.409877i	$0.865572\pi$
$54$		0			0
$55$	−6.70820			−0.904534
$56$		0			0
$57$	6.70820			0.888523
$58$		0			0
$59$	3.73607	+	6.47106i	0.486395	+	0.842460i	0.999878	−	0.0156395i	$-0.00497842\pi$
$59$	3.73607	+	6.47106i	0.486395	+	0.842460i	−0.513483	+	0.858100i	$0.671645\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$		0			0
$63$	−5.00000	+	1.73205i	−0.629941	+	0.218218i
$64$		0			0
$65$	−1.11803	+	1.93649i	−0.138675	+	0.240192i
$66$		0			0
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$		0			0
$69$	−8.41641			−1.01322
$70$		0			0
$71$	−8.94427			−1.06149			−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427			−1.06149			−0.530745	+	0.847532i	$0.678088\pi$
$72$		0			0
$73$	−5.35410	−	9.27358i	−0.626650	−	1.08539i	−0.988219	−	0.153045i	$-0.951092\pi$
$73$	−5.35410	−	9.27358i	−0.626650	−	1.08539i	0.361569	−	0.932345i	$-0.382241\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	5.35410	−	9.27358i	0.602384	−	1.04336i	−0.390076	−	0.920783i	$-0.627551\pi$
$79$	5.35410	−	9.27358i	0.602384	−	1.04336i	0.992459	−	0.122576i	$-0.0391155\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	16.7082			1.81226
$86$		0			0
$87$	−5.00000	−	8.66025i	−0.536056	−	0.928477i
$88$		0			0
$89$	1.11803	−	1.93649i	0.118511	−	0.205268i	−0.800667	−	0.599110i	$-0.795521\pi$
$89$	1.11803	−	1.93649i	0.118511	−	0.205268i	0.919178	+	0.393842i	$0.128854\pi$
$90$		0			0
$91$	−2.00000	−	1.73205i	−0.209657	−	0.181568i
$92$		0			0
$93$	−5.59017	+	9.68246i	−0.579674	+	1.00402i
$94$		0			0
$95$	−3.35410	−	5.80948i	−0.344124	−	0.596040i
$96$		0			0
$97$	−17.4164			−1.76837			−0.884184	−	0.467139i	$-0.845285\pi$
$97$	−17.4164			−1.76837			−0.884184	+	0.467139i	$0.845285\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	5.35410	−	9.27358i	0.527555	−	0.913753i	−0.471929	−	0.881637i	$-0.656442\pi$
$103$	5.35410	−	9.27358i	0.527555	−	0.913753i	0.999484	−	0.0321160i	$-0.0102246\pi$
$104$		0			0
$105$	10.0000	+	8.66025i	0.975900	+	0.845154i
$106$		0			0
$107$	−7.11803	+	12.3288i	−0.688126	+	1.19187i	0.284317	+	0.958730i	$0.408233\pi$
$107$	−7.11803	+	12.3288i	−0.688126	+	1.19187i	−0.972443	+	0.233139i	$0.925100\pi$
$108$		0			0
$109$	−5.35410	−	9.27358i	−0.512830	−	0.888248i	−0.999889	−	0.0148787i	$-0.995264\pi$
$109$	−5.35410	−	9.27358i	−0.512830	−	0.888248i	0.487059	−	0.873369i	$-0.338070\pi$
$110$		0			0
$111$	19.4721			1.84821
$112$		0			0
$113$	−14.9443			−1.40584			−0.702919	−	0.711269i	$-0.748121\pi$
$113$	−14.9443			−1.40584			−0.702919	+	0.711269i	$0.748121\pi$
$114$		0			0
$115$	4.20820	+	7.28882i	0.392417	+	0.679686i
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		0			0
$119$	−3.73607	+	19.4132i	−0.342485	+	1.77960i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$		0			0
$125$	11.1803			1.00000
$126$		0			0
$127$	−15.4164			−1.36798			−0.683992	−	0.729489i	$-0.739758\pi$
$127$	−15.4164			−1.36798			−0.683992	+	0.729489i	$0.739758\pi$
$128$		0			0
$129$	8.94427	+	15.4919i	0.787499	+	1.36399i
$130$		0			0
$131$	−1.88197	+	3.25966i	−0.164428	+	0.284798i	−0.936452	−	0.350796i	$-0.885911\pi$
$131$	−1.88197	+	3.25966i	−0.164428	+	0.284798i	0.772024	+	0.635593i	$0.219245\pi$
$132$		0			0
$133$	7.50000	−	2.59808i	0.650332	−	0.225282i
$134$		0			0
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$		0			0
$137$	1.88197	+	3.25966i	0.160787	+	0.278492i	0.935151	−	0.354249i	$-0.115263\pi$
$137$	1.88197	+	3.25966i	0.160787	+	0.278492i	−0.774364	+	0.632740i	$0.781930\pi$
$138$		0			0
$139$	−3.41641			−0.289776			−0.144888	−	0.989448i	$-0.546282\pi$
$139$	−3.41641			−0.289776			−0.144888	+	0.989448i	$0.546282\pi$
$140$		0			0
$141$	3.29180			0.277219
$142$		0			0
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	−5.00000	+	8.66025i	−0.415227	+	0.719195i
$146$		0			0
$147$	−12.2984	+	9.68246i	−1.01435	+	0.798596i
$148$		0			0
$149$	6.35410	−	11.0056i	0.520548	−	0.901616i	−0.479166	−	0.877724i	$-0.659061\pi$
$149$	6.35410	−	11.0056i	0.520548	−	0.901616i	0.999715	−	0.0238920i	$-0.00760577\pi$
$150$		0			0
$151$	−3.20820	−	5.55677i	−0.261080	−	0.452204i	0.705449	−	0.708760i	$-0.250745\pi$
$151$	−3.20820	−	5.55677i	−0.261080	−	0.452204i	−0.966529	+	0.256557i	$0.917412\pi$
$152$		0			0
$153$	−14.9443			−1.20817
$154$		0			0
$155$	11.1803			0.898027
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$		0			0
$159$	1.64590	−	2.85078i	0.130528	−	0.226081i
$160$		0			0
$161$	−9.40983	+	3.25966i	−0.741598	+	0.256897i
$162$		0			0
$163$	5.20820	−	9.02087i	0.407938	−	0.706569i	−0.586721	−	0.809789i	$-0.699581\pi$
$163$	5.20820	−	9.02087i	0.407938	−	0.706569i	0.994659	+	0.103220i	$0.0329146\pi$
$164$		0			0
$165$	−7.50000	−	12.9904i	−0.583874	−	1.01130i
$166$		0			0
$167$	−13.5279			−1.04682			−0.523409	−	0.852082i	$-0.675340\pi$
$167$	−13.5279			−1.04682			−0.523409	+	0.852082i	$0.675340\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$		0			0
$173$	−5.20820	+	9.02087i	−0.395972	+	0.685844i	−0.993225	−	0.116209i	$-0.962926\pi$
$173$	−5.20820	+	9.02087i	−0.395972	+	0.685844i	0.597252	+	0.802053i	$0.296259\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.35410	+	14.4697i	−0.627933	+	1.08761i
$178$		0			0
$179$	10.0623	+	17.4284i	0.752092	+	1.30266i	0.946807	+	0.321802i	$0.104288\pi$
$179$	10.0623	+	17.4284i	0.752092	+	1.30266i	−0.194715	+	0.980860i	$0.562378\pi$
$180$		0			0
$181$	1.41641			0.105281			0.0526404	−	0.998614i	$-0.483236\pi$
$181$	1.41641			0.105281			0.0526404	+	0.998614i	$0.483236\pi$
$182$		0			0
$183$	−6.70820			−0.495885
$184$		0			0
$185$	−9.73607	−	16.8634i	−0.715810	−	1.23982i
$186$		0			0
$187$	11.2082	−	19.4132i	0.819625	−	1.41963i
$188$		0			0
$189$	4.47214	+	3.87298i	0.325300	+	0.281718i
$190$		0			0
$191$	−5.59017	+	9.68246i	−0.404491	+	0.700598i	−0.994262	−	0.106972i	$-0.965884\pi$
$191$	−5.59017	+	9.68246i	−0.404491	+	0.700598i	0.589772	+	0.807570i	$0.299218\pi$
$192$		0			0
$193$	6.35410	+	11.0056i	0.457378	+	0.792202i	0.998821	−	0.0485349i	$-0.0154552\pi$
$193$	6.35410	+	11.0056i	0.457378	+	0.792202i	−0.541443	+	0.840737i	$0.682122\pi$
$194$		0			0
$195$	−5.00000			−0.358057
$196$		0			0
$197$	−26.9443			−1.91970			−0.959850	−	0.280514i	$-0.909495\pi$
$197$	−26.9443			−1.91970			−0.959850	+	0.280514i	$0.909495\pi$
$198$		0			0
$199$	−3.64590	−	6.31488i	−0.258451	−	0.447650i	0.707376	−	0.706837i	$-0.249879\pi$
$199$	−3.64590	−	6.31488i	−0.258451	−	0.447650i	−0.965827	+	0.259187i	$0.916545\pi$
$200$		0			0
$201$	3.35410	−	5.80948i	0.236580	−	0.409769i
$202$		0			0
$203$	−8.94427	−	7.74597i	−0.627765	−	0.543660i
$204$		0			0
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$		0			0
$207$	−3.76393	−	6.51932i	−0.261611	−	0.453124i
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	−10.0000	−	17.3205i	−0.685189	−	1.18678i
$214$		0			0
$215$	8.94427	−	15.4919i	0.609994	−	1.05654i
$216$		0			0
$217$	−2.50000	+	12.9904i	−0.169711	+	0.881845i
$218$		0			0
$219$	11.9721	−	20.7363i	0.809002	−	1.40123i
$220$		0			0
$221$	−3.73607	−	6.47106i	−0.251315	−	0.435291i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.97214	−	10.3440i	−0.396385	−	0.686558i	0.596892	−	0.802321i	$-0.296402\pi$
$227$	−5.97214	−	10.3440i	−0.396385	−	0.686558i	−0.993277	+	0.115763i	$0.963069\pi$
$228$		0			0
$229$	8.06231	−	13.9643i	0.532772	−	0.922788i	−0.466495	−	0.884524i	$-0.654484\pi$
$229$	8.06231	−	13.9643i	0.532772	−	0.922788i	0.999268	−	0.0382649i	$-0.0121831\pi$
$230$		0			0
$231$	16.7705	−	5.80948i	1.10342	−	0.382235i
$232$		0			0
$233$	2.97214	−	5.14789i	0.194711	−	0.337250i	−0.752095	−	0.659055i	$-0.770956\pi$
$233$	2.97214	−	5.14789i	0.194711	−	0.337250i	0.946806	+	0.321806i	$0.104290\pi$
$234$		0			0
$235$	−1.64590	−	2.85078i	−0.107367	−	0.185964i
$236$		0			0
$237$	23.9443			1.55535
$238$		0			0
$239$	7.41641			0.479728			0.239864	−	0.970807i	$-0.422897\pi$
$239$	7.41641			0.479728			0.239864	+	0.970807i	$0.422897\pi$
$240$		0			0
$241$	4.35410	+	7.54153i	0.280472	+	0.485792i	0.971501	−	0.237035i	$-0.0761756\pi$
$241$	4.35410	+	7.54153i	0.280472	+	0.485792i	−0.691029	+	0.722827i	$0.742842\pi$
$242$		0			0
$243$	−8.94427	+	15.4919i	−0.573775	+	0.993808i
$244$		0			0
$245$	14.5344	+	5.80948i	0.928571	+	0.371154i
$246$		0			0
$247$	−1.50000	+	2.59808i	−0.0954427	+	0.165312i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.4721			−0.660995			−0.330498	−	0.943807i	$-0.607217\pi$
$251$	−10.4721			−0.660995			−0.330498	+	0.943807i	$0.607217\pi$
$252$		0			0
$253$	11.2918			0.709909
$254$		0			0
$255$	18.6803	+	32.3553i	1.16981	+	2.02617i
$256$		0			0
$257$	8.97214	−	15.5402i	0.559666	−	0.969371i	−0.437858	−	0.899044i	$-0.644263\pi$
$257$	8.97214	−	15.5402i	0.559666	−	0.969371i	0.997524	−	0.0703264i	$-0.0224041\pi$
$258$		0			0
$259$	21.7705	−	7.54153i	1.35275	−	0.468608i
$260$		0			0
$261$	4.47214	−	7.74597i	0.276818	−	0.479463i
$262$		0			0
$263$	−7.06231	−	12.2323i	−0.435480	−	0.754274i	0.561854	−	0.827236i	$-0.310088\pi$
$263$	−7.06231	−	12.2323i	−0.435480	−	0.754274i	−0.997335	+	0.0729620i	$0.976755\pi$
$264$		0			0
$265$	−3.29180			−0.202213
$266$		0			0
$267$	5.00000			0.305995
$268$		0			0
$269$	−2.26393	−	3.92125i	−0.138034	−	0.239083i	0.788718	−	0.614755i	$-0.210745\pi$
$269$	−2.26393	−	3.92125i	−0.138034	−	0.239083i	−0.926753	+	0.375672i	$0.877412\pi$
$270$		0			0
$271$	3.20820	−	5.55677i	0.194885	−	0.337550i	−0.751978	−	0.659188i	$-0.770900\pi$
$271$	3.20820	−	5.55677i	0.194885	−	0.337550i	0.946863	+	0.321638i	$0.104233\pi$
$272$		0			0
$273$	1.11803	−	5.80948i	0.0676665	−	0.351605i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.2082	−	22.8773i	−0.793604	−	1.37456i	−0.923722	−	0.383064i	$-0.874869\pi$
$277$	−13.2082	−	22.8773i	−0.793604	−	1.37456i	0.130118	−	0.991499i	$-0.458464\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	9.05573			0.540219			0.270110	−	0.962830i	$-0.412940\pi$
$281$	9.05573			0.540219			0.270110	+	0.962830i	$0.412940\pi$
$282$		0			0
$283$	−7.06231	−	12.2323i	−0.419811	−	0.727133i	0.576110	−	0.817372i	$-0.304570\pi$
$283$	−7.06231	−	12.2323i	−0.419811	−	0.727133i	−0.995920	+	0.0902393i	$0.971237\pi$
$284$		0			0
$285$	7.50000	−	12.9904i	0.444262	−	0.769484i
$286$		0			0
$287$	8.94427	+	7.74597i	0.527964	+	0.457230i
$288$		0			0
$289$	−19.4164	+	33.6302i	−1.14214	+	1.97825i
$290$		0			0
$291$	−19.4721	−	33.7267i	−1.14148	−	1.97710i
$292$		0			0
$293$	2.94427			0.172006			0.0860031	−	0.996295i	$-0.472591\pi$
$293$	2.94427			0.172006			0.0860031	+	0.996295i	$0.472591\pi$
$294$		0			0
$295$	16.7082			0.972789
$296$		0			0
$297$	−3.35410	−	5.80948i	−0.194625	−	0.337100i
$298$		0			0
$299$	1.88197	−	3.25966i	0.108837	−	0.188511i
$300$		0			0
$301$	16.0000	+	13.8564i	0.922225	+	0.798670i
$302$		0			0
$303$	−10.0623	+	17.4284i	−0.578064	+	1.00124i
$304$		0			0
$305$	3.35410	+	5.80948i	0.192055	+	0.332650i
$306$		0			0
$307$	7.41641			0.423277			0.211638	−	0.977348i	$-0.432120\pi$
$307$	7.41641			0.423277			0.211638	+	0.977348i	$0.432120\pi$
$308$		0			0
$309$	23.9443			1.36214
$310$		0			0
$311$	−16.1180	−	27.9173i	−0.913970	−	1.58304i	−0.808403	−	0.588630i	$-0.799667\pi$
$311$	−16.1180	−	27.9173i	−0.913970	−	1.58304i	−0.105567	−	0.994412i	$-0.533666\pi$
$312$		0			0
$313$	16.2082	−	28.0734i	0.916142	−	1.58680i	0.110921	−	0.993829i	$-0.464620\pi$
$313$	16.2082	−	28.0734i	0.916142	−	1.58680i	0.805221	−	0.592975i	$-0.202047\pi$
$314$		0			0
$315$	−2.23607	+	11.6190i	−0.125988	+	0.654654i
$316$		0			0
$317$	1.88197	−	3.25966i	0.105702	−	0.183081i	−0.808323	−	0.588739i	$-0.799624\pi$
$317$	1.88197	−	3.25966i	0.105702	−	0.183081i	0.914025	+	0.405659i	$0.132958\pi$
$318$		0			0
$319$	6.70820	+	11.6190i	0.375587	+	0.650536i
$320$		0			0
$321$	−31.8328			−1.77673
$322$		0			0
$323$	22.4164			1.24728
$324$		0			0
$325$		0			0
$326$		0			0
$327$	11.9721	−	20.7363i	0.662061	−	1.14672i
$328$		0			0
$329$	3.68034	−	1.27491i	0.202904	−	0.0702879i
$330$		0			0
$331$	−14.2082	+	24.6093i	−0.780954	+	1.35265i	0.150433	+	0.988620i	$0.451933\pi$
$331$	−14.2082	+	24.6093i	−0.780954	+	1.35265i	−0.931387	+	0.364031i	$0.881400\pi$
$332$		0			0
$333$	8.70820	+	15.0831i	0.477207	+	0.826546i
$334$		0			0
$335$	−6.70820			−0.366508
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	−16.7082	−	28.9395i	−0.907465	−	1.57178i
$340$		0			0
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	−9.40983	+	16.2983i	−0.506608	+	0.877471i
$346$		0			0
$347$	−17.5344	−	30.3705i	−0.941298	−	1.63038i	−0.762999	−	0.646400i	$-0.776274\pi$
$347$	−17.5344	−	30.3705i	−0.941298	−	1.63038i	−0.178299	−	0.983976i	$-0.557060\pi$
$348$		0			0
$349$	−2.58359			−0.138297			−0.0691483	−	0.997606i	$-0.522028\pi$
$349$	−2.58359			−0.138297			−0.0691483	+	0.997606i	$0.522028\pi$
$350$		0			0
$351$	−2.23607			−0.119352
$352$		0			0
$353$	−15.3541	−	26.5941i	−0.817216	−	1.41546i	−0.907725	−	0.419565i	$-0.862183\pi$
$353$	−15.3541	−	26.5941i	−0.817216	−	1.41546i	0.0905091	−	0.995896i	$-0.471151\pi$
$354$		0			0
$355$	−10.0000	+	17.3205i	−0.530745	+	0.919277i
$356$		0			0
$357$	−41.7705	+	14.4697i	−2.21073	+	0.765819i
$358$		0			0
$359$	−2.97214	+	5.14789i	−0.156863	+	0.271695i	−0.933736	−	0.357963i	$-0.883472\pi$
$359$	−2.97214	+	5.14789i	−0.156863	+	0.271695i	0.776873	+	0.629658i	$0.216805\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	4.47214			0.234726
$364$		0			0
$365$	−23.9443			−1.25330
$366$		0			0
$367$	0.354102	+	0.613323i	0.0184840	+	0.0320152i	0.875119	−	0.483907i	$-0.160783\pi$
$367$	0.354102	+	0.613323i	0.0184840	+	0.0320152i	−0.856635	+	0.515922i	$0.827449\pi$
$368$		0			0
$369$	−4.47214	+	7.74597i	−0.232810	+	0.403239i
$370$		0			0
$371$	0.736068	−	3.82472i	0.0382147	−	0.198570i
$372$		0			0
$373$	14.2082	−	24.6093i	0.735673	−	1.27422i	−0.218755	−	0.975780i	$-0.570199\pi$
$373$	14.2082	−	24.6093i	0.735673	−	1.27422i	0.954427	−	0.298443i	$-0.0964673\pi$
$374$		0			0
$375$	12.5000	+	21.6506i	0.645497	+	1.11803i
$376$		0			0
$377$	4.47214			0.230327
$378$		0			0
$379$	−11.4164			−0.586421			−0.293211	−	0.956048i	$-0.594724\pi$
$379$	−11.4164			−0.586421			−0.293211	+	0.956048i	$0.594724\pi$
$380$		0			0
$381$	−17.2361	−	29.8537i	−0.883031	−	1.52945i
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	−13.4164	−	11.6190i	−0.683763	−	0.592157i
$386$		0			0
$387$	−8.00000	+	13.8564i	−0.406663	+	0.704361i
$388$		0			0
$389$	3.73607	+	6.47106i	0.189426	+	0.328096i	0.945059	−	0.326900i	$-0.106004\pi$
$389$	3.73607	+	6.47106i	0.189426	+	0.328096i	−0.755633	+	0.654995i	$0.772671\pi$
$390$		0			0
$391$	−28.1246			−1.42232
$392$		0			0
$393$	−8.41641			−0.424552
$394$		0			0
$395$	−11.9721	−	20.7363i	−0.602384	−	1.04336i
$396$		0			0
$397$	−7.06231	+	12.2323i	−0.354447	+	0.613920i	−0.987023	−	0.160578i	$-0.948664\pi$
$397$	−7.06231	+	12.2323i	−0.354447	+	0.613920i	0.632576	+	0.774498i	$0.281998\pi$
$398$		0			0
$399$	13.4164	+	11.6190i	0.671660	+	0.581675i
$400$		0			0
$401$	−4.88197	+	8.45581i	−0.243794	+	0.422263i	−0.961792	−	0.273782i	$-0.911725\pi$
$401$	−4.88197	+	8.45581i	−0.243794	+	0.422263i	0.717998	+	0.696045i	$0.245059\pi$
$402$		0			0
$403$	−2.50000	−	4.33013i	−0.124534	−	0.215699i
$404$		0			0
$405$	24.5967			1.22222
$406$		0			0
$407$	−26.1246			−1.29495
$408$		0			0
$409$	2.35410	+	4.07742i	0.116403	+	0.201616i	0.918340	−	0.395793i	$-0.129530\pi$
$409$	2.35410	+	4.07742i	0.116403	+	0.201616i	−0.801937	+	0.597409i	$0.796197\pi$
$410$		0			0
$411$	−4.20820	+	7.28882i	−0.207575	+	0.359531i
$412$		0			0
$413$	−3.73607	+	19.4132i	−0.183840	+	0.955260i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.81966	−	6.61585i	−0.187050	−	0.323979i
$418$		0			0
$419$	−15.0557			−0.735520			−0.367760	−	0.929921i	$-0.619875\pi$
$419$	−15.0557			−0.735520			−0.367760	+	0.929921i	$0.619875\pi$
$420$		0			0
$421$	−13.4164			−0.653876			−0.326938	−	0.945046i	$-0.606017\pi$
$421$	−13.4164			−0.653876			−0.326938	+	0.945046i	$0.606017\pi$
$422$		0			0
$423$	1.47214	+	2.54981i	0.0715777	+	0.123976i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.50000	+	2.59808i	−0.362950	+	0.125730i
$428$		0			0
$429$	−3.35410	+	5.80948i	−0.161938	+	0.280484i
$430$		0			0
$431$	6.68034	+	11.5707i	0.321781	+	0.557340i	0.980856	−	0.194737i	$-0.0623853\pi$
$431$	6.68034	+	11.5707i	0.321781	+	0.557340i	−0.659075	+	0.752077i	$0.729052\pi$
$432$		0			0
$433$	2.58359			0.124160			0.0620798	−	0.998071i	$-0.480227\pi$
$433$	2.58359			0.124160			0.0620798	+	0.998071i	$0.480227\pi$
$434$		0			0
$435$	−22.3607			−1.07211
$436$		0			0
$437$	5.64590	+	9.77898i	0.270080	+	0.467792i
$438$		0			0
$439$	−8.06231	+	13.9643i	−0.384793	+	0.666481i	−0.991740	−	0.128261i	$-0.959060\pi$
$439$	−8.06231	+	13.9643i	−0.384793	+	0.666481i	0.606948	+	0.794742i	$0.292394\pi$
$440$		0			0
$441$	−13.0000	−	5.19615i	−0.619048	−	0.247436i
$442$		0			0
$443$	−1.11803	+	1.93649i	−0.0531194	+	0.0920055i	−0.891362	−	0.453291i	$-0.850250\pi$
$443$	−1.11803	+	1.93649i	−0.0531194	+	0.0920055i	0.838243	+	0.545297i	$0.183583\pi$
$444$		0			0
$445$	−2.50000	−	4.33013i	−0.118511	−	0.205268i
$446$		0			0
$447$	28.4164			1.34405
$448$		0			0
$449$	10.3607			0.488951			0.244475	−	0.969656i	$-0.421384\pi$
$449$	10.3607			0.488951			0.244475	+	0.969656i	$0.421384\pi$
$450$		0			0
$451$	−6.70820	−	11.6190i	−0.315877	−	0.547115i
$452$		0			0
$453$	7.17376	−	12.4253i	0.337053	−	0.583792i
$454$		0			0
$455$	−5.59017	+	1.93649i	−0.262071	+	0.0907841i
$456$		0			0
$457$	−17.0623	+	29.5528i	−0.798141	+	1.38242i	0.122684	+	0.992446i	$0.460850\pi$
$457$	−17.0623	+	29.5528i	−0.798141	+	1.38242i	−0.920825	+	0.389975i	$0.872484\pi$
$458$		0			0
$459$	8.35410	+	14.4697i	0.389936	+	0.675389i
$460$		0			0
$461$	−10.3607			−0.482545			−0.241272	−	0.970457i	$-0.577565\pi$
$461$	−10.3607			−0.482545			−0.241272	+	0.970457i	$0.577565\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	12.5000	+	21.6506i	0.579674	+	1.00402i
$466$		0			0
$467$	−10.8262	+	18.7516i	−0.500979	+	0.867720i	0.499021	+	0.866590i	$0.333693\pi$
$467$	−10.8262	+	18.7516i	−0.500979	+	0.867720i	−0.999999	+	0.00113029i	$0.999640\pi$
$468$		0			0
$469$	1.50000	−	7.79423i	0.0692636	−	0.359904i
$470$		0			0
$471$	7.82624	−	13.5554i	0.360614	−	0.624602i
$472$		0			0
$473$	−12.0000	−	20.7846i	−0.551761	−	0.955677i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.94427			0.134809
$478$		0			0
$479$	−14.9164	−	25.8360i	−0.681548	−	1.18048i	−0.974508	−	0.224351i	$-0.927974\pi$
$479$	−14.9164	−	25.8360i	−0.681548	−	1.18048i	0.292960	−	0.956125i	$-0.405360\pi$
$480$		0			0
$481$	−4.35410	+	7.54153i	−0.198530	+	0.343864i
$482$		0			0
$483$	−16.8328	−	14.5776i	−0.765920	−	0.663306i
$484$		0			0
$485$	−19.4721	+	33.7267i	−0.884184	+	1.53145i
$486$		0			0
$487$	15.9164	+	27.5680i	0.721241	+	1.24923i	0.960503	+	0.278271i	$0.0897614\pi$
$487$	15.9164	+	27.5680i	0.721241	+	1.24923i	−0.239261	+	0.970955i	$0.576905\pi$
$488$		0			0
$489$	23.2918			1.05329
$490$		0			0
$491$	34.4721			1.55571			0.777853	−	0.628446i	$-0.216309\pi$
$491$	34.4721			1.55571			0.777853	+	0.628446i	$0.216309\pi$
$492$		0			0
$493$	−16.7082	−	28.9395i	−0.752500	−	1.30337i
$494$		0			0
$495$	6.70820	−	11.6190i	0.301511	−	0.522233i
$496$		0			0
$497$	−17.8885	−	15.4919i	−0.802411	−	0.694908i
$498$		0			0
$499$	−0.208204	+	0.360620i	−0.00932049	+	0.0161436i	−0.870648	−	0.491907i	$-0.836300\pi$
$499$	−0.208204	+	0.360620i	−0.00932049	+	0.0161436i	0.861328	+	0.508050i	$0.169634\pi$
$500$		0			0
$501$	−15.1246	−	26.1966i	−0.675718	−	1.17038i
$502$		0			0
$503$	−3.05573			−0.136248			−0.0681241	−	0.997677i	$-0.521701\pi$
$503$	−3.05573			−0.136248			−0.0681241	+	0.997677i	$0.521701\pi$
$504$		0			0
$505$	20.1246			0.895533
$506$		0			0
$507$	1.11803	+	1.93649i	0.0496536	+	0.0860026i
$508$		0			0
$509$	7.88197	−	13.6520i	0.349362	−	0.605113i	−0.636774	−	0.771050i	$-0.719732\pi$
$509$	7.88197	−	13.6520i	0.349362	−	0.605113i	0.986136	+	0.165938i	$0.0530650\pi$
$510$		0			0
$511$	5.35410	−	27.8207i	0.236852	−	1.23072i
$512$		0			0
$513$	3.35410	−	5.80948i	0.148087	−	0.256495i
$514$		0			0
$515$	−11.9721	−	20.7363i	−0.527555	−	0.913753i
$516$		0			0
$517$	−4.41641			−0.194233
$518$		0			0
$519$	−23.2918			−1.02240
$520$		0			0
$521$	0.0278640	+	0.0482619i	0.00122075	+	0.00211439i	0.866635	−	0.498942i	$-0.166278\pi$
$521$	0.0278640	+	0.0482619i	0.00122075	+	0.00211439i	−0.865414	+	0.501057i	$0.832945\pi$
$522$		0			0
$523$	9.64590	−	16.7072i	0.421786	−	0.730554i	−0.574329	−	0.818625i	$-0.694737\pi$
$523$	9.64590	−	16.7072i	0.421786	−	0.730554i	0.996114	+	0.0880707i	$0.0280701\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.6803	+	32.3553i	−0.813728	+	1.40942i
$528$		0			0
$529$	4.41641	+	7.64944i	0.192018	+	0.332584i
$530$		0			0
$531$	−14.9443			−0.648526
$532$		0			0
$533$	−4.47214			−0.193710
$534$		0			0
$535$	15.9164	+	27.5680i	0.688126	+	1.19187i
$536$		0			0
$537$	−22.5000	+	38.9711i	−0.970947	+	1.68173i
$538$		0			0
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	−7.35410	+	12.7377i	−0.316178	+	0.547636i	−0.979687	−	0.200532i	$-0.935733\pi$
$541$	−7.35410	+	12.7377i	−0.316178	+	0.547636i	0.663510	+	0.748168i	$0.269066\pi$
$542$		0			0
$543$	1.58359	+	2.74286i	0.0679584	+	0.117707i
$544$		0			0
$545$	−23.9443			−1.02566
$546$		0			0
$547$	31.4164			1.34327			0.671634	−	0.740883i	$-0.265593\pi$
$547$	31.4164			1.34327			0.671634	+	0.740883i	$0.265593\pi$
$548$		0			0
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$	−6.70820	+	11.6190i	−0.285779	+	0.494984i
$552$		0			0
$553$	26.7705	−	9.27358i	1.13840	−	0.394353i
$554$		0			0
$555$	21.7705	−	37.7076i	0.924107	−	1.60060i
$556$		0			0
$557$	2.64590	+	4.58283i	0.112110	+	0.194181i	0.916621	−	0.399758i	$-0.130906\pi$
$557$	2.64590	+	4.58283i	0.112110	+	0.194181i	−0.804511	+	0.593938i	$0.797572\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	50.1246			2.11626
$562$		0			0
$563$	−18.2984	−	31.6937i	−0.771185	−	1.33573i	−0.936914	−	0.349560i	$-0.886331\pi$
$563$	−18.2984	−	31.6937i	−0.771185	−	1.33573i	0.165730	−	0.986171i	$-0.447002\pi$
$564$		0			0
$565$	−16.7082	+	28.9395i	−0.702919	+	1.21749i
$566$		0			0
$567$	−5.50000	+	28.5788i	−0.230978	+	1.20020i
$568$		0			0
$569$	−8.26393	+	14.3136i	−0.346442	+	0.600055i	−0.985615	−	0.169008i	$-0.945944\pi$
$569$	−8.26393	+	14.3136i	−0.346442	+	0.600055i	0.639173	+	0.769063i	$0.279277\pi$
$570$		0			0
$571$	2.06231	+	3.57202i	0.0863048	+	0.149484i	0.905946	−	0.423392i	$-0.139161\pi$
$571$	2.06231	+	3.57202i	0.0863048	+	0.149484i	−0.819642	+	0.572877i	$0.805827\pi$
$572$		0			0
$573$	−25.0000			−1.04439
$574$		0			0
$575$		0			0
$576$		0			0
$577$	16.3541	+	28.3261i	0.680830	+	1.17923i	0.974728	+	0.223396i	$0.0717142\pi$
$577$	16.3541	+	28.3261i	0.680830	+	1.17923i	−0.293898	+	0.955837i	$0.594953\pi$
$578$		0			0
$579$	−14.2082	+	24.6093i	−0.590473	+	1.02273i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.20820	+	3.82472i	−0.0914545	+	0.158404i
$584$		0			0
$585$	−2.23607	−	3.87298i	−0.0924500	−	0.160128i
$586$		0			0
$587$	41.8885			1.72893			0.864463	−	0.502697i	$-0.167659\pi$
$587$	41.8885			1.72893			0.864463	+	0.502697i	$0.167659\pi$
$588$		0			0
$589$	15.0000			0.618064
$590$		0			0
$591$	−30.1246	−	52.1774i	−1.23916	−	2.14629i
$592$		0			0
$593$	−16.1180	+	27.9173i	−0.661888	+	1.14642i	0.318231	+	0.948013i	$0.396911\pi$
$593$	−16.1180	+	27.9173i	−0.661888	+	1.14642i	−0.980119	+	0.198411i	$0.936422\pi$
$594$		0			0
$595$	33.4164	+	28.9395i	1.36994	+	1.18640i
$596$		0			0
$597$	8.15248	−	14.1205i	0.333659	−	0.577914i
$598$		0			0
$599$	20.5344	+	35.5667i	0.839015	+	1.45322i	0.890719	+	0.454553i	$0.150201\pi$
$599$	20.5344	+	35.5667i	0.839015	+	1.45322i	−0.0517049	+	0.998662i	$0.516466\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	6.00000			0.244339
$604$		0			0
$605$	−2.23607	−	3.87298i	−0.0909091	−	0.157459i
$606$		0			0
$607$	−8.06231	+	13.9643i	−0.327239	+	0.566794i	−0.981963	−	0.189074i	$-0.939452\pi$
$607$	−8.06231	+	13.9643i	−0.327239	+	0.566794i	0.654724	+	0.755868i	$0.272785\pi$
$608$		0			0
$609$	5.00000	−	25.9808i	0.202610	−	1.05279i
$610$		0			0
$611$	−0.736068	+	1.27491i	−0.0297781	+	0.0515772i
$612$		0			0
$613$	−11.0623	−	19.1605i	−0.446802	−	0.773884i	0.551373	−	0.834259i	$-0.314104\pi$
$613$	−11.0623	−	19.1605i	−0.446802	−	0.773884i	−0.998176	+	0.0603742i	$0.980771\pi$
$614$		0			0
$615$	22.3607			0.901670
$616$		0			0
$617$	4.47214			0.180041			0.0900207	−	0.995940i	$-0.471307\pi$
$617$	4.47214			0.180041			0.0900207	+	0.995940i	$0.471307\pi$
$618$		0			0
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$	−4.20820	+	7.28882i	−0.168869	+	0.292490i
$622$		0			0
$623$	5.59017	−	1.93649i	0.223965	−	0.0775839i
$624$		0			0
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$		0			0
$627$	−10.0623	−	17.4284i	−0.401850	−	0.696024i
$628$		0			0
$629$	65.0689			2.59447
$630$		0			0
$631$	30.8328			1.22744			0.613718	−	0.789526i	$-0.289673\pi$
$631$	30.8328			1.22744			0.613718	+	0.789526i	$0.289673\pi$
$632$		0			0
$633$	−4.47214	−	7.74597i	−0.177751	−	0.307875i
$634$		0			0
$635$	−17.2361	+	29.8537i	−0.683992	+	1.18471i
$636$		0			0
$637$	−1.00000	−	6.92820i	−0.0396214	−	0.274505i
$638$		0			0
$639$	8.94427	−	15.4919i	0.353830	−	0.612851i
$640$		0			0
$641$	2.97214	+	5.14789i	0.117392	+	0.203329i	0.918734	−	0.394878i	$-0.129213\pi$
$641$	2.97214	+	5.14789i	0.117392	+	0.203329i	−0.801341	+	0.598208i	$0.795880\pi$
$642$		0			0
$643$	18.8328			0.742694			0.371347	−	0.928494i	$-0.378896\pi$
$643$	18.8328			0.742694			0.371347	+	0.928494i	$0.378896\pi$
$644$		0			0
$645$	40.0000			1.57500
$646$		0			0
$647$	7.88197	+	13.6520i	0.309872	+	0.536714i	0.978334	−	0.207032i	$-0.0663804\pi$
$647$	7.88197	+	13.6520i	0.309872	+	0.536714i	−0.668462	+	0.743746i	$0.733047\pi$
$648$		0			0
$649$	11.2082	−	19.4132i	0.439960	−	0.762034i
$650$		0			0
$651$	−27.9508	+	9.68246i	−1.09548	+	0.379485i
$652$		0			0
$653$	−6.73607	+	11.6672i	−0.263603	+	0.456573i	−0.967197	−	0.254029i	$-0.918244\pi$
$653$	−6.73607	+	11.6672i	−0.263603	+	0.456573i	0.703594	+	0.710602i	$0.251577\pi$
$654$		0			0
$655$	4.20820	+	7.28882i	0.164428	+	0.284798i
$656$		0			0
$657$	21.4164			0.835534
$658$		0			0
$659$	−8.94427			−0.348419			−0.174210	−	0.984709i	$-0.555737\pi$
$659$	−8.94427			−0.348419			−0.174210	+	0.984709i	$0.555737\pi$
$660$		0			0
$661$	−3.35410	−	5.80948i	−0.130459	−	0.225962i	0.793394	−	0.608708i	$-0.208312\pi$
$661$	−3.35410	−	5.80948i	−0.130459	−	0.225962i	−0.923854	+	0.382746i	$0.874979\pi$
$662$		0			0
$663$	8.35410	−	14.4697i	0.324446	−	0.561958i
$664$		0			0
$665$	3.35410	−	17.4284i	0.130066	−	0.675845i
$666$		0			0
$667$	8.41641	−	14.5776i	0.325885	−	0.564449i
$668$		0			0
$669$	4.47214	+	7.74597i	0.172903	+	0.299476i
$670$		0			0
$671$	9.00000			0.347441
$672$		0			0
$673$	17.4164			0.671353			0.335677	−	0.941977i	$-0.391035\pi$
$673$	17.4164			0.671353			0.335677	+	0.941977i	$0.391035\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.4443	+	28.4823i	−0.632005	+	1.09466i	0.355137	+	0.934814i	$0.384434\pi$
$677$	−16.4443	+	28.4823i	−0.632005	+	1.09466i	−0.987141	+	0.159850i	$0.948899\pi$
$678$		0			0
$679$	−34.8328	−	30.1661i	−1.33676	−	1.15767i
$680$		0			0
$681$	13.3541	−	23.1300i	0.511730	−	0.886343i
$682$		0			0
$683$	−2.26393	−	3.92125i	−0.0866270	−	0.150042i	0.819456	−	0.573142i	$-0.194275\pi$
$683$	−2.26393	−	3.92125i	−0.0866270	−	0.150042i	−0.906083	+	0.423099i	$0.860942\pi$
$684$		0			0
$685$	8.41641			0.321574
$686$		0			0
$687$	36.0557			1.37561
$688$		0			0
$689$	0.736068	+	1.27491i	0.0280420	+	0.0485701i
$690$		0			0
$691$	0.916408	−	1.58726i	0.0348618	−	0.0603824i	−0.848068	−	0.529887i	$-0.822234\pi$
$691$	0.916408	−	1.58726i	0.0348618	−	0.0603824i	0.882930	+	0.469505i	$0.155568\pi$
$692$		0			0
$693$	12.0000	+	10.3923i	0.455842	+	0.394771i
$694$		0			0
$695$	−3.81966	+	6.61585i	−0.144888	+	0.250953i
$696$		0			0
$697$	16.7082	+	28.9395i	0.632868	+	1.09616i
$698$		0			0
$699$	13.2918			0.502742
$700$		0			0
$701$	22.3607			0.844551			0.422276	−	0.906467i	$-0.361231\pi$
$701$	22.3607			0.844551			0.422276	+	0.906467i	$0.361231\pi$
$702$		0			0
$703$	−13.0623	−	22.6246i	−0.492654	−	0.853302i
$704$		0			0
$705$	3.68034	−	6.37454i	0.138610	−	0.240079i
$706$		0			0
$707$	−4.50000	+	23.3827i	−0.169240	+	0.879396i
$708$		0			0
$709$	4.93769	−	8.55234i	0.185439	−	0.321190i	−0.758285	−	0.651923i	$-0.773963\pi$
$709$	4.93769	−	8.55234i	0.185439	−	0.321190i	0.943724	+	0.330733i	$0.107296\pi$
$710$		0			0
$711$	10.7082	+	18.5472i	0.401589	+	0.695573i
$712$		0			0
$713$	−18.8197			−0.704802
$714$		0			0
$715$	6.70820			0.250873
$716$		0			0
$717$	8.29180	+	14.3618i	0.309663	+	0.536352i
$718$		0			0
$719$	5.64590	−	9.77898i	0.210556	−	0.364694i	−0.741332	−	0.671138i	$-0.765806\pi$
$719$	5.64590	−	9.77898i	0.210556	−	0.364694i	0.951889	+	0.306444i	$0.0991391\pi$
$720$		0			0
$721$	26.7705	−	9.27358i	0.996986	−	0.345366i
$722$		0			0
$723$	−9.73607	+	16.8634i	−0.362088	+	0.627155i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−14.8328			−0.550119			−0.275059	−	0.961427i	$-0.588698\pi$
$727$	−14.8328			−0.550119			−0.275059	+	0.961427i	$0.588698\pi$
$728$		0			0
$729$	−7.00000			−0.259259
$730$		0			0
$731$	29.8885	+	51.7685i	1.10547	+	1.91473i
$732$		0			0
$733$	−7.64590	+	13.2431i	−0.282408	+	0.489144i	−0.971977	−	0.235075i	$-0.924466\pi$
$733$	−7.64590	+	13.2431i	−0.282408	+	0.489144i	0.689570	+	0.724219i	$0.257800\pi$
$734$		0			0
$735$	5.00000	+	34.6410i	0.184428	+	1.27775i
$736$		0			0
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$		0			0
$739$	17.9164	+	31.0321i	0.659066	+	1.14154i	0.980858	+	0.194725i	$0.0623814\pi$
$739$	17.9164	+	31.0321i	0.659066	+	1.14154i	−0.321792	+	0.946810i	$0.604285\pi$
$740$		0			0
$741$	−6.70820			−0.246432
$742$		0			0
$743$	−15.0557			−0.552341			−0.276171	−	0.961109i	$-0.589065\pi$
$743$	−15.0557			−0.552341			−0.276171	+	0.961109i	$0.589065\pi$
$744$		0			0
$745$	−14.2082	−	24.6093i	−0.520548	−	0.901616i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−35.5902	+	12.3288i	−1.30044	+	0.450484i
$750$		0			0
$751$	15.0623	−	26.0887i	0.549631	−	0.951989i	−0.448668	−	0.893698i	$-0.648102\pi$
$751$	15.0623	−	26.0887i	0.549631	−	0.951989i	0.998300	−	0.0582911i	$-0.0185651\pi$
$752$		0			0
$753$	−11.7082	−	20.2792i	−0.426671	−	0.739015i
$754$		0			0
$755$	−14.3475			−0.522160
$756$		0			0
$757$	0.832816			0.0302692			0.0151346	−	0.999885i	$-0.495182\pi$
$757$	0.832816			0.0302692			0.0151346	+	0.999885i	$0.495182\pi$
$758$		0			0
$759$	12.6246	+	21.8665i	0.458244	+	0.793703i
$760$		0			0
$761$	−16.7705	+	29.0474i	−0.607931	+	1.05297i	0.383650	+	0.923478i	$0.374667\pi$
$761$	−16.7705	+	29.0474i	−0.607931	+	1.05297i	−0.991581	+	0.129488i	$0.958667\pi$
$762$		0			0
$763$	5.35410	−	27.8207i	0.193832	−	1.00718i
$764$		0			0
$765$	−16.7082	+	28.9395i	−0.604086	+	1.04631i
$766$		0			0
$767$	−3.73607	−	6.47106i	−0.134902	−	0.233656i
$768$		0			0
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$		0			0
$771$	40.1246			1.44505
$772$		0			0
$773$	−5.53444	−	9.58593i	−0.199060	−	0.344782i	0.749164	−	0.662385i	$-0.230456\pi$
$773$	−5.53444	−	9.58593i	−0.199060	−	0.344782i	−0.948224	+	0.317603i	$0.897122\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	38.9443	+	33.7267i	1.39712	+	1.20994i
$778$		0			0
$779$	6.70820	−	11.6190i	0.240346	−	0.416292i
$780$		0			0
$781$	13.4164	+	23.2379i	0.480077	+	0.831517i
$782$		0			0
$783$	−10.0000			−0.357371
$784$		0			0
$785$	−15.6525			−0.558661
$786$		0			0
$787$	−3.20820	−	5.55677i	−0.114360	−	0.198078i	0.803164	−	0.595758i	$-0.203148\pi$
$787$	−3.20820	−	5.55677i	−0.114360	−	0.198078i	−0.917524	+	0.397681i	$0.869815\pi$
$788$		0			0
$789$	15.7918	−	27.3522i	0.562203	−	0.973764i
$790$		0			0
$791$	−29.8885	−	25.8842i	−1.06271	−	0.920338i
$792$		0			0
$793$	1.50000	−	2.59808i	0.0532666	−	0.0922604i
$794$		0			0
$795$	−3.68034	−	6.37454i	−0.130528	−	0.226081i
$796$		0			0
$797$	26.9443			0.954415			0.477208	−	0.878791i	$-0.341649\pi$
$797$	26.9443			0.954415			0.477208	+	0.878791i	$0.341649\pi$
$798$		0			0
$799$	11.0000			0.389152
$800$		0			0
$801$	2.23607	+	3.87298i	0.0790076	+	0.136845i
$802$		0			0
$803$	−16.0623	+	27.8207i	−0.566826	+	0.981772i
$804$		0			0
$805$	−4.20820	+	21.8665i	−0.148320	+	0.770692i
$806$		0			0
$807$	5.06231	−	8.76817i	0.178202	−	0.308654i
$808$		0			0
$809$	2.20820	+	3.82472i	0.0776363	+	0.134470i	0.902230	−	0.431256i	$-0.141929\pi$
$809$	2.20820	+	3.82472i	0.0776363	+	0.134470i	−0.824593	+	0.565726i	$0.808596\pi$
$810$		0			0
$811$	−38.8328			−1.36360			−0.681802	−	0.731536i	$-0.738804\pi$
$811$	−38.8328			−1.36360			−0.681802	+	0.731536i	$0.738804\pi$
$812$		0			0
$813$	14.3475			0.503190
$814$		0			0
$815$	−11.6459	−	20.1713i	−0.407938	−	0.706569i
$816$		0			0
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$		0			0
$819$	5.00000	−	1.73205i	0.174714	−	0.0605228i
$820$		0			0
$821$	−16.8820	+	29.2404i	−0.589185	+	1.02050i	0.405155	+	0.914248i	$0.367218\pi$
$821$	−16.8820	+	29.2404i	−0.589185	+	1.02050i	−0.994339	+	0.106250i	$0.966116\pi$
$822$		0			0
$823$	−3.06231	−	5.30407i	−0.106745	−	0.184888i	0.807705	−	0.589587i	$-0.200710\pi$
$823$	−3.06231	−	5.30407i	−0.106745	−	0.184888i	−0.914450	+	0.404699i	$0.867376\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.8328			0.933068			0.466534	−	0.884503i	$-0.345502\pi$
$827$	26.8328			0.933068			0.466534	+	0.884503i	$0.345502\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	29.5344	−	51.1552i	1.02454	−	1.77455i
$832$		0			0
$833$	−41.0967	+	32.3553i	−1.42392	+	1.12104i
$834$		0			0
$835$	−15.1246	+	26.1966i	−0.523409	+	0.906571i
$836$		0			0
$837$	5.59017	+	9.68246i	0.193225	+	0.334675i
$838$		0			0
$839$	−29.8885			−1.03187			−0.515934	−	0.856629i	$-0.672555\pi$
$839$	−29.8885			−1.03187			−0.515934	+	0.856629i	$0.672555\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$		0			0
$843$	10.1246	+	17.5363i	0.348710	+	0.603984i
$844$		0			0
$845$	1.11803	−	1.93649i	0.0384615	−	0.0666173i
$846$		0			0
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$		0			0
$849$	15.7918	−	27.3522i	0.541973	−	0.938725i
$850$		0			0
$851$	16.3885	+	28.3858i	0.561792	+	0.973052i
$852$		0			0
$853$	28.2492			0.967235			0.483617	−	0.875279i	$-0.339323\pi$
$853$	28.2492			0.967235			0.483617	+	0.875279i	$0.339323\pi$
$854$		0			0
$855$	13.4164			0.458831
$856$		0			0
$857$	−21.6803	−	37.5515i	−0.740586	−	1.28273i	−0.952229	−	0.305386i	$-0.901215\pi$
$857$	−21.6803	−	37.5515i	−0.740586	−	1.28273i	0.211642	−	0.977347i	$-0.432119\pi$
$858$		0			0
$859$	3.64590	−	6.31488i	0.124396	−	0.215461i	−0.797100	−	0.603847i	$-0.793634\pi$
$859$	3.64590	−	6.31488i	0.124396	−	0.215461i	0.921497	+	0.388386i	$0.126967\pi$
$860$		0			0
$861$	−5.00000	+	25.9808i	−0.170400	+	0.885422i
$862$		0			0
$863$	3.02786	−	5.24441i	0.103070	−	0.178522i	−0.809878	−	0.586598i	$-0.800467\pi$
$863$	3.02786	−	5.24441i	0.103070	−	0.178522i	0.912948	+	0.408076i	$0.133800\pi$
$864$		0			0
$865$	11.6459	+	20.1713i	0.395972	+	0.685844i
$866$		0			0
$867$	−86.8328			−2.94900
$868$		0			0
$869$	−32.1246			−1.08975
$870$		0			0
$871$	1.50000	+	2.59808i	0.0508256	+	0.0880325i
$872$		0			0
$873$	17.4164	−	30.1661i	0.589456	−	1.02097i
$874$		0			0
$875$	22.3607	+	19.3649i	0.755929	+	0.654654i
$876$		0			0
$877$	4.06231	−	7.03612i	0.137174	−	0.237593i	−0.789252	−	0.614070i	$-0.789531\pi$
$877$	4.06231	−	7.03612i	0.137174	−	0.237593i	0.926426	+	0.376477i	$0.122865\pi$
$878$		0			0
$879$	3.29180	+	5.70156i	0.111030	+	0.192309i
$880$		0			0
$881$	−19.3050			−0.650400			−0.325200	−	0.945645i	$-0.605432\pi$
$881$	−19.3050			−0.650400			−0.325200	+	0.945645i	$0.605432\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	18.6803	+	32.3553i	0.627933	+	1.08761i
$886$		0			0
$887$	−7.88197	+	13.6520i	−0.264651	+	0.458388i	−0.967472	−	0.252978i	$-0.918590\pi$
$887$	−7.88197	+	13.6520i	−0.264651	+	0.458388i	0.702821	+	0.711366i	$0.251923\pi$
$888$		0			0
$889$	−30.8328	−	26.7020i	−1.03410	−	0.895556i
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$		0			0
$893$	−2.20820	−	3.82472i	−0.0738947	−	0.127989i
$894$		0			0
$895$	45.0000			1.50418
$896$		0			0
$897$	8.41641			0.281016
$898$		0			0
$899$	−11.1803	−	19.3649i	−0.372885	−	0.645856i
$900$		0			0
$901$	5.50000	−	9.52628i	0.183232	−	0.317366i
$902$		0			0
$903$	−8.94427	+	46.4758i	−0.297647	+	1.54662i
$904$		0			0
$905$	1.58359	−	2.74286i	0.0526404	−	0.0911758i
$906$		0			0
$907$	2.64590	+	4.58283i	0.0878556	+	0.152170i	0.906604	−	0.421981i	$-0.138665\pi$
$907$	2.64590	+	4.58283i	0.0878556	+	0.152170i	−0.818749	+	0.574152i	$0.805332\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−46.2492			−1.53231			−0.766153	−	0.642659i	$-0.777831\pi$
$911$	−46.2492			−1.53231			−0.766153	+	0.642659i	$0.777831\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−7.50000	+	12.9904i	−0.247942	+	0.429449i
$916$		0			0
$917$	−9.40983	+	3.25966i	−0.310740	+	0.107643i
$918$		0			0
$919$	−10.0623	+	17.4284i	−0.331925	+	0.574911i	−0.982889	−	0.184198i	$-0.941031\pi$
$919$	−10.0623	+	17.4284i	−0.331925	+	0.574911i	0.650964	+	0.759108i	$0.274365\pi$
$920$		0			0
$921$	8.29180	+	14.3618i	0.273224	+	0.473238i
$922$		0			0
$923$	8.94427			0.294404
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.7082	+	18.5472i	0.351704	+	0.609168i
$928$		0			0
$929$	23.5902	−	40.8594i	0.773968	−	1.34055i	−0.161404	−	0.986888i	$-0.551602\pi$
$929$	23.5902	−	40.8594i	0.773968	−	1.34055i	0.935372	−	0.353664i	$-0.115064\pi$
$930$		0			0
$931$	19.5000	+	7.79423i	0.639087	+	0.255446i
$932$		0			0
$933$	36.0410	−	62.4249i	1.17993	−	2.04370i
$934$		0			0
$935$	−25.0623	−	43.4092i	−0.819625	−	1.41963i
$936$		0			0
$937$	−1.41641			−0.0462720			−0.0231360	−	0.999732i	$-0.507365\pi$
$937$	−1.41641			−0.0462720			−0.0231360	+	0.999732i	$0.507365\pi$
$938$		0			0
$939$	72.4853			2.36547
$940$		0			0
$941$	−22.8820	−	39.6327i	−0.745931	−	1.29199i	−0.949759	−	0.312983i	$-0.898672\pi$
$941$	−22.8820	−	39.6327i	−0.745931	−	1.29199i	0.203828	−	0.979007i	$-0.434662\pi$
$942$		0			0
$943$	−8.41641	+	14.5776i	−0.274076	+	0.474713i
$944$		0			0
$945$	12.5000	−	4.33013i	0.406625	−	0.140859i
$946$		0			0
$947$	−15.7361	+	27.2557i	−0.511354	+	0.885690i	0.488560	+	0.872530i	$0.337522\pi$
$947$	−15.7361	+	27.2557i	−0.511354	+	0.885690i	−0.999913	+	0.0131599i	$0.995811\pi$
$948$		0			0
$949$	5.35410	+	9.27358i	0.173802	+	0.301033i
$950$		0			0
$951$	8.41641			0.272921
$952$		0			0
$953$	29.7771			0.964574			0.482287	−	0.876013i	$-0.339806\pi$
$953$	29.7771			0.964574			0.482287	+	0.876013i	$0.339806\pi$
$954$		0			0
$955$	12.5000	+	21.6506i	0.404491	+	0.700598i
$956$		0			0
$957$	−15.0000	+	25.9808i	−0.484881	+	0.839839i
$958$		0			0
$959$	−1.88197	+	9.77898i	−0.0607719	+	0.315780i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	−14.2361	−	24.6576i	−0.458751	−	0.794580i
$964$		0			0
$965$	28.4164			0.914757
$966$		0			0
$967$	−43.4164			−1.39618			−0.698089	−	0.716011i	$-0.745966\pi$
$967$	−43.4164			−1.39618			−0.698089	+	0.716011i	$0.745966\pi$
$968$		0			0
$969$	25.0623	+	43.4092i	0.805117	+	1.39450i
$970$		0			0
$971$	−12.3541	+	21.3979i	−0.396462	+	0.686692i	−0.993287	−	0.115679i	$-0.963095\pi$
$971$	−12.3541	+	21.3979i	−0.396462	+	0.686692i	0.596825	+	0.802372i	$0.296429\pi$
$972$		0			0
$973$	−6.83282	−	5.91739i	−0.219050	−	0.189703i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.8262	+	29.1439i	0.538319	+	0.932396i	0.998995	+	0.0448274i	$0.0142738\pi$
$977$	16.8262	+	29.1439i	0.538319	+	0.932396i	−0.460676	+	0.887569i	$0.652393\pi$
$978$		0			0
$979$	−6.70820			−0.214395
$980$		0			0
$981$	21.4164			0.683773
$982$		0			0
$983$	−0.736068	−	1.27491i	−0.0234769	−	0.0406632i	0.854048	−	0.520194i	$-0.174140\pi$
$983$	−0.736068	−	1.27491i	−0.0234769	−	0.0406632i	−0.877525	+	0.479531i	$0.840807\pi$
$984$		0			0
$985$	−30.1246	+	52.1774i	−0.959850	+	1.66251i
$986$		0			0
$987$	6.58359	+	5.70156i	0.209558	+	0.181483i
$988$		0			0
$989$	−15.0557	+	26.0773i	−0.478744	+	0.829209i
$990$		0			0
$991$	8.64590	+	14.9751i	0.274646	+	0.475701i	0.970046	−	0.242922i	$-0.0781060\pi$
$991$	8.64590	+	14.9751i	0.274646	+	0.475701i	−0.695400	+	0.718623i	$0.744773\pi$
$992$		0			0
$993$	−63.5410			−2.01641
$994$		0			0
$995$	−16.3050			−0.516902
$996$		0			0
$997$	0.208204	+	0.360620i	0.00659388	+	0.0114209i	0.869304	−	0.494279i	$-0.164568\pi$
$997$	0.208204	+	0.360620i	0.00659388	+	0.0114209i	−0.862710	+	0.505700i	$0.831234\pi$
$998$		0			0
$999$	9.73607	−	16.8634i	0.308036	−	0.533533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.j.625.2		4
4.3	odd	2		91.2.e.b.79.1	yes	4
7.4	even	3	inner	1456.2.r.j.417.2		4
12.11	even	2		819.2.j.c.352.2		4
28.3	even	6		637.2.e.h.508.1		4
28.11	odd	6		91.2.e.b.53.1	✓	4
28.19	even	6		637.2.a.e.1.2		2
28.23	odd	6		637.2.a.f.1.2		2
28.27	even	2		637.2.e.h.79.1		4
52.51	odd	2		1183.2.e.d.170.2		4
84.11	even	6		819.2.j.c.235.2		4
84.23	even	6		5733.2.a.v.1.1		2
84.47	odd	6		5733.2.a.w.1.1		2
364.51	odd	6		8281.2.a.z.1.1		2
364.103	even	6		8281.2.a.ba.1.1		2
364.207	odd	6		1183.2.e.d.508.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.1	✓	4	28.11	odd	6
91.2.e.b.79.1	yes	4	4.3	odd	2
637.2.a.e.1.2		2	28.19	even	6
637.2.a.f.1.2		2	28.23	odd	6
637.2.e.h.79.1		4	28.27	even	2
637.2.e.h.508.1		4	28.3	even	6
819.2.j.c.235.2		4	84.11	even	6
819.2.j.c.352.2		4	12.11	even	2
1183.2.e.d.170.2		4	52.51	odd	2
1183.2.e.d.508.2		4	364.207	odd	6
1456.2.r.j.417.2		4	7.4	even	3	inner
1456.2.r.j.625.2		4	1.1	even	1	trivial
5733.2.a.v.1.1		2	84.23	even	6
5733.2.a.w.1.1		2	84.47	odd	6
8281.2.a.z.1.1		2	364.51	odd	6
8281.2.a.ba.1.1		2	364.103	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11803 + 1.93649i) q^{3} +(1.11803 - 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.11803 + 1.93649i) q^{3} +(1.11803 - 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +5.00000 q^{15} +(3.73607 + 6.47106i) q^{17} +(1.50000 - 2.59808i) q^{19} +(-1.11803 + 5.80948i) q^{21} +(-1.88197 + 3.25966i) q^{23} +2.23607 q^{27} -4.47214 q^{29} +(2.50000 + 4.33013i) q^{31} +(3.35410 - 5.80948i) q^{33} +(5.59017 - 1.93649i) q^{35} +(4.35410 - 7.54153i) q^{37} +(-1.11803 - 1.93649i) q^{39} +4.47214 q^{41} +8.00000 q^{43} +(2.23607 + 3.87298i) q^{45} +(0.736068 - 1.27491i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-8.35410 + 14.4697i) q^{51} +(-0.736068 - 1.27491i) q^{53} -6.70820 q^{55} +6.70820 q^{57} +(3.73607 + 6.47106i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-5.00000 + 1.73205i) q^{63} +(-1.11803 + 1.93649i) q^{65} +(-1.50000 - 2.59808i) q^{67} -8.41641 q^{69} -8.94427 q^{71} +(-5.35410 - 9.27358i) q^{73} +(1.50000 - 7.79423i) q^{77} +(5.35410 - 9.27358i) q^{79} +(5.50000 + 9.52628i) q^{81} +16.7082 q^{85} +(-5.00000 - 8.66025i) q^{87} +(1.11803 - 1.93649i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(-5.59017 + 9.68246i) q^{93} +(-3.35410 - 5.80948i) q^{95} -17.4164 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 8 * q^7 - 4 * q^9	\( 4 q + 8 q^{7} - 4 q^{9} - 6 q^{11} - 4 q^{13} + 20 q^{15} + 6 q^{17} + 6 q^{19} - 12 q^{23} + 10 q^{31} + 4 q^{37} + 32 q^{43} - 6 q^{47} + 4 q^{49} - 20 q^{51} + 6 q^{53} + 6 q^{59} - 6 q^{61} - 20 q^{63} - 6 q^{67} + 20 q^{69} - 8 q^{73} + 6 q^{77} + 8 q^{79} + 22 q^{81} + 40 q^{85} - 20 q^{87} - 8 q^{91} - 16 q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q + 8 * q^7 - 4 * q^9 - 6 * q^11 - 4 * q^13 + 20 * q^15 + 6 * q^17 + 6 * q^19 - 12 * q^23 + 10 * q^31 + 4 * q^37 + 32 * q^43 - 6 * q^47 + 4 * q^49 - 20 * q^51 + 6 * q^53 + 6 * q^59 - 6 * q^61 - 20 * q^63 - 6 * q^67 + 20 * q^69 - 8 * q^73 + 6 * q^77 + 8 * q^79 + 22 * q^81 + 40 * q^85 - 20 * q^87 - 8 * q^91 - 16 * q^97 + 24 * q^99

Introduction

L-functions

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