LMFDB - Embedded newform 1456.2.s.h.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(113,1456)]

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, 4]))

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

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

chi := DirichletCharacter("1456.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.s (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1456.113
Dual form			1456.2.s.h.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 + 2.26728i) q^{3} +2.61803 q^{5} +(0.500000 + 0.866025i) q^{7} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$	\(q+(-1.30902 + 2.26728i) q^{3} +2.61803 q^{5} +(0.500000 + 0.866025i) q^{7} +(-1.92705 - 3.33775i) q^{9} +(0.927051 - 1.60570i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(-3.42705 + 5.93583i) q^{15} +(0.736068 + 1.27491i) q^{17} +(-0.927051 - 1.60570i) q^{19} -2.61803 q^{21} +(-2.23607 + 3.87298i) q^{23} +1.85410 q^{25} +2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +4.70820 q^{31} +(2.42705 + 4.20378i) q^{33} +(1.30902 + 2.26728i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-2.61803 - 9.06914i) q^{39} +(-0.381966 + 0.661585i) q^{41} +(6.28115 + 10.8793i) q^{43} +(-5.04508 - 8.73834i) q^{45} +2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} -3.85410 q^{51} +3.76393 q^{53} +(2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +(-1.11803 - 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(1.92705 - 3.33775i) q^{63} +(-6.54508 + 6.80185i) q^{65} +(-6.35410 + 11.0056i) q^{67} +(-5.85410 - 10.1396i) q^{69} +(-7.09017 - 12.2805i) q^{71} -2.00000 q^{73} +(-2.42705 + 4.20378i) q^{75} +1.85410 q^{77} -4.00000 q^{79} +(2.85410 - 4.94345i) q^{81} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +(-9.28115 - 16.0754i) q^{87} +(-2.45492 + 4.25204i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(-6.16312 + 10.6748i) q^{93} +(-2.42705 - 4.20378i) q^{95} +(-9.42705 - 16.3281i) q^{97} -7.14590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9	$ 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} - 3 q^{11} - 10 q^{13} - 7 q^{15} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 6 q^{25} - 3 q^{29} - 8 q^{31} + 3 q^{33} + 3 q^{35} - 8 q^{37} - 6 q^{39} - 6 q^{41} + 5 q^{43} - 9 q^{45} - 2 q^{49} - 2 q^{51} + 24 q^{53} + 3 q^{55} + 6 q^{57} + 12 q^{61} + q^{63} - 15 q^{65} - 12 q^{67} - 10 q^{69} - 6 q^{71} - 8 q^{73} - 3 q^{75} - 6 q^{77} - 16 q^{79} - 2 q^{81} + q^{85} - 17 q^{87} - 21 q^{89} - 14 q^{91} - 9 q^{93} - 3 q^{95} - 31 q^{97} - 42 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9 - 3 * q^11 - 10 * q^13 - 7 * q^15 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 6 * q^25 - 3 * q^29 - 8 * q^31 + 3 * q^33 + 3 * q^35 - 8 * q^37 - 6 * q^39 - 6 * q^41 + 5 * q^43 - 9 * q^45 - 2 * q^49 - 2 * q^51 + 24 * q^53 + 3 * q^55 + 6 * q^57 + 12 * q^61 + q^63 - 15 * q^65 - 12 * q^67 - 10 * q^69 - 6 * q^71 - 8 * q^73 - 3 * q^75 - 6 * q^77 - 16 * q^79 - 2 * q^81 + q^85 - 17 * q^87 - 21 * q^89 - 14 * q^91 - 9 * q^93 - 3 * q^95 - 31 * q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	0.189234	+	0.981932i	$0.439400\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	−0.944995	+	0.327085i	$0.893934\pi$
$4$		0			0
$5$	2.61803			1.17082			0.585410	−	0.810737i	$-0.300933\pi$
$5$	2.61803			1.17082			0.585410	+	0.810737i	$0.300933\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	−1.92705	−	3.33775i	−0.642350	−	1.11258i
$10$		0			0
$11$	0.927051	−	1.60570i	0.279516	−	0.484137i	−0.691748	−	0.722139i	$-0.743159\pi$
$11$	0.927051	−	1.60570i	0.279516	−	0.484137i	0.971265	+	0.238002i	$0.0764925\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$		0			0
$15$	−3.42705	+	5.93583i	−0.884861	+	1.53262i
$16$		0			0
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	0.941375	−	0.337363i	$-0.109535\pi$
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	−0.762852	+	0.646573i	$0.776202\pi$
$18$		0			0
$19$	−0.927051	−	1.60570i	−0.212680	−	0.368373i	0.739872	−	0.672747i	$-0.234886\pi$
$19$	−0.927051	−	1.60570i	−0.212680	−	0.368373i	−0.952552	+	0.304375i	$0.901553\pi$
$20$		0			0
$21$	−2.61803			−0.571302
$22$		0			0
$23$	−2.23607	+	3.87298i	−0.466252	+	0.807573i	−0.999257	−	0.0385394i	$-0.987729\pi$
$23$	−2.23607	+	3.87298i	−0.466252	+	0.807573i	0.533005	+	0.846112i	$0.321063\pi$
$24$		0			0
$25$	1.85410			0.370820
$26$		0			0
$27$	2.23607			0.430331
$28$		0			0
$29$	−3.54508	+	6.14027i	−0.658306	+	1.14022i	0.322748	+	0.946485i	$0.395393\pi$
$29$	−3.54508	+	6.14027i	−0.658306	+	1.14022i	−0.981054	+	0.193734i	$0.937940\pi$
$30$		0			0
$31$	4.70820			0.845618			0.422809	−	0.906219i	$-0.361044\pi$
$31$	4.70820			0.845618			0.422809	+	0.906219i	$0.361044\pi$
$32$		0			0
$33$	2.42705	+	4.20378i	0.422495	+	0.731783i
$34$		0			0
$35$	1.30902	+	2.26728i	0.221264	+	0.383241i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	−2.61803	−	9.06914i	−0.419221	−	1.45222i
$40$		0			0
$41$	−0.381966	+	0.661585i	−0.0596531	+	0.103322i	−0.894310	−	0.447449i	$-0.852333\pi$
$41$	−0.381966	+	0.661585i	−0.0596531	+	0.103322i	0.834657	+	0.550771i	$0.185666\pi$
$42$		0			0
$43$	6.28115	+	10.8793i	0.957867	+	1.65907i	0.727667	+	0.685931i	$0.240605\pi$
$43$	6.28115	+	10.8793i	0.957867	+	1.65907i	0.230200	+	0.973143i	$0.426062\pi$
$44$		0			0
$45$	−5.04508	−	8.73834i	−0.752077	−	1.30264i
$46$		0			0
$47$	2.23607			0.326164			0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607			0.326164			0.163082	+	0.986613i	$0.447856\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−3.85410			−0.539682
$52$		0			0
$53$	3.76393			0.517016			0.258508	−	0.966009i	$-0.416769\pi$
$53$	3.76393			0.517016			0.258508	+	0.966009i	$0.416769\pi$
$54$		0			0
$55$	2.42705	−	4.20378i	0.327263	−	0.566837i
$56$		0			0
$57$	4.85410			0.642942
$58$		0			0
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	0.784024	−	0.620730i	$-0.213164\pi$
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	−0.929580	+	0.368620i	$0.879830\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		0			0
$63$	1.92705	−	3.33775i	0.242786	−	0.420517i
$64$		0			0
$65$	−6.54508	+	6.80185i	−0.811818	+	0.843666i
$66$		0			0
$67$	−6.35410	+	11.0056i	−0.776277	+	1.34455i	0.157797	+	0.987472i	$0.449561\pi$
$67$	−6.35410	+	11.0056i	−0.776277	+	1.34455i	−0.934074	+	0.357080i	$0.883772\pi$
$68$		0			0
$69$	−5.85410	−	10.1396i	−0.704751	−	1.22066i
$70$		0			0
$71$	−7.09017	−	12.2805i	−0.841448	−	1.45743i	−0.888670	−	0.458547i	$-0.848370\pi$
$71$	−7.09017	−	12.2805i	−0.841448	−	1.45743i	0.0472218	−	0.998884i	$-0.484963\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$	−2.42705	+	4.20378i	−0.280252	+	0.485410i
$76$		0			0
$77$	1.85410			0.211295
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	2.85410	−	4.94345i	0.317122	−	0.549272i
$82$		0			0
$83$	−6.70820			−0.736321			−0.368161	−	0.929762i	$-0.620012\pi$
$83$	−6.70820			−0.736321			−0.368161	+	0.929762i	$0.620012\pi$
$84$		0			0
$85$	1.92705	+	3.33775i	0.209018	+	0.362030i
$86$		0			0
$87$	−9.28115	−	16.0754i	−0.995044	−	1.72347i
$88$		0			0
$89$	−2.45492	+	4.25204i	−0.260220	+	0.450715i	−0.966300	−	0.257417i	$-0.917129\pi$
$89$	−2.45492	+	4.25204i	−0.260220	+	0.450715i	0.706080	+	0.708132i	$0.250462\pi$
$90$		0			0
$91$	−3.50000	−	0.866025i	−0.366900	−	0.0907841i
$92$		0			0
$93$	−6.16312	+	10.6748i	−0.639086	+	1.10693i
$94$		0			0
$95$	−2.42705	−	4.20378i	−0.249010	−	0.431298i
$96$		0			0
$97$	−9.42705	−	16.3281i	−0.957172	−	1.65787i	−0.729318	−	0.684175i	$-0.760162\pi$
$97$	−9.42705	−	16.3281i	−0.957172	−	1.65787i	−0.227854	−	0.973695i	$-0.573171\pi$
$98$		0			0
$99$	−7.14590			−0.718190
$100$		0			0
$101$	5.78115	−	10.0133i	0.575246	−	0.996356i	−0.420769	−	0.907168i	$-0.638240\pi$
$101$	5.78115	−	10.0133i	0.575246	−	0.996356i	0.996015	−	0.0891877i	$-0.0284271\pi$
$102$		0			0
$103$	8.70820			0.858045			0.429022	−	0.903294i	$-0.358858\pi$
$103$	8.70820			0.858045			0.429022	+	0.903294i	$0.358858\pi$
$104$		0			0
$105$	−6.85410			−0.668892
$106$		0			0
$107$	−1.69098	+	2.92887i	−0.163473	+	0.283144i	−0.936112	−	0.351702i	$-0.885603\pi$
$107$	−1.69098	+	2.92887i	−0.163473	+	0.283144i	0.772639	+	0.634846i	$0.218936\pi$
$108$		0			0
$109$	−2.70820			−0.259399			−0.129699	−	0.991553i	$-0.541401\pi$
$109$	−2.70820			−0.259399			−0.129699	+	0.991553i	$0.541401\pi$
$110$		0			0
$111$	−5.23607	−	9.06914i	−0.496986	−	0.860804i
$112$		0			0
$113$	−0.736068	−	1.27491i	−0.0692435	−	0.119933i	0.829325	−	0.558766i	$-0.188725\pi$
$113$	−0.736068	−	1.27491i	−0.0692435	−	0.119933i	−0.898568	+	0.438833i	$0.855392\pi$
$114$		0			0
$115$	−5.85410	+	10.1396i	−0.545898	+	0.945523i
$116$		0			0
$117$	13.4894	+	3.33775i	1.24709	+	0.308575i
$118$		0			0
$119$	−0.736068	+	1.27491i	−0.0674752	+	0.116871i
$120$		0			0
$121$	3.78115	+	6.54915i	0.343741	+	0.595377i
$122$		0			0
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$		0			0
$125$	−8.23607			−0.736656
$126$		0			0
$127$	−10.4271	+	18.0602i	−0.925251	+	1.60258i	−0.134094	+	0.990969i	$0.542813\pi$
$127$	−10.4271	+	18.0602i	−0.925251	+	1.60258i	−0.791157	+	0.611613i	$0.790521\pi$
$128$		0			0
$129$	−32.8885			−2.89567
$130$		0			0
$131$	15.3262			1.33906			0.669530	−	0.742785i	$-0.266496\pi$
$131$	15.3262			1.33906			0.669530	+	0.742785i	$0.266496\pi$
$132$		0			0
$133$	0.927051	−	1.60570i	0.0803855	−	0.139232i
$134$		0			0
$135$	5.85410			0.503841
$136$		0			0
$137$	1.30902	+	2.26728i	0.111837	+	0.193707i	0.916511	−	0.400010i	$-0.130993\pi$
$137$	1.30902	+	2.26728i	0.111837	+	0.193707i	−0.804674	+	0.593717i	$0.797660\pi$
$138$		0			0
$139$	2.28115	+	3.95107i	0.193485	+	0.335126i	0.946403	−	0.322989i	$-0.104688\pi$
$139$	2.28115	+	3.95107i	0.193485	+	0.335126i	−0.752918	+	0.658114i	$0.771354\pi$
$140$		0			0
$141$	−2.92705	+	5.06980i	−0.246502	+	0.426954i
$142$		0			0
$143$	1.85410	+	6.42280i	0.155048	+	0.537101i
$144$		0			0
$145$	−9.28115	+	16.0754i	−0.770758	+	1.33499i
$146$		0			0
$147$	−1.30902	−	2.26728i	−0.107966	−	0.187002i
$148$		0			0
$149$	−0.927051	−	1.60570i	−0.0759470	−	0.131544i	0.825551	−	0.564328i	$-0.190865\pi$
$149$	−0.927051	−	1.60570i	−0.0759470	−	0.131544i	−0.901498	+	0.432784i	$0.857531\pi$
$150$		0			0
$151$	1.29180			0.105125			0.0525624	−	0.998618i	$-0.483261\pi$
$151$	1.29180			0.105125			0.0525624	+	0.998618i	$0.483261\pi$
$152$		0			0
$153$	2.83688	−	4.91362i	0.229348	−	0.397243i
$154$		0			0
$155$	12.3262			0.990067
$156$		0			0
$157$	14.8541			1.18549			0.592743	−	0.805392i	$-0.298045\pi$
$157$	14.8541			1.18549			0.592743	+	0.805392i	$0.298045\pi$
$158$		0			0
$159$	−4.92705	+	8.53390i	−0.390741	+	0.676783i
$160$		0			0
$161$	−4.47214			−0.352454
$162$		0			0
$163$	−1.85410	−	3.21140i	−0.145224	−	0.251536i	0.784232	−	0.620467i	$-0.213057\pi$
$163$	−1.85410	−	3.21140i	−0.145224	−	0.251536i	−0.929457	+	0.368931i	$0.879724\pi$
$164$		0			0
$165$	6.35410	+	11.0056i	0.494666	+	0.856787i
$166$		0			0
$167$	7.11803	−	12.3288i	0.550810	−	0.954031i	−0.447406	−	0.894331i	$-0.647652\pi$
$167$	7.11803	−	12.3288i	0.550810	−	0.954031i	0.998216	−	0.0597001i	$-0.0190144\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−3.57295	+	6.18853i	−0.273230	+	0.473249i
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	0.927051	+	1.60570i	0.0700785	+	0.121379i
$176$		0			0
$177$	5.85410			0.440021
$178$		0			0
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	9.70820			0.721605			0.360803	−	0.932642i	$-0.382503\pi$
$181$	9.70820			0.721605			0.360803	+	0.932642i	$0.382503\pi$
$182$		0			0
$183$	−15.7082			−1.16118
$184$		0			0
$185$	−5.23607	+	9.06914i	−0.384963	+	0.666776i
$186$		0			0
$187$	2.72949			0.199600
$188$		0			0
$189$	1.11803	+	1.93649i	0.0813250	+	0.140859i
$190$		0			0
$191$	10.6910	+	18.5173i	0.773572	+	1.33987i	0.935593	+	0.353079i	$0.114865\pi$
$191$	10.6910	+	18.5173i	0.773572	+	1.33987i	−0.162021	+	0.986787i	$0.551801\pi$
$192$		0			0
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$		0			0
$195$	−6.85410	−	23.7433i	−0.490832	−	1.70029i
$196$		0			0
$197$	8.39919	−	14.5478i	0.598417	−	1.03649i	−0.394638	−	0.918837i	$-0.629130\pi$
$197$	8.39919	−	14.5478i	0.598417	−	1.03649i	0.993055	−	0.117652i	$-0.0375368\pi$
$198$		0			0
$199$	−12.2082	−	21.1452i	−0.865417	−	1.49895i	−0.866633	−	0.498946i	$-0.833720\pi$
$199$	−12.2082	−	21.1452i	−0.865417	−	1.49895i	0.00121626	−	0.999999i	$-0.499613\pi$
$200$		0			0
$201$	−16.6353	−	28.8131i	−1.17336	−	2.03232i
$202$		0			0
$203$	−7.09017			−0.497632
$204$		0			0
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$		0			0
$207$	17.2361			1.19799
$208$		0			0
$209$	−3.43769			−0.237790
$210$		0			0
$211$	2.35410	−	4.07742i	0.162063	−	0.280701i	−0.773545	−	0.633741i	$-0.781519\pi$
$211$	2.35410	−	4.07742i	0.162063	−	0.280701i	0.935608	+	0.353039i	$0.114852\pi$
$212$		0			0
$213$	37.1246			2.54374
$214$		0			0
$215$	16.4443	+	28.4823i	1.12149	+	1.94248i
$216$		0			0
$217$	2.35410	+	4.07742i	0.159807	+	0.276794i
$218$		0			0
$219$	2.61803	−	4.53457i	0.176910	−	0.306418i
$220$		0			0
$221$	−5.15248	−	1.27491i	−0.346593	−	0.0857595i
$222$		0			0
$223$	10.1353	−	17.5548i	0.678707	−	1.17555i	−0.296664	−	0.954982i	$-0.595874\pi$
$223$	10.1353	−	17.5548i	0.678707	−	1.17555i	0.975371	−	0.220573i	$-0.0707926\pi$
$224$		0			0
$225$	−3.57295	−	6.18853i	−0.238197	−	0.412569i
$226$		0			0
$227$	0.736068	+	1.27491i	0.0488545	+	0.0846186i	0.889419	−	0.457094i	$-0.151110\pi$
$227$	0.736068	+	1.27491i	0.0488545	+	0.0846186i	−0.840564	+	0.541712i	$0.817776\pi$
$228$		0			0
$229$	−13.1246			−0.867299			−0.433649	−	0.901082i	$-0.642774\pi$
$229$	−13.1246			−0.867299			−0.433649	+	0.901082i	$0.642774\pi$
$230$		0			0
$231$	−2.42705	+	4.20378i	−0.159688	+	0.276588i
$232$		0			0
$233$	2.61803			0.171513			0.0857566	−	0.996316i	$-0.472669\pi$
$233$	2.61803			0.171513			0.0857566	+	0.996316i	$0.472669\pi$
$234$		0			0
$235$	5.85410			0.381880
$236$		0			0
$237$	5.23607	−	9.06914i	0.340119	−	0.589104i
$238$		0			0
$239$	24.7082			1.59824			0.799120	−	0.601171i	$-0.205299\pi$
$239$	24.7082			1.59824			0.799120	+	0.601171i	$0.205299\pi$
$240$		0			0
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	−0.925287	−	0.379267i	$-0.876176\pi$
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	0.134189	−	0.990956i	$-0.457157\pi$
$242$		0			0
$243$	10.8262	+	18.7516i	0.694503	+	1.20292i
$244$		0			0
$245$	−1.30902	+	2.26728i	−0.0836300	+	0.144851i
$246$		0			0
$247$	6.48936	+	1.60570i	0.412908	+	0.102168i
$248$		0			0
$249$	8.78115	−	15.2094i	0.556483	−	0.963857i
$250$		0			0
$251$	0.381966	+	0.661585i	0.0241095	+	0.0417588i	0.877828	−	0.478975i	$-0.158992\pi$
$251$	0.381966	+	0.661585i	0.0241095	+	0.0417588i	−0.853719	+	0.520734i	$0.825658\pi$
$252$		0			0
$253$	4.14590	+	7.18091i	0.260650	+	0.451460i
$254$		0			0
$255$	−10.0902			−0.631871
$256$		0			0
$257$	−8.37132	+	14.4996i	−0.522189	+	0.904457i	0.477478	+	0.878644i	$0.341551\pi$
$257$	−8.37132	+	14.4996i	−0.522189	+	0.904457i	−0.999667	+	0.0258138i	$0.991782\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$		0			0
$261$	27.3262			1.69145
$262$		0			0
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	9.85410			0.605333
$266$		0			0
$267$	−6.42705	−	11.1320i	−0.393329	−	0.681266i
$268$		0			0
$269$	14.3713	+	24.8919i	0.876235	+	1.51768i	0.855441	+	0.517900i	$0.173286\pi$
$269$	14.3713	+	24.8919i	0.876235	+	1.51768i	0.0207937	+	0.999784i	$0.493381\pi$
$270$		0			0
$271$	−4.20820	+	7.28882i	−0.255630	+	0.442764i	−0.965066	−	0.262005i	$-0.915616\pi$
$271$	−4.20820	+	7.28882i	−0.255630	+	0.442764i	0.709436	+	0.704770i	$0.248950\pi$
$272$		0			0
$273$	6.54508	−	6.80185i	0.396127	−	0.411667i
$274$		0			0
$275$	1.71885	−	2.97713i	0.103650	−	0.179528i
$276$		0			0
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$		0			0
$279$	−9.07295	−	15.7148i	−0.543183	−	0.940821i
$280$		0			0
$281$	20.1803			1.20386			0.601929	−	0.798550i	$-0.294399\pi$
$281$	20.1803			1.20386			0.601929	+	0.798550i	$0.294399\pi$
$282$		0			0
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	−0.594812	−	0.803865i	$-0.702774\pi$
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	0.993573	+	0.113190i	$0.0361069\pi$
$284$		0			0
$285$	12.7082			0.752769
$286$		0			0
$287$	−0.763932			−0.0450935
$288$		0			0
$289$	7.41641	−	12.8456i	0.436259	−	0.755623i
$290$		0			0
$291$	49.3607			2.89357
$292$		0			0
$293$	3.38197	+	5.85774i	0.197577	+	0.342213i	0.947742	−	0.319037i	$-0.103360\pi$
$293$	3.38197	+	5.85774i	0.197577	+	0.342213i	−0.750166	+	0.661250i	$0.770026\pi$
$294$		0			0
$295$	−2.92705	−	5.06980i	−0.170419	−	0.295175i
$296$		0			0
$297$	2.07295	−	3.59045i	0.120285	−	0.208339i
$298$		0			0
$299$	−4.47214	−	15.4919i	−0.258630	−	0.895922i
$300$		0			0
$301$	−6.28115	+	10.8793i	−0.362040	+	0.627071i
$302$		0			0
$303$	15.1353	+	26.2150i	0.869498	+	1.50601i
$304$		0			0
$305$	7.85410	+	13.6037i	0.449725	+	0.778946i
$306$		0			0
$307$	4.85410			0.277038			0.138519	−	0.990360i	$-0.455766\pi$
$307$	4.85410			0.277038			0.138519	+	0.990360i	$0.455766\pi$
$308$		0			0
$309$	−11.3992	+	19.7440i	−0.648477	+	1.12320i
$310$		0			0
$311$	−3.32624			−0.188614			−0.0943068	−	0.995543i	$-0.530063\pi$
$311$	−3.32624			−0.188614			−0.0943068	+	0.995543i	$0.530063\pi$
$312$		0			0
$313$	25.1246			1.42013			0.710064	−	0.704138i	$-0.248666\pi$
$313$	25.1246			1.42013			0.710064	+	0.704138i	$0.248666\pi$
$314$		0			0
$315$	5.04508	−	8.73834i	0.284258	−	0.492350i
$316$		0			0
$317$	26.2361			1.47356			0.736782	−	0.676130i	$-0.236344\pi$
$317$	26.2361			1.47356			0.736782	+	0.676130i	$0.236344\pi$
$318$		0			0
$319$	6.57295	+	11.3847i	0.368014	+	0.637420i
$320$		0			0
$321$	−4.42705	−	7.66788i	−0.247094	−	0.427979i
$322$		0			0
$323$	1.36475	−	2.36381i	0.0759364	−	0.131526i
$324$		0			0
$325$	−4.63525	+	4.81710i	−0.257118	+	0.267205i
$326$		0			0
$327$	3.54508	−	6.14027i	0.196044	−	0.339558i
$328$		0			0
$329$	1.11803	+	1.93649i	0.0616392	+	0.106762i
$330$		0			0
$331$	−5.07295	−	8.78661i	−0.278834	−	0.482956i	0.692261	−	0.721647i	$-0.256615\pi$
$331$	−5.07295	−	8.78661i	−0.278834	−	0.482956i	−0.971095	+	0.238692i	$0.923281\pi$
$332$		0			0
$333$	15.4164			0.844814
$334$		0			0
$335$	−16.6353	+	28.8131i	−0.908881	+	1.57423i
$336$		0			0
$337$	−11.5623			−0.629839			−0.314919	−	0.949118i	$-0.601978\pi$
$337$	−11.5623			−0.629839			−0.314919	+	0.949118i	$0.601978\pi$
$338$		0			0
$339$	3.85410			0.209326
$340$		0			0
$341$	4.36475	−	7.55996i	0.236364	−	0.409395i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−15.3262	−	26.5458i	−0.825137	−	1.42918i
$346$		0			0
$347$	15.3820	+	26.6423i	0.825747	+	1.43024i	0.901347	+	0.433098i	$0.142580\pi$
$347$	15.3820	+	26.6423i	0.825747	+	1.43024i	−0.0755997	+	0.997138i	$0.524087\pi$
$348$		0			0
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	0.443720	+	0.896166i	$0.353659\pi$
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	−0.997962	+	0.0638103i	$0.979675\pi$
$350$		0			0
$351$	−5.59017	+	5.80948i	−0.298381	+	0.310087i
$352$		0			0
$353$	−11.0729	+	19.1789i	−0.589354	+	1.02079i	0.404964	+	0.914333i	$0.367284\pi$
$353$	−11.0729	+	19.1789i	−0.589354	+	1.02079i	−0.994317	+	0.106458i	$0.966049\pi$
$354$		0			0
$355$	−18.5623	−	32.1509i	−0.985185	−	1.70639i
$356$		0			0
$357$	−1.92705	−	3.33775i	−0.101990	−	0.176652i
$358$		0			0
$359$	22.0902			1.16587			0.582937	−	0.812517i	$-0.301903\pi$
$359$	22.0902			1.16587			0.582937	+	0.812517i	$0.301903\pi$
$360$		0			0
$361$	7.78115	−	13.4774i	0.409534	−	0.709334i
$362$		0			0
$363$	−19.7984			−1.03915
$364$		0			0
$365$	−5.23607			−0.274068
$366$		0			0
$367$	−0.708204	+	1.22665i	−0.0369679	+	0.0640304i	−0.883917	−	0.467643i	$-0.845103\pi$
$367$	−0.708204	+	1.22665i	−0.0369679	+	0.0640304i	0.846949	+	0.531673i	$0.178437\pi$
$368$		0			0
$369$	2.94427			0.153273
$370$		0			0
$371$	1.88197	+	3.25966i	0.0977068	+	0.169233i
$372$		0			0
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	0.999287	+	0.0377522i	$0.0120198\pi$
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	−0.466949	+	0.884284i	$0.654647\pi$
$374$		0			0
$375$	10.7812	−	18.6735i	0.556736	−	0.964296i
$376$		0			0
$377$	−7.09017	−	24.5611i	−0.365162	−	1.26496i
$378$		0			0
$379$	−3.07295	+	5.32250i	−0.157847	+	0.273399i	−0.934092	−	0.357032i	$-0.883789\pi$
$379$	−3.07295	+	5.32250i	−0.157847	+	0.273399i	0.776245	+	0.630431i	$0.217122\pi$
$380$		0			0
$381$	−27.2984	−	47.2822i	−1.39854	−	2.42234i
$382$		0			0
$383$	−10.9894	−	19.0341i	−0.561530	−	0.972598i	−0.997363	−	0.0725709i	$-0.976880\pi$
$383$	−10.9894	−	19.0341i	−0.561530	−	0.972598i	0.435833	−	0.900027i	$-0.356454\pi$
$384$		0			0
$385$	4.85410			0.247388
$386$		0			0
$387$	24.2082	−	41.9298i	1.23057	−	2.13141i
$388$		0			0
$389$	−11.8885			−0.602773			−0.301387	−	0.953502i	$-0.597449\pi$
$389$	−11.8885			−0.602773			−0.301387	+	0.953502i	$0.597449\pi$
$390$		0			0
$391$	−6.58359			−0.332947
$392$		0			0
$393$	−20.0623	+	34.7489i	−1.01201	+	1.75285i
$394$		0			0
$395$	−10.4721			−0.526910
$396$		0			0
$397$	−0.708204	−	1.22665i	−0.0355437	−	0.0615636i	0.847706	−	0.530466i	$-0.177983\pi$
$397$	−0.708204	−	1.22665i	−0.0355437	−	0.0615636i	−0.883250	+	0.468902i	$0.844650\pi$
$398$		0			0
$399$	2.42705	+	4.20378i	0.121505	+	0.210452i
$400$		0			0
$401$	−17.7254	+	30.7013i	−0.885165	+	1.53315i	−0.0396416	+	0.999214i	$0.512622\pi$
$401$	−17.7254	+	30.7013i	−0.885165	+	1.53315i	−0.845524	+	0.533938i	$0.820712\pi$
$402$		0			0
$403$	−11.7705	+	12.2323i	−0.586331	+	0.609333i
$404$		0			0
$405$	7.47214	−	12.9421i	0.371293	−	0.643099i
$406$		0			0
$407$	3.70820	+	6.42280i	0.183809	+	0.318366i
$408$		0			0
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	0.630500	−	0.776189i	$-0.282850\pi$
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	−0.987450	+	0.157935i	$0.949516\pi$
$410$		0			0
$411$	−6.85410			−0.338088
$412$		0			0
$413$	1.11803	−	1.93649i	0.0550149	−	0.0952885i
$414$		0			0
$415$	−17.5623			−0.862100
$416$		0			0
$417$	−11.9443			−0.584914
$418$		0			0
$419$	−5.97214	+	10.3440i	−0.291758	+	0.505340i	−0.974226	−	0.225576i	$-0.927574\pi$
$419$	−5.97214	+	10.3440i	−0.291758	+	0.505340i	0.682468	+	0.730916i	$0.260907\pi$
$420$		0			0
$421$	1.41641			0.0690315			0.0345157	−	0.999404i	$-0.489011\pi$
$421$	1.41641			0.0690315			0.0345157	+	0.999404i	$0.489011\pi$
$422$		0			0
$423$	−4.30902	−	7.46344i	−0.209512	−	0.362885i
$424$		0			0
$425$	1.36475	+	2.36381i	0.0661999	+	0.114662i
$426$		0			0
$427$	−3.00000	+	5.19615i	−0.145180	+	0.251459i
$428$		0			0
$429$	−16.9894	−	4.20378i	−0.820254	−	0.202960i
$430$		0			0
$431$	3.89919	−	6.75359i	0.187817	−	0.325309i	−0.756705	−	0.653756i	$-0.773192\pi$
$431$	3.89919	−	6.75359i	0.187817	−	0.325309i	0.944522	+	0.328448i	$0.106525\pi$
$432$		0			0
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$		0			0
$435$	−24.2984	−	42.0860i	−1.16502	−	2.01787i
$436$		0			0
$437$	8.29180			0.396650
$438$		0			0
$439$	7.42705	−	12.8640i	0.354474	−	0.613967i	−0.632554	−	0.774516i	$-0.717993\pi$
$439$	7.42705	−	12.8640i	0.354474	−	0.613967i	0.987028	+	0.160550i	$0.0513267\pi$
$440$		0			0
$441$	3.85410			0.183529
$442$		0			0
$443$	5.23607			0.248773			0.124387	−	0.992234i	$-0.460304\pi$
$443$	5.23607			0.248773			0.124387	+	0.992234i	$0.460304\pi$
$444$		0			0
$445$	−6.42705	+	11.1320i	−0.304671	+	0.527706i
$446$		0			0
$447$	4.85410			0.229591
$448$		0			0
$449$	−9.76393	−	16.9116i	−0.460788	−	0.798109i	0.538212	−	0.842809i	$-0.319100\pi$
$449$	−9.76393	−	16.9116i	−0.460788	−	0.798109i	−0.999000	+	0.0447005i	$0.985767\pi$
$450$		0			0
$451$	0.708204	+	1.22665i	0.0333480	+	0.0577605i
$452$		0			0
$453$	−1.69098	+	2.92887i	−0.0794493	+	0.137610i
$454$		0			0
$455$	−9.16312	−	2.26728i	−0.429574	−	0.106292i
$456$		0			0
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	−0.988055	−	0.154098i	$-0.950753\pi$
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	0.627481	+	0.778632i	$0.284086\pi$
$458$		0			0
$459$	1.64590	+	2.85078i	0.0768239	+	0.133063i
$460$		0			0
$461$	6.10739	+	10.5783i	0.284450	+	0.492681i	0.972476	−	0.233005i	$-0.0748558\pi$
$461$	6.10739	+	10.5783i	0.284450	+	0.492681i	−0.688026	+	0.725686i	$0.741523\pi$
$462$		0			0
$463$	−6.70820			−0.311757			−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820			−0.311757			−0.155878	+	0.987776i	$0.549821\pi$
$464$		0			0
$465$	−16.1353	+	27.9471i	−0.748255	+	1.29601i
$466$		0			0
$467$	−2.34752			−0.108630			−0.0543152	−	0.998524i	$-0.517298\pi$
$467$	−2.34752			−0.108630			−0.0543152	+	0.998524i	$0.517298\pi$
$468$		0			0
$469$	−12.7082			−0.586810
$470$		0			0
$471$	−19.4443	+	33.6785i	−0.895945	+	1.55182i
$472$		0			0
$473$	23.2918			1.07096
$474$		0			0
$475$	−1.71885	−	2.97713i	−0.0788661	−	0.136600i
$476$		0			0
$477$	−7.25329	−	12.5631i	−0.332105	−	0.575223i
$478$		0			0
$479$	12.4894	−	21.6322i	0.570653	−	0.988400i	−0.425846	−	0.904796i	$-0.640023\pi$
$479$	12.4894	−	21.6322i	0.570653	−	0.988400i	0.996499	−	0.0836047i	$-0.0266433\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$		0			0
$483$	5.85410	−	10.1396i	0.266371	−	0.461368i
$484$		0			0
$485$	−24.6803	−	42.7476i	−1.12068	−	1.94107i
$486$		0			0
$487$	14.9894	+	25.9623i	0.679233	+	1.17647i	0.975212	+	0.221271i	$0.0710206\pi$
$487$	14.9894	+	25.9623i	0.679233	+	1.17647i	−0.295980	+	0.955194i	$0.595646\pi$
$488$		0			0
$489$	9.70820			0.439020
$490$		0			0
$491$	6.19098	−	10.7231i	0.279395	−	0.483927i	−0.691839	−	0.722051i	$-0.743199\pi$
$491$	6.19098	−	10.7231i	0.279395	−	0.483927i	0.971235	+	0.238125i	$0.0765327\pi$
$492$		0			0
$493$	−10.4377			−0.470090
$494$		0			0
$495$	−18.7082			−0.840871
$496$		0			0
$497$	7.09017	−	12.2805i	0.318038	−	0.550857i
$498$		0			0
$499$	−14.8541			−0.664961			−0.332480	−	0.943110i	$-0.607886\pi$
$499$	−14.8541			−0.664961			−0.332480	+	0.943110i	$0.607886\pi$
$500$		0			0
$501$	18.6353	+	32.2772i	0.832562	+	1.44204i
$502$		0			0
$503$	13.3090	+	23.0519i	0.593420	+	1.02783i	0.993768	+	0.111470i	$0.0355559\pi$
$503$	13.3090	+	23.0519i	0.593420	+	1.02783i	−0.400348	+	0.916363i	$0.631111\pi$
$504$		0			0
$505$	15.1353	−	26.2150i	0.673510	−	1.16655i
$506$		0			0
$507$	30.1074	+	15.8710i	1.33712	+	0.704855i
$508$		0			0
$509$	9.29837	−	16.1053i	0.412143	−	0.713853i	−0.582981	−	0.812486i	$-0.698114\pi$
$509$	9.29837	−	16.1053i	0.412143	−	0.713853i	0.995124	+	0.0986331i	$0.0314470\pi$
$510$		0			0
$511$	−1.00000	−	1.73205i	−0.0442374	−	0.0766214i
$512$		0			0
$513$	−2.07295	−	3.59045i	−0.0915229	−	0.158522i
$514$		0			0
$515$	22.7984			1.00462
$516$		0			0
$517$	2.07295	−	3.59045i	0.0911682	−	0.157908i
$518$		0			0
$519$	−23.5623			−1.03427
$520$		0			0
$521$	18.6525			0.817180			0.408590	−	0.912718i	$-0.366021\pi$
$521$	18.6525			0.817180			0.408590	+	0.912718i	$0.366021\pi$
$522$		0			0
$523$	0.562306	−	0.973942i	0.0245879	−	0.0425875i	−0.853470	−	0.521143i	$-0.825506\pi$
$523$	0.562306	−	0.973942i	0.0245879	−	0.0425875i	0.878058	+	0.478555i	$0.158839\pi$
$524$		0			0
$525$	−4.85410			−0.211850
$526$		0			0
$527$	3.46556	+	6.00252i	0.150962	+	0.261474i
$528$		0			0
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$		0			0
$531$	−4.30902	+	7.46344i	−0.186995	+	0.323886i
$532$		0			0
$533$	−0.763932	−	2.64634i	−0.0330896	−	0.114626i
$534$		0			0
$535$	−4.42705	+	7.66788i	−0.191398	+	0.331511i
$536$		0			0
$537$	−11.7812	−	20.4056i	−0.508394	−	0.880565i
$538$		0			0
$539$	0.927051	+	1.60570i	0.0399309	+	0.0691624i
$540$		0			0
$541$	35.2705			1.51640			0.758199	−	0.652023i	$-0.226080\pi$
$541$	35.2705			1.51640			0.758199	+	0.652023i	$0.226080\pi$
$542$		0			0
$543$	−12.7082	+	22.0113i	−0.545361	+	0.944593i
$544$		0			0
$545$	−7.09017			−0.303710
$546$		0			0
$547$	3.00000			0.128271			0.0641354	−	0.997941i	$-0.479571\pi$
$547$	3.00000			0.128271			0.0641354	+	0.997941i	$0.479571\pi$
$548$		0			0
$549$	11.5623	−	20.0265i	0.493467	−	0.854710i
$550$		0			0
$551$	13.1459			0.560034
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$		0			0
$555$	−13.7082	−	23.7433i	−0.581881	−	1.00785i
$556$		0			0
$557$	13.9894	−	24.2303i	0.592748	−	1.02667i	−0.401112	−	0.916029i	$-0.631376\pi$
$557$	13.9894	−	24.2303i	0.592748	−	1.02667i	0.993860	−	0.110641i	$-0.0352904\pi$
$558$		0			0
$559$	−43.9681	−	10.8793i	−1.85965	−	0.460144i
$560$		0			0
$561$	−3.57295	+	6.18853i	−0.150850	+	0.261280i
$562$		0			0
$563$	−10.5279	−	18.2348i	−0.443697	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$563$	−10.5279	−	18.2348i	−0.443697	−	0.768505i	−0.997960	+	0.0638360i	$0.979667\pi$
$564$		0			0
$565$	−1.92705	−	3.33775i	−0.0810716	−	0.140420i
$566$		0			0
$567$	5.70820			0.239722
$568$		0			0
$569$	−7.47214	+	12.9421i	−0.313248	+	0.542562i	−0.979064	−	0.203555i	$-0.934751\pi$
$569$	−7.47214	+	12.9421i	−0.313248	+	0.542562i	0.665815	+	0.746117i	$0.268084\pi$
$570$		0			0
$571$	−24.6869			−1.03312			−0.516558	−	0.856252i	$-0.672787\pi$
$571$	−24.6869			−1.03312			−0.516558	+	0.856252i	$0.672787\pi$
$572$		0			0
$573$	−55.9787			−2.33854
$574$		0			0
$575$	−4.14590	+	7.18091i	−0.172896	+	0.299464i
$576$		0			0
$577$	−43.8328			−1.82478			−0.912392	−	0.409318i	$-0.865767\pi$
$577$	−43.8328			−1.82478			−0.912392	+	0.409318i	$0.865767\pi$
$578$		0			0
$579$	7.85410	+	13.6037i	0.326405	+	0.565351i
$580$		0			0
$581$	−3.35410	−	5.80948i	−0.139152	−	0.241018i
$582$		0			0
$583$	3.48936	−	6.04374i	0.144514	−	0.250306i
$584$		0			0
$585$	35.3156	+	8.73834i	1.46012	+	0.361286i
$586$		0			0
$587$	−9.95492	+	17.2424i	−0.410883	+	0.711671i	−0.994987	−	0.100009i	$-0.968113\pi$
$587$	−9.95492	+	17.2424i	−0.410883	+	0.711671i	0.584103	+	0.811679i	$0.301446\pi$
$588$		0			0
$589$	−4.36475	−	7.55996i	−0.179846	−	0.311503i
$590$		0			0
$591$	21.9894	+	38.0867i	0.904521	+	1.56668i
$592$		0			0
$593$	43.7984			1.79858			0.899292	−	0.437349i	$-0.144083\pi$
$593$	43.7984			1.79858			0.899292	+	0.437349i	$0.144083\pi$
$594$		0			0
$595$	−1.92705	+	3.33775i	−0.0790014	+	0.136834i
$596$		0			0
$597$	63.9230			2.61619
$598$		0			0
$599$	−29.5066			−1.20561			−0.602803	−	0.797890i	$-0.705950\pi$
$599$	−29.5066			−1.20561			−0.602803	+	0.797890i	$0.705950\pi$
$600$		0			0
$601$	−20.1976	+	34.9832i	−0.823876	+	1.42699i	0.0788998	+	0.996883i	$0.474859\pi$
$601$	−20.1976	+	34.9832i	−0.823876	+	1.42699i	−0.902776	+	0.430112i	$0.858474\pi$
$602$		0			0
$603$	48.9787			1.99457
$604$		0			0
$605$	9.89919	+	17.1459i	0.402459	+	0.697080i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$		0			0
$609$	9.28115	−	16.0754i	0.376091	−	0.651409i
$610$		0			0
$611$	−5.59017	+	5.80948i	−0.226154	+	0.235026i
$612$		0			0
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	0.271187	+	0.962527i	$0.412584\pi$
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	−0.969166	+	0.246409i	$0.920749\pi$
$614$		0			0
$615$	−2.61803	−	4.53457i	−0.105569	−	0.182851i
$616$		0			0
$617$	−0.0278640	−	0.0482619i	−0.00112176	−	0.00194295i	0.865464	−	0.500971i	$-0.167024\pi$
$617$	−0.0278640	−	0.0482619i	−0.00112176	−	0.00194295i	−0.866586	+	0.499028i	$0.833690\pi$
$618$		0			0
$619$	−9.41641			−0.378477			−0.189239	−	0.981931i	$-0.560602\pi$
$619$	−9.41641			−0.378477			−0.189239	+	0.981931i	$0.560602\pi$
$620$		0			0
$621$	−5.00000	+	8.66025i	−0.200643	+	0.347524i
$622$		0			0
$623$	−4.90983			−0.196708
$624$		0			0
$625$	−30.8328			−1.23331
$626$		0			0
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$		0			0
$629$	−5.88854			−0.234792
$630$		0			0
$631$	17.1976	+	29.7870i	0.684624	+	1.18580i	0.973555	+	0.228454i	$0.0733669\pi$
$631$	17.1976	+	29.7870i	0.684624	+	1.18580i	−0.288931	+	0.957350i	$0.593300\pi$
$632$		0			0
$633$	6.16312	+	10.6748i	0.244962	+	0.424287i
$634$		0			0
$635$	−27.2984	+	47.2822i	−1.08330	+	1.87634i
$636$		0			0
$637$	−1.00000	−	3.46410i	−0.0396214	−	0.137253i
$638$		0			0
$639$	−27.3262	+	47.3304i	−1.08101	+	1.87236i
$640$		0			0
$641$	23.7533	+	41.1419i	0.938199	+	1.62501i	0.768829	+	0.639455i	$0.220840\pi$
$641$	23.7533	+	41.1419i	0.938199	+	1.62501i	0.169370	+	0.985553i	$0.445827\pi$
$642$		0			0
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	0.788723	−	0.614749i	$-0.210743\pi$
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$	−86.1033			−3.39032
$646$		0			0
$647$	12.3820	−	21.4462i	0.486785	−	0.843137i	−0.513099	−	0.858329i	$-0.671503\pi$
$647$	12.3820	−	21.4462i	0.486785	−	0.843137i	0.999885	+	0.0151924i	$0.00483607\pi$
$648$		0			0
$649$	−4.14590			−0.162741
$650$		0			0
$651$	−12.3262			−0.483103
$652$		0			0
$653$	0.190983	−	0.330792i	0.00747374	−	0.0129449i	−0.862264	−	0.506458i	$-0.830954\pi$
$653$	0.190983	−	0.330792i	0.00747374	−	0.0129449i	0.869738	+	0.493514i	$0.164288\pi$
$654$		0			0
$655$	40.1246			1.56780
$656$		0			0
$657$	3.85410	+	6.67550i	0.150363	+	0.260436i
$658$		0			0
$659$	−11.9443	−	20.6881i	−0.465283	−	0.805893i	0.533931	−	0.845528i	$-0.320714\pi$
$659$	−11.9443	−	20.6881i	−0.465283	−	0.805893i	−0.999214	+	0.0396343i	$0.987381\pi$
$660$		0			0
$661$	24.2705	−	42.0378i	0.944013	−	1.63508i	0.186299	−	0.982493i	$-0.440351\pi$
$661$	24.2705	−	42.0378i	0.944013	−	1.63508i	0.757715	−	0.652586i	$-0.226316\pi$
$662$		0			0
$663$	9.63525	−	10.0133i	0.374202	−	0.388882i
$664$		0			0
$665$	2.42705	−	4.20378i	0.0941170	−	0.163015i
$666$		0			0
$667$	−15.8541	−	27.4601i	−0.613873	−	1.06326i
$668$		0			0
$669$	26.5344	+	45.9590i	1.02588	+	1.77688i
$670$		0			0
$671$	11.1246			0.429461
$672$		0			0
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	−0.188165	−	0.982137i	$-0.560254\pi$
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	0.944639	−	0.328113i	$-0.106413\pi$
$674$		0			0
$675$	4.14590			0.159576
$676$		0			0
$677$	43.7426			1.68117			0.840583	−	0.541682i	$-0.182212\pi$
$677$	43.7426			1.68117			0.840583	+	0.541682i	$0.182212\pi$
$678$		0			0
$679$	9.42705	−	16.3281i	0.361777	−	0.626616i
$680$		0			0
$681$	−3.85410			−0.147690
$682$		0			0
$683$	0.736068	+	1.27491i	0.0281649	+	0.0487830i	0.879764	−	0.475410i	$-0.157700\pi$
$683$	0.736068	+	1.27491i	0.0281649	+	0.0487830i	−0.851599	+	0.524193i	$0.824367\pi$
$684$		0			0
$685$	3.42705	+	5.93583i	0.130941	+	0.226796i
$686$		0			0
$687$	17.1803	−	29.7572i	0.655471	−	1.13531i
$688$		0			0
$689$	−9.40983	+	9.77898i	−0.358486	+	0.372550i
$690$		0			0
$691$	−2.92705	+	5.06980i	−0.111350	+	0.192864i	−0.916315	−	0.400458i	$-0.868851\pi$
$691$	−2.92705	+	5.06980i	−0.111350	+	0.192864i	0.804965	+	0.593323i	$0.202184\pi$
$692$		0			0
$693$	−3.57295	−	6.18853i	−0.135725	−	0.235083i
$694$		0			0
$695$	5.97214	+	10.3440i	0.226536	+	0.392372i
$696$		0			0
$697$	−1.12461			−0.0425977
$698$		0			0
$699$	−3.42705	+	5.93583i	−0.129623	+	0.224514i
$700$		0			0
$701$	11.2361			0.424380			0.212190	−	0.977228i	$-0.431940\pi$
$701$	11.2361			0.424380			0.212190	+	0.977228i	$0.431940\pi$
$702$		0			0
$703$	7.41641			0.279715
$704$		0			0
$705$	−7.66312	+	13.2729i	−0.288610	+	0.499887i
$706$		0			0
$707$	11.5623			0.434845
$708$		0			0
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	0.555420	−	0.831570i	$-0.312557\pi$
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	−0.997871	+	0.0652231i	$0.979224\pi$
$710$		0			0
$711$	7.70820	+	13.3510i	0.289080	+	0.500702i
$712$		0			0
$713$	−10.5279	+	18.2348i	−0.394272	+	0.682898i
$714$		0			0
$715$	4.85410	+	16.8151i	0.181533	+	0.628849i
$716$		0			0
$717$	−32.3435	+	56.0205i	−1.20789	+	2.09212i
$718$		0			0
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	0.931779	−	0.363027i	$-0.118257\pi$
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	−0.780280	+	0.625430i	$0.784923\pi$
$720$		0			0
$721$	4.35410	+	7.54153i	0.162155	+	0.280861i
$722$		0			0
$723$	64.3050			2.39153
$724$		0			0
$725$	−6.57295	+	11.3847i	−0.244113	+	0.422816i
$726$		0			0
$727$	30.7082			1.13890			0.569452	−	0.822025i	$-0.307155\pi$
$727$	30.7082			1.13890			0.569452	+	0.822025i	$0.307155\pi$
$728$		0			0
$729$	−39.5623			−1.46527
$730$		0			0
$731$	−9.24671	+	16.0158i	−0.342002	+	0.592365i
$732$		0			0
$733$	−32.2705			−1.19194			−0.595969	−	0.803007i	$-0.703232\pi$
$733$	−32.2705			−1.19194			−0.595969	+	0.803007i	$0.703232\pi$
$734$		0			0
$735$	−3.42705	−	5.93583i	−0.126409	−	0.218946i
$736$		0			0
$737$	11.7812	+	20.4056i	0.433964	+	0.751648i
$738$		0			0
$739$	−3.43769	+	5.95426i	−0.126458	+	0.219031i	−0.922302	−	0.386470i	$-0.873694\pi$
$739$	−3.43769	+	5.95426i	−0.126458	+	0.219031i	0.795844	+	0.605502i	$0.207027\pi$
$740$		0			0
$741$	−12.1353	+	12.6113i	−0.445800	+	0.463289i
$742$		0			0
$743$	19.6631	−	34.0575i	0.721370	−	1.24945i	−0.239081	−	0.971000i	$-0.576846\pi$
$743$	19.6631	−	34.0575i	0.721370	−	1.24945i	0.960451	−	0.278450i	$-0.0898205\pi$
$744$		0			0
$745$	−2.42705	−	4.20378i	−0.0889203	−	0.154014i
$746$		0			0
$747$	12.9271	+	22.3903i	0.472976	+	0.819219i
$748$		0			0
$749$	−3.38197			−0.123574
$750$		0			0
$751$	11.3541	−	19.6659i	0.414317	−	0.717618i	−0.581039	−	0.813875i	$-0.697354\pi$
$751$	11.3541	−	19.6659i	0.414317	−	0.717618i	0.995356	+	0.0962572i	$0.0306871\pi$
$752$		0			0
$753$	−2.00000			−0.0728841
$754$		0			0
$755$	3.38197			0.123082
$756$		0			0
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$		0			0
$759$	−21.7082			−0.787958
$760$		0			0
$761$	14.4271	+	24.9884i	0.522980	+	0.905828i	0.999642	+	0.0267417i	$0.00851317\pi$
$761$	14.4271	+	24.9884i	0.522980	+	0.905828i	−0.476662	+	0.879087i	$0.658154\pi$
$762$		0			0
$763$	−1.35410	−	2.34537i	−0.0490218	−	0.0849082i
$764$		0			0
$765$	7.42705	−	12.8640i	0.268526	−	0.465100i
$766$		0			0
$767$	7.82624	+	1.93649i	0.282589	+	0.0699227i
$768$		0			0
$769$	9.20820	−	15.9491i	0.332056	−	0.575138i	−0.650859	−	0.759199i	$-0.725591\pi$
$769$	9.20820	−	15.9491i	0.332056	−	0.575138i	0.982915	+	0.184061i	$0.0589243\pi$
$770$		0			0
$771$	−21.9164	−	37.9603i	−0.789300	−	1.36711i
$772$		0			0
$773$	−12.6803	−	21.9630i	−0.456080	−	0.789954i	0.542669	−	0.839946i	$-0.317414\pi$
$773$	−12.6803	−	21.9630i	−0.456080	−	0.789954i	−0.998750	+	0.0499924i	$0.984080\pi$
$774$		0			0
$775$	8.72949			0.313573
$776$		0			0
$777$	5.23607	−	9.06914i	0.187843	−	0.325353i
$778$		0			0
$779$	1.41641			0.0507481
$780$		0			0
$781$	−26.2918			−0.940794
$782$		0			0
$783$	−7.92705	+	13.7301i	−0.283290	+	0.490672i
$784$		0			0
$785$	38.8885			1.38799
$786$		0			0
$787$	1.29180	+	2.23746i	0.0460476	+	0.0797567i	0.888131	−	0.459591i	$-0.152004\pi$
$787$	1.29180	+	2.23746i	0.0460476	+	0.0797567i	−0.842083	+	0.539348i	$0.818671\pi$
$788$		0			0
$789$	11.7812	+	20.4056i	0.419420	+	0.726457i
$790$		0			0
$791$	0.736068	−	1.27491i	0.0261716	−	0.0453305i
$792$		0			0
$793$	−21.0000	−	5.19615i	−0.745732	−	0.184521i
$794$		0			0
$795$	−12.8992	+	22.3420i	−0.457487	+	0.792391i
$796$		0			0
$797$	4.09017	+	7.08438i	0.144881	+	0.250942i	0.929329	−	0.369254i	$-0.120387\pi$
$797$	4.09017	+	7.08438i	0.144881	+	0.250942i	−0.784447	+	0.620195i	$0.787053\pi$
$798$		0			0
$799$	1.64590	+	2.85078i	0.0582277	+	0.100853i
$800$		0			0
$801$	18.9230			0.668611
$802$		0			0
$803$	−1.85410	+	3.21140i	−0.0654298	+	0.113328i
$804$		0			0
$805$	−11.7082			−0.412660
$806$		0			0
$807$	−75.2492			−2.64890
$808$		0			0
$809$	2.20820	−	3.82472i	0.0776363	−	0.134470i	−0.824593	−	0.565726i	$-0.808596\pi$
$809$	2.20820	−	3.82472i	0.0776363	−	0.134470i	0.902230	+	0.431256i	$0.141929\pi$
$810$		0			0
$811$	−39.2705			−1.37897			−0.689487	−	0.724298i	$-0.742164\pi$
$811$	−39.2705			−1.37897			−0.689487	+	0.724298i	$0.742164\pi$
$812$		0			0
$813$	−11.0172	−	19.0824i	−0.386391	−	0.669249i
$814$		0			0
$815$	−4.85410	−	8.40755i	−0.170032	−	0.294504i
$816$		0			0
$817$	11.6459	−	20.1713i	0.407438	−	0.705704i
$818$		0			0
$819$	3.85410	+	13.3510i	0.134673	+	0.466522i
$820$		0			0
$821$	3.68034	−	6.37454i	0.128445	−	0.222473i	−0.794629	−	0.607095i	$-0.792335\pi$
$821$	3.68034	−	6.37454i	0.128445	−	0.222473i	0.923074	+	0.384622i	$0.125668\pi$
$822$		0			0
$823$	−19.2082	−	33.2696i	−0.669556	−	1.15970i	−0.978028	−	0.208472i	$-0.933151\pi$
$823$	−19.2082	−	33.2696i	−0.669556	−	1.15970i	0.308473	−	0.951233i	$-0.400182\pi$
$824$		0			0
$825$	4.50000	+	7.79423i	0.156670	+	0.271360i
$826$		0			0
$827$	−15.9787			−0.555634			−0.277817	−	0.960634i	$-0.589611\pi$
$827$	−15.9787			−0.555634			−0.277817	+	0.960634i	$0.589611\pi$
$828$		0			0
$829$	−3.78115	+	6.54915i	−0.131325	+	0.227461i	−0.924188	−	0.381939i	$-0.875256\pi$
$829$	−3.78115	+	6.54915i	−0.131325	+	0.227461i	0.792863	+	0.609400i	$0.208590\pi$
$830$		0			0
$831$	−13.0902			−0.454093
$832$		0			0
$833$	−1.47214			−0.0510065
$834$		0			0
$835$	18.6353	−	32.2772i	0.644900	−	1.11700i
$836$		0			0
$837$	10.5279			0.363896
$838$		0			0
$839$	6.87132	+	11.9015i	0.237224	+	0.410885i	0.959917	−	0.280285i	$-0.0904290\pi$
$839$	6.87132	+	11.9015i	0.237224	+	0.410885i	−0.722692	+	0.691170i	$0.757096\pi$
$840$		0			0
$841$	−10.6353	−	18.4208i	−0.366733	−	0.635200i
$842$		0			0
$843$	−26.4164	+	45.7546i	−0.909829	+	1.57587i
$844$		0			0
$845$	−1.30902	−	34.0093i	−0.0450316	−	1.16995i
$846$		0			0
$847$	−3.78115	+	6.54915i	−0.129922	+	0.225031i
$848$		0			0
$849$	17.5623	+	30.4188i	0.602737	+	1.04397i
$850$		0			0
$851$	−8.94427	−	15.4919i	−0.306606	−	0.531057i
$852$		0			0
$853$	14.1246			0.483617			0.241809	−	0.970324i	$-0.422259\pi$
$853$	14.1246			0.483617			0.241809	+	0.970324i	$0.422259\pi$
$854$		0			0
$855$	−9.35410	+	16.2018i	−0.319904	+	0.554089i
$856$		0			0
$857$	−26.4508			−0.903544			−0.451772	−	0.892133i	$-0.649208\pi$
$857$	−26.4508			−0.903544			−0.451772	+	0.892133i	$0.649208\pi$
$858$		0			0
$859$	44.2492			1.50976			0.754882	−	0.655861i	$-0.227694\pi$
$859$	44.2492			1.50976			0.754882	+	0.655861i	$0.227694\pi$
$860$		0			0
$861$	1.00000	−	1.73205i	0.0340799	−	0.0590281i
$862$		0			0
$863$	−11.8885			−0.404691			−0.202345	−	0.979314i	$-0.564856\pi$
$863$	−11.8885			−0.404691			−0.202345	+	0.979314i	$0.564856\pi$
$864$		0			0
$865$	11.7812	+	20.4056i	0.400571	+	0.693810i
$866$		0			0
$867$	19.4164	+	33.6302i	0.659416	+	1.14214i
$868$		0			0
$869$	−3.70820	+	6.42280i	−0.125792	+	0.217878i
$870$		0			0
$871$	−12.7082	−	44.0225i	−0.430601	−	1.49165i
$872$		0			0
$873$	−36.3328	+	62.9303i	−1.22968	+	2.12987i
$874$		0			0
$875$	−4.11803	−	7.13264i	−0.139215	−	0.241127i
$876$		0			0
$877$	−0.354102	−	0.613323i	−0.0119572	−	0.0207104i	0.859985	−	0.510319i	$-0.170473\pi$
$877$	−0.354102	−	0.613323i	−0.0119572	−	0.0207104i	−0.871942	+	0.489609i	$0.837140\pi$
$878$		0			0
$879$	−17.7082			−0.597283
$880$		0			0
$881$	18.2984	−	31.6937i	0.616488	−	1.06779i	−0.373634	−	0.927576i	$-0.621888\pi$
$881$	18.2984	−	31.6937i	0.616488	−	1.06779i	0.990122	−	0.140212i	$-0.0447784\pi$
$882$		0			0
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$		0			0
$885$	15.3262			0.515186
$886$		0			0
$887$	27.3262	−	47.3304i	0.917525	−	1.58920i	0.114364	−	0.993439i	$-0.463517\pi$
$887$	27.3262	−	47.3304i	0.917525	−	1.58920i	0.803161	−	0.595761i	$-0.203150\pi$
$888$		0			0
$889$	−20.8541			−0.699424
$890$		0			0
$891$	−5.29180	−	9.16566i	−0.177282	−	0.307061i
$892$		0			0
$893$	−2.07295	−	3.59045i	−0.0693686	−	0.120150i
$894$		0			0
$895$	−11.7812	+	20.4056i	−0.393801	+	0.682082i
$896$		0			0
$897$	40.9787	+	10.1396i	1.36824	+	0.338551i
$898$		0			0
$899$	−16.6910	+	28.9096i	−0.556675	+	0.964190i
$900$		0			0
$901$	2.77051	+	4.79866i	0.0922991	+	0.159867i
$902$		0			0
$903$	−16.4443	−	28.4823i	−0.547231	−	0.947832i
$904$		0			0
$905$	25.4164			0.844870
$906$		0			0
$907$	−12.0000	+	20.7846i	−0.398453	+	0.690142i	−0.993535	−	0.113523i	$-0.963786\pi$
$907$	−12.0000	+	20.7846i	−0.398453	+	0.690142i	0.595082	+	0.803665i	$0.297120\pi$
$908$		0			0
$909$	−44.5623			−1.47804
$910$		0			0
$911$	22.6869			0.751651			0.375826	−	0.926690i	$-0.377359\pi$
$911$	22.6869			0.751651			0.375826	+	0.926690i	$0.377359\pi$
$912$		0			0
$913$	−6.21885	+	10.7714i	−0.205814	+	0.356480i
$914$		0			0
$915$	−41.1246			−1.35954
$916$		0			0
$917$	7.66312	+	13.2729i	0.253058	+	0.438310i
$918$		0			0
$919$	−15.0000	−	25.9808i	−0.494804	−	0.857026i	0.505178	−	0.863015i	$-0.331427\pi$
$919$	−15.0000	−	25.9808i	−0.494804	−	0.857026i	−0.999982	+	0.00598907i	$0.998094\pi$
$920$		0			0
$921$	−6.35410	+	11.0056i	−0.209375	+	0.362648i
$922$		0			0
$923$	49.6312	+	12.2805i	1.63363	+	0.404219i
$924$		0			0
$925$	−3.70820	+	6.42280i	−0.121925	+	0.211180i
$926$		0			0
$927$	−16.7812	−	29.0658i	−0.551165	−	0.954646i
$928$		0			0
$929$	−5.53444	−	9.58593i	−0.181579	−	0.314504i	0.760839	−	0.648940i	$-0.224788\pi$
$929$	−5.53444	−	9.58593i	−0.181579	−	0.314504i	−0.942418	+	0.334436i	$0.891454\pi$
$930$		0			0
$931$	1.85410			0.0607657
$932$		0			0
$933$	4.35410	−	7.54153i	0.142547	−	0.246898i
$934$		0			0
$935$	7.14590			0.233696
$936$		0			0
$937$	−15.8754			−0.518626			−0.259313	−	0.965793i	$-0.583496\pi$
$937$	−15.8754			−0.518626			−0.259313	+	0.965793i	$0.583496\pi$
$938$		0			0
$939$	−32.8885	+	56.9646i	−1.07328	+	1.85897i
$940$		0			0
$941$	20.3475			0.663310			0.331655	−	0.943401i	$-0.392393\pi$
$941$	20.3475			0.663310			0.331655	+	0.943401i	$0.392393\pi$
$942$		0			0
$943$	−1.70820	−	2.95870i	−0.0556268	−	0.0963484i
$944$		0			0
$945$	2.92705	+	5.06980i	0.0952170	+	0.164921i
$946$		0			0
$947$	−18.4336	+	31.9280i	−0.599012	+	1.03752i	0.393955	+	0.919130i	$0.371107\pi$
$947$	−18.4336	+	31.9280i	−0.599012	+	1.03752i	−0.992967	+	0.118390i	$0.962227\pi$
$948$		0			0
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$		0			0
$951$	−34.3435	+	59.4846i	−1.11366	+	1.92892i
$952$		0			0
$953$	−13.3885	−	23.1896i	−0.433697	−	0.751186i	0.563491	−	0.826122i	$-0.309458\pi$
$953$	−13.3885	−	23.1896i	−0.433697	−	0.751186i	−0.997188	+	0.0749362i	$0.976125\pi$
$954$		0			0
$955$	27.9894	+	48.4790i	0.905714	+	1.56874i
$956$		0			0
$957$	−34.4164			−1.11252
$958$		0			0
$959$	−1.30902	+	2.26728i	−0.0422704	+	0.0732144i
$960$		0			0
$961$	−8.83282			−0.284930
$962$		0			0
$963$	13.0344			0.420029
$964$		0			0
$965$	7.85410	−	13.6037i	0.252832	−	0.437919i
$966$		0			0
$967$	39.0000			1.25416			0.627078	−	0.778957i	$-0.284251\pi$
$967$	39.0000			1.25416			0.627078	+	0.778957i	$0.284251\pi$
$968$		0			0
$969$	3.57295	+	6.18853i	0.114780	+	0.198804i
$970$		0			0
$971$	15.7918	+	27.3522i	0.506783	+	0.877774i	0.999969	+	0.00784995i	$0.00249874\pi$
$971$	15.7918	+	27.3522i	0.506783	+	0.877774i	−0.493186	+	0.869924i	$0.664168\pi$
$972$		0			0
$973$	−2.28115	+	3.95107i	−0.0731304	+	0.126666i
$974$		0			0
$975$	−4.85410	−	16.8151i	−0.155456	−	0.538514i
$976$		0			0
$977$	11.2639	−	19.5097i	0.360365	−	0.624171i	−0.627656	−	0.778491i	$-0.715985\pi$
$977$	11.2639	−	19.5097i	0.360365	−	0.624171i	0.988021	+	0.154320i	$0.0493188\pi$
$978$		0			0
$979$	4.55166	+	7.88371i	0.145472	+	0.251965i
$980$		0			0
$981$	5.21885	+	9.03931i	0.166625	+	0.288603i
$982$		0			0
$983$	−18.3820			−0.586294			−0.293147	−	0.956067i	$-0.594702\pi$
$983$	−18.3820			−0.586294			−0.293147	+	0.956067i	$0.594702\pi$
$984$		0			0
$985$	21.9894	−	38.0867i	0.700639	−	1.21354i
$986$		0			0
$987$	−5.85410			−0.186338
$988$		0			0
$989$	−56.1803			−1.78643
$990$		0			0
$991$	−8.07295	+	13.9828i	−0.256446	+	0.444177i	−0.965287	−	0.261191i	$-0.915885\pi$
$991$	−8.07295	+	13.9828i	−0.256446	+	0.444177i	0.708842	+	0.705368i	$0.249218\pi$
$992$		0			0
$993$	26.5623			0.842929
$994$		0			0
$995$	−31.9615	−	55.3589i	−1.01325	−	1.75500i
$996$		0			0
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	0.158352	−	0.987383i	$-0.449382\pi$
$998$		0			0
$999$	−4.47214	+	7.74597i	−0.141492	+	0.245072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.h.113.1		4
4.3	odd	2		91.2.f.a.22.1	✓	4
12.11	even	2		819.2.o.c.568.2		4
13.3	even	3	inner	1456.2.s.h.1121.1		4
28.3	even	6		637.2.g.c.373.1		4
28.11	odd	6		637.2.g.b.373.1		4
28.19	even	6		637.2.h.f.165.2		4
28.23	odd	6		637.2.h.g.165.2		4
28.27	even	2		637.2.f.c.295.1		4
52.3	odd	6		91.2.f.a.29.1	yes	4
52.7	even	12		1183.2.c.c.337.4		4
52.19	even	12		1183.2.c.c.337.1		4
52.35	odd	6		1183.2.a.g.1.2		2
52.43	odd	6		1183.2.a.c.1.1		2
156.107	even	6		819.2.o.c.757.2		4
364.3	even	6		637.2.h.f.471.2		4
364.55	even	6		637.2.f.c.393.1		4
364.107	odd	6		637.2.g.b.263.1		4
364.139	even	6		8281.2.a.bb.1.2		2
364.159	even	6		637.2.g.c.263.1		4
364.251	even	6		8281.2.a.n.1.1		2
364.263	odd	6		637.2.h.g.471.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.1	✓	4	4.3	odd	2
91.2.f.a.29.1	yes	4	52.3	odd	6
637.2.f.c.295.1		4	28.27	even	2
637.2.f.c.393.1		4	364.55	even	6
637.2.g.b.263.1		4	364.107	odd	6
637.2.g.b.373.1		4	28.11	odd	6
637.2.g.c.263.1		4	364.159	even	6
637.2.g.c.373.1		4	28.3	even	6
637.2.h.f.165.2		4	28.19	even	6
637.2.h.f.471.2		4	364.3	even	6
637.2.h.g.165.2		4	28.23	odd	6
637.2.h.g.471.2		4	364.263	odd	6
819.2.o.c.568.2		4	12.11	even	2
819.2.o.c.757.2		4	156.107	even	6
1183.2.a.c.1.1		2	52.43	odd	6
1183.2.a.g.1.2		2	52.35	odd	6
1183.2.c.c.337.1		4	52.19	even	12
1183.2.c.c.337.4		4	52.7	even	12
1456.2.s.h.113.1		4	1.1	even	1	trivial
1456.2.s.h.1121.1		4	13.3	even	3	inner
8281.2.a.n.1.1		2	364.251	even	6
8281.2.a.bb.1.2		2	364.139	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.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 2.26728i) q^{3} +2.61803 q^{5} +(0.500000 + 0.866025i) q^{7} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\)	\(q+(-1.30902 + 2.26728i) q^{3} +2.61803 q^{5} +(0.500000 + 0.866025i) q^{7} +(-1.92705 - 3.33775i) q^{9} +(0.927051 - 1.60570i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(-3.42705 + 5.93583i) q^{15} +(0.736068 + 1.27491i) q^{17} +(-0.927051 - 1.60570i) q^{19} -2.61803 q^{21} +(-2.23607 + 3.87298i) q^{23} +1.85410 q^{25} +2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +4.70820 q^{31} +(2.42705 + 4.20378i) q^{33} +(1.30902 + 2.26728i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-2.61803 - 9.06914i) q^{39} +(-0.381966 + 0.661585i) q^{41} +(6.28115 + 10.8793i) q^{43} +(-5.04508 - 8.73834i) q^{45} +2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} -3.85410 q^{51} +3.76393 q^{53} +(2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +(-1.11803 - 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(1.92705 - 3.33775i) q^{63} +(-6.54508 + 6.80185i) q^{65} +(-6.35410 + 11.0056i) q^{67} +(-5.85410 - 10.1396i) q^{69} +(-7.09017 - 12.2805i) q^{71} -2.00000 q^{73} +(-2.42705 + 4.20378i) q^{75} +1.85410 q^{77} -4.00000 q^{79} +(2.85410 - 4.94345i) q^{81} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +(-9.28115 - 16.0754i) q^{87} +(-2.45492 + 4.25204i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(-6.16312 + 10.6748i) q^{93} +(-2.42705 - 4.20378i) q^{95} +(-9.42705 - 16.3281i) q^{97} -7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9	\( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} - 3 q^{11} - 10 q^{13} - 7 q^{15} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 6 q^{25} - 3 q^{29} - 8 q^{31} + 3 q^{33} + 3 q^{35} - 8 q^{37} - 6 q^{39} - 6 q^{41} + 5 q^{43} - 9 q^{45} - 2 q^{49} - 2 q^{51} + 24 q^{53} + 3 q^{55} + 6 q^{57} + 12 q^{61} + q^{63} - 15 q^{65} - 12 q^{67} - 10 q^{69} - 6 q^{71} - 8 q^{73} - 3 q^{75} - 6 q^{77} - 16 q^{79} - 2 q^{81} + q^{85} - 17 q^{87} - 21 q^{89} - 14 q^{91} - 9 q^{93} - 3 q^{95} - 31 q^{97} - 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9 - 3 * q^11 - 10 * q^13 - 7 * q^15 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 6 * q^25 - 3 * q^29 - 8 * q^31 + 3 * q^33 + 3 * q^35 - 8 * q^37 - 6 * q^39 - 6 * q^41 + 5 * q^43 - 9 * q^45 - 2 * q^49 - 2 * q^51 + 24 * q^53 + 3 * q^55 + 6 * q^57 + 12 * q^61 + q^63 - 15 * q^65 - 12 * q^67 - 10 * q^69 - 6 * q^71 - 8 * q^73 - 3 * q^75 - 6 * q^77 - 16 * q^79 - 2 * q^81 + q^85 - 17 * q^87 - 21 * q^89 - 14 * q^91 - 9 * q^93 - 3 * q^95 - 31 * q^97 - 42 * q^99

Introduction

L-functions

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