LMFDB - Embedded newform 315.2.j.c.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.2.j.c.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +9.46410 q^{8} +O(q^{10})$	\(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +9.46410 q^{8} +(1.36603 + 2.36603i) q^{10} +(0.366025 + 0.633975i) q^{11} +2.26795 q^{13} +(-7.09808 - 1.36603i) q^{14} +(-7.46410 + 12.9282i) q^{16} +(1.63397 + 2.83013i) q^{17} +(-2.23205 + 3.86603i) q^{19} -5.46410 q^{20} -2.00000 q^{22} +(-2.36603 + 4.09808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.09808 + 5.36603i) q^{26} +(9.46410 - 10.9282i) q^{28} +4.19615 q^{29} +(0.232051 + 0.401924i) q^{31} +(-10.9282 - 18.9282i) q^{32} -8.92820 q^{34} +(2.59808 + 0.500000i) q^{35} +(1.59808 - 2.76795i) q^{37} +(-6.09808 - 10.5622i) q^{38} +(4.73205 - 8.19615i) q^{40} +0.732051 q^{41} +3.19615 q^{43} +(2.00000 - 3.46410i) q^{44} +(-6.46410 - 11.1962i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-5.50000 + 4.33013i) q^{49} +2.73205 q^{50} +(-6.19615 - 10.7321i) q^{52} +(6.19615 + 10.7321i) q^{53} +0.732051 q^{55} +(8.19615 + 23.6603i) q^{56} +(-5.73205 + 9.92820i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} -1.26795 q^{62} +29.8564 q^{64} +(1.13397 - 1.96410i) q^{65} +(7.33013 + 12.6962i) q^{67} +(8.92820 - 15.4641i) q^{68} +(-4.73205 + 5.46410i) q^{70} -6.19615 q^{71} +(-6.33013 - 10.9641i) q^{73} +(4.36603 + 7.56218i) q^{74} +24.3923 q^{76} +(-1.26795 + 1.46410i) q^{77} +(3.69615 - 6.40192i) q^{79} +(7.46410 + 12.9282i) q^{80} +(-1.00000 + 1.73205i) q^{82} -15.1244 q^{83} +3.26795 q^{85} +(-4.36603 + 7.56218i) q^{86} +(3.46410 + 6.00000i) q^{88} +(7.56218 - 13.0981i) q^{89} +(1.96410 + 5.66987i) q^{91} +25.8564 q^{92} +(2.73205 + 4.73205i) q^{94} +(2.23205 + 3.86603i) q^{95} +14.9282 q^{97} +(-2.73205 - 18.9282i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8	$ 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8} + 2 q^{10} - 2 q^{11} + 16 q^{13} - 18 q^{14} - 16 q^{16} + 10 q^{17} - 2 q^{19} - 8 q^{20} - 8 q^{22} - 6 q^{23} - 2 q^{25} - 2 q^{26} + 24 q^{28} - 4 q^{29} - 6 q^{31} - 16 q^{32} - 8 q^{34} - 4 q^{37} - 14 q^{38} + 12 q^{40} - 4 q^{41} - 8 q^{43} + 8 q^{44} - 12 q^{46} + 4 q^{47} - 22 q^{49} + 4 q^{50} - 4 q^{52} + 4 q^{53} - 4 q^{55} + 12 q^{56} - 16 q^{58} + 10 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} + 8 q^{65} + 12 q^{67} + 8 q^{68} - 12 q^{70} - 4 q^{71} - 8 q^{73} + 14 q^{74} + 56 q^{76} - 12 q^{77} - 6 q^{79} + 16 q^{80} - 4 q^{82} - 12 q^{83} + 20 q^{85} - 14 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{92} + 4 q^{94} + 2 q^{95} + 32 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8 + 2 * q^10 - 2 * q^11 + 16 * q^13 - 18 * q^14 - 16 * q^16 + 10 * q^17 - 2 * q^19 - 8 * q^20 - 8 * q^22 - 6 * q^23 - 2 * q^25 - 2 * q^26 + 24 * q^28 - 4 * q^29 - 6 * q^31 - 16 * q^32 - 8 * q^34 - 4 * q^37 - 14 * q^38 + 12 * q^40 - 4 * q^41 - 8 * q^43 + 8 * q^44 - 12 * q^46 + 4 * q^47 - 22 * q^49 + 4 * q^50 - 4 * q^52 + 4 * q^53 - 4 * q^55 + 12 * q^56 - 16 * q^58 + 10 * q^59 - 8 * q^61 - 12 * q^62 + 64 * q^64 + 8 * q^65 + 12 * q^67 + 8 * q^68 - 12 * q^70 - 4 * q^71 - 8 * q^73 + 14 * q^74 + 56 * q^76 - 12 * q^77 - 6 * q^79 + 16 * q^80 - 4 * q^82 - 12 * q^83 + 20 * q^85 - 14 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^92 + 4 * q^94 + 2 * q^95 + 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.36603	+	2.36603i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$2$	−1.36603	+	2.36603i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$3$		0			0
$3$		0			0
$4$	−2.73205	−	4.73205i	−1.36603	−	2.36603i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$8$	9.46410			3.34607
$9$		0			0
$10$	1.36603	+	2.36603i	0.431975	+	0.748203i
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	0.915916	−	0.401371i	$-0.131466\pi$
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	−0.805555	+	0.592521i	$0.798133\pi$
$12$		0			0
$13$	2.26795			0.629016			0.314508	−	0.949255i	$-0.398160\pi$
$13$	2.26795			0.629016			0.314508	+	0.949255i	$0.398160\pi$
$14$	−7.09808	−	1.36603i	−1.89704	−	0.365086i
$15$		0			0
$16$	−7.46410	+	12.9282i	−1.86603	+	3.23205i
$17$	1.63397	+	2.83013i	0.396297	+	0.686407i	0.993266	−	0.115858i	$-0.0369617\pi$
$17$	1.63397	+	2.83013i	0.396297	+	0.686407i	−0.596969	+	0.802264i	$0.703628\pi$
$18$		0			0
$19$	−2.23205	+	3.86603i	−0.512068	+	0.886927i	0.487835	+	0.872936i	$0.337787\pi$
$19$	−2.23205	+	3.86603i	−0.512068	+	0.886927i	−0.999902	+	0.0139909i	$0.995546\pi$
$20$	−5.46410			−1.22181
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	−0.999971	−	0.00766135i	$-0.997561\pi$
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	0.506620	+	0.862169i	$0.330895\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.09808	+	5.36603i	−0.607583	+	1.05236i
$27$		0			0
$28$	9.46410	−	10.9282i	1.78855	−	2.06524i
$29$	4.19615			0.779206			0.389603	−	0.920983i	$-0.372612\pi$
$29$	4.19615			0.779206			0.389603	+	0.920983i	$0.372612\pi$
$30$		0			0
$31$	0.232051	+	0.401924i	0.0416776	+	0.0721876i	0.886112	−	0.463472i	$-0.153396\pi$
$31$	0.232051	+	0.401924i	0.0416776	+	0.0721876i	−0.844434	+	0.535659i	$0.820063\pi$
$32$	−10.9282	−	18.9282i	−1.93185	−	3.34607i
$33$		0			0
$34$	−8.92820			−1.53117
$35$	2.59808	+	0.500000i	0.439155	+	0.0845154i
$36$		0			0
$37$	1.59808	−	2.76795i	0.262722	−	0.455048i	−0.704242	−	0.709960i	$-0.748713\pi$
$37$	1.59808	−	2.76795i	0.262722	−	0.455048i	0.966964	+	0.254912i	$0.0820464\pi$
$38$	−6.09808	−	10.5622i	−0.989239	−	1.71341i
$39$		0			0
$40$	4.73205	−	8.19615i	0.748203	−	1.29593i
$41$	0.732051			0.114327			0.0571636	−	0.998365i	$-0.481794\pi$
$41$	0.732051			0.114327			0.0571636	+	0.998365i	$0.481794\pi$
$42$		0			0
$43$	3.19615			0.487409			0.243704	−	0.969850i	$-0.421637\pi$
$43$	3.19615			0.487409			0.243704	+	0.969850i	$0.421637\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	−6.46410	−	11.1962i	−0.953080	−	1.65078i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	2.73205			0.386370
$51$		0			0
$52$	−6.19615	−	10.7321i	−0.859252	−	1.48827i
$53$	6.19615	+	10.7321i	0.851107	+	1.47416i	0.880210	+	0.474584i	$0.157402\pi$
$53$	6.19615	+	10.7321i	0.851107	+	1.47416i	−0.0291032	+	0.999576i	$0.509265\pi$
$54$		0			0
$55$	0.732051			0.0987097
$56$	8.19615	+	23.6603i	1.09526	+	3.16173i
$57$		0			0
$58$	−5.73205	+	9.92820i	−0.752655	+	1.30364i
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	0.859571	−	0.511017i	$-0.170731\pi$
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	−0.872339	+	0.488901i	$0.837398\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$	−1.26795			−0.161030
$63$		0			0
$64$	29.8564			3.73205
$65$	1.13397	−	1.96410i	0.140652	−	0.243617i
$66$		0			0
$67$	7.33013	+	12.6962i	0.895518	+	1.55108i	0.833163	+	0.553028i	$0.186528\pi$
$67$	7.33013	+	12.6962i	0.895518	+	1.55108i	0.0623548	+	0.998054i	$0.480139\pi$
$68$	8.92820	−	15.4641i	1.08270	−	1.87530i
$69$		0			0
$70$	−4.73205	+	5.46410i	−0.565588	+	0.653085i
$71$	−6.19615			−0.735348			−0.367674	−	0.929955i	$-0.619846\pi$
$71$	−6.19615			−0.735348			−0.367674	+	0.929955i	$0.619846\pi$
$72$		0			0
$73$	−6.33013	−	10.9641i	−0.740885	−	1.28325i	−0.952093	−	0.305810i	$-0.901073\pi$
$73$	−6.33013	−	10.9641i	−0.740885	−	1.28325i	0.211207	−	0.977441i	$-0.432260\pi$
$74$	4.36603	+	7.56218i	0.507540	+	0.879085i
$75$		0			0
$76$	24.3923			2.79799
$77$	−1.26795	+	1.46410i	−0.144496	+	0.166850i
$78$		0			0
$79$	3.69615	−	6.40192i	0.415850	−	0.720273i	−0.579668	−	0.814853i	$-0.696818\pi$
$79$	3.69615	−	6.40192i	0.415850	−	0.720273i	0.995517	+	0.0945803i	$0.0301509\pi$
$80$	7.46410	+	12.9282i	0.834512	+	1.44542i
$81$		0			0
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	−15.1244			−1.66011			−0.830057	−	0.557679i	$-0.811692\pi$
$83$	−15.1244			−1.66011			−0.830057	+	0.557679i	$0.811692\pi$
$84$		0			0
$85$	3.26795			0.354459
$86$	−4.36603	+	7.56218i	−0.470801	+	0.815451i
$87$		0			0
$88$	3.46410	+	6.00000i	0.369274	+	0.639602i
$89$	7.56218	−	13.0981i	0.801589	−	1.38839i	−0.116980	−	0.993134i	$-0.537321\pi$
$89$	7.56218	−	13.0981i	0.801589	−	1.38839i	0.918570	−	0.395259i	$-0.129345\pi$
$90$		0			0
$91$	1.96410	+	5.66987i	0.205894	+	0.594364i
$92$	25.8564			2.69572
$93$		0			0
$94$	2.73205	+	4.73205i	0.281790	+	0.488074i
$95$	2.23205	+	3.86603i	0.229004	+	0.396646i
$96$		0			0
$97$	14.9282			1.51573			0.757865	−	0.652412i	$-0.226243\pi$
$97$	14.9282			1.51573			0.757865	+	0.652412i	$0.226243\pi$
$98$	−2.73205	−	18.9282i	−0.275979	−	1.91204i
$99$		0			0
$100$	−2.73205	+	4.73205i	−0.273205	+	0.473205i
$101$	−3.63397	−	6.29423i	−0.361594	−	0.626299i	0.626629	−	0.779317i	$-0.284434\pi$
$101$	−3.63397	−	6.29423i	−0.361594	−	0.626299i	−0.988223	+	0.153018i	$0.951101\pi$
$102$		0			0
$103$	4.59808	−	7.96410i	0.453062	−	0.784726i	−0.545513	−	0.838103i	$-0.683665\pi$
$103$	4.59808	−	7.96410i	0.453062	−	0.784726i	0.998574	+	0.0533764i	$0.0169983\pi$
$104$	21.4641			2.10473
$105$		0			0
$106$	−33.8564			−3.28842
$107$	1.09808	−	1.90192i	0.106155	−	0.183866i	−0.808054	−	0.589108i	$-0.799479\pi$
$107$	1.09808	−	1.90192i	0.106155	−	0.183866i	0.914210	+	0.405242i	$0.132813\pi$
$108$		0			0
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	−38.7846	−	7.46410i	−3.66480	−	0.705291i
$113$	−8.92820			−0.839895			−0.419947	−	0.907548i	$-0.637951\pi$
$113$	−8.92820			−0.839895			−0.419947	+	0.907548i	$0.637951\pi$
$114$		0			0
$115$	2.36603	+	4.09808i	0.220633	+	0.382148i
$116$	−11.4641	−	19.8564i	−1.06442	−	1.84362i
$117$		0			0
$118$	0.535898			0.0493334
$119$	−5.66025	+	6.53590i	−0.518875	+	0.599145i
$120$		0			0
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$	−5.46410	−	9.46410i	−0.494697	−	0.856840i
$123$		0			0
$124$	1.26795	−	2.19615i	0.113865	−	0.197220i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.80385			0.426273			0.213136	−	0.977022i	$-0.431632\pi$
$127$	4.80385			0.426273			0.213136	+	0.977022i	$0.431632\pi$
$128$	−18.9282	+	32.7846i	−1.67303	+	2.89778i
$129$		0			0
$130$	3.09808	+	5.36603i	0.271719	+	0.470632i
$131$	7.73205	−	13.3923i	0.675552	−	1.17009i	−0.300755	−	0.953702i	$-0.597239\pi$
$131$	7.73205	−	13.3923i	0.675552	−	1.17009i	0.976307	−	0.216390i	$-0.0694281\pi$
$132$		0			0
$133$	−11.5981	−	2.23205i	−1.00568	−	0.193543i
$134$	−40.0526			−3.46001
$135$		0			0
$136$	15.4641	+	26.7846i	1.32604	+	2.29676i
$137$	1.09808	+	1.90192i	0.0938150	+	0.162492i	0.909113	−	0.416549i	$-0.136760\pi$
$137$	1.09808	+	1.90192i	0.0938150	+	0.162492i	−0.815298	+	0.579041i	$0.803427\pi$
$138$		0			0
$139$	5.92820			0.502824			0.251412	−	0.967880i	$-0.419105\pi$
$139$	5.92820			0.502824			0.251412	+	0.967880i	$0.419105\pi$
$140$	−4.73205	−	13.6603i	−0.399931	−	1.15450i
$141$		0			0
$142$	8.46410	−	14.6603i	0.710292	−	1.23026i
$143$	0.830127	+	1.43782i	0.0694187	+	0.120237i
$144$		0			0
$145$	2.09808	−	3.63397i	0.174236	−	0.301785i
$146$	34.5885			2.86256
$147$		0			0
$148$	−17.4641			−1.43554
$149$	2.92820	−	5.07180i	0.239888	−	0.415498i	−0.720794	−	0.693149i	$-0.756223\pi$
$149$	2.92820	−	5.07180i	0.239888	−	0.415498i	0.960682	+	0.277651i	$0.0895560\pi$
$150$		0			0
$151$	4.46410	+	7.73205i	0.363283	+	0.629225i	0.988499	−	0.151227i	$-0.0483223\pi$
$151$	4.46410	+	7.73205i	0.363283	+	0.629225i	−0.625216	+	0.780452i	$0.714989\pi$
$152$	−21.1244	+	36.5885i	−1.71341	+	2.96772i
$153$		0			0
$154$	−1.73205	−	5.00000i	−0.139573	−	0.402911i
$155$	0.464102			0.0372775
$156$		0			0
$157$	−3.19615	−	5.53590i	−0.255081	−	0.441813i	0.709837	−	0.704366i	$-0.248769\pi$
$157$	−3.19615	−	5.53590i	−0.255081	−	0.441813i	−0.964917	+	0.262553i	$0.915435\pi$
$158$	10.0981	+	17.4904i	0.803360	+	1.39146i
$159$		0			0
$160$	−21.8564			−1.72790
$161$	−12.2942	−	2.36603i	−0.968921	−	0.186469i
$162$		0			0
$163$	−10.9282	+	18.9282i	−0.855963	+	1.48257i	0.0197859	+	0.999804i	$0.493702\pi$
$163$	−10.9282	+	18.9282i	−0.855963	+	1.48257i	−0.875749	+	0.482767i	$0.839632\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$		0			0
$166$	20.6603	−	35.7846i	1.60355	−	2.77742i
$167$	17.6603			1.36659			0.683296	−	0.730142i	$-0.260546\pi$
$167$	17.6603			1.36659			0.683296	+	0.730142i	$0.260546\pi$
$168$		0			0
$169$	−7.85641			−0.604339
$170$	−4.46410	+	7.73205i	−0.342381	+	0.593021i
$171$		0			0
$172$	−8.73205	−	15.1244i	−0.665813	−	1.15322i
$173$	7.26795	−	12.5885i	0.552572	−	0.957083i	−0.445516	−	0.895274i	$-0.646980\pi$
$173$	7.26795	−	12.5885i	0.552572	−	0.957083i	0.998088	−	0.0618087i	$-0.0196869\pi$
$174$		0			0
$175$	1.73205	−	2.00000i	0.130931	−	0.151186i
$176$	−10.9282			−0.823744
$177$		0			0
$178$	20.6603	+	35.7846i	1.54855	+	2.68217i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	−24.3205			−1.80773			−0.903865	−	0.427819i	$-0.859282\pi$
$181$	−24.3205			−1.80773			−0.903865	+	0.427819i	$0.859282\pi$
$182$	−16.0981	−	3.09808i	−1.19327	−	0.229645i
$183$		0			0
$184$	−22.3923	+	38.7846i	−1.65078	+	2.85924i
$185$	−1.59808	−	2.76795i	−0.117493	−	0.203504i
$186$		0			0
$187$	−1.19615	+	2.07180i	−0.0874713	+	0.151505i
$188$	−10.9282			−0.797021
$189$		0			0
$190$	−12.1962			−0.884802
$191$	−4.46410	+	7.73205i	−0.323011	+	0.559472i	−0.981108	−	0.193462i	$-0.938028\pi$
$191$	−4.46410	+	7.73205i	−0.323011	+	0.559472i	0.658097	+	0.752933i	$0.271362\pi$
$192$		0			0
$193$	−0.598076	−	1.03590i	−0.0430505	−	0.0745656i	0.843697	−	0.536819i	$-0.180374\pi$
$193$	−0.598076	−	1.03590i	−0.0430505	−	0.0745656i	−0.886748	+	0.462254i	$0.847041\pi$
$194$	−20.3923	+	35.3205i	−1.46408	+	2.53586i
$195$		0			0
$196$	35.5167	+	14.1962i	2.53690	+	1.01401i
$197$	0.339746			0.0242059			0.0121029	−	0.999927i	$-0.496147\pi$
$197$	0.339746			0.0242059			0.0121029	+	0.999927i	$0.496147\pi$
$198$		0			0
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	−0.932075	−	0.362267i	$-0.882003\pi$
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	0.152305	−	0.988334i	$-0.451330\pi$
$200$	−4.73205	−	8.19615i	−0.334607	−	0.579555i
$201$		0			0
$202$	19.8564			1.39709
$203$	3.63397	+	10.4904i	0.255055	+	0.736280i
$204$		0			0
$205$	0.366025	−	0.633975i	0.0255643	−	0.0442787i
$206$	12.5622	+	21.7583i	0.875248	+	1.51597i
$207$		0			0
$208$	−16.9282	+	29.3205i	−1.17376	+	2.03301i
$209$	−3.26795			−0.226049
$210$		0			0
$211$	7.07180			0.486843			0.243421	−	0.969921i	$-0.421730\pi$
$211$	7.07180			0.486843			0.243421	+	0.969921i	$0.421730\pi$
$212$	33.8564	−	58.6410i	2.32527	−	4.02748i
$213$		0			0
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	1.59808	−	2.76795i	0.108988	−	0.188773i
$216$		0			0
$217$	−0.803848	+	0.928203i	−0.0545687	+	0.0630105i
$218$	30.0526			2.03542
$219$		0			0
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	3.70577	+	6.41858i	0.249277	+	0.431761i
$222$		0			0
$223$	−20.3923			−1.36557			−0.682785	−	0.730619i	$-0.739231\pi$
$223$	−20.3923			−1.36557			−0.682785	+	0.730619i	$0.739231\pi$
$224$	37.8564	−	43.7128i	2.52939	−	2.92069i
$225$		0			0
$226$	12.1962	−	21.1244i	0.811276	−	1.40517i
$227$	−0.830127	−	1.43782i	−0.0550975	−	0.0954316i	0.837161	−	0.546956i	$-0.184214\pi$
$227$	−0.830127	−	1.43782i	−0.0550975	−	0.0954316i	−0.892259	+	0.451525i	$0.850880\pi$
$228$		0			0
$229$	1.50000	−	2.59808i	0.0991228	−	0.171686i	−0.812199	−	0.583380i	$-0.801730\pi$
$229$	1.50000	−	2.59808i	0.0991228	−	0.171686i	0.911322	+	0.411695i	$0.135063\pi$
$230$	−12.9282			−0.852460
$231$		0			0
$232$	39.7128			2.60727
$233$	8.66025	−	15.0000i	0.567352	−	0.982683i	−0.429474	−	0.903079i	$-0.641301\pi$
$233$	8.66025	−	15.0000i	0.567352	−	0.982683i	0.996827	−	0.0796037i	$-0.0253655\pi$
$234$		0			0
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	−0.535898	+	0.928203i	−0.0348840	+	0.0604209i
$237$		0			0
$238$	−7.73205	−	22.3205i	−0.501194	−	1.44682i
$239$	−7.07180			−0.457437			−0.228718	−	0.973493i	$-0.573453\pi$
$239$	−7.07180			−0.457437			−0.228718	+	0.973493i	$0.573453\pi$
$240$		0			0
$241$	−6.73205	−	11.6603i	−0.433650	−	0.751103i	0.563535	−	0.826092i	$-0.309441\pi$
$241$	−6.73205	−	11.6603i	−0.433650	−	0.751103i	−0.997184	+	0.0749893i	$0.976108\pi$
$242$	14.2942	+	24.7583i	0.918868	+	1.59153i
$243$		0			0
$244$	21.8564			1.39921
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		0			0
$247$	−5.06218	+	8.76795i	−0.322099	+	0.557891i
$248$	2.19615	+	3.80385i	0.139456	+	0.241545i
$249$		0			0
$250$	1.36603	−	2.36603i	0.0863950	−	0.149641i
$251$	24.5885			1.55201			0.776005	−	0.630727i	$-0.217243\pi$
$251$	24.5885			1.55201			0.776005	+	0.630727i	$0.217243\pi$
$252$		0			0
$253$	−3.46410			−0.217786
$254$	−6.56218	+	11.3660i	−0.411748	+	0.713168i
$255$		0			0
$256$	−21.8564	−	37.8564i	−1.36603	−	2.36603i
$257$	−2.83013	+	4.90192i	−0.176538	+	0.305774i	−0.940693	−	0.339260i	$-0.889823\pi$
$257$	−2.83013	+	4.90192i	−0.176538	+	0.305774i	0.764154	+	0.645034i	$0.223157\pi$
$258$		0			0
$259$	8.30385	+	1.59808i	0.515976	+	0.0992996i
$260$	−12.3923			−0.768538
$261$		0			0
$262$	21.1244	+	36.5885i	1.30507	+	2.26044i
$263$	4.19615	+	7.26795i	0.258746	+	0.448161i	0.965906	−	0.258892i	$-0.0833575\pi$
$263$	4.19615	+	7.26795i	0.258746	+	0.448161i	−0.707160	+	0.707053i	$0.750024\pi$
$264$		0			0
$265$	12.3923			0.761253
$266$	21.1244	−	24.3923i	1.29522	−	1.49559i
$267$		0			0
$268$	40.0526	−	69.3731i	2.44660	−	4.23763i
$269$	−6.26795	−	10.8564i	−0.382164	−	0.661927i	0.609208	−	0.793011i	$-0.291488\pi$
$269$	−6.26795	−	10.8564i	−0.382164	−	0.661927i	−0.991371	+	0.131084i	$0.958154\pi$
$270$		0			0
$271$	−1.53590	+	2.66025i	−0.0932992	+	0.161599i	−0.908897	−	0.417020i	$-0.863075\pi$
$271$	−1.53590	+	2.66025i	−0.0932992	+	0.161599i	0.815598	+	0.578619i	$0.196408\pi$
$272$	−48.7846			−2.95800
$273$		0			0
$274$	−6.00000			−0.362473
$275$	0.366025	−	0.633975i	0.0220722	−	0.0382301i
$276$		0			0
$277$	7.33013	+	12.6962i	0.440425	+	0.762838i	0.997721	−	0.0674759i	$-0.0214946\pi$
$277$	7.33013	+	12.6962i	0.440425	+	0.762838i	−0.557296	+	0.830314i	$0.688161\pi$
$278$	−8.09808	+	14.0263i	−0.485690	+	0.841240i
$279$		0			0
$280$	24.5885	+	4.73205i	1.46944	+	0.282794i
$281$	−13.8564			−0.826604			−0.413302	−	0.910594i	$-0.635625\pi$
$281$	−13.8564			−0.826604			−0.413302	+	0.910594i	$0.635625\pi$
$282$		0			0
$283$	12.0622	+	20.8923i	0.717022	+	1.24192i	0.962174	+	0.272434i	$0.0878287\pi$
$283$	12.0622	+	20.8923i	0.717022	+	1.24192i	−0.245152	+	0.969485i	$0.578838\pi$
$284$	16.9282	+	29.3205i	1.00450	+	1.73985i
$285$		0			0
$286$	−4.53590			−0.268213
$287$	0.633975	+	1.83013i	0.0374223	+	0.108029i
$288$		0			0
$289$	3.16025	−	5.47372i	0.185897	−	0.321984i
$290$	5.73205	+	9.92820i	0.336598	+	0.583004i
$291$		0			0
$292$	−34.5885	+	59.9090i	−2.02414	+	3.50591i
$293$	−18.9282			−1.10580			−0.552899	−	0.833248i	$-0.686478\pi$
$293$	−18.9282			−1.10580			−0.552899	+	0.833248i	$0.686478\pi$
$294$		0			0
$295$	−0.196152			−0.0114204
$296$	15.1244	−	26.1962i	0.879085	−	1.52262i
$297$		0			0
$298$	8.00000	+	13.8564i	0.463428	+	0.802680i
$299$	−5.36603	+	9.29423i	−0.310325	+	0.537499i
$300$		0			0
$301$	2.76795	+	7.99038i	0.159542	+	0.460558i
$302$	−24.3923			−1.40362
$303$		0			0
$304$	−33.3205	−	57.7128i	−1.91106	−	3.31006i
$305$	2.00000	+	3.46410i	0.114520	+	0.198354i
$306$		0			0
$307$	−32.1244			−1.83343			−0.916717	−	0.399537i	$-0.869171\pi$
$307$	−32.1244			−1.83343			−0.916717	+	0.399537i	$0.869171\pi$
$308$	10.3923	+	2.00000i	0.592157	+	0.113961i
$309$		0			0
$310$	−0.633975	+	1.09808i	−0.0360073	+	0.0623665i
$311$	4.56218	+	7.90192i	0.258697	+	0.448077i	0.965893	−	0.258941i	$-0.0833734\pi$
$311$	4.56218	+	7.90192i	0.258697	+	0.448077i	−0.707196	+	0.707018i	$0.750040\pi$
$312$		0			0
$313$	6.33013	−	10.9641i	0.357800	−	0.619728i	−0.629793	−	0.776763i	$-0.716860\pi$
$313$	6.33013	−	10.9641i	0.357800	−	0.619728i	0.987593	+	0.157035i	$0.0501936\pi$
$314$	17.4641			0.985556
$315$		0			0
$316$	−40.3923			−2.27224
$317$	−14.2224	+	24.6340i	−0.798811	+	1.38358i	0.121579	+	0.992582i	$0.461204\pi$
$317$	−14.2224	+	24.6340i	−0.798811	+	1.38358i	−0.920391	+	0.391000i	$0.872129\pi$
$318$		0			0
$319$	1.53590	+	2.66025i	0.0859938	+	0.148946i
$320$	14.9282	−	25.8564i	0.834512	−	1.44542i
$321$		0			0
$322$	22.3923	−	25.8564i	1.24787	−	1.44092i
$323$	−14.5885			−0.811723
$324$		0			0
$325$	−1.13397	−	1.96410i	−0.0629016	−	0.108949i
$326$	−29.8564	−	51.7128i	−1.65359	−	2.86411i
$327$		0			0
$328$	6.92820			0.382546
$329$	5.19615	+	1.00000i	0.286473	+	0.0551318i
$330$		0			0
$331$	−4.03590	+	6.99038i	−0.221833	+	0.384226i	−0.955365	−	0.295429i	$-0.904537\pi$
$331$	−4.03590	+	6.99038i	−0.221833	+	0.384226i	0.733532	+	0.679655i	$0.237871\pi$
$332$	41.3205	+	71.5692i	2.26776	+	3.92787i
$333$		0			0
$334$	−24.1244	+	41.7846i	−1.32003	+	2.28635i
$335$	14.6603			0.800975
$336$		0			0
$337$	17.9808			0.979475			0.489737	−	0.871870i	$-0.337093\pi$
$337$	17.9808			0.979475			0.489737	+	0.871870i	$0.337093\pi$
$338$	10.7321	−	18.5885i	0.583747	−	1.01108i
$339$		0			0
$340$	−8.92820	−	15.4641i	−0.484200	−	0.838659i
$341$	−0.169873	+	0.294229i	−0.00919914	+	0.0159334i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	30.2487			1.63090
$345$		0			0
$346$	19.8564	+	34.3923i	1.06749	+	1.84894i
$347$	−10.5359	−	18.2487i	−0.565597	−	0.979642i	−0.996994	−	0.0774801i	$-0.975313\pi$
$347$	−10.5359	−	18.2487i	−0.565597	−	0.979642i	0.431397	−	0.902162i	$-0.358021\pi$
$348$		0			0
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$	2.36603	+	6.83013i	0.126469	+	0.365086i
$351$		0			0
$352$	8.00000	−	13.8564i	0.426401	−	0.738549i
$353$	−1.56218	−	2.70577i	−0.0831463	−	0.144014i	0.821453	−	0.570276i	$-0.193164\pi$
$353$	−1.56218	−	2.70577i	−0.0831463	−	0.144014i	−0.904600	+	0.426262i	$0.859830\pi$
$354$		0			0
$355$	−3.09808	+	5.36603i	−0.164429	+	0.284799i
$356$	−82.6410			−4.37997
$357$		0			0
$358$	27.3205			1.44393
$359$	−0.633975	+	1.09808i	−0.0334599	+	0.0579542i	−0.882270	−	0.470743i	$-0.843986\pi$
$359$	−0.633975	+	1.09808i	−0.0334599	+	0.0579542i	0.848811	+	0.528697i	$0.177319\pi$
$360$		0			0
$361$	−0.464102	−	0.803848i	−0.0244264	−	0.0423078i
$362$	33.2224	−	57.5429i	1.74613	−	3.02439i
$363$		0			0
$364$	21.4641	−	24.7846i	1.12502	−	1.29907i
$365$	−12.6603			−0.662668
$366$		0			0
$367$	−5.59808	−	9.69615i	−0.292217	−	0.506135i	0.682117	−	0.731244i	$-0.261060\pi$
$367$	−5.59808	−	9.69615i	−0.292217	−	0.506135i	−0.974334	+	0.225108i	$0.927726\pi$
$368$	−35.3205	−	61.1769i	−1.84121	−	3.18907i
$369$		0			0
$370$	8.73205			0.453958
$371$	−21.4641	+	24.7846i	−1.11436	+	1.28675i
$372$		0			0
$373$	−13.2583	+	22.9641i	−0.686490	+	1.18904i	0.286476	+	0.958088i	$0.407516\pi$
$373$	−13.2583	+	22.9641i	−0.686490	+	1.18904i	−0.972966	+	0.230949i	$0.925817\pi$
$374$	−3.26795	−	5.66025i	−0.168982	−	0.292685i
$375$		0			0
$376$	9.46410	−	16.3923i	0.488074	−	0.845369i
$377$	9.51666			0.490133
$378$		0			0
$379$	6.32051			0.324663			0.162331	−	0.986736i	$-0.448099\pi$
$379$	6.32051			0.324663			0.162331	+	0.986736i	$0.448099\pi$
$380$	12.1962	−	21.1244i	0.625649	−	1.08366i
$381$		0			0
$382$	−12.1962	−	21.1244i	−0.624009	−	1.08082i
$383$	−11.6603	+	20.1962i	−0.595811	+	1.03198i	0.397621	+	0.917550i	$0.369836\pi$
$383$	−11.6603	+	20.1962i	−0.595811	+	1.03198i	−0.993432	+	0.114425i	$0.963497\pi$
$384$		0			0
$385$	0.633975	+	1.83013i	0.0323103	+	0.0932719i
$386$	3.26795			0.166334
$387$		0			0
$388$	−40.7846	−	70.6410i	−2.07052	−	3.58625i
$389$	2.70577	+	4.68653i	0.137188	+	0.237617i	0.926431	−	0.376464i	$-0.122860\pi$
$389$	2.70577	+	4.68653i	0.137188	+	0.237617i	−0.789243	+	0.614081i	$0.789527\pi$
$390$		0			0
$391$	−15.4641			−0.782053
$392$	−52.0526	+	40.9808i	−2.62905	+	2.06984i
$393$		0			0
$394$	−0.464102	+	0.803848i	−0.0233811	+	0.0404973i
$395$	−3.69615	−	6.40192i	−0.185974	−	0.322116i
$396$		0			0
$397$	15.5981	−	27.0167i	0.782845	−	1.35593i	−0.147433	−	0.989072i	$-0.547101\pi$
$397$	15.5981	−	27.0167i	0.782845	−	1.35593i	0.930278	−	0.366855i	$-0.119566\pi$
$398$	60.1051			3.01280
$399$		0			0
$400$	14.9282			0.746410
$401$	−8.19615	+	14.1962i	−0.409296	+	0.708922i	−0.994811	−	0.101740i	$-0.967559\pi$
$401$	−8.19615	+	14.1962i	−0.409296	+	0.708922i	0.585515	+	0.810662i	$0.300892\pi$
$402$		0			0
$403$	0.526279	+	0.911543i	0.0262158	+	0.0454072i
$404$	−19.8564	+	34.3923i	−0.987893	+	1.71108i
$405$		0			0
$406$	−29.7846	−	5.73205i	−1.47819	−	0.284477i
$407$	2.33975			0.115977
$408$		0			0
$409$	−1.57180	−	2.72243i	−0.0777203	−	0.134616i	0.824546	−	0.565795i	$-0.191431\pi$
$409$	−1.57180	−	2.72243i	−0.0777203	−	0.134616i	−0.902266	+	0.431180i	$0.858097\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$		0			0
$412$	−50.2487			−2.47558
$413$	0.339746	−	0.392305i	0.0167178	−	0.0193041i
$414$		0			0
$415$	−7.56218	+	13.0981i	−0.371213	+	0.642959i
$416$	−24.7846	−	42.9282i	−1.21517	−	2.10473i
$417$		0			0
$418$	4.46410	−	7.73205i	0.218346	−	0.378187i
$419$	35.4641			1.73253			0.866267	−	0.499581i	$-0.166513\pi$
$419$	35.4641			1.73253			0.866267	+	0.499581i	$0.166513\pi$
$420$		0			0
$421$	0.0717968			0.00349916			0.00174958	−	0.999998i	$-0.499443\pi$
$421$	0.0717968			0.00349916			0.00174958	+	0.999998i	$0.499443\pi$
$422$	−9.66025	+	16.7321i	−0.470254	+	0.814503i
$423$		0			0
$424$	58.6410	+	101.569i	2.84786	+	4.93264i
$425$	1.63397	−	2.83013i	0.0792594	−	0.137281i
$426$		0			0
$427$	−10.3923	−	2.00000i	−0.502919	−	0.0967868i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	4.36603	+	7.56218i	0.210548	+	0.364681i
$431$	8.66025	+	15.0000i	0.417150	+	0.722525i	0.995651	−	0.0931566i	$-0.0296957\pi$
$431$	8.66025	+	15.0000i	0.417150	+	0.722525i	−0.578502	+	0.815681i	$0.696362\pi$
$432$		0			0
$433$	15.1962			0.730280			0.365140	−	0.930953i	$-0.381021\pi$
$433$	15.1962			0.730280			0.365140	+	0.930953i	$0.381021\pi$
$434$	−1.09808	−	3.16987i	−0.0527093	−	0.152159i
$435$		0			0
$436$	−30.0526	+	52.0526i	−1.43926	+	2.49287i
$437$	−10.5622	−	18.2942i	−0.505257	−	0.875132i
$438$		0			0
$439$	−0.267949	+	0.464102i	−0.0127885	+	0.0221504i	−0.872349	−	0.488884i	$-0.837404\pi$
$439$	−0.267949	+	0.464102i	−0.0127885	+	0.0221504i	0.859560	+	0.511034i	$0.170737\pi$
$440$	6.92820			0.330289
$441$		0			0
$442$	−20.2487			−0.963133
$443$	4.73205	−	8.19615i	0.224827	−	0.389411i	−0.731441	−	0.681905i	$-0.761152\pi$
$443$	4.73205	−	8.19615i	0.224827	−	0.389411i	0.956267	+	0.292494i	$0.0944851\pi$
$444$		0			0
$445$	−7.56218	−	13.0981i	−0.358482	−	0.620908i
$446$	27.8564	−	48.2487i	1.31904	−	2.28464i
$447$		0			0
$448$	25.8564	+	74.6410i	1.22160	+	3.52646i
$449$	35.8564			1.69217			0.846084	−	0.533049i	$-0.178954\pi$
$449$	35.8564			1.69217			0.846084	+	0.533049i	$0.178954\pi$
$450$		0			0
$451$	0.267949	+	0.464102i	0.0126172	+	0.0218537i
$452$	24.3923	+	42.2487i	1.14732	+	1.98721i
$453$		0			0
$454$	4.53590			0.212880
$455$	5.89230	+	1.13397i	0.276236	+	0.0531615i
$456$		0			0
$457$	8.33013	−	14.4282i	0.389667	−	0.674923i	−0.602738	−	0.797939i	$-0.705923\pi$
$457$	8.33013	−	14.4282i	0.389667	−	0.674923i	0.992405	+	0.123016i	$0.0392568\pi$
$458$	4.09808	+	7.09808i	0.191491	+	0.331671i
$459$		0			0
$460$	12.9282	−	22.3923i	0.602781	−	1.04405i
$461$	−16.9808			−0.790873			−0.395436	−	0.918493i	$-0.629407\pi$
$461$	−16.9808			−0.790873			−0.395436	+	0.918493i	$0.629407\pi$
$462$		0			0
$463$	25.7321			1.19587			0.597935	−	0.801545i	$-0.295988\pi$
$463$	25.7321			1.19587			0.597935	+	0.801545i	$0.295988\pi$
$464$	−31.3205	+	54.2487i	−1.45402	+	2.51843i
$465$		0			0
$466$	23.6603	+	40.9808i	1.09604	+	1.89840i
$467$	−0.0717968	+	0.124356i	−0.00332236	+	0.00575449i	−0.867682	−	0.497120i	$-0.834391\pi$
$467$	−0.0717968	+	0.124356i	−0.00332236	+	0.00575449i	0.864359	+	0.502874i	$0.167724\pi$
$468$		0			0
$469$	−25.3923	+	29.3205i	−1.17251	+	1.35390i
$470$	5.46410			0.252040
$471$		0			0
$472$	−0.928203	−	1.60770i	−0.0427240	−	0.0740002i
$473$	1.16987	+	2.02628i	0.0537908	+	0.0931684i
$474$		0			0
$475$	4.46410			0.204827
$476$	46.3923	+	8.92820i	2.12639	+	0.409224i
$477$		0			0
$478$	9.66025	−	16.7321i	0.441850	−	0.765306i
$479$	4.39230	+	7.60770i	0.200690	+	0.347604i	0.948751	−	0.316025i	$-0.102348\pi$
$479$	4.39230	+	7.60770i	0.200690	+	0.347604i	−0.748061	+	0.663630i	$0.769015\pi$
$480$		0			0
$481$	3.62436	−	6.27757i	0.165256	−	0.286232i
$482$	36.7846			1.67549
$483$		0			0
$484$	−57.1769			−2.59895
$485$	7.46410	−	12.9282i	0.338927	−	0.587039i
$486$		0			0
$487$	0.205771	+	0.356406i	0.00932439	+	0.0161503i	0.870650	−	0.491903i	$-0.163699\pi$
$487$	0.205771	+	0.356406i	0.00932439	+	0.0161503i	−0.861326	+	0.508053i	$0.830365\pi$
$488$	−18.9282	+	32.7846i	−0.856840	+	1.48409i
$489$		0			0
$490$	−17.7583	−	7.09808i	−0.802240	−	0.320658i
$491$	38.2487			1.72614			0.863070	−	0.505084i	$-0.168539\pi$
$491$	38.2487			1.72614			0.863070	+	0.505084i	$0.168539\pi$
$492$		0			0
$493$	6.85641	+	11.8756i	0.308797	+	0.534852i
$494$	−13.8301	−	23.9545i	−0.622247	−	1.07776i
$495$		0			0
$496$	−6.92820			−0.311086
$497$	−5.36603	−	15.4904i	−0.240699	−	0.694839i
$498$		0			0
$499$	6.76795	−	11.7224i	0.302975	−	0.524768i	−0.673833	−	0.738883i	$-0.735353\pi$
$499$	6.76795	−	11.7224i	0.302975	−	0.524768i	0.976808	+	0.214115i	$0.0686868\pi$
$500$	2.73205	+	4.73205i	0.122181	+	0.211624i
$501$		0			0
$502$	−33.5885	+	58.1769i	−1.49913	+	2.59656i
$503$	−14.3923			−0.641721			−0.320861	−	0.947126i	$-0.603972\pi$
$503$	−14.3923			−0.641721			−0.320861	+	0.947126i	$0.603972\pi$
$504$		0			0
$505$	−7.26795			−0.323419
$506$	4.73205	−	8.19615i	0.210365	−	0.364363i
$507$		0			0
$508$	−13.1244	−	22.7321i	−0.582299	−	1.00857i
$509$	2.26795	−	3.92820i	0.100525	−	0.174115i	−0.811376	−	0.584525i	$-0.801281\pi$
$509$	2.26795	−	3.92820i	0.100525	−	0.174115i	0.911901	+	0.410410i	$0.134614\pi$
$510$		0			0
$511$	21.9282	−	25.3205i	0.970047	−	1.12011i
$512$	43.7128			1.93185
$513$		0			0
$514$	−7.73205	−	13.3923i	−0.341046	−	0.590709i
$515$	−4.59808	−	7.96410i	−0.202615	−	0.350940i
$516$		0			0
$517$	1.46410			0.0643911
$518$	−15.1244	+	17.4641i	−0.664526	+	0.767329i
$519$		0			0
$520$	10.7321	−	18.5885i	0.470632	−	0.815158i
$521$	−2.73205	−	4.73205i	−0.119693	−	0.207315i	0.799953	−	0.600063i	$-0.204858\pi$
$521$	−2.73205	−	4.73205i	−0.119693	−	0.207315i	−0.919646	+	0.392748i	$0.871524\pi$
$522$		0			0
$523$	13.8660	−	24.0167i	0.606319	−	1.05018i	−0.385523	−	0.922698i	$-0.625979\pi$
$523$	13.8660	−	24.0167i	0.606319	−	1.05018i	0.991842	−	0.127477i	$-0.0406878\pi$
$524$	−84.4974			−3.69129
$525$		0			0
$526$	−22.9282			−0.999717
$527$	−0.758330	+	1.31347i	−0.0330334	+	0.0572155i
$528$		0			0
$529$	0.303848	+	0.526279i	0.0132108	+	0.0228817i
$530$	−16.9282	+	29.3205i	−0.735314	+	1.27360i
$531$		0			0
$532$	21.1244	+	60.9808i	0.915857	+	2.64385i
$533$	1.66025			0.0719136
$534$		0			0
$535$	−1.09808	−	1.90192i	−0.0474740	−	0.0822273i
$536$	69.3731	+	120.158i	2.99646	+	5.19002i
$537$		0			0
$538$	34.2487			1.47657
$539$	−4.75833	−	1.90192i	−0.204956	−	0.0819217i
$540$		0			0
$541$	−2.89230	+	5.00962i	−0.124350	+	0.215380i	−0.921479	−	0.388429i	$-0.873018\pi$
$541$	−2.89230	+	5.00962i	−0.124350	+	0.215380i	0.797129	+	0.603809i	$0.206351\pi$
$542$	−4.19615	−	7.26795i	−0.180240	−	0.312185i
$543$		0			0
$544$	35.7128	−	61.8564i	1.53117	−	2.65207i
$545$	−11.0000			−0.471188
$546$		0			0
$547$	−26.2487			−1.12231			−0.561157	−	0.827709i	$-0.689644\pi$
$547$	−26.2487			−1.12231			−0.561157	+	0.827709i	$0.689644\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$		0			0
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−9.36603	+	16.2224i	−0.399006	+	0.691099i
$552$		0			0
$553$	19.2058	+	3.69615i	0.816712	+	0.157176i
$554$	−40.0526			−1.70167
$555$		0			0
$556$	−16.1962	−	28.0526i	−0.686870	−	1.18969i
$557$	7.39230	+	12.8038i	0.313222	+	0.542516i	0.979058	−	0.203582i	$-0.0652583\pi$
$557$	7.39230	+	12.8038i	0.313222	+	0.542516i	−0.665836	+	0.746098i	$0.731925\pi$
$558$		0			0
$559$	7.24871			0.306588
$560$	−25.8564	+	29.8564i	−1.09263	+	1.26166i
$561$		0			0
$562$	18.9282	−	32.7846i	0.798438	−	1.38294i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$		0			0
$565$	−4.46410	+	7.73205i	−0.187806	+	0.325290i
$566$	−65.9090			−2.77036
$567$		0			0
$568$	−58.6410			−2.46052
$569$	16.2224	−	28.0981i	0.680080	−	1.17793i	−0.294876	−	0.955535i	$-0.595278\pi$
$569$	16.2224	−	28.0981i	0.680080	−	1.17793i	0.974956	−	0.222397i	$-0.0713882\pi$
$570$		0			0
$571$	−9.30385	−	16.1147i	−0.389354	−	0.674381i	0.603009	−	0.797734i	$-0.293968\pi$
$571$	−9.30385	−	16.1147i	−0.389354	−	0.674381i	−0.992363	+	0.123354i	$0.960635\pi$
$572$	4.53590	−	7.85641i	0.189655	−	0.328493i
$573$		0			0
$574$	−5.19615	−	1.00000i	−0.216883	−	0.0417392i
$575$	4.73205			0.197340
$576$		0			0
$577$	−14.3301	−	24.8205i	−0.596571	−	1.03329i	−0.993323	−	0.115365i	$-0.963196\pi$
$577$	−14.3301	−	24.8205i	−0.596571	−	1.03329i	0.396752	−	0.917926i	$-0.370137\pi$
$578$	8.63397	+	14.9545i	0.359126	+	0.622024i
$579$		0			0
$580$	−22.9282			−0.952042
$581$	−13.0981	−	37.8109i	−0.543400	−	1.56866i
$582$		0			0
$583$	−4.53590	+	7.85641i	−0.187858	+	0.325379i
$584$	−59.9090	−	103.765i	−2.47905	−	4.29384i
$585$		0			0
$586$	25.8564	−	44.7846i	1.06812	−	1.85004i
$587$	−40.7321			−1.68119			−0.840596	−	0.541663i	$-0.817795\pi$
$587$	−40.7321			−1.68119			−0.840596	+	0.541663i	$0.817795\pi$
$588$		0			0
$589$	−2.07180			−0.0853669
$590$	0.267949	−	0.464102i	0.0110313	−	0.0191068i
$591$		0			0
$592$	23.8564	+	41.3205i	0.980492	+	1.69826i
$593$	13.9545	−	24.1699i	0.573042	−	0.992538i	−0.423209	−	0.906032i	$-0.639097\pi$
$593$	13.9545	−	24.1699i	0.573042	−	0.992538i	0.996251	−	0.0865058i	$-0.0275701\pi$
$594$		0			0
$595$	2.83013	+	8.16987i	0.116024	+	0.334932i
$596$	−32.0000			−1.31077
$597$		0			0
$598$	−14.6603	−	25.3923i	−0.599502	−	1.03837i
$599$	−19.1244	−	33.1244i	−0.781400	−	1.35342i	−0.931126	−	0.364697i	$-0.881173\pi$
$599$	−19.1244	−	33.1244i	−0.781400	−	1.35342i	0.149726	−	0.988727i	$-0.452161\pi$
$600$		0			0
$601$	−0.0717968			−0.00292865			−0.00146433	−	0.999999i	$-0.500466\pi$
$601$	−0.0717968			−0.00292865			−0.00146433	+	0.999999i	$0.500466\pi$
$602$	−22.6865	−	4.36603i	−0.924634	−	0.177946i
$603$		0			0
$604$	24.3923	−	42.2487i	0.992509	−	1.71908i
$605$	−5.23205	−	9.06218i	−0.212713	−	0.368430i
$606$		0			0
$607$	−1.59808	+	2.76795i	−0.0648639	+	0.112348i	−0.896634	−	0.442773i	$-0.853995\pi$
$607$	−1.59808	+	2.76795i	−0.0648639	+	0.112348i	0.831770	+	0.555121i	$0.187328\pi$
$608$	97.5692			3.95695
$609$		0			0
$610$	−10.9282			−0.442470
$611$	2.26795	−	3.92820i	0.0917514	−	0.158918i
$612$		0			0
$613$	13.4641	+	23.3205i	0.543810	+	0.941906i	0.998681	+	0.0513490i	$0.0163521\pi$
$613$	13.4641	+	23.3205i	0.543810	+	0.941906i	−0.454871	+	0.890557i	$0.650315\pi$
$614$	43.8827	−	76.0070i	1.77096	−	3.06739i
$615$		0			0
$616$	−12.0000	+	13.8564i	−0.483494	+	0.558291i
$617$	36.2487			1.45932			0.729659	−	0.683811i	$-0.239679\pi$
$617$	36.2487			1.45932			0.729659	+	0.683811i	$0.239679\pi$
$618$		0			0
$619$	15.0359	+	26.0429i	0.604344	+	1.04675i	0.992155	+	0.125015i	$0.0398980\pi$
$619$	15.0359	+	26.0429i	0.604344	+	1.04675i	−0.387811	+	0.921739i	$0.626769\pi$
$620$	−1.26795	−	2.19615i	−0.0509221	−	0.0881996i
$621$		0			0
$622$	−24.9282			−0.999530
$623$	39.2942	+	7.56218i	1.57429	+	0.302972i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.2942	+	29.9545i	0.691216	+	1.19722i
$627$		0			0
$628$	−17.4641	+	30.2487i	−0.696894	+	1.20705i
$629$	10.4449			0.416464
$630$		0			0
$631$	48.7846			1.94208			0.971042	−	0.238908i	$-0.0767893\pi$
$631$	48.7846			1.94208			0.971042	+	0.238908i	$0.0767893\pi$
$632$	34.9808	−	60.5885i	1.39146	−	2.41008i
$633$		0			0
$634$	−38.8564	−	67.3013i	−1.54319	−	2.67287i
$635$	2.40192	−	4.16025i	0.0953174	−	0.165095i
$636$		0			0
$637$	−12.4737	+	9.82051i	−0.494227	+	0.389103i
$638$	−8.39230			−0.332255
$639$		0			0
$640$	18.9282	+	32.7846i	0.748203	+	1.29593i
$641$	1.90192	+	3.29423i	0.0751215	+	0.130114i	0.901139	−	0.433530i	$-0.142732\pi$
$641$	1.90192	+	3.29423i	0.0751215	+	0.130114i	−0.826018	+	0.563644i	$0.809399\pi$
$642$		0			0
$643$	4.51666			0.178120			0.0890599	−	0.996026i	$-0.471614\pi$
$643$	4.51666			0.178120			0.0890599	+	0.996026i	$0.471614\pi$
$644$	22.3923	+	64.6410i	0.882380	+	2.54721i
$645$		0			0
$646$	19.9282	−	34.5167i	0.784065	−	1.35804i
$647$	−13.9545	−	24.1699i	−0.548607	−	0.950216i	−0.998370	−	0.0570678i	$-0.981825\pi$
$647$	−13.9545	−	24.1699i	−0.548607	−	0.950216i	0.449763	−	0.893148i	$-0.351508\pi$
$648$		0			0
$649$	0.0717968	−	0.124356i	0.00281827	−	0.00488139i
$650$	6.19615			0.243033
$651$		0			0
$652$	119.426			4.67707
$653$	−22.2942	+	38.6147i	−0.872441	+	1.51111i	−0.0129762	+	0.999916i	$0.504131\pi$
$653$	−22.2942	+	38.6147i	−0.872441	+	1.51111i	−0.859464	+	0.511196i	$0.829203\pi$
$654$		0			0
$655$	−7.73205	−	13.3923i	−0.302116	−	0.523281i
$656$	−5.46410	+	9.46410i	−0.213337	+	0.369511i
$657$		0			0
$658$	−9.46410	+	10.9282i	−0.368949	+	0.426026i
$659$	−2.92820			−0.114067			−0.0570333	−	0.998372i	$-0.518164\pi$
$659$	−2.92820			−0.114067			−0.0570333	+	0.998372i	$0.518164\pi$
$660$		0			0
$661$	−5.23205	−	9.06218i	−0.203503	−	0.352478i	0.746152	−	0.665776i	$-0.231899\pi$
$661$	−5.23205	−	9.06218i	−0.203503	−	0.352478i	−0.949655	+	0.313298i	$0.898566\pi$
$662$	−11.0263	−	19.0981i	−0.428549	−	0.742268i
$663$		0			0
$664$	−143.138			−5.55485
$665$	−7.73205	+	8.92820i	−0.299836	+	0.346221i
$666$		0			0
$667$	−9.92820	+	17.1962i	−0.384422	+	0.665838i
$668$	−48.2487	−	83.5692i	−1.86680	−	3.23339i
$669$		0			0
$670$	−20.0263	+	34.6865i	−0.773683	+	1.34006i
$671$	−2.92820			−0.113042
$672$		0			0
$673$	−27.3397			−1.05387			−0.526935	−	0.849906i	$-0.676659\pi$
$673$	−27.3397			−1.05387			−0.526935	+	0.849906i	$0.676659\pi$
$674$	−24.5622	+	42.5429i	−0.946100	+	1.63869i
$675$		0			0
$676$	21.4641	+	37.1769i	0.825542	+	1.42988i
$677$	−16.5622	+	28.6865i	−0.636536	+	1.10251i	0.349651	+	0.936880i	$0.386300\pi$
$677$	−16.5622	+	28.6865i	−0.636536	+	1.10251i	−0.986187	+	0.165633i	$0.947033\pi$
$678$		0			0
$679$	12.9282	+	37.3205i	0.496139	+	1.43223i
$680$	30.9282			1.18604
$681$		0			0
$682$	−0.464102	−	0.803848i	−0.0177714	−	0.0307809i
$683$	−14.0263	−	24.2942i	−0.536701	−	0.929593i	−0.999079	−	0.0429101i	$-0.986337\pi$
$683$	−14.0263	−	24.2942i	−0.536701	−	0.929593i	0.462378	−	0.886683i	$-0.346996\pi$
$684$		0			0
$685$	2.19615			0.0839107
$686$	44.9545	−	23.2224i	1.71637	−	0.886637i
$687$		0			0
$688$	−23.8564	+	41.3205i	−0.909517	+	1.57533i
$689$	14.0526	+	24.3397i	0.535360	+	0.927270i
$690$		0			0
$691$	−4.42820	+	7.66987i	−0.168457	+	0.291776i	−0.937877	−	0.346967i	$-0.887212\pi$
$691$	−4.42820	+	7.66987i	−0.168457	+	0.291776i	0.769421	+	0.638742i	$0.220545\pi$
$692$	−79.4256			−3.01931
$693$		0			0
$694$	57.5692			2.18530
$695$	2.96410	−	5.13397i	0.112435	−	0.194743i
$696$		0			0
$697$	1.19615	+	2.07180i	0.0453075	+	0.0784749i
$698$	−30.0526	+	52.0526i	−1.13751	+	1.97022i
$699$		0			0
$700$	−14.1962	−	2.73205i	−0.536564	−	0.103262i
$701$	8.58846			0.324382			0.162191	−	0.986759i	$-0.448144\pi$
$701$	8.58846			0.324382			0.162191	+	0.986759i	$0.448144\pi$
$702$		0			0
$703$	7.13397	+	12.3564i	0.269063	+	0.466031i
$704$	10.9282	+	18.9282i	0.411872	+	0.713384i
$705$		0			0
$706$	8.53590			0.321253
$707$	12.5885	−	14.5359i	0.473438	−	0.546679i
$708$		0			0
$709$	0.535898	−	0.928203i	0.0201261	−	0.0348594i	−0.855787	−	0.517328i	$-0.826927\pi$
$709$	0.535898	−	0.928203i	0.0201261	−	0.0348594i	0.875913	+	0.482469i	$0.160260\pi$
$710$	−8.46410	−	14.6603i	−0.317652	−	0.550190i
$711$		0			0
$712$	71.5692	−	123.962i	2.68217	−	4.64565i
$713$	−2.19615			−0.0822466
$714$		0			0
$715$	1.66025			0.0620900
$716$	−27.3205	+	47.3205i	−1.02102	+	1.76845i
$717$		0			0
$718$	−1.73205	−	3.00000i	−0.0646396	−	0.111959i
$719$	−10.2679	+	17.7846i	−0.382930	+	0.663254i	−0.991480	−	0.130262i	$-0.958418\pi$
$719$	−10.2679	+	17.7846i	−0.382930	+	0.663254i	0.608550	+	0.793516i	$0.291752\pi$
$720$		0			0
$721$	23.8923	+	4.59808i	0.889796	+	0.171241i
$722$	2.53590			0.0943764
$723$		0			0
$724$	66.4449	+	115.086i	2.46940	+	4.27713i
$725$	−2.09808	−	3.63397i	−0.0779206	−	0.134962i
$726$		0			0
$727$	−13.3397			−0.494744			−0.247372	−	0.968921i	$-0.579567\pi$
$727$	−13.3397			−0.494744			−0.247372	+	0.968921i	$0.579567\pi$
$728$	18.5885	+	53.6603i	0.688934	+	1.98878i
$729$		0			0
$730$	17.2942	−	29.9545i	0.640088	−	1.10867i
$731$	5.22243	+	9.04552i	0.193159	+	0.334561i
$732$		0			0
$733$	0.669873	−	1.16025i	0.0247423	−	0.0428550i	−0.853389	−	0.521274i	$-0.825457\pi$
$733$	0.669873	−	1.16025i	0.0247423	−	0.0428550i	0.878131	+	0.478419i	$0.158790\pi$
$734$	30.5885			1.12904
$735$		0			0
$736$	103.426			3.81232
$737$	−5.36603	+	9.29423i	−0.197660	+	0.342357i
$738$		0			0
$739$	−13.8923	−	24.0622i	−0.511037	−	0.885142i	−0.999918	−	0.0127913i	$-0.995928\pi$
$739$	−13.8923	−	24.0622i	−0.511037	−	0.885142i	0.488881	−	0.872350i	$-0.337405\pi$
$740$	−8.73205	+	15.1244i	−0.320997	+	0.555982i
$741$		0			0
$742$	−29.3205	−	84.6410i	−1.07639	−	3.10727i
$743$	15.9090			0.583643			0.291822	−	0.956473i	$-0.405739\pi$
$743$	15.9090			0.583643			0.291822	+	0.956473i	$0.405739\pi$
$744$		0			0
$745$	−2.92820	−	5.07180i	−0.107281	−	0.185816i
$746$	−36.2224	−	62.7391i	−1.32620	−	2.29704i
$747$		0			0
$748$	13.0718			0.477952
$749$	5.70577	+	1.09808i	0.208484	+	0.0401228i
$750$		0			0
$751$	−9.03590	+	15.6506i	−0.329725	+	0.571100i	−0.982457	−	0.186489i	$-0.940289\pi$
$751$	−9.03590	+	15.6506i	−0.329725	+	0.571100i	0.652732	+	0.757588i	$0.273623\pi$
$752$	14.9282	+	25.8564i	0.544376	+	0.942886i
$753$		0			0
$754$	−13.0000	+	22.5167i	−0.473432	+	0.820008i
$755$	8.92820			0.324931
$756$		0			0
$757$	−27.8564			−1.01246			−0.506229	−	0.862399i	$-0.668961\pi$
$757$	−27.8564			−1.01246			−0.506229	+	0.862399i	$0.668961\pi$
$758$	−8.63397	+	14.9545i	−0.313600	+	0.543171i
$759$		0			0
$760$	21.1244	+	36.5885i	0.766261	+	1.32720i
$761$	23.3660	−	40.4711i	0.847018	−	1.46708i	−0.0368396	−	0.999321i	$-0.511729\pi$
$761$	23.3660	−	40.4711i	0.847018	−	1.46708i	0.883857	−	0.467757i	$-0.154938\pi$
$762$		0			0
$763$	19.0526	−	22.0000i	0.689749	−	0.796453i
$764$	48.7846			1.76497
$765$		0			0
$766$	−31.8564	−	55.1769i	−1.15102	−	1.99362i
$767$	−0.222432	−	0.385263i	−0.00803155	−	0.0139111i
$768$		0			0
$769$	52.3205			1.88673			0.943363	−	0.331763i	$-0.107643\pi$
$769$	52.3205			1.88673			0.943363	+	0.331763i	$0.107643\pi$
$770$	−5.19615	−	1.00000i	−0.187256	−	0.0360375i
$771$		0			0
$772$	−3.26795	+	5.66025i	−0.117616	+	0.203717i
$773$	21.7583	+	37.6865i	0.782593	+	1.35549i	0.930427	+	0.366478i	$0.119437\pi$
$773$	21.7583	+	37.6865i	0.782593	+	1.35549i	−0.147834	+	0.989012i	$0.547230\pi$
$774$		0			0
$775$	0.232051	−	0.401924i	0.00833551	−	0.0144375i
$776$	141.282			5.07173
$777$		0			0
$778$	−14.7846			−0.530054
$779$	−1.63397	+	2.83013i	−0.0585432	+	0.101400i
$780$		0			0
$781$	−2.26795	−	3.92820i	−0.0811536	−	0.140562i
$782$	21.1244	−	36.5885i	0.755405	−	1.30840i
$783$		0			0
$784$	−14.9282	−	103.426i	−0.533150	−	3.69377i
$785$	−6.39230			−0.228151
$786$		0			0
$787$	−6.73205	−	11.6603i	−0.239972	−	0.415643i	0.720734	−	0.693212i	$-0.243805\pi$
$787$	−6.73205	−	11.6603i	−0.239972	−	0.415643i	−0.960706	+	0.277568i	$0.910471\pi$
$788$	−0.928203	−	1.60770i	−0.0330659	−	0.0572718i
$789$		0			0
$790$	20.1962			0.718547
$791$	−7.73205	−	22.3205i	−0.274920	−	0.793626i
$792$		0			0
$793$	−4.53590	+	7.85641i	−0.161074	+	0.278989i
$794$	42.6147	+	73.8109i	1.51234	+	2.61945i
$795$		0			0
$796$	−60.1051	+	104.105i	−2.13037	+	3.68991i
$797$	3.94744			0.139826			0.0699128	−	0.997553i	$-0.477728\pi$
$797$	3.94744			0.139826			0.0699128	+	0.997553i	$0.477728\pi$
$798$		0			0
$799$	6.53590			0.231223
$800$	−10.9282	+	18.9282i	−0.386370	+	0.669213i
$801$		0			0
$802$	−22.3923	−	38.7846i	−0.790700	−	1.36953i
$803$	4.63397	−	8.02628i	0.163529	−	0.283241i
$804$		0			0
$805$	−8.19615	+	9.46410i	−0.288876	+	0.333566i
$806$	−2.87564			−0.101290
$807$		0			0
$808$	−34.3923	−	59.5692i	−1.20992	−	2.09564i
$809$	12.8564	+	22.2679i	0.452007	+	0.782899i	0.998511	−	0.0545574i	$-0.0173748\pi$
$809$	12.8564	+	22.2679i	0.452007	+	0.782899i	−0.546503	+	0.837457i	$0.684041\pi$
$810$		0			0
$811$	−3.46410			−0.121641			−0.0608205	−	0.998149i	$-0.519372\pi$
$811$	−3.46410			−0.121641			−0.0608205	+	0.998149i	$0.519372\pi$
$812$	39.7128	−	45.8564i	1.39365	−	1.60924i
$813$		0			0
$814$	−3.19615	+	5.53590i	−0.112025	+	0.194033i
$815$	10.9282	+	18.9282i	0.382798	+	0.663026i
$816$		0			0
$817$	−7.13397	+	12.3564i	−0.249586	+	0.432296i
$818$	8.58846			0.300288
$819$		0			0
$820$	−4.00000			−0.139686
$821$	−12.7583	+	22.0981i	−0.445269	+	0.771228i	−0.998071	−	0.0620844i	$-0.980225\pi$
$821$	−12.7583	+	22.0981i	−0.445269	+	0.771228i	0.552802	+	0.833313i	$0.313559\pi$
$822$		0			0
$823$	−19.5885	−	33.9282i	−0.682811	−	1.18266i	−0.974119	−	0.226034i	$-0.927424\pi$
$823$	−19.5885	−	33.9282i	−0.682811	−	1.18266i	0.291309	−	0.956629i	$-0.405909\pi$
$824$	43.5167	−	75.3731i	1.51597	−	2.62575i
$825$		0			0
$826$	0.464102	+	1.33975i	0.0161482	+	0.0466157i
$827$	3.75129			0.130445			0.0652225	−	0.997871i	$-0.479224\pi$
$827$	3.75129			0.130445			0.0652225	+	0.997871i	$0.479224\pi$
$828$		0			0
$829$	2.30385	+	3.99038i	0.0800159	+	0.138592i	0.903257	−	0.429101i	$-0.141170\pi$
$829$	2.30385	+	3.99038i	0.0800159	+	0.138592i	−0.823241	+	0.567693i	$0.807836\pi$
$830$	−20.6603	−	35.7846i	−0.717128	−	1.24210i
$831$		0			0
$832$	67.7128			2.34752
$833$	−21.2417	−	8.49038i	−0.735980	−	0.294174i
$834$		0			0
$835$	8.83013	−	15.2942i	0.305579	−	0.529279i
$836$	8.92820	+	15.4641i	0.308788	+	0.534837i
$837$		0			0
$838$	−48.4449	+	83.9090i	−1.67350	+	2.89859i
$839$	−18.4449			−0.636787			−0.318394	−	0.947959i	$-0.603143\pi$
$839$	−18.4449			−0.636787			−0.318394	+	0.947959i	$0.603143\pi$
$840$		0			0
$841$	−11.3923			−0.392838
$842$	−0.0980762	+	0.169873i	−0.00337993	+	0.00585421i
$843$		0			0
$844$	−19.3205	−	33.4641i	−0.665039	−	1.15188i
$845$	−3.92820	+	6.80385i	−0.135134	+	0.234059i
$846$		0			0
$847$	27.1865	+	5.23205i	0.934140	+	0.179775i
$848$	−184.995			−6.35275
$849$		0			0
$850$	4.46410	+	7.73205i	0.153117	+	0.265207i
$851$	7.56218	+	13.0981i	0.259228	+	0.448996i
$852$		0			0
$853$	−31.9808			−1.09500			−0.547500	−	0.836806i	$-0.684420\pi$
$853$	−31.9808			−1.09500			−0.547500	+	0.836806i	$0.684420\pi$
$854$	18.9282	−	21.8564i	0.647710	−	0.747911i
$855$		0			0
$856$	10.3923	−	18.0000i	0.355202	−	0.615227i
$857$	14.5622	+	25.2224i	0.497435	+	0.861582i	0.999996	−	0.00295983i	$-0.000942146\pi$
$857$	14.5622	+	25.2224i	0.497435	+	0.861582i	−0.502561	+	0.864542i	$0.667609\pi$
$858$		0			0
$859$	−3.73205	+	6.46410i	−0.127336	+	0.220552i	−0.922644	−	0.385654i	$-0.873976\pi$
$859$	−3.73205	+	6.46410i	−0.127336	+	0.220552i	0.795308	+	0.606206i	$0.207309\pi$
$860$	−17.4641			−0.595521
$861$		0			0
$862$	−47.3205			−1.61174
$863$	7.19615	−	12.4641i	0.244960	−	0.424283i	−0.717160	−	0.696908i	$-0.754559\pi$
$863$	7.19615	−	12.4641i	0.244960	−	0.424283i	0.962120	+	0.272625i	$0.0878919\pi$
$864$		0			0
$865$	−7.26795	−	12.5885i	−0.247118	−	0.428020i
$866$	−20.7583	+	35.9545i	−0.705397	+	1.22178i
$867$		0			0
$868$	6.58846	+	1.26795i	0.223627	+	0.0430370i
$869$	5.41154			0.183574
$870$		0			0
$871$	16.6244	+	28.7942i	0.563295	+	0.975655i
$872$	−52.0526	−	90.1577i	−1.76272	−	3.05312i
$873$		0			0
$874$	57.7128			1.95217
$875$	−0.866025	−	2.50000i	−0.0292770	−	0.0845154i
$876$		0			0
$877$	2.07180	−	3.58846i	0.0699596	−	0.121174i	−0.828924	−	0.559362i	$-0.811046\pi$
$877$	2.07180	−	3.58846i	0.0699596	−	0.121174i	0.898883	+	0.438188i	$0.144380\pi$
$878$	−0.732051	−	1.26795i	−0.0247055	−	0.0427912i
$879$		0			0
$880$	−5.46410	+	9.46410i	−0.184195	+	0.319035i
$881$	−9.85641			−0.332071			−0.166035	−	0.986120i	$-0.553097\pi$
$881$	−9.85641			−0.332071			−0.166035	+	0.986120i	$0.553097\pi$
$882$		0			0
$883$	53.5885			1.80340			0.901698	−	0.432367i	$-0.142322\pi$
$883$	53.5885			1.80340			0.901698	+	0.432367i	$0.142322\pi$
$884$	20.2487	−	35.0718i	0.681038	−	1.17959i
$885$		0			0
$886$	12.9282	+	22.3923i	0.434331	+	0.752284i
$887$	−12.6340	+	21.8827i	−0.424207	+	0.734749i	−0.996346	−	0.0854082i	$-0.972781\pi$
$887$	−12.6340	+	21.8827i	−0.424207	+	0.734749i	0.572139	+	0.820157i	$0.306114\pi$
$888$		0			0
$889$	4.16025	+	12.0096i	0.139530	+	0.402790i
$890$	41.3205			1.38507
$891$		0			0
$892$	55.7128	+	96.4974i	1.86540	+	3.23097i
$893$	4.46410	+	7.73205i	0.149385	+	0.258743i
$894$		0			0
$895$	−10.0000			−0.334263
$896$	−98.3538	−	18.9282i	−3.28577	−	0.632347i
$897$		0			0
$898$	−48.9808	+	84.8372i	−1.63451	+	2.83105i
$899$	0.973721	+	1.68653i	0.0324754	+	0.0562490i
$900$		0			0
$901$	−20.2487	+	35.0718i	−0.674582	+	1.16841i
$902$	−1.46410			−0.0487493
$903$		0			0
$904$	−84.4974			−2.81034
$905$	−12.1603	+	21.0622i	−0.404221	+	0.700130i
$906$		0			0
$907$	−16.7942	−	29.0885i	−0.557643	−	0.965866i	−0.997693	−	0.0678928i	$-0.978372\pi$
$907$	−16.7942	−	29.0885i	−0.557643	−	0.965866i	0.440049	−	0.897974i	$-0.354961\pi$
$908$	−4.53590	+	7.85641i	−0.150529	+	0.260724i
$909$		0			0
$910$	−10.7321	+	12.3923i	−0.355764	+	0.410801i
$911$	14.7321			0.488095			0.244047	−	0.969763i	$-0.421525\pi$
$911$	14.7321			0.488095			0.244047	+	0.969763i	$0.421525\pi$
$912$		0			0
$913$	−5.53590	−	9.58846i	−0.183211	−	0.317332i
$914$	22.7583	+	39.4186i	0.752779	+	1.30385i
$915$		0			0
$916$	−16.3923			−0.541617
$917$	40.1769	+	7.73205i	1.32676	+	0.255335i
$918$		0			0
$919$	15.4282	−	26.7224i	0.508929	−	0.881492i	−0.491017	−	0.871150i	$-0.663375\pi$
$919$	15.4282	−	26.7224i	0.508929	−	0.881492i	0.999947	−	0.0103417i	$-0.00329193\pi$
$920$	22.3923	+	38.7846i	0.738252	+	1.27869i
$921$		0			0
$922$	23.1962	−	40.1769i	0.763925	−	1.32316i
$923$	−14.0526			−0.462546
$924$		0			0
$925$	−3.19615			−0.105089
$926$	−35.1506	+	60.8827i	−1.15512	+	2.00073i
$927$		0			0
$928$	−45.8564	−	79.4256i	−1.50531	−	2.60727i
$929$	−26.2224	+	45.4186i	−0.860330	+	1.49014i	0.0112804	+	0.999936i	$0.496409\pi$
$929$	−26.2224	+	45.4186i	−0.860330	+	1.49014i	−0.871611	+	0.490199i	$0.836924\pi$
$930$		0			0
$931$	−4.46410	−	30.9282i	−0.146305	−	1.01363i
$932$	−94.6410			−3.10007
$933$		0			0
$934$	−0.196152	−	0.339746i	−0.00641830	−	0.0111168i
$935$	1.19615	+	2.07180i	0.0391184	+	0.0677550i
$936$		0			0
$937$	31.7321			1.03664			0.518320	−	0.855186i	$-0.326557\pi$
$937$	31.7321			1.03664			0.518320	+	0.855186i	$0.326557\pi$
$938$	−34.6865	−	100.131i	−1.13256	−	3.26941i
$939$		0			0
$940$	−5.46410	+	9.46410i	−0.178219	+	0.308685i
$941$	−15.0263	−	26.0263i	−0.489843	−	0.848432i	0.510089	−	0.860122i	$-0.329612\pi$
$941$	−15.0263	−	26.0263i	−0.489843	−	0.848432i	−0.999932	+	0.0116892i	$0.996279\pi$
$942$		0			0
$943$	−1.73205	+	3.00000i	−0.0564033	+	0.0976934i
$944$	2.92820			0.0953049
$945$		0			0
$946$	−6.39230			−0.207832
$947$	−2.83013	+	4.90192i	−0.0919668	+	0.159291i	−0.908339	−	0.418235i	$-0.862649\pi$
$947$	−2.83013	+	4.90192i	−0.0919668	+	0.159291i	0.816372	+	0.577527i	$0.195982\pi$
$948$		0			0
$949$	−14.3564	−	24.8660i	−0.466029	−	0.807185i
$950$	−6.09808	+	10.5622i	−0.197848	+	0.342682i
$951$		0			0
$952$	−53.5692	+	61.8564i	−1.73619	+	2.00478i
$953$	36.1051			1.16956			0.584780	−	0.811192i	$-0.301181\pi$
$953$	36.1051			1.16956			0.584780	+	0.811192i	$0.301181\pi$
$954$		0			0
$955$	4.46410	+	7.73205i	0.144455	+	0.250203i
$956$	19.3205	+	33.4641i	0.624870	+	1.08231i
$957$		0			0
$958$	−24.0000			−0.775405
$959$	−3.80385	+	4.39230i	−0.122833	+	0.141835i
$960$		0			0
$961$	15.3923	−	26.6603i	0.496526	−	0.860008i
$962$	9.90192	+	17.1506i	0.319251	+	0.552959i
$963$		0			0
$964$	−36.7846	+	63.7128i	−1.18475	+	2.05205i
$965$	−1.19615			−0.0385055
$966$		0			0
$967$	−10.1244			−0.325577			−0.162789	−	0.986661i	$-0.552049\pi$
$967$	−10.1244			−0.325577			−0.162789	+	0.986661i	$0.552049\pi$
$968$	49.5167	−	85.7654i	1.59153	−	2.75660i
$969$		0			0
$970$	20.3923	+	35.3205i	0.654757	+	1.13407i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$		0			0
$973$	5.13397	+	14.8205i	0.164588	+	0.475124i
$974$	−1.12436			−0.0360267
$975$		0			0
$976$	−29.8564	−	51.7128i	−0.955680	−	1.65529i
$977$	−8.29423	−	14.3660i	−0.265356	−	0.459610i	0.702301	−	0.711880i	$-0.252156\pi$
$977$	−8.29423	−	14.3660i	−0.265356	−	0.459610i	−0.967657	+	0.252270i	$0.918823\pi$
$978$		0			0
$979$	11.0718			0.353856
$980$	30.0526	−	23.6603i	0.959994	−	0.755799i
$981$		0			0
$982$	−52.2487	+	90.4974i	−1.66732	+	2.88789i
$983$	4.90192	+	8.49038i	0.156347	+	0.270801i	0.933549	−	0.358451i	$-0.116695\pi$
$983$	4.90192	+	8.49038i	0.156347	+	0.270801i	−0.777202	+	0.629252i	$0.783361\pi$
$984$		0			0
$985$	0.169873	−	0.294229i	0.00541260	−	0.00937490i
$986$	−37.4641			−1.19310
$987$		0			0
$988$	55.3205			1.75998
$989$	−7.56218	+	13.0981i	−0.240463	+	0.416495i
$990$		0			0
$991$	10.5526	+	18.2776i	0.335213	+	0.580606i	0.983526	−	0.180768i	$-0.0578584\pi$
$991$	10.5526	+	18.2776i	0.335213	+	0.580606i	−0.648313	+	0.761374i	$0.724525\pi$
$992$	5.07180	−	8.78461i	0.161030	−	0.278912i
$993$		0			0
$994$	43.9808	+	8.46410i	1.39499	+	0.268465i
$995$	−22.0000			−0.697447
$996$		0			0
$997$	27.9904	+	48.4808i	0.886464	+	1.53540i	0.844026	+	0.536302i	$0.180179\pi$
$997$	27.9904	+	48.4808i	0.886464	+	1.53540i	0.0424381	+	0.999099i	$0.486487\pi$
$998$	18.4904	+	32.0263i	0.585303	+	1.01377i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.c.226.1		4
3.2	odd	2		105.2.i.d.16.2	✓	4
7.2	even	3		2205.2.a.z.1.2		2
7.4	even	3	inner	315.2.j.c.46.1		4
7.5	odd	6		2205.2.a.ba.1.2		2
12.11	even	2		1680.2.bg.o.961.1		4
15.2	even	4		525.2.r.f.499.2		4
15.8	even	4		525.2.r.a.499.1		4
15.14	odd	2		525.2.i.f.226.1		4
21.2	odd	6		735.2.a.g.1.1		2
21.5	even	6		735.2.a.h.1.1		2
21.11	odd	6		105.2.i.d.46.2	yes	4
21.17	even	6		735.2.i.l.361.2		4
21.20	even	2		735.2.i.l.226.2		4
84.11	even	6		1680.2.bg.o.1201.1		4
105.32	even	12		525.2.r.a.424.1		4
105.44	odd	6		3675.2.a.bg.1.2		2
105.53	even	12		525.2.r.f.424.2		4
105.74	odd	6		525.2.i.f.151.1		4
105.89	even	6		3675.2.a.be.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.2	✓	4	3.2	odd	2
105.2.i.d.46.2	yes	4	21.11	odd	6
315.2.j.c.46.1		4	7.4	even	3	inner
315.2.j.c.226.1		4	1.1	even	1	trivial
525.2.i.f.151.1		4	105.74	odd	6
525.2.i.f.226.1		4	15.14	odd	2
525.2.r.a.424.1		4	105.32	even	12
525.2.r.a.499.1		4	15.8	even	4
525.2.r.f.424.2		4	105.53	even	12
525.2.r.f.499.2		4	15.2	even	4
735.2.a.g.1.1		2	21.2	odd	6
735.2.a.h.1.1		2	21.5	even	6
735.2.i.l.226.2		4	21.20	even	2
735.2.i.l.361.2		4	21.17	even	6
1680.2.bg.o.961.1		4	12.11	even	2
1680.2.bg.o.1201.1		4	84.11	even	6
2205.2.a.z.1.2		2	7.2	even	3
2205.2.a.ba.1.2		2	7.5	odd	6
3675.2.a.be.1.2		2	105.89	even	6
3675.2.a.bg.1.2		2	105.44	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +9.46410 q^{8} +O(q^{10})\)	\(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +9.46410 q^{8} +(1.36603 + 2.36603i) q^{10} +(0.366025 + 0.633975i) q^{11} +2.26795 q^{13} +(-7.09808 - 1.36603i) q^{14} +(-7.46410 + 12.9282i) q^{16} +(1.63397 + 2.83013i) q^{17} +(-2.23205 + 3.86603i) q^{19} -5.46410 q^{20} -2.00000 q^{22} +(-2.36603 + 4.09808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.09808 + 5.36603i) q^{26} +(9.46410 - 10.9282i) q^{28} +4.19615 q^{29} +(0.232051 + 0.401924i) q^{31} +(-10.9282 - 18.9282i) q^{32} -8.92820 q^{34} +(2.59808 + 0.500000i) q^{35} +(1.59808 - 2.76795i) q^{37} +(-6.09808 - 10.5622i) q^{38} +(4.73205 - 8.19615i) q^{40} +0.732051 q^{41} +3.19615 q^{43} +(2.00000 - 3.46410i) q^{44} +(-6.46410 - 11.1962i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-5.50000 + 4.33013i) q^{49} +2.73205 q^{50} +(-6.19615 - 10.7321i) q^{52} +(6.19615 + 10.7321i) q^{53} +0.732051 q^{55} +(8.19615 + 23.6603i) q^{56} +(-5.73205 + 9.92820i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} -1.26795 q^{62} +29.8564 q^{64} +(1.13397 - 1.96410i) q^{65} +(7.33013 + 12.6962i) q^{67} +(8.92820 - 15.4641i) q^{68} +(-4.73205 + 5.46410i) q^{70} -6.19615 q^{71} +(-6.33013 - 10.9641i) q^{73} +(4.36603 + 7.56218i) q^{74} +24.3923 q^{76} +(-1.26795 + 1.46410i) q^{77} +(3.69615 - 6.40192i) q^{79} +(7.46410 + 12.9282i) q^{80} +(-1.00000 + 1.73205i) q^{82} -15.1244 q^{83} +3.26795 q^{85} +(-4.36603 + 7.56218i) q^{86} +(3.46410 + 6.00000i) q^{88} +(7.56218 - 13.0981i) q^{89} +(1.96410 + 5.66987i) q^{91} +25.8564 q^{92} +(2.73205 + 4.73205i) q^{94} +(2.23205 + 3.86603i) q^{95} +14.9282 q^{97} +(-2.73205 - 18.9282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8	\( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8} + 2 q^{10} - 2 q^{11} + 16 q^{13} - 18 q^{14} - 16 q^{16} + 10 q^{17} - 2 q^{19} - 8 q^{20} - 8 q^{22} - 6 q^{23} - 2 q^{25} - 2 q^{26} + 24 q^{28} - 4 q^{29} - 6 q^{31} - 16 q^{32} - 8 q^{34} - 4 q^{37} - 14 q^{38} + 12 q^{40} - 4 q^{41} - 8 q^{43} + 8 q^{44} - 12 q^{46} + 4 q^{47} - 22 q^{49} + 4 q^{50} - 4 q^{52} + 4 q^{53} - 4 q^{55} + 12 q^{56} - 16 q^{58} + 10 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} + 8 q^{65} + 12 q^{67} + 8 q^{68} - 12 q^{70} - 4 q^{71} - 8 q^{73} + 14 q^{74} + 56 q^{76} - 12 q^{77} - 6 q^{79} + 16 q^{80} - 4 q^{82} - 12 q^{83} + 20 q^{85} - 14 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{92} + 4 q^{94} + 2 q^{95} + 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8 + 2 * q^10 - 2 * q^11 + 16 * q^13 - 18 * q^14 - 16 * q^16 + 10 * q^17 - 2 * q^19 - 8 * q^20 - 8 * q^22 - 6 * q^23 - 2 * q^25 - 2 * q^26 + 24 * q^28 - 4 * q^29 - 6 * q^31 - 16 * q^32 - 8 * q^34 - 4 * q^37 - 14 * q^38 + 12 * q^40 - 4 * q^41 - 8 * q^43 + 8 * q^44 - 12 * q^46 + 4 * q^47 - 22 * q^49 + 4 * q^50 - 4 * q^52 + 4 * q^53 - 4 * q^55 + 12 * q^56 - 16 * q^58 + 10 * q^59 - 8 * q^61 - 12 * q^62 + 64 * q^64 + 8 * q^65 + 12 * q^67 + 8 * q^68 - 12 * q^70 - 4 * q^71 - 8 * q^73 + 14 * q^74 + 56 * q^76 - 12 * q^77 - 6 * q^79 + 16 * q^80 - 4 * q^82 - 12 * q^83 + 20 * q^85 - 14 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^92 + 4 * q^94 + 2 * q^95 + 32 * q^97 - 4 * q^98

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