LMFDB - Embedded newform 315.2.bl.h.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.h.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(1.50000 + 0.866025i) q^{11} -3.46410i q^{12} +1.73205i q^{15} +(-2.00000 + 3.46410i) q^{16} +6.00000 q^{17} -6.92820i q^{19} +(1.00000 - 1.73205i) q^{20} +(-1.50000 + 4.33013i) q^{21} +(3.00000 - 1.73205i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(4.00000 - 3.46410i) q^{28} +(-7.50000 - 4.33013i) q^{29} +(-3.00000 + 1.73205i) q^{31} +(1.50000 + 2.59808i) q^{33} +(-2.00000 + 1.73205i) q^{35} +(3.00000 - 5.19615i) q^{36} -8.00000 q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{43} -3.46410i q^{44} +(-1.50000 + 2.59808i) q^{45} +(4.50000 - 7.79423i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(9.00000 + 5.19615i) q^{51} -13.8564i q^{53} +1.73205i q^{55} +(6.00000 - 10.3923i) q^{57} +(3.00000 - 1.73205i) q^{60} +(-3.00000 - 1.73205i) q^{61} +(-6.00000 + 5.19615i) q^{63} +8.00000 q^{64} +(-4.00000 - 6.92820i) q^{67} +(-6.00000 - 10.3923i) q^{68} +6.00000 q^{69} +1.73205i q^{71} -8.66025i q^{73} +(-1.50000 + 0.866025i) q^{75} +(-12.0000 + 6.92820i) q^{76} +(-1.50000 + 4.33013i) q^{77} +(0.500000 - 0.866025i) q^{79} -4.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(9.00000 - 1.73205i) q^{84} +(3.00000 + 5.19615i) q^{85} +(-7.50000 - 12.9904i) q^{87} +6.00000 q^{89} +(-6.00000 - 3.46410i) q^{92} -6.00000 q^{93} +(6.00000 - 3.46410i) q^{95} +(-1.50000 - 0.866025i) q^{97} +5.19615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 2 q^{4} + q^{5} + q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 2 * q^4 + q^5 + q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 2 q^{4} + q^{5} + q^{7} + 3 q^{9} + 3 q^{11} - 4 q^{16} + 12 q^{17} + 2 q^{20} - 3 q^{21} + 6 q^{23} - q^{25} + 8 q^{28} - 15 q^{29} - 6 q^{31} + 3 q^{33} - 4 q^{35} + 6 q^{36} - 16 q^{37} + 6 q^{41} - 10 q^{43} - 3 q^{45} + 9 q^{47} - 12 q^{48} - 13 q^{49} + 18 q^{51} + 12 q^{57} + 6 q^{60} - 6 q^{61} - 12 q^{63} + 16 q^{64} - 8 q^{67} - 12 q^{68} + 12 q^{69} - 3 q^{75} - 24 q^{76} - 3 q^{77} + q^{79} - 8 q^{80} - 9 q^{81} - 9 q^{83} + 18 q^{84} + 6 q^{85} - 15 q^{87} + 12 q^{89} - 12 q^{92} - 12 q^{93} + 12 q^{95} - 3 q^{97}+O(q^{100}) $ 2 * q + 3 * q^3 - 2 * q^4 + q^5 + q^7 + 3 * q^9 + 3 * q^11 - 4 * q^16 + 12 * q^17 + 2 * q^20 - 3 * q^21 + 6 * q^23 - q^25 + 8 * q^28 - 15 * q^29 - 6 * q^31 + 3 * q^33 - 4 * q^35 + 6 * q^36 - 16 * q^37 + 6 * q^41 - 10 * q^43 - 3 * q^45 + 9 * q^47 - 12 * q^48 - 13 * q^49 + 18 * q^51 + 12 * q^57 + 6 * q^60 - 6 * q^61 - 12 * q^63 + 16 * q^64 - 8 * q^67 - 12 * q^68 + 12 * q^69 - 3 * q^75 - 24 * q^76 - 3 * q^77 + q^79 - 8 * q^80 - 9 * q^81 - 9 * q^83 + 18 * q^84 + 6 * q^85 - 15 * q^87 + 12 * q^89 - 12 * q^92 - 12 * q^93 + 12 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		−	3.46410i		−	1.00000i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$		0			0
$15$			1.73205i			0.447214i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$		−	6.92820i		−	1.58944i	−0.606977	−	0.794719i	$-0.707618\pi$
$19$		−	6.92820i		−	1.58944i	0.606977	−	0.794719i	$-0.292382\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	−1.50000	+	4.33013i	−0.327327	+	0.944911i
$22$		0			0
$23$	3.00000	−	1.73205i	0.625543	−	0.361158i	−0.153481	−	0.988152i	$-0.549048\pi$
$23$	3.00000	−	1.73205i	0.625543	−	0.361158i	0.779024	+	0.626994i	$0.215715\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$			5.19615i			1.00000i
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$	−7.50000	−	4.33013i	−1.39272	−	0.804084i	−0.399100	−	0.916907i	$-0.630677\pi$
$29$	−7.50000	−	4.33013i	−1.39272	−	0.804084i	−0.993615	+	0.112823i	$0.964011\pi$
$30$		0			0
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$		0			0
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$		0			0
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$	3.00000	−	5.19615i	0.500000	−	0.866025i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$		−	3.46410i		−	0.522233i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$	−6.00000	+	3.46410i	−0.866025	+	0.500000i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$		0			0
$53$		−	13.8564i		−	1.90332i	−0.307148	−	0.951662i	$-0.599375\pi$
$53$		−	13.8564i		−	1.90332i	0.307148	−	0.951662i	$-0.400625\pi$
$54$		0			0
$55$			1.73205i			0.233550i
$56$		0			0
$57$	6.00000	−	10.3923i	0.794719	−	1.37649i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	3.00000	−	1.73205i	0.387298	−	0.223607i
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	0.295495	−	0.955344i	$-0.404516\pi$
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	−0.679605	+	0.733578i	$0.737849\pi$
$62$		0			0
$63$	−6.00000	+	5.19615i	−0.755929	+	0.654654i
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−6.00000	−	10.3923i	−0.727607	−	1.26025i
$69$	6.00000			0.722315
$70$		0			0
$71$			1.73205i			0.205557i	0.994704	+	0.102778i	$0.0327732\pi$
$71$			1.73205i			0.205557i	−0.994704	+	0.102778i	$0.967227\pi$
$72$		0			0
$73$		−	8.66025i		−	1.01361i	−0.862062	−	0.506803i	$-0.830827\pi$
$73$		−	8.66025i		−	1.01361i	0.862062	−	0.506803i	$-0.169173\pi$
$74$		0			0
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$	−12.0000	+	6.92820i	−1.37649	+	0.794719i
$77$	−1.50000	+	4.33013i	−0.170941	+	0.493464i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	−4.00000			−0.447214
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$	9.00000	−	1.73205i	0.981981	−	0.188982i
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$		0			0
$87$	−7.50000	−	12.9904i	−0.804084	−	1.39272i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$		0			0
$92$	−6.00000	−	3.46410i	−0.625543	−	0.361158i
$93$	−6.00000			−0.622171
$94$		0			0
$95$	6.00000	−	3.46410i	0.615587	−	0.355409i
$96$		0			0
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	0.421912	−	0.906637i	$-0.361359\pi$
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	−0.574214	+	0.818705i	$0.694692\pi$
$98$		0			0
$99$			5.19615i			0.522233i
$100$	2.00000			0.200000
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	10.5000	−	6.06218i	1.03460	−	0.597324i	0.116298	−	0.993214i	$-0.462897\pi$
$103$	10.5000	−	6.06218i	1.03460	−	0.597324i	0.918298	+	0.395890i	$0.129564\pi$
$104$		0			0
$105$	−4.50000	+	0.866025i	−0.439155	+	0.0845154i
$106$		0			0
$107$		−	6.92820i		−	0.669775i	−0.942258	−	0.334887i	$-0.891302\pi$
$107$		−	6.92820i		−	0.669775i	0.942258	−	0.334887i	$-0.108698\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$		0			0
$111$	−12.0000	−	6.92820i	−1.13899	−	0.657596i
$112$	−10.0000	−	3.46410i	−0.944911	−	0.327327i
$113$	−9.00000	+	5.19615i	−0.846649	+	0.488813i	−0.859519	−	0.511104i	$-0.829237\pi$
$113$	−9.00000	+	5.19615i	−0.846649	+	0.488813i	0.0128699	+	0.999917i	$0.495903\pi$
$114$		0			0
$115$	3.00000	+	1.73205i	0.279751	+	0.161515i
$116$			17.3205i			1.60817i
$117$		0			0
$118$		0			0
$119$	3.00000	+	15.5885i	0.275010	+	1.42899i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$			10.3923i			0.937043i
$124$	6.00000	+	3.46410i	0.538816	+	0.311086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$	−15.0000	+	8.66025i	−1.32068	+	0.762493i
$130$		0			0
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	3.00000	−	5.19615i	0.261116	−	0.452267i
$133$	18.0000	−	3.46410i	1.56080	−	0.300376i
$134$		0			0
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	15.0000	+	8.66025i	1.28154	+	0.739895i	0.977129	−	0.212647i	$-0.0682083\pi$
$137$	15.0000	+	8.66025i	1.28154	+	0.739895i	0.304407	+	0.952542i	$0.401542\pi$
$138$		0			0
$139$	15.0000	−	8.66025i	1.27228	−	0.734553i	0.296866	−	0.954919i	$-0.404058\pi$
$139$	15.0000	−	8.66025i	1.27228	−	0.734553i	0.975417	+	0.220366i	$0.0707252\pi$
$140$	5.00000	+	1.73205i	0.422577	+	0.146385i
$141$	13.5000	−	7.79423i	1.13691	−	0.656392i
$142$		0			0
$143$		0			0
$144$	−12.0000			−1.00000
$145$		−	8.66025i		−	0.719195i
$146$		0			0
$147$	−12.0000	−	1.73205i	−0.989743	−	0.142857i
$148$	8.00000	+	13.8564i	0.657596	+	1.13899i
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	−0.304216	−	0.952603i	$-0.598394\pi$
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	0.672870	+	0.739760i	$0.265061\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$	9.00000	+	15.5885i	0.727607	+	1.26025i
$154$		0			0
$155$	−3.00000	−	1.73205i	−0.240966	−	0.139122i
$156$		0			0
$157$	−1.50000	+	0.866025i	−0.119713	+	0.0691164i	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−1.50000	+	0.866025i	−0.119713	+	0.0691164i	0.438948	+	0.898513i	$0.355351\pi$
$158$		0			0
$159$	12.0000	−	20.7846i	0.951662	−	1.64833i
$160$		0			0
$161$	6.00000	+	6.92820i	0.472866	+	0.546019i
$162$		0			0
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$		0			0
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$		0			0
$171$	18.0000	−	10.3923i	1.37649	−	0.794719i
$172$	20.0000			1.52499
$173$	−1.50000	+	2.59808i	−0.114043	+	0.197528i	−0.917397	−	0.397974i	$-0.869713\pi$
$173$	−1.50000	+	2.59808i	−0.114043	+	0.197528i	0.803354	+	0.595502i	$0.203047\pi$
$174$		0			0
$175$	−2.50000	−	0.866025i	−0.188982	−	0.0654654i
$176$	−6.00000	+	3.46410i	−0.452267	+	0.261116i
$177$		0			0
$178$		0			0
$179$			15.5885i			1.16514i	0.812782	+	0.582568i	$0.197952\pi$
$179$			15.5885i			1.16514i	−0.812782	+	0.582568i	$0.802048\pi$
$180$	6.00000			0.447214
$181$			20.7846i			1.54491i	0.635071	+	0.772454i	$0.280971\pi$
$181$			20.7846i			1.54491i	−0.635071	+	0.772454i	$0.719029\pi$
$182$		0			0
$183$	−3.00000	−	5.19615i	−0.221766	−	0.384111i
$184$		0			0
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$		0			0
$187$	9.00000	+	5.19615i	0.658145	+	0.379980i
$188$	−18.0000			−1.31278
$189$	−13.5000	+	2.59808i	−0.981981	+	0.188982i
$190$		0			0
$191$	1.50000	+	0.866025i	0.108536	+	0.0626634i	0.553285	−	0.832992i	$-0.313374\pi$
$191$	1.50000	+	0.866025i	0.108536	+	0.0626634i	−0.444749	+	0.895655i	$0.646707\pi$
$192$	12.0000	+	6.92820i	0.866025	+	0.500000i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$		0			0
$195$		0			0
$196$	11.0000	+	8.66025i	0.785714	+	0.618590i
$197$			3.46410i			0.246807i	0.992357	+	0.123404i	$0.0393809\pi$
$197$			3.46410i			0.246807i	−0.992357	+	0.123404i	$0.960619\pi$
$198$		0			0
$199$			10.3923i			0.736691i	0.929689	+	0.368345i	$0.120076\pi$
$199$			10.3923i			0.736691i	−0.929689	+	0.368345i	$0.879924\pi$
$200$		0			0
$201$		−	13.8564i		−	0.977356i
$202$		0			0
$203$	7.50000	−	21.6506i	0.526397	−	1.51958i
$204$		−	20.7846i		−	1.45521i
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	9.00000	+	5.19615i	0.625543	+	0.361158i
$208$		0			0
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	−0.500000	−	0.866025i	−0.0344214	−	0.0596196i	0.848301	−	0.529514i	$-0.177626\pi$
$211$	−0.500000	−	0.866025i	−0.0344214	−	0.0596196i	−0.882723	+	0.469894i	$0.844292\pi$
$212$	−24.0000	+	13.8564i	−1.64833	+	0.951662i
$213$	−1.50000	+	2.59808i	−0.102778	+	0.178017i
$214$		0			0
$215$	−10.0000			−0.681994
$216$		0			0
$217$	−6.00000	−	6.92820i	−0.407307	−	0.470317i
$218$		0			0
$219$	7.50000	−	12.9904i	0.506803	−	0.877809i
$220$	3.00000	−	1.73205i	0.202260	−	0.116775i
$221$		0			0
$222$		0			0
$223$	−3.00000	−	1.73205i	−0.200895	−	0.115987i	0.396178	−	0.918174i	$-0.370336\pi$
$223$	−3.00000	−	1.73205i	−0.200895	−	0.115987i	−0.597073	+	0.802187i	$0.703670\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$	−24.0000			−1.58944
$229$	−24.0000	+	13.8564i	−1.58596	+	0.915657i	−0.592002	+	0.805936i	$0.701662\pi$
$229$	−24.0000	+	13.8564i	−1.58596	+	0.915657i	−0.993962	+	0.109721i	$0.965004\pi$
$230$		0			0
$231$	−6.00000	+	5.19615i	−0.394771	+	0.341882i
$232$		0			0
$233$		−	3.46410i		−	0.226941i	−0.993541	−	0.113470i	$-0.963803\pi$
$233$		−	3.46410i		−	0.226941i	0.993541	−	0.113470i	$-0.0361967\pi$
$234$		0			0
$235$	9.00000			0.587095
$236$		0			0
$237$	1.50000	−	0.866025i	0.0974355	−	0.0562544i
$238$		0			0
$239$	−7.50000	+	4.33013i	−0.485135	+	0.280093i	−0.722554	−	0.691315i	$-0.757032\pi$
$239$	−7.50000	+	4.33013i	−0.485135	+	0.280093i	0.237419	+	0.971407i	$0.423699\pi$
$240$	−6.00000	−	3.46410i	−0.387298	−	0.223607i
$241$	−9.00000	−	5.19615i	−0.579741	−	0.334714i	0.181289	−	0.983430i	$-0.441973\pi$
$241$	−9.00000	−	5.19615i	−0.579741	−	0.334714i	−0.761030	+	0.648716i	$0.775306\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$			6.92820i			0.443533i
$245$	−5.50000	−	4.33013i	−0.351382	−	0.276642i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−13.5000	+	7.79423i	−0.855528	+	0.493939i
$250$		0			0
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	15.0000	+	5.19615i	0.944911	+	0.327327i
$253$	6.00000			0.377217
$254$		0			0
$255$			10.3923i			0.650791i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	−4.00000	−	20.7846i	−0.248548	−	1.29149i
$260$		0			0
$261$		−	25.9808i		−	1.60817i
$262$		0			0
$263$	15.0000	+	8.66025i	0.924940	+	0.534014i	0.885208	−	0.465196i	$-0.154016\pi$
$263$	15.0000	+	8.66025i	0.924940	+	0.534014i	0.0397320	+	0.999210i	$0.487350\pi$
$264$		0			0
$265$	12.0000	−	6.92820i	0.737154	−	0.425596i
$266$		0			0
$267$	9.00000	+	5.19615i	0.550791	+	0.317999i
$268$	−8.00000	+	13.8564i	−0.488678	+	0.846415i
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$		0			0
$271$		−	17.3205i		−	1.05215i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$		−	17.3205i		−	1.05215i	0.850439	−	0.526073i	$-0.176336\pi$
$272$	−12.0000	+	20.7846i	−0.727607	+	1.26025i
$273$		0			0
$274$		0			0
$275$	−1.50000	+	0.866025i	−0.0904534	+	0.0522233i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$	−9.00000	−	5.19615i	−0.538816	−	0.311086i
$280$		0			0
$281$	−19.5000	−	11.2583i	−1.16327	−	0.671616i	−0.211186	−	0.977446i	$-0.567733\pi$
$281$	−19.5000	−	11.2583i	−1.16327	−	0.671616i	−0.952086	+	0.305830i	$0.901066\pi$
$282$		0			0
$283$	10.5000	−	6.06218i	0.624160	−	0.360359i	−0.154327	−	0.988020i	$-0.549321\pi$
$283$	10.5000	−	6.06218i	0.624160	−	0.360359i	0.778487	+	0.627661i	$0.215988\pi$
$284$	3.00000	−	1.73205i	0.178017	−	0.102778i
$285$	12.0000			0.710819
$286$		0			0
$287$	−12.0000	+	10.3923i	−0.708338	+	0.613438i
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$	−1.50000	−	2.59808i	−0.0879316	−	0.152302i
$292$	−15.0000	+	8.66025i	−0.877809	+	0.506803i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.50000	+	7.79423i	−0.261116	+	0.452267i
$298$		0			0
$299$		0			0
$300$	3.00000	+	1.73205i	0.173205	+	0.100000i
$301$	−25.0000	−	8.66025i	−1.44098	−	0.499169i
$302$		0			0
$303$		0			0
$304$	24.0000	+	13.8564i	1.37649	+	0.794719i
$305$		−	3.46410i		−	0.198354i
$306$		0			0
$307$		−	3.46410i		−	0.197707i	−0.995102	−	0.0988534i	$-0.968483\pi$
$307$		−	3.46410i		−	0.197707i	0.995102	−	0.0988534i	$-0.0315175\pi$
$308$	9.00000	−	1.73205i	0.512823	−	0.0986928i
$309$	21.0000			1.19465
$310$		0			0
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$		0			0
$313$	13.5000	+	7.79423i	0.763065	+	0.440556i	0.830395	−	0.557175i	$-0.188115\pi$
$313$	13.5000	+	7.79423i	0.763065	+	0.440556i	−0.0673300	+	0.997731i	$0.521448\pi$
$314$		0			0
$315$	−7.50000	−	2.59808i	−0.422577	−	0.146385i
$316$	−2.00000			−0.112509
$317$	3.00000	+	1.73205i	0.168497	+	0.0972817i	0.581877	−	0.813277i	$-0.302319\pi$
$317$	3.00000	+	1.73205i	0.168497	+	0.0972817i	−0.413380	+	0.910559i	$0.635652\pi$
$318$		0			0
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$		−	41.5692i		−	2.31297i
$324$	18.0000			1.00000
$325$		0			0
$326$		0			0
$327$	−16.5000	−	9.52628i	−0.912452	−	0.526804i
$328$		0			0
$329$	22.5000	+	7.79423i	1.24047	+	0.429710i
$330$		0			0
$331$	8.50000	−	14.7224i	0.467202	−	0.809218i	−0.532096	−	0.846684i	$-0.678595\pi$
$331$	8.50000	−	14.7224i	0.467202	−	0.809218i	0.999298	+	0.0374662i	$0.0119287\pi$
$332$	18.0000			0.987878
$333$	−12.0000	−	20.7846i	−0.657596	−	1.13899i
$334$		0			0
$335$	4.00000	−	6.92820i	0.218543	−	0.378528i
$336$	−12.0000	−	13.8564i	−0.654654	−	0.755929i
$337$	13.0000	+	22.5167i	0.708155	+	1.22656i	0.965541	+	0.260252i	$0.0838056\pi$
$337$	13.0000	+	22.5167i	0.708155	+	1.22656i	−0.257386	+	0.966309i	$0.582861\pi$
$338$		0			0
$339$	−18.0000			−0.977626
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$		0			0
$347$	24.0000	−	13.8564i	1.28839	−	0.743851i	0.310021	−	0.950730i	$-0.399664\pi$
$347$	24.0000	−	13.8564i	1.28839	−	0.743851i	0.978367	+	0.206879i	$0.0663306\pi$
$348$	−15.0000	+	25.9808i	−0.804084	+	1.39272i
$349$	−15.0000	−	8.66025i	−0.802932	−	0.463573i	0.0415636	−	0.999136i	$-0.486766\pi$
$349$	−15.0000	−	8.66025i	−0.802932	−	0.463573i	−0.844495	+	0.535563i	$0.820099\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	0.438733	+	0.898617i	$0.355427\pi$
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	−0.997592	+	0.0693543i	$0.977906\pi$
$354$		0			0
$355$	−1.50000	+	0.866025i	−0.0796117	+	0.0459639i
$356$	−6.00000	−	10.3923i	−0.317999	−	0.550791i
$357$	−9.00000	+	25.9808i	−0.476331	+	1.37505i
$358$		0			0
$359$			31.1769i			1.64545i	0.568436	+	0.822727i	$0.307549\pi$
$359$			31.1769i			1.64545i	−0.568436	+	0.822727i	$0.692451\pi$
$360$		0			0
$361$	−29.0000			−1.52632
$362$		0			0
$363$		−	13.8564i		−	0.727273i
$364$		0			0
$365$	7.50000	−	4.33013i	0.392568	−	0.226649i
$366$		0			0
$367$	−9.00000	−	5.19615i	−0.469796	−	0.271237i	0.246358	−	0.969179i	$-0.420766\pi$
$367$	−9.00000	−	5.19615i	−0.469796	−	0.271237i	−0.716154	+	0.697942i	$0.754099\pi$
$368$			13.8564i			0.722315i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$		0			0
$371$	36.0000	−	6.92820i	1.86903	−	0.359694i
$372$	6.00000	+	10.3923i	0.311086	+	0.538816i
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$		0			0
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−23.0000			−1.18143			−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000			−1.18143			−0.590715	+	0.806880i	$0.701154\pi$
$380$	−12.0000	−	6.92820i	−0.615587	−	0.355409i
$381$	3.00000	+	1.73205i	0.153695	+	0.0887357i
$382$		0			0
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	0.608290	−	0.793715i	$-0.291856\pi$
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	−0.991522	+	0.129937i	$0.958522\pi$
$384$		0			0
$385$	−4.50000	+	0.866025i	−0.229341	+	0.0441367i
$386$		0			0
$387$	−30.0000			−1.52499
$388$			3.46410i			0.175863i
$389$	−28.5000	−	16.4545i	−1.44501	−	0.834275i	−0.446830	−	0.894619i	$-0.647447\pi$
$389$	−28.5000	−	16.4545i	−1.44501	−	0.834275i	−0.998178	+	0.0603436i	$0.980780\pi$
$390$		0			0
$391$	18.0000	−	10.3923i	0.910299	−	0.525561i
$392$		0			0
$393$			10.3923i			0.524222i
$394$		0			0
$395$	1.00000			0.0503155
$396$	9.00000	−	5.19615i	0.452267	−	0.261116i
$397$			29.4449i			1.47780i	0.673818	+	0.738898i	$0.264653\pi$
$397$			29.4449i			1.47780i	−0.673818	+	0.738898i	$0.735347\pi$
$398$		0			0
$399$	30.0000	+	10.3923i	1.50188	+	0.520266i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−22.5000	+	12.9904i	−1.12360	+	0.648709i	−0.942317	−	0.334723i	$-0.891357\pi$
$401$	−22.5000	+	12.9904i	−1.12360	+	0.648709i	−0.181280	+	0.983432i	$0.558024\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−9.00000			−0.447214
$406$		0			0
$407$	−12.0000	−	6.92820i	−0.594818	−	0.343418i
$408$		0			0
$409$	9.00000	−	5.19615i	0.445021	−	0.256933i	−0.260704	−	0.965419i	$-0.583955\pi$
$409$	9.00000	−	5.19615i	0.445021	−	0.256933i	0.705725	+	0.708486i	$0.250621\pi$
$410$		0			0
$411$	15.0000	+	25.9808i	0.739895	+	1.28154i
$412$	−21.0000	−	12.1244i	−1.03460	−	0.597324i
$413$		0			0
$414$		0			0
$415$	−9.00000			−0.441793
$416$		0			0
$417$	30.0000			1.46911
$418$		0			0
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$	6.00000	+	6.92820i	0.292770	+	0.338062i
$421$	−11.5000	+	19.9186i	−0.560476	+	0.970772i	0.436979	+	0.899472i	$0.356048\pi$
$421$	−11.5000	+	19.9186i	−0.560476	+	0.970772i	−0.997455	+	0.0713008i	$0.977285\pi$
$422$		0			0
$423$	27.0000			1.31278
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	3.00000	−	8.66025i	0.145180	−	0.419099i
$428$	−12.0000	+	6.92820i	−0.580042	+	0.334887i
$429$		0			0
$430$		0			0
$431$		−	31.1769i		−	1.50174i	−0.660451	−	0.750870i	$-0.729635\pi$
$431$		−	31.1769i		−	1.50174i	0.660451	−	0.750870i	$-0.270365\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$		−	6.92820i		−	0.332948i	−0.986046	−	0.166474i	$-0.946762\pi$
$433$		−	6.92820i		−	0.332948i	0.986046	−	0.166474i	$-0.0532382\pi$
$434$		0			0
$435$	7.50000	−	12.9904i	0.359597	−	0.622841i
$436$	11.0000	+	19.0526i	0.526804	+	0.912452i
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$		0			0
$439$	−3.00000	−	1.73205i	−0.143182	−	0.0826663i	0.426698	−	0.904394i	$-0.359677\pi$
$439$	−3.00000	−	1.73205i	−0.143182	−	0.0826663i	−0.569880	+	0.821728i	$0.693010\pi$
$440$		0			0
$441$	−16.5000	−	12.9904i	−0.785714	−	0.618590i
$442$		0			0
$443$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$443$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$444$			27.7128i			1.31519i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$	9.00000			0.425685
$448$	4.00000	+	20.7846i	0.188982	+	0.981981i
$449$			5.19615i			0.245222i	0.992455	+	0.122611i	$0.0391267\pi$
$449$			5.19615i			0.245222i	−0.992455	+	0.122611i	$0.960873\pi$
$450$		0			0
$451$			10.3923i			0.489355i
$452$	18.0000	+	10.3923i	0.846649	+	0.488813i
$453$	12.0000	−	6.92820i	0.563809	−	0.325515i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.00000	+	13.8564i	−0.374224	+	0.648175i	−0.990211	−	0.139581i	$-0.955424\pi$
$457$	−8.00000	+	13.8564i	−0.374224	+	0.648175i	0.615986	+	0.787757i	$0.288758\pi$
$458$		0			0
$459$			31.1769i			1.45521i
$460$		−	6.92820i		−	0.323029i
$461$	12.0000	−	20.7846i	0.558896	−	0.968036i	−0.438693	−	0.898637i	$-0.644559\pi$
$461$	12.0000	−	20.7846i	0.558896	−	0.968036i	0.997589	−	0.0693989i	$-0.0221081\pi$
$462$		0			0
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	30.0000	−	17.3205i	1.39272	−	0.804084i
$465$	−3.00000	−	5.19615i	−0.139122	−	0.240966i
$466$		0			0
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$		0			0
$469$	16.0000	−	13.8564i	0.738811	−	0.639829i
$470$		0			0
$471$	−3.00000			−0.138233
$472$		0			0
$473$	−15.0000	+	8.66025i	−0.689701	+	0.398199i
$474$		0			0
$475$	6.00000	+	3.46410i	0.275299	+	0.158944i
$476$	24.0000	−	20.7846i	1.10004	−	0.952661i
$477$	36.0000	−	20.7846i	1.64833	−	0.951662i
$478$		0			0
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	−0.0814184	−	0.996680i	$-0.525945\pi$
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	0.903859	−	0.427830i	$-0.140722\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	3.00000	+	15.5885i	0.136505	+	0.709299i
$484$	−8.00000	+	13.8564i	−0.363636	+	0.629837i
$485$		−	1.73205i		−	0.0786484i
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$		0			0
$489$	21.0000	+	12.1244i	0.949653	+	0.548282i
$490$		0			0
$491$	3.00000	−	1.73205i	0.135388	−	0.0781664i	−0.430776	−	0.902459i	$-0.641760\pi$
$491$	3.00000	−	1.73205i	0.135388	−	0.0781664i	0.566164	+	0.824292i	$0.308427\pi$
$492$	18.0000	−	10.3923i	0.811503	−	0.468521i
$493$	−45.0000	−	25.9808i	−2.02670	−	1.17011i
$494$		0			0
$495$	−4.50000	+	2.59808i	−0.202260	+	0.116775i
$496$		−	13.8564i		−	0.622171i
$497$	−4.50000	+	0.866025i	−0.201853	+	0.0388465i
$498$		0			0
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$		0			0
$502$		0			0
$503$	39.0000			1.73892			0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000			1.73892			0.869462	+	0.494000i	$0.164466\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−19.5000	+	11.2583i	−0.866025	+	0.500000i
$508$	−2.00000	−	3.46410i	−0.0887357	−	0.153695i
$509$	21.0000	+	36.3731i	0.930809	+	1.61221i	0.781943	+	0.623350i	$0.214229\pi$
$509$	21.0000	+	36.3731i	0.930809	+	1.61221i	0.148866	+	0.988857i	$0.452438\pi$
$510$		0			0
$511$	22.5000	−	4.33013i	0.995341	−	0.191554i
$512$		0			0
$513$	36.0000			1.58944
$514$		0			0
$515$	10.5000	+	6.06218i	0.462685	+	0.267131i
$516$	30.0000	+	17.3205i	1.32068	+	0.762493i
$517$	13.5000	−	7.79423i	0.593729	−	0.342790i
$518$		0			0
$519$	−4.50000	+	2.59808i	−0.197528	+	0.114043i
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$			12.1244i			0.530161i	0.964226	+	0.265081i	$0.0853985\pi$
$523$			12.1244i			0.530161i	−0.964226	+	0.265081i	$0.914601\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$	−3.00000	−	3.46410i	−0.130931	−	0.151186i
$526$		0			0
$527$	−18.0000	+	10.3923i	−0.784092	+	0.452696i
$528$	−12.0000			−0.522233
$529$	−5.50000	+	9.52628i	−0.239130	+	0.414186i
$530$		0			0
$531$		0			0
$532$	−24.0000	−	27.7128i	−1.04053	−	1.20150i
$533$		0			0
$534$		0			0
$535$	6.00000	−	3.46410i	0.259403	−	0.149766i
$536$		0			0
$537$	−13.5000	+	23.3827i	−0.582568	+	1.00904i
$538$		0			0
$539$	−12.0000	−	1.73205i	−0.516877	−	0.0746047i
$540$	9.00000	+	5.19615i	0.387298	+	0.223607i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$		0			0
$543$	−18.0000	+	31.1769i	−0.772454	+	1.33793i
$544$		0			0
$545$	−5.50000	−	9.52628i	−0.235594	−	0.408061i
$546$		0			0
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	−0.975976	−	0.217880i	$-0.930086\pi$
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	0.676677	+	0.736280i	$0.263419\pi$
$548$		−	34.6410i		−	1.47979i
$549$		−	10.3923i		−	0.443533i
$550$		0			0
$551$	−30.0000	+	51.9615i	−1.27804	+	2.21364i
$552$		0			0
$553$	2.50000	+	0.866025i	0.106311	+	0.0368271i
$554$		0			0
$555$		−	13.8564i		−	0.588172i
$556$	−30.0000	−	17.3205i	−1.27228	−	0.734553i
$557$		−	10.3923i		−	0.440336i	−0.975462	−	0.220168i	$-0.929339\pi$
$557$		−	10.3923i		−	0.440336i	0.975462	−	0.220168i	$-0.0706606\pi$
$558$		0			0
$559$		0			0
$560$	−2.00000	−	10.3923i	−0.0845154	−	0.439155i
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$		0			0
$563$	7.50000	+	12.9904i	0.316087	+	0.547479i	0.979668	−	0.200625i	$-0.0642974\pi$
$563$	7.50000	+	12.9904i	0.316087	+	0.547479i	−0.663581	+	0.748105i	$0.730964\pi$
$564$	−27.0000	−	15.5885i	−1.13691	−	0.656392i
$565$	−9.00000	−	5.19615i	−0.378633	−	0.218604i
$566$		0			0
$567$	−22.5000	−	7.79423i	−0.944911	−	0.327327i
$568$		0			0
$569$	−31.5000	−	18.1865i	−1.32055	−	0.762419i	−0.336733	−	0.941600i	$-0.609322\pi$
$569$	−31.5000	−	18.1865i	−1.32055	−	0.762419i	−0.983816	+	0.179181i	$0.942655\pi$
$570$		0			0
$571$	6.50000	+	11.2583i	0.272017	+	0.471146i	0.969378	−	0.245573i	$-0.0789761\pi$
$571$	6.50000	+	11.2583i	0.272017	+	0.471146i	−0.697362	+	0.716720i	$0.745643\pi$
$572$		0			0
$573$	1.50000	+	2.59808i	0.0626634	+	0.108536i
$574$		0			0
$575$			3.46410i			0.144463i
$576$	12.0000	+	20.7846i	0.500000	+	0.866025i
$577$			39.8372i			1.65844i	0.558920	+	0.829222i	$0.311216\pi$
$577$			39.8372i			1.65844i	−0.558920	+	0.829222i	$0.688784\pi$
$578$		0			0
$579$		−	6.92820i		−	0.287926i
$580$	−15.0000	+	8.66025i	−0.622841	+	0.359597i
$581$	−22.5000	−	7.79423i	−0.933457	−	0.323359i
$582$		0			0
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	−0.715226	−	0.698893i	$-0.753676\pi$
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	0.962872	+	0.269957i	$0.0870095\pi$
$588$	9.00000	+	22.5167i	0.371154	+	0.928571i
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	16.0000	−	27.7128i	0.657596	−	1.13899i
$593$	3.00000			0.123195			0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000			0.123195			0.0615976	+	0.998101i	$0.480380\pi$
$594$		0			0
$595$	−12.0000	+	10.3923i	−0.491952	+	0.426043i
$596$	−9.00000	−	5.19615i	−0.368654	−	0.212843i
$597$	−9.00000	+	15.5885i	−0.368345	+	0.637993i
$598$		0			0
$599$	−9.00000	+	5.19615i	−0.367730	+	0.212309i	−0.672466	−	0.740128i	$-0.734765\pi$
$599$	−9.00000	+	5.19615i	−0.367730	+	0.212309i	0.304736	+	0.952437i	$0.401432\pi$
$600$		0			0
$601$	−3.00000	−	1.73205i	−0.122373	−	0.0706518i	0.437564	−	0.899187i	$-0.355841\pi$
$601$	−3.00000	−	1.73205i	−0.122373	−	0.0706518i	−0.559937	+	0.828535i	$0.689175\pi$
$602$		0			0
$603$	12.0000	−	20.7846i	0.488678	−	0.846415i
$604$	−16.0000			−0.651031
$605$	4.00000	−	6.92820i	0.162623	−	0.281672i
$606$		0			0
$607$	−1.50000	+	0.866025i	−0.0608831	+	0.0351509i	−0.530133	−	0.847915i	$-0.677858\pi$
$607$	−1.50000	+	0.866025i	−0.0608831	+	0.0351509i	0.469249	+	0.883066i	$0.344525\pi$
$608$		0			0
$609$	30.0000	−	25.9808i	1.21566	−	1.05279i
$610$		0			0
$611$		0			0
$612$	18.0000	−	31.1769i	0.727607	−	1.26025i
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$		0			0
$615$	−9.00000	+	5.19615i	−0.362915	+	0.209529i
$616$		0			0
$617$	21.0000	−	12.1244i	0.845428	−	0.488108i	−0.0136775	−	0.999906i	$-0.504354\pi$
$617$	21.0000	−	12.1244i	0.845428	−	0.488108i	0.859106	+	0.511798i	$0.171020\pi$
$618$		0			0
$619$	−24.0000	−	13.8564i	−0.964641	−	0.556936i	−0.0670430	−	0.997750i	$-0.521356\pi$
$619$	−24.0000	−	13.8564i	−0.964641	−	0.556936i	−0.897598	+	0.440814i	$0.854690\pi$
$620$			6.92820i			0.278243i
$621$	9.00000	+	15.5885i	0.361158	+	0.625543i
$622$		0			0
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	18.0000	−	10.3923i	0.718851	−	0.415029i
$628$	3.00000	+	1.73205i	0.119713	+	0.0691164i
$629$	−48.0000			−1.91389
$630$		0			0
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$		0			0
$633$		−	1.73205i		−	0.0688428i
$634$		0			0
$635$	1.00000	+	1.73205i	0.0396838	+	0.0687343i
$636$	−48.0000			−1.90332
$637$		0			0
$638$		0			0
$639$	−4.50000	+	2.59808i	−0.178017	+	0.102778i
$640$		0			0
$641$	18.0000	+	10.3923i	0.710957	+	0.410471i	0.811415	−	0.584470i	$-0.198698\pi$
$641$	18.0000	+	10.3923i	0.710957	+	0.410471i	−0.100458	+	0.994941i	$0.532031\pi$
$642$		0			0
$643$	13.5000	−	7.79423i	0.532388	−	0.307374i	−0.209600	−	0.977787i	$-0.567216\pi$
$643$	13.5000	−	7.79423i	0.532388	−	0.307374i	0.741988	+	0.670413i	$0.233883\pi$
$644$	6.00000	−	17.3205i	0.236433	−	0.682524i
$645$	−15.0000	−	8.66025i	−0.590624	−	0.340997i
$646$		0			0
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−3.00000	−	15.5885i	−0.117579	−	0.610960i
$652$	−14.0000	−	24.2487i	−0.548282	−	0.949653i
$653$	3.00000	−	1.73205i	0.117399	−	0.0677804i	−0.440151	−	0.897924i	$-0.645075\pi$
$653$	3.00000	−	1.73205i	0.117399	−	0.0677804i	0.557550	+	0.830144i	$0.311742\pi$
$654$		0			0
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	−24.0000			−0.937043
$657$	22.5000	−	12.9904i	0.877809	−	0.506803i
$658$		0			0
$659$	−21.0000	−	12.1244i	−0.818044	−	0.472298i	0.0316976	−	0.999498i	$-0.489909\pi$
$659$	−21.0000	−	12.1244i	−0.818044	−	0.472298i	−0.849741	+	0.527200i	$0.823242\pi$
$660$	6.00000			0.233550
$661$	21.0000	−	12.1244i	0.816805	−	0.471583i	−0.0325082	−	0.999471i	$-0.510350\pi$
$661$	21.0000	−	12.1244i	0.816805	−	0.471583i	0.849314	+	0.527889i	$0.177016\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.0000	+	13.8564i	0.465340	+	0.537328i
$666$		0			0
$667$	−30.0000			−1.16160
$668$		0			0
$669$	−3.00000	−	5.19615i	−0.115987	−	0.200895i
$670$		0			0
$671$	−3.00000	−	5.19615i	−0.115814	−	0.200595i
$672$		0			0
$673$	13.0000	−	22.5167i	0.501113	−	0.867953i	−0.498886	−	0.866668i	$-0.666257\pi$
$673$	13.0000	−	22.5167i	0.501113	−	0.867953i	0.999999	−	0.00128586i	$-0.000409302\pi$
$674$		0			0
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	26.0000			1.00000
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$	1.50000	−	4.33013i	0.0575647	−	0.166175i
$680$		0			0
$681$	−18.0000	+	10.3923i	−0.689761	+	0.398234i
$682$		0			0
$683$			17.3205i			0.662751i	0.943499	+	0.331375i	$0.107513\pi$
$683$			17.3205i			0.662751i	−0.943499	+	0.331375i	$0.892487\pi$
$684$	−36.0000	−	20.7846i	−1.37649	−	0.794719i
$685$			17.3205i			0.661783i
$686$		0			0
$687$	−48.0000			−1.83131
$688$	−20.0000	−	34.6410i	−0.762493	−	1.32068i
$689$		0			0
$690$		0			0
$691$	−18.0000	−	10.3923i	−0.684752	−	0.395342i	0.116891	−	0.993145i	$-0.462707\pi$
$691$	−18.0000	−	10.3923i	−0.684752	−	0.395342i	−0.801643	+	0.597803i	$0.796041\pi$
$692$	6.00000			0.228086
$693$	−13.5000	+	2.59808i	−0.512823	+	0.0986928i
$694$		0			0
$695$	15.0000	+	8.66025i	0.568982	+	0.328502i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	1.00000	+	5.19615i	0.0377964	+	0.196396i
$701$			13.8564i			0.523349i	0.965156	+	0.261675i	$0.0842747\pi$
$701$			13.8564i			0.523349i	−0.965156	+	0.261675i	$0.915725\pi$
$702$		0			0
$703$			55.4256i			2.09042i
$704$	12.0000	+	6.92820i	0.452267	+	0.261116i
$705$	13.5000	+	7.79423i	0.508439	+	0.293548i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	−0.324104	−	0.946021i	$-0.605063\pi$
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	0.981331	−	0.192328i	$-0.0616038\pi$
$710$		0			0
$711$	3.00000			0.112509
$712$		0			0
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$		0			0
$716$	27.0000	−	15.5885i	1.00904	−	0.582568i
$717$	−15.0000			−0.560185
$718$		0			0
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$	−6.00000	−	10.3923i	−0.223607	−	0.387298i
$721$	21.0000	+	24.2487i	0.782081	+	0.903069i
$722$		0			0
$723$	−9.00000	−	15.5885i	−0.334714	−	0.579741i
$724$	36.0000	−	20.7846i	1.33793	−	0.772454i
$725$	7.50000	−	4.33013i	0.278543	−	0.160817i
$726$		0			0
$727$	−1.50000	−	0.866025i	−0.0556319	−	0.0321191i	0.471926	−	0.881638i	$-0.343559\pi$
$727$	−1.50000	−	0.866025i	−0.0556319	−	0.0321191i	−0.527558	+	0.849519i	$0.676892\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−30.0000	+	51.9615i	−1.10959	+	1.92187i
$732$	−6.00000	+	10.3923i	−0.221766	+	0.384111i
$733$	−22.5000	+	12.9904i	−0.831056	+	0.479811i	−0.854214	−	0.519921i	$-0.825961\pi$
$733$	−22.5000	+	12.9904i	−0.831056	+	0.479811i	0.0231578	+	0.999732i	$0.492628\pi$
$734$		0			0
$735$	−4.50000	−	11.2583i	−0.165985	−	0.415270i
$736$		0			0
$737$		−	13.8564i		−	0.510407i
$738$		0			0
$739$	−31.0000			−1.14035			−0.570177	−	0.821522i	$-0.693125\pi$
$739$	−31.0000			−1.14035			−0.570177	+	0.821522i	$0.693125\pi$
$740$	−8.00000	+	13.8564i	−0.294086	+	0.509372i
$741$		0			0
$742$		0			0
$743$	−33.0000	+	19.0526i	−1.21065	+	0.698971i	−0.962901	−	0.269853i	$-0.913025\pi$
$743$	−33.0000	+	19.0526i	−1.21065	+	0.698971i	−0.247751	+	0.968824i	$0.579692\pi$
$744$		0			0
$745$	4.50000	+	2.59808i	0.164867	+	0.0951861i
$746$		0			0
$747$	−27.0000			−0.987878
$748$		−	20.7846i		−	0.759961i
$749$	18.0000	−	3.46410i	0.657706	−	0.126576i
$750$		0			0
$751$	2.50000	+	4.33013i	0.0912263	+	0.158009i	0.908027	−	0.418911i	$-0.137588\pi$
$751$	2.50000	+	4.33013i	0.0912263	+	0.158009i	−0.816801	+	0.576919i	$0.804255\pi$
$752$	18.0000	+	31.1769i	0.656392	+	1.13691i
$753$	27.0000	+	15.5885i	0.983935	+	0.568075i
$754$		0			0
$755$	8.00000			0.291150
$756$	18.0000	+	20.7846i	0.654654	+	0.755929i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$		0			0
$759$	9.00000	+	5.19615i	0.326679	+	0.188608i
$760$		0			0
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$		0			0
$763$	−5.50000	−	28.5788i	−0.199113	−	1.03462i
$764$		−	3.46410i		−	0.125327i
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$		0			0
$767$		0			0
$768$		−	27.7128i		−	1.00000i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$			5.19615i			0.187135i
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	9.00000			0.323708			0.161854	−	0.986815i	$-0.448253\pi$
$773$	9.00000			0.323708			0.161854	+	0.986815i	$0.448253\pi$
$774$		0			0
$775$		−	3.46410i		−	0.124434i
$776$		0			0
$777$	12.0000	−	34.6410i	0.430498	−	1.24274i
$778$		0			0
$779$	36.0000	−	20.7846i	1.28983	−	0.744686i
$780$		0			0
$781$	−1.50000	+	2.59808i	−0.0536742	+	0.0929665i
$782$		0			0
$783$	22.5000	−	38.9711i	0.804084	−	1.39272i
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	−1.50000	−	0.866025i	−0.0535373	−	0.0309098i
$786$		0			0
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.221162	−	0.975237i	$-0.429015\pi$
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.955161	+	0.296087i	$0.0956817\pi$
$788$	6.00000	−	3.46410i	0.213741	−	0.123404i
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$		0			0
$791$	−18.0000	−	20.7846i	−0.640006	−	0.739016i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	24.0000			0.851192
$796$	18.0000	−	10.3923i	0.637993	−	0.368345i
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	0.914255	−	0.405140i	$-0.132777\pi$
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	−0.807989	+	0.589197i	$0.799444\pi$
$798$		0			0
$799$	27.0000	−	46.7654i	0.955191	−	1.65444i
$800$		0			0
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$		0			0
$803$	7.50000	−	12.9904i	0.264669	−	0.458421i
$804$	−24.0000	+	13.8564i	−0.846415	+	0.488678i
$805$	−3.00000	+	8.66025i	−0.105736	+	0.305234i
$806$		0			0
$807$	−36.0000	−	20.7846i	−1.26726	−	0.731653i
$808$		0			0
$809$			6.92820i			0.243583i	0.992556	+	0.121791i	$0.0388639\pi$
$809$			6.92820i			0.243583i	−0.992556	+	0.121791i	$0.961136\pi$
$810$		0			0
$811$			55.4256i			1.94626i	0.230263	+	0.973128i	$0.426041\pi$
$811$			55.4256i			1.94626i	−0.230263	+	0.973128i	$0.573959\pi$
$812$	−45.0000	+	8.66025i	−1.57919	+	0.303915i
$813$	15.0000	−	25.9808i	0.526073	−	0.911185i
$814$		0			0
$815$	7.00000	+	12.1244i	0.245199	+	0.424698i
$816$	−36.0000	+	20.7846i	−1.26025	+	0.727607i
$817$	60.0000	+	34.6410i	2.09913	+	1.21194i
$818$		0			0
$819$		0			0
$820$	12.0000			0.419058
$821$	12.0000	+	6.92820i	0.418803	+	0.241796i	0.694565	−	0.719430i	$-0.255597\pi$
$821$	12.0000	+	6.92820i	0.418803	+	0.241796i	−0.275762	+	0.961226i	$0.588930\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		0			0
$825$	−3.00000			−0.104447
$826$		0			0
$827$			34.6410i			1.20459i	0.798275	+	0.602293i	$0.205746\pi$
$827$			34.6410i			1.20459i	−0.798275	+	0.602293i	$0.794254\pi$
$828$		−	20.7846i		−	0.722315i
$829$			45.0333i			1.56407i	0.623233	+	0.782036i	$0.285819\pi$
$829$			45.0333i			1.56407i	−0.623233	+	0.782036i	$0.714181\pi$
$830$		0			0
$831$	15.0000	−	8.66025i	0.520344	−	0.300421i
$832$		0			0
$833$	−39.0000	+	15.5885i	−1.35127	+	0.540108i
$834$		0			0
$835$		0			0
$836$	−24.0000			−0.830057
$837$	−9.00000	−	15.5885i	−0.311086	−	0.538816i
$838$		0			0
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	0.0705865	+	0.997506i	$0.477513\pi$
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	−0.899158	+	0.437623i	$0.855820\pi$
$840$		0			0
$841$	23.0000	+	39.8372i	0.793103	+	1.37370i
$842$		0			0
$843$	−19.5000	−	33.7750i	−0.671616	−	1.16327i
$844$	−1.00000	+	1.73205i	−0.0344214	+	0.0596196i
$845$	−13.0000			−0.447214
$846$		0			0
$847$	16.0000	−	13.8564i	0.549767	−	0.476112i
$848$	48.0000	+	27.7128i	1.64833	+	0.951662i
$849$	21.0000			0.720718
$850$		0			0
$851$	−24.0000	+	13.8564i	−0.822709	+	0.474991i
$852$	6.00000			0.205557
$853$	−18.0000	−	10.3923i	−0.616308	−	0.355826i	0.159122	−	0.987259i	$-0.449134\pi$
$853$	−18.0000	−	10.3923i	−0.616308	−	0.355826i	−0.775430	+	0.631433i	$0.782467\pi$
$854$		0			0
$855$	18.0000	+	10.3923i	0.615587	+	0.355409i
$856$		0			0
$857$	25.5000	−	44.1673i	0.871063	−	1.50873i	0.0101655	−	0.999948i	$-0.496764\pi$
$857$	25.5000	−	44.1673i	0.871063	−	1.50873i	0.860898	−	0.508778i	$-0.169903\pi$
$858$		0			0
$859$	−6.00000	+	3.46410i	−0.204717	+	0.118194i	−0.598854	−	0.800858i	$-0.704377\pi$
$859$	−6.00000	+	3.46410i	−0.204717	+	0.118194i	0.394137	+	0.919052i	$0.371044\pi$
$860$	10.0000	+	17.3205i	0.340997	+	0.590624i
$861$	−27.0000	+	5.19615i	−0.920158	+	0.177084i
$862$		0			0
$863$			55.4256i			1.88671i	0.331785	+	0.943355i	$0.392349\pi$
$863$			55.4256i			1.88671i	−0.331785	+	0.943355i	$0.607651\pi$
$864$		0			0
$865$	−3.00000			−0.102003
$866$		0			0
$867$	28.5000	+	16.4545i	0.967911	+	0.558824i
$868$	−6.00000	+	17.3205i	−0.203653	+	0.587896i
$869$	1.50000	−	0.866025i	0.0508840	−	0.0293779i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		−	5.19615i		−	0.175863i
$874$		0			0
$875$	−0.500000	−	2.59808i	−0.0169031	−	0.0878310i
$876$	−30.0000			−1.01361
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$		0			0
$879$		−	15.5885i		−	0.525786i
$880$	−6.00000	−	3.46410i	−0.202260	−	0.116775i
$881$	36.0000			1.21287			0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000			1.21287			0.606435	+	0.795133i	$0.292599\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$	1.00000	+	5.19615i	0.0335389	+	0.174273i
$890$		0			0
$891$	−13.5000	+	7.79423i	−0.452267	+	0.261116i
$892$			6.92820i			0.231973i
$893$	−54.0000	−	31.1769i	−1.80704	−	1.04330i
$894$		0			0
$895$	−13.5000	+	7.79423i	−0.451255	+	0.260532i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	30.0000			1.00056
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$		−	83.1384i		−	2.76974i
$902$		0			0
$903$	−30.0000	−	34.6410i	−0.998337	−	1.15278i
$904$		0			0
$905$	−18.0000	+	10.3923i	−0.598340	+	0.345452i
$906$		0			0
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$	24.0000			0.796468
$909$		0			0
$910$		0			0
$911$	43.5000	+	25.1147i	1.44122	+	0.832088i	0.997931	−	0.0642908i	$-0.0204785\pi$
$911$	43.5000	+	25.1147i	1.44122	+	0.832088i	0.443288	+	0.896379i	$0.353812\pi$
$912$	24.0000	+	41.5692i	0.794719	+	1.37649i
$913$	−13.5000	+	7.79423i	−0.446785	+	0.257951i
$914$		0			0
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	48.0000	+	27.7128i	1.58596	+	0.915657i
$917$	−12.0000	+	10.3923i	−0.396275	+	0.343184i
$918$		0			0
$919$	19.0000			0.626752			0.313376	−	0.949629i	$-0.398540\pi$
$919$	19.0000			0.626752			0.313376	+	0.949629i	$0.398540\pi$
$920$		0			0
$921$	3.00000	−	5.19615i	0.0988534	−	0.171219i
$922$		0			0
$923$		0			0
$924$	15.0000	+	5.19615i	0.493464	+	0.170941i
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$		0			0
$927$	31.5000	+	18.1865i	1.03460	+	0.597324i
$928$		0			0
$929$	24.0000	−	41.5692i	0.787414	−	1.36384i	−0.140132	−	0.990133i	$-0.544753\pi$
$929$	24.0000	−	41.5692i	0.787414	−	1.36384i	0.927546	−	0.373709i	$-0.121914\pi$
$930$		0			0
$931$	18.0000	+	45.0333i	0.589926	+	1.47591i
$932$	−6.00000	+	3.46410i	−0.196537	+	0.113470i
$933$			31.1769i			1.02069i
$934$		0			0
$935$			10.3923i			0.339865i
$936$		0			0
$937$		−	48.4974i		−	1.58434i	−0.610299	−	0.792171i	$-0.708951\pi$
$937$		−	48.4974i		−	1.58434i	0.610299	−	0.792171i	$-0.291049\pi$
$938$		0			0
$939$	13.5000	+	23.3827i	0.440556	+	0.763065i
$940$	−9.00000	−	15.5885i	−0.293548	−	0.508439i
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	−0.930553	−	0.366157i	$-0.880673\pi$
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	0.148176	−	0.988961i	$-0.452660\pi$
$942$		0			0
$943$	18.0000	+	10.3923i	0.586161	+	0.338420i
$944$		0			0
$945$	−9.00000	−	10.3923i	−0.292770	−	0.338062i
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$	−3.00000	−	1.73205i	−0.0974355	−	0.0562544i
$949$		0			0
$950$		0			0
$951$	3.00000	+	5.19615i	0.0972817	+	0.168497i
$952$		0			0
$953$		−	6.92820i		−	0.224427i	−0.993684	−	0.112213i	$-0.964206\pi$
$953$		−	6.92820i		−	0.224427i	0.993684	−	0.112213i	$-0.0357940\pi$
$954$		0			0
$955$			1.73205i			0.0560478i
$956$	15.0000	+	8.66025i	0.485135	+	0.280093i
$957$		−	25.9808i		−	0.839839i
$958$		0			0
$959$	−15.0000	+	43.3013i	−0.484375	+	1.39827i
$960$			13.8564i			0.447214i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$		0			0
$963$	18.0000	−	10.3923i	0.580042	−	0.334887i
$964$			20.7846i			0.669427i
$965$	2.00000	−	3.46410i	0.0643823	−	0.111513i
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$		0			0
$969$	36.0000	−	62.3538i	1.15649	−	2.00309i
$970$		0			0
$971$	−42.0000			−1.34784			−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000			−1.34784			−0.673922	+	0.738802i	$0.735392\pi$
$972$	27.0000	+	15.5885i	0.866025	+	0.500000i
$973$	30.0000	+	34.6410i	0.961756	+	1.11054i
$974$		0			0
$975$		0			0
$976$	12.0000	−	6.92820i	0.384111	−	0.221766i
$977$	24.0000	−	13.8564i	0.767828	−	0.443306i	−0.0642712	−	0.997932i	$-0.520472\pi$
$977$	24.0000	−	13.8564i	0.767828	−	0.443306i	0.832099	+	0.554627i	$0.187139\pi$
$978$		0			0
$979$	9.00000	+	5.19615i	0.287641	+	0.166070i
$980$	−2.00000	+	13.8564i	−0.0638877	+	0.442627i
$981$	−16.5000	−	28.5788i	−0.526804	−	0.912452i
$982$		0			0
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	−0.960489	−	0.278319i	$-0.910223\pi$
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	0.721276	+	0.692648i	$0.243556\pi$
$984$		0			0
$985$	−3.00000	+	1.73205i	−0.0955879	+	0.0551877i
$986$		0			0
$987$	27.0000	+	31.1769i	0.859419	+	0.992372i
$988$		0			0
$989$			34.6410i			1.10152i
$990$		0			0
$991$	37.0000			1.17534			0.587672	−	0.809099i	$-0.300045\pi$
$991$	37.0000			1.17534			0.587672	+	0.809099i	$0.300045\pi$
$992$		0			0
$993$	25.5000	−	14.7224i	0.809218	−	0.467202i
$994$		0			0
$995$	−9.00000	+	5.19615i	−0.285319	+	0.164729i
$996$	27.0000	+	15.5885i	0.855528	+	0.493939i
$997$	−22.5000	−	12.9904i	−0.712582	−	0.411409i	0.0994342	−	0.995044i	$-0.468297\pi$
$997$	−22.5000	−	12.9904i	−0.712582	−	0.411409i	−0.812016	+	0.583635i	$0.801630\pi$
$998$		0			0
$999$		−	41.5692i		−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.h.146.1	yes	2
3.2	odd	2		945.2.bl.a.251.1		2
7.6	odd	2		315.2.bl.e.146.1	yes	2
9.4	even	3		945.2.bl.c.881.1		2
9.5	odd	6		315.2.bl.e.41.1	✓	2
21.20	even	2		945.2.bl.c.251.1		2
63.13	odd	6		945.2.bl.a.881.1		2
63.41	even	6	inner	315.2.bl.h.41.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.e.41.1	✓	2	9.5	odd	6
315.2.bl.e.146.1	yes	2	7.6	odd	2
315.2.bl.h.41.1	yes	2	63.41	even	6	inner
315.2.bl.h.146.1	yes	2	1.1	even	1	trivial
945.2.bl.a.251.1		2	3.2	odd	2
945.2.bl.a.881.1		2	63.13	odd	6
945.2.bl.c.251.1		2	21.20	even	2
945.2.bl.c.881.1		2	9.4	even	3

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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(1.50000 + 0.866025i) q^{11} -3.46410i q^{12} +1.73205i q^{15} +(-2.00000 + 3.46410i) q^{16} +6.00000 q^{17} -6.92820i q^{19} +(1.00000 - 1.73205i) q^{20} +(-1.50000 + 4.33013i) q^{21} +(3.00000 - 1.73205i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(4.00000 - 3.46410i) q^{28} +(-7.50000 - 4.33013i) q^{29} +(-3.00000 + 1.73205i) q^{31} +(1.50000 + 2.59808i) q^{33} +(-2.00000 + 1.73205i) q^{35} +(3.00000 - 5.19615i) q^{36} -8.00000 q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{43} -3.46410i q^{44} +(-1.50000 + 2.59808i) q^{45} +(4.50000 - 7.79423i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(9.00000 + 5.19615i) q^{51} -13.8564i q^{53} +1.73205i q^{55} +(6.00000 - 10.3923i) q^{57} +(3.00000 - 1.73205i) q^{60} +(-3.00000 - 1.73205i) q^{61} +(-6.00000 + 5.19615i) q^{63} +8.00000 q^{64} +(-4.00000 - 6.92820i) q^{67} +(-6.00000 - 10.3923i) q^{68} +6.00000 q^{69} +1.73205i q^{71} -8.66025i q^{73} +(-1.50000 + 0.866025i) q^{75} +(-12.0000 + 6.92820i) q^{76} +(-1.50000 + 4.33013i) q^{77} +(0.500000 - 0.866025i) q^{79} -4.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(9.00000 - 1.73205i) q^{84} +(3.00000 + 5.19615i) q^{85} +(-7.50000 - 12.9904i) q^{87} +6.00000 q^{89} +(-6.00000 - 3.46410i) q^{92} -6.00000 q^{93} +(6.00000 - 3.46410i) q^{95} +(-1.50000 - 0.866025i) q^{97} +5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 2 q^{4} + q^{5} + q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 2 * q^4 + q^5 + q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 2 q^{4} + q^{5} + q^{7} + 3 q^{9} + 3 q^{11} - 4 q^{16} + 12 q^{17} + 2 q^{20} - 3 q^{21} + 6 q^{23} - q^{25} + 8 q^{28} - 15 q^{29} - 6 q^{31} + 3 q^{33} - 4 q^{35} + 6 q^{36} - 16 q^{37} + 6 q^{41} - 10 q^{43} - 3 q^{45} + 9 q^{47} - 12 q^{48} - 13 q^{49} + 18 q^{51} + 12 q^{57} + 6 q^{60} - 6 q^{61} - 12 q^{63} + 16 q^{64} - 8 q^{67} - 12 q^{68} + 12 q^{69} - 3 q^{75} - 24 q^{76} - 3 q^{77} + q^{79} - 8 q^{80} - 9 q^{81} - 9 q^{83} + 18 q^{84} + 6 q^{85} - 15 q^{87} + 12 q^{89} - 12 q^{92} - 12 q^{93} + 12 q^{95} - 3 q^{97}+O(q^{100}) \) 2 * q + 3 * q^3 - 2 * q^4 + q^5 + q^7 + 3 * q^9 + 3 * q^11 - 4 * q^16 + 12 * q^17 + 2 * q^20 - 3 * q^21 + 6 * q^23 - q^25 + 8 * q^28 - 15 * q^29 - 6 * q^31 + 3 * q^33 - 4 * q^35 + 6 * q^36 - 16 * q^37 + 6 * q^41 - 10 * q^43 - 3 * q^45 + 9 * q^47 - 12 * q^48 - 13 * q^49 + 18 * q^51 + 12 * q^57 + 6 * q^60 - 6 * q^61 - 12 * q^63 + 16 * q^64 - 8 * q^67 - 12 * q^68 + 12 * q^69 - 3 * q^75 - 24 * q^76 - 3 * q^77 + q^79 - 8 * q^80 - 9 * q^81 - 9 * q^83 + 18 * q^84 + 6 * q^85 - 15 * q^87 + 12 * q^89 - 12 * q^92 - 12 * q^93 + 12 * q^95 - 3 * q^97

Introduction

L-functions

Modular forms

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Database

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