LMFDB - Embedded newform 1710.2.l.g.1531.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (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:	$13.6544187456$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1531.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.g.1261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-3.50000 + 2.59808i) q^{19} +1.00000 q^{20} +(1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{26} +(0.500000 + 0.866025i) q^{28} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 - 0.866025i) q^{35} +5.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(5.00000 - 8.66025i) q^{43} +(-1.50000 - 2.59808i) q^{44} +9.00000 q^{46} -6.00000 q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.50000 + 2.59808i) q^{53} +(-1.50000 + 2.59808i) q^{55} +1.00000 q^{56} +(-6.00000 + 10.3923i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(5.00000 + 8.66025i) q^{67} +6.00000 q^{68} +(-0.500000 - 0.866025i) q^{70} +(2.00000 - 3.46410i) q^{73} +(2.50000 - 4.33013i) q^{74} +(4.00000 + 1.73205i) q^{76} -3.00000 q^{77} +(-7.00000 + 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(1.50000 + 2.59808i) q^{82} +18.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(-5.00000 - 8.66025i) q^{86} -3.00000 q^{88} +(7.50000 + 12.9904i) q^{89} +(1.00000 + 1.73205i) q^{91} +(4.50000 - 7.79423i) q^{92} +(-0.500000 - 4.33013i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(-3.00000 + 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} + q^{10} + 6 q^{11} - 2 q^{13} - q^{14} - q^{16} - 6 q^{17} - 7 q^{19} + 2 q^{20} + 3 q^{22} + 9 q^{23} - q^{25} - 4 q^{26} + q^{28} - 8 q^{31} + q^{32} + 6 q^{34} + q^{35} + 10 q^{37} + q^{38} + q^{40} - 3 q^{41} + 10 q^{43} - 3 q^{44} + 18 q^{46} - 12 q^{49} - 2 q^{50} - 2 q^{52} + 3 q^{53} - 3 q^{55} + 2 q^{56} - 12 q^{59} + 10 q^{61} - 4 q^{62} + 2 q^{64} + 4 q^{65} + 10 q^{67} + 12 q^{68} - q^{70} + 4 q^{73} + 5 q^{74} + 8 q^{76} - 6 q^{77} - 14 q^{79} - q^{80} + 3 q^{82} + 36 q^{83} - 6 q^{85} - 10 q^{86} - 6 q^{88} + 15 q^{89} + 2 q^{91} + 9 q^{92} - q^{95} - 8 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8 + q^10 + 6 * q^11 - 2 * q^13 - q^14 - q^16 - 6 * q^17 - 7 * q^19 + 2 * q^20 + 3 * q^22 + 9 * q^23 - q^25 - 4 * q^26 + q^28 - 8 * q^31 + q^32 + 6 * q^34 + q^35 + 10 * q^37 + q^38 + q^40 - 3 * q^41 + 10 * q^43 - 3 * q^44 + 18 * q^46 - 12 * q^49 - 2 * q^50 - 2 * q^52 + 3 * q^53 - 3 * q^55 + 2 * q^56 - 12 * q^59 + 10 * q^61 - 4 * q^62 + 2 * q^64 + 4 * q^65 + 10 * q^67 + 12 * q^68 - q^70 + 4 * q^73 + 5 * q^74 + 8 * q^76 - 6 * q^77 - 14 * q^79 - q^80 + 3 * q^82 + 36 * q^83 - 6 * q^85 - 10 * q^86 - 6 * q^88 + 15 * q^89 + 2 * q^91 + 9 * q^92 - q^95 - 8 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$	1.00000			0.223607
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.768613	+	0.639713i	$0.220947\pi$
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.169701	+	0.985496i	$0.445720\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	0.500000	+	4.33013i	0.0811107	+	0.702439i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$		0			0
$46$	9.00000			1.32698
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	1.00000			0.133631
$57$		0			0
$58$		0			0
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000			0.248069
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$		0			0
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$	2.50000	−	4.33013i	0.290619	−	0.503367i
$75$		0			0
$76$	4.00000	+	1.73205i	0.458831	+	0.198680i
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	4.50000	−	7.79423i	0.469157	−	0.812605i
$93$		0			0
$94$		0			0
$95$	−0.500000	−	4.33013i	−0.0512989	−	0.444262i
$96$		0			0
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	3.00000			0.291386
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$		0			0
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−9.00000			−0.839254
$116$		0			0
$117$		0			0
$118$	6.00000	+	10.3923i	0.552345	+	0.956689i
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	10.0000			0.905357
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	0.511859	−	0.859069i	$-0.328957\pi$
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	−0.999905	+	0.0137486i	$0.995624\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$		0			0
$133$	3.50000	−	2.59808i	0.303488	−	0.225282i
$134$	10.0000			0.863868
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	−1.00000			−0.0845154
$141$		0			0
$142$		0			0
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$		0			0
$145$		0			0
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$		0			0
$148$	−2.50000	−	4.33013i	−0.205499	−	0.355934i
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	3.50000	−	2.59808i	0.283887	−	0.210732i
$153$		0			0
$154$	−1.50000	+	2.59808i	−0.120873	+	0.209359i
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		0			0
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$	7.00000	+	12.1244i	0.556890	+	0.964562i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−4.50000	−	7.79423i	−0.354650	−	0.614271i
$162$		0			0
$163$	−22.0000			−1.72317			−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000			−1.72317			−0.861586	+	0.507611i	$0.830529\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	9.00000	−	15.5885i	0.698535	−	1.20990i
$167$	−10.5000	−	18.1865i	−0.812514	−	1.40732i	−0.911099	−	0.412188i	$-0.864765\pi$
$167$	−10.5000	−	18.1865i	−0.812514	−	1.40732i	0.0985846	−	0.995129i	$-0.468568\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−6.00000			−0.460179
$171$		0			0
$172$	−10.0000			−0.762493
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$		0			0
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		0			0
$178$	15.0000			1.12430
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$		0			0
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$	2.00000			0.148250
$183$		0			0
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$	−2.50000	+	4.33013i	−0.183804	+	0.318357i
$186$		0			0
$187$	−9.00000	+	15.5885i	−0.658145	+	1.13994i
$188$		0			0
$189$		0			0
$190$	−4.00000	−	1.73205i	−0.290191	−	0.125656i
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$		0			0
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	6.00000			0.422159
$203$		0			0
$204$		0			0
$205$	−1.50000	−	2.59808i	−0.104765	−	0.181458i
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$		0			0
$208$	2.00000			0.138675
$209$	−10.5000	+	7.79423i	−0.726300	+	0.539138i
$210$		0			0
$211$	12.5000	−	21.6506i	0.860535	−	1.49049i	−0.0108774	−	0.999941i	$-0.503462\pi$
$211$	12.5000	−	21.6506i	0.860535	−	1.49049i	0.871413	−	0.490550i	$-0.163204\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$		0			0
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	4.00000			0.271538
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$	3.00000			0.202260
$221$	12.0000			0.807207
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	−4.50000	+	7.79423i	−0.296721	+	0.513936i
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$		0			0
$236$	12.0000			0.781133
$237$		0			0
$238$	−3.00000	−	5.19615i	−0.194461	−	0.336817i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$		0			0
$244$	5.00000	−	8.66025i	0.320092	−	0.554416i
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$		0			0
$247$	8.00000	+	3.46410i	0.509028	+	0.220416i
$248$	4.00000			0.254000
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	13.5000	+	23.3827i	0.848738	+	1.47006i
$254$	−11.0000			−0.690201
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	−5.00000			−0.310685
$260$	−1.00000	−	1.73205i	−0.0620174	−	0.107417i
$261$		0			0
$262$	−4.50000	−	7.79423i	−0.278011	−	0.481529i
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	−0.536614	−	0.843828i	$-0.680297\pi$
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	0.999083	+	0.0428069i	$0.0136300\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$	−0.500000	−	4.33013i	−0.0306570	−	0.265497i
$267$		0			0
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.107031	+	0.994256i	$0.534134\pi$
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.807535	+	0.589819i	$0.799199\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	−3.00000	−	5.19615i	−0.181902	−	0.315063i
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	4.00000			0.239904
$279$		0			0
$280$	−0.500000	+	0.866025i	−0.0298807	+	0.0517549i
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$		0			0
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	−0.328291	−	0.944577i	$-0.606473\pi$
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	0.982173	−	0.187980i	$-0.0601941\pi$
$284$		0			0
$285$		0			0
$286$	−6.00000			−0.354787
$287$	1.50000	−	2.59808i	0.0885422	−	0.153360i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$	−4.00000			−0.234082
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	−5.00000			−0.290619
$297$		0			0
$298$	−9.00000	−	15.5885i	−0.521356	−	0.903015i
$299$	9.00000	−	15.5885i	0.520483	−	0.901504i
$300$		0			0
$301$	−5.00000	+	8.66025i	−0.288195	+	0.499169i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$		0			0
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$	−10.0000			−0.572598
$306$		0			0
$307$	8.00000	−	13.8564i	0.456584	−	0.790827i	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	8.00000	−	13.8564i	0.456584	−	0.790827i	0.998778	+	0.0494267i	$0.0157394\pi$
$308$	1.50000	+	2.59808i	0.0854704	+	0.148039i
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$	−6.50000	−	11.2583i	−0.366816	−	0.635344i
$315$		0			0
$316$	14.0000			0.787562
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	0.996061	−	0.0886679i	$-0.0282610\pi$
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	−0.574819	+	0.818280i	$0.694928\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−9.00000			−0.501550
$323$	−3.00000	−	25.9808i	−0.166924	−	1.44561i
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−11.0000	+	19.0526i	−0.609234	+	1.05522i
$327$		0			0
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$		0			0
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−9.00000	−	15.5885i	−0.493939	−	0.855528i
$333$		0			0
$334$	−21.0000			−1.14907
$335$	−10.0000			−0.546358
$336$		0			0
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	13.0000			0.701934
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$		0			0
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	−	12.9904i	0.397499	−	0.688489i
$357$		0			0
$358$	−7.50000	+	12.9904i	−0.396387	+	0.686563i
$359$	−6.00000	+	10.3923i	−0.316668	+	0.548485i	−0.979791	−	0.200026i	$-0.935897\pi$
$359$	−6.00000	+	10.3923i	−0.316668	+	0.548485i	0.663123	+	0.748511i	$0.269231\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	16.0000			0.840941
$363$		0			0
$364$	1.00000	−	1.73205i	0.0524142	−	0.0907841i
$365$	2.00000	+	3.46410i	0.104685	+	0.181319i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−9.00000			−0.469157
$369$		0			0
$370$	2.50000	+	4.33013i	0.129969	+	0.225113i
$371$	−1.50000	−	2.59808i	−0.0778761	−	0.134885i
$372$		0			0
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−3.50000	+	2.59808i	−0.179546	+	0.133278i
$381$		0			0
$382$	−3.00000	+	5.19615i	−0.153493	+	0.265858i
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$		0			0
$385$	1.50000	−	2.59808i	0.0764471	−	0.132410i
$386$	−5.00000	−	8.66025i	−0.254493	−	0.440795i
$387$		0			0
$388$	8.00000			0.406138
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$	−54.0000			−2.73090
$392$	6.00000			0.303046
$393$		0			0
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	−7.00000	−	12.1244i	−0.352208	−	0.610043i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$	10.0000			0.501255
$399$		0			0
$400$	1.00000			0.0500000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	3.00000	−	5.19615i	0.149256	−	0.258518i
$405$		0			0
$406$		0			0
$407$	15.0000			0.743522
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$	−3.00000			−0.148159
$411$		0			0
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	6.00000	−	10.3923i	0.295241	−	0.511372i
$414$		0			0
$415$	−9.00000	+	15.5885i	−0.441793	+	0.765207i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		0			0
$418$	1.50000	+	12.9904i	0.0733674	+	0.635380i
$419$	−21.0000			−1.02592			−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000			−1.02592			−0.512959	+	0.858413i	$0.671451\pi$
$420$		0			0
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	0.353233	+	0.935536i	$0.385082\pi$
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	−0.986814	+	0.161859i	$0.948251\pi$
$422$	−12.5000	−	21.6506i	−0.608490	−	1.05394i
$423$		0			0
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	6.00000			0.291043
$426$		0			0
$427$	−5.00000	−	8.66025i	−0.241967	−	0.419099i
$428$	3.00000	+	5.19615i	0.145010	+	0.251166i
$429$		0			0
$430$	10.0000			0.482243
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$		0			0
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	0.991693	−	0.128624i	$-0.0410559\pi$
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	−0.607238	+	0.794520i	$0.707723\pi$
$434$	2.00000	−	3.46410i	0.0960031	−	0.166282i
$435$		0			0
$436$	2.00000			0.0957826
$437$	−36.0000	−	15.5885i	−1.72211	−	0.745697i
$438$		0			0
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$		0			0
$442$	6.00000	−	10.3923i	0.285391	−	0.494312i
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$		0			0
$445$	−15.0000			−0.711068
$446$	−0.500000	−	0.866025i	−0.0236757	−	0.0410075i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$		0			0
$454$	−6.00000	+	10.3923i	−0.281594	+	0.487735i
$455$	−2.00000			−0.0937614
$456$		0			0
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$	−5.00000	+	8.66025i	−0.233635	+	0.404667i
$459$		0			0
$460$	4.50000	+	7.79423i	0.209814	+	0.363408i
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	−0.270326	−	0.962769i	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$		0			0
$463$	11.0000			0.511213			0.255607	−	0.966781i	$-0.417725\pi$
$463$	11.0000			0.511213			0.255607	+	0.966781i	$0.417725\pi$
$464$		0			0
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$	−5.00000	−	8.66025i	−0.230879	−	0.399893i
$470$		0			0
$471$		0			0
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	15.0000	−	25.9808i	0.689701	−	1.19460i
$474$		0			0
$475$	4.00000	+	1.73205i	0.183533	+	0.0794719i
$476$	−6.00000			−0.275010
$477$		0			0
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	−5.00000	−	8.66025i	−0.227980	−	0.394874i
$482$	10.0000			0.455488
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	11.0000			0.498458			0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000			0.498458			0.249229	+	0.968445i	$0.419823\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$		0			0
$490$	−3.00000	−	5.19615i	−0.135526	−	0.234738i
$491$	1.50000	−	2.59808i	0.0676941	−	0.117250i	−0.830192	−	0.557478i	$-0.811769\pi$
$491$	1.50000	−	2.59808i	0.0676941	−	0.117250i	0.897886	+	0.440228i	$0.145102\pi$
$492$		0			0
$493$		0			0
$494$	7.00000	−	5.19615i	0.314945	−	0.233786i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$		0			0
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	19.5000	+	33.7750i	0.869462	+	1.50595i	0.862547	+	0.505976i	$0.168868\pi$
$503$	19.5000	+	33.7750i	0.869462	+	1.50595i	0.00691465	+	0.999976i	$0.497799\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$	27.0000			1.20030
$507$		0			0
$508$	−5.50000	+	9.52628i	−0.244023	+	0.422660i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−6.00000			−0.264649
$515$	0.500000	−	0.866025i	0.0220326	−	0.0381616i
$516$		0			0
$517$		0			0
$518$	−2.50000	+	4.33013i	−0.109844	+	0.190255i
$519$		0			0
$520$	−2.00000			−0.0877058
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	−9.00000			−0.393167
$525$		0			0
$526$	−7.50000	−	12.9904i	−0.327016	−	0.566408i
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$	−1.50000	+	2.59808i	−0.0651558	+	0.112853i
$531$		0			0
$532$	−4.00000	−	1.73205i	−0.173422	−	0.0750939i
$533$	6.00000			0.259889
$534$		0			0
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$	−5.00000	−	8.66025i	−0.215967	−	0.374066i
$537$		0			0
$538$	15.0000	+	25.9808i	0.646696	+	1.12011i
$539$	−18.0000			−0.775315
$540$		0			0
$541$	2.00000	+	3.46410i	0.0859867	+	0.148933i	0.905811	−	0.423681i	$-0.139262\pi$
$541$	2.00000	+	3.46410i	0.0859867	+	0.148933i	−0.819825	+	0.572615i	$0.805929\pi$
$542$	1.00000	+	1.73205i	0.0429537	+	0.0743980i
$543$		0			0
$544$	−6.00000			−0.257248
$545$	−1.00000	−	1.73205i	−0.0428353	−	0.0741929i
$546$		0			0
$547$	−13.0000	−	22.5167i	−0.555840	−	0.962743i	−0.997838	−	0.0657267i	$-0.979063\pi$
$547$	−13.0000	−	22.5167i	−0.555840	−	0.962743i	0.441998	−	0.897016i	$-0.354270\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$		0			0
$550$	−3.00000			−0.127920
$551$		0			0
$552$		0			0
$553$	7.00000	−	12.1244i	0.297670	−	0.515580i
$554$	−5.00000	+	8.66025i	−0.212430	+	0.367939i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	0.968769	+	0.247964i	$0.0797613\pi$
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	−0.269642	+	0.962961i	$0.586905\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$		0			0
$562$	15.0000			0.632737
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	−11.0000	−	19.0526i	−0.462364	−	0.800839i
$567$		0			0
$568$		0			0
$569$	45.0000			1.88650			0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000			1.88650			0.943249	+	0.332086i	$0.107752\pi$
$570$		0			0
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$	−3.00000	+	5.19615i	−0.125436	+	0.217262i
$573$		0			0
$574$	−1.50000	−	2.59808i	−0.0626088	−	0.108442i
$575$	4.50000	−	7.79423i	0.187663	−	0.325042i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−19.0000			−0.790296
$579$		0			0
$580$		0			0
$581$	−18.0000			−0.746766
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	−0.962872	−	0.269957i	$-0.912990\pi$
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	0.715226	+	0.698893i	$0.246324\pi$
$588$		0			0
$589$	14.0000	−	10.3923i	0.576860	−	0.428207i
$590$	−12.0000			−0.494032
$591$		0			0
$592$	−2.50000	+	4.33013i	−0.102749	+	0.177967i
$593$	−6.00000	−	10.3923i	−0.246390	−	0.426761i	0.716131	−	0.697966i	$-0.245911\pi$
$593$	−6.00000	−	10.3923i	−0.246390	−	0.426761i	−0.962522	+	0.271205i	$0.912578\pi$
$594$		0			0
$595$	3.00000	+	5.19615i	0.122988	+	0.213021i
$596$	−18.0000			−0.737309
$597$		0			0
$598$	−9.00000	−	15.5885i	−0.368037	−	0.637459i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	17.0000			0.693444			0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000			0.693444			0.346722	+	0.937968i	$0.387295\pi$
$602$	5.00000	+	8.66025i	0.203785	+	0.352966i
$603$		0			0
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−49.0000			−1.98885			−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−49.0000			−1.98885			−0.994424	+	0.105453i	$0.966371\pi$
$608$	−4.00000	−	1.73205i	−0.162221	−	0.0702439i
$609$		0			0
$610$	−5.00000	+	8.66025i	−0.202444	+	0.350643i
$611$		0			0
$612$		0			0
$613$	3.50000	−	6.06218i	0.141364	−	0.244849i	−0.786647	−	0.617403i	$-0.788185\pi$
$613$	3.50000	−	6.06218i	0.141364	−	0.244849i	0.928010	+	0.372554i	$0.121518\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$		0			0
$616$	3.00000			0.120873
$617$	12.0000	+	20.7846i	0.483102	+	0.836757i	0.999812	−	0.0194037i	$-0.00617676\pi$
$617$	12.0000	+	20.7846i	0.483102	+	0.836757i	−0.516710	+	0.856161i	$0.672843\pi$
$618$		0			0
$619$	−19.0000			−0.763674			−0.381837	−	0.924230i	$-0.624709\pi$
$619$	−19.0000			−0.763674			−0.381837	+	0.924230i	$0.624709\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$		0			0
$623$	−7.50000	−	12.9904i	−0.300481	−	0.520449i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−8.00000			−0.319744
$627$		0			0
$628$	−13.0000			−0.518756
$629$	−15.0000	+	25.9808i	−0.598089	+	1.03592i
$630$		0			0
$631$	−16.0000	−	27.7128i	−0.636950	−	1.10323i	−0.986098	−	0.166162i	$-0.946862\pi$
$631$	−16.0000	−	27.7128i	−0.636950	−	1.10323i	0.349148	−	0.937067i	$-0.386471\pi$
$632$	7.00000	−	12.1244i	0.278445	−	0.482281i
$633$		0			0
$634$	15.0000			0.595726
$635$	11.0000			0.436522
$636$		0			0
$637$	6.00000	+	10.3923i	0.237729	+	0.411758i
$638$		0			0
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$		0			0
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	−0.307372	−	0.951589i	$-0.599450\pi$
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	0.977787	−	0.209603i	$-0.0672170\pi$
$644$	−4.50000	+	7.79423i	−0.177325	+	0.307136i
$645$		0			0
$646$	−24.0000	−	10.3923i	−0.944267	−	0.408880i
$647$	39.0000			1.53325			0.766624	−	0.642096i	$-0.221935\pi$
$647$	39.0000			1.53325			0.766624	+	0.642096i	$0.221935\pi$
$648$		0			0
$649$	−18.0000	+	31.1769i	−0.706562	+	1.22380i
$650$	1.00000	+	1.73205i	0.0392232	+	0.0679366i
$651$		0			0
$652$	11.0000	+	19.0526i	0.430793	+	0.746156i
$653$	15.0000			0.586995			0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000			0.586995			0.293498	+	0.955960i	$0.405181\pi$
$654$		0			0
$655$	4.50000	+	7.79423i	0.175830	+	0.304546i
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$		0			0
$658$		0			0
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	−0.999545	−	0.0301523i	$-0.990401\pi$
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	0.473660	−	0.880708i	$-0.342933\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$	2.50000	−	4.33013i	0.0971653	−	0.168295i
$663$		0			0
$664$	−18.0000			−0.698535
$665$	0.500000	+	4.33013i	0.0193892	+	0.167915i
$666$		0			0
$667$		0			0
$668$	−10.5000	+	18.1865i	−0.406257	+	0.703658i
$669$		0			0
$670$	−5.00000	+	8.66025i	−0.193167	+	0.334575i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$		0			0
$673$	32.0000			1.23351			0.616755	−	0.787155i	$-0.288447\pi$
$673$	32.0000			1.23351			0.616755	+	0.787155i	$0.288447\pi$
$674$	−11.0000	−	19.0526i	−0.423704	−	0.733877i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−33.0000			−1.26829			−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000			−1.26829			−0.634147	+	0.773213i	$0.718648\pi$
$678$		0			0
$679$	4.00000	−	6.92820i	0.153506	−	0.265880i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$		0			0
$682$	−6.00000	+	10.3923i	−0.229752	+	0.397942i
$683$	−30.0000			−1.14792			−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000			−1.14792			−0.573959	+	0.818884i	$0.694593\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$		0			0
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	−1.00000			−0.0380418			−0.0190209	−	0.999819i	$-0.506055\pi$
$691$	−1.00000			−0.0380418			−0.0190209	+	0.999819i	$0.506055\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$	15.0000	+	25.9808i	0.569392	+	0.986216i
$695$	−4.00000			−0.151729
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$		0			0
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−21.0000	+	36.3731i	−0.793159	+	1.37379i	0.130843	+	0.991403i	$0.458232\pi$
$701$	−21.0000	+	36.3731i	−0.793159	+	1.37379i	−0.924002	+	0.382389i	$0.875102\pi$
$702$		0			0
$703$	−17.5000	+	12.9904i	−0.660025	+	0.489942i
$704$	3.00000			0.113067
$705$		0			0
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$		0			0
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	−18.0000	−	31.1769i	−0.674105	−	1.16758i
$714$		0			0
$715$	6.00000			0.224387
$716$	7.50000	+	12.9904i	0.280288	+	0.485473i
$717$		0			0
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	−0.306253	−	0.951950i	$-0.599075\pi$
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	0.977539	−	0.210752i	$-0.0675914\pi$
$720$		0			0
$721$	1.00000			0.0372419
$722$	−13.0000	−	13.8564i	−0.483810	−	0.515682i
$723$		0			0
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$		0			0
$726$		0			0
$727$	20.0000	−	34.6410i	0.741759	−	1.28476i	−0.209935	−	0.977715i	$-0.567325\pi$
$727$	20.0000	−	34.6410i	0.741759	−	1.28476i	0.951694	−	0.307049i	$-0.0993415\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$		0			0
$730$	4.00000			0.148047
$731$	30.0000	+	51.9615i	1.10959	+	1.92187i
$732$		0			0
$733$	41.0000			1.51437			0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000			1.51437			0.757185	+	0.653201i	$0.226574\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	−4.50000	+	7.79423i	−0.165872	+	0.287299i
$737$	15.0000	+	25.9808i	0.552532	+	0.957014i
$738$		0			0
$739$	24.5000	−	42.4352i	0.901247	−	1.56101i	0.0753699	−	0.997156i	$-0.475986\pi$
$739$	24.5000	−	42.4352i	0.901247	−	1.56101i	0.825877	−	0.563850i	$-0.190680\pi$
$740$	5.00000			0.183804
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−19.5000	+	33.7750i	−0.715386	+	1.23908i	0.247425	+	0.968907i	$0.420416\pi$
$743$	−19.5000	+	33.7750i	−0.715386	+	1.23908i	−0.962811	+	0.270177i	$0.912918\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	11.5000	−	19.9186i	0.421045	−	0.729271i
$747$		0			0
$748$	18.0000			0.658145
$749$	6.00000			0.219235
$750$		0			0
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.00000	−	8.66025i	0.181969	−	0.315179i
$756$		0			0
$757$	3.50000	−	6.06218i	0.127210	−	0.220334i	−0.795385	−	0.606105i	$-0.792731\pi$
$757$	3.50000	−	6.06218i	0.127210	−	0.220334i	0.922595	+	0.385771i	$0.126065\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$		0			0
$760$	0.500000	+	4.33013i	0.0181369	+	0.157070i
$761$	−15.0000			−0.543750			−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000			−0.543750			−0.271875	+	0.962333i	$0.587644\pi$
$762$		0			0
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$	3.00000	+	5.19615i	0.108536	+	0.187990i
$765$		0			0
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	24.0000			0.866590
$768$		0			0
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$	−1.50000	−	2.59808i	−0.0540562	−	0.0936282i
$771$		0			0
$772$	−10.0000			−0.359908
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$		0			0
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	4.00000	−	6.92820i	0.143592	−	0.248708i
$777$		0			0
$778$		0			0
$779$	−1.50000	−	12.9904i	−0.0537431	−	0.465429i
$780$		0			0
$781$		0			0
$782$	−27.0000	+	46.7654i	−0.965518	+	1.67233i
$783$		0			0
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	6.50000	+	11.2583i	0.231995	+	0.401827i
$786$		0			0
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$	−1.50000	−	2.59808i	−0.0534353	−	0.0925526i
$789$		0			0
$790$	−14.0000			−0.498098
$791$	−6.00000			−0.213335
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$		0			0
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	6.00000	−	10.3923i	0.211735	−	0.366736i
$804$		0			0
$805$	9.00000			0.317208
$806$	8.00000			0.281788
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	21.5000	+	37.2391i	0.754967	+	1.30764i	0.945391	+	0.325939i	$0.105681\pi$
$811$	21.5000	+	37.2391i	0.754967	+	1.30764i	−0.190424	+	0.981702i	$0.560986\pi$
$812$		0			0
$813$		0			0
$814$	7.50000	−	12.9904i	0.262875	−	0.455313i
$815$	11.0000	−	19.0526i	0.385313	−	0.667382i
$816$		0			0
$817$	5.00000	+	43.3013i	0.174928	+	1.51492i
$818$	−5.00000			−0.174821
$819$		0			0
$820$	−1.50000	+	2.59808i	−0.0523823	+	0.0907288i
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$		0			0
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	−0.963119	−	0.269075i	$-0.913282\pi$
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	0.248534	−	0.968623i	$-0.420051\pi$
$824$	1.00000			0.0348367
$825$		0			0
$826$	−6.00000	−	10.3923i	−0.208767	−	0.361595i
$827$	24.0000	+	41.5692i	0.834562	+	1.44550i	0.894387	+	0.447295i	$0.147612\pi$
$827$	24.0000	+	41.5692i	0.834562	+	1.44550i	−0.0598250	+	0.998209i	$0.519054\pi$
$828$		0			0
$829$	8.00000			0.277851			0.138926	−	0.990303i	$-0.455635\pi$
$829$	8.00000			0.277851			0.138926	+	0.990303i	$0.455635\pi$
$830$	9.00000	+	15.5885i	0.312395	+	0.541083i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	18.0000	−	31.1769i	0.623663	−	1.08022i
$834$		0			0
$835$	21.0000			0.726735
$836$	12.0000	+	5.19615i	0.415029	+	0.179713i
$837$		0			0
$838$	−10.5000	+	18.1865i	−0.362716	+	0.628243i
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	0.481927	+	0.876211i	$0.339937\pi$
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	−0.999785	+	0.0207443i	$0.993396\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$		0			0
$844$	−25.0000			−0.860535
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$	2.00000			0.0687208
$848$	−3.00000			−0.103020
$849$		0			0
$850$	3.00000	−	5.19615i	0.102899	−	0.178227i
$851$	22.5000	+	38.9711i	0.771290	+	1.33591i
$852$		0			0
$853$	−19.0000	+	32.9090i	−0.650548	+	1.12678i	0.332443	+	0.943123i	$0.392127\pi$
$853$	−19.0000	+	32.9090i	−0.650548	+	1.12678i	−0.982990	+	0.183658i	$0.941206\pi$
$854$	−10.0000			−0.342193
$855$		0			0
$856$	6.00000			0.205076
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	−0.584967	−	0.811057i	$-0.698893\pi$
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	0.994880	+	0.101068i	$0.0322260\pi$
$858$		0			0
$859$	−8.50000	−	14.7224i	−0.290016	−	0.502323i	0.683797	−	0.729672i	$-0.260327\pi$
$859$	−8.50000	−	14.7224i	−0.290016	−	0.502323i	−0.973813	+	0.227349i	$0.926994\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$		0			0
$862$	30.0000			1.02180
$863$	39.0000			1.32758			0.663788	−	0.747921i	$-0.268948\pi$
$863$	39.0000			1.32758			0.663788	+	0.747921i	$0.268948\pi$
$864$		0			0
$865$	−10.5000	−	18.1865i	−0.357011	−	0.618361i
$866$	16.0000			0.543702
$867$		0			0
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−21.0000	+	36.3731i	−0.712376	+	1.23387i
$870$		0			0
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$		0			0
$874$	−31.5000	+	23.3827i	−1.06550	+	0.790931i
$875$	−1.00000			−0.0338062
$876$		0			0
$877$	−17.5000	+	30.3109i	−0.590933	+	1.02353i	0.403174	+	0.915123i	$0.367907\pi$
$877$	−17.5000	+	30.3109i	−0.590933	+	1.02353i	−0.994107	+	0.108403i	$0.965426\pi$
$878$	7.00000	+	12.1244i	0.236239	+	0.409177i
$879$		0			0
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−39.0000			−1.31394			−0.656972	−	0.753915i	$-0.728163\pi$
$881$	−39.0000			−1.31394			−0.656972	+	0.753915i	$0.728163\pi$
$882$		0			0
$883$	−13.0000	−	22.5167i	−0.437485	−	0.757746i	0.560010	−	0.828486i	$-0.310797\pi$
$883$	−13.0000	−	22.5167i	−0.437485	−	0.757746i	−0.997495	+	0.0707399i	$0.977464\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	−18.0000			−0.604722
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	5.50000	+	9.52628i	0.184464	+	0.319501i
$890$	−7.50000	+	12.9904i	−0.251401	+	0.435439i
$891$		0			0
$892$	−1.00000			−0.0334825
$893$		0			0
$894$		0			0
$895$	7.50000	−	12.9904i	0.250697	−	0.434221i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−1.50000	+	2.59808i	−0.0500556	+	0.0866989i
$899$		0			0
$900$		0			0
$901$	−18.0000			−0.599667
$902$	4.50000	+	7.79423i	0.149834	+	0.259519i
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−16.0000			−0.531858
$906$		0			0
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	0.937018	+	0.349281i	$0.113574\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$		0			0
$910$	−1.00000	+	1.73205i	−0.0331497	+	0.0574169i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	54.0000			1.78714
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$		0			0
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$	−4.50000	+	7.79423i	−0.148603	+	0.257388i
$918$		0			0
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$	9.00000			0.296721
$921$		0			0
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$		0			0
$924$		0			0
$925$	−2.50000	−	4.33013i	−0.0821995	−	0.142374i
$926$	5.50000	−	9.52628i	0.180741	−	0.313053i
$927$		0			0
$928$		0			0
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	21.0000	−	15.5885i	0.688247	−	0.510891i
$932$	−6.00000			−0.196537
$933$		0			0
$934$		0			0
$935$	−9.00000	−	15.5885i	−0.294331	−	0.509797i
$936$		0			0
$937$	2.00000	+	3.46410i	0.0653372	+	0.113167i	0.896843	−	0.442348i	$-0.145854\pi$
$937$	2.00000	+	3.46410i	0.0653372	+	0.113167i	−0.831506	+	0.555515i	$0.812521\pi$
$938$	−10.0000			−0.326512
$939$		0			0
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$		0			0
$943$	−27.0000			−0.879241
$944$	−6.00000	−	10.3923i	−0.195283	−	0.338241i
$945$		0			0
$946$	−15.0000	−	25.9808i	−0.487692	−	0.844707i
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721926\pi$
$948$		0			0
$949$	−8.00000			−0.259691
$950$	3.50000	−	2.59808i	0.113555	−	0.0842927i
$951$		0			0
$952$	−3.00000	+	5.19615i	−0.0972306	+	0.168408i
$953$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$953$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$954$		0			0
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$		0			0
$958$	12.0000			0.387702
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−10.0000			−0.322413
$963$		0			0
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	5.00000	+	8.66025i	0.160956	+	0.278783i
$966$		0			0
$967$	−22.0000	+	38.1051i	−0.707472	+	1.22538i	0.258320	+	0.966060i	$0.416831\pi$
$967$	−22.0000	+	38.1051i	−0.707472	+	1.22538i	−0.965792	+	0.259318i	$0.916502\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	−8.00000			−0.256865
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$		0			0
$973$	−2.00000	−	3.46410i	−0.0641171	−	0.111054i
$974$	5.50000	−	9.52628i	0.176231	−	0.305242i
$975$		0			0
$976$	−10.0000			−0.320092
$977$	24.0000			0.767828			0.383914	−	0.923369i	$-0.374576\pi$
$977$	24.0000			0.767828			0.383914	+	0.923369i	$0.374576\pi$
$978$		0			0
$979$	22.5000	+	38.9711i	0.719103	+	1.24552i
$980$	−6.00000			−0.191663
$981$		0			0
$982$	−1.50000	−	2.59808i	−0.0478669	−	0.0829079i
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	−0.785295	−	0.619122i	$-0.787489\pi$
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	0.928823	+	0.370525i	$0.120822\pi$
$984$		0			0
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$		0			0
$987$		0			0
$988$	−1.00000	−	8.66025i	−0.0318142	−	0.275519i
$989$	90.0000			2.86183
$990$		0			0
$991$	26.0000	−	45.0333i	0.825917	−	1.43053i	−0.0752991	−	0.997161i	$-0.523991\pi$
$991$	26.0000	−	45.0333i	0.825917	−	1.43053i	0.901216	−	0.433370i	$-0.142676\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$		0			0
$995$	−10.0000			−0.317021
$996$		0			0
$997$	24.5000	+	42.4352i	0.775923	+	1.34394i	0.934274	+	0.356555i	$0.116049\pi$
$997$	24.5000	+	42.4352i	0.775923	+	1.34394i	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−12.5000	−	21.6506i	−0.395681	−	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.g.1531.1		2
3.2	odd	2		570.2.i.a.391.1	yes	2
19.7	even	3	inner	1710.2.l.g.1261.1		2
57.26	odd	6		570.2.i.a.121.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.a.121.1	✓	2	57.26	odd	6
570.2.i.a.391.1	yes	2	3.2	odd	2
1710.2.l.g.1261.1		2	19.7	even	3	inner
1710.2.l.g.1531.1		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-3.50000 + 2.59808i) q^{19} +1.00000 q^{20} +(1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{26} +(0.500000 + 0.866025i) q^{28} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 - 0.866025i) q^{35} +5.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(5.00000 - 8.66025i) q^{43} +(-1.50000 - 2.59808i) q^{44} +9.00000 q^{46} -6.00000 q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.50000 + 2.59808i) q^{53} +(-1.50000 + 2.59808i) q^{55} +1.00000 q^{56} +(-6.00000 + 10.3923i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(5.00000 + 8.66025i) q^{67} +6.00000 q^{68} +(-0.500000 - 0.866025i) q^{70} +(2.00000 - 3.46410i) q^{73} +(2.50000 - 4.33013i) q^{74} +(4.00000 + 1.73205i) q^{76} -3.00000 q^{77} +(-7.00000 + 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(1.50000 + 2.59808i) q^{82} +18.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(-5.00000 - 8.66025i) q^{86} -3.00000 q^{88} +(7.50000 + 12.9904i) q^{89} +(1.00000 + 1.73205i) q^{91} +(4.50000 - 7.79423i) q^{92} +(-0.500000 - 4.33013i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(-3.00000 + 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} + q^{10} + 6 q^{11} - 2 q^{13} - q^{14} - q^{16} - 6 q^{17} - 7 q^{19} + 2 q^{20} + 3 q^{22} + 9 q^{23} - q^{25} - 4 q^{26} + q^{28} - 8 q^{31} + q^{32} + 6 q^{34} + q^{35} + 10 q^{37} + q^{38} + q^{40} - 3 q^{41} + 10 q^{43} - 3 q^{44} + 18 q^{46} - 12 q^{49} - 2 q^{50} - 2 q^{52} + 3 q^{53} - 3 q^{55} + 2 q^{56} - 12 q^{59} + 10 q^{61} - 4 q^{62} + 2 q^{64} + 4 q^{65} + 10 q^{67} + 12 q^{68} - q^{70} + 4 q^{73} + 5 q^{74} + 8 q^{76} - 6 q^{77} - 14 q^{79} - q^{80} + 3 q^{82} + 36 q^{83} - 6 q^{85} - 10 q^{86} - 6 q^{88} + 15 q^{89} + 2 q^{91} + 9 q^{92} - q^{95} - 8 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8 + q^10 + 6 * q^11 - 2 * q^13 - q^14 - q^16 - 6 * q^17 - 7 * q^19 + 2 * q^20 + 3 * q^22 + 9 * q^23 - q^25 - 4 * q^26 + q^28 - 8 * q^31 + q^32 + 6 * q^34 + q^35 + 10 * q^37 + q^38 + q^40 - 3 * q^41 + 10 * q^43 - 3 * q^44 + 18 * q^46 - 12 * q^49 - 2 * q^50 - 2 * q^52 + 3 * q^53 - 3 * q^55 + 2 * q^56 - 12 * q^59 + 10 * q^61 - 4 * q^62 + 2 * q^64 + 4 * q^65 + 10 * q^67 + 12 * q^68 - q^70 + 4 * q^73 + 5 * q^74 + 8 * q^76 - 6 * q^77 - 14 * q^79 - q^80 + 3 * q^82 + 36 * q^83 - 6 * q^85 - 10 * q^86 - 6 * q^88 + 15 * q^89 + 2 * q^91 + 9 * q^92 - q^95 - 8 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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