LMFDB - Embedded newform 714.2.i.i.613.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(205,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("714.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.i (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:	$5.70131870432$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	714.613
Dual form			714.2.i.i.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +2.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +3.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(1.50000 - 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} -1.00000 q^{34} +(-0.500000 + 2.59808i) q^{35} +1.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(2.00000 - 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +1.00000 q^{41} +(-2.00000 - 1.73205i) q^{42} -4.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{46} +(4.50000 + 7.79423i) q^{47} -1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +4.00000 q^{50} +(0.500000 + 0.866025i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{54} -2.00000 q^{55} +(2.00000 + 1.73205i) q^{56} -4.00000 q^{57} +(1.50000 + 2.59808i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(0.500000 - 0.866025i) q^{60} +3.00000 q^{62} +(-0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(1.00000 - 1.73205i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-0.500000 - 0.866025i) q^{68} -8.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +4.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 - 3.46410i) q^{75} +4.00000 q^{76} +(-5.00000 + 1.73205i) q^{77} +1.00000 q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +9.00000 q^{83} +(0.500000 - 2.59808i) q^{84} +1.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(3.00000 + 5.19615i) q^{89} -1.00000 q^{90} +(-2.00000 - 1.73205i) q^{91} +8.00000 q^{92} +(-1.50000 - 2.59808i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 4 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + q^{10} + 2 q^{11} + q^{12} + 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - q^{17} + q^{18} - 4 q^{19} + 2 q^{20} - 5 q^{21} + 4 q^{22} - 8 q^{23} - q^{24} + 4 q^{25} + q^{26} - 2 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 3 q^{31} + q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} - 4 q^{37} + 4 q^{38} + q^{39} + q^{40} + 2 q^{41} - 4 q^{42} - 8 q^{43} + 2 q^{44} - q^{45} + 8 q^{46} + 9 q^{47} - 2 q^{48} + 2 q^{49} + 8 q^{50} + q^{51} - q^{52} - q^{54} - 4 q^{55} + 4 q^{56} - 8 q^{57} + 3 q^{58} - 11 q^{59} + q^{60} + 6 q^{62} - q^{63} + 2 q^{64} - q^{65} + 2 q^{66} + 12 q^{67} - q^{68} - 16 q^{69} - 5 q^{70} + 8 q^{71} + q^{72} - 6 q^{73} + 4 q^{74} - 4 q^{75} + 8 q^{76} - 10 q^{77} + 2 q^{78} - q^{80} - q^{81} + q^{82} + 18 q^{83} + q^{84} + 2 q^{85} - 4 q^{86} + 3 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} - 4 q^{91} + 16 q^{92} - 3 q^{93} - 9 q^{94} - 4 q^{95} - q^{96} + 16 q^{97} - 11 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 4 * q^7 - 2 * q^8 - q^9 + q^10 + 2 * q^11 + q^12 + 2 * q^13 + q^14 - 2 * q^15 - q^16 - q^17 + q^18 - 4 * q^19 + 2 * q^20 - 5 * q^21 + 4 * q^22 - 8 * q^23 - q^24 + 4 * q^25 + q^26 - 2 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 3 * q^31 + q^32 - 2 * q^33 - 2 * q^34 - q^35 + 2 * q^36 - 4 * q^37 + 4 * q^38 + q^39 + q^40 + 2 * q^41 - 4 * q^42 - 8 * q^43 + 2 * q^44 - q^45 + 8 * q^46 + 9 * q^47 - 2 * q^48 + 2 * q^49 + 8 * q^50 + q^51 - q^52 - q^54 - 4 * q^55 + 4 * q^56 - 8 * q^57 + 3 * q^58 - 11 * q^59 + q^60 + 6 * q^62 - q^63 + 2 * q^64 - q^65 + 2 * q^66 + 12 * q^67 - q^68 - 16 * q^69 - 5 * q^70 + 8 * q^71 + q^72 - 6 * q^73 + 4 * q^74 - 4 * q^75 + 8 * q^76 - 10 * q^77 + 2 * q^78 - q^80 - q^81 + q^82 + 18 * q^83 + q^84 + 2 * q^85 - 4 * q^86 + 3 * q^87 - 2 * q^88 + 6 * q^89 - 2 * q^90 - 4 * q^91 + 16 * q^92 - 3 * q^93 - 9 * q^94 - 4 * q^95 - q^96 + 16 * q^97 - 11 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	1.00000			0.408248
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	1.00000			0.223607
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$	2.00000			0.426401
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	−0.699301	−	0.714827i	$-0.746505\pi$
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	0.968709	+	0.248199i	$0.0798387\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−1.00000			−0.171499
$35$	−0.500000	+	2.59808i	−0.0845154	+	0.439155i
$36$	1.00000			0.166667
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	1.00000			0.156174			0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000			0.156174			0.0780869	+	0.996947i	$0.475119\pi$
$42$	−2.00000	−	1.73205i	−0.308607	−	0.267261i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	−1.00000			−0.144338
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	4.00000			0.565685
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−2.00000			−0.269680
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$	−4.00000			−0.529813
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	3.00000			0.381000
$63$	−0.500000	+	2.59808i	−0.0629941	+	0.327327i
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	1.00000	−	1.73205i	0.123091	−	0.213201i
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	−8.00000			−0.963087
$70$	−2.50000	+	0.866025i	−0.298807	+	0.103510i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	4.00000			0.458831
$77$	−5.00000	+	1.73205i	−0.569803	+	0.197386i
$78$	1.00000			0.113228
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.500000	+	0.866025i	0.0552158	+	0.0956365i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	0.500000	−	2.59808i	0.0545545	−	0.283473i
$85$	1.00000			0.108465
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	−1.00000			−0.105409
$91$	−2.00000	−	1.73205i	−0.209657	−	0.181568i
$92$	8.00000			0.834058
$93$	−1.50000	−	2.59808i	−0.155543	−	0.269408i
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$	−2.00000			−0.201008
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$	−0.500000	+	0.866025i	−0.0495074	+	0.0857493i
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	−1.00000			−0.0980581
$105$	2.00000	+	1.73205i	0.195180	+	0.169031i
$106$		0			0
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$	−4.00000			−0.379663
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	−4.00000	+	6.92820i	−0.373002	+	0.646058i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	−11.0000			−1.01263
$119$	2.50000	−	0.866025i	0.229175	−	0.0793884i
$120$	1.00000			0.0912871
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	0.500000	−	0.866025i	0.0450835	−	0.0780869i
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$	−9.00000			−0.804984
$126$	−2.50000	+	0.866025i	−0.222718	+	0.0771517i
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	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	$0.748915\pi$
$132$	2.00000			0.174078
$133$	−2.00000	+	10.3923i	−0.173422	+	0.901127i
$134$	12.0000			1.03664
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	0.500000	−	0.866025i	0.0428746	−	0.0742611i
$137$	−10.0000	+	17.3205i	−0.854358	+	1.47979i	0.0228820	+	0.999738i	$0.492716\pi$
$137$	−10.0000	+	17.3205i	−0.854358	+	1.47979i	−0.877240	+	0.480053i	$0.840618\pi$
$138$	−4.00000	−	6.92820i	−0.340503	−	0.589768i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−2.00000	−	1.73205i	−0.169031	−	0.146385i
$141$	9.00000			0.757937
$142$	2.00000	+	3.46410i	0.167836	+	0.290701i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$	−6.00000			−0.496564
$147$	6.50000	+	2.59808i	0.536111	+	0.214286i
$148$	4.00000			0.328798
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	1.00000			0.0808452
$154$	−4.00000	−	3.46410i	−0.322329	−	0.279145i
$155$	−3.00000			−0.240966
$156$	0.500000	+	0.866025i	0.0400320	+	0.0693375i
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	−0.885288	−	0.465044i	$-0.846039\pi$
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	0.845383	+	0.534160i	$0.179372\pi$
$158$		0			0
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−4.00000	+	20.7846i	−0.315244	+	1.63806i
$162$	−1.00000			−0.0785674
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$	−0.500000	+	0.866025i	−0.0390434	+	0.0676252i
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$	2.50000	−	0.866025i	0.192879	−	0.0668153i
$169$	−12.0000			−0.923077
$170$	0.500000	+	0.866025i	0.0383482	+	0.0664211i
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$	3.00000			0.227429
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$	−2.00000			−0.150756
$177$	5.50000	+	9.52628i	0.413405	+	0.716039i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$	0.500000	−	2.59808i	0.0370625	−	0.192582i
$183$		0			0
$184$	4.00000	+	6.92820i	0.294884	+	0.510754i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	−9.00000			−0.656392
$189$	2.00000	+	1.73205i	0.145479	+	0.125988i
$190$	−4.00000			−0.290191
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	−1.00000			−0.0716115
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	1.00000			0.0712470			0.0356235	−	0.999365i	$-0.488658\pi$
$197$	1.00000			0.0712470			0.0356235	+	0.999365i	$0.488658\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$	2.50000	−	4.33013i	0.177220	−	0.306955i	−0.763707	−	0.645563i	$-0.776623\pi$
$199$	2.50000	−	4.33013i	0.177220	−	0.306955i	0.940927	+	0.338608i	$0.109956\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$	−6.00000	−	10.3923i	−0.423207	−	0.733017i
$202$	−14.0000			−0.985037
$203$	−6.00000	−	5.19615i	−0.421117	−	0.364698i
$204$	−1.00000			−0.0700140
$205$	−0.500000	−	0.866025i	−0.0349215	−	0.0604858i
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$	−4.00000	+	6.92820i	−0.278019	+	0.481543i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−8.00000			−0.553372
$210$	−0.500000	+	2.59808i	−0.0345033	+	0.179284i
$211$	3.00000			0.206529			0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000			0.206529			0.103264	+	0.994654i	$0.467071\pi$
$212$		0			0
$213$	2.00000	−	3.46410i	0.137038	−	0.237356i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	1.00000			0.0680414
$217$	−7.50000	+	2.59808i	−0.509133	+	0.176369i
$218$	16.0000			1.08366
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	−0.500000	+	0.866025i	−0.0336336	+	0.0582552i
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$	−4.00000			−0.266667
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	−0.982877	−	0.184263i	$-0.941010\pi$
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	0.651015	+	0.759065i	$0.274343\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	0.975533	−	0.219853i	$-0.0705577\pi$
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	−0.678165	+	0.734910i	$0.737224\pi$
$230$	−8.00000			−0.527504
$231$	−1.00000	+	5.19615i	−0.0657952	+	0.341882i
$232$	−3.00000			−0.196960
$233$	5.50000	+	9.52628i	0.360317	+	0.624087i	0.988013	−	0.154371i	$-0.0493352\pi$
$233$	5.50000	+	9.52628i	0.360317	+	0.624087i	−0.627696	+	0.778459i	$0.716002\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	−5.50000	−	9.52628i	−0.358020	−	0.620108i
$237$		0			0
$238$	2.00000	+	1.73205i	0.129641	+	0.112272i
$239$	13.0000			0.840900			0.420450	−	0.907316i	$-0.361872\pi$
$239$	13.0000			0.840900			0.420450	+	0.907316i	$0.361872\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	5.50000	−	4.33013i	0.351382	−	0.276642i
$246$	1.00000			0.0637577
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	−1.50000	+	2.59808i	−0.0952501	+	0.164978i
$249$	4.50000	−	7.79423i	0.285176	−	0.493939i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	23.0000			1.45175			0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000			1.45175			0.725874	+	0.687828i	$0.241436\pi$
$252$	−2.00000	−	1.73205i	−0.125988	−	0.109109i
$253$	−16.0000			−1.00591
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$	0.500000	−	0.866025i	0.0313112	−	0.0542326i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$	−4.00000			−0.249029
$259$	−2.00000	+	10.3923i	−0.124274	+	0.645746i
$260$	1.00000			0.0620174
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	−0.715944	−	0.698158i	$-0.754003\pi$
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	0.962594	+	0.270947i	$0.0873367\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$		0			0
$266$	−10.0000	+	3.46410i	−0.613139	+	0.212398i
$267$	6.00000			0.367194
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	2.50000	−	4.33013i	0.152428	−	0.264013i	−0.779692	−	0.626164i	$-0.784624\pi$
$269$	2.50000	−	4.33013i	0.152428	−	0.264013i	0.932119	+	0.362151i	$0.117958\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−9.00000	−	15.5885i	−0.546711	−	0.946931i	−0.998497	−	0.0548050i	$-0.982546\pi$
$271$	−9.00000	−	15.5885i	−0.546711	−	0.946931i	0.451786	−	0.892126i	$-0.350787\pi$
$272$	1.00000			0.0606339
$273$	−2.50000	+	0.866025i	−0.151307	+	0.0524142i
$274$	−20.0000			−1.20824
$275$	−4.00000	−	6.92820i	−0.241209	−	0.417786i
$276$	4.00000	−	6.92820i	0.240772	−	0.417029i
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	0.0477206	+	0.998861i	$0.484804\pi$
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	−0.888899	+	0.458103i	$0.848529\pi$
$278$		0			0
$279$	−3.00000			−0.179605
$280$	0.500000	−	2.59808i	0.0298807	−	0.155265i
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$	4.50000	+	7.79423i	0.267971	+	0.464140i
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	−0.605575	−	0.795788i	$-0.707057\pi$
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	0.991960	+	0.126550i	$0.0403903\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$	2.00000	+	3.46410i	0.118470	+	0.205196i
$286$	2.00000			0.118262
$287$	−2.00000	−	1.73205i	−0.118056	−	0.102240i
$288$	−1.00000			−0.0589256
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	1.50000	−	2.59808i	0.0880830	−	0.152564i
$291$	4.00000	−	6.92820i	0.234484	−	0.406138i
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	1.00000	+	6.92820i	0.0583212	+	0.404061i
$295$	11.0000			0.640445
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−1.00000	+	1.73205i	−0.0579284	+	0.100335i
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$	4.00000			0.230940
$301$	8.00000	+	6.92820i	0.461112	+	0.399335i
$302$	4.00000			0.230174
$303$	7.00000	+	12.1244i	0.402139	+	0.696526i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$		0			0
$306$	0.500000	+	0.866025i	0.0285831	+	0.0495074i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	1.00000	−	5.19615i	0.0569803	−	0.296078i
$309$	−14.0000			−0.796432
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$	−0.500000	+	0.866025i	−0.0283069	+	0.0490290i
$313$	−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	$0.905929\pi$
$314$	−1.00000			−0.0564333
$315$	2.50000	−	0.866025i	0.140859	−	0.0487950i
$316$		0			0
$317$	5.50000	+	9.52628i	0.308911	+	0.535049i	0.978124	−	0.208021i	$-0.0667022\pi$
$317$	5.50000	+	9.52628i	0.308911	+	0.535049i	−0.669214	+	0.743070i	$0.733369\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	12.0000			0.669775
$322$	−20.0000	+	6.92820i	−1.11456	+	0.386094i
$323$	4.00000			0.222566
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$	−8.00000	−	13.8564i	−0.442401	−	0.766261i
$328$	−1.00000			−0.0552158
$329$	4.50000	−	23.3827i	0.248093	−	1.28913i
$330$	−2.00000			−0.110096
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	0.992112	+	0.125353i	$0.0400062\pi$
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	−0.387498	+	0.921871i	$0.626660\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	−2.00000	+	3.46410i	−0.109599	+	0.189832i
$334$	1.00000	+	1.73205i	0.0547176	+	0.0947736i
$335$	−12.0000			−0.655630
$336$	2.00000	+	1.73205i	0.109109	+	0.0944911i
$337$	34.0000			1.85210			0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000			1.85210			0.926049	+	0.377403i	$0.123183\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	7.50000	−	12.9904i	0.407344	−	0.705541i
$340$	−0.500000	+	0.866025i	−0.0271163	+	0.0469668i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	−4.00000			−0.216295
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	4.00000			0.215666
$345$	4.00000	+	6.92820i	0.215353	+	0.373002i
$346$	10.5000	−	18.1865i	0.564483	−	0.977714i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	27.0000			1.44528			0.722638	−	0.691226i	$-0.242929\pi$
$349$	27.0000			1.44528			0.722638	+	0.691226i	$0.242929\pi$
$350$	−8.00000	−	6.92820i	−0.427618	−	0.370328i
$351$	−1.00000			−0.0533761
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−14.0000	+	24.2487i	−0.745145	+	1.29063i	0.204982	+	0.978766i	$0.434286\pi$
$353$	−14.0000	+	24.2487i	−0.745145	+	1.29063i	−0.950127	+	0.311863i	$0.899047\pi$
$354$	−5.50000	+	9.52628i	−0.292322	+	0.506316i
$355$	−2.00000	−	3.46410i	−0.106149	−	0.183855i
$356$	−6.00000			−0.317999
$357$	0.500000	−	2.59808i	0.0264628	−	0.137505i
$358$	21.0000			1.10988
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	8.00000	+	13.8564i	0.420471	+	0.728277i
$363$	7.00000			0.367405
$364$	2.50000	−	0.866025i	0.131036	−	0.0453921i
$365$	6.00000			0.314054
$366$		0			0
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$	−4.00000	+	6.92820i	−0.208514	+	0.361158i
$369$	−0.500000	−	0.866025i	−0.0260290	−	0.0450835i
$370$	−4.00000			−0.207950
$371$		0			0
$372$	3.00000			0.155543
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	0.508065	−	0.861319i	$-0.330361\pi$
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	−0.999956	+	0.00933789i	$0.997028\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	3.00000			0.154508
$378$	−0.500000	+	2.59808i	−0.0257172	+	0.133631i
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	1.50000	−	2.59808i	0.0767467	−	0.132929i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$	1.00000			0.0510310
$385$	4.00000	+	3.46410i	0.203859	+	0.176547i
$386$	14.0000			0.712581
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−4.00000	+	6.92820i	−0.203069	+	0.351726i
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	−0.839561	−	0.543266i	$-0.817187\pi$
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	0.890263	+	0.455448i	$0.150521\pi$
$390$	−0.500000	−	0.866025i	−0.0253185	−	0.0438529i
$391$	8.00000			0.404577
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$	6.00000			0.302660
$394$	0.500000	+	0.866025i	0.0251896	+	0.0436297i
$395$		0			0
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	4.00000	+	6.92820i	0.200754	+	0.347717i	0.948772	−	0.315963i	$-0.102327\pi$
$397$	4.00000	+	6.92820i	0.200754	+	0.347717i	−0.748017	+	0.663679i	$0.768994\pi$
$398$	5.00000			0.250627
$399$	8.00000	+	6.92820i	0.400501	+	0.346844i
$400$	−4.00000			−0.200000
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$	6.00000	−	10.3923i	0.299253	−	0.518321i
$403$	1.50000	−	2.59808i	0.0747203	−	0.129419i
$404$	−7.00000	−	12.1244i	−0.348263	−	0.603209i
$405$	1.00000			0.0496904
$406$	1.50000	−	7.79423i	0.0744438	−	0.386821i
$407$	−8.00000			−0.396545
$408$	−0.500000	−	0.866025i	−0.0247537	−	0.0428746i
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$	0.500000	−	0.866025i	0.0246932	−	0.0427699i
$411$	10.0000	+	17.3205i	0.493264	+	0.854358i
$412$	14.0000			0.689730
$413$	27.5000	−	9.52628i	1.35319	−	0.468758i
$414$	−8.00000			−0.393179
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	−4.00000	−	6.92820i	−0.195646	−	0.338869i
$419$	4.00000			0.195413			0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000			0.195413			0.0977064	+	0.995215i	$0.468849\pi$
$420$	−2.50000	+	0.866025i	−0.121988	+	0.0422577i
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	1.50000	+	2.59808i	0.0730189	+	0.126472i
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$		0			0
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$	4.00000			0.193801
$427$		0			0
$428$	−12.0000			−0.580042
$429$	−1.00000	−	1.73205i	−0.0482805	−	0.0836242i
$430$	−2.00000	+	3.46410i	−0.0964486	+	0.167054i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	19.0000			0.913082			0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000			0.913082			0.456541	+	0.889702i	$0.349088\pi$
$434$	−6.00000	−	5.19615i	−0.288009	−	0.249423i
$435$	−3.00000			−0.143839
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	−16.0000	+	27.7128i	−0.765384	+	1.32568i
$438$	−3.00000	+	5.19615i	−0.143346	+	0.248282i
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$	2.00000			0.0953463
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	−1.00000			−0.0475651
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	−0.929631	−	0.368492i	$-0.879874\pi$
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	0.145692	−	0.989330i	$-0.453459\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	2.00000			0.0945968
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	−2.00000	−	3.46410i	−0.0942809	−	0.163299i
$451$	1.00000	−	1.73205i	0.0470882	−	0.0815591i
$452$	−7.50000	+	12.9904i	−0.352770	+	0.611016i
$453$	−2.00000	−	3.46410i	−0.0939682	−	0.162758i
$454$	−10.0000			−0.469323
$455$	−0.500000	+	2.59808i	−0.0234404	+	0.121800i
$456$	4.00000			0.187317
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	0.854094	−	0.520119i	$-0.174112\pi$
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	−0.877483	+	0.479608i	$0.840779\pi$
$458$	−4.50000	+	7.79423i	−0.210271	+	0.364200i
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$	−4.00000	−	6.92820i	−0.186501	−	0.323029i
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$	−5.00000	+	1.73205i	−0.232621	+	0.0805823i
$463$	−18.0000			−0.836531			−0.418265	−	0.908325i	$-0.637362\pi$
$463$	−18.0000			−0.836531			−0.418265	+	0.908325i	$0.637362\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$	−1.50000	+	2.59808i	−0.0695608	+	0.120483i
$466$	−5.50000	+	9.52628i	−0.254783	+	0.441296i
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$	1.00000			0.0462250
$469$	−30.0000	+	10.3923i	−1.38527	+	0.479872i
$470$	9.00000			0.415139
$471$	0.500000	+	0.866025i	0.0230388	+	0.0399043i
$472$	5.50000	−	9.52628i	0.253158	−	0.438483i
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$		0			0
$475$	−16.0000			−0.734130
$476$	−0.500000	+	2.59808i	−0.0229175	+	0.119083i
$477$		0			0
$478$	6.50000	+	11.2583i	0.297303	+	0.514944i
$479$	−13.0000	+	22.5167i	−0.593985	+	1.02881i	0.399704	+	0.916644i	$0.369113\pi$
$479$	−13.0000	+	22.5167i	−0.593985	+	1.02881i	−0.993689	+	0.112168i	$0.964220\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	−18.0000			−0.819878
$483$	16.0000	+	13.8564i	0.728025	+	0.630488i
$484$	−7.00000			−0.318182
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	13.5000	−	23.3827i	0.611743	−	1.05957i	−0.379203	−	0.925313i	$-0.623802\pi$
$487$	13.5000	−	23.3827i	0.611743	−	1.05957i	0.990947	−	0.134257i	$-0.0428648\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$	6.50000	+	2.59808i	0.293640	+	0.117369i
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$	0.500000	+	0.866025i	0.0225417	+	0.0390434i
$493$	−1.50000	+	2.59808i	−0.0675566	+	0.117011i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$	1.00000	+	1.73205i	0.0449467	+	0.0778499i
$496$	−3.00000			−0.134704
$497$	−8.00000	−	6.92820i	−0.358849	−	0.310772i
$498$	9.00000			0.403300
$499$	−6.50000	−	11.2583i	−0.290980	−	0.503992i	0.683062	−	0.730361i	$-0.260648\pi$
$499$	−6.50000	−	11.2583i	−0.290980	−	0.503992i	−0.974042	+	0.226369i	$0.927315\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	1.00000	−	1.73205i	0.0446767	−	0.0773823i
$502$	11.5000	+	19.9186i	0.513270	+	0.889010i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	0.500000	−	2.59808i	0.0222718	−	0.115728i
$505$	14.0000			0.622992
$506$	−8.00000	−	13.8564i	−0.355643	−	0.615992i
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	−14.0000	−	24.2487i	−0.620539	−	1.07481i	−0.989385	−	0.145315i	$-0.953580\pi$
$509$	−14.0000	−	24.2487i	−0.620539	−	1.07481i	0.368846	−	0.929490i	$-0.379753\pi$
$510$	1.00000			0.0442807
$511$	15.0000	−	5.19615i	0.663561	−	0.229864i
$512$	−1.00000			−0.0441942
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$	7.00000	−	12.1244i	0.308757	−	0.534782i
$515$	−7.00000	+	12.1244i	−0.308457	+	0.534263i
$516$	−2.00000	−	3.46410i	−0.0880451	−	0.152499i
$517$	18.0000			0.791639
$518$	−10.0000	+	3.46410i	−0.439375	+	0.152204i
$519$	−21.0000			−0.921798
$520$	0.500000	+	0.866025i	0.0219265	+	0.0379777i
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$	1.50000	−	2.59808i	0.0656532	−	0.113715i
$523$	20.0000	+	34.6410i	0.874539	+	1.51475i	0.857253	+	0.514895i	$0.172169\pi$
$523$	20.0000	+	34.6410i	0.874539	+	1.51475i	0.0172859	+	0.999851i	$0.494497\pi$
$524$	−6.00000			−0.262111
$525$	−2.00000	+	10.3923i	−0.0872872	+	0.453557i
$526$	8.00000			0.348817
$527$	1.50000	+	2.59808i	0.0653410	+	0.113174i
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	11.0000			0.477359
$532$	−8.00000	−	6.92820i	−0.346844	−	0.300376i
$533$	1.00000			0.0433148
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$	−10.5000	−	18.1865i	−0.453108	−	0.784807i
$538$	5.00000			0.215565
$539$	13.0000	+	5.19615i	0.559950	+	0.223814i
$540$	−1.00000			−0.0430331
$541$	16.0000	+	27.7128i	0.687894	+	1.19147i	0.972518	+	0.232828i	$0.0747978\pi$
$541$	16.0000	+	27.7128i	0.687894	+	1.19147i	−0.284624	+	0.958639i	$0.591869\pi$
$542$	9.00000	−	15.5885i	0.386583	−	0.669582i
$543$	8.00000	−	13.8564i	0.343313	−	0.594635i
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	−16.0000			−0.685365
$546$	−2.00000	−	1.73205i	−0.0855921	−	0.0741249i
$547$	−41.0000			−1.75303			−0.876517	−	0.481371i	$-0.840139\pi$
$547$	−41.0000			−1.75303			−0.876517	+	0.481371i	$0.840139\pi$
$548$	−10.0000	−	17.3205i	−0.427179	−	0.739895i
$549$		0			0
$550$	4.00000	−	6.92820i	0.170561	−	0.295420i
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$	8.00000			0.340503
$553$		0			0
$554$	−28.0000			−1.18961
$555$	2.00000	+	3.46410i	0.0848953	+	0.147043i
$556$		0			0
$557$	−8.00000	+	13.8564i	−0.338971	+	0.587115i	−0.984239	−	0.176841i	$-0.943412\pi$
$557$	−8.00000	+	13.8564i	−0.338971	+	0.587115i	0.645269	+	0.763956i	$0.276745\pi$
$558$	−1.50000	−	2.59808i	−0.0635001	−	0.109985i
$559$	−4.00000			−0.169182
$560$	2.50000	−	0.866025i	0.105644	−	0.0365963i
$561$	2.00000			0.0844401
$562$	10.0000	+	17.3205i	0.421825	+	0.730622i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$	−4.50000	+	7.79423i	−0.189484	+	0.328196i
$565$	−7.50000	−	12.9904i	−0.315527	−	0.546509i
$566$	13.0000			0.546431
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	−4.00000			−0.167836
$569$	1.00000	+	1.73205i	0.0419222	+	0.0726113i	0.886225	−	0.463255i	$-0.153319\pi$
$569$	1.00000	+	1.73205i	0.0419222	+	0.0726113i	−0.844303	+	0.535866i	$0.819985\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$	1.00000	+	1.73205i	0.0418121	+	0.0724207i
$573$	−3.00000			−0.125327
$574$	0.500000	−	2.59808i	0.0208696	−	0.108442i
$575$	−32.0000			−1.33449
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	7.50000	−	12.9904i	0.312229	−	0.540797i	−0.666616	−	0.745402i	$-0.732258\pi$
$577$	7.50000	−	12.9904i	0.312229	−	0.540797i	0.978845	+	0.204605i	$0.0655910\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	−7.00000	−	12.1244i	−0.290910	−	0.503871i
$580$	3.00000			0.124568
$581$	−18.0000	−	15.5885i	−0.746766	−	0.646718i
$582$	8.00000			0.331611
$583$		0			0
$584$	3.00000	−	5.19615i	0.124141	−	0.215018i
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	−5.50000	+	4.33013i	−0.226816	+	0.178571i
$589$	−12.0000			−0.494451
$590$	5.50000	+	9.52628i	0.226431	+	0.392191i
$591$	0.500000	−	0.866025i	0.0205673	−	0.0356235i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	−11.0000	−	19.0526i	−0.451716	−	0.782395i	0.546777	−	0.837278i	$-0.315855\pi$
$593$	−11.0000	−	19.0526i	−0.451716	−	0.782395i	−0.998493	+	0.0548835i	$0.982521\pi$
$594$	−2.00000			−0.0820610
$595$	−2.00000	−	1.73205i	−0.0819920	−	0.0710072i
$596$	−2.00000			−0.0819232
$597$	−2.50000	−	4.33013i	−0.102318	−	0.177220i
$598$	4.00000	−	6.92820i	0.163572	−	0.283315i
$599$	−5.50000	+	9.52628i	−0.224724	+	0.389233i	−0.956237	−	0.292595i	$-0.905481\pi$
$599$	−5.50000	+	9.52628i	−0.224724	+	0.389233i	0.731513	+	0.681828i	$0.238815\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$	−2.00000	+	10.3923i	−0.0815139	+	0.423559i
$603$	−12.0000			−0.488678
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	−7.00000	+	12.1244i	−0.284356	+	0.492518i
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	0.855700	−	0.517472i	$-0.173127\pi$
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	−0.875994	+	0.482322i	$0.839794\pi$
$608$	−4.00000			−0.162221
$609$	−7.50000	+	2.59808i	−0.303915	+	0.105279i
$610$		0			0
$611$	4.50000	+	7.79423i	0.182051	+	0.315321i
$612$	−0.500000	+	0.866025i	−0.0202113	+	0.0350070i
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	−0.474509	−	0.880251i	$-0.657374\pi$
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	0.999574	−	0.0291886i	$-0.00929235\pi$
$614$	10.0000	+	17.3205i	0.403567	+	0.698999i
$615$	−1.00000			−0.0403239
$616$	5.00000	−	1.73205i	0.201456	−	0.0697863i
$617$	17.0000			0.684394			0.342197	−	0.939628i	$-0.388829\pi$
$617$	17.0000			0.684394			0.342197	+	0.939628i	$0.388829\pi$
$618$	−7.00000	−	12.1244i	−0.281581	−	0.487713i
$619$	−14.0000	+	24.2487i	−0.562708	+	0.974638i	0.434551	+	0.900647i	$0.356907\pi$
$619$	−14.0000	+	24.2487i	−0.562708	+	0.974638i	−0.997259	+	0.0739910i	$0.976426\pi$
$620$	1.50000	−	2.59808i	0.0602414	−	0.104341i
$621$	4.00000	+	6.92820i	0.160514	+	0.278019i
$622$	18.0000			0.721734
$623$	3.00000	−	15.5885i	0.120192	−	0.624538i
$624$	−1.00000			−0.0400320
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	−4.00000	+	6.92820i	−0.159745	+	0.276686i
$628$	−0.500000	−	0.866025i	−0.0199522	−	0.0345582i
$629$	4.00000			0.159490
$630$	2.00000	+	1.73205i	0.0796819	+	0.0690066i
$631$	−38.0000			−1.51276			−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000			−1.51276			−0.756378	+	0.654135i	$0.773033\pi$
$632$		0			0
$633$	1.50000	−	2.59808i	0.0596196	−	0.103264i
$634$	−5.50000	+	9.52628i	−0.218433	+	0.378337i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$		0			0
$637$	1.00000	+	6.92820i	0.0396214	+	0.274505i
$638$	6.00000			0.237542
$639$	−2.00000	−	3.46410i	−0.0791188	−	0.137038i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$	6.00000	+	10.3923i	0.236801	+	0.410152i
$643$	45.0000			1.77463			0.887313	−	0.461167i	$-0.152569\pi$
$643$	45.0000			1.77463			0.887313	+	0.461167i	$0.152569\pi$
$644$	−16.0000	−	13.8564i	−0.630488	−	0.546019i
$645$	4.00000			0.157500
$646$	2.00000	+	3.46410i	0.0786889	+	0.136293i
$647$	−16.5000	+	28.5788i	−0.648682	+	1.12355i	0.334756	+	0.942305i	$0.391346\pi$
$647$	−16.5000	+	28.5788i	−0.648682	+	1.12355i	−0.983438	+	0.181245i	$0.941987\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	11.0000	+	19.0526i	0.431788	+	0.747878i
$650$	4.00000			0.156893
$651$	−1.50000	+	7.79423i	−0.0587896	+	0.305480i
$652$	16.0000			0.626608
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	8.00000	−	13.8564i	0.312825	−	0.541828i
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	−0.500000	−	0.866025i	−0.0195217	−	0.0338126i
$657$	6.00000			0.234082
$658$	22.5000	−	7.79423i	0.877141	−	0.303851i
$659$	39.0000			1.51922			0.759612	−	0.650376i	$-0.225389\pi$
$659$	39.0000			1.51922			0.759612	+	0.650376i	$0.225389\pi$
$660$	−1.00000	−	1.73205i	−0.0389249	−	0.0674200i
$661$	−23.5000	+	40.7032i	−0.914044	+	1.58317i	−0.105749	+	0.994393i	$0.533724\pi$
$661$	−23.5000	+	40.7032i	−0.914044	+	1.58317i	−0.808295	+	0.588778i	$0.799609\pi$
$662$	−11.0000	+	19.0526i	−0.427527	+	0.740499i
$663$	0.500000	+	0.866025i	0.0194184	+	0.0336336i
$664$	−9.00000			−0.349268
$665$	10.0000	−	3.46410i	0.387783	−	0.134332i
$666$	−4.00000			−0.154997
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$		0			0
$672$	−0.500000	+	2.59808i	−0.0192879	+	0.100223i
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	17.0000	+	29.4449i	0.654816	+	1.13417i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$	15.0000			0.576072
$679$	−16.0000	−	13.8564i	−0.614024	−	0.531760i
$680$	−1.00000			−0.0383482
$681$	5.00000	+	8.66025i	0.191600	+	0.331862i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$	20.0000			0.764161
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	9.00000			0.343371
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$		0			0
$690$	−4.00000	+	6.92820i	−0.152277	+	0.263752i
$691$	23.5000	+	40.7032i	0.893982	+	1.54842i	0.835059	+	0.550160i	$0.185433\pi$
$691$	23.5000	+	40.7032i	0.893982	+	1.54842i	0.0589228	+	0.998263i	$0.481233\pi$
$692$	21.0000			0.798300
$693$	4.00000	+	3.46410i	0.151947	+	0.131590i
$694$	4.00000			0.151838
$695$		0			0
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$	−0.500000	+	0.866025i	−0.0189389	+	0.0328031i
$698$	13.5000	+	23.3827i	0.510983	+	0.885048i
$699$	11.0000			0.416058
$700$	2.00000	−	10.3923i	0.0755929	−	0.392792i
$701$	20.0000			0.755390			0.377695	−	0.925930i	$-0.376717\pi$
$701$	20.0000			0.755390			0.377695	+	0.925930i	$0.376717\pi$
$702$	−0.500000	−	0.866025i	−0.0188713	−	0.0326860i
$703$	−8.00000	+	13.8564i	−0.301726	+	0.522604i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	−4.50000	−	7.79423i	−0.169480	−	0.293548i
$706$	−28.0000			−1.05379
$707$	35.0000	−	12.1244i	1.31631	−	0.455983i
$708$	−11.0000			−0.413405
$709$	21.0000	+	36.3731i	0.788672	+	1.36602i	0.926781	+	0.375602i	$0.122564\pi$
$709$	21.0000	+	36.3731i	0.788672	+	1.36602i	−0.138109	+	0.990417i	$0.544103\pi$
$710$	2.00000	−	3.46410i	0.0750587	−	0.130005i
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−24.0000			−0.898807
$714$	2.50000	−	0.866025i	0.0935601	−	0.0324102i
$715$	−2.00000			−0.0747958
$716$	10.5000	+	18.1865i	0.392403	+	0.679663i
$717$	6.50000	−	11.2583i	0.242747	−	0.420450i
$718$	7.50000	−	12.9904i	0.279898	−	0.484797i
$719$	25.0000	+	43.3013i	0.932343	+	1.61486i	0.779305	+	0.626644i	$0.215572\pi$
$719$	25.0000	+	43.3013i	0.932343	+	1.61486i	0.153037	+	0.988220i	$0.451094\pi$
$720$	1.00000			0.0372678
$721$	−7.00000	+	36.3731i	−0.260694	+	1.35460i
$722$	3.00000			0.111648
$723$	9.00000	+	15.5885i	0.334714	+	0.579741i
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$	3.50000	+	6.06218i	0.129897	+	0.224989i
$727$	26.0000			0.964287			0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000			0.964287			0.482143	+	0.876092i	$0.339858\pi$
$728$	2.00000	+	1.73205i	0.0741249	+	0.0641941i
$729$	1.00000			0.0370370
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	32.0000			1.18114
$735$	−1.00000	−	6.92820i	−0.0368856	−	0.255551i
$736$	−8.00000			−0.294884
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$	0.500000	−	0.866025i	0.0184053	−	0.0318788i
$739$	−21.0000	+	36.3731i	−0.772497	+	1.33800i	0.163693	+	0.986511i	$0.447659\pi$
$739$	−21.0000	+	36.3731i	−0.772497	+	1.33800i	−0.936190	+	0.351494i	$0.885674\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$	−4.00000			−0.146944
$742$		0			0
$743$	−16.0000			−0.586983			−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000			−0.586983			−0.293492	+	0.955962i	$0.594817\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$	1.00000	−	1.73205i	0.0366372	−	0.0634574i
$746$	9.50000	−	16.4545i	0.347820	−	0.602441i
$747$	−4.50000	−	7.79423i	−0.164646	−	0.285176i
$748$	−2.00000			−0.0731272
$749$	6.00000	−	31.1769i	0.219235	−	1.13918i
$750$	−9.00000			−0.328634
$751$	13.5000	+	23.3827i	0.492622	+	0.853246i	0.999964	−	0.00849853i	$-0.00270520\pi$
$751$	13.5000	+	23.3827i	0.492622	+	0.853246i	−0.507342	+	0.861745i	$0.669372\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$	11.5000	−	19.9186i	0.419083	−	0.725874i
$754$	1.50000	+	2.59808i	0.0546268	+	0.0946164i
$755$	−4.00000			−0.145575
$756$	−2.50000	+	0.866025i	−0.0909241	+	0.0314970i
$757$	27.0000			0.981332			0.490666	−	0.871348i	$-0.336754\pi$
$757$	27.0000			0.981332			0.490666	+	0.871348i	$0.336754\pi$
$758$	4.00000	+	6.92820i	0.145287	+	0.251644i
$759$	−8.00000	+	13.8564i	−0.290382	+	0.502956i
$760$	2.00000	−	3.46410i	0.0725476	−	0.125656i
$761$	18.0000	+	31.1769i	0.652499	+	1.13016i	0.982514	+	0.186187i	$0.0596129\pi$
$761$	18.0000	+	31.1769i	0.652499	+	1.13016i	−0.330015	+	0.943976i	$0.607054\pi$
$762$	−8.00000			−0.289809
$763$	−40.0000	+	13.8564i	−1.44810	+	0.501636i
$764$	3.00000			0.108536
$765$	−0.500000	−	0.866025i	−0.0180775	−	0.0313112i
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−5.50000	+	9.52628i	−0.198593	+	0.343974i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−46.0000			−1.65880			−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000			−1.65880			−0.829401	+	0.558653i	$0.811318\pi$
$770$	−1.00000	+	5.19615i	−0.0360375	+	0.187256i
$771$	−14.0000			−0.504198
$772$	7.00000	+	12.1244i	0.251936	+	0.436365i
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	0.0729331	+	0.997337i	$0.476764\pi$
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	−0.900186	+	0.435507i	$0.856569\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	−6.00000	−	10.3923i	−0.215526	−	0.373303i
$776$	−8.00000			−0.287183
$777$	8.00000	+	6.92820i	0.286998	+	0.248548i
$778$	2.00000			0.0717035
$779$	−2.00000	−	3.46410i	−0.0716574	−	0.124114i
$780$	0.500000	−	0.866025i	0.0179029	−	0.0310087i
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	4.00000	+	6.92820i	0.143040	+	0.247752i
$783$	−3.00000			−0.107211
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	1.00000			0.0356915
$786$	3.00000	+	5.19615i	0.107006	+	0.185341i
$787$	−9.50000	+	16.4545i	−0.338638	+	0.586539i	−0.984177	−	0.177189i	$-0.943300\pi$
$787$	−9.50000	+	16.4545i	−0.338638	+	0.586539i	0.645538	+	0.763728i	$0.276633\pi$
$788$	−0.500000	+	0.866025i	−0.0178118	+	0.0308509i
$789$	−4.00000	−	6.92820i	−0.142404	−	0.246651i
$790$		0			0
$791$	−30.0000	−	25.9808i	−1.06668	−	0.923770i
$792$	2.00000			0.0710669
$793$		0			0
$794$	−4.00000	+	6.92820i	−0.141955	+	0.245873i
$795$		0			0
$796$	2.50000	+	4.33013i	0.0886102	+	0.153477i
$797$	40.0000			1.41687			0.708436	−	0.705775i	$-0.249401\pi$
$797$	40.0000			1.41687			0.708436	+	0.705775i	$0.249401\pi$
$798$	−2.00000	+	10.3923i	−0.0707992	+	0.367884i
$799$	−9.00000			−0.318397
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	15.0000	−	25.9808i	0.529668	−	0.917413i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$	12.0000			0.423207
$805$	20.0000	−	6.92820i	0.704907	−	0.244187i
$806$	3.00000			0.105670
$807$	−2.50000	−	4.33013i	−0.0880042	−	0.152428i
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	19.0000	−	32.9090i	0.668004	−	1.15702i	−0.310457	−	0.950587i	$-0.600482\pi$
$809$	19.0000	−	32.9090i	0.668004	−	1.15702i	0.978461	−	0.206430i	$-0.0661846\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	11.0000			0.386262			0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000			0.386262			0.193131	+	0.981173i	$0.438136\pi$
$812$	7.50000	−	2.59808i	0.263198	−	0.0911746i
$813$	−18.0000			−0.631288
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$	0.500000	−	0.866025i	0.0175035	−	0.0303170i
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	−26.0000			−0.909069
$819$	−0.500000	+	2.59808i	−0.0174714	+	0.0907841i
$820$	1.00000			0.0349215
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$	−10.0000	+	17.3205i	−0.348790	+	0.604122i
$823$	−17.5000	+	30.3109i	−0.610012	+	1.05657i	0.381226	+	0.924482i	$0.375502\pi$
$823$	−17.5000	+	30.3109i	−0.610012	+	1.05657i	−0.991238	+	0.132089i	$0.957831\pi$
$824$	7.00000	+	12.1244i	0.243857	+	0.422372i
$825$	−8.00000			−0.278524
$826$	22.0000	+	19.0526i	0.765478	+	0.662923i
$827$	−46.0000			−1.59958			−0.799788	−	0.600282i	$-0.795055\pi$
$827$	−46.0000			−1.59958			−0.799788	+	0.600282i	$0.795055\pi$
$828$	−4.00000	−	6.92820i	−0.139010	−	0.240772i
$829$	27.0000	−	46.7654i	0.937749	−	1.62423i	0.168091	−	0.985771i	$-0.446240\pi$
$829$	27.0000	−	46.7654i	0.937749	−	1.62423i	0.769657	−	0.638457i	$-0.220427\pi$
$830$	4.50000	−	7.79423i	0.156197	−	0.270542i
$831$	14.0000	+	24.2487i	0.485655	+	0.841178i
$832$	1.00000			0.0346688
$833$	−6.50000	−	2.59808i	−0.225212	−	0.0900180i
$834$		0			0
$835$	−1.00000	−	1.73205i	−0.0346064	−	0.0599401i
$836$	4.00000	−	6.92820i	0.138343	−	0.239617i
$837$	−1.50000	+	2.59808i	−0.0518476	+	0.0898027i
$838$	2.00000	+	3.46410i	0.0690889	+	0.119665i
$839$	−26.0000			−0.897620			−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000			−0.897620			−0.448810	+	0.893627i	$0.648152\pi$
$840$	−2.00000	−	1.73205i	−0.0690066	−	0.0597614i
$841$	−20.0000			−0.689655
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$	10.0000	−	17.3205i	0.344418	−	0.596550i
$844$	−1.50000	+	2.59808i	−0.0516321	+	0.0894295i
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$	9.00000			0.309426
$847$	3.50000	−	18.1865i	0.120261	−	0.624897i
$848$		0			0
$849$	−6.50000	−	11.2583i	−0.223079	−	0.386385i
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$	−16.0000	+	27.7128i	−0.548473	+	0.949983i
$852$	2.00000	+	3.46410i	0.0685189	+	0.118678i
$853$	16.0000			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	−0.629066	−	0.777352i	$-0.716563\pi$
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	0.987739	+	0.156112i	$0.0498959\pi$
$858$	1.00000	−	1.73205i	0.0341394	−	0.0591312i
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$	−4.00000			−0.136399
$861$	−2.50000	+	0.866025i	−0.0851998	+	0.0295141i
$862$		0			0
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	0.745649	−	0.666339i	$-0.232140\pi$
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	−0.949891	+	0.312581i	$0.898806\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−10.5000	+	18.1865i	−0.357011	+	0.618361i
$866$	9.50000	+	16.4545i	0.322823	+	0.559146i
$867$	−1.00000			−0.0339618
$868$	1.50000	−	7.79423i	0.0509133	−	0.264553i
$869$		0			0
$870$	−1.50000	−	2.59808i	−0.0508548	−	0.0880830i
$871$	6.00000	−	10.3923i	0.203302	−	0.352130i
$872$	−8.00000	+	13.8564i	−0.270914	+	0.469237i
$873$	−4.00000	−	6.92820i	−0.135379	−	0.234484i
$874$	−32.0000			−1.08242
$875$	18.0000	+	15.5885i	0.608511	+	0.526986i
$876$	−6.00000			−0.202721
$877$	−15.0000	−	25.9808i	−0.506514	−	0.877308i	−0.999972	−	0.00753813i	$-0.997601\pi$
$877$	−15.0000	−	25.9808i	−0.506514	−	0.877308i	0.493458	−	0.869770i	$-0.335733\pi$
$878$	−0.500000	+	0.866025i	−0.0168742	+	0.0292269i
$879$		0			0
$880$	1.00000	+	1.73205i	0.0337100	+	0.0583874i
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	6.50000	+	2.59808i	0.218866	+	0.0874818i
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−0.500000	−	0.866025i	−0.0168168	−	0.0291276i
$885$	5.50000	−	9.52628i	0.184880	−	0.320222i
$886$	16.5000	−	28.5788i	0.554328	−	0.960125i
$887$	13.0000	+	22.5167i	0.436497	+	0.756035i	0.997417	−	0.0718351i	$-0.0228855\pi$
$887$	13.0000	+	22.5167i	0.436497	+	0.756035i	−0.560919	+	0.827871i	$0.689552\pi$
$888$	4.00000			0.134231
$889$	16.0000	+	13.8564i	0.536623	+	0.464729i
$890$	6.00000			0.201120
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$	1.00000	+	1.73205i	0.0334450	+	0.0579284i
$895$	−21.0000			−0.701953
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$	−8.00000			−0.267112
$898$	−3.00000	−	5.19615i	−0.100111	−	0.173398i
$899$	4.50000	−	7.79423i	0.150083	−	0.259952i
$900$	2.00000	−	3.46410i	0.0666667	−	0.115470i
$901$		0			0
$902$	2.00000			0.0665927
$903$	10.0000	−	3.46410i	0.332779	−	0.115278i
$904$	−15.0000			−0.498893
$905$	−8.00000	−	13.8564i	−0.265929	−	0.460603i
$906$	2.00000	−	3.46410i	0.0664455	−	0.115087i
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	0.151460	+	0.988463i	$0.451603\pi$
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	−0.931764	+	0.363064i	$0.881731\pi$
$908$	−5.00000	−	8.66025i	−0.165931	−	0.287401i
$909$	14.0000			0.464351
$910$	−2.50000	+	0.866025i	−0.0828742	+	0.0287085i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$		0			0
$916$	−9.00000			−0.297368
$917$	3.00000	−	15.5885i	0.0990687	−	0.514776i
$918$	1.00000			0.0330049
$919$	−29.0000	−	50.2295i	−0.956622	−	1.65692i	−0.730613	−	0.682792i	$-0.760765\pi$
$919$	−29.0000	−	50.2295i	−0.956622	−	1.65692i	−0.226009	−	0.974125i	$-0.572568\pi$
$920$	4.00000	−	6.92820i	0.131876	−	0.228416i
$921$	10.0000	−	17.3205i	0.329511	−	0.570730i
$922$	−10.0000	−	17.3205i	−0.329332	−	0.570421i
$923$	4.00000			0.131662
$924$	−4.00000	−	3.46410i	−0.131590	−	0.113961i
$925$	−16.0000			−0.526077
$926$	−9.00000	−	15.5885i	−0.295758	−	0.512268i
$927$	−7.00000	+	12.1244i	−0.229910	+	0.398216i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	2.50000	+	4.33013i	0.0820223	+	0.142067i	0.904118	−	0.427282i	$-0.140529\pi$
$929$	2.50000	+	4.33013i	0.0820223	+	0.142067i	−0.822096	+	0.569349i	$0.807195\pi$
$930$	−3.00000			−0.0983739
$931$	22.0000	−	17.3205i	0.721021	−	0.567657i
$932$	−11.0000			−0.360317
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$	−1.50000	+	2.59808i	−0.0490815	+	0.0850117i
$935$	1.00000	−	1.73205i	0.0327035	−	0.0566441i
$936$	0.500000	+	0.866025i	0.0163430	+	0.0283069i
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	−24.0000	−	20.7846i	−0.783628	−	0.678642i
$939$	−8.00000			−0.261070
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	1.00000	−	1.73205i	0.0325991	−	0.0564632i	−0.849266	−	0.527966i	$-0.822955\pi$
$941$	1.00000	−	1.73205i	0.0325991	−	0.0564632i	0.881865	+	0.471503i	$0.156288\pi$
$942$	−0.500000	+	0.866025i	−0.0162909	+	0.0282166i
$943$	−4.00000	−	6.92820i	−0.130258	−	0.225613i
$944$	11.0000			0.358020
$945$	0.500000	−	2.59808i	0.0162650	−	0.0845154i
$946$	−8.00000			−0.260102
$947$	−7.00000	−	12.1244i	−0.227469	−	0.393989i	0.729588	−	0.683887i	$-0.239712\pi$
$947$	−7.00000	−	12.1244i	−0.227469	−	0.393989i	−0.957057	+	0.289898i	$0.906379\pi$
$948$		0			0
$949$	−3.00000	+	5.19615i	−0.0973841	+	0.168674i
$950$	−8.00000	−	13.8564i	−0.259554	−	0.449561i
$951$	11.0000			0.356699
$952$	−2.50000	+	0.866025i	−0.0810255	+	0.0280680i
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$		0			0
$955$	−1.50000	+	2.59808i	−0.0485389	+	0.0840718i
$956$	−6.50000	+	11.2583i	−0.210225	+	0.364120i
$957$	−3.00000	−	5.19615i	−0.0969762	−	0.167968i
$958$	−26.0000			−0.840022
$959$	50.0000	−	17.3205i	1.61458	−	0.559308i
$960$	−1.00000			−0.0322749
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$	−14.0000			−0.450676
$966$	−4.00000	+	20.7846i	−0.128698	+	0.668734i
$967$	−52.0000			−1.67221			−0.836104	−	0.548572i	$-0.815172\pi$
$967$	−52.0000			−1.67221			−0.836104	+	0.548572i	$0.815172\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$	2.00000	−	3.46410i	0.0642493	−	0.111283i
$970$	4.00000	−	6.92820i	0.128432	−	0.222451i
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	0.998339	−	0.0576061i	$-0.0183467\pi$
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	−0.549058	+	0.835784i	$0.685013\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	27.0000			0.865136
$975$	−2.00000	−	3.46410i	−0.0640513	−	0.110940i
$976$		0			0
$977$	26.0000	−	45.0333i	0.831814	−	1.44074i	−0.0647848	−	0.997899i	$-0.520636\pi$
$977$	26.0000	−	45.0333i	0.831814	−	1.44074i	0.896599	−	0.442844i	$-0.146031\pi$
$978$	−8.00000	−	13.8564i	−0.255812	−	0.443079i
$979$	12.0000			0.383522
$980$	1.00000	+	6.92820i	0.0319438	+	0.221313i
$981$	−16.0000			−0.510841
$982$	14.0000	+	24.2487i	0.446758	+	0.773807i
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	−0.945705	−	0.325027i	$-0.894626\pi$
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	0.754334	+	0.656490i	$0.227960\pi$
$984$	−0.500000	+	0.866025i	−0.0159394	+	0.0276079i
$985$	−0.500000	−	0.866025i	−0.0159313	−	0.0275939i
$986$	−3.00000			−0.0955395
$987$	−18.0000	−	15.5885i	−0.572946	−	0.496186i
$988$	4.00000			0.127257
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	−0.993364	−	0.115015i	$-0.963308\pi$
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	0.596288	+	0.802771i	$0.296642\pi$
$992$	−1.50000	−	2.59808i	−0.0476250	−	0.0824890i
$993$	22.0000			0.698149
$994$	2.00000	−	10.3923i	0.0634361	−	0.329624i
$995$	−5.00000			−0.158511
$996$	4.50000	+	7.79423i	0.142588	+	0.246970i
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	−0.755235	−	0.655454i	$-0.772477\pi$
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	0.945257	+	0.326326i	$0.105811\pi$
$998$	6.50000	−	11.2583i	0.205754	−	0.356376i
$999$	2.00000	+	3.46410i	0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.i.i.613.1	yes	2
7.2	even	3	inner	714.2.i.i.205.1	✓	2
7.3	odd	6		4998.2.a.m.1.1		1
7.4	even	3		4998.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.i.i.205.1	✓	2	7.2	even	3	inner
714.2.i.i.613.1	yes	2	1.1	even	1	trivial
4998.2.a.e.1.1		1	7.4	even	3
4998.2.a.m.1.1		1	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +2.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +3.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(1.50000 - 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} -1.00000 q^{34} +(-0.500000 + 2.59808i) q^{35} +1.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(2.00000 - 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +1.00000 q^{41} +(-2.00000 - 1.73205i) q^{42} -4.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{46} +(4.50000 + 7.79423i) q^{47} -1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +4.00000 q^{50} +(0.500000 + 0.866025i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{54} -2.00000 q^{55} +(2.00000 + 1.73205i) q^{56} -4.00000 q^{57} +(1.50000 + 2.59808i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(0.500000 - 0.866025i) q^{60} +3.00000 q^{62} +(-0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(1.00000 - 1.73205i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-0.500000 - 0.866025i) q^{68} -8.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +4.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 - 3.46410i) q^{75} +4.00000 q^{76} +(-5.00000 + 1.73205i) q^{77} +1.00000 q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +9.00000 q^{83} +(0.500000 - 2.59808i) q^{84} +1.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(3.00000 + 5.19615i) q^{89} -1.00000 q^{90} +(-2.00000 - 1.73205i) q^{91} +8.00000 q^{92} +(-1.50000 - 2.59808i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + q^{10} + 2 q^{11} + q^{12} + 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - q^{17} + q^{18} - 4 q^{19} + 2 q^{20} - 5 q^{21} + 4 q^{22} - 8 q^{23} - q^{24} + 4 q^{25} + q^{26} - 2 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 3 q^{31} + q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} - 4 q^{37} + 4 q^{38} + q^{39} + q^{40} + 2 q^{41} - 4 q^{42} - 8 q^{43} + 2 q^{44} - q^{45} + 8 q^{46} + 9 q^{47} - 2 q^{48} + 2 q^{49} + 8 q^{50} + q^{51} - q^{52} - q^{54} - 4 q^{55} + 4 q^{56} - 8 q^{57} + 3 q^{58} - 11 q^{59} + q^{60} + 6 q^{62} - q^{63} + 2 q^{64} - q^{65} + 2 q^{66} + 12 q^{67} - q^{68} - 16 q^{69} - 5 q^{70} + 8 q^{71} + q^{72} - 6 q^{73} + 4 q^{74} - 4 q^{75} + 8 q^{76} - 10 q^{77} + 2 q^{78} - q^{80} - q^{81} + q^{82} + 18 q^{83} + q^{84} + 2 q^{85} - 4 q^{86} + 3 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} - 4 q^{91} + 16 q^{92} - 3 q^{93} - 9 q^{94} - 4 q^{95} - q^{96} + 16 q^{97} - 11 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 4 * q^7 - 2 * q^8 - q^9 + q^10 + 2 * q^11 + q^12 + 2 * q^13 + q^14 - 2 * q^15 - q^16 - q^17 + q^18 - 4 * q^19 + 2 * q^20 - 5 * q^21 + 4 * q^22 - 8 * q^23 - q^24 + 4 * q^25 + q^26 - 2 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 3 * q^31 + q^32 - 2 * q^33 - 2 * q^34 - q^35 + 2 * q^36 - 4 * q^37 + 4 * q^38 + q^39 + q^40 + 2 * q^41 - 4 * q^42 - 8 * q^43 + 2 * q^44 - q^45 + 8 * q^46 + 9 * q^47 - 2 * q^48 + 2 * q^49 + 8 * q^50 + q^51 - q^52 - q^54 - 4 * q^55 + 4 * q^56 - 8 * q^57 + 3 * q^58 - 11 * q^59 + q^60 + 6 * q^62 - q^63 + 2 * q^64 - q^65 + 2 * q^66 + 12 * q^67 - q^68 - 16 * q^69 - 5 * q^70 + 8 * q^71 + q^72 - 6 * q^73 + 4 * q^74 - 4 * q^75 + 8 * q^76 - 10 * q^77 + 2 * q^78 - q^80 - q^81 + q^82 + 18 * q^83 + q^84 + 2 * q^85 - 4 * q^86 + 3 * q^87 - 2 * q^88 + 6 * q^89 - 2 * q^90 - 4 * q^91 + 16 * q^92 - 3 * q^93 - 9 * q^94 - 4 * q^95 - q^96 + 16 * q^97 - 11 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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