LMFDB - Embedded newform 1071.2.i.c.613.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(613,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1071.613");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.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:	$8.55197805648$
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 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1071.613
Dual form			1071.2.i.c.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(2.00000 + 3.46410i) q^{19} +3.00000 q^{20} +6.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(0.500000 + 0.866025i) q^{26} +(0.500000 + 2.59808i) q^{28} +7.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(2.50000 - 4.33013i) q^{32} -1.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(4.50000 + 7.79423i) q^{40} -3.00000 q^{41} -8.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-2.00000 + 3.46410i) q^{46} +(3.50000 + 6.06218i) q^{47} +(1.00000 - 6.92820i) q^{49} -4.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-2.00000 + 3.46410i) q^{53} +18.0000 q^{55} +(-6.00000 + 5.19615i) q^{56} +(3.50000 + 6.06218i) q^{58} +(-2.50000 + 4.33013i) q^{59} +(-2.00000 - 3.46410i) q^{61} -7.00000 q^{62} +7.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-1.50000 - 7.79423i) q^{70} +16.0000 q^{71} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} +4.00000 q^{76} +(3.00000 + 15.5885i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-1.50000 - 2.59808i) q^{82} -9.00000 q^{83} -3.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(9.00000 - 15.5885i) q^{88} +(-7.00000 - 12.1244i) q^{89} +(-2.00000 + 1.73205i) q^{91} +4.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +(-6.00000 + 10.3923i) q^{95} +8.00000 q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 3 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 + 3 * q^5 - 4 * q^7 + 6 * q^8	$ 2 q + q^{2} + q^{4} + 3 q^{5} - 4 q^{7} + 6 q^{8} - 3 q^{10} + 6 q^{11} + 2 q^{13} - 5 q^{14} + q^{16} - q^{17} + 4 q^{19} + 6 q^{20} + 12 q^{22} + 4 q^{23} - 4 q^{25} + q^{26} + q^{28} + 14 q^{29} - 7 q^{31} + 5 q^{32} - 2 q^{34} - 15 q^{35} - 8 q^{37} - 4 q^{38} + 9 q^{40} - 6 q^{41} - 16 q^{43} - 6 q^{44} - 4 q^{46} + 7 q^{47} + 2 q^{49} - 8 q^{50} + q^{52} - 4 q^{53} + 36 q^{55} - 12 q^{56} + 7 q^{58} - 5 q^{59} - 4 q^{61} - 14 q^{62} + 14 q^{64} + 3 q^{65} - 4 q^{67} + q^{68} - 3 q^{70} + 32 q^{71} + 2 q^{73} + 8 q^{74} + 8 q^{76} + 6 q^{77} + 8 q^{79} - 3 q^{80} - 3 q^{82} - 18 q^{83} - 6 q^{85} - 8 q^{86} + 18 q^{88} - 14 q^{89} - 4 q^{91} + 8 q^{92} - 7 q^{94} - 12 q^{95} + 16 q^{97} + 13 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 3 * q^5 - 4 * q^7 + 6 * q^8 - 3 * q^10 + 6 * q^11 + 2 * q^13 - 5 * q^14 + q^16 - q^17 + 4 * q^19 + 6 * q^20 + 12 * q^22 + 4 * q^23 - 4 * q^25 + q^26 + q^28 + 14 * q^29 - 7 * q^31 + 5 * q^32 - 2 * q^34 - 15 * q^35 - 8 * q^37 - 4 * q^38 + 9 * q^40 - 6 * q^41 - 16 * q^43 - 6 * q^44 - 4 * q^46 + 7 * q^47 + 2 * q^49 - 8 * q^50 + q^52 - 4 * q^53 + 36 * q^55 - 12 * q^56 + 7 * q^58 - 5 * q^59 - 4 * q^61 - 14 * q^62 + 14 * q^64 + 3 * q^65 - 4 * q^67 + q^68 - 3 * q^70 + 32 * q^71 + 2 * q^73 + 8 * q^74 + 8 * q^76 + 6 * q^77 + 8 * q^79 - 3 * q^80 - 3 * q^82 - 18 * q^83 - 6 * q^85 - 8 * q^86 + 18 * q^88 - 14 * q^89 - 4 * q^91 + 8 * q^92 - 7 * q^94 - 12 * q^95 + 16 * q^97 + 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	3.00000			1.06066
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$		0			0
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$		0			0
$16$	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			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	6.00000			1.27920
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$	0.500000	+	2.59808i	0.0944911	+	0.490990i
$29$	7.00000			1.29987			0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$30$		0			0
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	−1.00000			−0.171499
$35$	−7.50000	−	2.59808i	−1.26773	−	0.439155i
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	4.50000	+	7.79423i	0.711512	+	1.23238i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	0.999926	+	0.0121990i	$0.00388317\pi$
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	−0.489398	+	0.872060i	$0.662783\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−4.00000			−0.565685
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	18.0000			2.42712
$56$	−6.00000	+	5.19615i	−0.801784	+	0.694365i
$57$		0			0
$58$	3.50000	+	6.06218i	0.459573	+	0.796003i
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	−0.981608	−	0.190909i	$-0.938857\pi$
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	0.656136	+	0.754643i	$0.272190\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	−7.00000			−0.889001
$63$		0			0
$64$	7.00000			0.875000
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	0.500000	+	0.866025i	0.0606339	+	0.105021i
$69$		0			0
$70$	−1.50000	−	7.79423i	−0.179284	−	0.931589i
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$		0			0
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	4.00000			0.458831
$77$	3.00000	+	15.5885i	0.341882	+	1.77647i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	−9.00000			−0.987878			−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000			−0.987878			−0.493939	+	0.869496i	$0.664443\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	9.00000	−	15.5885i	0.959403	−	1.66174i
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$		0			0
$91$	−2.00000	+	1.73205i	−0.209657	+	0.181568i
$92$	4.00000			0.417029
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	6.50000	−	2.59808i	0.656599	−	0.262445i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	−9.00000	−	15.5885i	−0.886796	−	1.53598i	−0.843641	−	0.536908i	$-0.819592\pi$
$103$	−9.00000	−	15.5885i	−0.886796	−	1.53598i	−0.0431555	−	0.999068i	$-0.513741\pi$
$104$	3.00000			0.294174
$105$		0			0
$106$	−4.00000			−0.388514
$107$	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			0
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$	9.00000	+	15.5885i	0.858116	+	1.48630i
$111$		0			0
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	−13.0000			−1.22294			−0.611469	−	0.791269i	$-0.709421\pi$
$113$	−13.0000			−1.22294			−0.611469	+	0.791269i	$0.709421\pi$
$114$		0			0
$115$	−6.00000	+	10.3923i	−0.559503	+	0.969087i
$116$	3.50000	−	6.06218i	0.324967	−	0.562859i
$117$		0			0
$118$	−5.00000			−0.460287
$119$	−0.500000	−	2.59808i	−0.0458349	−	0.238165i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	2.00000	−	3.46410i	0.181071	−	0.313625i
$123$		0			0
$124$	3.50000	+	6.06218i	0.314309	+	0.544400i
$125$	3.00000			0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$	−1.50000	+	2.59808i	−0.131559	+	0.227866i
$131$	−1.00000	−	1.73205i	−0.0873704	−	0.151330i	0.819028	−	0.573753i	$-0.194513\pi$
$131$	−1.00000	−	1.73205i	−0.0873704	−	0.151330i	−0.906399	+	0.422423i	$0.861180\pi$
$132$		0			0
$133$	−10.0000	−	3.46410i	−0.867110	−	0.300376i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	−0.767853	−	0.640626i	$-0.778675\pi$
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	0.938725	+	0.344668i	$0.112008\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	−6.00000	+	5.19615i	−0.507093	+	0.439155i
$141$		0			0
$142$	8.00000	+	13.8564i	0.671345	+	1.16280i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$	10.5000	+	18.1865i	0.871978	+	1.51031i
$146$	2.00000			0.165521
$147$		0			0
$148$	−8.00000			−0.657596
$149$	−11.0000	−	19.0526i	−0.901155	−	1.56085i	−0.825997	−	0.563675i	$-0.809387\pi$
$149$	−11.0000	−	19.0526i	−0.901155	−	1.56085i	−0.0751583	−	0.997172i	$-0.523946\pi$
$150$		0			0
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$	6.00000	+	10.3923i	0.486664	+	0.842927i
$153$		0			0
$154$	−12.0000	+	10.3923i	−0.966988	+	0.837436i
$155$	−21.0000			−1.68676
$156$		0			0
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	15.0000			1.18585
$161$	−10.0000	−	3.46410i	−0.788110	−	0.273009i
$162$		0			0
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−1.50000	−	2.59808i	−0.115045	−	0.199263i
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	−8.50000	−	14.7224i	−0.646243	−	1.11933i	−0.984013	−	0.178097i	$-0.943006\pi$
$173$	−8.50000	−	14.7224i	−0.646243	−	1.11933i	0.337770	−	0.941229i	$-0.390327\pi$
$174$		0			0
$175$	−2.00000	−	10.3923i	−0.151186	−	0.785584i
$176$	6.00000			0.452267
$177$		0			0
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	−0.583920	−	0.811811i	$-0.698482\pi$
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	0.995009	+	0.0997838i	$0.0318151\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−2.50000	−	0.866025i	−0.185312	−	0.0641941i
$183$		0			0
$184$	6.00000	+	10.3923i	0.442326	+	0.766131i
$185$	12.0000	−	20.7846i	0.882258	−	1.52811i
$186$		0			0
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	7.00000			0.510527
$189$		0			0
$190$	−12.0000			−0.870572
$191$	−6.50000	−	11.2583i	−0.470323	−	0.814624i	0.529101	−	0.848559i	$-0.322529\pi$
$191$	−6.50000	−	11.2583i	−0.470323	−	0.814624i	−0.999424	+	0.0339349i	$0.989196\pi$
$192$		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
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$	13.0000			0.926212			0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000			0.926212			0.463106	+	0.886303i	$0.346735\pi$
$198$		0			0
$199$	7.50000	−	12.9904i	0.531661	−	0.920864i	−0.467656	−	0.883911i	$-0.654901\pi$
$199$	7.50000	−	12.9904i	0.531661	−	0.920864i	0.999317	−	0.0369532i	$-0.0117652\pi$
$200$	−6.00000	+	10.3923i	−0.424264	+	0.734847i
$201$		0			0
$202$	6.00000			0.422159
$203$	−14.0000	+	12.1244i	−0.982607	+	0.850963i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	9.00000	−	15.5885i	0.627060	−	1.08610i
$207$		0			0
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$	24.0000			1.66011
$210$		0			0
$211$	−23.0000			−1.58339			−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000			−1.58339			−0.791693	+	0.610920i	$0.790800\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−12.0000	−	20.7846i	−0.818393	−	1.41750i
$216$		0			0
$217$	−3.50000	−	18.1865i	−0.237595	−	1.23458i
$218$		0			0
$219$		0			0
$220$	9.00000	−	15.5885i	0.606780	−	1.05097i
$221$	−0.500000	+	0.866025i	−0.0336336	+	0.0582552i
$222$		0			0
$223$	−20.0000			−1.33930			−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000			−1.33930			−0.669650	+	0.742677i	$0.733556\pi$
$224$	2.50000	+	12.9904i	0.167038	+	0.867956i
$225$		0			0
$226$	−6.50000	−	11.2583i	−0.432374	−	0.748893i
$227$	−1.00000	+	1.73205i	−0.0663723	+	0.114960i	−0.897302	−	0.441417i	$-0.854476\pi$
$227$	−1.00000	+	1.73205i	−0.0663723	+	0.114960i	0.830930	+	0.556378i	$0.187809\pi$
$228$		0			0
$229$	−11.5000	−	19.9186i	−0.759941	−	1.31626i	−0.942880	−	0.333133i	$-0.891894\pi$
$229$	−11.5000	−	19.9186i	−0.759941	−	1.31626i	0.182939	−	0.983124i	$-0.441439\pi$
$230$	−12.0000			−0.791257
$231$		0			0
$232$	21.0000			1.37872
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	0.680135	−	0.733087i	$-0.261921\pi$
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	−0.974939	+	0.222470i	$0.928588\pi$
$234$		0			0
$235$	−10.5000	+	18.1865i	−0.684944	+	1.18636i
$236$	2.50000	+	4.33013i	0.162736	+	0.281867i
$237$		0			0
$238$	2.00000	−	1.73205i	0.129641	−	0.112272i
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$		0			0
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$	12.5000	−	21.6506i	0.803530	−	1.39176i
$243$		0			0
$244$	−4.00000			−0.256074
$245$	19.5000	−	7.79423i	1.24581	−	0.497955i
$246$		0			0
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$	−10.5000	+	18.1865i	−0.666751	+	1.15485i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	1.00000			0.0631194			0.0315597	−	0.999502i	$-0.489953\pi$
$251$	1.00000			0.0631194			0.0315597	+	0.999502i	$0.489953\pi$
$252$		0			0
$253$	24.0000			1.50887
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	20.0000	+	6.92820i	1.24274	+	0.430498i
$260$	3.00000			0.186052
$261$		0			0
$262$	1.00000	−	1.73205i	0.0617802	−	0.107006i
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$	−2.00000	−	10.3923i	−0.122628	−	0.637193i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$		0			0
$271$	−5.00000	−	8.66025i	−0.303728	−	0.526073i	0.673249	−	0.739416i	$-0.264898\pi$
$271$	−5.00000	−	8.66025i	−0.303728	−	0.526073i	−0.976977	+	0.213343i	$0.931565\pi$
$272$	−1.00000			−0.0606339
$273$		0			0
$274$	4.00000			0.241649
$275$	12.0000	+	20.7846i	0.723627	+	1.25336i
$276$		0			0
$277$	−8.00000	+	13.8564i	−0.480673	+	0.832551i	−0.999754	−	0.0221745i	$-0.992941\pi$
$277$	−8.00000	+	13.8564i	−0.480673	+	0.832551i	0.519081	+	0.854725i	$0.326274\pi$
$278$	4.00000	+	6.92820i	0.239904	+	0.415526i
$279$		0			0
$280$	−22.5000	−	7.79423i	−1.34463	−	0.465794i
$281$	4.00000			0.238620			0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000			0.238620			0.119310	+	0.992857i	$0.461932\pi$
$282$		0			0
$283$	−8.50000	+	14.7224i	−0.505273	+	0.875158i	0.494709	+	0.869059i	$0.335275\pi$
$283$	−8.50000	+	14.7224i	−0.505273	+	0.875158i	−0.999981	+	0.00609896i	$0.998059\pi$
$284$	8.00000	−	13.8564i	0.474713	−	0.822226i
$285$		0			0
$286$	6.00000			0.354787
$287$	6.00000	−	5.19615i	0.354169	−	0.306719i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−10.5000	+	18.1865i	−0.616581	+	1.06795i
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$		0			0
$295$	−15.0000			−0.873334
$296$	−12.0000	−	20.7846i	−0.697486	−	1.20808i
$297$		0			0
$298$	11.0000	−	19.0526i	0.637213	−	1.10369i
$299$	2.00000	+	3.46410i	0.115663	+	0.200334i
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$	12.0000			0.690522
$303$		0			0
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	6.00000	−	10.3923i	0.343559	−	0.595062i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	15.0000	+	5.19615i	0.854704	+	0.296078i
$309$		0			0
$310$	−10.5000	−	18.1865i	−0.596360	−	1.03293i
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	−0.972250	−	0.233944i	$-0.924837\pi$
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	0.688726	+	0.725022i	$0.258170\pi$
$312$		0			0
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	−17.0000			−0.959366
$315$		0			0
$316$	8.00000			0.450035
$317$	−8.50000	−	14.7224i	−0.477408	−	0.826894i	0.522257	−	0.852788i	$-0.325090\pi$
$317$	−8.50000	−	14.7224i	−0.477408	−	0.826894i	−0.999665	+	0.0258939i	$0.991757\pi$
$318$		0			0
$319$	21.0000	−	36.3731i	1.17577	−	2.03650i
$320$	10.5000	+	18.1865i	0.586968	+	1.01666i
$321$		0			0
$322$	−2.00000	−	10.3923i	−0.111456	−	0.579141i
$323$	−4.00000			−0.222566
$324$		0			0
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$		0			0
$328$	−9.00000			−0.496942
$329$	−17.5000	−	6.06218i	−0.964806	−	0.334219i
$330$		0			0
$331$	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
$333$		0			0
$334$	3.00000	+	5.19615i	0.164153	+	0.284321i
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$		0			0
$340$	−1.50000	+	2.59808i	−0.0813489	+	0.140900i
$341$	21.0000	+	36.3731i	1.13721	+	1.96971i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−24.0000			−1.29399
$345$		0			0
$346$	8.50000	−	14.7224i	0.456963	−	0.791483i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	11.0000			0.588817			0.294408	−	0.955680i	$-0.404877\pi$
$349$	11.0000			0.588817			0.294408	+	0.955680i	$0.404877\pi$
$350$	8.00000	−	6.92820i	0.427618	−	0.370328i
$351$		0			0
$352$	−15.0000	−	25.9808i	−0.799503	−	1.38478i
$353$	8.00000	−	13.8564i	0.425797	−	0.737502i	−0.570697	−	0.821160i	$-0.693327\pi$
$353$	8.00000	−	13.8564i	0.425797	−	0.737502i	0.996495	+	0.0836583i	$0.0266604\pi$
$354$		0			0
$355$	24.0000	+	41.5692i	1.27379	+	2.20627i
$356$	−14.0000			−0.741999
$357$		0			0
$358$	11.0000			0.581368
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	0.993207	−	0.116358i	$-0.0371219\pi$
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	−0.597372	+	0.801964i	$0.703789\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$		0			0
$364$	0.500000	+	2.59808i	0.0262071	+	0.136176i
$365$	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	$-0.147978\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	24.0000			1.24770
$371$	−2.00000	−	10.3923i	−0.103835	−	0.539542i
$372$		0			0
$373$	2.50000	+	4.33013i	0.129445	+	0.224205i	0.923462	−	0.383691i	$-0.125347\pi$
$373$	2.50000	+	4.33013i	0.129445	+	0.224205i	−0.794017	+	0.607896i	$0.792014\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$		0			0
$376$	10.5000	+	18.1865i	0.541496	+	0.937899i
$377$	7.00000			0.360518
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$		0			0
$382$	6.50000	−	11.2583i	0.332569	−	0.576026i
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$		0			0
$385$	−36.0000	+	31.1769i	−1.83473	+	1.58892i
$386$	10.0000			0.508987
$387$		0			0
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	3.00000	−	20.7846i	0.151523	−	1.04978i
$393$		0			0
$394$	6.50000	+	11.2583i	0.327465	+	0.567186i
$395$	−12.0000	+	20.7846i	−0.603786	+	1.04579i
$396$		0			0
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$	15.0000			0.751882
$399$		0			0
$400$	−4.00000			−0.200000
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	−3.50000	+	6.06218i	−0.174347	+	0.301979i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$		0			0
$406$	−17.5000	−	6.06218i	−0.868510	−	0.300861i
$407$	−48.0000			−2.37927
$408$		0			0
$409$	−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	$0.944436\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$		0			0
$412$	−18.0000			−0.886796
$413$	−2.50000	−	12.9904i	−0.123017	−	0.639215i
$414$		0			0
$415$	−13.5000	−	23.3827i	−0.662689	−	1.14781i
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$		0			0
$418$	12.0000	+	20.7846i	0.586939	+	1.01661i
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−15.0000			−0.731055			−0.365528	−	0.930800i	$-0.619111\pi$
$421$	−15.0000			−0.731055			−0.365528	+	0.930800i	$0.619111\pi$
$422$	−11.5000	−	19.9186i	−0.559811	−	0.969622i
$423$		0			0
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	10.0000	+	3.46410i	0.483934	+	0.167640i
$428$	12.0000			0.580042
$429$		0			0
$430$	12.0000	−	20.7846i	0.578691	−	1.00232i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−21.0000			−1.00920			−0.504598	−	0.863355i	$-0.668359\pi$
$433$	−21.0000			−1.00920			−0.504598	+	0.863355i	$0.668359\pi$
$434$	14.0000	−	12.1244i	0.672022	−	0.581988i
$435$		0			0
$436$		0			0
$437$	−8.00000	+	13.8564i	−0.382692	+	0.662842i
$438$		0			0
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$	54.0000			2.57435
$441$		0			0
$442$	−1.00000			−0.0475651
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$		0			0
$445$	21.0000	−	36.3731i	0.995495	−	1.72425i
$446$	−10.0000	−	17.3205i	−0.473514	−	0.820150i
$447$		0			0
$448$	−14.0000	+	12.1244i	−0.661438	+	0.572822i
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$	−6.50000	+	11.2583i	−0.305734	+	0.529547i
$453$		0			0
$454$	−2.00000			−0.0938647
$455$	−7.50000	−	2.59808i	−0.351605	−	0.121800i
$456$		0			0
$457$	15.5000	+	26.8468i	0.725059	+	1.25584i	0.958950	+	0.283577i	$0.0915211\pi$
$457$	15.5000	+	26.8468i	0.725059	+	1.25584i	−0.233890	+	0.972263i	$0.575146\pi$
$458$	11.5000	−	19.9186i	0.537360	−	0.930734i
$459$		0			0
$460$	6.00000	+	10.3923i	0.279751	+	0.484544i
$461$	−32.0000			−1.49039			−0.745194	−	0.666847i	$-0.767643\pi$
$461$	−32.0000			−1.49039			−0.745194	+	0.666847i	$0.767643\pi$
$462$		0			0
$463$	−30.0000			−1.39422			−0.697109	−	0.716965i	$-0.745531\pi$
$463$	−30.0000			−1.39422			−0.697109	+	0.716965i	$0.745531\pi$
$464$	3.50000	+	6.06218i	0.162483	+	0.281430i
$465$		0			0
$466$	4.50000	−	7.79423i	0.208458	−	0.361061i
$467$	−13.5000	−	23.3827i	−0.624705	−	1.08202i	−0.988598	−	0.150581i	$-0.951886\pi$
$467$	−13.5000	−	23.3827i	−0.624705	−	1.08202i	0.363892	−	0.931441i	$-0.381448\pi$
$468$		0			0
$469$	−2.00000	−	10.3923i	−0.0923514	−	0.479872i
$470$	−21.0000			−0.968658
$471$		0			0
$472$	−7.50000	+	12.9904i	−0.345215	+	0.597931i
$473$	−24.0000	+	41.5692i	−1.10352	+	1.91135i
$474$		0			0
$475$	−16.0000			−0.734130
$476$	−2.50000	−	0.866025i	−0.114587	−	0.0396942i
$477$		0			0
$478$	−10.5000	−	18.1865i	−0.480259	−	0.831833i
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	−0.957351	−	0.288929i	$-0.906701\pi$
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	0.728895	+	0.684626i	$0.240034\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$	14.0000			0.637683
$483$		0			0
$484$	−25.0000			−1.13636
$485$	12.0000	+	20.7846i	0.544892	+	0.943781i
$486$		0			0
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	−0.430486	−	0.902597i	$-0.641658\pi$
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$	−6.00000	−	10.3923i	−0.271607	−	0.470438i
$489$		0			0
$490$	16.5000	+	12.9904i	0.745394	+	0.586846i
$491$	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			0
$493$	−3.50000	+	6.06218i	−0.157632	+	0.273027i
$494$	−2.00000	+	3.46410i	−0.0899843	+	0.155857i
$495$		0			0
$496$	−7.00000			−0.314309
$497$	−32.0000	+	27.7128i	−1.43540	+	1.24309i
$498$		0			0
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	0.948995	−	0.315291i	$-0.102102\pi$
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	−0.747547	+	0.664208i	$0.768769\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	0.500000	+	0.866025i	0.0223161	+	0.0386526i
$503$	26.0000			1.15928			0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000			1.15928			0.579641	+	0.814872i	$0.303193\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	12.0000	+	20.7846i	0.533465	+	0.923989i
$507$		0			0
$508$	−2.00000	+	3.46410i	−0.0887357	+	0.153695i
$509$	−4.00000	−	6.92820i	−0.177297	−	0.307087i	0.763657	−	0.645622i	$-0.223402\pi$
$509$	−4.00000	−	6.92820i	−0.177297	−	0.307087i	−0.940954	+	0.338535i	$0.890069\pi$
$510$		0			0
$511$	1.00000	+	5.19615i	0.0442374	+	0.229864i
$512$	11.0000			0.486136
$513$		0			0
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$	27.0000	−	46.7654i	1.18976	−	2.06073i
$516$		0			0
$517$	42.0000			1.84716
$518$	4.00000	+	20.7846i	0.175750	+	0.913223i
$519$		0			0
$520$	4.50000	+	7.79423i	0.197338	+	0.341800i
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$		0			0
$523$	−16.0000	−	27.7128i	−0.699631	−	1.21180i	−0.968594	−	0.248646i	$-0.920014\pi$
$523$	−16.0000	−	27.7128i	−0.699631	−	1.21180i	0.268963	−	0.963150i	$-0.413319\pi$
$524$	−2.00000			−0.0873704
$525$		0			0
$526$	−16.0000			−0.697633
$527$	−3.50000	−	6.06218i	−0.152462	−	0.264073i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$		0			0
$532$	−8.00000	+	6.92820i	−0.346844	+	0.300376i
$533$	−3.00000			−0.129944
$534$		0			0
$535$	−18.0000	+	31.1769i	−0.778208	+	1.34790i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	9.00000			0.388018
$539$	−33.0000	−	25.9808i	−1.42141	−	1.11907i
$540$		0			0
$541$	4.00000	+	6.92820i	0.171973	+	0.297867i	0.939110	−	0.343617i	$-0.111652\pi$
$541$	4.00000	+	6.92820i	0.171973	+	0.297867i	−0.767136	+	0.641484i	$0.778319\pi$
$542$	5.00000	−	8.66025i	0.214768	−	0.371990i
$543$		0			0
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$		0			0
$546$		0			0
$547$	−27.0000			−1.15444			−0.577218	−	0.816590i	$-0.695862\pi$
$547$	−27.0000			−1.15444			−0.577218	+	0.816590i	$0.695862\pi$
$548$	−2.00000	−	3.46410i	−0.0854358	−	0.147979i
$549$		0			0
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	14.0000	+	24.2487i	0.596420	+	1.03303i
$552$		0			0
$553$	−20.0000	−	6.92820i	−0.850487	−	0.294617i
$554$	−16.0000			−0.679775
$555$		0			0
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	−0.491496	−	0.870880i	$-0.663550\pi$
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	0.999952	−	0.00979220i	$-0.00311700\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	−1.50000	−	7.79423i	−0.0633866	−	0.329366i
$561$		0			0
$562$	2.00000	+	3.46410i	0.0843649	+	0.146124i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	−19.5000	−	33.7750i	−0.820371	−	1.42092i
$566$	−17.0000			−0.714563
$567$		0			0
$568$	48.0000			2.01404
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	0.921869	+	0.387503i	$0.126662\pi$
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	−0.125347	+	0.992113i	$0.540004\pi$
$570$		0			0
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	−0.192950	−	0.981209i	$-0.561806\pi$
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	0.946227	−	0.323505i	$-0.104861\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$		0			0
$574$	7.50000	+	2.59808i	0.313044	+	0.108442i
$575$	−16.0000			−0.667246
$576$		0			0
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	−0.783930	−	0.620850i	$-0.786788\pi$
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	0.929636	+	0.368478i	$0.120121\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$		0			0
$580$	21.0000			0.871978
$581$	18.0000	−	15.5885i	0.746766	−	0.646718i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$	3.00000	−	5.19615i	0.124141	−	0.215018i
$585$		0			0
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$	−28.0000			−1.15372
$590$	−7.50000	−	12.9904i	−0.308770	−	0.534806i
$591$		0			0
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$	6.00000	−	5.19615i	0.245976	−	0.213021i
$596$	−22.0000			−0.901155
$597$		0			0
$598$	−2.00000	+	3.46410i	−0.0817861	+	0.141658i
$599$	9.50000	−	16.4545i	0.388159	−	0.672312i	−0.604043	−	0.796952i	$-0.706444\pi$
$599$	9.50000	−	16.4545i	0.388159	−	0.672312i	0.992202	+	0.124640i	$0.0397776\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$	20.0000	+	6.92820i	0.815139	+	0.282372i
$603$		0			0
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$		0			0
$607$	18.5000	+	32.0429i	0.750892	+	1.30058i	0.947391	+	0.320079i	$0.103709\pi$
$607$	18.5000	+	32.0429i	0.750892	+	1.30058i	−0.196499	+	0.980504i	$0.562957\pi$
$608$	20.0000			0.811107
$609$		0			0
$610$	12.0000			0.485866
$611$	3.50000	+	6.06218i	0.141595	+	0.245249i
$612$		0			0
$613$	1.00000	−	1.73205i	0.0403896	−	0.0699569i	−0.845124	−	0.534570i	$-0.820473\pi$
$613$	1.00000	−	1.73205i	0.0403896	−	0.0699569i	0.885514	+	0.464614i	$0.153807\pi$
$614$	2.00000	+	3.46410i	0.0807134	+	0.139800i
$615$		0			0
$616$	9.00000	+	46.7654i	0.362620	+	1.88423i
$617$	−27.0000			−1.08698			−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000			−1.08698			−0.543490	+	0.839416i	$0.682897\pi$
$618$		0			0
$619$	−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	$0.976426\pi$
$620$	−10.5000	+	18.1865i	−0.421690	+	0.730389i
$621$		0			0
$622$	−10.0000			−0.400963
$623$	35.0000	+	12.1244i	1.40225	+	0.485752i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$		0			0
$628$	8.50000	+	14.7224i	0.339187	+	0.587489i
$629$	8.00000			0.318981
$630$		0			0
$631$	34.0000			1.35352			0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000			1.35352			0.676759	+	0.736204i	$0.263384\pi$
$632$	12.0000	+	20.7846i	0.477334	+	0.826767i
$633$		0			0
$634$	8.50000	−	14.7224i	0.337578	−	0.584702i
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$		0			0
$637$	1.00000	−	6.92820i	0.0396214	−	0.274505i
$638$	42.0000			1.66280
$639$		0			0
$640$	4.50000	−	7.79423i	0.177878	−	0.308094i
$641$	−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
$643$	−41.0000			−1.61688			−0.808441	−	0.588577i	$-0.799688\pi$
$643$	−41.0000			−1.61688			−0.808441	+	0.588577i	$0.799688\pi$
$644$	−8.00000	+	6.92820i	−0.315244	+	0.273009i
$645$		0			0
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	−3.50000	+	6.06218i	−0.137599	+	0.238329i	−0.926587	−	0.376080i	$-0.877272\pi$
$647$	−3.50000	+	6.06218i	−0.137599	+	0.238329i	0.788988	+	0.614408i	$0.210605\pi$
$648$		0			0
$649$	15.0000	+	25.9808i	0.588802	+	1.01983i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	8.00000			0.313304
$653$	23.0000	+	39.8372i	0.900060	+	1.55895i	0.827415	+	0.561591i	$0.189811\pi$
$653$	23.0000	+	39.8372i	0.900060	+	1.55895i	0.0726446	+	0.997358i	$0.476856\pi$
$654$		0			0
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$		0			0
$658$	−3.50000	−	18.1865i	−0.136444	−	0.708985i
$659$	25.0000			0.973862			0.486931	−	0.873441i	$-0.338116\pi$
$659$	25.0000			0.973862			0.486931	+	0.873441i	$0.338116\pi$
$660$		0			0
$661$	−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			0
$664$	−27.0000			−1.04780
$665$	−6.00000	−	31.1769i	−0.232670	−	1.20899i
$666$		0			0
$667$	14.0000	+	24.2487i	0.542082	+	0.938914i
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$		0			0
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	−5.00000	−	8.66025i	−0.192593	−	0.333581i
$675$		0			0
$676$	−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	$0.870116\pi$
$678$		0			0
$679$	−16.0000	+	13.8564i	−0.614024	+	0.531760i
$680$	−9.00000			−0.345134
$681$		0			0
$682$	−21.0000	+	36.3731i	−0.804132	+	1.39280i
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	−0.932349	−	0.361559i	$-0.882245\pi$
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	0.779294	+	0.626659i	$0.215578\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	−21.5000	−	37.2391i	−0.817899	−	1.41664i	−0.907228	−	0.420640i	$-0.861806\pi$
$691$	−21.5000	−	37.2391i	−0.817899	−	1.41664i	0.0893292	−	0.996002i	$-0.471528\pi$
$692$	−17.0000			−0.646243
$693$		0			0
$694$		0			0
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$		0			0
$697$	1.50000	−	2.59808i	0.0568166	−	0.0984092i
$698$	5.50000	+	9.52628i	0.208178	+	0.360575i
$699$		0			0
$700$	−10.0000	−	3.46410i	−0.377964	−	0.130931i
$701$	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			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	21.0000	−	36.3731i	0.791467	−	1.37086i
$705$		0			0
$706$	16.0000			0.602168
$707$	3.00000	+	15.5885i	0.112827	+	0.586264i
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	−24.0000	+	41.5692i	−0.900704	+	1.56007i
$711$		0			0
$712$	−21.0000	−	36.3731i	−0.787008	−	1.36314i
$713$	−28.0000			−1.04861
$714$		0			0
$715$	18.0000			0.673162
$716$	−5.50000	−	9.52628i	−0.205545	−	0.356014i
$717$		0			0
$718$	−7.50000	+	12.9904i	−0.279898	+	0.484797i
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	0.999848	−	0.0174426i	$-0.00555244\pi$
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	−0.515030	+	0.857172i	$0.672219\pi$
$720$		0			0
$721$	45.0000	+	15.5885i	1.67589	+	0.580544i
$722$	3.00000			0.111648
$723$		0			0
$724$		0			0
$725$	−14.0000	+	24.2487i	−0.519947	+	0.900575i
$726$		0			0
$727$	30.0000			1.11264			0.556319	−	0.830969i	$-0.312213\pi$
$727$	30.0000			1.11264			0.556319	+	0.830969i	$0.312213\pi$
$728$	−6.00000	+	5.19615i	−0.222375	+	0.192582i
$729$		0			0
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	32.0000			1.18114
$735$		0			0
$736$	20.0000			0.737210
$737$	12.0000	+	20.7846i	0.442026	+	0.765611i
$738$		0			0
$739$	−19.0000	+	32.9090i	−0.698926	+	1.21058i	0.269913	+	0.962885i	$0.413005\pi$
$739$	−19.0000	+	32.9090i	−0.698926	+	1.21058i	−0.968839	+	0.247691i	$0.920328\pi$
$740$	−12.0000	−	20.7846i	−0.441129	−	0.764057i
$741$		0			0
$742$	8.00000	−	6.92820i	0.293689	−	0.254342i
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$		0			0
$745$	33.0000	−	57.1577i	1.20903	−	2.09410i
$746$	−2.50000	+	4.33013i	−0.0915315	+	0.158537i
$747$		0			0
$748$	6.00000			0.219382
$749$	−30.0000	−	10.3923i	−1.09618	−	0.379727i
$750$		0			0
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$		0			0
$754$	3.50000	+	6.06218i	0.127462	+	0.220771i
$755$	36.0000			1.31017
$756$		0			0
$757$	−5.00000			−0.181728			−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000			−0.181728			−0.0908640	+	0.995863i	$0.528963\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$		0			0
$760$	−18.0000	+	31.1769i	−0.652929	+	1.13091i
$761$	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	$0.607054\pi$
$762$		0			0
$763$		0			0
$764$	−13.0000			−0.470323
$765$		0			0
$766$	−4.00000	+	6.92820i	−0.144526	+	0.250326i
$767$	−2.50000	+	4.33013i	−0.0902698	+	0.156352i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$	−45.0000	−	15.5885i	−1.62169	−	0.561769i
$771$		0			0
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$		0			0
$775$	−14.0000	−	24.2487i	−0.502895	−	0.871039i
$776$	24.0000			0.861550
$777$		0			0
$778$	−18.0000			−0.645331
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	48.0000	−	83.1384i	1.71758	−	2.97493i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$		0			0
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$	−51.0000			−1.82027
$786$		0			0
$787$	19.5000	−	33.7750i	0.695100	−	1.20395i	−0.275047	−	0.961431i	$-0.588693\pi$
$787$	19.5000	−	33.7750i	0.695100	−	1.20395i	0.970147	−	0.242518i	$-0.0779732\pi$
$788$	6.50000	−	11.2583i	0.231553	−	0.401061i
$789$		0			0
$790$	−24.0000			−0.853882
$791$	26.0000	−	22.5167i	0.924454	−	0.800600i
$792$		0			0
$793$	−2.00000	−	3.46410i	−0.0710221	−	0.123014i
$794$	−10.0000	+	17.3205i	−0.354887	+	0.614682i
$795$		0			0
$796$	−7.50000	−	12.9904i	−0.265830	−	0.460432i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	−7.00000			−0.247642
$800$	10.0000	+	17.3205i	0.353553	+	0.612372i
$801$		0			0
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$		0			0
$805$	−6.00000	−	31.1769i	−0.211472	−	1.09884i
$806$	−7.00000			−0.246564
$807$		0			0
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	−23.0000			−0.807639			−0.403820	−	0.914839i	$-0.632318\pi$
$811$	−23.0000			−0.807639			−0.403820	+	0.914839i	$0.632318\pi$
$812$	3.50000	+	18.1865i	0.122826	+	0.638222i
$813$		0			0
$814$	−24.0000	−	41.5692i	−0.841200	−	1.45700i
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$		0			0
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	−26.0000			−0.909069
$819$		0			0
$820$	−9.00000			−0.314294
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.859396	+	0.511311i	$0.170840\pi$
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.0131101	+	0.999914i	$0.495827\pi$
$822$		0			0
$823$	−20.5000	+	35.5070i	−0.714585	+	1.23770i	0.248534	+	0.968623i	$0.420051\pi$
$823$	−20.5000	+	35.5070i	−0.714585	+	1.23770i	−0.963119	+	0.269075i	$0.913282\pi$
$824$	−27.0000	−	46.7654i	−0.940590	−	1.62915i
$825$		0			0
$826$	10.0000	−	8.66025i	0.347945	−	0.301329i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$	13.5000	−	23.3827i	0.468592	−	0.811625i
$831$		0			0
$832$	7.00000			0.242681
$833$	5.50000	+	4.33013i	0.190564	+	0.150030i
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$		0			0
$838$	−12.0000	−	20.7846i	−0.414533	−	0.717992i
$839$	−46.0000			−1.58810			−0.794048	−	0.607855i	$-0.792030\pi$
$839$	−46.0000			−1.58810			−0.794048	+	0.607855i	$0.792030\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−7.50000	−	12.9904i	−0.258467	−	0.447678i
$843$		0			0
$844$	−11.5000	+	19.9186i	−0.395846	+	0.685626i
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$	62.5000	+	21.6506i	2.14753	+	0.743925i
$848$	−4.00000			−0.137361
$849$		0			0
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	16.0000	−	27.7128i	0.548473	−	0.949983i
$852$		0			0
$853$	16.0000			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$854$	2.00000	+	10.3923i	0.0684386	+	0.355617i
$855$		0			0
$856$	18.0000	+	31.1769i	0.615227	+	1.06561i
$857$	4.50000	−	7.79423i	0.153717	−	0.266246i	−0.778874	−	0.627180i	$-0.784209\pi$
$857$	4.50000	−	7.79423i	0.153717	−	0.266246i	0.932591	+	0.360935i	$0.117542\pi$
$858$		0			0
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	0.906516	+	0.422172i	$0.138732\pi$
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	−0.0876464	+	0.996152i	$0.527935\pi$
$860$	−24.0000			−0.818393
$861$		0			0
$862$	12.0000			0.408722
$863$	−18.0000	−	31.1769i	−0.612727	−	1.06127i	−0.990779	−	0.135490i	$-0.956739\pi$
$863$	−18.0000	−	31.1769i	−0.612727	−	1.06127i	0.378052	−	0.925785i	$-0.376594\pi$
$864$		0			0
$865$	25.5000	−	44.1673i	0.867026	−	1.50173i
$866$	−10.5000	−	18.1865i	−0.356805	−	0.618004i
$867$		0			0
$868$	−17.5000	−	6.06218i	−0.593989	−	0.205764i
$869$	48.0000			1.62829
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$		0			0
$873$		0			0
$874$	−16.0000			−0.541208
$875$	−6.00000	+	5.19615i	−0.202837	+	0.175662i
$876$		0			0
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	−17.5000	+	30.3109i	−0.590596	+	1.02294i
$879$		0			0
$880$	9.00000	+	15.5885i	0.303390	+	0.525487i
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−32.0000			−1.07689			−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000			−1.07689			−0.538443	+	0.842662i	$0.680987\pi$
$884$	0.500000	+	0.866025i	0.0168168	+	0.0291276i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−9.00000	−	15.5885i	−0.302190	−	0.523409i	0.674441	−	0.738328i	$-0.264385\pi$
$887$	−9.00000	−	15.5885i	−0.302190	−	0.523409i	−0.976632	+	0.214919i	$0.931051\pi$
$888$		0			0
$889$	8.00000	−	6.92820i	0.268311	−	0.232364i
$890$	42.0000			1.40784
$891$		0			0
$892$	−10.0000	+	17.3205i	−0.334825	+	0.579934i
$893$	−14.0000	+	24.2487i	−0.468492	+	0.811452i
$894$		0			0
$895$	33.0000			1.10307
$896$	7.50000	+	2.59808i	0.250557	+	0.0867956i
$897$		0			0
$898$	−7.00000	−	12.1244i	−0.233593	−	0.404595i
$899$	−24.5000	+	42.4352i	−0.817121	+	1.41529i
$900$		0			0
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$	−18.0000			−0.599334
$903$		0			0
$904$	−39.0000			−1.29712
$905$		0			0
$906$		0			0
$907$	−6.50000	+	11.2583i	−0.215829	+	0.373827i	−0.953529	−	0.301302i	$-0.902579\pi$
$907$	−6.50000	+	11.2583i	−0.215829	+	0.373827i	0.737700	+	0.675129i	$0.235912\pi$
$908$	1.00000	+	1.73205i	0.0331862	+	0.0574801i
$909$		0			0
$910$	−1.50000	−	7.79423i	−0.0497245	−	0.258376i
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$		0			0
$913$	−27.0000	+	46.7654i	−0.893570	+	1.54771i
$914$	−15.5000	+	26.8468i	−0.512694	+	0.888013i
$915$		0			0
$916$	−23.0000			−0.759941
$917$	5.00000	+	1.73205i	0.165115	+	0.0571974i
$918$		0			0
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$	−18.0000	+	31.1769i	−0.593442	+	1.02787i
$921$		0			0
$922$	−16.0000	−	27.7128i	−0.526932	−	0.912673i
$923$	16.0000			0.526646
$924$		0			0
$925$	32.0000			1.05215
$926$	−15.0000	−	25.9808i	−0.492931	−	0.853781i
$927$		0			0
$928$	17.5000	−	30.3109i	0.574466	−	0.995004i
$929$	−7.50000	−	12.9904i	−0.246067	−	0.426201i	0.716364	−	0.697727i	$-0.245805\pi$
$929$	−7.50000	−	12.9904i	−0.246067	−	0.426201i	−0.962431	+	0.271526i	$0.912472\pi$
$930$		0			0
$931$	26.0000	−	10.3923i	0.852116	−	0.340594i
$932$	−9.00000			−0.294805
$933$		0			0
$934$	13.5000	−	23.3827i	0.441733	−	0.765105i
$935$	−9.00000	+	15.5885i	−0.294331	+	0.509797i
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	8.00000	−	6.92820i	0.261209	−	0.226214i
$939$		0			0
$940$	10.5000	+	18.1865i	0.342472	+	0.593179i
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$	−6.00000	−	10.3923i	−0.195387	−	0.338420i
$944$	−5.00000			−0.162736
$945$		0			0
$946$	−48.0000			−1.56061
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	0.974244	+	0.225497i	$0.0724007\pi$
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	−0.291835	+	0.956469i	$0.594266\pi$
$948$		0			0
$949$	1.00000	−	1.73205i	0.0324614	−	0.0562247i
$950$	−8.00000	−	13.8564i	−0.259554	−	0.449561i
$951$		0			0
$952$	−1.50000	−	7.79423i	−0.0486153	−	0.252612i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	19.5000	−	33.7750i	0.631005	−	1.09293i
$956$	−10.5000	+	18.1865i	−0.339594	+	0.588195i
$957$		0			0
$958$	−10.0000			−0.323085
$959$	2.00000	+	10.3923i	0.0645834	+	0.335585i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$	4.00000	−	6.92820i	0.128965	−	0.223374i
$963$		0			0
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$	30.0000			0.965734
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$	−37.5000	−	64.9519i	−1.20530	−	2.08763i
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	0.659762	−	0.751475i	$-0.270657\pi$
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	−0.980677	+	0.195633i	$0.937324\pi$
$972$		0			0
$973$	−16.0000	+	13.8564i	−0.512936	+	0.444216i
$974$	25.0000			0.801052
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	−18.0000	+	31.1769i	−0.575871	+	0.997438i	0.420075	+	0.907489i	$0.362004\pi$
$977$	−18.0000	+	31.1769i	−0.575871	+	0.997438i	−0.995946	+	0.0899487i	$0.971330\pi$
$978$		0			0
$979$	−84.0000			−2.68465
$980$	3.00000	−	20.7846i	0.0958315	−	0.663940i
$981$		0			0
$982$	14.0000	+	24.2487i	0.446758	+	0.773807i
$983$	4.00000	−	6.92820i	0.127580	−	0.220975i	−0.795158	−	0.606402i	$-0.792612\pi$
$983$	4.00000	−	6.92820i	0.127580	−	0.220975i	0.922739	+	0.385426i	$0.125946\pi$
$984$		0			0
$985$	19.5000	+	33.7750i	0.621322	+	1.07616i
$986$	−7.00000			−0.222925
$987$		0			0
$988$	4.00000			0.127257
$989$	−16.0000	−	27.7128i	−0.508770	−	0.881216i
$990$		0			0
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.166250	+	0.986084i	$0.553166\pi$
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.770849	+	0.637018i	$0.780168\pi$
$992$	17.5000	+	30.3109i	0.555626	+	0.962372i
$993$		0			0
$994$	−40.0000	−	13.8564i	−1.26872	−	0.439499i
$995$	45.0000			1.42660
$996$		0			0
$997$	16.0000	−	27.7128i	0.506725	−	0.877674i	−0.493245	−	0.869891i	$-0.664189\pi$
$997$	16.0000	−	27.7128i	0.506725	−	0.877674i	0.999970	−	0.00778294i	$-0.00247741\pi$
$998$	−4.50000	+	7.79423i	−0.142445	+	0.246722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.i.c.613.1		2
3.2	odd	2		357.2.i.a.256.1	yes	2
7.2	even	3	inner	1071.2.i.c.919.1		2
7.3	odd	6		7497.2.a.f.1.1		1
7.4	even	3		7497.2.a.c.1.1		1
21.2	odd	6		357.2.i.a.205.1	✓	2
21.11	odd	6		2499.2.a.l.1.1		1
21.17	even	6		2499.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.a.205.1	✓	2	21.2	odd	6
357.2.i.a.256.1	yes	2	3.2	odd	2
1071.2.i.c.613.1		2	1.1	even	1	trivial
1071.2.i.c.919.1		2	7.2	even	3	inner
2499.2.a.i.1.1		1	21.17	even	6
2499.2.a.l.1.1		1	21.11	odd	6
7497.2.a.c.1.1		1	7.4	even	3
7497.2.a.f.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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(2.00000 + 3.46410i) q^{19} +3.00000 q^{20} +6.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(0.500000 + 0.866025i) q^{26} +(0.500000 + 2.59808i) q^{28} +7.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(2.50000 - 4.33013i) q^{32} -1.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(4.50000 + 7.79423i) q^{40} -3.00000 q^{41} -8.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-2.00000 + 3.46410i) q^{46} +(3.50000 + 6.06218i) q^{47} +(1.00000 - 6.92820i) q^{49} -4.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-2.00000 + 3.46410i) q^{53} +18.0000 q^{55} +(-6.00000 + 5.19615i) q^{56} +(3.50000 + 6.06218i) q^{58} +(-2.50000 + 4.33013i) q^{59} +(-2.00000 - 3.46410i) q^{61} -7.00000 q^{62} +7.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-1.50000 - 7.79423i) q^{70} +16.0000 q^{71} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} +4.00000 q^{76} +(3.00000 + 15.5885i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-1.50000 - 2.59808i) q^{82} -9.00000 q^{83} -3.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(9.00000 - 15.5885i) q^{88} +(-7.00000 - 12.1244i) q^{89} +(-2.00000 + 1.73205i) q^{91} +4.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +(-6.00000 + 10.3923i) q^{95} +8.00000 q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 3 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 + 3 * q^5 - 4 * q^7 + 6 * q^8	\( 2 q + q^{2} + q^{4} + 3 q^{5} - 4 q^{7} + 6 q^{8} - 3 q^{10} + 6 q^{11} + 2 q^{13} - 5 q^{14} + q^{16} - q^{17} + 4 q^{19} + 6 q^{20} + 12 q^{22} + 4 q^{23} - 4 q^{25} + q^{26} + q^{28} + 14 q^{29} - 7 q^{31} + 5 q^{32} - 2 q^{34} - 15 q^{35} - 8 q^{37} - 4 q^{38} + 9 q^{40} - 6 q^{41} - 16 q^{43} - 6 q^{44} - 4 q^{46} + 7 q^{47} + 2 q^{49} - 8 q^{50} + q^{52} - 4 q^{53} + 36 q^{55} - 12 q^{56} + 7 q^{58} - 5 q^{59} - 4 q^{61} - 14 q^{62} + 14 q^{64} + 3 q^{65} - 4 q^{67} + q^{68} - 3 q^{70} + 32 q^{71} + 2 q^{73} + 8 q^{74} + 8 q^{76} + 6 q^{77} + 8 q^{79} - 3 q^{80} - 3 q^{82} - 18 q^{83} - 6 q^{85} - 8 q^{86} + 18 q^{88} - 14 q^{89} - 4 q^{91} + 8 q^{92} - 7 q^{94} - 12 q^{95} + 16 q^{97} + 13 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 3 * q^5 - 4 * q^7 + 6 * q^8 - 3 * q^10 + 6 * q^11 + 2 * q^13 - 5 * q^14 + q^16 - q^17 + 4 * q^19 + 6 * q^20 + 12 * q^22 + 4 * q^23 - 4 * q^25 + q^26 + q^28 + 14 * q^29 - 7 * q^31 + 5 * q^32 - 2 * q^34 - 15 * q^35 - 8 * q^37 - 4 * q^38 + 9 * q^40 - 6 * q^41 - 16 * q^43 - 6 * q^44 - 4 * q^46 + 7 * q^47 + 2 * q^49 - 8 * q^50 + q^52 - 4 * q^53 + 36 * q^55 - 12 * q^56 + 7 * q^58 - 5 * q^59 - 4 * q^61 - 14 * q^62 + 14 * q^64 + 3 * q^65 - 4 * q^67 + q^68 - 3 * q^70 + 32 * q^71 + 2 * q^73 + 8 * q^74 + 8 * q^76 + 6 * q^77 + 8 * q^79 - 3 * q^80 - 3 * q^82 - 18 * q^83 - 6 * q^85 - 8 * q^86 + 18 * q^88 - 14 * q^89 - 4 * q^91 + 8 * q^92 - 7 * q^94 - 12 * q^95 + 16 * q^97 + 13 * q^98

Introduction

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