LMFDB - Embedded newform 1890.2.k.d.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(541,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1890.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.k (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:	$15.0917259820$
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			1621.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1890.1621
Dual form			1890.2.k.d.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-3.50000 - 6.06218i) q^{19} +1.00000 q^{20} +2.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(0.500000 + 2.59808i) q^{28} -2.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +5.00000 q^{34} +(-2.50000 - 0.866025i) q^{35} +(-3.00000 - 5.19615i) q^{37} +(-3.50000 + 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-2.00000 + 3.46410i) q^{46} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(2.00000 - 3.46410i) q^{53} +2.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +(1.00000 + 1.73205i) q^{58} +(2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(3.00000 - 5.19615i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(0.500000 + 2.59808i) q^{70} +1.00000 q^{71} +(-8.00000 + 13.8564i) q^{73} +(-3.00000 + 5.19615i) q^{74} +7.00000 q^{76} +(1.00000 + 5.19615i) q^{77} +(1.00000 + 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{80} -15.0000 q^{83} +5.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(-8.00000 - 13.8564i) q^{89} +(2.00000 - 1.73205i) q^{91} +4.00000 q^{92} +(-3.50000 + 6.06218i) q^{95} -10.0000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 2 q^{8} - q^{10} - 2 q^{11} + 2 q^{13} - 5 q^{14} - q^{16} - 5 q^{17} - 7 q^{19} + 2 q^{20} + 4 q^{22} - 4 q^{23} - q^{25} - q^{26} + q^{28} - 4 q^{29} + 6 q^{31} - q^{32} + 10 q^{34} - 5 q^{35} - 6 q^{37} - 7 q^{38} - q^{40} + 4 q^{43} - 2 q^{44} - 4 q^{46} + 2 q^{49} + 2 q^{50} - q^{52} + 4 q^{53} + 4 q^{55} + 4 q^{56} + 2 q^{58} + 4 q^{61} - 12 q^{62} + 2 q^{64} - q^{65} + 6 q^{67} - 5 q^{68} + q^{70} + 2 q^{71} - 16 q^{73} - 6 q^{74} + 14 q^{76} + 2 q^{77} + 2 q^{79} - q^{80} - 30 q^{83} + 10 q^{85} - 2 q^{86} - 2 q^{88} - 16 q^{89} + 4 q^{91} + 8 q^{92} - 7 q^{95} - 20 q^{97} - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8 - q^10 - 2 * q^11 + 2 * q^13 - 5 * q^14 - q^16 - 5 * q^17 - 7 * q^19 + 2 * q^20 + 4 * q^22 - 4 * q^23 - q^25 - q^26 + q^28 - 4 * q^29 + 6 * q^31 - q^32 + 10 * q^34 - 5 * q^35 - 6 * q^37 - 7 * q^38 - q^40 + 4 * q^43 - 2 * q^44 - 4 * q^46 + 2 * q^49 + 2 * q^50 - q^52 + 4 * q^53 + 4 * q^55 + 4 * q^56 + 2 * q^58 + 4 * q^61 - 12 * q^62 + 2 * q^64 - q^65 + 6 * q^67 - 5 * q^68 + q^70 + 2 * q^71 - 16 * q^73 - 6 * q^74 + 14 * q^76 + 2 * q^77 + 2 * q^79 - q^80 - 30 * q^83 + 10 * q^85 - 2 * q^86 - 2 * q^88 - 16 * q^89 + 4 * q^91 + 8 * q^92 - 7 * q^95 - 20 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		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
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	2.00000			0.426401
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		0			0
$28$	0.500000	+	2.59808i	0.0944911	+	0.490990i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	5.00000			0.857493
$35$	−2.50000	−	0.866025i	−0.422577	−	0.146385i
$36$		0			0
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	1.00000			0.141421
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		0			0
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	3.00000	−	5.19615i	0.366508	−	0.634811i	−0.622509	−	0.782613i	$-0.713886\pi$
$67$	3.00000	−	5.19615i	0.366508	−	0.634811i	0.989017	+	0.147802i	$0.0472198\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$		0			0
$70$	0.500000	+	2.59808i	0.0597614	+	0.310530i
$71$	1.00000			0.118678			0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000			0.118678			0.0593391	+	0.998238i	$0.481101\pi$
$72$		0			0
$73$	−8.00000	+	13.8564i	−0.936329	+	1.62177i	−0.164083	+	0.986447i	$0.552466\pi$
$73$	−8.00000	+	13.8564i	−0.936329	+	1.62177i	−0.772246	+	0.635323i	$0.780867\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	7.00000			0.802955
$77$	1.00000	+	5.19615i	0.113961	+	0.592157i
$78$		0			0
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$		0			0
$83$	−15.0000			−1.64646			−0.823232	−	0.567705i	$-0.807831\pi$
$83$	−15.0000			−1.64646			−0.823232	+	0.567705i	$0.807831\pi$
$84$		0			0
$85$	5.00000			0.542326
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$		0			0
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	0.0349934	−	0.999388i	$-0.488859\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	4.00000			0.417029
$93$		0			0
$94$		0			0
$95$	−3.50000	+	6.06218i	−0.359092	+	0.621966i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$		0			0
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	0.344865	−	0.938652i	$-0.387925\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−4.00000			−0.388514
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$		0			0
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$		0			0
$118$		0			0
$119$	2.50000	+	12.9904i	0.229175	+	1.19083i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	2.00000	−	3.46410i	0.181071	−	0.313625i
$123$		0			0
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$		0			0
$133$	−17.5000	−	6.06218i	−1.51744	−	0.525657i
$134$	−6.00000			−0.518321
$135$		0			0
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$	2.00000	−	1.73205i	0.169031	−	0.146385i
$141$		0			0
$142$	−0.500000	−	0.866025i	−0.0419591	−	0.0726752i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$		0			0
$145$	1.00000	+	1.73205i	0.0830455	+	0.143839i
$146$	16.0000			1.32417
$147$		0			0
$148$	6.00000			0.493197
$149$	−2.50000	−	4.33013i	−0.204808	−	0.354738i	0.745264	−	0.666770i	$-0.232324\pi$
$149$	−2.50000	−	4.33013i	−0.204808	−	0.354738i	−0.950072	+	0.312032i	$0.898990\pi$
$150$		0			0
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.0615699	+	0.998103i	$0.519611\pi$
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.833597	+	0.552372i	$0.813723\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$		0			0
$154$	4.00000	−	3.46410i	0.322329	−	0.279145i
$155$	−6.00000			−0.481932
$156$		0			0
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	−0.0535803	−	0.998564i	$-0.517063\pi$
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	0.891572	−	0.452880i	$-0.149603\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$		0			0
$160$	1.00000			0.0790569
$161$	−10.0000	−	3.46410i	−0.788110	−	0.273009i
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$	7.50000	+	12.9904i	0.582113	+	1.00825i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−2.50000	−	4.33013i	−0.191741	−	0.332106i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$	2.00000			0.150756
$177$		0			0
$178$	−8.00000	+	13.8564i	−0.599625	+	1.03858i
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	−0.676927	−	0.736050i	$-0.736689\pi$
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	0.975901	+	0.218212i	$0.0700223\pi$
$180$		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
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	−5.00000	−	8.66025i	−0.365636	−	0.633300i
$188$		0			0
$189$		0			0
$190$	7.00000			0.507833
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$	5.00000	+	8.66025i	0.358979	+	0.621770i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	3.00000			0.211079
$203$	−4.00000	+	3.46410i	−0.280745	+	0.243132i
$204$		0			0
$205$		0			0
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$		0			0
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	14.0000			0.968400
$210$		0			0
$211$	−3.00000			−0.206529			−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000			−0.206529			−0.103264	+	0.994654i	$0.532929\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		0			0
$217$	−3.00000	−	15.5885i	−0.203653	−	1.05821i
$218$	−10.0000			−0.677285
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$	−2.50000	+	4.33013i	−0.168168	+	0.291276i
$222$		0			0
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$		0			0
$226$	9.00000	+	15.5885i	0.598671	+	1.03693i
$227$	−14.0000	+	24.2487i	−0.929213	+	1.60944i	−0.144571	+	0.989494i	$0.546180\pi$
$227$	−14.0000	+	24.2487i	−0.929213	+	1.60944i	−0.784642	+	0.619949i	$0.787153\pi$
$228$		0			0
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	0.703060	−	0.711131i	$-0.251817\pi$
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	−0.967387	+	0.253302i	$0.918483\pi$
$230$	4.00000			0.263752
$231$		0			0
$232$	−2.00000			−0.131306
$233$	6.50000	+	11.2583i	0.425829	+	0.737558i	0.996497	−	0.0836229i	$-0.0266491\pi$
$233$	6.50000	+	11.2583i	0.425829	+	0.737558i	−0.570668	+	0.821181i	$0.693316\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	10.0000	−	8.66025i	0.648204	−	0.561361i
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	−4.00000			−0.256074
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	−3.50000	−	6.06218i	−0.222700	−	0.385727i
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	3.50000	+	6.06218i	0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$		0			0
$259$	−15.0000	−	5.19615i	−0.932055	−	0.322873i
$260$	1.00000			0.0620174
$261$		0			0
$262$	−7.00000	+	12.1244i	−0.432461	+	0.749045i
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	−4.00000			−0.245718
$266$	3.50000	+	18.1865i	0.214599	+	1.11509i
$267$		0			0
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	5.00000			0.303170
$273$		0			0
$274$	−17.0000			−1.02701
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−15.5000	+	26.8468i	−0.931305	+	1.61307i	−0.150210	+	0.988654i	$0.547995\pi$
$277$	−15.5000	+	26.8468i	−0.931305	+	1.61307i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−2.50000	−	4.33013i	−0.149940	−	0.259704i
$279$		0			0
$280$	−2.50000	−	0.866025i	−0.149404	−	0.0517549i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	0.936039	−	0.351895i	$-0.114463\pi$
$284$	−0.500000	+	0.866025i	−0.0296695	+	0.0513892i
$285$		0			0
$286$	2.00000			0.118262
$287$		0			0
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$		0			0
$292$	−8.00000	−	13.8564i	−0.468165	−	0.810885i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$		0			0
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	−2.50000	+	4.33013i	−0.144821	+	0.250838i
$299$	−2.00000	−	3.46410i	−0.115663	−	0.200334i
$300$		0			0
$301$	4.00000	−	3.46410i	0.230556	−	0.199667i
$302$	22.0000			1.26596
$303$		0			0
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−5.00000	−	1.73205i	−0.284901	−	0.0986928i
$309$		0			0
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$	2.50000	−	4.33013i	0.141762	−	0.245539i	−0.786398	−	0.617720i	$-0.788057\pi$
$311$	2.50000	−	4.33013i	0.141762	−	0.245539i	0.928160	+	0.372181i	$0.121390\pi$
$312$		0			0
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−21.0000			−1.18510
$315$		0			0
$316$	−2.00000			−0.112509
$317$	4.00000	+	6.92820i	0.224662	+	0.389127i	0.956218	−	0.292655i	$-0.0945387\pi$
$317$	4.00000	+	6.92820i	0.224662	+	0.389127i	−0.731556	+	0.681782i	$0.761205\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	2.00000	+	10.3923i	0.111456	+	0.579141i
$323$	35.0000			1.94745
$324$		0			0
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	13.5000	+	23.3827i	0.742027	+	1.28523i	0.951571	+	0.307429i	$0.0994688\pi$
$331$	13.5000	+	23.3827i	0.742027	+	1.28523i	−0.209544	+	0.977799i	$0.567198\pi$
$332$	7.50000	−	12.9904i	0.411616	−	0.712940i
$333$		0			0
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	−6.00000			−0.327815
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		0			0
$340$	−2.50000	+	4.33013i	−0.135582	+	0.234834i
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	2.00000			0.107833
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	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	$0.132425\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$	2.00000	−	1.73205i	0.106904	−	0.0925820i
$351$		0			0
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.0836583	+	0.996495i	$0.526660\pi$
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.821160	+	0.570697i	$0.806673\pi$
$354$		0			0
$355$	−0.500000	−	0.866025i	−0.0265372	−	0.0459639i
$356$	16.0000			0.847998
$357$		0			0
$358$	−8.00000			−0.422813
$359$	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
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$		0			0
$364$	0.500000	+	2.59808i	0.0262071	+	0.136176i
$365$	16.0000			0.837478
$366$		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
$370$	6.00000			0.311925
$371$	−2.00000	−	10.3923i	−0.103835	−	0.539542i
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$	−5.00000	+	8.66025i	−0.258544	+	0.447811i
$375$		0			0
$376$		0			0
$377$	−2.00000			−0.103005
$378$		0			0
$379$	19.0000			0.975964			0.487982	−	0.872854i	$-0.337733\pi$
$379$	19.0000			0.975964			0.487982	+	0.872854i	$0.337733\pi$
$380$	−3.50000	−	6.06218i	−0.179546	−	0.310983i
$381$		0			0
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	4.00000	−	3.46410i	0.203859	−	0.176547i
$386$	−4.00000			−0.203595
$387$		0			0
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	17.5000	−	30.3109i	0.887285	−	1.53682i	0.0442134	−	0.999022i	$-0.485922\pi$
$389$	17.5000	−	30.3109i	0.887285	−	1.53682i	0.843072	−	0.537801i	$-0.180745\pi$
$390$		0			0
$391$	20.0000			1.01144
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$		0			0
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$	1.00000	−	1.73205i	0.0503155	−	0.0871489i
$396$		0			0
$397$	−16.5000	−	28.5788i	−0.828111	−	1.43433i	−0.899518	−	0.436884i	$-0.856082\pi$
$397$	−16.5000	−	28.5788i	−0.828111	−	1.43433i	0.0714068	−	0.997447i	$-0.477251\pi$
$398$		0			0
$399$		0			0
$400$	1.00000			0.0500000
$401$	−2.00000	−	3.46410i	−0.0998752	−	0.172989i	0.811758	−	0.583994i	$-0.198511\pi$
$401$	−2.00000	−	3.46410i	−0.0998752	−	0.172989i	−0.911633	+	0.411005i	$0.865178\pi$
$402$		0			0
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$		0			0
$406$	5.00000	+	1.73205i	0.248146	+	0.0859602i
$407$	12.0000			0.594818
$408$		0			0
$409$	1.00000	−	1.73205i	0.0494468	−	0.0856444i	−0.840243	−	0.542211i	$-0.817588\pi$
$409$	1.00000	−	1.73205i	0.0494468	−	0.0856444i	0.889689	+	0.456566i	$0.150921\pi$
$410$		0			0
$411$		0			0
$412$	13.0000			0.640464
$413$		0			0
$414$		0			0
$415$	7.50000	+	12.9904i	0.368161	+	0.637673i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	−7.00000	−	12.1244i	−0.342381	−	0.593022i
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	1.50000	+	2.59808i	0.0730189	+	0.126472i
$423$		0			0
$424$	2.00000	−	3.46410i	0.0971286	−	0.168232i
$425$	−2.50000	−	4.33013i	−0.121268	−	0.210042i
$426$		0			0
$427$	10.0000	+	3.46410i	0.483934	+	0.167640i
$428$	3.00000			0.145010
$429$		0			0
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$		0			0
$433$	−38.0000			−1.82616			−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000			−1.82616			−0.913082	+	0.407777i	$0.866304\pi$
$434$	−12.0000	+	10.3923i	−0.576018	+	0.498847i
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	−14.0000	+	24.2487i	−0.669711	+	1.15997i
$438$		0			0
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	0.814344	−	0.580383i	$-0.197097\pi$
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	−0.909798	+	0.415051i	$0.863764\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	5.00000			0.237826
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	0.501129	−	0.865373i	$-0.332918\pi$
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	−0.999999	+	0.00130426i	$0.999585\pi$
$444$		0			0
$445$	−8.00000	+	13.8564i	−0.379236	+	0.656857i
$446$	−8.50000	−	14.7224i	−0.402487	−	0.697127i
$447$		0			0
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	20.0000			0.943858			0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000			0.943858			0.471929	+	0.881636i	$0.343558\pi$
$450$		0			0
$451$		0			0
$452$	9.00000	−	15.5885i	0.423324	−	0.733219i
$453$		0			0
$454$	28.0000			1.31411
$455$	−2.50000	−	0.866025i	−0.117202	−	0.0405999i
$456$		0			0
$457$	−14.0000	−	24.2487i	−0.654892	−	1.13431i	−0.981921	−	0.189292i	$-0.939381\pi$
$457$	−14.0000	−	24.2487i	−0.654892	−	1.13431i	0.327028	−	0.945015i	$-0.393953\pi$
$458$	−4.00000	+	6.92820i	−0.186908	+	0.323734i
$459$		0			0
$460$	−2.00000	−	3.46410i	−0.0932505	−	0.161515i
$461$	38.0000			1.76984			0.884918	−	0.465746i	$-0.154214\pi$
$461$	38.0000			1.76984			0.884918	+	0.465746i	$0.154214\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	6.50000	−	11.2583i	0.301107	−	0.521532i
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$		0			0
$469$	−3.00000	−	15.5885i	−0.138527	−	0.719808i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$		0			0
$475$	7.00000			0.321182
$476$	−12.5000	−	4.33013i	−0.572937	−	0.198471i
$477$		0			0
$478$	−10.5000	−	18.1865i	−0.480259	−	0.831833i
$479$	8.00000	−	13.8564i	0.365529	−	0.633115i	−0.623332	−	0.781958i	$-0.714221\pi$
$479$	8.00000	−	13.8564i	0.365529	−	0.633115i	0.988861	+	0.148842i	$0.0475547\pi$
$480$		0			0
$481$	−3.00000	−	5.19615i	−0.136788	−	0.236924i
$482$	10.0000			0.455488
$483$		0			0
$484$	−7.00000			−0.318182
$485$	5.00000	+	8.66025i	0.227038	+	0.393242i
$486$		0			0
$487$	−9.50000	+	16.4545i	−0.430486	+	0.745624i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−9.50000	+	16.4545i	−0.430486	+	0.745624i	0.566429	+	0.824110i	$0.308325\pi$
$488$	2.00000	+	3.46410i	0.0905357	+	0.156813i
$489$		0			0
$490$	5.50000	+	4.33013i	0.248465	+	0.195615i
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$		0			0
$493$	5.00000	−	8.66025i	0.225189	−	0.390038i
$494$	−3.50000	+	6.06218i	−0.157472	+	0.272750i
$495$		0			0
$496$	−6.00000			−0.269408
$497$	2.00000	−	1.73205i	0.0897123	−	0.0776931i
$498$		0			0
$499$	13.5000	+	23.3827i	0.604343	+	1.04675i	0.992155	+	0.125014i	$0.0398977\pi$
$499$	13.5000	+	23.3827i	0.604343	+	1.04675i	−0.387812	+	0.921739i	$0.626769\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−9.00000	−	15.5885i	−0.401690	−	0.695747i
$503$	28.0000			1.24846			0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000			1.24846			0.624229	+	0.781241i	$0.285413\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	−4.00000	−	6.92820i	−0.177822	−	0.307996i
$507$		0			0
$508$	3.50000	−	6.06218i	0.155287	−	0.268966i
$509$	−22.5000	−	38.9711i	−0.997295	−	1.72737i	−0.562303	−	0.826931i	$-0.690085\pi$
$509$	−22.5000	−	38.9711i	−0.997295	−	1.72737i	−0.434992	−	0.900434i	$-0.643249\pi$
$510$		0			0
$511$	8.00000	+	41.5692i	0.353899	+	1.83891i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.00000	−	1.73205i	0.0441081	−	0.0763975i
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$		0			0
$517$		0			0
$518$	3.00000	+	15.5885i	0.131812	+	0.684917i
$519$		0			0
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$		0			0
$523$	16.0000	+	27.7128i	0.699631	+	1.21180i	0.968594	+	0.248646i	$0.0799857\pi$
$523$	16.0000	+	27.7128i	0.699631	+	1.21180i	−0.268963	+	0.963150i	$0.586681\pi$
$524$	14.0000			0.611593
$525$		0			0
$526$	−16.0000			−0.697633
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	2.00000	+	3.46410i	0.0868744	+	0.150471i
$531$		0			0
$532$	14.0000	−	12.1244i	0.606977	−	0.525657i
$533$		0			0
$534$		0			0
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$	3.00000	−	5.19615i	0.129580	−	0.224440i
$537$		0			0
$538$	3.00000			0.129339
$539$	11.0000	+	8.66025i	0.473804	+	0.373024i
$540$		0			0
$541$	14.0000	+	24.2487i	0.601907	+	1.04253i	0.992532	+	0.121984i	$0.0389256\pi$
$541$	14.0000	+	24.2487i	0.601907	+	1.04253i	−0.390625	+	0.920550i	$0.627741\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$		0			0
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	−10.0000			−0.428353
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$	8.50000	+	14.7224i	0.363102	+	0.628911i
$549$		0			0
$550$	−1.00000	+	1.73205i	−0.0426401	+	0.0738549i
$551$	7.00000	+	12.1244i	0.298210	+	0.516515i
$552$		0			0
$553$	5.00000	+	1.73205i	0.212622	+	0.0736543i
$554$	31.0000			1.31706
$555$		0			0
$556$	−2.50000	+	4.33013i	−0.106024	+	0.183638i
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$	0.500000	+	2.59808i	0.0211289	+	0.109789i
$561$		0			0
$562$	−9.00000	−	15.5885i	−0.379642	−	0.657559i
$563$	9.50000	−	16.4545i	0.400377	−	0.693474i	−0.593394	−	0.804912i	$-0.702212\pi$
$563$	9.50000	−	16.4545i	0.400377	−	0.693474i	0.993771	+	0.111438i	$0.0355457\pi$
$564$		0			0
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$	−26.0000			−1.09286
$567$		0			0
$568$	1.00000			0.0419591
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	0.963849	+	0.266450i	$0.0858508\pi$
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	−0.251172	+	0.967943i	$0.580816\pi$
$570$		0			0
$571$	23.5000	−	40.7032i	0.983444	−	1.70338i	0.334790	−	0.942293i	$-0.391335\pi$
$571$	23.5000	−	40.7032i	0.983444	−	1.70338i	0.648655	−	0.761083i	$-0.275332\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		0			0
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	−0.682730	−	0.730670i	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		0			0
$580$	−2.00000			−0.0830455
$581$	−30.0000	+	25.9808i	−1.24461	+	1.07786i
$582$		0			0
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$	−8.00000	+	13.8564i	−0.331042	+	0.573382i
$585$		0			0
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	3.00000			0.123823			0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000			0.123823			0.0619116	+	0.998082i	$0.480280\pi$
$588$		0			0
$589$	−42.0000			−1.73058
$590$		0			0
$591$		0			0
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	13.5000	+	23.3827i	0.554379	+	0.960212i	0.997952	+	0.0639736i	$0.0203773\pi$
$593$	13.5000	+	23.3827i	0.554379	+	0.960212i	−0.443573	+	0.896238i	$0.646289\pi$
$594$		0			0
$595$	10.0000	−	8.66025i	0.409960	−	0.355036i
$596$	5.00000			0.204808
$597$		0			0
$598$	−2.00000	+	3.46410i	−0.0817861	+	0.141658i
$599$	−4.50000	+	7.79423i	−0.183865	+	0.318464i	−0.943193	−	0.332244i	$-0.892194\pi$
$599$	−4.50000	+	7.79423i	−0.183865	+	0.318464i	0.759328	+	0.650708i	$0.225528\pi$
$600$		0			0
$601$	25.0000			1.01977			0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000			1.01977			0.509886	+	0.860242i	$0.329688\pi$
$602$	−5.00000	−	1.73205i	−0.203785	−	0.0705931i
$603$		0			0
$604$	−11.0000	−	19.0526i	−0.447584	−	0.775238i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	−15.5000	−	26.8468i	−0.629126	−	1.08968i	−0.987728	−	0.156187i	$-0.950080\pi$
$607$	−15.5000	−	26.8468i	−0.629126	−	1.08968i	0.358602	−	0.933491i	$-0.383254\pi$
$608$	7.00000			0.283887
$609$		0			0
$610$	−4.00000			−0.161955
$611$		0			0
$612$		0			0
$613$	1.50000	−	2.59808i	0.0605844	−	0.104935i	−0.834142	−	0.551549i	$-0.814037\pi$
$613$	1.50000	−	2.59808i	0.0605844	−	0.104935i	0.894727	+	0.446614i	$0.147370\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$		0			0
$616$	1.00000	+	5.19615i	0.0402911	+	0.209359i
$617$	−25.0000			−1.00646			−0.503231	−	0.864152i	$-0.667856\pi$
$617$	−25.0000			−1.00646			−0.503231	+	0.864152i	$0.667856\pi$
$618$		0			0
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$		0			0
$622$	−5.00000			−0.200482
$623$	−40.0000	−	13.8564i	−1.60257	−	0.555145i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$	10.5000	+	18.1865i	0.418996	+	0.725722i
$629$	30.0000			1.19618
$630$		0			0
$631$	26.0000			1.03504			0.517522	−	0.855670i	$-0.326855\pi$
$631$	26.0000			1.03504			0.517522	+	0.855670i	$0.326855\pi$
$632$	1.00000	+	1.73205i	0.0397779	+	0.0688973i
$633$		0			0
$634$	4.00000	−	6.92820i	0.158860	−	0.275154i
$635$	3.50000	+	6.06218i	0.138893	+	0.240570i
$636$		0			0
$637$	1.00000	−	6.92820i	0.0396214	−	0.274505i
$638$	−4.00000			−0.158362
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	−0.486409	−	0.873731i	$-0.661693\pi$
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	0.999878	−	0.0156233i	$-0.00497325\pi$
$642$		0			0
$643$	26.0000			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$	8.00000	−	6.92820i	0.315244	−	0.273009i
$645$		0			0
$646$	−17.5000	−	30.3109i	−0.688528	−	1.19257i
$647$	−18.0000	+	31.1769i	−0.707653	+	1.22569i	0.258073	+	0.966126i	$0.416913\pi$
$647$	−18.0000	+	31.1769i	−0.707653	+	1.22569i	−0.965726	+	0.259565i	$0.916421\pi$
$648$		0			0
$649$		0			0
$650$	1.00000			0.0392232
$651$		0			0
$652$	−4.00000			−0.156652
$653$	8.00000	+	13.8564i	0.313064	+	0.542243i	0.979024	−	0.203744i	$-0.0653112\pi$
$653$	8.00000	+	13.8564i	0.313064	+	0.542243i	−0.665960	+	0.745988i	$0.731978\pi$
$654$		0			0
$655$	−7.00000	+	12.1244i	−0.273513	+	0.473738i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	13.5000	−	23.3827i	0.524692	−	0.908794i
$663$		0			0
$664$	−15.0000			−0.582113
$665$	3.50000	+	18.1865i	0.135724	+	0.705244i
$666$		0			0
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$		0			0
$670$	3.00000	+	5.19615i	0.115900	+	0.200745i
$671$	−8.00000			−0.308837
$672$		0			0
$673$	−30.0000			−1.15642			−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000			−1.15642			−0.578208	+	0.815890i	$0.696248\pi$
$674$	9.00000	+	15.5885i	0.346667	+	0.600445i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−20.0000	−	34.6410i	−0.768662	−	1.33136i	−0.938288	−	0.345854i	$-0.887589\pi$
$677$	−20.0000	−	34.6410i	−0.768662	−	1.33136i	0.169626	−	0.985509i	$-0.445744\pi$
$678$		0			0
$679$	−20.0000	+	17.3205i	−0.767530	+	0.664700i
$680$	5.00000			0.191741
$681$		0			0
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$		0			0
$685$	−17.0000			−0.649537
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	1.50000	+	2.59808i	0.0570627	+	0.0988355i	0.893146	−	0.449768i	$-0.148493\pi$
$691$	1.50000	+	2.59808i	0.0570627	+	0.0988355i	−0.836083	+	0.548603i	$0.815160\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−4.00000			−0.151838
$695$	−2.50000	−	4.33013i	−0.0948304	−	0.164251i
$696$		0			0
$697$		0			0
$698$	2.00000	+	3.46410i	0.0757011	+	0.131118i
$699$		0			0
$700$	−2.50000	−	0.866025i	−0.0944911	−	0.0327327i
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$		0			0
$703$	−21.0000	+	36.3731i	−0.792030	+	1.37184i
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	34.0000			1.27961
$707$	1.50000	+	7.79423i	0.0564133	+	0.293132i
$708$		0			0
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	−0.500000	+	0.866025i	−0.0187647	+	0.0325014i
$711$		0			0
$712$	−8.00000	−	13.8564i	−0.299813	−	0.519291i
$713$	−24.0000			−0.898807
$714$		0			0
$715$	2.00000			0.0747958
$716$	4.00000	+	6.92820i	0.149487	+	0.258919i
$717$		0			0
$718$	7.50000	−	12.9904i	0.279898	−	0.484797i
$719$	−2.50000	−	4.33013i	−0.0932343	−	0.161486i	0.815636	−	0.578565i	$-0.196387\pi$
$719$	−2.50000	−	4.33013i	−0.0932343	−	0.161486i	−0.908870	+	0.417079i	$0.863054\pi$
$720$		0			0
$721$	−32.5000	−	11.2583i	−1.21036	−	0.419282i
$722$	30.0000			1.11648
$723$		0			0
$724$		0			0
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$		0			0
$727$	−37.0000			−1.37225			−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000			−1.37225			−0.686127	+	0.727482i	$0.740691\pi$
$728$	2.00000	−	1.73205i	0.0741249	−	0.0641941i
$729$		0			0
$730$	−8.00000	−	13.8564i	−0.296093	−	0.512849i
$731$	−5.00000	+	8.66025i	−0.184932	+	0.320311i
$732$		0			0
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	0.999136	+	0.0415715i	$0.0132364\pi$
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	−0.463566	+	0.886062i	$0.653430\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	4.00000			0.147442
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$		0			0
$739$	21.5000	−	37.2391i	0.790890	−	1.36986i	−0.134526	−	0.990910i	$-0.542951\pi$
$739$	21.5000	−	37.2391i	0.790890	−	1.36986i	0.925416	−	0.378952i	$-0.123715\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$		0			0
$742$	−8.00000	+	6.92820i	−0.293689	+	0.254342i
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	−2.50000	+	4.33013i	−0.0915929	+	0.158644i
$746$	−5.50000	+	9.52628i	−0.201369	+	0.348782i
$747$		0			0
$748$	10.0000			0.365636
$749$	−7.50000	−	2.59808i	−0.274044	−	0.0949316i
$750$		0			0
$751$	25.0000	+	43.3013i	0.912263	+	1.58009i	0.810860	+	0.585240i	$0.199000\pi$
$751$	25.0000	+	43.3013i	0.912263	+	1.58009i	0.101403	+	0.994845i	$0.467667\pi$
$752$		0			0
$753$		0			0
$754$	1.00000	+	1.73205i	0.0364179	+	0.0630776i
$755$	22.0000			0.800662
$756$		0			0
$757$	19.0000			0.690567			0.345283	−	0.938498i	$-0.387783\pi$
$757$	19.0000			0.690567			0.345283	+	0.938498i	$0.387783\pi$
$758$	−9.50000	−	16.4545i	−0.345056	−	0.597654i
$759$		0			0
$760$	−3.50000	+	6.06218i	−0.126958	+	0.219898i
$761$	−17.0000	−	29.4449i	−0.616250	−	1.06738i	−0.990164	−	0.139912i	$-0.955318\pi$
$761$	−17.0000	−	29.4449i	−0.616250	−	1.06738i	0.373914	−	0.927463i	$-0.378015\pi$
$762$		0			0
$763$	−5.00000	−	25.9808i	−0.181012	−	0.940567i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	−17.0000	+	29.4449i	−0.614235	+	1.06389i
$767$		0			0
$768$		0			0
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$	−5.00000	−	1.73205i	−0.180187	−	0.0624188i
$771$		0			0
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	16.0000	−	27.7128i	0.575480	−	0.996761i	−0.420509	−	0.907288i	$-0.638149\pi$
$773$	16.0000	−	27.7128i	0.575480	−	0.996761i	0.995989	−	0.0894724i	$-0.0285181\pi$
$774$		0			0
$775$	3.00000	+	5.19615i	0.107763	+	0.186651i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	−35.0000			−1.25481
$779$		0			0
$780$		0			0
$781$	−1.00000	+	1.73205i	−0.0357828	+	0.0619777i
$782$	−10.0000	−	17.3205i	−0.357599	−	0.619380i
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	−21.0000			−0.749522
$786$		0			0
$787$	−4.00000	+	6.92820i	−0.142585	+	0.246964i	−0.928469	−	0.371409i	$-0.878875\pi$
$787$	−4.00000	+	6.92820i	−0.142585	+	0.246964i	0.785885	+	0.618373i	$0.212208\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$		0			0
$790$	−2.00000			−0.0711568
$791$	−36.0000	+	31.1769i	−1.28001	+	1.10852i
$792$		0			0
$793$	2.00000	+	3.46410i	0.0710221	+	0.123014i
$794$	−16.5000	+	28.5788i	−0.585563	+	1.01423i
$795$		0			0
$796$		0			0
$797$	−36.0000			−1.27519			−0.637593	−	0.770374i	$-0.720070\pi$
$797$	−36.0000			−1.27519			−0.637593	+	0.770374i	$0.720070\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−2.00000	+	3.46410i	−0.0706225	+	0.122322i
$803$	−16.0000	−	27.7128i	−0.564628	−	0.977964i
$804$		0			0
$805$	2.00000	+	10.3923i	0.0704907	+	0.366281i
$806$	−6.00000			−0.211341
$807$		0			0
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	14.0000	−	24.2487i	0.492214	−	0.852539i	−0.507746	−	0.861507i	$-0.669521\pi$
$809$	14.0000	−	24.2487i	0.492214	−	0.852539i	0.999960	+	0.00896753i	$0.00285449\pi$
$810$		0			0
$811$	7.00000			0.245803			0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000			0.245803			0.122902	+	0.992419i	$0.460780\pi$
$812$	−1.00000	−	5.19615i	−0.0350931	−	0.182349i
$813$		0			0
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−7.00000	−	12.1244i	−0.244899	−	0.424178i
$818$	−2.00000			−0.0699284
$819$		0			0
$820$		0			0
$821$	−23.0000	−	39.8372i	−0.802706	−	1.39033i	−0.917829	−	0.396976i	$-0.870060\pi$
$821$	−23.0000	−	39.8372i	−0.802706	−	1.39033i	0.115124	−	0.993351i	$-0.463274\pi$
$822$		0			0
$823$	−24.0000	+	41.5692i	−0.836587	+	1.44901i	0.0561440	+	0.998423i	$0.482119\pi$
$823$	−24.0000	+	41.5692i	−0.836587	+	1.44901i	−0.892731	+	0.450589i	$0.851214\pi$
$824$	−6.50000	−	11.2583i	−0.226438	−	0.392203i
$825$		0			0
$826$		0			0
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$		0			0
$829$	−9.00000	+	15.5885i	−0.312583	+	0.541409i	−0.978921	−	0.204240i	$-0.934528\pi$
$829$	−9.00000	+	15.5885i	−0.312583	+	0.541409i	0.666338	+	0.745650i	$0.267861\pi$
$830$	7.50000	−	12.9904i	0.260329	−	0.450903i
$831$		0			0
$832$	1.00000			0.0346688
$833$	27.5000	+	21.6506i	0.952819	+	0.750150i
$834$		0			0
$835$	4.00000	+	6.92820i	0.138426	+	0.239760i
$836$	−7.00000	+	12.1244i	−0.242100	+	0.419330i
$837$		0			0
$838$	8.00000	+	13.8564i	0.276355	+	0.478662i
$839$	−13.0000			−0.448810			−0.224405	−	0.974496i	$-0.572044\pi$
$839$	−13.0000			−0.448810			−0.224405	+	0.974496i	$0.572044\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	1.00000	+	1.73205i	0.0344623	+	0.0596904i
$843$		0			0
$844$	1.50000	−	2.59808i	0.0516321	−	0.0894295i
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	17.5000	+	6.06218i	0.601307	+	0.208299i
$848$	−4.00000			−0.137361
$849$		0			0
$850$	−2.50000	+	4.33013i	−0.0857493	+	0.148522i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$	13.0000			0.445112			0.222556	−	0.974920i	$-0.428560\pi$
$853$	13.0000			0.445112			0.222556	+	0.974920i	$0.428560\pi$
$854$	−2.00000	−	10.3923i	−0.0684386	−	0.355617i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−2.50000	+	4.33013i	−0.0853984	+	0.147914i	−0.905561	−	0.424216i	$-0.860550\pi$
$857$	−2.50000	+	4.33013i	−0.0853984	+	0.147914i	0.820163	+	0.572131i	$0.193883\pi$
$858$		0			0
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	0.968657	+	0.248402i	$0.0799054\pi$
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	−0.269206	+	0.963083i	$0.586761\pi$
$860$	2.00000			0.0681994
$861$		0			0
$862$	3.00000			0.102180
$863$	2.00000	+	3.46410i	0.0680808	+	0.117919i	0.898056	−	0.439880i	$-0.144979\pi$
$863$	2.00000	+	3.46410i	0.0680808	+	0.117919i	−0.829976	+	0.557800i	$0.811646\pi$
$864$		0			0
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	19.0000	+	32.9090i	0.645646	+	1.11829i
$867$		0			0
$868$	15.0000	+	5.19615i	0.509133	+	0.176369i
$869$	−4.00000			−0.135691
$870$		0			0
$871$	3.00000	−	5.19615i	0.101651	−	0.176065i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$		0			0
$874$	28.0000			0.947114
$875$	2.00000	−	1.73205i	0.0676123	−	0.0585540i
$876$		0			0
$877$	24.5000	+	42.4352i	0.827306	+	1.43294i	0.900144	+	0.435593i	$0.143461\pi$
$877$	24.5000	+	42.4352i	0.827306	+	1.43294i	−0.0728377	+	0.997344i	$0.523206\pi$
$878$	−2.00000	+	3.46410i	−0.0674967	+	0.116908i
$879$		0			0
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	−58.0000			−1.95407			−0.977035	−	0.213080i	$-0.931651\pi$
$881$	−58.0000			−1.95407			−0.977035	+	0.213080i	$0.931651\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−2.50000	−	4.33013i	−0.0840841	−	0.145638i
$885$		0			0
$886$	−10.5000	+	18.1865i	−0.352754	+	0.610989i
$887$	−19.0000	−	32.9090i	−0.637958	−	1.10497i	−0.985880	−	0.167452i	$-0.946446\pi$
$887$	−19.0000	−	32.9090i	−0.637958	−	1.10497i	0.347923	−	0.937523i	$-0.386887\pi$
$888$		0			0
$889$	−14.0000	+	12.1244i	−0.469545	+	0.406638i
$890$	16.0000			0.536321
$891$		0			0
$892$	−8.50000	+	14.7224i	−0.284601	+	0.492943i
$893$		0			0
$894$		0			0
$895$	−8.00000			−0.267411
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$		0			0
$898$	−10.0000	−	17.3205i	−0.333704	−	0.577993i
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$		0			0
$903$		0			0
$904$	−18.0000			−0.598671
$905$		0			0
$906$		0			0
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	−0.650868	−	0.759191i	$-0.725595\pi$
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	0.982913	+	0.184073i	$0.0589282\pi$
$908$	−14.0000	−	24.2487i	−0.464606	−	0.804722i
$909$		0			0
$910$	0.500000	+	2.59808i	0.0165748	+	0.0861254i
$911$	35.0000			1.15960			0.579801	−	0.814758i	$-0.303130\pi$
$911$	35.0000			1.15960			0.579801	+	0.814758i	$0.303130\pi$
$912$		0			0
$913$	15.0000	−	25.9808i	0.496428	−	0.859838i
$914$	−14.0000	+	24.2487i	−0.463079	+	0.802076i
$915$		0			0
$916$	8.00000			0.264327
$917$	−35.0000	−	12.1244i	−1.15580	−	0.400381i
$918$		0			0
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	−2.00000	+	3.46410i	−0.0659380	+	0.114208i
$921$		0			0
$922$	−19.0000	−	32.9090i	−0.625732	−	1.08380i
$923$	1.00000			0.0329154
$924$		0			0
$925$	6.00000			0.197279
$926$	−12.0000	−	20.7846i	−0.394344	−	0.683025i
$927$		0			0
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	−20.0000	−	34.6410i	−0.656179	−	1.13653i	−0.981597	−	0.190965i	$-0.938838\pi$
$929$	−20.0000	−	34.6410i	−0.656179	−	1.13653i	0.325418	−	0.945570i	$-0.394495\pi$
$930$		0			0
$931$	−45.5000	+	18.1865i	−1.49120	+	0.596040i
$932$	−13.0000			−0.425829
$933$		0			0
$934$	−1.50000	+	2.59808i	−0.0490815	+	0.0850117i
$935$	−5.00000	+	8.66025i	−0.163517	+	0.283221i
$936$		0			0
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$	−12.0000	+	10.3923i	−0.391814	+	0.339321i
$939$		0			0
$940$		0			0
$941$	−16.5000	+	28.5788i	−0.537885	+	0.931644i	0.461133	+	0.887331i	$0.347443\pi$
$941$	−16.5000	+	28.5788i	−0.537885	+	0.931644i	−0.999018	+	0.0443125i	$0.985890\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	4.00000			0.130051
$947$	26.5000	+	45.8993i	0.861134	+	1.49153i	0.870835	+	0.491575i	$0.163579\pi$
$947$	26.5000	+	45.8993i	0.861134	+	1.49153i	−0.00970072	+	0.999953i	$0.503088\pi$
$948$		0			0
$949$	−8.00000	+	13.8564i	−0.259691	+	0.449798i
$950$	−3.50000	−	6.06218i	−0.113555	−	0.196683i
$951$		0			0
$952$	2.50000	+	12.9904i	0.0810255	+	0.421021i
$953$	59.0000			1.91120			0.955599	−	0.294671i	$-0.0952101\pi$
$953$	59.0000			1.91120			0.955599	+	0.294671i	$0.0952101\pi$
$954$		0			0
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$	−10.5000	+	18.1865i	−0.339594	+	0.588195i
$957$		0			0
$958$	−16.0000			−0.516937
$959$	−8.50000	−	44.1673i	−0.274479	−	1.42624i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	−3.00000	+	5.19615i	−0.0967239	+	0.167531i
$963$		0			0
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	−4.00000			−0.128765
$966$		0			0
$967$	49.0000			1.57573			0.787867	−	0.615846i	$-0.211185\pi$
$967$	49.0000			1.57573			0.787867	+	0.615846i	$0.211185\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$		0			0
$970$	5.00000	−	8.66025i	0.160540	−	0.278064i
$971$	−17.0000	−	29.4449i	−0.545556	−	0.944931i	−0.998572	−	0.0534281i	$-0.982985\pi$
$971$	−17.0000	−	29.4449i	−0.545556	−	0.944931i	0.453016	−	0.891503i	$-0.350348\pi$
$972$		0			0
$973$	10.0000	−	8.66025i	0.320585	−	0.277635i
$974$	19.0000			0.608799
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	−22.5000	+	38.9711i	−0.719839	+	1.24680i	0.241225	+	0.970469i	$0.422451\pi$
$977$	−22.5000	+	38.9711i	−0.719839	+	1.24680i	−0.961063	+	0.276328i	$0.910882\pi$
$978$		0			0
$979$	32.0000			1.02272
$980$	1.00000	−	6.92820i	0.0319438	−	0.221313i
$981$		0			0
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	0.308165	+	0.951333i	$0.400285\pi$
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	−0.977961	+	0.208788i	$0.933048\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$	−10.0000			−0.318465
$987$		0			0
$988$	7.00000			0.222700
$989$	−4.00000	−	6.92820i	−0.127193	−	0.220304i
$990$		0			0
$991$	−14.0000	+	24.2487i	−0.444725	+	0.770286i	−0.998033	−	0.0626908i	$-0.980032\pi$
$991$	−14.0000	+	24.2487i	−0.444725	+	0.770286i	0.553308	+	0.832977i	$0.313365\pi$
$992$	3.00000	+	5.19615i	0.0952501	+	0.164978i
$993$		0			0
$994$	−2.50000	−	0.866025i	−0.0792952	−	0.0274687i
$995$		0			0
$996$		0			0
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$	13.5000	−	23.3827i	0.427335	−	0.740166i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.k.d.1621.1	yes	2
3.2	odd	2		1890.2.k.bf.1621.1	yes	2
7.2	even	3	inner	1890.2.k.d.541.1	✓	2
21.2	odd	6		1890.2.k.bf.541.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.k.d.541.1	✓	2	7.2	even	3	inner
1890.2.k.d.1621.1	yes	2	1.1	even	1	trivial
1890.2.k.bf.541.1	yes	2	21.2	odd	6
1890.2.k.bf.1621.1	yes	2	3.2	odd	2

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-3.50000 - 6.06218i) q^{19} +1.00000 q^{20} +2.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(0.500000 + 2.59808i) q^{28} -2.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +5.00000 q^{34} +(-2.50000 - 0.866025i) q^{35} +(-3.00000 - 5.19615i) q^{37} +(-3.50000 + 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-2.00000 + 3.46410i) q^{46} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(2.00000 - 3.46410i) q^{53} +2.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +(1.00000 + 1.73205i) q^{58} +(2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(3.00000 - 5.19615i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(0.500000 + 2.59808i) q^{70} +1.00000 q^{71} +(-8.00000 + 13.8564i) q^{73} +(-3.00000 + 5.19615i) q^{74} +7.00000 q^{76} +(1.00000 + 5.19615i) q^{77} +(1.00000 + 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{80} -15.0000 q^{83} +5.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(-8.00000 - 13.8564i) q^{89} +(2.00000 - 1.73205i) q^{91} +4.00000 q^{92} +(-3.50000 + 6.06218i) q^{95} -10.0000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 2 q^{8} - q^{10} - 2 q^{11} + 2 q^{13} - 5 q^{14} - q^{16} - 5 q^{17} - 7 q^{19} + 2 q^{20} + 4 q^{22} - 4 q^{23} - q^{25} - q^{26} + q^{28} - 4 q^{29} + 6 q^{31} - q^{32} + 10 q^{34} - 5 q^{35} - 6 q^{37} - 7 q^{38} - q^{40} + 4 q^{43} - 2 q^{44} - 4 q^{46} + 2 q^{49} + 2 q^{50} - q^{52} + 4 q^{53} + 4 q^{55} + 4 q^{56} + 2 q^{58} + 4 q^{61} - 12 q^{62} + 2 q^{64} - q^{65} + 6 q^{67} - 5 q^{68} + q^{70} + 2 q^{71} - 16 q^{73} - 6 q^{74} + 14 q^{76} + 2 q^{77} + 2 q^{79} - q^{80} - 30 q^{83} + 10 q^{85} - 2 q^{86} - 2 q^{88} - 16 q^{89} + 4 q^{91} + 8 q^{92} - 7 q^{95} - 20 q^{97} - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8 - q^10 - 2 * q^11 + 2 * q^13 - 5 * q^14 - q^16 - 5 * q^17 - 7 * q^19 + 2 * q^20 + 4 * q^22 - 4 * q^23 - q^25 - q^26 + q^28 - 4 * q^29 + 6 * q^31 - q^32 + 10 * q^34 - 5 * q^35 - 6 * q^37 - 7 * q^38 - q^40 + 4 * q^43 - 2 * q^44 - 4 * q^46 + 2 * q^49 + 2 * q^50 - q^52 + 4 * q^53 + 4 * q^55 + 4 * q^56 + 2 * q^58 + 4 * q^61 - 12 * q^62 + 2 * q^64 - q^65 + 6 * q^67 - 5 * q^68 + q^70 + 2 * q^71 - 16 * q^73 - 6 * q^74 + 14 * q^76 + 2 * q^77 + 2 * q^79 - q^80 - 30 * q^83 + 10 * q^85 - 2 * q^86 - 2 * q^88 - 16 * q^89 + 4 * q^91 + 8 * q^92 - 7 * q^95 - 20 * q^97 - 13 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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