LMFDB - Embedded newform 1710.2.l.q.1531.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29654208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 12 $ x^6 + 14x^4 + 49x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1531.2
Root			$-2.86514i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.q.1261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.75353 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.75353 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +2.20905 q^{11} +(1.60452 + 2.77912i) q^{13} +(0.876763 - 1.51860i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.58581 - 6.21081i) q^{17} +(0.727762 + 4.29772i) q^{19} -1.00000 q^{20} +(1.10452 - 1.91309i) q^{22} +(1.10452 + 1.91309i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.20905 q^{26} +(-0.876763 - 1.51860i) q^{28} +(3.83229 + 6.63772i) q^{29} -3.20905 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.58581 - 6.21081i) q^{34} +(0.876763 - 1.51860i) q^{35} -1.00000 q^{37} +(4.08581 + 1.51860i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(5.23481 - 9.06696i) q^{41} +(1.35805 - 2.35221i) q^{43} +(-1.10452 - 1.91309i) q^{44} +2.20905 q^{46} +(-4.96257 - 8.59543i) q^{47} -3.92515 q^{49} -1.00000 q^{50} +(1.60452 - 2.77912i) q^{52} +(5.48129 + 9.49387i) q^{53} +(1.10452 - 1.91309i) q^{55} -1.75353 q^{56} +7.66457 q^{58} +(3.00000 - 5.19615i) q^{59} +(2.98129 + 5.16374i) q^{61} +(-1.60452 + 2.77912i) q^{62} +1.00000 q^{64} +3.20905 q^{65} +(-0.0187126 - 0.0324111i) q^{67} -7.17162 q^{68} +(-0.876763 - 1.51860i) q^{70} +(3.58581 - 6.21081i) q^{71} +(5.98129 - 10.3599i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(3.35805 - 2.77912i) q^{76} +3.87362 q^{77} +(-0.604525 + 1.04707i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-5.23481 - 9.06696i) q^{82} -14.8362 q^{83} +(-3.58581 - 6.21081i) q^{85} +(-1.35805 - 2.35221i) q^{86} -2.20905 q^{88} +(-5.48129 - 9.49387i) q^{89} +(2.81357 + 4.87325i) q^{91} +(1.10452 - 1.91309i) q^{92} -9.92515 q^{94} +(4.08581 + 1.51860i) q^{95} +(-5.62324 + 9.73973i) q^{97} +(-1.96257 + 3.39928i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8} - 3 q^{10} - 8 q^{11} - q^{13} + q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 2 q^{26} - q^{28} + 6 q^{29} + 2 q^{31} + 3 q^{32} + 4 q^{34} + q^{35} - 6 q^{37} - q^{38} - 3 q^{40} + 8 q^{41} - 11 q^{43} + 4 q^{44} - 8 q^{46} + 36 q^{49} - 6 q^{50} - q^{52} + 18 q^{53} - 4 q^{55} - 2 q^{56} + 12 q^{58} + 18 q^{59} + 3 q^{61} + q^{62} + 6 q^{64} - 2 q^{65} - 15 q^{67} + 8 q^{68} - q^{70} - 4 q^{71} + 21 q^{73} - 3 q^{74} + q^{76} - 32 q^{77} + 7 q^{79} + 3 q^{80} - 8 q^{82} - 4 q^{83} + 4 q^{85} + 11 q^{86} + 8 q^{88} - 18 q^{89} - 15 q^{91} - 4 q^{92} - q^{95} - 38 q^{97} + 18 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8 - 3 * q^10 - 8 * q^11 - q^13 + q^14 - 3 * q^16 - 4 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 2 * q^26 - q^28 + 6 * q^29 + 2 * q^31 + 3 * q^32 + 4 * q^34 + q^35 - 6 * q^37 - q^38 - 3 * q^40 + 8 * q^41 - 11 * q^43 + 4 * q^44 - 8 * q^46 + 36 * q^49 - 6 * q^50 - q^52 + 18 * q^53 - 4 * q^55 - 2 * q^56 + 12 * q^58 + 18 * q^59 + 3 * q^61 + q^62 + 6 * q^64 - 2 * q^65 - 15 * q^67 + 8 * q^68 - q^70 - 4 * q^71 + 21 * q^73 - 3 * q^74 + q^76 - 32 * q^77 + 7 * q^79 + 3 * q^80 - 8 * q^82 - 4 * q^83 + 4 * q^85 + 11 * q^86 + 8 * q^88 - 18 * q^89 - 15 * q^91 - 4 * q^92 - q^95 - 38 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.75353			0.662770			0.331385	−	0.943496i	$-0.392484\pi$
$7$	1.75353			0.662770			0.331385	+	0.943496i	$0.392484\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.20905			0.666054			0.333027	−	0.942917i	$-0.391930\pi$
$11$	2.20905			0.666054			0.333027	+	0.942917i	$0.391930\pi$
$12$		0			0
$13$	1.60452	+	2.77912i	0.445015	+	0.770789i	0.998053	−	0.0623671i	$-0.0198650\pi$
$13$	1.60452	+	2.77912i	0.445015	+	0.770789i	−0.553038	+	0.833156i	$0.686532\pi$
$14$	0.876763	−	1.51860i	0.234325	−	0.405862i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.58581	−	6.21081i	0.869687	−	1.50634i	0.00737071	−	0.999973i	$-0.497654\pi$
$17$	3.58581	−	6.21081i	0.869687	−	1.50634i	0.862317	−	0.506370i	$-0.169013\pi$
$18$		0			0
$19$	0.727762	+	4.29772i	0.166960	+	0.985964i
$19$	0.727762	+	4.29772i	0.166960	+	0.985964i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	1.10452	−	1.91309i	0.235485	−	0.407873i
$23$	1.10452	+	1.91309i	0.230309	+	0.398908i	0.957899	−	0.287105i	$-0.0926929\pi$
$23$	1.10452	+	1.91309i	0.230309	+	0.398908i	−0.727590	+	0.686012i	$0.759360\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.20905			0.629346
$27$		0			0
$28$	−0.876763	−	1.51860i	−0.165693	−	0.286988i
$29$	3.83229	+	6.63772i	0.711638	+	1.23259i	0.964242	+	0.265023i	$0.0853796\pi$
$29$	3.83229	+	6.63772i	0.711638	+	1.23259i	−0.252604	+	0.967570i	$0.581287\pi$
$30$		0			0
$31$	−3.20905			−0.576362			−0.288181	−	0.957576i	$-0.593051\pi$
$31$	−3.20905			−0.576362			−0.288181	+	0.957576i	$0.593051\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−3.58581	−	6.21081i	−0.614962	−	1.06514i
$35$	0.876763	−	1.51860i	0.148200	−	0.256690i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	4.08581	+	1.51860i	0.662806	+	0.246349i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	5.23481	−	9.06696i	0.817540	−	1.41602i	−0.0899490	−	0.995946i	$-0.528670\pi$
$41$	5.23481	−	9.06696i	0.817540	−	1.41602i	0.907489	−	0.420075i	$-0.137996\pi$
$42$		0			0
$43$	1.35805	−	2.35221i	0.207101	−	0.358709i	−0.743699	−	0.668514i	$-0.766931\pi$
$43$	1.35805	−	2.35221i	0.207101	−	0.358709i	0.950800	+	0.309805i	$0.100264\pi$
$44$	−1.10452	−	1.91309i	−0.166513	−	0.288410i
$45$		0			0
$46$	2.20905			0.325707
$47$	−4.96257	−	8.59543i	−0.723866	−	1.25377i	−0.959439	−	0.281916i	$-0.909030\pi$
$47$	−4.96257	−	8.59543i	−0.723866	−	1.25377i	0.235573	−	0.971857i	$-0.424303\pi$
$48$		0			0
$49$	−3.92515			−0.560736
$50$	−1.00000			−0.141421
$51$		0			0
$52$	1.60452	−	2.77912i	0.222508	−	0.385394i
$53$	5.48129	+	9.49387i	0.752913	+	1.30408i	0.946405	+	0.322981i	$0.104685\pi$
$53$	5.48129	+	9.49387i	0.752913	+	1.30408i	−0.193493	+	0.981102i	$0.561982\pi$
$54$		0			0
$55$	1.10452	−	1.91309i	0.148934	−	0.257961i
$56$	−1.75353			−0.234325
$57$		0			0
$58$	7.66457			1.00641
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	2.98129	+	5.16374i	0.381715	+	0.661149i	0.991307	−	0.131565i	$-0.0420003\pi$
$61$	2.98129	+	5.16374i	0.381715	+	0.661149i	−0.609593	+	0.792715i	$0.708667\pi$
$62$	−1.60452	+	2.77912i	−0.203775	+	0.352948i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.20905			0.398034
$66$		0			0
$67$	−0.0187126	−	0.0324111i	−0.00228610	−	0.00395965i	0.864880	−	0.501979i	$-0.167394\pi$
$67$	−0.0187126	−	0.0324111i	−0.00228610	−	0.00395965i	−0.867166	+	0.498019i	$0.834061\pi$
$68$	−7.17162			−0.869687
$69$		0			0
$70$	−0.876763	−	1.51860i	−0.104793	−	0.181507i
$71$	3.58581	−	6.21081i	0.425558	−	0.737087i	−0.570915	−	0.821009i	$-0.693411\pi$
$71$	3.58581	−	6.21081i	0.425558	−	0.737087i	0.996472	+	0.0839219i	$0.0267446\pi$
$72$		0			0
$73$	5.98129	−	10.3599i	0.700057	−	1.21253i	−0.268389	−	0.963311i	$-0.586491\pi$
$73$	5.98129	−	10.3599i	0.700057	−	1.21253i	0.968446	−	0.249223i	$-0.0801753\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$		0			0
$76$	3.35805	−	2.77912i	0.385195	−	0.318787i
$77$	3.87362			0.441440
$78$		0			0
$79$	−0.604525	+	1.04707i	−0.0680144	+	0.117804i	−0.898027	−	0.439940i	$-0.855000\pi$
$79$	−0.604525	+	1.04707i	−0.0680144	+	0.117804i	0.830013	+	0.557744i	$0.188333\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	−5.23481	−	9.06696i	−0.578088	−	1.00128i
$83$	−14.8362			−1.62848			−0.814242	−	0.580525i	$-0.802847\pi$
$83$	−14.8362			−1.62848			−0.814242	+	0.580525i	$0.802847\pi$
$84$		0			0
$85$	−3.58581	−	6.21081i	−0.388936	−	0.673657i
$86$	−1.35805	−	2.35221i	−0.146442	−	0.253645i
$87$		0			0
$88$	−2.20905			−0.235485
$89$	−5.48129	−	9.49387i	−0.581015	−	1.00635i	−0.995359	−	0.0962277i	$-0.969322\pi$
$89$	−5.48129	−	9.49387i	−0.581015	−	1.00635i	0.414344	−	0.910120i	$-0.364011\pi$
$90$		0			0
$91$	2.81357	+	4.87325i	0.294943	+	0.510856i
$92$	1.10452	−	1.91309i	0.115155	−	0.199454i
$93$		0			0
$94$	−9.92515			−1.02370
$95$	4.08581	+	1.51860i	0.419195	+	0.155805i
$96$		0			0
$97$	−5.62324	+	9.73973i	−0.570953	+	0.988920i	0.425515	+	0.904951i	$0.360093\pi$
$97$	−5.62324	+	9.73973i	−0.570953	+	0.988920i	−0.996468	+	0.0839687i	$0.973240\pi$
$98$	−1.96257	+	3.39928i	−0.198250	+	0.343379i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.246475	+	0.426907i	0.0245252	+	0.0424788i	0.878027	−	0.478610i	$-0.158859\pi$
$101$	0.246475	+	0.426907i	0.0245252	+	0.0424788i	−0.853502	+	0.521089i	$0.825526\pi$
$102$		0			0
$103$	11.6787			1.15073			0.575367	−	0.817895i	$-0.304859\pi$
$103$	11.6787			1.15073			0.575367	+	0.817895i	$0.304859\pi$
$104$	−1.60452	−	2.77912i	−0.157337	−	0.272515i
$105$		0			0
$106$	10.9626			1.06478
$107$	−8.26058			−0.798580			−0.399290	−	0.916825i	$-0.630743\pi$
$107$	−8.26058			−0.798580			−0.399290	+	0.916825i	$0.630743\pi$
$108$		0			0
$109$	2.58581	−	4.47876i	0.247676	−	0.428987i	−0.715205	−	0.698915i	$-0.753667\pi$
$109$	2.58581	−	4.47876i	0.247676	−	0.428987i	0.962881	+	0.269928i	$0.0869999\pi$
$110$	−1.10452	−	1.91309i	−0.105312	−	0.182406i
$111$		0			0
$112$	−0.876763	+	1.51860i	−0.0828463	+	0.143494i
$113$	2.26058			0.212657			0.106329	−	0.994331i	$-0.466090\pi$
$113$	2.26058			0.212657			0.106329	+	0.994331i	$0.466090\pi$
$114$		0			0
$115$	2.20905			0.205995
$116$	3.83229	−	6.63772i	0.355819	−	0.616296i
$117$		0			0
$118$	−3.00000	−	5.19615i	−0.276172	−	0.478345i
$119$	6.28781	−	10.8908i	0.576403	−	0.998359i
$120$		0			0
$121$	−6.12010			−0.556373
$122$	5.96257			0.539826
$123$		0			0
$124$	1.60452	+	2.77912i	0.144091	+	0.249572i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.44386	+	11.1611i	0.571800	+	0.990387i	0.996381	+	0.0849972i	$0.0270881\pi$
$127$	6.44386	+	11.1611i	0.571800	+	0.990387i	−0.424581	+	0.905390i	$0.639579\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	1.60452	−	2.77912i	0.140726	−	0.243745i
$131$	−6.61158	+	11.4516i	−0.577656	+	1.00053i	0.418091	+	0.908405i	$0.362699\pi$
$131$	−6.61158	+	11.4516i	−0.577656	+	1.00053i	−0.995747	+	0.0921246i	$0.970634\pi$
$132$		0			0
$133$	1.27615	+	7.53615i	0.110656	+	0.653467i
$134$	−0.0374251			−0.00323304
$135$		0			0
$136$	−3.58581	+	6.21081i	−0.307481	+	0.532572i
$137$	−10.7161	−	18.5608i	−0.915538	−	1.58576i	−0.806111	−	0.591764i	$-0.798432\pi$
$137$	−10.7161	−	18.5608i	−0.915538	−	1.58576i	−0.109427	−	0.993995i	$-0.534902\pi$
$138$		0			0
$139$	−3.60452	−	6.24322i	−0.305732	−	0.529543i	0.671692	−	0.740830i	$-0.265568\pi$
$139$	−3.60452	−	6.24322i	−0.305732	−	0.529543i	−0.977424	+	0.211287i	$0.932234\pi$
$140$	−1.75353			−0.148200
$141$		0			0
$142$	−3.58581	−	6.21081i	−0.300915	−	0.521200i
$143$	3.54448	+	6.13921i	0.296404	+	0.513387i
$144$		0			0
$145$	7.66457			0.636508
$146$	−5.98129	−	10.3599i	−0.495015	−	0.857391i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−4.37676	+	7.58078i	−0.358558	+	0.621041i	−0.987720	−	0.156233i	$-0.950065\pi$
$149$	−4.37676	+	7.58078i	−0.358558	+	0.621041i	0.629162	+	0.777274i	$0.283398\pi$
$150$		0			0
$151$	8.67867			0.706261			0.353130	−	0.935574i	$-0.385117\pi$
$151$	8.67867			0.706261			0.353130	+	0.935574i	$0.385117\pi$
$152$	−0.727762	−	4.29772i	−0.0590293	−	0.348591i
$153$		0			0
$154$	1.93681	−	3.35466i	0.156073	−	0.270326i
$155$	−1.60452	+	2.77912i	−0.128879	+	0.223224i
$156$		0			0
$157$	−2.25353	+	3.90322i	−0.179851	+	0.311511i	−0.941829	−	0.336092i	$-0.890895\pi$
$157$	−2.25353	+	3.90322i	−0.179851	+	0.311511i	0.761978	+	0.647602i	$0.224228\pi$
$158$	0.604525	+	1.04707i	0.0480934	+	0.0833002i
$159$		0			0
$160$	1.00000			0.0790569
$161$	1.93681	+	3.35466i	0.152642	+	0.264384i
$162$		0			0
$163$	23.6271			1.85062			0.925311	−	0.379210i	$-0.123804\pi$
$163$	23.6271			1.85062			0.925311	+	0.379210i	$0.123804\pi$
$164$	−10.4696			−0.817540
$165$		0			0
$166$	−7.41810	+	12.8485i	−0.575756	+	0.997239i
$167$	4.89548	+	8.47921i	0.378823	+	0.656141i	0.990891	−	0.134664i	$-0.0429955\pi$
$167$	4.89548	+	8.47921i	0.378823	+	0.656141i	−0.612068	+	0.790805i	$0.709662\pi$
$168$		0			0
$169$	1.35100	−	2.34000i	0.103923	−	0.180000i
$170$	−7.17162			−0.550039
$171$		0			0
$172$	−2.71610			−0.207101
$173$	5.72776	−	9.92078i	0.435474	−	0.754263i	−0.561860	−	0.827232i	$-0.689914\pi$
$173$	5.72776	−	9.92078i	0.435474	−	0.754263i	0.997334	+	0.0729694i	$0.0232476\pi$
$174$		0			0
$175$	−0.876763	−	1.51860i	−0.0662770	−	0.114795i
$176$	−1.10452	+	1.91309i	−0.0832567	+	0.144205i
$177$		0			0
$178$	−10.9626			−0.821680
$179$	−6.62715			−0.495336			−0.247668	−	0.968845i	$-0.579664\pi$
$179$	−6.62715			−0.495336			−0.247668	+	0.968845i	$0.579664\pi$
$180$		0			0
$181$	−5.13029	−	8.88592i	−0.381331	−	0.660485i	0.609922	−	0.792462i	$-0.291201\pi$
$181$	−5.13029	−	8.88592i	−0.381331	−	0.660485i	−0.991253	+	0.131977i	$0.957868\pi$
$182$	5.62715			0.417112
$183$		0			0
$184$	−1.10452	−	1.91309i	−0.0814267	−	0.141035i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$		0			0
$187$	7.92124	−	13.7200i	0.579258	−	1.00330i
$188$	−4.96257	+	8.59543i	−0.361933	+	0.626886i
$189$		0			0
$190$	3.35805	−	2.77912i	0.243619	−	0.201618i
$191$	−25.2543			−1.82734			−0.913668	−	0.406460i	$-0.866763\pi$
$191$	−25.2543			−1.82734			−0.913668	+	0.406460i	$0.866763\pi$
$192$		0			0
$193$	−1.43681	+	2.48863i	−0.103424	+	0.179136i	−0.913093	−	0.407751i	$-0.866313\pi$
$193$	−1.43681	+	2.48863i	−0.103424	+	0.179136i	0.809669	+	0.586886i	$0.199647\pi$
$194$	5.62324	+	9.73973i	0.403725	+	0.699272i
$195$		0			0
$196$	1.96257	+	3.39928i	0.140184	+	0.242806i
$197$	14.8877			1.06071			0.530353	−	0.847777i	$-0.322059\pi$
$197$	14.8877			1.06071			0.530353	+	0.847777i	$0.322059\pi$
$198$		0			0
$199$	0.772238	+	1.33755i	0.0547425	+	0.0948168i	0.892098	−	0.451842i	$-0.149233\pi$
$199$	0.772238	+	1.33755i	0.0547425	+	0.0948168i	−0.837356	+	0.546659i	$0.815900\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	0.492950			0.0346838
$203$	6.72001	+	11.6394i	0.471652	+	0.816926i
$204$		0			0
$205$	−5.23481	−	9.06696i	−0.365615	−	0.633264i
$206$	5.83934	−	10.1140i	0.406846	−	0.704678i
$207$		0			0
$208$	−3.20905			−0.222508
$209$	1.60766	+	9.49387i	0.111204	+	0.656705i
$210$		0			0
$211$	−6.38381	+	11.0571i	−0.439480	+	0.761201i	−0.997649	−	0.0685256i	$-0.978171\pi$
$211$	−6.38381	+	11.0571i	−0.439480	+	0.761201i	0.558170	+	0.829727i	$0.311504\pi$
$212$	5.48129	−	9.49387i	0.376456	−	0.652042i
$213$		0			0
$214$	−4.13029	+	7.15387i	−0.282341	+	0.489028i
$215$	−1.35805	−	2.35221i	−0.0926182	−	0.160419i
$216$		0			0
$217$	−5.62715			−0.381996
$218$	−2.58581	−	4.47876i	−0.175133	−	0.303340i
$219$		0			0
$220$	−2.20905			−0.148934
$221$	23.0141			1.54810
$222$		0			0
$223$	−3.57876	+	6.19860i	−0.239652	+	0.415089i	−0.960614	−	0.277885i	$-0.910367\pi$
$223$	−3.57876	+	6.19860i	−0.239652	+	0.415089i	0.720963	+	0.692974i	$0.243700\pi$
$224$	0.876763	+	1.51860i	0.0585812	+	0.101466i
$225$		0			0
$226$	1.13029	−	1.95772i	0.0751856	−	0.130225i
$227$	14.2606			0.946508			0.473254	−	0.880926i	$-0.343079\pi$
$227$	14.2606			0.946508			0.473254	+	0.880926i	$0.343079\pi$
$228$		0			0
$229$	−21.2090			−1.40153			−0.700767	−	0.713390i	$-0.747159\pi$
$229$	−21.2090			−1.40153			−0.700767	+	0.713390i	$0.747159\pi$
$230$	1.10452	−	1.91309i	0.0728302	−	0.126146i
$231$		0			0
$232$	−3.83229	−	6.63772i	−0.251602	−	0.435787i
$233$	−2.70200	+	4.68000i	−0.177014	+	0.306597i	−0.940856	−	0.338806i	$-0.889977\pi$
$233$	−2.70200	+	4.68000i	−0.177014	+	0.306597i	0.763842	+	0.645403i	$0.223310\pi$
$234$		0			0
$235$	−9.92515			−0.647445
$236$	−6.00000			−0.390567
$237$		0			0
$238$	−6.28781	−	10.8908i	−0.407578	−	0.705946i
$239$	−21.4322			−1.38633			−0.693167	−	0.720777i	$-0.743785\pi$
$239$	−21.4322			−1.38633			−0.693167	+	0.720777i	$0.743785\pi$
$240$		0			0
$241$	3.18643	+	5.51905i	0.205256	+	0.355513i	0.950214	−	0.311598i	$-0.100864\pi$
$241$	3.18643	+	5.51905i	0.205256	+	0.355513i	−0.744958	+	0.667111i	$0.767531\pi$
$242$	−3.06005	+	5.30016i	−0.196707	+	0.340707i
$243$		0			0
$244$	2.98129	−	5.16374i	0.190857	−	0.330575i
$245$	−1.96257	+	3.39928i	−0.125384	+	0.217172i
$246$		0			0
$247$	−10.7761	+	8.91833i	−0.685670	+	0.567460i
$248$	3.20905			0.203775
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	9.13420	+	15.8209i	0.576546	+	0.998606i	0.995872	+	0.0907706i	$0.0289330\pi$
$251$	9.13420	+	15.8209i	0.576546	+	0.998606i	−0.419326	+	0.907836i	$0.637734\pi$
$252$		0			0
$253$	2.43995	+	4.22612i	0.153398	+	0.265694i
$254$	12.8877			0.808648
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	−1.75353			−0.108959
$260$	−1.60452	−	2.77912i	−0.0995084	−	0.172354i
$261$		0			0
$262$	6.61158	+	11.4516i	0.408464	+	0.707481i
$263$	−15.3136	+	26.5239i	−0.944275	+	1.63553i	−0.187080	+	0.982345i	$0.559902\pi$
$263$	−15.3136	+	26.5239i	−0.944275	+	1.63553i	−0.757195	+	0.653188i	$0.773431\pi$
$264$		0			0
$265$	10.9626			0.673426
$266$	7.16457	+	2.66290i	0.439288	+	0.163273i
$267$		0			0
$268$	−0.0187126	+	0.0324111i	−0.00114305	+	0.00197982i
$269$	−8.79486	+	15.2331i	−0.536232	+	0.928781i	0.462870	+	0.886426i	$0.346820\pi$
$269$	−8.79486	+	15.2331i	−0.536232	+	0.928781i	−0.999103	+	0.0423555i	$0.986514\pi$
$270$		0			0
$271$	−9.45552	+	16.3774i	−0.574382	+	0.994859i	0.421726	+	0.906723i	$0.361424\pi$
$271$	−9.45552	+	16.3774i	−0.574382	+	0.994859i	−0.996108	+	0.0881360i	$0.971909\pi$
$272$	3.58581	+	6.21081i	0.217422	+	0.376586i
$273$		0			0
$274$	−21.4322			−1.29477
$275$	−1.10452	−	1.91309i	−0.0666054	−	0.115364i
$276$		0			0
$277$	24.9110			1.49676			0.748380	−	0.663270i	$-0.230832\pi$
$277$	24.9110			1.49676			0.748380	+	0.663270i	$0.230832\pi$
$278$	−7.20905			−0.432370
$279$		0			0
$280$	−0.876763	+	1.51860i	−0.0523966	+	0.0907535i
$281$	13.4439	+	23.2855i	0.801994	+	1.38909i	0.918302	+	0.395880i	$0.129561\pi$
$281$	13.4439	+	23.2855i	0.801994	+	1.38909i	−0.116308	+	0.993213i	$0.537106\pi$
$282$		0			0
$283$	−12.8877	+	22.3222i	−0.766096	+	1.32692i	0.173570	+	0.984822i	$0.444470\pi$
$283$	−12.8877	+	22.3222i	−0.766096	+	1.32692i	−0.939665	+	0.342095i	$0.888864\pi$
$284$	−7.17162			−0.425558
$285$		0			0
$286$	7.08895			0.419178
$287$	9.17938	−	15.8991i	0.541841	−	0.938497i
$288$		0			0
$289$	−17.2161	−	29.8192i	−1.01271	−	1.75407i
$290$	3.83229	−	6.63772i	0.225040	−	0.389780i
$291$		0			0
$292$	−11.9626			−0.700057
$293$	−1.53037			−0.0894055			−0.0447027	−	0.999000i	$-0.514234\pi$
$293$	−1.53037			−0.0894055			−0.0447027	+	0.999000i	$0.514234\pi$
$294$		0			0
$295$	−3.00000	−	5.19615i	−0.174667	−	0.302532i
$296$	1.00000			0.0581238
$297$		0			0
$298$	4.37676	+	7.58078i	0.253539	+	0.439143i
$299$	−3.54448	+	6.13921i	−0.204982	+	0.355040i
$300$		0			0
$301$	2.38137	−	4.12466i	0.137260	−	0.237742i
$302$	4.33934	−	7.51595i	0.249701	−	0.432494i
$303$		0			0
$304$	−4.08581	−	1.51860i	−0.234337	−	0.0870975i
$305$	5.96257			0.341416
$306$		0			0
$307$	8.88381	−	15.3872i	0.507026	−	0.878195i	−0.492941	−	0.870063i	$-0.664078\pi$
$307$	8.88381	−	15.3872i	0.507026	−	0.878195i	0.999967	−	0.00813199i	$-0.00258852\pi$
$308$	−1.93681	−	3.35466i	−0.110360	−	0.191149i
$309$		0			0
$310$	1.60452	+	2.77912i	0.0911309	+	0.157843i
$311$	−11.4040			−0.646661			−0.323331	−	0.946286i	$-0.604803\pi$
$311$	−11.4040			−0.646661			−0.323331	+	0.946286i	$0.604803\pi$
$312$		0			0
$313$	5.13420	+	8.89269i	0.290202	+	0.502645i	0.973857	−	0.227160i	$-0.0729441\pi$
$313$	5.13420	+	8.89269i	0.290202	+	0.502645i	−0.683655	+	0.729805i	$0.739611\pi$
$314$	2.25353	+	3.90322i	0.127174	+	0.220271i
$315$		0			0
$316$	1.20905			0.0680144
$317$	−12.4064	−	21.4886i	−0.696815	−	1.20692i	−0.969565	−	0.244834i	$-0.921267\pi$
$317$	−12.4064	−	21.4886i	−0.696815	−	1.20692i	0.272750	−	0.962085i	$-0.412067\pi$
$318$		0			0
$319$	8.46571	+	14.6630i	0.473989	+	0.820973i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	3.87362			0.215869
$323$	29.3019	+	10.8908i	1.63040	+	0.605981i
$324$		0			0
$325$	1.60452	−	2.77912i	0.0890030	−	0.154158i
$326$	11.8136	−	20.4617i	0.654293	−	1.13327i
$327$		0			0
$328$	−5.23481	+	9.06696i	−0.289044	+	0.500639i
$329$	−8.70200	−	15.0723i	−0.479757	−	0.830963i
$330$		0			0
$331$	−9.75353			−0.536102			−0.268051	−	0.963405i	$-0.586380\pi$
$331$	−9.75353			−0.536102			−0.268051	+	0.963405i	$0.586380\pi$
$332$	7.41810	+	12.8485i	0.407121	+	0.705154i
$333$		0			0
$334$	9.79095			0.535737
$335$	−0.0374251			−0.00204475
$336$		0			0
$337$	−11.3206	+	19.6079i	−0.616674	+	1.06811i	0.373415	+	0.927665i	$0.378187\pi$
$337$	−11.3206	+	19.6079i	−0.616674	+	1.06811i	−0.990088	+	0.140446i	$0.955146\pi$
$338$	−1.35100	−	2.34000i	−0.0734847	−	0.127279i
$339$		0			0
$340$	−3.58581	+	6.21081i	−0.194468	+	0.336828i
$341$	−7.08895			−0.383888
$342$		0			0
$343$	−19.1575			−1.03441
$344$	−1.35805	+	2.35221i	−0.0732211	+	0.126823i
$345$		0			0
$346$	−5.72776	−	9.92078i	−0.307926	−	0.533344i
$347$	−12.6271	+	21.8709i	−0.677861	+	1.17409i	0.297763	+	0.954640i	$0.403760\pi$
$347$	−12.6271	+	21.8709i	−0.677861	+	1.17409i	−0.975624	+	0.219450i	$0.929574\pi$
$348$		0			0
$349$	29.2169			1.56394			0.781972	−	0.623314i	$-0.214214\pi$
$349$	29.2169			1.56394			0.781972	+	0.623314i	$0.214214\pi$
$350$	−1.75353			−0.0937299
$351$		0			0
$352$	1.10452	+	1.91309i	0.0588714	+	0.101968i
$353$	32.9189			1.75209			0.876047	−	0.482225i	$-0.160171\pi$
$353$	32.9189			1.75209			0.876047	+	0.482225i	$0.160171\pi$
$354$		0			0
$355$	−3.58581	−	6.21081i	−0.190315	−	0.329636i
$356$	−5.48129	+	9.49387i	−0.290508	+	0.503174i
$357$		0			0
$358$	−3.31357	+	5.73928i	−0.175128	+	0.303330i
$359$	−1.62324	+	2.81153i	−0.0856712	+	0.148387i	−0.905677	−	0.423968i	$-0.860637\pi$
$359$	−1.62324	+	2.81153i	−0.0856712	+	0.148387i	0.820006	+	0.572355i	$0.193970\pi$
$360$		0			0
$361$	−17.9407	+	6.25543i	−0.944249	+	0.329233i
$362$	−10.2606			−0.539284
$363$		0			0
$364$	2.81357	−	4.87325i	0.147471	−	0.255428i
$365$	−5.98129	−	10.3599i	−0.313075	−	0.542262i
$366$		0			0
$367$	6.02262	+	10.4315i	0.314378	+	0.544519i	0.979305	−	0.202389i	$-0.0648706\pi$
$367$	6.02262	+	10.4315i	0.314378	+	0.544519i	−0.664927	+	0.746909i	$0.731537\pi$
$368$	−2.20905			−0.115155
$369$		0			0
$370$	0.500000	+	0.866025i	0.0259938	+	0.0450225i
$371$	9.61158	+	16.6477i	0.499008	+	0.864307i
$372$		0			0
$373$	−3.86580			−0.200164			−0.100082	−	0.994979i	$-0.531910\pi$
$373$	−3.86580			−0.200164			−0.100082	+	0.994979i	$0.531910\pi$
$374$	−7.92124	−	13.7200i	−0.409597	−	0.709444i
$375$		0			0
$376$	4.96257	+	8.59543i	0.255925	+	0.443276i
$377$	−12.2980	+	21.3008i	−0.633379	+	1.09705i
$378$		0			0
$379$	−23.0593			−1.18448			−0.592240	−	0.805762i	$-0.701756\pi$
$379$	−23.0593			−1.18448			−0.592240	+	0.805762i	$0.701756\pi$
$380$	−0.727762	−	4.29772i	−0.0373334	−	0.220468i
$381$		0			0
$382$	−12.6271	+	21.8709i	−0.646061	+	1.11901i
$383$	1.03743	−	1.79687i	0.0530099	−	0.0918159i	−0.838303	−	0.545205i	$-0.816452\pi$
$383$	1.03743	−	1.79687i	0.0530099	−	0.0918159i	0.891313	+	0.453389i	$0.149785\pi$
$384$		0			0
$385$	1.93681	−	3.35466i	0.0987091	−	0.170969i
$386$	1.43681	+	2.48863i	0.0731318	+	0.126668i
$387$		0			0
$388$	11.2465			0.570953
$389$	−9.83229	−	17.0300i	−0.498517	−	0.863456i	0.501482	−	0.865168i	$-0.332788\pi$
$389$	−9.83229	−	17.0300i	−0.498517	−	0.863456i	−0.999999	+	0.00171186i	$0.999455\pi$
$390$		0			0
$391$	15.8425			0.801188
$392$	3.92515			0.198250
$393$		0			0
$394$	7.44386	−	12.8931i	0.375016	−	0.649547i
$395$	0.604525	+	1.04707i	0.0304169	+	0.0526837i
$396$		0			0
$397$	4.42515	−	7.66458i	0.222092	−	0.384674i	−0.733351	−	0.679850i	$-0.762045\pi$
$397$	4.42515	−	7.66458i	0.222092	−	0.384674i	0.955443	+	0.295176i	$0.0953782\pi$
$398$	1.54448			0.0774176
$399$		0			0
$400$	1.00000			0.0500000
$401$	−0.925150	+	1.60241i	−0.0461998	+	0.0800204i	−0.888201	−	0.459456i	$-0.848044\pi$
$401$	−0.925150	+	1.60241i	−0.0461998	+	0.0800204i	0.842001	+	0.539476i	$0.181378\pi$
$402$		0			0
$403$	−5.14900	−	8.91833i	−0.256490	−	0.444254i
$404$	0.246475	−	0.426907i	0.0122626	−	0.0212394i
$405$		0			0
$406$	13.4400			0.667017
$407$	−2.20905			−0.109499
$408$		0			0
$409$	−9.02967	−	15.6399i	−0.446489	−	0.773341i	0.551666	−	0.834065i	$-0.313992\pi$
$409$	−9.02967	−	15.6399i	−0.446489	−	0.773341i	−0.998155	+	0.0607241i	$0.980659\pi$
$410$	−10.4696			−0.517058
$411$		0			0
$412$	−5.83934	−	10.1140i	−0.287684	−	0.498282i
$413$	5.26058	−	9.11158i	0.258856	−	0.448352i
$414$		0			0
$415$	−7.41810	+	12.8485i	−0.364140	+	0.630709i
$416$	−1.60452	+	2.77912i	−0.0786683	+	0.136258i
$417$		0			0
$418$	9.02576	+	3.35466i	0.441464	+	0.164082i
$419$	1.44770			0.0707248			0.0353624	−	0.999375i	$-0.488741\pi$
$419$	1.44770			0.0707248			0.0353624	+	0.999375i	$0.488741\pi$
$420$		0			0
$421$	8.58581	−	14.8711i	0.418447	−	0.724771i	−0.577337	−	0.816506i	$-0.695908\pi$
$421$	8.58581	−	14.8711i	0.418447	−	0.724771i	0.995783	+	0.0917350i	$0.0292413\pi$
$422$	6.38381	+	11.0571i	0.310759	+	0.538251i
$423$		0			0
$424$	−5.48129	−	9.49387i	−0.266195	−	0.461063i
$425$	−7.17162			−0.347875
$426$		0			0
$427$	5.22776	+	9.05475i	0.252989	+	0.438190i
$428$	4.13029	+	7.15387i	0.199645	+	0.345795i
$429$		0			0
$430$	−2.71610			−0.130982
$431$	−9.53429	−	16.5139i	−0.459250	−	0.795445i	0.539671	−	0.841876i	$-0.318549\pi$
$431$	−9.53429	−	16.5139i	−0.459250	−	0.795445i	−0.998922	+	0.0464309i	$0.985215\pi$
$432$		0			0
$433$	7.94386	+	13.7592i	0.381758	+	0.661224i	0.991314	−	0.131519i	$-0.0419856\pi$
$433$	7.94386	+	13.7592i	0.381758	+	0.661224i	−0.609556	+	0.792743i	$0.708652\pi$
$434$	−2.81357	+	4.87325i	−0.135056	+	0.233924i
$435$		0			0
$436$	−5.17162			−0.247676
$437$	−7.41810	+	6.13921i	−0.354856	+	0.293678i
$438$		0			0
$439$	−1.68329	+	2.91554i	−0.0803389	+	0.139151i	−0.903396	−	0.428808i	$-0.858934\pi$
$439$	−1.68329	+	2.91554i	−0.0803389	+	0.139151i	0.823057	+	0.567959i	$0.192267\pi$
$440$	−1.10452	+	1.91309i	−0.0526562	+	0.0912031i
$441$		0			0
$442$	11.5071	−	19.9308i	0.547335	−	0.948011i
$443$	−11.7949	−	20.4293i	−0.560391	−	0.970625i	−0.997462	−	0.0711985i	$-0.977318\pi$
$443$	−11.7949	−	20.4293i	−0.560391	−	0.970625i	0.437071	−	0.899427i	$-0.356016\pi$
$444$		0			0
$445$	−10.9626			−0.519676
$446$	3.57876	+	6.19860i	0.169459	+	0.293512i
$447$		0			0
$448$	1.75353			0.0828463
$449$	10.9626			0.517356			0.258678	−	0.965964i	$-0.416713\pi$
$449$	10.9626			0.517356			0.258678	+	0.965964i	$0.416713\pi$
$450$		0			0
$451$	11.5640	−	20.0294i	0.544526	−	0.943146i
$452$	−1.13029	−	1.95772i	−0.0531643	−	0.0920832i
$453$		0			0
$454$	7.13029	−	12.3500i	0.334641	−	0.579615i
$455$	5.62715			0.263805
$456$		0			0
$457$	26.6491			1.24659			0.623296	−	0.781986i	$-0.285793\pi$
$457$	26.6491			1.24659			0.623296	+	0.781986i	$0.285793\pi$
$458$	−10.6045	+	18.3676i	−0.495517	+	0.858260i
$459$		0			0
$460$	−1.10452	−	1.91309i	−0.0514987	−	0.0891984i
$461$	2.20905	−	3.82619i	0.102886	−	0.178203i	−0.809987	−	0.586448i	$-0.800526\pi$
$461$	2.20905	−	3.82619i	0.102886	−	0.178203i	0.912872	+	0.408245i	$0.133859\pi$
$462$		0			0
$463$	−7.67867			−0.356858			−0.178429	−	0.983953i	$-0.557102\pi$
$463$	−7.67867			−0.356858			−0.178429	+	0.983953i	$0.557102\pi$
$464$	−7.66457			−0.355819
$465$		0			0
$466$	2.70200	+	4.68000i	0.125168	+	0.216797i
$467$	−24.0827			−1.11441			−0.557207	−	0.830374i	$-0.688127\pi$
$467$	−24.0827			−1.11441			−0.557207	+	0.830374i	$0.688127\pi$
$468$		0			0
$469$	−0.0328130	−	0.0568337i	−0.00151516	−	0.00262434i
$470$	−4.96257	+	8.59543i	−0.228907	+	0.396478i
$471$		0			0
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	3.35805	−	2.77912i	0.154078	−	0.127515i
$476$	−12.5756			−0.576403
$477$		0			0
$478$	−10.7161	+	18.5608i	−0.490143	+	0.848953i
$479$	0.451613	+	0.782216i	0.0206347	+	0.0357404i	0.876158	−	0.482023i	$-0.160098\pi$
$479$	0.451613	+	0.782216i	0.0206347	+	0.0357404i	−0.855524	+	0.517764i	$0.826765\pi$
$480$		0			0
$481$	−1.60452	−	2.77912i	−0.0731600	−	0.126717i
$482$	6.37285			0.290275
$483$		0			0
$484$	3.06005	+	5.30016i	0.139093	+	0.240916i
$485$	5.62324	+	9.73973i	0.255338	+	0.442258i
$486$		0			0
$487$	12.5727			0.569722			0.284861	−	0.958569i	$-0.408052\pi$
$487$	12.5727			0.569722			0.284861	+	0.958569i	$0.408052\pi$
$488$	−2.98129	−	5.16374i	−0.134957	−	0.233752i
$489$		0			0
$490$	1.96257	+	3.39928i	0.0886601	+	0.153564i
$491$	−14.5226	+	25.1539i	−0.655397	+	1.13518i	0.326397	+	0.945233i	$0.394165\pi$
$491$	−14.5226	+	25.1539i	−0.655397	+	1.13518i	−0.981794	+	0.189948i	$0.939168\pi$
$492$		0			0
$493$	54.9675			2.47561
$494$	2.33543	+	13.7916i	0.105076	+	0.620513i
$495$		0			0
$496$	1.60452	−	2.77912i	0.0720453	−	0.124786i
$497$	6.28781	−	10.8908i	0.282047	−	0.488520i
$498$		0			0
$499$	−9.63029	+	16.6801i	−0.431111	+	0.746706i	−0.996969	−	0.0777965i	$-0.975212\pi$
$499$	−9.63029	+	16.6801i	−0.431111	+	0.746706i	0.565858	+	0.824502i	$0.308545\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	18.2684			0.815359
$503$	8.52262	+	14.7616i	0.380005	+	0.658188i	0.991063	−	0.133398i	$-0.0425889\pi$
$503$	8.52262	+	14.7616i	0.380005	+	0.658188i	−0.611057	+	0.791586i	$0.709256\pi$
$504$		0			0
$505$	0.492950			0.0219360
$506$	4.87990			0.216938
$507$		0			0
$508$	6.44386	−	11.1611i	0.285900	−	0.495194i
$509$	−9.38067	−	16.2478i	−0.415791	−	0.720171i	0.579720	−	0.814816i	$-0.303162\pi$
$509$	−9.38067	−	16.2478i	−0.415791	−	0.720171i	−0.995511	+	0.0946444i	$0.969829\pi$
$510$		0			0
$511$	10.4883	−	18.1663i	0.463977	−	0.803631i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.00000			0.264649
$515$	5.83934	−	10.1140i	0.257312	−	0.445677i
$516$		0			0
$517$	−10.9626	−	18.9877i	−0.482133	−	0.835080i
$518$	−0.876763	+	1.51860i	−0.0385227	+	0.0667233i
$519$		0			0
$520$	−3.20905			−0.140726
$521$	−1.08895			−0.0477078			−0.0238539	−	0.999715i	$-0.507594\pi$
$521$	−1.08895			−0.0477078			−0.0238539	+	0.999715i	$0.507594\pi$
$522$		0			0
$523$	15.6600	+	27.1239i	0.684762	+	1.18604i	0.973511	+	0.228638i	$0.0734273\pi$
$523$	15.6600	+	27.1239i	0.684762	+	1.18604i	−0.288749	+	0.957405i	$0.593239\pi$
$524$	13.2232			0.577656
$525$		0			0
$526$	15.3136	+	26.5239i	0.667704	+	1.15650i
$527$	−11.5071	+	19.9308i	−0.501255	+	0.868199i
$528$		0			0
$529$	9.06005	−	15.6925i	0.393915	−	0.682281i
$530$	5.48129	−	9.49387i	0.238092	−	0.412387i
$531$		0			0
$532$	5.88842	−	4.87325i	0.255296	−	0.211282i
$533$	33.5975			1.45527
$534$		0			0
$535$	−4.13029	+	7.15387i	−0.178568	+	0.309289i
$536$	0.0187126	+	0.0324111i	0.000808260	+	0.00139995i
$537$		0			0
$538$	8.79486	+	15.2331i	0.379173	+	0.656748i
$539$	−8.67085			−0.373480
$540$		0			0
$541$	11.7246	+	20.3076i	0.504081	+	0.873094i	0.999989	+	0.00471871i	$0.00150202\pi$
$541$	11.7246	+	20.3076i	0.504081	+	0.873094i	−0.495908	+	0.868375i	$0.665165\pi$
$542$	9.45552	+	16.3774i	0.406150	+	0.703472i
$543$		0			0
$544$	7.17162			0.307481
$545$	−2.58581	−	4.47876i	−0.110764	−	0.191849i
$546$		0			0
$547$	4.60452	+	7.97527i	0.196875	+	0.340998i	0.947514	−	0.319715i	$-0.103587\pi$
$547$	4.60452	+	7.97527i	0.196875	+	0.340998i	−0.750638	+	0.660713i	$0.770254\pi$
$548$	−10.7161	+	18.5608i	−0.457769	+	0.792879i
$549$		0			0
$550$	−2.20905			−0.0941942
$551$	−25.7380	+	21.3008i	−1.09648	+	0.907443i
$552$		0			0
$553$	−1.06005	+	1.83606i	−0.0450779	+	0.0780772i
$554$	12.4555	−	21.5736i	0.529185	−	0.916575i
$555$		0			0
$556$	−3.60452	+	6.24322i	−0.152866	+	0.264772i
$557$	−1.55614	−	2.69531i	−0.0659357	−	0.114204i	0.831173	−	0.556014i	$-0.187670\pi$
$557$	−1.55614	−	2.69531i	−0.0659357	−	0.114204i	−0.897109	+	0.441810i	$0.854337\pi$
$558$		0			0
$559$	8.71610			0.368652
$560$	0.876763	+	1.51860i	0.0370500	+	0.0641724i
$561$		0			0
$562$	26.8877			1.13419
$563$	30.2684			1.27566			0.637830	−	0.770177i	$-0.279832\pi$
$563$	30.2684			1.27566			0.637830	+	0.770177i	$0.279832\pi$
$564$		0			0
$565$	1.13029	−	1.95772i	0.0475516	−	0.0823617i
$566$	12.8877	+	22.3222i	0.541711	+	0.938272i
$567$		0			0
$568$	−3.58581	+	6.21081i	−0.150457	+	0.260600i
$569$	4.36657			0.183056			0.0915282	−	0.995802i	$-0.470825\pi$
$569$	4.36657			0.183056			0.0915282	+	0.995802i	$0.470825\pi$
$570$		0			0
$571$	−43.4026			−1.81634			−0.908171	−	0.418599i	$-0.862521\pi$
$571$	−43.4026			−1.81634			−0.908171	+	0.418599i	$0.862521\pi$
$572$	3.54448	−	6.13921i	0.148202	−	0.256693i
$573$		0			0
$574$	−9.17938	−	15.8991i	−0.383140	−	0.663617i
$575$	1.10452	−	1.91309i	0.0460619	−	0.0797815i
$576$		0			0
$577$	−20.3354			−0.846575			−0.423287	−	0.905995i	$-0.639124\pi$
$577$	−20.3354			−0.846575			−0.423287	+	0.905995i	$0.639124\pi$
$578$	−34.4322			−1.43219
$579$		0			0
$580$	−3.83229	−	6.63772i	−0.159127	−	0.275616i
$581$	−26.0156			−1.07931
$582$		0			0
$583$	12.1084	+	20.9724i	0.501480	+	0.868589i
$584$	−5.98129	+	10.3599i	−0.247507	+	0.428695i
$585$		0			0
$586$	−0.765187	+	1.32534i	−0.0316096	+	0.0547494i
$587$	−6.38067	+	11.0517i	−0.263359	+	0.456151i	−0.967132	−	0.254274i	$-0.918164\pi$
$587$	−6.38067	+	11.0517i	−0.263359	+	0.456151i	0.703774	+	0.710424i	$0.251497\pi$
$588$		0			0
$589$	−2.33543	−	13.7916i	−0.0962295	−	0.568272i
$590$	−6.00000			−0.247016
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−18.4735	−	31.9971i	−0.758617	−	1.31396i	−0.943556	−	0.331214i	$-0.892542\pi$
$593$	−18.4735	−	31.9971i	−0.758617	−	1.31396i	0.184939	−	0.982750i	$-0.440791\pi$
$594$		0			0
$595$	−6.28781	−	10.8908i	−0.257775	−	0.446480i
$596$	8.75353			0.358558
$597$		0			0
$598$	3.54448	+	6.13921i	0.144944	+	0.251051i
$599$	−10.8090	−	18.7217i	−0.441642	−	0.764947i	0.556169	−	0.831069i	$-0.312271\pi$
$599$	−10.8090	−	18.7217i	−0.441642	−	0.764947i	−0.997812	+	0.0661222i	$0.978937\pi$
$600$		0			0
$601$	−36.0141			−1.46905			−0.734523	−	0.678584i	$-0.762594\pi$
$601$	−36.0141			−1.46905			−0.734523	+	0.678584i	$0.762594\pi$
$602$	−2.38137	−	4.12466i	−0.0970576	−	0.168109i
$603$		0			0
$604$	−4.33934	−	7.51595i	−0.176565	−	0.305820i
$605$	−3.06005	+	5.30016i	−0.124409	+	0.215482i
$606$		0			0
$607$	1.65047			0.0669907			0.0334953	−	0.999439i	$-0.489336\pi$
$607$	1.65047			0.0669907			0.0334953	+	0.999439i	$0.489336\pi$
$608$	−3.35805	+	2.77912i	−0.136187	+	0.112708i
$609$		0			0
$610$	2.98129	−	5.16374i	0.120709	−	0.209074i
$611$	15.9251	−	27.5832i	0.644263	−	1.11590i
$612$		0			0
$613$	−12.7691	+	22.1167i	−0.515739	+	0.893286i	0.484094	+	0.875016i	$0.339149\pi$
$613$	−12.7691	+	22.1167i	−0.515739	+	0.893286i	−0.999833	+	0.0182703i	$0.994184\pi$
$614$	−8.88381	−	15.3872i	−0.358522	−	0.620977i
$615$		0			0
$616$	−3.87362			−0.156073
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	0.719605	−	0.694383i	$-0.244323\pi$
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	−0.961156	+	0.276005i	$0.910989\pi$
$618$		0			0
$619$	14.7394			0.592427			0.296214	−	0.955122i	$-0.404276\pi$
$619$	14.7394			0.592427			0.296214	+	0.955122i	$0.404276\pi$
$620$	3.20905			0.128879
$621$		0			0
$622$	−5.70200	+	9.87615i	−0.228629	+	0.395998i
$623$	−9.61158	−	16.6477i	−0.385080	−	0.666977i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.2684			0.410408
$627$		0			0
$628$	4.50705			0.179851
$629$	−3.58581	+	6.21081i	−0.142976	+	0.247641i
$630$		0			0
$631$	10.6459	+	18.4392i	0.423805	+	0.734052i	0.996308	−	0.0858508i	$-0.0273608\pi$
$631$	10.6459	+	18.4392i	0.423805	+	0.734052i	−0.572503	+	0.819903i	$0.694027\pi$
$632$	0.604525	−	1.04707i	0.0240467	−	0.0416501i
$633$		0			0
$634$	−24.8129			−0.985445
$635$	12.8877			0.511434
$636$		0			0
$637$	−6.29800	−	10.9085i	−0.249536	−	0.432209i
$638$	16.9314			0.670322
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−19.3058	+	33.4387i	−0.762534	+	1.32075i	0.179006	+	0.983848i	$0.442712\pi$
$641$	−19.3058	+	33.4387i	−0.762534	+	1.32075i	−0.941540	+	0.336900i	$0.890622\pi$
$642$		0			0
$643$	6.27929	−	10.8760i	0.247631	−	0.428909i	−0.715237	−	0.698882i	$-0.753681\pi$
$643$	6.27929	−	10.8760i	0.247631	−	0.428909i	0.962868	+	0.269973i	$0.0870146\pi$
$644$	1.93681	−	3.35466i	0.0763211	−	0.132192i
$645$		0			0
$646$	24.0827	−	19.9308i	0.947520	−	0.784167i
$647$	24.2373			0.952865			0.476432	−	0.879211i	$-0.341930\pi$
$647$	24.2373			0.952865			0.476432	+	0.879211i	$0.341930\pi$
$648$		0			0
$649$	6.62715	−	11.4786i	0.260138	−	0.450573i
$650$	−1.60452	−	2.77912i	−0.0629346	−	0.109006i
$651$		0			0
$652$	−11.8136	−	20.4617i	−0.462655	−	0.801342i
$653$	5.35247			0.209458			0.104729	−	0.994501i	$-0.466602\pi$
$653$	5.35247			0.209458			0.104729	+	0.994501i	$0.466602\pi$
$654$		0			0
$655$	6.61158	+	11.4516i	0.258336	+	0.447450i
$656$	5.23481	+	9.06696i	0.204385	+	0.354005i
$657$		0			0
$658$	−17.4040			−0.678479
$659$	1.59747	+	2.76691i	0.0622288	+	0.107783i	0.895461	−	0.445139i	$-0.146846\pi$
$659$	1.59747	+	2.76691i	0.0622288	+	0.107783i	−0.833233	+	0.552923i	$0.813512\pi$
$660$		0			0
$661$	−18.6412	−	32.2876i	−0.725061	−	1.25584i	−0.958949	−	0.283578i	$-0.908478\pi$
$661$	−18.6412	−	32.2876i	−0.725061	−	1.25584i	0.233888	−	0.972263i	$-0.424855\pi$
$662$	−4.87676	+	8.44680i	−0.189541	+	0.328294i
$663$		0			0
$664$	14.8362			0.575756
$665$	7.16457	+	2.66290i	0.277830	+	0.103263i
$666$		0			0
$667$	−8.46571	+	14.6630i	−0.327794	+	0.567755i
$668$	4.89548	−	8.47921i	0.189412	−	0.328071i
$669$		0			0
$670$	−0.0187126	+	0.0324111i	−0.000722930	+	0.00125215i
$671$	6.58581	+	11.4070i	0.254242	+	0.440361i
$672$		0			0
$673$	0.940651			0.0362594			0.0181297	−	0.999836i	$-0.494229\pi$
$673$	0.940651			0.0362594			0.0181297	+	0.999836i	$0.494229\pi$
$674$	11.3206	+	19.6079i	0.436054	+	0.755268i
$675$		0			0
$676$	−2.70200			−0.103923
$677$	−30.8129			−1.18423			−0.592117	−	0.805852i	$-0.701708\pi$
$677$	−30.8129			−1.18423			−0.592117	+	0.805852i	$0.701708\pi$
$678$		0			0
$679$	−9.86049	+	17.0789i	−0.378411	+	0.655427i
$680$	3.58581	+	6.21081i	0.137510	+	0.238174i
$681$		0			0
$682$	−3.54448	+	6.13921i	−0.135725	+	0.235083i
$683$	8.26058			0.316082			0.158041	−	0.987433i	$-0.449482\pi$
$683$	8.26058			0.316082			0.158041	+	0.987433i	$0.449482\pi$
$684$		0			0
$685$	−21.4322			−0.818882
$686$	−9.57876	+	16.5909i	−0.365719	+	0.633444i
$687$		0			0
$688$	1.35805	+	2.35221i	0.0517752	+	0.0896772i
$689$	−17.5897	+	30.4663i	−0.670115	+	1.16067i
$690$		0			0
$691$	5.97668			0.227363			0.113682	−	0.993517i	$-0.463736\pi$
$691$	5.97668			0.227363			0.113682	+	0.993517i	$0.463736\pi$
$692$	−11.4555			−0.435474
$693$		0			0
$694$	12.6271	+	21.8709i	0.479320	+	0.830207i
$695$	−7.20905			−0.273455
$696$		0			0
$697$	−37.5421	−	65.0248i	−1.42201	−	2.46299i
$698$	14.6084	−	25.3026i	0.552937	−	0.957716i
$699$		0			0
$700$	−0.876763	+	1.51860i	−0.0331385	+	0.0573976i
$701$	22.0593	−	38.2079i	0.833170	−	1.44309i	−0.0623415	−	0.998055i	$-0.519857\pi$
$701$	22.0593	−	38.2079i	0.833170	−	1.44309i	0.895512	−	0.445038i	$-0.146810\pi$
$702$		0			0
$703$	−0.727762	−	4.29772i	−0.0274481	−	0.162091i
$704$	2.20905			0.0832567
$705$		0			0
$706$	16.4594	−	28.5086i	0.619459	−	1.07293i
$707$	0.432200	+	0.748592i	0.0162546	+	0.0281537i
$708$		0			0
$709$	−14.4135	−	24.9649i	−0.541310	−	0.937576i	−0.998829	−	0.0483765i	$-0.984595\pi$
$709$	−14.4135	−	24.9649i	−0.541310	−	0.937576i	0.457519	−	0.889200i	$-0.348738\pi$
$710$	−7.17162			−0.269146
$711$		0			0
$712$	5.48129	+	9.49387i	0.205420	+	0.355798i
$713$	−3.54448	−	6.13921i	−0.132742	−	0.229915i
$714$		0			0
$715$	7.08895			0.265112
$716$	3.31357	+	5.73928i	0.123834	+	0.214487i
$717$		0			0
$718$	1.62324	+	2.81153i	0.0605787	+	0.104925i
$719$	22.7988	−	39.4886i	0.850251	−	1.47268i	−0.0307311	−	0.999528i	$-0.509784\pi$
$719$	22.7988	−	39.4886i	0.850251	−	1.47268i	0.880982	−	0.473150i	$-0.156883\pi$
$720$		0			0
$721$	20.4788			0.762672
$722$	−3.55300	+	18.6648i	−0.132229	+	0.694633i
$723$		0			0
$724$	−5.13029	+	8.88592i	−0.190666	+	0.330243i
$725$	3.83229	−	6.63772i	0.142328	−	0.246519i
$726$		0			0
$727$	−2.56710	+	4.44635i	−0.0952085	+	0.164906i	−0.909696	−	0.415276i	$-0.863685\pi$
$727$	−2.56710	+	4.44635i	−0.0952085	+	0.164906i	0.814487	+	0.580182i	$0.197018\pi$
$728$	−2.81357	−	4.87325i	−0.104278	−	0.180615i
$729$		0			0
$730$	−11.9626			−0.442755
$731$	−9.73942	−	16.8692i	−0.360226	−	0.623929i
$732$		0			0
$733$	17.7910			0.657124			0.328562	−	0.944482i	$-0.393436\pi$
$733$	17.7910			0.657124			0.328562	+	0.944482i	$0.393436\pi$
$734$	12.0452			0.444598
$735$		0			0
$736$	−1.10452	+	1.91309i	−0.0407133	+	0.0705176i
$737$	−0.0413370	−	0.0715978i	−0.00152267	−	0.00263734i
$738$		0			0
$739$	5.36971	−	9.30061i	0.197528	−	0.342129i	−0.750198	−	0.661213i	$-0.770042\pi$
$739$	5.36971	−	9.30061i	0.197528	−	0.342129i	0.947726	+	0.319084i	$0.103375\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	19.2232			0.705704
$743$	16.5367	−	28.6424i	0.606674	−	1.05079i	−0.385111	−	0.922870i	$-0.625837\pi$
$743$	16.5367	−	28.6424i	0.606674	−	1.05079i	0.991785	−	0.127919i	$-0.0408298\pi$
$744$		0			0
$745$	4.37676	+	7.58078i	0.160352	+	0.277738i
$746$	−1.93290	+	3.34788i	−0.0707685	+	0.122575i
$747$		0			0
$748$	−15.8425			−0.579258
$749$	−14.4851			−0.529275
$750$		0			0
$751$	−12.0600	−	20.8886i	−0.440077	−	0.762237i	0.557617	−	0.830098i	$-0.311716\pi$
$751$	−12.0600	−	20.8886i	−0.440077	−	0.762237i	−0.997695	+	0.0678616i	$0.978382\pi$
$752$	9.92515			0.361933
$753$		0			0
$754$	12.2980	+	21.3008i	0.447867	+	0.775728i
$755$	4.33934	−	7.51595i	0.157925	−	0.273534i
$756$		0			0
$757$	15.5827	−	26.9900i	0.566362	−	0.980968i	−0.430560	−	0.902562i	$-0.641684\pi$
$757$	15.5827	−	26.9900i	0.566362	−	0.980968i	0.996922	−	0.0784055i	$-0.0249829\pi$
$758$	−11.5297	+	19.9700i	−0.418777	+	0.725342i
$759$		0			0
$760$	−4.08581	−	1.51860i	−0.148208	−	0.0550853i
$761$	−11.5586			−0.418998			−0.209499	−	0.977809i	$-0.567183\pi$
$761$	−11.5586			−0.418998			−0.209499	+	0.977809i	$0.567183\pi$
$762$		0			0
$763$	4.53429	−	7.85362i	0.164152	−	0.284320i
$764$	12.6271	+	21.8709i	0.456834	+	0.791260i
$765$		0			0
$766$	−1.03743	−	1.79687i	−0.0374837	−	0.0649237i
$767$	19.2543			0.695232
$768$		0			0
$769$	7.22385	+	12.5121i	0.260499	+	0.451197i	0.966375	−	0.257139i	$-0.0827797\pi$
$769$	7.22385	+	12.5121i	0.260499	+	0.451197i	−0.705876	+	0.708336i	$0.749446\pi$
$770$	−1.93681	−	3.35466i	−0.0697979	−	0.120893i
$771$		0			0
$772$	2.87362			0.103424
$773$	−18.9509	−	32.8239i	−0.681617	−	1.18060i	−0.974487	−	0.224443i	$-0.927944\pi$
$773$	−18.9509	−	32.8239i	−0.681617	−	1.18060i	0.292870	−	0.956152i	$-0.405390\pi$
$774$		0			0
$775$	1.60452	+	2.77912i	0.0576362	+	0.0998289i
$776$	5.62324	−	9.73973i	0.201862	−	0.349636i
$777$		0			0
$778$	−19.6646			−0.705009
$779$	42.7769	+	15.8991i	1.53264	+	0.569646i
$780$		0			0
$781$	7.92124	−	13.7200i	0.283444	−	0.490940i
$782$	7.92124	−	13.7200i	0.283263	−	0.490626i
$783$		0			0
$784$	1.96257	−	3.39928i	0.0700920	−	0.121403i
$785$	2.25353	+	3.90322i	0.0804318	+	0.139312i
$786$		0			0
$787$	−46.6491			−1.66286			−0.831430	−	0.555630i	$-0.812477\pi$
$787$	−46.6491			−1.66286			−0.831430	+	0.555630i	$0.812477\pi$
$788$	−7.44386	−	12.8931i	−0.265177	−	0.459299i
$789$		0			0
$790$	1.20905			0.0430161
$791$	3.96398			0.140943
$792$		0			0
$793$	−9.56710	+	16.5707i	−0.339738	+	0.588443i
$794$	−4.42515	−	7.66458i	−0.157043	−	0.272006i
$795$		0			0
$796$	0.772238	−	1.33755i	0.0273712	−	0.0474084i
$797$	−1.79877			−0.0637158			−0.0318579	−	0.999492i	$-0.510142\pi$
$797$	−1.79877			−0.0637158			−0.0318579	+	0.999492i	$0.510142\pi$
$798$		0			0
$799$	−71.1794			−2.51815
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	0.925150	+	1.60241i	0.0326682	+	0.0565829i
$803$	13.2130	−	22.8855i	0.466275	−	0.807612i
$804$		0			0
$805$	3.87362			0.136527
$806$	−10.2980			−0.362732
$807$		0			0
$808$	−0.246475	−	0.426907i	−0.00867096	−	0.0150185i
$809$	39.9251			1.40369			0.701847	−	0.712328i	$-0.252359\pi$
$809$	39.9251			1.40369			0.701847	+	0.712328i	$0.252359\pi$
$810$		0			0
$811$	6.98834	+	12.1042i	0.245394	+	0.425034i	0.962242	−	0.272195i	$-0.0877494\pi$
$811$	6.98834	+	12.1042i	0.245394	+	0.425034i	−0.716849	+	0.697229i	$0.754416\pi$
$812$	6.72001	−	11.6394i	0.235826	−	0.408463i
$813$		0			0
$814$	−1.10452	+	1.91309i	−0.0387136	+	0.0670539i
$815$	11.8136	−	20.4617i	0.413811	−	0.716742i
$816$		0			0
$817$	11.0975	+	4.12466i	0.388251	+	0.144304i
$818$	−18.0593			−0.631430
$819$		0			0
$820$	−5.23481	+	9.06696i	−0.182808	+	0.316632i
$821$	−10.5819	−	18.3284i	−0.369311	−	0.639665i	0.620147	−	0.784486i	$-0.287073\pi$
$821$	−10.5819	−	18.3284i	−0.369311	−	0.639665i	−0.989458	+	0.144820i	$0.953740\pi$
$822$		0			0
$823$	17.8994	+	31.0026i	0.623933	+	1.08068i	0.988746	+	0.149603i	$0.0477997\pi$
$823$	17.8994	+	31.0026i	0.623933	+	1.08068i	−0.364813	+	0.931081i	$0.618867\pi$
$824$	−11.6787			−0.406846
$825$		0			0
$826$	−5.26058	−	9.11158i	−0.183039	−	0.317033i
$827$	15.2878	+	26.4793i	0.531609	+	0.920774i	0.999319	+	0.0368923i	$0.0117459\pi$
$827$	15.2878	+	26.4793i	0.531609	+	0.920774i	−0.467710	+	0.883882i	$0.654921\pi$
$828$		0			0
$829$	−54.3136			−1.88639			−0.943195	−	0.332238i	$-0.892196\pi$
$829$	−54.3136			−1.88639			−0.943195	+	0.332238i	$0.892196\pi$
$830$	7.41810	+	12.8485i	0.257486	+	0.445979i
$831$		0			0
$832$	1.60452	+	2.77912i	0.0556269	+	0.0963486i
$833$	−14.0749	+	24.3784i	−0.487665	+	0.844660i
$834$		0			0
$835$	9.79095			0.338830
$836$	7.41810	−	6.13921i	0.256560	−	0.212329i
$837$		0			0
$838$	0.723850	−	1.25375i	0.0250050	−	0.0433099i
$839$	19.7988	−	34.2925i	0.683530	−	1.18391i	−0.290367	−	0.956915i	$-0.593777\pi$
$839$	19.7988	−	34.2925i	0.683530	−	1.18391i	0.973896	−	0.226993i	$-0.0728893\pi$
$840$		0			0
$841$	−14.8729	+	25.7605i	−0.512857	+	0.888294i
$842$	−8.58581	−	14.8711i	−0.295887	−	0.512491i
$843$		0			0
$844$	12.7676			0.439480
$845$	−1.35100	−	2.34000i	−0.0464758	−	0.0804985i
$846$		0			0
$847$	−10.7317			−0.368747
$848$	−10.9626			−0.376456
$849$		0			0
$850$	−3.58581	+	6.21081i	−0.122992	+	0.213029i
$851$	−1.10452	−	1.91309i	−0.0378626	−	0.0655800i
$852$		0			0
$853$	11.7761	−	20.3969i	0.403208	−	0.698376i	−0.590903	−	0.806742i	$-0.701229\pi$
$853$	11.7761	−	20.3969i	0.403208	−	0.698376i	0.994111	+	0.108366i	$0.0345619\pi$
$854$	10.4555			0.357781
$855$		0			0
$856$	8.26058			0.282341
$857$	27.9251	−	48.3678i	0.953905	−	1.65221i	0.217051	−	0.976160i	$-0.430356\pi$
$857$	27.9251	−	48.3678i	0.953905	−	1.65221i	0.736854	−	0.676051i	$-0.236310\pi$
$858$		0			0
$859$	−14.2949	−	24.7594i	−0.487734	−	0.844781i	0.512166	−	0.858886i	$-0.328843\pi$
$859$	−14.2949	−	24.7594i	−0.487734	−	0.844781i	−0.999901	+	0.0141057i	$0.995510\pi$
$860$	−1.35805	+	2.35221i	−0.0463091	+	0.0802097i
$861$		0			0
$862$	−19.0686			−0.649478
$863$	−2.31210			−0.0787048			−0.0393524	−	0.999225i	$-0.512529\pi$
$863$	−2.31210			−0.0787048			−0.0393524	+	0.999225i	$0.512529\pi$
$864$		0			0
$865$	−5.72776	−	9.92078i	−0.194750	−	0.337316i
$866$	15.8877			0.539887
$867$		0			0
$868$	2.81357	+	4.87325i	0.0954989	+	0.165409i
$869$	−1.33543	+	2.31302i	−0.0453012	+	0.0784640i
$870$		0			0
$871$	0.0600496	−	0.104009i	0.00203470	−	0.00352421i
$872$	−2.58581	+	4.47876i	−0.0875667	+	0.151670i
$873$		0			0
$874$	1.60766	+	9.49387i	0.0543800	+	0.321135i
$875$	−1.75353			−0.0592800
$876$		0			0
$877$	4.78390	−	8.28596i	0.161541	−	0.279797i	−0.773881	−	0.633331i	$-0.781687\pi$
$877$	4.78390	−	8.28596i	0.161541	−	0.279797i	0.935421	+	0.353535i	$0.115020\pi$
$878$	1.68329	+	2.91554i	0.0568082	+	0.0983947i
$879$		0			0
$880$	1.10452	+	1.91309i	0.0372335	+	0.0644904i
$881$	−23.5586			−0.793709			−0.396854	−	0.917882i	$-0.629898\pi$
$881$	−23.5586			−0.793709			−0.396854	+	0.917882i	$0.629898\pi$
$882$		0			0
$883$	−28.5195	−	49.3972i	−0.959757	−	1.66235i	−0.723086	−	0.690758i	$-0.757277\pi$
$883$	−28.5195	−	49.3972i	−0.959757	−	1.66235i	−0.236671	−	0.971590i	$-0.576056\pi$
$884$	−11.5071	−	19.9308i	−0.387024	−	0.670345i
$885$		0			0
$886$	−23.5897			−0.792512
$887$	18.6271	+	32.2632i	0.625438	+	1.08329i	0.988456	+	0.151509i	$0.0484132\pi$
$887$	18.6271	+	32.2632i	0.625438	+	1.08329i	−0.363017	+	0.931782i	$0.618253\pi$
$888$		0			0
$889$	11.2995	+	19.5713i	0.378972	+	0.656399i
$890$	−5.48129	+	9.49387i	−0.183733	+	0.318235i
$891$		0			0
$892$	7.15752			0.239652
$893$	33.3291	−	27.5832i	1.11532	−	0.923036i
$894$		0			0
$895$	−3.31357	+	5.73928i	−0.110761	+	0.191843i
$896$	0.876763	−	1.51860i	0.0292906	−	0.0507328i
$897$		0			0
$898$	5.48129	−	9.49387i	0.182913	−	0.316814i
$899$	−12.2980	−	21.3008i	−0.410161	−	0.710420i
$900$		0			0
$901$	78.6195			2.61919
$902$	−11.5640	−	20.0294i	−0.385038	−	0.666905i
$903$		0			0
$904$	−2.26058			−0.0751856
$905$	−10.2606			−0.341073
$906$		0			0
$907$	−22.1342	+	38.3376i	−0.734954	+	1.27298i	0.219789	+	0.975547i	$0.429463\pi$
$907$	−22.1342	+	38.3376i	−0.734954	+	1.27298i	−0.954744	+	0.297430i	$0.903870\pi$
$908$	−7.13029	−	12.3500i	−0.236627	−	0.409850i
$909$		0			0
$910$	2.81357	−	4.87325i	0.0932691	−	0.161547i
$911$	−52.1935			−1.72925			−0.864625	−	0.502418i	$-0.832444\pi$
$911$	−52.1935			−1.72925			−0.864625	+	0.502418i	$0.832444\pi$
$912$		0			0
$913$	−32.7739			−1.08466
$914$	13.3245	−	23.0788i	0.440737	−	0.763378i
$915$		0			0
$916$	10.6045	+	18.3676i	0.350383	+	0.606882i
$917$	−11.5936	+	20.0806i	−0.382853	+	0.663121i
$918$		0			0
$919$	−4.38067			−0.144505			−0.0722526	−	0.997386i	$-0.523019\pi$
$919$	−4.38067			−0.144505			−0.0722526	+	0.997386i	$0.523019\pi$
$920$	−2.20905			−0.0728302
$921$		0			0
$922$	−2.20905	−	3.82619i	−0.0727512	−	0.126009i
$923$	23.0141			0.757518
$924$		0			0
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	−3.83934	+	6.64993i	−0.126168	+	0.218530i
$927$		0			0
$928$	−3.83229	+	6.63772i	−0.125801	+	0.217894i
$929$	−4.88529	+	8.46156i	−0.160281	+	0.277615i	−0.934969	−	0.354728i	$-0.884573\pi$
$929$	−4.88529	+	8.46156i	−0.160281	+	0.277615i	0.774688	+	0.632343i	$0.217907\pi$
$930$		0			0
$931$	−2.85658	−	16.8692i	−0.0936205	−	0.552865i
$932$	5.40400			0.177014
$933$		0			0
$934$	−12.0413	+	20.8562i	−0.394005	+	0.682436i
$935$	−7.92124	−	13.7200i	−0.259052	−	0.448692i
$936$		0			0
$937$	22.2871	+	38.6024i	0.728088	+	1.26109i	0.957690	+	0.287801i	$0.0929242\pi$
$937$	22.2871	+	38.6024i	0.728088	+	1.26109i	−0.229602	+	0.973285i	$0.573742\pi$
$938$	−0.0656259			−0.00214276
$939$		0			0
$940$	4.96257	+	8.59543i	0.161861	+	0.280352i
$941$	−1.26449	−	2.19016i	−0.0412211	−	0.0713970i	0.844679	−	0.535274i	$-0.179791\pi$
$941$	−1.26449	−	2.19016i	−0.0412211	−	0.0713970i	−0.885900	+	0.463877i	$0.846458\pi$
$942$		0			0
$943$	23.1279			0.753149
$944$	3.00000	+	5.19615i	0.0976417	+	0.169120i
$945$		0			0
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	−2.66066	+	4.60840i	−0.0864599	+	0.149753i	−0.906012	−	0.423251i	$-0.860889\pi$
$947$	−2.66066	+	4.60840i	−0.0864599	+	0.149753i	0.819552	+	0.573004i	$0.194222\pi$
$948$		0			0
$949$	38.3885			1.24614
$950$	−0.727762	−	4.29772i	−0.0236117	−	0.139436i
$951$		0			0
$952$	−6.28781	+	10.8908i	−0.203789	+	0.352973i
$953$	5.01410	−	8.68468i	0.162423	−	0.281324i	−0.773314	−	0.634023i	$-0.781403\pi$
$953$	5.01410	−	8.68468i	0.162423	−	0.281324i	0.935737	+	0.352699i	$0.114736\pi$
$954$		0			0
$955$	−12.6271	+	21.8709i	−0.408605	+	0.707725i
$956$	10.7161	+	18.5608i	0.346583	+	0.600300i
$957$		0			0
$958$	0.903226			0.0291819
$959$	−18.7910	−	32.5469i	−0.606791	−	1.05099i
$960$		0			0
$961$	−20.7020			−0.667806
$962$	−3.20905			−0.103464
$963$		0			0
$964$	3.18643	−	5.51905i	0.102628	−	0.177757i
$965$	1.43681	+	2.48863i	0.0462526	+	0.0801119i
$966$		0			0
$967$	−16.3955	+	28.3978i	−0.527243	+	0.913212i	0.472253	+	0.881463i	$0.343441\pi$
$967$	−16.3955	+	28.3978i	−0.527243	+	0.913212i	−0.999496	+	0.0317485i	$0.989892\pi$
$968$	6.12010			0.196707
$969$		0			0
$970$	11.2465			0.361103
$971$	14.8877	−	25.7863i	0.477770	−	0.827522i	−0.521905	−	0.853003i	$-0.674779\pi$
$971$	14.8877	−	25.7863i	0.477770	−	0.827522i	0.999675	+	0.0254817i	$0.00811196\pi$
$972$		0			0
$973$	−6.32062	−	10.9476i	−0.202630	−	0.350965i
$974$	6.28634	−	10.8883i	0.201427	−	0.348882i
$975$		0			0
$976$	−5.96257			−0.190857
$977$	−49.7084			−1.59031			−0.795157	−	0.606404i	$-0.792611\pi$
$977$	−49.7084			−1.59031			−0.795157	+	0.606404i	$0.792611\pi$
$978$		0			0
$979$	−12.1084	−	20.9724i	−0.386987	−	0.670282i
$980$	3.92515			0.125384
$981$		0			0
$982$	14.5226	+	25.1539i	0.463436	+	0.802694i
$983$	−13.3510	+	23.1246i	−0.425831	+	0.737561i	−0.996498	−	0.0836212i	$-0.973351\pi$
$983$	−13.3510	+	23.1246i	−0.425831	+	0.737561i	0.570667	+	0.821182i	$0.306685\pi$
$984$		0			0
$985$	7.44386	−	12.8931i	0.237181	−	0.410810i
$986$	27.4837	−	47.6032i	0.875260	−	1.51600i
$987$		0			0
$988$	13.1116	+	4.87325i	0.417135	+	0.155039i
$989$	6.00000			0.190789
$990$		0			0
$991$	21.9580	−	38.0323i	0.697518	−	1.20814i	−0.271807	−	0.962352i	$-0.587621\pi$
$991$	21.9580	−	38.0323i	0.697518	−	1.20814i	0.969325	−	0.245784i	$-0.0790455\pi$
$992$	−1.60452	−	2.77912i	−0.0509437	−	0.0882371i
$993$		0			0
$994$	−6.28781	−	10.8908i	−0.199437	−	0.345436i
$995$	1.54448			0.0489632
$996$		0			0
$997$	−29.2239	−	50.6173i	−0.925531	−	1.60307i	−0.790705	−	0.612197i	$-0.790286\pi$
$997$	−29.2239	−	50.6173i	−0.925531	−	1.60307i	−0.134826	−	0.990869i	$-0.543048\pi$
$998$	9.63029	+	16.6801i	0.304841	+	0.528001i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.q.1531.2		6
3.2	odd	2		570.2.i.j.391.2	yes	6
19.7	even	3	inner	1710.2.l.q.1261.2		6
57.26	odd	6		570.2.i.j.121.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.2	✓	6	57.26	odd	6
570.2.i.j.391.2	yes	6	3.2	odd	2
1710.2.l.q.1261.2		6	19.7	even	3	inner
1710.2.l.q.1531.2		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.75353 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.75353 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +2.20905 q^{11} +(1.60452 + 2.77912i) q^{13} +(0.876763 - 1.51860i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.58581 - 6.21081i) q^{17} +(0.727762 + 4.29772i) q^{19} -1.00000 q^{20} +(1.10452 - 1.91309i) q^{22} +(1.10452 + 1.91309i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.20905 q^{26} +(-0.876763 - 1.51860i) q^{28} +(3.83229 + 6.63772i) q^{29} -3.20905 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.58581 - 6.21081i) q^{34} +(0.876763 - 1.51860i) q^{35} -1.00000 q^{37} +(4.08581 + 1.51860i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(5.23481 - 9.06696i) q^{41} +(1.35805 - 2.35221i) q^{43} +(-1.10452 - 1.91309i) q^{44} +2.20905 q^{46} +(-4.96257 - 8.59543i) q^{47} -3.92515 q^{49} -1.00000 q^{50} +(1.60452 - 2.77912i) q^{52} +(5.48129 + 9.49387i) q^{53} +(1.10452 - 1.91309i) q^{55} -1.75353 q^{56} +7.66457 q^{58} +(3.00000 - 5.19615i) q^{59} +(2.98129 + 5.16374i) q^{61} +(-1.60452 + 2.77912i) q^{62} +1.00000 q^{64} +3.20905 q^{65} +(-0.0187126 - 0.0324111i) q^{67} -7.17162 q^{68} +(-0.876763 - 1.51860i) q^{70} +(3.58581 - 6.21081i) q^{71} +(5.98129 - 10.3599i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(3.35805 - 2.77912i) q^{76} +3.87362 q^{77} +(-0.604525 + 1.04707i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-5.23481 - 9.06696i) q^{82} -14.8362 q^{83} +(-3.58581 - 6.21081i) q^{85} +(-1.35805 - 2.35221i) q^{86} -2.20905 q^{88} +(-5.48129 - 9.49387i) q^{89} +(2.81357 + 4.87325i) q^{91} +(1.10452 - 1.91309i) q^{92} -9.92515 q^{94} +(4.08581 + 1.51860i) q^{95} +(-5.62324 + 9.73973i) q^{97} +(-1.96257 + 3.39928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8} - 3 q^{10} - 8 q^{11} - q^{13} + q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 2 q^{26} - q^{28} + 6 q^{29} + 2 q^{31} + 3 q^{32} + 4 q^{34} + q^{35} - 6 q^{37} - q^{38} - 3 q^{40} + 8 q^{41} - 11 q^{43} + 4 q^{44} - 8 q^{46} + 36 q^{49} - 6 q^{50} - q^{52} + 18 q^{53} - 4 q^{55} - 2 q^{56} + 12 q^{58} + 18 q^{59} + 3 q^{61} + q^{62} + 6 q^{64} - 2 q^{65} - 15 q^{67} + 8 q^{68} - q^{70} - 4 q^{71} + 21 q^{73} - 3 q^{74} + q^{76} - 32 q^{77} + 7 q^{79} + 3 q^{80} - 8 q^{82} - 4 q^{83} + 4 q^{85} + 11 q^{86} + 8 q^{88} - 18 q^{89} - 15 q^{91} - 4 q^{92} - q^{95} - 38 q^{97} + 18 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8 - 3 * q^10 - 8 * q^11 - q^13 + q^14 - 3 * q^16 - 4 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 2 * q^26 - q^28 + 6 * q^29 + 2 * q^31 + 3 * q^32 + 4 * q^34 + q^35 - 6 * q^37 - q^38 - 3 * q^40 + 8 * q^41 - 11 * q^43 + 4 * q^44 - 8 * q^46 + 36 * q^49 - 6 * q^50 - q^52 + 18 * q^53 - 4 * q^55 - 2 * q^56 + 12 * q^58 + 18 * q^59 + 3 * q^61 + q^62 + 6 * q^64 - 2 * q^65 - 15 * q^67 + 8 * q^68 - q^70 - 4 * q^71 + 21 * q^73 - 3 * q^74 + q^76 - 32 * q^77 + 7 * q^79 + 3 * q^80 - 8 * q^82 - 4 * q^83 + 4 * q^85 + 11 * q^86 + 8 * q^88 - 18 * q^89 - 15 * q^91 - 4 * q^92 - q^95 - 38 * q^97 + 18 * q^98

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