LMFDB - Embedded newform 1755.2.i.f.1171.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not 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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.4
Root			$0.252952 - 1.56266i$ of defining polynomial
Character	$\chi$	$=$	1755.1171
Dual form			1755.2.i.f.586.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247048 + 0.427900i) q^{2} +(0.877935 - 1.52063i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.14269 + 3.71125i) q^{7} +1.85576 q^{8} +O(q^{10})$	\(q+(0.247048 + 0.427900i) q^{2} +(0.877935 - 1.52063i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.14269 + 3.71125i) q^{7} +1.85576 q^{8} -0.494096 q^{10} +(2.24265 + 3.88439i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.05870 + 1.83371i) q^{14} +(-1.29741 - 2.24718i) q^{16} -1.57196 q^{17} +1.86934 q^{19} +(0.877935 + 1.52063i) q^{20} +(-1.10808 + 1.91926i) q^{22} +(-2.62890 + 4.55339i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.494096 q^{26} +7.52458 q^{28} +(-0.375154 - 0.649786i) q^{29} +(-5.10067 + 8.83463i) q^{31} +(2.49680 - 4.32459i) q^{32} +(-0.388349 - 0.672641i) q^{34} -4.28539 q^{35} +2.78257 q^{37} +(0.461818 + 0.799892i) q^{38} +(-0.927880 + 1.60713i) q^{40} +(-3.18008 + 5.50806i) q^{41} +(-3.79662 - 6.57594i) q^{43} +7.87560 q^{44} -2.59786 q^{46} +(-4.13510 - 7.16221i) q^{47} +(-5.68226 + 9.84197i) q^{49} +(0.247048 - 0.427900i) q^{50} +(-0.877935 - 1.52063i) q^{52} -0.0752567 q^{53} -4.48530 q^{55} +(3.97632 + 6.88719i) q^{56} +(0.185362 - 0.321057i) q^{58} +(5.72037 - 9.90797i) q^{59} +(5.98002 + 10.3577i) q^{61} -5.04044 q^{62} -2.72231 q^{64} +(0.500000 + 0.866025i) q^{65} +(6.44874 - 11.1696i) q^{67} +(-1.38008 + 2.39036i) q^{68} +(-1.05870 - 1.83371i) q^{70} -14.4466 q^{71} +9.37293 q^{73} +(0.687429 + 1.19066i) q^{74} +(1.64116 - 2.84258i) q^{76} +(-9.61062 + 16.6461i) q^{77} +(3.04959 + 5.28205i) q^{79} +2.59482 q^{80} -3.14253 q^{82} +(0.306089 + 0.530162i) q^{83} +(0.785980 - 1.36136i) q^{85} +(1.87589 - 3.24914i) q^{86} +(4.16182 + 7.20849i) q^{88} +16.2485 q^{89} +4.28539 q^{91} +(4.61600 + 7.99515i) q^{92} +(2.04314 - 3.53882i) q^{94} +(-0.934672 + 1.61890i) q^{95} +(7.49702 + 12.9852i) q^{97} -5.61517 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.247048	+	0.427900i	0.174689	+	0.302571i	0.940054	−	0.341026i	$-0.110775\pi$
$2$	0.247048	+	0.427900i	0.174689	+	0.302571i	−0.765364	+	0.643597i	$0.777441\pi$
$3$		0			0
$3$		0			0
$4$	0.877935	−	1.52063i	0.438967	−	0.760314i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	2.14269	+	3.71125i	0.809862	+	1.40272i	0.912959	+	0.408050i	$0.133791\pi$
$7$	2.14269	+	3.71125i	0.809862	+	1.40272i	−0.103098	+	0.994671i	$0.532875\pi$
$8$	1.85576			0.656110
$9$		0			0
$10$	−0.494096			−0.156247
$11$	2.24265	+	3.88439i	0.676185	+	1.17119i	0.976121	+	0.217227i	$0.0697012\pi$
$11$	2.24265	+	3.88439i	0.676185	+	1.17119i	−0.299936	+	0.953959i	$0.596965\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−1.05870	+	1.83371i	−0.282948	+	0.490081i
$15$		0			0
$16$	−1.29741	−	2.24718i	−0.324352	−	0.561794i
$17$	−1.57196			−0.381256			−0.190628	−	0.981662i	$-0.561052\pi$
$17$	−1.57196			−0.381256			−0.190628	+	0.981662i	$0.561052\pi$
$18$		0			0
$19$	1.86934			0.428857			0.214429	−	0.976740i	$-0.431211\pi$
$19$	1.86934			0.428857			0.214429	+	0.976740i	$0.431211\pi$
$20$	0.877935	+	1.52063i	0.196312	+	0.340023i
$21$		0			0
$22$	−1.10808	+	1.91926i	−0.236244	+	0.409187i
$23$	−2.62890	+	4.55339i	−0.548163	+	0.949447i	0.450237	+	0.892909i	$0.351339\pi$
$23$	−2.62890	+	4.55339i	−0.548163	+	0.949447i	−0.998400	+	0.0565377i	$0.981994\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.494096			0.0969002
$27$		0			0
$28$	7.52458			1.42201
$29$	−0.375154	−	0.649786i	−0.0696644	−	0.120662i	0.829089	−	0.559116i	$-0.188860\pi$
$29$	−0.375154	−	0.649786i	−0.0696644	−	0.120662i	−0.898754	+	0.438454i	$0.855526\pi$
$30$		0			0
$31$	−5.10067	+	8.83463i	−0.916108	+	1.58675i	−0.110837	+	0.993839i	$0.535353\pi$
$31$	−5.10067	+	8.83463i	−0.916108	+	1.58675i	−0.805271	+	0.592907i	$0.797980\pi$
$32$	2.49680	−	4.32459i	0.441377	−	0.764487i
$33$		0			0
$34$	−0.388349	−	0.672641i	−0.0666014	−	0.115357i
$35$	−4.28539			−0.724362
$36$		0			0
$37$	2.78257			0.457452			0.228726	−	0.973491i	$-0.426544\pi$
$37$	2.78257			0.457452			0.228726	+	0.973491i	$0.426544\pi$
$38$	0.461818	+	0.799892i	0.0749167	+	0.129760i
$39$		0			0
$40$	−0.927880	+	1.60713i	−0.146711	+	0.254110i
$41$	−3.18008	+	5.50806i	−0.496645	+	0.860214i	−0.999993	−	0.00386999i	$-0.998768\pi$
$41$	−3.18008	+	5.50806i	−0.496645	+	0.860214i	0.503348	+	0.864084i	$0.332101\pi$
$42$		0			0
$43$	−3.79662	−	6.57594i	−0.578979	−	1.00282i	−0.995597	−	0.0937394i	$-0.970118\pi$
$43$	−3.79662	−	6.57594i	−0.578979	−	1.00282i	0.416618	−	0.909082i	$-0.363215\pi$
$44$	7.87560			1.18729
$45$		0			0
$46$	−2.59786			−0.383033
$47$	−4.13510	−	7.16221i	−0.603167	−	1.04472i	−0.992338	−	0.123550i	$-0.960572\pi$
$47$	−4.13510	−	7.16221i	−0.603167	−	1.04472i	0.389171	−	0.921165i	$-0.372761\pi$
$48$		0			0
$49$	−5.68226	+	9.84197i	−0.811752	+	1.40600i
$50$	0.247048	−	0.427900i	0.0349379	−	0.0605141i
$51$		0			0
$52$	−0.877935	−	1.52063i	−0.121748	−	0.210873i
$53$	−0.0752567			−0.0103373			−0.00516865	−	0.999987i	$-0.501645\pi$
$53$	−0.0752567			−0.0103373			−0.00516865	+	0.999987i	$0.501645\pi$
$54$		0			0
$55$	−4.48530			−0.604798
$56$	3.97632	+	6.88719i	0.531358	+	0.920340i
$57$		0			0
$58$	0.185362	−	0.321057i	0.0243392	−	0.0421568i
$59$	5.72037	−	9.90797i	0.744728	−	1.28991i	−0.205593	−	0.978638i	$-0.565912\pi$
$59$	5.72037	−	9.90797i	0.744728	−	1.28991i	0.950322	−	0.311270i	$-0.100754\pi$
$60$		0			0
$61$	5.98002	+	10.3577i	0.765663	+	1.32617i	0.939895	+	0.341463i	$0.110923\pi$
$61$	5.98002	+	10.3577i	0.765663	+	1.32617i	−0.174232	+	0.984705i	$0.555744\pi$
$62$	−5.04044			−0.640137
$63$		0			0
$64$	−2.72231			−0.340289
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	6.44874	−	11.1696i	0.787839	−	1.36458i	−0.139449	−	0.990229i	$-0.544533\pi$
$67$	6.44874	−	11.1696i	0.787839	−	1.36458i	0.927288	−	0.374348i	$-0.122134\pi$
$68$	−1.38008	+	2.39036i	−0.167359	+	0.289874i
$69$		0			0
$70$	−1.05870	−	1.83371i	−0.126538	−	0.219171i
$71$	−14.4466			−1.71450			−0.857250	−	0.514900i	$-0.827829\pi$
$71$	−14.4466			−1.71450			−0.857250	+	0.514900i	$0.827829\pi$
$72$		0			0
$73$	9.37293			1.09702			0.548509	−	0.836144i	$-0.315196\pi$
$73$	9.37293			1.09702			0.548509	+	0.836144i	$0.315196\pi$
$74$	0.687429	+	1.19066i	0.0799120	+	0.138412i
$75$		0			0
$76$	1.64116	−	2.84258i	0.188254	−	0.326066i
$77$	−9.61062	+	16.6461i	−1.09523	+	1.89700i
$78$		0			0
$79$	3.04959	+	5.28205i	0.343106	+	0.594277i	0.985008	−	0.172510i	$-0.0551877\pi$
$79$	3.04959	+	5.28205i	0.343106	+	0.594277i	−0.641902	+	0.766787i	$0.721854\pi$
$80$	2.59482			0.290109
$81$		0			0
$82$	−3.14253			−0.347034
$83$	0.306089	+	0.530162i	0.0335976	+	0.0581928i	0.882335	−	0.470621i	$-0.155970\pi$
$83$	0.306089	+	0.530162i	0.0335976	+	0.0581928i	−0.848738	+	0.528814i	$0.822637\pi$
$84$		0			0
$85$	0.785980	−	1.36136i	0.0852515	−	0.147660i
$86$	1.87589	−	3.24914i	0.202283	−	0.350364i
$87$		0			0
$88$	4.16182	+	7.20849i	0.443652	+	0.768427i
$89$	16.2485			1.72234			0.861169	−	0.508319i	$-0.169733\pi$
$89$	16.2485			1.72234			0.861169	+	0.508319i	$0.169733\pi$
$90$		0			0
$91$	4.28539			0.449230
$92$	4.61600	+	7.99515i	0.481252	+	0.833552i
$93$		0			0
$94$	2.04314	−	3.53882i	0.210734	−	0.365001i
$95$	−0.934672	+	1.61890i	−0.0958954	+	0.166096i
$96$		0			0
$97$	7.49702	+	12.9852i	0.761207	+	1.31845i	0.942229	+	0.334971i	$0.108726\pi$
$97$	7.49702	+	12.9852i	0.761207	+	1.31845i	−0.181021	+	0.983479i	$0.557940\pi$
$98$	−5.61517			−0.567218
$99$		0			0
$100$	−1.75587			−0.175587
$101$	5.44487	+	9.43079i	0.541785	+	0.938399i	0.998802	+	0.0489409i	$0.0155846\pi$
$101$	5.44487	+	9.43079i	0.541785	+	0.938399i	−0.457017	+	0.889458i	$0.651082\pi$
$102$		0			0
$103$	0.768667	−	1.33137i	0.0757390	−	0.131184i	−0.825668	−	0.564156i	$-0.809202\pi$
$103$	0.768667	−	1.33137i	0.0757390	−	0.131184i	0.901407	+	0.432972i	$0.142535\pi$
$104$	0.927880	−	1.60713i	0.0909861	−	0.157593i
$105$		0			0
$106$	−0.0185920	−	0.0322023i	−0.00180582	−	0.00312776i
$107$	5.43803			0.525715			0.262857	−	0.964835i	$-0.415335\pi$
$107$	5.43803			0.525715			0.262857	+	0.964835i	$0.415335\pi$
$108$		0			0
$109$	1.44466			0.138374			0.0691868	−	0.997604i	$-0.477960\pi$
$109$	1.44466			0.138374			0.0691868	+	0.997604i	$0.477960\pi$
$110$	−1.10808	−	1.91926i	−0.105652	−	0.182994i
$111$		0			0
$112$	5.55989	−	9.63002i	0.525360	−	0.909951i
$113$	2.23239	−	3.86661i	0.210006	−	0.363740i	−0.741710	−	0.670720i	$-0.765985\pi$
$113$	2.23239	−	3.86661i	0.210006	−	0.363740i	0.951716	+	0.306980i	$0.0993185\pi$
$114$		0			0
$115$	−2.62890	−	4.55339i	−0.245146	−	0.424605i
$116$	−1.31744			−0.122322
$117$		0			0
$118$	5.65282			0.520384
$119$	−3.36823	−	5.83394i	−0.308765	−	0.534796i
$120$		0			0
$121$	−4.55897	+	7.89637i	−0.414452	+	0.717851i
$122$	−2.95470	+	5.11770i	−0.267506	+	0.463335i
$123$		0			0
$124$	8.95612	+	15.5124i	0.804283	+	1.39306i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−3.92097			−0.347930			−0.173965	−	0.984752i	$-0.555658\pi$
$127$	−3.92097			−0.347930			−0.173965	+	0.984752i	$0.555658\pi$
$128$	−5.66615	−	9.81406i	−0.500821	−	0.867448i
$129$		0			0
$130$	−0.247048	+	0.427900i	−0.0216675	+	0.0375293i
$131$	0.387214	−	0.670674i	0.0338310	−	0.0585971i	−0.848614	−	0.529012i	$-0.822563\pi$
$131$	0.387214	−	0.670674i	0.0338310	−	0.0585971i	0.882445	+	0.470415i	$0.155896\pi$
$132$		0			0
$133$	4.00543	+	6.93761i	0.347315	+	0.601567i
$134$	6.37259			0.550508
$135$		0			0
$136$	−2.91718			−0.250146
$137$	2.35405	+	4.07733i	0.201120	+	0.348350i	0.948890	−	0.315608i	$-0.102209\pi$
$137$	2.35405	+	4.07733i	0.201120	+	0.348350i	−0.747770	+	0.663958i	$0.768875\pi$
$138$		0			0
$139$	3.48346	−	6.03352i	0.295463	−	0.511757i	−0.679630	−	0.733555i	$-0.737859\pi$
$139$	3.48346	−	6.03352i	0.295463	−	0.511757i	0.975092	+	0.221799i	$0.0711928\pi$
$140$	−3.76229	+	6.51647i	−0.317971	+	0.550743i
$141$		0			0
$142$	−3.56901	−	6.18171i	−0.299505	−	0.518758i
$143$	4.48530			0.375080
$144$		0			0
$145$	0.750308			0.0623097
$146$	2.31556	+	4.01067i	0.191637	+	0.331926i
$147$		0			0
$148$	2.44292	−	4.23126i	0.200807	−	0.347807i
$149$	−4.11863	+	7.13367i	−0.337411	+	0.584413i	−0.983945	−	0.178472i	$-0.942885\pi$
$149$	−4.11863	+	7.13367i	−0.337411	+	0.584413i	0.646534	+	0.762885i	$0.276218\pi$
$150$		0			0
$151$	4.38594	+	7.59667i	0.356923	+	0.618208i	0.987445	−	0.157963i	$-0.0504926\pi$
$151$	4.38594	+	7.59667i	0.356923	+	0.618208i	−0.630522	+	0.776171i	$0.717159\pi$
$152$	3.46905			0.281377
$153$		0			0
$154$	−9.49714			−0.765301
$155$	−5.10067	−	8.83463i	−0.409696	−	0.709614i
$156$		0			0
$157$	6.69687	−	11.5993i	0.534468	−	0.925726i	−0.464721	−	0.885457i	$-0.653845\pi$
$157$	6.69687	−	11.5993i	0.534468	−	0.925726i	0.999189	−	0.0402687i	$-0.0128214\pi$
$158$	−1.50679	+	2.60984i	−0.119874	+	0.207628i
$159$		0			0
$160$	2.49680	+	4.32459i	0.197390	+	0.341889i
$161$	−22.5317			−1.77575
$162$		0			0
$163$	−0.242444			−0.0189897			−0.00949486	−	0.999955i	$-0.503022\pi$
$163$	−0.242444			−0.0189897			−0.00949486	+	0.999955i	$0.503022\pi$
$164$	5.58380	+	9.67143i	0.436022	+	0.755212i
$165$		0			0
$166$	−0.151237	+	0.261951i	−0.0117383	+	0.0203313i
$167$	2.54305	−	4.40470i	0.196787	−	0.340846i	−0.750698	−	0.660646i	$-0.770282\pi$
$167$	2.54305	−	4.40470i	0.196787	−	0.340846i	0.947485	+	0.319800i	$0.103616\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.776699			0.0595701
$171$		0			0
$172$	−13.3327			−1.01661
$173$	−11.5855	−	20.0667i	−0.880831	−	1.52564i	−0.850418	−	0.526107i	$-0.823651\pi$
$173$	−11.5855	−	20.0667i	−0.880831	−	1.52564i	−0.0304130	−	0.999537i	$-0.509682\pi$
$174$		0			0
$175$	2.14269	−	3.71125i	0.161972	−	0.280544i
$176$	5.81927	−	10.0793i	0.438644	−	0.759753i
$177$		0			0
$178$	4.01416	+	6.95273i	0.300874	+	0.521129i
$179$	−13.9237			−1.04070			−0.520352	−	0.853952i	$-0.674199\pi$
$179$	−13.9237			−1.04070			−0.520352	+	0.853952i	$0.674199\pi$
$180$		0			0
$181$	13.6884			1.01745			0.508725	−	0.860929i	$-0.330117\pi$
$181$	13.6884			1.01745			0.508725	+	0.860929i	$0.330117\pi$
$182$	1.05870	+	1.83371i	0.0784757	+	0.135924i
$183$		0			0
$184$	−4.87860	+	8.44999i	−0.359655	+	0.622942i
$185$	−1.39129	+	2.40978i	−0.102289	+	0.177170i
$186$		0			0
$187$	−3.52536	−	6.10610i	−0.257800	−	0.446522i
$188$	−14.5214			−1.05908
$189$		0			0
$190$	−0.923636			−0.0670076
$191$	−3.92168	−	6.79255i	−0.283763	−	0.491491i	0.688546	−	0.725193i	$-0.258249\pi$
$191$	−3.92168	−	6.79255i	−0.283763	−	0.491491i	−0.972308	+	0.233702i	$0.924916\pi$
$192$		0			0
$193$	10.3259	−	17.8850i	0.743274	−	1.28739i	−0.207723	−	0.978188i	$-0.566605\pi$
$193$	10.3259	−	17.8850i	0.743274	−	1.28739i	0.950997	−	0.309200i	$-0.100061\pi$
$194$	−3.70425	+	6.41595i	−0.265950	+	0.460638i
$195$		0			0
$196$	9.97731	+	17.2812i	0.712665	+	1.23437i
$197$	−4.38617			−0.312502			−0.156251	−	0.987717i	$-0.549941\pi$
$197$	−4.38617			−0.312502			−0.156251	+	0.987717i	$0.549941\pi$
$198$		0			0
$199$	−13.3916			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$199$	−13.3916			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$200$	−0.927880	−	1.60713i	−0.0656110	−	0.113642i
$201$		0			0
$202$	−2.69029	+	4.65972i	−0.189288	+	0.327856i
$203$	1.60768	−	2.78458i	0.112837	−	0.195440i
$204$		0			0
$205$	−3.18008	−	5.50806i	−0.222106	−	0.384699i
$206$	0.759591			0.0529232
$207$		0			0
$208$	−2.59482			−0.179918
$209$	4.19229	+	7.26126i	0.289987	+	0.502272i
$210$		0			0
$211$	3.03493	−	5.25665i	0.208933	−	0.361883i	−0.742446	−	0.669906i	$-0.766334\pi$
$211$	3.03493	−	5.25665i	0.208933	−	0.361883i	0.951379	+	0.308023i	$0.0996675\pi$
$212$	−0.0660704	+	0.114437i	−0.00453774	+	0.00785959i
$213$		0			0
$214$	1.34345	+	2.32693i	0.0918367	+	0.159066i
$215$	7.59324			0.517855
$216$		0			0
$217$	−43.7167			−2.96768
$218$	0.356901	+	0.618170i	0.0241724	+	0.0418678i
$219$		0			0
$220$	−3.93780	+	6.82047i	−0.265487	+	0.459836i
$221$	−0.785980	+	1.36136i	−0.0528707	+	0.0915748i
$222$		0			0
$223$	11.4941	+	19.9083i	0.769700	+	1.33316i	0.937726	+	0.347377i	$0.112928\pi$
$223$	11.4941	+	19.9083i	0.769700	+	1.33316i	−0.168026	+	0.985783i	$0.553739\pi$
$224$	21.3995			1.42982
$225$		0			0
$226$	2.20603			0.146743
$227$	−9.41732	−	16.3113i	−0.625050	−	1.08262i	−0.988531	−	0.151016i	$-0.951745\pi$
$227$	−9.41732	−	16.3113i	−0.625050	−	1.08262i	0.363482	−	0.931601i	$-0.381588\pi$
$228$		0			0
$229$	2.70463	−	4.68455i	0.178727	−	0.309564i	−0.762718	−	0.646731i	$-0.776135\pi$
$229$	2.70463	−	4.68455i	0.178727	−	0.309564i	0.941445	+	0.337167i	$0.109469\pi$
$230$	1.29893	−	2.24981i	0.0856488	−	0.148348i
$231$		0			0
$232$	−0.696196	−	1.20585i	−0.0457075	−	0.0791677i
$233$	7.45934			0.488677			0.244339	−	0.969690i	$-0.421429\pi$
$233$	7.45934			0.488677			0.244339	+	0.969690i	$0.421429\pi$
$234$		0			0
$235$	8.27021			0.539489
$236$	−10.0442	−	17.3971i	−0.653823	−	1.13245i
$237$		0			0
$238$	1.66423	−	2.88253i	0.107876	−	0.186846i
$239$	3.84036	−	6.65171i	0.248412	−	0.430263i	−0.714673	−	0.699459i	$-0.753424\pi$
$239$	3.84036	−	6.65171i	0.248412	−	0.430263i	0.963086	+	0.269196i	$0.0867578\pi$
$240$		0			0
$241$	−14.6400	−	25.3573i	−0.943048	−	1.63341i	−0.759614	−	0.650375i	$-0.774612\pi$
$241$	−14.6400	−	25.3573i	−0.943048	−	1.63341i	−0.183434	−	0.983032i	$-0.558721\pi$
$242$	−4.50514			−0.289601
$243$		0			0
$244$	21.0003			1.34440
$245$	−5.68226	−	9.84197i	−0.363027	−	0.628780i
$246$		0			0
$247$	0.934672	−	1.61890i	0.0594718	−	0.103008i
$248$	−9.46562	+	16.3949i	−0.601068	+	1.04108i
$249$		0			0
$250$	0.247048	+	0.427900i	0.0156247	+	0.0270627i
$251$	26.6402			1.68152			0.840758	−	0.541412i	$-0.182110\pi$
$251$	26.6402			1.68152			0.840758	+	0.541412i	$0.182110\pi$
$252$		0			0
$253$	−23.5828			−1.48264
$254$	−0.968667	−	1.67778i	−0.0607796	−	0.105273i
$255$		0			0
$256$	0.0773104	−	0.133905i	0.00483190	−	0.00836909i
$257$	−0.356142	+	0.616855i	−0.0222155	+	0.0384784i	−0.876919	−	0.480637i	$-0.840405\pi$
$257$	−0.356142	+	0.616855i	−0.0222155	+	0.0384784i	0.854704	+	0.519116i	$0.173739\pi$
$258$		0			0
$259$	5.96220	+	10.3268i	0.370473	+	0.641678i
$260$	1.75587			0.108894
$261$		0			0
$262$	0.382641			0.0236397
$263$	−6.60152	−	11.4342i	−0.407067	−	0.705061i	0.587493	−	0.809230i	$-0.300115\pi$
$263$	−6.60152	−	11.4342i	−0.407067	−	0.705061i	−0.994560	+	0.104169i	$0.966782\pi$
$264$		0			0
$265$	0.0376283	−	0.0651742i	0.00231149	−	0.00400362i
$266$	−1.97907	+	3.42784i	−0.121344	+	0.210175i
$267$		0			0
$268$	−11.3231	−	19.6123i	−0.691671	−	1.19801i
$269$	18.3263			1.11737			0.558687	−	0.829379i	$-0.311305\pi$
$269$	18.3263			1.11737			0.558687	+	0.829379i	$0.311305\pi$
$270$		0			0
$271$	−28.9102			−1.75617			−0.878084	−	0.478507i	$-0.841178\pi$
$271$	−28.9102			−1.75617			−0.878084	+	0.478507i	$0.841178\pi$
$272$	2.03947	+	3.53247i	0.123661	+	0.214187i
$273$		0			0
$274$	−1.16313	+	2.01459i	−0.0702670	+	0.121706i
$275$	2.24265	−	3.88439i	0.135237	−	0.234237i
$276$		0			0
$277$	−13.0652	−	22.6297i	−0.785014	−	1.35968i	−0.928991	−	0.370103i	$-0.879322\pi$
$277$	−13.0652	−	22.6297i	−0.785014	−	1.35968i	0.143977	−	0.989581i	$-0.454011\pi$
$278$	3.44232			0.206457
$279$		0			0
$280$	−7.95265			−0.475261
$281$	13.8389	+	23.9697i	0.825559	+	1.42991i	0.901491	+	0.432798i	$0.142474\pi$
$281$	13.8389	+	23.9697i	0.825559	+	1.42991i	−0.0759316	+	0.997113i	$0.524193\pi$
$282$		0			0
$283$	−13.0720	+	22.6414i	−0.777053	+	1.34589i	0.156581	+	0.987665i	$0.449953\pi$
$283$	−13.0720	+	22.6414i	−0.777053	+	1.34589i	−0.933634	+	0.358229i	$0.883381\pi$
$284$	−12.6832	+	21.9680i	−0.752610	+	1.30356i
$285$		0			0
$286$	1.10808	+	1.91926i	0.0655224	+	0.113488i
$287$	−27.2557			−1.60885
$288$		0			0
$289$	−14.5289			−0.854644
$290$	0.185362	+	0.321057i	0.0108848	+	0.0188531i
$291$		0			0
$292$	8.22882	−	14.2527i	0.481555	−	0.834078i
$293$	2.00825	−	3.47840i	0.117323	−	0.203210i	−0.801383	−	0.598152i	$-0.795902\pi$
$293$	2.00825	−	3.47840i	0.117323	−	0.203210i	0.918706	+	0.394942i	$0.129235\pi$
$294$		0			0
$295$	5.72037	+	9.90797i	0.333053	+	0.576864i
$296$	5.16379			0.300139
$297$		0			0
$298$	−4.06999			−0.235768
$299$	2.62890	+	4.55339i	0.152033	+	0.263329i
$300$		0			0
$301$	16.2700	−	28.1804i	0.937786	−	1.62429i
$302$	−2.16708	+	3.75348i	−0.124701	+	0.215989i
$303$		0			0
$304$	−2.42530	−	4.20075i	−0.139101	−	0.240929i
$305$	−11.9600			−0.684830
$306$		0			0
$307$	−7.51331			−0.428807			−0.214404	−	0.976745i	$-0.568781\pi$
$307$	−7.51331			−0.428807			−0.214404	+	0.976745i	$0.568781\pi$
$308$	16.8750	+	29.2284i	0.961542	+	1.66544i
$309$		0			0
$310$	2.52022	−	4.36515i	0.143139	−	0.247924i
$311$	10.5200	−	18.2213i	0.596537	−	1.03323i	−0.396791	−	0.917909i	$-0.629876\pi$
$311$	10.5200	−	18.2213i	0.596537	−	1.03323i	0.993328	−	0.115323i	$-0.0367905\pi$
$312$		0			0
$313$	3.25007	+	5.62929i	0.183705	+	0.318186i	0.943139	−	0.332398i	$-0.107858\pi$
$313$	3.25007	+	5.62929i	0.183705	+	0.318186i	−0.759435	+	0.650584i	$0.774524\pi$
$314$	6.61779			0.373463
$315$		0			0
$316$	10.7094			0.602449
$317$	−5.72790	−	9.92101i	−0.321711	−	0.557220i	0.659130	−	0.752029i	$-0.270925\pi$
$317$	−5.72790	−	9.92101i	−0.321711	−	0.557220i	−0.980841	+	0.194809i	$0.937591\pi$
$318$		0			0
$319$	1.68268	−	2.91449i	0.0942120	−	0.163180i
$320$	1.36116	−	2.35759i	0.0760909	−	0.131793i
$321$		0			0
$322$	−5.56641	−	9.64130i	−0.310204	−	0.537289i
$323$	−2.93853			−0.163504
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−0.0598954	−	0.103742i	−0.00331730	−	0.00574573i
$327$		0			0
$328$	−5.90146	+	10.2216i	−0.325854	+	0.564395i
$329$	17.7205	−	30.6928i	0.976964	−	1.69215i
$330$		0			0
$331$	12.1797	+	21.0958i	0.669456	+	1.15953i	0.978057	+	0.208340i	$0.0668060\pi$
$331$	12.1797	+	21.0958i	0.669456	+	1.15953i	−0.308601	+	0.951192i	$0.599861\pi$
$332$	1.07490			0.0589931
$333$		0			0
$334$	2.51302			0.137507
$335$	6.44874	+	11.1696i	0.352332	+	0.610258i
$336$		0			0
$337$	−5.80009	+	10.0460i	−0.315951	+	0.547243i	−0.979639	−	0.200766i	$-0.935657\pi$
$337$	−5.80009	+	10.0460i	−0.315951	+	0.547243i	0.663688	+	0.748009i	$0.268990\pi$
$338$	0.247048	−	0.427900i	0.0134376	−	0.0232747i
$339$		0			0
$340$	−1.38008	−	2.39036i	−0.0748452	−	0.129636i
$341$	−45.7561			−2.47783
$342$		0			0
$343$	−18.7037			−1.00990
$344$	−7.04561	−	12.2034i	−0.379874	−	0.657961i
$345$		0			0
$346$	5.72436	−	9.91488i	0.307744	−	0.533028i
$347$	−6.09100	+	10.5499i	−0.326982	+	0.566349i	−0.981911	−	0.189341i	$-0.939365\pi$
$347$	−6.09100	+	10.5499i	−0.326982	+	0.566349i	0.654930	+	0.755690i	$0.272698\pi$
$348$		0			0
$349$	−3.95551	−	6.85114i	−0.211734	−	0.366733i	0.740524	−	0.672030i	$-0.234578\pi$
$349$	−3.95551	−	6.85114i	−0.211734	−	0.366733i	−0.952257	+	0.305297i	$0.901244\pi$
$350$	2.11739			0.113179
$351$		0			0
$352$	22.3978			1.19381
$353$	10.6294	+	18.4107i	0.565747	+	0.979903i	0.996980	+	0.0776620i	$0.0247455\pi$
$353$	10.6294	+	18.4107i	0.565747	+	0.979903i	−0.431233	+	0.902241i	$0.641921\pi$
$354$		0			0
$355$	7.22332	−	12.5112i	0.383374	−	0.664023i
$356$	14.2651	−	24.7079i	0.756050	−	1.30952i
$357$		0			0
$358$	−3.43981	−	5.95793i	−0.181800	−	0.314886i
$359$	7.59638			0.400922			0.200461	−	0.979702i	$-0.435756\pi$
$359$	7.59638			0.400922			0.200461	+	0.979702i	$0.435756\pi$
$360$		0			0
$361$	−15.5056			−0.816082
$362$	3.38169	+	5.85725i	0.177738	+	0.307850i
$363$		0			0
$364$	3.76229	−	6.51647i	0.197197	−	0.341556i
$365$	−4.68647	+	8.11720i	−0.245301	+	0.424873i
$366$		0			0
$367$	−10.8071	−	18.7184i	−0.564124	−	0.977092i	−0.997131	−	0.0757010i	$-0.975881\pi$
$367$	−10.8071	−	18.7184i	−0.564124	−	0.977092i	0.433006	−	0.901391i	$-0.357453\pi$
$368$	13.6430			0.711191
$369$		0			0
$370$	−1.37486			−0.0714754
$371$	−0.161252	−	0.279297i	−0.00837178	−	0.0145004i
$372$		0			0
$373$	6.00668	−	10.4039i	0.311014	−	0.538692i	−0.667568	−	0.744549i	$-0.732665\pi$
$373$	6.00668	−	10.4039i	0.311014	−	0.538692i	0.978582	+	0.205857i	$0.0659981\pi$
$374$	1.74186	−	3.01700i	0.0900697	−	0.156005i
$375$		0			0
$376$	−7.67376	−	13.2913i	−0.395744	−	0.685448i
$377$	−0.750308			−0.0386429
$378$		0			0
$379$	−3.44005			−0.176704			−0.0883518	−	0.996089i	$-0.528160\pi$
$379$	−3.44005			−0.176704			−0.0883518	+	0.996089i	$0.528160\pi$
$380$	1.64116	+	2.84258i	0.0841899	+	0.145821i
$381$		0			0
$382$	1.93768	−	3.35617i	0.0991406	−	0.171717i
$383$	13.4494	−	23.2950i	0.687232	−	1.19032i	−0.285498	−	0.958379i	$-0.592159\pi$
$383$	13.4494	−	23.2950i	0.687232	−	1.19032i	0.972730	−	0.231941i	$-0.0745076\pi$
$384$		0			0
$385$	−9.61062	−	16.6461i	−0.489803	−	0.848363i
$386$	10.2040			0.519368
$387$		0			0
$388$	26.3276			1.33658
$389$	1.66758	+	2.88833i	0.0845494	+	0.146444i	0.905199	−	0.424988i	$-0.139722\pi$
$389$	1.66758	+	2.88833i	0.0845494	+	0.146444i	−0.820650	+	0.571432i	$0.806388\pi$
$390$		0			0
$391$	4.13252	−	7.15774i	0.208991	−	0.361982i
$392$	−10.5449	+	18.2643i	−0.532599	+	0.922488i
$393$		0			0
$394$	−1.08359	−	1.87684i	−0.0545907	−	0.0945538i
$395$	−6.09918			−0.306883
$396$		0			0
$397$	0.768687			0.0385793			0.0192897	−	0.999814i	$-0.493860\pi$
$397$	0.768687			0.0385793			0.0192897	+	0.999814i	$0.493860\pi$
$398$	−3.30836	−	5.73025i	−0.165833	−	0.287232i
$399$		0			0
$400$	−1.29741	+	2.24718i	−0.0648704	+	0.112359i
$401$	14.8015	−	25.6370i	0.739153	−	1.28025i	−0.213723	−	0.976894i	$-0.568559\pi$
$401$	14.8015	−	25.6370i	0.739153	−	1.28025i	0.952877	−	0.303357i	$-0.0981075\pi$
$402$		0			0
$403$	5.10067	+	8.83463i	0.254083	+	0.440084i
$404$	19.1210			0.951303
$405$		0			0
$406$	1.58870			0.0788457
$407$	6.24034	+	10.8086i	0.309322	+	0.535762i
$408$		0			0
$409$	8.10055	−	14.0306i	0.400546	−	0.693766i	−0.593246	−	0.805021i	$-0.702154\pi$
$409$	8.10055	−	14.0306i	0.400546	−	0.693766i	0.993792	+	0.111255i	$0.0354871\pi$
$410$	1.57126	−	2.72151i	0.0775992	−	0.134406i
$411$		0			0
$412$	−1.34968	−	2.33771i	−0.0664939	−	0.115171i
$413$	49.0279			2.41251
$414$		0			0
$415$	−0.612178			−0.0300506
$416$	−2.49680	−	4.32459i	−0.122416	−	0.212030i
$417$		0			0
$418$	−2.07139	+	3.58776i	−0.101315	+	0.175483i
$419$	5.70634	−	9.88368i	0.278773	−	0.482849i	−0.692307	−	0.721603i	$-0.743406\pi$
$419$	5.70634	−	9.88368i	0.278773	−	0.482849i	0.971080	+	0.238754i	$0.0767389\pi$
$420$		0			0
$421$	−5.19917	−	9.00522i	−0.253392	−	0.438888i	0.711066	−	0.703126i	$-0.248213\pi$
$421$	−5.19917	−	9.00522i	−0.253392	−	0.438888i	−0.964458	+	0.264238i	$0.914880\pi$
$422$	2.99909			0.145994
$423$		0			0
$424$	−0.139658			−0.00678241
$425$	0.785980	+	1.36136i	0.0381256	+	0.0660355i
$426$		0			0
$427$	−25.6267	+	44.3868i	−1.24016	+	2.14803i
$428$	4.77424	−	8.26922i	0.230771	−	0.399708i
$429$		0			0
$430$	1.87589	+	3.24914i	0.0904637	+	0.156688i
$431$	0.879972			0.0423868			0.0211934	−	0.999775i	$-0.493253\pi$
$431$	0.879972			0.0423868			0.0211934	+	0.999775i	$0.493253\pi$
$432$		0			0
$433$	31.4562			1.51169			0.755845	−	0.654750i	$-0.227226\pi$
$433$	31.4562			1.51169			0.755845	+	0.654750i	$0.227226\pi$
$434$	−10.8001	−	18.7064i	−0.518422	−	0.897934i
$435$		0			0
$436$	1.26832	−	2.19679i	0.0607415	−	0.105207i
$437$	−4.91432	+	8.51185i	−0.235084	+	0.407177i
$438$		0			0
$439$	2.88207	+	4.99189i	0.137554	+	0.238250i	0.926570	−	0.376122i	$-0.122743\pi$
$439$	2.88207	+	4.99189i	0.137554	+	0.238250i	−0.789016	+	0.614372i	$0.789409\pi$
$440$	−8.32364			−0.396814
$441$		0			0
$442$	−0.776699			−0.0369438
$443$	2.06423	+	3.57535i	0.0980746	+	0.169870i	0.910888	−	0.412654i	$-0.135398\pi$
$443$	2.06423	+	3.57535i	0.0980746	+	0.169870i	−0.812813	+	0.582525i	$0.802065\pi$
$444$		0			0
$445$	−8.12425	+	14.0716i	−0.385126	+	0.667058i
$446$	−5.67917	+	9.83662i	−0.268917	+	0.465777i
$447$		0			0
$448$	−5.83307	−	10.1032i	−0.275587	−	0.477330i
$449$	30.3402			1.43184			0.715921	−	0.698181i	$-0.246007\pi$
$449$	30.3402			1.43184			0.715921	+	0.698181i	$0.246007\pi$
$450$		0			0
$451$	−28.5272			−1.34329
$452$	−3.91978	−	6.78927i	−0.184371	−	0.319340i
$453$		0			0
$454$	4.65306	−	8.05934i	0.218379	−	0.378243i
$455$	−2.14269	+	3.71125i	−0.100451	+	0.173986i
$456$		0			0
$457$	4.23141	+	7.32902i	0.197937	+	0.342837i	0.947859	−	0.318689i	$-0.103242\pi$
$457$	4.23141	+	7.32902i	0.197937	+	0.342837i	−0.749922	+	0.661526i	$0.769909\pi$
$458$	2.67269			0.124887
$459$		0			0
$460$	−9.23201			−0.430444
$461$	8.81541	+	15.2687i	0.410575	+	0.711136i	0.994953	−	0.100345i	$-0.0319948\pi$
$461$	8.81541	+	15.2687i	0.410575	+	0.711136i	−0.584378	+	0.811482i	$0.698661\pi$
$462$		0			0
$463$	0.627193	−	1.08633i	0.0291481	−	0.0504860i	−0.851083	−	0.525031i	$-0.824054\pi$
$463$	0.627193	−	1.08633i	0.0291481	−	0.0504860i	0.880231	+	0.474545i	$0.157387\pi$
$464$	−0.973456	+	1.68608i	−0.0451916	+	0.0782741i
$465$		0			0
$466$	1.84281	+	3.19185i	0.0853667	+	0.147859i
$467$	−11.3158			−0.523634			−0.261817	−	0.965117i	$-0.584322\pi$
$467$	−11.3158			−0.523634			−0.261817	+	0.965117i	$0.584322\pi$
$468$		0			0
$469$	55.2707			2.55216
$470$	2.04314	+	3.53882i	0.0942429	+	0.163234i
$471$		0			0
$472$	10.6156	−	18.3868i	0.488624	−	0.846321i
$473$	17.0290	−	29.4951i	0.782994	−	1.35618i
$474$		0			0
$475$	−0.934672	−	1.61890i	−0.0428857	−	0.0742802i
$476$	−11.8283			−0.542151
$477$		0			0
$478$	3.79502			0.173580
$479$	−16.6918	−	28.9110i	−0.762667	−	1.32098i	−0.941471	−	0.337094i	$-0.890556\pi$
$479$	−16.6918	−	28.9110i	−0.762667	−	1.32098i	0.178804	−	0.983885i	$-0.442777\pi$
$480$		0			0
$481$	1.39129	−	2.40978i	0.0634372	−	0.109876i
$482$	7.23358	−	12.5289i	0.329481	−	0.570677i
$483$		0			0
$484$	8.00495	+	13.8650i	0.363862	+	0.630227i
$485$	−14.9940			−0.680844
$486$		0			0
$487$	−42.2806			−1.91592			−0.957959	−	0.286904i	$-0.907374\pi$
$487$	−42.2806			−1.91592			−0.957959	+	0.286904i	$0.907374\pi$
$488$	11.0975	+	19.2214i	0.502360	+	0.870112i
$489$		0			0
$490$	2.80758	−	4.86288i	0.126834	−	0.219682i
$491$	5.73286	−	9.92961i	0.258720	−	0.448117i	−0.707179	−	0.707035i	$-0.750033\pi$
$491$	5.73286	−	9.92961i	0.258720	−	0.448117i	0.965899	+	0.258918i	$0.0833659\pi$
$492$		0			0
$493$	0.589727	+	1.02144i	0.0265600	+	0.0460032i
$494$	0.923636			0.0415563
$495$		0			0
$496$	26.4706			1.18857
$497$	−30.9547	−	53.6151i	−1.38851	−	2.40497i
$498$		0			0
$499$	−3.35426	+	5.80976i	−0.150157	+	0.260080i	−0.931285	−	0.364291i	$-0.881311\pi$
$499$	−3.35426	+	5.80976i	−0.150157	+	0.260080i	0.781128	+	0.624371i	$0.214645\pi$
$500$	0.877935	−	1.52063i	0.0392624	−	0.0680045i
$501$		0			0
$502$	6.58141	+	11.3993i	0.293743	+	0.508777i
$503$	−13.1409			−0.585925			−0.292963	−	0.956124i	$-0.594641\pi$
$503$	−13.1409			−0.585925			−0.292963	+	0.956124i	$0.594641\pi$
$504$		0			0
$505$	−10.8897			−0.484587
$506$	−5.82609	−	10.0911i	−0.259001	−	0.448603i
$507$		0			0
$508$	−3.44235	+	5.96233i	−0.152730	+	0.264536i
$509$	−15.5601	+	26.9508i	−0.689687	+	1.19457i	0.282252	+	0.959340i	$0.408919\pi$
$509$	−15.5601	+	26.9508i	−0.689687	+	1.19457i	−0.971939	+	0.235233i	$0.924415\pi$
$510$		0			0
$511$	20.0833	+	34.7853i	0.888433	+	1.53881i
$512$	−22.5882			−0.998267
$513$		0			0
$514$	−0.351936			−0.0155232
$515$	0.768667	+	1.33137i	0.0338715	+	0.0586672i
$516$		0			0
$517$	18.5472	−	32.1247i	0.815705	−	1.41284i
$518$	−2.94590	+	5.10244i	−0.129435	+	0.224189i
$519$		0			0
$520$	0.927880	+	1.60713i	0.0406902	+	0.0704775i
$521$	−10.6889			−0.468287			−0.234144	−	0.972202i	$-0.575229\pi$
$521$	−10.6889			−0.468287			−0.234144	+	0.972202i	$0.575229\pi$
$522$		0			0
$523$	−22.8750			−1.00025			−0.500127	−	0.865952i	$-0.666713\pi$
$523$	−22.8750			−1.00025			−0.500127	+	0.865952i	$0.666713\pi$
$524$	−0.679897	−	1.17762i	−0.0297014	−	0.0514444i
$525$		0			0
$526$	3.26178	−	5.64958i	0.142221	−	0.246333i
$527$	8.01805	−	13.8877i	0.349272	−	0.604957i
$528$		0			0
$529$	−2.32222	−	4.02220i	−0.100966	−	0.174878i
$530$	0.0371840			0.00161517
$531$		0			0
$532$	14.0660			0.609840
$533$	3.18008	+	5.50806i	0.137744	+	0.238580i
$534$		0			0
$535$	−2.71902	+	4.70948i	−0.117553	+	0.203608i
$536$	11.9673	−	20.7280i	0.516909	−	0.895313i
$537$		0			0
$538$	4.52747	+	7.84181i	0.195193	+	0.338085i
$539$	−50.9733			−2.19558
$540$		0			0
$541$	−13.5880			−0.584192			−0.292096	−	0.956389i	$-0.594353\pi$
$541$	−13.5880			−0.584192			−0.292096	+	0.956389i	$0.594353\pi$
$542$	−7.14220	−	12.3707i	−0.306784	−	0.531365i
$543$		0			0
$544$	−3.92487	+	6.79808i	−0.168278	+	0.291465i
$545$	−0.722331	+	1.25111i	−0.0309413	+	0.0535919i
$546$		0			0
$547$	−11.9818	−	20.7531i	−0.512305	−	0.887338i	−0.999898	−	0.0142675i	$-0.995458\pi$
$547$	−11.9818	−	20.7531i	−0.512305	−	0.887338i	0.487593	−	0.873071i	$-0.337875\pi$
$548$	8.26680			0.353140
$549$		0			0
$550$	2.21617			0.0944978
$551$	−0.701293	−	1.21467i	−0.0298761	−	0.0517469i
$552$		0			0
$553$	−13.0687	+	22.6356i	−0.555737	+	0.962564i
$554$	6.45548	−	11.1812i	0.274267	−	0.475045i
$555$		0			0
$556$	−6.11649	−	10.5941i	−0.259397	−	0.449289i
$557$	−0.501996			−0.0212702			−0.0106351	−	0.999943i	$-0.503385\pi$
$557$	−0.501996			−0.0212702			−0.0106351	+	0.999943i	$0.503385\pi$
$558$		0			0
$559$	−7.59324			−0.321160
$560$	5.55989	+	9.63002i	0.234948	+	0.406942i
$561$		0			0
$562$	−6.83774	+	11.8433i	−0.288433	+	0.499580i
$563$	8.45763	−	14.6490i	0.356447	−	0.617384i	−0.630918	−	0.775850i	$-0.717321\pi$
$563$	8.45763	−	14.6490i	0.356447	−	0.617384i	0.987364	+	0.158466i	$0.0506548\pi$
$564$		0			0
$565$	2.23239	+	3.86661i	0.0939173	+	0.162670i
$566$	−12.9177			−0.542971
$567$		0			0
$568$	−26.8095			−1.12490
$569$	−12.0627	−	20.8931i	−0.505693	−	0.875885i	−0.999978	−	0.00658582i	$-0.997904\pi$
$569$	−12.0627	−	20.8931i	−0.505693	−	0.875885i	0.494286	−	0.869300i	$-0.335430\pi$
$570$		0			0
$571$	7.32786	−	12.6922i	0.306661	−	0.531153i	−0.670968	−	0.741486i	$-0.734121\pi$
$571$	7.32786	−	12.6922i	0.306661	−	0.531153i	0.977630	+	0.210333i	$0.0674548\pi$
$572$	3.93780	−	6.82047i	0.164648	−	0.285178i
$573$		0			0
$574$	−6.73347	−	11.6627i	−0.281050	−	0.486792i
$575$	5.25780			0.219265
$576$		0			0
$577$	4.42835			0.184355			0.0921774	−	0.995743i	$-0.470617\pi$
$577$	4.42835			0.184355			0.0921774	+	0.995743i	$0.470617\pi$
$578$	−3.58935	−	6.21693i	−0.149297	−	0.258590i
$579$		0			0
$580$	0.658722	−	1.14094i	0.0273519	−	0.0473749i
$581$	−1.31171	+	2.27195i	−0.0544189	+	0.0942563i
$582$		0			0
$583$	−0.168774	−	0.292326i	−0.00698992	−	0.0121069i
$584$	17.3939			0.719765
$585$		0			0
$586$	1.98454			0.0819806
$587$	−3.40578	−	5.89899i	−0.140572	−	0.243477i	0.787140	−	0.616774i	$-0.211561\pi$
$587$	−3.40578	−	5.89899i	−0.140572	−	0.243477i	−0.927712	+	0.373297i	$0.878227\pi$
$588$		0			0
$589$	−9.53492	+	16.5150i	−0.392879	+	0.680487i
$590$	−2.82641	+	4.89548i	−0.116361	+	0.201544i
$591$		0			0
$592$	−3.61013	−	6.25293i	−0.148375	−	0.256994i
$593$	−9.71004			−0.398744			−0.199372	−	0.979924i	$-0.563890\pi$
$593$	−9.71004			−0.398744			−0.199372	+	0.979924i	$0.563890\pi$
$594$		0			0
$595$	6.73645			0.276168
$596$	7.23177	+	12.5258i	0.296225	+	0.513077i
$597$		0			0
$598$	−1.29893	+	2.24981i	−0.0531171	+	0.0920016i
$599$	11.1367	−	19.2893i	0.455032	−	0.788138i	−0.543658	−	0.839307i	$-0.682961\pi$
$599$	11.1367	−	19.2893i	0.455032	−	0.788138i	0.998690	+	0.0511684i	$0.0162945\pi$
$600$		0			0
$601$	−6.77115	−	11.7280i	−0.276201	−	0.478394i	0.694236	−	0.719747i	$-0.255742\pi$
$601$	−6.77115	−	11.7280i	−0.276201	−	0.478394i	−0.970437	+	0.241353i	$0.922409\pi$
$602$	16.0779			0.655285
$603$		0			0
$604$	15.4023			0.626710
$605$	−4.55897	−	7.89637i	−0.185348	−	0.321033i
$606$		0			0
$607$	2.38199	−	4.12572i	0.0966818	−	0.167458i	−0.813627	−	0.581387i	$-0.802510\pi$
$607$	2.38199	−	4.12572i	0.0966818	−	0.167458i	0.910309	+	0.413929i	$0.135844\pi$
$608$	4.66739	−	8.08415i	0.189288	−	0.327856i
$609$		0			0
$610$	−2.95470	−	5.11770i	−0.119633	−	0.207210i
$611$	−8.27021			−0.334577
$612$		0			0
$613$	−7.58211			−0.306238			−0.153119	−	0.988208i	$-0.548932\pi$
$613$	−7.58211			−0.306238			−0.153119	+	0.988208i	$0.548932\pi$
$614$	−1.85615	−	3.21494i	−0.0749080	−	0.129745i
$615$		0			0
$616$	−17.8350	+	30.8911i	−0.718593	+	1.24464i
$617$	7.28208	−	12.6129i	0.293166	−	0.507778i	−0.681391	−	0.731920i	$-0.738625\pi$
$617$	7.28208	−	12.6129i	0.293166	−	0.507778i	0.974556	+	0.224142i	$0.0719580\pi$
$618$		0			0
$619$	21.3509	+	36.9808i	0.858165	+	1.48639i	0.873677	+	0.486506i	$0.161729\pi$
$619$	21.3509	+	36.9808i	0.858165	+	1.48639i	−0.0155124	+	0.999880i	$0.504938\pi$
$620$	−17.9122			−0.719373
$621$		0			0
$622$	10.3958			0.416835
$623$	34.8155	+	60.3023i	1.39486	+	2.41596i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.60585	+	2.78141i	−0.0641825	+	0.111167i
$627$		0			0
$628$	−11.7588	−	20.3669i	−0.469228	−	0.812727i
$629$	−4.37409			−0.174406
$630$		0			0
$631$	−35.7936			−1.42492			−0.712461	−	0.701712i	$-0.752419\pi$
$631$	−35.7936			−1.42492			−0.712461	+	0.701712i	$0.752419\pi$
$632$	5.65931	+	9.80221i	0.225115	+	0.389911i
$633$		0			0
$634$	2.83013	−	4.90193i	0.112399	−	0.194681i
$635$	1.96048	−	3.39566i	0.0777994	−	0.134753i
$636$		0			0
$637$	5.68226	+	9.84197i	0.225140	+	0.389953i
$638$	1.66281			0.0658313
$639$		0			0
$640$	11.3323			0.447948
$641$	5.73418	+	9.93189i	0.226486	+	0.392286i	0.956764	−	0.290864i	$-0.0939428\pi$
$641$	5.73418	+	9.93189i	0.226486	+	0.392286i	−0.730278	+	0.683150i	$0.760609\pi$
$642$		0			0
$643$	14.4978	−	25.1109i	0.571738	−	0.990279i	−0.424650	−	0.905358i	$-0.639603\pi$
$643$	14.4978	−	25.1109i	0.571738	−	0.990279i	0.996388	−	0.0849212i	$-0.0270639\pi$
$644$	−19.7814	+	34.2623i	−0.779494	+	1.35012i
$645$		0			0
$646$	−0.725959	−	1.25740i	−0.0285625	−	0.0494716i
$647$	11.2588			0.442630			0.221315	−	0.975202i	$-0.428965\pi$
$647$	11.2588			0.442630			0.221315	+	0.975202i	$0.428965\pi$
$648$		0			0
$649$	51.3151			2.01430
$650$	−0.247048	−	0.427900i	−0.00969002	−	0.0167836i
$651$		0			0
$652$	−0.212850	+	0.368668i	−0.00833586	+	0.0144381i
$653$	−17.2419	+	29.8639i	−0.674729	+	1.16866i	0.301820	+	0.953365i	$0.402406\pi$
$653$	−17.2419	+	29.8639i	−0.674729	+	1.16866i	−0.976548	+	0.215299i	$0.930927\pi$
$654$		0			0
$655$	0.387214	+	0.670674i	0.0151297	+	0.0262054i
$656$	16.5034			0.644351
$657$		0			0
$658$	17.5113			0.682660
$659$	15.2334	+	26.3850i	0.593408	+	1.02781i	0.993769	+	0.111455i	$0.0355512\pi$
$659$	15.2334	+	26.3850i	0.593408	+	1.02781i	−0.400362	+	0.916357i	$0.631115\pi$
$660$		0			0
$661$	−10.7408	+	18.6036i	−0.417769	+	0.723597i	−0.995715	−	0.0924779i	$-0.970521\pi$
$661$	−10.7408	+	18.6036i	−0.417769	+	0.723597i	0.577946	+	0.816075i	$0.303855\pi$
$662$	−6.01793	+	10.4234i	−0.233893	+	0.405115i
$663$		0			0
$664$	0.568028	+	0.983853i	0.0220438	+	0.0381809i
$665$	−8.01086			−0.310648
$666$		0			0
$667$	3.94497			0.152750
$668$	−4.46527	−	7.73407i	−0.172766	−	0.299240i
$669$		0			0
$670$	−3.18630	+	5.51883i	−0.123097	+	0.213211i
$671$	−26.8222	+	46.4574i	−1.03546	+	1.79347i
$672$		0			0
$673$	−4.55275	−	7.88559i	−0.175496	−	0.303967i	0.764837	−	0.644224i	$-0.222819\pi$
$673$	−4.55275	−	7.88559i	−0.175496	−	0.303967i	−0.940333	+	0.340256i	$0.889486\pi$
$674$	−5.73160			−0.220773
$675$		0			0
$676$	−1.75587			−0.0675334
$677$	1.72288	+	2.98411i	0.0662155	+	0.114689i	0.897233	−	0.441558i	$-0.145574\pi$
$677$	1.72288	+	2.98411i	0.0662155	+	0.114689i	−0.831017	+	0.556247i	$0.812241\pi$
$678$		0			0
$679$	−32.1276	+	55.6467i	−1.23295	+	2.13552i
$680$	1.45859	−	2.52635i	0.0559343	−	0.0968811i
$681$		0			0
$682$	−11.3040	−	19.5790i	−0.432851	−	0.749720i
$683$	−36.2676			−1.38774			−0.693870	−	0.720100i	$-0.744096\pi$
$683$	−36.2676			−1.38774			−0.693870	+	0.720100i	$0.744096\pi$
$684$		0			0
$685$	−4.70810			−0.179887
$686$	−4.62071	−	8.00330i	−0.176419	−	0.305567i
$687$		0			0
$688$	−9.85153	+	17.0633i	−0.375586	+	0.650534i
$689$	−0.0376283	+	0.0651742i	−0.00143353	+	0.00248294i
$690$		0			0
$691$	19.1163	+	33.1104i	0.727218	+	1.25958i	0.958055	+	0.286586i	$0.0925204\pi$
$691$	19.1163	+	33.1104i	0.727218	+	1.25958i	−0.230837	+	0.972993i	$0.574146\pi$
$692$	−40.6853			−1.54662
$693$		0			0
$694$	−6.01907			−0.228481
$695$	3.48346	+	6.03352i	0.132135	+	0.228865i
$696$		0			0
$697$	4.99895	−	8.65844i	0.189349	−	0.327962i
$698$	1.95440	−	3.38512i	0.0739752	−	0.128129i
$699$		0			0
$700$	−3.76229	−	6.51647i	−0.142201	−	0.246300i
$701$	2.09523			0.0791359			0.0395679	−	0.999217i	$-0.487402\pi$
$701$	2.09523			0.0791359			0.0395679	+	0.999217i	$0.487402\pi$
$702$		0			0
$703$	5.20159			0.196182
$704$	−6.10519	−	10.5745i	−0.230098	−	0.398542i
$705$		0			0
$706$	−5.25195	+	9.09665i	−0.197660	+	0.342357i
$707$	−23.3334	+	40.4146i	−0.877542	+	1.51995i
$708$		0			0
$709$	9.93869	+	17.2143i	0.373255	+	0.646497i	0.990064	−	0.140616i	$-0.0449082\pi$
$709$	9.93869	+	17.2143i	0.373255	+	0.646497i	−0.616809	+	0.787113i	$0.711575\pi$
$710$	7.13803			0.267885
$711$		0			0
$712$	30.1533			1.13004
$713$	−26.8183	−	46.4507i	−1.00435	−	1.73959i
$714$		0			0
$715$	−2.24265	+	3.88439i	−0.0838704	+	0.145268i
$716$	−12.2241	+	21.1727i	−0.456835	+	0.791261i
$717$		0			0
$718$	1.87667	+	3.25049i	0.0700367	+	0.121307i
$719$	15.9997			0.596687			0.298344	−	0.954459i	$-0.403566\pi$
$719$	15.9997			0.596687			0.298344	+	0.954459i	$0.403566\pi$
$720$		0			0
$721$	6.58807			0.245353
$722$	−3.83061	−	6.63482i	−0.142561	−	0.246922i
$723$		0			0
$724$	12.0175	−	20.8149i	0.446627	−	0.773581i
$725$	−0.375154	+	0.649786i	−0.0139329	+	0.0241325i
$726$		0			0
$727$	15.2862	+	26.4765i	0.566934	+	0.981959i	0.996867	+	0.0790977i	$0.0252039\pi$
$727$	15.2862	+	26.4765i	0.566934	+	0.981959i	−0.429933	+	0.902861i	$0.641463\pi$
$728$	7.95265			0.294745
$729$		0			0
$730$	−4.63113			−0.171406
$731$	5.96813	+	10.3371i	0.220739	+	0.382332i
$732$		0			0
$733$	−13.8308	+	23.9556i	−0.510852	+	0.884821i	0.489069	+	0.872245i	$0.337337\pi$
$733$	−13.8308	+	23.9556i	−0.510852	+	0.884821i	−0.999921	+	0.0125762i	$0.995997\pi$
$734$	5.33973	−	9.24868i	0.197093	−	0.341375i
$735$		0			0
$736$	13.1277	+	22.7378i	0.483893	+	0.838127i
$737$	57.8491			2.13090
$738$		0			0
$739$	−2.03805			−0.0749710			−0.0374855	−	0.999297i	$-0.511935\pi$
$739$	−2.03805			−0.0749710			−0.0374855	+	0.999297i	$0.511935\pi$
$740$	2.44292	+	4.23126i	0.0898034	+	0.155544i
$741$		0			0
$742$	0.0796739	−	0.137999i	0.00292492	−	0.00506611i
$743$	4.23249	−	7.33089i	0.155275	−	0.268944i	−0.777884	−	0.628408i	$-0.783707\pi$
$743$	4.23249	−	7.33089i	0.155275	−	0.268944i	0.933159	+	0.359463i	$0.117040\pi$
$744$		0			0
$745$	−4.11863	−	7.13367i	−0.150895	−	0.261358i
$746$	5.93575			0.217323
$747$		0			0
$748$	−12.3801			−0.452662
$749$	11.6520	+	20.1819i	0.425756	+	0.737431i
$750$		0			0
$751$	9.34897	−	16.1929i	0.341149	−	0.590887i	−0.643497	−	0.765448i	$-0.722517\pi$
$751$	9.34897	−	16.1929i	0.341149	−	0.590887i	0.984646	+	0.174561i	$0.0558506\pi$
$752$	−10.7298	+	18.5846i	−0.391277	+	0.677711i
$753$		0			0
$754$	−0.185362	−	0.321057i	−0.00675049	−	0.0116922i
$755$	−8.77188			−0.319241
$756$		0			0
$757$	−4.02963			−0.146459			−0.0732296	−	0.997315i	$-0.523331\pi$
$757$	−4.02963			−0.146459			−0.0732296	+	0.997315i	$0.523331\pi$
$758$	−0.849858	−	1.47200i	−0.0308682	−	0.0534653i
$759$		0			0
$760$	−1.73453	+	3.00429i	−0.0629179	+	0.108977i
$761$	8.21661	−	14.2316i	0.297852	−	0.515895i	−0.677792	−	0.735253i	$-0.737063\pi$
$761$	8.21661	−	14.2316i	0.297852	−	0.515895i	0.975644	+	0.219359i	$0.0703965\pi$
$762$		0			0
$763$	3.09547	+	5.36151i	0.112063	+	0.194100i
$764$	−13.7719			−0.498250
$765$		0			0
$766$	13.2906			0.480208
$767$	−5.72037	−	9.90797i	−0.206550	−	0.357756i
$768$		0			0
$769$	13.5335	−	23.4407i	0.488031	−	0.845295i	−0.511874	−	0.859060i	$-0.671049\pi$
$769$	13.5335	−	23.4407i	0.488031	−	0.845295i	0.999905	+	0.0137657i	$0.00438191\pi$
$770$	4.74857	−	8.22477i	0.171127	−	0.296400i
$771$		0			0
$772$	−18.1309	−	31.4037i	−0.652546	−	1.13024i
$773$	50.3630			1.81143			0.905716	−	0.423886i	$-0.139334\pi$
$773$	50.3630			1.81143			0.905716	+	0.423886i	$0.139334\pi$
$774$		0			0
$775$	10.2013			0.366443
$776$	13.9127	+	24.0975i	0.499436	+	0.865048i
$777$		0			0
$778$	−0.823942	+	1.42711i	−0.0295398	+	0.0511644i
$779$	−5.94466	+	10.2965i	−0.212990	+	0.368909i
$780$		0			0
$781$	−32.3988	−	56.1163i	−1.15932	−	2.00800i
$782$	4.08372			0.146034
$783$		0			0
$784$	29.4889			1.05317
$785$	6.69687	+	11.5993i	0.239021	+	0.413997i
$786$		0			0
$787$	17.9756	−	31.1346i	0.640760	−	1.10983i	−0.344503	−	0.938785i	$-0.611953\pi$
$787$	17.9756	−	31.1346i	0.640760	−	1.10983i	0.985263	−	0.171044i	$-0.0547141\pi$
$788$	−3.85077	+	6.66973i	−0.137178	+	0.237599i
$789$		0			0
$790$	−1.50679	−	2.60984i	−0.0536092	−	0.0928539i
$791$	19.1333			0.680302
$792$		0			0
$793$	11.9600			0.424714
$794$	0.189903	+	0.328921i	0.00673939	+	0.0116730i
$795$		0			0
$796$	−11.7569	+	20.3636i	−0.416713	+	0.721769i
$797$	−16.1395	+	27.9544i	−0.571690	+	0.990196i	0.424703	+	0.905333i	$0.360379\pi$
$797$	−16.1395	+	27.9544i	−0.571690	+	0.990196i	−0.996393	+	0.0848631i	$0.972955\pi$
$798$		0			0
$799$	6.50022	+	11.2587i	0.229961	+	0.398304i
$800$	−4.99361			−0.176551
$801$		0			0
$802$	14.6268			0.516489
$803$	21.0202	+	36.4081i	0.741787	+	1.28481i
$804$		0			0
$805$	11.2658	−	19.5130i	0.397069	−	0.687743i
$806$	−2.52022	+	4.36515i	−0.0887710	+	0.153756i
$807$		0			0
$808$	10.1044	+	17.5013i	0.355471	+	0.615693i
$809$	−42.4707			−1.49319			−0.746594	−	0.665279i	$-0.768312\pi$
$809$	−42.4707			−1.49319			−0.746594	+	0.665279i	$0.768312\pi$
$810$		0			0
$811$	−14.1284			−0.496116			−0.248058	−	0.968745i	$-0.579792\pi$
$811$	−14.1284			−0.496116			−0.248058	+	0.968745i	$0.579792\pi$
$812$	−2.82288	−	4.88937i	−0.0990636	−	0.171583i
$813$		0			0
$814$	−3.08333	+	5.34048i	−0.108071	+	0.187184i
$815$	0.121222	−	0.209963i	0.00424623	−	0.00735468i
$816$		0			0
$817$	−7.09719	−	12.2927i	−0.248299	−	0.430067i
$818$	8.00489			0.279885
$819$		0			0
$820$	−11.1676			−0.389990
$821$	−22.0898	−	38.2606i	−0.770939	−	1.33531i	−0.937049	−	0.349198i	$-0.886454\pi$
$821$	−22.0898	−	38.2606i	−0.770939	−	1.33531i	0.166110	−	0.986107i	$-0.446879\pi$
$822$		0			0
$823$	13.1598	−	22.7934i	0.458721	−	0.794529i	−0.540172	−	0.841554i	$-0.681641\pi$
$823$	13.1598	−	22.7934i	0.458721	−	0.794529i	0.998894	+	0.0470259i	$0.0149743\pi$
$824$	1.42646	−	2.47070i	0.0496932	−	0.0860711i
$825$		0			0
$826$	12.1123	+	20.9790i	0.421439	+	0.729954i
$827$	52.3359			1.81990			0.909949	−	0.414720i	$-0.136121\pi$
$827$	52.3359			1.81990			0.909949	+	0.414720i	$0.136121\pi$
$828$		0			0
$829$	−44.0239			−1.52901			−0.764506	−	0.644617i	$-0.777017\pi$
$829$	−44.0239			−1.52901			−0.764506	+	0.644617i	$0.777017\pi$
$830$	−0.151237	−	0.261951i	−0.00524953	−	0.00909245i
$831$		0			0
$832$	−1.36116	+	2.35759i	−0.0471896	+	0.0817347i
$833$	8.93229	−	15.4712i	0.309485	−	0.536045i
$834$		0			0
$835$	2.54305	+	4.40470i	0.0880059	+	0.152431i
$836$	14.7222			0.509179
$837$		0			0
$838$	5.63896			0.194795
$839$	3.99553	+	6.92046i	0.137941	+	0.238921i	0.926717	−	0.375760i	$-0.122618\pi$
$839$	3.99553	+	6.92046i	0.137941	+	0.238921i	−0.788776	+	0.614681i	$0.789285\pi$
$840$		0			0
$841$	14.2185	−	24.6272i	0.490294	−	0.849214i
$842$	2.56889	−	4.44944i	0.0885297	−	0.153338i
$843$		0			0
$844$	−5.32894	−	9.23000i	−0.183430	−	0.317710i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−39.0739			−1.34259
$848$	0.0976386	+	0.169115i	0.00335292	+	0.00580743i
$849$		0			0
$850$	−0.388349	+	0.672641i	−0.0133203	+	0.0230714i
$851$	−7.31510	+	12.6701i	−0.250758	+	0.434326i
$852$		0			0
$853$	8.36352	+	14.4860i	0.286361	+	0.495992i	0.972938	−	0.231065i	$-0.0742209\pi$
$853$	8.36352	+	14.4860i	0.286361	+	0.495992i	−0.686577	+	0.727057i	$0.740888\pi$
$854$	−25.3241			−0.866573
$855$		0			0
$856$	10.0917			0.344927
$857$	11.7587	+	20.3667i	0.401669	+	0.695712i	0.993928	−	0.110037i	$-0.0350968\pi$
$857$	11.7587	+	20.3667i	0.401669	+	0.695712i	−0.592258	+	0.805748i	$0.701763\pi$
$858$		0			0
$859$	9.92549	−	17.1914i	0.338653	−	0.586565i	−0.645526	−	0.763738i	$-0.723362\pi$
$859$	9.92549	−	17.1914i	0.338653	−	0.586565i	0.984180	+	0.177173i	$0.0566953\pi$
$860$	6.66637	−	11.5465i	0.227321	−	0.393732i
$861$		0			0
$862$	0.217395	+	0.376540i	0.00740451	+	0.0128250i
$863$	−11.3010			−0.384690			−0.192345	−	0.981327i	$-0.561609\pi$
$863$	−11.3010			−0.384690			−0.192345	+	0.981327i	$0.561609\pi$
$864$		0			0
$865$	23.1711			0.787839
$866$	7.77120	+	13.4601i	0.264076	+	0.457393i
$867$		0			0
$868$	−38.3804	+	66.4768i	−1.30272	+	2.25637i
$869$	−13.6783	+	23.6916i	−0.464006	+	0.803682i
$870$		0			0
$871$	−6.44874	−	11.1696i	−0.218507	−	0.378466i
$872$	2.68095			0.0907883
$873$		0			0
$874$	−4.85629			−0.164266
$875$	2.14269	+	3.71125i	0.0724362	+	0.125463i
$876$		0			0
$877$	−23.6189	+	40.9091i	−0.797552	+	1.38140i	0.123653	+	0.992325i	$0.460539\pi$
$877$	−23.6189	+	40.9091i	−0.797552	+	1.38140i	−0.921206	+	0.389076i	$0.872794\pi$
$878$	−1.42402	+	2.46647i	−0.0480583	+	0.0832395i
$879$		0			0
$880$	5.81927	+	10.0793i	0.196167	+	0.339772i
$881$	−5.64812			−0.190290			−0.0951450	−	0.995463i	$-0.530331\pi$
$881$	−5.64812			−0.190290			−0.0951450	+	0.995463i	$0.530331\pi$
$882$		0			0
$883$	16.3032			0.548645			0.274323	−	0.961638i	$-0.411546\pi$
$883$	16.3032			0.548645			0.274323	+	0.961638i	$0.411546\pi$
$884$	1.38008	+	2.39036i	0.0464170	+	0.0803967i
$885$		0			0
$886$	−1.01993	+	1.76657i	−0.0342652	+	0.0593490i
$887$	−18.8459	+	32.6420i	−0.632783	+	1.09601i	0.354197	+	0.935171i	$0.384754\pi$
$887$	−18.8459	+	32.6420i	−0.632783	+	1.09601i	−0.986980	+	0.160842i	$0.948579\pi$
$888$		0			0
$889$	−8.40143	−	14.5517i	−0.281775	−	0.488048i
$890$	−8.02832			−0.269110
$891$		0			0
$892$	40.3642			1.35149
$893$	−7.72993	−	13.3886i	−0.258672	−	0.448034i
$894$		0			0
$895$	6.96183	−	12.0582i	0.232708	−	0.403063i
$896$	24.2816	−	42.0570i	0.811192	−	1.40503i
$897$		0			0
$898$	7.49548	+	12.9826i	0.250127	+	0.433233i
$899$	7.65416			0.255280
$900$		0			0
$901$	0.118300			0.00394116
$902$	−7.04759	−	12.2068i	−0.234659	−	0.406442i
$903$		0			0
$904$	4.14278	−	7.17550i	0.137787	−	0.238654i
$905$	−6.84419	+	11.8545i	−0.227509	+	0.394057i
$906$		0			0
$907$	−11.9264	−	20.6571i	−0.396009	−	0.685908i	0.597220	−	0.802077i	$-0.296272\pi$
$907$	−11.9264	−	20.6571i	−0.396009	−	0.685908i	−0.993229	+	0.116169i	$0.962939\pi$
$908$	−33.0712			−1.09751
$909$		0			0
$910$	−2.11739			−0.0701908
$911$	23.3805	+	40.4962i	0.774630	+	1.34170i	0.935002	+	0.354642i	$0.115397\pi$
$911$	23.3805	+	40.4962i	0.774630	+	1.34170i	−0.160372	+	0.987057i	$0.551269\pi$
$912$		0			0
$913$	−1.37290	+	2.37794i	−0.0454364	+	0.0786982i
$914$	−2.09072	+	3.62124i	−0.0691550	+	0.119780i
$915$		0			0
$916$	−4.74897	−	8.22546i	−0.156910	−	0.271777i
$917$	3.31872			0.109594
$918$		0			0
$919$	−12.3909			−0.408738			−0.204369	−	0.978894i	$-0.565514\pi$
$919$	−12.3909			−0.408738			−0.204369	+	0.978894i	$0.565514\pi$
$920$	−4.87860	−	8.44999i	−0.160843	−	0.278588i
$921$		0			0
$922$	−4.35566	+	7.54422i	−0.143446	+	0.248456i
$923$	−7.22332	+	12.5112i	−0.237758	+	0.411810i
$924$		0			0
$925$	−1.39129	−	2.40978i	−0.0457452	−	0.0792330i
$926$	0.619787			0.0203675
$927$		0			0
$928$	−3.74675			−0.122993
$929$	5.11063	+	8.85188i	0.167674	+	0.290421i	0.937602	−	0.347711i	$-0.113041\pi$
$929$	5.11063	+	8.85188i	0.167674	+	0.290421i	−0.769927	+	0.638132i	$0.779708\pi$
$930$		0			0
$931$	−10.6221	+	18.3980i	−0.348126	+	0.602971i
$932$	6.54881	−	11.3429i	0.214513	−	0.371548i
$933$		0			0
$934$	−2.79555	−	4.84204i	−0.0914733	−	0.158436i
$935$	7.05071			0.230583
$936$		0			0
$937$	23.8520			0.779212			0.389606	−	0.920982i	$-0.372611\pi$
$937$	23.8520			0.779212			0.389606	+	0.920982i	$0.372611\pi$
$938$	13.6545	+	23.6503i	0.445836	+	0.772210i
$939$		0			0
$940$	7.26070	−	12.5759i	0.236818	−	0.410181i
$941$	−12.6596	+	21.9271i	−0.412692	+	0.714804i	−0.995183	−	0.0980332i	$-0.968745\pi$
$941$	−12.6596	+	21.9271i	−0.412692	+	0.714804i	0.582491	+	0.812837i	$0.302078\pi$
$942$		0			0
$943$	−16.7202	−	28.9602i	−0.544485	−	0.943075i
$944$	−29.6866			−0.966216
$945$		0			0
$946$	16.8279			0.547122
$947$	−11.5509	−	20.0068i	−0.375355	−	0.650134i	0.615025	−	0.788508i	$-0.289146\pi$
$947$	−11.5509	−	20.0068i	−0.375355	−	0.650134i	−0.990380	+	0.138374i	$0.955813\pi$
$948$		0			0
$949$	4.68647	−	8.11720i	0.152129	−	0.263495i
$950$	0.461818	−	0.799892i	0.0149833	−	0.0259519i
$951$		0			0
$952$	−6.25062	−	10.8264i	−0.202584	−	0.350885i
$953$	−46.4511			−1.50470			−0.752350	−	0.658764i	$-0.771080\pi$
$953$	−46.4511			−1.50470			−0.752350	+	0.658764i	$0.771080\pi$
$954$		0			0
$955$	7.84336			0.253805
$956$	−6.74318	−	11.6795i	−0.218090	−	0.377743i
$957$		0			0
$958$	8.24734	−	14.2848i	0.266460	−	0.461521i
$959$	−10.0880	+	17.4729i	−0.325759	+	0.564231i
$960$		0			0
$961$	−36.5337	−	63.2783i	−1.17851	−	2.04124i
$962$	1.37486			0.0443272
$963$		0			0
$964$	−51.4120			−1.65587
$965$	10.3259	+	17.8850i	0.332402	+	0.575737i
$966$		0			0
$967$	3.87128	−	6.70525i	0.124492	−	0.215626i	−0.797042	−	0.603923i	$-0.793603\pi$
$967$	3.87128	−	6.70525i	0.124492	−	0.215626i	0.921534	+	0.388297i	$0.126937\pi$
$968$	−8.46035	+	14.6538i	−0.271926	+	0.470990i
$969$		0			0
$970$	−3.70425	−	6.41595i	−0.118936	−	0.206004i
$971$	2.78737			0.0894511			0.0447256	−	0.998999i	$-0.485759\pi$
$971$	2.78737			0.0894511			0.0447256	+	0.998999i	$0.485759\pi$
$972$		0			0
$973$	29.8559			0.957136
$974$	−10.4453	−	18.0919i	−0.334690	−	0.579701i
$975$		0			0
$976$	15.5171	−	26.8763i	0.496689	−	0.860290i
$977$	−5.73927	+	9.94071i	−0.183616	+	0.318031i	−0.943109	−	0.332483i	$-0.892113\pi$
$977$	−5.73927	+	9.94071i	−0.183616	+	0.318031i	0.759494	+	0.650515i	$0.225447\pi$
$978$		0			0
$979$	36.4397	+	63.1154i	1.16462	+	2.01718i
$980$	−19.9546			−0.637427
$981$		0			0
$982$	5.66517			0.180783
$983$	−14.4750	−	25.0714i	−0.461679	−	0.799652i	0.537366	−	0.843349i	$-0.319420\pi$
$983$	−14.4750	−	25.0714i	−0.461679	−	0.799652i	−0.999045	+	0.0436975i	$0.986086\pi$
$984$		0			0
$985$	2.19308	−	3.79853i	0.0698775	−	0.121031i
$986$	−0.291382	+	0.504688i	−0.00927949	+	0.0160725i
$987$		0			0
$988$	−1.64116	−	2.84258i	−0.0522123	−	0.0904344i
$989$	39.9237			1.26950
$990$		0			0
$991$	−5.40688			−0.171755			−0.0858776	−	0.996306i	$-0.527369\pi$
$991$	−5.40688			−0.171755			−0.0858776	+	0.996306i	$0.527369\pi$
$992$	25.4708	+	44.1167i	0.808697	+	1.40071i
$993$		0			0
$994$	15.2946	−	26.4910i	0.485115	−	0.840244i
$995$	6.69579	−	11.5974i	0.212271	−	0.367664i
$996$		0			0
$997$	18.4622	+	31.9774i	0.584703	+	1.01273i	0.994912	+	0.100743i	$0.0321221\pi$
$997$	18.4622	+	31.9774i	0.584703	+	1.01273i	−0.410210	+	0.911991i	$0.634545\pi$
$998$	−3.31466			−0.104924
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.1171.4		16
3.2	odd	2		585.2.i.e.391.5	yes	16
9.2	odd	6		585.2.i.e.196.5	✓	16
9.4	even	3		5265.2.a.ba.1.5		8
9.5	odd	6		5265.2.a.bf.1.4		8
9.7	even	3	inner	1755.2.i.f.586.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.5	✓	16	9.2	odd	6
585.2.i.e.391.5	yes	16	3.2	odd	2
1755.2.i.f.586.4		16	9.7	even	3	inner
1755.2.i.f.1171.4		16	1.1	even	1	trivial
5265.2.a.ba.1.5		8	9.4	even	3
5265.2.a.bf.1.4		8	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.247048 + 0.427900i) q^{2} +(0.877935 - 1.52063i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.14269 + 3.71125i) q^{7} +1.85576 q^{8} +O(q^{10})\)	\(q+(0.247048 + 0.427900i) q^{2} +(0.877935 - 1.52063i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.14269 + 3.71125i) q^{7} +1.85576 q^{8} -0.494096 q^{10} +(2.24265 + 3.88439i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.05870 + 1.83371i) q^{14} +(-1.29741 - 2.24718i) q^{16} -1.57196 q^{17} +1.86934 q^{19} +(0.877935 + 1.52063i) q^{20} +(-1.10808 + 1.91926i) q^{22} +(-2.62890 + 4.55339i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.494096 q^{26} +7.52458 q^{28} +(-0.375154 - 0.649786i) q^{29} +(-5.10067 + 8.83463i) q^{31} +(2.49680 - 4.32459i) q^{32} +(-0.388349 - 0.672641i) q^{34} -4.28539 q^{35} +2.78257 q^{37} +(0.461818 + 0.799892i) q^{38} +(-0.927880 + 1.60713i) q^{40} +(-3.18008 + 5.50806i) q^{41} +(-3.79662 - 6.57594i) q^{43} +7.87560 q^{44} -2.59786 q^{46} +(-4.13510 - 7.16221i) q^{47} +(-5.68226 + 9.84197i) q^{49} +(0.247048 - 0.427900i) q^{50} +(-0.877935 - 1.52063i) q^{52} -0.0752567 q^{53} -4.48530 q^{55} +(3.97632 + 6.88719i) q^{56} +(0.185362 - 0.321057i) q^{58} +(5.72037 - 9.90797i) q^{59} +(5.98002 + 10.3577i) q^{61} -5.04044 q^{62} -2.72231 q^{64} +(0.500000 + 0.866025i) q^{65} +(6.44874 - 11.1696i) q^{67} +(-1.38008 + 2.39036i) q^{68} +(-1.05870 - 1.83371i) q^{70} -14.4466 q^{71} +9.37293 q^{73} +(0.687429 + 1.19066i) q^{74} +(1.64116 - 2.84258i) q^{76} +(-9.61062 + 16.6461i) q^{77} +(3.04959 + 5.28205i) q^{79} +2.59482 q^{80} -3.14253 q^{82} +(0.306089 + 0.530162i) q^{83} +(0.785980 - 1.36136i) q^{85} +(1.87589 - 3.24914i) q^{86} +(4.16182 + 7.20849i) q^{88} +16.2485 q^{89} +4.28539 q^{91} +(4.61600 + 7.99515i) q^{92} +(2.04314 - 3.53882i) q^{94} +(-0.934672 + 1.61890i) q^{95} +(7.49702 + 12.9852i) q^{97} -5.61517 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

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