LMFDB - Embedded newform 1755.2.i.e.586.5

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} - x^{15} + 11 x^{14} - 4 x^{13} + 74 x^{12} - 18 x^{11} + 289 x^{10} - 4 x^{9} + 784 x^{8} + \cdots + 81 $ x^16 - x^15 + 11x^14 - 4x^13 + 74x^12 - 18x^11 + 289x^10 - 4x^9 + 784x^8 - 9x^7 + 1221x^6 + 133x^5 + 1245x^4 - 14x^3 + 391x^2 + 63x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			586.5
Root			$-0.237622 + 0.411573i$ of defining polynomial
Character	$\chi$	$=$	1755.586
Dual form			1755.2.i.e.1171.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.237622 - 0.411573i) q^{2} +(0.887072 + 1.53645i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.24774 + 2.16115i) q^{7} +1.79364 q^{8} +O(q^{10})$	\(q+(0.237622 - 0.411573i) q^{2} +(0.887072 + 1.53645i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.24774 + 2.16115i) q^{7} +1.79364 q^{8} +0.475244 q^{10} +(-1.50314 + 2.60351i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.592980 + 1.02707i) q^{14} +(-1.34794 + 2.33469i) q^{16} +1.86238 q^{17} -6.61778 q^{19} +(-0.887072 + 1.53645i) q^{20} +(0.714357 + 1.23730i) q^{22} +(2.00144 + 3.46660i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.475244 q^{26} -4.42734 q^{28} +(3.77429 - 6.53727i) q^{29} +(0.552970 + 0.957772i) q^{31} +(2.43424 + 4.21622i) q^{32} +(0.442542 - 0.766505i) q^{34} -2.49548 q^{35} -10.2065 q^{37} +(-1.57253 + 2.72370i) q^{38} +(0.896819 + 1.55334i) q^{40} +(-1.96768 - 3.40812i) q^{41} +(-3.18735 + 5.52065i) q^{43} -5.33357 q^{44} +1.90235 q^{46} +(-0.0661868 + 0.114639i) q^{47} +(0.386290 + 0.669074i) q^{49} +(0.237622 + 0.411573i) q^{50} +(0.887072 - 1.53645i) q^{52} +6.91685 q^{53} -3.00628 q^{55} +(-2.23799 + 3.87632i) q^{56} +(-1.79371 - 3.10680i) q^{58} +(0.402461 + 0.697082i) q^{59} +(2.39312 - 4.14500i) q^{61} +0.525591 q^{62} -3.07804 q^{64} +(0.500000 - 0.866025i) q^{65} +(-2.07699 - 3.59746i) q^{67} +(1.65206 + 2.86146i) q^{68} +(-0.592980 + 1.02707i) q^{70} +5.44325 q^{71} -6.33787 q^{73} +(-2.42528 + 4.20071i) q^{74} +(-5.87045 - 10.1679i) q^{76} +(-3.75105 - 6.49701i) q^{77} +(2.31771 - 4.01440i) q^{79} -2.69587 q^{80} -1.87025 q^{82} +(-7.26757 + 12.5878i) q^{83} +(0.931190 + 1.61287i) q^{85} +(1.51477 + 2.62365i) q^{86} +(-2.69609 + 4.66976i) q^{88} -5.77819 q^{89} +2.49548 q^{91} +(-3.55085 + 6.15025i) q^{92} +(0.0314549 + 0.0544814i) q^{94} +(-3.30889 - 5.73117i) q^{95} +(-3.03607 + 5.25864i) q^{97} +0.367164 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 5 q^{4} + 8 q^{5} + 6 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q - q^2 - 5 * q^4 + 8 * q^5 + 6 * q^7 + 12 * q^8	$ 16 q - q^{2} - 5 q^{4} + 8 q^{5} + 6 q^{7} + 12 q^{8} - 2 q^{10} - 9 q^{11} - 8 q^{13} + 3 q^{14} + 13 q^{16} - 12 q^{17} - 22 q^{19} + 5 q^{20} + 4 q^{22} - 3 q^{23} - 8 q^{25} + 2 q^{26} - 26 q^{28} - 8 q^{29} + 18 q^{31} - 3 q^{32} + 9 q^{34} + 12 q^{35} - 36 q^{37} + 8 q^{38} + 6 q^{40} + 17 q^{41} + 17 q^{43} - 10 q^{44} + 6 q^{46} - 11 q^{47} + 16 q^{49} - q^{50} - 5 q^{52} - 20 q^{53} - 18 q^{55} + q^{56} + 10 q^{58} - 7 q^{59} + 21 q^{61} + 58 q^{62} - 20 q^{64} + 8 q^{65} + 13 q^{67} + 16 q^{68} - 3 q^{70} + 68 q^{71} - 32 q^{73} + 4 q^{74} + 2 q^{76} - 18 q^{77} + 37 q^{79} + 26 q^{80} + 2 q^{82} - 3 q^{83} - 6 q^{85} + 2 q^{86} + 19 q^{88} - 28 q^{89} - 12 q^{91} + 14 q^{92} + 44 q^{94} - 11 q^{95} + 17 q^{97} - 90 q^{98}+O(q^{100}) $ 16 * q - q^2 - 5 * q^4 + 8 * q^5 + 6 * q^7 + 12 * q^8 - 2 * q^10 - 9 * q^11 - 8 * q^13 + 3 * q^14 + 13 * q^16 - 12 * q^17 - 22 * q^19 + 5 * q^20 + 4 * q^22 - 3 * q^23 - 8 * q^25 + 2 * q^26 - 26 * q^28 - 8 * q^29 + 18 * q^31 - 3 * q^32 + 9 * q^34 + 12 * q^35 - 36 * q^37 + 8 * q^38 + 6 * q^40 + 17 * q^41 + 17 * q^43 - 10 * q^44 + 6 * q^46 - 11 * q^47 + 16 * q^49 - q^50 - 5 * q^52 - 20 * q^53 - 18 * q^55 + q^56 + 10 * q^58 - 7 * q^59 + 21 * q^61 + 58 * q^62 - 20 * q^64 + 8 * q^65 + 13 * q^67 + 16 * q^68 - 3 * q^70 + 68 * q^71 - 32 * q^73 + 4 * q^74 + 2 * q^76 - 18 * q^77 + 37 * q^79 + 26 * q^80 + 2 * q^82 - 3 * q^83 - 6 * q^85 + 2 * q^86 + 19 * q^88 - 28 * q^89 - 12 * q^91 + 14 * q^92 + 44 * q^94 - 11 * q^95 + 17 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.237622	−	0.411573i	0.168024	−	0.291026i	−0.769701	−	0.638404i	$-0.779595\pi$
$2$	0.237622	−	0.411573i	0.168024	−	0.291026i	0.937725	+	0.347378i	$0.112928\pi$
$3$		0			0
$3$		0			0
$4$	0.887072	+	1.53645i	0.443536	+	0.768227i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.24774	+	2.16115i	−0.471601	+	0.816838i	−0.999472	−	0.0324871i	$-0.989657\pi$
$7$	−1.24774	+	2.16115i	−0.471601	+	0.816838i	0.527871	+	0.849325i	$0.322991\pi$
$8$	1.79364			0.634147
$9$		0			0
$10$	0.475244			0.150285
$11$	−1.50314	+	2.60351i	−0.453213	+	0.784989i	−0.998584	−	0.0532067i	$-0.983056\pi$
$11$	−1.50314	+	2.60351i	−0.453213	+	0.784989i	0.545370	+	0.838195i	$0.316389\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	0.592980	+	1.02707i	0.158481	+	0.274497i
$15$		0			0
$16$	−1.34794	+	2.33469i	−0.336984	+	0.583674i
$17$	1.86238			0.451693			0.225847	−	0.974163i	$-0.427485\pi$
$17$	1.86238			0.451693			0.225847	+	0.974163i	$0.427485\pi$
$18$		0			0
$19$	−6.61778			−1.51822			−0.759112	−	0.650960i	$-0.774366\pi$
$19$	−6.61778			−1.51822			−0.759112	+	0.650960i	$0.774366\pi$
$20$	−0.887072	+	1.53645i	−0.198355	+	0.343561i
$21$		0			0
$22$	0.714357	+	1.23730i	0.152301	+	0.263794i
$23$	2.00144	+	3.46660i	0.417330	+	0.722836i	0.995670	−	0.0929594i	$-0.0296327\pi$
$23$	2.00144	+	3.46660i	0.417330	+	0.722836i	−0.578340	+	0.815796i	$0.696299\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.475244			−0.0932029
$27$		0			0
$28$	−4.42734			−0.836689
$29$	3.77429	−	6.53727i	0.700869	−	1.21394i	−0.267293	−	0.963615i	$-0.586129\pi$
$29$	3.77429	−	6.53727i	0.700869	−	1.21394i	0.968162	−	0.250325i	$-0.0805375\pi$
$30$		0			0
$31$	0.552970	+	0.957772i	0.0993164	+	0.172021i	0.911402	−	0.411517i	$-0.135001\pi$
$31$	0.552970	+	0.957772i	0.0993164	+	0.172021i	−0.812086	+	0.583538i	$0.801668\pi$
$32$	2.43424	+	4.21622i	0.430316	+	0.745329i
$33$		0			0
$34$	0.442542	−	0.766505i	0.0758953	−	0.131455i
$35$	−2.49548			−0.421813
$36$		0			0
$37$	−10.2065			−1.67793			−0.838966	−	0.544183i	$-0.816840\pi$
$37$	−10.2065			−1.67793			−0.838966	+	0.544183i	$0.816840\pi$
$38$	−1.57253	+	2.72370i	−0.255098	+	0.441843i
$39$		0			0
$40$	0.896819	+	1.55334i	0.141799	+	0.245604i
$41$	−1.96768	−	3.40812i	−0.307299	−	0.532258i	0.670471	−	0.741936i	$-0.266092\pi$
$41$	−1.96768	−	3.40812i	−0.307299	−	0.532258i	−0.977771	+	0.209677i	$0.932759\pi$
$42$		0			0
$43$	−3.18735	+	5.52065i	−0.486066	+	0.841891i	−0.999872	−	0.0160156i	$-0.994902\pi$
$43$	−3.18735	+	5.52065i	−0.486066	+	0.841891i	0.513806	+	0.857907i	$0.328235\pi$
$44$	−5.33357			−0.804066
$45$		0			0
$46$	1.90235			0.280486
$47$	−0.0661868	+	0.114639i	−0.00965434	+	0.0167218i	−0.870812	−	0.491616i	$-0.836406\pi$
$47$	−0.0661868	+	0.114639i	−0.00965434	+	0.0167218i	0.861158	+	0.508338i	$0.169740\pi$
$48$		0			0
$49$	0.386290	+	0.669074i	0.0551843	+	0.0955820i
$50$	0.237622	+	0.411573i	0.0336048	+	0.0582052i
$51$		0			0
$52$	0.887072	−	1.53645i	0.123015	−	0.213068i
$53$	6.91685			0.950102			0.475051	−	0.879958i	$-0.342430\pi$
$53$	6.91685			0.950102			0.475051	+	0.879958i	$0.342430\pi$
$54$		0			0
$55$	−3.00628			−0.405366
$56$	−2.23799	+	3.87632i	−0.299064	+	0.517995i
$57$		0			0
$58$	−1.79371	−	3.10680i	−0.235526	−	0.407942i
$59$	0.402461	+	0.697082i	0.0523959	+	0.0907524i	0.891034	−	0.453937i	$-0.149981\pi$
$59$	0.402461	+	0.697082i	0.0523959	+	0.0907524i	−0.838638	+	0.544689i	$0.816648\pi$
$60$		0			0
$61$	2.39312	−	4.14500i	0.306407	−	0.530713i	−0.671166	−	0.741307i	$-0.734206\pi$
$61$	2.39312	−	4.14500i	0.306407	−	0.530713i	0.977574	+	0.210594i	$0.0675397\pi$
$62$	0.525591			0.0667501
$63$		0			0
$64$	−3.07804			−0.384754
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$		0			0
$67$	−2.07699	−	3.59746i	−0.253745	−	0.439499i	0.710809	−	0.703385i	$-0.248329\pi$
$67$	−2.07699	−	3.59746i	−0.253745	−	0.439499i	−0.964554	+	0.263886i	$0.914996\pi$
$68$	1.65206	+	2.86146i	0.200342	+	0.347003i
$69$		0			0
$70$	−0.592980	+	1.02707i	−0.0708747	+	0.122759i
$71$	5.44325			0.645995			0.322997	−	0.946400i	$-0.395310\pi$
$71$	5.44325			0.645995			0.322997	+	0.946400i	$0.395310\pi$
$72$		0			0
$73$	−6.33787			−0.741792			−0.370896	−	0.928674i	$-0.620949\pi$
$73$	−6.33787			−0.741792			−0.370896	+	0.928674i	$0.620949\pi$
$74$	−2.42528	+	4.20071i	−0.281933	+	0.488322i
$75$		0			0
$76$	−5.87045	−	10.1679i	−0.673387	−	1.16634i
$77$	−3.75105	−	6.49701i	−0.427472	−	0.740403i
$78$		0			0
$79$	2.31771	−	4.01440i	0.260763	−	0.451655i	−0.705682	−	0.708529i	$-0.749359\pi$
$79$	2.31771	−	4.01440i	0.260763	−	0.451655i	0.966445	+	0.256874i	$0.0826925\pi$
$80$	−2.69587			−0.301408
$81$		0			0
$82$	−1.87025			−0.206535
$83$	−7.26757	+	12.5878i	−0.797719	+	1.38169i	0.123379	+	0.992360i	$0.460627\pi$
$83$	−7.26757	+	12.5878i	−0.797719	+	1.38169i	−0.921098	+	0.389331i	$0.872706\pi$
$84$		0			0
$85$	0.931190	+	1.61287i	0.101002	+	0.174940i
$86$	1.51477	+	2.62365i	0.163341	+	0.282916i
$87$		0			0
$88$	−2.69609	+	4.66976i	−0.287404	+	0.497798i
$89$	−5.77819			−0.612487			−0.306243	−	0.951953i	$-0.599072\pi$
$89$	−5.77819			−0.612487			−0.306243	+	0.951953i	$0.599072\pi$
$90$		0			0
$91$	2.49548			0.261597
$92$	−3.55085	+	6.15025i	−0.370201	+	0.641208i
$93$		0			0
$94$	0.0314549	+	0.0544814i	0.00324432	+	0.00561933i
$95$	−3.30889	−	5.73117i	−0.339485	−	0.588005i
$96$		0			0
$97$	−3.03607	+	5.25864i	−0.308267	+	0.533934i	−0.977983	−	0.208683i	$-0.933082\pi$
$97$	−3.03607	+	5.25864i	−0.308267	+	0.533934i	0.669717	+	0.742617i	$0.266416\pi$
$98$	0.367164			0.0370891
$99$		0			0
$100$	−1.77414			−0.177414
$101$	−2.32176	+	4.02141i	−0.231024	+	0.400146i	−0.958110	−	0.286401i	$-0.907541\pi$
$101$	−2.32176	+	4.02141i	−0.231024	+	0.400146i	0.727086	+	0.686547i	$0.240874\pi$
$102$		0			0
$103$	6.38750	+	11.0635i	0.629379	+	1.09012i	0.987677	+	0.156509i	$0.0500239\pi$
$103$	6.38750	+	11.0635i	0.629379	+	1.09012i	−0.358298	+	0.933607i	$0.616643\pi$
$104$	−0.896819	−	1.55334i	−0.0879403	−	0.152317i
$105$		0			0
$106$	1.64359	−	2.84679i	0.159640	−	0.276505i
$107$	−10.4025			−1.00565			−0.502826	−	0.864388i	$-0.667706\pi$
$107$	−10.4025			−1.00565			−0.502826	+	0.864388i	$0.667706\pi$
$108$		0			0
$109$	18.4320			1.76546			0.882732	−	0.469877i	$-0.155702\pi$
$109$	18.4320			1.76546			0.882732	+	0.469877i	$0.155702\pi$
$110$	−0.714357	+	1.23730i	−0.0681113	+	0.117972i
$111$		0			0
$112$	−3.36375	−	5.82618i	−0.317844	−	0.550522i
$113$	−8.00969	−	13.8732i	−0.753489	−	1.30508i	−0.946122	−	0.323810i	$-0.895036\pi$
$113$	−8.00969	−	13.8732i	−0.753489	−	1.30508i	0.192634	−	0.981271i	$-0.438297\pi$
$114$		0			0
$115$	−2.00144	+	3.46660i	−0.186636	+	0.323262i
$116$	13.3923			1.24344
$117$		0			0
$118$	0.382534			0.0352151
$119$	−2.32377	+	4.02488i	−0.213019	+	0.368960i
$120$		0			0
$121$	0.981147	+	1.69940i	0.0891952	+	0.154491i
$122$	−1.13731	−	1.96989i	−0.102968	−	0.178345i
$123$		0			0
$124$	−0.981048	+	1.69923i	−0.0881008	+	0.152595i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.77944			−0.246636			−0.123318	−	0.992367i	$-0.539353\pi$
$127$	−2.77944			−0.246636			−0.123318	+	0.992367i	$0.539353\pi$
$128$	−5.59988	+	9.69928i	−0.494964	+	0.857303i
$129$		0			0
$130$	−0.237622	−	0.411573i	−0.0208408	−	0.0360973i
$131$	7.23156	+	12.5254i	0.631824	+	1.09435i	0.987179	+	0.159620i	$0.0510269\pi$
$131$	7.23156	+	12.5254i	0.631824	+	1.09435i	−0.355354	+	0.934732i	$0.615640\pi$
$132$		0			0
$133$	8.25727	−	14.3020i	0.715996	−	1.24014i
$134$	−1.97416			−0.170541
$135$		0			0
$136$	3.34043			0.286440
$137$	9.09964	−	15.7610i	0.777434	−	1.34656i	−0.155982	−	0.987760i	$-0.549854\pi$
$137$	9.09964	−	15.7610i	0.777434	−	1.34656i	0.933416	−	0.358796i	$-0.116813\pi$
$138$		0			0
$139$	11.3373	+	19.6368i	0.961618	+	1.66557i	0.718439	+	0.695590i	$0.244857\pi$
$139$	11.3373	+	19.6368i	0.961618	+	1.66557i	0.243179	+	0.969982i	$0.421810\pi$
$140$	−2.21367	−	3.83419i	−0.187089	−	0.324048i
$141$		0			0
$142$	1.29343	−	2.24029i	0.108543	−	0.188001i
$143$	3.00628			0.251398
$144$		0			0
$145$	7.54859			0.626876
$146$	−1.50602	+	2.60850i	−0.124639	+	0.215881i
$147$		0			0
$148$	−9.05387	−	15.6818i	−0.744223	−	1.28903i
$149$	9.19585	+	15.9277i	0.753353	+	1.30485i	0.946189	+	0.323615i	$0.104898\pi$
$149$	9.19585	+	15.9277i	0.753353	+	1.30485i	−0.192836	+	0.981231i	$0.561768\pi$
$150$		0			0
$151$	3.82184	−	6.61962i	0.311017	−	0.538697i	−0.667566	−	0.744551i	$-0.732664\pi$
$151$	3.82184	−	6.61962i	0.311017	−	0.538697i	0.978583	+	0.205854i	$0.0659971\pi$
$152$	−11.8699			−0.962776
$153$		0			0
$154$	−3.56533			−0.287302
$155$	−0.552970	+	0.957772i	−0.0444156	+	0.0769301i
$156$		0			0
$157$	4.74578	+	8.21993i	0.378754	+	0.656022i	0.990881	−	0.134738i	$-0.0430192\pi$
$157$	4.74578	+	8.21993i	0.378754	+	0.656022i	−0.612127	+	0.790760i	$0.709686\pi$
$158$	−1.10148	−	1.90782i	−0.0876289	−	0.151778i
$159$		0			0
$160$	−2.43424	+	4.21622i	−0.192443	+	0.333321i
$161$	−9.98912			−0.787253
$162$		0			0
$163$	3.32480			0.260418			0.130209	−	0.991487i	$-0.458435\pi$
$163$	3.32480			0.260418			0.130209	+	0.991487i	$0.458435\pi$
$164$	3.49094	−	6.04649i	0.272597	−	0.472151i
$165$		0			0
$166$	3.45386	+	5.98227i	0.268072	+	0.464314i
$167$	1.13639	+	1.96829i	0.0879365	+	0.152311i	0.906639	−	0.421908i	$-0.138639\pi$
$167$	1.13639	+	1.96829i	0.0879365	+	0.152311i	−0.818702	+	0.574218i	$0.805306\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	0.885084			0.0678828
$171$		0			0
$172$	−11.3096			−0.862351
$173$	−7.19723	+	12.4660i	−0.547195	+	0.947770i	0.451270	+	0.892388i	$0.350971\pi$
$173$	−7.19723	+	12.4660i	−0.547195	+	0.947770i	−0.998465	+	0.0553826i	$0.982362\pi$
$174$		0			0
$175$	−1.24774	−	2.16115i	−0.0943203	−	0.163368i
$176$	−4.05227	−	7.01874i	−0.305451	−	0.529057i
$177$		0			0
$178$	−1.37302	+	2.37815i	−0.102912	+	0.178250i
$179$	19.8554			1.48407			0.742033	−	0.670364i	$-0.233862\pi$
$179$	19.8554			1.48407			0.742033	+	0.670364i	$0.233862\pi$
$180$		0			0
$181$	−20.2602			−1.50593			−0.752964	−	0.658061i	$-0.771377\pi$
$181$	−20.2602			−1.50593			−0.752964	+	0.658061i	$0.771377\pi$
$182$	0.592980	−	1.02707i	0.0439546	−	0.0761317i
$183$		0			0
$184$	3.58986	+	6.21783i	0.264648	+	0.458384i
$185$	−5.10323	−	8.83906i	−0.375197	−	0.649861i
$186$		0			0
$187$	−2.79942	+	4.84873i	−0.204714	+	0.354574i
$188$	−0.234850			−0.0171282
$189$		0			0
$190$	−3.14506			−0.228167
$191$	7.21227	−	12.4920i	0.521862	−	0.903891i	−0.477815	−	0.878461i	$-0.658571\pi$
$191$	7.21227	−	12.4920i	0.521862	−	0.903891i	0.999677	−	0.0254305i	$-0.00809564\pi$
$192$		0			0
$193$	12.1134	+	20.9810i	0.871942	+	1.51025i	0.859985	+	0.510319i	$0.170473\pi$
$193$	12.1134	+	20.9810i	0.871942	+	1.51025i	0.0119565	+	0.999929i	$0.496194\pi$
$194$	1.44287	+	2.49913i	0.103592	+	0.179427i
$195$		0			0
$196$	−0.685334	+	1.18703i	−0.0489524	+	0.0847881i
$197$	−1.94373			−0.138485			−0.0692426	−	0.997600i	$-0.522058\pi$
$197$	−1.94373			−0.138485			−0.0692426	+	0.997600i	$0.522058\pi$
$198$		0			0
$199$	7.57304			0.536839			0.268419	−	0.963302i	$-0.413499\pi$
$199$	7.57304			0.536839			0.268419	+	0.963302i	$0.413499\pi$
$200$	−0.896819	+	1.55334i	−0.0634147	+	0.109837i
$201$		0			0
$202$	1.10340	+	1.91115i	0.0776352	+	0.134468i
$203$	9.41868	+	16.3136i	0.661061	+	1.14499i
$204$		0			0
$205$	1.96768	−	3.40812i	0.137429	−	0.238033i
$206$	6.07123			0.423003
$207$		0			0
$208$	2.69587			0.186925
$209$	9.94745	−	17.2295i	0.688079	−	1.19179i
$210$		0			0
$211$	−7.58831	−	13.1433i	−0.522401	−	0.904824i	−0.999660	−	0.0260620i	$-0.991703\pi$
$211$	−7.58831	−	13.1433i	−0.522401	−	0.904824i	0.477260	−	0.878762i	$-0.341630\pi$
$212$	6.13574	+	10.6274i	0.421405	+	0.729894i
$213$		0			0
$214$	−2.47187	+	4.28141i	−0.168974	+	0.292671i
$215$	−6.37469			−0.434751
$216$		0			0
$217$	−2.75985			−0.187351
$218$	4.37984	−	7.58610i	0.296640	−	0.513796i
$219$		0			0
$220$	−2.66678	−	4.61901i	−0.179795	−	0.311413i
$221$	−0.931190	−	1.61287i	−0.0626386	−	0.108493i
$222$		0			0
$223$	11.4679	−	19.8631i	0.767950	−	1.33013i	−0.170722	−	0.985319i	$-0.554610\pi$
$223$	11.4679	−	19.8631i	0.767950	−	1.33013i	0.938673	−	0.344810i	$-0.112057\pi$
$224$	−12.1492			−0.811751
$225$		0			0
$226$	−7.61311			−0.506417
$227$	−8.32539	+	14.4200i	−0.552576	+	0.957089i	0.445512	+	0.895276i	$0.353022\pi$
$227$	−8.32539	+	14.4200i	−0.552576	+	0.957089i	−0.998088	+	0.0618130i	$0.980312\pi$
$228$		0			0
$229$	6.35958	+	11.0151i	0.420253	+	0.727899i	0.995964	−	0.0897539i	$-0.0286081\pi$
$229$	6.35958	+	11.0151i	0.420253	+	0.727899i	−0.575711	+	0.817653i	$0.695275\pi$
$230$	0.951173	+	1.64748i	0.0627185	+	0.108632i
$231$		0			0
$232$	6.76972	−	11.7255i	0.444454	−	0.769816i
$233$	19.7105			1.29128			0.645638	−	0.763644i	$-0.276591\pi$
$233$	19.7105			1.29128			0.645638	+	0.763644i	$0.276591\pi$
$234$		0			0
$235$	−0.132374			−0.00863511
$236$	−0.714023	+	1.23672i	−0.0464789	+	0.0805039i
$237$		0			0
$238$	1.10435	+	1.91280i	0.0715847	+	0.123988i
$239$	6.88845	+	11.9311i	0.445577	+	0.771761i	0.998092	−	0.0617412i	$-0.0196654\pi$
$239$	6.88845	+	11.9311i	0.445577	+	0.771761i	−0.552516	+	0.833503i	$0.686332\pi$
$240$		0			0
$241$	0.962799	−	1.66762i	0.0620194	−	0.107421i	−0.833349	−	0.552748i	$-0.813579\pi$
$241$	0.962799	−	1.66762i	0.0620194	−	0.107421i	0.895368	+	0.445327i	$0.146913\pi$
$242$	0.932568			0.0599477
$243$		0			0
$244$	8.49147			0.543611
$245$	−0.386290	+	0.669074i	−0.0246792	+	0.0427455i
$246$		0			0
$247$	3.30889	+	5.73117i	0.210540	+	0.364665i
$248$	0.991828	+	1.71790i	0.0629811	+	0.109087i
$249$		0			0
$250$	−0.237622	+	0.411573i	−0.0150285	+	0.0260302i
$251$	11.5406			0.728436			0.364218	−	0.931314i	$-0.381336\pi$
$251$	11.5406			0.728436			0.364218	+	0.931314i	$0.381336\pi$
$252$		0			0
$253$	−12.0338			−0.756558
$254$	−0.660457	+	1.14394i	−0.0414407	+	0.0717774i
$255$		0			0
$256$	−0.416729	−	0.721796i	−0.0260456	−	0.0451123i
$257$	−8.98850	−	15.5685i	−0.560687	−	0.971139i	−0.997437	−	0.0715554i	$-0.977204\pi$
$257$	−8.98850	−	15.5685i	−0.560687	−	0.971139i	0.436750	−	0.899583i	$-0.356130\pi$
$258$		0			0
$259$	12.7350	−	22.0577i	0.791315	−	1.37060i
$260$	1.77414			0.110028
$261$		0			0
$262$	6.87350			0.424647
$263$	−2.96942	+	5.14319i	−0.183102	+	0.317142i	−0.942935	−	0.332976i	$-0.891947\pi$
$263$	−2.96942	+	5.14319i	−0.183102	+	0.317142i	0.759833	+	0.650118i	$0.225281\pi$
$264$		0			0
$265$	3.45842	+	5.99017i	0.212449	+	0.367973i
$266$	−3.92422	−	6.79694i	−0.240609	−	0.416747i
$267$		0			0
$268$	3.68488	−	6.38241i	0.225090	−	0.389868i
$269$	1.31308			0.0800597			0.0400299	−	0.999198i	$-0.487255\pi$
$269$	1.31308			0.0800597			0.0400299	+	0.999198i	$0.487255\pi$
$270$		0			0
$271$	−17.1495			−1.04176			−0.520879	−	0.853631i	$-0.674396\pi$
$271$	−17.1495			−1.04176			−0.520879	+	0.853631i	$0.674396\pi$
$272$	−2.51037	+	4.34809i	−0.152214	+	0.263642i
$273$		0			0
$274$	−4.32454	−	7.49033i	−0.261255	−	0.452507i
$275$	−1.50314	−	2.60351i	−0.0906427	−	0.156998i
$276$		0			0
$277$	−14.5936	+	25.2769i	−0.876847	+	1.51874i	−0.0220645	+	0.999757i	$0.507024\pi$
$277$	−14.5936	+	25.2769i	−0.876847	+	1.51874i	−0.854782	+	0.518987i	$0.826309\pi$
$278$	10.7760			0.646299
$279$		0			0
$280$	−4.47599			−0.267491
$281$	6.76359	−	11.7149i	0.403482	−	0.698852i	−0.590661	−	0.806920i	$-0.701133\pi$
$281$	6.76359	−	11.7149i	0.403482	−	0.698852i	0.994144	+	0.108068i	$0.0344664\pi$
$282$		0			0
$283$	8.63655	+	14.9590i	0.513390	+	0.889217i	0.999879	+	0.0155309i	$0.00494383\pi$
$283$	8.63655	+	14.9590i	0.513390	+	0.889217i	−0.486490	+	0.873686i	$0.661723\pi$
$284$	4.82855	+	8.36330i	0.286522	+	0.496270i
$285$		0			0
$286$	0.714357	−	1.23730i	0.0422408	−	0.0731632i
$287$	9.82060			0.579691
$288$		0			0
$289$	−13.5315			−0.795973
$290$	1.79371	−	3.10680i	0.105330	−	0.182437i
$291$		0			0
$292$	−5.62215	−	9.73785i	−0.329011	−	0.569865i
$293$	3.46977	+	6.00982i	0.202706	+	0.351098i	0.949400	−	0.314071i	$-0.101693\pi$
$293$	3.46977	+	6.00982i	0.202706	+	0.351098i	−0.746693	+	0.665169i	$0.768360\pi$
$294$		0			0
$295$	−0.402461	+	0.697082i	−0.0234322	+	0.0405857i
$296$	−18.3067			−1.06406
$297$		0			0
$298$	8.74053			0.506326
$299$	2.00144	−	3.46660i	0.115746	−	0.200479i
$300$		0			0
$301$	−7.95396	−	13.7767i	−0.458459	−	0.794074i
$302$	−1.81630	−	3.14593i	−0.104517	−	0.181028i
$303$		0			0
$304$	8.92035	−	15.4505i	0.511617	−	0.886147i
$305$	4.78624			0.274059
$306$		0			0
$307$	−16.0084			−0.913645			−0.456823	−	0.889558i	$-0.651013\pi$
$307$	−16.0084			−0.913645			−0.456823	+	0.889558i	$0.651013\pi$
$308$	6.65491	−	11.5266i	0.379198	−	0.656791i
$309$		0			0
$310$	0.262796	+	0.455175i	0.0149258	+	0.0258522i
$311$	−6.48175	−	11.2267i	−0.367546	−	0.636609i	0.621635	−	0.783307i	$-0.286469\pi$
$311$	−6.48175	−	11.2267i	−0.367546	−	0.636609i	−0.989181	+	0.146698i	$0.953135\pi$
$312$		0			0
$313$	9.24933	−	16.0203i	0.522803	−	0.905522i	−0.476845	−	0.878988i	$-0.658220\pi$
$313$	9.24933	−	16.0203i	0.522803	−	0.905522i	0.999648	−	0.0265342i	$-0.00844709\pi$
$314$	4.51080			0.254559
$315$		0			0
$316$	8.22391			0.462631
$317$	15.5849	−	26.9938i	0.875333	−	1.51612i	0.0189261	−	0.999821i	$-0.493975\pi$
$317$	15.5849	−	26.9938i	0.875333	−	1.51612i	0.856407	−	0.516301i	$-0.172691\pi$
$318$		0			0
$319$	11.3466	+	19.6528i	0.635286	+	1.10035i
$320$	−1.53902	−	2.66566i	−0.0860337	−	0.149015i
$321$		0			0
$322$	−2.37363	+	4.11125i	−0.132277	+	0.229111i
$323$	−12.3248			−0.685772
$324$		0			0
$325$	1.00000			0.0554700
$326$	0.790045	−	1.36840i	0.0437565	−	0.0757886i
$327$		0			0
$328$	−3.52930	−	6.11292i	−0.194873	−	0.337530i
$329$	−0.165168	−	0.286079i	−0.00910600	−	0.0157721i
$330$		0			0
$331$	10.7108	−	18.5516i	0.588716	−	1.01969i	−0.405684	−	0.914013i	$-0.632967\pi$
$331$	10.7108	−	18.5516i	0.588716	−	1.01969i	0.994401	−	0.105674i	$-0.0336999\pi$
$332$	−25.7874			−1.41527
$333$		0			0
$334$	1.08012			0.0591018
$335$	2.07699	−	3.59746i	0.113478	−	0.196550i
$336$		0			0
$337$	10.7896	+	18.6881i	0.587747	+	1.01801i	0.994527	+	0.104482i	$0.0333184\pi$
$337$	10.7896	+	18.6881i	0.587747	+	1.01801i	−0.406780	+	0.913526i	$0.633348\pi$
$338$	0.237622	+	0.411573i	0.0129249	+	0.0223866i
$339$		0			0
$340$	−1.65206	+	2.86146i	−0.0895958	+	0.155184i
$341$	−3.32476			−0.180046
$342$		0			0
$343$	−19.3963			−1.04730
$344$	−5.71695	+	9.90204i	−0.308237	+	0.533882i
$345$		0			0
$346$	3.42044	+	5.92437i	0.183884	+	0.318496i
$347$	−0.00650665	−	0.0112698i	−0.000349295	−	0.000604997i	0.865851	−	0.500302i	$-0.166778\pi$
$347$	−0.00650665	−	0.0112698i	−0.000349295	−	0.000604997i	−0.866200	+	0.499697i	$0.833445\pi$
$348$		0			0
$349$	6.51289	−	11.2807i	0.348627	−	0.603840i	−0.637379	−	0.770551i	$-0.719981\pi$
$349$	6.51289	−	11.2807i	0.348627	−	0.603840i	0.986006	+	0.166711i	$0.0533147\pi$
$350$	−1.18596			−0.0633923
$351$		0			0
$352$	−14.6360			−0.780100
$353$	7.29075	−	12.6280i	0.388048	−	0.672118i	−0.604139	−	0.796879i	$-0.706483\pi$
$353$	7.29075	−	12.6280i	0.388048	−	0.672118i	0.992187	+	0.124760i	$0.0398162\pi$
$354$		0			0
$355$	2.72162	+	4.71399i	0.144449	+	0.250193i
$356$	−5.12567	−	8.87792i	−0.271660	−	0.470529i
$357$		0			0
$358$	4.71808	−	8.17196i	0.249359	−	0.431902i
$359$	28.3828			1.49799			0.748995	−	0.662576i	$-0.230537\pi$
$359$	28.3828			1.49799			0.748995	+	0.662576i	$0.230537\pi$
$360$		0			0
$361$	24.7950			1.30500
$362$	−4.81426	+	8.33855i	−0.253032	+	0.438265i
$363$		0			0
$364$	2.21367	+	3.83419i	0.116028	+	0.200966i
$365$	−3.16894	−	5.48876i	−0.165870	−	0.287295i
$366$		0			0
$367$	−2.40226	+	4.16084i	−0.125397	+	0.217194i	−0.921888	−	0.387456i	$-0.873354\pi$
$367$	−2.40226	+	4.16084i	−0.125397	+	0.217194i	0.796491	+	0.604650i	$0.206687\pi$
$368$	−10.7913			−0.562534
$369$		0			0
$370$	−4.85056			−0.252168
$371$	−8.63043	+	14.9483i	−0.448070	+	0.776079i
$372$		0			0
$373$	2.06426	+	3.57540i	0.106883	+	0.185127i	0.914506	−	0.404572i	$-0.132580\pi$
$373$	2.06426	+	3.57540i	0.106883	+	0.185127i	−0.807623	+	0.589699i	$0.799246\pi$
$374$	1.33040	+	2.30433i	0.0687936	+	0.119154i
$375$		0			0
$376$	−0.118715	+	0.205621i	−0.00612227	+	0.0106041i
$377$	−7.54859			−0.388772
$378$		0			0
$379$	15.4974			0.796050			0.398025	−	0.917375i	$-0.369696\pi$
$379$	15.4974			0.796050			0.398025	+	0.917375i	$0.369696\pi$
$380$	5.87045	−	10.1679i	0.301148	−	0.521603i
$381$		0			0
$382$	−3.42759	−	5.93675i	−0.175371	−	0.303751i
$383$	1.07069	+	1.85449i	0.0547099	+	0.0947602i	0.892083	−	0.451871i	$-0.149243\pi$
$383$	1.07069	+	1.85449i	0.0547099	+	0.0947602i	−0.837373	+	0.546631i	$0.815910\pi$
$384$		0			0
$385$	3.75105	−	6.49701i	0.191171	−	0.331119i
$386$	11.5136			0.586028
$387$		0			0
$388$	−10.7729			−0.546909
$389$	8.29210	−	14.3623i	0.420426	−	0.728199i	−0.575555	−	0.817763i	$-0.695214\pi$
$389$	8.29210	−	14.3623i	0.420426	−	0.728199i	0.995981	+	0.0895637i	$0.0285473\pi$
$390$		0			0
$391$	3.72745	+	6.45613i	0.188505	+	0.326500i
$392$	0.692864	+	1.20008i	0.0349949	+	0.0606130i
$393$		0			0
$394$	−0.461873	+	0.799988i	−0.0232688	+	0.0403028i
$395$	4.63542			0.233234
$396$		0			0
$397$	4.60300			0.231018			0.115509	−	0.993306i	$-0.463150\pi$
$397$	4.60300			0.231018			0.115509	+	0.993306i	$0.463150\pi$
$398$	1.79952	−	3.11686i	0.0902018	−	0.156234i
$399$		0			0
$400$	−1.34794	−	2.33469i	−0.0673968	−	0.116735i
$401$	5.21156	+	9.02668i	0.260253	+	0.450771i	0.966309	−	0.257385i	$-0.0828608\pi$
$401$	5.21156	+	9.02668i	0.260253	+	0.450771i	−0.706056	+	0.708156i	$0.749527\pi$
$402$		0			0
$403$	0.552970	−	0.957772i	0.0275454	−	0.0477100i
$404$	−8.23829			−0.409870
$405$		0			0
$406$	8.95233			0.444297
$407$	15.3417	−	26.5727i	0.760462	−	1.31716i
$408$		0			0
$409$	−18.3965	−	31.8638i	−0.909651	−	1.57556i	−0.814550	−	0.580093i	$-0.803016\pi$
$409$	−18.3965	−	31.8638i	−0.909651	−	1.57556i	−0.0951006	−	0.995468i	$-0.530317\pi$
$410$	−0.935126	−	1.61969i	−0.0461826	−	0.0799906i
$411$		0			0
$412$	−11.3323	+	19.6282i	−0.558304	+	0.967011i
$413$	−2.00867			−0.0988399
$414$		0			0
$415$	−14.5351			−0.713502
$416$	2.43424	−	4.21622i	0.119348	−	0.206717i
$417$		0			0
$418$	−4.72746	−	8.18820i	−0.231228	−	0.400498i
$419$	−12.8064	−	22.1813i	−0.625634	−	1.08363i	−0.988418	−	0.151756i	$-0.951507\pi$
$419$	−12.8064	−	22.1813i	−0.625634	−	1.08363i	0.362784	−	0.931873i	$-0.381826\pi$
$420$		0			0
$421$	−4.15123	+	7.19014i	−0.202318	+	0.350426i	−0.949275	−	0.314447i	$-0.898181\pi$
$421$	−4.15123	+	7.19014i	−0.202318	+	0.350426i	0.746957	+	0.664873i	$0.231514\pi$
$422$	−7.21259			−0.351103
$423$		0			0
$424$	12.4063			0.602504
$425$	−0.931190	+	1.61287i	−0.0451693	+	0.0782356i
$426$		0			0
$427$	5.97198	+	10.3438i	0.289004	+	0.500570i
$428$	−9.22781	−	15.9830i	−0.446043	−	0.772569i
$429$		0			0
$430$	−1.51477	+	2.62365i	−0.0730485	+	0.126524i
$431$	1.12921			0.0543923			0.0271961	−	0.999630i	$-0.491342\pi$
$431$	1.12921			0.0543923			0.0271961	+	0.999630i	$0.491342\pi$
$432$		0			0
$433$	24.7868			1.19118			0.595588	−	0.803290i	$-0.296919\pi$
$433$	24.7868			1.19118			0.595588	+	0.803290i	$0.296919\pi$
$434$	−0.655801	+	1.13588i	−0.0314795	+	0.0545240i
$435$		0			0
$436$	16.3505	+	28.3199i	0.783046	+	1.35628i
$437$	−13.2451	−	22.9412i	−0.633600	−	1.09743i
$438$		0			0
$439$	17.1709	−	29.7408i	0.819520	−	1.41945i	−0.0865163	−	0.996250i	$-0.527573\pi$
$439$	17.1709	−	29.7408i	0.819520	−	1.41945i	0.906036	−	0.423200i	$-0.139093\pi$
$440$	−5.39217			−0.257062
$441$		0			0
$442$	−0.885084			−0.0420992
$443$	8.58860	−	14.8759i	0.408057	−	0.706775i	−0.586615	−	0.809866i	$-0.699540\pi$
$443$	8.58860	−	14.8759i	0.408057	−	0.706775i	0.994672	+	0.103091i	$0.0328732\pi$
$444$		0			0
$445$	−2.88910	−	5.00406i	−0.136956	−	0.237215i
$446$	−5.45007	−	9.43979i	−0.258068	−	0.446987i
$447$		0			0
$448$	3.84059	−	6.65209i	0.181451	−	0.314282i
$449$	−7.37552			−0.348072			−0.174036	−	0.984739i	$-0.555681\pi$
$449$	−7.37552			−0.348072			−0.174036	+	0.984739i	$0.555681\pi$
$450$		0			0
$451$	11.8308			0.557089
$452$	14.2103	−	24.6130i	0.668398	−	1.15770i
$453$		0			0
$454$	3.95659	+	6.85301i	0.185692	+	0.321628i
$455$	1.24774	+	2.16115i	0.0584950	+	0.101316i
$456$		0			0
$457$	−8.88483	+	15.3890i	−0.415615	+	0.719866i	−0.995493	−	0.0948374i	$-0.969767\pi$
$457$	−8.88483	+	15.3890i	−0.415615	+	0.719866i	0.579878	+	0.814703i	$0.303100\pi$
$458$	6.04470			0.282450
$459$		0			0
$460$	−7.10170			−0.331118
$461$	−7.79084	+	13.4941i	−0.362856	+	0.628485i	−0.988430	−	0.151680i	$-0.951532\pi$
$461$	−7.79084	+	13.4941i	−0.362856	+	0.628485i	0.625574	+	0.780165i	$0.284865\pi$
$462$		0			0
$463$	−1.91706	−	3.32045i	−0.0890935	−	0.154314i	0.818035	−	0.575169i	$-0.195064\pi$
$463$	−1.91706	−	3.32045i	−0.0890935	−	0.154314i	−0.907128	+	0.420854i	$0.861730\pi$
$464$	10.1750	+	17.6236i	0.472363	+	0.818157i
$465$		0			0
$466$	4.68364	−	8.11230i	0.216965	−	0.375795i
$467$	15.3789			0.711652			0.355826	−	0.934552i	$-0.384200\pi$
$467$	15.3789			0.711652			0.355826	+	0.934552i	$0.384200\pi$
$468$		0			0
$469$	10.3662			0.478666
$470$	−0.0314549	+	0.0544814i	−0.00145090	+	0.00251304i
$471$		0			0
$472$	0.721868	+	1.25031i	0.0332267	+	0.0575503i
$473$	−9.58205	−	16.5966i	−0.440583	−	0.763112i
$474$		0			0
$475$	3.30889	−	5.73117i	0.151822	−	0.262964i
$476$	−8.24539			−0.377927
$477$		0			0
$478$	6.54738			0.299470
$479$	10.8178	−	18.7370i	0.494278	−	0.856115i	−0.505700	−	0.862709i	$-0.668766\pi$
$479$	10.8178	−	18.7370i	0.494278	−	0.856115i	0.999978	+	0.00659439i	$0.00209908\pi$
$480$		0			0
$481$	5.10323	+	8.83906i	0.232687	+	0.403026i
$482$	−0.457564	−	0.792524i	−0.0208415	−	0.0360985i
$483$		0			0
$484$	−1.74070	+	3.01497i	−0.0791225	+	0.137044i
$485$	−6.07215			−0.275722
$486$		0			0
$487$	−13.1986			−0.598086			−0.299043	−	0.954240i	$-0.596667\pi$
$487$	−13.1986			−0.598086			−0.299043	+	0.954240i	$0.596667\pi$
$488$	4.29239	−	7.43463i	0.194307	−	0.336550i
$489$		0			0
$490$	0.183582	+	0.317973i	0.00829338	+	0.0143646i
$491$	−15.1570	−	26.2526i	−0.684024	−	1.18476i	−0.973743	−	0.227652i	$-0.926895\pi$
$491$	−15.1570	−	26.2526i	−0.684024	−	1.18476i	0.289719	−	0.957112i	$-0.406438\pi$
$492$		0			0
$493$	7.02917	−	12.1749i	0.316578	−	0.548329i
$494$	3.14506			0.141503
$495$		0			0
$496$	−2.98147			−0.133872
$497$	−6.79176	+	11.7637i	−0.304652	+	0.527673i
$498$		0			0
$499$	−18.2081	−	31.5373i	−0.815106	−	1.41181i	−0.909252	−	0.416247i	$-0.863345\pi$
$499$	−18.2081	−	31.5373i	−0.815106	−	1.41181i	0.0941452	−	0.995558i	$-0.469988\pi$
$500$	−0.887072	−	1.53645i	−0.0396711	−	0.0687123i
$501$		0			0
$502$	2.74230	−	4.74980i	0.122395	−	0.211994i
$503$	3.37170			0.150337			0.0751684	−	0.997171i	$-0.476051\pi$
$503$	3.37170			0.150337			0.0751684	+	0.997171i	$0.476051\pi$
$504$		0			0
$505$	−4.64353			−0.206634
$506$	−2.85949	+	4.95278i	−0.127120	+	0.220178i
$507$		0			0
$508$	−2.46557	−	4.27049i	−0.109392	−	0.189472i
$509$	14.5760	+	25.2464i	0.646072	+	1.11903i	0.984053	+	0.177876i	$0.0569226\pi$
$509$	14.5760	+	25.2464i	0.646072	+	1.11903i	−0.337981	+	0.941153i	$0.609744\pi$
$510$		0			0
$511$	7.90802	−	13.6971i	0.349830	−	0.605924i
$512$	−22.7956			−1.00743
$513$		0			0
$514$	−8.54345			−0.376835
$515$	−6.38750	+	11.0635i	−0.281467	+	0.487515i
$516$		0			0
$517$	−0.198976	−	0.344637i	−0.00875096	−	0.0151571i
$518$	−6.05223	−	10.4828i	−0.265920	−	0.460587i
$519$		0			0
$520$	0.896819	−	1.55334i	0.0393281	−	0.0681183i
$521$	3.09509			0.135598			0.0677991	−	0.997699i	$-0.478402\pi$
$521$	3.09509			0.135598			0.0677991	+	0.997699i	$0.478402\pi$
$522$		0			0
$523$	11.6267			0.508400			0.254200	−	0.967152i	$-0.418188\pi$
$523$	11.6267			0.508400			0.254200	+	0.967152i	$0.418188\pi$
$524$	−12.8298	+	22.2219i	−0.560474	+	0.970769i
$525$		0			0
$526$	1.41120	+	2.44427i	0.0615311	+	0.106575i
$527$	1.02984	+	1.78374i	0.0448606	+	0.0777008i
$528$		0			0
$529$	3.48845	−	6.04217i	0.151672	−	0.262703i
$530$	3.28719			0.142786
$531$		0			0
$532$	29.2992			1.27028
$533$	−1.96768	+	3.40812i	−0.0852295	+	0.147622i
$534$		0			0
$535$	−5.20127	−	9.00887i	−0.224871	−	0.389487i
$536$	−3.72537	−	6.45254i	−0.160912	−	0.278707i
$537$		0			0
$538$	0.312016	−	0.540427i	0.0134520	−	0.0232995i
$539$	−2.32259			−0.100041
$540$		0			0
$541$	19.7270			0.848132			0.424066	−	0.905631i	$-0.360603\pi$
$541$	19.7270			0.848132			0.424066	+	0.905631i	$0.360603\pi$
$542$	−4.07509	+	7.05827i	−0.175040	+	0.303179i
$543$		0			0
$544$	4.53347	+	7.85220i	0.194371	+	0.336660i
$545$	9.21599	+	15.9626i	0.394770	+	0.683761i
$546$		0			0
$547$	5.38353	−	9.32455i	0.230183	−	0.398689i	−0.727679	−	0.685918i	$-0.759401\pi$
$547$	5.38353	−	9.32455i	0.230183	−	0.398689i	0.957862	+	0.287229i	$0.0927342\pi$
$548$	32.2881			1.37928
$549$		0			0
$550$	−1.42871			−0.0609206
$551$	−24.9775	+	43.2622i	−1.06408	+	1.84303i
$552$		0			0
$553$	5.78380	+	10.0178i	0.245952	+	0.426002i
$554$	6.93553	+	12.0127i	0.294663	+	0.510371i
$555$		0			0
$556$	−20.1140	+	34.8385i	−0.853024	+	1.47748i
$557$	−34.4423			−1.45937			−0.729683	−	0.683786i	$-0.760332\pi$
$557$	−34.4423			−1.45937			−0.729683	+	0.683786i	$0.760332\pi$
$558$		0			0
$559$	6.37469			0.269621
$560$	3.36375	−	5.82618i	0.142144	−	0.246201i
$561$		0			0
$562$	−3.21435	−	5.56742i	−0.135589	−	0.234848i
$563$	10.7378	+	18.5984i	0.452544	+	0.783828i	0.998543	−	0.0539570i	$-0.0171834\pi$
$563$	10.7378	+	18.5984i	0.452544	+	0.783828i	−0.546000	+	0.837785i	$0.683850\pi$
$564$		0			0
$565$	8.00969	−	13.8732i	0.336970	−	0.583650i
$566$	8.20893			0.345047
$567$		0			0
$568$	9.76321			0.409655
$569$	−22.9248	+	39.7070i	−0.961059	+	1.66460i	−0.241208	+	0.970474i	$0.577543\pi$
$569$	−22.9248	+	39.7070i	−0.961059	+	1.66460i	−0.719851	+	0.694129i	$0.755790\pi$
$570$		0			0
$571$	22.9690	+	39.7834i	0.961221	+	1.66488i	0.719443	+	0.694552i	$0.244397\pi$
$571$	22.9690	+	39.7834i	0.961221	+	1.66488i	0.241778	+	0.970332i	$0.422269\pi$
$572$	2.66678	+	4.61901i	0.111504	+	0.193130i
$573$		0			0
$574$	2.33359	−	4.04189i	0.0974021	−	0.168705i
$575$	−4.00289			−0.166932
$576$		0			0
$577$	−44.0303			−1.83301			−0.916503	−	0.400028i	$-0.869000\pi$
$577$	−44.0303			−1.83301			−0.916503	+	0.400028i	$0.869000\pi$
$578$	−3.21539	+	5.56922i	−0.133743	+	0.231649i
$579$		0			0
$580$	6.69614	+	11.5981i	0.278042	+	0.481583i
$581$	−18.1361	−	31.4126i	−0.752411	−	1.30321i
$582$		0			0
$583$	−10.3970	+	18.0081i	−0.430599	+	0.745820i
$584$	−11.3678			−0.470405
$585$		0			0
$586$	3.29798			0.136238
$587$	−11.0945	+	19.2162i	−0.457917	+	0.793136i	−0.998851	−	0.0479296i	$-0.984738\pi$
$587$	−11.0945	+	19.2162i	−0.457917	+	0.793136i	0.540934	+	0.841065i	$0.318071\pi$
$588$		0			0
$589$	−3.65944	−	6.33833i	−0.150784	−	0.261166i
$590$	0.191267	+	0.331284i	0.00787433	+	0.0136387i
$591$		0			0
$592$	13.7577	−	23.8290i	0.565437	−	0.979365i
$593$	8.38651			0.344392			0.172196	−	0.985063i	$-0.444914\pi$
$593$	8.38651			0.344392			0.172196	+	0.985063i	$0.444914\pi$
$594$		0			0
$595$	−4.64753			−0.190530
$596$	−16.3148	+	28.2580i	−0.668278	+	1.15749i
$597$		0			0
$598$	−0.951173	−	1.64748i	−0.0388964	−	0.0673705i
$599$	20.4216	+	35.3712i	0.834402	+	1.44523i	0.894516	+	0.447035i	$0.147520\pi$
$599$	20.4216	+	35.3712i	0.834402	+	1.44523i	−0.0601143	+	0.998192i	$0.519147\pi$
$600$		0			0
$601$	4.18193	−	7.24331i	0.170584	−	0.295461i	−0.768040	−	0.640402i	$-0.778768\pi$
$601$	4.18193	−	7.24331i	0.170584	−	0.295461i	0.938624	+	0.344941i	$0.112101\pi$
$602$	−7.56014			−0.308128
$603$		0			0
$604$	13.5610			0.551789
$605$	−0.981147	+	1.69940i	−0.0398893	+	0.0690903i
$606$		0			0
$607$	−15.0802	−	26.1197i	−0.612087	−	1.06017i	−0.990888	−	0.134688i	$-0.956997\pi$
$607$	−15.0802	−	26.1197i	−0.612087	−	1.06017i	0.378801	−	0.925478i	$-0.376337\pi$
$608$	−16.1092	−	27.9020i	−0.653316	−	1.13158i
$609$		0			0
$610$	1.13731	−	1.96989i	0.0460485	−	0.0797583i
$611$	0.132374			0.00535527
$612$		0			0
$613$	−6.73660			−0.272089			−0.136044	−	0.990703i	$-0.543439\pi$
$613$	−6.73660			−0.272089			−0.136044	+	0.990703i	$0.543439\pi$
$614$	−3.80393	+	6.58861i	−0.153514	+	0.265895i
$615$		0			0
$616$	−6.72803	−	11.6533i	−0.271080	−	0.469524i
$617$	−3.48508	−	6.03634i	−0.140304	−	0.243014i	0.787307	−	0.616561i	$-0.211475\pi$
$617$	−3.48508	−	6.03634i	−0.140304	−	0.243014i	−0.927611	+	0.373547i	$0.878141\pi$
$618$		0			0
$619$	−17.6414	+	30.5557i	−0.709066	+	1.22814i	0.256138	+	0.966640i	$0.417550\pi$
$619$	−17.6414	+	30.5557i	−0.709066	+	1.22814i	−0.965204	+	0.261498i	$0.915783\pi$
$620$	−1.96210			−0.0787997
$621$		0			0
$622$	−6.16082			−0.247026
$623$	7.20968	−	12.4875i	0.288850	−	0.500302i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.39569	−	7.61355i	−0.175687	−	0.304299i
$627$		0			0
$628$	−8.41969	+	14.5833i	−0.335982	+	0.581938i
$629$	−19.0083			−0.757911
$630$		0			0
$631$	6.42382			0.255728			0.127864	−	0.991792i	$-0.459188\pi$
$631$	6.42382			0.255728			0.127864	+	0.991792i	$0.459188\pi$
$632$	4.15714	−	7.20037i	0.165362	−	0.286415i
$633$		0			0
$634$	−7.40661	−	12.8286i	−0.294154	−	0.509490i
$635$	−1.38972	−	2.40707i	−0.0551494	−	0.0955216i
$636$		0			0
$637$	0.386290	−	0.669074i	0.0153054	−	0.0265097i
$638$	10.7848			0.426973
$639$		0			0
$640$	−11.1998			−0.442709
$641$	24.7537	−	42.8746i	0.977711	−	1.69345i	0.307029	−	0.951700i	$-0.400665\pi$
$641$	24.7537	−	42.8746i	0.977711	−	1.69345i	0.670682	−	0.741745i	$-0.266002\pi$
$642$		0			0
$643$	19.0192	+	32.9423i	0.750046	+	1.29912i	0.947800	+	0.318866i	$0.103302\pi$
$643$	19.0192	+	32.9423i	0.750046	+	1.29912i	−0.197754	+	0.980252i	$0.563365\pi$
$644$	−8.86107	−	15.3478i	−0.349175	−	0.604789i
$645$		0			0
$646$	−2.92865	+	5.07257i	−0.115226	+	0.199577i
$647$	−44.2290			−1.73882			−0.869410	−	0.494091i	$-0.835501\pi$
$647$	−44.2290			−1.73882			−0.869410	+	0.494091i	$0.835501\pi$
$648$		0			0
$649$	−2.41982			−0.0949861
$650$	0.237622	−	0.411573i	0.00932029	−	0.0161432i
$651$		0			0
$652$	2.94934	+	5.10840i	0.115505	+	0.200060i
$653$	18.3836	+	31.8414i	0.719407	+	1.24605i	0.961235	+	0.275731i	$0.0889198\pi$
$653$	18.3836	+	31.8414i	0.719407	+	1.24605i	−0.241828	+	0.970319i	$0.577747\pi$
$654$		0			0
$655$	−7.23156	+	12.5254i	−0.282560	+	0.489409i
$656$	10.6092			0.414220
$657$		0			0
$658$	−0.156990			−0.00612011
$659$	13.9797	−	24.2135i	0.544570	−	0.943224i	−0.454063	−	0.890969i	$-0.650026\pi$
$659$	13.9797	−	24.2135i	0.544570	−	0.943224i	0.998634	−	0.0522543i	$-0.0166406\pi$
$660$		0			0
$661$	−1.33600	−	2.31401i	−0.0519642	−	0.0900046i	0.838873	−	0.544327i	$-0.183215\pi$
$661$	−1.33600	−	2.31401i	−0.0519642	−	0.0900046i	−0.890837	+	0.454322i	$0.849881\pi$
$662$	−5.09022	−	8.81652i	−0.197837	−	0.342664i
$663$		0			0
$664$	−13.0354	+	22.5779i	−0.505871	+	0.876194i
$665$	16.5145			0.640407
$666$		0			0
$667$	30.2161			1.16997
$668$	−2.01612	+	3.49202i	−0.0780060	+	0.135110i
$669$		0			0
$670$	−0.987078	−	1.70967i	−0.0381341	−	0.0660503i
$671$	7.19438	+	12.4610i	0.277736	+	0.481053i
$672$		0			0
$673$	11.2433	−	19.4740i	0.433398	−	0.750668i	−0.563765	−	0.825935i	$-0.690648\pi$
$673$	11.2433	−	19.4740i	0.433398	−	0.750668i	0.997163	+	0.0752673i	$0.0239810\pi$
$674$	10.2554			0.395022
$675$		0			0
$676$	−1.77414			−0.0682363
$677$	18.6555	−	32.3124i	0.716991	−	1.24186i	−0.245196	−	0.969474i	$-0.578852\pi$
$677$	18.6555	−	32.3124i	0.716991	−	1.24186i	0.962187	−	0.272391i	$-0.0878145\pi$
$678$		0			0
$679$	−7.57646	−	13.1228i	−0.290758	−	0.503608i
$680$	1.67022	+	2.89290i	0.0640499	+	0.110938i
$681$		0			0
$682$	−0.790036	+	1.36838i	−0.0302521	+	0.0523981i
$683$	21.6591			0.828762			0.414381	−	0.910103i	$-0.363998\pi$
$683$	21.6591			0.828762			0.414381	+	0.910103i	$0.363998\pi$
$684$		0			0
$685$	18.1993			0.695358
$686$	−4.60899	+	7.98300i	−0.175972	+	0.304792i
$687$		0			0
$688$	−8.59268	−	14.8830i	−0.327593	−	0.567408i
$689$	−3.45842	−	5.99017i	−0.131755	−	0.228207i
$690$		0			0
$691$	−15.0718	+	26.1051i	−0.573357	+	0.993084i	0.422861	+	0.906195i	$0.361026\pi$
$691$	−15.0718	+	26.1051i	−0.573357	+	0.993084i	−0.996218	+	0.0868893i	$0.972307\pi$
$692$	−25.5378			−0.970803
$693$		0			0
$694$	−0.00618448			−0.000234760
$695$	−11.3373	+	19.6368i	−0.430049	+	0.744866i
$696$		0			0
$697$	−3.66456	−	6.34721i	−0.138805	−	0.240418i
$698$	−3.09521	−	5.36106i	−0.117155	−	0.202919i
$699$		0			0
$700$	2.21367	−	3.83419i	0.0836689	−	0.144919i
$701$	10.1845			0.384664			0.192332	−	0.981330i	$-0.438395\pi$
$701$	10.1845			0.384664			0.192332	+	0.981330i	$0.438395\pi$
$702$		0			0
$703$	67.5442			2.54748
$704$	4.62672	−	8.01371i	0.174376	−	0.302028i
$705$		0			0
$706$	−3.46488	−	6.00135i	−0.130403	−	0.225864i
$707$	−5.79392	−	10.0354i	−0.217903	−	0.377419i
$708$		0			0
$709$	−16.2836	+	28.2040i	−0.611543	+	1.05922i	0.379438	+	0.925217i	$0.376117\pi$
$709$	−16.2836	+	28.2040i	−0.611543	+	1.05922i	−0.990981	+	0.134006i	$0.957216\pi$
$710$	2.58687			0.0970834
$711$		0			0
$712$	−10.3640			−0.388407
$713$	−2.21348	+	3.83385i	−0.0828954	+	0.143579i
$714$		0			0
$715$	1.50314	+	2.60351i	0.0562142	+	0.0973659i
$716$	17.6132	+	30.5070i	0.658236	+	1.14010i
$717$		0			0
$718$	6.74438	−	11.6816i	0.251698	−	0.435954i
$719$	28.8233			1.07493			0.537464	−	0.843287i	$-0.319382\pi$
$719$	28.8233			1.07493			0.537464	+	0.843287i	$0.319382\pi$
$720$		0			0
$721$	−31.8797			−1.18726
$722$	5.89184	−	10.2050i	0.219272	−	0.379790i
$723$		0			0
$724$	−17.9723	−	31.1289i	−0.667933	−	1.15689i
$725$	3.77429	+	6.53727i	0.140174	+	0.242788i
$726$		0			0
$727$	−11.8436	+	20.5138i	−0.439256	+	0.760813i	−0.997632	−	0.0687744i	$-0.978091\pi$
$727$	−11.8436	+	20.5138i	−0.439256	+	0.760813i	0.558376	+	0.829588i	$0.311424\pi$
$728$	4.47599			0.165891
$729$		0			0
$730$	−3.01203			−0.111480
$731$	−5.93605	+	10.2815i	−0.219553	+	0.380277i
$732$		0			0
$733$	−11.3349	−	19.6326i	−0.418664	−	0.725148i	0.577141	−	0.816644i	$-0.304168\pi$
$733$	−11.3349	−	19.6326i	−0.418664	−	0.725148i	−0.995805	+	0.0914967i	$0.970835\pi$
$734$	1.14166	+	1.97741i	0.0421394	+	0.0729876i
$735$		0			0
$736$	−9.74397	+	16.8770i	−0.359167	+	0.622096i
$737$	12.4880			0.460003
$738$		0			0
$739$	5.54302			0.203903			0.101952	−	0.994789i	$-0.467491\pi$
$739$	5.54302			0.203903			0.101952	+	0.994789i	$0.467491\pi$
$740$	9.05387	−	15.6818i	0.332827	−	0.576473i
$741$		0			0
$742$	4.10156	+	7.10410i	0.150573	+	0.260800i
$743$	22.0684	+	38.2235i	0.809610	+	1.40229i	0.913134	+	0.407659i	$0.133655\pi$
$743$	22.0684	+	38.2235i	0.809610	+	1.40229i	−0.103524	+	0.994627i	$0.533012\pi$
$744$		0			0
$745$	−9.19585	+	15.9277i	−0.336910	+	0.583545i
$746$	1.96205			0.0718358
$747$		0			0
$748$	−9.93313			−0.363191
$749$	12.9797	−	22.4815i	0.474267	−	0.821455i
$750$		0			0
$751$	−12.0674	−	20.9014i	−0.440347	−	0.762704i	0.557368	−	0.830266i	$-0.311811\pi$
$751$	−12.0674	−	20.9014i	−0.440347	−	0.762704i	−0.997715	+	0.0675620i	$0.978478\pi$
$752$	−0.178431	−	0.309052i	−0.00650672	−	0.0112700i
$753$		0			0
$754$	−1.79371	+	3.10680i	−0.0653230	+	0.113143i
$755$	7.64368			0.278182
$756$		0			0
$757$	−10.9814			−0.399126			−0.199563	−	0.979885i	$-0.563952\pi$
$757$	−10.9814			−0.399126			−0.199563	+	0.979885i	$0.563952\pi$
$758$	3.68253	−	6.37832i	0.133755	−	0.231671i
$759$		0			0
$760$	−5.93495	−	10.2796i	−0.215283	−	0.372882i
$761$	20.6439	+	35.7562i	0.748339	+	1.29616i	0.948618	+	0.316422i	$0.102482\pi$
$761$	20.6439	+	35.7562i	0.748339	+	1.29616i	−0.200279	+	0.979739i	$0.564185\pi$
$762$		0			0
$763$	−22.9983	+	39.8343i	−0.832595	+	1.44210i
$764$	25.5912			0.925858
$765$		0			0
$766$	1.01768			0.0367703
$767$	0.402461	−	0.697082i	0.0145320	−	0.0251702i
$768$		0			0
$769$	16.9547	+	29.3664i	0.611403	+	1.05898i	0.991004	+	0.133830i	$0.0427278\pi$
$769$	16.9547	+	29.3664i	0.611403	+	1.05898i	−0.379602	+	0.925150i	$0.623939\pi$
$770$	−1.78266	−	3.08766i	−0.0642427	−	0.111272i
$771$		0			0
$772$	−21.4909	+	37.2234i	−0.773475	+	1.33970i
$773$	−38.5022			−1.38483			−0.692414	−	0.721500i	$-0.743453\pi$
$773$	−38.5022			−1.38483			−0.692414	+	0.721500i	$0.743453\pi$
$774$		0			0
$775$	−1.10594			−0.0397266
$776$	−5.44562	+	9.43209i	−0.195486	+	0.338592i
$777$		0			0
$778$	−3.94077	−	6.82561i	−0.141283	−	0.244710i
$779$	13.0217	+	22.5542i	0.466549	+	0.808087i
$780$		0			0
$781$	−8.18196	+	14.1716i	−0.292773	+	0.507098i
$782$	3.54289			0.126694
$783$		0			0
$784$	−2.08278			−0.0743849
$785$	−4.74578	+	8.21993i	−0.169384	+	0.293382i
$786$		0			0
$787$	−3.56557	−	6.17575i	−0.127099	−	0.220142i	0.795452	−	0.606016i	$-0.207233\pi$
$787$	−3.56557	−	6.17575i	−0.127099	−	0.220142i	−0.922551	+	0.385874i	$0.873900\pi$
$788$	−1.72423	−	2.98645i	−0.0614231	−	0.106388i
$789$		0			0
$790$	1.10148	−	1.90782i	0.0391888	−	0.0678770i
$791$	39.9761			1.42138
$792$		0			0
$793$	−4.78624			−0.169964
$794$	1.09377	−	1.89447i	0.0388165	−	0.0672322i
$795$		0			0
$796$	6.71783	+	11.6356i	0.238107	+	0.412414i
$797$	1.42162	+	2.46232i	0.0503564	+	0.0872199i	0.890105	−	0.455756i	$-0.150631\pi$
$797$	1.42162	+	2.46232i	0.0503564	+	0.0872199i	−0.839748	+	0.542976i	$0.817298\pi$
$798$		0			0
$799$	−0.123265	+	0.213501i	−0.00436080	+	0.00755313i
$800$	−4.86847			−0.172126
$801$		0			0
$802$	4.95352			0.174915
$803$	9.52671	−	16.5007i	0.336190	−	0.582298i
$804$		0			0
$805$	−4.99456	−	8.65083i	−0.176035	−	0.304902i
$806$	−0.262796	−	0.455175i	−0.00925658	−	0.0160329i
$807$		0			0
$808$	−4.16440	+	7.21296i	−0.146503	+	0.253751i
$809$	−49.2285			−1.73078			−0.865391	−	0.501098i	$-0.832930\pi$
$809$	−49.2285			−1.73078			−0.865391	+	0.501098i	$0.832930\pi$
$810$		0			0
$811$	14.4236			0.506480			0.253240	−	0.967404i	$-0.418504\pi$
$811$	14.4236			0.506480			0.253240	+	0.967404i	$0.418504\pi$
$812$	−16.7101	+	28.9427i	−0.586409	+	1.01569i
$813$		0			0
$814$	−7.29106	−	12.6285i	−0.255552	−	0.442628i
$815$	1.66240	+	2.87936i	0.0582313	+	0.100860i
$816$		0			0
$817$	21.0932	−	36.5344i	0.737957	−	1.27818i
$818$	−17.4857			−0.611372
$819$		0			0
$820$	6.98188			0.243818
$821$	−15.3555	+	26.5966i	−0.535912	+	0.928227i	0.463206	+	0.886250i	$0.346699\pi$
$821$	−15.3555	+	26.5966i	−0.535912	+	0.928227i	−0.999119	+	0.0419768i	$0.986634\pi$
$822$		0			0
$823$	19.8972	+	34.4629i	0.693572	+	1.20130i	0.970660	+	0.240457i	$0.0772973\pi$
$823$	19.8972	+	34.4629i	0.693572	+	1.20130i	−0.277088	+	0.960845i	$0.589369\pi$
$824$	11.4569	+	19.8439i	0.399118	+	0.691293i
$825$		0			0
$826$	−0.477303	+	0.826712i	−0.0166075	+	0.0287650i
$827$	31.7524			1.10414			0.552069	−	0.833798i	$-0.313838\pi$
$827$	31.7524			1.10414			0.552069	+	0.833798i	$0.313838\pi$
$828$		0			0
$829$	6.91750			0.240255			0.120127	−	0.992758i	$-0.461670\pi$
$829$	6.91750			0.240255			0.120127	+	0.992758i	$0.461670\pi$
$830$	−3.45386	+	5.98227i	−0.119885	+	0.207648i
$831$		0			0
$832$	1.53902	+	2.66566i	0.0533558	+	0.0924150i
$833$	0.719418	+	1.24607i	0.0249264	+	0.0431737i
$834$		0			0
$835$	−1.13639	+	1.96829i	−0.0393264	+	0.0681153i
$836$	35.2964			1.22075
$837$		0			0
$838$	−12.1723			−0.420486
$839$	16.0617	−	27.8198i	0.554513	−	0.960445i	−0.443428	−	0.896310i	$-0.646238\pi$
$839$	16.0617	−	27.8198i	0.554513	−	0.960445i	0.997941	−	0.0641348i	$-0.0204288\pi$
$840$		0			0
$841$	−13.9906	−	24.2324i	−0.482434	−	0.835601i
$842$	1.97284	+	3.41707i	0.0679887	+	0.117760i
$843$		0			0
$844$	13.4627	−	23.3182i	0.463407	−	0.802644i
$845$	−1.00000			−0.0344010
$846$		0			0
$847$	−4.89687			−0.168258
$848$	−9.32347	+	16.1487i	−0.320169	+	0.554550i
$849$		0			0
$850$	0.442542	+	0.766505i	0.0151791	+	0.0262909i
$851$	−20.4277	−	35.3817i	−0.700251	−	1.21287i
$852$		0			0
$853$	−19.8130	+	34.3171i	−0.678384	+	1.17500i	0.297083	+	0.954852i	$0.403986\pi$
$853$	−19.8130	+	34.3171i	−0.678384	+	1.17500i	−0.975467	+	0.220144i	$0.929347\pi$
$854$	5.67629			0.194239
$855$		0			0
$856$	−18.6584			−0.637731
$857$	−1.12803	+	1.95380i	−0.0385327	+	0.0667405i	−0.884649	−	0.466258i	$-0.845602\pi$
$857$	−1.12803	+	1.95380i	−0.0385327	+	0.0667405i	0.846116	+	0.532999i	$0.178935\pi$
$858$		0			0
$859$	−6.67248	−	11.5571i	−0.227662	−	0.394322i	0.729453	−	0.684031i	$-0.239775\pi$
$859$	−6.67248	−	11.5571i	−0.227662	−	0.394322i	−0.957115	+	0.289709i	$0.906441\pi$
$860$	−5.65481	−	9.79442i	−0.192827	−	0.333987i
$861$		0			0
$862$	0.268326	−	0.464754i	0.00913921	−	0.0158296i
$863$	−45.5215			−1.54957			−0.774786	−	0.632224i	$-0.782142\pi$
$863$	−45.5215			−1.54957			−0.774786	+	0.632224i	$0.782142\pi$
$864$		0			0
$865$	−14.3945			−0.489426
$866$	5.88987	−	10.2016i	0.200146	−	0.346663i
$867$		0			0
$868$	−2.44819	−	4.24038i	−0.0830969	−	0.143928i
$869$	6.96769	+	12.0684i	0.236363	+	0.409392i
$870$		0			0
$871$	−2.07699	+	3.59746i	−0.0703762	+	0.121895i
$872$	33.0603			1.11956
$873$		0			0
$874$	−12.5893			−0.425840
$875$	1.24774	−	2.16115i	0.0421813	−	0.0730602i
$876$		0			0
$877$	−26.1599	−	45.3103i	−0.883358	−	1.53002i	−0.847584	−	0.530661i	$-0.821944\pi$
$877$	−26.1599	−	45.3103i	−0.883358	−	1.53002i	−0.0357738	−	0.999360i	$-0.511390\pi$
$878$	−8.16034	−	14.1341i	−0.275398	−	0.477003i
$879$		0			0
$880$	4.05227	−	7.01874i	0.136602	−	0.236602i
$881$	45.1831			1.52226			0.761128	−	0.648601i	$-0.224646\pi$
$881$	45.1831			1.52226			0.761128	+	0.648601i	$0.224646\pi$
$882$		0			0
$883$	−7.24302			−0.243747			−0.121873	−	0.992546i	$-0.538890\pi$
$883$	−7.24302			−0.243747			−0.121873	+	0.992546i	$0.538890\pi$
$884$	1.65206	−	2.86146i	0.0555649	−	0.0962413i
$885$		0			0
$886$	−4.08168	−	7.06967i	−0.137127	−	0.237510i
$887$	15.2434	+	26.4023i	0.511823	+	0.886504i	0.999906	+	0.0137067i	$0.00436312\pi$
$887$	15.2434	+	26.4023i	0.511823	+	0.886504i	−0.488083	+	0.872797i	$0.662304\pi$
$888$		0			0
$889$	3.46802	−	6.00679i	0.116314	−	0.201461i
$890$	−2.74605			−0.0920477
$891$		0			0
$892$	40.6916			1.36245
$893$	0.438010	−	0.758656i	0.0146574	−	0.0253874i
$894$		0			0
$895$	9.92772	+	17.1953i	0.331847	+	0.574776i
$896$	−13.9744	−	24.2043i	−0.466851	−	0.808610i
$897$		0			0
$898$	−1.75258	+	3.03557i	−0.0584845	+	0.101298i
$899$	8.34829			0.278431
$900$		0			0
$901$	12.8818			0.429155
$902$	2.81125	−	4.86922i	0.0936043	−	0.162127i
$903$		0			0
$904$	−14.3665	−	24.8835i	−0.477822	−	0.827612i
$905$	−10.1301	−	17.5458i	−0.336736	−	0.583244i
$906$		0			0
$907$	−6.72909	+	11.6551i	−0.223436	+	0.387002i	−0.955849	−	0.293858i	$-0.905061\pi$
$907$	−6.72909	+	11.6551i	−0.223436	+	0.387002i	0.732413	+	0.680860i	$0.238394\pi$
$908$	−29.5409			−0.980348
$909$		0			0
$910$	1.18596			0.0393142
$911$	−15.3374	+	26.5651i	−0.508149	+	0.880140i	0.491806	+	0.870705i	$0.336337\pi$
$911$	−15.3374	+	26.5651i	−0.508149	+	0.880140i	−0.999955	+	0.00943566i	$0.996996\pi$
$912$		0			0
$913$	−21.8483	−	37.8424i	−0.723074	−	1.25240i
$914$	4.22246	+	7.31351i	0.139666	+	0.241909i
$915$		0			0
$916$	−11.2828	+	19.5424i	−0.372794	+	0.645699i
$917$	−36.0924			−1.19188
$918$		0			0
$919$	−19.6999			−0.649839			−0.324919	−	0.945742i	$-0.605337\pi$
$919$	−19.6999			−0.649839			−0.324919	+	0.945742i	$0.605337\pi$
$920$	−3.58986	+	6.21783i	−0.118354	+	0.204996i
$921$		0			0
$922$	3.70255	+	6.41300i	0.121937	+	0.211201i
$923$	−2.72162	−	4.71399i	−0.0895833	−	0.155163i
$924$		0			0
$925$	5.10323	−	8.83906i	0.167793	−	0.290626i
$926$	−1.82214			−0.0598794
$927$		0			0
$928$	36.7501			1.20638
$929$	1.45936	−	2.52769i	0.0478802	−	0.0829309i	−0.841092	−	0.540892i	$-0.818087\pi$
$929$	1.45936	−	2.52769i	0.0478802	−	0.0829309i	0.888972	+	0.457961i	$0.151420\pi$
$930$		0			0
$931$	−2.55638	−	4.42778i	−0.0837820	−	0.145115i
$932$	17.4846	+	30.2842i	0.572727	+	0.991993i
$933$		0			0
$934$	3.65437	−	6.32955i	0.119575	−	0.207109i
$935$	−5.59883			−0.183101
$936$		0			0
$937$	−34.7949			−1.13670			−0.568351	−	0.822786i	$-0.692418\pi$
$937$	−34.7949			−1.13670			−0.568351	+	0.822786i	$0.692418\pi$
$938$	2.46323	−	4.26644i	0.0804274	−	0.139304i
$939$		0			0
$940$	−0.117425	−	0.203386i	−0.00382998	−	0.00663372i
$941$	−0.357443	−	0.619109i	−0.0116523	−	0.0201824i	0.860140	−	0.510057i	$-0.170376\pi$
$941$	−0.357443	−	0.619109i	−0.0116523	−	0.0201824i	−0.871793	+	0.489875i	$0.837042\pi$
$942$		0			0
$943$	7.87639	−	13.6423i	0.256490	−	0.444255i
$944$	−2.16997			−0.0706264
$945$		0			0
$946$	−9.10762			−0.296114
$947$	8.19183	−	14.1887i	0.266199	−	0.461070i	−0.701678	−	0.712494i	$-0.747566\pi$
$947$	8.19183	−	14.1887i	0.266199	−	0.461070i	0.967877	+	0.251424i	$0.0808990\pi$
$948$		0			0
$949$	3.16894	+	5.48876i	0.102868	+	0.178173i
$950$	−1.57253	−	2.72370i	−0.0510196	−	0.0883685i
$951$		0			0
$952$	−4.16799	+	7.21918i	−0.135085	+	0.233975i
$953$	−8.97837			−0.290838			−0.145419	−	0.989370i	$-0.546453\pi$
$953$	−8.97837			−0.290838			−0.145419	+	0.989370i	$0.546453\pi$
$954$		0			0
$955$	14.4245			0.466767
$956$	−12.2211	+	21.1676i	−0.395258	+	0.684608i
$957$		0			0
$958$	−5.14109	−	8.90463i	−0.166101	−	0.287696i
$959$	22.7080	+	39.3313i	0.733278	+	1.27008i
$960$		0			0
$961$	14.8884	−	25.7875i	0.480273	−	0.831856i
$962$	4.85056			0.156388
$963$		0			0
$964$	3.41629			0.110031
$965$	−12.1134	+	20.9810i	−0.389944	+	0.675403i
$966$		0			0
$967$	−0.152998	−	0.265000i	−0.00492008	−	0.00852182i	0.863555	−	0.504255i	$-0.168233\pi$
$967$	−0.152998	−	0.265000i	−0.00492008	−	0.00852182i	−0.868475	+	0.495733i	$0.834899\pi$
$968$	1.75982	+	3.04810i	0.0565628	+	0.0979697i
$969$		0			0
$970$	−1.44287	+	2.49913i	−0.0463279	+	0.0802423i
$971$	−24.9695			−0.801310			−0.400655	−	0.916229i	$-0.631217\pi$
$971$	−24.9695			−0.801310			−0.400655	+	0.916229i	$0.631217\pi$
$972$		0			0
$973$	−56.5841			−1.81400
$974$	−3.13628	+	5.43219i	−0.100493	+	0.174059i
$975$		0			0
$976$	6.45154	+	11.1744i	0.206509	+	0.357684i
$977$	11.7457	+	20.3442i	0.375780	+	0.650870i	0.990443	−	0.137920i	$-0.0440416\pi$
$977$	11.7457	+	20.3442i	0.375780	+	0.650870i	−0.614664	+	0.788789i	$0.710708\pi$
$978$		0			0
$979$	8.68542	−	15.0436i	0.277587	−	0.480795i
$980$	−1.37067			−0.0437844
$981$		0			0
$982$	−14.4065			−0.459729
$983$	−2.20491	+	3.81902i	−0.0703257	+	0.121808i	−0.899044	−	0.437858i	$-0.855737\pi$
$983$	−2.20491	+	3.81902i	−0.0703257	+	0.121808i	0.828718	+	0.559666i	$0.189071\pi$
$984$		0			0
$985$	−0.971866	−	1.68332i	−0.0309662	−	0.0536351i
$986$	−3.34057	−	5.78603i	−0.106385	−	0.184265i
$987$		0			0
$988$	−5.87045	+	10.1679i	−0.186764	+	0.323484i
$989$	−25.5172			−0.811399
$990$		0			0
$991$	−55.1403			−1.75159			−0.875794	−	0.482685i	$-0.839662\pi$
$991$	−55.1403			−1.75159			−0.875794	+	0.482685i	$0.839662\pi$
$992$	−2.69212	+	4.66289i	−0.0854749	+	0.148047i
$993$		0			0
$994$	3.22774	+	5.59061i	0.102378	+	0.177323i
$995$	3.78652	+	6.55845i	0.120041	+	0.207917i
$996$		0			0
$997$	17.5331	−	30.3683i	0.555280	−	0.961772i	−0.442602	−	0.896718i	$-0.645945\pi$
$997$	17.5331	−	30.3683i	0.555280	−	0.961772i	0.997882	−	0.0650543i	$-0.0207221\pi$
$998$	−17.3066			−0.547830
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.e.586.5		16
3.2	odd	2		585.2.i.f.196.4	✓	16
9.2	odd	6		5265.2.a.bb.1.5		8
9.4	even	3	inner	1755.2.i.e.1171.5		16
9.5	odd	6		585.2.i.f.391.4	yes	16
9.7	even	3		5265.2.a.be.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.f.196.4	✓	16	3.2	odd	2
585.2.i.f.391.4	yes	16	9.5	odd	6
1755.2.i.e.586.5		16	1.1	even	1	trivial
1755.2.i.e.1171.5		16	9.4	even	3	inner
5265.2.a.bb.1.5		8	9.2	odd	6
5265.2.a.be.1.4		8	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.237622 - 0.411573i) q^{2} +(0.887072 + 1.53645i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.24774 + 2.16115i) q^{7} +1.79364 q^{8} +O(q^{10})\)	\(q+(0.237622 - 0.411573i) q^{2} +(0.887072 + 1.53645i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.24774 + 2.16115i) q^{7} +1.79364 q^{8} +0.475244 q^{10} +(-1.50314 + 2.60351i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.592980 + 1.02707i) q^{14} +(-1.34794 + 2.33469i) q^{16} +1.86238 q^{17} -6.61778 q^{19} +(-0.887072 + 1.53645i) q^{20} +(0.714357 + 1.23730i) q^{22} +(2.00144 + 3.46660i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.475244 q^{26} -4.42734 q^{28} +(3.77429 - 6.53727i) q^{29} +(0.552970 + 0.957772i) q^{31} +(2.43424 + 4.21622i) q^{32} +(0.442542 - 0.766505i) q^{34} -2.49548 q^{35} -10.2065 q^{37} +(-1.57253 + 2.72370i) q^{38} +(0.896819 + 1.55334i) q^{40} +(-1.96768 - 3.40812i) q^{41} +(-3.18735 + 5.52065i) q^{43} -5.33357 q^{44} +1.90235 q^{46} +(-0.0661868 + 0.114639i) q^{47} +(0.386290 + 0.669074i) q^{49} +(0.237622 + 0.411573i) q^{50} +(0.887072 - 1.53645i) q^{52} +6.91685 q^{53} -3.00628 q^{55} +(-2.23799 + 3.87632i) q^{56} +(-1.79371 - 3.10680i) q^{58} +(0.402461 + 0.697082i) q^{59} +(2.39312 - 4.14500i) q^{61} +0.525591 q^{62} -3.07804 q^{64} +(0.500000 - 0.866025i) q^{65} +(-2.07699 - 3.59746i) q^{67} +(1.65206 + 2.86146i) q^{68} +(-0.592980 + 1.02707i) q^{70} +5.44325 q^{71} -6.33787 q^{73} +(-2.42528 + 4.20071i) q^{74} +(-5.87045 - 10.1679i) q^{76} +(-3.75105 - 6.49701i) q^{77} +(2.31771 - 4.01440i) q^{79} -2.69587 q^{80} -1.87025 q^{82} +(-7.26757 + 12.5878i) q^{83} +(0.931190 + 1.61287i) q^{85} +(1.51477 + 2.62365i) q^{86} +(-2.69609 + 4.66976i) q^{88} -5.77819 q^{89} +2.49548 q^{91} +(-3.55085 + 6.15025i) q^{92} +(0.0314549 + 0.0544814i) q^{94} +(-3.30889 - 5.73117i) q^{95} +(-3.03607 + 5.25864i) q^{97} +0.367164 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 5 q^{4} + 8 q^{5} + 6 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q - q^2 - 5 * q^4 + 8 * q^5 + 6 * q^7 + 12 * q^8	\( 16 q - q^{2} - 5 q^{4} + 8 q^{5} + 6 q^{7} + 12 q^{8} - 2 q^{10} - 9 q^{11} - 8 q^{13} + 3 q^{14} + 13 q^{16} - 12 q^{17} - 22 q^{19} + 5 q^{20} + 4 q^{22} - 3 q^{23} - 8 q^{25} + 2 q^{26} - 26 q^{28} - 8 q^{29} + 18 q^{31} - 3 q^{32} + 9 q^{34} + 12 q^{35} - 36 q^{37} + 8 q^{38} + 6 q^{40} + 17 q^{41} + 17 q^{43} - 10 q^{44} + 6 q^{46} - 11 q^{47} + 16 q^{49} - q^{50} - 5 q^{52} - 20 q^{53} - 18 q^{55} + q^{56} + 10 q^{58} - 7 q^{59} + 21 q^{61} + 58 q^{62} - 20 q^{64} + 8 q^{65} + 13 q^{67} + 16 q^{68} - 3 q^{70} + 68 q^{71} - 32 q^{73} + 4 q^{74} + 2 q^{76} - 18 q^{77} + 37 q^{79} + 26 q^{80} + 2 q^{82} - 3 q^{83} - 6 q^{85} + 2 q^{86} + 19 q^{88} - 28 q^{89} - 12 q^{91} + 14 q^{92} + 44 q^{94} - 11 q^{95} + 17 q^{97} - 90 q^{98}+O(q^{100}) \) 16 * q - q^2 - 5 * q^4 + 8 * q^5 + 6 * q^7 + 12 * q^8 - 2 * q^10 - 9 * q^11 - 8 * q^13 + 3 * q^14 + 13 * q^16 - 12 * q^17 - 22 * q^19 + 5 * q^20 + 4 * q^22 - 3 * q^23 - 8 * q^25 + 2 * q^26 - 26 * q^28 - 8 * q^29 + 18 * q^31 - 3 * q^32 + 9 * q^34 + 12 * q^35 - 36 * q^37 + 8 * q^38 + 6 * q^40 + 17 * q^41 + 17 * q^43 - 10 * q^44 + 6 * q^46 - 11 * q^47 + 16 * q^49 - q^50 - 5 * q^52 - 20 * q^53 - 18 * q^55 + q^56 + 10 * q^58 - 7 * q^59 + 21 * q^61 + 58 * q^62 - 20 * q^64 + 8 * q^65 + 13 * q^67 + 16 * q^68 - 3 * q^70 + 68 * q^71 - 32 * q^73 + 4 * q^74 + 2 * q^76 - 18 * q^77 + 37 * q^79 + 26 * q^80 + 2 * q^82 - 3 * q^83 - 6 * q^85 + 2 * q^86 + 19 * q^88 - 28 * q^89 - 12 * q^91 + 14 * q^92 + 44 * q^94 - 11 * q^95 + 17 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more