LMFDB - Embedded newform 531.2.i.c.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			64.5
Character	$\chi$	$=$	531.64
Dual form			531.2.i.c.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.61370 + 0.880659i) q^{2} +(4.46370 + 3.39321i) q^{4} +(-0.422705 + 1.06091i) q^{5} +(-3.24336 + 1.50054i) q^{7} +(5.58292 + 8.23419i) q^{8} +O(q^{10})$	\(q+(2.61370 + 0.880659i) q^{2} +(4.46370 + 3.39321i) q^{4} +(-0.422705 + 1.06091i) q^{5} +(-3.24336 + 1.50054i) q^{7} +(5.58292 + 8.23419i) q^{8} +(-2.03912 + 2.40064i) q^{10} +(1.24288 - 4.47645i) q^{11} +(0.233736 - 0.440872i) q^{13} +(-9.79864 + 1.06567i) q^{14} +(4.34051 + 15.6331i) q^{16} +(-3.12785 - 1.44710i) q^{17} +(3.33146 - 0.733309i) q^{19} +(-5.48672 + 3.30125i) q^{20} +(7.19075 - 10.6056i) q^{22} +(1.36389 - 8.31938i) q^{23} +(2.68313 + 2.54159i) q^{25} +(0.999173 - 0.946467i) q^{26} +(-19.5690 - 4.30747i) q^{28} +(4.38942 - 1.47897i) q^{29} +(-1.07570 - 0.236779i) q^{31} +(-1.34544 + 24.8152i) q^{32} +(-6.90086 - 6.53684i) q^{34} +(-0.220951 - 4.07519i) q^{35} +(-1.37727 + 2.03133i) q^{37} +(9.35324 + 1.01723i) q^{38} +(-11.0956 + 2.44234i) q^{40} +(0.568080 + 3.46513i) q^{41} +(0.990022 + 3.56574i) q^{43} +(20.7374 - 15.7642i) q^{44} +(10.8914 - 20.5433i) q^{46} +(-0.881582 - 2.21260i) q^{47} +(3.73606 - 4.39843i) q^{49} +(4.77462 + 9.00589i) q^{50} +(2.53930 - 1.17480i) q^{52} +(-4.59132 - 5.40532i) q^{53} +(4.22374 + 3.21080i) q^{55} +(-30.4631 - 18.3290i) q^{56} +12.7751 q^{58} +(4.50924 + 6.21826i) q^{59} +(-14.5736 - 4.91042i) q^{61} +(-2.60304 - 1.56620i) q^{62} +(-13.3597 + 33.5303i) q^{64} +(0.368924 + 0.434331i) q^{65} +(-0.642743 - 0.947975i) q^{67} +(-9.05145 - 17.0728i) q^{68} +(3.01136 - 10.8459i) q^{70} +(-3.14974 - 7.90526i) q^{71} +(-5.00415 + 0.544234i) q^{73} +(-5.38869 + 4.09638i) q^{74} +(17.3589 + 8.03108i) q^{76} +(2.68598 + 16.3837i) q^{77} +(-2.43897 + 1.46748i) q^{79} +(-18.4201 - 2.00330i) q^{80} +(-1.56681 + 9.55712i) q^{82} +(0.350818 + 6.47046i) q^{83} +(2.85739 - 2.70667i) q^{85} +(-0.552575 + 10.1917i) q^{86} +(43.7988 - 14.7576i) q^{88} +(-4.14450 + 1.39644i) q^{89} +(-0.0965432 + 1.78064i) q^{91} +(34.3174 - 32.5072i) q^{92} +(-0.355644 - 6.55946i) q^{94} +(-0.630249 + 3.84435i) q^{95} +(-9.65402 - 1.04994i) q^{97} +(13.6385 - 8.20599i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{3}{29}\right)$

Coefficient data

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

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

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

$2$	2.61370	+	0.880659i	1.84817	+	0.622720i	0.994854	+	0.101322i	$0.0323071\pi$
$2$	2.61370	+	0.880659i	1.84817	+	0.622720i	0.853313	+	0.521398i	$0.174589\pi$
$3$		0			0
$3$		0			0
$4$	4.46370	+	3.39321i	2.23185	+	1.69661i
$5$	−0.422705	+	1.06091i	−0.189039	+	0.474453i	−0.992696	−	0.120640i	$-0.961505\pi$
$5$	−0.422705	+	1.06091i	−0.189039	+	0.474453i	0.803657	+	0.595093i	$0.202885\pi$
$6$		0			0
$7$	−3.24336	+	1.50054i	−1.22587	+	0.567150i	−0.922602	−	0.385754i	$-0.873941\pi$
$7$	−3.24336	+	1.50054i	−1.22587	+	0.567150i	−0.303273	+	0.952904i	$0.598079\pi$
$8$	5.58292	+	8.23419i	1.97386	+	2.91122i
$9$		0			0
$10$	−2.03912	+	2.40064i	−0.644828	+	0.759150i
$11$	1.24288	−	4.47645i	0.374743	−	1.34970i	−0.500382	−	0.865805i	$-0.666807\pi$
$11$	1.24288	−	4.47645i	0.374743	−	1.34970i	0.875125	−	0.483897i	$-0.160779\pi$
$12$		0			0
$13$	0.233736	−	0.440872i	0.0648266	−	0.122276i	−0.848981	−	0.528424i	$-0.822783\pi$
$13$	0.233736	−	0.440872i	0.0648266	−	0.122276i	0.913807	+	0.406148i	$0.133128\pi$
$14$	−9.79864	+	1.06567i	−2.61880	+	0.284811i
$15$		0			0
$16$	4.34051	+	15.6331i	1.08513	+	3.90828i
$17$	−3.12785	−	1.44710i	−0.758614	−	0.350972i	0.00215268	−	0.999998i	$-0.499315\pi$
$17$	−3.12785	−	1.44710i	−0.758614	−	0.350972i	−0.760767	+	0.649025i	$0.775177\pi$
$18$		0			0
$19$	3.33146	−	0.733309i	0.764289	−	0.168233i	0.184314	−	0.982867i	$-0.440994\pi$
$19$	3.33146	−	0.733309i	0.764289	−	0.168233i	0.579974	+	0.814635i	$0.303063\pi$
$20$	−5.48672	+	3.30125i	−1.22687	+	0.738182i
$21$		0			0
$22$	7.19075	−	10.6056i	1.53307	−	2.26111i
$23$	1.36389	−	8.31938i	0.284391	−	1.73471i	−0.328465	−	0.944516i	$-0.606531\pi$
$23$	1.36389	−	8.31938i	0.284391	−	1.73471i	0.612856	−	0.790195i	$-0.290021\pi$
$24$		0			0
$25$	2.68313	+	2.54159i	0.536626	+	0.508319i
$26$	0.999173	−	0.946467i	0.195954	−	0.185618i
$27$		0			0
$28$	−19.5690	−	4.30747i	−3.69820	−	0.814035i
$29$	4.38942	−	1.47897i	0.815095	−	0.274638i	0.119282	−	0.992860i	$-0.461941\pi$
$29$	4.38942	−	1.47897i	0.815095	−	0.274638i	0.695813	+	0.718223i	$0.255044\pi$
$30$		0			0
$31$	−1.07570	−	0.236779i	−0.193201	−	0.0425268i	0.117316	−	0.993095i	$-0.462571\pi$
$31$	−1.07570	−	0.236779i	−0.193201	−	0.0425268i	−0.310517	+	0.950568i	$0.600502\pi$
$32$	−1.34544	+	24.8152i	−0.237842	+	4.38674i
$33$		0			0
$34$	−6.90086	−	6.53684i	−1.18349	−	1.12106i
$35$	−0.220951	−	4.07519i	−0.0373475	−	0.688833i
$36$		0			0
$37$	−1.37727	+	2.03133i	−0.226422	+	0.333948i	−0.923883	−	0.382675i	$-0.875003\pi$
$37$	−1.37727	+	2.03133i	−0.226422	+	0.333948i	0.697461	+	0.716623i	$0.254313\pi$
$38$	9.35324	+	1.01723i	1.51730	+	0.165016i
$39$		0			0
$40$	−11.0956	+	2.44234i	−1.75438	+	0.386167i
$41$	0.568080	+	3.46513i	0.0887192	+	0.541163i	0.993366	+	0.115000i	$0.0366868\pi$
$41$	0.568080	+	3.46513i	0.0887192	+	0.541163i	−0.904646	+	0.426163i	$0.859865\pi$
$42$		0			0
$43$	0.990022	+	3.56574i	0.150977	+	0.543770i	0.999884	+	0.0152278i	$0.00484735\pi$
$43$	0.990022	+	3.56574i	0.150977	+	0.543770i	−0.848907	+	0.528542i	$0.822739\pi$
$44$	20.7374	−	15.7642i	3.12628	−	2.37654i
$45$		0			0
$46$	10.8914	−	20.5433i	1.60584	−	3.02894i
$47$	−0.881582	−	2.21260i	−0.128592	−	0.322742i	0.850558	−	0.525882i	$-0.176265\pi$
$47$	−0.881582	−	2.21260i	−0.128592	−	0.322742i	−0.979150	+	0.203140i	$0.934885\pi$
$48$		0			0
$49$	3.73606	−	4.39843i	0.533723	−	0.628347i
$50$	4.77462	+	9.00589i	0.675234	+	1.27363i
$51$		0			0
$52$	2.53930	−	1.17480i	0.352137	−	0.162916i
$53$	−4.59132	−	5.40532i	−0.630666	−	0.742477i	0.350304	−	0.936636i	$-0.386078\pi$
$53$	−4.59132	−	5.40532i	−0.630666	−	0.742477i	−0.980970	+	0.194159i	$0.937802\pi$
$54$		0			0
$55$	4.22374	+	3.21080i	0.569529	+	0.432945i
$56$	−30.4631	−	18.3290i	−4.07080	−	2.44932i
$57$		0			0
$58$	12.7751			1.67745
$59$	4.50924	+	6.21826i	0.587053	+	0.809548i
$59$	4.50924	+	6.21826i	0.587053	+	0.809548i
$60$		0			0
$61$	−14.5736	−	4.91042i	−1.86596	−	0.628715i	−0.988952	−	0.148239i	$-0.952639\pi$
$61$	−14.5736	−	4.91042i	−1.86596	−	0.628715i	−0.877008	−	0.480476i	$-0.840464\pi$
$62$	−2.60304	−	1.56620i	−0.330586	−	0.198907i
$63$		0			0
$64$	−13.3597	+	33.5303i	−1.66996	+	4.19128i
$65$	0.368924	+	0.434331i	0.0457594	+	0.0538721i
$66$		0			0
$67$	−0.642743	−	0.947975i	−0.0785236	−	0.115814i	0.786399	−	0.617719i	$-0.211943\pi$
$67$	−0.642743	−	0.947975i	−0.0785236	−	0.115814i	−0.864923	+	0.501905i	$0.832633\pi$
$68$	−9.05145	−	17.0728i	−1.09765	−	2.07039i
$69$		0			0
$70$	3.01136	−	10.8459i	0.359926	−	1.29634i
$71$	−3.14974	−	7.90526i	−0.373806	−	0.938182i	−0.988745	−	0.149608i	$-0.952199\pi$
$71$	−3.14974	−	7.90526i	−0.373806	−	0.938182i	0.614939	−	0.788574i	$-0.289180\pi$
$72$		0			0
$73$	−5.00415	+	0.544234i	−0.585691	+	0.0636978i	−0.396167	−	0.918178i	$-0.629660\pi$
$73$	−5.00415	+	0.544234i	−0.585691	+	0.0636978i	−0.189524	+	0.981876i	$0.560694\pi$
$74$	−5.38869	+	4.09638i	−0.626423	+	0.476194i
$75$		0			0
$76$	17.3589	+	8.03108i	1.99120	+	0.921228i
$77$	2.68598	+	16.3837i	0.306095	+	1.86710i
$78$		0			0
$79$	−2.43897	+	1.46748i	−0.274406	+	0.165105i	−0.646105	−	0.763249i	$-0.723603\pi$
$79$	−2.43897	+	1.46748i	−0.274406	+	0.165105i	0.371699	+	0.928353i	$0.378775\pi$
$80$	−18.4201	−	2.00330i	−2.05943	−	0.223976i
$81$		0			0
$82$	−1.56681	+	9.55712i	−0.173025	+	1.05541i
$83$	0.350818	+	6.47046i	0.0385073	+	0.710225i	0.952508	+	0.304513i	$0.0984937\pi$
$83$	0.350818	+	6.47046i	0.0385073	+	0.710225i	−0.914001	+	0.405712i	$0.867024\pi$
$84$		0			0
$85$	2.85739	−	2.70667i	0.309928	−	0.293579i
$86$	−0.552575	+	10.1917i	−0.0595857	+	1.09899i
$87$		0			0
$88$	43.7988	−	14.7576i	4.66897	−	1.57316i
$89$	−4.14450	+	1.39644i	−0.439316	+	0.148023i	−0.530263	−	0.847833i	$-0.677907\pi$
$89$	−4.14450	+	1.39644i	−0.439316	+	0.148023i	0.0909477	+	0.995856i	$0.471010\pi$
$90$		0			0
$91$	−0.0965432	+	1.78064i	−0.0101205	+	0.186661i
$92$	34.3174	−	32.5072i	3.57784	−	3.38911i
$93$		0			0
$94$	−0.355644	−	6.55946i	−0.0366819	−	0.676557i
$95$	−0.630249	+	3.84435i	−0.0646622	+	0.394422i
$96$		0			0
$97$	−9.65402	−	1.04994i	−0.980217	−	0.106605i	−0.396042	−	0.918233i	$-0.629616\pi$
$97$	−9.65402	−	1.04994i	−0.980217	−	0.106605i	−0.584175	+	0.811627i	$0.698582\pi$
$98$	13.6385	−	8.20599i	1.37769	−	0.828930i
$99$		0			0
$100$	3.35250	+	20.4493i	0.335250	+	2.04493i
$101$	−6.33538	−	2.93106i	−0.630394	−	0.291651i	0.0785562	−	0.996910i	$-0.474969\pi$
$101$	−6.33538	−	2.93106i	−0.630394	−	0.291651i	−0.708951	+	0.705258i	$0.750831\pi$
$102$		0			0
$103$	−7.14362	+	5.43044i	−0.703882	+	0.535077i	−0.894766	−	0.446536i	$-0.852658\pi$
$103$	−7.14362	+	5.43044i	−0.703882	+	0.535077i	0.190884	+	0.981613i	$0.438865\pi$
$104$	4.93515	−	0.536730i	0.483931	−	0.0526307i
$105$		0			0
$106$	−7.24010	−	18.1713i	−0.703220	−	1.76495i
$107$	−1.14051	+	4.10773i	−0.110257	+	0.397110i	−0.997999	−	0.0632318i	$-0.979859\pi$
$107$	−1.14051	+	4.10773i	−0.110257	+	0.397110i	0.887742	+	0.460342i	$0.152273\pi$
$108$		0			0
$109$	3.65503	+	6.89411i	0.350088	+	0.660336i	0.994545	−	0.104304i	$-0.0332615\pi$
$109$	3.65503	+	6.89411i	0.350088	+	0.660336i	−0.644457	+	0.764640i	$0.722917\pi$
$110$	8.21198	+	12.1118i	0.782981	+	1.15481i
$111$		0			0
$112$	−37.5359	−	44.1907i	−3.54681	−	4.17563i
$113$	1.19164	−	2.99080i	0.112100	−	0.281351i	−0.862213	−	0.506545i	$-0.830922\pi$
$113$	1.19164	−	2.99080i	0.112100	−	0.281351i	0.974314	+	0.225194i	$0.0723017\pi$
$114$		0			0
$115$	8.24958	+	4.96361i	0.769278	+	0.462859i
$116$	24.6115	+	8.29258i	2.28512	+	0.769947i
$117$		0			0
$118$	6.30966	+	20.2238i	0.580851	+	1.86175i
$119$	12.3161			1.12902
$120$		0			0
$121$	−9.06845	−	5.45631i	−0.824405	−	0.496028i
$122$	−33.7667	−	25.6688i	−3.05709	−	2.32394i
$123$		0			0
$124$	−3.99816	−	4.70699i	−0.359045	−	0.422700i
$125$	−9.01292	+	4.16982i	−0.806140	+	0.372960i
$126$		0			0
$127$	−7.57778	−	14.2932i	−0.672419	−	1.26832i	−0.951382	−	0.308015i	$-0.900335\pi$
$127$	−7.57778	−	14.2932i	−0.672419	−	1.26832i	0.278963	−	0.960302i	$-0.410009\pi$
$128$	−32.2698	+	37.9909i	−2.85227	+	3.35796i
$129$		0			0
$130$	0.581760	+	1.46011i	0.0510238	+	0.128060i
$131$	1.95854	−	3.69420i	0.171118	−	0.322764i	−0.783089	−	0.621910i	$-0.786357\pi$
$131$	1.95854	−	3.69420i	0.171118	−	0.322764i	0.954207	+	0.299146i	$0.0967018\pi$
$132$		0			0
$133$	−9.70475	+	7.37736i	−0.841509	+	0.639698i
$134$	−0.845097	−	3.04376i	−0.0730053	−	0.262941i
$135$		0			0
$136$	−5.54685	−	33.8343i	−0.475638	−	2.90126i
$137$	−19.6835	+	4.33267i	−1.68168	+	0.370165i	−0.950185	−	0.311686i	$-0.899106\pi$
$137$	−19.6835	+	4.33267i	−1.68168	+	0.370165i	−0.731491	+	0.681851i	$0.761175\pi$
$138$		0			0
$139$	21.9813	+	2.39061i	1.86443	+	0.202769i	0.969778	−	0.243989i	$-0.0784562\pi$
$139$	21.9813	+	2.39061i	1.86443	+	0.202769i	0.894655	+	0.446758i	$0.147422\pi$
$140$	12.8417	−	18.9402i	1.08533	−	1.60074i
$141$		0			0
$142$	−1.27066	−	23.4359i	−0.106631	−	1.96669i
$143$	−1.68304	−	1.59426i	−0.140743	−	0.133319i
$144$		0			0
$145$	−0.286379	+	5.28195i	−0.0237825	+	0.438642i
$146$	−13.5586	−	2.98448i	−1.12212	−	0.246998i
$147$		0			0
$148$	−13.0405	+	4.39384i	−1.07192	+	0.361172i
$149$	14.0077	+	3.08333i	1.14756	+	0.252596i	0.747735	−	0.663997i	$-0.231141\pi$
$149$	14.0077	+	3.08333i	1.14756	+	0.252596i	0.399821	+	0.916593i	$0.369072\pi$
$150$		0			0
$151$	10.0234	−	9.49464i	0.815690	−	0.772663i	−0.161083	−	0.986941i	$-0.551499\pi$
$151$	10.0234	−	9.49464i	0.815690	−	0.772663i	0.976773	+	0.214278i	$0.0687399\pi$
$152$	24.6375	+	23.3378i	1.99836	+	1.89295i
$153$		0			0
$154$	−7.40814	+	45.1876i	−0.596965	+	3.64132i
$155$	0.705905	−	1.04113i	0.0566997	−	0.0836257i
$156$		0			0
$157$	20.2504	−	12.1843i	1.61616	−	0.972410i	0.636613	−	0.771184i	$-0.280335\pi$
$157$	20.2504	−	12.1843i	1.61616	−	0.972410i	0.979545	−	0.201226i	$-0.0644926\pi$
$158$	−7.66710	+	1.68766i	−0.609962	+	0.134263i
$159$		0			0
$160$	−25.7579	−	11.9169i	−2.03634	−	0.942112i
$161$	8.05995	+	29.0293i	0.635213	+	2.28783i
$162$		0			0
$163$	−1.30865	+	0.142325i	−0.102502	+	0.0111477i	−0.159226	−	0.987242i	$-0.550900\pi$
$163$	−1.30865	+	0.142325i	−0.102502	+	0.0111477i	0.0567244	+	0.998390i	$0.481934\pi$
$164$	−9.22221	+	17.3949i	−0.720133	+	1.35832i
$165$		0			0
$166$	−4.78133	+	17.2208i	−0.371103	+	1.33659i
$167$	10.7489	−	12.6546i	0.831777	−	0.979244i	−0.168202	−	0.985753i	$-0.553796\pi$
$167$	10.7489	−	12.6546i	0.831777	−	0.979244i	0.999979	+	0.00650896i	$0.00207188\pi$
$168$		0			0
$169$	7.15570	+	10.5539i	0.550438	+	0.811836i
$170$	9.85203	−	4.55803i	0.755616	−	0.349585i
$171$		0			0
$172$	−7.68015	+	19.2757i	−0.585606	+	1.46976i
$173$	−10.1235	−	7.69567i	−0.769674	−	0.585091i	0.144930	−	0.989442i	$-0.453704\pi$
$173$	−10.1235	−	7.69567i	−0.769674	−	0.585091i	−0.914604	+	0.404351i	$0.867497\pi$
$174$		0			0
$175$	−12.5161	−	4.21717i	−0.946129	−	0.318788i
$176$	75.3756			5.68165
$177$		0			0
$178$	−12.0623			−0.904105
$179$	9.24601	+	3.11534i	0.691079	+	0.232852i	0.642859	−	0.765985i	$-0.277748\pi$
$179$	9.24601	+	3.11534i	0.691079	+	0.232852i	0.0482209	+	0.998837i	$0.484645\pi$
$180$		0			0
$181$	1.67781	+	1.27544i	0.124711	+	0.0948025i	0.665670	−	0.746246i	$-0.268146\pi$
$181$	1.67781	+	1.27544i	0.124711	+	0.0948025i	−0.540960	+	0.841049i	$0.681939\pi$
$182$	−1.82047	+	4.56903i	−0.134942	+	0.338679i
$183$		0			0
$184$	76.1178	−	35.2159i	5.61148	−	2.59615i
$185$	−1.57287	−	2.31981i	−0.115640	−	0.170556i
$186$		0			0
$187$	−10.3654	+	12.2031i	−0.757993	+	0.892378i
$188$	3.57273	−	12.8678i	0.260568	−	0.938480i
$189$		0			0
$190$	−5.03284	+	9.49295i	−0.365121	+	0.688691i
$191$	0.640381	−	0.0696456i	0.0463363	−	0.00503938i	−0.0849215	−	0.996388i	$-0.527064\pi$
$191$	0.640381	−	0.0696456i	0.0463363	−	0.00503938i	0.131258	+	0.991348i	$0.458098\pi$
$192$		0			0
$193$	4.91357	+	17.6971i	0.353686	+	1.27386i	0.899856	+	0.436188i	$0.143672\pi$
$193$	4.91357	+	17.6971i	0.353686	+	1.27386i	−0.546169	+	0.837675i	$0.683914\pi$
$194$	−24.3081	−	11.2461i	−1.74522	−	0.807425i
$195$		0			0
$196$	31.6014	−	6.95600i	2.25725	−	0.496857i
$197$	−3.09833	+	1.86420i	−0.220747	+	0.132819i	−0.621632	−	0.783309i	$-0.713530\pi$
$197$	−3.09833	+	1.86420i	−0.220747	+	0.132819i	0.400885	+	0.916128i	$0.368703\pi$
$198$		0			0
$199$	−8.33655	+	12.2955i	−0.590962	+	0.871604i	−0.999147	−	0.0412955i	$-0.986852\pi$
$199$	−8.33655	+	12.2955i	−0.590962	+	0.871604i	0.408185	+	0.912899i	$0.366162\pi$
$200$	−5.94828	+	36.2829i	−0.420607	+	2.56559i
$201$		0			0
$202$	−13.9775	−	13.2402i	−0.983457	−	0.931580i
$203$	−12.0172	+	11.3833i	−0.843444	+	0.798952i
$204$		0			0
$205$	−3.91632	−	0.862048i	−0.273528	−	0.0602080i
$206$	−23.4537	+	7.90246i	−1.63409	+	0.550591i
$207$		0			0
$208$	7.90673	+	1.74040i	0.548233	+	0.120675i
$209$	0.857981	−	15.8245i	0.0593478	−	1.09461i
$210$		0			0
$211$	11.0043	+	10.4239i	0.757569	+	0.717608i	0.965462	−	0.260544i	$-0.0839019\pi$
$211$	11.0043	+	10.4239i	0.757569	+	0.717608i	−0.207893	+	0.978152i	$0.566661\pi$
$212$	−2.15285	−	39.7070i	−0.147858	−	2.72709i
$213$		0			0
$214$	−6.59846	+	9.73200i	−0.451061	+	0.665266i
$215$	−4.20141	−	0.456931i	−0.286534	−	0.0311624i
$216$		0			0
$217$	3.84418	−	0.846167i	0.260960	−	0.0574416i
$218$	3.48179	+	21.2380i	0.235817	+	1.43842i
$219$		0			0
$220$	7.95855	+	28.6641i	0.536565	+	1.93253i
$221$	−1.36907	+	1.04074i	−0.0920938	+	0.0700079i
$222$		0			0
$223$	−5.16805	+	9.74798i	−0.346078	+	0.652773i	−0.994054	−	0.108888i	$-0.965271\pi$
$223$	−5.16805	+	9.74798i	−0.346078	+	0.652773i	0.647976	+	0.761661i	$0.275616\pi$
$224$	−32.8723	−	82.5034i	−2.19638	−	5.51249i
$225$		0			0
$226$	5.74848	−	6.76763i	0.382383	−	0.450176i
$227$	6.57230	+	12.3967i	0.436219	+	0.822797i	0.999995	−	0.00313113i	$-0.000996670\pi$
$227$	6.57230	+	12.3967i	0.436219	+	0.822797i	−0.563776	+	0.825928i	$0.690652\pi$
$228$		0			0
$229$	13.4097	−	6.20398i	0.886137	−	0.409971i	0.0766155	−	0.997061i	$-0.475589\pi$
$229$	13.4097	−	6.20398i	0.886137	−	0.409971i	0.809522	+	0.587090i	$0.199727\pi$
$230$	17.1907	+	20.2385i	1.13352	+	1.33449i
$231$		0			0
$232$	36.6839	+	27.8864i	2.40841	+	1.83083i
$233$	8.88489	+	5.34586i	0.582068	+	0.350219i	0.775939	−	0.630808i	$-0.217277\pi$
$233$	8.88489	+	5.34586i	0.582068	+	0.350219i	−0.193870	+	0.981027i	$0.562104\pi$
$234$		0			0
$235$	2.72002			0.177435
$236$	−0.971985	+	43.0572i	−0.0632709	+	2.80279i
$237$		0			0
$238$	32.1907	+	10.8463i	2.08662	+	0.703063i
$239$	4.45730	+	2.68187i	0.288319	+	0.173475i	0.652364	−	0.757906i	$-0.273777\pi$
$239$	4.45730	+	2.68187i	0.288319	+	0.173475i	−0.364046	+	0.931381i	$0.618605\pi$
$240$		0			0
$241$	−1.39012	+	3.48895i	−0.0895457	+	0.224743i	−0.966928	−	0.255049i	$-0.917908\pi$
$241$	−1.39012	+	3.48895i	−0.0895457	+	0.224743i	0.877382	+	0.479792i	$0.159288\pi$
$242$	−18.8971	−	22.2474i	−1.21475	−	1.43012i
$243$		0			0
$244$	−48.3901	−	71.3700i	−3.09786	−	4.56900i
$245$	3.08708	+	5.82286i	0.197226	+	0.372009i
$246$		0			0
$247$	0.455385	−	1.64015i	0.0289754	−	0.104360i
$248$	−4.05586	−	10.1794i	−0.257547	−	0.646395i
$249$		0			0
$250$	−27.2293	+	2.96136i	−1.72213	+	0.187293i
$251$	−22.7060	+	17.2607i	−1.43319	+	1.08948i	−0.452982	+	0.891519i	$0.649640\pi$
$251$	−22.7060	+	17.2607i	−1.43319	+	1.08948i	−0.980209	+	0.197965i	$0.936567\pi$
$252$		0			0
$253$	−35.5462	−	16.4454i	−2.23477	−	1.03391i
$254$	−7.21862	−	44.0316i	−0.452936	−	2.76279i
$255$		0			0
$256$	−55.9463	+	33.6618i	−3.49664	+	2.10386i
$257$	−13.7430	−	1.49464i	−0.857263	−	0.0932330i	−0.331079	−	0.943603i	$-0.607413\pi$
$257$	−13.7430	−	1.49464i	−0.857263	−	0.0932330i	−0.526185	+	0.850370i	$0.676378\pi$
$258$		0			0
$259$	1.41891	−	8.65497i	0.0881668	−	0.537794i
$260$	0.172987	+	3.19056i	0.0107282	+	0.197870i
$261$		0			0
$262$	8.37237	−	7.93073i	0.517247	−	0.489962i
$263$	0.105003	−	1.93667i	0.00647479	−	0.119420i	−0.993509	−	0.113752i	$-0.963713\pi$
$263$	0.105003	−	1.93667i	0.00647479	−	0.119420i	0.999984	−	0.00566820i	$-0.00180425\pi$
$264$		0			0
$265$	7.67532	−	2.58612i	0.471491	−	0.158864i
$266$	−31.8623	+	10.7357i	−1.95360	+	0.658245i
$267$		0			0
$268$	0.347672	−	6.41244i	0.0212375	−	0.391702i
$269$	−4.94163	+	4.68096i	−0.301297	+	0.285403i	−0.823379	−	0.567492i	$-0.807914\pi$
$269$	−4.94163	+	4.68096i	−0.301297	+	0.285403i	0.522083	+	0.852895i	$0.325155\pi$
$270$		0			0
$271$	−0.266202	−	4.90981i	−0.0161706	−	0.298249i	−0.995421	−	0.0955930i	$-0.969525\pi$
$271$	−0.266202	−	4.90981i	−0.0161706	−	0.298249i	0.979250	−	0.202656i	$-0.0649575\pi$
$272$	9.04615	−	55.1791i	0.548503	−	3.34572i
$273$		0			0
$274$	−55.2625	−	6.01016i	−3.33853	−	0.363087i
$275$	14.7121	−	8.85200i	0.887175	−	0.533796i
$276$		0			0
$277$	0.482332	+	2.94210i	0.0289805	+	0.176773i	0.997351	−	0.0727450i	$-0.0231759\pi$
$277$	0.482332	+	2.94210i	0.0289805	+	0.176773i	−0.968370	+	0.249518i	$0.919728\pi$
$278$	55.3474	+	25.6064i	3.31951	+	1.53577i
$279$		0			0
$280$	32.3224	−	24.5708i	1.93163	−	1.46839i
$281$	9.58826	−	1.04279i	0.571988	−	0.0622074i	0.182445	−	0.983216i	$-0.441599\pi$
$281$	9.58826	−	1.04279i	0.571988	−	0.0622074i	0.389542	+	0.921009i	$0.372633\pi$
$282$		0			0
$283$	−0.536163	−	1.34567i	−0.0318716	−	0.0799916i	0.912180	−	0.409791i	$-0.134398\pi$
$283$	−0.536163	−	1.34567i	−0.0318716	−	0.0799916i	−0.944051	+	0.329799i	$0.893019\pi$
$284$	12.7647	−	45.9745i	0.757448	−	2.72808i
$285$		0			0
$286$	−2.99496	−	5.64910i	−0.177096	−	0.334038i
$287$	−7.04205	−	10.3862i	−0.415679	−	0.613081i
$288$		0			0
$289$	−3.31623	−	3.90417i	−0.195073	−	0.229657i
$290$	−5.40010	+	13.5532i	−0.317105	+	0.795873i
$291$		0			0
$292$	−24.1837	−	14.5509i	−1.41524	−	0.851524i
$293$	−19.6052	−	6.60577i	−1.14535	−	0.385913i	−0.318271	−	0.948000i	$-0.603102\pi$
$293$	−19.6052	−	6.60577i	−1.14535	−	0.385913i	−0.827078	+	0.562087i	$0.809999\pi$
$294$		0			0
$295$	−8.50309	+	2.15541i	−0.495069	+	0.125493i
$296$	−24.4155			−1.41912
$297$		0			0
$298$	33.8966	+	20.3949i	1.96358	+	1.18145i
$299$	−3.34899	−	2.54584i	−0.193677	−	0.147230i
$300$		0			0
$301$	−8.56152	−	10.0794i	−0.493478	−	0.580967i
$302$	34.5596	−	15.9890i	1.98868	−	0.920063i
$303$		0			0
$304$	25.9241	+	48.8981i	1.48685	+	2.80450i
$305$	11.3698	−	13.3856i	0.651036	−	0.766458i
$306$		0			0
$307$	0.0193825	+	0.0486463i	0.00110622	+	0.00277639i	0.929529	−	0.368750i	$-0.120214\pi$
$307$	0.0193825	+	0.0486463i	0.00110622	+	0.00277639i	−0.928423	+	0.371526i	$0.878835\pi$
$308$	−43.6041	+	82.2461i	−2.48458	+	4.68641i
$309$		0			0
$310$	2.76191	−	2.09955i	0.156866	−	0.119246i
$311$	5.35906	+	19.3016i	0.303884	+	1.09449i	0.945006	+	0.327053i	$0.106056\pi$
$311$	5.35906	+	19.3016i	0.303884	+	1.09449i	−0.641122	+	0.767439i	$0.721531\pi$
$312$		0			0
$313$	1.63871	+	9.99567i	0.0926252	+	0.564989i	0.991841	+	0.127483i	$0.0406898\pi$
$313$	1.63871	+	9.99567i	0.0926252	+	0.564989i	−0.899216	+	0.437506i	$0.855862\pi$
$314$	63.6587	−	14.0123i	3.59247	−	0.790762i
$315$		0			0
$316$	−15.8663	−	1.72557i	−0.892550	−	0.0970707i
$317$	−10.2828	+	15.1660i	−0.577541	+	0.851810i	−0.998471	−	0.0552837i	$-0.982394\pi$
$317$	−10.2828	+	15.1660i	−0.577541	+	0.851810i	0.420929	+	0.907093i	$0.361704\pi$
$318$		0			0
$319$	−1.16500	−	21.4872i	−0.0652277	−	1.20305i
$320$	−29.9254	−	28.3468i	−1.67288	−	1.58464i
$321$		0			0
$322$	−4.49861	+	82.9721i	−0.250698	+	4.62385i
$323$	−11.4815	−	2.52726i	−0.638845	−	0.140620i
$324$		0			0
$325$	1.74766	−	0.588855i	0.0969428	−	0.0326638i
$326$	−3.54577	−	0.780484i	−0.196382	−	0.0432270i
$327$		0			0
$328$	−25.3610	+	24.0232i	−1.40033	+	1.32646i
$329$	6.17938	+	5.85342i	0.340680	+	0.322710i
$330$		0			0
$331$	2.09918	−	12.8044i	0.115381	−	0.703795i	−0.864261	−	0.503044i	$-0.832214\pi$
$331$	2.09918	−	12.8044i	0.115381	−	0.703795i	0.979642	−	0.200751i	$-0.0643382\pi$
$332$	−20.3897	+	30.0726i	−1.11903	+	1.65045i
$333$		0			0
$334$	39.2389	−	23.6093i	2.14706	−	1.29184i
$335$	1.27741	−	0.281178i	0.0697922	−	0.0153624i
$336$		0			0
$337$	18.3371	+	8.48364i	0.998885	+	0.462133i	0.850035	−	0.526726i	$-0.176581\pi$
$337$	18.3371	+	8.48364i	0.998885	+	0.462133i	0.148850	+	0.988860i	$0.452443\pi$
$338$	9.40851	+	33.8864i	0.511755	+	1.84318i
$339$		0			0
$340$	21.9388	−	2.38599i	1.18980	−	0.129399i
$341$	−2.39690	+	4.52103i	−0.129799	+	0.244828i
$342$		0			0
$343$	1.17500	−	4.23197i	0.0634441	−	0.228505i
$344$	−23.8337	+	28.0592i	−1.28503	+	1.51285i
$345$		0			0
$346$	−19.6825	−	29.0295i	−1.05814	−	1.56064i
$347$	−1.05950	+	0.490178i	−0.0568770	+	0.0263141i	−0.448121	−	0.893973i	$-0.647907\pi$
$347$	−1.05950	+	0.490178i	−0.0568770	+	0.0263141i	0.391244	+	0.920287i	$0.372045\pi$
$348$		0			0
$349$	−5.26612	+	13.2170i	−0.281889	+	0.707488i	0.718045	+	0.695997i	$0.245037\pi$
$349$	−5.26612	+	13.2170i	−0.281889	+	0.707488i	−0.999934	+	0.0114913i	$0.996342\pi$
$350$	−28.9995	−	22.0448i	−1.55009	−	1.17835i
$351$		0			0
$352$	109.412	+	36.8651i	5.83166	+	1.96492i
$353$	21.8595			1.16347			0.581733	−	0.813380i	$-0.302375\pi$
$353$	21.8595			1.16347			0.581733	+	0.813380i	$0.302375\pi$
$354$		0			0
$355$	9.71818			0.515787
$356$	−23.2382	−	7.82986i	−1.23162	−	0.414982i
$357$		0			0
$358$	21.4228	+	16.2852i	1.13223	+	0.860698i
$359$	4.56185	−	11.4494i	0.240765	−	0.604275i	−0.758088	−	0.652152i	$-0.773866\pi$
$359$	4.56185	−	11.4494i	0.240765	−	0.604275i	0.998853	+	0.0478771i	$0.0152456\pi$
$360$		0			0
$361$	−6.68306	+	3.09191i	−0.351740	+	0.162732i
$362$	3.26207	+	4.81119i	0.171451	+	0.252871i
$363$		0			0
$364$	−6.47302	+	7.62062i	−0.339278	+	0.399429i
$365$	1.53790	−	5.53900i	0.0804971	−	0.289924i
$366$		0			0
$367$	14.5872	−	27.5143i	0.761444	−	1.43624i	−0.133963	−	0.990986i	$-0.542770\pi$
$367$	14.5872	−	27.5143i	0.761444	−	1.43624i	0.895407	−	0.445249i	$-0.146885\pi$
$368$	135.978	−	14.7885i	7.08833	−	0.770902i
$369$		0			0
$370$	−2.06806	−	7.44847i	−0.107513	−	0.387228i
$371$	23.0022	+	10.6419i	1.19421	+	0.552502i
$372$		0			0
$373$	−13.8087	+	3.03954i	−0.714990	+	0.157381i	−0.557545	−	0.830147i	$-0.688257\pi$
$373$	−13.8087	+	3.03954i	−0.714990	+	0.157381i	−0.157445	+	0.987528i	$0.550326\pi$
$374$	−37.8388	+	22.7669i	−1.95660	+	1.17725i
$375$		0			0
$376$	13.2972	−	19.6119i	0.685751	−	1.01141i
$377$	0.373928	−	2.28086i	0.0192583	−	0.117470i
$378$		0			0
$379$	−4.21265	−	3.99043i	−0.216389	−	0.204975i	0.571825	−	0.820376i	$-0.306236\pi$
$379$	−4.21265	−	3.99043i	−0.216389	−	0.204975i	−0.788214	+	0.615401i	$0.788994\pi$
$380$	−15.8579	+	15.0214i	−0.813495	+	0.770583i
$381$		0			0
$382$	1.73510	+	0.381924i	0.0887754	+	0.0195409i
$383$	27.5711	−	9.28977i	1.40882	−	0.474685i	0.490815	−	0.871264i	$-0.336699\pi$
$383$	27.5711	−	9.28977i	1.40882	−	0.474685i	0.918001	+	0.396579i	$0.129803\pi$
$384$		0			0
$385$	−18.5170	−	4.07591i	−0.943715	−	0.207727i
$386$	−2.74248	+	50.5821i	−0.139589	+	2.57456i
$387$		0			0
$388$	−39.5299	−	37.4448i	−2.00683	−	1.90097i
$389$	−0.726109	−	13.3923i	−0.0368152	−	0.679016i	−0.957451	−	0.288595i	$-0.906812\pi$
$389$	−0.726109	−	13.3923i	−0.0368152	−	0.679016i	0.920636	−	0.390422i	$-0.127671\pi$
$390$		0			0
$391$	−16.3050	+	24.0481i	−0.824579	+	1.21616i
$392$	57.0756	+	6.20734i	2.88275	+	0.313518i
$393$		0			0
$394$	−9.73984	+	2.14390i	−0.490686	+	0.108008i
$395$	−0.525899	−	3.20784i	−0.0264608	−	0.161404i
$396$		0			0
$397$	−1.08612	−	3.91184i	−0.0545107	−	0.196330i	0.931281	−	0.364301i	$-0.118692\pi$
$397$	−1.08612	−	3.91184i	−0.0545107	−	0.196330i	−0.985792	+	0.167971i	$0.946278\pi$
$398$	−32.6174	+	24.7951i	−1.63496	+	1.24287i
$399$		0			0
$400$	−28.0869	+	52.9774i	−1.40434	+	2.64887i
$401$	3.17411	+	7.96641i	0.158507	+	0.397824i	0.986685	−	0.162642i	$-0.0520015\pi$
$401$	3.17411	+	7.96641i	0.158507	+	0.397824i	−0.828178	+	0.560466i	$0.810622\pi$
$402$		0			0
$403$	−0.355819	+	0.418902i	−0.0177246	+	0.0208670i
$404$	−18.3335	−	34.5807i	−0.912127	−	1.72045i
$405$		0			0
$406$	−41.4343	+	19.1695i	−2.05635	+	0.951368i
$407$	7.38135	+	8.69000i	0.365880	+	0.430747i
$408$		0			0
$409$	0.930782	+	0.707562i	0.0460242	+	0.0349867i	0.627933	−	0.778267i	$-0.283901\pi$
$409$	0.930782	+	0.707562i	0.0460242	+	0.0349867i	−0.581909	+	0.813254i	$0.697694\pi$
$410$	−9.47693	−	5.70208i	−0.468032	−	0.281606i
$411$		0			0
$412$	−50.3136			−2.47877
$413$	−23.9558	−	13.4018i	−1.17879	−	0.659457i
$414$		0			0
$415$	−7.01286	−	2.36291i	−0.344248	−	0.115991i
$416$	10.6258	+	6.39335i	0.520975	+	0.313460i
$417$		0			0
$418$	16.1785	−	40.6050i	0.791318	−	1.98606i
$419$	−13.4637	−	15.8506i	−0.657743	−	0.774354i	0.327623	−	0.944809i	$-0.393752\pi$
$419$	−13.4637	−	15.8506i	−0.657743	−	0.774354i	−0.985366	+	0.170454i	$0.945477\pi$
$420$		0			0
$421$	8.83654	+	13.0329i	0.430666	+	0.635185i	0.979666	−	0.200637i	$-0.0643013\pi$
$421$	8.83654	+	13.0329i	0.430666	+	0.635185i	−0.548999	+	0.835823i	$0.684991\pi$
$422$	19.5822	+	36.9359i	0.953246	+	1.79801i
$423$		0			0
$424$	18.8754	−	67.9832i	0.916672	−	3.30155i
$425$	−4.71448	−	11.8325i	−0.228686	−	0.573958i
$426$		0			0
$427$	54.6357	−	5.94199i	2.64401	−	0.287553i
$428$	−19.0293	+	14.4657i	−0.919816	+	0.699226i
$429$		0			0
$430$	−10.5788	−	4.89429i	−0.510157	−	0.236024i
$431$	−2.40543	−	14.6725i	−0.115865	−	0.706748i	−0.979319	−	0.202320i	$-0.935152\pi$
$431$	−2.40543	−	14.6725i	−0.115865	−	0.706748i	0.863454	−	0.504428i	$-0.168296\pi$
$432$		0			0
$433$	4.33307	−	2.60712i	0.208234	−	0.125290i	−0.407617	−	0.913153i	$-0.633640\pi$
$433$	4.33307	−	2.60712i	0.208234	−	0.125290i	0.615851	+	0.787863i	$0.288812\pi$
$434$	10.7927	+	1.17378i	0.518067	+	0.0563432i
$435$		0			0
$436$	−7.07827	+	43.1755i	−0.338988	+	2.06773i
$437$	−1.55693	−	28.7158i	−0.0744779	−	1.37366i
$438$		0			0
$439$	6.49426	−	6.15169i	0.309954	−	0.293604i	−0.516871	−	0.856063i	$-0.672903\pi$
$439$	6.49426	−	6.15169i	0.309954	−	0.293604i	0.826825	+	0.562459i	$0.190145\pi$
$440$	−2.85757	+	52.7047i	−0.136229	+	2.51260i
$441$		0			0
$442$	−4.49489	+	1.51450i	−0.213800	+	0.0720376i
$443$	−23.4622	+	7.90534i	−1.11472	+	0.375594i	−0.815598	−	0.578619i	$-0.803592\pi$
$443$	−23.4622	+	7.90534i	−1.11472	+	0.375594i	−0.299126	+	0.954214i	$0.596695\pi$
$444$		0			0
$445$	0.270399	−	4.98722i	0.0128181	−	0.236417i
$446$	−22.0924	+	20.9270i	−1.04611	+	0.990924i
$447$		0			0
$448$	−6.98319	−	128.797i	−0.329925	−	6.08511i
$449$	−2.98163	+	18.1871i	−0.140712	+	0.858303i	0.818270	+	0.574834i	$0.194933\pi$
$449$	−2.98163	+	18.1871i	−0.140712	+	0.858303i	−0.958982	+	0.283469i	$0.908515\pi$
$450$		0			0
$451$	16.2176	+	1.76377i	0.763655	+	0.0830525i
$452$	15.4676	−	9.30652i	0.727533	−	0.437742i
$453$		0			0
$454$	6.26080	+	38.1892i	0.293834	+	1.79231i
$455$	−1.84828	−	0.855107i	−0.0866489	−	0.0400880i
$456$		0			0
$457$	−3.68703	+	2.80281i	−0.172472	+	0.131110i	−0.687849	−	0.725854i	$-0.741445\pi$
$457$	−3.68703	+	2.80281i	−0.172472	+	0.131110i	0.515377	+	0.856964i	$0.327652\pi$
$458$	40.5125	−	4.40600i	1.89303	−	0.205879i
$459$		0			0
$460$	19.9811	+	50.1487i	0.931621	+	2.33819i
$461$	3.79976	−	13.6855i	0.176973	−	0.637397i	−0.820832	−	0.571170i	$-0.806490\pi$
$461$	3.79976	−	13.6855i	0.176973	−	0.637397i	0.997805	−	0.0662277i	$-0.0210964\pi$
$462$		0			0
$463$	14.7717	+	27.8624i	0.686500	+	1.29488i	0.944430	+	0.328713i	$0.106615\pi$
$463$	14.7717	+	27.8624i	0.686500	+	1.29488i	−0.257930	+	0.966164i	$0.583040\pi$
$464$	42.1732	+	62.2008i	1.95784	+	2.88760i
$465$		0			0
$466$	18.5146	+	21.7970i	0.857671	+	1.00973i
$467$	0.531441	−	1.33382i	0.0245922	−	0.0617217i	−0.916168	−	0.400795i	$-0.868734\pi$
$467$	0.531441	−	1.33382i	0.0245922	−	0.0617217i	0.940760	+	0.339073i	$0.110113\pi$
$468$		0			0
$469$	3.50712	+	2.11016i	0.161944	+	0.0974383i
$470$	7.10933	+	2.39541i	0.327929	+	0.110492i
$471$		0			0
$472$	−26.0276	+	71.8460i	−1.19802	+	3.30698i
$473$	17.1923			0.790505
$474$		0			0
$475$	10.8025	+	6.49965i	0.495653	+	0.298224i
$476$	54.9755	+	41.7913i	2.51980	+	1.91550i
$477$		0			0
$478$	9.28824	+	10.9350i	0.424834	+	0.500153i
$479$	23.1773	−	10.7230i	1.05900	−	0.489944i	0.188477	−	0.982078i	$-0.439645\pi$
$479$	23.1773	−	10.7230i	1.05900	−	0.489944i	0.870520	+	0.492133i	$0.163783\pi$
$480$		0			0
$481$	0.573637	+	1.08200i	0.0261556	+	0.0493347i
$482$	−6.70594	+	7.89485i	−0.305447	+	0.359600i
$483$		0			0
$484$	−21.9644	−	55.1265i	−0.998382	−	2.50575i
$485$	5.19469	−	9.79822i	0.235879	−	0.444914i
$486$		0			0
$487$	29.1029	−	22.1235i	1.31878	−	1.00251i	0.320304	−	0.947315i	$-0.396215\pi$
$487$	29.1029	−	22.1235i	1.31878	−	1.00251i	0.998476	−	0.0551955i	$-0.0175782\pi$
$488$	−40.9299	−	147.416i	−1.85281	−	6.67322i
$489$		0			0
$490$	2.94077	+	17.9379i	0.132850	+	0.810351i
$491$	−5.66939	+	1.24793i	−0.255856	+	0.0563181i	−0.341046	−	0.940047i	$-0.610781\pi$
$491$	−5.66939	+	1.24793i	−0.255856	+	0.0563181i	0.0851902	+	0.996365i	$0.472850\pi$
$492$		0			0
$493$	−15.8696	−	1.72593i	−0.714733	−	0.0777319i
$494$	2.63465	−	3.88582i	0.118539	−	0.174831i
$495$		0			0
$496$	−0.967488	−	17.8443i	−0.0434415	−	0.801231i
$497$	22.0779	+	20.9133i	0.990329	+	0.938089i
$498$		0			0
$499$	1.89552	−	34.9608i	0.0848550	−	1.56506i	−0.577828	−	0.816159i	$-0.696099\pi$
$499$	1.89552	−	34.9608i	0.0848550	−	1.56506i	0.662683	−	0.748900i	$-0.269418\pi$
$500$	−54.3800	−	11.9699i	−2.43195	−	0.535312i
$501$		0			0
$502$	−74.5476	+	25.1180i	−3.32722	+	1.12107i
$503$	−17.2941	−	3.80673i	−0.771108	−	0.169734i	−0.188045	−	0.982160i	$-0.560215\pi$
$503$	−17.2941	−	3.80673i	−0.771108	−	0.169734i	−0.583063	+	0.812427i	$0.698146\pi$
$504$		0			0
$505$	5.78759	−	5.48229i	0.257544	−	0.243959i
$506$	−78.4243	−	74.2875i	−3.48639	−	3.30248i
$507$		0			0
$508$	14.6750	−	89.5135i	0.651098	−	3.97152i
$509$	3.88057	−	5.72342i	0.172003	−	0.253686i	−0.731910	−	0.681401i	$-0.761371\pi$
$509$	3.88057	−	5.72342i	0.172003	−	0.253686i	0.903914	+	0.427715i	$0.140681\pi$
$510$		0			0
$511$	15.4136	−	9.27406i	0.681858	−	0.410260i
$512$	−78.5097	+	17.2813i	−3.46967	+	0.763733i
$513$		0			0
$514$	−34.6038	−	16.0094i	−1.52631	−	0.706145i
$515$	−2.74156	−	9.87421i	−0.120808	−	0.435110i
$516$		0			0
$517$	−11.0003	+	1.19636i	−0.483794	+	0.0526157i
$518$	11.3307	−	21.3720i	0.497842	−	0.939030i
$519$		0			0
$520$	−1.51669	+	5.46262i	−0.0665112	+	0.239552i
$521$	2.53662	−	2.98634i	0.111131	−	0.130834i	−0.703784	−	0.710414i	$-0.748508\pi$
$521$	2.53662	−	2.98634i	0.111131	−	0.130834i	0.814915	+	0.579580i	$0.196783\pi$
$522$		0			0
$523$	21.1778	+	31.2349i	0.926039	+	1.36581i	0.930687	+	0.365816i	$0.119210\pi$
$523$	21.1778	+	31.2349i	0.926039	+	1.36581i	−0.00464826	+	0.999989i	$0.501480\pi$
$524$	21.2775	−	9.84404i	0.929514	−	0.430039i
$525$		0			0
$526$	1.98000	−	4.96942i	0.0863320	−	0.216677i
$527$	3.02198	+	2.29725i	0.131640	+	0.100070i
$528$		0			0
$529$	−45.5559	−	15.3496i	−1.98069	−	0.667372i
$530$	22.3385			0.970322
$531$		0			0
$532$	−68.3521			−2.96344
$533$	1.66046	+	0.559475i	0.0719226	+	0.0242335i
$534$		0			0
$535$	−3.87584	−	2.94633i	−0.167567	−	0.127381i
$536$	4.21742	−	10.5849i	0.182165	−	0.457200i
$537$		0			0
$538$	−17.0383	+	7.88275i	−0.734573	+	0.339850i
$539$	−15.0459	−	22.1910i	−0.648072	−	0.955835i
$540$		0			0
$541$	−16.6040	+	19.5477i	−0.713860	+	0.840421i	−0.992787	−	0.119891i	$-0.961745\pi$
$541$	−16.6040	+	19.5477i	−0.713860	+	0.840421i	0.278927	+	0.960312i	$0.410021\pi$
$542$	3.62809	−	13.0672i	0.155840	−	0.561285i
$543$		0			0
$544$	40.1182	−	75.6710i	1.72006	−	3.24437i
$545$	−8.85903	+	0.963477i	−0.379479	+	0.0412708i
$546$		0			0
$547$	−11.2448	−	40.5000i	−0.480792	−	1.73165i	−0.663209	−	0.748434i	$-0.730806\pi$
$547$	−11.2448	−	40.5000i	−0.480792	−	1.73165i	0.182418	−	0.983221i	$-0.441608\pi$
$548$	−102.563	−	47.4507i	−4.38127	−	2.02699i
$549$		0			0
$550$	46.2488	−	10.1801i	1.97205	−	0.434082i
$551$	13.5386	−	8.14593i	0.576765	−	0.347028i
$552$		0			0
$553$	5.70846	−	8.41934i	0.242748	−	0.358027i
$554$	−1.33031	+	8.11454i	−0.0565195	+	0.344754i
$555$		0			0
$556$	90.0062	+	85.2584i	3.81711	+	3.61576i
$557$	−31.8542	+	30.1739i	−1.34971	+	1.27851i	−0.421309	+	0.906917i	$0.638429\pi$
$557$	−31.8542	+	30.1739i	−1.34971	+	1.27851i	−0.928396	+	0.371592i	$0.878812\pi$
$558$		0			0
$559$	1.80344	+	0.396967i	0.0762773	+	0.0167899i
$560$	62.7489	−	21.1426i	2.65162	−	0.893436i
$561$		0			0
$562$	25.9792	+	5.71846i	1.09587	+	0.241219i
$563$	2.05406	−	37.8850i	0.0865685	−	1.59666i	−0.556497	−	0.830850i	$-0.687855\pi$
$563$	2.05406	−	37.8850i	0.0865685	−	1.59666i	0.643065	−	0.765811i	$-0.277662\pi$
$564$		0			0
$565$	2.66925	+	2.52845i	0.112296	+	0.106373i
$566$	−0.216296	−	3.98935i	−0.00909161	−	0.167685i
$567$		0			0
$568$	47.5086	−	70.0700i	1.99342	−	2.94007i
$569$	−2.67480	−	0.290902i	−0.112133	−	0.0121952i	0.0518802	−	0.998653i	$-0.483479\pi$
$569$	−2.67480	−	0.290902i	−0.112133	−	0.0121952i	−0.164014	+	0.986458i	$0.552444\pi$
$570$		0			0
$571$	36.7407	−	8.08724i	1.53755	−	0.338440i	0.636198	−	0.771526i	$-0.280506\pi$
$571$	36.7407	−	8.08724i	1.53755	−	0.338440i	0.901353	+	0.433085i	$0.142575\pi$
$572$	−2.10291	−	12.8272i	−0.0879271	−	0.536332i
$573$		0			0
$574$	−9.25908	−	33.3482i	−0.386467	−	1.39193i
$575$	24.8040	−	18.8555i	1.03440	−	0.786329i
$576$		0			0
$577$	−17.1166	+	32.2853i	−0.712573	+	1.34406i	0.217274	+	0.976111i	$0.430284\pi$
$577$	−17.1166	+	32.2853i	−0.712573	+	1.34406i	−0.929847	+	0.367945i	$0.880061\pi$
$578$	−5.22941	−	13.1248i	−0.217515	−	0.545920i
$579$		0			0
$580$	−19.2011	+	22.6053i	−0.797282	+	0.938632i
$581$	−10.8470	−	20.4596i	−0.450009	−	0.848807i
$582$		0			0
$583$	−29.9031	+	13.8347i	−1.23846	+	0.572973i
$584$	−32.4191	−	38.1667i	−1.34151	−	1.57935i
$585$		0			0
$586$	−45.4248	−	34.5310i	−1.87648	−	1.42646i
$587$	−15.5937	−	9.38239i	−0.643619	−	0.387253i	0.156003	−	0.987757i	$-0.450139\pi$
$587$	−15.5937	−	9.38239i	−0.643619	−	0.387253i	−0.799622	+	0.600504i	$0.794967\pi$
$588$		0			0
$589$	−3.75728			−0.154816
$590$	−24.1227	−	1.85472i	−0.993117	−	0.0763576i
$591$		0			0
$592$	−37.7340	−	12.7141i	−1.55086	−	0.522545i
$593$	−2.61735	−	1.57480i	−0.107481	−	0.0646695i	0.460798	−	0.887505i	$-0.347563\pi$
$593$	−2.61735	−	1.57480i	−0.107481	−	0.0646695i	−0.568280	+	0.822836i	$0.692391\pi$
$594$		0			0
$595$	−5.20610	+	13.0663i	−0.213429	+	0.535667i
$596$	52.0638	+	61.2942i	2.13261	+	2.51071i
$597$		0			0
$598$	−6.51126	−	9.60338i	−0.266265	−	0.392712i
$599$	3.62754	+	6.84226i	0.148217	+	0.279567i	0.946493	−	0.322725i	$-0.104599\pi$
$599$	3.62754	+	6.84226i	0.148217	+	0.279567i	−0.798276	+	0.602292i	$0.794254\pi$
$600$		0			0
$601$	12.0917	−	43.5504i	0.493231	−	1.77646i	−0.126850	−	0.991922i	$-0.540487\pi$
$601$	12.0917	−	43.5504i	0.493231	−	1.77646i	0.620082	−	0.784537i	$-0.287099\pi$
$602$	−13.5008	−	33.8843i	−0.550250	−	1.38102i
$603$		0			0
$604$	76.9586	−	8.36975i	3.13140	−	0.340560i
$605$	9.62193	−	7.31440i	0.391187	−	0.297373i
$606$		0			0
$607$	−27.2602	−	12.6119i	−1.10646	−	0.511902i	−0.220369	−	0.975416i	$-0.570726\pi$
$607$	−27.2602	−	12.6119i	−1.10646	−	0.511902i	−0.886090	+	0.463514i	$0.846588\pi$
$608$	13.7149	+	83.6573i	0.556214	+	3.39275i
$609$		0			0
$610$	41.5056	−	24.9731i	1.68051	−	1.01113i
$611$	−1.18153	−	0.128499i	−0.0477997	−	0.00519853i
$612$		0			0
$613$	0.349096	−	2.12939i	0.0140998	−	0.0860053i	−0.978839	−	0.204631i	$-0.934401\pi$
$613$	0.349096	−	2.12939i	0.0140998	−	0.0860053i	0.992939	+	0.118626i	$0.0378489\pi$
$614$	0.00781919	+	0.144216i	0.000315557	+	0.00582010i
$615$		0			0
$616$	−119.911	+	113.586i	−4.83136	+	4.57650i
$617$	0.915876	−	16.8923i	0.0368718	−	0.680060i	−0.920419	−	0.390933i	$-0.872152\pi$
$617$	0.915876	−	16.8923i	0.0368718	−	0.680060i	0.957291	−	0.289127i	$-0.0933649\pi$
$618$		0			0
$619$	4.50813	−	1.51896i	0.181197	−	0.0610524i	−0.227241	−	0.973839i	$-0.572970\pi$
$619$	4.50813	−	1.51896i	0.181197	−	0.0610524i	0.408437	+	0.912786i	$0.366074\pi$
$620$	6.68373	−	2.25201i	0.268425	−	0.0904429i
$621$		0			0
$622$	−2.99113	+	55.1681i	−0.119933	+	2.21204i
$623$	11.3467	−	10.7481i	0.454595	−	0.430615i
$624$		0			0
$625$	0.386435	+	7.12737i	0.0154574	+	0.285095i
$626$	−4.51969	+	27.5689i	−0.180643	+	1.10187i
$627$		0			0
$628$	131.735	+	14.3271i	5.25682	+	0.571713i
$629$	7.24742	−	4.36063i	0.288974	−	0.173870i
$630$		0			0
$631$	0.500603	+	3.05354i	0.0199287	+	0.121560i	0.994917	−	0.100695i	$-0.0321067\pi$
$631$	0.500603	+	3.05354i	0.0199287	+	0.121560i	−0.974989	+	0.222255i	$0.928658\pi$
$632$	−25.7001	−	11.8901i	−1.02230	−	0.472964i
$633$		0			0
$634$	−40.2324	+	30.5839i	−1.59783	+	1.21464i
$635$	18.3670	−	1.99753i	0.728870	−	0.0792694i
$636$		0			0
$637$	−1.06589	−	2.67519i	−0.0422323	−	0.105995i
$638$	15.8779	−	57.1872i	0.628614	−	2.26406i
$639$		0			0
$640$	−26.6643	−	50.2943i	−1.05400	−	1.98806i
$641$	−11.5903	−	17.0944i	−0.457788	−	0.675187i	0.526818	−	0.849978i	$-0.323385\pi$
$641$	−11.5903	−	17.0944i	−0.457788	−	0.675187i	−0.984605	+	0.174792i	$0.944075\pi$
$642$		0			0
$643$	−3.20516	−	3.77341i	−0.126399	−	0.148809i	0.695322	−	0.718698i	$-0.255262\pi$
$643$	−3.20516	−	3.77341i	−0.126399	−	0.148809i	−0.821721	+	0.569890i	$0.806986\pi$
$644$	−62.5255	+	156.927i	−2.46385	+	6.18380i
$645$		0			0
$646$	−27.7835	−	16.7168i	−1.09313	−	0.657712i
$647$	30.9165	+	10.4170i	1.21545	+	0.409533i	0.852724	−	0.522362i	$-0.174949\pi$
$647$	30.9165	+	10.4170i	1.21545	+	0.409533i	0.362728	+	0.931895i	$0.381846\pi$
$648$		0			0
$649$	33.4402	−	12.4569i	1.31264	−	0.488975i
$650$	5.08645			0.199507
$651$		0			0
$652$	−6.32437	−	3.80525i	−0.247682	−	0.149025i
$653$	16.6899	+	12.6873i	0.653126	+	0.496493i	0.878477	−	0.477784i	$-0.158560\pi$
$653$	16.6899	+	12.6873i	0.653126	+	0.496493i	−0.225351	+	0.974278i	$0.572353\pi$
$654$		0			0
$655$	3.09133	+	3.63939i	0.120788	+	0.142203i
$656$	−51.7050	+	23.9213i	−2.01874	+	0.933970i
$657$		0			0
$658$	10.9962	+	20.7410i	0.428677	+	0.808570i
$659$	−25.5069	+	30.0291i	−0.993609	+	1.16977i	−0.00813057	+	0.999967i	$0.502588\pi$
$659$	−25.5069	+	30.0291i	−0.993609	+	1.16977i	−0.985479	+	0.169800i	$0.945688\pi$
$660$		0			0
$661$	10.7340	+	26.9403i	0.417504	+	1.04786i	0.975888	+	0.218274i	$0.0700425\pi$
$661$	10.7340	+	26.9403i	0.417504	+	1.04786i	−0.558383	+	0.829583i	$0.688578\pi$
$662$	16.7630	−	31.6183i	0.651511	−	1.22888i
$663$		0			0
$664$	−51.3204	+	39.0127i	−1.99162	+	1.51399i
$665$	−3.72447	−	13.4143i	−0.144429	−	0.520185i
$666$		0			0
$667$	−6.31740	−	38.5344i	−0.244611	−	1.49206i
$668$	90.9198	−	20.0130i	3.51779	−	0.774325i
$669$		0			0
$670$	3.58638	+	0.390043i	0.138554	+	0.0150687i
$671$	−40.0945	+	59.1350i	−1.54783	+	2.28288i
$672$		0			0
$673$	2.07890	+	38.3431i	0.0801357	+	1.47802i	0.711586	+	0.702599i	$0.247977\pi$
$673$	2.07890	+	38.3431i	0.0801357	+	1.47802i	−0.631450	+	0.775417i	$0.717540\pi$
$674$	40.4565	+	38.3224i	1.55833	+	1.47613i
$675$		0			0
$676$	−3.87066	+	71.3901i	−0.148871	+	2.74577i
$677$	8.65444	+	1.90499i	0.332617	+	0.0732145i	0.378139	−	0.925749i	$-0.376564\pi$
$677$	8.65444	+	1.90499i	0.332617	+	0.0732145i	−0.0455221	+	0.998963i	$0.514495\pi$
$678$		0			0
$679$	32.8869	−	11.0809i	1.26208	−	0.425246i
$680$	38.2398	+	8.41721i	1.46643	+	0.322785i
$681$		0			0
$682$	−10.2463	+	9.70578i	−0.392350	+	0.371654i
$683$	1.44235	+	1.36627i	0.0551899	+	0.0522787i	0.714797	−	0.699332i	$-0.246519\pi$
$683$	1.44235	+	1.36627i	0.0551899	+	0.0522787i	−0.659608	+	0.751610i	$0.729277\pi$
$684$		0			0
$685$	3.72375	−	22.7139i	0.142277	−	0.867852i
$686$	6.79803	−	10.0263i	0.259550	−	0.382808i
$687$		0			0
$688$	−51.4463	+	30.9542i	−1.96137	+	1.18012i
$689$	−3.45621	+	0.760769i	−0.131671	+	0.0289830i
$690$		0			0
$691$	−22.8062	−	10.5513i	−0.867590	−	0.401390i	−0.0649750	−	0.997887i	$-0.520697\pi$
$691$	−22.8062	−	10.5513i	−0.867590	−	0.401390i	−0.802615	+	0.596497i	$0.796559\pi$
$692$	−19.0751	−	68.7022i	−0.725126	−	2.61167i
$693$		0			0
$694$	−3.20090	+	0.348119i	−0.121505	+	0.0132144i
$695$	−11.8278	+	22.3097i	−0.448656	+	0.846254i
$696$		0			0
$697$	3.23751	−	11.6605i	0.122630	−	0.441672i
$698$	−25.4037	+	29.9076i	−0.961545	+	1.13202i
$699$		0			0
$700$	−41.5583	−	61.2940i	−1.57076	−	2.31669i
$701$	27.2029	−	12.5854i	1.02744	−	0.475344i	0.167572	−	0.985860i	$-0.446407\pi$
$701$	27.2029	−	12.5854i	1.02744	−	0.475344i	0.859869	+	0.510515i	$0.170545\pi$
$702$		0			0
$703$	−3.09874	+	7.77725i	−0.116871	+	0.293324i
$704$	133.492	+	101.478i	5.03118	+	3.82460i
$705$		0			0
$706$	57.1343	+	19.2508i	2.15028	+	0.724513i
$707$	24.9461			0.938194
$708$		0			0
$709$	−35.7069			−1.34100			−0.670500	−	0.741910i	$-0.733920\pi$
$709$	−35.7069			−1.34100			−0.670500	+	0.741910i	$0.733920\pi$
$710$	25.4004	+	8.55840i	0.953261	+	0.321191i
$711$		0			0
$712$	−34.6369	−	26.3303i	−1.29807	−	0.986770i
$713$	−3.43700	+	8.62622i	−0.128717	+	0.323054i
$714$		0			0
$715$	2.40279	−	1.11165i	0.0898593	−	0.0415733i
$716$	30.7004	+	45.2797i	1.14733	+	1.69218i
$717$		0			0
$718$	22.0063	−	25.9078i	0.821269	−	0.966872i
$719$	−8.22926	+	29.6391i	−0.306900	+	1.10535i	0.635839	+	0.771822i	$0.280654\pi$
$719$	−8.22926	+	29.6391i	−0.306900	+	1.10535i	−0.942739	+	0.333532i	$0.891760\pi$
$720$		0			0
$721$	15.0207	−	28.3321i	0.559402	−	1.05514i
$722$	−20.1905	+	2.19585i	−0.751411	+	0.0817209i
$723$		0			0
$724$	3.16140	+	11.3863i	0.117492	+	0.423170i
$725$	15.5363	+	7.18787i	0.577004	+	0.266951i
$726$		0			0
$727$	7.01192	−	1.54344i	0.260058	−	0.0572430i	−0.0830277	−	0.996547i	$-0.526459\pi$
$727$	7.01192	−	1.54344i	0.260058	−	0.0572430i	0.343085	+	0.939304i	$0.388528\pi$
$728$	−15.2011	+	9.14618i	−0.563389	+	0.338980i
$729$		0			0
$730$	8.89757	−	13.1229i	0.329314	−	0.485702i
$731$	2.06333	−	12.5857i	0.0763149	−	0.465500i
$732$		0			0
$733$	−36.9815	−	35.0308i	−1.36594	−	1.29389i	−0.916193	−	0.400737i	$-0.868754\pi$
$733$	−36.9815	−	35.0308i	−1.36594	−	1.29389i	−0.449751	−	0.893154i	$-0.648487\pi$
$734$	62.3572	−	59.0679i	2.30165	−	2.18024i
$735$		0			0
$736$	204.612	+	45.0385i	7.54209	+	1.66014i
$737$	−5.04242	+	1.69899i	−0.185740	+	0.0625831i
$738$		0			0
$739$	5.47877	+	1.20597i	0.201540	+	0.0443623i	0.314593	−	0.949227i	$-0.398132\pi$
$739$	5.47877	+	1.20597i	0.201540	+	0.0443623i	−0.113053	+	0.993589i	$0.536063\pi$
$740$	0.850798	−	15.6920i	0.0312760	−	0.576851i
$741$		0			0
$742$	50.7489	+	48.0719i	1.86305	+	1.76478i
$743$	1.81953	+	33.5592i	0.0667519	+	1.23117i	0.819586	+	0.572956i	$0.194204\pi$
$743$	1.81953	+	33.5592i	0.0667519	+	1.23117i	−0.752834	+	0.658210i	$0.771314\pi$
$744$		0			0
$745$	−9.19226	+	13.5576i	−0.336778	+	0.496711i
$746$	−38.7688	−	4.21636i	−1.41943	−	0.154372i
$747$		0			0
$748$	−87.6757	+	19.2989i	−3.20574	+	0.705637i
$749$	−2.46474	−	15.0342i	−0.0900595	−	0.549339i
$750$		0			0
$751$	9.89349	+	35.6331i	0.361019	+	1.30027i	0.891672	+	0.452682i	$0.149533\pi$
$751$	9.89349	+	35.6331i	0.361019	+	1.30027i	−0.530653	+	0.847589i	$0.678053\pi$
$752$	30.7634	−	23.3857i	1.12182	−	0.852789i
$753$		0			0
$754$	2.98600	−	5.63219i	0.108744	−	0.205112i
$755$	5.83602	+	14.6473i	0.212395	+	0.533070i
$756$		0			0
$757$	6.17567	−	7.27056i	0.224459	−	0.264253i	−0.638393	−	0.769711i	$-0.720400\pi$
$757$	6.17567	−	7.27056i	0.224459	−	0.264253i	0.862851	+	0.505458i	$0.168676\pi$
$758$	−7.49641	−	14.1397i	−0.272282	−	0.513578i
$759$		0			0
$760$	−35.1737	+	16.2731i	−1.27588	+	0.590287i
$761$	−19.1297	−	22.5212i	−0.693450	−	0.816393i	0.296911	−	0.954905i	$-0.404044\pi$
$761$	−19.1297	−	22.5212i	−0.693450	−	0.816393i	−0.990361	+	0.138513i	$0.955768\pi$
$762$		0			0
$763$	−22.1994	−	16.8756i	−0.803674	−	0.610937i
$764$	3.09479	+	1.86207i	0.111966	+	0.0673674i
$765$		0			0
$766$	80.2437			2.89932
$767$	3.79543	−	0.534571i	0.137045	−	0.0193023i
$768$		0			0
$769$	37.4545	+	12.6199i	1.35064	+	0.455085i	0.899326	−	0.437279i	$-0.144058\pi$
$769$	37.4545	+	12.6199i	1.35064	+	0.455085i	0.451317	+	0.892364i	$0.350954\pi$
$770$	−44.8085	−	26.9604i	−1.61479	−	0.971585i
$771$		0			0
$772$	−38.1173	+	95.6671i	−1.37187	+	3.44314i
$773$	8.94785	+	10.5342i	0.321832	+	0.378890i	0.899158	−	0.437624i	$-0.144180\pi$
$773$	8.94785	+	10.5342i	0.321832	+	0.378890i	−0.577326	+	0.816513i	$0.695904\pi$
$774$		0			0
$775$	−2.28444	−	3.36930i	−0.0820596	−	0.121029i
$776$	−45.2522	−	85.3547i	−1.62446	−	3.06405i
$777$		0			0
$778$	9.89621	−	35.6429i	0.354796	−	1.27786i
$779$	4.43355	+	11.1274i	0.158848	+	0.398679i
$780$		0			0
$781$	−39.3023	+	4.27438i	−1.40635	+	0.152949i
$782$	−63.7945	+	48.4953i	−2.28129	+	1.73419i
$783$		0			0
$784$	84.9775	+	39.3148i	3.03491	+	1.40410i
$785$	4.36645	+	26.6342i	0.155845	+	0.950615i
$786$		0			0
$787$	44.4629	−	26.7525i	1.58493	−	0.953622i	0.596387	−	0.802697i	$-0.296602\pi$
$787$	44.4629	−	26.7525i	1.58493	−	0.953622i	0.988545	−	0.150926i	$-0.0482254\pi$
$788$	−20.1556	−	2.19206i	−0.718015	−	0.0780889i
$789$		0			0
$790$	1.45047	−	8.84748i	0.0516055	−	0.314779i
$791$	0.622880	+	11.4883i	0.0221471	+	0.408478i
$792$		0			0
$793$	−5.57124	+	5.27736i	−0.197840	+	0.187404i
$794$	0.606211	−	11.1809i	0.0215136	−	0.396795i
$795$		0			0
$796$	−78.9330	+	26.5956i	−2.79771	+	0.942657i
$797$	−25.8791	+	8.71968i	−0.916684	+	0.308867i	−0.737813	−	0.675006i	$-0.764141\pi$
$797$	−25.8791	+	8.71968i	−0.916684	+	0.308867i	−0.178872	+	0.983872i	$0.557245\pi$
$798$		0			0
$799$	−0.444397	+	8.19642i	−0.0157216	+	0.289968i
$800$	−66.6801	+	63.1627i	−2.35750	+	2.23314i
$801$		0			0
$802$	1.28048	+	23.6171i	0.0452155	+	0.833950i
$803$	−3.78332	+	23.0773i	−0.133511	+	0.814379i
$804$		0			0
$805$	−34.2044	−	3.71996i	−1.20555	−	0.131111i
$806$	−1.29891	+	0.781531i	−0.0457523	+	0.0275283i
$807$		0			0
$808$	−11.2350	−	68.5306i	−0.395247	−	2.41090i
$809$	−19.1127	−	8.84247i	−0.671966	−	0.310885i	0.0540740	−	0.998537i	$-0.482779\pi$
$809$	−19.1127	−	8.84247i	−0.671966	−	0.310885i	−0.726040	+	0.687652i	$0.758641\pi$
$810$		0			0
$811$	0.169473	−	0.128830i	0.00595099	−	0.00452382i	−0.602194	−	0.798349i	$-0.705707\pi$
$811$	0.169473	−	0.128830i	0.00595099	−	0.00452382i	0.608145	+	0.793826i	$0.291914\pi$
$812$	−92.2673	+	10.0347i	−3.23795	+	0.352148i
$813$		0			0
$814$	11.6397	+	29.2135i	0.407973	+	1.02393i
$815$	0.402181	−	1.44852i	0.0140878	−	0.0507396i
$816$		0			0
$817$	5.91301	+	11.1531i	0.206870	+	0.390198i
$818$	1.80967	+	2.66906i	0.0632735	+	0.0933215i
$819$		0			0
$820$	−14.5562	−	17.1368i	−0.508323	−	0.598445i
$821$	15.0100	−	37.6723i	0.523853	−	1.31477i	−0.394459	−	0.918914i	$-0.629068\pi$
$821$	15.0100	−	37.6723i	0.523853	−	1.31477i	0.918312	−	0.395858i	$-0.129553\pi$
$822$		0			0
$823$	−37.3966	−	22.5008i	−1.30356	−	0.784329i	−0.317114	−	0.948387i	$-0.602714\pi$
$823$	−37.3966	−	22.5008i	−1.30356	−	0.784329i	−0.986451	+	0.164059i	$0.947541\pi$
$824$	−84.5975	−	28.5042i	−2.94709	−	0.992991i
$825$		0			0
$826$	−50.8110	−	56.1251i	−1.76794	−	1.95284i
$827$	−26.8695			−0.934342			−0.467171	−	0.884167i	$-0.654727\pi$
$827$	−26.8695			−0.934342			−0.467171	+	0.884167i	$0.654727\pi$
$828$		0			0
$829$	−18.1378	−	10.9132i	−0.629953	−	0.379030i	0.164482	−	0.986380i	$-0.447405\pi$
$829$	−18.1378	−	10.9132i	−0.629953	−	0.379030i	−0.794434	+	0.607350i	$0.792232\pi$
$830$	−16.2486	−	12.3519i	−0.563998	−	0.428740i
$831$		0			0
$832$	11.6599	+	13.7271i	0.404235	+	0.475903i
$833$	−18.0508	+	8.35117i	−0.625422	+	0.289351i
$834$		0			0
$835$	8.88178	+	16.7528i	0.307367	+	0.579755i
$836$	57.5258	−	67.7246i	1.98957	−	2.34230i
$837$		0			0
$838$	−21.2310	−	53.2858i	−0.733412	−	1.84073i
$839$	5.67045	−	10.6956i	0.195766	−	0.369253i	−0.766123	−	0.642694i	$-0.777817\pi$
$839$	5.67045	−	10.6956i	0.195766	−	0.369253i	0.961889	+	0.273440i	$0.0881617\pi$
$840$		0			0
$841$	−6.00702	+	4.56642i	−0.207139	+	0.157463i
$842$	11.6185	+	41.8461i	0.400401	+	1.44211i
$843$		0			0
$844$	13.7496	+	83.8690i	0.473281	+	2.88689i
$845$	−14.2214	+	3.13038i	−0.489232	+	0.107688i
$846$		0			0
$847$	37.5996	+	4.08921i	1.29194	+	0.140507i
$848$	64.5732	−	95.2384i	2.21745	−	3.27050i
$849$		0			0
$850$	−1.90189	−	35.0784i	−0.0652344	−	1.20318i
$851$	15.0209	+	14.2286i	0.514911	+	0.487749i
$852$		0			0
$853$	−1.39015	+	25.6397i	−0.0475977	+	0.877888i	0.873083	+	0.487571i	$0.162117\pi$
$853$	−1.39015	+	25.6397i	−0.0475977	+	0.877888i	−0.920681	+	0.390316i	$0.872366\pi$
$854$	148.034	+	32.5848i	5.06563	+	1.11503i
$855$		0			0
$856$	−40.1912	+	13.5420i	−1.37371	+	0.462856i
$857$	33.6327	+	7.40313i	1.14887	+	0.252886i	0.748288	−	0.663374i	$-0.230876\pi$
$857$	33.6327	+	7.40313i	1.14887	+	0.252886i	0.400584	+	0.916260i	$0.368807\pi$
$858$		0			0
$859$	18.5634	−	17.5842i	0.633374	−	0.599964i	−0.302135	−	0.953265i	$-0.597699\pi$
$859$	18.5634	−	17.5842i	0.633374	−	0.599964i	0.935510	+	0.353301i	$0.114941\pi$
$860$	−17.2034	−	16.2959i	−0.586630	−	0.555685i
$861$		0			0
$862$	6.63436	−	40.4678i	0.225967	−	1.37834i
$863$	−14.4377	+	21.2939i	−0.491463	+	0.724854i	−0.989852	−	0.142099i	$-0.954615\pi$
$863$	−14.4377	+	21.2939i	−0.491463	+	0.724854i	0.498389	+	0.866954i	$0.333925\pi$
$864$		0			0
$865$	12.4436	−	7.48709i	0.423097	−	0.254569i
$866$	13.6213	−	2.99828i	0.462872	−	0.101886i
$867$		0			0
$868$	20.0305	+	9.26708i	0.679878	+	0.314545i
$869$	3.53776	+	12.7419i	0.120010	+	0.432238i
$870$		0			0
$871$	−0.568168	+	0.0617920i	−0.0192516	+	0.00209374i
$872$	−36.3617	+	68.5854i	−1.23136	+	2.32260i
$873$		0			0
$874$	21.2195	−	76.4258i	0.717761	−	2.58514i
$875$	22.9751	−	27.0484i	0.776702	−	0.914404i
$876$		0			0
$877$	−16.9850	−	25.0510i	−0.573543	−	0.845913i	0.424689	−	0.905339i	$-0.360383\pi$
$877$	−16.9850	−	25.0510i	−0.573543	−	0.845913i	−0.998233	+	0.0594259i	$0.981073\pi$
$878$	22.3916	−	10.3595i	0.755680	−	0.349615i
$879$		0			0
$880$	−31.8616	+	79.9667i	−1.07406	+	2.69568i
$881$	16.5957	+	12.6157i	0.559124	+	0.425035i	0.846194	−	0.532874i	$-0.178888\pi$
$881$	16.5957	+	12.6157i	0.559124	+	0.425035i	−0.287070	+	0.957910i	$0.592681\pi$
$882$		0			0
$883$	−38.9379	−	13.1197i	−1.31036	−	0.441513i	−0.424487	−	0.905434i	$-0.639545\pi$
$883$	−38.9379	−	13.1197i	−1.31036	−	0.441513i	−0.885876	+	0.463921i	$0.846442\pi$
$884$	−9.64259			−0.324315
$885$		0			0
$886$	−68.2852			−2.29409
$887$	47.6161	+	16.0437i	1.59879	+	0.538696i	0.970875	−	0.239585i	$-0.0770113\pi$
$887$	47.6161	+	16.0437i	1.59879	+	0.538696i	0.627917	+	0.778281i	$0.283908\pi$
$888$		0			0
$889$	46.0249	+	34.9872i	1.54363	+	1.17343i
$890$	5.09878	−	12.7970i	0.170912	−	0.428956i
$891$		0			0
$892$	−56.1456	+	25.9757i	−1.87989	+	0.869731i
$893$	−4.55948	−	6.72473i	−0.152577	−	0.225034i
$894$		0			0
$895$	−7.21343	+	8.49231i	−0.241118	+	0.283867i
$896$	47.6557	−	171.640i	1.59206	−	5.73410i
$897$		0			0
$898$	−23.8097	+	44.9099i	−0.794541	+	1.49866i
$899$	−5.07189	+	0.551601i	−0.169157	+	0.0183969i
$900$		0			0
$901$	6.53892	+	23.5511i	0.217843	+	0.784600i
$902$	40.8346	+	18.8921i	1.35964	+	0.629038i
$903$		0			0
$904$	31.2796	−	6.88517i	1.04035	−	0.228997i
$905$	−2.06234	+	1.24087i	−0.0685545	+	0.0412479i
$906$		0			0
$907$	−18.9891	+	28.0068i	−0.630522	+	0.929951i	0.369477	+	0.929240i	$0.379537\pi$
$907$	−18.9891	+	28.0068i	−0.630522	+	0.929951i	−1.00000		0.000711271i	$0.999774\pi$
$908$	−12.7278	+	77.6363i	−0.422388	+	2.57645i
$909$		0			0
$910$	−4.07781	−	3.86270i	−0.135178	−	0.128047i
$911$	−30.7244	+	29.1037i	−1.01795	+	0.964249i	−0.999367	−	0.0355780i	$-0.988673\pi$
$911$	−30.7244	+	29.1037i	−1.01795	+	0.964249i	−0.0185788	+	0.999827i	$0.505914\pi$
$912$		0			0
$913$	29.4007	+	6.47159i	0.973022	+	0.214178i
$914$	−12.1051	+	4.07870i	−0.400402	+	0.134911i
$915$		0			0
$916$	80.9082	+	17.8092i	2.67328	+	0.588434i
$917$	−0.808965	+	14.9205i	−0.0267144	+	0.492718i
$918$		0			0
$919$	−21.9793	−	20.8199i	−0.725031	−	0.686786i	0.233313	−	0.972402i	$-0.425043\pi$
$919$	−21.9793	−	20.8199i	−0.725031	−	0.686786i	−0.958344	+	0.285616i	$0.907802\pi$
$920$	5.18545	+	95.6400i	0.170959	+	3.15316i
$921$		0			0
$922$	21.9837	−	32.4235i	0.723995	−	1.06781i
$923$	−4.22142	−	0.459107i	−0.138950	−	0.0151117i
$924$		0			0
$925$	−8.85821	+	1.94984i	−0.291256	+	0.0641103i
$926$	14.0716	+	85.8330i	0.462421	+	2.82065i
$927$		0			0
$928$	30.7952	+	110.914i	1.01090	+	3.64093i
$929$	−25.6472	+	19.4965i	−0.841457	+	0.639659i	−0.934484	−	0.356005i	$-0.884139\pi$
$929$	−25.6472	+	19.4965i	−0.841457	+	0.639659i	0.0930274	+	0.995664i	$0.470346\pi$
$930$		0			0
$931$	9.22111	−	17.3929i	0.302210	−	0.570028i
$932$	21.5198	+	54.0106i	0.704904	+	1.76918i
$933$		0			0
$934$	2.56367	−	3.01818i	0.0838857	−	0.0987579i
$935$	−8.56487	−	16.1550i	−0.280101	−	0.528327i
$936$		0			0
$937$	10.1098	−	4.67728i	0.330272	−	0.152800i	−0.247744	−	0.968826i	$-0.579689\pi$
$937$	10.1098	−	4.67728i	0.330272	−	0.152800i	0.578016	+	0.816025i	$0.303827\pi$
$938$	7.30823	+	8.60392i	0.238622	+	0.280928i
$939$		0			0
$940$	12.1414	+	9.22962i	0.396007	+	0.301037i
$941$	−12.1409	−	7.30492i	−0.395781	−	0.238134i	0.303726	−	0.952760i	$-0.401769\pi$
$941$	−12.1409	−	7.30492i	−0.395781	−	0.238134i	−0.699507	+	0.714626i	$0.746597\pi$
$942$		0			0
$943$	29.6026			0.963992
$944$	−77.6382	+	97.4839i	−2.52691	+	3.17283i
$945$		0			0
$946$	44.9357	+	15.1406i	1.46098	+	0.492263i
$947$	−40.7951	−	24.5456i	−1.32566	−	0.797624i	−0.336113	−	0.941822i	$-0.609112\pi$
$947$	−40.7951	−	24.5456i	−1.32566	−	0.797624i	−0.989549	+	0.144198i	$0.953940\pi$
$948$		0			0
$949$	−0.929710	+	2.33340i	−0.0301797	+	0.0757453i
$950$	22.5106	+	26.5015i	0.730339	+	0.859822i
$951$		0			0
$952$	68.7600	+	101.413i	2.22852	+	3.28683i
$953$	−11.0627	−	20.8664i	−0.358355	−	0.675928i	0.637140	−	0.770748i	$-0.280117\pi$
$953$	−11.0627	−	20.8664i	−0.358355	−	0.675928i	−0.995494	+	0.0948198i	$0.969773\pi$
$954$		0			0
$955$	−0.196804	+	0.708825i	−0.00636844	+	0.0229371i
$956$	10.7959	+	27.0956i	0.349163	+	0.876334i
$957$		0			0
$958$	70.0218	−	7.61533i	2.26230	−	0.246040i
$959$	57.3394	−	43.5883i	1.85159	−	1.40754i
$960$		0			0
$961$	−27.0338	−	12.5072i	−0.872057	−	0.403457i
$962$	0.546449	+	3.33319i	0.0176182	+	0.107466i
$963$		0			0
$964$	−18.0438	+	10.8566i	−0.581153	+	0.349668i
$965$	−20.8520	−	2.26779i	−0.671249	−	0.0730027i
$966$		0			0
$967$	−6.68953	+	40.8043i	−0.215121	+	1.31218i	0.629578	+	0.776937i	$0.283228\pi$
$967$	−6.68953	+	40.8043i	−0.215121	+	1.31218i	−0.844699	+	0.535242i	$0.820220\pi$
$968$	−5.70017	−	105.133i	−0.183210	−	3.37912i
$969$		0			0
$970$	22.2063	−	21.0349i	0.713000	−	0.675390i
$971$	2.61284	−	48.1910i	0.0838501	−	1.54652i	−0.589846	−	0.807516i	$-0.700812\pi$
$971$	2.61284	−	48.1910i	0.0838501	−	1.54652i	0.673696	−	0.739008i	$-0.264706\pi$
$972$		0			0
$973$	−74.8806	+	25.2302i	−2.40056	+	0.808843i
$974$	95.5497	−	32.1944i	3.06161	−	1.03158i
$975$		0			0
$976$	13.5082	−	249.144i	0.432388	−	7.97492i
$977$	36.7202	−	34.7832i	1.17478	−	1.11281i	0.183234	−	0.983069i	$-0.441343\pi$
$977$	36.7202	−	34.7832i	1.17478	−	1.11281i	0.991548	−	0.129743i	$-0.0414152\pi$
$978$		0			0
$979$	1.10000	+	20.2883i	0.0351561	+	0.648415i
$980$	−5.97840	+	36.4666i	−0.190973	+	1.16488i
$981$		0			0
$982$	−15.9171	−	1.73109i	−0.507935	−	0.0552412i
$983$	−31.1441	+	18.7388i	−0.993343	+	0.597675i	−0.916781	−	0.399390i	$-0.869222\pi$
$983$	−31.1441	+	18.7388i	−0.993343	+	0.597675i	−0.0765621	+	0.997065i	$0.524394\pi$
$984$		0			0
$985$	−0.668071	−	4.07505i	−0.0212865	−	0.129842i
$986$	−39.9586	−	18.4868i	−1.27254	−	0.588740i
$987$		0			0
$988$	7.59807	−	5.77590i	0.241727	−	0.183756i
$989$	31.0150	−	3.37309i	0.986220	−	0.107258i
$990$		0			0
$991$	18.1018	+	45.4321i	0.575022	+	1.44320i	0.872570	+	0.488490i	$0.162452\pi$
$991$	18.1018	+	45.4321i	0.575022	+	1.44320i	−0.297547	+	0.954707i	$0.596169\pi$
$992$	7.32301	−	26.3751i	0.232506	−	0.837410i
$993$		0			0
$994$	39.2876	+	74.1042i	1.24613	+	2.35044i
$995$	−9.52049	−	14.0417i	−0.301820	−	0.445151i
$996$		0			0
$997$	13.2925	+	15.6491i	0.420977	+	0.495612i	0.931240	−	0.364406i	$-0.118728\pi$
$997$	13.2925	+	15.6491i	0.420977	+	0.495612i	−0.510263	+	0.860018i	$0.670452\pi$
$998$	35.7428	−	89.7078i	1.13142	−	2.83965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.64.5		140
3.2	odd	2		177.2.e.a.64.1	✓	140
59.12	even	29	inner	531.2.i.c.307.5		140
177.71	odd	58		177.2.e.a.130.1	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.64.1	✓	140	3.2	odd	2
177.2.e.a.130.1	yes	140	177.71	odd	58
531.2.i.c.64.5		140	1.1	even	1	trivial
531.2.i.c.307.5		140	59.12	even	29	inner

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(2.61370 + 0.880659i) q^{2} +(4.46370 + 3.39321i) q^{4} +(-0.422705 + 1.06091i) q^{5} +(-3.24336 + 1.50054i) q^{7} +(5.58292 + 8.23419i) q^{8} +O(q^{10})\)	\(q+(2.61370 + 0.880659i) q^{2} +(4.46370 + 3.39321i) q^{4} +(-0.422705 + 1.06091i) q^{5} +(-3.24336 + 1.50054i) q^{7} +(5.58292 + 8.23419i) q^{8} +(-2.03912 + 2.40064i) q^{10} +(1.24288 - 4.47645i) q^{11} +(0.233736 - 0.440872i) q^{13} +(-9.79864 + 1.06567i) q^{14} +(4.34051 + 15.6331i) q^{16} +(-3.12785 - 1.44710i) q^{17} +(3.33146 - 0.733309i) q^{19} +(-5.48672 + 3.30125i) q^{20} +(7.19075 - 10.6056i) q^{22} +(1.36389 - 8.31938i) q^{23} +(2.68313 + 2.54159i) q^{25} +(0.999173 - 0.946467i) q^{26} +(-19.5690 - 4.30747i) q^{28} +(4.38942 - 1.47897i) q^{29} +(-1.07570 - 0.236779i) q^{31} +(-1.34544 + 24.8152i) q^{32} +(-6.90086 - 6.53684i) q^{34} +(-0.220951 - 4.07519i) q^{35} +(-1.37727 + 2.03133i) q^{37} +(9.35324 + 1.01723i) q^{38} +(-11.0956 + 2.44234i) q^{40} +(0.568080 + 3.46513i) q^{41} +(0.990022 + 3.56574i) q^{43} +(20.7374 - 15.7642i) q^{44} +(10.8914 - 20.5433i) q^{46} +(-0.881582 - 2.21260i) q^{47} +(3.73606 - 4.39843i) q^{49} +(4.77462 + 9.00589i) q^{50} +(2.53930 - 1.17480i) q^{52} +(-4.59132 - 5.40532i) q^{53} +(4.22374 + 3.21080i) q^{55} +(-30.4631 - 18.3290i) q^{56} +12.7751 q^{58} +(4.50924 + 6.21826i) q^{59} +(-14.5736 - 4.91042i) q^{61} +(-2.60304 - 1.56620i) q^{62} +(-13.3597 + 33.5303i) q^{64} +(0.368924 + 0.434331i) q^{65} +(-0.642743 - 0.947975i) q^{67} +(-9.05145 - 17.0728i) q^{68} +(3.01136 - 10.8459i) q^{70} +(-3.14974 - 7.90526i) q^{71} +(-5.00415 + 0.544234i) q^{73} +(-5.38869 + 4.09638i) q^{74} +(17.3589 + 8.03108i) q^{76} +(2.68598 + 16.3837i) q^{77} +(-2.43897 + 1.46748i) q^{79} +(-18.4201 - 2.00330i) q^{80} +(-1.56681 + 9.55712i) q^{82} +(0.350818 + 6.47046i) q^{83} +(2.85739 - 2.70667i) q^{85} +(-0.552575 + 10.1917i) q^{86} +(43.7988 - 14.7576i) q^{88} +(-4.14450 + 1.39644i) q^{89} +(-0.0965432 + 1.78064i) q^{91} +(34.3174 - 32.5072i) q^{92} +(-0.355644 - 6.55946i) q^{94} +(-0.630249 + 3.84435i) q^{95} +(-9.65402 - 1.04994i) q^{97} +(13.6385 - 8.20599i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

L-functions

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