LMFDB - Embedded newform 531.2.i.c.19.4

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			19.4
Character	$\chi$	$=$	531.19
Dual form			531.2.i.c.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.454038 - 0.856407i) q^{2} +(0.595092 + 0.877695i) q^{4} +(-3.60206 + 0.792874i) q^{5} +(1.56865 - 1.19245i) q^{7} +(2.94914 - 0.320738i) q^{8} +O(q^{10})$	\(q+(0.454038 - 0.856407i) q^{2} +(0.595092 + 0.877695i) q^{4} +(-3.60206 + 0.792874i) q^{5} +(1.56865 - 1.19245i) q^{7} +(2.94914 - 0.320738i) q^{8} +(-0.956451 + 3.44483i) q^{10} +(0.731304 + 1.83543i) q^{11} +(0.326231 + 6.01697i) q^{13} +(-0.309001 - 1.88482i) q^{14} +(0.279337 - 0.701084i) q^{16} +(1.98052 + 1.50555i) q^{17} +(-0.510808 + 0.172111i) q^{19} +(-2.83946 - 2.68968i) q^{20} +(1.90392 + 0.207064i) q^{22} +(2.30855 - 1.38901i) q^{23} +(7.80833 - 3.61252i) q^{25} +(5.30110 + 2.45255i) q^{26} +(1.98010 + 0.667174i) q^{28} +(4.68698 + 8.84059i) q^{29} +(-6.98124 - 2.35225i) q^{31} +(3.36739 + 3.96440i) q^{32} +(2.18860 - 1.01255i) q^{34} +(-4.70490 + 5.53904i) q^{35} +(8.07738 + 0.878468i) q^{37} +(-0.0845291 + 0.515605i) q^{38} +(-10.3687 + 3.49361i) q^{40} +(-4.71579 - 2.83740i) q^{41} +(1.43226 - 3.59471i) q^{43} +(-1.17576 + 1.73411i) q^{44} +(-0.141387 - 2.60772i) q^{46} +(1.10146 + 0.242450i) q^{47} +(-0.833992 + 3.00377i) q^{49} +(0.451495 - 8.32733i) q^{50} +(-5.08693 + 3.86698i) q^{52} +(-2.40290 - 8.65448i) q^{53} +(-4.08947 - 6.03152i) q^{55} +(4.24369 - 4.01984i) q^{56} +9.69921 q^{58} +(-3.58219 + 6.79470i) q^{59} +(4.54005 - 8.56344i) q^{61} +(-5.18424 + 4.91077i) q^{62} +(6.39815 - 1.40834i) q^{64} +(-5.94580 - 21.4148i) q^{65} +(-10.7277 + 1.16671i) q^{67} +(-0.142824 + 2.63423i) q^{68} +(2.60747 + 6.54425i) q^{70} +(-1.03135 - 0.227018i) q^{71} +(-1.59885 - 9.75254i) q^{73} +(4.41977 - 6.51867i) q^{74} +(-0.455039 - 0.345912i) q^{76} +(3.33583 + 2.00710i) q^{77} +(-6.95616 - 6.58922i) q^{79} +(-0.450320 + 2.74683i) q^{80} +(-4.57111 + 2.75035i) q^{82} +(2.31576 - 2.72632i) q^{83} +(-8.32767 - 3.85279i) q^{85} +(-2.42823 - 2.85874i) q^{86} +(2.74541 + 5.17839i) q^{88} +(-2.07887 - 3.92116i) q^{89} +(7.68671 + 9.04949i) q^{91} +(2.59293 + 1.19962i) q^{92} +(0.707741 - 0.833217i) q^{94} +(1.70350 - 1.02496i) q^{95} +(-1.55157 + 9.46414i) q^{97} +(2.19378 + 2.07806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{19}{29}\right)$

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 $

$2$	0.454038	−	0.856407i	0.321054	−	0.605571i	−0.669482	−	0.742828i	$-0.733484\pi$
$2$	0.454038	−	0.856407i	0.321054	−	0.605571i	0.990535	+	0.137257i	$0.0438287\pi$
$3$		0			0
$3$		0			0
$4$	0.595092	+	0.877695i	0.297546	+	0.438847i
$5$	−3.60206	+	0.792874i	−1.61089	+	0.354584i	−0.927018	−	0.375017i	$-0.877637\pi$
$5$	−3.60206	+	0.792874i	−1.61089	+	0.354584i	−0.683873	+	0.729601i	$0.739706\pi$
$6$		0			0
$7$	1.56865	−	1.19245i	0.592893	−	0.450706i	−0.265205	−	0.964192i	$-0.585439\pi$
$7$	1.56865	−	1.19245i	0.592893	−	0.450706i	0.858098	+	0.513487i	$0.171646\pi$
$8$	2.94914	−	0.320738i	1.04268	−	0.113398i
$9$		0			0
$10$	−0.956451	+	3.44483i	−0.302457	+	1.08935i
$11$	0.731304	+	1.83543i	0.220496	+	0.553404i	0.997059	−	0.0766358i	$-0.0244179\pi$
$11$	0.731304	+	1.83543i	0.220496	+	0.553404i	−0.776563	+	0.630040i	$0.783039\pi$
$12$		0			0
$13$	0.326231	+	6.01697i	0.0904801	+	1.66881i	0.593728	+	0.804665i	$0.297655\pi$
$13$	0.326231	+	6.01697i	0.0904801	+	1.66881i	−0.503248	+	0.864142i	$0.667862\pi$
$14$	−0.309001	−	1.88482i	−0.0825839	−	0.503740i
$15$		0			0
$16$	0.279337	−	0.701084i	0.0698344	−	0.175271i
$17$	1.98052	+	1.50555i	0.480347	+	0.365150i	0.817150	−	0.576425i	$-0.195553\pi$
$17$	1.98052	+	1.50555i	0.480347	+	0.365150i	−0.336803	+	0.941575i	$0.609346\pi$
$18$		0			0
$19$	−0.510808	+	0.172111i	−0.117187	+	0.0394850i	−0.377284	−	0.926097i	$-0.623142\pi$
$19$	−0.510808	+	0.172111i	−0.117187	+	0.0394850i	0.260097	+	0.965583i	$0.416245\pi$
$20$	−2.83946	−	2.68968i	−0.634923	−	0.601431i
$21$		0			0
$22$	1.90392	+	0.207064i	0.405917	+	0.0441461i
$23$	2.30855	−	1.38901i	0.481366	−	0.289628i	−0.254115	−	0.967174i	$-0.581784\pi$
$23$	2.30855	−	1.38901i	0.481366	−	0.289628i	0.735481	+	0.677546i	$0.236956\pi$
$24$		0			0
$25$	7.80833	−	3.61252i	1.56167	−	0.722504i
$26$	5.30110	+	2.45255i	1.03963	+	0.480984i
$27$		0			0
$28$	1.98010	+	0.667174i	0.374204	+	0.126084i
$29$	4.68698	+	8.84059i	0.870351	+	1.64166i	0.762032	+	0.647540i	$0.224202\pi$
$29$	4.68698	+	8.84059i	0.870351	+	1.64166i	0.108319	+	0.994116i	$0.465453\pi$
$30$		0			0
$31$	−6.98124	−	2.35225i	−1.25387	−	0.422477i	−0.387493	−	0.921873i	$-0.626659\pi$
$31$	−6.98124	−	2.35225i	−1.25387	−	0.422477i	−0.866374	+	0.499395i	$0.833556\pi$
$32$	3.36739	+	3.96440i	0.595277	+	0.700814i
$33$		0			0
$34$	2.18860	−	1.01255i	0.375341	−	0.173651i
$35$	−4.70490	+	5.53904i	−0.795273	+	0.936268i
$36$		0			0
$37$	8.07738	+	0.878468i	1.32791	+	0.144419i	0.744427	−	0.667704i	$-0.232723\pi$
$37$	8.07738	+	0.878468i	1.32791	+	0.144419i	0.583486	+	0.812123i	$0.301688\pi$
$38$	−0.0845291	+	0.515605i	−0.0137124	+	0.0836421i
$39$		0			0
$40$	−10.3687	+	3.49361i	−1.63943	+	0.552389i
$41$	−4.71579	−	2.83740i	−0.736482	−	0.443127i	0.0972751	−	0.995258i	$-0.468987\pi$
$41$	−4.71579	−	2.83740i	−0.736482	−	0.443127i	−0.833758	+	0.552131i	$0.813815\pi$
$42$		0			0
$43$	1.43226	−	3.59471i	0.218418	−	0.548189i	−0.778411	−	0.627755i	$-0.783974\pi$
$43$	1.43226	−	3.59471i	0.218418	−	0.548189i	0.996830	+	0.0795660i	$0.0253534\pi$
$44$	−1.17576	+	1.73411i	−0.177252	+	0.261427i
$45$		0			0
$46$	−0.141387	−	2.60772i	−0.0208463	−	0.384488i
$47$	1.10146	+	0.242450i	0.160665	+	0.0353649i	0.294574	−	0.955629i	$-0.404822\pi$
$47$	1.10146	+	0.242450i	0.160665	+	0.0353649i	−0.133910	+	0.990994i	$0.542753\pi$
$48$		0			0
$49$	−0.833992	+	3.00377i	−0.119142	+	0.429109i
$50$	0.451495	−	8.32733i	0.0638510	−	1.17766i
$51$		0			0
$52$	−5.08693	+	3.86698i	−0.705430	+	0.536254i
$53$	−2.40290	−	8.65448i	−0.330064	−	1.18878i	−0.923403	−	0.383831i	$-0.874604\pi$
$53$	−2.40290	−	8.65448i	−0.330064	−	1.18878i	0.593339	−	0.804953i	$-0.297809\pi$
$54$		0			0
$55$	−4.08947	−	6.03152i	−0.551424	−	0.813289i
$56$	4.24369	−	4.01984i	0.567087	−	0.537173i
$57$		0			0
$58$	9.69921			1.27357
$59$	−3.58219	+	6.79470i	−0.466361	+	0.884594i
$59$	−3.58219	+	6.79470i	−0.466361	+	0.884594i
$60$		0			0
$61$	4.54005	−	8.56344i	0.581294	−	1.09644i	−0.402210	−	0.915548i	$-0.631758\pi$
$61$	4.54005	−	8.56344i	0.581294	−	1.09644i	0.983504	−	0.180889i	$-0.0578974\pi$
$62$	−5.18424	+	4.91077i	−0.658399	+	0.623668i
$63$		0			0
$64$	6.39815	−	1.40834i	0.799768	−	0.176042i
$65$	−5.94580	−	21.4148i	−0.737486	−	2.65618i
$66$		0			0
$67$	−10.7277	+	1.16671i	−1.31060	+	0.142536i	−0.736603	−	0.676325i	$-0.763571\pi$
$67$	−10.7277	+	1.16671i	−1.31060	+	0.142536i	−0.573992	+	0.818861i	$0.694606\pi$
$68$	−0.142824	+	2.63423i	−0.0173200	+	0.319448i
$69$		0			0
$70$	2.60747	+	6.54425i	0.311652	+	0.782187i
$71$	−1.03135	−	0.227018i	−0.122399	−	0.0269420i	0.153349	−	0.988172i	$-0.450994\pi$
$71$	−1.03135	−	0.227018i	−0.122399	−	0.0269420i	−0.275747	+	0.961230i	$0.588925\pi$
$72$		0			0
$73$	−1.59885	−	9.75254i	−0.187131	−	1.14145i	−0.898612	−	0.438743i	$-0.855424\pi$
$73$	−1.59885	−	9.75254i	−0.187131	−	1.14145i	0.711481	−	0.702705i	$-0.248025\pi$
$74$	4.41977	−	6.51867i	0.513787	−	0.757780i
$75$		0			0
$76$	−0.455039	−	0.345912i	−0.0521965	−	0.0396788i
$77$	3.33583	+	2.00710i	0.380153	+	0.228731i
$78$		0			0
$79$	−6.95616	−	6.58922i	−0.782629	−	0.741346i	0.187937	−	0.982181i	$-0.439820\pi$
$79$	−6.95616	−	6.58922i	−0.782629	−	0.741346i	−0.970566	+	0.240836i	$0.922579\pi$
$80$	−0.450320	+	2.74683i	−0.0503473	+	0.307105i
$81$		0			0
$82$	−4.57111	+	2.75035i	−0.504795	+	0.303725i
$83$	2.31576	−	2.72632i	0.254187	−	0.299252i	−0.620237	−	0.784414i	$-0.712964\pi$
$83$	2.31576	−	2.72632i	0.254187	−	0.299252i	0.874424	+	0.485162i	$0.161239\pi$
$84$		0			0
$85$	−8.32767	−	3.85279i	−0.903263	−	0.417894i
$86$	−2.42823	−	2.85874i	−0.261843	−	0.308266i
$87$		0			0
$88$	2.74541	+	5.17839i	0.292661	+	0.552018i
$89$	−2.07887	−	3.92116i	−0.220360	−	0.415643i	0.748542	−	0.663087i	$-0.230754\pi$
$89$	−2.07887	−	3.92116i	−0.220360	−	0.415643i	−0.968902	+	0.247444i	$0.920409\pi$
$90$		0			0
$91$	7.68671	+	9.04949i	0.805786	+	0.948644i
$92$	2.59293	+	1.19962i	0.270331	+	0.125069i
$93$		0			0
$94$	0.707741	−	0.833217i	0.0729979	−	0.0859398i
$95$	1.70350	−	1.02496i	0.174775	−	0.105159i
$96$		0			0
$97$	−1.55157	+	9.46414i	−0.157538	+	0.960937i	0.783192	+	0.621780i	$0.213590\pi$
$97$	−1.55157	+	9.46414i	−0.157538	+	0.960937i	−0.940730	+	0.339157i	$0.889858\pi$
$98$	2.19378	+	2.07806i	0.221605	+	0.209916i
$99$		0			0
$100$	7.81736	+	4.70355i	0.781736	+	0.470355i
$101$	7.67652	+	5.83554i	0.763843	+	0.580658i	0.912906	−	0.408170i	$-0.133833\pi$
$101$	7.67652	+	5.83554i	0.763843	+	0.580658i	−0.149064	+	0.988828i	$0.547626\pi$
$102$		0			0
$103$	−1.76370	+	2.60126i	−0.173782	+	0.256310i	−0.904599	−	0.426264i	$-0.859829\pi$
$103$	−1.76370	+	2.60126i	−0.173782	+	0.256310i	0.730816	+	0.682574i	$0.239140\pi$
$104$	2.89197	+	17.6402i	0.283581	+	1.72977i
$105$		0			0
$106$	−8.50276	−	1.87160i	−0.825861	−	0.181786i
$107$	−3.87188	−	9.71767i	−0.374308	−	0.939443i	−0.988627	−	0.150385i	$-0.951949\pi$
$107$	−3.87188	−	9.71767i	−0.374308	−	0.939443i	0.614319	−	0.789058i	$-0.289431\pi$
$108$		0			0
$109$	−0.519308	+	9.57807i	−0.0497407	+	0.917413i	0.862067	+	0.506795i	$0.169170\pi$
$109$	−0.519308	+	9.57807i	−0.0497407	+	0.917413i	−0.911807	+	0.410618i	$0.865313\pi$
$110$	−7.02221	+	0.763711i	−0.669541	+	0.0728170i
$111$		0			0
$112$	−0.397829	−	1.43285i	−0.0375913	−	0.135392i
$113$	4.09523	−	0.901428i	0.385247	−	0.0847993i	−0.0181242	−	0.999836i	$-0.505769\pi$
$113$	4.09523	−	0.901428i	0.385247	−	0.0847993i	0.403371	+	0.915036i	$0.367838\pi$
$114$		0			0
$115$	−7.21424	+	6.83369i	−0.672731	+	0.637245i
$116$	−4.97015	+	9.37470i	−0.461467	+	0.870419i
$117$		0			0
$118$	4.19258	+	6.15286i	0.385958	+	0.566417i
$119$	4.90204			0.449369
$120$		0			0
$121$	5.15194	−	4.88018i	0.468358	−	0.443652i
$122$	−5.27243	−	7.77626i	−0.477344	−	0.704029i
$123$		0			0
$124$	−2.08992	−	7.52720i	−0.187680	−	0.675963i
$125$	−10.5807	+	8.04324i	−0.946367	+	0.719409i
$126$		0			0
$127$	0.257141	−	4.74268i	0.0228176	−	0.420845i	−0.964702	−	0.263346i	$-0.915174\pi$
$127$	0.257141	−	4.74268i	0.0228176	−	0.420845i	0.987519	−	0.157499i	$-0.0503432\pi$
$128$	−1.08422	+	3.90499i	−0.0958321	+	0.345156i
$129$		0			0
$130$	−21.0394	−	4.63113i	−1.84528	−	0.406177i
$131$	−1.21302	−	22.3728i	−0.105982	−	1.95472i	−0.257530	−	0.966270i	$-0.582909\pi$
$131$	−1.21302	−	22.3728i	−0.105982	−	1.95472i	0.151548	−	0.988450i	$-0.451574\pi$
$132$		0			0
$133$	−0.596043	+	0.879098i	−0.0516835	+	0.0762274i
$134$	−3.87160	+	9.71699i	−0.334456	+	0.839420i
$135$		0			0
$136$	6.32371	+	3.80485i	0.542254	+	0.326263i
$137$	−5.27757	+	1.77822i	−0.450894	+	0.151924i	−0.535581	−	0.844484i	$-0.679907\pi$
$137$	−5.27757	+	1.77822i	−0.450894	+	0.151924i	0.0846875	+	0.996408i	$0.473011\pi$
$138$		0			0
$139$	3.63366	−	22.1643i	0.308203	−	1.87996i	−0.146346	−	0.989234i	$-0.546751\pi$
$139$	3.63366	−	22.1643i	0.308203	−	1.87996i	0.454549	−	0.890722i	$-0.349801\pi$
$140$	−7.66143	−	0.833231i	−0.647509	−	0.0704209i
$141$		0			0
$142$	−0.662692	+	0.780182i	−0.0556119	+	0.0654714i
$143$	−10.8052	+	4.99901i	−0.903574	+	0.418038i
$144$		0			0
$145$	−23.8923	−	28.1282i	−1.98415	−	2.33592i
$146$	−9.07808	−	3.05876i	−0.751307	−	0.253145i
$147$		0			0
$148$	4.03576	+	7.61225i	0.331737	+	0.625723i
$149$	16.8644	+	5.68228i	1.38159	+	0.465510i	0.909376	−	0.415976i	$-0.136560\pi$
$149$	16.8644	+	5.68228i	1.38159	+	0.465510i	0.472210	+	0.881486i	$0.343457\pi$
$150$		0			0
$151$	6.92769	+	3.20509i	0.563767	+	0.260826i	0.681007	−	0.732277i	$-0.261542\pi$
$151$	6.92769	+	3.20509i	0.563767	+	0.260826i	−0.117240	+	0.993104i	$0.537405\pi$
$152$	−1.45124	+	0.671415i	−0.117711	+	0.0544590i
$153$		0			0
$154$	3.23349	−	1.94553i	0.260562	−	0.156775i
$155$	27.0119	+	2.93772i	2.16965	+	0.235963i
$156$		0			0
$157$	9.55139	+	9.04755i	0.762284	+	0.722073i	0.966448	−	0.256863i	$-0.0826890\pi$
$157$	9.55139	+	9.04755i	0.762284	+	0.722073i	−0.204164	+	0.978937i	$0.565448\pi$
$158$	−8.80142	+	2.96554i	−0.700203	+	0.235926i
$159$		0			0
$160$	−15.2728	−	11.6101i	−1.20742	−	0.917860i
$161$	1.96497	−	4.93171i	0.154861	−	0.388673i
$162$		0			0
$163$	1.33331	+	8.13281i	0.104433	+	0.637011i	0.986230	+	0.165382i	$0.0528857\pi$
$163$	1.33331	+	8.13281i	0.104433	+	0.637011i	−0.881797	+	0.471629i	$0.843666\pi$
$164$	−0.315960	−	5.82754i	−0.0246723	−	0.455054i
$165$		0			0
$166$	−1.28340	−	3.22108i	−0.0996109	−	0.250004i
$167$	−0.931448	+	3.35477i	−0.0720776	+	0.259600i	−0.990806	−	0.135290i	$-0.956803\pi$
$167$	−0.931448	+	3.35477i	−0.0720776	+	0.259600i	0.918728	+	0.394890i	$0.129217\pi$
$168$		0			0
$169$	−23.1737	+	2.52029i	−1.78259	+	0.193869i
$170$	−7.08064	+	5.38256i	−0.543060	+	0.412824i
$171$		0			0
$172$	4.00739	−	0.882093i	0.305561	−	0.0672590i
$173$	−1.73245	−	2.55517i	−0.131716	−	0.194266i	0.756112	−	0.654442i	$-0.227097\pi$
$173$	−1.73245	−	2.55517i	−0.131716	−	0.194266i	−0.887828	+	0.460176i	$0.847786\pi$
$174$		0			0
$175$	7.94075	−	14.9779i	0.600265	−	1.13222i
$176$	1.49107			0.112394
$177$		0			0
$178$	−4.30200			−0.322448
$179$	−5.37488	+	10.1381i	−0.401738	+	0.757758i	−0.999019	−	0.0442739i	$-0.985903\pi$
$179$	−5.37488	+	10.1381i	−0.401738	+	0.757758i	0.597282	+	0.802031i	$0.296247\pi$
$180$		0			0
$181$	−1.95990	−	2.89063i	−0.145678	−	0.214859i	0.747849	−	0.663869i	$-0.231087\pi$
$181$	−1.95990	−	2.89063i	−0.145678	−	0.214859i	−0.893526	+	0.449010i	$0.851777\pi$
$182$	11.2401	−	2.47413i	0.833172	−	0.183395i
$183$		0			0
$184$	6.36272	−	4.83682i	0.469066	−	0.356575i
$185$	−29.7918	+	3.24005i	−2.19033	+	0.238213i
$186$		0			0
$187$	−1.31498	+	4.73613i	−0.0961608	+	0.346340i
$188$	0.442673	+	1.11103i	0.0322853	+	0.0810299i
$189$		0			0
$190$	−0.104330	−	1.92426i	−0.00756892	−	0.139601i
$191$	−3.91786	−	23.8979i	−0.283487	−	1.72919i	−0.617454	−	0.786607i	$-0.711836\pi$
$191$	−3.91786	−	23.8979i	−0.283487	−	1.72919i	0.333967	−	0.942585i	$-0.391613\pi$
$192$		0			0
$193$	−6.93810	+	17.4133i	−0.499415	+	1.25344i	0.436019	+	0.899937i	$0.356388\pi$
$193$	−6.93810	+	17.4133i	−0.499415	+	1.25344i	−0.935434	+	0.353501i	$0.884991\pi$
$194$	7.40068	+	5.62585i	0.531338	+	0.403913i
$195$		0			0
$196$	−3.13269	+	1.05553i	−0.223764	+	0.0753948i
$197$	10.8964	+	10.3216i	0.776336	+	0.735385i	0.969316	−	0.245818i	$-0.0790566\pi$
$197$	10.8964	+	10.3216i	0.776336	+	0.735385i	−0.192980	+	0.981203i	$0.561815\pi$
$198$		0			0
$199$	26.0870	+	2.83713i	1.84926	+	0.201119i	0.964347	−	0.264642i	$-0.0852536\pi$
$199$	26.0870	+	2.83713i	1.84926	+	0.201119i	0.884911	+	0.465760i	$0.154219\pi$
$200$	21.8692	−	13.1582i	1.54638	−	0.930428i
$201$		0			0
$202$	8.48303	−	3.92467i	0.596864	−	0.276139i
$203$	17.8942	+	8.27875i	1.25593	+	0.581054i
$204$		0			0
$205$	19.2363	+	6.48145i	1.34352	+	0.452684i
$206$	1.42695	+	2.69152i	0.0994205	+	0.187527i
$207$		0			0
$208$	4.30953	+	1.45205i	0.298812	+	0.100682i
$209$	−0.689455	−	0.811689i	−0.0476906	−	0.0561457i
$210$		0			0
$211$	2.40423	−	1.11231i	0.165514	−	0.0765749i	−0.335383	−	0.942082i	$-0.608866\pi$
$211$	2.40423	−	1.11231i	0.165514	−	0.0765749i	0.500897	+	0.865507i	$0.333004\pi$
$212$	6.16604	−	7.25923i	0.423485	−	0.498566i
$213$		0			0
$214$	−10.0803	−	1.09629i	−0.689073	−	0.0749412i
$215$	−2.30895	+	14.0840i	−0.157469	+	0.960520i
$216$		0			0
$217$	−13.7561	+	4.63496i	−0.933822	+	0.314641i
$218$	7.96694	+	4.79355i	0.539589	+	0.324660i
$219$		0			0
$220$	2.86022	−	7.17861i	0.192836	−	0.483982i
$221$	−8.41276	+	12.4079i	−0.565903	+	0.834645i
$222$		0			0
$223$	0.858196	+	15.8285i	0.0574691	+	1.05995i	0.875017	+	0.484093i	$0.160850\pi$
$223$	0.858196	+	15.8285i	0.0574691	+	1.05995i	−0.817547	+	0.575861i	$0.804667\pi$
$224$	10.0096	+	2.20329i	0.668796	+	0.147213i
$225$		0			0
$226$	1.08740	−	3.91647i	0.0723329	−	0.260520i
$227$	0.179815	−	3.31650i	0.0119348	−	0.220124i	−0.986482	−	0.163871i	$-0.947602\pi$
$227$	0.179815	−	3.31650i	0.0119348	−	0.220124i	0.998417	−	0.0562528i	$-0.0179153\pi$
$228$		0			0
$229$	3.85864	−	2.93326i	0.254986	−	0.193835i	−0.469870	−	0.882736i	$-0.655699\pi$
$229$	3.85864	−	2.93326i	0.254986	−	0.193835i	0.724856	+	0.688900i	$0.241906\pi$
$230$	2.57688	+	9.28108i	0.169914	+	0.611976i
$231$		0			0
$232$	16.6581	+	24.5688i	1.09366	+	1.61302i
$233$	2.77099	−	2.62482i	0.181533	−	0.171957i	−0.591537	−	0.806278i	$-0.701479\pi$
$233$	2.77099	−	2.62482i	0.181533	−	0.171957i	0.773070	+	0.634320i	$0.218720\pi$
$234$		0			0
$235$	−4.15976			−0.271353
$236$	−8.09540	+	0.899403i	−0.526966	+	0.0585461i
$237$		0			0
$238$	2.22571	−	4.19814i	0.144272	−	0.272125i
$239$	19.1146	−	18.1064i	1.23642	−	1.17120i	0.257654	−	0.966237i	$-0.417050\pi$
$239$	19.1146	−	18.1064i	1.23642	−	1.17120i	0.978769	−	0.204966i	$-0.0657082\pi$
$240$		0			0
$241$	11.5385	−	2.53982i	0.743261	−	0.163604i	0.172832	−	0.984951i	$-0.444708\pi$
$241$	11.5385	−	2.53982i	0.743261	−	0.163604i	0.570429	+	0.821347i	$0.306777\pi$
$242$	−1.84024	−	6.62794i	−0.118295	−	0.426060i
$243$		0			0
$244$	10.2178	−	1.11126i	0.654130	−	0.0711409i
$245$	0.622482	−	11.4810i	0.0397689	−	0.733495i
$246$		0			0
$247$	−1.20223	−	3.01737i	−0.0764960	−	0.191991i
$248$	−21.3431	−	4.69797i	−1.35529	−	0.298321i
$249$		0			0
$250$	2.08424	+	12.7133i	0.131819	+	0.804061i
$251$	−2.48782	+	3.66927i	−0.157030	+	0.231602i	−0.898063	−	0.439866i	$-0.855026\pi$
$251$	−2.48782	+	3.66927i	−0.157030	+	0.231602i	0.741033	+	0.671468i	$0.234336\pi$
$252$		0			0
$253$	4.23768	+	3.22140i	0.266421	+	0.202528i
$254$	−3.94492	−	2.37358i	−0.247526	−	0.148931i
$255$		0			0
$256$	12.3644	+	11.7122i	0.772777	+	0.732014i
$257$	−0.748886	+	4.56801i	−0.0467143	+	0.284944i	−0.999845	−	0.0176149i	$-0.994393\pi$
$257$	−0.748886	+	4.56801i	−0.0467143	+	0.284944i	0.953131	+	0.302559i	$0.0978410\pi$
$258$		0			0
$259$	13.7181	−	8.25391i	0.852401	−	0.512873i
$260$	15.2574	−	17.9624i	0.946224	−	1.11398i
$261$		0			0
$262$	−19.7110	−	9.11927i	−1.21775	−	0.563390i
$263$	−11.2124	−	13.2003i	−0.691387	−	0.813963i	0.298711	−	0.954344i	$-0.403443\pi$
$263$	−11.2124	−	13.2003i	−0.691387	−	0.813963i	−0.990098	+	0.140380i	$0.955167\pi$
$264$		0			0
$265$	15.5173	+	29.2688i	0.953221	+	1.79797i
$266$	0.482239	+	0.909599i	0.0295680	+	0.0557711i
$267$		0			0
$268$	−7.40797	−	8.72134i	−0.452514	−	0.532740i
$269$	−0.694763	−	0.321431i	−0.0423604	−	0.0195980i	0.398595	−	0.917127i	$-0.369498\pi$
$269$	−0.694763	−	0.321431i	−0.0423604	−	0.0195980i	−0.440955	+	0.897529i	$0.645360\pi$
$270$		0			0
$271$	−5.60669	+	6.60071i	−0.340582	+	0.400964i	−0.905613	−	0.424106i	$-0.860589\pi$
$271$	−5.60669	+	6.60071i	−0.340582	+	0.400964i	0.565030	+	0.825070i	$0.308864\pi$
$272$	1.60875	−	0.967954i	0.0975449	−	0.0586908i
$273$		0			0
$274$	−0.873339	+	5.32713i	−0.0527603	+	0.321824i
$275$	12.3408	+	11.6898i	0.744178	+	0.704923i
$276$		0			0
$277$	−16.7174	−	10.0585i	−1.00445	−	0.604357i	−0.0845113	−	0.996423i	$-0.526933\pi$
$277$	−16.7174	−	10.0585i	−1.00445	−	0.604357i	−0.919937	+	0.392066i	$0.871760\pi$
$278$	−17.3319	−	13.1754i	−1.03950	−	0.790205i
$279$		0			0
$280$	−12.0988	+	17.8444i	−0.723043	+	1.06641i
$281$	−3.65118	−	22.2712i	−0.217811	−	1.32859i	−0.838658	−	0.544658i	$-0.816659\pi$
$281$	−3.65118	−	22.2712i	−0.217811	−	1.32859i	0.620847	−	0.783932i	$-0.286789\pi$
$282$		0			0
$283$	11.5999	+	2.55333i	0.689542	+	0.151780i	0.545901	−	0.837850i	$-0.316188\pi$
$283$	11.5999	+	2.55333i	0.689542	+	0.151780i	0.143642	+	0.989630i	$0.454119\pi$
$284$	−0.414497	−	1.04031i	−0.0245958	−	0.0617309i
$285$		0			0
$286$	−0.624779	+	11.5234i	−0.0369439	+	0.681391i
$287$	−10.7809	+	1.17249i	−0.636375	+	0.0692100i
$288$		0			0
$289$	−2.89221	−	10.4168i	−0.170130	−	0.612753i
$290$	−34.9372	+	7.69025i	−2.05158	+	0.451587i
$291$		0			0
$292$	7.60829	−	7.20696i	0.445242	−	0.421755i
$293$	0.808234	−	1.52449i	0.0472175	−	0.0890617i	−0.858780	−	0.512344i	$-0.828777\pi$
$293$	0.808234	−	1.52449i	0.0472175	−	0.0890617i	0.905998	+	0.423282i	$0.139122\pi$
$294$		0			0
$295$	7.51592	−	27.3152i	0.437594	−	1.59035i
$296$	24.1031			1.40096
$297$		0			0
$298$	12.5234	−	11.8628i	0.725462	−	0.687194i
$299$	9.11074	+	13.4373i	0.526888	+	0.777102i
$300$		0			0
$301$	−2.03981	−	7.34675i	−0.117573	−	0.423460i
$302$	5.89030	−	4.47769i	0.338948	−	0.257662i
$303$		0			0
$304$	−0.0220233	+	0.406197i	−0.00126313	+	0.0232970i
$305$	−9.56381	+	34.4457i	−0.547622	+	1.97236i
$306$		0			0
$307$	−31.2202	−	6.87209i	−1.78183	−	0.392211i	−0.802854	−	0.596176i	$-0.796686\pi$
$307$	−31.2202	−	6.87209i	−1.78183	−	0.392211i	−0.978978	+	0.203965i	$0.934617\pi$
$308$	0.223502	+	4.12225i	0.0127352	+	0.234887i
$309$		0			0
$310$	14.7803	−	21.7993i	0.839466	−	1.23812i
$311$	3.46625	−	8.69963i	0.196553	−	0.493311i	−0.797357	−	0.603508i	$-0.793769\pi$
$311$	3.46625	−	8.69963i	0.196553	−	0.493311i	0.993910	+	0.110198i	$0.0351483\pi$
$312$		0			0
$313$	24.4439	+	14.7074i	1.38165	+	0.831311i	0.995827	−	0.0912616i	$-0.0290899\pi$
$313$	24.4439	+	14.7074i	1.38165	+	0.831311i	0.385823	+	0.922573i	$0.373918\pi$
$314$	12.0851	−	4.07194i	0.682001	−	0.229793i
$315$		0			0
$316$	1.64377	−	10.0266i	0.0924695	−	0.564039i
$317$	−9.78358	−	1.06403i	−0.549500	−	0.0597618i	−0.170842	−	0.985298i	$-0.554649\pi$
$317$	−9.78358	−	1.06403i	−0.549500	−	0.0597618i	−0.378658	+	0.925537i	$0.623614\pi$
$318$		0			0
$319$	−12.7987	+	15.0678i	−0.716590	+	0.843635i
$320$	−21.9299	+	10.1459i	−1.22592	+	0.567170i
$321$		0			0
$322$	−3.33138	−	3.92200i	−0.185650	−	0.218564i
$323$	−1.27079	−	0.428178i	−0.0707085	−	0.0238245i
$324$		0			0
$325$	24.2837	+	45.8040i	1.34702	+	2.54075i
$326$	7.57037	+	2.55076i	0.419284	+	0.141273i
$327$		0			0
$328$	−14.8176	−	6.85534i	−0.818163	−	0.378523i
$329$	2.01691	−	0.933124i	0.111196	−	0.0514448i
$330$		0			0
$331$	12.7308	−	7.65988i	0.699750	−	0.421025i	−0.120742	−	0.992684i	$-0.538527\pi$
$331$	12.7308	−	7.65988i	0.699750	−	0.421025i	0.820492	+	0.571659i	$0.193700\pi$
$332$	3.77096	+	0.410117i	0.206958	+	0.0225081i
$333$		0			0
$334$	2.45014	+	2.32089i	0.134066	+	0.126994i
$335$	37.7167	−	12.7083i	2.06069	−	0.694326i
$336$		0			0
$337$	−12.2794	−	9.33453i	−0.668899	−	0.508484i	0.214729	−	0.976674i	$-0.431113\pi$
$337$	−12.2794	−	9.33453i	−0.668899	−	0.508484i	−0.883628	+	0.468190i	$0.844906\pi$
$338$	−8.36335	+	20.9904i	−0.454906	+	1.14173i
$339$		0			0
$340$	−1.57415	−	9.60192i	−0.0853705	−	0.520737i
$341$	−0.788000	−	14.5338i	−0.0426726	−	0.787050i
$342$		0			0
$343$	7.37894	+	18.5198i	0.398425	+	0.999973i
$344$	3.07098	−	11.0607i	0.165576	−	0.596352i
$345$		0			0
$346$	−2.97487	+	0.323536i	−0.159930	+	0.0173934i
$347$	7.25962	−	5.51862i	0.389717	−	0.296255i	−0.391907	−	0.920005i	$-0.628185\pi$
$347$	7.25962	−	5.51862i	0.389717	−	0.296255i	0.781624	+	0.623750i	$0.214392\pi$
$348$		0			0
$349$	−19.8250	+	4.36382i	−1.06121	+	0.233590i	−0.711079	−	0.703112i	$-0.751793\pi$
$349$	−19.8250	+	4.36382i	−1.06121	+	0.233590i	−0.350129	+	0.936701i	$0.613862\pi$
$350$	−9.22173	−	13.6010i	−0.492922	−	0.727006i
$351$		0			0
$352$	−4.81381	+	9.07981i	−0.256577	+	0.483955i
$353$	0.182220			0.00969858			0.00484929	−	0.999988i	$-0.498456\pi$
$353$	0.182220			0.00969858			0.00484929	+	0.999988i	$0.498456\pi$
$354$		0			0
$355$	3.89499			0.206725
$356$	2.20447	−	4.15807i	0.116837	−	0.220377i
$357$		0			0
$358$	6.24194	+	9.20617i	0.329897	+	0.486561i
$359$	22.6091	−	4.97665i	1.19327	−	0.262658i	0.426441	−	0.904515i	$-0.359767\pi$
$359$	22.6091	−	4.97665i	1.19327	−	0.262658i	0.766824	+	0.641858i	$0.221836\pi$
$360$		0			0
$361$	−14.8945	+	11.3225i	−0.783919	+	0.595920i
$362$	−3.36542	+	0.366012i	−0.176883	+	0.0192372i
$363$		0			0
$364$	−3.36840	+	12.1319i	−0.176552	+	0.635882i
$365$	13.4917	+	33.8616i	0.706187	+	1.77240i
$366$		0			0
$367$	−0.294974	−	5.44048i	−0.0153975	−	0.283991i	−0.996084	−	0.0884066i	$-0.971823\pi$
$367$	−0.294974	−	5.44048i	−0.0153975	−	0.283991i	0.980687	−	0.195584i	$-0.0626603\pi$
$368$	−0.328947	−	2.00649i	−0.0171476	−	0.104596i
$369$		0			0
$370$	−10.7518	+	26.9850i	−0.558959	+	1.40288i
$371$	−14.0894	−	10.7105i	−0.731484	−	0.556060i
$372$		0			0
$373$	−0.183093	+	0.0616911i	−0.00948017	+	0.00319424i	−0.324038	−	0.946044i	$-0.605040\pi$
$373$	−0.183093	+	0.0616911i	−0.00948017	+	0.00319424i	0.314557	+	0.949238i	$0.398144\pi$
$374$	3.45900	+	3.27654i	0.178861	+	0.169426i
$375$		0			0
$376$	3.32612	+	0.361737i	0.171532	+	0.0186552i
$377$	−51.6645	+	31.0855i	−2.66086	+	1.60098i
$378$		0			0
$379$	30.1643	−	13.9555i	1.54944	−	0.716846i	0.555995	−	0.831186i	$-0.312338\pi$
$379$	30.1643	−	13.9555i	1.54944	−	0.716846i	0.993442	+	0.114340i	$0.0364755\pi$
$380$	1.91334	+	0.885207i	0.0981524	+	0.0454102i
$381$		0			0
$382$	−22.2452	−	7.49528i	−1.13816	−	0.383492i
$383$	6.22295	+	11.7377i	0.317978	+	0.599770i	0.990050	−	0.140716i	$-0.0449404\pi$
$383$	6.22295	+	11.7377i	0.317978	+	0.599770i	−0.672072	+	0.740486i	$0.734596\pi$
$384$		0			0
$385$	−13.6072	−	4.58482i	−0.693490	−	0.233664i
$386$	11.7627	+	13.8481i	0.598707	+	0.704852i
$387$		0			0
$388$	−9.22995	+	4.27023i	−0.468580	+	0.216788i
$389$	1.88575	−	2.22007i	0.0956111	−	0.112562i	−0.712276	−	0.701900i	$-0.752335\pi$
$389$	1.88575	−	2.22007i	0.0956111	−	0.112562i	0.807887	+	0.589338i	$0.200611\pi$
$390$		0			0
$391$	6.66336	+	0.724684i	0.336980	+	0.0366488i
$392$	−1.49613	+	9.12601i	−0.0755662	+	0.460933i
$393$		0			0
$394$	13.7869	−	4.64534i	0.694573	−	0.234029i
$395$	30.2809	+	18.2194i	1.52360	+	0.916720i
$396$		0			0
$397$	13.8879	−	34.8561i	0.697015	−	1.74938i	0.0355875	−	0.999367i	$-0.488670\pi$
$397$	13.8879	−	34.8561i	0.697015	−	1.74938i	0.661427	−	0.750009i	$-0.269951\pi$
$398$	14.2742	−	21.0529i	0.715502	−	1.05529i
$399$		0			0
$400$	−0.351520	−	6.48341i	−0.0175760	−	0.324170i
$401$	−20.4792	−	4.50781i	−1.02268	−	0.225109i	−0.328191	−	0.944611i	$-0.606439\pi$
$401$	−20.4792	−	4.50781i	−1.02268	−	0.225109i	−0.694490	+	0.719502i	$0.744370\pi$
$402$		0			0
$403$	11.8759	−	42.7733i	0.591583	−	2.13069i
$404$	−0.553588	+	10.2103i	−0.0275420	+	0.507983i
$405$		0			0
$406$	15.2146	−	11.5659i	0.755090	−	0.574005i
$407$	4.29465	+	15.4679i	0.212878	+	0.766717i
$408$		0			0
$409$	1.28587	+	1.89652i	0.0635823	+	0.0937769i	0.858151	−	0.513397i	$-0.171613\pi$
$409$	1.28587	+	1.89652i	0.0635823	+	0.0937769i	−0.794569	+	0.607174i	$0.792303\pi$
$410$	14.2848	−	13.5312i	0.705474	−	0.668260i
$411$		0			0
$412$	−3.33268			−0.164189
$413$	2.48318	+	14.9301i	0.122189	+	0.734662i
$414$		0			0
$415$	−6.17987	+	11.6565i	−0.303358	+	0.572194i
$416$	−22.7551	+	21.5548i	−1.11566	+	1.05681i
$417$		0			0
$418$	−1.00817	+	0.221916i	−0.0493114	+	0.0108543i
$419$	2.02756	+	7.30262i	0.0990529	+	0.356756i	0.996421	−	0.0845259i	$-0.0269376\pi$
$419$	2.02756	+	7.30262i	0.0990529	+	0.356756i	−0.897368	+	0.441282i	$0.854524\pi$
$420$		0			0
$421$	−29.4401	+	3.20180i	−1.43482	+	0.156046i	−0.792259	−	0.610185i	$-0.791095\pi$
$421$	−29.4401	+	3.20180i	−1.43482	+	0.156046i	−0.642564	+	0.766232i	$0.722129\pi$
$422$	0.139018	−	2.56403i	0.00676728	−	0.124815i
$423$		0			0
$424$	−9.86231	−	24.7525i	−0.478956	−	1.20209i
$425$	20.9034	+	4.60118i	1.01396	+	0.223190i
$426$		0			0
$427$	−3.08978	−	18.8468i	−0.149525	−	0.912062i
$428$	6.22503	−	9.18124i	0.300898	−	0.443792i
$429$		0			0
$430$	11.0133	+	8.37207i	0.531107	+	0.403737i
$431$	−16.3166	−	9.81735i	−0.785941	−	0.472885i	0.0651679	−	0.997874i	$-0.479242\pi$
$431$	−16.3166	−	9.81735i	−0.785941	−	0.472885i	−0.851109	+	0.524989i	$0.824069\pi$
$432$		0			0
$433$	−23.1519	−	21.9306i	−1.11261	−	1.05392i	−0.998169	−	0.0604872i	$-0.980735\pi$
$433$	−23.1519	−	21.9306i	−1.11261	−	1.05392i	−0.114438	−	0.993430i	$-0.536507\pi$
$434$	−2.27637	+	13.8852i	−0.109269	+	0.666512i
$435$		0			0
$436$	−8.71566	+	5.24404i	−0.417404	+	0.251144i
$437$	−0.940162	+	1.10684i	−0.0449741	+	0.0529475i
$438$		0			0
$439$	31.6299	+	14.6335i	1.50961	+	0.698421i	0.987956	−	0.154736i	$-0.0494526\pi$
$439$	31.6299	+	14.6335i	1.50961	+	0.698421i	0.521655	+	0.853156i	$0.325315\pi$
$440$	−13.9949	−	16.4761i	−0.667183	−	0.785468i
$441$		0			0
$442$	6.80649	+	12.8384i	0.323752	+	0.610660i
$443$	5.05965	+	9.54351i	0.240391	+	0.453426i	0.974125	−	0.226012i	$-0.0725687\pi$
$443$	5.05965	+	9.54351i	0.240391	+	0.453426i	−0.733733	+	0.679437i	$0.762224\pi$
$444$		0			0
$445$	10.5972	+	12.4760i	0.502356	+	0.591419i
$446$	13.9453	+	6.45178i	0.660328	+	0.305500i
$447$		0			0
$448$	8.35706	−	9.83869i	0.394834	−	0.464834i
$449$	−7.61582	+	4.58229i	−0.359413	+	0.216251i	−0.683794	−	0.729675i	$-0.739671\pi$
$449$	−7.61582	+	4.58229i	−0.359413	+	0.216251i	0.324382	+	0.945926i	$0.394844\pi$
$450$		0			0
$451$	1.75918	−	10.7305i	0.0828365	−	0.505280i
$452$	3.22822	+	3.05793i	0.151843	+	0.143833i
$453$		0			0
$454$	−2.75863	−	1.65981i	−0.129469	−	0.0778988i
$455$	−34.8631	−	26.5022i	−1.63441	−	1.24244i
$456$		0			0
$457$	−3.57752	+	5.27644i	−0.167349	+	0.246822i	−0.902111	−	0.431503i	$-0.857983\pi$
$457$	−3.57752	+	5.27644i	−0.167349	+	0.246822i	0.734762	+	0.678325i	$0.237294\pi$
$458$	−0.760096	−	4.63638i	−0.0355170	−	0.216644i
$459$		0			0
$460$	−10.2910	−	2.26523i	−0.479822	−	0.105617i
$461$	2.62599	+	6.59074i	0.122305	+	0.306962i	0.977363	−	0.211571i	$-0.0678579\pi$
$461$	2.62599	+	6.59074i	0.122305	+	0.306962i	−0.855058	+	0.518532i	$0.826479\pi$
$462$		0			0
$463$	0.589901	−	10.8801i	0.0274150	−	0.505640i	−0.952290	−	0.305195i	$-0.901278\pi$
$463$	0.589901	−	10.8801i	0.0274150	−	0.505640i	0.979705	−	0.200445i	$-0.0642388\pi$
$464$	7.50725	−	0.816462i	0.348515	−	0.0379033i
$465$		0			0
$466$	−0.989778	−	3.56486i	−0.0458506	−	0.165139i
$467$	−24.5008	+	5.39303i	−1.13376	+	0.249560i	−0.741930	−	0.670478i	$-0.766089\pi$
$467$	−24.5008	+	5.39303i	−1.13376	+	0.249560i	−0.391831	+	0.920037i	$0.628158\pi$
$468$		0			0
$469$	−15.4367	+	14.6224i	−0.712801	+	0.675201i
$470$	−1.88869	+	3.56245i	−0.0871188	+	0.164324i
$471$		0			0
$472$	−8.38504	+	21.1874i	−0.385953	+	0.975231i
$473$	7.64528			0.351530
$474$		0			0
$475$	−3.36680	+	3.18921i	−0.154480	+	0.146331i
$476$	2.91717	+	4.30250i	0.133708	+	0.197205i
$477$		0			0
$478$	−6.82763	−	24.5909i	−0.312288	−	1.12476i
$479$	−17.8783	+	13.5907i	−0.816881	+	0.620977i	−0.927895	−	0.372842i	$-0.878383\pi$
$479$	−17.8783	+	13.5907i	−0.816881	+	0.620977i	0.111014	+	0.993819i	$0.464590\pi$
$480$		0			0
$481$	−2.65063	+	48.8879i	−0.120858	+	2.22910i
$482$	3.06381	−	11.0348i	0.139553	−	0.502623i
$483$		0			0
$484$	7.34918	+	1.61768i	0.334054	+	0.0735308i
$485$	−1.91503	−	35.3206i	−0.0869569	−	1.60383i
$486$		0			0
$487$	−3.41544	+	5.03740i	−0.154768	+	0.228266i	−0.897166	−	0.441693i	$-0.854378\pi$
$487$	−3.41544	+	5.03740i	−0.154768	+	0.228266i	0.742398	+	0.669959i	$0.233688\pi$
$488$	10.6426	−	26.7109i	0.481768	−	1.20915i
$489$		0			0
$490$	−9.54978	−	5.74591i	−0.431415	−	0.259574i
$491$	−16.2996	+	5.49196i	−0.735588	+	0.247849i	−0.662067	−	0.749445i	$-0.730320\pi$
$491$	−16.2996	+	5.49196i	−0.735588	+	0.247849i	−0.0735218	+	0.997294i	$0.523424\pi$
$492$		0			0
$493$	−4.02730	+	24.5655i	−0.181381	+	1.10637i
$494$	−3.12995	−	0.340403i	−0.140823	−	0.0153155i
$495$		0			0
$496$	−3.59925	+	4.23736i	−0.161611	+	0.190263i
$497$	−1.88853	+	0.873729i	−0.0847124	+	0.0391921i
$498$		0			0
$499$	10.8733	+	12.8010i	0.486754	+	0.573051i	0.949631	−	0.313372i	$-0.101459\pi$
$499$	10.8733	+	12.8010i	0.486754	+	0.573051i	−0.462877	+	0.886423i	$0.653183\pi$
$500$	−13.3560	−	4.50016i	−0.597299	−	0.201253i
$501$		0			0
$502$	2.01282	+	3.79658i	0.0898365	+	0.169450i
$503$	−29.1391	−	9.81811i	−1.29925	−	0.437768i	−0.417152	−	0.908837i	$-0.636972\pi$
$503$	−29.1391	−	9.81811i	−1.29925	−	0.437768i	−0.882096	+	0.471069i	$0.843868\pi$
$504$		0			0
$505$	−32.2782	−	14.9335i	−1.43636	−	0.664531i
$506$	4.68290	−	2.16654i	0.208180	−	0.0963145i
$507$		0			0
$508$	4.31565	−	2.59664i	0.191476	−	0.115207i
$509$	−6.28798	−	0.683859i	−0.278710	−	0.0303115i	−0.0323033	−	0.999478i	$-0.510284\pi$
$509$	−6.28798	−	0.683859i	−0.278710	−	0.0303115i	−0.246406	+	0.969167i	$0.579250\pi$
$510$		0			0
$511$	−14.1375	−	13.3917i	−0.625406	−	0.592416i
$512$	7.96321	−	2.68312i	0.351928	−	0.118578i
$513$		0			0
$514$	3.57205	+	2.71540i	0.157556	+	0.119771i
$515$	4.29048	−	10.7683i	0.189061	−	0.474508i
$516$		0			0
$517$	0.360501	+	2.19896i	0.0158548	+	0.0967102i
$518$	−0.840161	−	15.4959i	−0.0369146	−	0.680849i
$519$		0			0
$520$	−24.4035	−	61.2483i	−1.07017	−	2.68591i
$521$	4.06265	−	14.6323i	0.177988	−	0.641055i	−0.819681	−	0.572820i	$-0.805849\pi$
$521$	4.06265	−	14.6323i	0.177988	−	0.641055i	0.997669	−	0.0682348i	$-0.0217367\pi$
$522$		0			0
$523$	−24.6084	+	2.67633i	−1.07605	+	0.117028i	−0.628943	−	0.777452i	$-0.716512\pi$
$523$	−24.6084	+	2.67633i	−1.07605	+	0.117028i	−0.447109	+	0.894479i	$0.647546\pi$
$524$	18.9146	−	14.3785i	0.826290	−	0.628129i
$525$		0			0
$526$	−16.3957	+	3.60896i	−0.714885	+	0.157358i
$527$	−10.2850	−	15.1693i	−0.448024	−	0.660785i
$528$		0			0
$529$	−7.37333	+	13.9076i	−0.320580	+	0.604678i
$530$	32.1114			1.39483
$531$		0			0
$532$	−1.12628			−0.0488304
$533$	15.5341	−	29.3004i	0.672856	−	1.26914i
$534$		0			0
$535$	21.6516	+	31.9338i	0.936082	+	1.38062i
$536$	−31.2632	+	6.88155i	−1.35036	+	0.297238i
$537$		0			0
$538$	−0.590725	+	0.449057i	−0.0254680	+	0.0193602i
$539$	−6.12311	+	0.665929i	−0.263741	+	0.0286836i
$540$		0			0
$541$	3.52645	−	12.7011i	0.151614	−	0.546064i	−0.848250	−	0.529595i	$-0.822344\pi$
$541$	3.52645	−	12.7011i	0.151614	−	0.546064i	0.999864	−	0.0164689i	$-0.00524245\pi$
$542$	3.10724	+	7.79858i	0.133467	+	0.334978i
$543$		0			0
$544$	0.700576	+	12.9214i	0.0300370	+	0.553999i
$545$	−5.72362	−	34.9126i	−0.245173	−	1.49549i
$546$		0			0
$547$	−0.294672	+	0.739572i	−0.0125993	+	0.0316218i	−0.935142	−	0.354274i	$-0.884728\pi$
$547$	−0.294672	+	0.739572i	−0.0125993	+	0.0316218i	0.922543	+	0.385895i	$0.126107\pi$
$548$	−4.70138	−	3.57389i	−0.200833	−	0.152669i
$549$		0			0
$550$	15.6144	−	5.26112i	0.665802	−	0.224335i
$551$	−3.91571	−	3.70916i	−0.166815	−	0.158016i
$552$		0			0
$553$	−18.7691	−	2.04126i	−0.798144	−	0.0868034i
$554$	−16.2045	+	9.74991i	−0.688463	+	0.414234i
$555$		0			0
$556$	21.6159	−	10.0006i	0.916718	−	0.424119i
$557$	20.8305	+	9.63720i	0.882615	+	0.408341i	0.808215	−	0.588887i	$-0.200434\pi$
$557$	20.8305	+	9.63720i	0.882615	+	0.408341i	0.0743999	+	0.997228i	$0.476296\pi$
$558$		0			0
$559$	22.0965	+	7.44519i	0.934584	+	0.314898i
$560$	2.56908	+	4.84579i	0.108563	+	0.204772i
$561$		0			0
$562$	−20.7310	−	6.98509i	−0.874485	−	0.294648i
$563$	13.1858	+	15.5235i	0.555716	+	0.654240i	0.966250	−	0.257606i	$-0.0829336\pi$
$563$	13.1858	+	15.5235i	0.555716	+	0.654240i	−0.410534	+	0.911845i	$0.634658\pi$
$564$		0			0
$565$	−14.0366	+	6.49400i	−0.590522	+	0.273205i
$566$	7.45349	−	8.77492i	0.313293	−	0.368838i
$567$		0			0
$568$	−3.11441	−	0.338712i	−0.130678	−	0.0142121i
$569$	−1.76110	+	10.7423i	−0.0738293	+	0.450339i	0.923879	+	0.382684i	$0.125000\pi$
$569$	−1.76110	+	10.7423i	−0.0738293	+	0.450339i	−0.997709	+	0.0676553i	$0.978448\pi$
$570$		0			0
$571$	−15.8273	+	5.33283i	−0.662351	+	0.223172i	−0.630344	−	0.776316i	$-0.717086\pi$
$571$	−15.8273	+	5.33283i	−0.662351	+	0.223172i	−0.0320066	+	0.999488i	$0.510190\pi$
$572$	−10.8177	−	6.50878i	−0.452310	−	0.272146i
$573$		0			0
$574$	−3.89080	+	9.76517i	−0.162399	+	0.407590i
$575$	13.0081	−	19.1855i	0.542476	−	0.800092i
$576$		0			0
$577$	−0.963395	−	17.7688i	−0.0401067	−	0.739724i	−0.947561	−	0.319574i	$-0.896460\pi$
$577$	−0.963395	−	17.7688i	−0.0401067	−	0.739724i	0.907455	−	0.420150i	$-0.138023\pi$
$578$	−10.2342	−	2.25272i	−0.425686	−	0.0937006i
$579$		0			0
$580$	10.4698	−	37.7090i	0.434737	−	1.56578i
$581$	0.381593	−	7.03807i	0.0158311	−	0.291988i
$582$		0			0
$583$	14.1275	−	10.7394i	0.585100	−	0.444781i
$584$	−7.84323	−	28.2488i	−0.324555	−	1.16894i
$585$		0			0
$586$	−0.938616	−	1.38435i	−0.0387739	−	0.0571872i
$587$	−22.2809	+	21.1056i	−0.919633	+	0.871123i	−0.991998	−	0.126255i	$-0.959704\pi$
$587$	−22.2809	+	21.1056i	−0.919633	+	0.871123i	0.0723646	+	0.997378i	$0.476945\pi$
$588$		0			0
$589$	3.97092			0.163619
$590$	−19.9804	−	18.8388i	−0.822579	−	0.775582i
$591$		0			0
$592$	2.87220	−	5.41754i	0.118047	−	0.222659i
$593$	−8.16572	+	7.73498i	−0.335326	+	0.317637i	−0.836772	−	0.547551i	$-0.815560\pi$
$593$	−8.16572	+	7.73498i	−0.335326	+	0.317637i	0.501446	+	0.865189i	$0.332801\pi$
$594$		0			0
$595$	−17.6575	+	3.88670i	−0.723885	+	0.159339i
$596$	5.04856	+	18.1833i	0.206797	+	0.744816i
$597$		0			0
$598$	15.6445	−	1.70144i	0.639750	−	0.0695770i
$599$	2.41003	−	44.4504i	0.0984711	−	1.81619i	−0.366011	−	0.930611i	$-0.619277\pi$
$599$	2.41003	−	44.4504i	0.0984711	−	1.81619i	0.464482	−	0.885583i	$-0.346241\pi$
$600$		0			0
$601$	−9.65143	−	24.2233i	−0.393690	−	0.988088i	−0.983559	−	0.180589i	$-0.942200\pi$
$601$	−9.65143	−	24.2233i	−0.393690	−	0.988088i	0.589869	−	0.807499i	$-0.299180\pi$
$602$	−7.21796	−	1.58879i	−0.294182	−	0.0647544i
$603$		0			0
$604$	1.30952	+	7.98772i	0.0532836	+	0.325016i
$605$	−14.6882	+	21.6635i	−0.597162	+	0.880748i
$606$		0			0
$607$	11.1356	+	8.46508i	0.451981	+	0.343587i	0.806269	−	0.591549i	$-0.201484\pi$
$607$	11.1356	+	8.46508i	0.451981	+	0.343587i	−0.354288	+	0.935136i	$0.615277\pi$
$608$	−2.40241	−	1.44548i	−0.0974306	−	0.0586220i
$609$		0			0
$610$	25.1572	+	23.8302i	1.01859	+	0.964857i
$611$	−1.09948	+	6.70655i	−0.0444803	+	0.271318i
$612$		0			0
$613$	7.11918	−	4.28347i	0.287541	−	0.173008i	−0.364474	−	0.931213i	$-0.618751\pi$
$613$	7.11918	−	4.28347i	0.287541	−	0.173008i	0.652015	+	0.758206i	$0.273924\pi$
$614$	−20.0605	+	23.6170i	−0.809575	+	0.953105i
$615$		0			0
$616$	10.4816	+	4.84929i	0.422315	+	0.195384i
$617$	14.3763	+	16.9251i	0.578769	+	0.681380i	0.971163	−	0.238418i	$-0.0766287\pi$
$617$	14.3763	+	16.9251i	0.578769	+	0.681380i	−0.392394	+	0.919797i	$0.628353\pi$
$618$		0			0
$619$	−4.74571	−	8.95136i	−0.190746	−	0.359786i	0.769631	−	0.638489i	$-0.220440\pi$
$619$	−4.74571	−	8.95136i	−0.190746	−	0.359786i	−0.960377	+	0.278703i	$0.910095\pi$
$620$	13.4961	+	25.4564i	0.542018	+	1.02235i
$621$		0			0
$622$	−5.87661	−	6.91848i	−0.235631	−	0.277406i
$623$	−7.93683	−	3.67197i	−0.317982	−	0.147114i
$624$		0			0
$625$	3.88612	−	4.57510i	0.155445	−	0.183004i
$626$	23.6940	−	14.2562i	0.947002	−	0.569792i
$627$		0			0
$628$	−2.25704	+	13.7673i	−0.0900657	+	0.549376i
$629$	14.6748	+	13.9007i	0.585124	+	0.554259i
$630$		0			0
$631$	15.7690	+	9.48788i	0.627753	+	0.377706i	0.793595	−	0.608446i	$-0.208207\pi$
$631$	15.7690	+	9.48788i	0.627753	+	0.377706i	−0.165842	+	0.986152i	$0.553034\pi$
$632$	−22.6281	−	17.2014i	−0.900097	−	0.684236i
$633$		0			0
$634$	−5.35336	+	7.89562i	−0.212609	+	0.313575i
$635$	2.83411	+	17.2873i	0.112468	+	0.686027i
$636$		0			0
$637$	−18.3456	−	4.03818i	−0.726881	−	0.159999i
$638$	7.09307	+	17.8023i	0.280817	+	0.704798i
$639$		0			0
$640$	0.809247	−	14.9257i	0.0319883	−	0.589989i
$641$	28.9047	−	3.14358i	1.14167	−	0.124164i	0.482316	−	0.875997i	$-0.339796\pi$
$641$	28.9047	−	3.14358i	1.14167	−	0.124164i	0.659353	+	0.751833i	$0.270830\pi$
$642$		0			0
$643$	−4.67964	−	16.8545i	−0.184547	−	0.664679i	−0.996696	−	0.0812277i	$-0.974116\pi$
$643$	−4.67964	−	16.8545i	−0.184547	−	0.664679i	0.812148	−	0.583451i	$-0.198298\pi$
$644$	5.49787	−	1.21017i	0.216647	−	0.0476875i
$645$		0			0
$646$	−0.943681	+	0.893902i	−0.0371286	+	0.0351701i
$647$	−8.37699	+	15.8007i	−0.329333	+	0.621188i	−0.991785	−	0.127916i	$-0.959171\pi$
$647$	−8.37699	+	15.8007i	−0.329333	+	0.621188i	0.662452	+	0.749105i	$0.269516\pi$
$648$		0			0
$649$	−15.0909	−	1.60588i	−0.592369	−	0.0630363i
$650$	50.2526			1.97107
$651$		0			0
$652$	−6.34469	+	6.01001i	−0.248477	+	0.235370i
$653$	16.9995	+	25.0724i	0.665241	+	0.981158i	0.999255	+	0.0385894i	$0.0122864\pi$
$653$	16.9995	+	25.0724i	0.665241	+	0.981158i	−0.334014	+	0.942568i	$0.608403\pi$
$654$		0			0
$655$	22.1082	+	79.6264i	0.863838	+	3.11126i
$656$	−3.30655	+	2.51357i	−0.129099	+	0.0981386i
$657$		0			0
$658$	0.116622	−	2.15097i	0.00454641	−	0.0838537i
$659$	−4.97240	+	17.9090i	−0.193697	+	0.697634i	0.801347	+	0.598200i	$0.204117\pi$
$659$	−4.97240	+	17.9090i	−0.193697	+	0.697634i	−0.995044	+	0.0994343i	$0.968297\pi$
$660$		0			0
$661$	19.0988	+	4.20396i	0.742857	+	0.163515i	0.570245	−	0.821475i	$-0.306848\pi$
$661$	19.0988	+	4.20396i	0.742857	+	0.163515i	0.172612	+	0.984990i	$0.444779\pi$
$662$	−0.779696	−	14.3807i	−0.0303038	−	0.558920i
$663$		0			0
$664$	5.95505	−	8.78304i	0.231101	−	0.340848i
$665$	1.44997	−	3.63915i	0.0562274	−	0.141120i
$666$		0			0
$667$	23.0998	+	13.8987i	0.894427	+	0.538159i
$668$	−3.49877	+	1.17887i	−0.135371	+	0.0456119i
$669$		0			0
$670$	6.24141	−	38.0709i	0.241127	−	1.47081i
$671$	19.0378	+	2.07048i	0.734945	+	0.0799301i
$672$		0			0
$673$	0.918729	−	1.08161i	0.0354144	−	0.0416931i	−0.744170	−	0.667991i	$-0.767155\pi$
$673$	0.918729	−	1.08161i	0.0354144	−	0.0416931i	0.779584	+	0.626298i	$0.215430\pi$
$674$	−13.5695	+	6.27790i	−0.522676	+	0.241816i
$675$		0			0
$676$	−16.0025	−	18.8396i	−0.615482	−	0.724602i
$677$	−29.4722	−	9.93033i	−1.13271	−	0.381654i	−0.310349	−	0.950623i	$-0.600446\pi$
$677$	−29.4722	−	9.93033i	−1.13271	−	0.381654i	−0.822359	+	0.568969i	$0.807342\pi$
$678$		0			0
$679$	8.85170	+	16.6961i	0.339697	+	0.640736i
$680$	−25.7952	−	8.69141i	−0.989200	−	0.333300i
$681$		0			0
$682$	−12.8046	−	5.92406i	−0.490315	−	0.226844i
$683$	17.6213	−	8.15250i	0.674262	−	0.311947i	−0.0527142	−	0.998610i	$-0.516787\pi$
$683$	17.6213	−	8.15250i	0.674262	−	0.311947i	0.726976	+	0.686663i	$0.240925\pi$
$684$		0			0
$685$	17.6002	−	10.5897i	0.672471	−	0.404612i
$686$	19.2108	+	2.08930i	0.733470	+	0.0797697i
$687$		0			0
$688$	−2.12011	−	2.00828i	−0.0808285	−	0.0765648i
$689$	51.2898	−	17.2816i	1.95399	−	0.658375i
$690$		0			0
$691$	−17.8107	−	13.5394i	−0.677553	−	0.515062i	0.208867	−	0.977944i	$-0.433022\pi$
$691$	−17.8107	−	13.5394i	−0.677553	−	0.515062i	−0.886420	+	0.462882i	$0.846815\pi$
$692$	1.21169	−	3.04112i	0.0460617	−	0.115606i
$693$		0			0
$694$	−1.43004	−	8.72285i	−0.0542836	−	0.331115i
$695$	4.48486	+	82.7184i	0.170121	+	3.13769i
$696$		0			0
$697$	−5.06787	−	12.7194i	−0.191959	−	0.481781i
$698$	−5.26411	+	18.9596i	−0.199250	+	0.717632i
$699$		0			0
$700$	17.8715	−	1.94364i	0.675478	−	0.0734626i
$701$	−9.17619	+	6.97556i	−0.346580	+	0.263463i	−0.763953	−	0.645272i	$-0.776744\pi$
$701$	−9.17619	+	6.97556i	−0.346580	+	0.263463i	0.417373	+	0.908735i	$0.362951\pi$
$702$		0			0
$703$	−4.27719	+	0.941480i	−0.161317	+	0.0355086i
$704$	7.26390	+	10.7135i	0.273769	+	0.403778i
$705$		0			0
$706$	0.0827348	−	0.156054i	0.00311376	−	0.00587318i
$707$	19.0004			0.714583
$708$		0			0
$709$	17.4864			0.656714			0.328357	−	0.944554i	$-0.393505\pi$
$709$	17.4864			0.656714			0.328357	+	0.944554i	$0.393505\pi$
$710$	1.76847	−	3.33569i	0.0663696	−	0.125186i
$711$		0			0
$712$	−7.38854	−	10.8973i	−0.276897	−	0.408393i
$713$	−19.3838	+	4.26671i	−0.725931	+	0.159789i
$714$		0			0
$715$	34.9573	−	26.5739i	1.30733	−	0.993807i
$716$	−12.0967	+	1.31560i	−0.452075	+	0.0491662i
$717$		0			0
$718$	6.00338	−	21.6222i	0.224044	−	0.806934i
$719$	−14.6095	−	36.6671i	−0.544843	−	1.36745i	−0.901322	−	0.433149i	$-0.857402\pi$
$719$	−14.6095	−	36.6671i	−0.544843	−	1.36745i	0.356479	−	0.934303i	$-0.383977\pi$
$720$		0			0
$721$	0.335265	+	6.18360i	0.0124859	+	0.230289i
$722$	2.93399	+	17.8966i	0.109192	+	0.666041i
$723$		0			0
$724$	1.37077	−	3.44038i	0.0509444	−	0.127861i
$725$	68.5343	+	52.0984i	2.54530	+	1.93489i
$726$		0			0
$727$	−2.08905	+	0.703882i	−0.0774784	+	0.0261055i	−0.357774	−	0.933808i	$-0.616464\pi$
$727$	−2.08905	+	0.703882i	−0.0774784	+	0.0261055i	0.280295	+	0.959914i	$0.409568\pi$
$728$	25.5717	+	24.2228i	0.947749	+	0.897755i
$729$		0			0
$730$	35.1250	+	3.82008i	1.30004	+	0.141387i
$731$	8.24866	−	4.96305i	0.305088	−	0.183565i
$732$		0			0
$733$	16.5415	−	7.65293i	0.610975	−	0.282667i	−0.0899004	−	0.995951i	$-0.528655\pi$
$733$	16.5415	−	7.65293i	0.610975	−	0.282667i	0.700876	+	0.713284i	$0.252793\pi$
$734$	−4.79319	−	2.21757i	−0.176920	−	0.0818519i
$735$		0			0
$736$	13.2804	+	4.47468i	0.489522	+	0.164939i
$737$	−9.98661	−	18.8367i	−0.367861	−	0.693860i
$738$		0			0
$739$	−1.76425	−	0.594445i	−0.0648990	−	0.0218670i	0.286665	−	0.958031i	$-0.407453\pi$
$739$	−1.76425	−	0.594445i	−0.0648990	−	0.0218670i	−0.351564	+	0.936164i	$0.614350\pi$
$740$	−20.5726	−	24.2199i	−0.756264	−	0.890343i
$741$		0			0
$742$	−15.5696	+	7.20328i	−0.571579	+	0.264441i
$743$	8.87470	−	10.4481i	0.325581	−	0.383304i	−0.574882	−	0.818236i	$-0.694952\pi$
$743$	8.87470	−	10.4481i	0.325581	−	0.383304i	0.900463	+	0.434933i	$0.143228\pi$
$744$		0			0
$745$	−65.2519	−	7.09658i	−2.39065	−	0.259998i
$746$	−0.0302984	+	0.184812i	−0.00110930	+	0.00676644i
$747$		0			0
$748$	−4.93941	+	1.66428i	−0.180603	+	0.0608521i
$749$	−17.6615	−	10.6266i	−0.645337	−	0.388286i
$750$		0			0
$751$	4.70684	−	11.8133i	0.171755	−	0.431073i	−0.817750	−	0.575574i	$-0.804779\pi$
$751$	4.70684	−	11.8133i	0.171755	−	0.431073i	0.989505	+	0.144502i	$0.0461579\pi$
$752$	0.477657	−	0.704491i	0.0174184	−	0.0256902i
$753$		0			0
$754$	3.16418	+	58.3599i	0.115233	+	2.12534i
$755$	−27.4952	−	6.05215i	−1.00065	−	0.220260i
$756$		0			0
$757$	−12.8473	+	46.2719i	−0.466944	+	1.68178i	0.236988	+	0.971513i	$0.423840\pi$
$757$	−12.8473	+	46.2719i	−0.466944	+	1.68178i	−0.703932	+	0.710268i	$0.748574\pi$
$758$	1.74417	−	32.1692i	0.0633510	−	1.16844i
$759$		0			0
$760$	4.69511	−	3.56913i	0.170310	−	0.129466i
$761$	3.99053	+	14.3726i	0.144657	+	0.521006i	0.999996	+	0.00293726i	$0.000934960\pi$
$761$	3.99053	+	14.3726i	0.144657	+	0.521006i	−0.855339	+	0.518068i	$0.826651\pi$
$762$		0			0
$763$	10.6068	+	15.6439i	0.383992	+	0.566346i
$764$	18.6436	−	17.6601i	0.674501	−	0.638921i
$765$		0			0
$766$	12.8777			0.465291
$767$	−42.0521	−	19.3373i	−1.51841	−	0.698229i
$768$		0			0
$769$	12.3235	−	23.2446i	0.444396	−	0.838220i	−0.555581	−	0.831462i	$-0.687504\pi$
$769$	12.3235	−	23.2446i	0.444396	−	0.838220i	0.999977	−	0.00675757i	$-0.00215102\pi$
$770$	−10.1047	+	9.57166i	−0.364147	+	0.344939i
$771$		0			0
$772$	−19.4124	+	4.27299i	−0.698667	+	0.153788i
$773$	9.15270	+	32.9651i	0.329200	+	1.18567i	0.924189	+	0.381937i	$0.124743\pi$
$773$	9.15270	+	32.9651i	0.329200	+	1.18567i	−0.594989	+	0.803734i	$0.702843\pi$
$774$		0			0
$775$	−63.0094	+	6.85268i	−2.26336	+	0.246156i
$776$	−1.54027	+	28.4087i	−0.0552926	+	1.01981i
$777$		0			0
$778$	−1.04508	−	2.62296i	−0.0374681	−	0.0940378i
$779$	2.89721	+	0.637724i	0.103803	+	0.0228488i
$780$		0			0
$781$	−0.337555	−	2.05900i	−0.0120787	−	0.0736766i
$782$	3.64604	−	5.37751i	0.130382	−	0.192299i
$783$		0			0
$784$	1.87293	+	1.42376i	0.0668903	+	0.0508487i
$785$	−41.5783	−	25.0168i	−1.48399	−	0.892888i
$786$		0			0
$787$	−20.4863	−	19.4057i	−0.730258	−	0.691737i	0.229266	−	0.973364i	$-0.426367\pi$
$787$	−20.4863	−	19.4057i	−0.730258	−	0.691737i	−0.959524	+	0.281626i	$0.909126\pi$
$788$	−2.57487	+	15.7060i	−0.0917260	+	0.559504i
$789$		0			0
$790$	29.3520	−	17.6605i	1.04430	−	0.628332i
$791$	5.34906	−	6.29740i	0.190191	−	0.223910i
$792$		0			0
$793$	53.0071	+	24.5237i	1.88234	+	0.870862i
$794$	−23.5453	−	27.7197i	−0.835592	−	0.983735i
$795$		0			0
$796$	13.0340	+	24.5848i	0.461979	+	0.871384i
$797$	−0.564908	−	1.06553i	−0.0200101	−	0.0377430i	0.873305	−	0.487173i	$-0.161972\pi$
$797$	−0.564908	−	1.06553i	−0.0200101	−	0.0377430i	−0.893316	+	0.449430i	$0.851627\pi$
$798$		0			0
$799$	1.81644	+	2.13848i	0.0642612	+	0.0756541i
$800$	40.6152	+	18.7906i	1.43596	+	0.664348i
$801$		0			0
$802$	−13.1588	+	15.4918i	−0.464655	+	0.547034i
$803$	16.7309	−	10.0666i	0.590420	−	0.355244i
$804$		0			0
$805$	−3.16773	+	19.3223i	−0.111648	+	0.681021i
$806$	−31.2392	−	29.5913i	−1.10035	−	1.04231i
$807$		0			0
$808$	24.5108	+	14.7477i	0.862287	+	0.518821i
$809$	−28.9270	−	21.9897i	−1.01702	−	0.773118i	−0.0428836	−	0.999080i	$-0.513654\pi$
$809$	−28.9270	−	21.9897i	−1.01702	−	0.773118i	−0.974136	+	0.225962i	$0.927448\pi$
$810$		0			0
$811$	−14.5324	+	21.4337i	−0.510301	+	0.752638i	−0.992343	−	0.123510i	$-0.960585\pi$
$811$	−14.5324	+	21.4337i	−0.510301	+	0.752638i	0.482042	+	0.876148i	$0.339895\pi$
$812$	3.38249	+	20.6323i	0.118702	+	0.724051i
$813$		0			0
$814$	15.1968	+	3.34506i	0.532647	+	0.117244i
$815$	−11.2510	−	28.2378i	−0.394104	−	0.989126i
$816$		0			0
$817$	−0.112922	+	2.08272i	−0.00395063	+	0.0728650i
$818$	2.20803	−	0.240137i	0.0772019	−	0.00839621i
$819$		0			0
$820$	5.75861	+	20.7406i	0.201099	+	0.724294i
$821$	−16.7576	+	3.68863i	−0.584844	+	0.128734i	−0.497530	−	0.867447i	$-0.665760\pi$
$821$	−16.7576	+	3.68863i	−0.584844	+	0.128734i	−0.0873145	+	0.996181i	$0.527828\pi$
$822$		0			0
$823$	−18.2365	+	17.2745i	−0.635684	+	0.602152i	−0.936133	−	0.351646i	$-0.885622\pi$
$823$	−18.2365	+	17.2745i	−0.635684	+	0.602152i	0.300449	+	0.953798i	$0.402864\pi$
$824$	−4.36707	+	8.23716i	−0.152134	+	0.286955i
$825$		0			0
$826$	13.9137	+	4.65222i	0.484119	+	0.161871i
$827$	8.28668			0.288156			0.144078	−	0.989566i	$-0.453978\pi$
$827$	8.28668			0.288156			0.144078	+	0.989566i	$0.453978\pi$
$828$		0			0
$829$	−1.96900	+	1.86514i	−0.0683862	+	0.0647789i	−0.721129	−	0.692800i	$-0.756377\pi$
$829$	−1.96900	+	1.86514i	−0.0683862	+	0.0647789i	0.652743	+	0.757579i	$0.273618\pi$
$830$	7.17679	+	10.5850i	0.249110	+	0.367410i
$831$		0			0
$832$	10.5612	+	38.0380i	0.366144	+	1.31873i
$833$	−6.17406	+	4.69340i	−0.213919	+	0.162617i
$834$		0			0
$835$	0.695223	−	12.8226i	0.0240592	−	0.443745i
$836$	0.302126	−	1.08816i	0.0104493	−	0.0376348i
$837$		0			0
$838$	7.17460	+	1.57925i	0.247843	+	0.0545543i
$839$	1.83159	+	33.7817i	0.0632335	+	1.16627i	0.842185	+	0.539189i	$0.181269\pi$
$839$	1.83159	+	33.7817i	0.0632335	+	1.16627i	−0.778951	+	0.627085i	$0.784248\pi$
$840$		0			0
$841$	−39.9137	+	58.8684i	−1.37634	+	2.02994i
$842$	−10.6249	+	26.6665i	−0.366158	+	0.918987i
$843$		0			0
$844$	2.40701	+	1.44825i	0.0828527	+	0.0498508i
$845$	81.4749	−	27.4521i	2.80282	−	0.944380i
$846$		0			0
$847$	2.26219	−	13.7987i	0.0777297	−	0.474130i
$848$	−6.73874	−	0.732882i	−0.231409	−	0.0251673i
$849$		0			0
$850$	13.4314	−	15.8127i	0.460694	−	0.542371i
$851$	19.8672	−	9.19157i	0.681040	−	0.315083i
$852$		0			0
$853$	27.0957	+	31.8995i	0.927739	+	1.09222i	0.995523	+	0.0945186i	$0.0301312\pi$
$853$	27.0957	+	31.8995i	0.927739	+	1.09222i	−0.0677843	+	0.997700i	$0.521593\pi$
$854$	−17.5434	−	5.91107i	−0.600324	−	0.202273i
$855$		0			0
$856$	−14.5355	−	27.4169i	−0.496814	−	0.937090i
$857$	38.6832	+	13.0339i	1.32139	+	0.445229i	0.889599	−	0.456743i	$-0.150984\pi$
$857$	38.6832	+	13.0339i	1.32139	+	0.445229i	0.431795	+	0.901972i	$0.357881\pi$
$858$		0			0
$859$	1.93898	+	0.897069i	0.0661572	+	0.0306076i	0.452689	−	0.891669i	$-0.350465\pi$
$859$	1.93898	+	0.897069i	0.0661572	+	0.0306076i	−0.386532	+	0.922276i	$0.626327\pi$
$860$	−13.7355	+	6.35471i	−0.468376	+	0.216694i
$861$		0			0
$862$	−15.8160	+	9.51616i	−0.538695	+	0.324122i
$863$	−27.3225	−	2.97150i	−0.930068	−	0.101151i	−0.369473	−	0.929241i	$-0.620462\pi$
$863$	−27.3225	−	2.97150i	−0.930068	−	0.101151i	−0.560595	+	0.828090i	$0.689427\pi$
$864$		0			0
$865$	8.26632	+	7.83028i	0.281063	+	0.266237i
$866$	−29.2934	+	9.87008i	−0.995429	+	0.335399i
$867$		0			0
$868$	−12.2542	−	9.31540i	−0.415935	−	0.316185i
$869$	7.00702	−	17.5863i	0.237697	−	0.596574i
$870$		0			0
$871$	−10.5197	−	64.1675i	−0.356448	−	2.17423i
$872$	1.54054	+	28.4136i	0.0521693	+	0.962206i
$873$		0			0
$874$	0.521040	+	1.30771i	0.0176244	+	0.0442340i
$875$	−7.00619	+	25.2340i	−0.236853	+	0.853066i
$876$		0			0
$877$	36.9467	−	4.01820i	1.24760	−	0.135685i	0.539616	−	0.841912i	$-0.318570\pi$
$877$	36.9467	−	4.01820i	1.24760	−	0.135685i	0.707986	+	0.706227i	$0.249604\pi$
$878$	26.8934	−	20.4439i	0.907609	−	0.689947i
$879$		0			0
$880$	−5.37094	+	1.18223i	−0.181054	+	0.0398531i
$881$	16.9578	+	25.0108i	0.571322	+	0.842637i	0.998093	−	0.0617228i	$-0.0196595\pi$
$881$	16.9578	+	25.0108i	0.571322	+	0.842637i	−0.426772	+	0.904359i	$0.640349\pi$
$882$		0			0
$883$	5.80372	−	10.9470i	0.195311	−	0.368395i	−0.766442	−	0.642313i	$-0.777975\pi$
$883$	5.80372	−	10.9470i	0.195311	−	0.368395i	0.961753	+	0.273918i	$0.0883197\pi$
$884$	−15.8967			−0.534664
$885$		0			0
$886$	10.4704			0.351760
$887$	−13.4236	+	25.3196i	−0.450720	+	0.850149i	0.549175	+	0.835707i	$0.314942\pi$
$887$	−13.4236	+	25.3196i	−0.450720	+	0.850149i	−0.999896	+	0.0144416i	$0.995403\pi$
$888$		0			0
$889$	−5.25207	−	7.74623i	−0.176149	−	0.259800i
$890$	15.4961	−	3.41094i	0.519429	−	0.114335i
$891$		0			0
$892$	−13.3819	+	10.1726i	−0.448059	+	0.340605i
$893$	−0.604363	+	0.0657285i	−0.0202242	+	0.00219952i
$894$		0			0
$895$	11.3224	−	40.7797i	0.378467	−	1.36311i
$896$	2.95578	+	7.41844i	0.0987455	+	0.247833i
$897$		0			0
$898$	0.466429	+	8.60277i	0.0155649	+	0.287078i
$899$	−11.9256	−	72.7432i	−0.397743	−	2.42612i
$900$		0			0
$901$	8.27077	−	20.7581i	0.275539	−	0.691551i
$902$	−8.39095	−	6.37864i	−0.279388	−	0.212385i
$903$		0			0
$904$	11.7883	−	3.97193i	0.392072	−	0.132104i
$905$	9.35158	+	8.85828i	0.310857	+	0.294459i
$906$		0			0
$907$	−38.2857	−	4.16382i	−1.27126	−	0.138258i	−0.552496	−	0.833515i	$-0.686325\pi$
$907$	−38.2857	−	4.16382i	−1.27126	−	0.138258i	−0.718760	+	0.695258i	$0.755290\pi$
$908$	3.01788	−	1.81580i	0.100152	−	0.0602594i
$909$		0			0
$910$	−38.5259	+	17.8240i	−1.27712	+	0.590859i
$911$	37.2143	+	17.2172i	1.23297	+	0.570431i	0.924637	−	0.380849i	$-0.124368\pi$
$911$	37.2143	+	17.2172i	1.23297	+	0.570431i	0.308329	+	0.951280i	$0.400230\pi$
$912$		0			0
$913$	6.69750	+	2.25665i	0.221655	+	0.0746842i
$914$	2.89445	+	5.45952i	0.0957400	+	0.180585i
$915$		0			0
$916$	4.87076	+	1.64115i	0.160934	+	0.0542251i
$917$	−28.5813	−	33.6486i	−0.943839	−	1.11117i
$918$		0			0
$919$	48.3929	−	22.3889i	1.59633	−	0.738543i	0.598304	−	0.801269i	$-0.295842\pi$
$919$	48.3929	−	22.3889i	1.59633	−	0.738543i	0.998031	+	0.0627265i	$0.0199796\pi$
$920$	−19.0839	+	22.4674i	−0.629179	+	0.740727i
$921$		0			0
$922$	6.83666	+	0.743531i	0.225153	+	0.0244869i
$923$	1.02950	−	6.27967i	0.0338864	−	0.206698i
$924$		0			0
$925$	66.2444	−	22.3203i	2.17810	−	0.733888i
$926$	−9.04994	−	5.44517i	−0.297399	−	0.178939i
$927$		0			0
$928$	−19.2647	+	48.3508i	−0.632396	+	1.58719i
$929$	−5.45843	+	8.05058i	−0.179085	+	0.264131i	−0.906628	−	0.421932i	$-0.861352\pi$
$929$	−5.45843	+	8.05058i	−0.179085	+	0.264131i	0.727542	+	0.686063i	$0.240662\pi$
$930$		0			0
$931$	−0.0909724	−	1.67789i	−0.00298150	−	0.0549905i
$932$	3.95278	+	0.870073i	0.129478	+	0.0285002i
$933$		0			0
$934$	−6.50566	+	23.4313i	−0.212872	+	0.766695i
$935$	0.981486	−	18.1024i	0.0320980	−	0.592013i
$936$		0			0
$937$	21.2649	−	16.1651i	0.694694	−	0.528092i	−0.197185	−	0.980366i	$-0.563180\pi$
$937$	21.2649	−	16.1651i	0.694694	−	0.528092i	0.891879	+	0.452274i	$0.149387\pi$
$938$	5.51389	+	19.8593i	0.180035	+	0.648428i
$939$		0			0
$940$	−2.47544	−	3.65100i	−0.0807400	−	0.119083i
$941$	9.62890	−	9.12098i	0.313893	−	0.297335i	−0.514491	−	0.857496i	$-0.672019\pi$
$941$	9.62890	−	9.12098i	0.313893	−	0.297335i	0.828384	+	0.560160i	$0.189260\pi$
$942$		0			0
$943$	−14.8278			−0.482860
$944$	3.76302	+	4.40943i	0.122476	+	0.143515i
$945$		0			0
$946$	3.47125	−	6.54747i	0.112860	−	0.212877i
$947$	31.4111	−	29.7542i	1.02072	−	0.966881i	0.0212649	−	0.999774i	$-0.493231\pi$
$947$	31.4111	−	29.7542i	1.02072	−	0.966881i	0.999459	+	0.0328930i	$0.0104721\pi$
$948$		0			0
$949$	58.1591	−	12.8018i	1.88793	−	0.415564i
$950$	1.20260	+	4.33137i	0.0390175	+	0.140528i
$951$		0			0
$952$	14.4568	−	1.57227i	0.468547	−	0.0509576i
$953$	1.57378	−	29.0266i	0.0509796	−	0.940264i	−0.855444	−	0.517895i	$-0.826716\pi$
$953$	1.57378	−	29.0266i	0.0509796	−	0.940264i	0.906424	−	0.422369i	$-0.138801\pi$
$954$		0			0
$955$	33.0604	+	82.9754i	1.06981	+	2.68502i
$956$	27.2668	+	6.00188i	0.881872	+	0.194115i
$957$		0			0
$958$	3.52177	+	21.4818i	0.113783	+	0.694046i
$959$	−6.15821	+	9.08267i	−0.198859	+	0.293295i
$960$		0			0
$961$	18.5257	+	14.0829i	0.597604	+	0.454286i
$962$	40.6645	+	24.4670i	1.31108	+	0.788848i
$963$		0			0
$964$	9.09566	+	8.61587i	0.292952	+	0.277498i
$965$	11.1849	−	68.2249i	0.360055	−	2.19624i
$966$		0			0
$967$	6.33376	−	3.81090i	0.203680	−	0.122550i	−0.410060	−	0.912059i	$-0.634492\pi$
$967$	6.33376	−	3.81090i	0.203680	−	0.122550i	0.613740	+	0.789509i	$0.289665\pi$
$968$	13.6285	−	16.0447i	0.438037	−	0.515697i
$969$		0			0
$970$	−31.1183	−	14.3969i	−0.999149	−	0.462255i
$971$	11.9797	+	14.1036i	0.384446	+	0.452605i	0.920013	−	0.391888i	$-0.128178\pi$
$971$	11.9797	+	14.1036i	0.384446	+	0.452605i	−0.535567	+	0.844493i	$0.679902\pi$
$972$		0			0
$973$	−20.7301	−	39.1010i	−0.664575	−	1.25352i
$974$	2.76332	+	5.21218i	0.0885426	+	0.167009i
$975$		0			0
$976$	−4.73549	−	5.57505i	−0.151579	−	0.178453i
$977$	4.09891	+	1.89636i	0.131136	+	0.0606699i	0.484360	−	0.874869i	$-0.339053\pi$
$977$	4.09891	+	1.89636i	0.131136	+	0.0606699i	−0.353224	+	0.935539i	$0.614915\pi$
$978$		0			0
$979$	5.67675	−	6.68319i	0.181430	−	0.213596i
$980$	10.4473	−	6.28590i	0.333725	−	0.200796i
$981$		0			0
$982$	−2.69727	+	16.4526i	−0.0860733	+	0.525024i
$983$	13.7096	+	12.9865i	0.437270	+	0.414204i	0.874409	−	0.485190i	$-0.161250\pi$
$983$	13.7096	+	12.9865i	0.437270	+	0.414204i	−0.437139	+	0.899394i	$0.644008\pi$
$984$		0			0
$985$	−47.4332	−	28.5396i	−1.51135	−	0.909348i
$986$	19.2095	+	14.6027i	0.611754	+	0.465044i
$987$		0			0
$988$	1.93289	−	2.85080i	0.0614935	−	0.0906961i
$989$	−1.68663	−	10.2880i	−0.0536318	−	0.327140i
$990$		0			0
$991$	−1.29766	−	0.285638i	−0.0412217	−	0.00907358i	0.194312	−	0.980940i	$-0.437753\pi$
$991$	−1.29766	−	0.285638i	−0.0412217	−	0.00907358i	−0.235533	+	0.971866i	$0.575684\pi$
$992$	−14.1833	−	35.5974i	−0.450320	−	1.13022i
$993$		0			0
$994$	−0.109199	+	2.01406i	−0.00346359	+	0.0638821i
$995$	−96.2165	+	10.4642i	−3.05027	+	0.331737i
$996$		0			0
$997$	−5.68693	−	20.4825i	−0.180107	−	0.648686i	−0.997374	−	0.0724270i	$-0.976926\pi$
$997$	−5.68693	−	20.4825i	−0.180107	−	0.648686i	0.817267	−	0.576259i	$-0.195488\pi$
$998$	15.8997	−	3.49980i	0.503297	−	0.110784i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.19.4		140
3.2	odd	2		177.2.e.a.19.2	✓	140
59.28	even	29	inner	531.2.i.c.28.4		140
177.146	odd	58		177.2.e.a.28.2	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.19.2	✓	140	3.2	odd	2
177.2.e.a.28.2	yes	140	177.146	odd	58
531.2.i.c.19.4		140	1.1	even	1	trivial
531.2.i.c.28.4		140	59.28	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)

\(f(q)\)	\(=\)	\(q+(0.454038 - 0.856407i) q^{2} +(0.595092 + 0.877695i) q^{4} +(-3.60206 + 0.792874i) q^{5} +(1.56865 - 1.19245i) q^{7} +(2.94914 - 0.320738i) q^{8} +O(q^{10})\)	\(q+(0.454038 - 0.856407i) q^{2} +(0.595092 + 0.877695i) q^{4} +(-3.60206 + 0.792874i) q^{5} +(1.56865 - 1.19245i) q^{7} +(2.94914 - 0.320738i) q^{8} +(-0.956451 + 3.44483i) q^{10} +(0.731304 + 1.83543i) q^{11} +(0.326231 + 6.01697i) q^{13} +(-0.309001 - 1.88482i) q^{14} +(0.279337 - 0.701084i) q^{16} +(1.98052 + 1.50555i) q^{17} +(-0.510808 + 0.172111i) q^{19} +(-2.83946 - 2.68968i) q^{20} +(1.90392 + 0.207064i) q^{22} +(2.30855 - 1.38901i) q^{23} +(7.80833 - 3.61252i) q^{25} +(5.30110 + 2.45255i) q^{26} +(1.98010 + 0.667174i) q^{28} +(4.68698 + 8.84059i) q^{29} +(-6.98124 - 2.35225i) q^{31} +(3.36739 + 3.96440i) q^{32} +(2.18860 - 1.01255i) q^{34} +(-4.70490 + 5.53904i) q^{35} +(8.07738 + 0.878468i) q^{37} +(-0.0845291 + 0.515605i) q^{38} +(-10.3687 + 3.49361i) q^{40} +(-4.71579 - 2.83740i) q^{41} +(1.43226 - 3.59471i) q^{43} +(-1.17576 + 1.73411i) q^{44} +(-0.141387 - 2.60772i) q^{46} +(1.10146 + 0.242450i) q^{47} +(-0.833992 + 3.00377i) q^{49} +(0.451495 - 8.32733i) q^{50} +(-5.08693 + 3.86698i) q^{52} +(-2.40290 - 8.65448i) q^{53} +(-4.08947 - 6.03152i) q^{55} +(4.24369 - 4.01984i) q^{56} +9.69921 q^{58} +(-3.58219 + 6.79470i) q^{59} +(4.54005 - 8.56344i) q^{61} +(-5.18424 + 4.91077i) q^{62} +(6.39815 - 1.40834i) q^{64} +(-5.94580 - 21.4148i) q^{65} +(-10.7277 + 1.16671i) q^{67} +(-0.142824 + 2.63423i) q^{68} +(2.60747 + 6.54425i) q^{70} +(-1.03135 - 0.227018i) q^{71} +(-1.59885 - 9.75254i) q^{73} +(4.41977 - 6.51867i) q^{74} +(-0.455039 - 0.345912i) q^{76} +(3.33583 + 2.00710i) q^{77} +(-6.95616 - 6.58922i) q^{79} +(-0.450320 + 2.74683i) q^{80} +(-4.57111 + 2.75035i) q^{82} +(2.31576 - 2.72632i) q^{83} +(-8.32767 - 3.85279i) q^{85} +(-2.42823 - 2.85874i) q^{86} +(2.74541 + 5.17839i) q^{88} +(-2.07887 - 3.92116i) q^{89} +(7.68671 + 9.04949i) q^{91} +(2.59293 + 1.19962i) q^{92} +(0.707741 - 0.833217i) q^{94} +(1.70350 - 1.02496i) q^{95} +(-1.55157 + 9.46414i) q^{97} +(2.19378 + 2.07806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 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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