LMFDB - Embedded newform 603.2.u.c.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.2
Root			$-0.165981 + 0.106669i$ of defining polynomial
Character	$\chi$	$=$	603.64
Dual form			603.2.u.c.424.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25667 - 0.368991i) q^{2} +(-0.239446 - 0.153882i) q^{4} +(1.35049 + 2.95717i) q^{5} +(4.00914 + 1.17719i) q^{7} +(1.95949 + 2.26138i) q^{8} +O(q^{10})$	\(q+(-1.25667 - 0.368991i) q^{2} +(-0.239446 - 0.153882i) q^{4} +(1.35049 + 2.95717i) q^{5} +(4.00914 + 1.17719i) q^{7} +(1.95949 + 2.26138i) q^{8} +(-0.605953 - 4.21450i) q^{10} +(0.0622997 + 0.136417i) q^{11} +(-0.628542 + 0.725376i) q^{13} +(-4.60379 - 2.95867i) q^{14} +(-1.39153 - 3.04702i) q^{16} +(0.311139 - 0.199957i) q^{17} +(-7.59646 + 2.23052i) q^{19} +(0.131686 - 0.915898i) q^{20} +(-0.0279533 - 0.194419i) q^{22} +(-0.206011 + 1.43284i) q^{23} +(-3.64670 + 4.20851i) q^{25} +(1.05753 - 0.679631i) q^{26} +(-0.778822 - 0.898809i) q^{28} -1.51049 q^{29} +(3.08248 + 3.55737i) q^{31} +(-0.227312 - 1.58099i) q^{32} +(-0.464780 + 0.136472i) q^{34} +(1.93317 + 13.4455i) q^{35} +4.71809 q^{37} +10.3693 q^{38} +(-4.04098 + 8.84852i) q^{40} +(-3.83945 + 2.46746i) q^{41} +(6.83054 - 4.38972i) q^{43} +(0.00607483 - 0.0422514i) q^{44} +(0.787594 - 1.72459i) q^{46} +(0.238631 - 1.65971i) q^{47} +(8.79864 + 5.65454i) q^{49} +(6.13559 - 3.94311i) q^{50} +(0.262124 - 0.0769666i) q^{52} +(7.23687 + 4.65086i) q^{53} +(-0.319274 + 0.368461i) q^{55} +(5.19381 + 11.3729i) q^{56} +(1.89818 + 0.557356i) q^{58} +(-6.70083 - 7.73317i) q^{59} +(-0.894613 + 1.95893i) q^{61} +(-2.56102 - 5.60785i) q^{62} +(-1.25115 + 8.70192i) q^{64} +(-2.99390 - 0.879088i) q^{65} +(-6.69173 - 4.71389i) q^{67} -0.105271 q^{68} +(2.53191 - 17.6098i) q^{70} +(4.93184 + 3.16950i) q^{71} +(-2.85782 + 6.25776i) q^{73} +(-5.92907 - 1.74093i) q^{74} +(2.16218 + 0.634873i) q^{76} +(0.0891792 + 0.620255i) q^{77} +(1.57181 - 1.81396i) q^{79} +(7.13129 - 8.22995i) q^{80} +(5.73539 - 1.68406i) q^{82} +(-0.453939 - 0.993987i) q^{83} +(1.01150 + 0.650049i) q^{85} +(-10.2035 + 2.99602i) q^{86} +(-0.186415 + 0.408192i) q^{88} +(1.38903 + 9.66095i) q^{89} +(-3.37382 + 2.16822i) q^{91} +(0.269818 - 0.311386i) q^{92} +(-0.912300 + 1.99766i) q^{94} +(-16.8550 - 19.4517i) q^{95} -3.44598 q^{97} +(-8.97050 - 10.3525i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 4 q^{4} - q^{5} - 8 q^{7} + 22 q^{8}+O(q^{10}) $ 20 * q + 4 * q^2 - 4 * q^4 - q^5 - 8 * q^7 + 22 * q^8	$ 20 q + 4 q^{2} - 4 q^{4} - q^{5} - 8 q^{7} + 22 q^{8} - 9 q^{10} + 12 q^{13} - 6 q^{14} + 8 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} - 2 q^{23} - 3 q^{25} + 31 q^{26} - 5 q^{28} + 6 q^{29} - 16 q^{32} - 8 q^{34} - 34 q^{35} + 24 q^{37} + 14 q^{38} - 11 q^{40} + 6 q^{41} - 22 q^{43} + 22 q^{44} + 15 q^{46} - 16 q^{47} + 42 q^{49} + 17 q^{50} + 2 q^{52} + q^{53} + 20 q^{55} - 11 q^{56} + 10 q^{58} + 26 q^{59} - 26 q^{61} - 11 q^{62} - 6 q^{64} - 9 q^{65} - 22 q^{67} + 52 q^{68} - 42 q^{70} - 20 q^{71} - 55 q^{73} - 37 q^{74} - 3 q^{76} + 70 q^{77} - 34 q^{79} - 40 q^{80} - 12 q^{82} - 56 q^{83} + 41 q^{85} + 33 q^{86} + 11 q^{88} + 3 q^{89} + 12 q^{91} + 18 q^{92} + 32 q^{94} - 74 q^{95} - 14 q^{97} - 95 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 4 * q^4 - q^5 - 8 * q^7 + 22 * q^8 - 9 * q^10 + 12 * q^13 - 6 * q^14 + 8 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 - 2 * q^23 - 3 * q^25 + 31 * q^26 - 5 * q^28 + 6 * q^29 - 16 * q^32 - 8 * q^34 - 34 * q^35 + 24 * q^37 + 14 * q^38 - 11 * q^40 + 6 * q^41 - 22 * q^43 + 22 * q^44 + 15 * q^46 - 16 * q^47 + 42 * q^49 + 17 * q^50 + 2 * q^52 + q^53 + 20 * q^55 - 11 * q^56 + 10 * q^58 + 26 * q^59 - 26 * q^61 - 11 * q^62 - 6 * q^64 - 9 * q^65 - 22 * q^67 + 52 * q^68 - 42 * q^70 - 20 * q^71 - 55 * q^73 - 37 * q^74 - 3 * q^76 + 70 * q^77 - 34 * q^79 - 40 * q^80 - 12 * q^82 - 56 * q^83 + 41 * q^85 + 33 * q^86 + 11 * q^88 + 3 * q^89 + 12 * q^91 + 18 * q^92 + 32 * q^94 - 74 * q^95 - 14 * q^97 - 95 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.25667	−	0.368991i	−0.888599	−	0.260916i	−0.194592	−	0.980884i	$-0.562338\pi$
$2$	−1.25667	−	0.368991i	−0.888599	−	0.260916i	−0.694007	+	0.719968i	$0.744156\pi$
$3$		0			0
$3$		0			0
$4$	−0.239446	−	0.153882i	−0.119723	−	0.0769412i
$5$	1.35049	+	2.95717i	0.603959	+	1.32248i	0.926630	+	0.375974i	$0.122692\pi$
$5$	1.35049	+	2.95717i	0.603959	+	1.32248i	−0.322672	+	0.946511i	$0.604581\pi$
$6$		0			0
$7$	4.00914	+	1.17719i	1.51531	+	0.444936i	0.930518	−	0.366246i	$-0.119357\pi$
$7$	4.00914	+	1.17719i	1.51531	+	0.444936i	0.584794	+	0.811182i	$0.301175\pi$
$8$	1.95949	+	2.26138i	0.692785	+	0.799517i
$9$		0			0
$10$	−0.605953	−	4.21450i	−0.191619	−	1.33274i
$11$	0.0622997	+	0.136417i	0.0187841	+	0.0411314i	0.918792	−	0.394743i	$-0.129166\pi$
$11$	0.0622997	+	0.136417i	0.0187841	+	0.0411314i	−0.900007	+	0.435875i	$0.856439\pi$
$12$		0			0
$13$	−0.628542	+	0.725376i	−0.174326	+	0.201183i	−0.836188	−	0.548442i	$-0.815221\pi$
$13$	−0.628542	+	0.725376i	−0.174326	+	0.201183i	0.661862	+	0.749626i	$0.269766\pi$
$14$	−4.60379	−	2.95867i	−1.23041	−	0.790739i
$15$		0			0
$16$	−1.39153	−	3.04702i	−0.347882	−	0.761755i
$17$	0.311139	−	0.199957i	0.0754622	−	0.0484966i	−0.502366	−	0.864655i	$-0.667537\pi$
$17$	0.311139	−	0.199957i	0.0754622	−	0.0484966i	0.577828	+	0.816159i	$0.303900\pi$
$18$		0			0
$19$	−7.59646	+	2.23052i	−1.74275	+	0.511717i	−0.989313	−	0.145806i	$-0.953423\pi$
$19$	−7.59646	+	2.23052i	−1.74275	+	0.511717i	−0.753435	+	0.657523i	$0.771604\pi$
$20$	0.131686	−	0.915898i	0.0294459	−	0.204801i
$21$		0			0
$22$	−0.0279533	−	0.194419i	−0.00595966	−	0.0414504i
$23$	−0.206011	+	1.43284i	−0.0429563	+	0.298768i	0.957006	+	0.290069i	$0.0936782\pi$
$23$	−0.206011	+	1.43284i	−0.0429563	+	0.298768i	−0.999962	+	0.00869922i	$0.997231\pi$
$24$		0			0
$25$	−3.64670	+	4.20851i	−0.729339	+	0.841702i
$26$	1.05753	−	0.679631i	0.207398	−	0.133287i
$27$		0			0
$28$	−0.778822	−	0.898809i	−0.147184	−	0.169859i
$29$	−1.51049			−0.280490			−0.140245	−	0.990117i	$-0.544789\pi$
$29$	−1.51049			−0.280490			−0.140245	+	0.990117i	$0.544789\pi$
$30$		0			0
$31$	3.08248	+	3.55737i	0.553630	+	0.638923i	0.961725	−	0.274016i	$-0.0883522\pi$
$31$	3.08248	+	3.55737i	0.553630	+	0.638923i	−0.408095	+	0.912939i	$0.633807\pi$
$32$	−0.227312	−	1.58099i	−0.0401835	−	0.279482i
$33$		0			0
$34$	−0.464780	+	0.136472i	−0.0797092	+	0.0234047i
$35$	1.93317	+	13.4455i	0.326765	+	2.27270i
$36$		0			0
$37$	4.71809			0.775648			0.387824	−	0.921733i	$-0.373227\pi$
$37$	4.71809			0.775648			0.387824	+	0.921733i	$0.373227\pi$
$38$	10.3693			1.68212
$39$		0			0
$40$	−4.04098	+	8.84852i	−0.638935	+	1.39907i
$41$	−3.83945	+	2.46746i	−0.599621	+	0.385353i	−0.804952	−	0.593339i	$-0.797809\pi$
$41$	−3.83945	+	2.46746i	−0.599621	+	0.385353i	0.205331	+	0.978693i	$0.434173\pi$
$42$		0			0
$43$	6.83054	−	4.38972i	1.04165	−	0.669426i	0.0962538	−	0.995357i	$-0.469314\pi$
$43$	6.83054	−	4.38972i	1.04165	−	0.669426i	0.945394	+	0.325931i	$0.105678\pi$
$44$	0.00607483	−	0.0422514i	0.000915816	−	0.00636964i
$45$		0			0
$46$	0.787594	−	1.72459i	0.116124	−	0.254277i
$47$	0.238631	−	1.65971i	0.0348079	−	0.242094i	−0.964988	−	0.262294i	$-0.915521\pi$
$47$	0.238631	−	1.65971i	0.0348079	−	0.242094i	0.999796	+	0.0201996i	$0.00643016\pi$
$48$		0			0
$49$	8.79864	+	5.65454i	1.25695	+	0.807792i
$50$	6.13559	−	3.94311i	0.867704	−	0.557639i
$51$		0			0
$52$	0.262124	−	0.0769666i	0.0363501	−	0.0106734i
$53$	7.23687	+	4.65086i	0.994061	+	0.638844i	0.933221	−	0.359303i	$-0.116986\pi$
$53$	7.23687	+	4.65086i	0.994061	+	0.638844i	0.0608403	+	0.998148i	$0.480622\pi$
$54$		0			0
$55$	−0.319274	+	0.368461i	−0.0430508	+	0.0496833i
$56$	5.19381	+	11.3729i	0.694052	+	1.51976i
$57$		0			0
$58$	1.89818	+	0.557356i	0.249243	+	0.0731844i
$59$	−6.70083	−	7.73317i	−0.872373	−	1.00677i	−0.999888	−	0.0149359i	$-0.995246\pi$
$59$	−6.70083	−	7.73317i	−0.872373	−	1.00677i	0.127515	−	0.991837i	$-0.459300\pi$
$60$		0			0
$61$	−0.894613	+	1.95893i	−0.114544	+	0.250815i	−0.958218	−	0.286040i	$-0.907661\pi$
$61$	−0.894613	+	1.95893i	−0.114544	+	0.250815i	0.843674	+	0.536856i	$0.180388\pi$
$62$	−2.56102	−	5.60785i	−0.325250	−	0.712197i
$63$		0			0
$64$	−1.25115	+	8.70192i	−0.156393	+	1.08774i
$65$	−2.99390	−	0.879088i	−0.371347	−	0.109037i
$66$		0			0
$67$	−6.69173	−	4.71389i	−0.817525	−	0.575893i
$67$	−6.69173	−	4.71389i	−0.817525	−	0.575893i
$68$	−0.105271			−0.0127659
$69$		0			0
$70$	2.53191	−	17.6098i	0.302621	−	2.10478i
$71$	4.93184	+	3.16950i	0.585302	+	0.376151i	0.799524	−	0.600634i	$-0.205085\pi$
$71$	4.93184	+	3.16950i	0.585302	+	0.376151i	−0.214222	+	0.976785i	$0.568722\pi$
$72$		0			0
$73$	−2.85782	+	6.25776i	−0.334483	+	0.732415i	−0.999901	−	0.0140556i	$-0.995526\pi$
$73$	−2.85782	+	6.25776i	−0.334483	+	0.732415i	0.665419	+	0.746470i	$0.268253\pi$
$74$	−5.92907	−	1.74093i	−0.689240	−	0.202379i
$75$		0			0
$76$	2.16218	+	0.634873i	0.248019	+	0.0728249i
$77$	0.0891792	+	0.620255i	0.0101629	+	0.0706846i
$78$		0			0
$79$	1.57181	−	1.81396i	0.176842	−	0.204087i	−0.660408	−	0.750907i	$-0.729617\pi$
$79$	1.57181	−	1.81396i	0.176842	−	0.204087i	0.837250	+	0.546820i	$0.184162\pi$
$80$	7.13129	−	8.22995i	0.797303	−	0.920136i
$81$		0			0
$82$	5.73539	−	1.68406i	0.633368	−	0.185974i
$83$	−0.453939	−	0.993987i	−0.0498262	−	0.109104i	0.883082	−	0.469219i	$-0.155465\pi$
$83$	−0.453939	−	0.993987i	−0.0498262	−	0.109104i	−0.932908	+	0.360115i	$0.882737\pi$
$84$		0			0
$85$	1.01150	+	0.650049i	0.109712	+	0.0705077i
$86$	−10.2035	+	2.99602i	−1.10027	+	0.323069i
$87$		0			0
$88$	−0.186415	+	0.408192i	−0.0198719	+	0.0435134i
$89$	1.38903	+	9.66095i	0.147237	+	1.02406i	0.920715	+	0.390235i	$0.127606\pi$
$89$	1.38903	+	9.66095i	0.147237	+	1.02406i	−0.773478	+	0.633823i	$0.781485\pi$
$90$		0			0
$91$	−3.37382	+	2.16822i	−0.353672	+	0.227291i
$92$	0.269818	−	0.311386i	0.0281304	−	0.0324642i
$93$		0			0
$94$	−0.912300	+	1.99766i	−0.0940965	+	0.206043i
$95$	−16.8550	−	19.4517i	−1.72929	−	1.99570i
$96$		0			0
$97$	−3.44598			−0.349887			−0.174943	−	0.984578i	$-0.555974\pi$
$97$	−3.44598			−0.349887			−0.174943	+	0.984578i	$0.555974\pi$
$98$	−8.97050	−	10.3525i	−0.906157	−	1.04576i
$99$		0			0
$100$	1.52080	−	0.446548i	0.152080	−	0.0446548i
$101$	5.66839	−	1.66439i	0.564026	−	0.165613i	0.0127244	−	0.999919i	$-0.495950\pi$
$101$	5.66839	−	1.66439i	0.564026	−	0.165613i	0.551302	+	0.834306i	$0.314131\pi$
$102$		0			0
$103$	4.73505	+	5.46454i	0.466559	+	0.538437i	0.939451	−	0.342683i	$-0.111336\pi$
$103$	4.73505	+	5.46454i	0.466559	+	0.538437i	−0.472892	+	0.881120i	$0.656790\pi$
$104$	−2.87197			−0.281620
$105$		0			0
$106$	−7.37823	−	8.51493i	−0.716637	−	0.827043i
$107$	−7.21826	+	15.8058i	−0.697815	+	1.52800i	0.144785	+	0.989463i	$0.453751\pi$
$107$	−7.21826	+	15.8058i	−0.697815	+	1.52800i	−0.842600	+	0.538540i	$0.818976\pi$
$108$		0			0
$109$	−2.51064	+	2.89744i	−0.240476	+	0.277524i	−0.863139	−	0.504966i	$-0.831505\pi$
$109$	−2.51064	+	2.89744i	−0.240476	+	0.277524i	0.622663	+	0.782490i	$0.286051\pi$
$110$	0.537180	−	0.345225i	0.0512181	−	0.0329159i
$111$		0			0
$112$	−1.99191	−	13.8540i	−0.188217	−	1.30908i
$113$	3.57527	−	7.82875i	0.336333	−	0.736467i	−0.663599	−	0.748088i	$-0.730972\pi$
$113$	3.57527	−	7.82875i	0.336333	−	0.736467i	0.999932	+	0.0116213i	$0.00369927\pi$
$114$		0			0
$115$	−4.51536	+	1.32583i	−0.421060	+	0.123634i
$116$	0.361679	+	0.232437i	0.0335811	+	0.0215812i
$117$		0			0
$118$	5.56725	+	12.1906i	0.512507	+	1.12223i
$119$	1.48278	−	0.435385i	0.135927	−	0.0399117i
$120$		0			0
$121$	7.18874	−	8.29625i	0.653522	−	0.754204i
$122$	1.84706	−	2.13162i	0.167225	−	0.192988i
$123$		0			0
$124$	−0.190670	−	1.32614i	−0.0171227	−	0.119091i
$125$	−1.77380	−	0.520834i	−0.158653	−	0.0465848i
$126$		0			0
$127$	14.0877	+	4.13652i	1.25008	+	0.367057i	0.838794	−	0.544449i	$-0.183261\pi$
$127$	14.0877	+	4.13652i	1.25008	+	0.367057i	0.411287	+	0.911506i	$0.365080\pi$
$128$	3.45617	−	7.56795i	0.305485	−	0.668919i
$129$		0			0
$130$	3.43796	+	2.20944i	0.301529	+	0.193781i
$131$	0.401852	−	2.79494i	0.0351099	−	0.244195i	−0.964707	−	0.263325i	$-0.915181\pi$
$131$	0.401852	−	2.79494i	0.0351099	−	0.244195i	0.999817	+	0.0191305i	$0.00608978\pi$
$132$		0			0
$133$	−33.0810			−2.86849
$134$	6.66991	+	8.39298i	0.576192	+	0.725043i
$135$		0			0
$136$	1.06185	+	0.311788i	0.0910530	+	0.0267356i
$137$	−0.815236	+	5.67009i	−0.0696503	+	0.484428i	0.924903	+	0.380202i	$0.124146\pi$
$137$	−0.815236	+	5.67009i	−0.0696503	+	0.484428i	−0.994554	+	0.104226i	$0.966763\pi$
$138$		0			0
$139$	−9.08369	−	19.8905i	−0.770469	−	1.68709i	−0.725618	−	0.688097i	$-0.758446\pi$
$139$	−9.08369	−	19.8905i	−0.770469	−	1.68709i	−0.0448502	−	0.998994i	$-0.514281\pi$
$140$	1.60613	−	3.51694i	0.135743	−	0.297236i
$141$		0			0
$142$	−5.02817	−	5.80282i	−0.421955	−	0.486962i
$143$	−0.138112	−	0.0405533i	−0.0115495	−	0.00339124i
$144$		0			0
$145$	−2.03990	−	4.46676i	−0.169404	−	0.370944i
$146$	5.90039	−	6.80941i	0.488320	−	0.563551i
$147$		0			0
$148$	−1.12973	−	0.726030i	−0.0928629	−	0.0596793i
$149$	4.56865	−	1.34148i	0.374279	−	0.109898i	−0.0891827	−	0.996015i	$-0.528425\pi$
$149$	4.56865	−	1.34148i	0.374279	−	0.109898i	0.463461	+	0.886117i	$0.346607\pi$
$150$		0			0
$151$	17.3012	−	11.1188i	1.40796	−	0.904838i	0.407989	−	0.912987i	$-0.366230\pi$
$151$	17.3012	−	11.1188i	1.40796	−	0.904838i	0.999967	+	0.00814880i	$0.00259387\pi$
$152$	−19.9293	−	12.8078i	−1.61648	−	1.03885i
$153$		0			0
$154$	0.116800	−	0.812361i	0.00941200	−	0.0654619i
$155$	−6.35688	+	13.9196i	−0.510596	+	1.11805i
$156$		0			0
$157$	1.47742	−	10.2757i	0.117911	−	0.820087i	−0.841939	−	0.539573i	$-0.818586\pi$
$157$	1.47742	−	10.2757i	0.117911	−	0.820087i	0.959850	−	0.280515i	$-0.0905051\pi$
$158$	−2.64458	+	1.69957i	−0.210391	+	0.135210i
$159$		0			0
$160$	4.36827	−	2.80732i	0.345342	−	0.221938i
$161$	−2.51265	+	5.50194i	−0.198025	+	0.433614i
$162$		0			0
$163$	−1.72259			−0.134924			−0.0674620	−	0.997722i	$-0.521490\pi$
$163$	−1.72259			−0.134924			−0.0674620	+	0.997722i	$0.521490\pi$
$164$	1.29904			0.101438
$165$		0			0
$166$	0.203678	+	1.41661i	0.0158085	+	0.109950i
$167$	11.7758	−	3.45767i	0.911236	−	0.267563i	0.207675	−	0.978198i	$-0.433410\pi$
$167$	11.7758	−	3.45767i	0.911236	−	0.267563i	0.703561	+	0.710635i	$0.251592\pi$
$168$		0			0
$169$	1.71899	+	11.9558i	0.132230	+	0.919678i
$170$	−1.03125	−	1.19013i	−0.0790934	−	0.0912787i
$171$		0			0
$172$	−2.31104			−0.176215
$173$	−14.9753	−	17.2824i	−1.13855	−	1.31396i	−0.942821	−	0.333300i	$-0.891838\pi$
$173$	−14.9753	−	17.2824i	−1.13855	−	1.31396i	−0.195730	−	0.980658i	$-0.562708\pi$
$174$		0			0
$175$	−19.5743	+	12.5797i	−1.47968	+	0.950933i
$176$	0.328975	−	0.379657i	0.0247974	−	0.0286177i
$177$		0			0
$178$	1.81925	−	12.6531i	0.136358	−	0.948394i
$179$	−3.36497	−	23.4039i	−0.251510	−	1.74929i	−0.589159	−	0.808017i	$-0.700541\pi$
$179$	−3.36497	−	23.4039i	−0.251510	−	1.74929i	0.337649	−	0.941272i	$-0.390368\pi$
$180$		0			0
$181$	0.788465	−	5.48390i	0.0586062	−	0.407615i	−0.939309	−	0.343073i	$-0.888532\pi$
$181$	0.788465	−	5.48390i	0.0586062	−	0.407615i	0.997915	−	0.0645420i	$-0.0205587\pi$
$182$	5.03982	−	1.47983i	0.373577	−	0.109692i
$183$		0			0
$184$	−3.64387	+	2.34177i	−0.268630	+	0.172638i
$185$	6.37174	+	13.9522i	0.468460	+	1.02578i
$186$		0			0
$187$	0.0466614	+	0.0299875i	0.00341222	+	0.00219290i
$188$	−0.312540	+	0.360690i	−0.0227943	+	0.0263060i
$189$		0			0
$190$	14.0036	+	30.6637i	1.01593	+	2.22458i
$191$	−2.91992	−	20.3085i	−0.211278	−	1.46947i	−0.768896	−	0.639373i	$-0.779194\pi$
$191$	−2.91992	−	20.3085i	−0.211278	−	1.46947i	0.557618	−	0.830097i	$-0.311715\pi$
$192$		0			0
$193$	−9.56885	−	11.0430i	−0.688781	−	0.794896i	0.298410	−	0.954438i	$-0.403544\pi$
$193$	−9.56885	−	11.0430i	−0.688781	−	0.794896i	−0.987191	+	0.159542i	$0.948998\pi$
$194$	4.33046	+	1.27154i	0.310909	+	0.0912911i
$195$		0			0
$196$	−1.23666	−	2.70791i	−0.0883330	−	0.193422i
$197$	12.8372	+	8.24996i	0.914612	+	0.587785i	0.911090	−	0.412208i	$-0.135242\pi$
$197$	12.8372	+	8.24996i	0.914612	+	0.587785i	0.00352230	+	0.999994i	$0.498879\pi$
$198$		0			0
$199$	−0.567438	−	0.166615i	−0.0402246	−	0.0118110i	0.261558	−	0.965188i	$-0.415764\pi$
$199$	−0.567438	−	0.166615i	−0.0402246	−	0.0118110i	−0.301783	+	0.953377i	$0.597582\pi$
$200$	−16.6627			−1.17823
$201$		0			0
$202$	−7.73743			−0.544404
$203$	−6.05575	−	1.77813i	−0.425030	−	0.124800i
$204$		0			0
$205$	−12.4818	−	8.02160i	−0.871770	−	0.560253i
$206$	−3.93402	−	8.61431i	−0.274097	−	0.600188i
$207$		0			0
$208$	3.08487	+	0.905799i	0.213897	+	0.0628058i
$209$	−0.777540	−	0.897329i	−0.0537835	−	0.0620695i
$210$		0			0
$211$	3.45407	+	24.0236i	0.237788	+	1.65385i	0.662898	+	0.748709i	$0.269326\pi$
$211$	3.45407	+	24.0236i	0.237788	+	1.65385i	−0.425110	+	0.905142i	$0.639765\pi$
$212$	−1.01715	−	2.22726i	−0.0698584	−	0.152969i
$213$		0			0
$214$	14.9032	−	17.1992i	1.01876	−	1.17571i
$215$	22.2057	+	14.2708i	1.51442	+	0.973257i
$216$		0			0
$217$	8.17039	+	17.8907i	0.554642	+	1.21450i
$218$	4.22417	−	2.71471i	0.286097	−	0.183863i
$219$		0			0
$220$	0.133148	−	0.0390959i	0.00897686	−	0.00263584i
$221$	−0.0505199	+	0.351374i	−0.00339834	+	0.0236359i
$222$		0			0
$223$	−1.77542	−	12.3484i	−0.118891	−	0.826907i	−0.958780	−	0.284149i	$-0.908289\pi$
$223$	−1.77542	−	12.3484i	−0.118891	−	0.826907i	0.839889	−	0.542758i	$-0.182620\pi$
$224$	0.949799	−	6.60600i	0.0634611	−	0.441382i
$225$		0			0
$226$	−7.38167	+	8.51890i	−0.491021	+	0.566669i
$227$	1.89772	−	1.21959i	0.125956	−	0.0809470i	−0.476146	−	0.879366i	$-0.657967\pi$
$227$	1.89772	−	1.21959i	0.125956	−	0.0809470i	0.602102	+	0.798419i	$0.294330\pi$
$228$		0			0
$229$	4.28084	+	4.94036i	0.282886	+	0.326468i	0.879354	−	0.476169i	$-0.157975\pi$
$229$	4.28084	+	4.94036i	0.282886	+	0.326468i	−0.596468	+	0.802637i	$0.703430\pi$
$230$	6.16354			0.406412
$231$		0			0
$232$	−2.95979	−	3.41577i	−0.194319	−	0.224257i
$233$	1.25509	+	8.72935i	0.0822237	+	0.571879i	0.988733	+	0.149692i	$0.0478282\pi$
$233$	1.25509	+	8.72935i	0.0822237	+	0.571879i	−0.906509	+	0.422187i	$0.861263\pi$
$234$		0			0
$235$	5.23032	−	1.53576i	0.341188	−	0.100182i
$236$	0.414486	+	2.88281i	0.0269807	+	0.187655i
$237$		0			0
$238$	−2.02402			−0.131198
$239$	26.6058			1.72098			0.860492	−	0.509464i	$-0.170156\pi$
$239$	26.6058			1.72098			0.860492	+	0.509464i	$0.170156\pi$
$240$		0			0
$241$	0.196911	−	0.431174i	0.0126841	−	0.0277744i	−0.903184	−	0.429254i	$-0.858777\pi$
$241$	0.196911	−	0.431174i	0.0126841	−	0.0277744i	0.915868	+	0.401479i	$0.131504\pi$
$242$	−12.0951	+	7.77305i	−0.777503	+	0.499671i
$243$		0			0
$244$	0.515656	−	0.331392i	0.0330115	−	0.0212152i
$245$	−4.83893	+	33.6555i	−0.309148	+	2.15017i
$246$		0			0
$247$	3.15673	−	6.91227i	0.200858	−	0.439817i
$248$	−2.00446	+	13.9413i	−0.127283	+	0.885273i
$249$		0			0
$250$	2.03689	+	1.30903i	0.128824	+	0.0827904i
$251$	22.2179	−	14.2786i	1.40238	−	0.901256i	0.402482	−	0.915428i	$-0.368148\pi$
$251$	22.2179	−	14.2786i	1.40238	−	0.901256i	0.999900	+	0.0141724i	$0.00451138\pi$
$252$		0			0
$253$	−0.208299	+	0.0611621i	−0.0130956	+	0.00384523i
$254$	−16.1772	−	10.3965i	−1.01505	−	0.652332i
$255$		0			0
$256$	4.37853	−	5.05309i	0.273658	−	0.315818i
$257$	4.26965	+	9.34922i	0.266333	+	0.583188i	0.994795	−	0.101898i	$-0.0324916\pi$
$257$	4.26965	+	9.34922i	0.266333	+	0.583188i	−0.728462	+	0.685087i	$0.759764\pi$
$258$		0			0
$259$	18.9155	+	5.55408i	1.17535	+	0.345114i
$260$	0.581600	+	0.671202i	0.0360693	+	0.0416262i
$261$		0			0
$262$	−1.53630	+	3.36403i	−0.0949131	+	0.207831i
$263$	−4.19564	−	9.18717i	−0.258714	−	0.566505i	0.735049	−	0.678014i	$-0.237159\pi$
$263$	−4.19564	−	9.18717i	−0.258714	−	0.566505i	−0.993763	+	0.111508i	$0.964432\pi$
$264$		0			0
$265$	−3.98001	+	27.6816i	−0.244490	+	1.70047i
$266$	41.5719	+	12.2066i	2.54894	+	0.748435i
$267$		0			0
$268$	0.876922	+	2.15846i	0.0535665	+	0.131849i
$269$	−21.3974			−1.30462			−0.652312	−	0.757950i	$-0.726201\pi$
$269$	−21.3974			−1.30462			−0.652312	+	0.757950i	$0.726201\pi$
$270$		0			0
$271$	−0.816462	+	5.67862i	−0.0495966	+	0.344952i	0.949880	+	0.312613i	$0.101204\pi$
$271$	−0.816462	+	5.67862i	−0.0495966	+	0.344952i	−0.999477	+	0.0323382i	$0.989705\pi$
$272$	−1.04223	−	0.669800i	−0.0631944	−	0.0406126i
$273$		0			0
$274$	3.11669	−	6.82461i	0.188286	−	0.412290i
$275$	−0.801302	−	0.235284i	−0.0483204	−	0.0141881i
$276$		0			0
$277$	−3.42232	−	1.00488i	−0.205627	−	0.0603777i	0.177297	−	0.984157i	$-0.443265\pi$
$277$	−3.42232	−	1.00488i	−0.205627	−	0.0603777i	−0.382924	+	0.923780i	$0.625083\pi$
$278$	4.07577	+	28.3476i	0.244448	+	1.70017i
$279$		0			0
$280$	−26.6172	+	30.7179i	−1.59068	+	1.83575i
$281$	−15.9051	+	18.3554i	−0.948818	+	1.09499i	0.0465560	+	0.998916i	$0.485175\pi$
$281$	−15.9051	+	18.3554i	−0.948818	+	1.09499i	−0.995374	+	0.0960784i	$0.969370\pi$
$282$		0			0
$283$	−5.31098	+	1.55945i	−0.315705	+	0.0926994i	−0.435746	−	0.900070i	$-0.643516\pi$
$283$	−5.31098	+	1.55945i	−0.315705	+	0.0926994i	0.120041	+	0.992769i	$0.461697\pi$
$284$	−0.693177	−	1.51785i	−0.0411325	−	0.0900676i
$285$		0			0
$286$	0.158597	+	0.101924i	0.00937804	+	0.00602690i
$287$	−18.2976	+	5.37265i	−1.08007	+	0.317137i
$288$		0			0
$289$	−7.00523	+	15.3393i	−0.412072	+	0.902313i
$290$	0.915283	+	6.36594i	0.0537473	+	0.373821i
$291$		0			0
$292$	1.64725	−	1.05862i	0.0963981	−	0.0619513i
$293$	−12.5427	+	14.4750i	−0.732750	+	0.845639i	−0.992778	−	0.119962i	$-0.961723\pi$
$293$	−12.5427	+	14.4750i	−0.732750	+	0.845639i	0.260028	+	0.965601i	$0.416268\pi$
$294$		0			0
$295$	13.8188	−	30.2590i	0.804564	−	1.76175i
$296$	9.24506	+	10.6694i	0.537358	+	0.620144i
$297$		0			0
$298$	−6.23628			−0.361258
$299$	−0.909862	−	1.05004i	−0.0526187	−	0.0607252i
$300$		0			0
$301$	32.5521	−	9.55816i	1.87627	−	0.550923i
$302$	−25.8447	+	7.58868i	−1.48719	+	0.436680i
$303$		0			0
$304$	17.3671	+	20.0427i	0.996073	+	1.14953i
$305$	−7.00105			−0.400879
$306$		0			0
$307$	−10.0758	−	11.6281i	−0.575058	−	0.663653i	0.391477	−	0.920188i	$-0.371964\pi$
$307$	−10.0758	−	11.6281i	−0.575058	−	0.663653i	−0.966535	+	0.256535i	$0.917419\pi$
$308$	0.0740927	−	0.162240i	0.00422183	−	0.00924451i
$309$		0			0
$310$	13.1247	−	15.1467i	0.745433	−	0.860275i
$311$	22.1252	−	14.2190i	1.25460	−	0.806284i	0.267066	−	0.963678i	$-0.413946\pi$
$311$	22.1252	−	14.2190i	1.25460	−	0.806284i	0.987536	+	0.157394i	$0.0503093\pi$
$312$		0			0
$313$	−1.76597	−	12.2826i	−0.0998183	−	0.694252i	−0.976867	−	0.213850i	$-0.931400\pi$
$313$	−1.76597	−	12.2826i	−0.0998183	−	0.694252i	0.877048	−	0.480402i	$-0.159509\pi$
$314$	−5.64825	+	12.3679i	−0.318749	+	0.697964i
$315$		0			0
$316$	−0.655500	+	0.192472i	−0.0368747	+	0.0108274i
$317$	−7.03882	−	4.52358i	−0.395340	−	0.254069i	0.327834	−	0.944735i	$-0.393681\pi$
$317$	−7.03882	−	4.52358i	−0.395340	−	0.254069i	−0.723174	+	0.690666i	$0.757318\pi$
$318$		0			0
$319$	−0.0941028	−	0.206056i	−0.00526875	−	0.0115369i
$320$	−27.4227	+	8.05203i	−1.53297	+	0.450122i
$321$		0			0
$322$	5.18774	−	5.98697i	0.289101	−	0.333641i
$323$	−1.91755	+	2.21297i	−0.106695	+	0.123133i
$324$		0			0
$325$	−0.760652	−	5.29045i	−0.0421934	−	0.293461i
$326$	2.16473	+	0.635622i	0.119893	+	0.0352038i
$327$		0			0
$328$	−13.1032	−	3.84746i	−0.723505	−	0.212440i
$329$	2.91050	−	6.37311i	0.160461	−	0.351361i
$330$		0			0
$331$	13.7220	+	8.81860i	0.754230	+	0.484714i	0.860391	−	0.509635i	$-0.170219\pi$
$331$	13.7220	+	8.81860i	0.754230	+	0.484714i	−0.106161	+	0.994349i	$0.533856\pi$
$332$	−0.0442635	+	0.307859i	−0.00242927	+	0.0168960i
$333$		0			0
$334$	−16.0741			−0.879534
$335$	4.90261	−	26.1546i	0.267858	−	1.42898i
$336$		0			0
$337$	3.09315	+	0.908232i	0.168495	+	0.0494745i	0.364892	−	0.931050i	$-0.381106\pi$
$337$	3.09315	+	0.908232i	0.168495	+	0.0494745i	−0.196397	+	0.980524i	$0.562924\pi$
$338$	2.25139	−	15.6588i	0.122460	−	0.851726i
$339$		0			0
$340$	−0.142167	−	0.311303i	−0.00771010	−	0.0168828i
$341$	−0.293250	+	0.642127i	−0.0158804	+	0.0347732i
$342$		0			0
$343$	9.46465	+	10.9228i	0.511043	+	0.589775i
$344$	23.3112	+	6.84479i	1.25686	+	0.369046i
$345$		0			0
$346$	12.4419	+	27.2440i	0.668882	+	1.46465i
$347$	15.5953	−	17.9979i	0.837200	−	0.966180i	−0.162590	−	0.986694i	$-0.551985\pi$
$347$	15.5953	−	17.9979i	0.837200	−	0.966180i	0.999790	+	0.0205137i	$0.00653017\pi$
$348$		0			0
$349$	0.905143	+	0.581700i	0.0484512	+	0.0311377i	0.564642	−	0.825336i	$-0.309014\pi$
$349$	0.905143	+	0.581700i	0.0484512	+	0.0311377i	−0.516191	+	0.856474i	$0.672651\pi$
$350$	29.2402	−	8.58570i	1.56296	−	0.458925i
$351$		0			0
$352$	0.201513	−	0.129505i	0.0107407	−	0.00690262i
$353$	7.44594	+	4.78521i	0.396307	+	0.254691i	0.723583	−	0.690238i	$-0.242494\pi$
$353$	7.44594	+	4.78521i	0.396307	+	0.254691i	−0.327275	+	0.944929i	$0.606130\pi$
$354$		0			0
$355$	−2.71233	+	18.8647i	−0.143955	+	1.00123i
$356$	1.15405	−	2.52702i	0.0611646	−	0.133932i
$357$		0			0
$358$	−4.40718	+	30.6526i	−0.232927	+	1.62004i
$359$	6.47557	−	4.16160i	0.341768	−	0.219641i	−0.358486	−	0.933535i	$-0.616707\pi$
$359$	6.47557	−	4.16160i	0.341768	−	0.219641i	0.700253	+	0.713894i	$0.253070\pi$
$360$		0			0
$361$	36.7472	−	23.6160i	1.93406	−	1.24295i
$362$	−3.01435	+	6.60050i	−0.158431	+	0.346915i
$363$		0			0
$364$	1.14150			0.0598307
$365$	−22.3647			−1.17062
$366$		0			0
$367$	−0.886613	−	6.16653i	−0.0462808	−	0.321890i	−0.999789	−	0.0205241i	$-0.993467\pi$
$367$	−0.886613	−	6.16653i	−0.0462808	−	0.321890i	0.953509	−	0.301366i	$-0.0974426\pi$
$368$	4.65256	−	1.36612i	0.242532	−	0.0712137i
$369$		0			0
$370$	−2.85894	−	19.8844i	−0.148629	−	1.03374i
$371$	23.5387	+	27.1651i	1.22207	+	1.41034i
$372$		0			0
$373$	16.8774			0.873876			0.436938	−	0.899492i	$-0.356063\pi$
$373$	16.8774			0.873876			0.436938	+	0.899492i	$0.356063\pi$
$374$	−0.0475728	−	0.0549020i	−0.00245993	−	0.00283891i
$375$		0			0
$376$	4.22083	−	2.71256i	0.217673	−	0.139890i
$377$	0.949403	−	1.09567i	0.0488968	−	0.0564299i
$378$		0			0
$379$	0.320260	−	2.22746i	0.0164507	−	0.114417i	−0.979942	−	0.199285i	$-0.936138\pi$
$379$	0.320260	−	2.22746i	0.0164507	−	0.114417i	0.996392	+	0.0848685i	$0.0270470\pi$
$380$	1.04258	+	7.25131i	0.0534833	+	0.371984i
$381$		0			0
$382$	−3.82428	+	26.5985i	−0.195667	+	1.36090i
$383$	−18.5805	+	5.45572i	−0.949419	+	0.278774i	−0.719545	−	0.694446i	$-0.755650\pi$
$383$	−18.5805	+	5.45572i	−0.949419	+	0.278774i	−0.229874	+	0.973220i	$0.573831\pi$
$384$		0			0
$385$	−1.71376	+	1.10137i	−0.0873413	+	0.0561309i
$386$	7.95009	+	17.4083i	0.404649	+	0.886058i
$387$		0			0
$388$	0.825126	+	0.530276i	0.0418894	+	0.0269207i
$389$	5.19746	−	5.99819i	0.263522	−	0.304120i	−0.608533	−	0.793528i	$-0.708242\pi$
$389$	5.19746	−	5.99819i	0.263522	−	0.304120i	0.872055	+	0.489408i	$0.162787\pi$
$390$		0			0
$391$	0.222408	+	0.487005i	0.0112477	+	0.0246289i
$392$	4.45383	+	30.9771i	0.224952	+	1.56458i
$393$		0			0
$394$	−13.0879	−	15.1043i	−0.659360	−	0.760942i
$395$	7.48690	+	2.19835i	0.376707	+	0.110611i
$396$		0			0
$397$	−8.51036	−	18.6351i	−0.427123	−	0.935269i	−0.993785	−	0.111318i	$-0.964493\pi$
$397$	−8.51036	−	18.6351i	−0.427123	−	0.935269i	0.566662	−	0.823950i	$-0.308235\pi$
$398$	0.651602	+	0.418759i	0.0326619	+	0.0209905i
$399$		0			0
$400$	17.8979	+	5.25529i	0.894894	+	0.262765i
$401$	2.90066			0.144852			0.0724260	−	0.997374i	$-0.476926\pi$
$401$	2.90066			0.144852			0.0724260	+	0.997374i	$0.476926\pi$
$402$		0			0
$403$	−4.51790			−0.225053
$404$	−1.61339	−	0.473735i	−0.0802693	−	0.0235692i
$405$		0			0
$406$	6.95395	+	4.46903i	0.345119	+	0.221794i
$407$	0.293935	+	0.643629i	0.0145698	+	0.0319035i
$408$		0			0
$409$	−34.8618	−	10.2363i	−1.72380	−	0.506155i	−0.738108	−	0.674683i	$-0.764281\pi$
$409$	−34.8618	−	10.2363i	−1.72380	−	0.506155i	−0.985697	+	0.168528i	$0.946099\pi$
$410$	12.7256	+	14.6862i	0.628475	+	0.725299i
$411$		0			0
$412$	−0.292891	−	2.03710i	−0.0144297	−	0.100361i
$413$	−17.7611	−	38.8915i	−0.873969	−	1.91372i
$414$		0			0
$415$	2.32634	−	2.68474i	0.114196	−	0.131789i
$416$	1.28969	+	0.828832i	0.0632321	+	0.0406368i
$417$		0			0
$418$	0.646003	+	1.41455i	0.0315971	+	0.0691879i
$419$	−1.13476	+	0.729268i	−0.0554368	+	0.0356271i	−0.568066	−	0.822983i	$-0.692308\pi$
$419$	−1.13476	+	0.729268i	−0.0554368	+	0.0356271i	0.512629	+	0.858610i	$0.328672\pi$
$420$		0			0
$421$	−16.3978	+	4.81483i	−0.799180	+	0.234660i	−0.655728	−	0.754997i	$-0.727638\pi$
$421$	−16.3978	+	4.81483i	−0.799180	+	0.234660i	−0.143452	+	0.989657i	$0.545820\pi$
$422$	4.52387	−	31.4642i	0.220218	−	1.53165i
$423$		0			0
$424$	3.66327	+	25.4786i	0.177904	+	1.23735i
$425$	−0.293108	+	2.03861i	−0.0142178	+	0.0988872i
$426$		0			0
$427$	−5.89266	+	6.80049i	−0.285166	+	0.329099i
$428$	4.16061	−	2.67386i	0.201111	−	0.129246i
$429$		0			0
$430$	−22.6395	−	26.1273i	−1.09177	−	1.25997i
$431$	17.6493			0.850139			0.425069	−	0.905161i	$-0.360250\pi$
$431$	17.6493			0.850139			0.425069	+	0.905161i	$0.360250\pi$
$432$		0			0
$433$	−19.8037	−	22.8547i	−0.951705	−	1.09833i	−0.995061	−	0.0992667i	$-0.968350\pi$
$433$	−19.8037	−	22.8547i	−0.951705	−	1.09833i	0.0433556	−	0.999060i	$-0.486195\pi$
$434$	−3.66598	−	25.4974i	−0.175973	−	1.22392i
$435$		0			0
$436$	1.04703	−	0.307435i	0.0501435	−	0.0147235i
$437$	−1.63103	−	11.3440i	−0.0780226	−	0.542659i
$438$		0			0
$439$	−12.0530			−0.575258			−0.287629	−	0.957742i	$-0.592867\pi$
$439$	−12.0530			−0.575258			−0.287629	+	0.957742i	$0.592867\pi$
$440$	−1.45884			−0.0695476
$441$		0			0
$442$	0.193141	−	0.422919i	0.00918676	−	0.0201162i
$443$	−15.2556	+	9.80417i	−0.724815	+	0.465810i	−0.850309	−	0.526284i	$-0.823585\pi$
$443$	−15.2556	+	9.80417i	−0.724815	+	0.465810i	0.125494	+	0.992094i	$0.459948\pi$
$444$		0			0
$445$	−26.6931	+	17.1546i	−1.26538	+	0.813208i
$446$	−2.32531	+	16.1729i	−0.110107	+	0.765809i
$447$		0			0
$448$	−15.2598	+	33.4144i	−0.720959	+	1.57868i
$449$	1.09793	−	7.63630i	0.0518147	−	0.360379i	−0.947375	−	0.320126i	$-0.896275\pi$
$449$	1.09793	−	7.63630i	0.0518147	−	0.360379i	0.999190	−	0.0402528i	$-0.0128163\pi$
$450$		0			0
$451$	−0.575802	−	0.370045i	−0.0271134	−	0.0174248i
$452$	−2.06079	+	1.32439i	−0.0969314	+	0.0622940i
$453$		0			0
$454$	−2.83482	+	0.832379i	−0.133045	+	0.0390655i
$455$	−10.9681	−	7.04877i	−0.514192	−	0.330451i
$456$		0			0
$457$	−11.0018	+	12.6968i	−0.514643	+	0.593929i	−0.952281	−	0.305222i	$-0.901269\pi$
$457$	−11.0018	+	12.6968i	−0.514643	+	0.593929i	0.437639	+	0.899151i	$0.355815\pi$
$458$	−3.55665	−	7.78798i	−0.166191	−	0.363908i
$459$		0			0
$460$	1.28521	+	0.377371i	0.0599231	+	0.0175950i
$461$	−13.2423	−	15.2824i	−0.616756	−	0.711774i	0.358332	−	0.933594i	$-0.383346\pi$
$461$	−13.2423	−	15.2824i	−0.616756	−	0.711774i	−0.975088	+	0.221820i	$0.928800\pi$
$462$		0			0
$463$	−3.76850	+	8.25186i	−0.175137	+	0.383496i	−0.976761	−	0.214332i	$-0.931242\pi$
$463$	−3.76850	+	8.25186i	−0.175137	+	0.383496i	0.801624	+	0.597829i	$0.203970\pi$
$464$	2.10188	+	4.60248i	0.0975774	+	0.213665i
$465$		0			0
$466$	1.64382	−	11.4330i	0.0761485	−	0.529624i
$467$	−20.7777	−	6.10089i	−0.961479	−	0.282316i	−0.236920	−	0.971529i	$-0.576138\pi$
$467$	−20.7777	−	6.10089i	−0.961479	−	0.282316i	−0.724558	+	0.689214i	$0.757956\pi$
$468$		0			0
$469$	−21.2789	−	26.7761i	−0.982570	−	1.23640i
$470$	−7.13946			−0.329319
$471$		0			0
$472$	4.35737	−	30.3062i	0.200564	−	1.39495i
$473$	1.02438	+	0.658326i	0.0471008	+	0.0302699i
$474$		0			0
$475$	18.3148	−	40.1038i	0.840341	−	1.84009i
$476$	−0.422045	−	0.123923i	−0.0193444	−	0.00568002i
$477$		0			0
$478$	−33.4346	−	9.81730i	−1.52926	−	0.449033i
$479$	−3.05707	−	21.2624i	−0.139681	−	0.971503i	−0.932274	−	0.361752i	$-0.882179\pi$
$479$	−3.05707	−	21.2624i	−0.139681	−	0.971503i	0.792593	−	0.609751i	$-0.208730\pi$
$480$		0			0
$481$	−2.96551	+	3.42239i	−0.135216	+	0.156047i
$482$	−0.406551	+	0.469184i	−0.0185179	+	0.0213708i
$483$		0			0
$484$	−2.99796	+	0.880280i	−0.136271	+	0.0400127i
$485$	−4.65378	−	10.1903i	−0.211317	−	0.462720i
$486$		0			0
$487$	30.2917	+	19.4673i	1.37265	+	0.882147i	0.998968	−	0.0454110i	$-0.0144597\pi$
$487$	30.2917	+	19.4673i	1.37265	+	0.882147i	0.373679	+	0.927558i	$0.378096\pi$
$488$	−6.18287	+	1.81545i	−0.279885	+	0.0821817i
$489$		0			0
$490$	18.4995	−	40.5082i	0.835722	−	1.82998i
$491$	−1.14805	−	7.98487i	−0.0518108	−	0.360352i	−0.999190	−	0.0402388i	$-0.987188\pi$
$491$	−1.14805	−	7.98487i	−0.0518108	−	0.360352i	0.947379	−	0.320113i	$-0.103721\pi$
$492$		0			0
$493$	−0.469970	+	0.302032i	−0.0211664	+	0.0136028i
$494$	−6.51753	+	7.52163i	−0.293237	+	0.338414i
$495$		0			0
$496$	6.55003	−	14.3426i	0.294105	−	0.644000i
$497$	16.0413	+	18.5127i	0.719552	+	0.830407i
$498$		0			0
$499$	18.9071			0.846398			0.423199	−	0.906037i	$-0.360907\pi$
$499$	18.9071			0.846398			0.423199	+	0.906037i	$0.360907\pi$
$500$	0.344581	+	0.397668i	0.0154101	+	0.0177842i
$501$		0			0
$502$	−33.1892	+	9.74523i	−1.48131	+	0.434951i
$503$	−26.9003	+	7.89864i	−1.19942	+	0.352183i	−0.819633	−	0.572889i	$-0.805823\pi$
$503$	−26.9003	+	7.89864i	−1.19942	+	0.352183i	−0.379792	+	0.925072i	$0.624004\pi$
$504$		0			0
$505$	12.5770	+	14.5146i	0.559669	+	0.645892i
$506$	0.284331			0.0126400
$507$		0			0
$508$	−2.73670	−	3.15832i	−0.121421	−	0.140128i
$509$	−3.23092	+	7.07473i	−0.143208	+	0.313582i	−0.967621	−	0.252407i	$-0.918778\pi$
$509$	−3.23092	+	7.07473i	−0.143208	+	0.313582i	0.824413	+	0.565988i	$0.191505\pi$
$510$		0			0
$511$	−18.8240	+	21.7240i	−0.832723	+	0.961014i
$512$	−21.3650	+	13.7305i	−0.944209	+	0.606806i
$513$		0			0
$514$	−1.91575	−	13.3243i	−0.0845001	−	0.587711i
$515$	−9.76491	+	21.3822i	−0.430293	+	0.942211i
$516$		0			0
$517$	0.241280	−	0.0708463i	0.0106115	−	0.00311582i
$518$	−21.7211	−	13.9593i	−0.954368	−	0.613335i
$519$		0			0
$520$	−3.87857	−	8.49289i	−0.170087	−	0.372438i
$521$	19.7764	−	5.80687i	0.866419	−	0.254404i	0.181827	−	0.983330i	$-0.441799\pi$
$521$	19.7764	−	5.80687i	0.866419	−	0.254404i	0.684591	+	0.728927i	$0.259981\pi$
$522$		0			0
$523$	22.7837	−	26.2938i	0.996262	−	1.14975i	0.00754216	−	0.999972i	$-0.497599\pi$
$523$	22.7837	−	26.2938i	0.996262	−	1.14975i	0.988720	−	0.149776i	$-0.0478553\pi$
$524$	−0.526314	+	0.607398i	−0.0229921	+	0.0265343i
$525$		0			0
$526$	1.88254	+	13.0934i	0.0820829	+	0.570899i
$527$	1.67040	+	0.490474i	0.0727638	+	0.0213654i
$528$		0			0
$529$	20.0577	+	5.88949i	0.872076	+	0.256065i
$530$	15.2158	−	33.3180i	0.660933	−	1.44724i
$531$		0			0
$532$	7.92111	+	5.09059i	0.343424	+	0.220705i
$533$	0.623415	−	4.33595i	0.0270031	−	0.187811i
$534$		0			0
$535$	−56.4885			−2.44221
$536$	−2.45253	−	24.3693i	−0.105933	−	1.05260i
$537$		0			0
$538$	26.8895	+	7.89547i	1.15929	+	0.340398i
$539$	−0.223225	+	1.55256i	−0.00961498	+	0.0668737i
$540$		0			0
$541$	15.8597	+	34.7279i	0.681862	+	1.49307i	0.860658	+	0.509183i	$0.170052\pi$
$541$	15.8597	+	34.7279i	0.681862	+	1.49307i	−0.178796	+	0.983886i	$0.557220\pi$
$542$	3.12138	−	6.83488i	0.134075	−	0.293583i
$543$		0			0
$544$	−0.386855	−	0.446455i	−0.0165863	−	0.0191416i
$545$	−11.9588	−	3.51142i	−0.512259	−	0.150413i
$546$		0			0
$547$	−12.5108	−	27.3949i	−0.534925	−	1.17132i	−0.963474	−	0.267803i	$-0.913702\pi$
$547$	−12.5108	−	27.3949i	−0.534925	−	1.17132i	0.428549	−	0.903519i	$-0.359025\pi$
$548$	1.06773	−	1.23223i	0.0456112	−	0.0526382i
$549$		0			0
$550$	0.920154	+	0.591347i	0.0392355	+	0.0252151i
$551$	11.4743	−	3.36917i	0.488824	−	0.143532i
$552$		0			0
$553$	8.43697	−	5.42211i	0.358777	−	0.230572i
$554$	3.92993	+	2.52561i	0.166967	+	0.107303i
$555$		0			0
$556$	−0.885749	+	6.16052i	−0.0375641	+	0.261264i
$557$	7.60418	−	16.6508i	0.322199	−	0.705518i	−0.677346	−	0.735665i	$-0.736870\pi$
$557$	7.60418	−	16.6508i	0.322199	−	0.705518i	0.999545	+	0.0301462i	$0.00959730\pi$
$558$		0			0
$559$	−1.10908	+	7.71383i	−0.0469092	+	0.326260i
$560$	38.2786	−	24.6001i	1.61756	−	1.03955i
$561$		0			0
$562$	26.7604	−	17.1979i	1.12882	−	0.725449i
$563$	15.0080	−	32.8630i	0.632512	−	1.38501i	−0.273547	−	0.961859i	$-0.588197\pi$
$563$	15.0080	−	32.8630i	0.632512	−	1.38501i	0.906060	−	0.423150i	$-0.139076\pi$
$564$		0			0
$565$	27.9793			1.17710
$566$	7.24957			0.304722
$567$		0			0
$568$	2.49647	+	17.3634i	0.104750	+	0.728550i
$569$	−16.4694	+	4.83585i	−0.690433	+	0.202730i	−0.608082	−	0.793874i	$-0.708061\pi$
$569$	−16.4694	+	4.83585i	−0.690433	+	0.202730i	−0.0823509	+	0.996603i	$0.526243\pi$
$570$		0			0
$571$	−1.12976	−	7.85769i	−0.0472792	−	0.328834i	−0.999710	−	0.0240792i	$-0.992335\pi$
$571$	−1.12976	−	7.85769i	−0.0472792	−	0.328834i	0.952431	−	0.304755i	$-0.0985745\pi$
$572$	0.0268299	+	0.0309633i	0.00112181	+	0.00129464i
$573$		0			0
$574$	24.9764			1.04250
$575$	−5.27887	−	6.09214i	−0.220144	−	0.254060i
$576$		0			0
$577$	9.74594	−	6.26333i	0.405729	−	0.260746i	−0.321822	−	0.946800i	$-0.604295\pi$
$577$	9.74594	−	6.26333i	0.405729	−	0.260746i	0.727550	+	0.686054i	$0.240659\pi$
$578$	14.4633	−	16.6916i	0.601595	−	0.694278i
$579$		0			0
$580$	−0.198910	+	1.38345i	−0.00825929	+	0.0574446i
$581$	−0.649792	−	4.51940i	−0.0269579	−	0.187496i
$582$		0			0
$583$	−0.183602	+	1.27698i	−0.00760403	+	0.0528872i
$584$	−19.7510	+	5.79942i	−0.817303	+	0.239982i
$585$		0			0
$586$	21.1031	−	13.5622i	0.871762	−	0.560247i
$587$	−2.72713	−	5.97159i	−0.112561	−	0.246474i	0.844965	−	0.534822i	$-0.179621\pi$
$587$	−2.72713	−	5.97159i	−0.112561	−	0.246474i	−0.957526	+	0.288348i	$0.906894\pi$
$588$		0			0
$589$	−31.3508	−	20.1479i	−1.29179	−	0.830180i
$590$	−28.5310	+	32.9266i	−1.17460	+	1.35556i
$591$		0			0
$592$	−6.56534	−	14.3761i	−0.269834	−	0.590854i
$593$	0.145444	+	1.01158i	0.00597265	+	0.0415407i	0.992590	−	0.121513i	$-0.0387747\pi$
$593$	0.145444	+	1.01158i	0.00597265	+	0.0415407i	−0.986617	+	0.163054i	$0.947866\pi$
$594$		0			0
$595$	3.28999	+	3.79686i	0.134877	+	0.155656i
$596$	−1.30037	−	0.381824i	−0.0532654	−	0.0156401i
$597$		0			0
$598$	0.755940	+	1.65528i	0.0309127	+	0.0676894i
$599$	−4.26028	−	2.73792i	−0.174070	−	0.111868i	0.450704	−	0.892673i	$-0.351173\pi$
$599$	−4.26028	−	2.73792i	−0.174070	−	0.111868i	−0.624775	+	0.780805i	$0.714809\pi$
$600$		0			0
$601$	−25.5526	−	7.50293i	−1.04231	−	0.306051i	−0.284605	−	0.958645i	$-0.591863\pi$
$601$	−25.5526	−	7.50293i	−1.04231	−	0.306051i	−0.757708	+	0.652594i	$0.773681\pi$
$602$	−44.4341			−1.81100
$603$		0			0
$604$	−5.85370			−0.238184
$605$	34.2417	+	10.0543i	1.39212	+	0.408764i
$606$		0			0
$607$	36.8178	+	23.6614i	1.49439	+	0.960386i	0.995604	+	0.0936600i	$0.0298567\pi$
$607$	36.8178	+	23.6614i	1.49439	+	0.960386i	0.498785	+	0.866726i	$0.333780\pi$
$608$	5.25320	+	11.5029i	0.213046	+	0.466505i
$609$		0			0
$610$	8.79800	+	2.58333i	0.356221	+	0.104596i
$611$	1.05393	+	1.21630i	0.0426373	+	0.0492061i
$612$		0			0
$613$	−0.107256	−	0.745982i	−0.00433203	−	0.0301299i	0.987541	−	0.157363i	$-0.0502994\pi$
$613$	−0.107256	−	0.745982i	−0.00433203	−	0.0301299i	−0.991873	+	0.127233i	$0.959390\pi$
$614$	8.37131	+	18.3306i	0.337838	+	0.739763i
$615$		0			0
$616$	−1.22788	+	1.41705i	−0.0494728	+	0.0570947i
$617$	8.00617	+	5.14525i	0.322316	+	0.207140i	0.691786	−	0.722103i	$-0.256824\pi$
$617$	8.00617	+	5.14525i	0.322316	+	0.207140i	−0.369470	+	0.929243i	$0.620461\pi$
$618$		0			0
$619$	−5.62194	−	12.3103i	−0.225965	−	0.494794i	0.762360	−	0.647153i	$-0.224040\pi$
$619$	−5.62194	−	12.3103i	−0.225965	−	0.494794i	−0.988325	+	0.152359i	$0.951313\pi$
$620$	3.66411	−	2.35478i	0.147154	−	0.0945703i
$621$		0			0
$622$	−33.0507	+	9.70455i	−1.32521	+	0.389117i
$623$	−5.80393	+	40.3672i	−0.232530	+	1.61728i
$624$		0			0
$625$	3.10721	+	21.6111i	0.124288	+	0.864444i
$626$	−2.31292	+	16.0867i	−0.0924431	+	0.642956i
$627$		0			0
$628$	−1.93501	+	2.23312i	−0.0772151	+	0.0891110i
$629$	1.46798	−	0.943413i	0.0585321	−	0.0376163i
$630$		0			0
$631$	11.3588	+	13.1087i	0.452185	+	0.521849i	0.935371	−	0.353668i	$-0.115066\pi$
$631$	11.3588	+	13.1087i	0.452185	+	0.521849i	−0.483186	+	0.875518i	$0.660520\pi$
$632$	7.18200			0.285684
$633$		0			0
$634$	7.17631	+	8.28190i	0.285008	+	0.328916i
$635$	6.79294	+	47.2460i	0.269570	+	1.87490i
$636$		0			0
$637$	−9.63199	+	2.82821i	−0.381633	+	0.112058i
$638$	0.0422231	+	0.293668i	0.00167163	+	0.0116264i
$639$		0			0
$640$	27.0472			1.06913
$641$	24.4921			0.967379			0.483689	−	0.875240i	$-0.339296\pi$
$641$	24.4921			0.967379			0.483689	+	0.875240i	$0.339296\pi$
$642$		0			0
$643$	10.4440	−	22.8692i	0.411872	−	0.901873i	−0.584055	−	0.811714i	$-0.698535\pi$
$643$	10.4440	−	22.8692i	0.411872	−	0.901873i	0.995927	−	0.0901598i	$-0.0287378\pi$
$644$	1.44830	−	0.930764i	0.0570709	−	0.0366772i
$645$		0			0
$646$	3.22628	−	2.07341i	0.126936	−	0.0815771i
$647$	−1.01574	+	7.06463i	−0.0399329	+	0.277739i	−0.999998	−	0.00203756i	$-0.999351\pi$
$647$	−1.01574	+	7.06463i	−0.0399329	+	0.277739i	0.960065	+	0.279777i	$0.0902605\pi$
$648$		0			0
$649$	0.637479	−	1.39588i	0.0250232	−	0.0547932i
$650$	−0.996243	+	6.92902i	−0.0390758	+	0.271778i
$651$		0			0
$652$	0.412468	+	0.265077i	0.0161535	+	0.0103812i
$653$	−17.3894	+	11.1755i	−0.680500	+	0.437331i	−0.834697	−	0.550710i	$-0.814357\pi$
$653$	−17.3894	+	11.1755i	−0.680500	+	0.437331i	0.154197	+	0.988040i	$0.450721\pi$
$654$		0			0
$655$	8.80780	−	2.58620i	0.344149	−	0.101051i
$656$	12.8611	+	8.26533i	0.502142	+	0.322707i
$657$		0			0
$658$	−6.00916	+	6.93494i	−0.234261	+	0.270352i
$659$	0.794947	+	1.74069i	0.0309667	+	0.0678077i	0.924483	−	0.381223i	$-0.124497\pi$
$659$	0.794947	+	1.74069i	0.0309667	+	0.0678077i	−0.893517	+	0.449030i	$0.851770\pi$
$660$		0			0
$661$	45.1174	+	13.2477i	1.75486	+	0.515275i	0.991433	−	0.130614i	$-0.0416949\pi$
$661$	45.1174	+	13.2477i	1.75486	+	0.515275i	0.763431	+	0.645889i	$0.223513\pi$
$662$	−13.9900	−	16.1454i	−0.543738	−	0.627507i
$663$		0			0
$664$	1.35829	−	2.97424i	0.0527118	−	0.115423i
$665$	−44.6757	−	97.8261i	−1.73245	−	3.79353i
$666$		0			0
$667$	0.311177	−	2.16429i	0.0120488	−	0.0838015i
$668$	−3.35173	−	0.984157i	−0.129682	−	0.0380782i
$669$		0			0
$670$	−15.8118	+	31.0587i	−0.610863	+	1.19990i
$671$	−0.322966			−0.0124680
$672$		0			0
$673$	1.41109	−	9.81436i	0.0543936	−	0.378316i	−0.944382	−	0.328850i	$-0.893339\pi$
$673$	1.41109	−	9.81436i	0.0543936	−	0.378316i	0.998776	−	0.0494659i	$-0.0157519\pi$
$674$	−3.55194	−	2.28269i	−0.136816	−	0.0879260i
$675$		0			0
$676$	1.42819	−	3.12729i	0.0549302	−	0.120280i
$677$	25.9152	+	7.60940i	0.996003	+	0.292453i	0.738815	−	0.673909i	$-0.235386\pi$
$677$	25.9152	+	7.60940i	0.996003	+	0.292453i	0.257188	+	0.966361i	$0.417204\pi$
$678$		0			0
$679$	−13.8154	−	4.05658i	−0.530188	−	0.155677i
$680$	0.512014	+	3.56114i	0.0196348	+	0.136563i
$681$		0			0
$682$	0.605457	−	0.698735i	0.0231842	−	0.0267559i
$683$	−1.95234	+	2.25312i	−0.0747041	+	0.0862131i	−0.791871	−	0.610688i	$-0.790893\pi$
$683$	−1.95234	+	2.25312i	−0.0747041	+	0.0862131i	0.717167	+	0.696901i	$0.245438\pi$
$684$		0			0
$685$	−17.8684	+	5.24662i	−0.682715	+	0.200463i
$686$	−7.86352	−	17.2187i	−0.300230	−	0.657413i
$687$		0			0
$688$	−22.8804	−	14.7044i	−0.872309	−	0.560599i
$689$	−7.92230	+	2.32620i	−0.301816	+	0.0886210i
$690$		0			0
$691$	9.72563	−	21.2962i	0.369980	−	0.810144i	−0.629471	−	0.777024i	$-0.716728\pi$
$691$	9.72563	−	21.2962i	0.369980	−	0.810144i	0.999451	−	0.0331202i	$-0.0105444\pi$
$692$	0.926311	+	6.44264i	0.0352131	+	0.244912i
$693$		0			0
$694$	−26.2392	+	16.8629i	−0.996027	+	0.640108i
$695$	46.5521	−	53.7240i	1.76582	−	2.03787i
$696$		0			0
$697$	−0.701215	+	1.53545i	−0.0265604	+	0.0581592i
$698$	−0.922823	−	1.06499i	−0.0349294	−	0.0403106i
$699$		0			0
$700$	6.62278			0.250317
$701$	14.3262	+	16.5334i	0.541095	+	0.624457i	0.958785	−	0.284133i	$-0.0917057\pi$
$701$	14.3262	+	16.5334i	0.541095	+	0.624457i	−0.417690	+	0.908590i	$0.637160\pi$
$702$		0			0
$703$	−35.8408	+	10.5238i	−1.35176	+	0.396912i
$704$	−1.26504	+	0.371449i	−0.0476780	+	0.0139995i
$705$		0			0
$706$	−7.59138	−	8.76091i	−0.285705	−	0.329721i
$707$	24.6847			0.928362
$708$		0			0
$709$	29.2614	+	33.7694i	1.09893	+	1.26824i	0.960625	+	0.277849i	$0.0896215\pi$
$709$	29.2614	+	33.7694i	1.09893	+	1.26824i	0.138310	+	0.990389i	$0.455833\pi$
$710$	10.3694	−	22.7058i	0.389156	−	0.852133i
$711$		0			0
$712$	−19.1252	+	22.0717i	−0.716748	+	0.827171i
$713$	−5.73218	+	3.68385i	−0.214672	+	0.137961i
$714$		0			0
$715$	−0.0665962	−	0.463187i	−0.00249056	−	0.0173222i
$716$	−2.79572	+	6.12177i	−0.104481	+	0.228781i
$717$		0			0
$718$	−9.67324	+	2.84032i	−0.361002	+	0.106000i
$719$	−9.93837	−	6.38700i	−0.370639	−	0.238195i	0.342040	−	0.939685i	$-0.388882\pi$
$719$	−9.93837	−	6.38700i	−0.370639	−	0.238195i	−0.712679	+	0.701490i	$0.752518\pi$
$720$		0			0
$721$	12.5507	+	27.4822i	0.467412	+	1.02349i
$722$	−54.8931	+	16.1181i	−2.04291	+	0.599853i
$723$		0			0
$724$	−1.03267	+	1.19176i	−0.0383789	+	0.0442916i
$725$	5.50828	−	6.35690i	0.204572	−	0.236089i
$726$		0			0
$727$	−0.347481	−	2.41678i	−0.0128874	−	0.0896336i	0.982363	−	0.186986i	$-0.0598718\pi$
$727$	−0.347481	−	2.41678i	−0.0128874	−	0.0896336i	−0.995250	+	0.0973521i	$0.968963\pi$
$728$	−11.5141	−	3.38085i	−0.426742	−	0.125303i
$729$		0			0
$730$	28.1050	+	8.25237i	1.04021	+	0.305434i
$731$	1.24749	−	2.73162i	0.0461401	−	0.101033i
$732$		0			0
$733$	10.9932	+	7.06489i	0.406043	+	0.260948i	0.727682	−	0.685914i	$-0.240598\pi$
$733$	10.9932	+	7.06489i	0.406043	+	0.260948i	−0.321640	+	0.946862i	$0.604234\pi$
$734$	−1.16122	+	8.07643i	−0.0428612	+	0.298107i
$735$		0			0
$736$	2.31214			0.0852265
$737$	0.226163	−	1.20654i	0.00833083	−	0.0444436i
$738$		0			0
$739$	−17.2305	−	5.05934i	−0.633835	−	0.186111i	−0.0509966	−	0.998699i	$-0.516240\pi$
$739$	−17.2305	−	5.05934i	−0.633835	−	0.186111i	−0.582838	+	0.812588i	$0.698058\pi$
$740$	0.621307	−	4.32128i	0.0228397	−	0.158854i
$741$		0			0
$742$	−19.5567	−	42.8231i	−0.717947	−	1.57209i
$743$	−10.3360	+	22.6328i	−0.379193	+	0.830317i	0.619770	+	0.784784i	$0.287226\pi$
$743$	−10.3360	+	22.6328i	−0.379193	+	0.830317i	−0.998963	+	0.0455330i	$0.985501\pi$
$744$		0			0
$745$	10.1369	+	11.6986i	0.371387	+	0.428604i
$746$	−21.2092	−	6.22759i	−0.776525	−	0.228008i
$747$		0			0
$748$	−0.00655833	−	0.0143607i	−0.000239796	−	0.000525081i
$749$	−47.5454	+	54.8703i	−1.73727	+	2.00492i
$750$		0			0
$751$	13.6348	+	8.76256i	0.497541	+	0.319751i	0.765232	−	0.643754i	$-0.222624\pi$
$751$	13.6348	+	8.76256i	0.497541	+	0.319751i	−0.267691	+	0.963505i	$0.586261\pi$
$752$	−5.38924	+	1.58242i	−0.196525	+	0.0577051i
$753$		0			0
$754$	−1.59738	+	1.02657i	−0.0581731	+	0.0373856i
$755$	56.2454	+	36.1468i	2.04698	+	1.31552i
$756$		0			0
$757$	3.61924	−	25.1724i	0.131544	−	0.914906i	−0.812000	−	0.583658i	$-0.801621\pi$
$757$	3.61924	−	25.1724i	0.131544	−	0.914906i	0.943544	−	0.331249i	$-0.107470\pi$
$758$	−1.22437	+	2.68100i	−0.0444712	+	0.0973784i
$759$		0			0
$760$	10.9604	−	76.2309i	0.397574	−	2.76519i
$761$	29.4607	−	18.9332i	1.06795	−	0.686329i	0.116206	−	0.993225i	$-0.462927\pi$
$761$	29.4607	−	18.9332i	1.06795	−	0.686329i	0.951743	+	0.306896i	$0.0992903\pi$
$762$		0			0
$763$	−13.4763	+	8.66072i	−0.487876	+	0.313539i
$764$	−2.42596	+	5.31210i	−0.0877680	+	0.192185i
$765$		0			0
$766$	25.3626			0.916389
$767$	9.82120			0.354623
$768$		0			0
$769$	1.41852	+	9.86605i	0.0511533	+	0.355779i	0.999282	+	0.0378917i	$0.0120642\pi$
$769$	1.41852	+	9.86605i	0.0511533	+	0.355779i	−0.948129	+	0.317887i	$0.897027\pi$
$770$	2.56002	−	0.751691i	0.0922568	−	0.0270891i
$771$		0			0
$772$	0.591890	+	4.11669i	0.0213026	+	0.148163i
$773$	−31.9798	−	36.9067i	−1.15023	−	1.32744i	−0.936549	−	0.350537i	$-0.885999\pi$
$773$	−31.9798	−	36.9067i	−1.15023	−	1.32744i	−0.213684	−	0.976903i	$-0.568546\pi$
$774$		0			0
$775$	−26.2121			−0.941567
$776$	−6.75238	−	7.79267i	−0.242396	−	0.279740i
$777$		0			0
$778$	−8.74476	+	5.61991i	−0.313515	+	0.201484i
$779$	23.6625	−	27.3080i	0.847797	−	0.978410i
$780$		0			0
$781$	−0.125123	+	0.870248i	−0.00447724	+	0.0311399i
$782$	−0.0997924	−	0.694071i	−0.00356857	−	0.0248199i
$783$		0			0
$784$	4.98595	−	34.6781i	0.178070	−	1.23850i
$785$	32.3821	−	9.50824i	1.15577	−	0.339364i
$786$		0			0
$787$	−37.6038	+	24.1665i	−1.34043	+	0.861442i	−0.996975	−	0.0777271i	$-0.975234\pi$
$787$	−37.6038	+	24.1665i	−1.34043	+	0.861442i	−0.343455	+	0.939169i	$0.611597\pi$
$788$	−1.80429	−	3.95084i	−0.0642750	−	0.140743i
$789$		0			0
$790$	−8.59738	−	5.52520i	−0.305881	−	0.196578i
$791$	23.5497	−	27.1778i	0.837330	−	0.966330i
$792$		0			0
$793$	−0.858659	−	1.88020i	−0.0304919	−	0.0667679i
$794$	3.81852	+	26.5584i	0.135514	+	0.942522i
$795$		0			0
$796$	0.110232	+	0.127214i	0.00390705	+	0.00450898i
$797$	−34.9900	−	10.2740i	−1.23941	−	0.363924i	−0.404617	−	0.914486i	$-0.632595\pi$
$797$	−34.9900	−	10.2740i	−1.23941	−	0.363924i	−0.834794	+	0.550563i	$0.814413\pi$
$798$		0			0
$799$	−0.257624	−	0.564117i	−0.00911407	−	0.0199570i
$800$	7.48256	+	4.80875i	0.264548	+	0.170015i
$801$		0			0
$802$	−3.64517	−	1.07032i	−0.128715	−	0.0377942i
$803$	−1.03171			−0.0364082
$804$		0			0
$805$	−19.6635			−0.693046
$806$	5.67751	+	1.66707i	0.199982	+	0.0587199i
$807$		0			0
$808$	14.8710	+	9.55700i	0.523159	+	0.336214i
$809$	12.2760	+	26.8806i	0.431599	+	0.945071i	0.993065	+	0.117571i	$0.0375106\pi$
$809$	12.2760	+	26.8806i	0.431599	+	0.945071i	−0.561465	+	0.827500i	$0.689762\pi$
$810$		0			0
$811$	−36.8081	−	10.8078i	−1.29251	−	0.379514i	−0.438009	−	0.898971i	$-0.644316\pi$
$811$	−36.8081	−	10.8078i	−1.29251	−	0.379514i	−0.854497	+	0.519457i	$0.826134\pi$
$812$	1.17640	+	1.35764i	0.0412835	+	0.0476437i
$813$		0			0
$814$	−0.131886	−	0.917288i	−0.00462260	−	0.0321509i
$815$	−2.32635	−	5.09400i	−0.0814885	−	0.178435i
$816$		0			0
$817$	−42.0966	+	48.5820i	−1.47277	+	1.69967i
$818$	40.0326	+	25.7274i	1.39971	+	0.899537i
$819$		0			0
$820$	1.75434	+	3.84147i	0.0612643	+	0.134150i
$821$	−30.1186	+	19.3561i	−1.05115	+	0.675532i	−0.947719	−	0.319105i	$-0.896618\pi$
$821$	−30.1186	+	19.3561i	−1.05115	+	0.675532i	−0.103428	+	0.994637i	$0.532981\pi$
$822$		0			0
$823$	25.9858	−	7.63012i	0.905808	−	0.265969i	0.204532	−	0.978860i	$-0.434433\pi$
$823$	25.9858	−	7.63012i	0.905808	−	0.265969i	0.701275	+	0.712891i	$0.252614\pi$
$824$	−3.07908	+	21.4155i	−0.107265	+	0.746043i
$825$		0			0
$826$	7.96926	+	55.4274i	0.277286	+	1.92857i
$827$	−2.37423	+	16.5131i	−0.0825600	+	0.574218i	0.905987	+	0.423305i	$0.139130\pi$
$827$	−2.37423	+	16.5131i	−0.0825600	+	0.574218i	−0.988547	+	0.150912i	$0.951779\pi$
$828$		0			0
$829$	26.2213	−	30.2610i	0.910704	−	1.05101i	−0.0877890	−	0.996139i	$-0.527980\pi$
$829$	26.2213	−	30.2610i	0.910704	−	1.05101i	0.998494	−	0.0548699i	$-0.0174744\pi$
$830$	−3.91409	+	2.51543i	−0.135860	+	0.0873119i
$831$		0			0
$832$	−5.52577	−	6.37707i	−0.191571	−	0.221085i
$833$	3.86826			0.134027
$834$		0			0
$835$	26.1280	+	30.1533i	0.904196	+	1.04350i
$836$	0.0480954	+	0.334511i	0.00166342	+	0.0115693i
$837$		0			0
$838$	1.69511	−	0.497730i	0.0585567	−	0.0171938i
$839$	2.49430	+	17.3482i	0.0861127	+	0.598927i	0.986491	+	0.163818i	$0.0523810\pi$
$839$	2.49430	+	17.3482i	0.0861127	+	0.598927i	−0.900378	+	0.435109i	$0.856710\pi$
$840$		0			0
$841$	−26.7184			−0.921325
$842$	22.3832			0.771377
$843$		0			0
$844$	2.86974	−	6.28386i	0.0987807	−	0.216299i
$845$	−33.0339	+	21.2296i	−1.13640	+	0.730320i
$846$		0			0
$847$	38.5869	−	24.7983i	1.32586	−	0.852080i
$848$	4.10094	−	28.5227i	0.140827	−	0.979473i
$849$		0			0
$850$	1.12057	−	2.45371i	0.0384352	−	0.0841614i
$851$	−0.971979	+	6.76027i	−0.0333190	+	0.231739i
$852$		0			0
$853$	−13.2261	−	8.49991i	−0.452853	−	0.291031i	0.294263	−	0.955725i	$-0.404926\pi$
$853$	−13.2261	−	8.49991i	−0.452853	−	0.291031i	−0.747116	+	0.664693i	$0.768562\pi$
$854$	9.91444	−	6.37163i	0.339265	−	0.218033i
$855$		0			0
$856$	−49.8869	+	14.6481i	−1.70510	+	0.500663i
$857$	−27.6728	−	17.7842i	−0.945285	−	0.607498i	−0.0253964	−	0.999677i	$-0.508085\pi$
$857$	−27.6728	−	17.7842i	−0.945285	−	0.607498i	−0.919889	+	0.392180i	$0.871721\pi$
$858$		0			0
$859$	−6.76834	+	7.81108i	−0.230933	+	0.266511i	−0.859375	−	0.511345i	$-0.829147\pi$
$859$	−6.76834	+	7.81108i	−0.230933	+	0.266511i	0.628443	+	0.777856i	$0.283693\pi$
$860$	−3.12105	−	6.83414i	−0.106427	−	0.233042i
$861$		0			0
$862$	−22.1794	−	6.51245i	−0.755432	−	0.221815i
$863$	22.4558	+	25.9153i	0.764403	+	0.882169i	0.995881	−	0.0906716i	$-0.0289014\pi$
$863$	22.4558	+	25.9153i	0.764403	+	0.882169i	−0.231477	+	0.972840i	$0.574356\pi$
$864$		0			0
$865$	30.8829	−	67.6242i	1.05005	−	2.29929i
$866$	16.4535	+	36.0282i	0.559113	+	1.22429i
$867$		0			0
$868$	0.796693	−	5.54112i	0.0270415	−	0.188078i
$869$	0.345379	+	0.101412i	0.0117162	+	0.00344018i
$870$		0			0
$871$	7.62537	−	1.89115i	0.258376	−	0.0640790i
$872$	−11.4718			−0.388483
$873$		0			0
$874$	−2.13619	+	14.8575i	−0.0722577	+	0.502563i
$875$	−6.49828	−	4.17619i	−0.219682	−	0.141181i
$876$		0			0
$877$	−16.2069	+	35.4882i	−0.547268	+	1.19835i	0.410777	+	0.911736i	$0.365257\pi$
$877$	−16.2069	+	35.4882i	−0.547268	+	1.19835i	−0.958046	+	0.286615i	$0.907470\pi$
$878$	15.1466	+	4.44744i	0.511173	+	0.150094i
$879$		0			0
$880$	1.56699	+	0.460109i	0.0528231	+	0.0155103i
$881$	3.48998	+	24.2734i	0.117581	+	0.817790i	0.960206	+	0.279291i	$0.0900995\pi$
$881$	3.48998	+	24.2734i	0.117581	+	0.817790i	−0.842626	+	0.538499i	$0.818991\pi$
$882$		0			0
$883$	−22.9420	+	26.4765i	−0.772060	+	0.891005i	−0.996509	−	0.0834811i	$-0.973396\pi$
$883$	−22.9420	+	26.4765i	−0.772060	+	0.891005i	0.224449	+	0.974486i	$0.427942\pi$
$884$	0.0661670	−	0.0763608i	0.00222544	−	0.00256829i
$885$		0			0
$886$	22.7889	−	6.69142i	0.765607	−	0.224803i
$887$	−15.9441	−	34.9127i	−0.535351	−	1.17225i	−0.963294	−	0.268449i	$-0.913489\pi$
$887$	−15.9441	−	34.9127i	−0.535351	−	1.17225i	0.427943	−	0.903806i	$-0.359238\pi$
$888$		0			0
$889$	51.6100	+	33.1678i	1.73094	+	1.11241i
$890$	39.8743	−	11.7082i	1.33659	−	0.392458i
$891$		0			0
$892$	−1.47508	+	3.22997i	−0.0493892	+	0.108147i
$893$	1.88928	+	13.1402i	0.0632223	+	0.439721i
$894$		0			0
$895$	64.6648	−	41.5576i	2.16151	−	1.38912i
$896$	22.7652	−	26.2724i	0.760531	−	0.877699i
$897$		0			0
$898$	−4.19747	+	9.19117i	−0.140071	+	0.306713i
$899$	−4.65604	−	5.37336i	−0.155288	−	0.179212i
$900$		0			0
$901$	3.18164			0.105996
$902$	0.587048	+	0.677490i	0.0195466	+	0.0225580i
$903$		0			0
$904$	24.7095	−	7.25535i	0.821824	−	0.241309i
$905$	17.2816	−	5.07434i	0.574460	−	0.168677i
$906$		0			0
$907$	18.0780	+	20.8631i	0.600270	+	0.692748i	0.971836	−	0.235658i	$-0.0757246\pi$
$907$	18.0780	+	20.8631i	0.600270	+	0.692748i	−0.371566	+	0.928406i	$0.621179\pi$
$908$	−0.642074			−0.0213080
$909$		0			0
$910$	11.1823	+	12.9051i	0.370691	+	0.427800i
$911$	16.3330	−	35.7643i	0.541136	−	1.18492i	−0.419663	−	0.907680i	$-0.637852\pi$
$911$	16.3330	−	35.7643i	0.541136	−	1.18492i	0.960800	−	0.277244i	$-0.0894209\pi$
$912$		0			0
$913$	0.107317	−	0.123850i	0.00355167	−	0.00409884i
$914$	18.5106	−	11.8960i	0.612277	−	0.393486i
$915$		0			0
$916$	−0.264796	−	1.84169i	−0.00874909	−	0.0608513i
$917$	4.90125	−	10.7322i	0.161854	−	0.354410i
$918$		0			0
$919$	−29.8753	+	8.77218i	−0.985495	+	0.289367i	−0.734491	−	0.678619i	$-0.762579\pi$
$919$	−29.8753	+	8.77218i	−0.985495	+	0.289367i	−0.251004	+	0.967986i	$0.580761\pi$
$920$	−11.8460	−	7.61298i	−0.390552	−	0.250992i
$921$		0			0
$922$	11.0021	+	24.0913i	0.362335	+	0.793403i
$923$	−5.39895	+	1.58527i	−0.177709	+	0.0521799i
$924$		0			0
$925$	−17.2054	+	19.8561i	−0.565711	+	0.652865i
$926$	7.78062	−	8.97931i	0.255687	−	0.295078i
$927$		0			0
$928$	0.343352	+	2.38806i	0.0112711	+	0.0783920i
$929$	3.84664	+	1.12948i	0.126204	+	0.0370569i	0.344225	−	0.938887i	$-0.388142\pi$
$929$	3.84664	+	1.12948i	0.126204	+	0.0370569i	−0.218020	+	0.975944i	$0.569960\pi$
$930$		0			0
$931$	−79.4511	−	23.3290i	−2.60391	−	0.764576i
$932$	1.04277	−	2.28334i	0.0341570	−	0.0747933i
$933$		0			0
$934$	23.8595	+	15.3336i	0.780708	+	0.501731i
$935$	−0.0256620	+	0.178483i	−0.000839238	+	0.00583703i
$936$		0			0
$937$	15.4008			0.503121			0.251561	−	0.967842i	$-0.419056\pi$
$937$	15.4008			0.503121			0.251561	+	0.967842i	$0.419056\pi$
$938$	16.8604	+	41.5004i	0.550513	+	1.35504i
$939$		0			0
$940$	−1.48870	−	0.437123i	−0.0485562	−	0.0142574i
$941$	−7.73230	+	53.7793i	−0.252066	+	1.75316i	0.333703	+	0.942678i	$0.391702\pi$
$941$	−7.73230	+	53.7793i	−0.252066	+	1.75316i	−0.585769	+	0.810478i	$0.699207\pi$
$942$		0			0
$943$	−2.74451	−	6.00965i	−0.0893737	−	0.195701i
$944$	−14.2387	+	31.1785i	−0.463431	+	1.01477i
$945$		0			0
$946$	−1.04438	−	1.20528i	−0.0339558	−	0.0391871i
$947$	23.2004	+	6.81224i	0.753911	+	0.221368i	0.636035	−	0.771660i	$-0.280573\pi$
$947$	23.2004	+	6.81224i	0.753911	+	0.221368i	0.117876	+	0.993028i	$0.462392\pi$
$948$		0			0
$949$	−2.74297	−	6.00626i	−0.0890404	−	0.194971i
$950$	−37.8136	+	43.6392i	−1.22684	+	1.41584i
$951$		0			0
$952$	3.89007	+	2.50000i	0.126078	+	0.0810254i
$953$	−27.3567	+	8.03266i	−0.886172	+	0.260203i	−0.692979	−	0.720957i	$-0.743702\pi$
$953$	−27.3567	+	8.03266i	−0.886172	+	0.260203i	−0.193192	+	0.981161i	$0.561884\pi$
$954$		0			0
$955$	56.1122	−	36.0611i	1.81575	−	1.16691i
$956$	−6.37064	−	4.09416i	−0.206041	−	0.132415i
$957$		0			0
$958$	−4.00391	+	27.8478i	−0.129360	+	0.899721i
$959$	−9.94316	+	21.7725i	−0.321081	+	0.703070i
$960$		0			0
$961$	1.25855	−	8.75339i	0.0405983	−	0.282367i
$962$	4.98950	−	3.20656i	0.160868	−	0.103384i
$963$		0			0
$964$	−0.113499	+	0.0729417i	−0.00365557	+	0.00234929i
$965$	19.7335	−	43.2102i	0.635242	−	1.39099i
$966$		0			0
$967$	0.672521			0.0216268			0.0108134	−	0.999942i	$-0.496558\pi$
$967$	0.672521			0.0216268			0.0108134	+	0.999942i	$0.496558\pi$
$968$	32.8472			1.05575
$969$		0			0
$970$	2.08811	+	14.5231i	0.0670450	+	0.466308i
$971$	−54.5205	+	16.0087i	−1.74965	+	0.513742i	−0.990540	−	0.137225i	$-0.956182\pi$
$971$	−54.5205	+	16.0087i	−1.74965	+	0.513742i	−0.759106	+	0.650967i	$0.774363\pi$
$972$		0			0
$973$	−13.0029	−	90.4370i	−0.416853	−	2.89928i
$974$	−30.8834	−	35.6413i	−0.989567	−	1.14202i
$975$		0			0
$976$	7.21378			0.230907
$977$	16.9419	+	19.5520i	0.542019	+	0.625524i	0.959005	−	0.283390i	$-0.0914589\pi$
$977$	16.9419	+	19.5520i	0.542019	+	0.625524i	−0.416986	+	0.908913i	$0.636913\pi$
$978$		0			0
$979$	−1.23138	+	0.791363i	−0.0393552	+	0.0252921i
$980$	6.33764	−	7.31403i	0.202449	−	0.233638i
$981$		0			0
$982$	−1.50363	+	10.4580i	−0.0479827	+	0.333727i
$983$	5.25671	+	36.5613i	0.167663	+	1.16612i	0.883698	+	0.468058i	$0.155046\pi$
$983$	5.25671	+	36.5613i	0.167663	+	1.16612i	−0.716035	+	0.698065i	$0.754045\pi$
$984$		0			0
$985$	−7.05998	+	49.1032i	−0.224950	+	1.56456i
$986$	0.702044	−	0.206139i	0.0223576	−	0.00656479i
$987$		0			0
$988$	−1.81954	+	1.16935i	−0.0578873	+	0.0372019i
$989$	4.88260	+	10.6914i	0.155258	+	0.339967i
$990$		0			0
$991$	−25.0967	−	16.1286i	−0.797222	−	0.512343i	0.0774864	−	0.996993i	$-0.475311\pi$
$991$	−25.0967	−	16.1286i	−0.797222	−	0.512343i	−0.874708	+	0.484650i	$0.838947\pi$
$992$	4.92349	−	5.68201i	0.156321	−	0.180404i
$993$		0			0
$994$	−13.3276	−	29.1834i	−0.422726	−	0.925641i
$995$	−0.273613	−	1.90302i	−0.00867412	−	0.0603298i
$996$		0			0
$997$	−20.8000	−	24.0045i	−0.658742	−	0.760229i	0.323829	−	0.946116i	$-0.395030\pi$
$997$	−20.8000	−	24.0045i	−0.658742	−	0.760229i	−0.982571	+	0.185887i	$0.940484\pi$
$998$	−23.7600	−	6.97655i	−0.752108	−	0.220839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.c.64.2		20
3.2	odd	2		67.2.e.c.64.1	yes	20
67.22	even	11	inner	603.2.u.c.424.2		20
201.89	odd	22		67.2.e.c.22.1	✓	20
201.92	odd	22		4489.2.a.l.1.4		10
201.176	even	22		4489.2.a.m.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.22.1	✓	20	201.89	odd	22
67.2.e.c.64.1	yes	20	3.2	odd	2
603.2.u.c.64.2		20	1.1	even	1	trivial
603.2.u.c.424.2		20	67.22	even	11	inner
4489.2.a.l.1.4		10	201.92	odd	22
4489.2.a.m.1.7		10	201.176	even	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25667 - 0.368991i) q^{2} +(-0.239446 - 0.153882i) q^{4} +(1.35049 + 2.95717i) q^{5} +(4.00914 + 1.17719i) q^{7} +(1.95949 + 2.26138i) q^{8} +O(q^{10})\)	\(q+(-1.25667 - 0.368991i) q^{2} +(-0.239446 - 0.153882i) q^{4} +(1.35049 + 2.95717i) q^{5} +(4.00914 + 1.17719i) q^{7} +(1.95949 + 2.26138i) q^{8} +(-0.605953 - 4.21450i) q^{10} +(0.0622997 + 0.136417i) q^{11} +(-0.628542 + 0.725376i) q^{13} +(-4.60379 - 2.95867i) q^{14} +(-1.39153 - 3.04702i) q^{16} +(0.311139 - 0.199957i) q^{17} +(-7.59646 + 2.23052i) q^{19} +(0.131686 - 0.915898i) q^{20} +(-0.0279533 - 0.194419i) q^{22} +(-0.206011 + 1.43284i) q^{23} +(-3.64670 + 4.20851i) q^{25} +(1.05753 - 0.679631i) q^{26} +(-0.778822 - 0.898809i) q^{28} -1.51049 q^{29} +(3.08248 + 3.55737i) q^{31} +(-0.227312 - 1.58099i) q^{32} +(-0.464780 + 0.136472i) q^{34} +(1.93317 + 13.4455i) q^{35} +4.71809 q^{37} +10.3693 q^{38} +(-4.04098 + 8.84852i) q^{40} +(-3.83945 + 2.46746i) q^{41} +(6.83054 - 4.38972i) q^{43} +(0.00607483 - 0.0422514i) q^{44} +(0.787594 - 1.72459i) q^{46} +(0.238631 - 1.65971i) q^{47} +(8.79864 + 5.65454i) q^{49} +(6.13559 - 3.94311i) q^{50} +(0.262124 - 0.0769666i) q^{52} +(7.23687 + 4.65086i) q^{53} +(-0.319274 + 0.368461i) q^{55} +(5.19381 + 11.3729i) q^{56} +(1.89818 + 0.557356i) q^{58} +(-6.70083 - 7.73317i) q^{59} +(-0.894613 + 1.95893i) q^{61} +(-2.56102 - 5.60785i) q^{62} +(-1.25115 + 8.70192i) q^{64} +(-2.99390 - 0.879088i) q^{65} +(-6.69173 - 4.71389i) q^{67} -0.105271 q^{68} +(2.53191 - 17.6098i) q^{70} +(4.93184 + 3.16950i) q^{71} +(-2.85782 + 6.25776i) q^{73} +(-5.92907 - 1.74093i) q^{74} +(2.16218 + 0.634873i) q^{76} +(0.0891792 + 0.620255i) q^{77} +(1.57181 - 1.81396i) q^{79} +(7.13129 - 8.22995i) q^{80} +(5.73539 - 1.68406i) q^{82} +(-0.453939 - 0.993987i) q^{83} +(1.01150 + 0.650049i) q^{85} +(-10.2035 + 2.99602i) q^{86} +(-0.186415 + 0.408192i) q^{88} +(1.38903 + 9.66095i) q^{89} +(-3.37382 + 2.16822i) q^{91} +(0.269818 - 0.311386i) q^{92} +(-0.912300 + 1.99766i) q^{94} +(-16.8550 - 19.4517i) q^{95} -3.44598 q^{97} +(-8.97050 - 10.3525i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 4 q^{4} - q^{5} - 8 q^{7} + 22 q^{8}+O(q^{10}) \) 20 * q + 4 * q^2 - 4 * q^4 - q^5 - 8 * q^7 + 22 * q^8	\( 20 q + 4 q^{2} - 4 q^{4} - q^{5} - 8 q^{7} + 22 q^{8} - 9 q^{10} + 12 q^{13} - 6 q^{14} + 8 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} - 2 q^{23} - 3 q^{25} + 31 q^{26} - 5 q^{28} + 6 q^{29} - 16 q^{32} - 8 q^{34} - 34 q^{35} + 24 q^{37} + 14 q^{38} - 11 q^{40} + 6 q^{41} - 22 q^{43} + 22 q^{44} + 15 q^{46} - 16 q^{47} + 42 q^{49} + 17 q^{50} + 2 q^{52} + q^{53} + 20 q^{55} - 11 q^{56} + 10 q^{58} + 26 q^{59} - 26 q^{61} - 11 q^{62} - 6 q^{64} - 9 q^{65} - 22 q^{67} + 52 q^{68} - 42 q^{70} - 20 q^{71} - 55 q^{73} - 37 q^{74} - 3 q^{76} + 70 q^{77} - 34 q^{79} - 40 q^{80} - 12 q^{82} - 56 q^{83} + 41 q^{85} + 33 q^{86} + 11 q^{88} + 3 q^{89} + 12 q^{91} + 18 q^{92} + 32 q^{94} - 74 q^{95} - 14 q^{97} - 95 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 4 * q^4 - q^5 - 8 * q^7 + 22 * q^8 - 9 * q^10 + 12 * q^13 - 6 * q^14 + 8 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 - 2 * q^23 - 3 * q^25 + 31 * q^26 - 5 * q^28 + 6 * q^29 - 16 * q^32 - 8 * q^34 - 34 * q^35 + 24 * q^37 + 14 * q^38 - 11 * q^40 + 6 * q^41 - 22 * q^43 + 22 * q^44 + 15 * q^46 - 16 * q^47 + 42 * q^49 + 17 * q^50 + 2 * q^52 + q^53 + 20 * q^55 - 11 * q^56 + 10 * q^58 + 26 * q^59 - 26 * q^61 - 11 * q^62 - 6 * q^64 - 9 * q^65 - 22 * q^67 + 52 * q^68 - 42 * q^70 - 20 * q^71 - 55 * q^73 - 37 * q^74 - 3 * q^76 + 70 * q^77 - 34 * q^79 - 40 * q^80 - 12 * q^82 - 56 * q^83 + 41 * q^85 + 33 * q^86 + 11 * q^88 + 3 * q^89 + 12 * q^91 + 18 * q^92 + 32 * q^94 - 74 * q^95 - 14 * q^97 - 95 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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