LMFDB - Embedded newform 603.2.z.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, degree $20$, 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:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	603.19
Dual form			603.2.z.c.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.322186 - 0.166098i) q^{2} +(-1.08390 - 1.52212i) q^{4} +(-2.74026 - 3.16243i) q^{5} +(-0.139020 - 2.91838i) q^{7} +(0.199567 + 1.38802i) q^{8} +O(q^{10})$	\(q+(-0.322186 - 0.166098i) q^{2} +(-1.08390 - 1.52212i) q^{4} +(-2.74026 - 3.16243i) q^{5} +(-0.139020 - 2.91838i) q^{7} +(0.199567 + 1.38802i) q^{8} +(0.357599 + 1.47404i) q^{10} +(3.69355 - 0.711873i) q^{11} +(-1.41341 + 0.565844i) q^{13} +(-0.439948 + 0.963352i) q^{14} +(-1.05607 + 3.05132i) q^{16} +(-0.661417 + 0.928830i) q^{17} +(0.223966 - 4.70162i) q^{19} +(-1.84344 + 7.59877i) q^{20} +(-1.30825 - 0.384137i) q^{22} +(-3.06447 - 2.92196i) q^{23} +(-1.78036 + 12.3827i) q^{25} +(0.549366 + 0.0524581i) q^{26} +(-4.29146 + 3.37484i) q^{28} +(-4.25355 + 7.36737i) q^{29} +(5.42003 + 2.16985i) q^{31} +(2.87685 - 2.74307i) q^{32} +(0.367376 - 0.189396i) q^{34} +(-8.84824 + 8.43678i) q^{35} +(-2.53337 - 4.38792i) q^{37} +(-0.853089 + 1.47759i) q^{38} +(3.84266 - 4.43466i) q^{40} +(-1.90109 - 0.181532i) q^{41} +(1.62245 + 3.55266i) q^{43} +(-5.08699 - 4.85044i) q^{44} +(0.501994 + 1.45042i) q^{46} +(1.00911 - 4.15959i) q^{47} +(-1.52933 + 0.146034i) q^{49} +(2.63035 - 3.69381i) q^{50} +(2.39328 + 1.53807i) q^{52} +(2.55985 - 5.60528i) q^{53} +(-12.3725 - 9.72988i) q^{55} +(4.02304 - 0.775377i) q^{56} +(2.59414 - 1.66715i) q^{58} +(0.656506 + 4.56610i) q^{59} +(0.0916683 + 0.0176676i) q^{61} +(-1.38585 - 1.59935i) q^{62} +(4.81373 - 1.41344i) q^{64} +(5.66256 + 2.91925i) q^{65} +(-3.83660 - 7.23052i) q^{67} +2.13070 q^{68} +(4.25211 - 1.24853i) q^{70} +(2.82358 + 3.96517i) q^{71} +(0.555307 + 0.107027i) q^{73} +(0.0873886 + 1.83451i) q^{74} +(-7.39920 + 4.75517i) q^{76} +(-2.59100 - 10.6802i) q^{77} +(-6.66672 - 5.24277i) q^{79} +(12.5435 - 5.02167i) q^{80} +(0.582352 + 0.374255i) q^{82} +(2.21585 - 6.40227i) q^{83} +(4.74982 - 0.453553i) q^{85} +(0.0673620 - 1.41410i) q^{86} +(1.72521 + 4.98466i) q^{88} +(-9.86134 - 2.89555i) q^{89} +(1.84784 + 4.04621i) q^{91} +(-1.12601 + 7.83160i) q^{92} +(-1.01602 + 1.17255i) q^{94} +(-15.4823 + 12.1754i) q^{95} +(5.77589 + 10.0041i) q^{97} +(0.516985 + 0.206970i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{33}\right)$	$1$

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 $

$2$	−0.322186	−	0.166098i	−0.227820	−	0.117449i	0.340538	−	0.940231i	$-0.389391\pi$
$2$	−0.322186	−	0.166098i	−0.227820	−	0.117449i	−0.568358	+	0.822781i	$0.692421\pi$
$3$		0			0
$3$		0			0
$4$	−1.08390	−	1.52212i	−0.541949	−	0.761061i
$5$	−2.74026	−	3.16243i	−1.22548	−	1.41428i	−0.879404	−	0.476077i	$-0.842058\pi$
$5$	−2.74026	−	3.16243i	−1.22548	−	1.41428i	−0.346079	−	0.938205i	$-0.612487\pi$
$6$		0			0
$7$	−0.139020	−	2.91838i	−0.0525445	−	1.10305i	−0.859074	−	0.511851i	$-0.828960\pi$
$7$	−0.139020	−	2.91838i	−0.0525445	−	1.10305i	0.806529	−	0.591194i	$-0.201343\pi$
$8$	0.199567	+	1.38802i	0.0705578	+	0.490740i
$9$		0			0
$10$	0.357599	+	1.47404i	0.113083	+	0.466133i
$11$	3.69355	−	0.711873i	1.11365	−	0.214638i	0.400943	−	0.916103i	$-0.368682\pi$
$11$	3.69355	−	0.711873i	1.11365	−	0.214638i	0.712704	+	0.701465i	$0.247470\pi$
$12$		0			0
$13$	−1.41341	+	0.565844i	−0.392009	+	0.156937i	−0.559289	−	0.828973i	$-0.688926\pi$
$13$	−1.41341	+	0.565844i	−0.392009	+	0.156937i	0.167280	+	0.985909i	$0.446502\pi$
$14$	−0.439948	+	0.963352i	−0.117581	+	0.257467i
$15$		0			0
$16$	−1.05607	+	3.05132i	−0.264018	+	0.762831i
$17$	−0.661417	+	0.928830i	−0.160417	+	0.225274i	−0.886959	−	0.461847i	$-0.847187\pi$
$17$	−0.661417	+	0.928830i	−0.160417	+	0.225274i	0.726542	+	0.687122i	$0.241126\pi$
$18$		0			0
$19$	0.223966	−	4.70162i	0.0513812	−	1.07862i	−0.815070	−	0.579363i	$-0.803301\pi$
$19$	0.223966	−	4.70162i	0.0513812	−	1.07862i	0.866451	−	0.499262i	$-0.166396\pi$
$20$	−1.84344	+	7.59877i	−0.412206	+	1.69914i
$21$		0			0
$22$	−1.30825	−	0.384137i	−0.278920	−	0.0818982i
$23$	−3.06447	−	2.92196i	−0.638985	−	0.609271i	0.299705	−	0.954032i	$-0.403112\pi$
$23$	−3.06447	−	2.92196i	−0.638985	−	0.609271i	−0.938691	+	0.344761i	$0.887960\pi$
$24$		0			0
$25$	−1.78036	+	12.3827i	−0.356072	+	2.47654i
$26$	0.549366	+	0.0524581i	0.107740	+	0.0102879i
$27$		0			0
$28$	−4.29146	+	3.37484i	−0.811009	+	0.637784i
$29$	−4.25355	+	7.36737i	−0.789865	+	1.36809i	0.136185	+	0.990683i	$0.456516\pi$
$29$	−4.25355	+	7.36737i	−0.789865	+	1.36809i	−0.926049	+	0.377402i	$0.876817\pi$
$30$		0			0
$31$	5.42003	+	2.16985i	0.973466	+	0.389717i	0.803219	−	0.595684i	$-0.203119\pi$
$31$	5.42003	+	2.16985i	0.973466	+	0.389717i	0.170248	+	0.985401i	$0.445543\pi$
$32$	2.87685	−	2.74307i	0.508560	−	0.484911i
$33$		0			0
$34$	0.367376	−	0.189396i	0.0630045	−	0.0324811i
$35$	−8.84824	+	8.43678i	−1.49563	+	1.42608i
$36$		0			0
$37$	−2.53337	−	4.38792i	−0.416483	−	0.721369i	0.579100	−	0.815256i	$-0.303404\pi$
$37$	−2.53337	−	4.38792i	−0.416483	−	0.721369i	−0.995583	+	0.0938872i	$0.970071\pi$
$38$	−0.853089	+	1.47759i	−0.138389	+	0.239697i
$39$		0			0
$40$	3.84266	−	4.43466i	0.607578	−	0.701182i
$41$	−1.90109	−	0.181532i	−0.296900	−	0.0283506i	−0.0544571	−	0.998516i	$-0.517343\pi$
$41$	−1.90109	−	0.181532i	−0.296900	−	0.0283506i	−0.242443	+	0.970166i	$0.577949\pi$
$42$		0			0
$43$	1.62245	+	3.55266i	0.247421	+	0.541776i	0.992071	−	0.125679i	$-0.0401110\pi$
$43$	1.62245	+	3.55266i	0.247421	+	0.541776i	−0.744650	+	0.667455i	$0.767384\pi$
$44$	−5.08699	−	4.85044i	−0.766893	−	0.731231i
$45$		0			0
$46$	0.501994	+	1.45042i	0.0740150	+	0.213852i
$47$	1.00911	−	4.15959i	0.147193	−	0.606739i	−0.849650	−	0.527347i	$-0.823187\pi$
$47$	1.00911	−	4.15959i	0.147193	−	0.606739i	0.996843	−	0.0793922i	$-0.0252980\pi$
$48$		0			0
$49$	−1.52933	+	0.146034i	−0.218476	+	0.0208620i
$50$	2.63035	−	3.69381i	0.371987	−	0.522383i
$51$		0			0
$52$	2.39328	+	1.53807i	0.331888	+	0.213291i
$53$	2.55985	−	5.60528i	0.351622	−	0.769945i	−0.648341	−	0.761350i	$-0.724537\pi$
$53$	2.55985	−	5.60528i	0.351622	−	0.769945i	0.999963	−	0.00859494i	$-0.00273589\pi$
$54$		0			0
$55$	−12.3725	−	9.72988i	−1.66831	−	1.31198i
$56$	4.02304	−	0.775377i	0.537601	−	0.103614i
$57$		0			0
$58$	2.59414	−	1.66715i	0.340627	−	0.218908i
$59$	0.656506	+	4.56610i	0.0854698	+	0.594455i	0.986876	+	0.161481i	$0.0516270\pi$
$59$	0.656506	+	4.56610i	0.0854698	+	0.594455i	−0.901406	+	0.432975i	$0.857464\pi$
$60$		0			0
$61$	0.0916683	+	0.0176676i	0.0117369	+	0.00226211i	0.195116	−	0.980780i	$-0.437492\pi$
$61$	0.0916683	+	0.0176676i	0.0117369	+	0.00226211i	−0.183379	+	0.983042i	$0.558704\pi$
$62$	−1.38585	−	1.59935i	−0.176003	−	0.203118i
$63$		0			0
$64$	4.81373	−	1.41344i	0.601717	−	0.176680i
$65$	5.66256	+	2.91925i	0.702354	+	0.362089i
$66$		0			0
$67$	−3.83660	−	7.23052i	−0.468716	−	0.883349i
$67$	−3.83660	−	7.23052i	−0.468716	−	0.883349i
$68$	2.13070			0.258386
$69$		0			0
$70$	4.25211	−	1.24853i	0.508224	−	0.149228i
$71$	2.82358	+	3.96517i	0.335098	+	0.470579i	0.947403	−	0.320042i	$-0.103697\pi$
$71$	2.82358	+	3.96517i	0.335098	+	0.470579i	−0.612306	+	0.790621i	$0.709758\pi$
$72$		0			0
$73$	0.555307	+	0.107027i	0.0649938	+	0.0125265i	0.221644	−	0.975128i	$-0.428858\pi$
$73$	0.555307	+	0.107027i	0.0649938	+	0.0125265i	−0.156651	+	0.987654i	$0.550070\pi$
$74$	0.0873886	+	1.83451i	0.0101587	+	0.213258i
$75$		0			0
$76$	−7.39920	+	4.75517i	−0.848746	+	0.545456i
$77$	−2.59100	−	10.6802i	−0.295271	−	1.21713i
$78$		0			0
$79$	−6.66672	−	5.24277i	−0.750065	−	0.589857i	0.168233	−	0.985747i	$-0.446194\pi$
$79$	−6.66672	−	5.24277i	−0.750065	−	0.589857i	−0.918298	+	0.395890i	$0.870436\pi$
$80$	12.5435	−	5.02167i	1.40241	−	0.561439i
$81$		0			0
$82$	0.582352	+	0.374255i	0.0643100	+	0.0413295i
$83$	2.21585	−	6.40227i	0.243221	−	0.702741i	−0.755638	−	0.654989i	$-0.772673\pi$
$83$	2.21585	−	6.40227i	0.243221	−	0.702741i	0.998859	−	0.0477517i	$-0.0152056\pi$
$84$		0			0
$85$	4.74982	−	0.453553i	0.515190	−	0.0491947i
$86$	0.0673620	−	1.41410i	0.00726383	−	0.152487i
$87$		0			0
$88$	1.72521	+	4.98466i	0.183908	+	0.531367i
$89$	−9.86134	−	2.89555i	−1.04530	−	0.306928i	−0.286383	−	0.958115i	$-0.592453\pi$
$89$	−9.86134	−	2.89555i	−1.04530	−	0.306928i	−0.758917	+	0.651187i	$0.774271\pi$
$90$		0			0
$91$	1.84784	+	4.04621i	0.193707	+	0.424158i
$92$	−1.12601	+	7.83160i	−0.117395	+	0.816501i
$93$		0			0
$94$	−1.01602	+	1.17255i	−0.104795	+	0.120939i
$95$	−15.4823	+	12.1754i	−1.58845	+	1.24917i
$96$		0			0
$97$	5.77589	+	10.0041i	0.586453	+	1.01577i	0.994693	+	0.102891i	$0.0328094\pi$
$97$	5.77589	+	10.0041i	0.586453	+	1.01577i	−0.408240	+	0.912875i	$0.633857\pi$
$98$	0.516985	+	0.206970i	0.0522234	+	0.0209071i
$99$		0			0
$100$	20.7777	−	10.7116i	2.07777	−	1.07116i
$101$	5.67494	−	2.92563i	0.564677	−	0.291111i	−0.152155	−	0.988357i	$-0.548621\pi$
$101$	5.67494	−	2.92563i	0.564677	−	0.291111i	0.716833	+	0.697245i	$0.245591\pi$
$102$		0			0
$103$	−8.07445	−	3.23252i	−0.795599	−	0.318510i	−0.0619859	−	0.998077i	$-0.519743\pi$
$103$	−8.07445	−	3.23252i	−0.795599	−	0.318510i	−0.733613	+	0.679567i	$0.762168\pi$
$104$	−1.06747	−	1.84892i	−0.104675	−	0.181302i
$105$		0			0
$106$	−1.75577	+	1.38076i	−0.170536	+	0.134111i
$107$	−0.652978	+	0.753577i	−0.0631257	+	0.0728510i	−0.786434	−	0.617674i	$-0.788075\pi$
$107$	−0.652978	+	0.753577i	−0.0631257	+	0.0728510i	0.723308	+	0.690525i	$0.242621\pi$
$108$		0			0
$109$	−0.493032	+	3.42911i	−0.0472239	+	0.328449i	0.952491	+	0.304567i	$0.0985117\pi$
$109$	−0.493032	+	3.42911i	−0.0472239	+	0.328449i	−0.999715	+	0.0238822i	$0.992397\pi$
$110$	2.37014	+	5.18988i	0.225984	+	0.494836i
$111$		0			0
$112$	9.05175	+	2.65783i	0.855310	+	0.251142i
$113$	−0.887877	−	2.56535i	−0.0835244	−	0.241328i	0.895503	−	0.445055i	$-0.146816\pi$
$113$	−0.887877	−	2.56535i	−0.0835244	−	0.241328i	−0.979028	+	0.203727i	$0.934695\pi$
$114$		0			0
$115$	−0.843065	+	17.6981i	−0.0786162	+	1.65036i
$116$	15.8245	−	1.51105i	1.46926	−	0.140298i
$117$		0			0
$118$	0.546904	−	1.58018i	0.0503466	−	0.145467i
$119$	2.80263	+	1.80114i	0.256917	+	0.165110i
$120$		0			0
$121$	2.92349	−	1.17039i	0.265772	−	0.106399i
$122$	−0.0265996	−	0.0209182i	−0.00240822	−	0.00189384i
$123$		0			0
$124$	−2.57198	−	10.6019i	−0.230971	−	0.952075i
$125$	26.4369	−	16.9900i	2.36459	−	1.51963i
$126$		0			0
$127$	0.490400	+	10.2948i	0.0435159	+	0.913512i	0.910077	+	0.414440i	$0.136023\pi$
$127$	0.490400	+	10.2948i	0.0435159	+	0.913512i	−0.866561	+	0.499072i	$0.833674\pi$
$128$	−9.59204	−	1.84871i	−0.847824	−	0.163405i
$129$		0			0
$130$	−1.33951	−	1.88108i	−0.117483	−	0.164982i
$131$	−6.64337	+	1.95067i	−0.580434	+	0.170431i	−0.558753	−	0.829334i	$-0.688720\pi$
$131$	−6.64337	+	1.95067i	−0.580434	+	0.170431i	−0.0216811	+	0.999765i	$0.506902\pi$
$132$		0			0
$133$	−13.7523			−1.19247
$134$	0.0351218	+	2.96682i	0.00303406	+	0.256295i
$135$		0			0
$136$	−1.42123	−	0.732697i	−0.121870	−	0.0628283i
$137$	−7.99208	+	2.34669i	−0.682810	+	0.200491i	−0.604700	−	0.796454i	$-0.706707\pi$
$137$	−7.99208	+	2.34669i	−0.682810	+	0.200491i	−0.0781102	+	0.996945i	$0.524889\pi$
$138$		0			0
$139$	−13.3909	−	15.4539i	−1.13580	−	1.31079i	−0.944222	−	0.329310i	$-0.893184\pi$
$139$	−13.3909	−	15.4539i	−1.13580	−	1.31079i	−0.191581	−	0.981477i	$-0.561361\pi$
$140$	22.4324	+	4.32349i	1.89588	+	0.365402i
$141$		0			0
$142$	−0.251111	−	1.74651i	−0.0210727	−	0.146564i
$143$	−4.81769	+	3.09614i	−0.402876	+	0.258912i
$144$		0			0
$145$	34.9546	−	6.73695i	2.90282	−	0.559474i
$146$	−0.161135	−	0.126718i	−0.0133356	−	0.0104873i
$147$		0			0
$148$	−3.93304	+	8.61215i	−0.323294	+	0.707915i
$149$	−1.14518	−	0.735966i	−0.0938172	−	0.0602927i	0.492891	−	0.870091i	$-0.335940\pi$
$149$	−1.14518	−	0.735966i	−0.0938172	−	0.0602927i	−0.586708	+	0.809798i	$0.699576\pi$
$150$		0			0
$151$	1.19058	−	1.67193i	0.0968876	−	0.136060i	−0.763286	−	0.646060i	$-0.776415\pi$
$151$	1.19058	−	1.67193i	0.0968876	−	0.136060i	0.860174	+	0.510001i	$0.170355\pi$
$152$	6.57065	−	0.627421i	0.532950	−	0.0508905i
$153$		0			0
$154$	−0.939186	+	3.87138i	−0.0756818	+	0.311964i
$155$	−7.99030	−	23.0864i	−0.641796	−	1.85435i
$156$		0			0
$157$	−13.3545	−	12.7335i	−1.06581	−	1.01624i	−0.999830	−	0.0184220i	$-0.994136\pi$
$157$	−13.3545	−	12.7335i	−1.06581	−	1.01624i	−0.0659750	−	0.997821i	$-0.521016\pi$
$158$	1.27711	+	2.79648i	0.101601	+	0.222476i
$159$		0			0
$160$	−16.5581	−	1.58111i	−1.30903	−	0.124997i
$161$	−8.10138	+	9.34950i	−0.638479	+	0.736844i
$162$		0			0
$163$	−1.18107	+	2.04567i	−0.0925084	+	0.160229i	−0.908566	−	0.417741i	$-0.862822\pi$
$163$	−1.18107	+	2.04567i	−0.0925084	+	0.160229i	0.816058	+	0.577971i	$0.196155\pi$
$164$	1.78428	+	3.09046i	0.139329	+	0.241324i
$165$		0			0
$166$	−1.77732	+	1.69467i	−0.137947	+	0.131532i
$167$	21.0530	−	10.8536i	1.62913	−	0.839874i	0.631194	−	0.775625i	$-0.282565\pi$
$167$	21.0530	−	10.8536i	1.62913	−	0.839874i	0.997934	−	0.0642483i	$-0.0204650\pi$
$168$		0			0
$169$	−7.73099	+	7.37149i	−0.594692	+	0.567037i
$170$	−1.60566	−	0.642808i	−0.123148	−	0.0493011i
$171$		0			0
$172$	3.64902	−	6.32029i	0.278235	−	0.481917i
$173$	10.4941	−	8.25267i	0.797854	−	0.627439i	−0.133709	−	0.991021i	$-0.542689\pi$
$173$	10.4941	−	8.25267i	0.797854	−	0.627439i	0.931562	+	0.363581i	$0.118446\pi$
$174$		0			0
$175$	36.3849	+	3.47434i	2.75044	+	0.262635i
$176$	−1.72850	+	12.0220i	−0.130291	+	0.906192i
$177$		0			0
$178$	2.69624	+	2.57086i	0.202092	+	0.192694i
$179$	−1.45117	−	0.426102i	−0.108466	−	0.0318484i	0.227049	−	0.973883i	$-0.427092\pi$
$179$	−1.45117	−	0.426102i	−0.108466	−	0.0318484i	−0.335515	+	0.942035i	$0.608910\pi$
$180$		0			0
$181$	4.16163	−	17.1545i	0.309332	−	1.27508i	−0.578791	−	0.815476i	$-0.696475\pi$
$181$	4.16163	−	17.1545i	0.309332	−	1.27508i	0.888123	−	0.459607i	$-0.152010\pi$
$182$	0.0767202	−	1.61055i	0.00568688	−	0.119382i
$183$		0			0
$184$	3.44418	−	4.83667i	0.253908	−	0.356564i
$185$	−6.93440	+	20.0356i	−0.509827	+	1.47305i
$186$		0			0
$187$	−1.78177	+	3.90152i	−0.130296	+	0.285308i
$188$	−7.42518	+	2.97259i	−0.541537	+	0.216799i
$189$		0			0
$190$	7.01047	−	1.35116i	0.508593	−	0.0980233i
$191$	−0.783539	−	3.22979i	−0.0566949	−	0.233700i	0.936414	−	0.350898i	$-0.114124\pi$
$191$	−0.783539	−	3.22979i	−0.0566949	−	0.233700i	−0.993108	+	0.117199i	$0.962609\pi$
$192$		0			0
$193$	−3.42809	−	23.8429i	−0.246760	−	1.71625i	−0.616703	−	0.787196i	$-0.711532\pi$
$193$	−3.42809	−	23.8429i	−0.246760	−	1.71625i	0.369943	−	0.929054i	$-0.379377\pi$
$194$	−0.199240	−	4.18256i	−0.0143046	−	0.300290i
$195$		0			0
$196$	1.87992	+	2.16955i	0.134280	+	0.154968i
$197$	−7.89220	−	11.0830i	−0.562296	−	0.789634i	0.431350	−	0.902185i	$-0.358037\pi$
$197$	−7.89220	−	11.0830i	−0.562296	−	0.789634i	−0.993646	+	0.112551i	$0.964098\pi$
$198$		0			0
$199$	−6.71277	−	3.46067i	−0.475856	−	0.245321i	0.203576	−	0.979059i	$-0.434743\pi$
$199$	−6.71277	−	3.46067i	−0.475856	−	0.245321i	−0.679432	+	0.733738i	$0.737774\pi$
$200$	−17.5427			−1.24046
$201$		0			0
$202$	−2.31433			−0.162835
$203$	22.0921	+	11.3893i	1.55056	+	0.799371i
$204$		0			0
$205$	4.63540	+	6.50951i	0.323751	+	0.454644i
$206$	2.06456	+	2.38262i	0.143844	+	0.166005i
$207$		0			0
$208$	−0.233909	−	4.91034i	−0.0162186	−	0.340471i
$209$	−2.51973	−	17.5251i	−0.174293	−	1.21224i
$210$		0			0
$211$	4.46549	+	18.4070i	0.307417	+	1.26719i	0.890577	+	0.454832i	$0.150301\pi$
$211$	4.46549	+	18.4070i	0.307417	+	1.26719i	−0.583160	+	0.812357i	$0.698184\pi$
$212$	−11.3065	+	2.17916i	−0.776537	+	0.149665i
$213$		0			0
$214$	0.335548	−	0.134333i	0.0229376	−	0.00918282i
$215$	6.78912	−	14.8661i	0.463014	−	1.01386i
$216$		0			0
$217$	5.57897	−	16.1194i	0.378725	−	1.09426i
$218$	0.728417	−	1.02292i	0.0493346	−	0.0692808i
$219$		0			0
$220$	−1.39948	+	29.3787i	−0.0943530	+	1.98071i
$221$	0.409280	−	1.68708i	0.0275312	−	0.113485i
$222$		0			0
$223$	16.4670	+	4.83516i	1.10271	+	0.323786i	0.781930	−	0.623366i	$-0.214235\pi$
$223$	16.4670	+	4.83516i	1.10271	+	0.323786i	0.320784	+	0.947152i	$0.396054\pi$
$224$	−8.40527	−	8.01441i	−0.561601	−	0.535485i
$225$		0			0
$226$	−0.140039	+	0.973995i	−0.00931527	+	0.0647892i
$227$	13.7423	+	1.31223i	0.912106	+	0.0870955i	0.540547	−	0.841314i	$-0.318217\pi$
$227$	13.7423	+	1.31223i	0.912106	+	0.0870955i	0.371559	+	0.928409i	$0.378823\pi$
$228$		0			0
$229$	8.76376	−	6.89189i	0.579125	−	0.455429i	−0.285126	−	0.958490i	$-0.592035\pi$
$229$	8.76376	−	6.89189i	0.579125	−	0.455429i	0.864251	+	0.503061i	$0.167793\pi$
$230$	3.21125	−	5.56204i	0.211743	−	0.366750i
$231$		0			0
$232$	−11.0749	−	4.43374i	−0.727105	−	0.291089i
$233$	−19.3569	+	18.4567i	−1.26811	+	1.20914i	−0.301334	+	0.953519i	$0.597432\pi$
$233$	−19.3569	+	18.4567i	−1.26811	+	1.20914i	−0.966777	+	0.255622i	$0.917720\pi$
$234$		0			0
$235$	−15.9196	+	8.20715i	−1.03848	+	0.535375i
$236$	6.23858	−	5.94847i	0.406097	−	0.387212i
$237$		0			0
$238$	−0.603801	−	1.04581i	−0.0391386	−	0.0677901i
$239$	0.120032	−	0.207902i	0.00776424	−	0.0134481i	−0.862117	−	0.506709i	$-0.830862\pi$
$239$	0.120032	−	0.207902i	0.00776424	−	0.0134481i	0.869881	+	0.493261i	$0.164195\pi$
$240$		0			0
$241$	2.45460	−	2.83276i	0.158115	−	0.182474i	−0.671165	−	0.741308i	$-0.734206\pi$
$241$	2.45460	−	2.83276i	0.158115	−	0.182474i	0.829279	+	0.558834i	$0.188751\pi$
$242$	−1.13631	−	0.108504i	−0.0730446	−	0.00697492i
$243$		0			0
$244$	−0.0724669	−	0.158680i	−0.00463922	−	0.0101585i
$245$	4.65260	+	4.43624i	0.297244	+	0.283421i
$246$		0			0
$247$	2.34383	+	6.77204i	0.149134	+	0.430895i
$248$	−1.93014	+	7.95616i	−0.122564	+	0.505216i
$249$		0			0
$250$	−11.3396	+	1.08280i	−0.717179	+	0.0684823i
$251$	−12.6423	+	17.7536i	−0.797972	+	1.12059i	0.192284	+	0.981339i	$0.438410\pi$
$251$	−12.6423	+	17.7536i	−0.797972	+	1.12059i	−0.990256	+	0.139256i	$0.955529\pi$
$252$		0			0
$253$	−13.3988	−	8.61090i	−0.842377	−	0.541363i
$254$	1.55194	−	3.39828i	0.0973775	−	0.213227i
$255$		0			0
$256$	−5.10384	−	4.01370i	−0.318990	−	0.250857i
$257$	0.597339	−	0.115128i	0.0372610	−	0.00718147i	−0.170587	−	0.985343i	$-0.554566\pi$
$257$	0.597339	−	0.115128i	0.0372610	−	0.00718147i	0.207848	+	0.978161i	$0.433354\pi$
$258$		0			0
$259$	−12.4534	+	8.00334i	−0.773819	+	0.497303i
$260$	−1.69418	−	11.7833i	−0.105069	−	0.730768i
$261$		0			0
$262$	2.46440	+	0.474975i	0.152251	+	0.0293440i
$263$	−10.7689	−	12.4280i	−0.664038	−	0.766341i	0.319393	−	0.947622i	$-0.396521\pi$
$263$	−10.7689	−	12.4280i	−0.664038	−	0.766341i	−0.983431	+	0.181282i	$0.941975\pi$
$264$		0			0
$265$	−24.7410	+	7.26461i	−1.51983	+	0.446261i
$266$	4.43078	+	2.28423i	0.271669	+	0.140055i
$267$		0			0
$268$	−6.84725	+	13.6769i	−0.418263	+	0.835452i
$269$	−10.2191			−0.623068			−0.311534	−	0.950235i	$-0.600843\pi$
$269$	−10.2191			−0.623068			−0.311534	+	0.950235i	$0.600843\pi$
$270$		0			0
$271$	−5.98629	+	1.75773i	−0.363641	+	0.106775i	−0.458449	−	0.888721i	$-0.651595\pi$
$271$	−5.98629	+	1.75773i	−0.363641	+	0.106775i	0.0948073	+	0.995496i	$0.469777\pi$
$272$	−2.13566	−	2.99911i	−0.129493	−	0.181848i
$273$		0			0
$274$	2.96472	+	0.571402i	0.179105	+	0.0345197i
$275$	2.23905	+	47.0034i	0.135020	+	2.83441i
$276$		0			0
$277$	−24.3381	+	15.6411i	−1.46233	+	0.939784i	−0.463783	+	0.885949i	$0.653508\pi$
$277$	−24.3381	+	15.6411i	−1.46233	+	0.939784i	−0.998550	+	0.0538352i	$0.982855\pi$
$278$	1.74749	+	7.20325i	0.104807	+	0.432022i
$279$		0			0
$280$	−13.4763	−	10.5978i	−0.805360	−	0.633342i
$281$	−4.32804	+	1.73268i	−0.258189	+	0.103363i	−0.497146	−	0.867667i	$-0.665619\pi$
$281$	−4.32804	+	1.73268i	−0.258189	+	0.103363i	0.238957	+	0.971030i	$0.423194\pi$
$282$		0			0
$283$	7.29878	+	4.69064i	0.433867	+	0.278830i	0.739290	−	0.673387i	$-0.235161\pi$
$283$	7.29878	+	4.69064i	0.433867	+	0.278830i	−0.305423	+	0.952217i	$0.598798\pi$
$284$	2.97499	−	8.59568i	0.176533	−	0.510060i
$285$		0			0
$286$	2.06645	−	0.197323i	0.122192	−	0.0116679i
$287$	−0.265491	+	5.57335i	−0.0156715	+	0.328984i
$288$		0			0
$289$	5.13490	+	14.8363i	0.302053	+	0.872725i
$290$	−12.3809	−	3.63535i	−0.727030	−	0.213475i
$291$		0			0
$292$	−0.438989	−	0.961252i	−0.0256899	−	0.0562530i
$293$	1.72254	−	11.9806i	0.100632	−	0.699911i	−0.875577	−	0.483079i	$-0.839518\pi$
$293$	1.72254	−	11.9806i	0.100632	−	0.699911i	0.976209	−	0.216832i	$-0.0695725\pi$
$294$		0			0
$295$	12.6410	−	14.5885i	0.735986	−	0.849373i
$296$	5.58495	−	4.39205i	0.324619	−	0.255283i
$297$		0			0
$298$	0.246720	+	0.427331i	0.0142921	+	0.0247546i
$299$	5.98472	+	2.39592i	0.346105	+	0.138560i
$300$		0			0
$301$	10.1425	−	5.22881i	0.584603	−	0.301384i
$302$	−0.661291	+	0.340919i	−0.0380530	+	0.0196177i
$303$		0			0
$304$	14.1096	+	5.64864i	0.809243	+	0.323972i
$305$	−0.195323	−	0.338309i	−0.0111841	−	0.0193715i
$306$		0			0
$307$	9.07612	−	7.13754i	0.518002	−	0.407361i	−0.324639	−	0.945838i	$-0.605243\pi$
$307$	9.07612	−	7.13754i	0.518002	−	0.407361i	0.842640	+	0.538477i	$0.181000\pi$
$308$	−13.4482	+	15.5201i	−0.766285	+	0.884340i
$309$		0			0
$310$	−1.26026	+	8.76530i	−0.0715779	+	0.497835i
$311$	8.89395	+	19.4750i	0.504330	+	1.10433i	0.975038	+	0.222039i	$0.0712711\pi$
$311$	8.89395	+	19.4750i	0.504330	+	1.10433i	−0.470708	+	0.882289i	$0.656002\pi$
$312$		0			0
$313$	9.43080	+	2.76913i	0.533060	+	0.156521i	0.537175	−	0.843471i	$-0.319492\pi$
$313$	9.43080	+	2.76913i	0.533060	+	0.156521i	−0.00411449	+	0.999992i	$0.501310\pi$
$314$	2.18762	+	6.32071i	0.123454	+	0.356698i
$315$		0			0
$316$	−0.754085	+	15.8302i	−0.0424206	+	0.890518i
$317$	−10.1298	+	0.967276i	−0.568945	+	0.0543277i	−0.375565	−	0.926796i	$-0.622551\pi$
$317$	−10.1298	+	0.967276i	−0.568945	+	0.0543277i	−0.193380	+	0.981124i	$0.561945\pi$
$318$		0			0
$319$	−10.4661	+	30.2397i	−0.585987	+	1.69310i
$320$	−17.6608	−	11.3499i	−0.987269	−	0.634479i
$321$		0			0
$322$	4.16309	−	1.66665i	0.232000	−	0.0928787i
$323$	4.21887	+	3.31776i	0.234744	+	0.184605i
$324$		0			0
$325$	−4.49029	−	18.5092i	−0.249076	−	1.02671i
$326$	0.720306	−	0.462912i	0.0398940	−	0.0256383i
$327$		0			0
$328$	−0.127425	−	2.67498i	−0.00703588	−	0.147701i
$329$	−12.2796	−	2.36669i	−0.676995	−	0.130480i
$330$		0			0
$331$	−0.592197	−	0.831625i	−0.0325501	−	0.0457102i	0.797980	−	0.602684i	$-0.205902\pi$
$331$	−0.592197	−	0.831625i	−0.0325501	−	0.0457102i	−0.830530	+	0.556973i	$0.811963\pi$
$332$	−12.1468	+	3.56662i	−0.666642	+	0.195744i
$333$		0			0
$334$	−8.58572			−0.469790
$335$	−12.3527	+	31.9465i	−0.674902	+	1.74543i
$336$		0			0
$337$	22.2882	+	11.4904i	1.21411	+	0.625919i	0.941763	−	0.336279i	$-0.109168\pi$
$337$	22.2882	+	11.4904i	1.21411	+	0.625919i	0.272351	+	0.962198i	$0.412199\pi$
$338$	3.71521	−	1.09088i	0.202081	−	0.0593362i
$339$		0			0
$340$	−5.83868	−	6.73820i	−0.316647	−	0.365430i
$341$	21.5638	+	4.15608i	1.16775	+	0.225065i
$342$		0			0
$343$	−2.27181	−	15.8008i	−0.122666	−	0.853163i
$344$	−4.60738	+	2.96099i	−0.248414	+	0.159646i
$345$		0			0
$346$	−4.75181	+	0.915837i	−0.255459	+	0.0492357i
$347$	−23.9846	−	18.8617i	−1.28756	−	1.01255i	−0.998473	−	0.0552454i	$-0.982406\pi$
$347$	−23.9846	−	18.8617i	−1.28756	−	1.01255i	−0.289087	−	0.957303i	$-0.593352\pi$
$348$		0			0
$349$	7.36861	−	16.1350i	0.394433	−	0.863687i	−0.603372	−	0.797460i	$-0.706177\pi$
$349$	7.36861	−	16.1350i	0.394433	−	0.863687i	0.997805	−	0.0662270i	$-0.0210962\pi$
$350$	−11.1456	−	7.16285i	−0.595758	−	0.382871i
$351$		0			0
$352$	8.67307	−	12.1796i	0.462276	−	0.649176i
$353$	7.00986	−	0.669361i	0.373097	−	0.0356265i	0.0931767	−	0.995650i	$-0.470298\pi$
$353$	7.00986	−	0.669361i	0.373097	−	0.0356265i	0.279921	+	0.960023i	$0.409692\pi$
$354$		0			0
$355$	4.80221	−	19.7950i	0.254875	−	1.05061i
$356$	6.28131	+	18.1487i	0.332909	+	0.961877i
$357$		0			0
$358$	0.396771	+	0.378321i	0.0209700	+	0.0199949i
$359$	−6.51222	−	14.2598i	−0.343702	−	0.752602i	0.656296	−	0.754503i	$-0.272122\pi$
$359$	−6.51222	−	14.2598i	−0.343702	−	0.752602i	−0.999998	+	0.00190126i	$0.999395\pi$
$360$		0			0
$361$	−3.14107	−	0.299936i	−0.165320	−	0.0157861i
$362$	−4.19015	+	4.83569i	−0.220229	+	0.254158i
$363$		0			0
$364$	4.15596	−	7.19833i	0.217831	−	0.377295i
$365$	−1.18322	−	2.04940i	−0.0619327	−	0.107271i
$366$		0			0
$367$	−22.8972	+	21.8324i	−1.19522	+	1.13964i	−0.208364	+	0.978051i	$0.566814\pi$
$367$	−22.8972	+	21.8324i	−1.19522	+	1.13964i	−0.986858	+	0.161591i	$0.948338\pi$
$368$	12.1521	−	6.26487i	0.633475	−	0.326579i
$369$		0			0
$370$	5.56205	−	5.30340i	0.289157	−	0.275711i
$371$	−16.7142	−	6.69137i	−0.867760	−	0.347399i
$372$		0			0
$373$	16.1518	−	27.9758i	0.836310	−	1.44853i	−0.0566492	−	0.998394i	$-0.518042\pi$
$373$	16.1518	−	27.9758i	0.836310	−	1.44853i	0.892959	−	0.450137i	$-0.148625\pi$
$374$	1.22210	−	0.961067i	0.0631931	−	0.0496956i
$375$		0			0
$376$	5.97499	+	0.570543i	0.308137	+	0.0294235i
$377$	1.84323	−	12.8200i	0.0949313	−	0.660261i
$378$		0			0
$379$	19.5365	+	18.6281i	1.00352	+	0.956859i	0.999069	−	0.0431309i	$-0.0137333\pi$
$379$	19.5365	+	18.6281i	1.00352	+	0.956859i	0.00445554	+	0.999990i	$0.498582\pi$
$380$	35.3136	+	10.3690i	1.81155	+	0.531920i
$381$		0			0
$382$	−0.284018	+	1.17074i	−0.0145316	+	0.0599001i
$383$	1.00107	−	21.0151i	0.0511525	−	1.07382i	−0.816719	−	0.577035i	$-0.804210\pi$
$383$	1.00107	−	21.0151i	0.0511525	−	1.07382i	0.867872	−	0.496788i	$-0.165487\pi$
$384$		0			0
$385$	−26.6755	+	37.4605i	−1.35951	+	1.90916i
$386$	−2.85578	+	8.25125i	−0.145356	+	0.419977i
$387$		0			0
$388$	8.96704	−	19.6351i	0.455233	−	0.996821i
$389$	31.0292	−	12.4222i	1.57324	−	0.629831i	0.589236	−	0.807961i	$-0.299429\pi$
$389$	31.0292	−	12.4222i	1.57324	−	0.629831i	0.984007	+	0.178130i	$0.0570047\pi$
$390$		0			0
$391$	4.74090	−	0.913733i	0.239757	−	0.0462094i
$392$	−0.507903	−	2.09361i	−0.0256530	−	0.105743i
$393$		0			0
$394$	0.701879	+	4.88168i	0.0353602	+	0.245935i
$395$	1.68867	+	35.4496i	0.0849664	+	1.78366i
$396$		0			0
$397$	−16.6953	−	19.2674i	−0.837913	−	0.967004i	0.161890	−	0.986809i	$-0.448241\pi$
$397$	−16.6953	−	19.2674i	−0.837913	−	0.967004i	−0.999804	+	0.0198051i	$0.993695\pi$
$398$	1.58795	+	2.22996i	0.0795966	+	0.111778i
$399$		0			0
$400$	−35.9034	−	18.5095i	−1.79517	−	0.925473i
$401$	−9.43023			−0.470923			−0.235462	−	0.971884i	$-0.575660\pi$
$401$	−9.43023			−0.470923			−0.235462	+	0.971884i	$0.575660\pi$
$402$		0			0
$403$	−8.88853			−0.442769
$404$	−10.6042	−	5.46686i	−0.527580	−	0.271987i
$405$		0			0
$406$	−5.22603	−	7.33893i	−0.259363	−	0.364225i
$407$	−12.4808	−	14.4036i	−0.618648	−	0.713958i
$408$		0			0
$409$	1.03927	+	21.8169i	0.0513884	+	1.07878i	0.866406	+	0.499340i	$0.166424\pi$
$409$	1.03927	+	21.8169i	0.0513884	+	1.07878i	−0.815018	+	0.579436i	$0.803273\pi$
$410$	−0.412242	−	2.86721i	−0.0203592	−	0.141601i
$411$		0			0
$412$	3.83159	+	15.7940i	0.188769	+	0.778116i
$413$	13.2344	−	2.55071i	0.651220	−	0.125512i
$414$		0			0
$415$	−26.3188	+	10.5364i	−1.29194	+	0.517214i
$416$	−2.51402	+	5.50493i	−0.123260	+	0.269901i
$417$		0			0
$418$	−2.09907	+	6.06485i	−0.102669	+	0.296642i
$419$	12.4202	−	17.4417i	0.606767	−	0.852085i	−0.390894	−	0.920436i	$-0.627834\pi$
$419$	12.4202	−	17.4417i	0.606767	−	0.852085i	0.997661	+	0.0683506i	$0.0217736\pi$
$420$		0			0
$421$	1.06974	−	22.4565i	0.0521357	−	1.09446i	−0.809560	−	0.587037i	$-0.800294\pi$
$421$	1.06974	−	22.4565i	0.0521357	−	1.09446i	0.861695	−	0.507426i	$-0.169403\pi$
$422$	1.61865	−	6.67218i	0.0787948	−	0.324797i
$423$		0			0
$424$	8.29112	+	2.43449i	0.402652	+	0.118229i
$425$	−10.3238	−	9.84376i	−0.500780	−	0.477493i
$426$		0			0
$427$	0.0388172	−	0.269979i	0.00187849	−	0.0130652i
$428$	1.85480	+	0.177112i	0.0896550	+	0.00856102i
$429$		0			0
$430$	−4.65659	+	3.66198i	−0.224561	+	0.176596i
$431$	−17.1268	+	29.6645i	−0.824968	+	1.42889i	0.0769755	+	0.997033i	$0.475474\pi$
$431$	−17.1268	+	29.6645i	−0.824968	+	1.42889i	−0.901944	+	0.431854i	$0.857860\pi$
$432$		0			0
$433$	10.2617	+	4.10815i	0.493144	+	0.197425i	0.604886	−	0.796312i	$-0.293219\pi$
$433$	10.2617	+	4.10815i	0.493144	+	0.197425i	−0.111742	+	0.993737i	$0.535643\pi$
$434$	−4.47487	+	4.26678i	−0.214800	+	0.204812i
$435$		0			0
$436$	5.75392	−	2.96635i	0.275563	−	0.142063i
$437$	−14.4243	+	13.7535i	−0.690007	+	0.657920i
$438$		0			0
$439$	−11.5205	−	19.9541i	−0.549844	−	0.952357i	−0.998285	−	0.0585448i	$-0.981354\pi$
$439$	−11.5205	−	19.9541i	−0.549844	−	0.952357i	0.448441	−	0.893812i	$-0.351979\pi$
$440$	11.0361	−	19.1151i	0.526127	−	0.911278i
$441$		0			0
$442$	−0.412085	+	0.475571i	−0.0196009	+	0.0226206i
$443$	23.1782	+	2.21325i	1.10123	+	0.105155i	0.629807	−	0.776752i	$-0.283134\pi$
$443$	23.1782	+	2.21325i	1.10123	+	0.105155i	0.471424	+	0.881907i	$0.343740\pi$
$444$		0			0
$445$	17.8657	+	39.1204i	0.846915	+	1.85448i
$446$	−4.50233	−	4.29297i	−0.213192	−	0.203278i
$447$		0			0
$448$	−4.79416	−	13.8518i	−0.226503	−	0.654437i
$449$	2.74364	−	11.3095i	0.129481	−	0.533726i	−0.869712	−	0.493559i	$-0.835696\pi$
$449$	2.74364	−	11.3095i	0.129481	−	0.533726i	0.999193	−	0.0401672i	$-0.0127891\pi$
$450$		0			0
$451$	−7.15100	+	0.682838i	−0.336727	+	0.0321536i
$452$	−2.94241	+	4.13204i	−0.138399	+	0.194355i
$453$		0			0
$454$	−4.20960	−	2.70535i	−0.197566	−	0.126968i
$455$	7.73229	−	16.9314i	0.362495	−	0.793754i
$456$		0			0
$457$	−22.6130	−	17.7831i	−1.05779	−	0.831857i	−0.0715957	−	0.997434i	$-0.522809\pi$
$457$	−22.6130	−	17.7831i	−1.05779	−	0.831857i	−0.986197	+	0.165576i	$0.947052\pi$
$458$	−3.96829	+	0.764825i	−0.185426	+	0.0357379i
$459$		0			0
$460$	27.8525	−	17.8997i	1.29863	−	0.834578i
$461$	−0.0543149	−	0.377768i	−0.00252970	−	0.0175944i	0.988517	−	0.151106i	$-0.0482836\pi$
$461$	−0.0543149	−	0.377768i	−0.00252970	−	0.0175944i	−0.991047	+	0.133512i	$0.957375\pi$
$462$		0			0
$463$	27.9111	+	5.37943i	1.29714	+	0.250003i	0.790664	−	0.612250i	$-0.209736\pi$
$463$	27.9111	+	5.37943i	1.29714	+	0.250003i	0.506477	+	0.862254i	$0.330948\pi$
$464$	−17.9882	−	20.7594i	−0.835079	−	0.963733i
$465$		0			0
$466$	9.30214	−	2.73135i	0.430913	−	0.126528i
$467$	16.8190	+	8.67079i	0.778290	+	0.401237i	0.801121	−	0.598503i	$-0.204237\pi$
$467$	16.8190	+	8.67079i	0.778290	+	0.401237i	−0.0228304	+	0.999739i	$0.507268\pi$
$468$		0			0
$469$	−20.5681	+	12.2019i	−0.949746	+	0.563430i
$470$	6.49227			0.299466
$471$		0			0
$472$	−6.20683	+	1.82249i	−0.285692	+	0.0838869i
$473$	8.52163	+	11.9670i	0.391825	+	0.550241i
$474$		0			0
$475$	57.8199	+	11.1439i	2.65296	+	0.511316i
$476$	−0.296210	−	6.21821i	−0.0135768	−	0.285011i
$477$		0			0
$478$	−0.0732048	+	0.0470459i	−0.00334831	+	0.00215183i
$479$	0.877495	+	3.61708i	0.0400938	+	0.165269i	0.988339	−	0.152271i	$-0.0486586\pi$
$479$	0.877495	+	3.61708i	0.0400938	+	0.165269i	−0.948245	+	0.317539i	$0.897143\pi$
$480$		0			0
$481$	6.06356	+	4.76844i	0.276475	+	0.217422i
$482$	−1.26135	+	0.504970i	−0.0574531	+	0.0230007i
$483$		0			0
$484$	−4.95025	−	3.18133i	−0.225011	−	0.144606i
$485$	15.8099	−	45.6798i	0.717892	−	2.07421i
$486$		0			0
$487$	24.5702	−	2.34617i	1.11338	−	0.106315i	0.477888	−	0.878421i	$-0.341402\pi$
$487$	24.5702	−	2.34617i	1.11338	−	0.106315i	0.635494	+	0.772105i	$0.280796\pi$
$488$	−0.00622903	+	0.130763i	−0.000281975	+	0.00591938i
$489$		0			0
$490$	−0.762148	−	2.20208i	−0.0344303	−	0.0994799i
$491$	24.1094	+	7.07915i	1.08804	+	0.319478i	0.776091	−	0.630621i	$-0.217200\pi$
$491$	24.1094	+	7.07915i	1.08804	+	0.319478i	0.311950	+	0.950099i	$0.399018\pi$
$492$		0			0
$493$	−4.02966	−	8.82373i	−0.181487	−	0.397401i
$494$	0.369677	−	2.57116i	0.0166326	−	0.115682i
$495$		0			0
$496$	−12.3449	+	14.2467i	−0.554301	+	0.639698i
$497$	11.1793	−	8.79154i	0.501462	−	0.394354i
$498$		0			0
$499$	10.0109	+	17.3394i	0.448150	+	0.776219i	0.998266	−	0.0588699i	$-0.0187497\pi$
$499$	10.0109	+	17.3394i	0.448150	+	0.776219i	−0.550116	+	0.835088i	$0.685416\pi$
$500$	−54.5157	−	21.8248i	−2.43802	−	0.976035i
$501$		0			0
$502$	7.02199	−	3.62009i	0.313407	−	0.161572i
$503$	−26.5491	+	13.6870i	−1.18376	+	0.610273i	−0.933735	−	0.357965i	$-0.883471\pi$
$503$	−26.5491	+	13.6870i	−1.18376	+	0.610273i	−0.250030	+	0.968238i	$0.580440\pi$
$504$		0			0
$505$	−24.8029	−	9.92960i	−1.10372	−	0.441861i
$506$	2.88665	+	4.99983i	0.128327	+	0.222270i
$507$		0			0
$508$	15.1383	−	11.9049i	0.671655	−	0.528196i
$509$	−14.1403	+	16.3188i	−0.626760	+	0.723320i	−0.976976	−	0.213349i	$-0.931563\pi$
$509$	−14.1403	+	16.3188i	−0.626760	+	0.723320i	0.350216	+	0.936669i	$0.386108\pi$
$510$		0			0
$511$	0.235146	−	1.63548i	0.0104023	−	0.0723493i
$512$	9.09373	+	19.9125i	0.401890	+	0.880017i
$513$		0			0
$514$	−0.211577	−	0.0621245i	−0.00933225	−	0.00274020i
$515$	11.9035	+	34.3929i	0.524530	+	1.51553i
$516$		0			0
$517$	0.766081	−	16.0820i	0.0336922	−	0.707286i
$518$	5.34166	−	0.510067i	0.234699	−	0.0224110i
$519$		0			0
$520$	−2.92192	+	8.44234i	−0.128135	+	0.370221i
$521$	5.87663	+	3.77668i	0.257460	+	0.165459i	0.663003	−	0.748616i	$-0.269281\pi$
$521$	5.87663	+	3.77668i	0.257460	+	0.165459i	−0.405544	+	0.914076i	$0.632918\pi$
$522$		0			0
$523$	12.8224	−	5.13333i	0.560686	−	0.224465i	−0.0739691	−	0.997261i	$-0.523567\pi$
$523$	12.8224	−	5.13333i	0.560686	−	0.224465i	0.634655	+	0.772796i	$0.281142\pi$
$524$	10.1699	+	7.99770i	0.444274	+	0.349381i
$525$		0			0
$526$	1.40532	+	5.79280i	0.0612748	+	0.252578i
$527$	−5.60033	+	3.59911i	−0.243954	+	0.156780i
$528$		0			0
$529$	−0.241297	−	5.06545i	−0.0104912	−	0.220237i
$530$	9.17783	+	1.76888i	0.398659	+	0.0768353i
$531$		0			0
$532$	14.9061	+	20.9326i	0.646260	+	0.907544i
$533$	2.78974	−	0.819142i	0.120837	−	0.0354810i
$534$		0			0
$535$	4.17246			0.180391
$536$	9.27047	−	6.76827i	0.400423	−	0.292345i
$537$		0			0
$538$	3.29244	+	1.69737i	0.141947	+	0.0731788i
$539$	−5.54471	+	1.62807i	−0.238828	+	0.0701261i
$540$		0			0
$541$	7.66409	+	8.84483i	0.329505	+	0.380269i	0.896194	−	0.443663i	$-0.146321\pi$
$541$	7.66409	+	8.84483i	0.329505	+	0.380269i	−0.566689	+	0.823932i	$0.691776\pi$
$542$	2.22065	+	0.427996i	0.0953853	+	0.0183840i
$543$		0			0
$544$	0.645049	+	4.48642i	0.0276563	+	0.192354i
$545$	12.1954	−	7.83748i	0.522392	−	0.335721i
$546$		0			0
$547$	−16.0273	+	3.08901i	−0.685278	+	0.132077i	−0.519995	−	0.854170i	$-0.674066\pi$
$547$	−16.0273	+	3.08901i	−0.685278	+	0.132077i	−0.165284	+	0.986246i	$0.552854\pi$
$548$	12.2346	+	9.62136i	0.522634	+	0.411004i
$549$		0			0
$550$	7.08580	−	15.5157i	0.302139	−	0.661593i
$551$	33.6859	+	21.6486i	1.43507	+	0.922262i
$552$		0			0
$553$	−14.3736	+	20.1849i	−0.611228	+	0.858349i
$554$	10.4393	−	0.996836i	0.443525	−	0.0423515i
$555$		0			0
$556$	−9.00840	+	37.1331i	−0.382041	+	1.57480i
$557$	2.68587	+	7.76032i	0.113804	+	0.328815i	0.987491	−	0.157673i	$-0.0503990\pi$
$557$	2.68587	+	7.76032i	0.113804	+	0.328815i	−0.873687	+	0.486488i	$0.838278\pi$
$558$		0			0
$559$	−4.30343	−	4.10332i	−0.182016	−	0.173552i
$560$	−16.3989	−	35.9087i	−0.692982	−	1.51742i
$561$		0			0
$562$	1.68223	+	0.160633i	0.0709605	+	0.00677590i
$563$	26.1410	−	30.1683i	1.10171	−	1.27144i	0.142178	−	0.989841i	$-0.454589\pi$
$563$	26.1410	−	30.1683i	1.10171	−	1.27144i	0.959532	−	0.281600i	$-0.0908652\pi$
$564$		0			0
$565$	−5.67973	+	9.83759i	−0.238948	+	0.413870i
$566$	−1.57245	−	2.72357i	−0.0660952	−	0.114480i
$567$		0			0
$568$	−4.94025	+	4.71052i	−0.207288	+	0.197649i
$569$	−18.8713	+	9.72885i	−0.791127	+	0.407854i	−0.805911	−	0.592036i	$-0.798324\pi$
$569$	−18.8713	+	9.72885i	−0.791127	+	0.407854i	0.0147841	+	0.999891i	$0.495294\pi$
$570$		0			0
$571$	15.5906	−	14.8656i	0.652447	−	0.622107i	−0.289775	−	0.957095i	$-0.593581\pi$
$571$	15.5906	−	14.8656i	0.652447	−	0.622107i	0.942223	+	0.334988i	$0.108732\pi$
$572$	9.93460	+	3.97721i	0.415386	+	0.166296i
$573$		0			0
$574$	1.01126	−	1.75156i	0.0422092	−	0.0731085i
$575$	41.6376	−	32.7441i	1.73641	−	1.36552i
$576$		0			0
$577$	−8.62656	−	0.823736i	−0.359128	−	0.0342926i	−0.0860673	−	0.996289i	$-0.527430\pi$
$577$	−8.62656	−	0.823736i	−0.359128	−	0.0342926i	−0.273061	+	0.961997i	$0.588036\pi$
$578$	0.809896	−	5.63295i	0.0336872	−	0.234300i
$579$		0			0
$580$	−48.1418	−	45.9031i	−1.99898	−	1.90602i
$581$	−18.9923	−	5.57665i	−0.787935	−	0.231359i
$582$		0			0
$583$	5.46467	−	22.5257i	0.226324	−	0.932918i
$584$	−0.0377342	+	0.792138i	−0.00156145	+	0.0327789i
$585$		0			0
$586$	−2.54493	+	3.57385i	−0.105130	+	0.147634i
$587$	−1.73883	+	5.02402i	−0.0717692	+	0.207363i	−0.975180	−	0.221412i	$-0.928934\pi$
$587$	−1.73883	+	5.02402i	−0.0717692	+	0.207363i	0.903411	+	0.428775i	$0.141055\pi$
$588$		0			0
$589$	11.4157	−	24.9969i	0.470377	−	1.02998i
$590$	−6.49586	+	2.60055i	−0.267430	+	0.107063i
$591$		0			0
$592$	16.0644	−	3.09615i	0.660242	−	0.127251i
$593$	−2.29798	−	9.47239i	−0.0943666	−	0.388985i	0.904967	−	0.425481i	$-0.139895\pi$
$593$	−2.29798	−	9.47239i	−0.0943666	−	0.388985i	−0.999334	+	0.0364969i	$0.988380\pi$
$594$		0			0
$595$	−1.98396	−	13.7987i	−0.0813344	−	0.565693i
$596$	0.121034	+	2.54082i	0.00495776	+	0.104076i
$597$		0			0
$598$	−1.53023	−	1.76598i	−0.0625759	−	0.0722164i
$599$	11.0977	+	15.5845i	0.453438	+	0.636765i	0.976497	−	0.215532i	$-0.0691485\pi$
$599$	11.0977	+	15.5845i	0.453438	+	0.636765i	−0.523058	+	0.852297i	$0.675209\pi$
$600$		0			0
$601$	33.4184	+	17.2284i	1.36317	+	0.702761i	0.975698	−	0.219121i	$-0.0703191\pi$
$601$	33.4184	+	17.2284i	1.36317	+	0.702761i	0.387469	+	0.921883i	$0.373349\pi$
$602$	−4.13626			−0.168581
$603$		0			0
$604$	−3.83534			−0.156058
$605$	−11.7124	−	6.03817i	−0.476178	−	0.245487i
$606$		0			0
$607$	−24.1077	−	33.8545i	−0.978501	−	1.37411i	−0.926844	−	0.375448i	$-0.877489\pi$
$607$	−24.1077	−	33.8545i	−0.978501	−	1.37411i	−0.0516577	−	0.998665i	$-0.516450\pi$
$608$	−12.2525	−	14.1402i	−0.496907	−	0.573461i
$609$		0			0
$610$	0.00673766	+	0.141441i	0.000272800	+	0.00572677i
$611$	0.927400	+	6.45021i	0.0375186	+	0.260947i
$612$		0			0
$613$	−2.94489	−	12.1390i	−0.118943	−	0.490289i	−0.999855	−	0.0170098i	$-0.994585\pi$
$613$	−2.94489	−	12.1390i	−0.118943	−	0.490289i	0.880913	−	0.473279i	$-0.156930\pi$
$614$	−4.10973	+	0.792085i	−0.165855	+	0.0319660i
$615$		0			0
$616$	14.3073	−	5.72779i	0.576458	−	0.230779i
$617$	15.0880	−	33.0380i	0.607418	−	1.33006i	−0.316908	−	0.948456i	$-0.602645\pi$
$617$	15.0880	−	33.0380i	0.607418	−	1.33006i	0.924326	−	0.381604i	$-0.124628\pi$
$618$		0			0
$619$	11.0858	−	32.0303i	0.445576	−	1.28741i	−0.469074	−	0.883159i	$-0.655412\pi$
$619$	11.0858	−	32.0303i	0.445576	−	1.28741i	0.914650	−	0.404248i	$-0.132467\pi$
$620$	−26.4797	+	37.1856i	−1.06345	+	1.49341i
$621$		0			0
$622$	0.369266	−	7.75184i	0.0148062	−	0.310821i
$623$	−7.07941	+	29.1817i	−0.283631	+	1.16914i
$624$		0			0
$625$	−66.1573	−	19.4255i	−2.64629	−	0.777022i
$626$	−2.57852	−	2.45861i	−0.103058	−	0.0982660i
$627$		0			0
$628$	−4.90701	+	34.1290i	−0.195811	+	1.36190i
$629$	5.75124	+	0.549177i	0.229317	+	0.0218971i
$630$		0			0
$631$	−4.04223	+	3.17884i	−0.160919	+	0.126548i	−0.695371	−	0.718651i	$-0.744760\pi$
$631$	−4.04223	+	3.17884i	−0.160919	+	0.126548i	0.534453	+	0.845198i	$0.320518\pi$
$632$	5.94662	−	10.2998i	0.236544	−	0.409706i
$633$		0			0
$634$	3.42433	+	1.37090i	0.135998	+	0.0544452i
$635$	31.2126	−	29.7612i	1.23864	−	1.18104i
$636$		0			0
$637$	2.07894	−	1.07177i	0.0823708	−	0.0424651i
$638$	8.39478	−	8.00441i	0.332353	−	0.316898i
$639$		0			0
$640$	20.4383	+	35.4001i	0.807893	+	1.39931i
$641$	−3.54387	+	6.13817i	−0.139975	+	0.242443i	−0.927487	−	0.373856i	$-0.878035\pi$
$641$	−3.54387	+	6.13817i	−0.139975	+	0.242443i	0.787512	+	0.616299i	$0.211369\pi$
$642$		0			0
$643$	−26.5109	+	30.5952i	−1.04549	+	1.20656i	−0.0675392	+	0.997717i	$0.521515\pi$
$643$	−26.5109	+	30.5952i	−1.04549	+	1.20656i	−0.977949	+	0.208842i	$0.933031\pi$
$644$	23.0122	+	2.19740i	0.906806	+	0.0865895i
$645$		0			0
$646$	−0.808186	−	1.76968i	−0.0317976	−	0.0696271i
$647$	−1.23538	−	1.17794i	−0.0485680	−	0.0463095i	0.665406	−	0.746481i	$-0.268258\pi$
$647$	−1.23538	−	1.17794i	−0.0485680	−	0.0463095i	−0.713974	+	0.700172i	$0.753107\pi$
$648$		0			0
$649$	5.67532	+	16.3978i	0.222776	+	0.643668i
$650$	−1.62764	+	6.70923i	−0.0638414	+	0.263158i
$651$		0			0
$652$	4.39392	−	0.419569i	0.172079	−	0.0164316i
$653$	11.3410	−	15.9262i	0.443808	−	0.623241i	−0.530709	−	0.847554i	$-0.678074\pi$
$653$	11.3410	−	15.9262i	0.443808	−	0.623241i	0.974517	+	0.224313i	$0.0720138\pi$
$654$		0			0
$655$	24.3734	+	15.6639i	0.952349	+	0.612038i
$656$	2.56160	−	5.60913i	0.100014	−	0.219000i
$657$		0			0
$658$	3.56320	+	2.80213i	0.138908	+	0.109238i
$659$	37.4405	−	7.21606i	1.45847	−	0.281098i	0.602500	−	0.798119i	$-0.294171\pi$
$659$	37.4405	−	7.21606i	1.45847	−	0.281098i	0.855973	+	0.517021i	$0.172959\pi$
$660$		0			0
$661$	−0.221567	+	0.142392i	−0.00861794	+	0.00553842i	−0.544943	−	0.838473i	$-0.683449\pi$
$661$	−0.221567	+	0.142392i	−0.00861794	+	0.00553842i	0.536325	+	0.844012i	$0.319812\pi$
$662$	0.0526661	+	0.366301i	0.00204693	+	0.0142367i
$663$		0			0
$664$	9.32871	+	1.79796i	0.362024	+	0.0697744i
$665$	37.6848	+	43.4906i	1.46135	+	1.68649i
$666$		0			0
$667$	34.5620	−	10.1483i	1.33825	−	0.392945i
$668$	−39.3397	−	20.2810i	−1.52210	−	0.784697i
$669$		0			0
$670$	9.28614	−	8.24095i	0.358755	−	0.318376i
$671$	0.351158			0.0135563
$672$		0			0
$673$	−1.38235	+	0.405894i	−0.0532856	+	0.0156461i	−0.308267	−	0.951300i	$-0.599749\pi$
$673$	−1.38235	+	0.405894i	−0.0532856	+	0.0156461i	0.254981	+	0.966946i	$0.417931\pi$
$674$	−5.27240	−	7.40405i	−0.203085	−	0.285193i
$675$		0			0
$676$	19.5999	+	3.77758i	0.753843	+	0.145291i
$677$	−1.95510	−	41.0427i	−0.0751407	−	1.57740i	−0.650506	−	0.759501i	$-0.725443\pi$
$677$	−1.95510	−	41.0427i	−0.0751407	−	1.57740i	0.575366	−	0.817896i	$-0.304860\pi$
$678$		0			0
$679$	28.3929	−	18.2470i	1.08962	−	0.700257i
$680$	1.57745	+	6.50234i	0.0604924	+	0.249353i
$681$		0			0
$682$	−6.25723	−	4.92074i	−0.239602	−	0.188425i
$683$	−39.6538	+	15.8750i	−1.51731	+	0.607440i	−0.972869	−	0.231359i	$-0.925683\pi$
$683$	−39.6538	+	15.8750i	−1.51731	+	0.607440i	−0.544442	+	0.838798i	$0.683259\pi$
$684$		0			0
$685$	29.3216	+	18.8439i	1.12032	+	0.719987i
$686$	−1.89254	+	5.46814i	−0.0722575	+	0.208774i
$687$		0			0
$688$	−12.5537	+	1.19874i	−0.478607	+	0.0457014i
$689$	−0.446398	+	9.37104i	−0.0170064	+	0.357008i
$690$		0			0
$691$	6.89167	+	19.9122i	0.262171	+	0.757495i	0.996867	+	0.0790976i	$0.0252039\pi$
$691$	6.89167	+	19.9122i	0.262171	+	0.757495i	−0.734695	+	0.678397i	$0.762675\pi$
$692$	−23.9362	−	7.02829i	−0.909916	−	0.267176i
$693$		0			0
$694$	4.59460	+	10.0608i	0.174408	+	0.381901i
$695$	−12.1774	+	84.6957i	−0.461915	+	3.21269i
$696$		0			0
$697$	1.42603	−	1.64572i	0.0540146	−	0.0623362i
$698$	−5.05406	+	3.97455i	−0.191299	+	0.150439i
$699$		0			0
$700$	−34.1492	−	59.1481i	−1.29072	−	2.23559i
$701$	−0.789684	−	0.316142i	−0.0298259	−	0.0119405i	0.356702	−	0.934218i	$-0.383901\pi$
$701$	−0.789684	−	0.316142i	−0.0298259	−	0.0119405i	−0.386527	+	0.922278i	$0.626326\pi$
$702$		0			0
$703$	−21.1977	+	10.9282i	−0.799486	+	0.412164i
$704$	16.7736	−	8.64738i	0.632178	−	0.325910i
$705$		0			0
$706$	−2.36966	−	0.948668i	−0.0891832	−	0.0357036i
$707$	−9.32705	−	16.1549i	−0.350780	−	0.607568i
$708$		0			0
$709$	17.7497	−	13.9585i	0.666603	−	0.524223i	−0.226536	−	0.974003i	$-0.572740\pi$
$709$	17.7497	−	13.9585i	0.666603	−	0.524223i	0.893139	+	0.449780i	$0.148498\pi$
$710$	−4.83512	+	5.58002i	−0.181459	+	0.209415i
$711$		0			0
$712$	2.05109	−	14.2656i	0.0768677	−	0.534627i
$713$	−10.2693	−	22.4866i	−0.384587	−	0.842128i
$714$		0			0
$715$	22.9931	+	6.75138i	0.859892	+	0.252487i
$716$	0.924342	+	2.67071i	0.0345443	+	0.0998092i
$717$		0			0
$718$	−0.270379	+	5.67596i	−0.0100905	+	0.211825i
$719$	4.89236	−	0.467164i	0.182454	−	0.0174223i	−0.00342887	−	0.999994i	$-0.501091\pi$
$719$	4.89236	−	0.467164i	0.182454	−	0.0174223i	0.185883	+	0.982572i	$0.440485\pi$
$720$		0			0
$721$	−8.31123	+	24.0137i	−0.309526	+	0.894318i
$722$	0.962190	+	0.618362i	0.0358090	+	0.0230131i
$723$		0			0
$724$	−30.6220	+	12.2592i	−1.13806	+	0.455610i
$725$	−83.6549	−	65.7869i	−3.10686	−	2.44326i
$726$		0			0
$727$	4.20101	+	17.3168i	0.155807	+	0.642245i	0.995127	+	0.0986065i	$0.0314385\pi$
$727$	4.20101	+	17.3168i	0.155807	+	0.642245i	−0.839320	+	0.543638i	$0.817046\pi$
$728$	−5.24746	+	3.37234i	−0.194484	+	0.124987i
$729$		0			0
$730$	0.0408153	+	0.856819i	0.00151064	+	0.0317123i
$731$	−4.37293	−	0.842813i	−0.161739	−	0.0311726i
$732$		0			0
$733$	−9.34722	−	13.1263i	−0.345248	−	0.484832i	0.605045	−	0.796191i	$-0.293155\pi$
$733$	−9.34722	−	13.1263i	−0.345248	−	0.484832i	−0.950292	+	0.311359i	$0.899216\pi$
$734$	11.0035	−	3.23091i	0.406145	−	0.119255i
$735$		0			0
$736$	−16.8312			−0.620404
$737$	−19.3179	−	23.9751i	−0.711584	−	0.883135i
$738$		0			0
$739$	−35.7394	−	18.4249i	−1.31470	−	0.677772i	−0.348920	−	0.937153i	$-0.613451\pi$
$739$	−35.7394	−	18.4249i	−1.31470	−	0.677772i	−0.965775	+	0.259380i	$0.916482\pi$
$740$	38.0129	−	11.1616i	1.39738	−	0.410308i
$741$		0			0
$742$	4.27366	+	4.93207i	0.156891	+	0.181062i
$743$	−3.74942	−	0.722641i	−0.137553	−	0.0265111i	0.120010	−	0.992773i	$-0.461707\pi$
$743$	−3.74942	−	0.722641i	−0.137553	−	0.0265111i	−0.257563	+	0.966262i	$0.582919\pi$
$744$		0			0
$745$	0.810666	+	5.63831i	0.0297005	+	0.206572i
$746$	−9.85062	+	6.33061i	−0.360657	+	0.231780i
$747$		0			0
$748$	7.86986	−	1.51679i	0.287750	−	0.0554593i
$749$	2.29000	+	1.80088i	0.0836749	+	0.0658026i
$750$		0			0
$751$	−15.0968	+	33.0573i	−0.550889	+	1.20628i	0.405477	+	0.914105i	$0.367105\pi$
$751$	−15.0968	+	33.0573i	−0.550889	+	1.20628i	−0.956366	+	0.292173i	$0.905622\pi$
$752$	11.6266	+	7.47194i	0.423977	+	0.272474i
$753$		0			0
$754$	−2.72324	+	3.82425i	−0.0991744	+	0.139271i
$755$	−8.54985	+	0.816412i	−0.311161	+	0.0297123i
$756$		0			0
$757$	−3.68340	+	15.1832i	−0.133875	+	0.551842i	0.864881	+	0.501978i	$0.167394\pi$
$757$	−3.68340	+	15.1832i	−0.133875	+	0.551842i	−0.998756	+	0.0498644i	$0.984121\pi$
$758$	−3.20031	−	9.24668i	−0.116240	−	0.335855i
$759$		0			0
$760$	−19.9895	−	19.0599i	−0.725094	−	0.691376i
$761$	17.8635	+	39.1157i	0.647553	+	1.41794i	0.893680	+	0.448705i	$0.148115\pi$
$761$	17.8635	+	39.1157i	0.647553	+	1.41794i	−0.246127	+	0.969238i	$0.579158\pi$
$762$		0			0
$763$	10.0760	+	0.962141i	0.364776	+	0.0348319i
$764$	−4.06686	+	4.69341i	−0.147134	+	0.169802i
$765$		0			0
$766$	−3.81311	+	6.60450i	−0.137773	+	0.238630i
$767$	−3.51161	−	6.08229i	−0.126797	−	0.219619i
$768$		0			0
$769$	22.0326	−	21.0080i	0.794514	−	0.757568i	−0.179572	−	0.983745i	$-0.557471\pi$
$769$	22.0326	−	21.0080i	0.794514	−	0.757568i	0.974086	+	0.226177i	$0.0726228\pi$
$770$	14.8166	−	7.63848i	0.533952	−	0.275272i
$771$		0			0
$772$	−32.5761	+	31.0613i	−1.17244	+	1.11792i
$773$	28.0043	+	11.2112i	1.00725	+	0.403240i	0.815844	−	0.578272i	$-0.196273\pi$
$773$	28.0043	+	11.2112i	1.00725	+	0.403240i	0.191401	+	0.981512i	$0.438697\pi$
$774$		0			0
$775$	−36.5182	+	63.2514i	−1.31177	+	2.27206i
$776$	−12.7333	+	10.0136i	−0.457098	+	0.359466i
$777$		0			0
$778$	−12.0605	−	1.15164i	−0.432389	−	0.0412881i
$779$	−1.27927	+	8.89754i	−0.0458347	+	0.318788i
$780$		0			0
$781$	13.2517	+	12.6355i	0.474185	+	0.452134i
$782$	−1.67922	−	0.493063i	−0.0600487	−	0.0176319i
$783$		0			0
$784$	1.16949	−	4.82071i	0.0417676	−	0.172168i
$785$	−3.67395	+	77.1258i	−0.131129	+	2.75274i
$786$		0			0
$787$	20.7225	−	29.1007i	0.738679	−	1.03733i	−0.258770	−	0.965939i	$-0.583317\pi$
$787$	20.7225	−	29.1007i	0.738679	−	1.03733i	0.997448	−	0.0713903i	$-0.0227436\pi$
$788$	−8.31540	+	24.0258i	−0.296224	+	0.855883i
$789$		0			0
$790$	5.34405	−	11.7018i	0.190133	−	0.416333i
$791$	−7.36325	+	2.94780i	−0.261807	+	0.104812i
$792$		0			0
$793$	−0.139562	+	0.0268984i	−0.00495599	+	0.000955189i
$794$	2.17871	+	8.98075i	0.0773194	+	0.318715i
$795$		0			0
$796$	2.00839	+	13.9687i	0.0711856	+	0.495107i
$797$	0.0436329	+	0.915967i	0.00154556	+	0.0324452i	0.999508	−	0.0313530i	$-0.00998161\pi$
$797$	0.0436329	+	0.915967i	0.00154556	+	0.0324452i	−0.997963	+	0.0637983i	$0.979679\pi$
$798$		0			0
$799$	3.19611	+	3.68851i	0.113070	+	0.130490i
$800$	28.8447	+	40.5067i	1.01981	+	1.43213i
$801$		0			0
$802$	3.03828	+	1.56634i	0.107286	+	0.0553095i
$803$	2.12724			0.0750688
$804$		0			0
$805$	51.7671			1.82455
$806$	2.86376	+	1.47637i	0.100872	+	0.0520029i
$807$		0			0
$808$	5.19338	+	7.29308i	0.182702	+	0.256570i
$809$	19.9349	+	23.0061i	0.700874	+	0.808852i	0.988870	−	0.148780i	$-0.0475346\pi$
$809$	19.9349	+	23.0061i	0.700874	+	0.808852i	−0.287996	+	0.957631i	$0.592989\pi$
$810$		0			0
$811$	1.26442	+	26.5435i	0.0443998	+	0.932067i	0.905687	+	0.423948i	$0.139356\pi$
$811$	1.26442	+	26.5435i	0.0443998	+	0.932067i	−0.861287	+	0.508119i	$0.830341\pi$
$812$	−6.60974	−	45.9718i	−0.231956	−	1.61329i
$813$		0			0
$814$	1.62871	+	6.71365i	0.0570864	+	0.235313i
$815$	9.70573	−	1.87063i	0.339977	−	0.0655252i
$816$		0			0
$817$	17.0666	−	6.83244i	0.597086	−	0.239037i
$818$	3.28891	−	7.20171i	0.114994	−	0.251802i
$819$		0			0
$820$	4.88397	−	14.1113i	0.170556	−	0.492788i
$821$	11.1578	−	15.6689i	0.389410	−	0.546849i	−0.572611	−	0.819827i	$-0.694069\pi$
$821$	11.1578	−	15.6689i	0.389410	−	0.546849i	0.962020	+	0.272978i	$0.0880087\pi$
$822$		0			0
$823$	−1.53571	+	32.2384i	−0.0535313	+	1.12376i	0.799083	+	0.601220i	$0.205319\pi$
$823$	−1.53571	+	32.2384i	−0.0535313	+	1.12376i	−0.852615	+	0.522540i	$0.824984\pi$
$824$	2.87542	−	11.8526i	0.100170	−	0.412906i
$825$		0			0
$826$	−4.68759	−	1.37640i	−0.163102	−	0.0478911i
$827$	−30.1000	−	28.7003i	−1.04668	−	0.998006i	−0.0466789	−	0.998910i	$-0.514864\pi$
$827$	−30.1000	−	28.7003i	−1.04668	−	0.998006i	−1.00000		0.000903979i	$0.999712\pi$
$828$		0			0
$829$	3.83431	−	26.6682i	0.133171	−	0.926225i	−0.808214	−	0.588890i	$-0.799565\pi$
$829$	3.83431	−	26.6682i	0.133171	−	0.926225i	0.941385	−	0.337335i	$-0.109526\pi$
$830$	10.2296	+	0.976809i	0.355075	+	0.0339056i
$831$		0			0
$832$	−6.00400	+	4.72159i	−0.208151	+	0.163692i
$833$	0.875887	−	1.51708i	0.0303477	−	0.0525637i
$834$		0			0
$835$	−92.0143	−	36.8370i	−3.18429	−	1.27480i
$836$	−23.9442	+	22.8308i	−0.828128	+	0.789618i
$837$		0			0
$838$	−6.89866	+	3.55651i	−0.238310	+	0.122857i
$839$	17.7853	−	16.9582i	0.614016	−	0.585463i	−0.317906	−	0.948122i	$-0.602980\pi$
$839$	17.7853	−	16.9582i	0.614016	−	0.585463i	0.931922	+	0.362659i	$0.118131\pi$
$840$		0			0
$841$	−21.6854	−	37.5602i	−0.747772	−	1.29518i
$842$	−4.07464	+	7.05748i	−0.140421	+	0.243217i
$843$		0			0
$844$	23.1776	−	26.7483i	0.797805	−	0.920716i
$845$	44.4968	+	4.24893i	1.53074	+	0.146168i
$846$		0			0
$847$	−3.82207	−	8.36917i	−0.131328	−	0.287568i
$848$	14.4001	+	13.7305i	0.494503	+	0.471508i
$849$		0			0
$850$	1.69116	+	4.88629i	0.0580064	+	0.167598i
$851$	−5.05792	+	20.8490i	−0.173383	+	0.714695i
$852$		0			0
$853$	23.7625	−	2.26905i	0.813613	−	0.0776906i	0.320050	−	0.947401i	$-0.396300\pi$
$853$	23.7625	−	2.26905i	0.813613	−	0.0776906i	0.493563	+	0.869710i	$0.335694\pi$
$854$	−0.0573494	+	0.0805360i	−0.00196246	+	0.00275589i
$855$		0			0
$856$	−1.17629	−	0.755958i	−0.0402049	−	0.0258381i
$857$	15.4550	−	33.8417i	0.527932	−	1.15601i	−0.438416	−	0.898772i	$-0.644460\pi$
$857$	15.4550	−	33.8417i	0.527932	−	1.15601i	0.966348	−	0.257238i	$-0.0828125\pi$
$858$		0			0
$859$	19.1125	+	15.0302i	0.652110	+	0.512825i	0.888526	−	0.458827i	$-0.151730\pi$
$859$	19.1125	+	15.0302i	0.652110	+	0.512825i	−0.236415	+	0.971652i	$0.575973\pi$
$860$	−29.9867	+	5.77947i	−1.02254	+	0.197078i
$861$		0			0
$862$	10.4452	−	6.71274i	0.355766	−	0.228637i
$863$	−4.47441	−	31.1202i	−0.152311	−	1.05934i	−0.912333	−	0.409448i	$-0.865721\pi$
$863$	−4.47441	−	31.1202i	−0.152311	−	1.05934i	0.760023	−	0.649897i	$-0.225188\pi$
$864$		0			0
$865$	−54.8552	−	10.5725i	−1.86513	−	0.359475i
$866$	−2.62381	−	3.02803i	−0.0891605	−	0.102897i
$867$		0			0
$868$	−30.5827	+	8.97990i	−1.03805	+	0.304798i
$869$	−28.3560	−	14.6186i	−0.961913	−	0.495901i
$870$		0			0
$871$	9.51405	+	8.04878i	0.322371	+	0.272722i
$872$	−4.85807			−0.164515
$873$		0			0
$874$	6.93173	−	2.03534i	0.234469	−	0.0688464i
$875$	−53.2585	−	74.7911i	−1.80047	−	2.52840i
$876$		0			0
$877$	−34.4800	−	6.64548i	−1.16431	−	0.224402i	−0.429750	−	0.902948i	$-0.641398\pi$
$877$	−34.4800	−	6.64548i	−1.16431	−	0.224402i	−0.734558	+	0.678546i	$0.762610\pi$
$878$	0.397400	+	8.34246i	0.0134116	+	0.281544i
$879$		0			0
$880$	42.7553	−	27.4772i	1.44128	−	0.926255i
$881$	−2.83874	−	11.7015i	−0.0956397	−	0.394232i	0.903791	−	0.427974i	$-0.140773\pi$
$881$	−2.83874	−	11.7015i	−0.0956397	−	0.394232i	−0.999431	+	0.0337422i	$0.989257\pi$
$882$		0			0
$883$	8.33568	+	6.55525i	0.280518	+	0.220602i	0.748498	−	0.663137i	$-0.230776\pi$
$883$	8.33568	+	6.55525i	0.280518	+	0.220602i	−0.467980	+	0.883739i	$0.655018\pi$
$884$	−3.01156	+	1.20565i	−0.101290	+	0.0405502i
$885$		0			0
$886$	−7.10008	−	4.56294i	−0.238532	−	0.153295i
$887$	−12.0455	+	34.8033i	−0.404450	+	1.16858i	0.540494	+	0.841348i	$0.318237\pi$
$887$	−12.0455	+	34.8033i	−0.404450	+	1.16858i	−0.944944	+	0.327233i	$0.893884\pi$
$888$		0			0
$889$	29.9759	−	2.86235i	1.00536	−	0.0960001i
$890$	0.741761	−	15.5715i	0.0248639	−	0.521957i
$891$		0			0
$892$	−10.4889	−	30.3057i	−0.351194	−	1.01471i
$893$	−19.3308	−	5.67604i	−0.646881	−	0.189941i
$894$		0			0
$895$	2.62907	+	5.75686i	0.0878801	+	0.192431i
$896$	−4.06177	+	28.2503i	−0.135694	+	0.943775i
$897$		0			0
$898$	−2.76244	+	3.18803i	−0.0921839	+	0.106386i
$899$	−39.0405	+	30.7018i	−1.30207	+	1.02396i
$900$		0			0
$901$	3.51323	+	6.08509i	0.117043	+	0.202724i
$902$	2.41737	+	0.967768i	0.0804895	+	0.0322232i
$903$		0			0
$904$	3.38357	−	1.74435i	0.112536	−	0.0580163i
$905$	−65.6538	+	33.8469i	−2.18241	+	1.12511i
$906$		0			0
$907$	0.738517	+	0.295658i	0.0245221	+	0.00981715i	0.383891	−	0.923378i	$-0.374584\pi$
$907$	0.738517	+	0.295658i	0.0245221	+	0.00981715i	−0.359369	+	0.933196i	$0.617008\pi$
$908$	−12.8978	−	22.3397i	−0.428030	−	0.741370i
$909$		0			0
$910$	−5.30350	+	4.17072i	−0.175809	+	0.138258i
$911$	16.4933	−	19.0343i	0.546449	−	0.630635i	−0.413603	−	0.910457i	$-0.635730\pi$
$911$	16.4933	−	19.0343i	0.546449	−	0.630635i	0.960052	+	0.279822i	$0.0902754\pi$
$912$		0			0
$913$	3.62674	−	25.2245i	0.120028	−	0.834810i
$914$	4.33185	+	9.48544i	0.143285	+	0.313750i
$915$		0			0
$916$	−19.9893	−	5.86940i	−0.660466	−	0.193930i
$917$	6.61636	+	19.1167i	0.218492	+	0.631290i
$918$		0			0
$919$	2.57647	−	54.0868i	0.0849899	−	1.78416i	−0.406872	−	0.913485i	$-0.633380\pi$
$919$	2.57647	−	54.0868i	0.0849899	−	1.78416i	0.491862	−	0.870673i	$-0.336317\pi$
$920$	−24.7336	+	2.36177i	−0.815443	+	0.0778654i
$921$		0			0
$922$	−0.0452472	+	0.130733i	−0.00149014	+	0.00430547i
$923$	−6.23455	−	4.00670i	−0.205213	−	0.131882i
$924$		0			0
$925$	58.8445	−	23.5578i	1.93479	−	0.774575i
$926$	−8.09906	−	6.36917i	−0.266151	−	0.209304i
$927$		0			0
$928$	7.97238	+	32.8626i	0.261706	+	1.07877i
$929$	−26.3979	+	16.9649i	−0.866087	+	0.556600i	−0.896553	−	0.442935i	$-0.853937\pi$
$929$	−26.3979	+	16.9649i	−0.866087	+	0.556600i	0.0304665	+	0.999536i	$0.490301\pi$
$930$		0			0
$931$	0.344076	+	7.22305i	0.0112766	+	0.236726i
$932$	49.0743	+	9.45830i	1.60748	+	0.309817i
$933$		0			0
$934$	−3.97864	−	5.58721i	−0.130185	−	0.182819i
$935$	17.2208	−	5.05649i	0.563181	−	0.165365i
$936$		0			0
$937$	19.6125			0.640711			0.320356	−	0.947297i	$-0.396198\pi$
$937$	19.6125			0.640711			0.320356	+	0.947297i	$0.396198\pi$
$938$	8.65345	−	0.514946i	0.282545	−	0.0168136i
$939$		0			0
$940$	29.7476	+	15.3359i	0.970259	+	0.500203i
$941$	40.4242	−	11.8696i	1.31779	−	0.386938i	0.454095	−	0.890953i	$-0.349963\pi$
$941$	40.4242	−	11.8696i	1.31779	−	0.386938i	0.863695	+	0.504015i	$0.168145\pi$
$942$		0			0
$943$	5.29540	+	6.11121i	0.172442	+	0.199008i
$944$	−14.6260	−	2.81892i	−0.476034	−	0.0917481i
$945$		0			0
$946$	−0.757857	−	5.27101i	−0.0246400	−	0.171375i
$947$	−5.19730	+	3.34010i	−0.168889	+	0.108539i	−0.622355	−	0.782735i	$-0.713824\pi$
$947$	−5.19730	+	3.34010i	−0.168889	+	0.108539i	0.453465	+	0.891274i	$0.350188\pi$
$948$		0			0
$949$	−0.845437	+	0.162945i	−0.0274441	+	0.00528941i
$950$	−16.7778	−	13.1942i	−0.544342	−	0.428075i
$951$		0			0
$952$	−1.94071	+	4.24957i	−0.0628988	+	0.137729i
$953$	4.32350	+	2.77854i	0.140052	+	0.0900058i	0.608790	−	0.793331i	$-0.291655\pi$
$953$	4.32350	+	2.77854i	0.140052	+	0.0900058i	−0.468739	+	0.883337i	$0.655291\pi$
$954$		0			0
$955$	−8.06689	+	11.3284i	−0.261039	+	0.366577i
$956$	−0.446555	+	0.0426409i	−0.0144426	+	0.00137910i
$957$		0			0
$958$	0.318075	−	1.31112i	0.0102765	−	0.0423605i
$959$	7.95959	+	22.9977i	0.257029	+	0.742635i
$960$		0			0
$961$	2.23272	+	2.12890i	0.0720233	+	0.0686741i
$962$	−1.16156	−	2.54347i	−0.0374503	−	0.0820048i
$963$		0			0
$964$	−6.97235	−	0.665778i	−0.224564	−	0.0214433i
$965$	−66.0077	+	76.1769i	−2.12486	+	2.45222i
$966$		0			0
$967$	−12.6032	+	21.8294i	−0.405291	+	0.701985i	−0.994355	−	0.106101i	$-0.966163\pi$
$967$	−12.6032	+	21.8294i	−0.405291	+	0.701985i	0.589064	+	0.808086i	$0.299497\pi$
$968$	2.20796	+	3.82430i	0.0709666	+	0.122918i
$969$		0			0
$970$	−12.6811	+	12.0914i	−0.407165	+	0.388231i
$971$	37.8736	−	19.5252i	1.21542	−	0.626593i	0.273320	−	0.961923i	$-0.411878\pi$
$971$	37.8736	−	19.5252i	1.21542	−	0.626593i	0.942101	+	0.335330i	$0.108848\pi$
$972$		0			0
$973$	−43.2389	+	41.2282i	−1.38618	+	1.32172i
$974$	−8.30587	−	3.32517i	−0.266137	−	0.106545i
$975$		0			0
$976$	−0.150718	+	0.261051i	−0.00482437	+	0.00835605i
$977$	5.44837	−	4.28464i	0.174309	−	0.137078i	−0.527193	−	0.849745i	$-0.676756\pi$
$977$	5.44837	−	4.28464i	0.174309	−	0.137078i	0.701502	+	0.712668i	$0.252513\pi$
$978$		0			0
$979$	−38.4846	−	3.67484i	−1.22997	−	0.117448i
$980$	1.70956	−	11.8903i	0.0546099	−	0.379821i
$981$		0			0
$982$	−6.59186	−	6.28533i	−0.210355	−	0.200573i
$983$	−55.6393	−	16.3372i	−1.77462	−	0.521075i	−0.780101	−	0.625654i	$-0.784832\pi$
$983$	−55.6393	−	16.3372i	−1.77462	−	0.521075i	−0.994517	+	0.104579i	$0.966650\pi$
$984$		0			0
$985$	−13.4227	+	55.3290i	−0.427682	+	1.76293i
$986$	−0.167307	+	3.51220i	−0.00532813	+	0.111851i
$987$		0			0
$988$	7.76741	−	10.9078i	0.247114	−	0.347023i
$989$	5.40881	−	15.6277i	0.171990	−	0.496933i
$990$		0			0
$991$	−4.79012	+	10.4889i	−0.152163	+	0.333191i	−0.970328	−	0.241793i	$-0.922264\pi$
$991$	−4.79012	+	10.4889i	−0.152163	+	0.333191i	0.818165	+	0.574984i	$0.194992\pi$
$992$	21.5447	−	8.62519i	0.684044	−	0.273850i
$993$		0			0
$994$	−5.06208	+	0.975637i	−0.160560	+	0.0309453i
$995$	7.45061	+	30.7118i	0.236200	+	0.973630i
$996$		0			0
$997$	−1.25320	−	8.71620i	−0.0396892	−	0.276045i	0.960307	−	0.278947i	$-0.0899853\pi$
$997$	−1.25320	−	8.71620i	−0.0396892	−	0.276045i	−0.999996	+	0.00290212i	$0.999076\pi$
$998$	−0.345327	−	7.24930i	−0.0109311	−	0.229473i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.19.2		100
3.2	odd	2		67.2.g.a.19.4	✓	100
67.60	even	33	inner	603.2.z.c.127.2		100
201.23	odd	66		4489.2.a.p.1.25		50
201.44	even	66		4489.2.a.q.1.26		50
201.194	odd	66		67.2.g.a.60.4	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.19.4	✓	100	3.2	odd	2
67.2.g.a.60.4	yes	100	201.194	odd	66
603.2.z.c.19.2		100	1.1	even	1	trivial
603.2.z.c.127.2		100	67.60	even	33	inner
4489.2.a.p.1.25		50	201.23	odd	66
4489.2.a.q.1.26		50	201.44	even	66

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.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.322186 - 0.166098i) q^{2} +(-1.08390 - 1.52212i) q^{4} +(-2.74026 - 3.16243i) q^{5} +(-0.139020 - 2.91838i) q^{7} +(0.199567 + 1.38802i) q^{8} +O(q^{10})\)	\(q+(-0.322186 - 0.166098i) q^{2} +(-1.08390 - 1.52212i) q^{4} +(-2.74026 - 3.16243i) q^{5} +(-0.139020 - 2.91838i) q^{7} +(0.199567 + 1.38802i) q^{8} +(0.357599 + 1.47404i) q^{10} +(3.69355 - 0.711873i) q^{11} +(-1.41341 + 0.565844i) q^{13} +(-0.439948 + 0.963352i) q^{14} +(-1.05607 + 3.05132i) q^{16} +(-0.661417 + 0.928830i) q^{17} +(0.223966 - 4.70162i) q^{19} +(-1.84344 + 7.59877i) q^{20} +(-1.30825 - 0.384137i) q^{22} +(-3.06447 - 2.92196i) q^{23} +(-1.78036 + 12.3827i) q^{25} +(0.549366 + 0.0524581i) q^{26} +(-4.29146 + 3.37484i) q^{28} +(-4.25355 + 7.36737i) q^{29} +(5.42003 + 2.16985i) q^{31} +(2.87685 - 2.74307i) q^{32} +(0.367376 - 0.189396i) q^{34} +(-8.84824 + 8.43678i) q^{35} +(-2.53337 - 4.38792i) q^{37} +(-0.853089 + 1.47759i) q^{38} +(3.84266 - 4.43466i) q^{40} +(-1.90109 - 0.181532i) q^{41} +(1.62245 + 3.55266i) q^{43} +(-5.08699 - 4.85044i) q^{44} +(0.501994 + 1.45042i) q^{46} +(1.00911 - 4.15959i) q^{47} +(-1.52933 + 0.146034i) q^{49} +(2.63035 - 3.69381i) q^{50} +(2.39328 + 1.53807i) q^{52} +(2.55985 - 5.60528i) q^{53} +(-12.3725 - 9.72988i) q^{55} +(4.02304 - 0.775377i) q^{56} +(2.59414 - 1.66715i) q^{58} +(0.656506 + 4.56610i) q^{59} +(0.0916683 + 0.0176676i) q^{61} +(-1.38585 - 1.59935i) q^{62} +(4.81373 - 1.41344i) q^{64} +(5.66256 + 2.91925i) q^{65} +(-3.83660 - 7.23052i) q^{67} +2.13070 q^{68} +(4.25211 - 1.24853i) q^{70} +(2.82358 + 3.96517i) q^{71} +(0.555307 + 0.107027i) q^{73} +(0.0873886 + 1.83451i) q^{74} +(-7.39920 + 4.75517i) q^{76} +(-2.59100 - 10.6802i) q^{77} +(-6.66672 - 5.24277i) q^{79} +(12.5435 - 5.02167i) q^{80} +(0.582352 + 0.374255i) q^{82} +(2.21585 - 6.40227i) q^{83} +(4.74982 - 0.453553i) q^{85} +(0.0673620 - 1.41410i) q^{86} +(1.72521 + 4.98466i) q^{88} +(-9.86134 - 2.89555i) q^{89} +(1.84784 + 4.04621i) q^{91} +(-1.12601 + 7.83160i) q^{92} +(-1.01602 + 1.17255i) q^{94} +(-15.4823 + 12.1754i) q^{95} +(5.77589 + 10.0041i) q^{97} +(0.516985 + 0.206970i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

L-functions

Modular forms

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