LMFDB - Embedded newform 603.2.z.c.55.2

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			55.2
Character	$\chi$	$=$	603.55
Dual form			603.2.z.c.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597030 + 0.239015i) q^{2} +(-1.14815 - 1.09476i) q^{4} +(-2.47647 + 1.59153i) q^{5} +(0.640337 - 0.503567i) q^{7} +(-0.958120 - 2.09799i) q^{8} +O(q^{10})$	\(q+(0.597030 + 0.239015i) q^{2} +(-1.14815 - 1.09476i) q^{4} +(-2.47647 + 1.59153i) q^{5} +(0.640337 - 0.503567i) q^{7} +(-0.958120 - 2.09799i) q^{8} +(-1.85892 + 0.358278i) q^{10} +(4.57279 + 2.35744i) q^{11} +(1.22728 + 1.72348i) q^{13} +(0.502660 - 0.147594i) q^{14} +(0.0803947 + 1.68769i) q^{16} +(3.65972 - 3.48954i) q^{17} +(5.10149 + 4.01186i) q^{19} +(4.58570 + 0.883821i) q^{20} +(2.16663 + 2.50042i) q^{22} +(1.85150 + 5.34955i) q^{23} +(1.52285 - 3.33458i) q^{25} +(0.320788 + 1.32231i) q^{26} +(-1.28649 - 0.122845i) q^{28} +(-2.07365 - 3.59167i) q^{29} +(-0.909392 + 1.27706i) q^{31} +(-1.86410 + 5.38595i) q^{32} +(3.01901 - 1.20863i) q^{34} +(-0.784333 + 2.26618i) q^{35} +(3.99330 - 6.91661i) q^{37} +(2.08685 + 3.61453i) q^{38} +(5.71177 + 3.67073i) q^{40} +(1.43537 + 5.91669i) q^{41} +(-6.96586 - 2.04536i) q^{43} +(-2.66943 - 7.71280i) q^{44} +(-0.173222 + 3.63637i) q^{46} +(5.14467 + 0.991554i) q^{47} +(-1.49386 + 6.15778i) q^{49} +(1.70620 - 1.62686i) q^{50} +(0.477688 - 3.32239i) q^{52} +(4.18385 - 1.22849i) q^{53} +(-15.0763 + 1.43961i) q^{55} +(-1.67000 - 0.860944i) q^{56} +(-0.379570 - 2.63997i) q^{58} +(-1.87516 - 4.10604i) q^{59} +(0.0838230 - 0.0432138i) q^{61} +(-0.848171 + 0.545086i) q^{62} +(-0.187328 + 0.216189i) q^{64} +(-5.78229 - 2.31488i) q^{65} +(-6.19207 - 5.35334i) q^{67} -8.02212 q^{68} +(-1.00992 + 1.16551i) q^{70} +(-0.640015 - 0.610253i) q^{71} +(6.08960 - 3.13941i) q^{73} +(4.03729 - 3.17496i) q^{74} +(-1.46526 - 10.1911i) q^{76} +(4.11526 - 0.793150i) q^{77} +(7.09030 - 0.677042i) q^{79} +(-2.88511 - 4.05156i) q^{80} +(-0.557215 + 3.87552i) q^{82} +(0.172253 + 3.61605i) q^{83} +(-3.50948 + 14.4663i) q^{85} +(-3.66996 - 2.88609i) q^{86} +(0.564599 - 11.8524i) q^{88} +(6.78300 + 7.82800i) q^{89} +(1.65376 + 0.485588i) q^{91} +(3.73067 - 8.16903i) q^{92} +(2.83453 + 1.82164i) q^{94} +(-19.0187 - 1.81606i) q^{95} +(6.75458 - 11.6993i) q^{97} +(-2.36368 + 3.31932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{4}{33}\right)$	$1$

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 $

$2$	0.597030	+	0.239015i	0.422164	+	0.169009i	0.573010	−	0.819548i	$-0.305776\pi$
$2$	0.597030	+	0.239015i	0.422164	+	0.169009i	−0.150846	+	0.988557i	$0.548200\pi$
$3$		0			0
$3$		0			0
$4$	−1.14815	−	1.09476i	−0.574076	−	0.547380i
$5$	−2.47647	+	1.59153i	−1.10751	+	0.711753i	−0.960749	−	0.277419i	$-0.910521\pi$
$5$	−2.47647	+	1.59153i	−1.10751	+	0.711753i	−0.146761	+	0.989172i	$0.546885\pi$
$6$		0			0
$7$	0.640337	−	0.503567i	0.242025	−	0.190330i	−0.489777	−	0.871848i	$-0.662922\pi$
$7$	0.640337	−	0.503567i	0.242025	−	0.190330i	0.731802	+	0.681517i	$0.238680\pi$
$8$	−0.958120	−	2.09799i	−0.338747	−	0.741752i
$9$		0			0
$10$	−1.85892	+	0.358278i	−0.587843	+	0.113297i
$11$	4.57279	+	2.35744i	1.37875	+	0.710794i	0.978622	−	0.205666i	$-0.0659360\pi$
$11$	4.57279	+	2.35744i	1.37875	+	0.710794i	0.400126	+	0.916460i	$0.368966\pi$
$12$		0			0
$13$	1.22728	+	1.72348i	0.340387	+	0.478007i	0.948918	−	0.315524i	$-0.102180\pi$
$13$	1.22728	+	1.72348i	0.340387	+	0.478007i	−0.608531	+	0.793530i	$0.708241\pi$
$14$	0.502660	−	0.147594i	0.134342	−	0.0394463i
$15$		0			0
$16$	0.0803947	+	1.68769i	0.0200987	+	0.421923i
$17$	3.65972	−	3.48954i	0.887613	−	0.846337i	−0.101297	−	0.994856i	$-0.532299\pi$
$17$	3.65972	−	3.48954i	0.887613	−	0.846337i	0.988910	+	0.148519i	$0.0474507\pi$
$18$		0			0
$19$	5.10149	+	4.01186i	1.17036	+	0.920383i	0.997909	−	0.0646351i	$-0.0205883\pi$
$19$	5.10149	+	4.01186i	1.17036	+	0.920383i	0.172453	+	0.985018i	$0.444831\pi$
$20$	4.58570	+	0.883821i	1.02539	+	0.197628i
$21$		0			0
$22$	2.16663	+	2.50042i	0.461927	+	0.533092i
$23$	1.85150	+	5.34955i	0.386064	+	1.11546i	0.955898	+	0.293698i	$0.0948861\pi$
$23$	1.85150	+	5.34955i	0.386064	+	1.11546i	−0.569835	+	0.821759i	$0.692993\pi$
$24$		0			0
$25$	1.52285	−	3.33458i	0.304570	−	0.666915i
$26$	0.320788	+	1.32231i	0.0629117	+	0.259326i
$27$		0			0
$28$	−1.28649	−	0.122845i	−0.243124	−	0.0232155i
$29$	−2.07365	−	3.59167i	−0.385067	−	0.666956i	0.606711	−	0.794922i	$-0.292488\pi$
$29$	−2.07365	−	3.59167i	−0.385067	−	0.666956i	−0.991779	+	0.127966i	$0.959155\pi$
$30$		0			0
$31$	−0.909392	+	1.27706i	−0.163332	+	0.229367i	−0.888128	−	0.459596i	$-0.847994\pi$
$31$	−0.909392	+	1.27706i	−0.163332	+	0.229367i	0.724797	+	0.688963i	$0.241934\pi$
$32$	−1.86410	+	5.38595i	−0.329529	+	0.952111i
$33$		0			0
$34$	3.01901	−	1.20863i	0.517757	−	0.207278i
$35$	−0.784333	+	2.26618i	−0.132576	+	0.383055i
$36$		0			0
$37$	3.99330	−	6.91661i	0.656495	−	1.13708i	−0.325021	−	0.945707i	$-0.605372\pi$
$37$	3.99330	−	6.91661i	0.656495	−	1.13708i	0.981517	−	0.191377i	$-0.0612952\pi$
$38$	2.08685	+	3.61453i	0.338532	+	0.586354i
$39$		0			0
$40$	5.71177	+	3.67073i	0.903110	+	0.580393i
$41$	1.43537	+	5.91669i	0.224168	+	0.924032i	0.967045	+	0.254605i	$0.0819454\pi$
$41$	1.43537	+	5.91669i	0.224168	+	0.924032i	−0.742877	+	0.669427i	$0.766539\pi$
$42$		0			0
$43$	−6.96586	−	2.04536i	−1.06228	−	0.311915i	−0.296514	−	0.955029i	$-0.595824\pi$
$43$	−6.96586	−	2.04536i	−1.06228	−	0.311915i	−0.765771	+	0.643114i	$0.777642\pi$
$44$	−2.66943	−	7.71280i	−0.402431	−	1.16275i
$45$		0			0
$46$	−0.173222	+	3.63637i	−0.0255402	+	0.536154i
$47$	5.14467	+	0.991554i	0.750428	+	0.144633i	0.550103	−	0.835097i	$-0.314588\pi$
$47$	5.14467	+	0.991554i	0.750428	+	0.144633i	0.200324	+	0.979730i	$0.435800\pi$
$48$		0			0
$49$	−1.49386	+	6.15778i	−0.213409	+	0.879682i
$50$	1.70620	−	1.62686i	0.241293	−	0.230072i
$51$		0			0
$52$	0.477688	−	3.32239i	0.0662434	−	0.460733i
$53$	4.18385	−	1.22849i	0.574696	−	0.168746i	0.0185462	−	0.999828i	$-0.494096\pi$
$53$	4.18385	−	1.22849i	0.574696	−	0.168746i	0.556150	+	0.831082i	$0.312278\pi$
$54$		0			0
$55$	−15.0763	+	1.43961i	−2.03289	+	0.194117i
$56$	−1.67000	−	0.860944i	−0.223163	−	0.115049i
$57$		0			0
$58$	−0.379570	−	2.63997i	−0.0498400	−	0.346645i
$59$	−1.87516	−	4.10604i	−0.244125	−	0.534560i	0.747415	−	0.664357i	$-0.231295\pi$
$59$	−1.87516	−	4.10604i	−0.244125	−	0.534560i	−0.991541	+	0.129797i	$0.958567\pi$
$60$		0			0
$61$	0.0838230	−	0.0432138i	0.0107324	−	0.00553295i	−0.452852	−	0.891586i	$-0.649593\pi$
$61$	0.0838230	−	0.0432138i	0.0107324	−	0.00553295i	0.463584	+	0.886053i	$0.346563\pi$
$62$	−0.848171	+	0.545086i	−0.107718	+	0.0692260i
$63$		0			0
$64$	−0.187328	+	0.216189i	−0.0234161	+	0.0270236i
$65$	−5.78229	−	2.31488i	−0.717205	−	0.287125i
$66$		0			0
$67$	−6.19207	−	5.35334i	−0.756481	−	0.654015i
$67$	−6.19207	−	5.35334i	−0.756481	−	0.654015i
$68$	−8.02212			−0.972825
$69$		0			0
$70$	−1.00992	+	1.16551i	−0.120709	+	0.139305i
$71$	−0.640015	−	0.610253i	−0.0759558	−	0.0724237i	0.651150	−	0.758949i	$-0.274287\pi$
$71$	−0.640015	−	0.610253i	−0.0759558	−	0.0724237i	−0.727106	+	0.686525i	$0.759135\pi$
$72$		0			0
$73$	6.08960	−	3.13941i	0.712734	−	0.367440i	−0.0634169	−	0.997987i	$-0.520200\pi$
$73$	6.08960	−	3.13941i	0.712734	−	0.367440i	0.776151	+	0.630547i	$0.217169\pi$
$74$	4.03729	−	3.17496i	0.469326	−	0.369082i
$75$		0			0
$76$	−1.46526	−	10.1911i	−0.168077	−	1.16900i
$77$	4.11526	−	0.793150i	0.468977	−	0.0903879i
$78$		0			0
$79$	7.09030	−	0.677042i	0.797722	−	0.0761732i	0.311769	−	0.950158i	$-0.399079\pi$
$79$	7.09030	−	0.677042i	0.797722	−	0.0761732i	0.485953	+	0.873985i	$0.338473\pi$
$80$	−2.88511	−	4.05156i	−0.322565	−	0.452979i
$81$		0			0
$82$	−0.557215	+	3.87552i	−0.0615341	+	0.427979i
$83$	0.172253	+	3.61605i	0.0189073	+	0.396913i	0.988408	+	0.151823i	$0.0485144\pi$
$83$	0.172253	+	3.61605i	0.0189073	+	0.396913i	−0.969500	+	0.245090i	$0.921183\pi$
$84$		0			0
$85$	−3.50948	+	14.4663i	−0.380657	+	1.56909i
$86$	−3.66996	−	2.88609i	−0.395742	−	0.311215i
$87$		0			0
$88$	0.564599	−	11.8524i	0.0601864	−	1.26347i
$89$	6.78300	+	7.82800i	0.718997	+	0.829767i	0.991186	−	0.132477i	$-0.0422931\pi$
$89$	6.78300	+	7.82800i	0.718997	+	0.829767i	−0.272189	+	0.962244i	$0.587748\pi$
$90$		0			0
$91$	1.65376	+	0.485588i	0.173361	+	0.0509034i
$92$	3.73067	−	8.16903i	0.388950	−	0.851681i
$93$		0			0
$94$	2.83453	+	1.82164i	0.292359	+	0.187888i
$95$	−19.0187	−	1.81606i	−1.95127	−	0.186324i
$96$		0			0
$97$	6.75458	−	11.6993i	0.685824	−	1.18788i	−0.287354	−	0.957825i	$-0.592776\pi$
$97$	6.75458	−	11.6993i	0.685824	−	1.18788i	0.973177	−	0.230057i	$-0.0738912\pi$
$98$	−2.36368	+	3.31932i	−0.238768	+	0.335302i
$99$		0			0
$100$	−5.39902	+	2.16144i	−0.539902	+	0.216144i
$101$	−14.3439	+	5.74244i	−1.42727	+	0.571394i	−0.951355	−	0.308096i	$-0.900308\pi$
$101$	−14.3439	+	5.74244i	−1.42727	+	0.571394i	−0.475918	+	0.879490i	$0.657884\pi$
$102$		0			0
$103$	−4.97060	+	6.98023i	−0.489767	+	0.687782i	−0.983310	−	0.181940i	$-0.941762\pi$
$103$	−4.97060	+	6.98023i	−0.489767	+	0.687782i	0.493542	+	0.869722i	$0.335702\pi$
$104$	2.43996	−	4.22613i	0.239257	−	0.414406i
$105$		0			0
$106$	2.79151	+	0.266557i	0.271135	+	0.0258903i
$107$	2.80355	+	1.80174i	0.271030	+	0.174180i	0.669095	−	0.743177i	$-0.266682\pi$
$107$	2.80355	+	1.80174i	0.271030	+	0.174180i	−0.398065	+	0.917357i	$0.630318\pi$
$108$		0			0
$109$	−7.18092	+	15.7240i	−0.687807	+	1.50609i	0.166347	+	0.986067i	$0.446803\pi$
$109$	−7.18092	+	15.7240i	−0.687807	+	1.50609i	−0.854154	+	0.520020i	$0.825924\pi$
$110$	−9.34508	−	2.74396i	−0.891019	−	0.261627i
$111$		0			0
$112$	0.901346	+	1.04021i	0.0851692	+	0.0982905i
$113$	−0.404665	+	8.49496i	−0.0380677	+	0.799139i	0.896433	+	0.443179i	$0.146149\pi$
$113$	−0.404665	+	8.49496i	−0.0380677	+	0.799139i	−0.934501	+	0.355960i	$0.884154\pi$
$114$		0			0
$115$	−13.0991	−	10.3013i	−1.22150	−	0.960598i
$116$	−1.55115	+	6.39393i	−0.144021	+	0.593662i
$117$		0			0
$118$	−0.138126	−	2.89962i	−0.0127155	−	0.266931i
$119$	0.586241	−	4.07739i	0.0537406	−	0.373774i
$120$		0			0
$121$	8.97228	+	12.5998i	0.815662	+	1.14544i
$122$	0.0603735	−	0.00576497i	0.00546596	−	0.000521936i
$123$		0			0
$124$	2.44220	−	0.470695i	0.219316	−	0.0422696i
$125$	−0.558934	−	3.88747i	−0.0499925	−	0.347706i
$126$		0			0
$127$	−2.51206	+	1.97550i	−0.222909	+	0.175298i	−0.723368	−	0.690463i	$-0.757407\pi$
$127$	−2.51206	+	1.97550i	−0.222909	+	0.175298i	0.500459	+	0.865760i	$0.333165\pi$
$128$	9.96817	−	5.13895i	0.881070	−	0.454223i
$129$		0			0
$130$	−2.89891	−	2.76410i	−0.254251	−	0.242428i
$131$	6.83673	−	7.89001i	0.597328	−	0.689353i	−0.373910	−	0.927465i	$-0.621983\pi$
$131$	6.83673	−	7.89001i	0.597328	−	0.689353i	0.971238	+	0.238112i	$0.0765285\pi$
$132$		0			0
$133$	5.28691			0.458433
$134$	−2.41732	−	4.67610i	−0.208825	−	0.403954i
$135$		0			0
$136$	−10.8275	−	4.33467i	−0.928448	−	0.371695i
$137$	−3.49471	+	4.03312i	−0.298574	+	0.344572i	−0.885137	−	0.465331i	$-0.845935\pi$
$137$	−3.49471	+	4.03312i	−0.298574	+	0.344572i	0.586563	+	0.809904i	$0.300481\pi$
$138$		0			0
$139$	13.9512	−	8.96588i	1.18332	−	0.760476i	0.207330	−	0.978271i	$-0.433523\pi$
$139$	13.9512	−	8.96588i	1.18332	−	0.760476i	0.975995	+	0.217795i	$0.0698863\pi$
$140$	3.38146	−	1.74326i	0.285785	−	0.147333i
$141$		0			0
$142$	−0.236249	−	0.517312i	−0.0198255	−	0.0434119i
$143$	1.54912	+	10.7743i	0.129544	+	0.900996i
$144$		0			0
$145$	10.8516	+	5.59438i	0.901174	+	0.464588i
$146$	4.38604	−	0.418816i	0.362991	−	0.0346615i
$147$		0			0
$148$	−12.1569	+	3.56960i	−0.999295	+	0.293419i
$149$	1.34599	−	9.36158i	0.110268	−	0.766930i	−0.857391	−	0.514666i	$-0.827916\pi$
$149$	1.34599	−	9.36158i	0.110268	−	0.766930i	0.967658	−	0.252264i	$-0.0811751\pi$
$150$		0			0
$151$	−2.48225	+	2.36682i	−0.202002	+	0.192609i	−0.784327	−	0.620347i	$-0.786992\pi$
$151$	−2.48225	+	2.36682i	−0.202002	+	0.192609i	0.582325	+	0.812956i	$0.302143\pi$
$152$	3.52900	−	14.5467i	0.286239	−	1.17989i
$153$		0			0
$154$	2.64650	+	0.510072i	0.213261	+	0.0411028i
$155$	0.219598	−	4.60992i	0.0176385	−	0.370278i
$156$		0			0
$157$	−3.40789	−	9.84646i	−0.271979	−	0.785833i	−0.995433	−	0.0954601i	$-0.969568\pi$
$157$	−3.40789	−	9.84646i	−0.271979	−	0.785833i	0.723454	−	0.690373i	$-0.242553\pi$
$158$	4.39495	+	1.29047i	0.349643	+	0.102664i
$159$		0			0
$160$	−3.95552	−	16.3049i	−0.312712	−	1.28901i
$161$	3.87944	+	2.49316i	0.305742	+	0.196489i
$162$		0			0
$163$	12.4707	+	21.5998i	0.976778	+	1.69183i	0.673939	+	0.738787i	$0.264601\pi$
$163$	12.4707	+	21.5998i	0.976778	+	1.69183i	0.302839	+	0.953042i	$0.402065\pi$
$164$	4.82933	−	8.36465i	0.377108	−	0.653169i
$165$		0			0
$166$	−0.761447	+	2.20006i	−0.0590998	+	0.170758i
$167$	7.61869	−	3.05007i	0.589552	−	0.236021i	−0.0576533	−	0.998337i	$-0.518362\pi$
$167$	7.61869	−	3.05007i	0.589552	−	0.236021i	0.647206	+	0.762316i	$0.275938\pi$
$168$		0			0
$169$	2.78773	−	8.05462i	0.214441	−	0.619586i
$170$	−5.55292	+	7.79798i	−0.425889	+	0.598078i
$171$		0			0
$172$	5.75869	+	9.97434i	0.439096	+	0.760536i
$173$	−12.5139	−	1.19493i	−0.951413	−	0.0908489i	−0.392206	−	0.919877i	$-0.628288\pi$
$173$	−12.5139	−	1.19493i	−0.951413	−	0.0908489i	−0.559206	+	0.829028i	$0.688894\pi$
$174$		0			0
$175$	−0.704044	−	2.90211i	−0.0532207	−	0.219379i
$176$	−3.61100	+	7.90699i	−0.272190	+	0.596012i
$177$		0			0
$178$	2.17865	+	6.29479i	0.163297	+	0.471814i
$179$	−12.1920	−	14.0703i	−0.911271	−	1.05166i	−0.998460	−	0.0554709i	$-0.982334\pi$
$179$	−12.1920	−	14.0703i	−0.911271	−	1.05166i	0.0871894	−	0.996192i	$-0.472211\pi$
$180$		0			0
$181$	−20.2807	−	3.90878i	−1.50745	−	0.290537i	−0.632428	−	0.774619i	$-0.717942\pi$
$181$	−20.2807	−	3.90878i	−1.50745	−	0.290537i	−0.875023	+	0.484082i	$0.839154\pi$
$182$	0.871282	+	0.685184i	0.0645837	+	0.0507892i
$183$		0			0
$184$	9.44935	−	9.00993i	0.696615	−	0.664221i
$185$	1.11869	+	23.4842i	0.0822478	+	1.72659i
$186$		0			0
$187$	24.9615	−	7.32936i	1.82537	−	0.535976i
$188$	−4.82135	−	6.77064i	−0.351633	−	0.493800i
$189$		0			0
$190$	−10.9206	−	5.62998i	−0.792266	−	0.408442i
$191$	−12.9749	+	2.50070i	−0.938828	+	0.180944i	−0.635639	−	0.771986i	$-0.719263\pi$
$191$	−12.9749	+	2.50070i	−0.938828	+	0.180944i	−0.303189	+	0.952931i	$0.598051\pi$
$192$		0			0
$193$	−8.10532	−	17.7482i	−0.583434	−	1.27754i	−0.939330	−	0.343016i	$-0.888551\pi$
$193$	−8.10532	−	17.7482i	−0.583434	−	1.27754i	0.355896	−	0.934526i	$-0.384176\pi$
$194$	6.82898	−	5.37037i	0.490292	−	0.385570i
$195$		0			0
$196$	8.45647	−	5.43464i	0.604033	−	0.388189i
$197$	−17.9662	−	17.1307i	−1.28004	−	1.22051i	−0.962192	−	0.272372i	$-0.912192\pi$
$197$	−17.9662	−	17.1307i	−1.28004	−	1.22051i	−0.317847	−	0.948142i	$-0.602960\pi$
$198$		0			0
$199$	−12.1801	−	4.87617i	−0.863423	−	0.345662i	−0.102679	−	0.994715i	$-0.532741\pi$
$199$	−12.1801	−	4.87617i	−0.863423	−	0.345662i	−0.760744	+	0.649052i	$0.775166\pi$
$200$	−8.45498			−0.597858
$201$		0			0
$202$	−9.93627			−0.699114
$203$	−3.13648	−	1.25566i	−0.220138	−	0.0881299i
$204$		0			0
$205$	−12.9712	−	12.3681i	−0.905951	−	0.863822i
$206$	−4.63597	+	2.97936i	−0.323003	+	0.207582i
$207$		0			0
$208$	−2.81003	+	2.20983i	−0.194841	+	0.153224i
$209$	13.8703	+	30.3718i	0.959432	+	2.10086i
$210$		0			0
$211$	6.72315	−	1.29578i	0.462840	−	0.0892052i	0.0475000	−	0.998871i	$-0.484875\pi$
$211$	6.72315	−	1.29578i	0.462840	−	0.0892052i	0.415340	+	0.909666i	$0.363662\pi$
$212$	−6.14860	−	3.16982i	−0.422287	−	0.217704i
$213$		0			0
$214$	1.24316	+	1.74578i	0.0849810	+	0.119339i
$215$	20.5060	−	6.02110i	1.39850	−	0.410636i
$216$		0			0
$217$	0.0607686	+	1.27569i	0.00412524	+	0.0865995i
$218$	−8.04549	+	7.67136i	−0.544910	+	0.519570i
$219$		0			0
$220$	18.8859	+	14.8520i	1.27329	+	1.00132i
$221$	10.5057	+	2.02480i	0.706687	+	0.136203i
$222$		0			0
$223$	10.4406	+	12.0491i	0.699154	+	0.806867i	0.988638	−	0.150316i	$-0.0480291\pi$
$223$	10.4406	+	12.0491i	0.699154	+	0.806867i	−0.289484	+	0.957183i	$0.593484\pi$
$224$	1.51854	+	4.38752i	0.101461	+	0.293154i
$225$		0			0
$226$	−2.27202	+	4.97503i	−0.151132	+	0.330934i
$227$	−0.938150	−	3.86711i	−0.0622672	−	0.256669i	0.932167	−	0.362029i	$-0.117916\pi$
$227$	−0.938150	−	3.86711i	−0.0622672	−	0.256669i	−0.994434	+	0.105360i	$0.966401\pi$
$228$		0			0
$229$	−15.2664	−	1.45777i	−1.00883	−	0.0963319i	−0.422467	−	0.906378i	$-0.638836\pi$
$229$	−15.2664	−	1.45777i	−1.00883	−	0.0963319i	−0.586366	+	0.810046i	$0.699442\pi$
$230$	−5.35841	−	9.28105i	−0.353323	−	0.611974i
$231$		0			0
$232$	−5.54848	+	7.79176i	−0.364276	+	0.511554i
$233$	−3.39495	+	9.80907i	−0.222411	+	0.642614i	0.777495	+	0.628889i	$0.216490\pi$
$233$	−3.39495	+	9.80907i	−0.222411	+	0.642614i	−0.999906	+	0.0137247i	$0.995631\pi$
$234$		0			0
$235$	−14.3187	+	5.73234i	−0.934049	+	0.373937i
$236$	−2.34215	+	6.76720i	−0.152461	+	0.440508i
$237$		0			0
$238$	1.32456	−	2.29421i	0.0858585	−	0.148711i
$239$	0.580154	+	1.00486i	0.0375270	+	0.0649987i	0.884179	−	0.467148i	$-0.154719\pi$
$239$	0.580154	+	1.00486i	0.0375270	+	0.0649987i	−0.846652	+	0.532147i	$0.821385\pi$
$240$		0			0
$241$	4.78817	+	3.07717i	0.308433	+	0.198218i	0.685696	−	0.727888i	$-0.259498\pi$
$241$	4.78817	+	3.07717i	0.308433	+	0.198218i	−0.377262	+	0.926106i	$0.623135\pi$
$242$	2.34518	+	9.66696i	0.150754	+	0.621416i
$243$		0			0
$244$	−0.143550	−	0.0421501i	−0.00918986	−	0.00269839i
$245$	−6.10078	−	17.6270i	−0.389765	−	1.12615i
$246$		0			0
$247$	−0.653373	+	13.7160i	−0.0415731	+	0.872727i
$248$	3.55057	+	0.684317i	0.225462	+	0.0434542i
$249$		0			0
$250$	0.595462	−	2.45453i	0.0376603	−	0.155238i
$251$	5.49267	−	5.23725i	0.346694	−	0.330572i	−0.496645	−	0.867954i	$-0.665435\pi$
$251$	5.49267	−	5.23725i	0.346694	−	0.330572i	0.843339	+	0.537381i	$0.180586\pi$
$252$		0			0
$253$	−4.14472	+	28.8271i	−0.260576	+	1.81235i
$254$	−1.97195	+	0.579016i	−0.123731	+	0.0363307i
$255$		0			0
$256$	7.74911	−	0.739950i	0.484319	−	0.0462469i
$257$	27.1525	+	13.9981i	1.69372	+	0.873175i	0.986012	+	0.166674i	$0.0533026\pi$
$257$	27.1525	+	13.9981i	1.69372	+	0.873175i	0.707711	+	0.706502i	$0.249728\pi$
$258$		0			0
$259$	−0.925912	−	6.43986i	−0.0575333	−	0.400153i
$260$	4.10471	+	8.98805i	0.254563	+	0.557415i
$261$		0			0
$262$	5.96756	−	3.07649i	0.368677	−	0.190066i
$263$	3.51168	−	2.25682i	0.216540	−	0.139162i	−0.427875	−	0.903838i	$-0.640738\pi$
$263$	3.51168	−	2.25682i	0.216540	−	0.139162i	0.644414	+	0.764676i	$0.277101\pi$
$264$		0			0
$265$	−8.40599	+	9.70103i	−0.516376	+	0.595930i
$266$	3.15644	+	1.26365i	0.193534	+	0.0774793i
$267$		0			0
$268$	1.24880	+	12.9253i	0.0762828	+	0.789537i
$269$	6.63103			0.404301			0.202150	−	0.979354i	$-0.435207\pi$
$269$	6.63103			0.404301			0.202150	+	0.979354i	$0.435207\pi$
$270$		0			0
$271$	17.7400	−	20.4731i	1.07763	−	1.24365i	0.109291	−	0.994010i	$-0.465142\pi$
$271$	17.7400	−	20.4731i	1.07763	−	1.24365i	0.968339	−	0.249641i	$-0.0803125\pi$
$272$	6.18349	+	5.89595i	0.374929	+	0.357494i
$273$		0			0
$274$	−3.05042	+	1.57260i	−0.184283	+	0.0950044i
$275$	14.8247	−	11.6583i	0.893965	−	0.703021i
$276$		0			0
$277$	1.32002	+	9.18096i	0.0793125	+	0.551630i	0.990273	+	0.139137i	$0.0444329\pi$
$277$	1.32002	+	9.18096i	0.0793125	+	0.551630i	−0.910961	+	0.412493i	$0.864658\pi$
$278$	10.4723	−	2.01836i	0.628084	−	0.121053i
$279$		0			0
$280$	5.50591	−	0.525751i	0.329041	−	0.0314196i
$281$	−8.93579	−	12.5486i	−0.533065	−	0.748585i	0.456959	−	0.889488i	$-0.348939\pi$
$281$	−8.93579	−	12.5486i	−0.533065	−	0.748585i	−0.990023	+	0.140903i	$0.954999\pi$
$282$		0			0
$283$	0.820413	−	5.70610i	0.0487685	−	0.339192i	−0.950800	−	0.309806i	$-0.899736\pi$
$283$	0.820413	−	5.70610i	0.0487685	−	0.339192i	0.999568	−	0.0293859i	$-0.00935518\pi$
$284$	0.0667534	+	1.40133i	0.00396108	+	0.0831534i
$285$		0			0
$286$	−1.65036	+	6.80287i	−0.0975877	+	0.402262i
$287$	3.89857	+	3.06587i	0.230126	+	0.180973i
$288$		0			0
$289$	0.407798	−	8.56072i	0.0239881	−	0.503572i
$290$	5.14158	+	5.93370i	0.301924	+	0.348439i
$291$		0			0
$292$	−10.4287	−	3.06214i	−0.610293	−	0.179198i
$293$	−2.96432	+	6.49096i	−0.173178	+	0.379206i	−0.976241	−	0.216688i	$-0.930475\pi$
$293$	−2.96432	+	6.49096i	−0.173178	+	0.379206i	0.803063	+	0.595894i	$0.203202\pi$
$294$		0			0
$295$	11.1787	+	7.18408i	0.650846	+	0.418274i
$296$	−18.3370	−	1.75098i	−1.06582	−	0.101773i
$297$		0			0
$298$	3.04115	−	5.26743i	0.176169	−	0.305134i
$299$	−6.94751	+	9.75642i	−0.401785	+	0.564228i
$300$		0			0
$301$	−5.49048	+	2.19806i	−0.316466	+	0.126694i
$302$	−2.04768	+	0.819767i	−0.117831	+	0.0471723i
$303$		0			0
$304$	−6.36065	+	8.93228i	−0.364808	+	0.512301i
$305$	−0.138809	+	0.240424i	−0.00794818	+	0.0137666i
$306$		0			0
$307$	27.2721	+	2.60417i	1.55650	+	0.148628i	0.837521	−	0.546405i	$-0.184004\pi$
$307$	27.2721	+	2.60417i	1.55650	+	0.148628i	0.718978	+	0.695033i	$0.244610\pi$
$308$	−5.59325	−	3.59456i	−0.318705	−	0.204819i
$309$		0			0
$310$	1.23295	−	2.69978i	0.0700266	−	0.153337i
$311$	−6.86144	−	2.01470i	−0.389076	−	0.114243i	0.0813428	−	0.996686i	$-0.474079\pi$
$311$	−6.86144	−	2.01470i	−0.389076	−	0.114243i	−0.470419	+	0.882443i	$0.655897\pi$
$312$		0			0
$313$	3.18149	+	3.67164i	0.179829	+	0.207533i	0.838506	−	0.544892i	$-0.183429\pi$
$313$	3.18149	+	3.67164i	0.179829	+	0.207533i	−0.658678	+	0.752425i	$0.728884\pi$
$314$	0.318835	−	6.69316i	0.0179929	−	0.377717i
$315$		0			0
$316$	−8.88194	−	6.98484i	−0.499648	−	0.392928i
$317$	−3.44708	+	14.2091i	−0.193608	+	0.798061i	0.789307	+	0.613999i	$0.210440\pi$
$317$	−3.44708	+	14.2091i	−0.193608	+	0.798061i	−0.982915	+	0.184062i	$0.941075\pi$
$318$		0			0
$319$	−1.01524	−	21.3125i	−0.0568424	−	1.19327i
$320$	0.119842	−	0.833522i	0.00669939	−	0.0465953i
$321$		0			0
$322$	1.72024	+	2.41573i	0.0958650	+	0.134624i
$323$	32.6695	−	3.11956i	1.81778	−	0.173577i
$324$		0			0
$325$	7.61603	−	1.46787i	0.422461	−	0.0814228i
$326$	2.28268	+	15.8764i	0.126426	+	0.879313i
$327$		0			0
$328$	11.0379	−	8.68031i	0.609467	−	0.479290i
$329$	3.79364	−	1.95576i	0.209150	−	0.107824i
$330$		0			0
$331$	−24.9000	−	23.7421i	−1.36863	−	1.30498i	−0.908955	−	0.416895i	$-0.863118\pi$
$331$	−24.9000	−	23.7421i	−1.36863	−	1.30498i	−0.459673	−	0.888088i	$-0.652033\pi$
$332$	3.76093	−	4.34034i	0.206408	−	0.238207i
$333$		0			0
$334$	5.27760			0.288777
$335$	23.8545	+	3.40253i	1.30331	+	0.185900i
$336$		0			0
$337$	−12.7566	−	5.10696i	−0.694895	−	0.278194i	−0.00279545	−	0.999996i	$-0.500890\pi$
$337$	−12.7566	−	5.10696i	−0.694895	−	0.278194i	−0.692099	+	0.721802i	$0.743314\pi$
$338$	3.58953	−	4.14254i	0.195245	−	0.225325i
$339$		0			0
$340$	19.8665	−	12.7674i	1.07741	−	0.692411i
$341$	−7.16905	+	3.69590i	−0.388226	+	0.200144i
$342$		0			0
$343$	4.51312	+	9.88236i	0.243686	+	0.533598i
$344$	2.38298	+	16.5740i	0.128482	+	0.893612i
$345$		0			0
$346$	−7.18555	−	3.70441i	−0.386298	−	0.199150i
$347$	−1.95121	+	0.186318i	−0.104747	+	0.0100021i	−0.147298	−	0.989092i	$-0.547058\pi$
$347$	−1.95121	+	0.186318i	−0.104747	+	0.0100021i	0.0425511	+	0.999094i	$0.486451\pi$
$348$		0			0
$349$	15.4653	−	4.54103i	0.827841	−	0.243076i	0.159752	−	0.987157i	$-0.448931\pi$
$349$	15.4653	−	4.54103i	0.827841	−	0.243076i	0.668089	+	0.744081i	$0.267112\pi$
$350$	0.273311	−	1.90092i	0.0146091	−	0.101609i
$351$		0			0
$352$	−21.2212	+	20.2343i	−1.13109	+	1.07849i
$353$	1.29560	−	5.34055i	0.0689580	−	0.284249i	−0.926884	−	0.375349i	$-0.877523\pi$
$353$	1.29560	−	5.34055i	0.0689580	−	0.284249i	0.995842	+	0.0910996i	$0.0290382\pi$
$354$		0			0
$355$	2.55621	+	0.492669i	0.135670	+	0.0261482i
$356$	0.781871	−	16.4135i	0.0414391	−	0.869913i
$357$		0			0
$358$	−3.91597	−	11.3144i	−0.206965	−	0.597987i
$359$	−17.7685	−	5.21730i	−0.937785	−	0.275358i	−0.223092	−	0.974797i	$-0.571615\pi$
$359$	−17.7685	−	5.21730i	−0.937785	−	0.275358i	−0.714692	+	0.699439i	$0.753433\pi$
$360$		0			0
$361$	5.45079	+	22.4685i	0.286884	+	1.18255i
$362$	−11.1739	−	7.18104i	−0.587288	−	0.377427i
$363$		0			0
$364$	−1.36717	−	2.36800i	−0.0716589	−	0.124117i
$365$	−10.0842	+	17.4664i	−0.527833	+	0.914234i
$366$		0			0
$367$	1.82950	−	5.28599i	0.0954990	−	0.275926i	−0.887126	−	0.461527i	$-0.847302\pi$
$367$	1.82950	−	5.28599i	0.0954990	−	0.275926i	0.982625	+	0.185601i	$0.0594230\pi$
$368$	−8.87954	+	3.55483i	−0.462878	+	0.185308i
$369$		0			0
$370$	−4.94518	+	14.2882i	−0.257088	+	0.742806i
$371$	2.06045	−	2.89350i	0.106973	−	0.150223i
$372$		0			0
$373$	1.73903	+	3.01208i	0.0900433	+	0.155960i	0.907529	−	0.419989i	$-0.137966\pi$
$373$	1.73903	+	3.01208i	0.0900433	+	0.155960i	−0.817486	+	0.575949i	$0.804633\pi$
$374$	16.6546	+	1.59032i	0.861188	+	0.0822335i
$375$		0			0
$376$	−2.84894	−	11.7435i	−0.146923	−	0.605625i
$377$	3.64521	−	7.98189i	0.187738	−	0.411088i
$378$		0			0
$379$	0.942741	+	2.72387i	0.0484254	+	0.139916i	0.966620	−	0.256213i	$-0.0824747\pi$
$379$	0.942741	+	2.72387i	0.0484254	+	0.139916i	−0.918195	+	0.396128i	$0.870353\pi$
$380$	19.8481	+	22.9060i	1.01819	+	1.17505i
$381$		0			0
$382$	−8.34408	−	1.60819i	−0.426920	−	0.0822821i
$383$	−18.7999	−	14.7844i	−0.960630	−	0.755447i	0.00901672	−	0.999959i	$-0.497130\pi$
$383$	−18.7999	−	14.7844i	−0.960630	−	0.755447i	−0.969646	+	0.244512i	$0.921372\pi$
$384$		0			0
$385$	−8.92897	+	8.51376i	−0.455063	+	0.433901i
$386$	−0.597043	−	12.5335i	−0.0303887	−	0.637937i
$387$		0			0
$388$	−20.5632	+	6.03789i	−1.04394	+	0.306528i
$389$	12.0149	+	16.8726i	0.609182	+	0.855477i	0.997825	−	0.0659117i	$-0.0209956\pi$
$389$	12.0149	+	16.8726i	0.609182	+	0.855477i	−0.388643	+	0.921388i	$0.627056\pi$
$390$		0			0
$391$	25.4434	+	13.1170i	1.28673	+	0.663355i
$392$	14.3503	−	2.76579i	0.724797	−	0.139693i
$393$		0			0
$394$	−6.63186	−	14.5217i	−0.334108	−	0.731595i
$395$	−16.4814	+	12.9611i	−0.829268	+	0.652143i
$396$		0			0
$397$	6.63162	−	4.26188i	0.332832	−	0.213898i	−0.363541	−	0.931578i	$-0.618432\pi$
$397$	6.63162	−	4.26188i	0.332832	−	0.213898i	0.696373	+	0.717680i	$0.254796\pi$
$398$	−6.10640	−	5.82244i	−0.306086	−	0.291852i
$399$		0			0
$400$	5.75017	+	2.30202i	0.287508	+	0.115101i
$401$	−6.56007			−0.327594			−0.163797	−	0.986494i	$-0.552374\pi$
$401$	−6.56007			−0.327594			−0.163797	+	0.986494i	$0.552374\pi$
$402$		0			0
$403$	−3.31707			−0.165235
$404$	22.7556	+	9.10996i	1.13213	+	0.453238i
$405$		0			0
$406$	−1.57245	−	1.49933i	−0.0780395	−	0.0744105i
$407$	34.5660	−	22.2142i	1.71337	−	1.10112i
$408$		0			0
$409$	−5.15713	+	4.05561i	−0.255003	+	0.200537i	−0.737474	−	0.675375i	$-0.763982\pi$
$409$	−5.15713	+	4.05561i	−0.255003	+	0.200537i	0.482471	+	0.875912i	$0.339739\pi$
$410$	−4.78807	−	10.4844i	−0.236466	−	0.517788i
$411$		0			0
$412$	13.3487	−	2.57275i	0.657642	−	0.126750i
$413$	−3.26840	−	1.68498i	−0.160827	−	0.0829123i
$414$		0			0
$415$	−6.18162	−	8.68087i	−0.303444	−	0.426127i
$416$	−11.5703	+	3.39736i	−0.567282	+	0.166569i
$417$		0			0
$418$	1.02170	+	21.4481i	0.0499729	+	1.04906i
$419$	−0.316875	+	0.302140i	−0.0154804	+	0.0147605i	−0.697780	−	0.716312i	$-0.745829\pi$
$419$	−0.316875	+	0.302140i	−0.0154804	+	0.0147605i	0.682299	+	0.731073i	$0.260980\pi$
$420$		0			0
$421$	14.1956	+	11.1635i	0.691850	+	0.544077i	0.901007	−	0.433805i	$-0.142829\pi$
$421$	14.1956	+	11.1635i	0.691850	+	0.544077i	−0.209156	+	0.977882i	$0.567072\pi$
$422$	4.32363	+	0.833311i	0.210471	+	0.0405650i
$423$		0			0
$424$	−6.58599	−	7.60064i	−0.319844	−	0.369120i
$425$	−6.06292	−	17.5177i	−0.294095	−	0.849731i
$426$		0			0
$427$	0.0319140	−	0.0698818i	0.00154443	−	0.00338182i
$428$	−1.24644	−	5.13789i	−0.0602488	−	0.248349i
$429$		0			0
$430$	13.6818	+	1.30645i	0.659796	+	0.0630028i
$431$	−3.12906	−	5.41970i	−0.150722	−	0.261058i	0.780771	−	0.624817i	$-0.214826\pi$
$431$	−3.12906	−	5.41970i	−0.150722	−	0.261058i	−0.931493	+	0.363759i	$0.881493\pi$
$432$		0			0
$433$	2.16043	−	3.03390i	0.103824	−	0.145800i	−0.759396	−	0.650629i	$-0.774505\pi$
$433$	2.16043	−	3.03390i	0.103824	−	0.145800i	0.863219	+	0.504829i	$0.168445\pi$
$434$	−0.268628	+	0.776149i	−0.0128946	+	0.0372564i
$435$		0			0
$436$	25.4588	−	10.1922i	1.21926	−	0.488116i
$437$	−12.0162	+	34.7186i	−0.574814	+	1.66082i
$438$		0			0
$439$	3.61468	−	6.26081i	0.172519	−	0.298812i	−0.766781	−	0.641909i	$-0.778143\pi$
$439$	3.61468	−	6.26081i	0.172519	−	0.298812i	0.939300	+	0.343097i	$0.111476\pi$
$440$	17.4652	+	30.2506i	0.832621	+	1.44214i
$441$		0			0
$442$	5.78823	+	3.71987i	0.275318	+	0.176936i
$443$	−1.65399	−	6.81782i	−0.0785832	−	0.323925i	0.918929	−	0.394424i	$-0.129056\pi$
$443$	−1.65399	−	6.81782i	−0.0785832	−	0.323925i	−0.997512	+	0.0704994i	$0.977541\pi$
$444$		0			0
$445$	−29.2564	−	8.59044i	−1.38688	−	0.407226i
$446$	3.35344	+	9.68912i	0.158790	+	0.458793i
$447$		0			0
$448$	−0.0110880	+	0.232766i	−0.000523859	+	0.0109972i
$449$	−23.3224	−	4.49502i	−1.10065	−	0.212133i	−0.393591	−	0.919286i	$-0.628767\pi$
$449$	−23.3224	−	4.49502i	−1.10065	−	0.212133i	−0.707061	+	0.707153i	$0.749979\pi$
$450$		0			0
$451$	−7.38457	+	30.4396i	−0.347726	+	1.43335i
$452$	9.76456	−	9.31049i	0.459286	−	0.437929i
$453$		0			0
$454$	0.364192	−	2.53301i	0.0170924	−	0.118880i
$455$	−4.86831	+	1.42946i	−0.228230	+	0.0670143i
$456$		0			0
$457$	−11.4881	+	1.09698i	−0.537392	+	0.0513147i	−0.360224	−	0.932866i	$-0.617300\pi$
$457$	−11.4881	+	1.09698i	−0.537392	+	0.0513147i	−0.177168	+	0.984181i	$0.556694\pi$
$458$	−8.76608	−	4.51923i	−0.409612	−	0.211170i
$459$		0			0
$460$	3.76236	+	26.1678i	0.175421	+	1.22008i
$461$	−9.41225	−	20.6099i	−0.438372	−	0.959901i	−0.991894	−	0.127066i	$-0.959444\pi$
$461$	−9.41225	−	20.6099i	−0.438372	−	0.959901i	0.553522	−	0.832834i	$-0.313283\pi$
$462$		0			0
$463$	−12.5354	+	6.46244i	−0.582569	+	0.300335i	−0.724206	−	0.689584i	$-0.757794\pi$
$463$	−12.5354	+	6.46244i	−0.582569	+	0.300335i	0.141637	+	0.989919i	$0.454763\pi$
$464$	5.89493	−	3.78844i	0.273665	−	0.175874i
$465$		0			0
$466$	−4.37140	+	5.04487i	−0.202501	+	0.233699i
$467$	−3.27341	−	1.31048i	−0.151475	−	0.0606416i	0.294686	−	0.955594i	$-0.404785\pi$
$467$	−3.27341	−	1.31048i	−0.151475	−	0.0606416i	−0.446161	+	0.894953i	$0.647209\pi$
$468$		0			0
$469$	−6.66078	−	0.309826i	−0.307566	−	0.0143065i
$470$	−9.91880			−0.457520
$471$		0			0
$472$	−6.81779	+	7.86815i	−0.313814	+	0.362161i
$473$	−27.0316	−	25.7746i	−1.24292	−	1.18512i
$474$		0			0
$475$	21.1466	−	10.9018i	0.970274	−	0.500211i
$476$	−5.13686	+	4.03967i	−0.235448	+	0.185158i
$477$		0			0
$478$	0.106194	+	0.738594i	0.00485719	+	0.0337825i
$479$	20.0507	−	3.86445i	0.916139	−	0.176571i	0.290673	−	0.956822i	$-0.406121\pi$
$479$	20.0507	−	3.86445i	0.916139	−	0.176571i	0.625466	+	0.780251i	$0.284909\pi$
$480$		0			0
$481$	16.8215	−	1.60626i	0.766996	−	0.0732392i
$482$	2.12319	+	2.98161i	0.0967087	+	0.135808i
$483$		0			0
$484$	3.49223	−	24.2890i	0.158738	−	1.10404i
$485$	1.89224	+	39.7230i	0.0859221	+	1.80373i
$486$		0			0
$487$	6.28243	−	25.8965i	0.284684	−	1.17348i	−0.632353	−	0.774680i	$-0.717911\pi$
$487$	6.28243	−	25.8965i	0.284684	−	1.17348i	0.917037	−	0.398803i	$-0.130574\pi$
$488$	−0.170975	−	0.134456i	−0.00773966	−	0.00608653i
$489$		0			0
$490$	0.570775	−	11.9820i	0.0257850	−	0.541294i
$491$	−7.27531	−	8.39615i	−0.328330	−	0.378913i	0.567452	−	0.823406i	$-0.307929\pi$
$491$	−7.27531	−	8.39615i	−0.328330	−	0.378913i	−0.895782	+	0.444493i	$0.853384\pi$
$492$		0			0
$493$	−20.1223	−	5.90843i	−0.906261	−	0.266102i
$494$	−3.66840	+	8.03268i	−0.165049	+	0.361408i
$495$		0			0
$496$	−2.22840	−	1.43210i	−0.100058	−	0.0643034i
$497$	−0.717129	−	0.0684775i	−0.0321676	−	0.00307164i
$498$		0			0
$499$	−14.2495	+	24.6809i	−0.637896	+	1.10487i	0.347998	+	0.937495i	$0.386862\pi$
$499$	−14.2495	+	24.6809i	−0.637896	+	1.10487i	−0.985894	+	0.167372i	$0.946472\pi$
$500$	−3.61411	+	5.07530i	−0.161628	+	0.226974i
$501$		0			0
$502$	4.53107	−	1.81397i	0.202231	−	0.0809612i
$503$	14.8536	−	5.94647i	0.662288	−	0.265140i	−0.0160708	−	0.999871i	$-0.505116\pi$
$503$	14.8536	−	5.94647i	0.662288	−	0.265140i	0.678359	+	0.734731i	$0.262691\pi$
$504$		0			0
$505$	26.3830	−	37.0497i	1.17403	−	1.64869i
$506$	−9.36463	+	16.2200i	−0.416309	+	0.721068i
$507$		0			0
$508$	5.04692	+	0.481923i	0.223921	+	0.0213819i
$509$	−11.2058	−	7.20154i	−0.496689	−	0.319203i	0.268201	−	0.963363i	$-0.413571\pi$
$509$	−11.2058	−	7.20154i	−0.496689	−	0.319203i	−0.764891	+	0.644160i	$0.777207\pi$
$510$		0			0
$511$	2.31850	−	5.07680i	0.102564	−	0.224584i
$512$	−16.7179	−	4.90881i	−0.738832	−	0.216941i
$513$		0			0
$514$	12.8651	+	14.8471i	0.567454	+	0.654877i
$515$	1.20029	−	25.1971i	0.0528910	−	1.11032i
$516$		0			0
$517$	21.1880	+	16.6624i	0.931846	+	0.732812i
$518$	0.986423	−	4.06609i	0.0433410	−	0.178654i
$519$		0			0
$520$	0.683533	+	14.3491i	0.0299749	+	0.629251i
$521$	−3.47035	+	24.1368i	−0.152039	+	1.05745i	0.760758	+	0.649036i	$0.224828\pi$
$521$	−3.47035	+	24.1368i	−0.152039	+	1.05745i	−0.912796	+	0.408415i	$0.866081\pi$
$522$		0			0
$523$	−25.9229	−	36.4036i	−1.13353	−	1.59182i	−0.740151	−	0.672441i	$-0.765246\pi$
$523$	−25.9229	−	36.4036i	−1.13353	−	1.59182i	−0.393378	−	0.919377i	$-0.628694\pi$
$524$	−16.4873	+	1.57434i	−0.720250	+	0.0687755i
$525$		0			0
$526$	2.63599	−	0.508046i	0.114935	−	0.0221519i
$527$	1.12824	+	7.84705i	0.0491467	+	0.341823i
$528$		0			0
$529$	−7.11039	+	5.59168i	−0.309148	+	0.243116i
$530$	−7.33732	+	3.78265i	−0.318713	+	0.164308i
$531$		0			0
$532$	−6.07017	−	5.78790i	−0.263175	−	0.250937i
$533$	−8.43568	+	9.73529i	−0.365390	+	0.421682i
$534$		0			0
$535$	−9.81042			−0.424142
$536$	−5.29852	+	18.1201i	−0.228861	+	0.782667i
$537$		0			0
$538$	3.95892	+	1.58491i	0.170681	+	0.0683304i
$539$	−21.3477	+	24.6365i	−0.919510	+	1.06117i
$540$		0			0
$541$	−31.5151	+	20.2535i	−1.35494	+	0.870766i	−0.997991	−	0.0633589i	$-0.979819\pi$
$541$	−31.5151	+	20.2535i	−1.35494	+	0.870766i	−0.356947	+	0.934125i	$0.616182\pi$
$542$	15.4847	−	7.98291i	0.665124	−	0.342895i
$543$		0			0
$544$	11.9724	+	26.2159i	0.513313	+	1.12400i
$545$	−7.24192	−	50.3686i	−0.310210	−	2.15756i
$546$		0			0
$547$	−3.06575	−	1.58050i	−0.131082	−	0.0675775i	0.391438	−	0.920204i	$-0.371978\pi$
$547$	−3.06575	−	1.58050i	−0.131082	−	0.0675775i	−0.522520	+	0.852627i	$0.675008\pi$
$548$	8.42776	−	0.804753i	0.360016	−	0.0343774i
$549$		0			0
$550$	11.6373	−	3.41702i	0.496216	−	0.145702i
$551$	3.83055	−	26.6421i	0.163187	−	1.13499i
$552$		0			0
$553$	4.19925	−	4.00398i	0.178570	−	0.170266i
$554$	−1.40629	+	5.79681i	−0.0597476	+	0.246283i
$555$		0			0
$556$	−25.8336	−	4.97901i	−1.09559	−	0.211157i
$557$	1.07741	−	22.6176i	0.0456513	−	0.958338i	−0.853606	−	0.520919i	$-0.825590\pi$
$557$	1.07741	−	22.6176i	0.0456513	−	0.958338i	0.899258	−	0.437419i	$-0.144107\pi$
$558$		0			0
$559$	−5.02395	−	14.5157i	−0.212490	−	0.613951i
$560$	−3.88767	−	1.14152i	−0.164284	−	0.0482382i
$561$		0			0
$562$	−2.33564	−	9.62765i	−0.0985232	−	0.406118i
$563$	4.23752	+	2.72329i	0.178590	+	0.114773i	0.626882	−	0.779114i	$-0.284331\pi$
$563$	4.23752	+	2.72329i	0.178590	+	0.114773i	−0.448291	+	0.893887i	$0.647967\pi$
$564$		0			0
$565$	−12.5178	−	21.6815i	−0.526629	−	0.912149i
$566$	1.85365	−	3.21062i	0.0779148	−	0.134952i
$567$		0			0
$568$	−0.667094	+	1.92744i	−0.0279906	+	0.0808737i
$569$	37.7824	−	15.1258i	1.58392	−	0.634107i	0.598027	−	0.801476i	$-0.295951\pi$
$569$	37.7824	−	15.1258i	1.58392	−	0.634107i	0.985894	+	0.167369i	$0.0535271\pi$
$570$		0			0
$571$	−1.06348	+	3.07272i	−0.0445052	+	0.128589i	−0.965064	−	0.262015i	$-0.915613\pi$
$571$	−1.06348	+	3.07272i	−0.0445052	+	0.128589i	0.920558	+	0.390605i	$0.127734\pi$
$572$	10.0167	−	14.0665i	0.418819	−	0.588149i
$573$		0			0
$574$	1.59478	+	2.76223i	0.0665647	+	0.115293i
$575$	20.6580	+	1.97260i	0.861499	+	0.0822632i
$576$		0			0
$577$	3.05261	+	12.5830i	0.127082	+	0.523838i	0.999391	+	0.0348843i	$0.0111063\pi$
$577$	3.05261	+	12.5830i	0.127082	+	0.523838i	−0.872310	+	0.488954i	$0.837379\pi$
$578$	2.28961	−	5.01354i	0.0952351	−	0.208536i
$579$		0			0
$580$	−6.33475	−	18.3031i	−0.263036	−	0.759993i
$581$	1.93122	+	2.22875i	0.0801205	+	0.0924640i
$582$		0			0
$583$	22.0280	+	4.24554i	0.912305	+	0.175832i
$584$	−12.4210	−	9.76800i	−0.513986	−	0.404203i
$585$		0			0
$586$	−3.32122	+	3.16678i	−0.137198	+	0.130818i
$587$	−1.20419	−	25.2791i	−0.0497022	−	1.04338i	−0.876659	−	0.481113i	$-0.840233\pi$
$587$	−1.20419	−	25.2791i	−0.0497022	−	1.04338i	0.826957	−	0.562266i	$-0.190070\pi$
$588$		0			0
$589$	−9.76264	+	2.86657i	−0.402263	+	0.118115i
$590$	4.95689	+	6.96097i	0.204072	+	0.286579i
$591$		0			0
$592$	11.9941	+	6.18341i	0.492956	+	0.254137i
$593$	41.4964	−	7.99777i	1.70405	−	0.328429i	0.757954	−	0.652308i	$-0.226199\pi$
$593$	41.4964	−	7.99777i	1.70405	−	0.328429i	0.946098	+	0.323879i	$0.104987\pi$
$594$		0			0
$595$	5.03748	+	11.0306i	0.206517	+	0.452209i
$596$	−11.7941	+	9.27497i	−0.483105	+	0.379918i
$597$		0			0
$598$	−6.47980	+	4.16431i	−0.264979	+	0.170291i
$599$	−28.0692	−	26.7639i	−1.14688	−	1.09354i	−0.994448	−	0.105229i	$-0.966443\pi$
$599$	−28.0692	−	26.7639i	−1.14688	−	1.09354i	−0.152427	−	0.988315i	$-0.548709\pi$
$600$		0			0
$601$	−25.6102	−	10.2528i	−1.04466	−	0.418219i	−0.215074	−	0.976598i	$-0.568999\pi$
$601$	−25.6102	−	10.2528i	−1.04466	−	0.418219i	−0.829586	+	0.558379i	$0.811423\pi$
$602$	−3.80335			−0.155013
$603$		0			0
$604$	5.44109			0.221395
$605$	−42.2725	−	16.9234i	−1.71862	−	0.688032i
$606$		0			0
$607$	−23.2782	−	22.1957i	−0.944832	−	0.900895i	0.0503711	−	0.998731i	$-0.483960\pi$
$607$	−23.2782	−	22.1957i	−0.944832	−	0.900895i	−0.995203	+	0.0978355i	$0.968808\pi$
$608$	−31.1173	+	19.9979i	−1.26197	+	0.811021i
$609$		0			0
$610$	−0.140338	+	0.110363i	−0.00568212	+	0.00446847i
$611$	4.60505	+	10.0836i	0.186300	+	0.407941i
$612$		0			0
$613$	23.8909	−	4.60459i	0.964944	−	0.185978i	0.317641	−	0.948211i	$-0.397109\pi$
$613$	23.8909	−	4.60459i	0.964944	−	0.185978i	0.647302	+	0.762233i	$0.275897\pi$
$614$	15.6598	+	8.07319i	0.631978	+	0.325807i
$615$		0			0
$616$	−5.60693	−	7.87384i	−0.225910	−	0.317246i
$617$	3.77878	−	1.10955i	0.152128	−	0.0446688i	−0.204782	−	0.978808i	$-0.565649\pi$
$617$	3.77878	−	1.10955i	0.152128	−	0.0446688i	0.356910	+	0.934139i	$0.383830\pi$
$618$		0			0
$619$	−0.883972	−	18.5569i	−0.0355298	−	0.745863i	−0.944403	−	0.328790i	$-0.893359\pi$
$619$	−0.883972	−	18.5569i	−0.0355298	−	0.745863i	0.908873	−	0.417073i	$-0.136944\pi$
$620$	−5.29889	+	5.05249i	−0.212809	+	0.202913i
$621$		0			0
$622$	−3.61494	−	2.84282i	−0.144946	−	0.113987i
$623$	8.28533	+	1.59687i	0.331945	+	0.0639771i
$624$		0			0
$625$	19.5743	+	22.5900i	0.782972	+	0.903598i
$626$	1.02187	+	2.95250i	0.0408422	+	0.118006i
$627$		0			0
$628$	−6.86673	+	15.0360i	−0.274012	+	0.600004i
$629$	−9.52137	−	39.2476i	−0.379642	−	1.56491i
$630$		0			0
$631$	−48.3559	−	4.61743i	−1.92502	−	0.183817i	−0.938249	−	0.345960i	$-0.887553\pi$
$631$	−48.3559	−	4.61743i	−1.92502	−	0.183817i	−0.986767	+	0.162143i	$0.948159\pi$
$632$	−8.21379	−	14.2267i	−0.326727	−	0.565908i
$633$		0			0
$634$	−5.45419	+	7.65934i	−0.216614	+	0.304191i
$635$	3.07695	−	8.89028i	0.122105	−	0.352800i
$636$		0			0
$637$	−12.4462	+	4.98270i	−0.493135	+	0.197422i
$638$	4.48786	−	12.9668i	0.177676	−	0.513362i
$639$		0			0
$640$	−16.5071	+	28.5911i	−0.652499	+	1.13016i
$641$	1.91580	+	3.31826i	0.0756695	+	0.131063i	0.901377	−	0.433035i	$-0.142557\pi$
$641$	1.91580	+	3.31826i	0.0756695	+	0.131063i	−0.825708	+	0.564098i	$0.809224\pi$
$642$		0			0
$643$	−21.1823	−	13.6131i	−0.835349	−	0.536846i	0.0516244	−	0.998667i	$-0.483560\pi$
$643$	−21.1823	−	13.6131i	−0.835349	−	0.536846i	−0.886974	+	0.461820i	$0.847197\pi$
$644$	−1.72477	−	7.10958i	−0.0679653	−	0.280157i
$645$		0			0
$646$	20.2503	+	5.94603i	0.796738	+	0.233943i
$647$	11.9201	+	34.4409i	0.468627	+	1.35401i	0.893625	+	0.448815i	$0.148154\pi$
$647$	11.9201	+	34.4409i	0.468627	+	1.35401i	−0.424997	+	0.905195i	$0.639725\pi$
$648$		0			0
$649$	1.10499	−	23.1966i	0.0433747	−	0.910547i
$650$	4.89784	+	0.943981i	0.192109	+	0.0370260i
$651$		0			0
$652$	9.32842	−	38.4523i	0.365329	−	1.50591i
$653$	−31.3716	+	29.9128i	−1.22767	+	1.17058i	−0.248256	+	0.968694i	$0.579857\pi$
$653$	−31.3716	+	29.9128i	−1.22767	+	1.17058i	−0.979410	+	0.201882i	$0.935294\pi$
$654$		0			0
$655$	−4.37376	+	30.4202i	−0.170897	+	1.18862i
$656$	−9.87016	+	2.89814i	−0.385365	+	0.113153i
$657$		0			0
$658$	2.73237	−	0.260910i	0.106519	−	0.0101713i
$659$	3.76398	+	1.94047i	0.146624	+	0.0755899i	0.529977	−	0.848012i	$-0.322200\pi$
$659$	3.76398	+	1.94047i	0.146624	+	0.0755899i	−0.383353	+	0.923602i	$0.625231\pi$
$660$		0			0
$661$	−1.14276	−	7.94809i	−0.0444483	−	0.309145i	−0.999902	−	0.0140036i	$-0.995542\pi$
$661$	−1.14276	−	7.94809i	−0.0444483	−	0.309145i	0.955454	−	0.295141i	$-0.0953667\pi$
$662$	−9.19133	−	20.1262i	−0.357231	−	0.782227i
$663$		0			0
$664$	7.42139	−	3.82599i	0.288006	−	0.148477i
$665$	−13.0929	+	8.41427i	−0.507719	+	0.326291i
$666$		0			0
$667$	15.3745	−	17.7431i	0.595301	−	0.687014i
$668$	−12.0865	−	4.83871i	−0.467641	−	0.187215i
$669$		0			0
$670$	13.4286	+	7.73297i	0.518791	+	0.298751i
$671$	0.485179			0.0187301
$672$		0			0
$673$	2.59382	−	2.99343i	0.0999846	−	0.115388i	−0.703552	−	0.710644i	$-0.748404\pi$
$673$	2.59382	−	2.99343i	0.0999846	−	0.115388i	0.803536	+	0.595256i	$0.202949\pi$
$674$	−6.39542	−	6.09802i	−0.246342	−	0.234887i
$675$		0			0
$676$	−12.0186	+	6.19603i	−0.462255	+	0.238309i
$677$	−4.77286	+	3.75342i	−0.183436	+	0.144256i	−0.705654	−	0.708556i	$-0.749347\pi$
$677$	−4.77286	+	3.75342i	−0.183436	+	0.144256i	0.522219	+	0.852812i	$0.325104\pi$
$678$		0			0
$679$	−1.56616	−	10.8929i	−0.0601036	−	0.418030i
$680$	33.7126	−	6.49758i	1.29282	−	0.249171i
$681$		0			0
$682$	−5.16351	+	0.493056i	−0.197721	+	0.0188801i
$683$	−4.70302	−	6.60447i	−0.179956	−	0.252713i	0.714738	−	0.699392i	$-0.246546\pi$
$683$	−4.70302	−	6.60447i	−0.179956	−	0.252713i	−0.894694	+	0.446679i	$0.852606\pi$
$684$		0			0
$685$	2.23573	−	15.5498i	0.0854227	−	0.594128i
$686$	0.332440	+	6.97877i	0.0126926	+	0.266451i
$687$		0			0
$688$	2.89192	−	11.9207i	0.110254	−	0.454471i
$689$	7.25204	+	5.70307i	0.276281	+	0.217270i
$690$		0			0
$691$	−1.27017	+	26.6641i	−0.0483195	+	1.01435i	0.836368	+	0.548168i	$0.184675\pi$
$691$	−1.27017	+	26.6641i	−0.0483195	+	1.01435i	−0.884688	+	0.466184i	$0.845628\pi$
$692$	13.0597	+	15.0717i	0.496454	+	0.572939i
$693$		0			0
$694$	−1.20946	−	0.355131i	−0.0459107	−	0.0134806i
$695$	−20.2802	+	44.4074i	−0.769272	+	1.68447i
$696$		0			0
$697$	25.8996	+	16.6447i	0.981017	+	0.630461i
$698$	10.3186	+	0.985311i	0.390566	+	0.0372946i
$699$		0			0
$700$	−2.36876	+	4.10282i	−0.0895309	+	0.155072i
$701$	−6.48440	+	9.10606i	−0.244912	+	0.343931i	−0.918673	−	0.395018i	$-0.870738\pi$
$701$	−6.48440	+	9.10606i	−0.244912	+	0.343931i	0.673761	+	0.738949i	$0.264678\pi$
$702$		0			0
$703$	48.1202	−	19.2644i	1.81489	−	0.726572i
$704$	−1.36626	+	0.546970i	−0.0514930	+	0.0206147i
$705$		0			0
$706$	2.04998	−	2.87880i	0.0771522	−	0.108345i
$707$	−6.29324	+	10.9002i	−0.236682	+	0.409945i
$708$		0			0
$709$	−23.5191	−	2.24581i	−0.883280	−	0.0843430i	−0.356451	−	0.934314i	$-0.616013\pi$
$709$	−23.5191	−	2.24581i	−0.883280	−	0.0843430i	−0.526829	+	0.849971i	$0.676619\pi$
$710$	1.40838	+	0.905110i	0.0528555	+	0.0339682i
$711$		0			0
$712$	9.92415	−	21.7308i	0.371923	−	0.814398i
$713$	−8.51544	−	2.50036i	−0.318906	−	0.0936392i
$714$		0			0
$715$	−20.9840	−	24.2168i	−0.784758	−	0.905658i
$716$	−1.40536	+	29.5021i	−0.0525207	+	1.10255i
$717$		0			0
$718$	−9.36130	−	7.36181i	−0.349361	−	0.274740i
$719$	3.35475	−	13.8285i	0.125111	−	0.515714i	−0.874422	−	0.485166i	$-0.838759\pi$
$719$	3.35475	−	13.8285i	0.125111	−	0.515714i	0.999533	−	0.0305488i	$-0.00972551\pi$
$720$		0			0
$721$	0.332152	+	6.97273i	0.0123700	+	0.259678i
$722$	−2.11601	+	14.7172i	−0.0787496	+	0.547716i
$723$		0			0
$724$	19.0061	+	26.6903i	0.706356	+	0.991939i
$725$	−15.1346	+	1.44517i	−0.562083	+	0.0536724i
$726$		0			0
$727$	26.5215	−	5.11161i	0.983629	−	0.189579i	0.328013	−	0.944673i	$-0.393621\pi$
$727$	26.5215	−	5.11161i	0.983629	−	0.189579i	0.655616	+	0.755094i	$0.272409\pi$
$728$	−0.565743	−	3.93483i	−0.0209678	−	0.145834i
$729$		0			0
$730$	−10.1953	+	8.01769i	−0.377346	+	0.296748i
$731$	−32.6305	+	16.8222i	−1.20688	+	0.622191i
$732$		0			0
$733$	0.876940	+	0.836161i	0.0323905	+	0.0308843i	0.706101	−	0.708111i	$-0.250452\pi$
$733$	0.876940	+	0.836161i	0.0323905	+	0.0308843i	−0.673711	+	0.738995i	$0.735301\pi$
$734$	2.35569	−	2.71861i	0.0869502	−	0.100346i
$735$		0			0
$736$	−32.2638			−1.18926
$737$	−15.6949	−	39.0771i	−0.578127	−	1.43942i
$738$		0			0
$739$	19.0049	+	7.60841i	0.699106	+	0.279880i	0.693864	−	0.720107i	$-0.255907\pi$
$739$	19.0049	+	7.60841i	0.699106	+	0.279880i	0.00524228	+	0.999986i	$0.498331\pi$
$740$	24.4251	−	28.1881i	0.897886	−	1.03622i
$741$		0			0
$742$	1.92174	−	1.23503i	0.0705492	−	0.0453392i
$743$	41.0341	−	21.1545i	1.50539	−	0.776085i	0.508987	−	0.860774i	$-0.330020\pi$
$743$	41.0341	−	21.1545i	1.50539	−	0.776085i	0.996407	+	0.0846899i	$0.0269900\pi$
$744$		0			0
$745$	11.5659	+	25.3258i	0.423742	+	0.927866i
$746$	0.318319	+	2.21395i	0.0116545	+	0.0810586i
$747$		0			0
$748$	−36.6835	−	18.9116i	−1.34128	−	0.691478i
$749$	2.70251	−	0.258059i	0.0987477	−	0.00942926i
$750$		0			0
$751$	−6.97758	+	2.04880i	−0.254616	+	0.0747619i	−0.406549	−	0.913629i	$-0.633268\pi$
$751$	−6.97758	+	2.04880i	−0.254616	+	0.0747619i	0.151934	+	0.988391i	$0.451450\pi$
$752$	−1.25983	+	8.76234i	−0.0459414	+	0.319530i
$753$		0			0
$754$	4.08408	−	3.89417i	0.148734	−	0.141817i
$755$	2.38034	−	9.81191i	0.0866295	−	0.357092i
$756$		0			0
$757$	27.6903	+	5.33686i	1.00642	+	0.193971i	0.665721	−	0.746201i	$-0.268124\pi$
$757$	27.6903	+	5.33686i	1.00642	+	0.193971i	0.340699	+	0.940172i	$0.389336\pi$
$758$	−0.0882008	+	1.85156i	−0.00320360	+	0.0672518i
$759$		0			0
$760$	14.4121	+	41.6410i	0.522781	+	1.51048i
$761$	11.9663	+	3.51361i	0.433776	+	0.127368i	0.491329	−	0.870974i	$-0.336511\pi$
$761$	11.9663	+	3.51361i	0.433776	+	0.127368i	−0.0575523	+	0.998342i	$0.518330\pi$
$762$		0			0
$763$	3.31988	+	13.6847i	0.120188	+	0.495421i
$764$	17.6348	+	11.3332i	0.638003	+	0.410020i
$765$		0			0
$766$	−7.69041	−	13.3202i	−0.277866	−	0.481278i
$767$	4.77530	−	8.27107i	0.172426	−	0.298651i
$768$		0			0
$769$	−10.8662	+	31.3958i	−0.391846	+	1.13216i	0.560766	+	0.827974i	$0.310507\pi$
$769$	−10.8662	+	31.3958i	−0.391846	+	1.13216i	−0.952612	+	0.304189i	$0.901615\pi$
$770$	−7.36578	+	2.94881i	−0.265444	+	0.106268i
$771$		0			0
$772$	−10.1239	+	29.2510i	−0.364366	+	1.05277i
$773$	12.6416	−	17.7526i	0.454687	−	0.638518i	−0.522061	−	0.852908i	$-0.674837\pi$
$773$	12.6416	−	17.7526i	0.454687	−	0.638518i	0.976748	+	0.214390i	$0.0687762\pi$
$774$		0			0
$775$	2.87359	+	4.97721i	0.103222	+	0.178787i
$776$	−31.0167	−	2.96173i	−1.11343	−	0.106320i
$777$		0			0
$778$	3.14048	+	12.9452i	0.112592	+	0.464108i
$779$	−16.4144	+	35.9425i	−0.588106	+	1.28777i
$780$		0			0
$781$	−1.48802	−	4.29936i	−0.0532456	−	0.153843i
$782$	12.0553	+	13.9126i	0.431097	+	0.497513i
$783$		0			0
$784$	−10.5125	−	2.02612i	−0.375448	−	0.0723616i
$785$	24.1104	+	18.9607i	0.860539	+	0.676735i
$786$		0			0
$787$	−10.0271	+	9.56079i	−0.357426	+	0.340805i	−0.847422	−	0.530919i	$-0.821847\pi$
$787$	−10.0271	+	9.56079i	−0.357426	+	0.340805i	0.489996	+	0.871725i	$0.336998\pi$
$788$	1.87387	+	39.3374i	0.0667538	+	1.40134i
$789$		0			0
$790$	−12.9378	+	3.79887i	−0.460305	+	0.135158i
$791$	4.01866	+	5.64342i	0.142887	+	0.200657i
$792$		0			0
$793$	0.177352	+	0.0914315i	0.00629797	+	0.00324683i
$794$	4.97793	−	0.959417i	0.176660	−	0.0340484i
$795$		0			0
$796$	8.64634	+	18.9328i	0.306461	+	0.671057i
$797$	4.64380	−	3.65193i	0.164492	−	0.129358i	−0.532520	−	0.846417i	$-0.678755\pi$
$797$	4.64380	−	3.65193i	0.164492	−	0.129358i	0.697012	+	0.717060i	$0.254512\pi$
$798$		0			0
$799$	22.2881	−	14.3237i	0.788498	−	0.506737i
$800$	15.1211	+	14.4180i	0.534612	+	0.509752i
$801$		0			0
$802$	−3.91656	−	1.56795i	−0.138298	−	0.0553663i
$803$	35.2474			1.24385
$804$		0			0
$805$	−13.5752			−0.478464
$806$	−1.98039	−	0.792828i	−0.0697562	−	0.0279262i
$807$		0			0
$808$	25.7908	+	24.5915i	0.907317	+	0.865125i
$809$	−2.40411	+	1.54502i	−0.0845238	+	0.0543202i	−0.582220	−	0.813031i	$-0.697816\pi$
$809$	−2.40411	+	1.54502i	−0.0845238	+	0.0543202i	0.497696	+	0.867351i	$0.334179\pi$
$810$		0			0
$811$	8.28666	−	6.51670i	0.290984	−	0.228832i	−0.461986	−	0.886887i	$-0.652863\pi$
$811$	8.28666	−	6.51670i	0.290984	−	0.228832i	0.752970	+	0.658055i	$0.228621\pi$
$812$	2.22651	+	4.87538i	0.0781353	+	0.171092i
$813$		0			0
$814$	25.9465	−	5.00077i	0.909423	−	0.175277i
$815$	−65.2599	−	33.6438i	−2.28596	−	1.17849i
$816$		0			0
$817$	−27.3306	−	38.3804i	−0.956176	−	1.34276i
$818$	−4.04831	+	1.18869i	−0.141546	+	0.0415616i
$819$		0			0
$820$	1.35290	+	28.4008i	0.0472452	+	0.991799i
$821$	−22.6016	+	21.5506i	−0.788802	+	0.752122i	−0.973009	−	0.230766i	$-0.925877\pi$
$821$	−22.6016	+	21.5506i	−0.788802	+	0.752122i	0.184207	+	0.982887i	$0.441028\pi$
$822$		0			0
$823$	−34.7009	−	27.2891i	−1.20960	−	0.951239i	−0.209949	−	0.977712i	$-0.567330\pi$
$823$	−34.7009	−	27.2891i	−1.20960	−	0.951239i	−0.999650	+	0.0264738i	$0.991572\pi$
$824$	19.4069	+	3.74037i	0.676071	+	0.130302i
$825$		0			0
$826$	−1.54860	−	1.78718i	−0.0538826	−	0.0621839i
$827$	−14.8113	−	42.7945i	−0.515041	−	1.48811i	−0.840107	−	0.542421i	$-0.817508\pi$
$827$	−14.8113	−	42.7945i	−0.515041	−	1.48811i	0.325066	−	0.945691i	$-0.394613\pi$
$828$		0			0
$829$	−9.42035	+	20.6277i	−0.327182	+	0.716429i	−0.999721	−	0.0236330i	$-0.992477\pi$
$829$	−9.42035	+	20.6277i	−0.327182	+	0.716429i	0.672538	+	0.740062i	$0.265204\pi$
$830$	−1.61576	−	6.66024i	−0.0560837	−	0.231180i
$831$		0			0
$832$	−0.602501	−	0.0575319i	−0.0208880	−	0.00199456i
$833$	16.0207	+	27.7486i	0.555084	+	0.961433i
$834$		0			0
$835$	−14.0132	+	19.6788i	−0.484946	+	0.681011i
$836$	17.3246	−	50.0561i	0.599184	−	1.73123i
$837$		0			0
$838$	−0.261400	+	0.104649i	−0.00902990	+	0.00361503i
$839$	16.3880	−	47.3500i	0.565777	−	1.63470i	−0.191413	−	0.981510i	$-0.561307\pi$
$839$	16.3880	−	47.3500i	0.565777	−	1.63470i	0.757190	−	0.653195i	$-0.226572\pi$
$840$		0			0
$841$	5.89994	−	10.2190i	0.203446	−	0.352379i
$842$	5.80694	+	10.0579i	0.200120	+	0.346618i
$843$		0			0
$844$	−9.13776	−	5.87248i	−0.314535	−	0.202139i
$845$	5.91544	+	24.3838i	0.203497	+	0.838827i
$846$		0			0
$847$	12.0901	+	3.54998i	0.415422	+	0.121979i
$848$	2.40967	+	6.96229i	0.0827485	+	0.239086i
$849$		0			0
$850$	0.567233	−	11.9077i	0.0194559	−	0.408430i
$851$	44.3943	+	8.55630i	1.52182	+	0.293306i
$852$		0			0
$853$	5.71991	−	23.5778i	0.195846	−	0.807289i	−0.786096	−	0.618105i	$-0.787901\pi$
$853$	5.71991	−	23.5778i	0.195846	−	0.807289i	0.981942	−	0.189184i	$-0.0605842\pi$
$854$	0.0357564	−	0.0340936i	0.00122356	−	0.00116666i
$855$		0			0
$856$	1.09388	−	7.60811i	0.0373881	−	0.260040i
$857$	25.8904	−	7.60210i	0.884399	−	0.259683i	0.192170	−	0.981362i	$-0.438447\pi$
$857$	25.8904	−	7.60210i	0.884399	−	0.259683i	0.692228	+	0.721679i	$0.256629\pi$
$858$		0			0
$859$	17.2248	−	1.64477i	0.587703	−	0.0561189i	0.203031	−	0.979172i	$-0.434921\pi$
$859$	17.2248	−	1.64477i	0.587703	−	0.0561189i	0.384672	+	0.923053i	$0.374315\pi$
$860$	−30.1356	−	15.5360i	−1.02762	−	0.529773i
$861$		0			0
$862$	−0.572757	−	3.98361i	−0.0195082	−	0.135682i
$863$	18.4454	+	40.3897i	0.627887	+	1.37488i	0.909641	+	0.415394i	$0.136356\pi$
$863$	18.4454	+	40.3897i	0.627887	+	1.37488i	−0.281754	+	0.959487i	$0.590916\pi$
$864$		0			0
$865$	32.8920	−	16.9570i	1.11836	−	0.576555i
$866$	2.01499	−	1.29495i	0.0684720	−	0.0440043i
$867$		0			0
$868$	1.32680	−	1.53121i	0.0450346	−	0.0519727i
$869$	34.0186	+	13.6190i	1.15400	+	0.461992i
$870$		0			0
$871$	1.62695	−	17.2420i	0.0551271	−	0.584221i
$872$	39.8690			1.35014
$873$		0			0
$874$	−15.4723	+	17.8560i	−0.523358	+	0.603988i
$875$	−2.31551	−	2.20783i	−0.0782784	−	0.0746383i
$876$		0			0
$877$	−0.555016	+	0.286131i	−0.0187416	+	0.00966195i	−0.467572	−	0.883955i	$-0.654871\pi$
$877$	−0.555016	+	0.286131i	−0.0187416	+	0.00966195i	0.448830	+	0.893617i	$0.351841\pi$
$878$	3.65450	−	2.87393i	0.123333	−	0.0969903i
$879$		0			0
$880$	−3.64168	−	25.3284i	−0.122761	−	0.853821i
$881$	−42.2005	+	8.13349i	−1.42177	+	0.274024i	−0.841438	−	0.540354i	$-0.818290\pi$
$881$	−42.2005	+	8.13349i	−1.42177	+	0.274024i	−0.580335	+	0.814378i	$0.697078\pi$
$882$		0			0
$883$	25.5237	−	2.43721i	0.858939	−	0.0820188i	0.343715	−	0.939074i	$-0.388315\pi$
$883$	25.5237	−	2.43721i	0.858939	−	0.0820188i	0.515224	+	0.857055i	$0.327709\pi$
$884$	−9.84541	−	13.8259i	−0.331137	−	0.465017i
$885$		0			0
$886$	0.642081	−	4.46577i	0.0215711	−	0.150030i
$887$	−1.81680	−	38.1392i	−0.0610020	−	1.28059i	−0.797155	−	0.603775i	$-0.793663\pi$
$887$	−1.81680	−	38.1392i	−0.0610020	−	1.28059i	0.736153	−	0.676815i	$-0.236640\pi$
$888$		0			0
$889$	−0.613765	+	2.52998i	−0.0205850	+	0.0848527i
$890$	−15.4137	−	12.1215i	−0.516668	−	0.406312i
$891$		0			0
$892$	1.20348	−	25.2641i	0.0402955	−	0.845906i
$893$	22.2675	+	25.6981i	0.745154	+	0.859954i
$894$		0			0
$895$	52.5863	+	15.4407i	1.75777	+	0.516127i
$896$	3.79519	−	8.31030i	0.126788	−	0.277628i
$897$		0			0
$898$	−12.8498	−	8.25805i	−0.428803	−	0.275575i
$899$	6.47255	+	0.618053i	0.215872	+	0.0206132i
$900$		0			0
$901$	11.0249	−	19.0956i	0.367292	−	0.636168i
$902$	−11.6843	+	16.4083i	−0.389045	+	0.546338i
$903$		0			0
$904$	18.2101	−	7.29021i	0.605658	−	0.242469i
$905$	56.4453	−	22.5973i	1.87631	−	0.751160i
$906$		0			0
$907$	−4.62354	+	6.49285i	−0.153522	+	0.215592i	−0.884173	−	0.467160i	$-0.845277\pi$
$907$	−4.62354	+	6.49285i	−0.153522	+	0.215592i	0.730651	+	0.682751i	$0.239217\pi$
$908$	−3.15642	+	5.46707i	−0.104749	+	0.181431i
$909$		0			0
$910$	−3.24819	−	0.310165i	−0.107676	−	0.0102819i
$911$	−4.49593	−	2.88936i	−0.148957	−	0.0957287i	0.464040	−	0.885815i	$-0.346400\pi$
$911$	−4.49593	−	2.88936i	−0.148957	−	0.0957287i	−0.612996	+	0.790086i	$0.710036\pi$
$912$		0			0
$913$	−7.73692	+	16.9415i	−0.256055	+	0.560682i
$914$	−7.12095	−	2.09090i	−0.235540	−	0.0691608i
$915$		0			0
$916$	15.9323	+	18.3868i	0.526416	+	0.607517i
$917$	0.404667	−	8.49502i	0.0133633	−	0.280530i
$918$		0			0
$919$	15.5935	+	12.2629i	0.514383	+	0.404515i	0.841325	−	0.540529i	$-0.181776\pi$
$919$	15.5935	+	12.2629i	0.514383	+	0.404515i	−0.326942	+	0.945044i	$0.606018\pi$
$920$	−9.06143	+	37.3517i	−0.298746	+	1.23145i
$921$		0			0
$922$	−0.693312	−	14.5544i	−0.0228330	−	0.479324i
$923$	0.266278	−	1.85200i	0.00876465	−	0.0609595i
$924$		0			0
$925$	−16.9827	−	23.8489i	−0.558389	−	0.784148i
$926$	−9.02862	+	0.862128i	−0.296699	+	0.0283313i
$927$		0			0
$928$	23.2100	−	4.47337i	0.761907	−	0.146846i
$929$	2.90665	+	20.2162i	0.0953641	+	0.663272i	0.980293	+	0.197547i	$0.0632974\pi$
$929$	2.90665	+	20.2162i	0.0953641	+	0.663272i	−0.884929	+	0.465725i	$0.845793\pi$
$930$		0			0
$931$	−32.3250	+	25.4207i	−1.05941	+	0.833129i
$932$	14.6365	−	7.54564i	0.479435	−	0.247166i
$933$		0			0
$934$	−1.64110	−	1.56479i	−0.0536985	−	0.0512014i
$935$	−50.1515	+	57.8779i	−1.64013	+	1.89281i
$936$		0			0
$937$	−20.1340			−0.657749			−0.328874	−	0.944374i	$-0.606669\pi$
$937$	−20.1340			−0.657749			−0.328874	+	0.944374i	$0.606669\pi$
$938$	−3.90263	−	1.77700i	−0.127425	−	0.0580211i
$939$		0			0
$940$	22.7156	+	9.09394i	0.740900	+	0.296612i
$941$	−25.3495	+	29.2549i	−0.826370	+	0.953682i	−0.999513	−	0.0312146i	$-0.990062\pi$
$941$	−25.3495	+	29.2549i	−0.826370	+	0.953682i	0.173142	+	0.984897i	$0.444608\pi$
$942$		0			0
$943$	−28.9940	+	18.6333i	−0.944176	+	0.606785i
$944$	6.77897	−	3.49480i	0.220637	−	0.113746i
$945$		0			0
$946$	−9.97818	−	21.8492i	−0.324419	−	0.710377i
$947$	4.95722	+	34.4782i	0.161088	+	1.12039i	0.896588	+	0.442867i	$0.146038\pi$
$947$	4.95722	+	34.4782i	0.161088	+	1.12039i	−0.735499	+	0.677525i	$0.763052\pi$
$948$		0			0
$949$	12.8844	+	6.64235i	0.418244	+	0.215620i
$950$	15.2309	−	1.45437i	0.494155	−	0.0471861i
$951$		0			0
$952$	−9.11603	+	2.67671i	−0.295452	+	0.0867526i
$953$	0.914735	−	6.36212i	0.0296312	−	0.206089i	−0.969628	−	0.244586i	$-0.921348\pi$
$953$	0.914735	−	6.36212i	0.0296312	−	0.206089i	0.999259	+	0.0384969i	$0.0122570\pi$
$954$		0			0
$955$	28.1519	−	26.8427i	0.910973	−	0.868611i
$956$	0.433972	−	1.78886i	0.0140357	−	0.0578558i
$957$		0			0
$958$	12.8945	+	2.48521i	0.416603	+	0.0802937i
$959$	−0.206853	+	4.34238i	−0.00667963	+	0.140223i
$960$		0			0
$961$	9.33521	+	26.9723i	0.301136	+	0.870075i
$962$	10.4269	+	3.06161i	0.336176	+	0.0987102i
$963$		0			0
$964$	−2.12878	−	8.77496i	−0.0685634	−	0.282622i
$965$	48.3193	+	31.0529i	1.55545	+	0.999629i
$966$		0			0
$967$	−12.0412	−	20.8560i	−0.387220	−	0.670685i	0.604855	−	0.796336i	$-0.293231\pi$
$967$	−12.0412	−	20.8560i	−0.387220	−	0.670685i	−0.992074	+	0.125651i	$0.959898\pi$
$968$	17.8377	−	30.8959i	0.573327	−	0.993031i
$969$		0			0
$970$	−8.36465	+	24.1681i	−0.268573	+	0.775990i
$971$	−21.3271	+	8.53808i	−0.684419	+	0.274000i	−0.687701	−	0.725994i	$-0.741380\pi$
$971$	−21.3271	+	8.53808i	−0.684419	+	0.274000i	0.00328121	+	0.999995i	$0.498956\pi$
$972$		0			0
$973$	4.41854	−	12.7665i	0.141652	−	0.409277i
$974$	9.94044	−	13.9594i	0.318512	−	0.447288i
$975$		0			0
$976$	0.0796705	+	0.137993i	0.00255019	+	0.00441706i
$977$	13.0843	+	1.24940i	0.418605	+	0.0399719i	0.302234	−	0.953234i	$-0.402268\pi$
$977$	13.0843	+	1.24940i	0.418605	+	0.0399719i	0.116371	+	0.993206i	$0.462874\pi$
$978$		0			0
$979$	12.5632	+	51.7863i	0.401522	+	1.65510i
$980$	−12.2928	+	26.9174i	−0.392678	+	0.859845i
$981$		0			0
$982$	−2.33677	−	6.75166i	−0.0745694	−	0.215454i
$983$	3.38655	+	3.90829i	0.108014	+	0.124655i	0.807182	−	0.590302i	$-0.200992\pi$
$983$	3.38655	+	3.90829i	0.108014	+	0.124655i	−0.699168	+	0.714957i	$0.746446\pi$
$984$		0			0
$985$	71.7568	+	13.8300i	2.28636	+	0.440660i
$986$	−10.6014	−	8.33702i	−0.337617	−	0.265505i
$987$		0			0
$988$	15.7659	−	15.0327i	0.501580	−	0.478255i
$989$	−1.95551	−	41.0512i	−0.0621816	−	1.30535i
$990$		0			0
$991$	9.59194	−	2.81645i	0.304698	−	0.0894674i	−0.125809	−	0.992054i	$-0.540153\pi$
$991$	9.59194	−	2.81645i	0.304698	−	0.0894674i	0.430508	+	0.902587i	$0.358335\pi$
$992$	−5.18300	−	7.27851i	−0.164560	−	0.231093i
$993$		0			0
$994$	−0.411780	−	0.212287i	−0.0130609	−	0.00673335i
$995$	37.9241	−	7.30928i	1.20228	−	0.231720i
$996$		0			0
$997$	23.3350	+	51.0965i	0.739027	+	1.61824i	0.785149	+	0.619307i	$0.212586\pi$
$997$	23.3350	+	51.0965i	0.739027	+	1.61824i	−0.0461219	+	0.998936i	$0.514686\pi$
$998$	−14.4065	+	11.3294i	−0.456029	+	0.358625i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.55.2		100
3.2	odd	2		67.2.g.a.55.4	yes	100
67.39	even	33	inner	603.2.z.c.307.2		100
201.113	even	66		4489.2.a.q.1.28		50
201.155	odd	66		4489.2.a.p.1.23		50
201.173	odd	66		67.2.g.a.39.4	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.39.4	✓	100	201.173	odd	66
67.2.g.a.55.4	yes	100	3.2	odd	2
603.2.z.c.55.2		100	1.1	even	1	trivial
603.2.z.c.307.2		100	67.39	even	33	inner
4489.2.a.p.1.23		50	201.155	odd	66
4489.2.a.q.1.28		50	201.113	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)

\(f(q)\)	\(=\)	\(q+(0.597030 + 0.239015i) q^{2} +(-1.14815 - 1.09476i) q^{4} +(-2.47647 + 1.59153i) q^{5} +(0.640337 - 0.503567i) q^{7} +(-0.958120 - 2.09799i) q^{8} +O(q^{10})\)	\(q+(0.597030 + 0.239015i) q^{2} +(-1.14815 - 1.09476i) q^{4} +(-2.47647 + 1.59153i) q^{5} +(0.640337 - 0.503567i) q^{7} +(-0.958120 - 2.09799i) q^{8} +(-1.85892 + 0.358278i) q^{10} +(4.57279 + 2.35744i) q^{11} +(1.22728 + 1.72348i) q^{13} +(0.502660 - 0.147594i) q^{14} +(0.0803947 + 1.68769i) q^{16} +(3.65972 - 3.48954i) q^{17} +(5.10149 + 4.01186i) q^{19} +(4.58570 + 0.883821i) q^{20} +(2.16663 + 2.50042i) q^{22} +(1.85150 + 5.34955i) q^{23} +(1.52285 - 3.33458i) q^{25} +(0.320788 + 1.32231i) q^{26} +(-1.28649 - 0.122845i) q^{28} +(-2.07365 - 3.59167i) q^{29} +(-0.909392 + 1.27706i) q^{31} +(-1.86410 + 5.38595i) q^{32} +(3.01901 - 1.20863i) q^{34} +(-0.784333 + 2.26618i) q^{35} +(3.99330 - 6.91661i) q^{37} +(2.08685 + 3.61453i) q^{38} +(5.71177 + 3.67073i) q^{40} +(1.43537 + 5.91669i) q^{41} +(-6.96586 - 2.04536i) q^{43} +(-2.66943 - 7.71280i) q^{44} +(-0.173222 + 3.63637i) q^{46} +(5.14467 + 0.991554i) q^{47} +(-1.49386 + 6.15778i) q^{49} +(1.70620 - 1.62686i) q^{50} +(0.477688 - 3.32239i) q^{52} +(4.18385 - 1.22849i) q^{53} +(-15.0763 + 1.43961i) q^{55} +(-1.67000 - 0.860944i) q^{56} +(-0.379570 - 2.63997i) q^{58} +(-1.87516 - 4.10604i) q^{59} +(0.0838230 - 0.0432138i) q^{61} +(-0.848171 + 0.545086i) q^{62} +(-0.187328 + 0.216189i) q^{64} +(-5.78229 - 2.31488i) q^{65} +(-6.19207 - 5.35334i) q^{67} -8.02212 q^{68} +(-1.00992 + 1.16551i) q^{70} +(-0.640015 - 0.610253i) q^{71} +(6.08960 - 3.13941i) q^{73} +(4.03729 - 3.17496i) q^{74} +(-1.46526 - 10.1911i) q^{76} +(4.11526 - 0.793150i) q^{77} +(7.09030 - 0.677042i) q^{79} +(-2.88511 - 4.05156i) q^{80} +(-0.557215 + 3.87552i) q^{82} +(0.172253 + 3.61605i) q^{83} +(-3.50948 + 14.4663i) q^{85} +(-3.66996 - 2.88609i) q^{86} +(0.564599 - 11.8524i) q^{88} +(6.78300 + 7.82800i) q^{89} +(1.65376 + 0.485588i) q^{91} +(3.73067 - 8.16903i) q^{92} +(2.83453 + 1.82164i) q^{94} +(-19.0187 - 1.81606i) q^{95} +(6.75458 - 11.6993i) q^{97} +(-2.36368 + 3.31932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 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

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