LMFDB - Embedded newform 675.2.r.a.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.2
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69452 - 1.88195i) q^{2} +(-0.461298 + 4.38896i) q^{4} +(2.12223 - 0.704374i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 - 3.59200i) q^{8} +O(q^{10})$	\(q+(-1.69452 - 1.88195i) q^{2} +(-0.461298 + 4.38896i) q^{4} +(2.12223 - 0.704374i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 - 3.59200i) q^{8} +(-4.92175 - 2.80036i) q^{10} +(-1.63896 - 1.82025i) q^{11} +(-1.19441 + 1.32652i) q^{13} +(5.12291 - 1.08891i) q^{14} +(-6.50420 - 1.38251i) q^{16} +(-3.67466 + 2.66979i) q^{17} +(5.85004 - 4.25031i) q^{19} +(2.11249 + 9.63931i) q^{20} +(-0.648378 + 6.16890i) q^{22} +(2.31553 - 0.492181i) q^{23} +(4.00772 - 2.98968i) q^{25} +4.52040 q^{26} +(-7.38384 - 5.36467i) q^{28} +(7.47301 - 3.32720i) q^{29} +(6.20029 + 2.76055i) q^{31} +(2.30859 + 3.99860i) q^{32} +(11.2512 + 2.39152i) q^{34} +(-0.932951 + 4.52939i) q^{35} +(1.53985 + 4.73917i) q^{37} +(-17.9119 - 3.80729i) q^{38} +(7.96211 - 11.1054i) q^{40} +(3.20347 - 3.55781i) q^{41} +(4.14034 - 7.17127i) q^{43} +(8.74507 - 6.35367i) q^{44} +(-4.84997 - 3.52371i) q^{46} +(9.25434 - 4.12030i) q^{47} +(1.36143 + 2.35806i) q^{49} +(-12.4176 - 2.47626i) q^{50} +(-5.27108 - 5.85413i) q^{52} +(2.52356 + 1.83348i) q^{53} +(-4.76039 - 2.70855i) q^{55} +(1.32108 + 12.5692i) q^{56} +(-18.9248 - 8.42585i) q^{58} +(-6.99016 + 7.76336i) q^{59} +(-1.76446 - 1.95963i) q^{61} +(-5.31128 - 16.3465i) q^{62} +(-0.496397 + 1.52775i) q^{64} +(-1.60044 + 3.65649i) q^{65} +(-1.48939 - 0.663118i) q^{67} +(-10.0225 - 17.3595i) q^{68} +(10.1050 - 5.91936i) q^{70} +(-8.24169 - 5.98794i) q^{71} +(-0.608028 + 1.87132i) q^{73} +(6.30959 - 10.9285i) q^{74} +(15.9558 + 27.6363i) q^{76} +(4.95496 - 1.05321i) q^{77} +(13.6290 - 6.06801i) q^{79} +(-14.7772 + 1.64738i) q^{80} -12.1240 q^{82} +(0.424422 + 4.03811i) q^{83} +(-5.91793 + 8.25424i) q^{85} +(-20.5119 + 4.35993i) q^{86} +(-14.6413 - 3.11211i) q^{88} +(-0.105993 + 0.326212i) q^{89} +(-1.14078 - 3.51095i) q^{91} +(1.09201 + 10.3898i) q^{92} +(-23.4358 - 10.4343i) q^{94} +(9.42133 - 13.1407i) q^{95} +(-10.0640 + 4.48076i) q^{97} +(2.13079 - 6.55791i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.69452	−	1.88195i	−1.19821	−	1.33074i	−0.930080	−	0.367358i	$-0.880263\pi$
$2$	−1.69452	−	1.88195i	−1.19821	−	1.33074i	−0.268125	−	0.963384i	$-0.586404\pi$
$3$		0			0
$3$		0			0
$4$	−0.461298	+	4.38896i	−0.230649	+	2.19448i
$5$	2.12223	−	0.704374i	0.949090	−	0.315005i
$5$	2.12223	−	0.704374i	0.949090	−	0.315005i
$6$		0			0
$7$	−1.03406	+	1.79105i	−0.390839	+	0.676953i	−0.992560	−	0.121753i	$-0.961148\pi$
$7$	−1.03406	+	1.79105i	−0.390839	+	0.676953i	0.601721	+	0.798706i	$0.294482\pi$
$8$	4.94396	−	3.59200i	1.74795	−	1.26996i
$9$		0			0
$10$	−4.92175	−	2.80036i	−1.55640	−	0.885552i
$11$	−1.63896	−	1.82025i	−0.494166	−	0.548827i	0.443541	−	0.896254i	$-0.353722\pi$
$11$	−1.63896	−	1.82025i	−0.494166	−	0.548827i	−0.937707	+	0.347427i	$0.887055\pi$
$12$		0			0
$13$	−1.19441	+	1.32652i	−0.331269	+	0.367911i	−0.885651	−	0.464351i	$-0.846288\pi$
$13$	−1.19441	+	1.32652i	−0.331269	+	0.367911i	0.554383	+	0.832262i	$0.312954\pi$
$14$	5.12291	−	1.08891i	1.36916	−	0.291023i
$15$		0			0
$16$	−6.50420	−	1.38251i	−1.62605	−	0.345628i
$17$	−3.67466	+	2.66979i	−0.891235	+	0.647520i	−0.936200	−	0.351469i	$-0.885682\pi$
$17$	−3.67466	+	2.66979i	−0.891235	+	0.647520i	0.0449649	+	0.998989i	$0.485682\pi$
$18$		0			0
$19$	5.85004	−	4.25031i	1.34209	−	0.975087i	0.342728	−	0.939435i	$-0.388649\pi$
$19$	5.85004	−	4.25031i	1.34209	−	0.975087i	0.999364	−	0.0356524i	$-0.0113509\pi$
$20$	2.11249	+	9.63931i	0.472367	+	2.15542i
$21$		0			0
$22$	−0.648378	+	6.16890i	−0.138235	+	1.31521i
$23$	2.31553	−	0.492181i	0.482821	−	0.102627i	0.0399305	−	0.999202i	$-0.487286\pi$
$23$	2.31553	−	0.492181i	0.482821	−	0.102627i	0.442891	+	0.896576i	$0.353953\pi$
$24$		0			0
$25$	4.00772	−	2.98968i	0.801543	−	0.597937i
$26$	4.52040			0.886523
$27$		0			0
$28$	−7.38384	−	5.36467i	−1.39541	−	1.01383i
$29$	7.47301	−	3.32720i	1.38770	−	0.617845i	0.429273	−	0.903175i	$-0.358770\pi$
$29$	7.47301	−	3.32720i	1.38770	−	0.617845i	0.958429	+	0.285330i	$0.0921031\pi$
$30$		0			0
$31$	6.20029	+	2.76055i	1.11361	+	0.495809i	0.879259	−	0.476344i	$-0.158038\pi$
$31$	6.20029	+	2.76055i	1.11361	+	0.495809i	0.234346	+	0.972153i	$0.424705\pi$
$32$	2.30859	+	3.99860i	0.408105	+	0.706859i
$33$		0			0
$34$	11.2512	+	2.39152i	1.92956	+	0.410141i
$35$	−0.932951	+	4.52939i	−0.157698	+	0.765606i
$36$		0			0
$37$	1.53985	+	4.73917i	0.253150	+	0.779115i	0.994189	+	0.107653i	$0.0343334\pi$
$37$	1.53985	+	4.73917i	0.253150	+	0.779115i	−0.741039	+	0.671462i	$0.765667\pi$
$38$	−17.9119	−	3.80729i	−2.90569	−	0.617624i
$39$		0			0
$40$	7.96211	−	11.1054i	1.25892	−	1.75592i
$41$	3.20347	−	3.55781i	0.500297	−	0.555636i	−0.439113	−	0.898432i	$-0.644707\pi$
$41$	3.20347	−	3.55781i	0.500297	−	0.555636i	0.939410	+	0.342796i	$0.111374\pi$
$42$		0			0
$43$	4.14034	−	7.17127i	0.631395	−	1.09361i	−0.355871	−	0.934535i	$-0.615816\pi$
$43$	4.14034	−	7.17127i	0.631395	−	1.09361i	0.987267	−	0.159074i	$-0.0508508\pi$
$44$	8.74507	−	6.35367i	1.31837	−	0.957851i
$45$		0			0
$46$	−4.84997	−	3.52371i	−0.715088	−	0.519542i
$47$	9.25434	−	4.12030i	1.34988	−	0.601007i	0.400839	−	0.916148i	$-0.368719\pi$
$47$	9.25434	−	4.12030i	1.34988	−	0.601007i	0.949045	+	0.315141i	$0.102052\pi$
$48$		0			0
$49$	1.36143	+	2.35806i	0.194489	+	0.336866i
$50$	−12.4176	−	2.47626i	−1.75611	−	0.350196i
$51$		0			0
$52$	−5.27108	−	5.85413i	−0.730967	−	0.811821i
$53$	2.52356	+	1.83348i	0.346638	+	0.251847i	0.747457	−	0.664310i	$-0.231274\pi$
$53$	2.52356	+	1.83348i	0.346638	+	0.251847i	−0.400819	+	0.916157i	$0.631274\pi$
$54$		0			0
$55$	−4.76039	−	2.70855i	−0.641891	−	0.365221i
$56$	1.32108	+	12.5692i	0.176537	+	1.67963i
$57$		0			0
$58$	−18.9248	−	8.42585i	−2.48494	−	1.10637i
$59$	−6.99016	+	7.76336i	−0.910041	+	1.01070i	0.0898499	+	0.995955i	$0.471361\pi$
$59$	−6.99016	+	7.76336i	−0.910041	+	1.01070i	−0.999891	+	0.0147480i	$0.995305\pi$
$60$		0			0
$61$	−1.76446	−	1.95963i	−0.225916	−	0.250905i	0.619521	−	0.784980i	$-0.287327\pi$
$61$	−1.76446	−	1.95963i	−0.225916	−	0.250905i	−0.845437	+	0.534075i	$0.820660\pi$
$62$	−5.31128	−	16.3465i	−0.674534	−	2.07600i
$63$		0			0
$64$	−0.496397	+	1.52775i	−0.0620496	+	0.190969i
$65$	−1.60044	+	3.65649i	−0.198510	+	0.453532i
$66$		0			0
$67$	−1.48939	−	0.663118i	−0.181958	−	0.0810127i	0.313736	−	0.949510i	$-0.398419\pi$
$67$	−1.48939	−	0.663118i	−0.181958	−	0.0810127i	−0.495693	+	0.868498i	$0.665086\pi$
$68$	−10.0225	−	17.3595i	−1.21541	−	2.10515i
$69$		0			0
$70$	10.1050	−	5.91936i	1.20778	−	0.707498i
$71$	−8.24169	−	5.98794i	−0.978109	−	0.710638i	−0.0208238	−	0.999783i	$-0.506629\pi$
$71$	−8.24169	−	5.98794i	−0.978109	−	0.710638i	−0.957285	+	0.289145i	$0.906629\pi$
$72$		0			0
$73$	−0.608028	+	1.87132i	−0.0711643	+	0.219021i	−0.980313	−	0.197451i	$-0.936734\pi$
$73$	−0.608028	+	1.87132i	−0.0711643	+	0.219021i	0.909148	+	0.416472i	$0.136734\pi$
$74$	6.30959	−	10.9285i	0.733475	−	1.27042i
$75$		0			0
$76$	15.9558	+	27.6363i	1.83026	+	3.17010i
$77$	4.95496	−	1.05321i	0.564670	−	0.120024i
$78$		0			0
$79$	13.6290	−	6.06801i	1.53338	−	0.682704i	0.545525	−	0.838094i	$-0.316330\pi$
$79$	13.6290	−	6.06801i	1.53338	−	0.682704i	0.987853	+	0.155390i	$0.0496635\pi$
$80$	−14.7772	+	1.64738i	−1.65214	+	0.184183i
$81$		0			0
$82$	−12.1240			−1.33887
$83$	0.424422	+	4.03811i	0.0465864	+	0.443240i	0.992808	+	0.119720i	$0.0381996\pi$
$83$	0.424422	+	4.03811i	0.0465864	+	0.443240i	−0.946221	+	0.323520i	$0.895134\pi$
$84$		0			0
$85$	−5.91793	+	8.25424i	−0.641890	+	0.895298i
$86$	−20.5119	+	4.35993i	−2.21185	+	0.470144i
$87$		0			0
$88$	−14.6413	−	3.11211i	−1.56077	−	0.331752i
$89$	−0.105993	+	0.326212i	−0.0112352	+	0.0345784i	−0.956517	−	0.291677i	$-0.905787\pi$
$89$	−0.105993	+	0.326212i	−0.0112352	+	0.0345784i	0.945282	+	0.326255i	$0.105787\pi$
$90$		0			0
$91$	−1.14078	−	3.51095i	−0.119586	−	0.368048i
$92$	1.09201	+	10.3898i	0.113850	+	1.08321i
$93$		0			0
$94$	−23.4358	−	10.4343i	−2.41722	−	1.07622i
$95$	9.42133	−	13.1407i	0.966608	−	1.34821i
$96$		0			0
$97$	−10.0640	+	4.48076i	−1.02184	+	0.454953i	−0.848098	−	0.529839i	$-0.822252\pi$
$97$	−10.0640	+	4.48076i	−1.02184	+	0.454953i	−0.173742	+	0.984791i	$0.555586\pi$
$98$	2.13079	−	6.55791i	0.215243	−	0.662449i
$99$		0			0
$100$	11.2729	+	18.9688i	1.12729	+	1.89688i
$101$	−6.38861	+	11.0654i	−0.635691	+	1.10105i	0.350677	+	0.936496i	$0.385951\pi$
$101$	−6.38861	+	11.0654i	−0.635691	+	1.10105i	−0.986368	+	0.164553i	$0.947382\pi$
$102$		0			0
$103$	0.959675	−	9.13070i	0.0945596	−	0.899674i	−0.839693	−	0.543062i	$-0.817265\pi$
$103$	0.959675	−	9.13070i	0.0945596	−	0.899674i	0.934252	−	0.356613i	$-0.116068\pi$
$104$	−1.14023	+	10.8486i	−0.111809	+	1.06379i
$105$		0			0
$106$	−0.825708	−	7.85609i	−0.0801999	−	0.763051i
$107$	−0.980681			−0.0948061			−0.0474030	−	0.998876i	$-0.515095\pi$
$107$	−0.980681			−0.0948061			−0.0474030	+	0.998876i	$0.515095\pi$
$108$		0			0
$109$	−2.74384	−	8.44467i	−0.262812	−	0.808853i	−0.992189	−	0.124741i	$-0.960190\pi$
$109$	−2.74384	−	8.44467i	−0.262812	−	0.808853i	0.729377	−	0.684112i	$-0.239810\pi$
$110$	2.96920	+	13.5485i	0.283103	+	1.29180i
$111$		0			0
$112$	9.20190	−	10.2197i	0.869498	−	0.965675i
$113$	−4.53863	+	5.04065i	−0.426958	+	0.474185i	−0.917788	−	0.397070i	$-0.870027\pi$
$113$	−4.53863	+	5.04065i	−0.426958	+	0.474185i	0.490830	+	0.871255i	$0.336694\pi$
$114$		0			0
$115$	4.56740	−	2.67552i	0.425913	−	0.249493i
$116$	11.1557	+	34.3336i	1.03578	+	3.18779i
$117$		0			0
$118$	26.4552			2.43540
$119$	−0.981908	−	9.34223i	−0.0900113	−	0.856401i
$120$		0			0
$121$	0.522693	−	4.97309i	0.0475175	−	0.452099i
$122$	−0.698024	+	6.64126i	−0.0631962	+	0.601271i
$123$		0			0
$124$	−14.9761	+	25.9394i	−1.34490	+	2.32943i
$125$	6.39944	−	9.16773i	0.572383	−	0.819986i
$126$		0			0
$127$	3.08193	−	9.48521i	0.273477	−	0.841676i	−0.716141	−	0.697955i	$-0.754093\pi$
$127$	3.08193	−	9.48521i	0.273477	−	0.841676i	0.989618	−	0.143721i	$-0.0459067\pi$
$128$	12.1523	−	5.41057i	1.07412	−	0.478231i
$129$		0			0
$130$	9.59332	−	3.18405i	0.841390	−	0.279259i
$131$	12.5686	+	5.59591i	1.09813	+	0.488917i	0.874139	−	0.485675i	$-0.161426\pi$
$131$	12.5686	+	5.59591i	1.09813	+	0.488917i	0.223986	+	0.974592i	$0.428093\pi$
$132$		0			0
$133$	1.56320	+	14.8728i	0.135546	+	1.28964i
$134$	1.27584	+	3.92662i	0.110215	+	0.339208i
$135$		0			0
$136$	−8.57746	+	26.3987i	−0.735511	+	2.26367i
$137$	−8.34276	−	1.77331i	−0.712770	−	0.151504i	−0.162764	−	0.986665i	$-0.552041\pi$
$137$	−8.34276	−	1.77331i	−0.712770	−	0.151504i	−0.550005	+	0.835161i	$0.685374\pi$
$138$		0			0
$139$	9.12603	−	1.93980i	0.774060	−	0.164532i	0.196086	−	0.980587i	$-0.437177\pi$
$139$	9.12603	−	1.93980i	0.774060	−	0.164532i	0.577974	+	0.816055i	$0.303843\pi$
$140$	−19.4489	−	6.18409i	−1.64374	−	0.522651i
$141$		0			0
$142$	2.69667	+	25.6571i	0.226300	+	2.15310i
$143$	4.37219			0.365621
$144$		0			0
$145$	13.5158	−	12.3249i	1.12243	−	1.02352i
$146$	4.55205	−	2.02670i	0.376730	−	0.167731i
$147$		0			0
$148$	−21.5104	+	4.57217i	−1.76814	+	0.375830i
$149$	3.47298	+	6.01538i	0.284518	+	0.492799i	0.972492	−	0.232936i	$-0.0748332\pi$
$149$	3.47298	+	6.01538i	0.284518	+	0.492799i	−0.687974	+	0.725735i	$0.741500\pi$
$150$		0			0
$151$	0.394205	−	0.682783i	0.0320800	−	0.0555641i	−0.849540	−	0.527525i	$-0.823120\pi$
$151$	0.394205	−	0.682783i	0.0320800	−	0.0555641i	0.881620	+	0.471961i	$0.156454\pi$
$152$	13.6553	−	42.0267i	1.10759	−	3.40881i
$153$		0			0
$154$	−10.3783	−	7.54031i	−0.836311	−	0.607616i
$155$	15.1029	+	1.49119i	1.21309	+	0.119776i
$156$		0			0
$157$	−1.94393	−	3.36698i	−0.155142	−	0.268714i	0.777969	−	0.628303i	$-0.216250\pi$
$157$	−1.94393	−	3.36698i	−0.155142	−	0.268714i	−0.933111	+	0.359589i	$0.882917\pi$
$158$	−34.5142	−	15.3667i	−2.74580	−	1.22251i
$159$		0			0
$160$	7.71587	+	6.85983i	0.609993	+	0.542318i
$161$	−1.51288	+	4.65617i	−0.119232	+	0.366958i
$162$		0			0
$163$	2.59370	+	7.98258i	0.203154	+	0.625244i	0.999784	+	0.0207767i	$0.00661392\pi$
$163$	2.59370	+	7.98258i	0.203154	+	0.625244i	−0.796630	+	0.604467i	$0.793386\pi$
$164$	14.1373	+	15.7011i	1.10394	+	1.22605i
$165$		0			0
$166$	6.88033	−	7.64139i	0.534018	−	0.593087i
$167$	−9.87343	−	4.39594i	−0.764029	−	0.340168i	−0.0125472	−	0.999921i	$-0.503994\pi$
$167$	−9.87343	−	4.39594i	−0.764029	−	0.340168i	−0.751482	+	0.659754i	$0.770661\pi$
$168$		0			0
$169$	1.02581	+	9.75997i	0.0789088	+	0.750767i
$170$	25.5621	−	2.84970i	1.96053	−	0.218562i
$171$		0			0
$172$	29.5645	+	21.4799i	2.25427	+	1.63783i
$173$	11.0146	+	12.2329i	0.837422	+	0.930051i	0.998379	−	0.0569100i	$-0.0181248\pi$
$173$	11.0146	+	12.2329i	0.837422	+	0.930051i	−0.160957	+	0.986961i	$0.551458\pi$
$174$		0			0
$175$	1.21044	+	10.2695i	0.0915009	+	0.776305i
$176$	8.14362	+	14.1052i	0.613849	+	1.06322i
$177$		0			0
$178$	0.793522	−	0.353299i	0.0594770	−	0.0264809i
$179$	0.422707	+	0.307115i	0.0315946	+	0.0229548i	0.603471	−	0.797385i	$-0.293784\pi$
$179$	0.422707	+	0.307115i	0.0315946	+	0.0229548i	−0.571876	+	0.820340i	$0.693784\pi$
$180$		0			0
$181$	−18.6716	+	13.5657i	−1.38785	+	1.00833i	−0.391756	+	0.920069i	$0.628132\pi$
$181$	−18.6716	+	13.5657i	−1.38785	+	1.00833i	−0.996097	+	0.0882646i	$0.971868\pi$
$182$	−4.67438	+	8.09626i	−0.346488	+	0.600134i
$183$		0			0
$184$	9.67997	−	10.7507i	0.713617	−	0.792552i
$185$	6.60606	+	8.97298i	0.485687	+	0.659706i
$186$		0			0
$187$	10.8823	+	2.31311i	0.795794	+	0.169151i
$188$	13.8148	+	42.5176i	1.00755	+	3.10092i
$189$		0			0
$190$	−40.6949	+	4.53672i	−2.95232	+	0.329128i
$191$	−0.982006	−	0.208732i	−0.0710555	−	0.0151033i	0.172247	−	0.985054i	$-0.444897\pi$
$191$	−0.982006	−	0.208732i	−0.0710555	−	0.0151033i	−0.243302	+	0.969951i	$0.578231\pi$
$192$		0			0
$193$	6.92614	+	11.9964i	0.498554	+	0.863521i	0.999999	−	0.00166856i	$-0.000531120\pi$
$193$	6.92614	+	11.9964i	0.498554	+	0.863521i	−0.501444	+	0.865190i	$0.667198\pi$
$194$	25.4861	+	11.3472i	1.82980	+	0.814679i
$195$		0			0
$196$	−10.9775	+	4.88748i	−0.784104	+	0.349105i
$197$	−6.40803	−	4.65571i	−0.456553	−	0.331705i	0.335624	−	0.941996i	$-0.391053\pi$
$197$	−6.40803	−	4.65571i	−0.456553	−	0.331705i	−0.792178	+	0.610291i	$0.791053\pi$
$198$		0			0
$199$	14.6161			1.03611			0.518053	−	0.855348i	$-0.326657\pi$
$199$	14.6161			1.03611			0.518053	+	0.855348i	$0.326657\pi$
$200$	9.07505	−	29.1766i	0.641703	−	2.06310i
$201$		0			0
$202$	31.6502	−	6.72746i	2.22690	−	0.473342i
$203$	−1.76839	+	16.8251i	−0.124116	+	1.18089i
$204$		0			0
$205$	4.29246	−	9.80692i	0.299799	−	0.684945i
$206$	−18.8097	+	13.6661i	−1.31054	+	0.952160i
$207$		0			0
$208$	9.60259	−	6.97669i	0.665820	−	0.483746i
$209$	−17.3246	−	3.68246i	−1.19837	−	0.254721i
$210$		0			0
$211$	−13.0287	+	2.76934i	−0.896933	+	0.190649i	−0.633238	−	0.773957i	$-0.718275\pi$
$211$	−13.0287	+	2.76934i	−0.896933	+	0.190649i	−0.263695	+	0.964606i	$0.584941\pi$
$212$	−9.21118	+	10.2300i	−0.632626	+	0.702603i
$213$		0			0
$214$	1.66178	+	1.84560i	0.113597	+	0.126162i
$215$	3.73549	−	18.1354i	0.254758	−	1.23683i
$216$		0			0
$217$	−11.3558	+	8.25045i	−0.770880	+	0.560077i
$218$	−11.2430	+	19.4734i	−0.761471	+	1.31891i
$219$		0			0
$220$	14.0837	−	19.6437i	0.949522	−	1.32438i
$221$	0.847490	−	8.06333i	0.0570084	−	0.542398i
$222$		0			0
$223$	2.44141	+	2.71146i	0.163489	+	0.181573i	0.819323	−	0.573332i	$-0.194350\pi$
$223$	2.44141	+	2.71146i	0.163489	+	0.181573i	−0.655834	+	0.754905i	$0.727683\pi$
$224$	−9.54893			−0.638014
$225$		0			0
$226$	17.1771			1.14260
$227$	−10.5152	−	11.6783i	−0.697915	−	0.775114i	0.285127	−	0.958490i	$-0.407964\pi$
$227$	−10.5152	−	11.6783i	−0.697915	−	0.775114i	−0.983043	+	0.183376i	$0.941297\pi$
$228$		0			0
$229$	−0.627978	+	5.97482i	−0.0414980	+	0.394827i	0.953983	+	0.299862i	$0.0969406\pi$
$229$	−0.627978	+	5.97482i	−0.0414980	+	0.394827i	−0.995481	+	0.0949650i	$0.969726\pi$
$230$	−12.7747	−	4.06193i	−0.842342	−	0.267835i
$231$		0			0
$232$	24.9950	−	43.2926i	1.64100	−	2.84230i
$233$	0.484321	−	0.351880i	0.0317289	−	0.0230524i	−0.571808	−	0.820388i	$-0.693758\pi$
$233$	0.484321	−	0.351880i	0.0317289	−	0.0230524i	0.603537	+	0.797335i	$0.293758\pi$
$234$		0			0
$235$	16.7376	−	15.2627i	1.09184	−	0.995630i
$236$	−30.8485	−	34.2608i	−2.00807	−	2.23019i
$237$		0			0
$238$	−15.9178	+	17.6785i	−1.03180	+	1.14593i
$239$	1.14937	−	0.244307i	0.0743469	−	0.0158029i	−0.170588	−	0.985342i	$-0.554567\pi$
$239$	1.14937	−	0.244307i	0.0743469	−	0.0158029i	0.244935	+	0.969540i	$0.421233\pi$
$240$		0			0
$241$	−17.5785	−	3.73642i	−1.13233	−	0.240684i	−0.396621	−	0.917982i	$-0.629817\pi$
$241$	−17.5785	−	3.73642i	−1.13233	−	0.240684i	−0.735709	+	0.677298i	$0.763151\pi$
$242$	−10.2448	+	7.44331i	−0.658563	+	0.478474i
$243$		0			0
$244$	9.41469	−	6.84017i	0.602714	−	0.437897i
$245$	4.55021	+	4.04539i	0.290702	+	0.258450i
$246$		0			0
$247$	−1.34920	+	12.8368i	−0.0858477	+	0.816787i
$248$	40.5699	−	8.62339i	2.57619	−	0.547586i
$249$		0			0
$250$	−28.0972	+	3.49144i	−1.77702	+	0.220818i
$251$	−0.313172			−0.0197673			−0.00988364	−	0.999951i	$-0.503146\pi$
$251$	−0.313172			−0.0197673			−0.00988364	+	0.999951i	$0.503146\pi$
$252$		0			0
$253$	−4.69096	−	3.40818i	−0.294918	−	0.214270i
$254$	−23.0731	+	10.2728i	−1.44773	+	0.644573i
$255$		0			0
$256$	−27.8398	−	12.3951i	−1.73999	−	0.774692i
$257$	−1.48530	−	2.57262i	−0.0926507	−	0.160476i	0.815975	−	0.578087i	$-0.196201\pi$
$257$	−1.48530	−	2.57262i	−0.0926507	−	0.160476i	−0.908626	+	0.417611i	$0.862867\pi$
$258$		0			0
$259$	−10.0804	−	2.14265i	−0.626365	−	0.133138i
$260$	−15.3099	−	8.71099i	−0.949482	−	0.540233i
$261$		0			0
$262$	−10.7665	−	33.1359i	−0.665158	−	2.04714i
$263$	−7.94955	−	1.68973i	−0.490190	−	0.104193i	−0.0438160	−	0.999040i	$-0.513952\pi$
$263$	−7.94955	−	1.68973i	−0.490190	−	0.104193i	−0.446374	+	0.894847i	$0.647285\pi$
$264$		0			0
$265$	6.64704	+	2.11353i	0.408324	+	0.129833i
$266$	25.3411	−	28.1441i	1.55376	−	1.72563i
$267$		0			0
$268$	3.59745	−	6.23097i	0.219749	−	0.380617i
$269$	−18.6230	+	13.5304i	−1.13547	+	0.824965i	−0.986481	−	0.163874i	$-0.947601\pi$
$269$	−18.6230	+	13.5304i	−1.13547	+	0.824965i	−0.148986	+	0.988839i	$0.547601\pi$
$270$		0			0
$271$	−18.3049	−	13.2993i	−1.11194	−	0.807874i	−0.128974	−	0.991648i	$-0.541169\pi$
$271$	−18.3049	−	13.2993i	−1.11194	−	0.807874i	−0.982969	+	0.183774i	$0.941169\pi$
$272$	27.5917	−	12.2846i	1.67299	−	0.744865i
$273$		0			0
$274$	10.7997	+	18.7056i	0.652432	+	1.13005i
$275$	−12.0105	−	2.39507i	−0.724259	−	0.144428i
$276$		0			0
$277$	−6.92921	−	7.69566i	−0.416336	−	0.462388i	0.498100	−	0.867120i	$-0.334031\pi$
$277$	−6.92921	−	7.69566i	−0.416336	−	0.462388i	−0.914435	+	0.404732i	$0.867365\pi$
$278$	−19.1148	−	13.8877i	−1.14643	−	0.832931i
$279$		0			0
$280$	11.6571	+	25.7443i	0.696643	+	1.53851i
$281$	−2.65920	−	25.3006i	−0.158635	−	1.50931i	−0.727060	−	0.686574i	$-0.759114\pi$
$281$	−2.65920	−	25.3006i	−0.158635	−	1.50931i	0.568425	−	0.822735i	$-0.307553\pi$
$282$		0			0
$283$	−15.1378	−	6.73980i	−0.899851	−	0.400639i	−0.0959386	−	0.995387i	$-0.530585\pi$
$283$	−15.1378	−	6.73980i	−0.899851	−	0.400639i	−0.803912	+	0.594748i	$0.797252\pi$
$284$	30.0827	−	33.4102i	1.78508	−	1.98253i
$285$		0			0
$286$	−7.40876	−	8.22826i	−0.438089	−	0.486547i
$287$	3.05963	+	9.41657i	0.180604	+	0.555842i
$288$		0			0
$289$	1.12201	−	3.45318i	0.0660004	−	0.203128i
$290$	−46.0977	−	4.55148i	−2.70695	−	0.267272i
$291$		0			0
$292$	−7.93266	−	3.53185i	−0.464224	−	0.206686i
$293$	6.06420	+	10.5035i	0.354274	+	0.613621i	0.986993	−	0.160760i	$-0.0513946\pi$
$293$	6.06420	+	10.5035i	0.354274	+	0.613621i	−0.632719	+	0.774381i	$0.718061\pi$
$294$		0			0
$295$	−9.36642	+	21.3993i	−0.545334	+	1.24592i
$296$	24.6360	+	17.8991i	1.43194	+	1.04037i
$297$		0			0
$298$	5.43564	−	16.7292i	0.314878	−	0.969095i
$299$	−2.11279	+	3.65946i	−0.122186	+	0.211632i
$300$		0			0
$301$	8.56274	+	14.8311i	0.493548	+	0.854851i
$302$	−1.95295	+	0.415113i	−0.112380	+	0.0238871i
$303$		0			0
$304$	−43.9259	+	19.5571i	−2.51933	+	1.12168i
$305$	−5.12490	−	2.91595i	−0.293451	−	0.166967i
$306$		0			0
$307$	−11.7705			−0.671776			−0.335888	−	0.941902i	$-0.609036\pi$
$307$	−11.7705			−0.671776			−0.335888	+	0.941902i	$0.609036\pi$
$308$	2.33678	+	22.2330i	0.133150	+	1.26684i
$309$		0			0
$310$	−22.7858	−	30.9498i	−1.29414	−	1.75783i
$311$	9.67624	−	2.05675i	0.548689	−	0.116628i	0.0747782	−	0.997200i	$-0.476175\pi$
$311$	9.67624	−	2.05675i	0.548689	−	0.116628i	0.473911	+	0.880573i	$0.342842\pi$
$312$		0			0
$313$	33.6648	+	7.15567i	1.90285	+	0.404462i	0.999691	−	0.0248538i	$-0.00791202\pi$
$313$	33.6648	+	7.15567i	1.90285	+	0.404462i	0.903154	+	0.429316i	$0.141245\pi$
$314$	−3.04248	+	9.36378i	−0.171697	+	0.528429i
$315$		0			0
$316$	20.3452	+	62.6162i	1.14451	+	3.52243i
$317$	2.32443	+	22.1155i	0.130553	+	1.24213i	0.842034	+	0.539425i	$0.181358\pi$
$317$	2.32443	+	22.1155i	0.130553	+	1.24213i	−0.711481	+	0.702706i	$0.751975\pi$
$318$		0			0
$319$	−18.3043	−	8.14961i	−1.02485	−	0.456290i
$320$	0.0226404	+	3.59189i	0.00126564	+	0.200793i
$321$		0			0
$322$	11.3263	−	5.04280i	0.631190	−	0.281024i
$323$	−10.1495	+	31.2368i	−0.564731	+	1.73806i
$324$		0			0
$325$	−0.820957	+	8.88722i	−0.0455385	+	0.492974i
$326$	10.6278	−	18.4078i	0.588618	−	1.01952i
$327$		0			0
$328$	3.05817	−	29.0965i	0.168859	−	1.60659i
$329$	−2.18991	+	20.8356i	−0.120734	+	1.14871i
$330$		0			0
$331$	1.36800	+	13.0156i	0.0751920	+	0.715404i	0.965563	+	0.260169i	$0.0837781\pi$
$331$	1.36800	+	13.0156i	0.0751920	+	0.715404i	−0.890371	+	0.455235i	$0.849555\pi$
$332$	−17.9189			−0.983426
$333$		0			0
$334$	8.45777	+	26.0303i	0.462788	+	1.42432i
$335$	−3.62790	−	0.358203i	−0.198214	−	0.0195707i
$336$		0			0
$337$	9.72209	−	10.7975i	0.529596	−	0.588176i	−0.417680	−	0.908594i	$-0.637157\pi$
$337$	9.72209	−	10.7975i	0.529596	−	0.588176i	0.947276	+	0.320418i	$0.103823\pi$
$338$	16.6295	−	18.4690i	0.904528	−	1.00458i
$339$		0			0
$340$	−33.4976	−	29.7812i	−1.81666	−	1.61511i
$341$	−5.13715	−	15.8105i	−0.278192	−	0.856188i
$342$		0			0
$343$	−20.1081			−1.08573
$344$	−5.28954	−	50.3266i	−0.285193	−	2.71343i
$345$		0			0
$346$	4.35739	−	41.4578i	0.234255	−	2.22878i
$347$	1.16703	−	11.1035i	0.0626493	−	0.596068i	−0.917490	−	0.397759i	$-0.869788\pi$
$347$	1.16703	−	11.1035i	0.0626493	−	0.596068i	0.980139	−	0.198310i	$-0.0635452\pi$
$348$		0			0
$349$	4.08628	−	7.07765i	0.218734	−	0.378858i	−0.735687	−	0.677321i	$-0.763141\pi$
$349$	4.08628	−	7.07765i	0.218734	−	0.378858i	0.954421	+	0.298463i	$0.0964740\pi$
$350$	17.2757	−	19.6799i	0.923424	−	1.05194i
$351$		0			0
$352$	3.49476	−	10.7558i	0.186272	−	0.573285i
$353$	20.5995	−	9.17150i	1.09640	−	0.488150i	0.222836	−	0.974856i	$-0.428468\pi$
$353$	20.5995	−	9.17150i	1.09640	−	0.488150i	0.873566	+	0.486706i	$0.161802\pi$
$354$		0			0
$355$	−21.7085	−	6.90255i	−1.15217	−	0.366349i
$356$	−1.38284	−	0.615679i	−0.0732903	−	0.0326309i
$357$		0			0
$358$	−0.138310	−	1.31593i	−0.00730989	−	0.0695489i
$359$	7.75846	+	23.8781i	0.409476	+	1.26024i	0.917100	+	0.398658i	$0.130524\pi$
$359$	7.75846	+	23.8781i	0.409476	+	1.26024i	−0.507624	+	0.861579i	$0.669476\pi$
$360$		0			0
$361$	10.2866	−	31.6589i	0.541400	−	1.66626i
$362$	57.1695	+	12.1518i	3.00476	+	0.638682i
$363$		0			0
$364$	15.9357	−	3.38723i	0.835256	−	0.177539i
$365$	0.0277319	+	4.39965i	0.00145155	+	0.230288i
$366$		0			0
$367$	0.674667	+	6.41903i	0.0352173	+	0.335071i	0.997918	+	0.0645007i	$0.0205455\pi$
$367$	0.674667	+	6.41903i	0.0352173	+	0.335071i	−0.962700	+	0.270570i	$0.912788\pi$
$368$	−15.7411			−0.820562
$369$		0			0
$370$	5.69263	−	27.6372i	0.295946	−	1.43679i
$371$	−5.89338	+	2.62390i	−0.305969	+	0.136226i
$372$		0			0
$373$	23.5755	−	5.01112i	1.22069	−	0.259466i	0.447875	−	0.894096i	$-0.352181\pi$
$373$	23.5755	−	5.01112i	1.22069	−	0.259466i	0.772816	+	0.634630i	$0.218848\pi$
$374$	−14.0871	−	24.3996i	−0.728428	−	1.26167i
$375$		0			0
$376$	30.9530	−	53.6121i	1.59628	−	2.76484i
$377$	−4.51220	+	13.8871i	−0.232390	+	0.715224i
$378$		0			0
$379$	−0.345496	−	0.251018i	−0.0177469	−	0.0128939i	0.578876	−	0.815415i	$-0.303491\pi$
$379$	−0.345496	−	0.251018i	−0.0177469	−	0.0128939i	−0.596623	+	0.802521i	$0.703491\pi$
$380$	53.3282	+	47.4117i	2.73568	+	2.43217i
$381$		0			0
$382$	1.27120	+	2.20179i	0.0650404	+	0.112653i
$383$	−20.8402	−	9.27864i	−1.06488	−	0.474117i	−0.201930	−	0.979400i	$-0.564721\pi$
$383$	−20.8402	−	9.27864i	−1.06488	−	0.474117i	−0.862953	+	0.505283i	$0.831388\pi$
$384$		0			0
$385$	9.77370	−	5.72529i	0.498114	−	0.291788i
$386$	10.8402	−	33.3628i	0.551753	−	1.69812i
$387$		0			0
$388$	−15.0234	−	46.2373i	−0.762698	−	2.34734i
$389$	−8.29913	−	9.21712i	−0.420783	−	0.467327i	0.495063	−	0.868857i	$-0.335145\pi$
$389$	−8.29913	−	9.21712i	−0.420783	−	0.467327i	−0.915846	+	0.401531i	$0.868478\pi$
$390$		0			0
$391$	−7.19475	+	7.99058i	−0.363854	+	0.404101i
$392$	15.2010	+	6.76791i	0.767765	+	0.341831i
$393$		0			0
$394$	2.09670	+	19.9488i	0.105630	+	1.00501i
$395$	24.6496	−	22.4776i	1.24026	−	1.13097i
$396$		0			0
$397$	−2.26012	−	1.64207i	−0.113432	−	0.0824133i	0.529623	−	0.848233i	$-0.322333\pi$
$397$	−2.26012	−	1.64207i	−0.113432	−	0.0824133i	−0.643055	+	0.765820i	$0.722333\pi$
$398$	−24.7672	−	27.5068i	−1.24147	−	1.37879i
$399$		0			0
$400$	−30.2003	+	13.9048i	−1.51001	+	0.695240i
$401$	18.1027	+	31.3549i	0.904008	+	1.56579i	0.822244	+	0.569136i	$0.192722\pi$
$401$	18.1027	+	31.3549i	0.904008	+	1.56579i	0.0817642	+	0.996652i	$0.473945\pi$
$402$		0			0
$403$	−11.0676	+	4.92761i	−0.551316	+	0.245462i
$404$	−45.6186	−	33.1438i	−2.26961	−	1.64897i
$405$		0			0
$406$	34.6605	−	25.1824i	1.72017	−	1.24978i
$407$	6.10273	−	10.5702i	0.302501	−	0.523947i
$408$		0			0
$409$	−14.8526	+	16.4955i	−0.734414	+	0.815649i	−0.988450	−	0.151546i	$-0.951575\pi$
$409$	−14.8526	+	16.4955i	−0.734414	+	0.815649i	0.254037	+	0.967195i	$0.418242\pi$
$410$	−25.7298	+	8.53979i	−1.27071	+	0.421750i
$411$		0			0
$412$	39.6316	+	8.42395i	1.95251	+	0.415018i
$413$	−6.67630	−	20.5475i	−0.328519	−	1.01108i
$414$		0			0
$415$	3.74506	+	8.27084i	0.183838	+	0.405999i
$416$	−8.06163	−	1.71355i	−0.395254	−	0.0840138i
$417$		0			0
$418$	22.4267	+	38.8441i	1.09692	+	1.89993i
$419$	29.2051	+	13.0030i	1.42676	+	0.635236i	0.967456	−	0.253041i	$-0.0814308\pi$
$419$	29.2051	+	13.0030i	1.42676	+	0.635236i	0.459308	+	0.888277i	$0.348097\pi$
$420$		0			0
$421$	−1.27594	+	0.568087i	−0.0621857	+	0.0276869i	−0.437594	−	0.899173i	$-0.644169\pi$
$421$	−1.27594	+	0.568087i	−0.0621857	+	0.0276869i	0.375408	+	0.926860i	$0.377503\pi$
$422$	27.2891	+	19.8267i	1.32841	+	0.965150i
$423$		0			0
$424$	19.0622			0.925745
$425$	−6.74513	+	21.6858i	−0.327187	+	1.05192i
$426$		0			0
$427$	5.33436	−	1.13385i	0.258148	−	0.0548710i
$428$	0.452387	−	4.30417i	0.0218669	−	0.208050i
$429$		0			0
$430$	−40.4599	+	23.7008i	−1.95115	+	1.14295i
$431$	0.506575	−	0.368048i	0.0244009	−	0.0177283i	−0.575518	−	0.817789i	$-0.695200\pi$
$431$	0.506575	−	0.368048i	0.0244009	−	0.0177283i	0.599919	+	0.800061i	$0.295200\pi$
$432$		0			0
$433$	−4.64257	+	3.37302i	−0.223108	+	0.162097i	−0.693724	−	0.720241i	$-0.744031\pi$
$433$	−4.64257	+	3.37302i	−0.223108	+	0.162097i	0.470617	+	0.882338i	$0.344031\pi$
$434$	34.7695	+	7.39049i	1.66899	+	0.354755i
$435$		0			0
$436$	38.3291	−	8.14710i	1.83563	−	0.390175i
$437$	11.4540	−	12.7210i	0.547920	−	0.608527i
$438$		0			0
$439$	−15.5049	−	17.2199i	−0.740007	−	0.821861i	0.249190	−	0.968455i	$-0.419836\pi$
$439$	−15.5049	−	17.2199i	−0.740007	−	0.821861i	−0.989197	+	0.146594i	$0.953169\pi$
$440$	−33.2643	+	3.70835i	−1.58581	+	0.176789i
$441$		0			0
$442$	−16.6109	+	12.0685i	−0.790100	+	0.574041i
$443$	−10.9667	+	18.9950i	−0.521046	+	0.902477i	0.478655	+	0.878003i	$0.341125\pi$
$443$	−10.9667	+	18.9950i	−0.521046	+	0.902477i	−0.999700	+	0.0244742i	$0.992209\pi$
$444$		0			0
$445$	0.00483427	+	0.766955i	0.000229167	+	0.0363572i
$446$	0.965829	−	9.18925i	0.0457333	−	0.435124i
$447$		0			0
$448$	−2.22298	−	2.46887i	−0.105026	−	0.116643i
$449$	12.6712			0.597990			0.298995	−	0.954255i	$-0.403349\pi$
$449$	12.6712			0.597990			0.298995	+	0.954255i	$0.403349\pi$
$450$		0			0
$451$	−11.7265			−0.552178
$452$	−20.0296	−	22.2451i	−0.942112	−	1.04632i
$453$		0			0
$454$	−4.15982	+	39.5781i	−0.195230	+	1.85749i
$455$	−4.89401	−	6.64751i	−0.229435	−	0.311640i
$456$		0			0
$457$	0.0638731	−	0.110631i	0.00298786	−	0.00517512i	−0.864528	−	0.502585i	$-0.832382\pi$
$457$	0.0638731	−	0.110631i	0.00298786	−	0.00517512i	0.867515	+	0.497410i	$0.165716\pi$
$458$	12.3084	−	8.94261i	0.575136	−	0.417861i
$459$		0			0
$460$	9.63581	+	21.2804i	0.449272	+	0.992203i
$461$	4.84829	+	5.38457i	0.225807	+	0.250785i	0.845393	−	0.534144i	$-0.179366\pi$
$461$	4.84829	+	5.38457i	0.225807	+	0.250785i	−0.619586	+	0.784929i	$0.712699\pi$
$462$		0			0
$463$	15.2392	−	16.9248i	0.708225	−	0.786564i	−0.276438	−	0.961032i	$-0.589154\pi$
$463$	15.2392	−	16.9248i	0.708225	−	0.786564i	0.984663	+	0.174468i	$0.0558206\pi$
$464$	−53.2058	+	11.3092i	−2.47002	+	0.525018i
$465$		0			0
$466$	−1.48291	−	0.315203i	−0.0686945	−	0.0146015i
$467$	7.87672	−	5.72277i	0.364491	−	0.264818i	−0.390432	−	0.920632i	$-0.627674\pi$
$467$	7.87672	−	5.72277i	0.364491	−	0.264818i	0.754923	+	0.655814i	$0.227674\pi$
$468$		0			0
$469$	2.72780	−	1.98186i	0.125958	−	0.0915138i
$470$	−57.0859	−	5.63641i	−2.63318	−	0.259988i
$471$		0			0
$472$	−6.67311	+	63.4904i	−0.307155	+	2.92238i
$473$	−19.8394	+	4.21699i	−0.912216	+	0.193897i
$474$		0			0
$475$	10.7382	−	34.5238i	0.492704	−	1.58406i
$476$	41.4556			1.90012
$477$		0			0
$478$	−2.40741	−	1.74909i	−0.110112	−	0.0800013i
$479$	10.2812	−	4.57749i	0.469761	−	0.209151i	−0.158183	−	0.987410i	$-0.550564\pi$
$479$	10.2812	−	4.57749i	0.469761	−	0.209151i	0.627944	+	0.778259i	$0.283897\pi$
$480$		0			0
$481$	−8.12582	−	3.61785i	−0.370506	−	0.164960i
$482$	22.7553	+	39.4133i	1.03648	+	1.79523i
$483$		0			0
$484$	21.5856	+	4.58816i	0.981163	+	0.208553i
$485$	−18.2019	+	16.5980i	−0.826506	+	0.753676i
$486$		0			0
$487$	−2.45081	−	7.54283i	−0.111057	−	0.341798i	0.880047	−	0.474886i	$-0.157511\pi$
$487$	−2.45081	−	7.54283i	−0.111057	−	0.341798i	−0.991104	+	0.133088i	$0.957511\pi$
$488$	−15.7624	−	3.35040i	−0.713531	−	0.151666i
$489$		0			0
$490$	−0.0971844	−	15.4183i	−0.00439035	−	0.696526i
$491$	−9.84430	+	10.9332i	−0.444267	+	0.493409i	−0.923134	−	0.384479i	$-0.874381\pi$
$491$	−9.84430	+	10.9332i	−0.444267	+	0.493409i	0.478867	+	0.877888i	$0.341048\pi$
$492$		0			0
$493$	−18.5778	+	32.1777i	−0.836702	+	1.44921i
$494$	26.4445	−	19.2131i	1.18980	−	0.864437i
$495$		0			0
$496$	−36.5114	−	26.5271i	−1.63941	−	1.19110i
$497$	19.2471	−	8.56938i	0.863352	−	0.384389i
$498$		0			0
$499$	−11.7212	−	20.3017i	−0.524714	−	0.908831i	−0.999586	−	0.0287762i	$-0.990839\pi$
$499$	−11.7212	−	20.3017i	−0.524714	−	0.908831i	0.474872	−	0.880055i	$-0.342494\pi$
$500$	37.2847	+	32.3159i	1.66742	+	1.44521i
$501$		0			0
$502$	0.530676	+	0.589376i	0.0236852	+	0.0263051i
$503$	11.6643	+	8.47463i	0.520087	+	0.377865i	0.816637	−	0.577152i	$-0.195836\pi$
$503$	11.6643	+	8.47463i	0.520087	+	0.377865i	−0.296550	+	0.955017i	$0.595836\pi$
$504$		0			0
$505$	−5.76393	+	27.9833i	−0.256491	+	1.24524i
$506$	1.53488	+	14.6034i	0.0682336	+	0.649200i
$507$		0			0
$508$	40.2085	+	17.9020i	1.78396	+	0.794272i
$509$	−0.258484	+	0.287075i	−0.0114571	+	0.0127244i	−0.748846	−	0.662744i	$-0.769392\pi$
$509$	−0.258484	+	0.287075i	−0.0114571	+	0.0127244i	0.737389	+	0.675468i	$0.236058\pi$
$510$		0			0
$511$	−2.72289	−	3.02407i	−0.120453	−	0.133777i
$512$	15.6267	+	48.0942i	0.690611	+	2.12548i
$513$		0			0
$514$	−2.32468	+	7.15462i	−0.102537	+	0.315577i
$515$	−4.39477	−	20.0534i	−0.193657	−	0.883659i
$516$		0			0
$517$	−22.6675	−	10.0922i	−0.996915	−	0.443855i
$518$	13.0490	+	22.6016i	0.573342	+	0.993057i
$519$		0			0
$520$	5.22162	+	23.8263i	0.228983	+	1.04485i
$521$	−35.3256	−	25.6656i	−1.54764	−	1.12443i	−0.945304	−	0.326190i	$-0.894235\pi$
$521$	−35.3256	−	25.6656i	−1.54764	−	1.12443i	−0.602340	−	0.798240i	$-0.705765\pi$
$522$		0			0
$523$	−6.03504	+	18.5739i	−0.263894	+	0.812182i	0.728052	+	0.685522i	$0.240426\pi$
$523$	−6.03504	+	18.5739i	−0.263894	+	0.812182i	−0.991946	+	0.126660i	$0.959574\pi$
$524$	−30.3581	+	52.5818i	−1.32620	+	2.29705i
$525$		0			0
$526$	10.2907	+	17.8239i	0.448694	+	0.777161i
$527$	−30.1540	+	6.40943i	−1.31353	+	0.279199i
$528$		0			0
$529$	−15.8921	+	7.07563i	−0.690962	+	0.307636i
$530$	−7.28596	−	16.0908i	−0.316482	−	0.698940i
$531$		0			0
$532$	−65.9973			−2.86135
$533$	0.893274	+	8.49894i	0.0386920	+	0.368130i
$534$		0			0
$535$	−2.08123	+	0.690766i	−0.0899795	+	0.0298644i
$536$	−9.74539	+	2.07145i	−0.420937	+	0.0894728i
$537$		0			0
$538$	57.0207	+	12.1201i	2.45834	+	0.522536i
$539$	2.06094	−	6.34291i	0.0887708	−	0.273208i
$540$		0			0
$541$	−5.67479	−	17.4652i	−0.243978	−	0.750888i	−0.995803	−	0.0915249i	$-0.970826\pi$
$541$	−5.67479	−	17.4652i	−0.243978	−	0.750888i	0.751824	−	0.659363i	$-0.229174\pi$
$542$	5.98935	+	56.9848i	0.257264	+	2.44771i
$543$		0			0
$544$	−19.1587	−	8.53001i	−0.821423	−	0.365721i
$545$	−11.7713	−	15.9888i	−0.504225	−	0.684887i
$546$		0			0
$547$	35.1535	−	15.6513i	1.50306	−	0.669203i	0.520278	−	0.853997i	$-0.325828\pi$
$547$	35.1535	−	15.6513i	1.50306	−	0.669203i	0.982777	+	0.184794i	$0.0591616\pi$
$548$	11.6315	−	35.7980i	0.496872	−	1.52922i
$549$		0			0
$550$	15.8446	+	26.6616i	0.675614	+	1.13686i
$551$	29.5758	−	51.2268i	1.25997	−	2.18234i
$552$		0			0
$553$	−3.22511	+	30.6849i	−0.137146	+	1.30485i
$554$	−2.74121	+	26.0809i	−0.116463	+	1.10807i
$555$		0			0
$556$	4.30388	+	40.9486i	0.182525	+	1.73661i
$557$	−34.0992			−1.44483			−0.722414	−	0.691461i	$-0.756968\pi$
$557$	−34.0992			−1.44483			−0.722414	+	0.691461i	$0.756968\pi$
$558$		0			0
$559$	4.56761	+	14.0577i	0.193189	+	0.594576i
$560$	12.3300	−	28.1702i	0.521039	−	1.19041i
$561$		0			0
$562$	−43.1085	+	47.8769i	−1.81842	+	2.01956i
$563$	16.6117	−	18.4492i	0.700100	−	0.777540i	−0.283292	−	0.959034i	$-0.591427\pi$
$563$	16.6117	−	18.4492i	0.700100	−	0.777540i	0.983392	+	0.181494i	$0.0580933\pi$
$564$		0			0
$565$	−6.08150	+	13.8943i	−0.255851	+	0.584538i
$566$	12.9674	+	39.9094i	0.545058	+	1.67752i
$567$		0			0
$568$	−62.2553			−2.61217
$569$	−2.96097	−	28.1717i	−0.124130	−	1.18102i	−0.862297	−	0.506403i	$-0.830975\pi$
$569$	−2.96097	−	28.1717i	−0.124130	−	1.18102i	0.738167	−	0.674618i	$-0.235692\pi$
$570$		0			0
$571$	−3.33890	+	31.7675i	−0.139729	+	1.32943i	0.669884	+	0.742465i	$0.266344\pi$
$571$	−3.33890	+	31.7675i	−0.139729	+	1.32943i	−0.809613	+	0.586964i	$0.800323\pi$
$572$	−2.01689	+	19.1894i	−0.0843303	+	0.802349i
$573$		0			0
$574$	12.5369	−	21.7146i	0.523282	−	0.906351i
$575$	7.80852	−	8.89522i	0.325638	−	0.370956i
$576$		0			0
$577$	−4.21265	+	12.9652i	−0.175375	+	0.539748i	−0.999650	−	0.0264408i	$-0.991583\pi$
$577$	−4.21265	+	12.9652i	−0.175375	+	0.539748i	0.824276	+	0.566189i	$0.191583\pi$
$578$	−8.39998	+	3.73991i	−0.349393	+	0.155560i
$579$		0			0
$580$	47.8585	+	65.0060i	1.98722	+	2.69923i
$581$	−7.67133	−	3.41550i	−0.318260	−	0.141699i
$582$		0			0
$583$	−0.798637	−	7.59853i	−0.0330762	−	0.314699i
$584$	3.71570	+	11.4358i	0.153757	+	0.473215i
$585$		0			0
$586$	9.49120	−	29.2109i	0.392078	−	1.20669i
$587$	−38.8559	−	8.25908i	−1.60376	−	0.340889i	−0.682815	−	0.730592i	$-0.739244\pi$
$587$	−38.8559	−	8.25908i	−1.60376	−	0.340889i	−0.920941	+	0.389703i	$0.872578\pi$
$588$		0			0
$589$	48.0051	−	10.2038i	1.97802	−	0.420441i
$590$	56.1441	−	18.6344i	2.31141	−	0.767165i
$591$		0			0
$592$	−3.46354	−	32.9534i	−0.142351	−	1.35438i
$593$	−16.9892			−0.697663			−0.348832	−	0.937185i	$-0.613421\pi$
$593$	−16.9892			−0.697663			−0.348832	+	0.937185i	$0.613421\pi$
$594$		0			0
$595$	−8.66425	−	19.1347i	−0.355200	−	0.784447i
$596$	−28.0034	+	12.4679i	−1.14706	+	0.510705i
$597$		0			0
$598$	10.4671	−	2.22485i	0.428032	−	0.0909810i
$599$	7.81800	+	13.5412i	0.319435	+	0.553277i	0.980370	−	0.197166i	$-0.0631736\pi$
$599$	7.81800	+	13.5412i	0.319435	+	0.553277i	−0.660935	+	0.750443i	$0.729840\pi$
$600$		0			0
$601$	−0.702116	+	1.21610i	−0.0286399	+	0.0496058i	−0.879990	−	0.474992i	$-0.842451\pi$
$601$	−0.702116	+	1.21610i	−0.0286399	+	0.0496058i	0.851350	+	0.524598i	$0.175784\pi$
$602$	13.4017	−	41.2462i	0.546213	−	1.68107i
$603$		0			0
$604$	2.81486	+	2.04512i	0.114535	+	0.0832147i
$605$	−2.39364	−	10.9222i	−0.0973152	−	0.444051i
$606$		0			0
$607$	−3.79337	−	6.57031i	−0.153968	−	0.266681i	0.778715	−	0.627378i	$-0.215872\pi$
$607$	−3.79337	−	6.57031i	−0.153968	−	0.266681i	−0.932683	+	0.360698i	$0.882539\pi$
$608$	30.5006	+	13.5798i	1.23696	+	0.550732i
$609$		0			0
$610$	3.19656	+	14.5859i	0.129425	+	0.590568i
$611$	−5.58777	+	17.1974i	−0.226057	+	0.695732i
$612$		0			0
$613$	9.44377	+	29.0649i	0.381430	+	1.17392i	0.939037	+	0.343816i	$0.111720\pi$
$613$	9.44377	+	29.0649i	0.381430	+	1.17392i	−0.557607	+	0.830105i	$0.688280\pi$
$614$	19.9453	+	22.1515i	0.804925	+	0.893960i
$615$		0			0
$616$	20.7140	−	23.0052i	0.834590	−	0.926906i
$617$	−0.925938	−	0.412254i	−0.0372768	−	0.0165967i	0.388014	−	0.921654i	$-0.373161\pi$
$617$	−0.925938	−	0.412254i	−0.0372768	−	0.0165967i	−0.425290	+	0.905057i	$0.639828\pi$
$618$		0			0
$619$	−4.81309	−	45.7935i	−0.193454	−	1.84059i	−0.473724	−	0.880673i	$-0.657091\pi$
$619$	−4.81309	−	45.7935i	−0.193454	−	1.84059i	0.280270	−	0.959921i	$-0.409576\pi$
$620$	−13.5117	+	65.5981i	−0.542644	+	2.63448i
$621$		0			0
$622$	−20.2673	−	14.7250i	−0.812644	−	0.590420i
$623$	−0.474659	−	0.527162i	−0.0190168	−	0.0211203i
$624$		0			0
$625$	7.12357	−	23.9636i	0.284943	−	0.958545i
$626$	−43.5789	−	75.4809i	−1.74176	−	3.01682i
$627$		0			0
$628$	15.6743	−	6.97863i	0.625471	−	0.278478i
$629$	−18.3110	−	13.3037i	−0.730108	−	0.530455i
$630$		0			0
$631$	−6.24556	+	4.53767i	−0.248632	+	0.180642i	−0.705120	−	0.709088i	$-0.749107\pi$
$631$	−6.24556	+	4.53767i	−0.248632	+	0.180642i	0.456488	+	0.889729i	$0.349107\pi$
$632$	45.5848	−	78.9552i	1.81327	−	3.14067i
$633$		0			0
$634$	37.6815	−	41.8496i	1.49653	−	1.66206i
$635$	−0.140565	−	22.3006i	−0.00557816	−	0.884973i
$636$		0			0
$637$	−4.75411	−	1.01052i	−0.188365	−	0.0400382i
$638$	15.6798	+	48.2575i	0.620770	+	1.91053i
$639$		0			0
$640$	21.9790	−	20.0422i	0.868795	−	0.792239i
$641$	27.3002	+	5.80283i	1.07829	+	0.229198i	0.712623	−	0.701547i	$-0.247507\pi$
$641$	27.3002	+	5.80283i	1.07829	+	0.229198i	0.365669	+	0.930745i	$0.380840\pi$
$642$		0			0
$643$	−3.87285	−	6.70797i	−0.152730	−	0.264537i	0.779500	−	0.626402i	$-0.215473\pi$
$643$	−3.87285	−	6.70797i	−0.152730	−	0.264537i	−0.932230	+	0.361866i	$0.882140\pi$
$644$	−19.7379	−	8.78787i	−0.777782	−	0.346291i
$645$		0			0
$646$	75.9847	−	33.8305i	2.98958	−	1.33105i
$647$	27.8778	+	20.2544i	1.09599	+	0.796283i	0.980401	−	0.197015i	$-0.0631246\pi$
$647$	27.8778	+	20.2544i	1.09599	+	0.796283i	0.115588	+	0.993297i	$0.463125\pi$
$648$		0			0
$649$	25.5879			1.00441
$650$	18.1165	−	13.5146i	0.710586	−	0.530085i
$651$		0			0
$652$	−36.2317	+	7.70129i	−1.41894	+	0.301606i
$653$	−1.25103	+	11.9028i	−0.0489567	+	0.465792i	0.942389	+	0.334518i	$0.108573\pi$
$653$	−1.25103	+	11.9028i	−0.0489567	+	0.465792i	−0.991346	+	0.131274i	$0.958093\pi$
$654$		0			0
$655$	30.6151	+	3.02280i	1.19623	+	0.118111i
$656$	−25.7547	+	18.7119i	−1.00555	+	0.730576i
$657$		0			0
$658$	42.9225	−	31.1850i	1.67329	−	1.21572i
$659$	9.12961	+	1.94056i	0.355639	+	0.0755934i	0.382267	−	0.924052i	$-0.375144\pi$
$659$	9.12961	+	1.94056i	0.355639	+	0.0755934i	−0.0266278	+	0.999645i	$0.508477\pi$
$660$		0			0
$661$	−4.71132	+	1.00142i	−0.183249	+	0.0389508i	−0.298622	−	0.954371i	$-0.596527\pi$
$661$	−4.71132	+	1.00142i	−0.183249	+	0.0389508i	0.115373	+	0.993322i	$0.463194\pi$
$662$	22.1767	−	24.6297i	0.861922	−	0.957261i
$663$		0			0
$664$	16.6032	+	18.4397i	0.644329	+	0.715600i
$665$	13.7935	+	30.4624i	0.534888	+	1.18128i
$666$		0			0
$667$	15.6664	−	11.3823i	0.606605	−	0.440724i
$668$	23.8482	−	41.3063i	0.922714	−	1.59819i
$669$		0			0
$670$	5.47342	+	7.43452i	0.211457	+	0.287221i
$671$	−0.675140	+	6.42352i	−0.0260635	+	0.247977i
$672$		0			0
$673$	−11.9310	−	13.2507i	−0.459907	−	0.510779i	0.467929	−	0.883766i	$-0.345000\pi$
$673$	−11.9310	−	13.2507i	−0.459907	−	0.510779i	−0.927837	+	0.372987i	$0.878334\pi$
$674$	−36.7946			−1.41728
$675$		0			0
$676$	−43.3093			−1.66574
$677$	−10.2517	−	11.3857i	−0.394005	−	0.437586i	0.513205	−	0.858266i	$-0.328458\pi$
$677$	−10.2517	−	11.3857i	−0.394005	−	0.437586i	−0.907209	+	0.420680i	$0.861792\pi$
$678$		0			0
$679$	2.38150	−	22.6584i	0.0913935	−	0.869551i
$680$	0.391213	+	62.0658i	0.0150024	+	2.38012i
$681$		0			0
$682$	−21.0497	+	36.4591i	−0.806034	+	1.39609i
$683$	22.9889	−	16.7024i	0.879645	−	0.639100i	−0.0535124	−	0.998567i	$-0.517042\pi$
$683$	22.9889	−	16.7024i	0.879645	−	0.639100i	0.933158	+	0.359468i	$0.117042\pi$
$684$		0			0
$685$	−18.9543	+	2.11305i	−0.724207	+	0.0807355i
$686$	34.0735	+	37.8425i	1.30093	+	1.44483i
$687$		0			0
$688$	−36.8439	+	40.9193i	−1.40466	+	1.56004i
$689$	−5.44631	+	1.15765i	−0.207488	+	0.0441029i
$690$		0			0
$691$	−21.4992	−	4.56981i	−0.817870	−	0.173844i	−0.220065	−	0.975485i	$-0.570627\pi$
$691$	−21.4992	−	4.56981i	−0.817870	−	0.173844i	−0.597805	+	0.801642i	$0.703960\pi$
$692$	−58.7708	+	42.6995i	−2.23413	+	1.62319i
$693$		0			0
$694$	−22.8739	+	16.6188i	−0.868280	+	0.630842i
$695$	18.0012	−	10.5448i	0.682824	−	0.399988i
$696$		0			0
$697$	−2.27302	+	21.6263i	−0.0860966	+	0.819155i
$698$	−20.2441	+	4.30301i	−0.766250	+	0.162871i
$699$		0			0
$700$	−45.6310	+	0.575266i	−1.72469	+	0.0217430i
$701$	−6.44692			−0.243497			−0.121748	−	0.992561i	$-0.538850\pi$
$701$	−6.44692			−0.243497			−0.121748	+	0.992561i	$0.538850\pi$
$702$		0			0
$703$	29.1511	+	21.1795i	1.09946	+	0.798801i
$704$	3.59447	−	1.60036i	0.135472	−	0.0603159i
$705$		0			0
$706$	−52.1666	−	23.2261i	−1.96332	−	0.874124i
$707$	−13.2125	−	22.8847i	−0.496906	−	0.860666i
$708$		0			0
$709$	4.80312	+	1.02094i	0.180385	+	0.0383420i	0.297218	−	0.954809i	$-0.403941\pi$
$709$	4.80312	+	1.02094i	0.180385	+	0.0383420i	−0.116833	+	0.993152i	$0.537274\pi$
$710$	23.7952	+	52.5509i	0.893017	+	1.97220i
$711$		0			0
$712$	0.647729	+	1.99351i	0.0242747	+	0.0747098i
$713$	15.7156	+	3.34046i	0.588555	+	0.125101i
$714$		0			0
$715$	9.27880	−	3.07966i	0.347007	−	0.115173i
$716$	−1.54291	+	1.71358i	−0.0576613	+	0.0640393i
$717$		0			0
$718$	31.7906	−	55.0629i	1.18641	−	2.05493i
$719$	−38.7957	+	28.1867i	−1.44683	+	1.05119i	−0.460277	+	0.887775i	$0.652250\pi$
$719$	−38.7957	+	28.1867i	−1.44683	+	1.05119i	−0.986558	+	0.163412i	$0.947750\pi$
$720$		0			0
$721$	15.3612	+	11.1605i	0.572080	+	0.415640i
$722$	−77.0113	+	34.2877i	−2.86607	+	1.27605i
$723$		0			0
$724$	−50.9263	−	88.2070i	−1.89266	−	3.27819i
$725$	20.0024	−	35.6764i	0.742871	−	1.32499i
$726$		0			0
$727$	6.94241	+	7.71033i	0.257480	+	0.285960i	0.858000	−	0.513649i	$-0.171707\pi$
$727$	6.94241	+	7.71033i	0.257480	+	0.285960i	−0.600521	+	0.799609i	$0.705040\pi$
$728$	−18.2513	−	13.2603i	−0.676437	−	0.491461i
$729$		0			0
$730$	8.23293	−	7.50747i	0.304715	−	0.277864i
$731$	3.93151	+	37.4058i	0.145412	+	1.38350i
$732$		0			0
$733$	−8.79421	−	3.91543i	−0.324822	−	0.144620i	0.237847	−	0.971303i	$-0.423558\pi$
$733$	−8.79421	−	3.91543i	−0.324822	−	0.144620i	−0.562668	+	0.826683i	$0.690225\pi$
$734$	10.9371	−	12.1469i	0.403695	−	0.448349i
$735$		0			0
$736$	7.31365	+	8.12263i	0.269585	+	0.299404i
$737$	1.23401	+	3.79789i	0.0454553	+	0.139897i
$738$		0			0
$739$	−10.9628	+	33.7400i	−0.403273	+	1.24115i	0.519056	+	0.854740i	$0.326284\pi$
$739$	−10.9628	+	33.7400i	−0.403273	+	1.24115i	−0.922329	+	0.386406i	$0.873716\pi$
$740$	−42.4294	+	24.8545i	−1.55974	+	0.913671i
$741$		0			0
$742$	14.9245	+	6.64481i	0.547895	+	0.243939i
$743$	−1.41943	−	2.45852i	−0.0520738	−	0.0901944i	0.838814	−	0.544419i	$-0.183250\pi$
$743$	−1.41943	−	2.45852i	−0.0520738	−	0.0901944i	−0.890887	+	0.454224i	$0.849916\pi$
$744$		0			0
$745$	11.6075	+	10.3197i	0.425268	+	0.378086i
$746$	−49.3797	−	35.8765i	−1.80792	−	1.31353i
$747$		0			0
$748$	−15.1721	+	46.6951i	−0.554749	+	1.70734i
$749$	1.01409	−	1.75645i	0.0370539	−	0.0641793i
$750$		0			0
$751$	−19.4018	−	33.6049i	−0.707983	−	1.22626i	−0.965604	−	0.260016i	$-0.916272\pi$
$751$	−19.4018	−	33.6049i	−0.707983	−	1.22626i	0.257622	−	0.966246i	$-0.417061\pi$
$752$	−65.8884	+	14.0050i	−2.40270	+	0.510710i
$753$		0			0
$754$	33.7809	−	15.0402i	1.23023	−	0.547734i
$755$	0.355659	−	1.72669i	0.0129438	−	0.0628407i
$756$		0			0
$757$	32.7437			1.19009			0.595046	−	0.803692i	$-0.297134\pi$
$757$	32.7437			1.19009			0.595046	+	0.803692i	$0.297134\pi$
$758$	0.113046	+	1.07556i	0.00410602	+	0.0390662i
$759$		0			0
$760$	−0.622811	−	98.8087i	−0.0225917	−	3.58417i
$761$	−0.437407	+	0.0929737i	−0.0158560	+	0.00337029i	−0.215833	−	0.976430i	$-0.569247\pi$
$761$	−0.437407	+	0.0929737i	−0.0158560	+	0.00337029i	0.199977	+	0.979801i	$0.435913\pi$
$762$		0			0
$763$	17.9621	+	3.81797i	0.650273	+	0.138220i
$764$	1.36911	−	4.21370i	0.0495328	−	0.152446i
$765$		0			0
$766$	17.8521	+	54.9431i	0.645022	+	1.98517i
$767$	−1.94918	−	18.5452i	−0.0703808	−	0.669629i
$768$		0			0
$769$	−6.84396	−	3.04713i	−0.246800	−	0.109882i	0.279609	−	0.960114i	$-0.409795\pi$
$769$	−6.84396	−	3.04713i	−0.246800	−	0.109882i	−0.526409	+	0.850232i	$0.676462\pi$
$770$	−27.3364	−	8.69204i	−0.985137	−	0.313239i
$771$		0			0
$772$	−55.8469	+	24.8646i	−2.00997	+	0.894897i
$773$	5.48853	−	16.8920i	0.197409	−	0.607562i	−0.802531	−	0.596610i	$-0.796514\pi$
$773$	5.48853	−	16.8920i	0.197409	−	0.607562i	0.999940	−	0.0109516i	$-0.00348607\pi$
$774$		0			0
$775$	33.1022	−	7.47343i	1.18906	−	0.268453i
$776$	−33.6609	+	58.3024i	−1.20836	+	2.09293i
$777$		0			0
$778$	−3.28316	+	31.2372i	−0.117707	+	1.11991i
$779$	3.61864	−	34.4290i	0.129651	−	1.23355i
$780$		0			0
$781$	2.60826	+	24.8160i	0.0933310	+	0.887985i
$782$	27.2295			0.973726
$783$		0			0
$784$	−5.59494	−	17.2195i	−0.199819	−	0.614981i
$785$	−6.49706	−	5.77625i	−0.231890	−	0.206163i
$786$		0			0
$787$	9.21203	−	10.2310i	0.328373	−	0.364695i	−0.556239	−	0.831022i	$-0.687756\pi$
$787$	9.21203	−	10.2310i	0.328373	−	0.364695i	0.884613	+	0.466327i	$0.154423\pi$
$788$	23.3897	−	25.9769i	0.833225	−	0.925390i
$789$		0			0
$790$	−84.0710	−	8.30081i	−2.99111	−	0.295329i
$791$	−4.33484	−	13.3413i	−0.154129	−	0.474361i
$792$		0			0
$793$	4.70698			0.167150
$794$	0.739510	+	7.03597i	0.0262442	+	0.249697i
$795$		0			0
$796$	−6.74238	+	64.1494i	−0.238977	+	2.27372i
$797$	2.44389	−	23.2520i	0.0865669	−	0.823629i	−0.861969	−	0.506961i	$-0.830769\pi$
$797$	2.44389	−	23.2520i	0.0865669	−	0.823629i	0.948536	−	0.316669i	$-0.102564\pi$
$798$		0			0
$799$	−23.0062	+	39.8478i	−0.813899	+	1.40972i
$800$	21.2067	+	9.12329i	0.749771	+	0.322557i
$801$		0			0
$802$	28.3330	−	87.1999i	1.00047	−	3.07914i
$803$	4.40281	−	1.96026i	0.155372	−	0.0691759i
$804$		0			0
$805$	0.0690018	+	10.9471i	0.00243199	+	0.385835i
$806$	28.0278	+	12.4788i	0.987236	+	0.439546i
$807$		0			0
$808$	8.16185	+	77.6548i	0.287133	+	2.73189i
$809$	3.98567	+	12.2666i	0.140129	+	0.431272i	0.996352	−	0.0853332i	$-0.0271955\pi$
$809$	3.98567	+	12.2666i	0.140129	+	0.431272i	−0.856224	+	0.516605i	$0.827195\pi$
$810$		0			0
$811$	−5.74344	+	17.6765i	−0.201679	+	0.620705i	0.798154	+	0.602454i	$0.205810\pi$
$811$	−5.74344	+	17.6765i	−0.201679	+	0.620705i	−0.999833	+	0.0182520i	$0.994190\pi$
$812$	−73.0288	−	15.5228i	−2.56281	−	0.544742i
$813$		0			0
$814$	−30.2339	+	6.42641i	−1.05970	+	0.225246i
$815$	11.1271	+	15.1139i	0.389767	+	0.529418i
$816$		0			0
$817$	−6.25895	−	59.5500i	−0.218973	−	2.08339i
$818$	56.2117			1.96540
$819$		0			0
$820$	41.0621	+	23.3634i	1.43395	+	0.815884i
$821$	−31.8397	+	14.1760i	−1.11121	+	0.494744i	−0.878472	−	0.477794i	$-0.841437\pi$
$821$	−31.8397	+	14.1760i	−1.11121	+	0.494744i	−0.232742	+	0.972538i	$0.574770\pi$
$822$		0			0
$823$	−25.4303	+	5.40537i	−0.886444	+	0.188419i	−0.628564	−	0.777758i	$-0.716357\pi$
$823$	−25.4303	+	5.40537i	−0.886444	+	0.188419i	−0.257879	+	0.966177i	$0.583024\pi$
$824$	−28.0528	−	48.5890i	−0.977267	−	1.69268i
$825$		0			0
$826$	−27.3564	+	47.3826i	−0.951850	+	1.64865i
$827$	10.5951	−	32.6084i	0.368428	−	1.13390i	−0.579379	−	0.815058i	$-0.696705\pi$
$827$	10.5951	−	32.6084i	0.368428	−	1.13390i	0.947807	−	0.318846i	$-0.103295\pi$
$828$		0			0
$829$	−11.1943	−	8.13310i	−0.388792	−	0.282474i	0.376168	−	0.926551i	$-0.377242\pi$
$829$	−11.1943	−	8.13310i	−0.388792	−	0.282474i	−0.764960	+	0.644077i	$0.777242\pi$
$830$	9.21926	−	21.0631i	0.320005	−	0.731111i
$831$		0			0
$832$	−1.43370	−	2.48324i	−0.0497046	−	0.0860908i
$833$	−11.2983	−	5.03033i	−0.391463	−	0.174291i
$834$		0			0
$835$	−24.0501	−	2.37460i	−0.832287	−	0.0821764i
$836$	24.1540	−	74.3384i	0.835384	−	2.57105i
$837$		0			0
$838$	−25.0176	−	76.9964i	−0.864220	−	2.65980i
$839$	−24.2283	−	26.9083i	−0.836455	−	0.928977i	0.161872	−	0.986812i	$-0.448247\pi$
$839$	−24.2283	−	26.9083i	−0.836455	−	0.928977i	−0.998326	+	0.0578349i	$0.981580\pi$
$840$		0			0
$841$	25.3708	−	28.1771i	0.874855	−	0.971625i
$842$	3.23122	+	1.43863i	0.111355	+	0.0495786i
$843$		0			0
$844$	−6.14439	−	58.4600i	−0.211499	−	2.01228i
$845$	9.05168	+	19.9903i	0.311387	+	0.687689i
$846$		0			0
$847$	8.36655	+	6.07866i	0.287478	+	0.208865i
$848$	−13.8790	−	15.4142i	−0.476606	−	0.529324i
$849$		0			0
$850$	52.2415	−	24.0530i	1.79187	−	0.825011i
$851$	5.89809	+	10.2158i	0.202184	+	0.350193i
$852$		0			0
$853$	−28.5948	+	12.7312i	−0.979066	+	0.435908i	−0.832943	−	0.553358i	$-0.813346\pi$
$853$	−28.5948	+	12.7312i	−0.979066	+	0.435908i	−0.146123	+	0.989266i	$0.546679\pi$
$854$	−11.1730	−	8.11768i	−0.382333	−	0.277781i
$855$		0			0
$856$	−4.84845	+	3.52261i	−0.165717	+	0.120400i
$857$	−6.62700	+	11.4783i	−0.226374	+	0.392091i	−0.956731	−	0.290975i	$-0.906021\pi$
$857$	−6.62700	+	11.4783i	−0.226374	+	0.392091i	0.730357	+	0.683066i	$0.239354\pi$
$858$		0			0
$859$	−18.1786	+	20.1893i	−0.620244	+	0.688851i	−0.968632	−	0.248499i	$-0.920063\pi$
$859$	−18.1786	+	20.1893i	−0.620244	+	0.688851i	0.348388	+	0.937351i	$0.386729\pi$
$860$	77.8725	+	24.7608i	2.65543	+	0.844335i
$861$		0			0
$862$	−1.55105	−	0.329686i	−0.0528290	−	0.0112291i
$863$	−17.1394	−	52.7496i	−0.583431	−	1.79562i	−0.605481	−	0.795859i	$-0.707019\pi$
$863$	−17.1394	−	52.7496i	−0.583431	−	1.79562i	0.0220503	−	0.999757i	$-0.492981\pi$
$864$		0			0
$865$	31.9920	+	18.2027i	1.08776	+	0.618910i
$866$	14.2148	+	3.02145i	0.483038	+	0.102673i
$867$		0			0
$868$	−30.9725	−	53.6460i	−1.05128	−	1.82086i
$869$	−33.3827	−	14.8629i	−1.13243	−	0.504190i
$870$		0			0
$871$	2.65857	−	1.18367i	0.0900823	−	0.0401072i
$872$	−43.8987	−	31.8943i	−1.48660	−	1.08008i
$873$		0			0
$874$	−43.3493			−1.46631
$875$	9.80243	+	20.9417i	0.331383	+	0.707960i
$876$		0			0
$877$	44.2699	−	9.40986i	1.49489	−	0.317748i	0.613331	−	0.789826i	$-0.289829\pi$
$877$	44.2699	−	9.40986i	1.49489	−	0.317748i	0.881557	+	0.472077i	$0.156496\pi$
$878$	−6.13376	+	58.3588i	−0.207004	+	1.96952i
$879$		0			0
$880$	27.2179	+	24.1983i	0.917517	+	0.815723i
$881$	−3.25840	+	2.36737i	−0.109778	+	0.0797587i	−0.641320	−	0.767273i	$-0.721613\pi$
$881$	−3.25840	+	2.36737i	−0.109778	+	0.0797587i	0.531542	+	0.847032i	$0.321613\pi$
$882$		0			0
$883$	−23.5316	+	17.0967i	−0.791900	+	0.575349i	−0.908527	−	0.417827i	$-0.862792\pi$
$883$	−23.5316	+	17.0967i	−0.791900	+	0.575349i	0.116626	+	0.993176i	$0.462792\pi$
$884$	34.9987	+	7.43920i	1.17713	+	0.250208i
$885$		0			0
$886$	54.3309	−	11.5484i	1.82528	−	0.387976i
$887$	−8.44114	+	9.37484i	−0.283426	+	0.314776i	−0.868000	−	0.496564i	$-0.834595\pi$
$887$	−8.44114	+	9.37484i	−0.283426	+	0.314776i	0.584574	+	0.811340i	$0.301262\pi$
$888$		0			0
$889$	13.8016	+	15.3282i	0.462890	+	0.514091i
$890$	1.43518	−	1.30872i	0.0481074	−	0.0438683i
$891$		0			0
$892$	−13.0267	+	9.46448i	−0.436167	+	0.316894i
$893$	36.6258	−	63.4377i	1.22563	−	2.12286i
$894$		0			0
$895$	1.11341	+	0.354024i	0.0372171	+	0.0118337i
$896$	−2.87568	+	27.3603i	−0.0960698	+	0.914044i
$897$		0			0
$898$	−21.4715	−	23.8466i	−0.716515	−	0.795770i
$899$	55.5197			1.85169
$900$		0			0
$901$	−14.1682			−0.472012
$902$	19.8707	+	22.0687i	0.661622	+	0.734806i
$903$		0			0
$904$	−4.33277	+	41.2235i	−0.144106	+	1.37107i
$905$	−30.0702	+	41.9414i	−0.999566	+	1.39418i
$906$		0			0
$907$	3.40353	−	5.89509i	0.113012	−	0.195743i	−0.803971	−	0.594668i	$-0.797283\pi$
$907$	3.40353	−	5.89509i	0.113012	−	0.195743i	0.916983	+	0.398925i	$0.130617\pi$
$908$	56.1061	−	40.7634i	1.86195	−	1.35278i
$909$		0			0
$910$	−4.21731	+	20.4746i	−0.139802	+	0.678727i
$911$	17.3545	+	19.2742i	0.574981	+	0.638581i	0.958548	−	0.284932i	$-0.0919710\pi$
$911$	17.3545	+	19.2742i	0.574981	+	0.638581i	−0.383567	+	0.923513i	$0.625304\pi$
$912$		0			0
$913$	6.65476	−	7.39086i	0.220240	−	0.244602i
$914$	−0.316437	+	0.0672608i	−0.0104668	+	0.00222479i
$915$		0			0
$916$	−25.9336	−	5.51235i	−0.856869	−	0.182133i
$917$	−23.0193	+	16.7245i	−0.760165	+	0.552292i
$918$		0			0
$919$	1.07405	−	0.780342i	0.0354296	−	0.0257411i	−0.569930	−	0.821694i	$-0.693030\pi$
$919$	1.07405	−	0.780342i	0.0354296	−	0.0257411i	0.605359	+	0.795952i	$0.293030\pi$
$920$	12.9706	−	29.6338i	0.427628	−	0.976996i
$921$		0			0
$922$	1.91800	−	18.2485i	0.0631658	−	0.600983i
$923$	17.7871	−	3.78076i	0.585468	−	0.124445i
$924$		0			0
$925$	20.3399	+	14.3896i	0.668772	+	0.473127i
$926$	−57.6748			−1.89531
$927$		0			0
$928$	30.5563	+	22.2004i	1.00306	+	0.728765i
$929$	−30.7141	+	13.6748i	−1.00770	+	0.448655i	−0.843129	−	0.537711i	$-0.819289\pi$
$929$	−30.7141	+	13.6748i	−1.00770	+	0.448655i	−0.164566	+	0.986366i	$0.552623\pi$
$930$		0			0
$931$	17.9869	+	8.00827i	0.589496	+	0.262460i
$932$	1.32097	+	2.28799i	0.0432698	+	0.0749455i
$933$		0			0
$934$	−24.1172	−	5.12627i	−0.789140	−	0.167737i
$935$	24.7241	−	2.75627i	0.808564	−	0.0901397i
$936$		0			0
$937$	5.34347	+	16.4455i	0.174563	+	0.537251i	0.999613	−	0.0278089i	$-0.00885300\pi$
$937$	5.34347	+	16.4455i	0.174563	+	0.537251i	−0.825050	+	0.565060i	$0.808853\pi$
$938$	−8.35207	−	1.77529i	−0.272705	−	0.0579652i
$939$		0			0
$940$	59.2665	+	80.5014i	1.93306	+	2.62566i
$941$	−24.2742	+	26.9592i	−0.791316	+	0.878845i	−0.994967	−	0.100198i	$-0.968052\pi$
$941$	−24.2742	+	26.9592i	−0.791316	+	0.878845i	0.203652	+	0.979043i	$0.434719\pi$
$942$		0			0
$943$	5.66663	−	9.81489i	0.184531	−	0.319617i
$944$	56.1983	−	40.8305i	1.82910	−	1.32892i
$945$		0			0
$946$	41.5544	+	30.1910i	1.35105	+	0.981595i
$947$	−10.7100	+	4.76839i	−0.348028	+	0.154952i	−0.573303	−	0.819343i	$-0.694338\pi$
$947$	−10.7100	+	4.76839i	−0.348028	+	0.154952i	0.225276	+	0.974295i	$0.427672\pi$
$948$		0			0
$949$	−1.75611	−	3.04168i	−0.0570059	−	0.0987370i
$950$	−83.1683	+	38.2923i	−2.69834	+	1.24237i
$951$		0			0
$952$	−38.4118	−	42.6606i	−1.24493	−	1.38264i
$953$	−0.574496	−	0.417395i	−0.0186097	−	0.0135208i	0.578442	−	0.815724i	$-0.303661\pi$
$953$	−0.574496	−	0.417395i	−0.0186097	−	0.0135208i	−0.597051	+	0.802203i	$0.703661\pi$
$954$		0			0
$955$	−2.23107	+	0.248722i	−0.0721957	+	0.00804847i
$956$	0.542050	+	5.15726i	0.0175311	+	0.166798i
$957$		0			0
$958$	−26.0363	−	11.5921i	−0.841196	−	0.374524i
$959$	11.8030	−	13.1086i	0.381139	−	0.423298i
$960$		0			0
$961$	10.0799	+	11.1949i	0.325159	+	0.361126i
$962$	6.96073	+	21.4229i	0.224423	+	0.690703i
$963$		0			0
$964$	24.5079	−	75.4277i	0.789348	−	2.42936i
$965$	23.1488	+	20.5806i	0.745187	+	0.662512i
$966$		0			0
$967$	25.5114	+	11.3584i	0.820392	+	0.365262i	0.773625	−	0.633644i	$-0.218441\pi$
$967$	25.5114	+	11.3584i	0.820392	+	0.365262i	0.0467673	+	0.998906i	$0.485108\pi$
$968$	−15.2792	−	26.4643i	−0.491090	−	0.850594i
$969$		0			0
$970$	62.0801	+	6.12952i	1.99327	+	0.196807i
$971$	24.9120	+	18.0996i	0.799465	+	0.580845i	0.910757	−	0.412942i	$-0.135499\pi$
$971$	24.9120	+	18.0996i	0.799465	+	0.580845i	−0.111292	+	0.993788i	$0.535499\pi$
$972$		0			0
$973$	−5.96262	+	18.3511i	−0.191153	+	0.588308i
$974$	−10.0423	+	17.3938i	−0.321776	+	0.557333i
$975$		0			0
$976$	8.76719	+	15.1852i	0.280631	+	0.486067i
$977$	24.5833	−	5.22535i	0.786491	−	0.167174i	0.202876	−	0.979204i	$-0.434971\pi$
$977$	24.5833	−	5.22535i	0.786491	−	0.167174i	0.583615	+	0.812031i	$0.301638\pi$
$978$		0			0
$979$	0.767507	−	0.341716i	0.0245296	−	0.0109213i
$980$	−19.8541	+	18.1046i	−0.634215	+	0.578329i
$981$		0			0
$982$	37.2571			1.18892
$983$	4.95289	+	47.1236i	0.157973	+	1.50301i	0.730381	+	0.683040i	$0.239342\pi$
$983$	4.95289	+	47.1236i	0.157973	+	1.50301i	−0.572409	+	0.819968i	$0.693991\pi$
$984$		0			0
$985$	−16.8787	−	5.36683i	−0.537799	−	0.171001i
$986$	92.0373	−	19.5631i	2.93106	−	0.623017i
$987$		0			0
$988$	−55.7179	−	11.8432i	−1.77262	−	0.376782i
$989$	6.05751	−	18.6431i	0.192617	−	0.592816i
$990$		0			0
$991$	14.2923	+	43.9872i	0.454010	+	1.39730i	0.872294	+	0.488982i	$0.162632\pi$
$991$	14.2923	+	43.9872i	0.454010	+	1.39730i	−0.418284	+	0.908316i	$0.637368\pi$
$992$	3.27562	+	31.1655i	0.104001	+	0.989504i
$993$		0			0
$994$	−48.7418	−	21.7012i	−1.54600	−	0.688321i
$995$	31.0187	−	10.2952i	0.983359	−	0.326379i
$996$		0			0
$997$	−47.2632	+	21.0429i	−1.49684	+	0.666436i	−0.981659	−	0.190645i	$-0.938942\pi$
$997$	−47.2632	+	21.0429i	−1.49684	+	0.666436i	−0.515182	+	0.857081i	$0.672275\pi$
$998$	−18.3451	+	56.4605i	−0.580705	+	1.78722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.2		224
3.2	odd	2		225.2.q.a.196.27	yes	224
9.4	even	3	inner	675.2.r.a.496.27		224
9.5	odd	6		225.2.q.a.121.2	yes	224
25.6	even	5	inner	675.2.r.a.181.27		224
75.56	odd	10		225.2.q.a.106.2	yes	224
225.31	even	15	inner	675.2.r.a.631.2		224
225.131	odd	30		225.2.q.a.31.27	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.27	✓	224	225.131	odd	30
225.2.q.a.106.2	yes	224	75.56	odd	10
225.2.q.a.121.2	yes	224	9.5	odd	6
225.2.q.a.196.27	yes	224	3.2	odd	2
675.2.r.a.46.2		224	1.1	even	1	trivial
675.2.r.a.181.27		224	25.6	even	5	inner
675.2.r.a.496.27		224	9.4	even	3	inner
675.2.r.a.631.2		224	225.31	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69452 - 1.88195i) q^{2} +(-0.461298 + 4.38896i) q^{4} +(2.12223 - 0.704374i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 - 3.59200i) q^{8} +O(q^{10})\)	\(q+(-1.69452 - 1.88195i) q^{2} +(-0.461298 + 4.38896i) q^{4} +(2.12223 - 0.704374i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 - 3.59200i) q^{8} +(-4.92175 - 2.80036i) q^{10} +(-1.63896 - 1.82025i) q^{11} +(-1.19441 + 1.32652i) q^{13} +(5.12291 - 1.08891i) q^{14} +(-6.50420 - 1.38251i) q^{16} +(-3.67466 + 2.66979i) q^{17} +(5.85004 - 4.25031i) q^{19} +(2.11249 + 9.63931i) q^{20} +(-0.648378 + 6.16890i) q^{22} +(2.31553 - 0.492181i) q^{23} +(4.00772 - 2.98968i) q^{25} +4.52040 q^{26} +(-7.38384 - 5.36467i) q^{28} +(7.47301 - 3.32720i) q^{29} +(6.20029 + 2.76055i) q^{31} +(2.30859 + 3.99860i) q^{32} +(11.2512 + 2.39152i) q^{34} +(-0.932951 + 4.52939i) q^{35} +(1.53985 + 4.73917i) q^{37} +(-17.9119 - 3.80729i) q^{38} +(7.96211 - 11.1054i) q^{40} +(3.20347 - 3.55781i) q^{41} +(4.14034 - 7.17127i) q^{43} +(8.74507 - 6.35367i) q^{44} +(-4.84997 - 3.52371i) q^{46} +(9.25434 - 4.12030i) q^{47} +(1.36143 + 2.35806i) q^{49} +(-12.4176 - 2.47626i) q^{50} +(-5.27108 - 5.85413i) q^{52} +(2.52356 + 1.83348i) q^{53} +(-4.76039 - 2.70855i) q^{55} +(1.32108 + 12.5692i) q^{56} +(-18.9248 - 8.42585i) q^{58} +(-6.99016 + 7.76336i) q^{59} +(-1.76446 - 1.95963i) q^{61} +(-5.31128 - 16.3465i) q^{62} +(-0.496397 + 1.52775i) q^{64} +(-1.60044 + 3.65649i) q^{65} +(-1.48939 - 0.663118i) q^{67} +(-10.0225 - 17.3595i) q^{68} +(10.1050 - 5.91936i) q^{70} +(-8.24169 - 5.98794i) q^{71} +(-0.608028 + 1.87132i) q^{73} +(6.30959 - 10.9285i) q^{74} +(15.9558 + 27.6363i) q^{76} +(4.95496 - 1.05321i) q^{77} +(13.6290 - 6.06801i) q^{79} +(-14.7772 + 1.64738i) q^{80} -12.1240 q^{82} +(0.424422 + 4.03811i) q^{83} +(-5.91793 + 8.25424i) q^{85} +(-20.5119 + 4.35993i) q^{86} +(-14.6413 - 3.11211i) q^{88} +(-0.105993 + 0.326212i) q^{89} +(-1.14078 - 3.51095i) q^{91} +(1.09201 + 10.3898i) q^{92} +(-23.4358 - 10.4343i) q^{94} +(9.42133 - 13.1407i) q^{95} +(-10.0640 + 4.48076i) q^{97} +(2.13079 - 6.55791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more