LMFDB - Embedded newform 441.2.bb.d.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.d.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16438 + 0.359164i) q^{2} +(-0.425690 - 0.290231i) q^{4} +(0.478452 - 0.0721150i) q^{5} +(1.90196 - 1.83918i) q^{7} +(-1.91089 - 2.39618i) q^{8} +O(q^{10})$	\(q+(1.16438 + 0.359164i) q^{2} +(-0.425690 - 0.290231i) q^{4} +(0.478452 - 0.0721150i) q^{5} +(1.90196 - 1.83918i) q^{7} +(-1.91089 - 2.39618i) q^{8} +(0.583002 + 0.0878735i) q^{10} +(2.56776 - 2.38253i) q^{11} +(0.866309 + 3.79555i) q^{13} +(2.87517 - 1.45839i) q^{14} +(-0.987928 - 2.51720i) q^{16} +(-0.0251704 - 0.335876i) q^{17} +(3.24669 - 5.62343i) q^{19} +(-0.224602 - 0.108163i) q^{20} +(3.84558 - 1.85193i) q^{22} +(0.169582 - 2.26291i) q^{23} +(-4.55415 + 1.40477i) q^{25} +(-0.354511 + 4.73062i) q^{26} +(-1.34343 + 0.230913i) q^{28} +(5.84248 + 2.81359i) q^{29} +(2.13461 + 3.69724i) q^{31} +(0.211833 + 2.82672i) q^{32} +(0.0913266 - 0.400128i) q^{34} +(0.777362 - 1.01712i) q^{35} +(-4.62031 + 3.15007i) q^{37} +(5.80012 - 5.38172i) q^{38} +(-1.08707 - 1.00865i) q^{40} +(2.67167 + 3.35017i) q^{41} +(-5.28773 + 6.63061i) q^{43} +(-1.78456 + 0.268978i) q^{44} +(1.01022 - 2.57399i) q^{46} +(-4.71078 - 1.45308i) q^{47} +(0.234867 - 6.99606i) q^{49} -5.80731 q^{50} +(0.732806 - 1.86716i) q^{52} +(-7.44857 - 5.07835i) q^{53} +(1.05673 - 1.32510i) q^{55} +(-8.04143 - 1.04297i) q^{56} +(5.79234 + 5.37451i) q^{58} +(12.3025 + 1.85430i) q^{59} +(-7.55952 + 5.15399i) q^{61} +(1.15758 + 5.07168i) q^{62} +(-1.97205 + 8.64012i) q^{64} +(0.688204 + 1.75351i) q^{65} +(-2.35068 - 4.07149i) q^{67} +(-0.0867667 + 0.150284i) q^{68} +(1.27046 - 0.905112i) q^{70} +(-12.8903 + 6.20766i) q^{71} +(7.72629 - 2.38325i) q^{73} +(-6.51120 + 2.00844i) q^{74} +(-3.01417 + 1.45155i) q^{76} +(0.501868 - 9.25403i) q^{77} +(0.516002 - 0.893742i) q^{79} +(-0.654204 - 1.13311i) q^{80} +(1.90759 + 4.86045i) q^{82} +(-2.93736 + 12.8694i) q^{83} +(-0.0362645 - 0.158885i) q^{85} +(-8.53842 + 5.82140i) q^{86} +(-10.6157 - 1.60006i) q^{88} +(1.38129 + 1.28165i) q^{89} +(8.62836 + 5.62567i) q^{91} +(-0.728956 + 0.914082i) q^{92} +(-4.96325 - 3.38389i) q^{94} +(1.14785 - 2.92467i) q^{95} -0.104657 q^{97} +(2.78621 - 8.06173i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	1.16438	+	0.359164i	0.823343	+	0.253968i	0.677671	−	0.735365i	$-0.262989\pi$
$2$	1.16438	+	0.359164i	0.823343	+	0.253968i	0.145672	+	0.989333i	$0.453466\pi$
$3$		0			0
$3$		0			0
$4$	−0.425690	−	0.290231i	−0.212845	−	0.145115i
$5$	0.478452	−	0.0721150i	0.213970	−	0.0322508i	−0.0411822	−	0.999152i	$-0.513112\pi$
$5$	0.478452	−	0.0721150i	0.213970	−	0.0322508i	0.255152	+	0.966901i	$0.417874\pi$
$6$		0			0
$7$	1.90196	−	1.83918i	0.718871	−	0.695143i
$7$	1.90196	−	1.83918i	0.718871	−	0.695143i
$8$	−1.91089	−	2.39618i	−0.675603	−	0.847179i
$9$		0			0
$10$	0.583002	+	0.0878735i	0.184362	+	0.0277880i
$11$	2.56776	−	2.38253i	0.774209	−	0.718361i	−0.190498	−	0.981688i	$-0.561010\pi$
$11$	2.56776	−	2.38253i	0.774209	−	0.718361i	0.964707	+	0.263327i	$0.0848197\pi$
$12$		0			0
$13$	0.866309	+	3.79555i	0.240271	+	1.05270i	0.940771	+	0.339043i	$0.110103\pi$
$13$	0.866309	+	3.79555i	0.240271	+	1.05270i	−0.700500	+	0.713653i	$0.747040\pi$
$14$	2.87517	−	1.45839i	0.768421	−	0.389771i
$15$		0			0
$16$	−0.987928	−	2.51720i	−0.246982	−	0.629300i
$17$	−0.0251704	−	0.335876i	−0.00610472	−	0.0814618i	0.993319	−	0.115399i	$-0.0368145\pi$
$17$	−0.0251704	−	0.335876i	−0.00610472	−	0.0814618i	−0.999424	+	0.0339368i	$0.989196\pi$
$18$		0			0
$19$	3.24669	−	5.62343i	0.744841	−	1.29010i	−0.205428	−	0.978672i	$-0.565859\pi$
$19$	3.24669	−	5.62343i	0.744841	−	1.29010i	0.950269	−	0.311430i	$-0.100808\pi$
$20$	−0.224602	−	0.108163i	−0.0502226	−	0.0241859i
$21$		0			0
$22$	3.84558	−	1.85193i	0.819880	−	0.394833i
$23$	0.169582	−	2.26291i	0.0353602	−	0.471850i	−0.951214	−	0.308533i	$-0.900162\pi$
$23$	0.169582	−	2.26291i	0.0353602	−	0.471850i	0.986574	−	0.163316i	$-0.0522191\pi$
$24$		0			0
$25$	−4.55415	+	1.40477i	−0.910830	+	0.280954i
$26$	−0.354511	+	4.73062i	−0.0695253	+	0.927750i
$27$		0			0
$28$	−1.34343	+	0.230913i	−0.253884	+	0.0436385i
$29$	5.84248	+	2.81359i	1.08492	+	0.522471i	0.888887	−	0.458126i	$-0.151479\pi$
$29$	5.84248	+	2.81359i	1.08492	+	0.522471i	0.196035	+	0.980597i	$0.437194\pi$
$30$		0			0
$31$	2.13461	+	3.69724i	0.383386	+	0.664045i	0.991544	−	0.129772i	$-0.0414244\pi$
$31$	2.13461	+	3.69724i	0.383386	+	0.664045i	−0.608157	+	0.793816i	$0.708091\pi$
$32$	0.211833	+	2.82672i	0.0374472	+	0.499698i
$33$		0			0
$34$	0.0913266	−	0.400128i	0.0156624	−	0.0686214i
$35$	0.777362	−	1.01712i	0.131398	−	0.171924i
$36$		0			0
$37$	−4.62031	+	3.15007i	−0.759574	+	0.517869i	−0.880069	−	0.474845i	$-0.842504\pi$
$37$	−4.62031	+	3.15007i	−0.759574	+	0.517869i	0.120495	+	0.992714i	$0.461552\pi$
$38$	5.80012	−	5.38172i	0.940903	−	0.873031i
$39$		0			0
$40$	−1.08707	−	1.00865i	−0.171881	−	0.159482i
$41$	2.67167	+	3.35017i	0.417245	+	0.523209i	0.945388	−	0.325947i	$-0.105683\pi$
$41$	2.67167	+	3.35017i	0.417245	+	0.523209i	−0.528143	+	0.849155i	$0.677112\pi$
$42$		0			0
$43$	−5.28773	+	6.63061i	−0.806371	+	1.01116i	0.193179	+	0.981164i	$0.438120\pi$
$43$	−5.28773	+	6.63061i	−0.806371	+	1.01116i	−0.999550	+	0.0299942i	$0.990451\pi$
$44$	−1.78456	+	0.268978i	−0.269032	+	0.0405500i
$45$		0			0
$46$	1.01022	−	2.57399i	0.148948	−	0.379514i
$47$	−4.71078	−	1.45308i	−0.687138	−	0.211954i	−0.0685245	−	0.997649i	$-0.521829\pi$
$47$	−4.71078	−	1.45308i	−0.687138	−	0.211954i	−0.618614	+	0.785695i	$0.712305\pi$
$48$		0			0
$49$	0.234867	−	6.99606i	0.0335524	−	0.999437i
$50$	−5.80731			−0.821278
$51$		0			0
$52$	0.732806	−	1.86716i	0.101622	−	0.258928i
$53$	−7.44857	−	5.07835i	−1.02314	−	0.697565i	−0.0692124	−	0.997602i	$-0.522049\pi$
$53$	−7.44857	−	5.07835i	−1.02314	−	0.697565i	−0.953928	+	0.300037i	$0.903001\pi$
$54$		0			0
$55$	1.05673	−	1.32510i	0.142490	−	0.178677i
$56$	−8.04143	−	1.04297i	−1.07458	−	0.139372i
$57$		0			0
$58$	5.79234	+	5.37451i	0.760572	+	0.705707i
$59$	12.3025	+	1.85430i	1.60165	+	0.241409i	0.888253	−	0.459355i	$-0.151919\pi$
$59$	12.3025	+	1.85430i	1.60165	+	0.241409i	0.713393	+	0.700764i	$0.247157\pi$
$60$		0			0
$61$	−7.55952	+	5.15399i	−0.967897	+	0.659901i	−0.940525	−	0.339724i	$-0.889666\pi$
$61$	−7.55952	+	5.15399i	−0.967897	+	0.659901i	−0.0273718	+	0.999625i	$0.508714\pi$
$62$	1.15758	+	5.07168i	0.147013	+	0.644104i
$63$		0			0
$64$	−1.97205	+	8.64012i	−0.246506	+	1.08001i
$65$	0.688204	+	1.75351i	0.0853612	+	0.217497i
$66$		0			0
$67$	−2.35068	−	4.07149i	−0.287181	−	0.497412i	0.685955	−	0.727644i	$-0.259385\pi$
$67$	−2.35068	−	4.07149i	−0.287181	−	0.497412i	−0.973136	+	0.230232i	$0.926051\pi$
$68$	−0.0867667	+	0.150284i	−0.0105220	+	0.0182246i
$69$		0			0
$70$	1.27046	−	0.905112i	0.151849	−	0.108182i
$71$	−12.8903	+	6.20766i	−1.52980	+	0.736714i	−0.994179	−	0.107743i	$-0.965637\pi$
$71$	−12.8903	+	6.20766i	−1.52980	+	0.736714i	−0.535623	+	0.844457i	$0.679923\pi$
$72$		0			0
$73$	7.72629	−	2.38325i	0.904294	−	0.278938i	0.192476	−	0.981302i	$-0.438348\pi$
$73$	7.72629	−	2.38325i	0.904294	−	0.278938i	0.711818	+	0.702364i	$0.247872\pi$
$74$	−6.51120	+	2.00844i	−0.756912	+	0.233476i
$75$		0			0
$76$	−3.01417	+	1.45155i	−0.345750	+	0.166504i
$77$	0.501868	−	9.25403i	0.0571932	−	1.05459i
$78$		0			0
$79$	0.516002	−	0.893742i	0.0580548	−	0.100554i	−0.835537	−	0.549434i	$-0.814844\pi$
$79$	0.516002	−	0.893742i	0.0580548	−	0.100554i	0.893592	+	0.448880i	$0.148177\pi$
$80$	−0.654204	−	1.13311i	−0.0731422	−	0.126686i
$81$		0			0
$82$	1.90759	+	4.86045i	0.210658	+	0.536747i
$83$	−2.93736	+	12.8694i	−0.322417	+	1.41260i	0.510821	+	0.859687i	$0.329342\pi$
$83$	−2.93736	+	12.8694i	−0.322417	+	1.41260i	−0.833238	+	0.552915i	$0.813515\pi$
$84$		0			0
$85$	−0.0362645	−	0.158885i	−0.00393344	−	0.0172335i
$86$	−8.53842	+	5.82140i	−0.920721	+	0.627737i
$87$		0			0
$88$	−10.6157	−	1.60006i	−1.13164	−	0.170567i
$89$	1.38129	+	1.28165i	0.146416	+	0.135854i	0.749981	−	0.661460i	$-0.230063\pi$
$89$	1.38129	+	1.28165i	0.146416	+	0.135854i	−0.603564	+	0.797314i	$0.706253\pi$
$90$		0			0
$91$	8.62836	+	5.62567i	0.904498	+	0.589730i
$92$	−0.728956	+	0.914082i	−0.0759989	+	0.0952996i
$93$		0			0
$94$	−4.96325	−	3.38389i	−0.511921	−	0.349022i
$95$	1.14785	−	2.92467i	0.117767	−	0.300065i
$96$		0			0
$97$	−0.104657			−0.0106263			−0.00531317	−	0.999986i	$-0.501691\pi$
$97$	−0.104657			−0.0106263			−0.00531317	+	0.999986i	$0.501691\pi$
$98$	2.78621	−	8.06173i	0.281450	−	0.814358i
$99$		0			0
$100$	2.34636	+	0.723758i	0.234636	+	0.0723758i
$101$	1.58961	−	4.05026i	0.158172	−	0.403015i	−0.829716	−	0.558186i	$-0.811498\pi$
$101$	1.58961	−	4.05026i	0.158172	−	0.403015i	0.987888	+	0.155171i	$0.0495927\pi$
$102$		0			0
$103$	5.12165	−	0.771965i	0.504652	−	0.0760640i	0.108218	−	0.994127i	$-0.465486\pi$
$103$	5.12165	−	0.771965i	0.504652	−	0.0760640i	0.396434	+	0.918063i	$0.370248\pi$
$104$	7.43941	−	9.32872i	0.729494	−	0.914756i
$105$		0			0
$106$	−6.84902	−	8.58840i	−0.665236	−	0.834179i
$107$	7.51758	+	6.97530i	0.726752	+	0.674327i	0.954101	−	0.299486i	$-0.0968152\pi$
$107$	7.51758	+	6.97530i	0.726752	+	0.674327i	−0.227349	+	0.973813i	$0.573006\pi$
$108$		0			0
$109$	−0.535156	+	0.496553i	−0.0512587	+	0.0475611i	−0.705386	−	0.708823i	$-0.749226\pi$
$109$	−0.535156	+	0.496553i	−0.0512587	+	0.0475611i	0.654128	+	0.756384i	$0.273036\pi$
$110$	1.70637	−	1.16338i	0.162696	−	0.110924i
$111$		0			0
$112$	−6.50856	−	2.97063i	−0.615001	−	0.280698i
$113$	1.22163	−	5.35233i	0.114922	−	0.503505i	−0.884402	−	0.466726i	$-0.845433\pi$
$113$	1.22163	−	5.35233i	0.114922	−	0.503505i	0.999323	−	0.0367784i	$-0.0117096\pi$
$114$		0			0
$115$	−0.0820532	−	1.09492i	−0.00765150	−	0.102102i
$116$	−1.67050	−	2.89339i	−0.155102	−	0.268644i
$117$		0			0
$118$	13.6588	+	6.57773i	1.25739	+	0.605529i
$119$	−0.665607	−	0.592528i	−0.0610161	−	0.0543169i
$120$		0			0
$121$	0.0948966	−	1.26631i	0.00862696	−	0.115119i
$122$	−10.6533	+	3.28611i	−0.964504	+	0.297510i
$123$		0			0
$124$	0.164373	−	2.19341i	0.0147612	−	0.196974i
$125$	−4.25733	+	2.05022i	−0.380788	+	0.183378i
$126$		0			0
$127$	3.98417	+	1.91867i	0.353538	+	0.170255i	0.602220	−	0.798330i	$-0.294283\pi$
$127$	3.98417	+	1.91867i	0.353538	+	0.170255i	−0.248682	+	0.968585i	$0.579997\pi$
$128$	−2.56480	+	4.44236i	−0.226698	+	0.392653i
$129$		0			0
$130$	0.171532	+	2.28894i	0.0150444	+	0.200753i
$131$	5.69783	+	14.5178i	0.497822	+	1.26843i	0.930305	+	0.366787i	$0.119542\pi$
$131$	5.69783	+	14.5178i	0.497822	+	1.26843i	−0.432483	+	0.901642i	$0.642362\pi$
$132$		0			0
$133$	−4.16741	−	16.6667i	−0.361361	−	1.44519i
$134$	−1.27475	−	5.58505i	−0.110122	−	0.482475i
$135$		0			0
$136$	−0.756722	+	0.702135i	−0.0648884	+	0.0602076i
$137$	−11.5919	−	1.74720i	−0.990363	−	0.149273i	−0.366174	−	0.930547i	$-0.619332\pi$
$137$	−11.5919	−	1.74720i	−0.990363	−	0.149273i	−0.624189	+	0.781273i	$0.714570\pi$
$138$		0			0
$139$	−5.45746	−	6.84344i	−0.462896	−	0.580453i	0.494520	−	0.869166i	$-0.335344\pi$
$139$	−5.45746	−	6.84344i	−0.462896	−	0.580453i	−0.957416	+	0.288713i	$0.906773\pi$
$140$	−0.626114	+	0.207362i	−0.0529163	+	0.0175253i
$141$		0			0
$142$	−17.2389	+	2.59834i	−1.44665	+	0.218048i
$143$	11.2675	+	7.68205i	0.942235	+	0.642405i
$144$		0			0
$145$	2.99825	+	0.924838i	0.248991	+	0.0768036i
$146$	9.85234			0.815385
$147$		0			0
$148$	2.88107			0.236822
$149$	5.15279	+	1.58943i	0.422133	+	0.130211i	0.498542	−	0.866866i	$-0.333869\pi$
$149$	5.15279	+	1.58943i	0.422133	+	0.130211i	−0.0764085	+	0.997077i	$0.524345\pi$
$150$		0			0
$151$	0.935832	+	0.638040i	0.0761569	+	0.0519229i	0.600800	−	0.799399i	$-0.294849\pi$
$151$	0.935832	+	0.638040i	0.0761569	+	0.0519229i	−0.524643	+	0.851322i	$0.675801\pi$
$152$	−19.6788	+	2.96611i	−1.59616	+	0.240583i
$153$		0			0
$154$	3.90809	−	10.5950i	0.314922	−	0.853768i
$155$	1.28793	+	1.61502i	0.103449	+	0.129721i
$156$		0			0
$157$	20.1181	+	3.03231i	1.60560	+	0.242005i	0.889815	−	0.456321i	$-0.150833\pi$
$157$	20.1181	+	3.03231i	1.60560	+	0.242005i	0.715780	+	0.698325i	$0.246071\pi$
$158$	0.921824	−	0.855328i	0.0733364	−	0.0680462i
$159$		0			0
$160$	0.305201	+	1.33717i	0.0241282	+	0.105713i
$161$	−3.83935	−	4.61585i	−0.302583	−	0.363780i
$162$		0			0
$163$	−2.30035	−	5.86119i	−0.180177	−	0.459084i	0.812040	−	0.583601i	$-0.198357\pi$
$163$	−2.30035	−	5.86119i	−0.180177	−	0.459084i	−0.992217	+	0.124518i	$0.960262\pi$
$164$	−0.164982	−	2.20154i	−0.0128830	−	0.171911i
$165$		0			0
$166$	−8.04245	+	13.9299i	−0.624215	+	1.08117i
$167$	13.3927	+	6.44960i	1.03636	+	0.499085i	0.873122	−	0.487502i	$-0.162092\pi$
$167$	13.3927	+	6.44960i	1.03636	+	0.499085i	0.163238	+	0.986587i	$0.447806\pi$
$168$		0			0
$169$	−1.94311	+	0.935750i	−0.149470	+	0.0719808i
$170$	0.0148402	−	0.198028i	0.00113819	−	0.0151881i
$171$		0			0
$172$	4.17534	−	1.28792i	0.318367	−	0.0982032i
$173$	0.355483	−	4.74359i	0.0270269	−	0.360648i	−0.967251	−	0.253822i	$-0.918312\pi$
$173$	0.355483	−	4.74359i	0.0270269	−	0.360648i	0.994278	−	0.106826i	$-0.0340688\pi$
$174$		0			0
$175$	−6.07817	+	11.0477i	−0.459466	+	0.835126i
$176$	−8.53407	−	4.10979i	−0.643280	−	0.309787i
$177$		0			0
$178$	1.14803	+	1.98844i	0.0860481	+	0.149040i
$179$	−1.67556	−	22.3588i	−0.125237	−	1.67117i	−0.606872	−	0.794800i	$-0.707576\pi$
$179$	−1.67556	−	22.3588i	−0.125237	−	1.67117i	0.481635	−	0.876372i	$-0.340043\pi$
$180$		0			0
$181$	−3.56581	+	15.6229i	−0.265045	+	1.16124i	0.650655	+	0.759374i	$0.274495\pi$
$181$	−3.56581	+	15.6229i	−0.265045	+	1.16124i	−0.915699	+	0.401864i	$0.868363\pi$
$182$	8.02617	+	9.64943i	0.594939	+	0.715263i
$183$		0			0
$184$	−5.74640	+	3.91783i	−0.423630	+	0.288826i
$185$	−1.98343	+	1.84035i	−0.145825	+	0.135305i
$186$		0			0
$187$	−0.864867	−	0.802479i	−0.0632453	−	0.0586831i
$188$	1.58360	+	1.98578i	0.115496	+	0.144828i
$189$		0			0
$190$	2.38698	−	2.99317i	0.173169	−	0.217148i
$191$	6.54747	−	0.986873i	0.473758	−	0.0714076i	0.0921766	−	0.995743i	$-0.470618\pi$
$191$	6.54747	−	0.986873i	0.473758	−	0.0714076i	0.381582	+	0.924335i	$0.375379\pi$
$192$		0			0
$193$	0.855841	−	2.18065i	0.0616048	−	0.156966i	−0.896757	−	0.442523i	$-0.854083\pi$
$193$	0.855841	−	2.18065i	0.0616048	−	0.156966i	0.958362	+	0.285557i	$0.0921786\pi$
$194$	−0.121861	−	0.0375892i	−0.00874912	−	0.00269875i
$195$		0			0
$196$	−2.13045	+	2.90999i	−0.152175	+	0.207856i
$197$	−0.848986			−0.0604878			−0.0302439	−	0.999543i	$-0.509628\pi$
$197$	−0.848986			−0.0604878			−0.0302439	+	0.999543i	$0.509628\pi$
$198$		0			0
$199$	0.565966	−	1.44206i	0.0401202	−	0.102225i	−0.909409	−	0.415902i	$-0.863466\pi$
$199$	0.565966	−	1.44206i	0.0401202	−	0.102225i	0.949530	+	0.313678i	$0.101561\pi$
$200$	12.0686	+	8.22821i	0.853377	+	0.581822i
$201$		0			0
$202$	3.30562	−	4.14512i	0.232583	−	0.291649i
$203$	16.2868	−	5.39403i	1.14311	−	0.378586i
$204$		0			0
$205$	1.51986	+	1.41023i	0.106152	+	0.0984946i
$206$	6.24083	+	0.940653i	0.434819	+	0.0655384i
$207$		0			0
$208$	8.69830	−	5.93040i	0.603119	−	0.411199i
$209$	−5.06129	−	22.1749i	−0.350097	−	1.53387i
$210$		0			0
$211$	−1.65577	+	7.25438i	−0.113988	+	0.499412i	0.885413	+	0.464805i	$0.153875\pi$
$211$	−1.65577	+	7.25438i	−0.113988	+	0.499412i	−0.999401	+	0.0346079i	$0.988982\pi$
$212$	1.69689	+	4.32361i	0.116543	+	0.296947i
$213$		0			0
$214$	6.24806	+	10.8220i	0.427109	+	0.739774i
$215$	−2.05176	+	3.55375i	−0.139929	+	0.242364i
$216$		0			0
$217$	10.8598	+	3.10608i	0.737212	+	0.210854i
$218$	−0.801471	+	0.385968i	−0.0542824	+	0.0261410i
$219$		0			0
$220$	−0.834427	+	0.257387i	−0.0562570	+	0.0173530i
$221$	1.25303	−	0.386508i	0.0842877	−	0.0259993i
$222$		0			0
$223$	−5.04353	+	2.42883i	−0.337740	+	0.162647i	−0.595064	−	0.803678i	$-0.702873\pi$
$223$	−5.04353	+	2.42883i	−0.337740	+	0.162647i	0.257325	+	0.966325i	$0.417159\pi$
$224$	5.60173	+	4.98669i	0.374281	+	0.333187i
$225$		0			0
$226$	3.34482	−	5.79339i	0.222494	−	0.385371i
$227$	−4.67080	−	8.09007i	−0.310012	−	0.536957i	0.668353	−	0.743845i	$-0.267000\pi$
$227$	−4.67080	−	8.09007i	−0.310012	−	0.536957i	−0.978365	+	0.206888i	$0.933666\pi$
$228$		0			0
$229$	−6.96150	−	17.7376i	−0.460029	−	1.17213i	−0.953237	−	0.302223i	$-0.902271\pi$
$229$	−6.96150	−	17.7376i	−0.460029	−	1.17213i	0.493208	−	0.869911i	$-0.335824\pi$
$230$	0.297716	−	1.30438i	0.0196308	−	0.0860083i
$231$		0			0
$232$	−4.42248	−	19.3761i	−0.290350	−	1.27211i
$233$	−12.7829	+	8.71526i	−0.837438	+	0.570956i	−0.904344	−	0.426804i	$-0.859640\pi$
$233$	−12.7829	+	8.71526i	−0.837438	+	0.570956i	0.0669063	+	0.997759i	$0.478687\pi$
$234$		0			0
$235$	−2.35867	−	0.355513i	−0.153863	−	0.0231911i
$236$	−4.69887	−	4.35992i	−0.305870	−	0.283806i
$237$		0			0
$238$	−0.562207	−	0.928991i	−0.0364424	−	0.0602176i
$239$	−5.81621	+	7.29330i	−0.376220	+	0.471764i	−0.933509	−	0.358554i	$-0.883270\pi$
$239$	−5.81621	+	7.29330i	−0.376220	+	0.471764i	0.557289	+	0.830318i	$0.311841\pi$
$240$		0			0
$241$	−12.2263	−	8.33574i	−0.787565	−	0.536952i	0.101445	−	0.994841i	$-0.467653\pi$
$241$	−12.2263	−	8.33574i	−0.787565	−	0.536952i	−0.889010	+	0.457889i	$0.848606\pi$
$242$	0.565308	−	1.44038i	0.0363394	−	0.0925912i
$243$		0			0
$244$	4.71386			0.301774
$245$	−0.392148	−	3.36422i	−0.0250534	−	0.214932i
$246$		0			0
$247$	24.1566	+	7.45133i	1.53705	+	0.474117i
$248$	4.78028	−	12.1799i	0.303548	−	0.773427i
$249$		0			0
$250$	−5.69353	+	0.858162i	−0.360091	+	0.0542749i
$251$	6.59780	−	8.27338i	0.416449	−	0.522211i	−0.528718	−	0.848798i	$-0.677327\pi$
$251$	6.59780	−	8.27338i	0.416449	−	0.522211i	0.945167	+	0.326587i	$0.105898\pi$
$252$		0			0
$253$	−4.95602	−	6.21465i	−0.311582	−	0.390712i
$254$	3.94997	+	3.66504i	0.247843	+	0.229965i
$255$		0			0
$256$	8.41113	−	7.80438i	0.525695	−	0.487774i
$257$	0.755069	−	0.514797i	0.0470999	−	0.0321122i	−0.539541	−	0.841959i	$-0.681402\pi$
$257$	0.755069	−	0.514797i	0.0470999	−	0.0321122i	0.586641	+	0.809847i	$0.300450\pi$
$258$		0			0
$259$	−2.99408	+	14.4889i	−0.186043	+	0.900294i
$260$	0.215962	−	0.946192i	0.0133934	−	0.0586803i
$261$		0			0
$262$	1.42016	+	18.9508i	0.0877380	+	1.17078i
$263$	5.19424	+	8.99669i	0.320291	+	0.554760i	0.980548	−	0.196280i	$-0.0628861\pi$
$263$	5.19424	+	8.99669i	0.320291	+	0.554760i	−0.660257	+	0.751039i	$0.729553\pi$
$264$		0			0
$265$	−3.93001	−	1.89259i	−0.241419	−	0.116261i
$266$	1.13363	−	20.9032i	0.0695074	−	1.28166i
$267$		0			0
$268$	−0.181012	+	2.41543i	−0.0110571	+	0.147546i
$269$	−0.387486	+	0.119524i	−0.0236254	+	0.00728748i	−0.306545	−	0.951856i	$-0.599173\pi$
$269$	−0.387486	+	0.119524i	−0.0236254	+	0.00728748i	0.282920	+	0.959144i	$0.408697\pi$
$270$		0			0
$271$	−1.17146	+	15.6320i	−0.0711609	+	0.949576i	0.841341	+	0.540504i	$0.181766\pi$
$271$	−1.17146	+	15.6320i	−0.0711609	+	0.949576i	−0.912502	+	0.409072i	$0.865853\pi$
$272$	−0.820599	+	0.395180i	−0.0497561	+	0.0239613i
$273$		0			0
$274$	−12.8699	−	6.19780i	−0.777497	−	0.374423i
$275$	−8.34705	+	14.4575i	−0.503346	+	0.871821i
$276$		0			0
$277$	−0.937936	−	12.5159i	−0.0563551	−	0.752007i	−0.951777	−	0.306789i	$-0.900745\pi$
$277$	−0.937936	−	12.5159i	−0.0563551	−	0.752007i	0.895422	−	0.445218i	$-0.146874\pi$
$278$	−3.89665	−	9.92850i	−0.233706	−	0.595472i
$279$		0			0
$280$	−3.92265	+	0.0808987i	−0.234423	+	0.00483462i
$281$	0.550915	+	2.41372i	0.0328648	+	0.143990i	0.988698	−	0.149918i	$-0.0479011\pi$
$281$	0.550915	+	2.41372i	0.0328648	+	0.143990i	−0.955834	+	0.293908i	$0.905044\pi$
$282$		0			0
$283$	16.5720	−	15.3765i	0.985102	−	0.914041i	−0.0112023	−	0.999937i	$-0.503566\pi$
$283$	16.5720	−	15.3765i	0.985102	−	0.914041i	0.996304	+	0.0858964i	$0.0273754\pi$
$284$	7.28895	+	1.09863i	0.432519	+	0.0651918i
$285$		0			0
$286$	10.3606	+	12.9917i	0.612632	+	0.768217i
$287$	11.2429	+	1.45820i	0.663650	+	0.0860749i
$288$		0			0
$289$	16.6979	−	2.51681i	0.982232	−	0.148048i
$290$	3.15894	+	2.15373i	0.185499	+	0.126471i
$291$		0			0
$292$	−3.98070	−	1.22788i	−0.232953	−	0.0718565i
$293$	−14.8118			−0.865315			−0.432657	−	0.901558i	$-0.642424\pi$
$293$	−14.8118			−0.865315			−0.432657	+	0.901558i	$0.642424\pi$
$294$		0			0
$295$	6.01987			0.350490
$296$	16.3771	+	5.05166i	0.951898	+	0.293622i
$297$		0			0
$298$	5.42895	+	3.70140i	0.314491	+	0.214416i
$299$	8.73590	−	1.31673i	0.505210	−	0.0761482i
$300$		0			0
$301$	2.13782	+	22.3362i	0.123222	+	1.28744i
$302$	0.860505	+	1.07904i	0.0495165	+	0.0620918i
$303$		0			0
$304$	−17.3628	−	2.61702i	−0.995823	−	0.150096i
$305$	−3.24519	+	3.01109i	−0.185819	+	0.172415i
$306$		0			0
$307$	−5.30365	−	23.2368i	−0.302695	−	1.32619i	−0.866041	−	0.499973i	$-0.833343\pi$
$307$	−5.30365	−	23.2368i	−0.302695	−	1.32619i	0.563346	−	0.826221i	$-0.309514\pi$
$308$	−2.89945	+	3.79370i	−0.165211	+	0.216166i
$309$		0			0
$310$	0.919590	+	2.34308i	0.0522292	+	0.133078i
$311$	0.917379	+	12.2416i	0.0520198	+	0.694156i	0.960864	+	0.277020i	$0.0893469\pi$
$311$	0.917379	+	12.2416i	0.0520198	+	0.694156i	−0.908844	+	0.417135i	$0.863034\pi$
$312$		0			0
$313$	−6.16297	+	10.6746i	−0.348352	+	0.603363i	−0.985957	−	0.167001i	$-0.946592\pi$
$313$	−6.16297	+	10.6746i	−0.348352	+	0.603363i	0.637605	+	0.770363i	$0.279925\pi$
$314$	22.3360	+	10.7565i	1.26049	+	0.607022i
$315$		0			0
$316$	−0.479048	+	0.230698i	−0.0269486	+	0.0129778i
$317$	2.32511	−	31.0264i	0.130591	−	1.74262i	−0.419717	−	0.907655i	$-0.637871\pi$
$317$	2.32511	−	31.0264i	0.130591	−	1.74262i	0.550308	−	0.834962i	$-0.314510\pi$
$318$		0			0
$319$	21.7056	−	6.69528i	1.21528	−	0.374864i
$320$	−0.320449	+	4.27610i	−0.0179136	+	0.239041i
$321$		0			0
$322$	−2.81263	−	6.75357i	−0.156742	−	0.376362i
$323$	−1.97049	−	0.948939i	−0.109641	−	0.0528004i
$324$		0			0
$325$	−9.27717	−	16.0685i	−0.514605	−	0.891322i
$326$	−0.573353	−	7.65087i	−0.0317551	−	0.423742i
$327$		0			0
$328$	2.92234	−	12.8036i	0.161359	−	0.706962i
$329$	−11.6322	+	5.90025i	−0.641302	+	0.325292i
$330$		0			0
$331$	7.99384	−	5.45011i	0.439381	−	0.299565i	−0.323351	−	0.946279i	$-0.604810\pi$
$331$	7.99384	−	5.45011i	0.439381	−	0.299565i	0.762733	+	0.646714i	$0.223857\pi$
$332$	4.98551	−	4.62588i	0.273615	−	0.253878i
$333$		0			0
$334$	13.2778	+	12.3200i	0.726528	+	0.674120i
$335$	−1.41830	−	1.77849i	−0.0774901	−	0.0971695i
$336$		0			0
$337$	−19.8317	+	24.8682i	−1.08030	+	1.35466i	−0.149656	+	0.988738i	$0.547817\pi$
$337$	−19.8317	+	24.8682i	−1.08030	+	1.35466i	−0.930647	+	0.365919i	$0.880755\pi$
$338$	−2.59861	+	0.391677i	−0.141346	+	0.0213044i
$339$		0			0
$340$	−0.0306759	+	0.0781610i	−0.00166364	+	0.00423888i
$341$	14.2900	+	4.40787i	0.773845	+	0.238700i
$342$		0			0
$343$	−12.4203	−	13.7382i	−0.670632	−	0.741790i
$344$	25.9924			1.40142
$345$		0			0
$346$	2.11765	−	5.39568i	0.113845	−	0.290073i
$347$	−21.4375	−	14.6158i	−1.15082	−	0.784619i	−0.171156	−	0.985244i	$-0.554750\pi$
$347$	−21.4375	−	14.6158i	−1.15082	−	0.784619i	−0.979668	+	0.200625i	$0.935703\pi$
$348$		0			0
$349$	14.0924	−	17.6713i	0.754350	−	0.945924i	−0.245374	−	0.969428i	$-0.578911\pi$
$349$	14.0924	−	17.6713i	0.754350	−	0.945924i	0.999724	+	0.0235040i	$0.00748224\pi$
$350$	−11.0452	+	10.6807i	−0.590393	+	0.570906i
$351$		0			0
$352$	7.27869	+	6.75363i	0.387955	+	0.359970i
$353$	−16.8785	−	2.54402i	−0.898350	−	0.135404i	−0.316397	−	0.948627i	$-0.602473\pi$
$353$	−16.8785	−	2.54402i	−0.898350	−	0.135404i	−0.581953	+	0.813223i	$0.697711\pi$
$354$		0			0
$355$	−5.71974	+	3.89965i	−0.303572	+	0.206972i
$356$	−0.216027	−	0.946478i	−0.0114494	−	0.0501632i
$357$		0			0
$358$	6.07948	−	26.6359i	0.321310	−	1.40775i
$359$	1.08167	+	2.75605i	0.0570883	+	0.145459i	0.956572	−	0.291495i	$-0.0941527\pi$
$359$	1.08167	+	2.75605i	0.0570883	+	0.145459i	−0.899484	+	0.436954i	$0.856057\pi$
$360$		0			0
$361$	−11.5819	−	20.0605i	−0.609576	−	1.05582i
$362$	−9.76314	+	16.9103i	−0.513139	+	0.888784i
$363$		0			0
$364$	−2.04027	−	4.89901i	−0.106939	−	0.256778i
$365$	3.52479	−	1.69745i	0.184496	−	0.0888487i
$366$		0			0
$367$	−30.6947	+	9.46806i	−1.60225	+	0.494229i	−0.961796	−	0.273768i	$-0.911730\pi$
$367$	−30.6947	+	9.46806i	−1.60225	+	0.494229i	−0.640454	+	0.767997i	$0.721254\pi$
$368$	−5.86373	+	1.80872i	−0.305668	+	0.0942861i
$369$		0			0
$370$	−2.97046	+	1.43050i	−0.154427	+	0.0743680i
$371$	−23.5068	+	4.04044i	−1.22041	+	0.209769i
$372$		0			0
$373$	−9.31752	+	16.1384i	−0.482443	+	0.835615i	−0.999797	−	0.0201562i	$-0.993584\pi$
$373$	−9.31752	+	16.1384i	−0.482443	+	0.835615i	0.517354	+	0.855771i	$0.326917\pi$
$374$	−0.718814	−	1.24502i	−0.0371690	−	0.0643785i
$375$		0			0
$376$	5.51994	+	14.0646i	0.284669	+	0.725325i
$377$	−5.61773	+	24.6129i	−0.289328	+	1.26763i
$378$		0			0
$379$	−3.21589	−	14.0898i	−0.165189	−	0.723742i	−0.987876	−	0.155247i	$-0.950383\pi$
$379$	−3.21589	−	14.0898i	−0.165189	−	0.723742i	0.822686	−	0.568496i	$-0.192474\pi$
$380$	−1.33746	+	0.911864i	−0.0686102	+	0.0467777i
$381$		0			0
$382$	7.97821	+	1.20252i	0.408201	+	0.0615264i
$383$	−15.9543	−	14.8034i	−0.815224	−	0.756418i	0.157714	−	0.987485i	$-0.449588\pi$
$383$	−15.9543	−	14.8034i	−0.815224	−	0.756418i	−0.972938	+	0.231067i	$0.925778\pi$
$384$		0			0
$385$	−0.427235	−	4.46380i	−0.0217739	−	0.227496i
$386$	1.77974	−	2.23172i	0.0905862	−	0.113592i
$387$		0			0
$388$	0.0445516	+	0.0303748i	0.00226177	+	0.00154205i
$389$	−2.16278	+	5.51067i	−0.109657	+	0.279402i	−0.975160	−	0.221502i	$-0.928904\pi$
$389$	−2.16278	+	5.51067i	−0.109657	+	0.279402i	0.865503	+	0.500904i	$0.166999\pi$
$390$		0			0
$391$	−0.764325			−0.0386536
$392$	−17.2126	+	12.8059i	−0.869370	+	0.646797i
$393$		0			0
$394$	−0.988545	−	0.304926i	−0.0498022	−	0.0153619i
$395$	0.182430	−	0.464824i	0.00917905	−	0.0233878i
$396$		0			0
$397$	−30.7867	+	4.64035i	−1.54514	+	0.232892i	−0.865596	−	0.500742i	$-0.833060\pi$
$397$	−30.7867	+	4.64035i	−1.54514	+	0.232892i	−0.679544	+	0.733635i	$0.737822\pi$
$398$	1.17694	−	1.47583i	0.0589945	−	0.0739767i
$399$		0			0
$400$	8.03525	+	10.0759i	0.401763	+	0.503794i
$401$	−3.26789	−	3.03216i	−0.163191	−	0.151419i	0.594351	−	0.804206i	$-0.297409\pi$
$401$	−3.26789	−	3.03216i	−0.163191	−	0.151419i	−0.757541	+	0.652787i	$0.773600\pi$
$402$		0			0
$403$	−12.1838	+	11.3050i	−0.606921	+	0.563140i
$404$	−1.85219	+	1.26280i	−0.0921499	+	0.0628267i
$405$		0			0
$406$	20.9014	−	0.431060i	1.03732	−	0.0213932i
$407$	−4.35869	+	19.0967i	−0.216052	+	0.946587i
$408$		0			0
$409$	2.15951	+	28.8167i	0.106781	+	1.42489i	0.751125	+	0.660159i	$0.229511\pi$
$409$	2.15951	+	28.8167i	0.106781	+	1.42489i	−0.644344	+	0.764735i	$0.722870\pi$
$410$	1.26320	+	2.18793i	0.0623850	+	0.108054i
$411$		0			0
$412$	−2.40429	−	1.15784i	−0.118451	−	0.0570428i
$413$	26.8091	−	19.0996i	1.31919	−	0.939831i
$414$		0			0
$415$	−0.477308	+	6.36923i	−0.0234301	+	0.312653i
$416$	−10.5454	+	3.25283i	−0.517032	+	0.159483i
$417$		0			0
$418$	2.07118	−	27.6380i	0.101305	−	1.35182i
$419$	−4.22512	+	2.03471i	−0.206411	+	0.0994021i	−0.534233	−	0.845337i	$-0.679400\pi$
$419$	−4.22512	+	2.03471i	−0.206411	+	0.0994021i	0.327822	+	0.944739i	$0.393685\pi$
$420$		0			0
$421$	12.3161	+	5.93113i	0.600250	+	0.289065i	0.709228	−	0.704979i	$-0.249043\pi$
$421$	12.3161	+	5.93113i	0.600250	+	0.289065i	−0.108978	+	0.994044i	$0.534758\pi$
$422$	−4.53346	+	7.85219i	−0.220685	+	0.382238i
$423$		0			0
$424$	2.06476	+	27.5523i	0.100274	+	1.33806i
$425$	0.586457	+	1.49427i	0.0284474	+	0.0724827i
$426$		0			0
$427$	−4.89877	+	23.7059i	−0.237068	+	1.14721i
$428$	−1.17572	−	5.15115i	−0.0568304	−	0.248990i
$429$		0			0
$430$	−3.66541	+	3.40101i	−0.176762	+	0.164011i
$431$	17.3702	+	2.61814i	0.836695	+	0.126111i	0.553394	−	0.832920i	$-0.313332\pi$
$431$	17.3702	+	2.61814i	0.836695	+	0.126111i	0.283301	+	0.959031i	$0.408571\pi$
$432$		0			0
$433$	8.35451	+	10.4762i	0.401492	+	0.503455i	0.940945	−	0.338561i	$-0.109940\pi$
$433$	8.35451	+	10.4762i	0.401492	+	0.503455i	−0.539452	+	0.842016i	$0.681369\pi$
$434$	11.5294	+	7.51712i	0.553428	+	0.360833i
$435$		0			0
$436$	0.371926	−	0.0560588i	0.0178120	−	0.00268473i
$437$	−12.1747	−	8.30059i	−0.582397	−	0.397071i
$438$		0			0
$439$	20.4582	+	6.31051i	0.976415	+	0.301184i	0.741590	−	0.670854i	$-0.234072\pi$
$439$	20.4582	+	6.31051i	0.976415	+	0.301184i	0.234825	+	0.972038i	$0.424548\pi$
$440$	−5.19449			−0.247638
$441$		0			0
$442$	1.59782			0.0760007
$443$	4.06343	+	1.25340i	0.193059	+	0.0595509i	0.389777	−	0.920909i	$-0.372552\pi$
$443$	4.06343	+	1.25340i	0.193059	+	0.0595509i	−0.196718	+	0.980460i	$0.563028\pi$
$444$		0			0
$445$	0.753306	+	0.513596i	0.0357101	+	0.0243468i
$446$	−6.74494	+	1.01664i	−0.319382	+	0.0481391i
$447$		0			0
$448$	12.1399	+	20.0601i	0.573558	+	0.947749i
$449$	−22.8896	−	28.7026i	−1.08023	−	1.35456i	−0.930691	−	0.365805i	$-0.880794\pi$
$449$	−22.8896	−	28.7026i	−1.08023	−	1.35456i	−0.149535	−	0.988756i	$-0.547778\pi$
$450$		0			0
$451$	14.8421	+	2.23709i	0.698887	+	0.105340i
$452$	−2.07345	+	1.92388i	−0.0975268	+	0.0904917i
$453$		0			0
$454$	−2.53294	−	11.0975i	−0.118877	−	0.520832i
$455$	4.53395	+	2.06938i	0.212555	+	0.0970139i
$456$		0			0
$457$	−9.04556	−	23.0477i	−0.423133	−	1.07813i	−0.970472	−	0.241215i	$-0.922454\pi$
$457$	−9.04556	−	23.0477i	−0.423133	−	1.07813i	0.547338	−	0.836911i	$-0.315641\pi$
$458$	−1.73513	−	23.1537i	−0.0810772	−	1.08190i
$459$		0			0
$460$	−0.282851	+	0.489913i	−0.0131880	+	0.0228423i
$461$	−26.9651	−	12.9857i	−1.25589	−	0.604805i	−0.316806	−	0.948490i	$-0.602610\pi$
$461$	−26.9651	−	12.9857i	−1.25589	−	0.604805i	−0.939085	+	0.343685i	$0.888325\pi$
$462$		0			0
$463$	−6.14531	+	2.95943i	−0.285597	+	0.137536i	−0.571198	−	0.820812i	$-0.693521\pi$
$463$	−6.14531	+	2.95943i	−0.285597	+	0.137536i	0.285601	+	0.958349i	$0.407807\pi$
$464$	1.31042	−	17.4863i	0.0608346	−	0.811782i
$465$		0			0
$466$	−18.0144	+	5.55672i	−0.834503	+	0.257410i
$467$	0.363371	−	4.84885i	0.0168148	−	0.224378i	−0.982465	−	0.186445i	$-0.940303\pi$
$467$	0.363371	−	4.84885i	0.0168148	−	0.224378i	0.999280	−	0.0379334i	$-0.0120775\pi$
$468$		0			0
$469$	−11.9591	−	3.42049i	−0.552219	−	0.157943i
$470$	−2.61871	−	1.26110i	−0.120792	−	0.0581704i
$471$		0			0
$472$	−19.0655	−	33.0224i	−0.877559	−	1.51998i
$473$	2.22001	+	29.6240i	0.102076	+	1.36211i
$474$		0			0
$475$	−6.88628	+	30.1708i	−0.315964	+	1.38433i
$476$	0.111373	+	0.445413i	0.00510477	+	0.0204155i
$477$		0			0
$478$	−9.39179	+	6.40321i	−0.429570	+	0.292876i
$479$	−24.8770	+	23.0825i	−1.13666	+	1.05467i	−0.138731	+	0.990330i	$0.544302\pi$
$479$	−24.8770	+	23.0825i	−1.13666	+	1.05467i	−0.997928	+	0.0643360i	$0.979507\pi$
$480$		0			0
$481$	−15.9589	−	14.8077i	−0.727662	−	0.675172i
$482$	−11.2422	−	14.0972i	−0.512067	−	0.642112i
$483$		0			0
$484$	−0.407918	+	0.511513i	−0.0185417	+	0.0232506i
$485$	−0.0500735	+	0.00754737i	−0.00227372	+	0.000342708i
$486$		0			0
$487$	−2.82654	+	7.20192i	−0.128083	+	0.326350i	−0.980502	−	0.196509i	$-0.937039\pi$
$487$	−2.82654	+	7.20192i	−0.128083	+	0.326350i	0.852419	+	0.522859i	$0.175135\pi$
$488$	26.7953	+	8.26526i	1.21297	+	0.374151i
$489$		0			0
$490$	0.751696	−	4.05808i	0.0339582	−	0.183325i
$491$	−7.86421			−0.354907			−0.177453	−	0.984129i	$-0.556786\pi$
$491$	−7.86421			−0.354907			−0.177453	+	0.984129i	$0.556786\pi$
$492$		0			0
$493$	0.797959	−	2.03317i	0.0359383	−	0.0915693i
$494$	25.4513	+	17.3524i	1.14511	+	0.780721i
$495$		0			0
$496$	7.19786	−	9.02583i	0.323194	−	0.405272i
$497$	−13.0999	+	35.5143i	−0.587610	+	1.59303i
$498$		0			0
$499$	−3.50221	−	3.24957i	−0.156780	−	0.145471i	0.597882	−	0.801584i	$-0.296009\pi$
$499$	−3.50221	−	3.24957i	−0.156780	−	0.145471i	−0.754663	+	0.656113i	$0.772199\pi$
$500$	2.40734	+	0.362849i	0.107660	+	0.0162271i
$501$		0			0
$502$	10.6539	−	7.26368i	0.475505	−	0.324194i
$503$	−0.922903	−	4.04350i	−0.0411502	−	0.180291i	0.950176	−	0.311713i	$-0.100903\pi$
$503$	−0.922903	−	4.04350i	−0.0411502	−	0.180291i	−0.991326	+	0.131422i	$0.958046\pi$
$504$		0			0
$505$	0.468467	−	2.05249i	0.0208465	−	0.0913345i
$506$	−3.53862	−	9.01625i	−0.157311	−	0.400821i
$507$		0			0
$508$	−1.13916	−	1.97309i	−0.0505422	−	0.0875417i
$509$	−8.55705	+	14.8213i	−0.379285	+	0.656940i	−0.990958	−	0.134170i	$-0.957163\pi$
$509$	−8.55705	+	14.8213i	−0.379285	+	0.656940i	0.611674	+	0.791110i	$0.290497\pi$
$510$		0			0
$511$	10.3119	−	18.7428i	0.456170	−	0.829134i
$512$	21.8400	−	10.5176i	0.965202	−	0.464817i
$513$		0			0
$514$	1.06409	−	0.328227i	0.0469348	−	0.0144775i
$515$	2.39480	−	0.738697i	0.105527	−	0.0325509i
$516$		0			0
$517$	−15.5582	+	7.49242i	−0.684248	+	0.329516i
$518$	−8.69014	+	15.7952i	−0.381823	+	0.694001i
$519$		0			0
$520$	2.88666	−	4.99984i	0.126588	−	0.219257i
$521$	17.5214	+	30.3479i	0.767625	+	1.32957i	0.938847	+	0.344334i	$0.111895\pi$
$521$	17.5214	+	30.3479i	0.767625	+	1.32957i	−0.171222	+	0.985232i	$0.554772\pi$
$522$		0			0
$523$	−0.0195189	−	0.0497334i	−0.000853502	−	0.00217469i	0.930446	−	0.366428i	$-0.119419\pi$
$523$	−0.0195189	−	0.0497334i	−0.000853502	−	0.00217469i	−0.931300	+	0.364253i	$0.881324\pi$
$524$	1.78801	−	7.83379i	0.0781096	−	0.342221i
$525$		0			0
$526$	2.81679	+	12.3412i	0.122818	+	0.538101i
$527$	1.18809	−	0.810023i	0.0517538	−	0.0352852i
$528$		0			0
$529$	17.6511	+	2.66048i	0.767439	+	0.115673i
$530$	−3.89628	−	3.61522i	−0.169244	−	0.157035i
$531$		0			0
$532$	−3.06317	+	8.30438i	−0.132805	+	0.360040i
$533$	−10.4012	+	13.0427i	−0.450528	+	0.564944i
$534$		0			0
$535$	4.09983	+	2.79521i	0.177251	+	0.120848i
$536$	−5.26415	+	13.4128i	−0.227377	+	0.579346i
$537$		0			0
$538$	−0.494110			−0.0213026
$539$	−16.0653	−	18.5238i	−0.691980	−	0.797876i
$540$		0			0
$541$	−18.3452	−	5.65875i	−0.788723	−	0.243289i	−0.125878	−	0.992046i	$-0.540175\pi$
$541$	−18.3452	−	5.65875i	−0.788723	−	0.243289i	−0.662845	+	0.748757i	$0.730651\pi$
$542$	−6.97848	+	17.7809i	−0.299751	+	0.763754i
$543$		0			0
$544$	0.944094	−	0.142299i	0.0404777	−	0.00610103i
$545$	−0.220238	+	0.276169i	−0.00943395	+	0.0118298i
$546$		0			0
$547$	6.65592	+	8.34625i	0.284586	+	0.356860i	0.903492	−	0.428606i	$-0.140995\pi$
$547$	6.65592	+	8.34625i	0.284586	+	0.356860i	−0.618905	+	0.785466i	$0.712424\pi$
$548$	4.42747	+	4.10809i	0.189132	+	0.175489i
$549$		0			0
$550$	−14.9118	+	13.8361i	−0.635841	+	0.589974i
$551$	34.7907	−	23.7199i	1.48213	−	1.01050i
$552$		0			0
$553$	−0.662335	−	2.64888i	−0.0281654	−	0.112642i
$554$	3.40315	−	14.9102i	0.144586	−	0.633472i
$555$		0			0
$556$	0.337012	+	4.49711i	0.0142925	+	0.190720i
$557$	−8.96714	−	15.5315i	−0.379950	−	0.658093i	0.611105	−	0.791550i	$-0.290725\pi$
$557$	−8.96714	−	15.5315i	−0.379950	−	0.658093i	−0.991055	+	0.133457i	$0.957392\pi$
$558$		0			0
$559$	−29.7476	−	14.3257i	−1.25819	−	0.605912i
$560$	−3.32826	−	0.951937i	−0.140645	−	0.0402267i
$561$		0			0
$562$	−0.225445	+	3.00836i	−0.00950983	+	0.126900i
$563$	8.12445	−	2.50606i	0.342405	−	0.105618i	−0.118783	−	0.992920i	$-0.537899\pi$
$563$	8.12445	−	2.50606i	0.342405	−	0.105618i	0.461188	+	0.887302i	$0.347423\pi$
$564$		0			0
$565$	0.198510	−	2.64893i	0.00835138	−	0.111441i
$566$	24.8188	−	11.9521i	1.04321	−	0.502385i
$567$		0			0
$568$	39.5067	+	19.0254i	1.65767	+	0.798290i
$569$	20.6457	−	35.7595i	0.865514	−	1.49911i	−0.00102143	−	0.999999i	$-0.500325\pi$
$569$	20.6457	−	35.7595i	0.865514	−	1.49911i	0.866536	−	0.499115i	$-0.166342\pi$
$570$		0			0
$571$	−1.26106	−	16.8276i	−0.0527736	−	0.704215i	−0.959358	−	0.282191i	$-0.908939\pi$
$571$	−1.26106	−	16.8276i	−0.0527736	−	0.704215i	0.906585	−	0.422024i	$-0.138680\pi$
$572$	−2.56690	−	6.54035i	−0.107327	−	0.273466i
$573$		0			0
$574$	12.5674	+	5.73597i	0.524551	+	0.239415i
$575$	2.40657	+	10.5439i	0.100361	+	0.439709i
$576$		0			0
$577$	−7.84027	+	7.27471i	−0.326395	+	0.302850i	−0.826300	−	0.563230i	$-0.809559\pi$
$577$	−7.84027	+	7.27471i	−0.326395	+	0.302850i	0.499905	+	0.866080i	$0.333368\pi$
$578$	20.3467	+	3.06678i	0.846313	+	0.127561i
$579$		0			0
$580$	−1.00791	−	1.26388i	−0.0418512	−	0.0524797i
$581$	18.0824	+	29.8794i	0.750184	+	1.23961i
$582$		0			0
$583$	−31.2255	+	4.70648i	−1.29323	+	0.194923i
$584$	−20.4748	−	13.9595i	−0.847254	−	0.577648i
$585$		0			0
$586$	−17.2466	−	5.31987i	−0.712450	−	0.219762i
$587$	−47.8313			−1.97421			−0.987105	−	0.160072i	$-0.948828\pi$
$587$	−47.8313			−1.97421			−0.987105	+	0.160072i	$0.948828\pi$
$588$		0			0
$589$	27.7216			1.14225
$590$	7.00943	+	2.16212i	0.288574	+	0.0890132i
$591$		0			0
$592$	12.4939	+	8.51819i	0.513496	+	0.350095i
$593$	−12.7059	+	1.91510i	−0.521768	+	0.0786439i	−0.404646	−	0.914474i	$-0.632605\pi$
$593$	−12.7059	+	1.91510i	−0.521768	+	0.0786439i	−0.117123	+	0.993117i	$0.537367\pi$
$594$		0			0
$595$	−0.361191	−	0.235496i	−0.0148074	−	0.00965439i
$596$	−1.73219	−	2.17210i	−0.0709534	−	0.0889728i
$597$		0			0
$598$	10.6448	+	1.60445i	0.435300	+	0.0656110i
$599$	28.5281	−	26.4702i	1.16563	−	1.08154i	0.170259	−	0.985399i	$-0.445539\pi$
$599$	28.5281	−	26.4702i	1.16563	−	1.08154i	0.995367	−	0.0961443i	$-0.0306510\pi$
$600$		0			0
$601$	−7.47487	−	32.7496i	−0.304907	−	1.33588i	−0.862621	−	0.505850i	$-0.831179\pi$
$601$	−7.47487	−	32.7496i	−0.304907	−	1.33588i	0.557715	−	0.830033i	$-0.311678\pi$
$602$	−5.53312	+	26.7757i	−0.225513	+	1.09130i
$603$		0			0
$604$	−0.213196	−	0.543215i	−0.00867482	−	0.0221031i
$605$	−0.0459163	−	0.612710i	−0.00186676	−	0.0249102i
$606$		0			0
$607$	15.3229	−	26.5400i	0.621937	−	1.07723i	−0.367187	−	0.930147i	$-0.619679\pi$
$607$	15.3229	−	26.5400i	0.621937	−	1.07723i	0.989125	−	0.147080i	$-0.0469874\pi$
$608$	16.5836	+	7.98624i	0.672553	+	0.323885i
$609$		0			0
$610$	−4.86011	+	2.34051i	−0.196780	+	0.0947644i
$611$	1.43426	−	19.1388i	0.0580238	−	0.774274i
$612$		0			0
$613$	5.40164	−	1.66619i	0.218170	−	0.0672966i	−0.183743	−	0.982974i	$-0.558821\pi$
$613$	5.40164	−	1.66619i	0.218170	−	0.0672966i	0.401913	+	0.915678i	$0.368345\pi$
$614$	2.17036	−	28.9614i	0.0875884	−	1.16879i
$615$		0			0
$616$	−23.1334	+	16.4809i	−0.932070	+	0.664034i
$617$	27.0291	+	13.0165i	1.08815	+	0.524026i	0.889914	−	0.456128i	$-0.150764\pi$
$617$	27.0291	+	13.0165i	1.08815	+	0.524026i	0.198237	+	0.980154i	$0.436479\pi$
$618$		0			0
$619$	7.37348	+	12.7712i	0.296365	+	0.513319i	0.975302	−	0.220878i	$-0.0708921\pi$
$619$	7.37348	+	12.7712i	0.296365	+	0.513319i	−0.678936	+	0.734197i	$0.737559\pi$
$620$	−0.0795331	−	1.06130i	−0.00319412	−	0.0426226i
$621$		0			0
$622$	−3.32856	+	14.5834i	−0.133463	+	0.584739i
$623$	4.98433	−	0.102794i	0.199693	−	0.00411836i
$624$		0			0
$625$	17.7997	−	12.1356i	0.711988	−	0.485425i
$626$	−11.0100	+	10.2158i	−0.440047	+	0.408304i
$627$		0			0
$628$	−7.68399	−	7.12970i	−0.306625	−	0.284506i
$629$	1.17433	+	1.47256i	0.0468235	+	0.0587149i
$630$		0			0
$631$	4.85334	−	6.08590i	0.193209	−	0.242276i	−0.675786	−	0.737098i	$-0.736195\pi$
$631$	4.85334	−	6.08590i	0.193209	−	0.242276i	0.868994	+	0.494822i	$0.164767\pi$
$632$	−3.12759	+	0.471409i	−0.124409	+	0.0187516i
$633$		0			0
$634$	13.8509	−	35.2915i	0.550089	−	1.40160i
$635$	2.04460	+	0.630675i	0.0811374	+	0.0250276i
$636$		0			0
$637$	26.7574	−	5.16930i	1.06016	−	0.204815i
$638$	27.6783			1.09579
$639$		0			0
$640$	−0.906772	+	2.31042i	−0.0358433	+	0.0913273i
$641$	−1.71913	−	1.17208i	−0.0679015	−	0.0462945i	0.528894	−	0.848688i	$-0.322607\pi$
$641$	−1.71913	−	1.17208i	−0.0679015	−	0.0462945i	−0.596795	+	0.802394i	$0.703559\pi$
$642$		0			0
$643$	−3.39064	+	4.25173i	−0.133714	+	0.167672i	−0.844181	−	0.536059i	$-0.819912\pi$
$643$	−3.39064	+	4.25173i	−0.133714	+	0.167672i	0.710467	+	0.703731i	$0.248484\pi$
$644$	0.294715	+	3.07922i	0.0116134	+	0.121338i
$645$		0			0
$646$	−1.95358	−	1.81266i	−0.0768626	−	0.0713181i
$647$	35.3311	+	5.32530i	1.38901	+	0.209359i	0.800597	−	0.599203i	$-0.204516\pi$
$647$	35.3311	+	5.32530i	1.38901	+	0.209359i	0.588410	+	0.808563i	$0.299754\pi$
$648$		0			0
$649$	36.0077	−	24.5497i	1.41343	−	0.963659i
$650$	−5.03093	−	22.0419i	−0.197329	−	0.864556i
$651$		0			0
$652$	−0.721862	+	3.16268i	−0.0282703	+	0.123860i
$653$	−15.9219	−	40.5683i	−0.623071	−	1.58756i	−0.797787	−	0.602940i	$-0.793996\pi$
$653$	−15.9219	−	40.5683i	−0.623071	−	1.58756i	0.174716	−	0.984619i	$-0.444099\pi$
$654$		0			0
$655$	3.77309	+	6.53519i	0.147427	+	0.255351i
$656$	5.79362	−	10.0349i	0.226203	−	0.391795i
$657$		0			0
$658$	−15.6635	+	2.69229i	−0.610625	+	0.104956i
$659$	35.2017	−	16.9523i	1.37127	−	0.660366i	0.404147	−	0.914694i	$-0.367568\pi$
$659$	35.2017	−	16.9523i	1.37127	−	0.660366i	0.967118	+	0.254328i	$0.0818542\pi$
$660$		0			0
$661$	−12.9097	+	3.98211i	−0.502129	+	0.154886i	−0.535464	−	0.844558i	$-0.679863\pi$
$661$	−12.9097	+	3.98211i	−0.502129	+	0.154886i	0.0333354	+	0.999444i	$0.489387\pi$
$662$	11.2654	−	3.47491i	0.437841	−	0.135056i
$663$		0			0
$664$	36.4505	−	17.5536i	1.41455	−	0.681213i
$665$	−3.19583	−	7.67370i	−0.123929	−	0.297573i
$666$		0			0
$667$	7.35769	−	12.7439i	0.284891	−	0.493445i
$668$	−3.82928	−	6.63251i	−0.148159	−	0.256620i
$669$		0			0
$670$	−1.01267	−	2.58025i	−0.0391230	−	0.0996838i
$671$	−7.13147	+	31.2450i	−0.275307	+	1.20620i
$672$		0			0
$673$	−3.22835	−	14.1443i	−0.124444	−	0.545225i	−0.998260	−	0.0589677i	$-0.981219\pi$
$673$	−3.22835	−	14.1443i	−0.124444	−	0.545225i	0.873816	−	0.486257i	$-0.161638\pi$
$674$	−32.0235	+	21.8332i	−1.23350	+	0.840985i
$675$		0			0
$676$	1.09874	+	0.165609i	0.0422594	+	0.00636958i
$677$	29.7279	+	27.5834i	1.14254	+	1.06012i	0.997498	+	0.0706918i	$0.0225207\pi$
$677$	29.7279	+	27.5834i	1.14254	+	1.06012i	0.145037	+	0.989426i	$0.453670\pi$
$678$		0			0
$679$	−0.199054	+	0.192483i	−0.00763898	+	0.00738683i
$680$	−0.311421	+	0.390509i	−0.0119424	+	0.0149753i
$681$		0			0
$682$	15.0558	+	10.2649i	0.576518	+	0.393063i
$683$	1.28225	−	3.26713i	0.0490641	−	0.125013i	−0.904241	−	0.427023i	$-0.859562\pi$
$683$	1.28225	−	3.26713i	0.0490641	−	0.125013i	0.953305	+	0.302010i	$0.0976576\pi$
$684$		0			0
$685$	−5.67217			−0.216722
$686$	−9.52769	−	20.4574i	−0.363769	−	0.781066i
$687$		0			0
$688$	21.9144	+	6.75971i	0.835480	+	0.257712i
$689$	12.8224	−	32.6708i	0.488493	−	1.24466i
$690$		0			0
$691$	27.8663	−	4.20016i	1.06008	−	0.159782i	0.404220	−	0.914662i	$-0.367543\pi$
$691$	27.8663	−	4.20016i	1.06008	−	0.159782i	0.655863	+	0.754880i	$0.272305\pi$
$692$	−1.52806	+	1.91613i	−0.0580882	+	0.0728403i
$693$		0			0
$694$	−19.7119	−	24.7180i	−0.748255	−	0.938282i
$695$	−3.10465	−	2.88069i	−0.117766	−	0.109271i
$696$		0			0
$697$	1.05799	−	0.981675i	0.0400744	−	0.0371836i
$698$	22.7559	−	15.5147i	0.861322	−	0.587240i
$699$		0			0
$700$	5.79380	−	2.93882i	0.218985	−	0.111077i
$701$	−3.42531	+	15.0073i	−0.129372	+	0.566817i	0.868140	+	0.496320i	$0.165316\pi$
$701$	−3.42531	+	15.0073i	−0.129372	+	0.566817i	−0.997512	+	0.0704971i	$0.977541\pi$
$702$		0			0
$703$	2.71351	+	36.2093i	0.102342	+	1.36566i
$704$	15.5216	+	26.8842i	0.584993	+	1.01324i
$705$		0			0
$706$	−18.7393	−	9.02435i	−0.705261	−	0.339636i
$707$	−4.42577	−	10.6270i	−0.166448	−	0.399668i
$708$		0			0
$709$	1.88110	−	25.1016i	0.0706463	−	0.942709i	−0.843449	−	0.537209i	$-0.819479\pi$
$709$	1.88110	−	25.1016i	0.0706463	−	0.942709i	0.914095	−	0.405499i	$-0.132902\pi$
$710$	−8.06059	+	2.48636i	−0.302508	+	0.0933115i
$711$		0			0
$712$	0.431571	−	5.75891i	0.0161738	−	0.215824i
$713$	8.72853	−	4.20344i	0.326886	−	0.157420i
$714$		0			0
$715$	5.94495	+	2.86294i	0.222328	+	0.107068i
$716$	−5.77593	+	10.0042i	−0.215857	+	0.373875i
$717$		0			0
$718$	0.269602	+	3.59759i	0.0100615	+	0.134261i
$719$	6.59793	+	16.8112i	0.246061	+	0.626954i	0.999534	−	0.0305254i	$-0.00971804\pi$
$719$	6.59793	+	16.8112i	0.246061	+	0.626954i	−0.753473	+	0.657479i	$0.771623\pi$
$720$		0			0
$721$	8.32138	−	10.8879i	0.309904	−	0.405485i
$722$	−6.28079	−	27.5179i	−0.233747	−	1.02411i
$723$		0			0
$724$	6.05217	−	5.61559i	0.224927	−	0.208702i
$725$	−30.5600	−	4.60618i	−1.13497	−	0.171069i
$726$		0			0
$727$	15.8416	+	19.8647i	0.587531	+	0.736740i	0.983377	−	0.181577i	$-0.0581201\pi$
$727$	15.8416	+	19.8647i	0.587531	+	0.736740i	−0.395846	+	0.918317i	$0.629549\pi$
$728$	−3.00774	−	31.4252i	−0.111474	−	1.16469i
$729$		0			0
$730$	4.71387	−	0.710502i	0.174468	−	0.0262969i
$731$	2.36015	+	1.60913i	0.0872934	+	0.0595157i
$732$		0			0
$733$	35.7234	+	11.0192i	1.31947	+	0.407004i	0.872968	−	0.487777i	$-0.162192\pi$
$733$	35.7234	+	11.0192i	1.31947	+	0.407004i	0.446505	+	0.894781i	$0.352668\pi$
$734$	−39.1409			−1.44472
$735$		0			0
$736$	6.43253			0.237106
$737$	−15.7364	−	4.85405i	−0.579659	−	0.178801i
$738$		0			0
$739$	−5.03505	−	3.43284i	−0.185217	−	0.126279i	0.467162	−	0.884172i	$-0.345277\pi$
$739$	−5.03505	−	3.43284i	−0.185217	−	0.126279i	−0.652379	+	0.757893i	$0.726229\pi$
$740$	1.37845	−	0.207768i	0.0506730	−	0.00763772i
$741$		0			0
$742$	−28.8221	−	3.73820i	−1.05809	−	0.137234i
$743$	29.4648	+	36.9477i	1.08096	+	1.35548i	0.930261	+	0.366899i	$0.119581\pi$
$743$	29.4648	+	36.9477i	1.08096	+	1.35548i	0.150698	+	0.988580i	$0.451848\pi$
$744$		0			0
$745$	2.57999	+	0.388870i	0.0945233	+	0.0142471i
$746$	−16.6455	+	15.4448i	−0.609435	+	0.565473i
$747$		0			0
$748$	0.135261	+	0.592619i	0.00494564	+	0.0216683i
$749$	27.1269	−	0.559451i	0.991195	−	0.0204419i
$750$		0			0
$751$	10.0770	+	25.6758i	0.367715	+	0.936923i	0.988264	+	0.152755i	$0.0488147\pi$
$751$	10.0770	+	25.6758i	0.367715	+	0.936923i	−0.620549	+	0.784168i	$0.713090\pi$
$752$	0.996211	+	13.2935i	0.0363281	+	0.484765i
$753$		0			0
$754$	−15.3812	+	26.6411i	−0.560152	+	0.970212i
$755$	0.493763	+	0.237784i	0.0179699	+	0.00865384i
$756$		0			0
$757$	−20.5176	+	9.88077i	−0.745726	+	0.359123i	−0.767848	−	0.640633i	$-0.778672\pi$
$757$	−20.5176	+	9.88077i	−0.745726	+	0.359123i	0.0221216	+	0.999755i	$0.492958\pi$
$758$	1.31601	−	17.5609i	0.0477995	−	0.637841i
$759$		0			0
$760$	−9.20147	+	2.83828i	−0.333773	+	0.102955i
$761$	3.97581	−	53.0534i	0.144123	−	1.92319i	−0.192050	−	0.981385i	$-0.561513\pi$
$761$	3.97581	−	53.0534i	0.144123	−	1.92319i	0.336172	−	0.941800i	$-0.390868\pi$
$762$		0			0
$763$	−0.104596	+	1.92867i	−0.00378664	+	0.0698224i
$764$	−3.07362	−	1.48018i	−0.111200	−	0.0535509i
$765$		0			0
$766$	−13.2600	−	22.9670i	−0.479103	−	0.829831i
$767$	3.61966	+	48.3011i	0.130698	+	1.74405i
$768$		0			0
$769$	−6.46382	+	28.3198i	−0.233091	+	1.02124i	0.713968	+	0.700179i	$0.246896\pi$
$769$	−6.46382	+	28.3198i	−0.233091	+	1.02124i	−0.947059	+	0.321060i	$0.895961\pi$
$770$	1.10577	−	5.35102i	0.0398493	−	0.192837i
$771$		0			0
$772$	−0.997214	+	0.679889i	−0.0358905	+	0.0244698i
$773$	6.53636	−	6.06486i	0.235097	−	0.218138i	−0.553823	−	0.832635i	$-0.686831\pi$
$773$	6.53636	−	6.06486i	0.235097	−	0.218138i	0.788919	+	0.614497i	$0.210641\pi$
$774$		0			0
$775$	−14.9151	−	13.8392i	−0.535766	−	0.497118i
$776$	0.199989	+	0.250778i	0.00717918	+	0.00900241i
$777$		0			0
$778$	−4.49753	+	5.63973i	−0.161244	+	0.202194i
$779$	27.5135	−	4.14699i	0.985774	−	0.148581i
$780$		0			0
$781$	−18.3093	+	46.6514i	−0.655160	+	1.66932i
$782$	−0.889967	−	0.274518i	−0.0318252	−	0.00981676i
$783$		0			0
$784$	−17.8425	+	6.32039i	−0.637232	+	0.225728i
$785$	9.84420			0.351355
$786$		0			0
$787$	6.30813	−	16.0729i	0.224861	−	0.572936i	−0.773268	−	0.634079i	$-0.781379\pi$
$787$	6.30813	−	16.0729i	0.224861	−	0.572936i	0.998129	+	0.0611433i	$0.0194747\pi$
$788$	0.361405	+	0.246402i	0.0128745	+	0.00877771i
$789$		0			0
$790$	0.379367	−	0.475711i	0.0134973	−	0.0169250i
$791$	−7.52038	−	12.4267i	−0.267394	−	0.441842i
$792$		0			0
$793$	−26.1111	−	24.2276i	−0.927232	−	0.860346i
$794$	−37.5141	−	5.65435i	−1.33133	−	0.200665i
$795$		0			0
$796$	−0.659456	+	0.449609i	−0.0233738	+	0.0159360i
$797$	0.752292	+	3.29601i	0.0266476	+	0.116751i	0.986502	−	0.163746i	$-0.0523579\pi$
$797$	0.752292	+	3.29601i	0.0266476	+	0.116751i	−0.959855	+	0.280497i	$0.909501\pi$
$798$		0			0
$799$	−0.369483	+	1.61881i	−0.0130714	+	0.0572694i
$800$	−4.93560	−	12.5757i	−0.174500	−	0.444619i
$801$		0			0
$802$	−2.71603	−	4.70430i	−0.0959064	−	0.166115i
$803$	14.1611	−	24.5278i	0.499735	−	0.865566i
$804$		0			0
$805$	−2.16982	−	1.93159i	−0.0764761	−	0.0680795i
$806$	−18.2470	+	8.78729i	−0.642723	+	0.309519i
$807$		0			0
$808$	−12.7427	+	3.93061i	−0.448287	+	0.138278i
$809$	−11.7089	+	3.61171i	−0.411662	+	0.126981i	−0.493667	−	0.869651i	$-0.664344\pi$
$809$	−11.7089	+	3.61171i	−0.411662	+	0.126981i	0.0820050	+	0.996632i	$0.473868\pi$
$810$		0			0
$811$	−3.22236	+	1.55181i	−0.113152	+	0.0544913i	−0.489604	−	0.871945i	$-0.662859\pi$
$811$	−3.22236	+	1.55181i	−0.113152	+	0.0544913i	0.376451	+	0.926436i	$0.377144\pi$
$812$	−8.49866	−	2.43075i	−0.298244	−	0.0853027i
$813$		0			0
$814$	−11.9340	+	20.6703i	−0.418287	+	0.724495i
$815$	−1.52329	−	2.63841i	−0.0533584	−	0.0924194i
$816$		0			0
$817$	20.1191	+	51.2627i	0.703879	+	1.79345i
$818$	−7.83544	+	34.3293i	−0.273960	+	1.20030i
$819$		0			0
$820$	−0.237700	−	1.04143i	−0.00830084	−	0.0363684i
$821$	−26.7879	+	18.2636i	−0.934903	+	0.637406i	−0.931949	−	0.362590i	$-0.881893\pi$
$821$	−26.7879	+	18.2636i	−0.934903	+	0.637406i	−0.00295371	+	0.999996i	$0.500940\pi$
$822$		0			0
$823$	−25.5125	−	3.84539i	−0.889310	−	0.134042i	−0.311532	−	0.950236i	$-0.600842\pi$
$823$	−25.5125	−	3.84539i	−0.889310	−	0.134042i	−0.577778	+	0.816194i	$0.696080\pi$
$824$	−11.6367	−	10.7973i	−0.405384	−	0.376141i
$825$		0			0
$826$	38.0760	−	12.6104i	1.32483	−	0.438771i
$827$	−5.37221	+	6.73653i	−0.186810	+	0.234252i	−0.866413	−	0.499328i	$-0.833580\pi$
$827$	−5.37221	+	6.73653i	−0.186810	+	0.234252i	0.679603	+	0.733580i	$0.262152\pi$
$828$		0			0
$829$	−35.9939	−	24.5402i	−1.25012	−	0.852318i	−0.256661	−	0.966502i	$-0.582622\pi$
$829$	−35.9939	−	24.5402i	−1.25012	−	0.852318i	−0.993460	+	0.114184i	$0.963575\pi$
$830$	−2.84337	+	7.24478i	−0.0986948	+	0.251470i
$831$		0			0
$832$	−34.5024			−1.19616
$833$	−2.35572	+	0.0972075i	−0.0816208	+	0.00336804i
$834$		0			0
$835$	6.87289	+	2.12001i	0.237846	+	0.0733658i
$836$	−4.28131	+	10.9086i	−0.148072	+	0.377282i
$837$		0			0
$838$	−5.65045	+	0.851668i	−0.195192	+	0.0294204i
$839$	26.0318	−	32.6429i	0.898719	−	1.12696i	−0.0926298	−	0.995701i	$-0.529527\pi$
$839$	26.0318	−	32.6429i	0.898719	−	1.12696i	0.991348	−	0.131257i	$-0.0419013\pi$
$840$		0			0
$841$	8.13710	+	10.2036i	0.280590	+	0.351848i
$842$	12.2104	+	11.3296i	0.420799	+	0.390444i
$843$		0			0
$844$	2.81029	−	2.60757i	0.0967341	−	0.0897562i
$845$	−0.862201	+	0.587839i	−0.0296606	+	0.0202223i
$846$		0			0
$847$	−2.14847	−	2.58299i	−0.0738223	−	0.0887526i
$848$	−5.42457	+	23.7666i	−0.186280	+	0.816148i
$849$		0			0
$850$	0.146172	+	1.95054i	0.00501367	+	0.0669028i
$851$	6.34482	+	10.9895i	0.217498	+	0.376717i
$852$		0			0
$853$	51.3099	+	24.7095i	1.75682	+	0.846039i	0.974896	+	0.222663i	$0.0714749\pi$
$853$	51.3099	+	24.7095i	1.75682	+	0.846039i	0.781922	+	0.623376i	$0.214239\pi$
$854$	−14.2184	+	25.8433i	−0.486542	+	0.884340i
$855$		0			0
$856$	2.34880	−	31.3425i	0.0802803	−	1.07127i
$857$	−20.5900	+	6.35118i	−0.703341	+	0.216952i	−0.625739	−	0.780032i	$-0.715203\pi$
$857$	−20.5900	+	6.35118i	−0.703341	+	0.216952i	−0.0776021	+	0.996984i	$0.524726\pi$
$858$		0			0
$859$	0.645342	−	8.61149i	0.0220188	−	0.293820i	−0.975313	−	0.220825i	$-0.929125\pi$
$859$	0.645342	−	8.61149i	0.0220188	−	0.293820i	0.997332	−	0.0729954i	$-0.0232558\pi$
$860$	1.90482	−	0.917314i	0.0649539	−	0.0312802i
$861$		0			0
$862$	19.2853	+	9.28729i	0.656858	+	0.316326i
$863$	−4.07461	+	7.05743i	−0.138701	+	0.240238i	−0.927005	−	0.375048i	$-0.877626\pi$
$863$	−4.07461	+	7.05743i	−0.138701	+	0.240238i	0.788304	+	0.615286i	$0.210959\pi$
$864$		0			0
$865$	−0.172003	−	2.29522i	−0.00584827	−	0.0780397i
$866$	5.96516	+	15.1990i	0.202704	+	0.516482i
$867$		0			0
$868$	−3.72143	−	4.47408i	−0.126314	−	0.151860i
$869$	−0.804400	−	3.52431i	−0.0272874	−	0.119554i
$870$		0			0
$871$	13.4171	−	12.4493i	0.454622	−	0.421828i
$872$	2.21246	+	0.333474i	0.0749233	+	0.0112929i
$873$		0			0
$874$	−11.1948	−	14.0378i	−0.378669	−	0.474836i
$875$	−4.32654	+	11.7294i	−0.146264	+	0.396527i
$876$		0			0
$877$	17.2811	−	2.60470i	0.583540	−	0.0879545i	0.149364	−	0.988782i	$-0.452278\pi$
$877$	17.2811	−	2.60470i	0.583540	−	0.0879545i	0.434177	+	0.900828i	$0.357039\pi$
$878$	21.5546	+	14.6957i	0.727433	+	0.495955i
$879$		0			0
$880$	−4.37952	−	1.35090i	−0.147634	−	0.0455389i
$881$	6.01851			0.202769			0.101384	−	0.994847i	$-0.467673\pi$
$881$	6.01851			0.202769			0.101384	+	0.994847i	$0.467673\pi$
$882$		0			0
$883$	0.267947			0.00901712			0.00450856	−	0.999990i	$-0.498565\pi$
$883$	0.267947			0.00901712			0.00450856	+	0.999990i	$0.498565\pi$
$884$	−0.645578	−	0.199134i	−0.0217131	−	0.00669762i
$885$		0			0
$886$	4.28120	+	2.91888i	0.143830	+	0.0980615i
$887$	−4.39966	+	0.663141i	−0.147726	+	0.0222661i	−0.222489	−	0.974935i	$-0.571418\pi$
$887$	−4.39966	+	0.663141i	−0.147726	+	0.0222661i	0.0747629	+	0.997201i	$0.476180\pi$
$888$		0			0
$889$	11.1065	−	3.67835i	0.372500	−	0.123368i
$890$	0.692671	+	0.868582i	0.0232184	+	0.0291150i
$891$		0			0
$892$	2.85190	+	0.429855i	0.0954888	+	0.0143926i
$893$	−23.4657	+	21.7730i	−0.785251	+	0.728606i
$894$		0			0
$895$	−2.41408	−	10.5768i	−0.0806937	−	0.353542i
$896$	3.29215	+	13.1663i	0.109983	+	0.439855i
$897$		0			0
$898$	−16.3433	−	41.6420i	−0.545382	−	1.38961i
$899$	2.06886	+	27.6070i	0.0690003	+	0.920745i
$900$		0			0
$901$	−1.51821	+	2.62962i	−0.0505789	+	0.0876053i
$902$	16.4784	+	7.93558i	0.548671	+	0.264226i
$903$		0			0
$904$	−15.1596	+	7.30047i	−0.504200	+	0.242810i
$905$	−0.579428	+	7.73194i	−0.0192609	+	0.257018i
$906$		0			0
$907$	−15.0937	+	4.65581i	−0.501180	+	0.154593i	−0.535029	−	0.844833i	$-0.679699\pi$
$907$	−15.0937	+	4.65581i	−0.501180	+	0.154593i	0.0338496	+	0.999427i	$0.489223\pi$
$908$	−0.359671	+	4.79948i	−0.0119361	+	0.159276i
$909$		0			0
$910$	4.53601	+	4.03798i	0.150367	+	0.133858i
$911$	11.2611	+	5.42304i	0.373095	+	0.179673i	0.611029	−	0.791608i	$-0.290756\pi$
$911$	11.2611	+	5.42304i	0.373095	+	0.179673i	−0.237934	+	0.971281i	$0.576470\pi$
$912$		0			0
$913$	23.1194	+	40.0439i	0.765140	+	1.32526i
$914$	−2.25457	−	30.0852i	−0.0745746	−	0.995129i
$915$		0			0
$916$	−2.18456	+	9.57117i	−0.0721798	+	0.316240i
$917$	37.5379	+	17.1330i	1.23961	+	0.565780i
$918$		0			0
$919$	−31.9759	+	21.8008i	−1.05479	+	0.719141i	−0.961027	−	0.276454i	$-0.910841\pi$
$919$	−31.9759	+	21.8008i	−1.05479	+	0.719141i	−0.0937589	+	0.995595i	$0.529888\pi$
$920$	−2.46684	+	2.28890i	−0.0813294	+	0.0754627i
$921$		0			0
$922$	−26.7337	−	24.8052i	−0.880428	−	0.816917i
$923$	−34.7285	−	43.5482i	−1.14310	−	1.43341i
$924$		0			0
$925$	16.6164	−	20.8364i	0.546345	−	0.685096i
$926$	−8.21842	+	1.23873i	−0.270074	+	0.0407071i
$927$		0			0
$928$	−6.71560	+	17.1111i	−0.220450	+	0.561698i
$929$	10.0477	+	3.09929i	0.329653	+	0.101684i	0.455164	−	0.890408i	$-0.349581\pi$
$929$	10.0477	+	3.09929i	0.329653	+	0.101684i	−0.125511	+	0.992092i	$0.540057\pi$
$930$		0			0
$931$	−38.5793	−	24.0348i	−1.26438	−	0.787708i
$932$	7.97101			0.261099
$933$		0			0
$934$	2.16464	−	5.51541i	0.0708291	−	0.180470i
$935$	−0.471668	−	0.321578i	−0.0154252	−	0.0105167i
$936$		0			0
$937$	−10.2021	+	12.7930i	−0.333288	+	0.417930i	−0.920032	−	0.391842i	$-0.871838\pi$
$937$	−10.2021	+	12.7930i	−0.333288	+	0.417930i	0.586744	+	0.809772i	$0.300409\pi$
$938$	−12.6964	−	8.27803i	−0.414553	−	0.270287i
$939$		0			0
$940$	0.900883	+	0.835898i	0.0293836	+	0.0272640i
$941$	−4.27020	−	0.643630i	−0.139205	−	0.0209817i	0.0790702	−	0.996869i	$-0.474805\pi$
$941$	−4.27020	−	0.643630i	−0.139205	−	0.0209817i	−0.218275	+	0.975887i	$0.570043\pi$
$942$		0			0
$943$	8.03420	−	5.47763i	0.261630	−	0.178376i
$944$	−7.48631	−	32.7997i	−0.243659	−	1.06754i
$945$		0			0
$946$	−8.05494	+	35.2910i	−0.261889	+	1.14741i
$947$	−18.1492	−	46.2433i	−0.589769	−	1.50271i	−0.844424	−	0.535675i	$-0.820057\pi$
$947$	−18.1492	−	46.2433i	−0.589769	−	1.50271i	0.254655	−	0.967032i	$-0.418038\pi$
$948$		0			0
$949$	15.7391	+	27.2609i	0.510912	+	0.884926i
$950$	−18.8545	+	32.6570i	−0.611722	+	1.05953i
$951$		0			0
$952$	−0.147901	+	2.72717i	−0.00479350	+	0.0883882i
$953$	−22.4248	+	10.7992i	−0.726411	+	0.349821i	−0.760272	−	0.649605i	$-0.774934\pi$
$953$	−22.4248	+	10.7992i	−0.726411	+	0.349821i	0.0338604	+	0.999427i	$0.489220\pi$
$954$		0			0
$955$	3.06148	−	0.944342i	0.0990673	−	0.0305582i
$956$	4.59265	−	1.41664i	0.148537	−	0.0458175i
$957$		0			0
$958$	−37.2568	+	17.9419i	−1.20371	+	0.579677i
$959$	−25.2607	+	17.9964i	−0.815710	+	0.581135i
$960$		0			0
$961$	6.38692	−	11.0625i	0.206030	−	0.356854i
$962$	−13.2638	−	22.9737i	−0.427644	−	0.740700i
$963$		0			0
$964$	2.78532	+	7.09689i	0.0897093	+	0.228575i
$965$	0.252221	−	1.10505i	0.00811930	−	0.0355730i
$966$		0			0
$967$	5.68287	+	24.8983i	0.182749	+	0.800675i	0.980314	+	0.197443i	$0.0632636\pi$
$967$	5.68287	+	24.8983i	0.182749	+	0.800675i	−0.797566	+	0.603232i	$0.793879\pi$
$968$	−3.21564	+	2.19239i	−0.103355	+	0.0704660i
$969$		0			0
$970$	−0.0610155	−	0.00919660i	−0.00195909	−	0.000295285i
$971$	−38.2013	−	35.4456i	−1.22594	−	1.13750i	−0.986005	−	0.166715i	$-0.946684\pi$
$971$	−38.2013	−	35.4456i	−1.22594	−	1.13750i	−0.239933	−	0.970789i	$-0.577126\pi$
$972$		0			0
$973$	−22.9661	−	2.97869i	−0.736260	−	0.0954923i
$974$	−5.87785	+	7.37059i	−0.188338	+	0.236169i
$975$		0			0
$976$	20.4419	+	13.9370i	0.654328	+	0.446113i
$977$	6.39499	−	16.2942i	0.204594	−	0.521297i	−0.791341	−	0.611375i	$-0.790617\pi$
$977$	6.39499	−	16.2942i	0.204594	−	0.521297i	0.995935	+	0.0900786i	$0.0287118\pi$
$978$		0			0
$979$	6.60039			0.210949
$980$	−0.809465	+	1.54593i	−0.0258574	+	0.0493829i
$981$		0			0
$982$	−9.15694	−	2.82454i	−0.292210	−	0.0901348i
$983$	−6.01807	+	15.3338i	−0.191946	+	0.489072i	−0.994154	−	0.107974i	$-0.965564\pi$
$983$	−6.01807	+	15.3338i	−0.191946	+	0.489072i	0.802207	+	0.597046i	$0.203659\pi$
$984$		0			0
$985$	−0.406199	+	0.0612247i	−0.0129426	+	0.00195078i
$986$	1.65937	−	2.08079i	0.0528451	−	0.0662657i
$987$		0			0
$988$	−8.12064	−	10.1830i	−0.258352	−	0.323963i
$989$	14.1078	+	13.0901i	0.448601	+	0.416241i
$990$		0			0
$991$	9.97278	−	9.25339i	0.316796	−	0.293944i	−0.505706	−	0.862706i	$-0.668768\pi$
$991$	9.97278	−	9.25339i	0.316796	−	0.293944i	0.822502	+	0.568762i	$0.192578\pi$
$992$	−9.99889	+	6.81713i	−0.317465	+	0.216444i
$993$		0			0
$994$	−28.0087	+	36.6472i	−0.888383	+	1.16238i
$995$	0.166793	−	0.730770i	0.00528771	−	0.0231670i
$996$		0			0
$997$	−1.92714	−	25.7159i	−0.0610332	−	0.814432i	−0.940786	−	0.339001i	$-0.889911\pi$
$997$	−1.92714	−	25.7159i	−0.0610332	−	0.814432i	0.879753	−	0.475431i	$-0.157708\pi$
$998$	−2.91078	−	5.04162i	−0.0921391	−	0.159590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.100.3		48
3.2	odd	2		49.2.g.a.2.2	✓	48
12.11	even	2		784.2.bg.c.737.1		48
21.2	odd	6		343.2.e.d.246.6		48
21.5	even	6		343.2.e.c.246.6		48
21.11	odd	6		343.2.g.i.312.3		48
21.17	even	6		343.2.g.h.312.3		48
21.20	even	2		343.2.g.g.128.2		48
49.25	even	21	inner	441.2.bb.d.172.3		48
147.5	even	42		2401.2.a.i.1.8		24
147.44	odd	42		2401.2.a.h.1.8		24
147.74	odd	42		49.2.g.a.25.2	yes	48
147.83	even	14		343.2.g.h.177.3		48
147.89	even	42		343.2.e.c.99.6		48
147.107	odd	42		343.2.e.d.99.6		48
147.113	odd	14		343.2.g.i.177.3		48
147.122	even	42		343.2.g.g.67.2		48
588.515	even	42		784.2.bg.c.417.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.2.2	✓	48	3.2	odd	2
49.2.g.a.25.2	yes	48	147.74	odd	42
343.2.e.c.99.6		48	147.89	even	42
343.2.e.c.246.6		48	21.5	even	6
343.2.e.d.99.6		48	147.107	odd	42
343.2.e.d.246.6		48	21.2	odd	6
343.2.g.g.67.2		48	147.122	even	42
343.2.g.g.128.2		48	21.20	even	2
343.2.g.h.177.3		48	147.83	even	14
343.2.g.h.312.3		48	21.17	even	6
343.2.g.i.177.3		48	147.113	odd	14
343.2.g.i.312.3		48	21.11	odd	6
441.2.bb.d.100.3		48	1.1	even	1	trivial
441.2.bb.d.172.3		48	49.25	even	21	inner
784.2.bg.c.417.1		48	588.515	even	42
784.2.bg.c.737.1		48	12.11	even	2
2401.2.a.h.1.8		24	147.44	odd	42
2401.2.a.i.1.8		24	147.5	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16438 + 0.359164i) q^{2} +(-0.425690 - 0.290231i) q^{4} +(0.478452 - 0.0721150i) q^{5} +(1.90196 - 1.83918i) q^{7} +(-1.91089 - 2.39618i) q^{8} +O(q^{10})\)	\(q+(1.16438 + 0.359164i) q^{2} +(-0.425690 - 0.290231i) q^{4} +(0.478452 - 0.0721150i) q^{5} +(1.90196 - 1.83918i) q^{7} +(-1.91089 - 2.39618i) q^{8} +(0.583002 + 0.0878735i) q^{10} +(2.56776 - 2.38253i) q^{11} +(0.866309 + 3.79555i) q^{13} +(2.87517 - 1.45839i) q^{14} +(-0.987928 - 2.51720i) q^{16} +(-0.0251704 - 0.335876i) q^{17} +(3.24669 - 5.62343i) q^{19} +(-0.224602 - 0.108163i) q^{20} +(3.84558 - 1.85193i) q^{22} +(0.169582 - 2.26291i) q^{23} +(-4.55415 + 1.40477i) q^{25} +(-0.354511 + 4.73062i) q^{26} +(-1.34343 + 0.230913i) q^{28} +(5.84248 + 2.81359i) q^{29} +(2.13461 + 3.69724i) q^{31} +(0.211833 + 2.82672i) q^{32} +(0.0913266 - 0.400128i) q^{34} +(0.777362 - 1.01712i) q^{35} +(-4.62031 + 3.15007i) q^{37} +(5.80012 - 5.38172i) q^{38} +(-1.08707 - 1.00865i) q^{40} +(2.67167 + 3.35017i) q^{41} +(-5.28773 + 6.63061i) q^{43} +(-1.78456 + 0.268978i) q^{44} +(1.01022 - 2.57399i) q^{46} +(-4.71078 - 1.45308i) q^{47} +(0.234867 - 6.99606i) q^{49} -5.80731 q^{50} +(0.732806 - 1.86716i) q^{52} +(-7.44857 - 5.07835i) q^{53} +(1.05673 - 1.32510i) q^{55} +(-8.04143 - 1.04297i) q^{56} +(5.79234 + 5.37451i) q^{58} +(12.3025 + 1.85430i) q^{59} +(-7.55952 + 5.15399i) q^{61} +(1.15758 + 5.07168i) q^{62} +(-1.97205 + 8.64012i) q^{64} +(0.688204 + 1.75351i) q^{65} +(-2.35068 - 4.07149i) q^{67} +(-0.0867667 + 0.150284i) q^{68} +(1.27046 - 0.905112i) q^{70} +(-12.8903 + 6.20766i) q^{71} +(7.72629 - 2.38325i) q^{73} +(-6.51120 + 2.00844i) q^{74} +(-3.01417 + 1.45155i) q^{76} +(0.501868 - 9.25403i) q^{77} +(0.516002 - 0.893742i) q^{79} +(-0.654204 - 1.13311i) q^{80} +(1.90759 + 4.86045i) q^{82} +(-2.93736 + 12.8694i) q^{83} +(-0.0362645 - 0.158885i) q^{85} +(-8.53842 + 5.82140i) q^{86} +(-10.6157 - 1.60006i) q^{88} +(1.38129 + 1.28165i) q^{89} +(8.62836 + 5.62567i) q^{91} +(-0.728956 + 0.914082i) q^{92} +(-4.96325 - 3.38389i) q^{94} +(1.14785 - 2.92467i) q^{95} -0.104657 q^{97} +(2.78621 - 8.06173i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

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