LMFDB - Embedded newform 738.2.u.c.487.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [738,2,Mod(289,738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(738, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("738.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.u (of order $20$, degree $8$, 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:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			487.3
Character	$\chi$	$=$	738.487
Dual form			738.2.u.c.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.31414 + 0.751911i) q^{5} +(0.764846 - 0.121140i) q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.31414 + 0.751911i) q^{5} +(0.764846 - 0.121140i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.751911 + 2.31414i) q^{10} +(1.70745 + 0.869989i) q^{11} +(-0.213300 + 1.34672i) q^{13} +(0.547569 + 0.547569i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.491498 - 0.964619i) q^{17} +(0.449778 + 2.83979i) q^{19} +(-1.43022 + 1.96853i) q^{20} +(0.299778 + 1.89272i) q^{22} +(3.18930 - 2.31716i) q^{23} +(0.744808 + 0.541135i) q^{25} +(-1.21490 + 0.619020i) q^{26} +(-0.121140 + 0.764846i) q^{28} +(-0.899058 - 1.76450i) q^{29} +(1.32338 + 4.07295i) q^{31} -1.00000i q^{32} +(1.06929 - 0.169359i) q^{34} +(1.86105 + 0.294761i) q^{35} +(-1.51684 + 4.66835i) q^{37} +(-2.03306 + 2.03306i) q^{38} -2.43324 q^{40} +(-0.192001 - 6.40024i) q^{41} +(4.54823 + 6.26011i) q^{43} +(-1.35504 + 1.35504i) q^{44} +(3.74925 + 1.21821i) q^{46} +(-2.08040 - 0.329502i) q^{47} +(-6.08708 + 1.97781i) q^{49} +0.920633i q^{50} +(-1.21490 - 0.619020i) q^{52} +(-1.82528 - 3.58232i) q^{53} +(3.29713 + 3.29713i) q^{55} +(-0.689977 + 0.351561i) q^{56} +(0.899058 - 1.76450i) q^{58} +(3.46306 - 2.51606i) q^{59} +(0.203993 - 0.280773i) q^{61} +(-2.51722 + 3.46466i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-1.50622 + 2.95613i) q^{65} +(-8.51861 + 4.34045i) q^{67} +(0.765526 + 0.765526i) q^{68} +(0.855430 + 1.67888i) q^{70} +(-1.74337 - 0.888290i) q^{71} -5.73369i q^{73} +(-4.66835 + 1.51684i) q^{74} +(-2.83979 - 0.449778i) q^{76} +(1.41132 + 0.458567i) q^{77} +(2.17036 - 2.17036i) q^{79} +(-1.43022 - 1.96853i) q^{80} +(5.06505 - 3.91730i) q^{82} +3.37700 q^{83} +(1.86271 - 1.86271i) q^{85} +(-2.39115 + 7.35920i) q^{86} +(-1.89272 - 0.299778i) q^{88} +(1.80343 - 0.285636i) q^{89} +1.05587i q^{91} +(1.21821 + 3.74925i) q^{92} +(-0.956253 - 1.87675i) q^{94} +(-1.09442 + 6.90987i) q^{95} +(2.73955 - 1.39587i) q^{97} +(-5.17798 - 3.76202i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4}+O(q^{10}) $ 24 * q + 6 * q^4	$ 24 q + 6 q^{4} + 4 q^{10} - 4 q^{11} + 2 q^{13} - 6 q^{16} - 10 q^{17} - 8 q^{19} - 10 q^{20} + 4 q^{22} + 4 q^{23} + 6 q^{25} + 8 q^{26} + 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} - 8 q^{38} + 16 q^{40} - 4 q^{41} - 20 q^{43} + 4 q^{44} + 20 q^{46} + 12 q^{47} + 40 q^{49} + 8 q^{52} - 26 q^{53} - 4 q^{55} - 14 q^{58} + 8 q^{59} + 40 q^{61} + 6 q^{64} + 12 q^{65} + 8 q^{67} + 10 q^{68} - 60 q^{70} - 48 q^{71} + 10 q^{74} + 8 q^{76} + 20 q^{77} + 28 q^{79} - 10 q^{80} - 2 q^{82} + 80 q^{83} - 30 q^{85} + 8 q^{86} + 16 q^{88} - 58 q^{89} - 4 q^{92} - 8 q^{94} + 68 q^{95} - 86 q^{97} - 2 q^{98}+O(q^{100}) $ 24 * q + 6 * q^4 + 4 * q^10 - 4 * q^11 + 2 * q^13 - 6 * q^16 - 10 * q^17 - 8 * q^19 - 10 * q^20 + 4 * q^22 + 4 * q^23 + 6 * q^25 + 8 * q^26 + 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 - 8 * q^38 + 16 * q^40 - 4 * q^41 - 20 * q^43 + 4 * q^44 + 20 * q^46 + 12 * q^47 + 40 * q^49 + 8 * q^52 - 26 * q^53 - 4 * q^55 - 14 * q^58 + 8 * q^59 + 40 * q^61 + 6 * q^64 + 12 * q^65 + 8 * q^67 + 10 * q^68 - 60 * q^70 - 48 * q^71 + 10 * q^74 + 8 * q^76 + 20 * q^77 + 28 * q^79 - 10 * q^80 - 2 * q^82 + 80 * q^83 - 30 * q^85 + 8 * q^86 + 16 * q^88 - 58 * q^89 - 4 * q^92 - 8 * q^94 + 68 * q^95 - 86 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.31414	+	0.751911i	1.03492	+	0.336265i	0.776732	−	0.629831i	$-0.216876\pi$
$5$	2.31414	+	0.751911i	1.03492	+	0.336265i	0.258184	+	0.966096i	$0.416876\pi$
$6$		0			0
$7$	0.764846	−	0.121140i	0.289084	−	0.0457865i	−0.0102080	−	0.999948i	$-0.503249\pi$
$7$	0.764846	−	0.121140i	0.289084	−	0.0457865i	0.299292	+	0.954161i	$0.403249\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$		0			0
$10$	0.751911	+	2.31414i	0.237775	+	0.731797i
$11$	1.70745	+	0.869989i	0.514815	+	0.262311i	0.692040	−	0.721859i	$-0.256712\pi$
$11$	1.70745	+	0.869989i	0.514815	+	0.262311i	−0.177225	+	0.984170i	$0.556712\pi$
$12$		0			0
$13$	−0.213300	+	1.34672i	−0.0591587	+	0.373514i	0.940292	+	0.340369i	$0.110552\pi$
$13$	−0.213300	+	1.34672i	−0.0591587	+	0.373514i	−0.999451	+	0.0331443i	$0.989448\pi$
$14$	0.547569	+	0.547569i	0.146344	+	0.146344i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.491498	−	0.964619i	0.119206	−	0.233955i	−0.823691	−	0.567038i	$-0.808089\pi$
$17$	0.491498	−	0.964619i	0.119206	−	0.233955i	0.942897	+	0.333084i	$0.108089\pi$
$18$		0			0
$19$	0.449778	+	2.83979i	0.103186	+	0.651492i	0.984019	+	0.178064i	$0.0569835\pi$
$19$	0.449778	+	2.83979i	0.103186	+	0.651492i	−0.880833	+	0.473428i	$0.843017\pi$
$20$	−1.43022	+	1.96853i	−0.319807	+	0.440176i
$21$		0			0
$22$	0.299778	+	1.89272i	0.0639128	+	0.403530i
$23$	3.18930	−	2.31716i	0.665016	−	0.483162i	−0.203337	−	0.979109i	$-0.565179\pi$
$23$	3.18930	−	2.31716i	0.665016	−	0.483162i	0.868353	+	0.495946i	$0.165179\pi$
$24$		0			0
$25$	0.744808	+	0.541135i	0.148962	+	0.108227i
$26$	−1.21490	+	0.619020i	−0.238261	+	0.121400i
$27$		0			0
$28$	−0.121140	+	0.764846i	−0.0228932	+	0.144542i
$29$	−0.899058	−	1.76450i	−0.166951	−	0.327660i	0.792340	−	0.610080i	$-0.208863\pi$
$29$	−0.899058	−	1.76450i	−0.166951	−	0.327660i	−0.959291	+	0.282420i	$0.908863\pi$
$30$		0			0
$31$	1.32338	+	4.07295i	0.237686	+	0.731523i	0.996754	+	0.0805113i	$0.0256553\pi$
$31$	1.32338	+	4.07295i	0.237686	+	0.731523i	−0.759067	+	0.651012i	$0.774345\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	1.06929	−	0.169359i	0.183381	−	0.0290448i
$35$	1.86105	+	0.294761i	0.314575	+	0.0498237i
$36$		0			0
$37$	−1.51684	+	4.66835i	−0.249367	+	0.767473i	0.745520	+	0.666483i	$0.232201\pi$
$37$	−1.51684	+	4.66835i	−0.249367	+	0.767473i	−0.994887	+	0.100990i	$0.967799\pi$
$38$	−2.03306	+	2.03306i	−0.329806	+	0.329806i
$39$		0			0
$40$	−2.43324			−0.384728
$41$	−0.192001	−	6.40024i	−0.0299855	−	0.999550i
$41$	−0.192001	−	6.40024i	−0.0299855	−	0.999550i
$42$		0			0
$43$	4.54823	+	6.26011i	0.693599	+	0.954657i	0.999996	+	0.00275366i	$0.000876518\pi$
$43$	4.54823	+	6.26011i	0.693599	+	0.954657i	−0.306397	+	0.951904i	$0.599123\pi$
$44$	−1.35504	+	1.35504i	−0.204280	+	0.204280i
$45$		0			0
$46$	3.74925	+	1.21821i	0.552797	+	0.179615i
$47$	−2.08040	−	0.329502i	−0.303457	−	0.0480629i	0.00284912	−	0.999996i	$-0.499093\pi$
$47$	−2.08040	−	0.329502i	−0.303457	−	0.0480629i	−0.306306	+	0.951933i	$0.599093\pi$
$48$		0			0
$49$	−6.08708	+	1.97781i	−0.869583	+	0.282545i
$50$			0.920633i			0.130197i
$51$		0			0
$52$	−1.21490	−	0.619020i	−0.168476	−	0.0858427i
$53$	−1.82528	−	3.58232i	−0.250722	−	0.492069i	0.731003	−	0.682374i	$-0.239052\pi$
$53$	−1.82528	−	3.58232i	−0.250722	−	0.492069i	−0.981725	+	0.190305i	$0.939052\pi$
$54$		0			0
$55$	3.29713	+	3.29713i	0.444585	+	0.444585i
$56$	−0.689977	+	0.351561i	−0.0922021	+	0.0469793i
$57$		0			0
$58$	0.899058	−	1.76450i	0.118052	−	0.231690i
$59$	3.46306	−	2.51606i	0.450853	−	0.327564i	−0.339080	−	0.940758i	$-0.610116\pi$
$59$	3.46306	−	2.51606i	0.450853	−	0.327564i	0.789932	+	0.613194i	$0.210116\pi$
$60$		0			0
$61$	0.203993	−	0.280773i	0.0261186	−	0.0359492i	−0.795758	−	0.605615i	$-0.792927\pi$
$61$	0.203993	−	0.280773i	0.0261186	−	0.0359492i	0.821877	+	0.569666i	$0.192927\pi$
$62$	−2.51722	+	3.46466i	−0.319687	+	0.440012i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−1.50622	+	2.95613i	−0.186824	+	0.366662i
$66$		0			0
$67$	−8.51861	+	4.34045i	−1.04071	+	0.530270i	−0.888882	−	0.458136i	$-0.848517\pi$
$67$	−8.51861	+	4.34045i	−1.04071	+	0.530270i	−0.151832	+	0.988406i	$0.548517\pi$
$68$	0.765526	+	0.765526i	0.0928337	+	0.0928337i
$69$		0			0
$70$	0.855430	+	1.67888i	0.102243	+	0.200664i
$71$	−1.74337	−	0.888290i	−0.206900	−	0.105421i	0.347470	−	0.937691i	$-0.387041\pi$
$71$	−1.74337	−	0.888290i	−0.206900	−	0.105421i	−0.554370	+	0.832270i	$0.687041\pi$
$72$		0			0
$73$		−	5.73369i		−	0.671077i	−0.942026	−	0.335539i	$-0.891082\pi$
$73$		−	5.73369i		−	0.671077i	0.942026	−	0.335539i	$-0.108918\pi$
$74$	−4.66835	+	1.51684i	−0.542685	+	0.176329i
$75$		0			0
$76$	−2.83979	−	0.449778i	−0.325746	−	0.0515931i
$77$	1.41132	+	0.458567i	0.160835	+	0.0522586i
$78$		0			0
$79$	2.17036	−	2.17036i	0.244185	−	0.244185i	−0.574394	−	0.818579i	$-0.694762\pi$
$79$	2.17036	−	2.17036i	0.244185	−	0.244185i	0.818579	+	0.574394i	$0.194762\pi$
$80$	−1.43022	−	1.96853i	−0.159903	−	0.220088i
$81$		0			0
$82$	5.06505	−	3.91730i	0.559341	−	0.432594i
$83$	3.37700			0.370674			0.185337	−	0.982675i	$-0.440662\pi$
$83$	3.37700			0.370674			0.185337	+	0.982675i	$0.440662\pi$
$84$		0			0
$85$	1.86271	−	1.86271i	0.202039	−	0.202039i
$86$	−2.39115	+	7.35920i	−0.257844	+	0.793563i
$87$		0			0
$88$	−1.89272	−	0.299778i	−0.201765	−	0.0319564i
$89$	1.80343	−	0.285636i	0.191164	−	0.0302773i	−0.0601185	−	0.998191i	$-0.519148\pi$
$89$	1.80343	−	0.285636i	0.191164	−	0.0302773i	0.251282	+	0.967914i	$0.419148\pi$
$90$		0			0
$91$			1.05587i			0.110686i
$92$	1.21821	+	3.74925i	0.127007	+	0.390887i
$93$		0			0
$94$	−0.956253	−	1.87675i	−0.0986300	−	0.193572i
$95$	−1.09442	+	6.90987i	−0.112285	+	0.708938i
$96$		0			0
$97$	2.73955	−	1.39587i	0.278159	−	0.141729i	−0.309346	−	0.950950i	$-0.600110\pi$
$97$	2.73955	−	1.39587i	0.278159	−	0.141729i	0.587505	+	0.809220i	$0.300110\pi$
$98$	−5.17798	−	3.76202i	−0.523055	−	0.380022i
$99$		0			0
$100$	−0.744808	+	0.541135i	−0.0744808	+	0.0541135i
$101$	−0.868554	−	5.48383i	−0.0864243	−	0.545662i	−0.992471	−	0.122483i	$-0.960914\pi$
$101$	−0.868554	−	5.48383i	−0.0864243	−	0.545662i	0.906046	−	0.423179i	$-0.139086\pi$
$102$		0			0
$103$	7.39553	−	10.1791i	0.728703	−	1.00297i	−0.270487	−	0.962724i	$-0.587185\pi$
$103$	7.39553	−	10.1791i	0.728703	−	1.00297i	0.999190	−	0.0402497i	$-0.0128153\pi$
$104$	−0.213300	−	1.34672i	−0.0209158	−	0.132057i
$105$		0			0
$106$	1.82528	−	3.58232i	0.177287	−	0.347945i
$107$	7.59916	+	5.52111i	0.734638	+	0.533746i	0.891027	−	0.453949i	$-0.149985\pi$
$107$	7.59916	+	5.52111i	0.734638	+	0.533746i	−0.156389	+	0.987696i	$0.549985\pi$
$108$		0			0
$109$	−4.86413	−	4.86413i	−0.465899	−	0.465899i	0.434684	−	0.900583i	$-0.356860\pi$
$109$	−4.86413	−	4.86413i	−0.465899	−	0.465899i	−0.900583	+	0.434684i	$0.856860\pi$
$110$	−0.729430	+	4.60544i	−0.0695484	+	0.439111i
$111$		0			0
$112$	−0.689977	−	0.351561i	−0.0651967	−	0.0332194i
$113$	−5.26138	−	16.1929i	−0.494949	−	1.52330i	−0.817037	−	0.576586i	$-0.804385\pi$
$113$	−5.26138	−	16.1929i	−0.494949	−	1.52330i	0.322088	−	0.946710i	$-0.395615\pi$
$114$		0			0
$115$	9.12281	−	2.96418i	0.850706	−	0.276411i
$116$	1.95597	−	0.309794i	0.181607	−	0.0287637i
$117$		0			0
$118$	4.07108	+	1.32277i	0.374773	+	0.121771i
$119$	0.259066	−	0.797325i	0.0237486	−	0.0730906i
$120$		0			0
$121$	−4.30714	−	5.92826i	−0.391558	−	0.538933i
$122$	0.347054			0.0314208
$123$		0			0
$124$	−4.28255			−0.384585
$125$	−5.83439	−	8.03035i	−0.521844	−	0.718256i
$126$		0			0
$127$	−0.100465	+	0.309199i	−0.00891482	+	0.0274370i	−0.955415	−	0.295266i	$-0.904592\pi$
$127$	−0.100465	+	0.309199i	−0.00891482	+	0.0274370i	0.946500	+	0.322703i	$0.104592\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$		0			0
$130$	−3.27689	+	0.519009i	−0.287402	+	0.0455201i
$131$	0.903005	−	0.293404i	0.0788960	−	0.0256348i	−0.269303	−	0.963055i	$-0.586793\pi$
$131$	0.903005	−	0.293404i	0.0788960	−	0.0256348i	0.348199	+	0.937421i	$0.386793\pi$
$132$		0			0
$133$	0.688022	+	2.11751i	0.0596590	+	0.183612i
$134$	−8.51861	−	4.34045i	−0.735896	−	0.374958i
$135$		0			0
$136$	−0.169359	+	1.06929i	−0.0145224	+	0.0916907i
$137$	−6.22745	−	6.22745i	−0.532047	−	0.532047i	0.389134	−	0.921181i	$-0.372774\pi$
$137$	−6.22745	−	6.22745i	−0.532047	−	0.532047i	−0.921181	+	0.389134i	$0.872774\pi$
$138$		0			0
$139$	−15.4867	−	11.2518i	−1.31357	−	0.954361i	−0.999988	−	0.00479869i	$-0.998473\pi$
$139$	−15.4867	−	11.2518i	−1.31357	−	0.954361i	−0.313577	−	0.949563i	$-0.601527\pi$
$140$	−0.855430	+	1.67888i	−0.0722971	+	0.141891i
$141$		0			0
$142$	−0.306084	−	1.93254i	−0.0256860	−	0.162175i
$143$	−1.53583	+	2.11389i	−0.128433	+	0.176773i
$144$		0			0
$145$	−0.753803	−	4.75932i	−0.0625999	−	0.395240i
$146$	4.63865	−	3.37018i	0.383897	−	0.278918i
$147$		0			0
$148$	−3.97114	−	2.88520i	−0.326426	−	0.237162i
$149$	10.0142	−	5.10248i	0.820394	−	0.418011i	0.00717819	−	0.999974i	$-0.497715\pi$
$149$	10.0142	−	5.10248i	0.820394	−	0.418011i	0.813215	+	0.581963i	$0.197715\pi$
$150$		0			0
$151$	2.29873	−	14.5136i	0.187068	−	1.18110i	−0.698158	−	0.715943i	$-0.745997\pi$
$151$	2.29873	−	14.5136i	0.187068	−	1.18110i	0.885227	−	0.465160i	$-0.154003\pi$
$152$	−1.30531	−	2.56181i	−0.105874	−	0.207790i
$153$		0			0
$154$	0.458567	+	1.41132i	0.0369524	+	0.113728i
$155$			10.4205i			0.836991i
$156$		0			0
$157$	−14.0907	+	2.23175i	−1.12456	+	0.178113i	−0.690892	−	0.722958i	$-0.742782\pi$
$157$	−14.0907	+	2.23175i	−1.12456	+	0.178113i	−0.433671	+	0.901071i	$0.642782\pi$
$158$	3.03157	+	0.480153i	0.241178	+	0.0381989i
$159$		0			0
$160$	0.751911	−	2.31414i	0.0594438	−	0.182949i
$161$	2.15862	−	2.15862i	0.170123	−	0.170123i
$162$		0			0
$163$	−7.95104			−0.622773			−0.311387	−	0.950283i	$-0.600793\pi$
$163$	−7.95104			−0.622773			−0.311387	+	0.950283i	$0.600793\pi$
$164$	6.14633	+	1.79518i	0.479947	+	0.140180i
$165$		0			0
$166$	1.98495	+	2.73205i	0.154062	+	0.212048i
$167$	−3.93143	+	3.93143i	−0.304223	+	0.304223i	−0.842664	−	0.538440i	$-0.819014\pi$
$167$	−3.93143	+	3.93143i	−0.304223	+	0.304223i	0.538440	+	0.842664i	$0.319014\pi$
$168$		0			0
$169$	10.5956	+	3.44271i	0.815044	+	0.264824i
$170$	2.60183	+	0.412089i	0.199551	+	0.0316058i
$171$		0			0
$172$	−7.35920	+	2.39115i	−0.561134	+	0.182323i
$173$			4.77457i			0.363004i	0.983391	+	0.181502i	$0.0580959\pi$
$173$			4.77457i			0.363004i	−0.983391	+	0.181502i	$0.941904\pi$
$174$		0			0
$175$	0.635216	+	0.323659i	0.0480178	+	0.0244663i
$176$	−0.869989	−	1.70745i	−0.0655779	−	0.128704i
$177$		0			0
$178$	1.29112	+	1.29112i	0.0967732	+	0.0967732i
$179$	12.7648	−	6.50400i	0.954087	−	0.486132i	0.0936036	−	0.995610i	$-0.470161\pi$
$179$	12.7648	−	6.50400i	0.954087	−	0.486132i	0.860484	+	0.509478i	$0.170161\pi$
$180$		0			0
$181$	9.14517	−	17.9484i	0.679755	−	1.33409i	−0.250835	−	0.968030i	$-0.580705\pi$
$181$	9.14517	−	17.9484i	0.679755	−	1.33409i	0.930590	−	0.366064i	$-0.119295\pi$
$182$	−0.854220	+	0.620627i	−0.0633190	+	0.0460039i
$183$		0			0
$184$	−2.31716	+	3.18930i	−0.170824	+	0.235119i
$185$	−7.02037	+	9.66272i	−0.516148	+	0.710417i
$186$		0			0
$187$	1.67842	−	1.21944i	0.122738	−	0.0891743i
$188$	0.956253	−	1.87675i	0.0697419	−	0.136876i
$189$		0			0
$190$	−6.23348	+	3.17612i	−0.452225	+	0.230420i
$191$	12.8209	+	12.8209i	0.927686	+	0.927686i	0.997556	−	0.0698705i	$-0.0222586\pi$
$191$	12.8209	+	12.8209i	0.927686	+	0.927686i	−0.0698705	+	0.997556i	$0.522259\pi$
$192$		0			0
$193$	−1.42534	−	2.79739i	−0.102598	−	0.201360i	0.834001	−	0.551763i	$-0.186045\pi$
$193$	−1.42534	−	2.79739i	−0.102598	−	0.201360i	−0.936599	+	0.350403i	$0.886045\pi$
$194$	2.73955	+	1.39587i	0.196688	+	0.100218i
$195$		0			0
$196$		−	6.40034i		−	0.457167i
$197$	1.86008	−	0.604378i	0.132526	−	0.0430602i	−0.242003	−	0.970275i	$-0.577804\pi$
$197$	1.86008	−	0.604378i	0.132526	−	0.0430602i	0.374529	+	0.927215i	$0.377804\pi$
$198$		0			0
$199$	−2.06562	−	0.327162i	−0.146428	−	0.0231919i	0.0827903	−	0.996567i	$-0.473617\pi$
$199$	−2.06562	−	0.327162i	−0.146428	−	0.0231919i	−0.229218	+	0.973375i	$0.573617\pi$
$200$	−0.875574	−	0.284491i	−0.0619124	−	0.0201166i
$201$		0			0
$202$	3.92599	−	3.92599i	0.276232	−	0.276232i
$203$	−0.901392	−	1.24066i	−0.0632653	−	0.0870772i
$204$		0			0
$205$	4.36810	−	14.9555i	0.305081	−	1.04453i
$206$	12.5820			0.876631
$207$		0			0
$208$	0.964147	−	0.964147i	0.0668516	−	0.0668516i
$209$	−1.70261	+	5.24009i	−0.117772	+	0.362465i
$210$		0			0
$211$	−16.1045	−	2.55070i	−1.10868	−	0.175598i	−0.424867	−	0.905256i	$-0.639679\pi$
$211$	−16.1045	−	2.55070i	−1.10868	−	0.175598i	−0.683812	+	0.729658i	$0.739679\pi$
$212$	3.97103	−	0.628949i	0.272731	−	0.0431964i
$213$		0			0
$214$			9.39308i			0.642098i
$215$	5.81823	+	17.9067i	0.396800	+	1.22122i
$216$		0			0
$217$	1.50558	+	2.95486i	0.102205	+	0.200589i
$218$	1.07610	−	6.79423i	0.0728827	−	0.460163i
$219$		0			0
$220$	−4.15463	+	2.11689i	−0.280105	+	0.142721i
$221$	1.19424	+	0.867665i	0.0803331	+	0.0583654i
$222$		0			0
$223$	8.50658	−	6.18039i	0.569643	−	0.413870i	−0.265333	−	0.964157i	$-0.585482\pi$
$223$	8.50658	−	6.18039i	0.569643	−	0.413870i	0.834975	+	0.550287i	$0.185482\pi$
$224$	−0.121140	−	0.764846i	−0.00809398	−	0.0511034i
$225$		0			0
$226$	10.0077	−	13.7745i	0.665705	−	0.916264i
$227$	3.49222	+	22.0490i	0.231787	+	1.46344i	0.779302	+	0.626648i	$0.215574\pi$
$227$	3.49222	+	22.0490i	0.231787	+	1.46344i	−0.547516	+	0.836795i	$0.684426\pi$
$228$		0			0
$229$	−10.8186	+	21.2328i	−0.714915	+	1.40310i	0.191833	+	0.981428i	$0.438557\pi$
$229$	−10.8186	+	21.2328i	−0.714915	+	1.40310i	−0.906748	+	0.421672i	$0.861443\pi$
$230$	7.76033	+	5.63821i	0.511701	+	0.371772i
$231$		0			0
$232$	1.40032	+	1.40032i	0.0919353	+	0.0919353i
$233$	0.698709	−	4.41148i	0.0457740	−	0.289005i	−0.954174	−	0.299254i	$-0.903262\pi$
$233$	0.698709	−	4.41148i	0.0457740	−	0.289005i	0.999947	+	0.0102485i	$0.00326225\pi$
$234$		0			0
$235$	−4.56658	−	2.32679i	−0.297891	−	0.151783i
$236$	1.32277	+	4.07108i	0.0861052	+	0.265004i
$237$		0			0
$238$	0.797325	−	0.259066i	0.0516829	−	0.0167928i
$239$	−17.2772	+	2.73645i	−1.11757	+	0.177006i	−0.687778	−	0.725921i	$-0.741414\pi$
$239$	−17.2772	+	2.73645i	−1.11757	+	0.177006i	−0.429794	+	0.902927i	$0.641414\pi$
$240$		0			0
$241$	15.1092	+	4.90928i	0.973270	+	0.316234i	0.752135	−	0.659009i	$-0.229024\pi$
$241$	15.1092	+	4.90928i	0.973270	+	0.316234i	0.221134	+	0.975243i	$0.429024\pi$
$242$	2.26440	−	6.96909i	0.145561	−	0.447990i
$243$		0			0
$244$	0.203993	+	0.280773i	0.0130593	+	0.0179746i
$245$	−15.5735			−0.994956
$246$		0			0
$247$	−3.92034			−0.249445
$248$	−2.51722	−	3.46466i	−0.159844	−	0.220006i
$249$		0			0
$250$	3.06732	−	9.44024i	0.193994	−	0.597053i
$251$	12.0287	+	3.90837i	0.759246	+	0.246694i	0.662955	−	0.748659i	$-0.269302\pi$
$251$	12.0287	+	3.90837i	0.759246	+	0.246694i	0.0962912	+	0.995353i	$0.469302\pi$
$252$		0			0
$253$	7.46148	−	1.18178i	0.469099	−	0.0742980i
$254$	−0.309199	+	0.100465i	−0.0194009	+	0.00630373i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.46012	−	3.80112i	−0.465349	−	0.237107i	0.205563	−	0.978644i	$-0.434097\pi$
$257$	−7.46012	−	3.80112i	−0.465349	−	0.237107i	−0.670913	+	0.741536i	$0.734097\pi$
$258$		0			0
$259$	−0.594626	+	3.75432i	−0.0369483	+	0.233282i
$260$	−2.34600	−	2.34600i	−0.145492	−	0.145492i
$261$		0			0
$262$	0.768142	+	0.558088i	0.0474560	+	0.0344788i
$263$	6.65709	−	13.0653i	0.410494	−	0.805639i	−0.589504	−	0.807765i	$-0.700677\pi$
$263$	6.65709	−	13.0653i	0.410494	−	0.805639i	0.999998	+	0.00212633i	$0.000676832\pi$
$264$		0			0
$265$	−1.53038	−	9.66245i	−0.0940106	−	0.593559i
$266$	−1.30869	+	1.80126i	−0.0802412	+	0.110443i
$267$		0			0
$268$	−1.49562	−	9.44295i	−0.0913593	−	0.576820i
$269$	12.3637	−	8.98279i	0.753831	−	0.547690i	−0.143181	−	0.989697i	$-0.545733\pi$
$269$	12.3637	−	8.98279i	0.753831	−	0.547690i	0.897012	+	0.442006i	$0.145733\pi$
$270$		0			0
$271$	−7.60210	−	5.52325i	−0.461795	−	0.335514i	0.332440	−	0.943124i	$-0.392128\pi$
$271$	−7.60210	−	5.52325i	−0.461795	−	0.335514i	−0.794235	+	0.607611i	$0.792128\pi$
$272$	−0.964619	+	0.491498i	−0.0584886	+	0.0298014i
$273$		0			0
$274$	1.37771	−	8.69852i	0.0832305	−	0.525497i
$275$	0.800941	+	1.57193i	0.0482985	+	0.0947912i
$276$		0			0
$277$	7.10673	+	21.8723i	0.427002	+	1.31418i	0.901064	+	0.433686i	$0.142787\pi$
$277$	7.10673	+	21.8723i	0.427002	+	1.31418i	−0.474062	+	0.880492i	$0.657213\pi$
$278$		−	19.1426i		−	1.14810i
$279$		0			0
$280$	−1.86105	+	0.294761i	−0.111219	+	0.0176154i
$281$	−8.40657	−	1.33147i	−0.501494	−	0.0794288i	−0.0994375	−	0.995044i	$-0.531704\pi$
$281$	−8.40657	−	1.33147i	−0.501494	−	0.0794288i	−0.402056	+	0.915615i	$0.631704\pi$
$282$		0			0
$283$	−5.91672	+	18.2098i	−0.351713	+	1.08246i	0.606179	+	0.795329i	$0.292702\pi$
$283$	−5.91672	+	18.2098i	−0.351713	+	1.08246i	−0.957891	+	0.287132i	$0.907298\pi$
$284$	1.38354	−	1.38354i	0.0820982	−	0.0820982i
$285$		0			0
$286$	−2.61291			−0.154505
$287$	−0.922174	−	4.87194i	−0.0544342	−	0.287582i
$288$		0			0
$289$	9.30343	+	12.8051i	0.547261	+	0.753240i
$290$	3.40730	−	3.40730i	0.200083	−	0.200083i
$291$		0			0
$292$	5.45306	+	1.77181i	0.319116	+	0.103687i
$293$	−29.0923	−	4.60776i	−1.69959	−	0.269188i	−0.770068	−	0.637961i	$-0.779778\pi$
$293$	−29.0923	−	4.60776i	−1.69959	−	0.269188i	−0.929519	+	0.368773i	$0.879778\pi$
$294$		0			0
$295$	9.90588	−	3.21862i	0.576743	−	0.187395i
$296$		−	4.90860i		−	0.285307i
$297$		0			0
$298$	10.0142	+	5.10248i	0.580106	+	0.295579i
$299$	2.44030	+	4.78936i	0.141126	+	0.276976i
$300$		0			0
$301$	4.23704	+	4.23704i	0.244219	+	0.244219i
$302$	13.0929	−	6.67119i	0.753414	−	0.383884i
$303$		0			0
$304$	1.30531	−	2.56181i	0.0748645	−	0.146930i
$305$	0.683186	−	0.496363i	0.0391191	−	0.0284217i
$306$		0			0
$307$	−7.08538	+	9.75219i	−0.404384	+	0.556587i	−0.961838	−	0.273621i	$-0.911779\pi$
$307$	−7.08538	+	9.75219i	−0.404384	+	0.556587i	0.557453	+	0.830208i	$0.311779\pi$
$308$	−0.872247	+	1.20054i	−0.0497009	+	0.0684074i
$309$		0			0
$310$	−8.43033	+	6.12499i	−0.478810	+	0.347876i
$311$	−10.9841	+	21.5576i	−0.622854	+	1.22242i	0.336891	+	0.941544i	$0.390625\pi$
$311$	−10.9841	+	21.5576i	−0.622854	+	1.22242i	−0.959744	+	0.280875i	$0.909375\pi$
$312$		0			0
$313$	−10.7310	+	5.46771i	−0.606551	+	0.309053i	−0.730158	−	0.683278i	$-0.760554\pi$
$313$	−10.7310	+	5.46771i	−0.606551	+	0.309053i	0.123607	+	0.992331i	$0.460554\pi$
$314$	−10.0879	−	10.0879i	−0.569291	−	0.569291i
$315$		0			0
$316$	1.39346	+	2.73481i	0.0783881	+	0.153845i
$317$	−18.8240	−	9.59131i	−1.05726	−	0.538702i	−0.163176	−	0.986597i	$-0.552174\pi$
$317$	−18.8240	−	9.59131i	−1.05726	−	0.538702i	−0.894086	+	0.447895i	$0.852174\pi$
$318$		0			0
$319$		−	3.79497i		−	0.212477i
$320$	2.31414	−	0.751911i	0.129365	−	0.0420331i
$321$		0			0
$322$	3.01517	+	0.477556i	0.168029	+	0.0266132i
$323$	2.96038	+	0.961885i	0.164720	+	0.0535207i
$324$		0			0
$325$	−0.887626	+	0.887626i	−0.0492366	+	0.0492366i
$326$	−4.67350	−	6.43252i	−0.258841	−	0.356265i
$327$		0			0
$328$	2.16039	+	6.02766i	0.119287	+	0.332822i
$329$	−1.63110			−0.0899253
$330$		0			0
$331$	9.24927	−	9.24927i	0.508386	−	0.508386i	−0.405645	−	0.914031i	$-0.632953\pi$
$331$	9.24927	−	9.24927i	0.508386	−	0.508386i	0.914031	+	0.405645i	$0.132953\pi$
$332$	−1.04355	+	3.21172i	−0.0572723	+	0.176266i
$333$		0			0
$334$	−5.49143	−	0.869757i	−0.300478	−	0.0475910i
$335$	−22.9769	+	3.63919i	−1.25536	+	0.198830i
$336$		0			0
$337$			34.7407i			1.89244i	0.323517	+	0.946222i	$0.395135\pi$
$337$			34.7407i			1.89244i	−0.323517	+	0.946222i	$0.604865\pi$
$338$	3.44271	+	10.5956i	0.187259	+	0.576323i
$339$		0			0
$340$	1.19593	+	2.34715i	0.0648584	+	0.127292i
$341$	−1.28381	+	8.10568i	−0.0695224	+	0.438947i
$342$		0			0
$343$	−9.24593	+	4.71103i	−0.499233	+	0.254372i
$344$	−6.26011	−	4.54823i	−0.337522	−	0.245224i
$345$		0			0
$346$	−3.86271	+	2.80642i	−0.207661	+	0.150874i
$347$	−2.90719	−	18.3552i	−0.156066	−	0.985361i	−0.934067	−	0.357098i	$-0.883766\pi$
$347$	−2.90719	−	18.3552i	−0.156066	−	0.985361i	0.778001	−	0.628263i	$-0.216234\pi$
$348$		0			0
$349$	4.47452	−	6.15864i	0.239515	−	0.329665i	−0.672290	−	0.740288i	$-0.734689\pi$
$349$	4.47452	−	6.15864i	0.239515	−	0.329665i	0.911805	+	0.410624i	$0.134689\pi$
$350$	0.111525	+	0.704142i	0.00596127	+	0.0376380i
$351$		0			0
$352$	0.869989	−	1.70745i	0.0463706	−	0.0910073i
$353$	−5.29884	−	3.84984i	−0.282029	−	0.204906i	0.437773	−	0.899086i	$-0.355767\pi$
$353$	−5.29884	−	3.84984i	−0.282029	−	0.204906i	−0.719802	+	0.694179i	$0.755767\pi$
$354$		0			0
$355$	−3.36649	−	3.36649i	−0.178675	−	0.178675i
$356$	−0.285636	+	1.80343i	−0.0151387	+	0.0955818i
$357$		0			0
$358$	12.7648	+	6.50400i	0.674642	+	0.343747i
$359$	6.07771	+	18.7053i	0.320770	+	0.987227i	0.973314	+	0.229477i	$0.0737015\pi$
$359$	6.07771	+	18.7053i	0.320770	+	0.987227i	−0.652545	+	0.757750i	$0.726299\pi$
$360$		0			0
$361$	10.2080	−	3.31677i	0.537262	−	0.174567i
$362$	19.8960	−	3.15121i	1.04571	−	0.165624i
$363$		0			0
$364$	−1.00420	−	0.326283i	−0.0526342	−	0.0171019i
$365$	4.31122	−	13.2686i	0.225660	−	0.694509i
$366$		0			0
$367$	11.9527	+	16.4515i	0.623926	+	0.858760i	0.997631	−	0.0687874i	$-0.0219130\pi$
$367$	11.9527	+	16.4515i	0.623926	+	0.858760i	−0.373706	+	0.927547i	$0.621913\pi$
$368$	−3.94220			−0.205501
$369$		0			0
$370$	−11.9438			−0.620927
$371$	−1.83002	−	2.51880i	−0.0950098	−	0.130770i
$372$		0			0
$373$	−4.14940	+	12.7705i	−0.214848	+	0.661234i	0.784317	+	0.620361i	$0.213014\pi$
$373$	−4.14940	+	12.7705i	−0.214848	+	0.661234i	−0.999164	+	0.0408728i	$0.986986\pi$
$374$	1.97310	+	0.641098i	0.102026	+	0.0331504i
$375$		0			0
$376$	2.08040	−	0.329502i	0.107288	−	0.0169928i
$377$	2.56806	−	0.834414i	0.132262	−	0.0429745i
$378$		0			0
$379$	7.01391	+	21.5866i	0.360280	+	1.10883i	0.952884	+	0.303335i	$0.0981000\pi$
$379$	7.01391	+	21.5866i	0.360280	+	1.10883i	−0.592604	+	0.805494i	$0.701900\pi$
$380$	−6.23348	−	3.17612i	−0.319771	−	0.162931i
$381$		0			0
$382$	−2.83638	+	17.9082i	−0.145122	+	0.916264i
$383$	−12.6672	−	12.6672i	−0.647261	−	0.647261i	0.305069	−	0.952330i	$-0.401320\pi$
$383$	−12.6672	−	12.6672i	−0.647261	−	0.647261i	−0.952330	+	0.305069i	$0.901320\pi$
$384$		0			0
$385$	2.92121	+	2.12238i	0.148879	+	0.108167i
$386$	1.42534	−	2.79739i	0.0725479	−	0.142383i
$387$		0			0
$388$	0.480984	+	3.03681i	0.0244183	+	0.154171i
$389$	−8.52127	+	11.7285i	−0.432046	+	0.594660i	−0.968421	−	0.249320i	$-0.919793\pi$
$389$	−8.52127	+	11.7285i	−0.432046	+	0.594660i	0.536376	+	0.843979i	$0.319793\pi$
$390$		0			0
$391$	−0.667645	−	4.21535i	−0.0337643	−	0.213179i
$392$	5.17798	−	3.76202i	0.261528	−	0.190011i
$393$		0			0
$394$	1.58228	+	1.14960i	0.0797142	+	0.0579158i
$395$	6.65445	−	3.39061i	0.334822	−	0.170600i
$396$		0			0
$397$	1.83389	−	11.5787i	0.0920402	−	0.581119i	−0.897963	−	0.440072i	$-0.854953\pi$
$397$	1.83389	−	11.5787i	0.0920402	−	0.581119i	0.990003	−	0.141047i	$-0.0450469\pi$
$398$	−0.949460	−	1.86342i	−0.0475921	−	0.0934048i
$399$		0			0
$400$	−0.284491	−	0.875574i	−0.0142246	−	0.0437787i
$401$			7.12396i			0.355753i	0.984053	+	0.177877i	$0.0569228\pi$
$401$			7.12396i			0.355753i	−0.984053	+	0.177877i	$0.943077\pi$
$402$		0			0
$403$	−5.76741	+	0.913468i	−0.287295	+	0.0455031i
$404$	5.48383	+	0.868554i	0.272831	+	0.0432122i
$405$		0			0
$406$	0.473890	−	1.45848i	0.0235188	−	0.0723833i
$407$	−6.65134	+	6.65134i	−0.329695	+	0.329695i
$408$		0			0
$409$	−23.1629			−1.14533			−0.572665	−	0.819790i	$-0.694090\pi$
$409$	−23.1629			−1.14533			−0.572665	+	0.819790i	$0.694090\pi$
$410$	14.6667	−	5.25673i	0.724338	−	0.259612i
$411$		0			0
$412$	7.39553	+	10.1791i	0.364351	+	0.501487i
$413$	2.34391	−	2.34391i	0.115336	−	0.115336i
$414$		0			0
$415$	7.81487	+	2.53920i	0.383617	+	0.124645i
$416$	1.34672	+	0.213300i	0.0660285	+	0.0104579i
$417$		0			0
$418$	−5.24009	+	1.70261i	−0.256301	+	0.0832774i
$419$			27.6513i			1.35085i	0.737428	+	0.675426i	$0.236040\pi$
$419$			27.6513i			1.35085i	−0.737428	+	0.675426i	$0.763960\pi$
$420$		0			0
$421$	11.9168	+	6.07192i	0.580790	+	0.295927i	0.719597	−	0.694392i	$-0.244327\pi$
$421$	11.9168	+	6.07192i	0.580790	+	0.295927i	−0.138807	+	0.990319i	$0.544327\pi$
$422$	−7.40243	−	14.5281i	−0.360345	−	0.707216i
$423$		0			0
$424$	2.84294	+	2.84294i	0.138065	+	0.138065i
$425$	0.888060	−	0.452489i	0.0430773	−	0.0219490i
$426$		0			0
$427$	0.122011	−	0.239459i	0.00590451	−	0.0115882i
$428$	−7.59916	+	5.52111i	−0.367319	+	0.266873i
$429$		0			0
$430$	−11.0669	+	15.2323i	−0.533694	+	0.734567i
$431$	−13.5992	+	18.7177i	−0.655049	+	0.901598i	−0.999305	−	0.0372781i	$-0.988131\pi$
$431$	−13.5992	+	18.7177i	−0.655049	+	0.901598i	0.344256	+	0.938876i	$0.388131\pi$
$432$		0			0
$433$	10.5995	−	7.70099i	0.509380	−	0.370086i	−0.303209	−	0.952924i	$-0.598058\pi$
$433$	10.5995	−	7.70099i	0.509380	−	0.370086i	0.812588	+	0.582838i	$0.198058\pi$
$434$	−1.50558	+	2.95486i	−0.0722701	+	0.141838i
$435$		0			0
$436$	6.12916	−	3.12296i	0.293533	−	0.149563i
$437$	8.01474	+	8.01474i	0.383397	+	0.383397i
$438$		0			0
$439$	−2.90888	−	5.70900i	−0.138833	−	0.272476i	0.811113	−	0.584890i	$-0.198862\pi$
$439$	−2.90888	−	5.70900i	−0.138833	−	0.272476i	−0.949946	+	0.312414i	$0.898862\pi$
$440$	−4.15463	−	2.11689i	−0.198064	−	0.100919i
$441$		0			0
$442$			1.47616i			0.0702137i
$443$	25.7972	−	8.38201i	1.22566	−	0.398241i	0.376520	−	0.926408i	$-0.377120\pi$
$443$	25.7972	−	8.38201i	1.22566	−	0.398241i	0.849141	+	0.528167i	$0.177120\pi$
$444$		0			0
$445$	4.38818	+	0.695019i	0.208020	+	0.0329471i
$446$	10.0001	+	3.24923i	0.473518	+	0.153855i
$447$		0			0
$448$	0.547569	−	0.547569i	0.0258702	−	0.0258702i
$449$	−12.7995	−	17.6170i	−0.604046	−	0.831398i	0.392025	−	0.919955i	$-0.371775\pi$
$449$	−12.7995	−	17.6170i	−0.604046	−	0.831398i	−0.996071	+	0.0885562i	$0.971775\pi$
$450$		0			0
$451$	5.24031	−	11.0951i	0.246757	−	0.522449i
$452$	17.0262			0.800844
$453$		0			0
$454$	−15.7853	+	15.7853i	−0.740843	+	0.740843i
$455$	−0.793923	+	2.44344i	−0.0372197	+	0.114550i
$456$		0			0
$457$	−22.1854	−	3.51383i	−1.03779	−	0.164370i	−0.385789	−	0.922587i	$-0.626071\pi$
$457$	−22.1854	−	3.51383i	−1.03779	−	0.164370i	−0.652002	+	0.758217i	$0.726071\pi$
$458$	−23.5367	+	3.72785i	−1.09980	+	0.174191i
$459$		0			0
$460$			9.59229i			0.447243i
$461$	−0.129129	−	0.397419i	−0.00601414	−	0.0185096i	0.948004	−	0.318257i	$-0.103098\pi$
$461$	−0.129129	−	0.397419i	−0.00601414	−	0.0185096i	−0.954019	+	0.299748i	$0.903098\pi$
$462$		0			0
$463$	10.7351	+	21.0688i	0.498902	+	0.979151i	0.993903	+	0.110258i	$0.0351678\pi$
$463$	10.7351	+	21.0688i	0.498902	+	0.979151i	−0.495001	+	0.868893i	$0.664832\pi$
$464$	−0.309794	+	1.95597i	−0.0143818	+	0.0908034i
$465$		0			0
$466$	3.97965	−	2.02773i	0.184354	−	0.0939329i
$467$	27.3165	+	19.8466i	1.26406	+	0.918393i	0.998949	−	0.0458256i	$-0.0145919\pi$
$467$	27.3165	+	19.8466i	1.26406	+	0.918393i	0.265110	+	0.964218i	$0.414592\pi$
$468$		0			0
$469$	−5.98962	+	4.35171i	−0.276575	+	0.200943i
$470$	−0.801757	−	5.06209i	−0.0369823	−	0.233497i
$471$		0			0
$472$	−2.51606	+	3.46306i	−0.115811	+	0.159400i
$473$	2.31966	+	14.6457i	0.106658	+	0.673411i
$474$		0			0
$475$	−1.20171	+	2.35849i	−0.0551382	+	0.108215i
$476$	0.678245	+	0.492774i	0.0310873	+	0.0225862i
$477$		0			0
$478$	−12.3691	−	12.3691i	−0.565751	−	0.565751i
$479$	−1.32292	+	8.35260i	−0.0604458	+	0.381640i	0.938857	+	0.344307i	$0.111886\pi$
$479$	−1.32292	+	8.35260i	−0.0604458	+	0.381640i	−0.999303	+	0.0373327i	$0.988114\pi$
$480$		0			0
$481$	−5.96344	−	3.03852i	−0.271909	−	0.138545i
$482$	4.90928	+	15.1092i	0.223612	+	0.688205i
$483$		0			0
$484$	6.96909	−	2.26440i	0.316777	−	0.102927i
$485$	7.38928	−	1.17035i	0.335530	−	0.0531427i
$486$		0			0
$487$	5.54282	+	1.80097i	0.251169	+	0.0816099i	0.431896	−	0.901924i	$-0.357845\pi$
$487$	5.54282	+	1.80097i	0.251169	+	0.0816099i	−0.180726	+	0.983533i	$0.557845\pi$
$488$	−0.107246	+	0.330068i	−0.00485478	+	0.0149415i
$489$		0			0
$490$	−9.15389	−	12.5992i	−0.413530	−	0.569176i
$491$	−2.17917			−0.0983444			−0.0491722	−	0.998790i	$-0.515658\pi$
$491$	−2.17917			−0.0983444			−0.0491722	+	0.998790i	$0.515658\pi$
$492$		0			0
$493$	−2.14396			−0.0965590
$494$	−2.30432	−	3.17162i	−0.103676	−	0.142698i
$495$		0			0
$496$	1.32338	−	4.07295i	0.0594216	−	0.182881i
$497$	−1.44101	−	0.468214i	−0.0646383	−	0.0210023i
$498$		0			0
$499$	4.50542	−	0.713589i	0.201690	−	0.0319446i	−0.0547717	−	0.998499i	$-0.517443\pi$
$499$	4.50542	−	0.713589i	0.201690	−	0.0319446i	0.256462	+	0.966554i	$0.417443\pi$
$500$	9.44024	−	3.06732i	0.422180	−	0.137175i
$501$		0			0
$502$	3.90837	+	12.0287i	0.174439	+	0.536868i
$503$	−23.6295	−	12.0398i	−1.05359	−	0.536828i	−0.160649	−	0.987012i	$-0.551359\pi$
$503$	−23.6295	−	12.0398i	−1.05359	−	0.536828i	−0.892936	+	0.450183i	$0.851359\pi$
$504$		0			0
$505$	2.11340	−	13.3435i	0.0940449	−	0.593776i
$506$	5.34183	+	5.34183i	0.237473	+	0.237473i
$507$		0			0
$508$	−0.263020	−	0.191096i	−0.0116696	−	0.00847849i
$509$	18.8242	−	36.9445i	0.834367	−	1.63754i	0.0657422	−	0.997837i	$-0.479059\pi$
$509$	18.8242	−	36.9445i	0.834367	−	1.63754i	0.768624	−	0.639700i	$-0.220941\pi$
$510$		0			0
$511$	−0.694577	−	4.38538i	−0.0307263	−	0.193998i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$		0			0
$514$	−1.30978	−	8.26961i	−0.0577718	−	0.364757i
$515$	24.7681	−	17.9951i	1.09141	−	0.792957i
$516$		0			0
$517$	−3.26551	−	2.37253i	−0.143617	−	0.104344i
$518$	−3.38682	+	1.72567i	−0.148808	+	0.0758216i
$519$		0			0
$520$	0.519009	−	3.27689i	0.0227600	−	0.143701i
$521$	16.4215	+	32.2289i	0.719437	+	1.41197i	0.903294	+	0.429022i	$0.141142\pi$
$521$	16.4215	+	32.2289i	0.719437	+	1.41197i	−0.183857	+	0.982953i	$0.558858\pi$
$522$		0			0
$523$	3.28998	+	10.1255i	0.143861	+	0.442758i	0.996863	−	0.0791497i	$-0.0252205\pi$
$523$	3.28998	+	10.1255i	0.143861	+	0.442758i	−0.853002	+	0.521908i	$0.825221\pi$
$524$			0.949476i			0.0414781i
$525$		0			0
$526$	14.4830	−	2.29388i	0.631487	−	0.100018i
$527$	4.57929	+	0.725288i	0.199477	+	0.0315940i
$528$		0			0
$529$	−2.30498	+	7.09401i	−0.100217	+	0.308435i
$530$	6.91755	−	6.91755i	0.300479	−	0.300479i
$531$		0			0
$532$	−2.22648			−0.0965304
$533$	8.66031	+	1.10660i	0.375120	+	0.0479321i
$534$		0			0
$535$	13.4342	+	18.4905i	0.580810	+	0.799416i
$536$	6.76041	−	6.76041i	0.292005	−	0.292005i
$537$		0			0
$538$	14.5345	+	4.72253i	0.626625	+	0.203603i
$539$	−12.1141	−	1.91868i	−0.521789	−	0.0826433i
$540$		0			0
$541$	22.2634	−	7.23382i	0.957178	−	0.311006i	0.211549	−	0.977367i	$-0.432149\pi$
$541$	22.2634	−	7.23382i	0.957178	−	0.311006i	0.745629	+	0.666361i	$0.232149\pi$
$542$		−	9.39672i		−	0.403624i
$543$		0			0
$544$	−0.964619	−	0.491498i	−0.0413577	−	0.0210728i
$545$	−7.59890	−	14.9137i	−0.325501	−	0.638832i
$546$		0			0
$547$	3.03293	+	3.03293i	0.129679	+	0.129679i	0.768967	−	0.639288i	$-0.220771\pi$
$547$	3.03293	+	3.03293i	0.129679	+	0.129679i	−0.639288	+	0.768967i	$0.720771\pi$
$548$	7.84704	−	3.99827i	0.335209	−	0.170798i
$549$		0			0
$550$	−0.800941	+	1.57193i	−0.0341522	+	0.0670275i
$551$	4.60643	−	3.34677i	0.196241	−	0.142577i
$552$		0			0
$553$	1.39707	−	1.92291i	0.0594096	−	0.0817704i
$554$	−13.5178	+	18.6057i	−0.574317	+	0.790479i
$555$		0			0
$556$	15.4867	−	11.2518i	0.656783	−	0.477181i
$557$	−13.7726	+	27.0302i	−0.583563	+	1.14531i	0.390832	+	0.920462i	$0.372187\pi$
$557$	−13.7726	+	27.0302i	−0.583563	+	1.14531i	−0.974395	+	0.224844i	$0.927813\pi$
$558$		0			0
$559$	−9.40077	+	4.78993i	−0.397610	+	0.202592i
$560$	−1.33236	−	1.33236i	−0.0563027	−	0.0563027i
$561$		0			0
$562$	−3.86407	−	7.58367i	−0.162996	−	0.319898i
$563$	−6.34322	−	3.23203i	−0.267335	−	0.136214i	0.315185	−	0.949030i	$-0.397933\pi$
$563$	−6.34322	−	3.23203i	−0.267335	−	0.136214i	−0.582520	+	0.812816i	$0.697933\pi$
$564$		0			0
$565$		−	41.4287i		−	1.74292i
$566$	−18.2098	+	5.91672i	−0.765415	+	0.248698i
$567$		0			0
$568$	1.93254	+	0.306084i	0.0810875	+	0.0128430i
$569$	5.32173	+	1.72913i	0.223098	+	0.0724891i	0.418433	−	0.908248i	$-0.362579\pi$
$569$	5.32173	+	1.72913i	0.223098	+	0.0724891i	−0.195335	+	0.980737i	$0.562579\pi$
$570$		0			0
$571$	21.3425	−	21.3425i	0.893157	−	0.893157i	−0.101662	−	0.994819i	$-0.532416\pi$
$571$	21.3425	−	21.3425i	0.893157	−	0.893157i	0.994819	+	0.101662i	$0.0324159\pi$
$572$	−1.53583	−	2.11389i	−0.0642164	−	0.0883863i
$573$		0			0
$574$	3.39944	−	3.60971i	0.141890	−	0.150666i
$575$	3.62932			0.151353
$576$		0			0
$577$	−12.8553	+	12.8553i	−0.535175	+	0.535175i	−0.922108	−	0.386933i	$-0.873534\pi$
$577$	−12.8553	+	12.8553i	−0.535175	+	0.535175i	0.386933	+	0.922108i	$0.373534\pi$
$578$	−4.89110	+	15.0533i	−0.203443	+	0.626133i
$579$		0			0
$580$	4.75932	+	0.753803i	0.197620	+	0.0313000i
$581$	2.58288	−	0.409089i	0.107156	−	0.0169719i
$582$		0			0
$583$		−	7.70460i		−	0.319092i
$584$	1.77181	+	5.45306i	0.0733179	+	0.225649i
$585$		0			0
$586$	−13.3722	−	26.2445i	−0.552402	−	1.08415i
$587$	4.20437	−	26.5453i	0.173533	−	1.09564i	−0.735073	−	0.677988i	$-0.762852\pi$
$587$	4.20437	−	26.5453i	0.173533	−	1.09564i	0.908606	−	0.417655i	$-0.137148\pi$
$588$		0			0
$589$	−10.9711	+	5.59005i	−0.452056	+	0.230334i
$590$	8.42645	+	6.12217i	0.346911	+	0.252046i
$591$		0			0
$592$	3.97114	−	2.88520i	0.163213	−	0.118581i
$593$	−0.889337	−	5.61505i	−0.0365207	−	0.230583i	0.962676	−	0.270656i	$-0.0872407\pi$
$593$	−0.889337	−	5.61505i	−0.0365207	−	0.230583i	−0.999197	+	0.0400737i	$0.987241\pi$
$594$		0			0
$595$	1.19903	−	1.65033i	0.0491556	−	0.0676569i
$596$	1.75819	+	11.1008i	0.0720185	+	0.454707i
$597$		0			0
$598$	−2.44030	+	4.78936i	−0.0997913	+	0.195851i
$599$	0.0983430	+	0.0714504i	0.00401819	+	0.00291938i	0.589793	−	0.807555i	$-0.299210\pi$
$599$	0.0983430	+	0.0714504i	0.00401819	+	0.00291938i	−0.585774	+	0.810474i	$0.699210\pi$
$600$		0			0
$601$	−23.7773	−	23.7773i	−0.969896	−	0.969896i	0.0296638	−	0.999560i	$-0.490556\pi$
$601$	−23.7773	−	23.7773i	−0.969896	−	0.969896i	−0.999560	+	0.0296638i	$0.990556\pi$
$602$	−0.937369	+	5.91831i	−0.0382043	+	0.241212i
$603$		0			0
$604$	13.0929	+	6.67119i	0.532744	+	0.271447i
$605$	−5.50981	−	16.9574i	−0.224005	−	0.689418i
$606$		0			0
$607$	−15.8182	+	5.13964i	−0.642040	+	0.208611i	−0.611901	−	0.790934i	$-0.709595\pi$
$607$	−15.8182	+	5.13964i	−0.642040	+	0.208611i	−0.0301389	+	0.999546i	$0.509595\pi$
$608$	2.83979	−	0.449778i	0.115169	−	0.0182409i
$609$		0			0
$610$	0.803133	+	0.260954i	0.0325179	+	0.0105657i
$611$	0.887496	−	2.73143i	0.0359043	−	0.110502i
$612$		0			0
$613$	1.69647	+	2.33499i	0.0685197	+	0.0943093i	0.841901	−	0.539631i	$-0.181436\pi$
$613$	1.69647	+	2.33499i	0.0685197	+	0.0943093i	−0.773382	+	0.633941i	$0.781436\pi$
$614$	−12.0544			−0.486475
$615$		0			0
$616$	−1.48395			−0.0597902
$617$	−18.4240	−	25.3585i	−0.741724	−	1.02090i	−0.998518	−	0.0544288i	$-0.982666\pi$
$617$	−18.4240	−	25.3585i	−0.741724	−	1.02090i	0.256794	−	0.966466i	$-0.417334\pi$
$618$		0			0
$619$	−6.39522	+	19.6825i	−0.257046	+	0.791105i	0.736374	+	0.676575i	$0.236536\pi$
$619$	−6.39522	+	19.6825i	−0.257046	+	0.791105i	−0.993420	+	0.114531i	$0.963464\pi$
$620$	−9.91045	−	3.22010i	−0.398013	−	0.129322i
$621$		0			0
$622$	−23.8968	+	3.78488i	−0.958174	+	0.151760i
$623$	1.34475	−	0.436934i	0.0538761	−	0.0175054i
$624$		0			0
$625$	−8.88597	−	27.3482i	−0.355439	−	1.09393i
$626$	−10.7310	−	5.46771i	−0.428897	−	0.218534i
$627$		0			0
$628$	2.23175	−	14.0907i	0.0890567	−	0.562282i
$629$	3.75766	+	3.75766i	0.149828	+	0.149828i
$630$		0			0
$631$	5.73368	+	4.16576i	0.228254	+	0.165836i	0.696034	−	0.718008i	$-0.254946\pi$
$631$	5.73368	+	4.16576i	0.228254	+	0.165836i	−0.467780	+	0.883845i	$0.654946\pi$
$632$	−1.39346	+	2.73481i	−0.0554288	+	0.108785i
$633$		0			0
$634$	−3.30494	−	20.8666i	−0.131256	−	0.828718i
$635$	−0.464980	+	0.639991i	−0.0184522	+	0.0253973i
$636$		0			0
$637$	−1.36519	−	8.61948i	−0.0540908	−	0.341516i
$638$	3.07019	−	2.23063i	0.121550	−	0.0883113i
$639$		0			0
$640$	1.96853	+	1.43022i	0.0778129	+	0.0565344i
$641$	44.6481	−	22.7493i	1.76349	−	0.898545i	0.816466	−	0.577394i	$-0.195930\pi$
$641$	44.6481	−	22.7493i	1.76349	−	0.898545i	0.947028	−	0.321151i	$-0.104070\pi$
$642$		0			0
$643$	5.00859	−	31.6230i	0.197519	−	1.24709i	−0.667217	−	0.744863i	$-0.732515\pi$
$643$	5.00859	−	31.6230i	0.197519	−	1.24709i	0.864737	−	0.502226i	$-0.167485\pi$
$644$	1.38592	+	2.72003i	0.0546130	+	0.107184i
$645$		0			0
$646$	0.961885	+	2.96038i	0.0378449	+	0.116475i
$647$			25.2616i			0.993138i	0.867997	+	0.496569i	$0.165407\pi$
$647$			25.2616i			0.993138i	−0.867997	+	0.496569i	$0.834593\pi$
$648$		0			0
$649$	8.10195	−	1.28322i	0.318029	−	0.0503709i
$650$	−1.23984	−	0.196371i	−0.0486304	−	0.00770230i
$651$		0			0
$652$	2.45701	−	7.56189i	0.0962238	−	0.296146i
$653$	15.0916	−	15.0916i	0.590578	−	0.590578i	−0.347210	−	0.937788i	$-0.612871\pi$
$653$	15.0916	−	15.0916i	0.590578	−	0.590578i	0.937788	+	0.347210i	$0.112871\pi$
$654$		0			0
$655$	2.31030			0.0902708
$656$	−3.60664	+	5.29076i	−0.140816	+	0.206570i
$657$		0			0
$658$	−0.958735	−	1.31959i	−0.0373754	−	0.0514428i
$659$	32.0138	−	32.0138i	1.24708	−	1.24708i	0.290076	−	0.957004i	$-0.406320\pi$
$659$	32.0138	−	32.0138i	1.24708	−	1.24708i	0.957004	−	0.290076i	$-0.0936805\pi$
$660$		0			0
$661$	−17.1198	−	5.56258i	−0.665885	−	0.216359i	−0.0434797	−	0.999054i	$-0.513844\pi$
$661$	−17.1198	−	5.56258i	−0.665885	−	0.216359i	−0.622405	+	0.782695i	$0.713844\pi$
$662$	12.9194	+	2.04623i	0.502127	+	0.0795290i
$663$		0			0
$664$	−3.21172	+	1.04355i	−0.124639	+	0.0404976i
$665$			5.41756i			0.210084i
$666$		0			0
$667$	−6.95601	−	3.54427i	−0.269338	−	0.137234i
$668$	−2.52413	−	4.95389i	−0.0976617	−	0.191672i
$669$		0			0
$670$	−16.4497	−	16.4497i	−0.635506	−	0.635506i
$671$	0.592577	−	0.301933i	0.0228762	−	0.0116560i
$672$		0			0
$673$	−6.05006	+	11.8739i	−0.233213	+	0.457705i	−0.977721	−	0.209907i	$-0.932684\pi$
$673$	−6.05006	+	11.8739i	−0.233213	+	0.457705i	0.744509	+	0.667613i	$0.232684\pi$
$674$	−28.1058	+	20.4201i	−1.08259	+	0.786551i
$675$		0			0
$676$	−6.54842	+	9.01313i	−0.251862	+	0.346659i
$677$	−21.8833	+	30.1198i	−0.841043	+	1.15760i	0.144723	+	0.989472i	$0.453771\pi$
$677$	−21.8833	+	30.1198i	−0.841043	+	1.15760i	−0.985766	+	0.168124i	$0.946229\pi$
$678$		0			0
$679$	1.92624	−	1.39949i	0.0739222	−	0.0537076i
$680$	−1.19593	+	2.34715i	−0.0458618	+	0.0900089i
$681$		0			0
$682$	−7.31224	+	3.72577i	−0.280000	+	0.142667i
$683$	23.2969	+	23.2969i	0.891432	+	0.891432i	0.994658	−	0.103226i	$-0.0329165\pi$
$683$	23.2969	+	23.2969i	0.891432	+	0.891432i	−0.103226	+	0.994658i	$0.532916\pi$
$684$		0			0
$685$	−9.72873	−	19.0937i	−0.371716	−	0.729533i
$686$	−9.24593	−	4.71103i	−0.353011	−	0.179868i
$687$		0			0
$688$		−	7.73792i		−	0.295005i
$689$	5.21372	−	1.69404i	0.198627	−	0.0645378i
$690$		0			0
$691$	11.0811	+	1.75507i	0.421544	+	0.0667660i	0.363603	−	0.931554i	$-0.381546\pi$
$691$	11.0811	+	1.75507i	0.421544	+	0.0667660i	0.0579411	+	0.998320i	$0.481546\pi$
$692$	−4.54089	−	1.47542i	−0.172619	−	0.0560872i
$693$		0			0
$694$	13.1409	−	13.1409i	0.498822	−	0.498822i
$695$	−27.3782	−	37.6828i	−1.03851	−	1.42939i
$696$		0			0
$697$	−6.26817	−	2.96050i	−0.237424	−	0.112137i
$698$	7.61250			0.288137
$699$		0			0
$700$	−0.504110	+	0.504110i	−0.0190536	+	0.0190536i
$701$	−7.94928	+	24.4654i	−0.300240	+	0.924045i	0.681170	+	0.732125i	$0.261471\pi$
$701$	−7.94928	+	24.4654i	−0.300240	+	0.924045i	−0.981411	+	0.191920i	$0.938529\pi$
$702$		0			0
$703$	−13.9394	−	2.20778i	−0.525734	−	0.0832680i
$704$	1.89272	−	0.299778i	0.0713346	−	0.0112983i
$705$		0			0
$706$		−	6.54973i		−	0.246502i
$707$	−1.32862	−	4.08907i	−0.0499679	−	0.153785i
$708$		0			0
$709$	1.76599	+	3.46596i	0.0663233	+	0.130167i	0.921788	−	0.387694i	$-0.126728\pi$
$709$	1.76599	+	3.46596i	0.0663233	+	0.130167i	−0.855465	+	0.517861i	$0.826728\pi$
$710$	0.744774	−	4.70232i	0.0279509	−	0.176475i
$711$		0			0
$712$	−1.62690	+	0.828947i	−0.0609707	+	0.0310661i
$713$	13.6584	+	9.92338i	0.511510	+	0.371634i
$714$		0			0
$715$	−5.14360	+	3.73704i	−0.192360	+	0.139757i
$716$	2.24113	+	14.1499i	0.0837548	+	0.528807i
$717$		0			0
$718$	−11.5605	+	15.9117i	−0.431434	+	0.593818i
$719$	5.26564	+	33.2459i	0.196375	+	1.23986i	0.867091	+	0.498150i	$0.165987\pi$
$719$	5.26564	+	33.2459i	0.196375	+	1.23986i	−0.670716	+	0.741714i	$0.734013\pi$
$720$		0			0
$721$	4.42335	−	8.68131i	0.164734	−	0.323309i
$722$	8.68343	+	6.30888i	0.323164	+	0.234792i
$723$		0			0
$724$	14.2439	+	14.2439i	0.529372	+	0.529372i
$725$	0.285207	−	1.80073i	0.0105923	−	0.0668773i
$726$		0			0
$727$	−36.3179	−	18.5049i	−1.34696	−	0.686308i	−0.376236	−	0.926524i	$-0.622782\pi$
$727$	−36.3179	−	18.5049i	−1.34696	−	0.686308i	−0.970719	+	0.240216i	$0.922782\pi$
$728$	−0.326283	−	1.00420i	−0.0120928	−	0.0372180i
$729$		0			0
$730$	13.2686	−	4.31122i	0.491092	−	0.159565i
$731$	8.27407	−	1.31048i	0.306027	−	0.0484700i
$732$		0			0
$733$	−18.8746	−	6.13273i	−0.697149	−	0.226517i	−0.0610611	−	0.998134i	$-0.519448\pi$
$733$	−18.8746	−	6.13273i	−0.697149	−	0.226517i	−0.636088	+	0.771617i	$0.719448\pi$
$734$	−6.28390	+	19.3399i	−0.231943	+	0.713847i
$735$		0			0
$736$	−2.31716	−	3.18930i	−0.0854118	−	0.117559i
$737$	−18.3212			−0.674871
$738$		0			0
$739$	6.22606			0.229029			0.114515	−	0.993422i	$-0.463469\pi$
$739$	6.22606			0.229029			0.114515	+	0.993422i	$0.463469\pi$
$740$	−7.02037	−	9.66272i	−0.258074	−	0.355209i
$741$		0			0
$742$	0.962098	−	2.96103i	0.0353197	−	0.108703i
$743$	−10.6206	−	3.45085i	−0.389633	−	0.126599i	0.107648	−	0.994189i	$-0.465668\pi$
$743$	−10.6206	−	3.45085i	−0.389633	−	0.126599i	−0.497281	+	0.867590i	$0.665668\pi$
$744$		0			0
$745$	27.0109	−	4.27810i	0.989602	−	0.156737i
$746$	−12.7705	+	4.14940i	−0.467563	+	0.151920i
$747$		0			0
$748$	0.641098	+	1.97310i	0.0234409	+	0.0721435i
$749$	6.48101	+	3.30224i	0.236811	+	0.120661i
$750$		0			0
$751$	5.99299	−	37.8382i	0.218687	−	1.38074i	−0.596999	−	0.802242i	$-0.703640\pi$
$751$	5.99299	−	37.8382i	0.218687	−	1.38074i	0.815686	−	0.578495i	$-0.196360\pi$
$752$	1.48940	+	1.48940i	0.0543128	+	0.0543128i
$753$		0			0
$754$	2.18452	+	1.58715i	0.0795557	+	0.0578006i
$755$	16.2326	−	31.8582i	0.590764	−	1.15944i
$756$		0			0
$757$	6.92466	+	43.7206i	0.251681	+	1.58905i	0.712575	+	0.701596i	$0.247529\pi$
$757$	6.92466	+	43.7206i	0.251681	+	1.58905i	−0.460894	+	0.887455i	$0.652471\pi$
$758$	−13.3412	+	18.3627i	−0.484576	+	0.666962i
$759$		0			0
$760$	−1.09442	−	6.90987i	−0.0396986	−	0.250647i
$761$	26.0808	−	18.9488i	0.945429	−	0.686895i	−0.00429204	−	0.999991i	$-0.501366\pi$
$761$	26.0808	−	18.9488i	0.945429	−	0.686895i	0.949721	+	0.313096i	$0.101366\pi$
$762$		0			0
$763$	−4.30955	−	3.13107i	−0.156016	−	0.113352i
$764$	−16.1552	+	8.23151i	−0.584476	+	0.297805i
$765$		0			0
$766$	2.80238	−	17.6935i	0.101254	−	0.639292i
$767$	2.64977	+	5.20046i	0.0956776	+	0.187778i
$768$		0			0
$769$	0.494981	+	1.52340i	0.0178495	+	0.0549350i	0.959585	−	0.281421i	$-0.0908056\pi$
$769$	0.494981	+	1.52340i	0.0178495	+	0.0549350i	−0.941735	+	0.336356i	$0.890806\pi$
$770$			3.61081i			0.130125i
$771$		0			0
$772$	3.10093	−	0.491139i	0.111605	−	0.0176765i
$773$	−4.09040	−	0.647855i	−0.147121	−	0.0233017i	0.0824393	−	0.996596i	$-0.473729\pi$
$773$	−4.09040	−	0.647855i	−0.147121	−	0.0233017i	−0.229561	+	0.973294i	$0.573729\pi$
$774$		0			0
$775$	−1.21835	+	3.74969i	−0.0437644	+	0.134693i
$776$	−2.17412	+	2.17412i	−0.0780463	+	0.0780463i
$777$		0			0
$778$	−14.4973			−0.519752
$779$	18.0890	−	3.42393i	0.648105	−	0.122675i
$780$		0			0
$781$	−2.20391	−	3.03342i	−0.0788621	−	0.108544i
$782$	3.01785	−	3.01785i	0.107918	−	0.107918i
$783$		0			0
$784$	6.08708	+	1.97781i	0.217396	+	0.0706362i
$785$	−34.2861	−	5.43038i	−1.22372	−	0.193819i
$786$		0			0
$787$	38.8428	−	12.6208i	1.38460	−	0.449882i	0.480418	−	0.877040i	$-0.340485\pi$
$787$	38.8428	−	12.6208i	1.38460	−	0.449882i	0.904177	+	0.427157i	$0.140485\pi$
$788$			1.95581i			0.0696728i
$789$		0			0
$790$	6.65445	+	3.39061i	0.236755	+	0.120633i
$791$	−5.98574	−	11.7477i	−0.212828	−	0.417699i
$792$		0			0
$793$	0.334611	+	0.334611i	0.0118824	+	0.0118824i
$794$	10.4453	−	5.32215i	0.370690	−	0.188876i
$795$		0			0
$796$	0.949460	−	1.86342i	0.0336527	−	0.0660472i
$797$	−7.00031	+	5.08602i	−0.247964	+	0.180156i	−0.704824	−	0.709382i	$-0.748974\pi$
$797$	−7.00031	+	5.08602i	−0.247964	+	0.180156i	0.456860	+	0.889539i	$0.348974\pi$
$798$		0			0
$799$	−1.34035	+	1.84484i	−0.0474183	+	0.0652658i
$800$	0.541135	−	0.744808i	0.0191320	−	0.0263329i
$801$		0			0
$802$	−5.76340	+	4.18736i	−0.203513	+	0.147861i
$803$	4.98824	−	9.78998i	0.176031	−	0.345481i
$804$		0			0
$805$	6.61846	−	3.37227i	0.233270	−	0.118857i
$806$	−4.12901	−	4.12901i	−0.145438	−	0.145438i
$807$		0			0
$808$	2.52064	+	4.94704i	0.0886759	+	0.174036i
$809$	−9.49659	−	4.83875i	−0.333882	−	0.170122i	0.279010	−	0.960288i	$-0.409994\pi$
$809$	−9.49659	−	4.83875i	−0.333882	−	0.170122i	−0.612892	+	0.790167i	$0.709994\pi$
$810$		0			0
$811$		−	27.9832i		−	0.982624i	−0.870984	−	0.491312i	$-0.836518\pi$
$811$		−	27.9832i		−	0.982624i	0.870984	−	0.491312i	$-0.163482\pi$
$812$	1.45848	−	0.473890i	0.0511827	−	0.0166303i
$813$		0			0
$814$	−9.29061	−	1.47149i	−0.325636	−	0.0515756i
$815$	−18.3998	−	5.97847i	−0.644518	−	0.209417i
$816$		0			0
$817$	−15.7317	+	15.7317i	−0.550382	+	0.550382i
$818$	−13.6148	−	18.7391i	−0.476030	−	0.655199i
$819$		0			0
$820$	12.8737	+	8.77580i	0.449568	+	0.306464i
$821$	−11.1940			−0.390675			−0.195337	−	0.980736i	$-0.562580\pi$
$821$	−11.1940			−0.390675			−0.195337	+	0.980736i	$0.562580\pi$
$822$		0			0
$823$	−26.3592	+	26.3592i	−0.918825	+	0.918825i	−0.996944	−	0.0781190i	$-0.975109\pi$
$823$	−26.3592	+	26.3592i	−0.918825	+	0.918825i	0.0781190	+	0.996944i	$0.475109\pi$
$824$	−3.88806	+	11.9662i	−0.135447	+	0.416863i
$825$		0			0
$826$	3.27398	+	0.518548i	0.113916	+	0.0180426i
$827$	−27.7671	+	4.39788i	−0.965557	+	0.152929i	−0.619252	−	0.785193i	$-0.712564\pi$
$827$	−27.7671	+	4.39788i	−0.965557	+	0.152929i	−0.346305	+	0.938122i	$0.612564\pi$
$828$		0			0
$829$		−	35.1987i		−	1.22250i	−0.791437	−	0.611250i	$-0.790667\pi$
$829$		−	35.1987i		−	1.22250i	0.791437	−	0.611250i	$-0.209333\pi$
$830$	2.53920	+	7.81487i	0.0881370	+	0.271258i
$831$		0			0
$832$	0.619020	+	1.21490i	0.0214607	+	0.0421189i
$833$	−1.08395	+	6.84381i	−0.0375567	+	0.237124i
$834$		0			0
$835$	−12.0540	+	6.14181i	−0.417145	+	0.212546i
$836$	−4.45749	−	3.23856i	−0.154166	−	0.112008i
$837$		0			0
$838$	−22.3703	+	16.2530i	−0.772770	+	0.561451i
$839$	−8.72142	−	55.0649i	−0.301097	−	1.90105i	−0.418933	−	0.908017i	$-0.637596\pi$
$839$	−8.72142	−	55.0649i	−0.301097	−	1.90105i	0.117836	−	0.993033i	$-0.462404\pi$
$840$		0			0
$841$	14.7406	−	20.2887i	0.508297	−	0.699611i
$842$	2.09224	+	13.2099i	0.0721034	+	0.455243i
$843$		0			0
$844$	7.40243	−	14.5281i	0.254802	−	0.500077i
$845$	21.9311	+	15.9339i	0.754452	+	0.548141i
$846$		0			0
$847$	−4.01244	−	4.01244i	−0.137869	−	0.137869i
$848$	−0.628949	+	3.97103i	−0.0215982	+	0.136366i
$849$		0			0
$850$	0.888060	+	0.452489i	0.0304602	+	0.0155203i
$851$	5.97968	+	18.4036i	0.204981	+	0.630866i
$852$		0			0
$853$	2.90870	−	0.945093i	0.0995919	−	0.0323594i	−0.258797	−	0.965932i	$-0.583326\pi$
$853$	2.90870	−	0.945093i	0.0995919	−	0.0323594i	0.358389	+	0.933572i	$0.383326\pi$
$854$	0.265443	−	0.0420420i	0.00908326	−	0.00143865i
$855$		0			0
$856$	−8.93335	−	2.90262i	−0.305336	−	0.0992095i
$857$	1.49279	−	4.59433i	0.0509927	−	0.156939i	−0.922317	−	0.386433i	$-0.873707\pi$
$857$	1.49279	−	4.59433i	0.0509927	−	0.156939i	0.973310	+	0.229494i	$0.0737070\pi$
$858$		0			0
$859$	0.924855	+	1.27295i	0.0315557	+	0.0434326i	0.824503	−	0.565857i	$-0.191455\pi$
$859$	0.924855	+	1.27295i	0.0315557	+	0.0434326i	−0.792948	+	0.609290i	$0.791455\pi$
$860$	−18.8282			−0.642035
$861$		0			0
$862$	−23.1363			−0.788025
$863$	−28.0756	−	38.6428i	−0.955706	−	1.31542i	−0.948946	−	0.315439i	$-0.897848\pi$
$863$	−28.0756	−	38.6428i	−0.955706	−	1.31542i	−0.00675970	−	0.999977i	$-0.502152\pi$
$864$		0			0
$865$	−3.59005	+	11.0490i	−0.122065	+	0.375679i
$866$	12.4605	+	4.04865i	0.423424	+	0.137579i
$867$		0			0
$868$	−3.27549	+	0.518787i	−0.111177	+	0.0176088i
$869$	5.59397	−	1.81759i	0.189763	−	0.0616576i
$870$		0			0
$871$	−4.02836	−	12.3980i	−0.136496	−	0.420091i
$872$	6.12916	+	3.12296i	0.207560	+	0.105757i
$873$		0			0
$874$	−1.77311	+	11.1950i	−0.0599765	+	0.378677i
$875$	−5.43520	−	5.43520i	−0.183743	−	0.183743i
$876$		0			0
$877$	17.6825	+	12.8471i	0.597096	+	0.433815i	0.844847	−	0.535008i	$-0.179692\pi$
$877$	17.6825	+	12.8471i	0.597096	+	0.433815i	−0.247751	+	0.968824i	$0.579692\pi$
$878$	2.90888	−	5.70900i	0.0981700	−	0.192669i
$879$		0			0
$880$	−0.729430	−	4.60544i	−0.0245891	−	0.155249i
$881$	5.80881	−	7.99514i	0.195704	−	0.269363i	−0.699876	−	0.714265i	$-0.746761\pi$
$881$	5.80881	−	7.99514i	0.195704	−	0.269363i	0.895580	+	0.444901i	$0.146761\pi$
$882$		0			0
$883$	0.0424055	+	0.267738i	0.00142706	+	0.00901009i	0.988392	−	0.151928i	$-0.0485481\pi$
$883$	0.0424055	+	0.267738i	0.00142706	+	0.00901009i	−0.986965	+	0.160938i	$0.948548\pi$
$884$	−1.19424	+	0.867665i	−0.0401666	+	0.0291827i
$885$		0			0
$886$	21.9444	+	15.9435i	0.737236	+	0.535633i
$887$	−24.0394	+	12.2487i	−0.807164	+	0.411271i	−0.808331	−	0.588729i	$-0.799629\pi$
$887$	−24.0394	+	12.2487i	−0.807164	+	0.411271i	0.00116658	+	0.999999i	$0.499629\pi$
$888$		0			0
$889$	−0.0393838	+	0.248660i	−0.00132089	+	0.00833978i
$890$	2.01702	+	3.95863i	0.0676108	+	0.132694i
$891$		0			0
$892$	3.24923	+	10.0001i	0.108792	+	0.334828i
$893$		−	6.05609i		−	0.202659i
$894$		0			0
$895$	34.4301	−	5.45319i	1.15087	−	0.182280i
$896$	0.764846	+	0.121140i	0.0255517	+	0.00404699i
$897$		0			0
$898$	6.72910	−	20.7100i	0.224553	−	0.691103i
$899$	5.99693	−	5.99693i	0.200009	−	0.200009i
$900$		0			0
$901$	−4.35269			−0.145009
$902$	12.0563	−	2.28206i	0.401432	−	0.0759841i
$903$		0			0
$904$	10.0077	+	13.7745i	0.332852	+	0.458132i
$905$	34.6588	−	34.6588i	1.15210	−	1.15210i
$906$		0			0
$907$	12.9029	+	4.19242i	0.428435	+	0.139207i	0.515294	−	0.857014i	$-0.327683\pi$
$907$	12.9029	+	4.19242i	0.428435	+	0.139207i	−0.0868588	+	0.996221i	$0.527683\pi$
$908$	−22.0490	−	3.49222i	−0.731722	−	0.115893i
$909$		0			0
$910$	−2.44344	+	0.793923i	−0.0809994	+	0.0263183i
$911$			24.3266i			0.805977i	0.915205	+	0.402989i	$0.132029\pi$
$911$			24.3266i			0.805977i	−0.915205	+	0.402989i	$0.867971\pi$
$912$		0			0
$913$	5.76606	+	2.93795i	0.190829	+	0.0972320i
$914$	−10.1975	−	20.0138i	−0.337304	−	0.661997i
$915$		0			0
$916$	−16.8504	−	16.8504i	−0.556753	−	0.556753i
$917$	0.655117	−	0.333799i	0.0216339	−	0.0110230i
$918$		0			0
$919$	7.59676	−	14.9095i	0.250594	−	0.491819i	−0.731103	−	0.682267i	$-0.760994\pi$
$919$	7.59676	−	14.9095i	0.250594	−	0.491819i	0.981697	+	0.190448i	$0.0609942\pi$
$920$	−7.76033	+	5.63821i	−0.255850	+	0.185886i
$921$		0			0
$922$	0.245618	−	0.338064i	0.00808900	−	0.0111336i
$923$	1.56814	−	2.15836i	0.0516160	−	0.0710433i
$924$		0			0
$925$	−3.65596	+	2.65621i	−0.120207	+	0.0873357i
$926$	−10.7351	+	21.0688i	−0.352777	+	0.692364i
$927$		0			0
$928$	−1.76450	+	0.899058i	−0.0579226	+	0.0295130i
$929$	17.2358	+	17.2358i	0.565488	+	0.565488i	0.930861	−	0.365373i	$-0.119059\pi$
$929$	17.2358	+	17.2358i	0.565488	+	0.565488i	−0.365373	+	0.930861i	$0.619059\pi$
$930$		0			0
$931$	−8.35440	−	16.3964i	−0.273805	−	0.537372i
$932$	3.97965	+	2.02773i	0.130358	+	0.0664206i
$933$		0			0
$934$			33.7651i			1.10483i
$935$	4.80101	−	1.55994i	0.157010	−	0.0510155i
$936$		0			0
$937$	13.0319	+	2.06405i	0.425735	+	0.0674297i	0.365625	−	0.930762i	$-0.380855\pi$
$937$	13.0319	+	2.06405i	0.425735	+	0.0674297i	0.0601091	+	0.998192i	$0.480855\pi$
$938$	−7.04122	−	2.28783i	−0.229904	−	0.0747003i
$939$		0			0
$940$	3.62406	−	3.62406i	0.118204	−	0.118204i
$941$	−33.0734	−	45.5216i	−1.07816	−	1.48396i	−0.861528	−	0.507710i	$-0.830492\pi$
$941$	−33.0734	−	45.5216i	−1.07816	−	1.48396i	−0.216634	−	0.976253i	$-0.569508\pi$
$942$		0			0
$943$	−15.4428	−	19.9674i	−0.502886	−	0.650229i
$944$	−4.28058			−0.139321
$945$		0			0
$946$	−10.4852	+	10.4852i	−0.340903	+	0.340903i
$947$	−7.84188	+	24.1348i	−0.254827	+	0.784277i	0.739037	+	0.673665i	$0.235281\pi$
$947$	−7.84188	+	24.1348i	−0.254827	+	0.784277i	−0.993864	+	0.110612i	$0.964719\pi$
$948$		0			0
$949$	7.72168	+	1.22299i	0.250656	+	0.0397001i
$950$	−2.61440	+	0.414081i	−0.0848224	+	0.0134346i
$951$		0			0
$952$			0.838357i			0.0271713i
$953$	15.9665	+	49.1399i	0.517206	+	1.59180i	0.779232	+	0.626736i	$0.215610\pi$
$953$	15.9665	+	49.1399i	0.517206	+	1.59180i	−0.262025	+	0.965061i	$0.584390\pi$
$954$		0			0
$955$	20.0292	+	39.3095i	0.648129	+	1.27203i
$956$	2.73645	−	17.2772i	0.0885030	−	0.558786i
$957$		0			0
$958$	−7.53499	+	3.83927i	−0.243444	+	0.124041i
$959$	−5.51743	−	4.00865i	−0.178167	−	0.129446i
$960$		0			0
$961$	10.2419	−	7.44121i	0.330385	−	0.240039i
$962$	−1.04700	−	6.61052i	−0.0337568	−	0.213132i
$963$		0			0
$964$	−9.33800	+	12.8527i	−0.300757	+	0.413956i
$965$	−1.19506	−	7.54529i	−0.0384702	−	0.242892i
$966$		0			0
$967$	−20.3168	+	39.8740i	−0.653344	+	1.28226i	0.292073	+	0.956396i	$0.405655\pi$
$967$	−20.3168	+	39.8740i	−0.653344	+	1.28226i	−0.945417	+	0.325864i	$0.894345\pi$
$968$	5.92826	+	4.30714i	0.190542	+	0.138437i
$969$		0			0
$970$	5.29014	+	5.29014i	0.169856	+	0.169856i
$971$	6.03360	−	38.0947i	0.193628	−	1.22252i	−0.679003	−	0.734135i	$-0.737588\pi$
$971$	6.03360	−	38.0947i	0.193628	−	1.22252i	0.872631	−	0.488381i	$-0.162412\pi$
$972$		0			0
$973$	−13.2080	−	6.72980i	−0.423428	−	0.215747i
$974$	1.80097	+	5.54282i	0.0577069	+	0.177604i
$975$		0			0
$976$	−0.330068	+	0.107246i	−0.0105652	+	0.00343285i
$977$	35.5535	−	5.63113i	1.13746	−	0.180156i	0.440832	−	0.897590i	$-0.354684\pi$
$977$	35.5535	−	5.63113i	1.13746	−	0.180156i	0.696626	+	0.717434i	$0.254684\pi$
$978$		0			0
$979$	3.32777	+	1.08126i	0.106356	+	0.0345572i
$980$	4.81248	−	14.8113i	0.153729	−	0.473130i
$981$		0			0
$982$	−1.28088	−	1.76298i	−0.0408746	−	0.0562590i
$983$	−19.4487			−0.620316			−0.310158	−	0.950685i	$-0.600382\pi$
$983$	−19.4487			−0.620316			−0.310158	+	0.950685i	$0.600382\pi$
$984$		0			0
$985$	4.75894			0.151633
$986$	−1.26019	−	1.73450i	−0.0401325	−	0.0552377i
$987$		0			0
$988$	1.21145	−	3.72847i	0.0385414	−	0.118618i
$989$	29.0114	+	9.42638i	0.922509	+	0.299741i
$990$		0			0
$991$	−23.1497	+	3.66655i	−0.735374	+	0.116472i	−0.512878	−	0.858462i	$-0.671421\pi$
$991$	−23.1497	+	3.66655i	−0.735374	+	0.116472i	−0.222496	+	0.974934i	$0.571421\pi$
$992$	4.07295	−	1.32338i	0.129316	−	0.0420174i
$993$		0			0
$994$	−0.468214	−	1.44101i	−0.0148508	−	0.0457062i
$995$	−4.53414	−	2.31026i	−0.143742	−	0.0732401i
$996$		0			0
$997$	−4.11136	+	25.9581i	−0.130208	+	0.822101i	0.832986	+	0.553294i	$0.186629\pi$
$997$	−4.11136	+	25.9581i	−0.130208	+	0.822101i	−0.963194	+	0.268807i	$0.913371\pi$
$998$	3.22553	+	3.22553i	0.102102	+	0.102102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.c.487.3	✓	24
3.2	odd	2		738.2.u.d.487.1	yes	24
41.8	even	20	inner	738.2.u.c.541.3	yes	24
123.8	odd	20		738.2.u.d.541.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.u.c.487.3	✓	24	1.1	even	1	trivial
738.2.u.c.541.3	yes	24	41.8	even	20	inner
738.2.u.d.487.1	yes	24	3.2	odd	2
738.2.u.d.541.1	yes	24	123.8	odd	20

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.31414 + 0.751911i) q^{5} +(0.764846 - 0.121140i) q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.31414 + 0.751911i) q^{5} +(0.764846 - 0.121140i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.751911 + 2.31414i) q^{10} +(1.70745 + 0.869989i) q^{11} +(-0.213300 + 1.34672i) q^{13} +(0.547569 + 0.547569i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.491498 - 0.964619i) q^{17} +(0.449778 + 2.83979i) q^{19} +(-1.43022 + 1.96853i) q^{20} +(0.299778 + 1.89272i) q^{22} +(3.18930 - 2.31716i) q^{23} +(0.744808 + 0.541135i) q^{25} +(-1.21490 + 0.619020i) q^{26} +(-0.121140 + 0.764846i) q^{28} +(-0.899058 - 1.76450i) q^{29} +(1.32338 + 4.07295i) q^{31} -1.00000i q^{32} +(1.06929 - 0.169359i) q^{34} +(1.86105 + 0.294761i) q^{35} +(-1.51684 + 4.66835i) q^{37} +(-2.03306 + 2.03306i) q^{38} -2.43324 q^{40} +(-0.192001 - 6.40024i) q^{41} +(4.54823 + 6.26011i) q^{43} +(-1.35504 + 1.35504i) q^{44} +(3.74925 + 1.21821i) q^{46} +(-2.08040 - 0.329502i) q^{47} +(-6.08708 + 1.97781i) q^{49} +0.920633i q^{50} +(-1.21490 - 0.619020i) q^{52} +(-1.82528 - 3.58232i) q^{53} +(3.29713 + 3.29713i) q^{55} +(-0.689977 + 0.351561i) q^{56} +(0.899058 - 1.76450i) q^{58} +(3.46306 - 2.51606i) q^{59} +(0.203993 - 0.280773i) q^{61} +(-2.51722 + 3.46466i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-1.50622 + 2.95613i) q^{65} +(-8.51861 + 4.34045i) q^{67} +(0.765526 + 0.765526i) q^{68} +(0.855430 + 1.67888i) q^{70} +(-1.74337 - 0.888290i) q^{71} -5.73369i q^{73} +(-4.66835 + 1.51684i) q^{74} +(-2.83979 - 0.449778i) q^{76} +(1.41132 + 0.458567i) q^{77} +(2.17036 - 2.17036i) q^{79} +(-1.43022 - 1.96853i) q^{80} +(5.06505 - 3.91730i) q^{82} +3.37700 q^{83} +(1.86271 - 1.86271i) q^{85} +(-2.39115 + 7.35920i) q^{86} +(-1.89272 - 0.299778i) q^{88} +(1.80343 - 0.285636i) q^{89} +1.05587i q^{91} +(1.21821 + 3.74925i) q^{92} +(-0.956253 - 1.87675i) q^{94} +(-1.09442 + 6.90987i) q^{95} +(2.73955 - 1.39587i) q^{97} +(-5.17798 - 3.76202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4}+O(q^{10}) \) 24 * q + 6 * q^4	\( 24 q + 6 q^{4} + 4 q^{10} - 4 q^{11} + 2 q^{13} - 6 q^{16} - 10 q^{17} - 8 q^{19} - 10 q^{20} + 4 q^{22} + 4 q^{23} + 6 q^{25} + 8 q^{26} + 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} - 8 q^{38} + 16 q^{40} - 4 q^{41} - 20 q^{43} + 4 q^{44} + 20 q^{46} + 12 q^{47} + 40 q^{49} + 8 q^{52} - 26 q^{53} - 4 q^{55} - 14 q^{58} + 8 q^{59} + 40 q^{61} + 6 q^{64} + 12 q^{65} + 8 q^{67} + 10 q^{68} - 60 q^{70} - 48 q^{71} + 10 q^{74} + 8 q^{76} + 20 q^{77} + 28 q^{79} - 10 q^{80} - 2 q^{82} + 80 q^{83} - 30 q^{85} + 8 q^{86} + 16 q^{88} - 58 q^{89} - 4 q^{92} - 8 q^{94} + 68 q^{95} - 86 q^{97} - 2 q^{98}+O(q^{100}) \) 24 * q + 6 * q^4 + 4 * q^10 - 4 * q^11 + 2 * q^13 - 6 * q^16 - 10 * q^17 - 8 * q^19 - 10 * q^20 + 4 * q^22 + 4 * q^23 + 6 * q^25 + 8 * q^26 + 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 - 8 * q^38 + 16 * q^40 - 4 * q^41 - 20 * q^43 + 4 * q^44 + 20 * q^46 + 12 * q^47 + 40 * q^49 + 8 * q^52 - 26 * q^53 - 4 * q^55 - 14 * q^58 + 8 * q^59 + 40 * q^61 + 6 * q^64 + 12 * q^65 + 8 * q^67 + 10 * q^68 - 60 * q^70 - 48 * q^71 + 10 * q^74 + 8 * q^76 + 20 * q^77 + 28 * q^79 - 10 * q^80 - 2 * q^82 + 80 * q^83 - 30 * q^85 + 8 * q^86 + 16 * q^88 - 58 * q^89 - 4 * q^92 - 8 * q^94 + 68 * q^95 - 86 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more