LMFDB - Embedded newform 414.2.i.c.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	414.55
Dual form			414.2.i.c.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(0.841254 - 0.540641i) q^{4} +(-0.459493 - 3.19584i) q^{5} +(-0.497033 + 1.08835i) q^{7} +(-0.654861 + 0.755750i) q^{8} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.841254 - 0.540641i) q^{4} +(-0.459493 - 3.19584i) q^{5} +(-0.497033 + 1.08835i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(1.34125 + 2.93694i) q^{10} +(0.544078 + 0.159756i) q^{11} +(-2.44815 - 5.36070i) q^{13} +(0.170276 - 1.18430i) q^{14} +(0.415415 - 0.909632i) q^{16} +(0.127214 + 0.0817557i) q^{17} +(-3.91978 + 2.51909i) q^{19} +(-2.11435 - 2.44009i) q^{20} -0.567047 q^{22} +(-4.67421 - 1.07322i) q^{23} +(-5.20482 + 1.52827i) q^{25} +(3.85927 + 4.45383i) q^{26} +(0.170276 + 1.18430i) q^{28} +(-3.56996 - 2.29427i) q^{29} +(2.64478 - 3.05224i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-0.145095 - 0.0426036i) q^{34} +(3.70658 + 1.08835i) q^{35} +(1.33908 - 9.31349i) q^{37} +(3.05129 - 3.52138i) q^{38} +(2.71616 + 1.74557i) q^{40} +(-0.673415 - 4.68370i) q^{41} +(-2.29057 - 2.64346i) q^{43} +(0.544078 - 0.159756i) q^{44} +(4.78723 - 0.287130i) q^{46} +2.38905 q^{47} +(3.64656 + 4.20835i) q^{49} +(4.56342 - 2.93273i) q^{50} +(-4.95773 - 3.18614i) q^{52} +(1.21682 - 2.66446i) q^{53} +(0.260554 - 1.81219i) q^{55} +(-0.497033 - 1.08835i) q^{56} +(4.07172 + 1.19557i) q^{58} +(0.411888 + 0.901910i) q^{59} +(-1.33083 + 1.53586i) q^{61} +(-1.67773 + 3.67372i) q^{62} +(-0.142315 - 0.989821i) q^{64} +(-16.0071 + 10.2871i) q^{65} +(1.25598 - 0.368789i) q^{67} +0.151220 q^{68} -3.86306 q^{70} +(1.48145 - 0.434992i) q^{71} +(-3.24226 + 2.08368i) q^{73} +(1.33908 + 9.31349i) q^{74} +(-1.93560 + 4.23838i) q^{76} +(-0.444295 + 0.512744i) q^{77} +(3.52408 + 7.71665i) q^{79} +(-3.09792 - 0.909632i) q^{80} +(1.96569 + 4.30426i) q^{82} +(0.787149 - 5.47474i) q^{83} +(0.202824 - 0.444124i) q^{85} +(2.94253 + 1.89105i) q^{86} +(-0.477031 + 0.306569i) q^{88} +(11.5896 + 13.3752i) q^{89} +7.05114 q^{91} +(-4.51242 + 1.62422i) q^{92} +(-2.29227 + 0.673072i) q^{94} +(9.85172 + 11.3695i) q^{95} +(0.420422 + 2.92410i) q^{97} +(-4.68448 - 3.01053i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$		0			0
$3$		0			0
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.459493	−	3.19584i	−0.205492	−	1.42922i	−0.787637	−	0.616140i	$-0.788696\pi$
$5$	−0.459493	−	3.19584i	−0.205492	−	1.42922i	0.582145	−	0.813085i	$-0.302214\pi$
$6$		0			0
$7$	−0.497033	+	1.08835i	−0.187861	+	0.411358i	−0.980004	−	0.198977i	$-0.936238\pi$
$7$	−0.497033	+	1.08835i	−0.187861	+	0.411358i	0.792143	+	0.610335i	$0.208965\pi$
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$		0			0
$10$	1.34125	+	2.93694i	0.424142	+	0.928741i
$11$	0.544078	+	0.159756i	0.164046	+	0.0481682i	0.362724	−	0.931897i	$-0.381847\pi$
$11$	0.544078	+	0.159756i	0.164046	+	0.0481682i	−0.198678	+	0.980065i	$0.563665\pi$
$12$		0			0
$13$	−2.44815	−	5.36070i	−0.678995	−	1.48679i	−0.863705	−	0.503998i	$-0.831862\pi$
$13$	−2.44815	−	5.36070i	−0.678995	−	1.48679i	0.184710	−	0.982793i	$-0.440865\pi$
$14$	0.170276	−	1.18430i	0.0455082	−	0.316516i
$15$		0			0
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	0.127214	+	0.0817557i	0.0308540	+	0.0198287i	0.555977	−	0.831198i	$-0.312344\pi$
$17$	0.127214	+	0.0817557i	0.0308540	+	0.0198287i	−0.525123	+	0.851026i	$0.675981\pi$
$18$		0			0
$19$	−3.91978	+	2.51909i	−0.899259	+	0.577918i	−0.906570	−	0.422055i	$-0.861309\pi$
$19$	−3.91978	+	2.51909i	−0.899259	+	0.577918i	0.00731173	+	0.999973i	$0.497673\pi$
$20$	−2.11435	−	2.44009i	−0.472784	−	0.545622i
$21$		0			0
$22$	−0.567047			−0.120895
$23$	−4.67421	−	1.07322i	−0.974639	−	0.223782i
$23$	−4.67421	−	1.07322i	−0.974639	−	0.223782i
$24$		0			0
$25$	−5.20482	+	1.52827i	−1.04096	+	0.305655i
$26$	3.85927	+	4.45383i	0.756865	+	0.873468i
$27$		0			0
$28$	0.170276	+	1.18430i	0.0321791	+	0.223811i
$29$	−3.56996	−	2.29427i	−0.662925	−	0.426036i	0.165444	−	0.986219i	$-0.447094\pi$
$29$	−3.56996	−	2.29427i	−0.662925	−	0.426036i	−0.828369	+	0.560183i	$0.810731\pi$
$30$		0			0
$31$	2.64478	−	3.05224i	0.475016	−	0.548198i	−0.466784	−	0.884372i	$-0.654587\pi$
$31$	2.64478	−	3.05224i	0.475016	−	0.548198i	0.941800	+	0.336173i	$0.109133\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$		0			0
$34$	−0.145095	−	0.0426036i	−0.0248835	−	0.00730646i
$35$	3.70658	+	1.08835i	0.626527	+	0.183965i
$36$		0			0
$37$	1.33908	−	9.31349i	0.220143	−	1.53113i	−0.517350	−	0.855774i	$-0.673081\pi$
$37$	1.33908	−	9.31349i	0.220143	−	1.53113i	0.737493	−	0.675355i	$-0.236009\pi$
$38$	3.05129	−	3.52138i	0.494985	−	0.571243i
$39$		0			0
$40$	2.71616	+	1.74557i	0.429463	+	0.275999i
$41$	−0.673415	−	4.68370i	−0.105170	−	0.731471i	−0.972359	−	0.233492i	$-0.924985\pi$
$41$	−0.673415	−	4.68370i	−0.105170	−	0.731471i	0.867189	−	0.497979i	$-0.165924\pi$
$42$		0			0
$43$	−2.29057	−	2.64346i	−0.349308	−	0.403123i	0.553721	−	0.832702i	$-0.313207\pi$
$43$	−2.29057	−	2.64346i	−0.349308	−	0.403123i	−0.903029	+	0.429579i	$0.858662\pi$
$44$	0.544078	−	0.159756i	0.0820228	−	0.0240841i
$45$		0			0
$46$	4.78723	−	0.287130i	0.705838	−	0.0423350i
$47$	2.38905			0.348478			0.174239	−	0.984703i	$-0.444253\pi$
$47$	2.38905			0.348478			0.174239	+	0.984703i	$0.444253\pi$
$48$		0			0
$49$	3.64656	+	4.20835i	0.520937	+	0.601193i
$50$	4.56342	−	2.93273i	0.645365	−	0.414751i
$51$		0			0
$52$	−4.95773	−	3.18614i	−0.687513	−	0.441838i
$53$	1.21682	−	2.66446i	0.167143	−	0.365992i	−0.807463	−	0.589918i	$-0.799160\pi$
$53$	1.21682	−	2.66446i	0.167143	−	0.365992i	0.974606	+	0.223926i	$0.0718874\pi$
$54$		0			0
$55$	0.260554	−	1.81219i	0.0351331	−	0.244356i
$56$	−0.497033	−	1.08835i	−0.0664188	−	0.145437i
$57$		0			0
$58$	4.07172	+	1.19557i	0.534644	+	0.156986i
$59$	0.411888	+	0.901910i	0.0536233	+	0.117419i	0.934547	−	0.355840i	$-0.115805\pi$
$59$	0.411888	+	0.901910i	0.0536233	+	0.117419i	−0.880924	+	0.473258i	$0.843078\pi$
$60$		0			0
$61$	−1.33083	+	1.53586i	−0.170395	+	0.196647i	−0.834524	−	0.550972i	$-0.814257\pi$
$61$	−1.33083	+	1.53586i	−0.170395	+	0.196647i	0.664129	+	0.747618i	$0.268803\pi$
$62$	−1.67773	+	3.67372i	−0.213072	+	0.466563i
$63$		0			0
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−16.0071	+	10.2871i	−1.98543	+	1.27596i
$66$		0			0
$67$	1.25598	−	0.368789i	0.153442	−	0.0450547i	−0.204109	−	0.978948i	$-0.565430\pi$
$67$	1.25598	−	0.368789i	0.153442	−	0.0450547i	0.357552	+	0.933893i	$0.383612\pi$
$68$	0.151220			0.0183381
$69$		0			0
$70$	−3.86306			−0.461724
$71$	1.48145	−	0.434992i	0.175815	−	0.0516240i	−0.192640	−	0.981270i	$-0.561705\pi$
$71$	1.48145	−	0.434992i	0.175815	−	0.0516240i	0.368455	+	0.929645i	$0.379887\pi$
$72$		0			0
$73$	−3.24226	+	2.08368i	−0.379478	+	0.243876i	−0.716449	−	0.697639i	$-0.754234\pi$
$73$	−3.24226	+	2.08368i	−0.379478	+	0.243876i	0.336971	+	0.941515i	$0.390598\pi$
$74$	1.33908	+	9.31349i	0.155665	+	1.08267i
$75$		0			0
$76$	−1.93560	+	4.23838i	−0.222029	+	0.486176i
$77$	−0.444295	+	0.512744i	−0.0506321	+	0.0584326i
$78$		0			0
$79$	3.52408	+	7.71665i	0.396489	+	0.868191i	0.997614	+	0.0690356i	$0.0219922\pi$
$79$	3.52408	+	7.71665i	0.396489	+	0.868191i	−0.601125	+	0.799155i	$0.705281\pi$
$80$	−3.09792	−	0.909632i	−0.346358	−	0.101700i
$81$		0			0
$82$	1.96569	+	4.30426i	0.217074	+	0.475326i
$83$	0.787149	−	5.47474i	0.0864009	−	0.600931i	−0.899915	−	0.436065i	$-0.856372\pi$
$83$	0.787149	−	5.47474i	0.0864009	−	0.600931i	0.986316	−	0.164866i	$-0.0527192\pi$
$84$		0			0
$85$	0.202824	−	0.444124i	0.0219994	−	0.0481720i
$86$	2.94253	+	1.89105i	0.317301	+	0.203917i
$87$		0			0
$88$	−0.477031	+	0.306569i	−0.0508516	+	0.0326804i
$89$	11.5896	+	13.3752i	1.22850	+	1.41776i	0.876248	+	0.481860i	$0.160039\pi$
$89$	11.5896	+	13.3752i	1.22850	+	1.41776i	0.352252	+	0.935905i	$0.385416\pi$
$90$		0			0
$91$	7.05114			0.739160
$92$	−4.51242	+	1.62422i	−0.470452	+	0.169336i
$93$		0			0
$94$	−2.29227	+	0.673072i	−0.236430	+	0.0694221i
$95$	9.85172	+	11.3695i	1.01077	+	1.16649i
$96$		0			0
$97$	0.420422	+	2.92410i	0.0426874	+	0.296897i	0.999970	+	0.00774339i	$0.00246482\pi$
$97$	0.420422	+	2.92410i	0.0426874	+	0.296897i	−0.957283	+	0.289154i	$0.906626\pi$
$98$	−4.68448	−	3.01053i	−0.473204	−	0.304110i
$99$		0			0
$100$	−3.55233	+	4.09960i	−0.355233	+	0.409960i
$101$	−0.343376	+	2.38823i	−0.0341672	+	0.237638i	−0.999748	−	0.0224668i	$-0.992848\pi$
$101$	−0.343376	+	2.38823i	−0.0341672	+	0.237638i	0.965580	+	0.260105i	$0.0837571\pi$
$102$		0			0
$103$	17.5097	+	5.14132i	1.72528	+	0.506589i	0.985991	−	0.166796i	$-0.0533421\pi$
$103$	17.5097	+	5.14132i	1.72528	+	0.506589i	0.739292	+	0.673385i	$0.235160\pi$
$104$	5.65455	+	1.66032i	0.554474	+	0.162808i
$105$		0			0
$106$	−0.416864	+	2.89935i	−0.0404894	+	0.281610i
$107$	11.7816	−	13.5967i	1.13897	−	1.31444i	0.196370	−	0.980530i	$-0.437085\pi$
$107$	11.7816	−	13.5967i	1.13897	−	1.31444i	0.942603	−	0.333915i	$-0.108370\pi$
$108$		0			0
$109$	−3.16279	−	2.03260i	−0.302941	−	0.194688i	0.380335	−	0.924849i	$-0.375809\pi$
$109$	−3.16279	−	2.03260i	−0.302941	−	0.194688i	−0.683275	+	0.730161i	$0.739445\pi$
$110$	0.260554	+	1.81219i	0.0248429	+	0.172786i
$111$		0			0
$112$	0.783524	+	0.904235i	0.0740360	+	0.0854421i
$113$	−8.84192	+	2.59622i	−0.831778	+	0.244232i	−0.669780	−	0.742559i	$-0.733612\pi$
$113$	−8.84192	+	2.59622i	−0.831778	+	0.244232i	−0.161997	+	0.986791i	$0.551794\pi$
$114$		0			0
$115$	−1.28208	+	15.4312i	−0.119554	+	1.43896i
$116$	−4.24362			−0.394010
$117$		0			0
$118$	−0.649301	−	0.749334i	−0.0597730	−	0.0689817i
$119$	−0.152209	+	0.0978186i	−0.0139529	+	0.00896702i
$120$		0			0
$121$	−8.98329	−	5.77321i	−0.816663	−	0.524837i
$122$	0.844220	−	1.84858i	0.0764321	−	0.167363i
$123$		0			0
$124$	0.574766	−	3.99758i	0.0516155	−	0.358993i
$125$	0.569431	+	1.24688i	0.0509315	+	0.111524i
$126$		0			0
$127$	−10.8003	−	3.17124i	−0.958367	−	0.281402i	−0.235101	−	0.971971i	$-0.575542\pi$
$127$	−10.8003	−	3.17124i	−0.958367	−	0.281402i	−0.723267	+	0.690569i	$0.757360\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$		0			0
$130$	12.4604	−	14.3801i	1.09285	−	1.26122i
$131$	−5.92140	+	12.9661i	−0.517355	+	1.13285i	0.453076	+	0.891472i	$0.350326\pi$
$131$	−5.92140	+	12.9661i	−0.517355	+	1.13285i	−0.970431	+	0.241378i	$0.922401\pi$
$132$		0			0
$133$	−0.793392	−	5.51816i	−0.0687958	−	0.478485i
$134$	−1.10120	+	0.707701i	−0.0951295	+	0.0611360i
$135$		0			0
$136$	−0.145095	+	0.0426036i	−0.0124418	+	0.00365323i
$137$	17.9556			1.53405			0.767024	−	0.641618i	$-0.221736\pi$
$137$	17.9556			1.53405			0.767024	+	0.641618i	$0.221736\pi$
$138$		0			0
$139$	15.4382			1.30945			0.654723	−	0.755869i	$-0.272785\pi$
$139$	15.4382			1.30945			0.654723	+	0.755869i	$0.272785\pi$
$140$	3.70658	−	1.08835i	0.313263	−	0.0919824i
$141$		0			0
$142$	−1.29889	+	0.834743i	−0.109000	+	0.0700501i
$143$	−0.475582	−	3.30775i	−0.0397702	−	0.276608i
$144$		0			0
$145$	−5.69177	+	12.4632i	−0.472676	+	1.03502i
$146$	2.52389	−	2.91272i	0.208878	−	0.241059i
$147$		0			0
$148$	−3.90875	−	8.55897i	−0.321297	−	0.703543i
$149$	11.2893	+	3.31485i	0.924858	+	0.271563i	0.709282	−	0.704925i	$-0.249019\pi$
$149$	11.2893	+	3.31485i	0.924858	+	0.271563i	0.215575	+	0.976487i	$0.430837\pi$
$150$		0			0
$151$	−4.67292	−	10.2323i	−0.380277	−	0.832691i	−0.998895	−	0.0469988i	$-0.985034\pi$
$151$	−4.67292	−	10.2323i	−0.380277	−	0.832691i	0.618618	−	0.785692i	$-0.287693\pi$
$152$	0.663109	−	4.61202i	0.0537852	−	0.374084i
$153$		0			0
$154$	0.281841	−	0.617146i	0.0227114	−	0.0497311i
$155$	−10.9697	−	7.04982i	−0.881110	−	0.566255i
$156$		0			0
$157$	3.83924	−	2.46733i	0.306405	−	0.196914i	−0.378398	−	0.925643i	$-0.623525\pi$
$157$	3.83924	−	2.46733i	0.306405	−	0.196914i	0.684803	+	0.728729i	$0.259888\pi$
$158$	−5.55536	−	6.41122i	−0.441960	−	0.510050i
$159$		0			0
$160$	3.22871			0.255252
$161$	3.49127	−	4.55375i	0.275151	−	0.358886i
$162$		0			0
$163$	−10.5595	+	3.10055i	−0.827085	+	0.242854i	−0.667764	−	0.744373i	$-0.732749\pi$
$163$	−10.5595	+	3.10055i	−0.827085	+	0.242854i	−0.159321	+	0.987227i	$0.550930\pi$
$164$	−3.09871	−	3.57611i	−0.241969	−	0.279247i
$165$		0			0
$166$	0.787149	+	5.47474i	0.0610946	+	0.424922i
$167$	11.4291	+	7.34502i	0.884409	+	0.568375i	0.902128	−	0.431468i	$-0.142004\pi$
$167$	11.4291	+	7.34502i	0.884409	+	0.568375i	−0.0177196	+	0.999843i	$0.505641\pi$
$168$		0			0
$169$	−14.2305	+	16.4229i	−1.09465	+	1.26330i
$170$	−0.0694846	+	0.483276i	−0.00532922	+	0.0370656i
$171$		0			0
$172$	−3.35611	−	0.985442i	−0.255901	−	0.0751393i
$173$	−10.0680	−	2.95624i	−0.765457	−	0.224758i	−0.124380	−	0.992235i	$-0.539694\pi$
$173$	−10.0680	−	2.95624i	−0.765457	−	0.224758i	−0.641077	+	0.767476i	$0.721512\pi$
$174$		0			0
$175$	0.923671	−	6.42427i	0.0698229	−	0.485629i
$176$	0.371337	−	0.428546i	0.0279906	−	0.0323029i
$177$		0			0
$178$	−14.8884	−	9.56820i	−1.11593	−	0.717167i
$179$	−2.47729	−	17.2300i	−0.185162	−	1.28783i	−0.844326	−	0.535829i	$-0.819999\pi$
$179$	−2.47729	−	17.2300i	−0.185162	−	1.28783i	0.659165	−	0.751999i	$-0.270910\pi$
$180$		0			0
$181$	11.2379	+	12.9693i	0.835308	+	0.963997i	0.999749	−	0.0223899i	$-0.00712752\pi$
$181$	11.2379	+	12.9693i	0.835308	+	0.963997i	−0.164441	+	0.986387i	$0.552582\pi$
$182$	−6.76552	+	1.98653i	−0.501493	+	0.147252i
$183$		0			0
$184$	3.87204	−	2.82972i	0.285450	−	0.208610i
$185$	−30.3798			−2.23356
$186$		0			0
$187$	0.0561536	+	0.0648047i	0.00410636	+	0.00473899i
$188$	2.00979	−	1.29162i	0.146579	−	0.0942008i
$189$		0			0
$190$	−12.6558	−	8.13340i	−0.918149	−	0.590059i
$191$	−3.32989	+	7.29145i	−0.240943	+	0.527591i	−0.991013	−	0.133767i	$-0.957292\pi$
$191$	−3.32989	+	7.29145i	−0.240943	+	0.527591i	0.750070	+	0.661358i	$0.230020\pi$
$192$		0			0
$193$	2.31213	−	16.0812i	0.166430	−	1.15755i	−0.719758	−	0.694225i	$-0.755747\pi$
$193$	2.31213	−	16.0812i	0.166430	−	1.15755i	0.886189	−	0.463324i	$-0.153343\pi$
$194$	−1.22721	−	2.68721i	−0.0881082	−	0.192930i
$195$		0			0
$196$	5.34289	+	1.56881i	0.381635	+	0.112058i
$197$	−8.46731	−	18.5408i	−0.603271	−	1.32098i	−0.927083	−	0.374857i	$-0.877692\pi$
$197$	−8.46731	−	18.5408i	−0.603271	−	1.32098i	0.323812	−	0.946121i	$-0.395035\pi$
$198$		0			0
$199$	10.4596	−	12.0711i	0.741464	−	0.855695i	−0.252248	−	0.967663i	$-0.581170\pi$
$199$	10.4596	−	12.0711i	0.741464	−	0.855695i	0.993712	+	0.111968i	$0.0357154\pi$
$200$	2.25344	−	4.93435i	0.159342	−	0.348911i
$201$		0			0
$202$	−0.343376	−	2.38823i	−0.0241598	−	0.168035i
$203$	4.27136	−	2.74504i	0.299791	−	0.192664i
$204$		0			0
$205$	−14.6590	+	4.30426i	−1.02383	+	0.300622i
$206$	−18.2489			−1.27146
$207$		0			0
$208$	−5.89326			−0.408624
$209$	−2.53510	+	0.744373i	−0.175357	+	0.0514894i
$210$		0			0
$211$	19.0873	−	12.2667i	1.31403	−	0.844473i	0.319360	−	0.947633i	$-0.396532\pi$
$211$	19.0873	−	12.2667i	1.31403	−	0.844473i	0.994665	+	0.103161i	$0.0328956\pi$
$212$	−0.416864	−	2.89935i	−0.0286303	−	0.199128i
$213$		0			0
$214$	−7.47375	+	16.3652i	−0.510895	+	1.11870i
$215$	−7.39557	+	8.53495i	−0.504374	+	0.582079i
$216$		0			0
$217$	2.00736	+	4.39551i	0.136269	+	0.298387i
$218$	3.60733	+	1.05921i	0.244319	+	0.0717386i
$219$		0			0
$220$	−0.760554	−	1.66538i	−0.0512766	−	0.112280i
$221$	0.126828	−	0.882109i	0.00853138	−	0.0593371i
$222$		0			0
$223$	5.01547	−	10.9823i	0.335860	−	0.735432i	−0.664065	−	0.747675i	$-0.731170\pi$
$223$	5.01547	−	10.9823i	0.335860	−	0.735432i	0.999925	+	0.0122434i	$0.00389729\pi$
$224$	−1.00654	−	0.646863i	−0.0672521	−	0.0432203i
$225$		0			0
$226$	7.75232	−	4.98211i	0.515676	−	0.331405i
$227$	4.46773	+	5.15604i	0.296534	+	0.342218i	0.884391	−	0.466746i	$-0.154574\pi$
$227$	4.46773	+	5.15604i	0.296534	+	0.342218i	−0.587858	+	0.808964i	$0.700028\pi$
$228$		0			0
$229$	12.8490			0.849088			0.424544	−	0.905407i	$-0.360434\pi$
$229$	12.8490			0.849088			0.424544	+	0.905407i	$0.360434\pi$
$230$	−3.11732	−	15.1673i	−0.205550	−	1.00010i
$231$		0			0
$232$	4.07172	−	1.19557i	0.267322	−	0.0784928i
$233$	−3.66525	−	4.22992i	−0.240119	−	0.277112i	0.622881	−	0.782317i	$-0.285962\pi$
$233$	−3.66525	−	4.22992i	−0.240119	−	0.277112i	−0.862999	+	0.505205i	$0.831417\pi$
$234$		0			0
$235$	−1.09775	−	7.63502i	−0.0716093	−	0.498054i
$236$	0.834112	+	0.536051i	0.0542960	+	0.0348939i
$237$		0			0
$238$	0.118484	−	0.136738i	0.00768021	−	0.00886343i
$239$	−0.322011	+	2.23963i	−0.0208291	+	0.144870i	−0.997582	−	0.0694984i	$-0.977860\pi$
$239$	−0.322011	+	2.23963i	−0.0208291	+	0.144870i	0.976753	+	0.214368i	$0.0687692\pi$
$240$		0			0
$241$	−6.40569	−	1.88088i	−0.412627	−	0.121158i	0.0688290	−	0.997628i	$-0.478074\pi$
$241$	−6.40569	−	1.88088i	−0.412627	−	0.121158i	−0.481456	+	0.876470i	$0.659892\pi$
$242$	10.2459	+	3.00847i	0.658632	+	0.193392i
$243$		0			0
$244$	−0.289217	+	2.01155i	−0.0185152	+	0.128776i
$245$	11.7737	−	13.5875i	0.752192	−	0.868076i
$246$		0			0
$247$	23.1003	+	14.8457i	1.46984	+	0.944606i
$248$	0.574766	+	3.99758i	0.0364977	+	0.253847i
$249$		0			0
$250$	−0.897652	−	1.03595i	−0.0567725	−	0.0655190i
$251$	7.31337	−	2.14740i	0.461616	−	0.135543i	−0.0426521	−	0.999090i	$-0.513581\pi$
$251$	7.31337	−	2.14740i	0.461616	−	0.135543i	0.504268	+	0.863547i	$0.331763\pi$
$252$		0			0
$253$	−2.37168	−	1.33065i	−0.149106	−	0.0836570i
$254$	11.2562			0.706277
$255$		0			0
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	10.8867	−	6.99649i	0.679096	−	0.436429i	−0.155098	−	0.987899i	$-0.549569\pi$
$257$	10.8867	−	6.99649i	0.679096	−	0.436429i	0.834195	+	0.551470i	$0.185933\pi$
$258$		0			0
$259$	9.47078	+	6.08650i	0.588486	+	0.378197i
$260$	−7.90436	+	17.3081i	−0.490208	+	1.07341i
$261$		0			0
$262$	2.02858	−	14.1091i	0.125326	−	0.871662i
$263$	−7.07570	−	15.4936i	−0.436306	−	0.955377i	−0.992262	−	0.124165i	$-0.960375\pi$
$263$	−7.07570	−	15.4936i	−0.436306	−	0.955377i	0.555955	−	0.831212i	$-0.312353\pi$
$264$		0			0
$265$	−9.07432	−	2.66446i	−0.557431	−	0.163677i
$266$	2.31590	+	5.07111i	0.141997	+	0.310930i
$267$		0			0
$268$	0.857215	−	0.989279i	0.0523627	−	0.0604298i
$269$	4.12469	−	9.03182i	0.251487	−	0.550680i	−0.741216	−	0.671267i	$-0.765750\pi$
$269$	4.12469	−	9.03182i	0.251487	−	0.550680i	0.992703	+	0.120587i	$0.0384778\pi$
$270$		0			0
$271$	0.135310	+	0.941103i	0.00821951	+	0.0571679i	0.993518	−	0.113672i	$-0.0362611\pi$
$271$	0.135310	+	0.941103i	0.00821951	+	0.0571679i	−0.985299	+	0.170839i	$0.945352\pi$
$272$	0.127214	−	0.0817557i	0.00771351	−	0.00495717i
$273$		0			0
$274$	−17.2283	+	5.05867i	−1.04080	+	0.305606i
$275$	−3.07598			−0.185488
$276$		0			0
$277$	−25.4857			−1.53129			−0.765644	−	0.643265i	$-0.777580\pi$
$277$	−25.4857			−1.53129			−0.765644	+	0.643265i	$0.777580\pi$
$278$	−14.8128	+	4.34943i	−0.888413	+	0.260861i
$279$		0			0
$280$	−3.24982	+	2.08853i	−0.194214	+	0.124814i
$281$	1.54510	+	10.7464i	0.0921728	+	0.641076i	0.982570	+	0.185892i	$0.0595174\pi$
$281$	1.54510	+	10.7464i	0.0921728	+	0.641076i	−0.890397	+	0.455184i	$0.849574\pi$
$282$		0			0
$283$	−10.5773	+	23.1610i	−0.628755	+	1.37678i	0.280223	+	0.959935i	$0.409592\pi$
$283$	−10.5773	+	23.1610i	−0.628755	+	1.37678i	−0.908977	+	0.416846i	$0.863136\pi$
$284$	1.01110	−	1.16687i	0.0599976	−	0.0692409i
$285$		0			0
$286$	1.38822	+	3.03977i	0.0820870	+	0.179745i
$287$	5.43222	+	1.59504i	0.320654	+	0.0941525i
$288$		0			0
$289$	−7.05256	−	15.4429i	−0.414856	−	0.908408i
$290$	1.94991	−	13.5619i	0.114503	−	0.796385i
$291$		0			0
$292$	−1.60104	+	3.50580i	−0.0936940	+	0.205161i
$293$	−5.21294	−	3.35016i	−0.304543	−	0.195718i	0.379439	−	0.925217i	$-0.376117\pi$
$293$	−5.21294	−	3.35016i	−0.304543	−	0.195718i	−0.683982	+	0.729499i	$0.739753\pi$
$294$		0			0
$295$	2.69310	−	1.73075i	0.156798	−	0.100768i
$296$	6.16176	+	7.11105i	0.358145	+	0.413321i
$297$		0			0
$298$	−11.7659			−0.681582
$299$	5.68995	+	27.6844i	0.329059	+	1.60103i
$300$		0			0
$301$	4.01550	−	1.17906i	0.231449	−	0.0679597i
$302$	7.36640	+	8.50128i	0.423889	+	0.489194i
$303$		0			0
$304$	0.663109	+	4.61202i	0.0380319	+	0.264518i
$305$	5.51987	+	3.54741i	0.316067	+	0.203124i
$306$		0			0
$307$	−7.50267	+	8.65854i	−0.428200	+	0.494169i	−0.928317	−	0.371788i	$-0.878745\pi$
$307$	−7.50267	+	8.65854i	−0.428200	+	0.494169i	0.500118	+	0.865958i	$0.333290\pi$
$308$	−0.0965545	+	0.671552i	−0.00550171	+	0.0382652i
$309$		0			0
$310$	12.5115	+	3.67372i	0.710608	+	0.208653i
$311$	−16.1527	−	4.74286i	−0.915935	−	0.268943i	−0.210398	−	0.977616i	$-0.567476\pi$
$311$	−16.1527	−	4.74286i	−0.915935	−	0.268943i	−0.705537	+	0.708673i	$0.749294\pi$
$312$		0			0
$313$	4.21377	−	29.3074i	0.238176	−	1.65655i	−0.422858	−	0.906196i	$-0.638973\pi$
$313$	4.21377	−	29.3074i	0.238176	−	1.65655i	0.661034	−	0.750356i	$-0.270118\pi$
$314$	−2.98860	+	3.44903i	−0.168656	+	0.194640i
$315$		0			0
$316$	7.13658	+	4.58640i	0.401464	+	0.258005i
$317$	3.03974	+	21.1418i	0.170729	+	1.18744i	0.877349	+	0.479852i	$0.159310\pi$
$317$	3.03974	+	21.1418i	0.170729	+	1.18744i	−0.706621	+	0.707593i	$0.749781\pi$
$318$		0			0
$319$	−1.57581	−	1.81859i	−0.0882286	−	0.101821i
$320$	−3.09792	+	0.909632i	−0.173179	+	0.0508500i
$321$		0			0
$322$	−2.06691	+	5.35290i	−0.115185	+	0.298305i
$323$	−0.704602			−0.0392051
$324$		0			0
$325$	20.9348	+	24.1600i	1.16125	+	1.34016i
$326$	9.25825	−	5.94992i	0.512767	−	0.329535i
$327$		0			0
$328$	3.98070	+	2.55824i	0.219797	+	0.141255i
$329$	−1.18744	+	2.60012i	−0.0654654	+	0.143349i
$330$		0			0
$331$	−1.34990	+	9.38878i	−0.0741974	+	0.516054i	0.918500	+	0.395421i	$0.129401\pi$
$331$	−1.34990	+	9.38878i	−0.0741974	+	0.516054i	−0.992697	+	0.120633i	$0.961508\pi$
$332$	−2.29768	−	5.03121i	−0.126101	−	0.276124i
$333$		0			0
$334$	−13.0355	−	3.82755i	−0.713268	−	0.209434i
$335$	−1.75571	−	3.84446i	−0.0959244	−	0.210045i
$336$		0			0
$337$	−23.5960	+	27.2313i	−1.28536	+	1.48338i	−0.497589	+	0.867413i	$0.665781\pi$
$337$	−23.5960	+	27.2313i	−1.28536	+	1.48338i	−0.787769	+	0.615970i	$0.788764\pi$
$338$	9.02720	−	19.7668i	0.491015	−	1.07517i
$339$		0			0
$340$	−0.0694846	−	0.483276i	−0.00376833	−	0.0262093i
$341$	1.92658	−	1.23814i	0.104330	−	0.0670489i
$342$		0			0
$343$	−14.4287	+	4.23664i	−0.779076	+	0.228757i
$344$	3.49779			0.188588
$345$		0			0
$346$	10.4931			0.564110
$347$	−13.6104	+	3.99637i	−0.730643	+	0.214536i	−0.625834	−	0.779956i	$-0.715241\pi$
$347$	−13.6104	+	3.99637i	−0.730643	+	0.214536i	−0.104809	+	0.994492i	$0.533423\pi$
$348$		0			0
$349$	19.8958	−	12.7862i	1.06500	−	0.684432i	0.113953	−	0.993486i	$-0.463649\pi$
$349$	19.8958	−	12.7862i	1.06500	−	0.684432i	0.951044	+	0.309054i	$0.100012\pi$
$350$	0.923671	+	6.42427i	0.0493723	+	0.343392i
$351$		0			0
$352$	−0.235560	+	0.515804i	−0.0125554	+	0.0274925i
$353$	16.5810	−	19.1355i	0.882520	−	1.01848i	−0.117158	−	0.993113i	$-0.537378\pi$
$353$	16.5810	−	19.1355i	0.882520	−	1.01848i	0.999678	−	0.0253689i	$-0.00807605\pi$
$354$		0			0
$355$	−2.07088	−	4.53459i	−0.109911	−	0.240671i
$356$	16.9810	+	4.98607i	0.899991	+	0.264261i
$357$		0			0
$358$	7.23119	+	15.8341i	0.382180	+	0.836858i
$359$	−2.70519	+	18.8150i	−0.142775	+	0.993020i	0.784898	+	0.619625i	$0.212715\pi$
$359$	−2.70519	+	18.8150i	−0.142775	+	0.993020i	−0.927673	+	0.373395i	$0.878194\pi$
$360$		0			0
$361$	1.12596	−	2.46552i	0.0592613	−	0.129764i
$362$	−14.4366	−	9.27782i	−0.758769	−	0.487631i
$363$		0			0
$364$	5.93179	−	3.81213i	0.310910	−	0.199810i
$365$	8.14890	+	9.40433i	0.426533	+	0.492245i
$366$		0			0
$367$	−9.04960			−0.472386			−0.236193	−	0.971706i	$-0.575900\pi$
$367$	−9.04960			−0.472386			−0.236193	+	0.971706i	$0.575900\pi$
$368$	−2.91797	+	3.80598i	−0.152110	+	0.198400i
$369$		0			0
$370$	29.1492	−	8.55897i	1.51539	−	0.444960i
$371$	2.29507	+	2.64865i	0.119154	+	0.137511i
$372$		0			0
$373$	−2.19117	−	15.2399i	−0.113455	−	0.789094i	−0.964515	−	0.264027i	$-0.914949\pi$
$373$	−2.19117	−	15.2399i	−0.113455	−	0.789094i	0.851061	−	0.525067i	$-0.175960\pi$
$374$	−0.0721366	−	0.0463594i	−0.00373009	−	0.00239719i
$375$		0			0
$376$	−1.56449	+	1.80552i	−0.0806826	+	0.0931126i
$377$	−3.55912	+	24.7542i	−0.183304	+	1.27491i
$378$		0			0
$379$	12.9964	+	3.81609i	0.667581	+	0.196020i	0.597926	−	0.801552i	$-0.295992\pi$
$379$	12.9964	+	3.81609i	0.667581	+	0.196020i	0.0696556	+	0.997571i	$0.477810\pi$
$380$	14.4346	+	4.23838i	0.740480	+	0.217424i
$381$		0			0
$382$	1.14077	−	7.93424i	0.0583669	−	0.405951i
$383$	−21.5666	+	24.8891i	−1.10200	+	1.27178i	−0.142584	+	0.989783i	$0.545541\pi$
$383$	−21.5666	+	24.8891i	−1.10200	+	1.27178i	−0.959416	+	0.281993i	$0.909004\pi$
$384$		0			0
$385$	1.84280	+	1.18430i	0.0939178	+	0.0603573i
$386$	2.31213	+	16.0812i	0.117684	+	0.818511i
$387$		0			0
$388$	1.93457	+	2.23261i	0.0982128	+	0.113344i
$389$	−7.65832	+	2.24869i	−0.388292	+	0.114013i	−0.470051	−	0.882639i	$-0.655764\pi$
$389$	−7.65832	+	2.24869i	−0.388292	+	0.114013i	0.0817587	+	0.996652i	$0.473946\pi$
$390$		0			0
$391$	−0.506885	−	0.518672i	−0.0256343	−	0.0262304i
$392$	−5.56845			−0.281249
$393$		0			0
$394$	13.3479	+	15.4043i	0.672456	+	0.776056i
$395$	23.0419	−	14.8081i	1.15936	−	0.745078i
$396$		0			0
$397$	20.4451	+	13.1393i	1.02611	+	0.659441i	0.941514	−	0.336974i	$-0.109404\pi$
$397$	20.4451	+	13.1393i	1.02611	+	0.659441i	0.0845963	+	0.996415i	$0.473040\pi$
$398$	−6.63513	+	14.5289i	−0.332589	+	0.728269i
$399$		0			0
$400$	−0.771994	+	5.36934i	−0.0385997	+	0.268467i
$401$	−8.62438	−	18.8848i	−0.430681	−	0.943060i	−0.993216	−	0.116286i	$-0.962901\pi$
$401$	−8.62438	−	18.8848i	−0.430681	−	0.943060i	0.562535	−	0.826774i	$-0.309826\pi$
$402$		0			0
$403$	−22.8370	−	6.70554i	−1.13759	−	0.334027i
$404$	1.00231	+	2.19475i	0.0498668	+	0.109193i
$405$		0			0
$406$	−3.32498	+	3.83723i	−0.165016	+	0.190438i
$407$	2.21645	−	4.85334i	0.109865	−	0.240571i
$408$		0			0
$409$	0.306631	+	2.13267i	0.0151619	+	0.105454i	0.995997	−	0.0893860i	$-0.0284905\pi$
$409$	0.306631	+	2.13267i	0.0151619	+	0.105454i	−0.980835	+	0.194840i	$0.937581\pi$
$410$	12.8525	−	8.25981i	0.634740	−	0.407923i
$411$		0			0
$412$	17.5097	−	5.14132i	0.862642	−	0.253294i
$413$	−1.18632			−0.0583748
$414$		0			0
$415$	−17.8581			−0.876620
$416$	5.65455	−	1.66032i	0.277237	−	0.0814041i
$417$		0			0
$418$	2.22270	−	1.42844i	0.108716	−	0.0698674i
$419$	−1.62874	−	11.3281i	−0.0795691	−	0.553415i	−0.990142	−	0.140067i	$-0.955268\pi$
$419$	−1.62874	−	11.3281i	−0.0795691	−	0.553415i	0.910573	−	0.413348i	$-0.135641\pi$
$420$		0			0
$421$	1.54740	−	3.38834i	0.0754158	−	0.165138i	−0.868169	−	0.496269i	$-0.834703\pi$
$421$	1.54740	−	3.38834i	0.0754158	−	0.165138i	0.943585	+	0.331131i	$0.107430\pi$
$422$	−14.8582	+	17.1473i	−0.723287	+	0.834718i
$423$		0			0
$424$	1.21682	+	2.66446i	0.0590939	+	0.129398i
$425$	−0.787073	−	0.231105i	−0.0381786	−	0.0112103i
$426$		0			0
$427$	−1.01009	−	2.21178i	−0.0488816	−	0.107036i
$428$	2.56039	−	17.8079i	0.123761	−	0.860778i
$429$		0			0
$430$	4.69143	−	10.2728i	0.226241	−	0.495398i
$431$	27.0140	+	17.3608i	1.30122	+	0.836241i	0.993344	−	0.115186i	$-0.0367466\pi$
$431$	27.0140	+	17.3608i	1.30122	+	0.836241i	0.307873	+	0.951428i	$0.400383\pi$
$432$		0			0
$433$	−5.13129	+	3.29768i	−0.246594	+	0.158476i	−0.658100	−	0.752931i	$-0.728639\pi$
$433$	−5.13129	+	3.29768i	−0.246594	+	0.158476i	0.411506	+	0.911407i	$0.365003\pi$
$434$	−3.16441	−	3.65192i	−0.151897	−	0.175298i
$435$		0			0
$436$	−3.75962			−0.180053
$437$	21.0254	−	7.56796i	1.00578	−	0.362024i
$438$		0			0
$439$	−24.0664	+	7.06652i	−1.14862	+	0.337267i	−0.800003	−	0.599997i	$-0.795169\pi$
$439$	−24.0664	+	7.06652i	−1.14862	+	0.337267i	−0.348622	+	0.937263i	$0.613350\pi$
$440$	1.19894	+	1.38365i	0.0571572	+	0.0659629i
$441$		0			0
$442$	0.126828	+	0.882109i	0.00603260	+	0.0419576i
$443$	5.87864	+	3.77797i	0.279303	+	0.179497i	0.672791	−	0.739833i	$-0.265095\pi$
$443$	5.87864	+	3.77797i	0.279303	+	0.179497i	−0.393488	+	0.919330i	$0.628732\pi$
$444$		0			0
$445$	37.4196	−	43.1845i	1.77386	−	2.04714i
$446$	−1.71822	+	11.9505i	−0.0813602	+	0.565872i
$447$		0			0
$448$	1.14801	+	0.337086i	0.0542383	+	0.0159258i
$449$	−25.9983	−	7.63380i	−1.22694	−	0.360261i	−0.396844	−	0.917886i	$-0.629895\pi$
$449$	−25.9983	−	7.63380i	−1.22694	−	0.360261i	−0.830093	+	0.557625i	$0.811713\pi$
$450$		0			0
$451$	0.381858	−	2.65588i	0.0179810	−	0.125061i
$452$	−6.03467	+	6.96438i	−0.283847	+	0.327577i
$453$		0			0
$454$	−5.73938	−	3.68848i	−0.269362	−	0.173109i
$455$	−3.23995	−	22.5343i	−0.151891	−	1.05643i
$456$		0			0
$457$	−1.83627	−	2.11917i	−0.0858972	−	0.0991306i	0.711174	−	0.703016i	$-0.248164\pi$
$457$	−1.83627	−	2.11917i	−0.0858972	−	0.0991306i	−0.797071	+	0.603886i	$0.793618\pi$
$458$	−12.3286	+	3.61999i	−0.576076	+	0.169151i
$459$		0			0
$460$	7.26417	+	13.6747i	0.338694	+	0.637585i
$461$	14.2268			0.662609			0.331305	−	0.943524i	$-0.392511\pi$
$461$	14.2268			0.662609			0.331305	+	0.943524i	$0.392511\pi$
$462$		0			0
$463$	7.82793	+	9.03392i	0.363795	+	0.419842i	0.907908	−	0.419170i	$-0.137679\pi$
$463$	7.82793	+	9.03392i	0.363795	+	0.419842i	−0.544113	+	0.839012i	$0.683134\pi$
$464$	−3.56996	+	2.29427i	−0.165731	+	0.106509i
$465$		0			0
$466$	4.70849	+	3.02596i	0.218117	+	0.140175i
$467$	−12.6570	+	27.7149i	−0.585694	+	1.28249i	0.352315	+	0.935881i	$0.385395\pi$
$467$	−12.6570	+	27.7149i	−0.585694	+	1.28249i	−0.938009	+	0.346610i	$0.887333\pi$
$468$		0			0
$469$	−0.222892	+	1.55025i	−0.0102922	+	0.0715837i
$470$	3.20432	+	7.01648i	0.147804	+	0.323646i
$471$		0			0
$472$	−0.951347	−	0.279341i	−0.0437893	−	0.0128577i
$473$	−0.823940	−	1.80418i	−0.0378848	−	0.0829562i
$474$		0			0
$475$	16.5519	−	19.1019i	0.759452	−	0.876455i
$476$	−0.0751614	+	0.164580i	−0.00344502	+	0.00754353i
$477$		0			0
$478$	−0.322011	−	2.23963i	−0.0147284	−	0.102438i
$479$	17.3254	−	11.1343i	0.791616	−	0.508741i	−0.0812541	−	0.996693i	$-0.525893\pi$
$479$	17.3254	−	11.1343i	0.791616	−	0.508741i	0.872870	+	0.487953i	$0.162256\pi$
$480$		0			0
$481$	−53.2051	+	15.6224i	−2.42594	+	0.712322i
$482$	6.67612			0.304089
$483$		0			0
$484$	−10.6785			−0.485384
$485$	9.15178	−	2.68721i	0.415561	−	0.122020i
$486$		0			0
$487$	25.5866	−	16.4435i	1.15944	−	0.745127i	0.187944	−	0.982180i	$-0.439818\pi$
$487$	25.5866	−	16.4435i	1.15944	−	0.745127i	0.971497	+	0.237052i	$0.0761813\pi$
$488$	−0.289217	−	2.01155i	−0.0130922	−	0.0910585i
$489$		0			0
$490$	−7.46870	+	16.3542i	−0.337402	+	0.738807i
$491$	−12.6480	+	14.5966i	−0.570798	+	0.658736i	−0.965601	−	0.260030i	$-0.916268\pi$
$491$	−12.6480	+	14.5966i	−0.570798	+	0.658736i	0.394802	+	0.918766i	$0.370813\pi$
$492$		0			0
$493$	−0.266580	−	0.583730i	−0.0120062	−	0.0262899i
$494$	−26.3471	−	7.73620i	−1.18541	−	0.348068i
$495$		0			0
$496$	−1.67773	−	3.67372i	−0.0753324	−	0.164955i
$497$	−0.262904	+	1.82854i	−0.0117929	+	0.0820212i
$498$		0			0
$499$	−0.413293	+	0.904985i	−0.0185015	+	0.0405127i	−0.918657	−	0.395056i	$-0.870725\pi$
$499$	−0.413293	+	0.904985i	−0.0185015	+	0.0405127i	0.900156	+	0.435568i	$0.143453\pi$
$500$	1.15315	+	0.741085i	0.0515705	+	0.0331423i
$501$		0			0
$502$	−6.41213	+	4.12083i	−0.286187	+	0.183921i
$503$	−26.2152	−	30.2540i	−1.16888	−	1.34896i	−0.925373	−	0.379059i	$-0.876248\pi$
$503$	−26.2152	−	30.2540i	−1.16888	−	1.34896i	−0.243506	−	0.969899i	$-0.578298\pi$
$504$		0			0
$505$	7.79020			0.346659
$506$	2.65050	+	0.608566i	0.117829	+	0.0270541i
$507$		0			0
$508$	−10.8003	+	3.17124i	−0.479184	+	0.140701i
$509$	9.05687	+	10.4522i	0.401439	+	0.463285i	0.920094	−	0.391699i	$-0.128112\pi$
$509$	9.05687	+	10.4522i	0.401439	+	0.463285i	−0.518655	+	0.854984i	$0.673567\pi$
$510$		0			0
$511$	−0.656258	−	4.56437i	−0.0290311	−	0.201916i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$		0			0
$514$	−8.47462	+	9.78023i	−0.373799	+	0.431387i
$515$	8.38525	−	58.3207i	0.369498	−	2.56992i
$516$		0			0
$517$	1.29983	+	0.381664i	0.0571664	+	0.0167856i
$518$	−10.8019	−	3.17173i	−0.474609	−	0.139358i
$519$		0			0
$520$	2.70791	−	18.8340i	0.118750	−	0.825923i
$521$	−1.16054	+	1.33933i	−0.0508441	+	0.0586772i	−0.780602	−	0.625029i	$-0.785087\pi$
$521$	−1.16054	+	1.33933i	−0.0508441	+	0.0586772i	0.729758	+	0.683706i	$0.239633\pi$
$522$		0			0
$523$	−32.1950	−	20.6905i	−1.40779	−	0.904732i	−0.407825	−	0.913060i	$-0.633713\pi$
$523$	−32.1950	−	20.6905i	−1.40779	−	0.904732i	−0.999965	+	0.00832773i	$0.997349\pi$
$524$	2.02858	+	14.1091i	0.0886189	+	0.616358i
$525$		0			0
$526$	11.1541	+	12.8726i	0.486344	+	0.561270i
$527$	0.585992	−	0.172063i	0.0255262	−	0.00749517i
$528$		0			0
$529$	20.6964	+	10.0329i	0.899844	+	0.436213i
$530$	9.45741			0.410804
$531$		0			0
$532$	−3.65079	−	4.21323i	−0.158282	−	0.182667i
$533$	−23.4593	+	15.0764i	−1.01614	+	0.653031i
$534$		0			0
$535$	−48.8666	−	31.4046i	−2.11269	−	1.35774i
$536$	−0.543780	+	1.19071i	−0.0234877	+	0.0514309i
$537$		0			0
$538$	−1.41306	+	9.82802i	−0.0609212	+	0.423716i
$539$	1.31170	+	2.87223i	0.0564991	+	0.123716i
$540$		0			0
$541$	−13.3313	−	3.91443i	−0.573159	−	0.168295i	−0.0177068	−	0.999843i	$-0.505637\pi$
$541$	−13.3313	−	3.91443i	−0.573159	−	0.168295i	−0.555452	+	0.831549i	$0.687455\pi$
$542$	−0.394968	−	0.864860i	−0.0169653	−	0.0371489i
$543$		0			0
$544$	−0.0990281	+	0.114284i	−0.00424579	+	0.00489991i
$545$	−5.04260	+	11.0418i	−0.216001	+	0.472977i
$546$		0			0
$547$	1.83095	+	12.7345i	0.0782858	+	0.544490i	0.990788	+	0.135419i	$0.0432380\pi$
$547$	1.83095	+	12.7345i	0.0782858	+	0.544490i	−0.912503	+	0.409071i	$0.865853\pi$
$548$	15.1052	−	9.70752i	0.645262	−	0.414685i
$549$		0			0
$550$	2.95138	−	0.866603i	0.125847	−	0.0369521i
$551$	19.7729			0.842355
$552$		0			0
$553$	−10.1500			−0.431622
$554$	24.4534	−	7.18015i	1.03892	−	0.305056i
$555$		0			0
$556$	12.9874	−	8.34649i	0.550788	−	0.353970i
$557$	−1.27876	−	8.89394i	−0.0541826	−	0.376848i	−0.998813	−	0.0487117i	$-0.984488\pi$
$557$	−1.27876	−	8.89394i	−0.0541826	−	0.376848i	0.944630	−	0.328137i	$-0.106421\pi$
$558$		0			0
$559$	−8.56313	+	18.7506i	−0.362182	+	0.793067i
$560$	2.52977	−	2.91951i	0.106902	−	0.123372i
$561$		0			0
$562$	−4.51012	−	9.87578i	−0.190248	−	0.416585i
$563$	3.02452	+	0.888079i	0.127468	+	0.0374281i	0.344844	−	0.938660i	$-0.387932\pi$
$563$	3.02452	+	0.888079i	0.127468	+	0.0374281i	−0.217376	+	0.976088i	$0.569750\pi$
$564$		0			0
$565$	12.3599	+	27.0644i	0.519986	+	1.13861i
$566$	3.62362	−	25.2028i	0.152312	−	1.05935i
$567$		0			0
$568$	−0.641396	+	1.40446i	−0.0269124	+	0.0589299i
$569$	−15.1047	−	9.70721i	−0.633223	−	0.406948i	0.184279	−	0.982874i	$-0.441005\pi$
$569$	−15.1047	−	9.70721i	−0.633223	−	0.406948i	−0.817502	+	0.575926i	$0.804641\pi$
$570$		0			0
$571$	1.89782	−	1.21966i	0.0794213	−	0.0510410i	−0.500327	−	0.865836i	$-0.666787\pi$
$571$	1.89782	−	1.21966i	0.0794213	−	0.0510410i	0.579749	+	0.814795i	$0.303151\pi$
$572$	−2.18839	−	2.52553i	−0.0915011	−	0.105598i
$573$		0			0
$574$	−5.66155			−0.236309
$575$	25.9686	−	1.55755i	1.08296	−	0.0649544i
$576$		0			0
$577$	26.7821	−	7.86394i	1.11495	−	0.327380i	0.328177	−	0.944616i	$-0.393566\pi$
$577$	26.7821	−	7.86394i	1.11495	−	0.327380i	0.786778	+	0.617236i	$0.211748\pi$
$578$	11.1177	+	12.8305i	0.462434	+	0.533677i
$579$		0			0
$580$	1.94991	+	13.5619i	0.0809658	+	0.563129i
$581$	5.56720	+	3.57782i	0.230966	+	0.148433i
$582$		0			0
$583$	1.08771	−	1.25528i	0.0450482	−	0.0519884i
$584$	0.548493	−	3.81486i	0.0226968	−	0.157860i
$585$		0			0
$586$	5.94563	+	1.74579i	0.245612	+	0.0721181i
$587$	−14.4421	−	4.24058i	−0.596088	−	0.175027i	−0.0302483	−	0.999542i	$-0.509630\pi$
$587$	−14.4421	−	4.24058i	−0.596088	−	0.175027i	−0.565840	+	0.824515i	$0.691448\pi$
$588$		0			0
$589$	−2.67809	+	18.6265i	−0.110349	+	0.767493i
$590$	−2.09640	+	2.41938i	−0.0863076	+	0.0996043i
$591$		0			0
$592$	−7.91558	−	5.08703i	−0.325328	−	0.209076i
$593$	−2.94209	−	20.4627i	−0.120817	−	0.840302i	−0.956634	−	0.291293i	$-0.905914\pi$
$593$	−2.94209	−	20.4627i	−0.120817	−	0.840302i	0.835816	−	0.549009i	$-0.184995\pi$
$594$		0			0
$595$	0.382552	+	0.441488i	0.0156831	+	0.0180993i
$596$	11.2893	−	3.31485i	0.462429	−	0.135781i
$597$		0			0
$598$	−13.2591	−	24.9600i	−0.542204	−	1.02069i
$599$	−23.3328			−0.953354			−0.476677	−	0.879079i	$-0.658159\pi$
$599$	−23.3328			−0.953354			−0.476677	+	0.879079i	$0.658159\pi$
$600$		0			0
$601$	18.2016	+	21.0057i	0.742457	+	0.856842i	0.993814	−	0.111053i	$-0.0354223\pi$
$601$	18.2016	+	21.0057i	0.742457	+	0.856842i	−0.251357	+	0.967894i	$0.580877\pi$
$602$	−3.52066	+	2.26259i	−0.143491	+	0.0922164i
$603$		0			0
$604$	−9.46310	−	6.08157i	−0.385048	−	0.247455i
$605$	−14.3225	+	31.3619i	−0.582293	+	1.27504i
$606$		0			0
$607$	−0.851274	+	5.92074i	−0.0345521	+	0.240315i	−0.999777	−	0.0211046i	$-0.993282\pi$
$607$	−0.851274	+	5.92074i	−0.0345521	+	0.240315i	0.965225	+	0.261420i	$0.0841908\pi$
$608$	−1.93560	−	4.23838i	−0.0784991	−	0.171889i
$609$		0			0
$610$	−6.29570	−	1.84858i	−0.254906	−	0.0748470i
$611$	−5.84875	−	12.8070i	−0.236615	−	0.518114i
$612$		0			0
$613$	17.3336	−	20.0041i	0.700099	−	0.807957i	−0.288667	−	0.957430i	$-0.593212\pi$
$613$	17.3336	−	20.0041i	0.700099	−	0.807957i	0.988766	+	0.149472i	$0.0477575\pi$
$614$	4.75936	−	10.4216i	0.192072	−	0.420580i
$615$		0			0
$616$	−0.0965545	−	0.671552i	−0.00389029	−	0.0270576i
$617$	−8.74112	+	5.61758i	−0.351904	+	0.226155i	−0.704635	−	0.709570i	$-0.748889\pi$
$617$	−8.74112	+	5.61758i	−0.351904	+	0.226155i	0.352731	+	0.935725i	$0.385253\pi$
$618$		0			0
$619$	31.5027	−	9.25004i	1.26620	−	0.371790i	0.421402	−	0.906874i	$-0.361538\pi$
$619$	31.5027	−	9.25004i	1.26620	−	0.371790i	0.844799	+	0.535083i	$0.179720\pi$
$620$	−13.0397			−0.523689
$621$		0			0
$622$	16.8346			0.675006
$623$	−20.3173	+	5.96570i	−0.813996	+	0.239011i
$624$		0			0
$625$	−19.0939	+	12.2709i	−0.763757	+	0.490837i
$626$	4.21377	+	29.3074i	0.168416	+	1.17136i
$627$		0			0
$628$	1.89584	−	4.15130i	0.0756521	−	0.165655i
$629$	0.931781	−	1.07533i	0.0371526	−	0.0428763i
$630$		0			0
$631$	−8.95480	−	19.6083i	−0.356485	−	0.780594i	−0.999887	−	0.0150646i	$-0.995205\pi$
$631$	−8.95480	−	19.6083i	−0.356485	−	0.780594i	0.643401	−	0.765529i	$-0.277523\pi$
$632$	−8.13963	−	2.39001i	−0.323777	−	0.0950696i
$633$		0			0
$634$	−8.87296	−	19.4291i	−0.352390	−	0.771627i
$635$	−5.17215	+	35.9731i	−0.205250	+	1.42755i
$636$		0			0
$637$	13.6324	−	29.8508i	0.540136	−	1.18273i
$638$	2.02434	+	1.30096i	0.0801443	+	0.0515056i
$639$		0			0
$640$	2.71616	−	1.74557i	0.107366	−	0.0689998i
$641$	13.0180	+	15.0236i	0.514181	+	0.593397i	0.952164	−	0.305587i	$-0.0988525\pi$
$641$	13.0180	+	15.0236i	0.514181	+	0.593397i	−0.437983	+	0.898983i	$0.644307\pi$
$642$		0			0
$643$	−41.4485			−1.63457			−0.817284	−	0.576235i	$-0.804521\pi$
$643$	−41.4485			−1.63457			−0.817284	+	0.576235i	$0.804521\pi$
$644$	0.475103	−	5.71838i	0.0187217	−	0.225336i
$645$		0			0
$646$	0.676061	−	0.198509i	0.0265993	−	0.00781024i
$647$	−3.92796	−	4.53311i	−0.154424	−	0.178215i	0.673266	−	0.739400i	$-0.264891\pi$
$647$	−3.92796	−	4.53311i	−0.154424	−	0.178215i	−0.827690	+	0.561185i	$0.810345\pi$
$648$		0			0
$649$	0.0800142	+	0.556511i	0.00314083	+	0.0218450i
$650$	−26.8935	−	17.2834i	−1.05485	−	0.677910i
$651$		0			0
$652$	−7.20694	+	8.31725i	−0.282246	+	0.325729i
$653$	4.79551	−	33.3535i	0.187663	−	1.30522i	−0.650376	−	0.759612i	$-0.725389\pi$
$653$	4.79551	−	33.3535i	0.187663	−	1.30522i	0.838039	−	0.545611i	$-0.183702\pi$
$654$		0			0
$655$	44.1583	+	12.9661i	1.72541	+	0.506626i
$656$	−4.54019	−	1.33312i	−0.177265	−	0.0520496i
$657$		0			0
$658$	0.406797	−	2.82934i	0.0158586	−	0.110299i
$659$	3.96455	−	4.57533i	0.154437	−	0.178230i	−0.673259	−	0.739407i	$-0.735106\pi$
$659$	3.96455	−	4.57533i	0.154437	−	0.178230i	0.827696	+	0.561177i	$0.189651\pi$
$660$		0			0
$661$	40.5021	+	26.0291i	1.57535	+	1.01242i	0.977533	+	0.210782i	$0.0676011\pi$
$661$	40.5021	+	26.0291i	1.57535	+	1.01242i	0.597816	+	0.801633i	$0.296035\pi$
$662$	−1.34990	−	9.38878i	−0.0524655	−	0.364905i
$663$		0			0
$664$	3.62206	+	4.18008i	0.140563	+	0.162219i
$665$	−17.2706	+	5.07111i	−0.669726	+	0.196649i
$666$		0			0
$667$	14.2245	+	14.5553i	0.550774	+	0.563582i
$668$	13.5858			0.525649
$669$		0			0
$670$	2.76770	+	3.19409i	0.106925	+	0.123399i
$671$	−0.969438	+	0.623020i	−0.0374247	+	0.0240514i
$672$		0			0
$673$	16.9093	+	10.8669i	0.651804	+	0.418889i	0.824325	−	0.566117i	$-0.191555\pi$
$673$	16.9093	+	10.8669i	0.651804	+	0.418889i	−0.172521	+	0.985006i	$0.555191\pi$
$674$	14.9683	−	32.7760i	0.576557	−	1.26248i
$675$		0			0
$676$	−3.09258	+	21.5094i	−0.118945	+	0.827284i
$677$	15.4694	+	33.8732i	0.594536	+	1.30185i	0.932662	+	0.360751i	$0.117480\pi$
$677$	15.4694	+	33.8732i	0.594536	+	1.30185i	−0.338126	+	0.941101i	$0.609793\pi$
$678$		0			0
$679$	−3.39141	−	0.995807i	−0.130150	−	0.0382156i
$680$	0.202824	+	0.444124i	0.00777796	+	0.0170314i
$681$		0			0
$682$	−1.49972	+	1.73076i	−0.0574271	+	0.0662744i
$683$	14.1178	−	30.9136i	0.540201	−	1.18288i	−0.421008	−	0.907057i	$-0.638324\pi$
$683$	14.1178	−	30.9136i	0.540201	−	1.18288i	0.961210	−	0.275819i	$-0.0889490\pi$
$684$		0			0
$685$	−8.25046	−	57.3832i	−0.315234	−	2.19250i
$686$	12.6506	−	8.13006i	0.483003	−	0.310407i
$687$		0			0
$688$	−3.35611	+	0.985442i	−0.127950	+	0.0375696i
$689$	−17.2623			−0.657643
$690$		0			0
$691$	−45.9303			−1.74727			−0.873636	−	0.486580i	$-0.838244\pi$
$691$	−45.9303			−1.74727			−0.873636	+	0.486580i	$0.838244\pi$
$692$	−10.0680	+	2.95624i	−0.382729	+	0.112379i
$693$		0			0
$694$	11.9331	−	7.66897i	0.452976	−	0.291110i
$695$	−7.09372	−	49.3379i	−0.269080	−	1.87149i
$696$		0			0
$697$	0.297251	−	0.650890i	0.0112592	−	0.0246542i
$698$	−15.4876	+	17.8736i	−0.586213	+	0.676526i
$699$		0			0
$700$	−2.69618	−	5.90382i	−0.101906	−	0.223143i
$701$	4.02727	+	1.18251i	0.152108	+	0.0446629i	0.356900	−	0.934143i	$-0.383834\pi$
$701$	4.02727	+	1.18251i	0.152108	+	0.0446629i	−0.204792	+	0.978805i	$0.565652\pi$
$702$		0			0
$703$	18.2126	+	39.8801i	0.686902	+	1.50411i
$704$	0.0806993	−	0.561276i	0.00304147	−	0.0211539i
$705$		0			0
$706$	−10.5183	+	23.0318i	−0.395861	+	0.866815i
$707$	−2.42857	−	1.56074i	−0.0913356	−	0.0586978i
$708$		0			0
$709$	−15.4593	+	9.93506i	−0.580585	+	0.373119i	−0.797725	−	0.603021i	$-0.793963\pi$
$709$	−15.4593	+	9.93506i	−0.580585	+	0.373119i	0.217140	+	0.976140i	$0.430327\pi$
$710$	3.26454	+	3.76748i	0.122516	+	0.141391i
$711$		0			0
$712$	−17.6979			−0.663256
$713$	−15.6380	+	11.4284i	−0.585646	+	0.427996i
$714$		0			0
$715$	−10.3525	+	3.03977i	−0.387162	+	0.113681i
$716$	−11.3993	−	13.1554i	−0.426010	−	0.491642i
$717$		0			0
$718$	−2.70519	−	18.8150i	−0.100957	−	0.702171i
$719$	−17.9159	−	11.5138i	−0.668150	−	0.429394i	0.162108	−	0.986773i	$-0.448171\pi$
$719$	−17.9159	−	11.5138i	−0.668150	−	0.429394i	−0.830258	+	0.557379i	$0.811807\pi$
$720$		0			0
$721$	−14.2985	+	16.5013i	−0.532503	+	0.614541i
$722$	−0.385738	+	2.68287i	−0.0143557	+	0.0998460i
$723$		0			0
$724$	16.4656	+	4.83475i	0.611941	+	0.179682i
$725$	22.0873	+	6.48541i	0.820301	+	0.240862i
$726$		0			0
$727$	0.782890	−	5.44512i	0.0290358	−	0.201948i	−0.970140	−	0.242547i	$-0.922017\pi$
$727$	0.782890	−	5.44512i	0.0290358	−	0.201948i	0.999176	+	0.0405983i	$0.0129264\pi$
$728$	−4.61751	+	5.32889i	−0.171136	+	0.197502i
$729$		0			0
$730$	−10.4683	−	6.72758i	−0.387450	−	0.248999i
$731$	−0.0752755	−	0.523553i	−0.00278417	−	0.0193643i
$732$		0			0
$733$	31.0630	+	35.8487i	1.14734	+	1.32410i	0.938152	+	0.346225i	$0.112537\pi$
$733$	31.0630	+	35.8487i	1.14734	+	1.32410i	0.209188	+	0.977875i	$0.432918\pi$
$734$	8.68303	−	2.54957i	0.320497	−	0.0941063i
$735$		0			0
$736$	1.72750	−	4.47389i	0.0636766	−	0.164910i
$737$	0.742267			0.0273418
$738$		0			0
$739$	−14.7195	−	16.9872i	−0.541466	−	0.624885i	0.417408	−	0.908719i	$-0.362939\pi$
$739$	−14.7195	−	16.9872i	−0.541466	−	0.624885i	−0.958873	+	0.283835i	$0.908393\pi$
$740$	−25.5571	+	16.4245i	−0.939497	+	0.603778i
$741$		0			0
$742$	−2.94831	−	1.89477i	−0.108236	−	0.0695591i
$743$	4.36881	−	9.56635i	0.160276	−	0.350955i	−0.812408	−	0.583090i	$-0.801844\pi$
$743$	4.36881	−	9.56635i	0.160276	−	0.350955i	0.972684	+	0.232134i	$0.0745709\pi$
$744$		0			0
$745$	5.40636	−	37.6021i	0.198074	−	1.37763i
$746$	6.39600	+	14.0053i	0.234174	+	0.512770i
$747$		0			0
$748$	0.0822755	+	0.0241583i	0.00300829	+	0.000883314i
$749$	8.94214	+	19.5806i	0.326739	+	0.715458i
$750$		0			0
$751$	−19.0370	+	21.9698i	−0.694669	+	0.801691i	−0.988022	−	0.154313i	$-0.950684\pi$
$751$	−19.0370	+	21.9698i	−0.694669	+	0.801691i	0.293353	+	0.956004i	$0.405229\pi$
$752$	0.992446	−	2.17315i	0.0361908	−	0.0792467i
$753$		0			0
$754$	−3.55912	−	24.7542i	−0.129616	−	0.901496i
$755$	−30.5536	+	19.6356i	−1.11196	+	0.714612i
$756$		0			0
$757$	9.36715	−	2.75044i	0.340455	−	0.0999666i	−0.107036	−	0.994255i	$-0.534136\pi$
$757$	9.36715	−	2.75044i	0.340455	−	0.0999666i	0.447491	+	0.894289i	$0.352318\pi$
$758$	−13.5451			−0.491980
$759$		0			0
$760$	−15.0440			−0.545703
$761$	8.11283	−	2.38214i	0.294090	−	0.0863525i	−0.131360	−	0.991335i	$-0.541934\pi$
$761$	8.11283	−	2.38214i	0.294090	−	0.0863525i	0.425449	+	0.904982i	$0.360116\pi$
$762$		0			0
$763$	3.78420	−	2.43196i	0.136997	−	0.0880428i
$764$	1.14077	+	7.93424i	0.0412716	+	0.287051i
$765$		0			0
$766$	13.6809	−	29.9570i	0.494311	−	1.08239i
$767$	3.82650	−	4.41602i	0.138167	−	0.159453i
$768$		0			0
$769$	−10.8038	−	23.6570i	−0.389595	−	0.853095i	−0.998220	−	0.0596366i	$-0.981006\pi$
$769$	−10.8038	−	23.6570i	−0.389595	−	0.853095i	0.608625	−	0.793458i	$-0.291721\pi$
$770$	−2.10181	−	0.617146i	−0.0757439	−	0.0222404i
$771$		0			0
$772$	−6.74906	−	14.7784i	−0.242904	−	0.531886i
$773$	2.12196	−	14.7586i	0.0763218	−	0.530829i	−0.915412	−	0.402518i	$-0.868135\pi$
$773$	2.12196	−	14.7586i	0.0763218	−	0.530829i	0.991734	−	0.128312i	$-0.0409558\pi$
$774$		0			0
$775$	−9.10095	+	19.9283i	−0.326916	+	0.715845i
$776$	−2.48520	−	1.59714i	−0.0892136	−	0.0573341i
$777$		0			0
$778$	6.71458	−	4.31520i	0.240729	−	0.154707i
$779$	14.4383	+	16.6627i	0.517306	+	0.597002i
$780$		0			0
$781$	0.875515			0.0313284
$782$	0.632479	+	0.354856i	0.0226174	+	0.0126896i
$783$		0			0
$784$	5.34289	−	1.56881i	0.190817	−	0.0560291i
$785$	−9.64931	−	11.1359i	−0.344399	−	0.397457i
$786$		0			0
$787$	4.54765	+	31.6296i	0.162106	+	1.12747i	0.894655	+	0.446758i	$0.147422\pi$
$787$	4.54765	+	31.6296i	0.162106	+	1.12747i	−0.732549	+	0.680715i	$0.761669\pi$
$788$	−17.1471	−	11.0198i	−0.610839	−	0.392562i
$789$		0			0
$790$	−17.9366	+	20.7000i	−0.638156	+	0.736472i
$791$	1.56913	−	10.9135i	0.0557917	−	0.388040i
$792$		0			0
$793$	11.4914	+	3.37417i	0.408070	+	0.119820i
$794$	−23.3187	−	6.84699i	−0.827549	−	0.242990i
$795$		0			0
$796$	2.27310	−	15.8097i	0.0805677	−	0.560361i
$797$	19.4503	−	22.4468i	0.688964	−	0.795107i	−0.298254	−	0.954487i	$-0.596404\pi$
$797$	19.4503	−	22.4468i	0.688964	−	0.795107i	0.987217	+	0.159380i	$0.0509496\pi$
$798$		0			0
$799$	0.303921	+	0.195318i	0.0107520	+	0.00690986i
$800$	−0.771994	−	5.36934i	−0.0272941	−	0.189835i
$801$		0			0
$802$	13.5955	+	15.6900i	0.480073	+	0.554034i
$803$	−2.09692	+	0.615712i	−0.0739988	+	0.0217280i
$804$		0			0
$805$	−16.1573	−	9.06515i	−0.569470	−	0.319505i
$806$	23.8011			0.838357
$807$		0			0
$808$	−1.58004	−	1.82347i	−0.0555857	−	0.0641493i
$809$	21.4809	−	13.8050i	0.755229	−	0.485356i	−0.105500	−	0.994419i	$-0.533644\pi$
$809$	21.4809	−	13.8050i	0.755229	−	0.485356i	0.860729	+	0.509063i	$0.170008\pi$
$810$		0			0
$811$	−14.6318	−	9.40331i	−0.513794	−	0.330195i	0.257919	−	0.966167i	$-0.416963\pi$
$811$	−14.6318	−	9.40331i	−0.513794	−	0.330195i	−0.771713	+	0.635971i	$0.780600\pi$
$812$	2.10922	−	4.61855i	0.0740191	−	0.162079i
$813$		0			0
$814$	−0.759321	+	5.28119i	−0.0266142	+	0.185106i
$815$	14.7609	+	32.3219i	0.517052	+	1.13219i
$816$		0			0
$817$	15.6376	+	4.59162i	0.547091	+	0.160640i
$818$	−0.895052	−	1.95989i	−0.0312948	−	0.0685260i
$819$		0			0
$820$	−10.0048	+	11.5462i	−0.349384	+	0.403211i
$821$	−4.72084	+	10.3372i	−0.164758	+	0.360770i	−0.973946	−	0.226780i	$-0.927180\pi$
$821$	−4.72084	+	10.3372i	−0.164758	+	0.360770i	0.809188	+	0.587550i	$0.199907\pi$
$822$		0			0
$823$	−1.59889	−	11.1205i	−0.0557338	−	0.387637i	−0.998527	−	0.0542589i	$-0.982720\pi$
$823$	−1.59889	−	11.1205i	−0.0557338	−	0.387637i	0.942793	−	0.333379i	$-0.108189\pi$
$824$	−15.3520	+	9.86611i	−0.534811	+	0.343702i
$825$		0			0
$826$	1.13826	−	0.334224i	0.0396052	−	0.0116291i
$827$	40.8122			1.41918			0.709589	−	0.704615i	$-0.248880\pi$
$827$	40.8122			1.41918			0.709589	+	0.704615i	$0.248880\pi$
$828$		0			0
$829$	−20.7003			−0.718950			−0.359475	−	0.933155i	$-0.617044\pi$
$829$	−20.7003			−0.718950			−0.359475	+	0.933155i	$0.617044\pi$
$830$	17.1347	−	5.03121i	0.594755	−	0.174636i
$831$		0			0
$832$	−4.95773	+	3.18614i	−0.171878	+	0.110460i
$833$	0.119838	+	0.833490i	0.00415213	+	0.0288787i
$834$		0			0
$835$	18.2220	−	39.9005i	0.630597	−	1.38081i
$836$	−1.73023	+	1.99679i	−0.0598411	+	0.0690603i
$837$		0			0
$838$	4.75427	+	10.4104i	0.164233	+	0.359621i
$839$	49.7208	+	14.5993i	1.71655	+	0.504026i	0.984224	−	0.176925i	$-0.0566151\pi$
$839$	49.7208	+	14.5993i	1.71655	+	0.504026i	0.732329	+	0.680951i	$0.238433\pi$
$840$		0			0
$841$	−4.56611	−	9.99839i	−0.157452	−	0.344772i
$842$	−0.530117	+	3.68704i	−0.0182690	+	0.127064i
$843$		0			0
$844$	9.42541	−	20.6388i	0.324436	−	0.710416i
$845$	59.0237	+	37.9322i	2.03048	+	1.30491i
$846$		0			0
$847$	10.7483	−	6.90749i	0.369315	−	0.237344i
$848$	−1.91819	−	2.21371i	−0.0658711	−	0.0760193i
$849$		0			0
$850$	0.820301			0.0281361
$851$	−16.2545	+	42.0961i	−0.557198	+	1.44303i
$852$		0			0
$853$	52.0041	−	15.2698i	1.78059	−	0.522827i	0.785241	−	0.619191i	$-0.212539\pi$
$853$	52.0041	−	15.2698i	1.78059	−	0.522827i	0.995346	+	0.0963633i	$0.0307211\pi$
$854$	1.59230	+	1.83762i	0.0544875	+	0.0628819i
$855$		0			0
$856$	2.56039	+	17.8079i	0.0875124	+	0.608662i
$857$	11.1654	+	7.17555i	0.381402	+	0.245112i	0.717268	−	0.696798i	$-0.245392\pi$
$857$	11.1654	+	7.17555i	0.381402	+	0.245112i	−0.335866	+	0.941910i	$0.609029\pi$
$858$		0			0
$859$	18.9577	−	21.8783i	0.646827	−	0.746478i	−0.333739	−	0.942665i	$-0.608311\pi$
$859$	18.9577	−	21.8783i	0.646827	−	0.746478i	0.980566	+	0.196187i	$0.0628560\pi$
$860$	−1.60721	+	11.1784i	−0.0548055	+	0.381180i
$861$		0			0
$862$	−30.8108	−	9.04687i	−1.04942	−	0.308138i
$863$	−5.20557	−	1.52849i	−0.177200	−	0.0520305i	0.191929	−	0.981409i	$-0.438526\pi$
$863$	−5.20557	−	1.52849i	−0.177200	−	0.0520305i	−0.369129	+	0.929378i	$0.620344\pi$
$864$		0			0
$865$	−4.82149	+	33.5342i	−0.163935	+	1.14020i
$866$	3.99437	−	4.60975i	0.135734	−	0.156646i
$867$		0			0
$868$	4.06509	+	2.61248i	0.137978	+	0.0886733i
$869$	0.684593	+	4.76145i	0.0232232	+	0.161521i
$870$		0			0
$871$	−5.05179	−	5.83008i	−0.171174	−	0.197545i
$872$	3.60733	−	1.05921i	0.122160	−	0.0358693i
$873$		0			0
$874$	−18.0416	+	13.1849i	−0.610265	+	0.445987i
$875$	−1.64007			−0.0554445
$876$		0			0
$877$	9.38270	+	10.8282i	0.316831	+	0.365643i	0.891719	−	0.452590i	$-0.149500\pi$
$877$	9.38270	+	10.8282i	0.316831	+	0.365643i	−0.574888	+	0.818232i	$0.694954\pi$
$878$	21.1006	−	13.5606i	0.712112	−	0.457647i
$879$		0			0
$880$	−1.54019	−	0.989821i	−0.0519199	−	0.0333669i
$881$	14.5394	−	31.8369i	0.489846	−	1.07261i	−0.489791	−	0.871840i	$-0.662927\pi$
$881$	14.5394	−	31.8369i	0.489846	−	1.07261i	0.979638	−	0.200774i	$-0.0643457\pi$
$882$		0			0
$883$	0.921384	−	6.40837i	0.0310071	−	0.215659i	−0.968427	−	0.249297i	$-0.919800\pi$
$883$	0.921384	−	6.40837i	0.0310071	−	0.215659i	0.999434	+	0.0336385i	$0.0107095\pi$
$884$	−0.370209	−	0.810646i	−0.0124515	−	0.0272650i
$885$		0			0
$886$	−6.70489	−	1.96873i	−0.225255	−	0.0661409i
$887$	11.8202	+	25.8826i	0.396882	+	0.869051i	0.997577	+	0.0695725i	$0.0221635\pi$
$887$	11.8202	+	25.8826i	0.396882	+	0.869051i	−0.600695	+	0.799479i	$0.705109\pi$
$888$		0			0
$889$	8.81950	−	10.1783i	0.295797	−	0.341368i
$890$	−23.7373	+	51.9775i	−0.795678	+	1.74229i
$891$		0			0
$892$	−1.71822	−	11.9505i	−0.0575303	−	0.400132i
$893$	−9.36453	+	6.01822i	−0.313372	+	0.201392i
$894$		0			0
$895$	−53.9260	+	15.8341i	−1.80255	+	0.529275i
$896$	−1.19647			−0.0399714
$897$		0			0
$898$	27.0959			0.904202
$899$	−16.4444	+	4.82852i	−0.548453	+	0.161040i
$900$		0			0
$901$	0.372632	−	0.239476i	0.0124142	−	0.00797810i
$902$	0.381858	+	2.65588i	0.0127145	+	0.0884312i
$903$		0			0
$904$	3.82813	−	8.38244i	0.127322	−	0.278796i
$905$	36.2840	−	41.8739i	1.20612	−	1.39194i
$906$		0			0
$907$	19.1575	+	41.9492i	0.636116	+	1.39290i	0.903198	+	0.429225i	$0.141213\pi$
$907$	19.1575	+	41.9492i	0.636116	+	1.39290i	−0.267082	+	0.963674i	$0.586059\pi$
$908$	6.54606	+	1.92210i	0.217239	+	0.0637870i
$909$		0			0
$910$	9.45736	+	20.7087i	0.313508	+	0.686488i
$911$	−2.99109	+	20.8035i	−0.0990991	+	0.689250i	0.878341	+	0.478035i	$0.158651\pi$
$911$	−2.99109	+	20.8035i	−0.0990991	+	0.689250i	−0.977440	+	0.211214i	$0.932258\pi$
$912$		0			0
$913$	1.30289	−	2.85294i	0.0431194	−	0.0944184i
$914$	2.35893	+	1.51599i	0.0780265	+	0.0501446i
$915$		0			0
$916$	10.8093	−	6.94672i	0.357149	−	0.229526i
$917$	−11.1685	−	12.8891i	−0.368816	−	0.425636i
$918$		0			0
$919$	12.2512			0.404130			0.202065	−	0.979372i	$-0.435235\pi$
$919$	12.2512			0.404130			0.202065	+	0.979372i	$0.435235\pi$
$920$	−10.8225	−	11.0742i	−0.356808	−	0.365105i
$921$		0			0
$922$	−13.6505	+	4.00816i	−0.449556	+	0.132002i
$923$	−5.95866	−	6.87667i	−0.196132	−	0.226348i
$924$		0			0
$925$	7.26390	+	50.5215i	0.238835	+	1.66114i
$926$	−10.0560	−	6.46260i	−0.330461	−	0.212374i
$927$		0			0
$928$	2.77898	−	3.20711i	0.0912245	−	0.105279i
$929$	1.50358	−	10.4576i	0.0493308	−	0.343103i	−0.950176	−	0.311713i	$-0.899097\pi$
$929$	1.50358	−	10.4576i	0.0493308	−	0.343103i	0.999507	−	0.0313905i	$-0.00999355\pi$
$930$		0			0
$931$	−24.8949	−	7.30981i	−0.815898	−	0.239569i
$932$	−5.37028	−	1.57686i	−0.175909	−	0.0516516i
$933$		0			0
$934$	4.33608	−	30.1581i	0.141881	−	0.986803i
$935$	0.181304	−	0.209235i	0.00592926	−	0.00684273i
$936$		0			0
$937$	−3.56590	−	2.29166i	−0.116493	−	0.0748653i	0.481097	−	0.876667i	$-0.340238\pi$
$937$	−3.56590	−	2.29166i	−0.116493	−	0.0748653i	−0.597590	+	0.801802i	$0.703875\pi$
$938$	−0.222892	−	1.55025i	−0.00727768	−	0.0506173i
$939$		0			0
$940$	−5.05129	−	5.82950i	−0.164755	−	0.190137i
$941$	4.22571	−	1.24078i	0.137754	−	0.0404483i	−0.212129	−	0.977242i	$-0.568040\pi$
$941$	4.22571	−	1.24078i	0.137754	−	0.0404483i	0.349883	+	0.936793i	$0.386221\pi$
$942$		0			0
$943$	−1.87896	+	22.6153i	−0.0611873	+	0.736456i
$944$	0.991510			0.0322709
$945$		0			0
$946$	1.29886	+	1.49897i	0.0422296	+	0.0487356i
$947$	−43.0988	+	27.6979i	−1.40052	+	0.900062i	−0.999869	−	0.0161668i	$-0.994854\pi$
$947$	−43.0988	+	27.6979i	−1.40052	+	0.900062i	−0.400655	+	0.916229i	$0.631217\pi$
$948$		0			0
$949$	19.1075	+	12.2796i	0.620256	+	0.398614i
$950$	−10.4998	+	22.9913i	−0.340658	+	0.745937i
$951$		0			0
$952$	0.0257491	−	0.179089i	0.000834534	−	0.00580431i
$953$	18.4410	+	40.3801i	0.597362	+	1.30804i	0.930890	+	0.365300i	$0.119034\pi$
$953$	18.4410	+	40.3801i	0.597362	+	1.30804i	−0.333527	+	0.942740i	$0.608239\pi$
$954$		0			0
$955$	24.8324	+	7.29145i	0.803558	+	0.235946i
$956$	0.939944	+	2.05819i	0.0304000	+	0.0665666i
$957$		0			0
$958$	−13.4867	+	15.5644i	−0.435734	+	0.502864i
$959$	−8.92452	+	19.5420i	−0.288188	+	0.631043i
$960$		0			0
$961$	2.09046	+	14.5395i	0.0674342	+	0.469015i
$962$	46.6486	−	29.9792i	1.50401	−	0.966569i
$963$		0			0
$964$	−6.40569	+	1.88088i	−0.206313	+	0.0605791i
$965$	−52.4554			−1.68860
$966$		0			0
$967$	20.0385			0.644393			0.322197	−	0.946673i	$-0.395579\pi$
$967$	20.0385			0.644393			0.322197	+	0.946673i	$0.395579\pi$
$968$	10.2459	−	3.00847i	0.329316	−	0.0966959i
$969$		0			0
$970$	−8.02400	+	5.15671i	−0.257635	+	0.165572i
$971$	1.95186	+	13.5755i	0.0626383	+	0.435659i	0.996874	+	0.0790035i	$0.0251738\pi$
$971$	1.95186	+	13.5755i	0.0626383	+	0.435659i	−0.934236	+	0.356655i	$0.883917\pi$
$972$		0			0
$973$	−7.67327	+	16.8021i	−0.245994	+	0.538651i
$974$	−19.9175	+	22.9860i	−0.638198	+	0.736520i
$975$		0			0
$976$	0.844220	+	1.84858i	0.0270228	+	0.0591718i
$977$	−12.5084	−	3.67280i	−0.400180	−	0.117503i	0.0754485	−	0.997150i	$-0.475961\pi$
$977$	−12.5084	−	3.67280i	−0.400180	−	0.117503i	−0.475628	+	0.879646i	$0.657779\pi$
$978$		0			0
$979$	4.16891	+	9.12865i	0.133239	+	0.291753i
$980$	2.55866	−	17.7959i	0.0817335	−	0.568469i
$981$		0			0
$982$	8.02337	−	17.5687i	0.256036	−	0.560640i
$983$	11.0387	+	7.09415i	0.352080	+	0.226268i	0.704711	−	0.709494i	$-0.251077\pi$
$983$	11.0387	+	7.09415i	0.352080	+	0.226268i	−0.352631	+	0.935762i	$0.614713\pi$
$984$		0			0
$985$	−55.3629	+	35.5796i	−1.76401	+	1.13366i
$986$	0.420238	+	0.484980i	0.0133831	+	0.0154449i
$987$		0			0
$988$	27.4594			0.873599
$989$	7.86958	+	14.8143i	0.250238	+	0.471069i
$990$		0			0
$991$	−28.3790	+	8.33283i	−0.901490	+	0.264701i	−0.699455	−	0.714677i	$-0.746574\pi$
$991$	−28.3790	+	8.33283i	−0.901490	+	0.264701i	−0.202035	+	0.979378i	$0.564755\pi$
$992$	2.64478	+	3.05224i	0.0839718	+	0.0969087i
$993$		0			0
$994$	−0.262904	−	1.82854i	−0.00833881	−	0.0579977i
$995$	−43.3834	−	27.8808i	−1.37534	−	0.883880i
$996$		0			0
$997$	−5.78472	+	6.67593i	−0.183204	+	0.211429i	−0.839921	−	0.542708i	$-0.817399\pi$
$997$	−5.78472	+	6.67593i	−0.183204	+	0.211429i	0.656717	+	0.754137i	$0.271944\pi$
$998$	0.141588	−	0.984764i	0.00448188	−	0.0311722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.c.55.1		10
3.2	odd	2		46.2.c.b.9.1	✓	10
12.11	even	2		368.2.m.a.193.1		10
23.8	even	11		9522.2.a.bz.1.5		5
23.15	odd	22		9522.2.a.bw.1.1		5
23.18	even	11	inner	414.2.i.c.271.1		10
69.8	odd	22		1058.2.a.j.1.5		5
69.38	even	22		1058.2.a.k.1.5		5
69.41	odd	22		46.2.c.b.41.1	yes	10
276.107	odd	22		8464.2.a.bv.1.1		5
276.179	even	22		368.2.m.a.225.1		10
276.215	even	22		8464.2.a.bu.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.b.9.1	✓	10	3.2	odd	2
46.2.c.b.41.1	yes	10	69.41	odd	22
368.2.m.a.193.1		10	12.11	even	2
368.2.m.a.225.1		10	276.179	even	22
414.2.i.c.55.1		10	1.1	even	1	trivial
414.2.i.c.271.1		10	23.18	even	11	inner
1058.2.a.j.1.5		5	69.8	odd	22
1058.2.a.k.1.5		5	69.38	even	22
8464.2.a.bu.1.1		5	276.215	even	22
8464.2.a.bv.1.1		5	276.107	odd	22
9522.2.a.bw.1.1		5	23.15	odd	22
9522.2.a.bz.1.5		5	23.8	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.841254 - 0.540641i) q^{4} +(-0.459493 - 3.19584i) q^{5} +(-0.497033 + 1.08835i) q^{7} +(-0.654861 + 0.755750i) q^{8} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.841254 - 0.540641i) q^{4} +(-0.459493 - 3.19584i) q^{5} +(-0.497033 + 1.08835i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(1.34125 + 2.93694i) q^{10} +(0.544078 + 0.159756i) q^{11} +(-2.44815 - 5.36070i) q^{13} +(0.170276 - 1.18430i) q^{14} +(0.415415 - 0.909632i) q^{16} +(0.127214 + 0.0817557i) q^{17} +(-3.91978 + 2.51909i) q^{19} +(-2.11435 - 2.44009i) q^{20} -0.567047 q^{22} +(-4.67421 - 1.07322i) q^{23} +(-5.20482 + 1.52827i) q^{25} +(3.85927 + 4.45383i) q^{26} +(0.170276 + 1.18430i) q^{28} +(-3.56996 - 2.29427i) q^{29} +(2.64478 - 3.05224i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-0.145095 - 0.0426036i) q^{34} +(3.70658 + 1.08835i) q^{35} +(1.33908 - 9.31349i) q^{37} +(3.05129 - 3.52138i) q^{38} +(2.71616 + 1.74557i) q^{40} +(-0.673415 - 4.68370i) q^{41} +(-2.29057 - 2.64346i) q^{43} +(0.544078 - 0.159756i) q^{44} +(4.78723 - 0.287130i) q^{46} +2.38905 q^{47} +(3.64656 + 4.20835i) q^{49} +(4.56342 - 2.93273i) q^{50} +(-4.95773 - 3.18614i) q^{52} +(1.21682 - 2.66446i) q^{53} +(0.260554 - 1.81219i) q^{55} +(-0.497033 - 1.08835i) q^{56} +(4.07172 + 1.19557i) q^{58} +(0.411888 + 0.901910i) q^{59} +(-1.33083 + 1.53586i) q^{61} +(-1.67773 + 3.67372i) q^{62} +(-0.142315 - 0.989821i) q^{64} +(-16.0071 + 10.2871i) q^{65} +(1.25598 - 0.368789i) q^{67} +0.151220 q^{68} -3.86306 q^{70} +(1.48145 - 0.434992i) q^{71} +(-3.24226 + 2.08368i) q^{73} +(1.33908 + 9.31349i) q^{74} +(-1.93560 + 4.23838i) q^{76} +(-0.444295 + 0.512744i) q^{77} +(3.52408 + 7.71665i) q^{79} +(-3.09792 - 0.909632i) q^{80} +(1.96569 + 4.30426i) q^{82} +(0.787149 - 5.47474i) q^{83} +(0.202824 - 0.444124i) q^{85} +(2.94253 + 1.89105i) q^{86} +(-0.477031 + 0.306569i) q^{88} +(11.5896 + 13.3752i) q^{89} +7.05114 q^{91} +(-4.51242 + 1.62422i) q^{92} +(-2.29227 + 0.673072i) q^{94} +(9.85172 + 11.3695i) q^{95} +(0.420422 + 2.92410i) q^{97} +(-4.68448 - 3.01053i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

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Database

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