LMFDB - Embedded newform 450.2.l.c.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.2
Root			$0.543374 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	450.109
Dual form			450.2.l.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(1.36682 + 1.76969i) q^{5} -0.533559i q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(1.36682 + 1.76969i) q^{5} -0.533559i q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.23511 + 0.0655797i) q^{10} +(-1.16034 - 0.843033i) q^{11} +(3.86406 + 5.31842i) q^{13} +(0.431658 + 0.313618i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.911505 + 0.296166i) q^{17} +(-0.0657863 + 0.202470i) q^{19} +(1.26071 - 1.84679i) q^{20} +(1.36406 - 0.443209i) q^{22} +(2.21243 - 3.04515i) q^{23} +(-1.26362 + 4.83769i) q^{25} -6.57392 q^{26} +(-0.507445 + 0.164879i) q^{28} +(1.91420 + 5.89130i) q^{29} +(-0.722398 + 2.22331i) q^{31} -1.00000i q^{32} +(-0.775373 + 0.563341i) q^{34} +(0.944235 - 0.729278i) q^{35} +(-2.38812 - 3.28696i) q^{37} +(-0.125133 - 0.172231i) q^{38} +(0.753056 + 2.10545i) q^{40} +(-6.42486 + 4.66793i) q^{41} +11.3607i q^{43} +(-0.443209 + 1.36406i) q^{44} +(1.16314 + 3.57979i) q^{46} +(9.65219 - 3.13619i) q^{47} +6.71531 q^{49} +(-3.17104 - 3.86581i) q^{50} +(3.86406 - 5.31842i) q^{52} +(3.07528 - 0.999220i) q^{53} +(-0.0940579 - 3.20571i) q^{55} +(0.164879 - 0.507445i) q^{56} +(-5.89130 - 1.91420i) q^{58} +(-6.08749 + 4.42282i) q^{59} +(-10.1710 - 7.38968i) q^{61} +(-1.37408 - 1.89126i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-4.13050 + 14.1075i) q^{65} +(-6.57451 - 2.13619i) q^{67} -0.958413i q^{68} +(0.0349907 + 1.19256i) q^{70} +(-3.12869 - 9.62913i) q^{71} +(8.21552 - 11.3077i) q^{73} +4.06291 q^{74} +0.212889 q^{76} +(-0.449808 + 0.619107i) q^{77} +(-4.79840 - 14.7679i) q^{79} +(-2.14598 - 0.628316i) q^{80} -7.94156i q^{82} +(15.5315 + 5.04650i) q^{83} +(0.721739 + 2.01789i) q^{85} +(-9.19103 - 6.67767i) q^{86} +(-0.843033 - 1.16034i) q^{88} +(-4.54845 - 3.30464i) q^{89} +(2.83769 - 2.06170i) q^{91} +(-3.57979 - 1.16314i) q^{92} +(-3.13619 + 9.65219i) q^{94} +(-0.448227 + 0.160317i) q^{95} +(5.29318 - 1.71986i) q^{97} +(-3.94716 + 5.43280i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 - 4 * q^5	$ 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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
$5$	1.36682	+	1.76969i	0.611259	+	0.791430i
$5$	1.36682	+	1.76969i	0.611259	+	0.791430i
$6$		0			0
$7$		−	0.533559i		−	0.201666i	−0.994903	−	0.100833i	$-0.967849\pi$
$7$		−	0.533559i		−	0.201666i	0.994903	−	0.100833i	$-0.0321508\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		0			0
$10$	−2.23511	+	0.0655797i	−0.706803	+	0.0207381i
$11$	−1.16034	−	0.843033i	−0.349854	−	0.254184i	0.398954	−	0.916971i	$-0.369373\pi$
$11$	−1.16034	−	0.843033i	−0.349854	−	0.254184i	−0.748808	+	0.662787i	$0.769373\pi$
$12$		0			0
$13$	3.86406	+	5.31842i	1.07170	+	1.47506i	0.868347	+	0.495957i	$0.165183\pi$
$13$	3.86406	+	5.31842i	1.07170	+	1.47506i	0.203349	+	0.979106i	$0.434817\pi$
$14$	0.431658	+	0.313618i	0.115366	+	0.0838180i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.911505	+	0.296166i	0.221072	+	0.0718308i	0.417459	−	0.908696i	$-0.362921\pi$
$17$	0.911505	+	0.296166i	0.221072	+	0.0718308i	−0.196387	+	0.980527i	$0.562921\pi$
$18$		0			0
$19$	−0.0657863	+	0.202470i	−0.0150924	+	0.0464497i	−0.958319	−	0.285700i	$-0.907774\pi$
$19$	−0.0657863	+	0.202470i	−0.0150924	+	0.0464497i	0.943227	+	0.332150i	$0.107774\pi$
$20$	1.26071	−	1.84679i	0.281903	−	0.412954i
$21$		0			0
$22$	1.36406	−	0.443209i	0.290818	−	0.0944924i
$23$	2.21243	−	3.04515i	0.461324	−	0.634957i	−0.513459	−	0.858114i	$-0.671636\pi$
$23$	2.21243	−	3.04515i	0.461324	−	0.634957i	0.974783	+	0.223157i	$0.0716362\pi$
$24$		0			0
$25$	−1.26362	+	4.83769i	−0.252724	+	0.967538i
$26$	−6.57392			−1.28925
$27$		0			0
$28$	−0.507445	+	0.164879i	−0.0958981	+	0.0311592i
$29$	1.91420	+	5.89130i	0.355458	+	1.09399i	0.955743	+	0.294201i	$0.0950537\pi$
$29$	1.91420	+	5.89130i	0.355458	+	1.09399i	−0.600285	+	0.799786i	$0.704946\pi$
$30$		0			0
$31$	−0.722398	+	2.22331i	−0.129747	+	0.399319i	−0.994736	−	0.102471i	$-0.967325\pi$
$31$	−0.722398	+	2.22331i	−0.129747	+	0.399319i	0.864989	+	0.501790i	$0.167325\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−0.775373	+	0.563341i	−0.132975	+	0.0966122i
$35$	0.944235	−	0.729278i	0.159605	−	0.123270i
$36$		0			0
$37$	−2.38812	−	3.28696i	−0.392604	−	0.540373i	0.566264	−	0.824224i	$-0.308388\pi$
$37$	−2.38812	−	3.28696i	−0.392604	−	0.540373i	−0.958869	+	0.283850i	$0.908388\pi$
$38$	−0.125133	−	0.172231i	−0.0202993	−	0.0279395i
$39$		0			0
$40$	0.753056	+	2.10545i	0.119069	+	0.332900i
$41$	−6.42486	+	4.66793i	−1.00339	+	0.729009i	−0.962813	−	0.270167i	$-0.912921\pi$
$41$	−6.42486	+	4.66793i	−1.00339	+	0.729009i	−0.0405813	+	0.999176i	$0.512921\pi$
$42$		0			0
$43$			11.3607i			1.73250i	0.499614	+	0.866248i	$0.333475\pi$
$43$			11.3607i			1.73250i	−0.499614	+	0.866248i	$0.666525\pi$
$44$	−0.443209	+	1.36406i	−0.0668162	+	0.205639i
$45$		0			0
$46$	1.16314	+	3.57979i	0.171496	+	0.527811i
$47$	9.65219	−	3.13619i	1.40792	−	0.457460i	0.496175	−	0.868223i	$-0.334737\pi$
$47$	9.65219	−	3.13619i	1.40792	−	0.457460i	0.911742	+	0.410763i	$0.134737\pi$
$48$		0			0
$49$	6.71531			0.959331
$50$	−3.17104	−	3.86581i	−0.448453	−	0.546709i
$51$		0			0
$52$	3.86406	−	5.31842i	0.535848	−	0.737532i
$53$	3.07528	−	0.999220i	0.422423	−	0.137253i	−0.0900889	−	0.995934i	$-0.528715\pi$
$53$	3.07528	−	0.999220i	0.422423	−	0.137253i	0.512512	+	0.858680i	$0.328715\pi$
$54$		0			0
$55$	−0.0940579	−	3.20571i	−0.0126828	−	0.432258i
$56$	0.164879	−	0.507445i	0.0220329	−	0.0678102i
$57$		0			0
$58$	−5.89130	−	1.91420i	−0.773566	−	0.251347i
$59$	−6.08749	+	4.42282i	−0.792524	+	0.575802i	−0.908711	−	0.417425i	$-0.862933\pi$
$59$	−6.08749	+	4.42282i	−0.792524	+	0.575802i	0.116188	+	0.993227i	$0.462933\pi$
$60$		0			0
$61$	−10.1710	−	7.38968i	−1.30227	−	0.946151i	−0.302290	−	0.953216i	$-0.597751\pi$
$61$	−10.1710	−	7.38968i	−1.30227	−	0.946151i	−0.999975	+	0.00706498i	$0.997751\pi$
$62$	−1.37408	−	1.89126i	−0.174509	−	0.240191i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−4.13050	+	14.1075i	−0.512325	+	1.74982i
$66$		0			0
$67$	−6.57451	−	2.13619i	−0.803204	−	0.260977i	−0.121487	−	0.992593i	$-0.538766\pi$
$67$	−6.57451	−	2.13619i	−0.803204	−	0.260977i	−0.681717	+	0.731616i	$0.738766\pi$
$68$		−	0.958413i		−	0.116225i
$69$		0			0
$70$	0.0349907	+	1.19256i	0.00418218	+	0.142538i
$71$	−3.12869	−	9.62913i	−0.371308	−	1.14277i	−0.945936	−	0.324353i	$-0.894853\pi$
$71$	−3.12869	−	9.62913i	−0.371308	−	1.14277i	0.574628	−	0.818415i	$-0.305147\pi$
$72$		0			0
$73$	8.21552	−	11.3077i	0.961554	−	1.32347i	0.0153549	−	0.999882i	$-0.495112\pi$
$73$	8.21552	−	11.3077i	0.961554	−	1.32347i	0.946199	−	0.323584i	$-0.104888\pi$
$74$	4.06291			0.472304
$75$		0			0
$76$	0.212889			0.0244201
$77$	−0.449808	+	0.619107i	−0.0512604	+	0.0705538i
$78$		0			0
$79$	−4.79840	−	14.7679i	−0.539862	−	1.66152i	−0.732903	−	0.680333i	$-0.761835\pi$
$79$	−4.79840	−	14.7679i	−0.539862	−	1.66152i	0.193041	−	0.981191i	$-0.438165\pi$
$80$	−2.14598	−	0.628316i	−0.239928	−	0.0702478i
$81$		0			0
$82$		−	7.94156i		−	0.876999i
$83$	15.5315	+	5.04650i	1.70481	+	0.553926i	0.989455	−	0.144838i	$-0.0462662\pi$
$83$	15.5315	+	5.04650i	1.70481	+	0.553926i	0.715352	+	0.698764i	$0.246266\pi$
$84$		0			0
$85$	0.721739	+	2.01789i	0.0782835	+	0.218871i
$86$	−9.19103	−	6.67767i	−0.991094	−	0.720072i
$87$		0			0
$88$	−0.843033	−	1.16034i	−0.0898676	−	0.123692i
$89$	−4.54845	−	3.30464i	−0.482135	−	0.350291i	0.320017	−	0.947412i	$-0.396311\pi$
$89$	−4.54845	−	3.30464i	−0.482135	−	0.350291i	−0.802152	+	0.597120i	$0.796311\pi$
$90$		0			0
$91$	2.83769	−	2.06170i	0.297471	−	0.216125i
$92$	−3.57979	−	1.16314i	−0.373219	−	0.121266i
$93$		0			0
$94$	−3.13619	+	9.65219i	−0.323473	+	0.995548i
$95$	−0.448227	+	0.160317i	−0.0459871	+	0.0164482i
$96$		0			0
$97$	5.29318	−	1.71986i	0.537441	−	0.174625i	−0.0277049	−	0.999616i	$-0.508820\pi$
$97$	5.29318	−	1.71986i	0.537441	−	0.174625i	0.565146	+	0.824991i	$0.308820\pi$
$98$	−3.94716	+	5.43280i	−0.398724	+	0.548796i
$99$		0			0
$100$	4.99140	−	0.293155i	0.499140	−	0.0293155i
$101$	9.42708			0.938029			0.469015	−	0.883190i	$-0.344609\pi$
$101$	9.42708			0.938029			0.469015	+	0.883190i	$0.344609\pi$
$102$		0			0
$103$	7.60723	−	2.47174i	0.749562	−	0.243548i	0.0907695	−	0.995872i	$-0.471067\pi$
$103$	7.60723	−	2.47174i	0.749562	−	0.243548i	0.658793	+	0.752324i	$0.271067\pi$
$104$	2.03145	+	6.25217i	0.199200	+	0.613076i
$105$		0			0
$106$	−0.999220	+	3.07528i	−0.0970529	+	0.298698i
$107$		−	18.9260i		−	1.82964i	−0.403857	−	0.914822i	$-0.632331\pi$
$107$		−	18.9260i		−	1.82964i	0.403857	−	0.914822i	$-0.367669\pi$
$108$		0			0
$109$	−2.14813	+	1.56071i	−0.205754	+	0.149489i	−0.685891	−	0.727705i	$-0.740587\pi$
$109$	−2.14813	+	1.56071i	−0.205754	+	0.149489i	0.480137	+	0.877194i	$0.340587\pi$
$110$	2.64876	+	1.80817i	0.252549	+	0.172403i
$111$		0			0
$112$	0.313618	+	0.431658i	0.0296341	+	0.0407879i
$113$	−1.80029	−	2.47788i	−0.169357	−	0.233099i	0.715899	−	0.698203i	$-0.246017\pi$
$113$	−1.80029	−	2.47788i	−0.169357	−	0.233099i	−0.885256	+	0.465104i	$0.846017\pi$
$114$		0			0
$115$	8.41296	−	0.246843i	0.784513	−	0.0230182i
$116$	5.01144	−	3.64102i	0.465301	−	0.338061i
$117$		0			0
$118$		−	7.52455i		−	0.692691i
$119$	0.158022	−	0.486342i	0.0144859	−	0.0445829i
$120$		0			0
$121$	−2.76351	−	8.50522i	−0.251229	−	0.773202i
$122$	11.9567	−	3.88498i	1.08251	−	0.351730i
$123$		0			0
$124$	2.33773			0.209934
$125$	−10.2884	+	4.37602i	−0.920219	+	0.391404i
$126$		0			0
$127$	−3.81036	+	5.24451i	−0.338115	+	0.465375i	−0.943890	−	0.330261i	$-0.892863\pi$
$127$	−3.81036	+	5.24451i	−0.338115	+	0.465375i	0.605775	+	0.795636i	$0.292863\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	−8.98535	−	11.6338i	−0.788068	−	1.02035i
$131$	2.92266	−	8.99503i	0.255354	−	0.785900i	−0.738405	−	0.674357i	$-0.764421\pi$
$131$	2.92266	−	8.99503i	0.255354	−	0.785900i	0.993760	−	0.111543i	$-0.0355792\pi$
$132$		0			0
$133$	0.108029	+	0.0351009i	0.00936734	+	0.00304363i
$134$	5.59261	−	4.06327i	0.483128	−	0.351013i
$135$		0			0
$136$	0.775373	+	0.563341i	0.0664877	+	0.0483061i
$137$	−7.25096	−	9.98010i	−0.619492	−	0.852657i	0.377824	−	0.925877i	$-0.376672\pi$
$137$	−7.25096	−	9.98010i	−0.619492	−	0.852657i	−0.997316	+	0.0732202i	$0.976672\pi$
$138$		0			0
$139$	3.67227	+	2.66806i	0.311478	+	0.226302i	0.732530	−	0.680734i	$-0.238339\pi$
$139$	3.67227	+	2.66806i	0.311478	+	0.226302i	−0.421052	+	0.907036i	$0.638339\pi$
$140$	−0.985369	−	0.672662i	−0.0832789	−	0.0568503i
$141$		0			0
$142$	9.62913	+	3.12869i	0.808059	+	0.262554i
$143$		−	9.42867i		−	0.788465i
$144$		0			0
$145$	−7.80943	+	11.4399i	−0.648538	+	0.950030i
$146$	4.31916	+	13.2930i	0.357456	+	1.10014i
$147$		0			0
$148$	−2.38812	+	3.28696i	−0.196302	+	0.270187i
$149$	11.0750			0.907303			0.453651	−	0.891179i	$-0.350121\pi$
$149$	11.0750			0.907303			0.453651	+	0.891179i	$0.350121\pi$
$150$		0			0
$151$	−1.63387			−0.132962			−0.0664812	−	0.997788i	$-0.521177\pi$
$151$	−1.63387			−0.132962			−0.0664812	+	0.997788i	$0.521177\pi$
$152$	−0.125133	+	0.172231i	−0.0101496	+	0.0139698i
$153$		0			0
$154$	−0.236478	−	0.727804i	−0.0190559	−	0.0586481i
$155$	−4.92196	+	1.76044i	−0.395342	+	0.141402i
$156$		0			0
$157$			6.64544i			0.530364i	0.964198	+	0.265182i	$0.0854320\pi$
$157$			6.64544i			0.530364i	−0.964198	+	0.265182i	$0.914568\pi$
$158$	14.7679	+	4.79840i	1.17487	+	0.381740i
$159$		0			0
$160$	1.76969	−	1.36682i	0.139906	−	0.108056i
$161$	−1.62477	−	1.18046i	−0.128050	−	0.0930335i
$162$		0			0
$163$	−5.94451	−	8.18191i	−0.465610	−	0.640857i	0.510051	−	0.860144i	$-0.329627\pi$
$163$	−5.94451	−	8.18191i	−0.465610	−	0.640857i	−0.975660	+	0.219288i	$0.929627\pi$
$164$	6.42486	+	4.66793i	0.501697	+	0.364504i
$165$		0			0
$166$	−13.2119	+	9.59902i	−1.02544	+	0.745028i
$167$	−12.1625	−	3.95185i	−0.941166	−	0.305803i	−0.202045	−	0.979376i	$-0.564759\pi$
$167$	−12.1625	−	3.95185i	−0.941166	−	0.305803i	−0.739121	+	0.673573i	$0.764759\pi$
$168$		0			0
$169$	−9.33741	+	28.7376i	−0.718262	+	2.21058i
$170$	−2.05673	−	0.602186i	−0.157744	−	0.0461856i
$171$		0			0
$172$	10.8047	−	3.51066i	0.823851	−	0.267685i
$173$	−8.02770	+	11.0492i	−0.610335	+	0.840054i	−0.996605	−	0.0823317i	$-0.973763\pi$
$173$	−8.02770	+	11.0492i	−0.610335	+	0.840054i	0.386270	+	0.922386i	$0.373763\pi$
$174$		0			0
$175$	2.58119	+	0.674216i	0.195120	+	0.0509659i
$176$	1.43425			0.108111
$177$		0			0
$178$	5.34703	−	1.73735i	0.400776	−	0.130220i
$179$	0.924399	+	2.84501i	0.0690928	+	0.212646i	0.979641	−	0.200757i	$-0.0643401\pi$
$179$	0.924399	+	2.84501i	0.0690928	+	0.212646i	−0.910548	+	0.413403i	$0.864340\pi$
$180$		0			0
$181$	2.35559	−	7.24976i	0.175090	−	0.538871i	−0.824548	−	0.565792i	$-0.808570\pi$
$181$	2.35559	−	7.24976i	0.175090	−	0.538871i	0.999638	+	0.0269215i	$0.00857041\pi$
$182$			3.50758i			0.259999i
$183$		0			0
$184$	3.04515	−	2.21243i	0.224491	−	0.163102i
$185$	2.55279	−	8.71891i	0.187685	−	0.641027i
$186$		0			0
$187$	−0.807974	−	1.11208i	−0.0590849	−	0.0813234i
$188$	−5.96538	−	8.21065i	−0.435070	−	0.598823i
$189$		0			0
$190$	0.133762	−	0.456855i	0.00970408	−	0.0331438i
$191$	−6.79610	+	4.93766i	−0.491749	+	0.357276i	−0.805856	−	0.592111i	$-0.798295\pi$
$191$	−6.79610	+	4.93766i	−0.491749	+	0.357276i	0.314108	+	0.949387i	$0.398295\pi$
$192$		0			0
$193$			10.5266i			0.757723i	0.925453	+	0.378861i	$0.123684\pi$
$193$			10.5266i			0.757723i	−0.925453	+	0.378861i	$0.876316\pi$
$194$	−1.71986	+	5.29318i	−0.123479	+	0.380028i
$195$		0			0
$196$	−2.07515	−	6.38664i	−0.148225	−	0.456189i
$197$	−9.70843	+	3.15446i	−0.691697	+	0.224746i	−0.633709	−	0.773571i	$-0.718468\pi$
$197$	−9.70843	+	3.15446i	−0.691697	+	0.224746i	−0.0579878	+	0.998317i	$0.518468\pi$
$198$		0			0
$199$	−3.84318			−0.272436			−0.136218	−	0.990679i	$-0.543495\pi$
$199$	−3.84318			−0.272436			−0.136218	+	0.990679i	$0.543495\pi$
$200$	−2.69670	+	4.21044i	−0.190686	+	0.297723i
$201$		0			0
$202$	−5.54110	+	7.62667i	−0.389870	+	0.536610i
$203$	3.14336	−	1.02134i	0.220620	−	0.0716839i
$204$		0			0
$205$	−17.0424	−	4.98981i	−1.19029	−	0.348503i
$206$	−2.47174	+	7.60723i	−0.172214	+	0.530021i
$207$		0			0
$208$	−6.25217	−	2.03145i	−0.433510	−	0.140856i
$209$	0.247023	−	0.179472i	0.0170869	−	0.0124144i
$210$		0			0
$211$	−4.24669	−	3.08540i	−0.292354	−	0.212408i	0.431934	−	0.901905i	$-0.357831\pi$
$211$	−4.24669	−	3.08540i	−0.292354	−	0.212408i	−0.724288	+	0.689498i	$0.757831\pi$
$212$	−1.90063	−	2.61599i	−0.130536	−	0.179667i
$213$		0			0
$214$	15.3114	+	11.1244i	1.04667	+	0.760450i
$215$	−20.1050	+	15.5281i	−1.37115	+	1.05900i
$216$		0			0
$217$	1.18627	+	0.385442i	0.0805292	+	0.0261655i
$218$		−	2.65524i		−	0.179836i
$219$		0			0
$220$	−3.01974	+	1.08007i	−0.203591	+	0.0728185i
$221$	1.94697	+	5.99217i	0.130968	+	0.403077i
$222$		0			0
$223$	11.3315	−	15.5964i	0.758811	−	1.04441i	−0.238501	−	0.971142i	$-0.576656\pi$
$223$	11.3315	−	15.5964i	0.758811	−	1.04441i	0.997312	−	0.0732716i	$-0.0233440\pi$
$224$	−0.533559			−0.0356499
$225$		0			0
$226$	3.06283			0.203736
$227$	−4.96066	+	6.82776i	−0.329250	+	0.453174i	−0.941263	−	0.337673i	$-0.890360\pi$
$227$	−4.96066	+	6.82776i	−0.329250	+	0.453174i	0.612013	+	0.790848i	$0.290360\pi$
$228$		0			0
$229$	−1.84041	−	5.66419i	−0.121618	−	0.374300i	0.871652	−	0.490125i	$-0.163049\pi$
$229$	−1.84041	−	5.66419i	−0.121618	−	0.374300i	−0.993270	+	0.115825i	$0.963049\pi$
$230$	−4.74532	+	6.95132i	−0.312897	+	0.458357i
$231$		0			0
$232$			6.19448i			0.406688i
$233$	−1.99049	−	0.646750i	−0.130401	−	0.0423700i	0.243089	−	0.970004i	$-0.421839\pi$
$233$	−1.99049	−	0.646750i	−0.130401	−	0.0423700i	−0.373491	+	0.927634i	$0.621839\pi$
$234$		0			0
$235$	18.7429	+	12.7948i	1.22265	+	0.834642i
$236$	6.08749	+	4.42282i	0.396262	+	0.287901i
$237$		0			0
$238$	0.300576	+	0.413707i	0.0194834	+	0.0268167i
$239$	−8.00797	−	5.81813i	−0.517993	−	0.376344i	0.297855	−	0.954611i	$-0.403729\pi$
$239$	−8.00797	−	5.81813i	−0.517993	−	0.376344i	−0.815847	+	0.578268i	$0.803729\pi$
$240$		0			0
$241$	17.3588	−	12.6119i	1.11818	−	0.812406i	0.134249	−	0.990948i	$-0.457138\pi$
$241$	17.3588	−	12.6119i	1.11818	−	0.812406i	0.983932	+	0.178542i	$0.0571379\pi$
$242$	8.50522	+	2.76351i	0.546736	+	0.177645i
$243$		0			0
$244$	−3.88498	+	11.9567i	−0.248711	+	0.765452i
$245$	9.17861	+	11.8840i	0.586400	+	0.759243i
$246$		0			0
$247$	−1.33102	+	0.432474i	−0.0846907	+	0.0275177i
$248$	−1.37408	+	1.89126i	−0.0872543	+	0.120095i
$249$		0			0
$250$	2.50707	−	10.8956i	0.158561	−	0.689100i
$251$	4.10753			0.259265			0.129632	−	0.991562i	$-0.458620\pi$
$251$	4.10753			0.259265			0.129632	+	0.991562i	$0.458620\pi$
$252$		0			0
$253$	−5.13432	+	1.66824i	−0.322792	+	0.104881i
$254$	−2.00323	−	6.16529i	−0.125694	−	0.386845i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$			30.7748i			1.91968i	0.280552	+	0.959839i	$0.409482\pi$
$257$			30.7748i			1.91968i	−0.280552	+	0.959839i	$0.590518\pi$
$258$		0			0
$259$	−1.75379	+	1.27420i	−0.108975	+	0.0791751i
$260$	14.6934	−	0.431116i	0.911247	−	0.0267367i
$261$		0			0
$262$	5.55924	+	7.65163i	0.343451	+	0.472719i
$263$	16.6771	+	22.9541i	1.02836	+	1.41541i	0.906174	+	0.422904i	$0.138989\pi$
$263$	16.6771	+	22.9541i	1.02836	+	1.41541i	0.122183	+	0.992508i	$0.461011\pi$
$264$		0			0
$265$	5.97166	+	4.07655i	0.366836	+	0.250421i
$266$	−0.0918954	+	0.0667659i	−0.00563447	+	0.00409368i
$267$		0			0
$268$			6.91285i			0.422269i
$269$	3.29621	−	10.1447i	0.200974	−	0.618533i	−0.798881	−	0.601489i	$-0.794574\pi$
$269$	3.29621	−	10.1447i	0.200974	−	0.618533i	0.999855	−	0.0170443i	$-0.00542564\pi$
$270$		0			0
$271$	7.05917	+	21.7259i	0.428814	+	1.31975i	0.899295	+	0.437343i	$0.144080\pi$
$271$	7.05917	+	21.7259i	0.428814	+	1.31975i	−0.470481	+	0.882410i	$0.655920\pi$
$272$	−0.911505	+	0.296166i	−0.0552681	+	0.0179577i
$273$		0			0
$274$	12.3361			0.745250
$275$	5.54456	−	4.54807i	0.334349	−	0.274259i
$276$		0			0
$277$	−18.4912	+	25.4510i	−1.11103	+	1.52920i	−0.291141	+	0.956680i	$0.594035\pi$
$277$	−18.4912	+	25.4510i	−1.11103	+	1.52920i	−0.819889	+	0.572522i	$0.805965\pi$
$278$	−4.31701	+	1.40268i	−0.258917	+	0.0841273i
$279$		0			0
$280$	1.12338	−	0.401800i	0.0671348	−	0.0240121i
$281$	3.33074	−	10.2510i	0.198695	−	0.611522i	−0.801218	−	0.598372i	$-0.795814\pi$
$281$	3.33074	−	10.2510i	0.198695	−	0.611522i	0.999914	−	0.0131494i	$-0.00418569\pi$
$282$		0			0
$283$	3.96046	+	1.28683i	0.235425	+	0.0764943i	0.424354	−	0.905497i	$-0.360501\pi$
$283$	3.96046	+	1.28683i	0.235425	+	0.0764943i	−0.188928	+	0.981991i	$0.560501\pi$
$284$	−8.19103	+	5.95113i	−0.486048	+	0.353135i
$285$		0			0
$286$	7.62795	+	5.54203i	0.451050	+	0.327707i
$287$	2.49062	+	3.42804i	0.147017	+	0.202351i
$288$		0			0
$289$	−13.0102	−	9.45244i	−0.765304	−	0.556026i
$290$	−4.66479	−	13.0422i	−0.273926	−	0.765862i
$291$		0			0
$292$	−13.2930	−	4.31916i	−0.777914	−	0.252760i
$293$		−	17.9603i		−	1.04925i	−0.851333	−	0.524626i	$-0.824205\pi$
$293$		−	17.9603i		−	1.04925i	0.851333	−	0.524626i	$-0.175795\pi$
$294$		0			0
$295$	−16.1475	−	4.72779i	−0.940145	−	0.275263i
$296$	−1.25551	−	3.86406i	−0.0729749	−	0.224594i
$297$		0			0
$298$	−6.50975	+	8.95990i	−0.377099	+	0.519033i
$299$	24.7443			1.43100
$300$		0			0
$301$	6.06163			0.349386
$302$	0.960365	−	1.32183i	0.0552628	−	0.0760627i
$303$		0			0
$304$	−0.0657863	−	0.202470i	−0.00377311	−	0.0116124i
$305$	−0.824473	−	28.0999i	−0.0472092	−	1.60900i
$306$		0			0
$307$		−	20.8174i		−	1.18811i	−0.804423	−	0.594056i	$-0.797526\pi$
$307$		−	20.8174i		−	1.18811i	0.804423	−	0.594056i	$-0.202474\pi$
$308$	0.727804	+	0.236478i	0.0414705	+	0.0134746i
$309$		0			0
$310$	1.46883	−	5.01671i	0.0834240	−	0.284930i
$311$	−15.7375	−	11.4339i	−0.892390	−	0.648359i	0.0441099	−	0.999027i	$-0.485955\pi$
$311$	−15.7375	−	11.4339i	−0.892390	−	0.648359i	−0.936500	+	0.350667i	$0.885955\pi$
$312$		0			0
$313$	3.45800	+	4.75953i	0.195458	+	0.269024i	0.895485	−	0.445092i	$-0.146829\pi$
$313$	3.45800	+	4.75953i	0.195458	+	0.269024i	−0.700027	+	0.714116i	$0.746829\pi$
$314$	−5.37627	−	3.90609i	−0.303401	−	0.220433i
$315$		0			0
$316$	−12.5624	+	9.12709i	−0.706688	+	0.513439i
$317$	10.2344	+	3.32534i	0.574818	+	0.186770i	0.581978	−	0.813205i	$-0.302279\pi$
$317$	10.2344	+	3.32534i	0.574818	+	0.186770i	−0.00715959	+	0.999974i	$0.502279\pi$
$318$		0			0
$319$	2.74545	−	8.44962i	0.153716	−	0.473088i
$320$	0.0655797	+	2.23511i	0.00366602	+	0.124946i
$321$		0			0
$322$	1.91003	−	0.620606i	0.106442	−	0.0345850i
$323$	−0.119929	+	0.165068i	−0.00667304	+	0.00918465i
$324$		0			0
$325$	−30.6116	+	11.9727i	−1.69802	+	0.664123i
$326$	10.1134			0.560129
$327$		0			0
$328$	−7.55288	+	2.45408i	−0.417038	+	0.135504i
$329$	−1.67334	−	5.15002i	−0.0922543	−	0.283930i
$330$		0			0
$331$	−0.190692	+	0.586889i	−0.0104814	+	0.0322584i	−0.956160	−	0.292843i	$-0.905399\pi$
$331$	−0.190692	+	0.586889i	−0.0104814	+	0.0322584i	0.945679	+	0.325102i	$0.105399\pi$
$332$		−	16.3308i		−	0.896270i
$333$		0			0
$334$	10.3461	−	7.51686i	0.566112	−	0.411304i
$335$	−5.20576	−	14.5546i	−0.284421	−	0.795205i
$336$		0			0
$337$	9.05814	+	12.4675i	0.493429	+	0.679146i	0.981016	−	0.193928i	$-0.0621229\pi$
$337$	9.05814	+	12.4675i	0.493429	+	0.679146i	−0.487587	+	0.873074i	$0.662123\pi$
$338$	−17.7608	−	24.4456i	−0.966060	−	1.32967i
$339$		0			0
$340$	1.69610	−	1.30998i	0.0919837	−	0.0710434i
$341$	2.71255	−	1.97078i	0.146893	−	0.106724i
$342$		0			0
$343$		−	7.31793i		−	0.395131i
$344$	−3.51066	+	10.8047i	−0.189282	+	0.582551i
$345$		0			0
$346$	−4.22041	−	12.9891i	−0.226891	−	0.698298i
$347$	21.5477	−	7.00126i	1.15674	−	0.375847i	0.333061	−	0.942905i	$-0.391919\pi$
$347$	21.5477	−	7.00126i	1.15674	−	0.375847i	0.823678	+	0.567058i	$0.191919\pi$
$348$		0			0
$349$	16.9543			0.907544			0.453772	−	0.891118i	$-0.350078\pi$
$349$	16.9543			0.907544			0.453772	+	0.891118i	$0.350078\pi$
$350$	−2.06264	+	1.69194i	−0.110253	+	0.0904378i
$351$		0			0
$352$	−0.843033	+	1.16034i	−0.0449338	+	0.0618461i
$353$	−5.76583	+	1.87343i	−0.306884	+	0.0997127i	−0.458411	−	0.888740i	$-0.651581\pi$
$353$	−5.76583	+	1.87343i	−0.306884	+	0.0997127i	0.151526	+	0.988453i	$0.451581\pi$
$354$		0			0
$355$	12.7642	−	18.6981i	0.677456	−	0.992392i
$356$	−1.73735	+	5.34703i	−0.0920796	+	0.283392i
$357$		0			0
$358$	−2.84501	−	0.924399i	−0.150363	−	0.0488560i
$359$	−15.2894	+	11.1084i	−0.806943	+	0.586279i	−0.912943	−	0.408088i	$-0.866196\pi$
$359$	−15.2894	+	11.1084i	−0.806943	+	0.586279i	0.105999	+	0.994366i	$0.466196\pi$
$360$		0			0
$361$	15.3347	+	11.1413i	0.807087	+	0.586383i
$362$	4.48060	+	6.16702i	0.235495	+	0.324131i
$363$		0			0
$364$	−2.83769	−	2.06170i	−0.148735	−	0.108063i
$365$	31.2403	−	0.916613i	1.63519	−	0.0479777i
$366$		0			0
$367$	−23.8224	−	7.74036i	−1.24352	−	0.404044i	−0.387924	−	0.921691i	$-0.626808\pi$
$367$	−23.8224	−	7.74036i	−1.24352	−	0.404044i	−0.855594	+	0.517648i	$0.826808\pi$
$368$			3.76401i			0.196213i
$369$		0			0
$370$	5.55325	+	7.19010i	0.288700	+	0.373795i
$371$	−0.533143	−	1.64085i	−0.0276794	−	0.0851885i
$372$		0			0
$373$	6.99196	−	9.62360i	0.362030	−	0.498291i	−0.588683	−	0.808364i	$-0.700353\pi$
$373$	6.99196	−	9.62360i	0.362030	−	0.498291i	0.950713	+	0.310073i	$0.100353\pi$
$374$	1.37461			0.0710792
$375$		0			0
$376$	10.1489			0.523390
$377$	−23.9358	+	32.9448i	−1.23276	+	1.69675i
$378$		0			0
$379$	−8.50366	−	26.1716i	−0.436804	−	1.34434i	−0.891227	−	0.453558i	$-0.850155\pi$
$379$	−8.50366	−	26.1716i	−0.436804	−	1.34434i	0.454423	−	0.890786i	$-0.349845\pi$
$380$	0.290981	+	0.376748i	0.0149270	+	0.0193268i
$381$		0			0
$382$		−	8.40045i		−	0.429804i
$383$	−20.9531	−	6.80809i	−1.07066	−	0.347877i	−0.279912	−	0.960026i	$-0.590305\pi$
$383$	−20.9531	−	6.80809i	−1.07066	−	0.347877i	−0.790743	+	0.612149i	$0.790305\pi$
$384$		0			0
$385$	−1.71043	+	0.0501855i	−0.0871718	+	0.00255769i
$386$	−8.51621	−	6.18739i	−0.433464	−	0.314930i
$387$		0			0
$388$	−3.27137	−	4.50265i	−0.166078	−	0.228587i
$389$	−14.1491	−	10.2799i	−0.717386	−	0.521212i	0.168162	−	0.985759i	$-0.446217\pi$
$389$	−14.1491	−	10.2799i	−0.717386	−	0.521212i	−0.885548	+	0.464548i	$0.846217\pi$
$390$		0			0
$391$	2.91851	−	2.12042i	0.147595	−	0.107234i
$392$	6.38664	+	2.07515i	0.322574	+	0.104811i
$393$		0			0
$394$	3.15446	−	9.70843i	0.158919	−	0.489104i
$395$	19.5762	−	28.6768i	0.984985	−	1.44288i
$396$		0			0
$397$	23.3000	−	7.57062i	1.16939	−	0.379959i	0.340976	−	0.940072i	$-0.389242\pi$
$397$	23.3000	−	7.57062i	1.16939	−	0.379959i	0.828416	+	0.560113i	$0.189242\pi$
$398$	2.25896	−	3.10920i	0.113232	−	0.155850i
$399$		0			0
$400$	−1.82123	−	4.65651i	−0.0910617	−	0.232826i
$401$	−1.04105			−0.0519875			−0.0259937	−	0.999662i	$-0.508275\pi$
$401$	−1.04105			−0.0519875			−0.0259937	+	0.999662i	$0.508275\pi$
$402$		0			0
$403$	−14.6159	+	4.74899i	−0.728069	+	0.236564i
$404$	−2.91313	−	8.96568i	−0.144934	−	0.446059i
$405$		0			0
$406$	−1.02134	+	3.14336i	−0.0506882	+	0.156002i
$407$			5.82724i			0.288845i
$408$		0			0
$409$	18.0061	−	13.0822i	0.890345	−	0.646873i	−0.0456231	−	0.998959i	$-0.514527\pi$
$409$	18.0061	−	13.0822i	0.890345	−	0.646873i	0.935968	+	0.352085i	$0.114527\pi$
$410$	14.0541	−	10.8547i	0.694084	−	0.536074i
$411$		0			0
$412$	−4.70153	−	6.47109i	−0.231628	−	0.318808i
$413$	2.35984	+	3.24804i	0.116120	+	0.159825i
$414$		0			0
$415$	12.2980	+	34.3837i	0.603686	+	1.68783i
$416$	5.31842	−	3.86406i	0.260757	−	0.189451i
$417$		0			0
$418$			0.305337i			0.0149345i
$419$	−7.14737	+	21.9973i	−0.349172	+	1.07464i	0.610141	+	0.792293i	$0.291113\pi$
$419$	−7.14737	+	21.9973i	−0.349172	+	1.07464i	−0.959312	+	0.282347i	$0.908887\pi$
$420$		0			0
$421$	3.01643	+	9.28363i	0.147012	+	0.452457i	0.997264	−	0.0739190i	$-0.0235506\pi$
$421$	3.01643	+	9.28363i	0.147012	+	0.452457i	−0.850252	+	0.526376i	$0.823551\pi$
$422$	4.99228	−	1.62209i	0.243021	−	0.0789622i
$423$		0			0
$424$	3.23354			0.157035
$425$	−2.58456	+	4.03534i	−0.125369	+	0.195743i
$426$		0			0
$427$	−3.94283	+	5.42684i	−0.190807	+	0.262623i
$428$	−17.9997	+	5.84845i	−0.870048	+	0.282696i
$429$		0			0
$430$	−0.745034	−	25.3925i	−0.0359287	−	1.22453i
$431$	−2.62448	+	8.07731i	−0.126417	+	0.389070i	−0.994157	−	0.107948i	$-0.965572\pi$
$431$	−2.62448	+	8.07731i	−0.126417	+	0.389070i	0.867740	+	0.497019i	$0.165572\pi$
$432$		0			0
$433$	−20.9272	−	6.79967i	−1.00570	−	0.326771i	−0.240558	−	0.970635i	$-0.577330\pi$
$433$	−20.9272	−	6.79967i	−1.00570	−	0.326771i	−0.765140	+	0.643864i	$0.777330\pi$
$434$	−1.00910	+	0.733154i	−0.0484384	+	0.0351925i
$435$		0			0
$436$	2.14813	+	1.56071i	0.102877	+	0.0747445i
$437$	0.471002	+	0.648279i	0.0225311	+	0.0310114i
$438$		0			0
$439$	−31.0325	−	22.5464i	−1.48110	−	1.07608i	−0.977201	−	0.212318i	$-0.931899\pi$
$439$	−31.0325	−	22.5464i	−1.48110	−	1.07608i	−0.503898	−	0.863763i	$-0.668101\pi$
$440$	0.901164	−	3.07787i	0.0429613	−	0.146732i
$441$		0			0
$442$	−5.99217	−	1.94697i	−0.285018	−	0.0926080i
$443$			12.7478i			0.605666i	0.953044	+	0.302833i	$0.0979324\pi$
$443$			12.7478i			0.605666i	−0.953044	+	0.302833i	$0.902068\pi$
$444$		0			0
$445$	−0.368702	−	12.5662i	−0.0174782	−	0.595695i
$446$	5.95730	+	18.3347i	0.282087	+	0.868173i
$447$		0			0
$448$	0.313618	−	0.431658i	0.0148171	−	0.0203939i
$449$	18.0358			0.851161			0.425580	−	0.904921i	$-0.360070\pi$
$449$	18.0358			0.851161			0.425580	+	0.904921i	$0.360070\pi$
$450$		0			0
$451$	11.3902			0.536344
$452$	−1.80029	+	2.47788i	−0.0846783	+	0.116550i
$453$		0			0
$454$	−2.60797	−	8.02651i	−0.122398	−	0.376703i
$455$	7.52718	+	2.20387i	0.352880	+	0.103319i
$456$		0			0
$457$		−	21.1495i		−	0.989334i	−0.869083	−	0.494667i	$-0.835290\pi$
$457$		−	21.1495i		−	0.989334i	0.869083	−	0.494667i	$-0.164710\pi$
$458$	5.66419	+	1.84041i	0.264670	+	0.0859966i
$459$		0			0
$460$	−2.83451	−	7.92492i	−0.132160	−	0.369502i
$461$	25.8954	+	18.8141i	1.20607	+	0.876260i	0.994868	−	0.101183i	$-0.0322627\pi$
$461$	25.8954	+	18.8141i	1.20607	+	0.876260i	0.211200	+	0.977443i	$0.432263\pi$
$462$		0			0
$463$	16.9150	+	23.2815i	0.786108	+	1.08198i	0.994582	+	0.103957i	$0.0331503\pi$
$463$	16.9150	+	23.2815i	0.786108	+	1.08198i	−0.208474	+	0.978028i	$0.566850\pi$
$464$	−5.01144	−	3.64102i	−0.232650	−	0.169030i
$465$		0			0
$466$	1.69321	−	1.23019i	0.0784366	−	0.0569875i
$467$	−4.94859	−	1.60789i	−0.228993	−	0.0744045i	0.192273	−	0.981342i	$-0.438414\pi$
$467$	−4.94859	−	1.60789i	−0.228993	−	0.0744045i	−0.421266	+	0.906937i	$0.638414\pi$
$468$		0			0
$469$	−1.13978	+	3.50789i	−0.0526303	+	0.161979i
$470$	−21.3680	+	7.64270i	−0.985633	+	0.352532i
$471$		0			0
$472$	−7.15627	+	2.32521i	−0.329394	+	0.107027i
$473$	9.57747	−	13.1823i	0.440373	−	0.606121i
$474$		0			0
$475$	−0.896356	−	0.574099i	−0.0411276	−	0.0263414i
$476$	−0.511370			−0.0234386
$477$		0			0
$478$	9.41393	−	3.05877i	0.430583	−	0.139905i
$479$	−12.2490	−	37.6985i	−0.559670	−	1.72249i	−0.683279	−	0.730157i	$-0.739447\pi$
$479$	−12.2490	−	37.6985i	−0.559670	−	1.72249i	0.123609	−	0.992331i	$-0.460553\pi$
$480$		0			0
$481$	8.25361	−	25.4020i	0.376332	−	1.15823i
$482$			21.4567i			0.977326i
$483$		0			0
$484$	−7.23497	+	5.25652i	−0.328862	+	0.238933i
$485$	10.2784	+	7.01657i	0.466719	+	0.318606i
$486$		0			0
$487$	3.19936	+	4.40354i	0.144977	+	0.199544i	0.875330	−	0.483527i	$-0.160644\pi$
$487$	3.19936	+	4.40354i	0.144977	+	0.199544i	−0.730353	+	0.683070i	$0.760644\pi$
$488$	−7.38968	−	10.1710i	−0.334515	−	0.460420i
$489$		0			0
$490$	−15.0094	+	0.440388i	−0.678057	+	0.0198947i
$491$	0.707053	−	0.513704i	0.0319088	−	0.0231831i	−0.571717	−	0.820451i	$-0.693722\pi$
$491$	0.707053	−	0.513704i	0.0319088	−	0.0231831i	0.603625	+	0.797268i	$0.293722\pi$
$492$		0			0
$493$			5.93687i			0.267383i
$494$	0.432474	−	1.33102i	0.0194579	−	0.0598854i
$495$		0			0
$496$	−0.722398	−	2.22331i	−0.0324366	−	0.0998297i
$497$	−5.13771	+	1.66934i	−0.230458	+	0.0748803i
$498$		0			0
$499$	34.9604			1.56504			0.782522	−	0.622623i	$-0.213933\pi$
$499$	34.9604			1.56504			0.782522	+	0.622623i	$0.213933\pi$
$500$	7.34113	+	8.43255i	0.328305	+	0.377115i
$501$		0			0
$502$	−2.41434	+	3.32306i	−0.107757	+	0.148315i
$503$	0.304076	−	0.0988002i	0.0135581	−	0.00440528i	−0.302230	−	0.953235i	$-0.597731\pi$
$503$	0.304076	−	0.0988002i	0.0135581	−	0.00440528i	0.315788	+	0.948830i	$0.397731\pi$
$504$		0			0
$505$	12.8851	+	16.6830i	0.573379	+	0.742385i
$506$	1.66824	−	5.13432i	0.0741624	−	0.228248i
$507$		0			0
$508$	6.16529	+	2.00323i	0.273541	+	0.0888788i
$509$	−16.6867	+	12.1236i	−0.739624	+	0.537368i	−0.892593	−	0.450863i	$-0.851116\pi$
$509$	−16.6867	+	12.1236i	−0.739624	+	0.537368i	0.152969	+	0.988231i	$0.451116\pi$
$510$		0			0
$511$	−6.03333	−	4.38347i	−0.266899	−	0.193913i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$		0			0
$514$	−24.8973	−	18.0890i	−1.09817	−	0.797870i
$515$	14.7719	+	10.0840i	0.650928	+	0.444356i
$516$		0			0
$517$	−13.8437	−	4.49809i	−0.608845	−	0.197826i
$518$		−	2.16780i		−	0.0952477i
$519$		0			0
$520$	−8.28779	+	12.1406i	−0.363444	+	0.532402i
$521$	1.30417	+	4.01383i	0.0571368	+	0.175849i	0.975552	−	0.219769i	$-0.0705304\pi$
$521$	1.30417	+	4.01383i	0.0571368	+	0.175849i	−0.918415	+	0.395618i	$0.870530\pi$
$522$		0			0
$523$	−12.6714	+	17.4407i	−0.554081	+	0.762627i	−0.990559	−	0.137088i	$-0.956226\pi$
$523$	−12.6714	+	17.4407i	−0.554081	+	0.762627i	0.436478	+	0.899715i	$0.356226\pi$
$524$	−9.45794			−0.413172
$525$		0			0
$526$	−28.3729			−1.23712
$527$	−1.31694	+	1.81261i	−0.0573668	+	0.0789586i
$528$		0			0
$529$	2.72931	+	8.39994i	0.118666	+	0.365215i
$530$	−6.80806	+	2.43504i	−0.295723	+	0.105771i
$531$		0			0
$532$		−	0.113589i		−	0.00492470i
$533$	−49.6520	−	16.1329i	−2.15067	−	0.698795i
$534$		0			0
$535$	33.4932	−	25.8684i	1.44804	−	1.11839i
$536$	−5.59261	−	4.06327i	−0.241564	−	0.175507i
$537$		0			0
$538$	6.26977	+	8.62960i	0.270309	+	0.372048i
$539$	−7.79201	−	5.66123i	−0.335626	−	0.243846i
$540$		0			0
$541$	7.22987	−	5.25281i	0.310837	−	0.225836i	−0.421419	−	0.906866i	$-0.638468\pi$
$541$	7.22987	−	5.25281i	0.310837	−	0.225836i	0.732255	+	0.681030i	$0.238468\pi$
$542$	−21.7259	−	7.05917i	−0.933206	−	0.303217i
$543$		0			0
$544$	0.296166	−	0.911505i	0.0126980	−	0.0390805i
$545$	−5.69809	−	1.66833i	−0.244079	−	0.0714634i
$546$		0			0
$547$	11.4874	−	3.73249i	0.491167	−	0.159590i	−0.0529536	−	0.998597i	$-0.516864\pi$
$547$	11.4874	−	3.73249i	0.491167	−	0.159590i	0.544120	+	0.839007i	$0.316864\pi$
$548$	−7.25096	+	9.98010i	−0.309746	+	0.426329i
$549$		0			0
$550$	0.420459	+	7.15893i	0.0179284	+	0.305258i
$551$	−1.31874			−0.0561801
$552$		0			0
$553$	−7.87957	+	2.56023i	−0.335073	+	0.108872i
$554$	−9.72142	−	29.9194i	−0.413023	−	1.27116i
$555$		0			0
$556$	1.40268	−	4.31701i	0.0594870	−	0.183082i
$557$		−	8.23596i		−	0.348969i	−0.984660	−	0.174484i	$-0.944174\pi$
$557$		−	8.23596i		−	0.348969i	0.984660	−	0.174484i	$-0.0558259\pi$
$558$		0			0
$559$	−60.4211	+	43.8985i	−2.55554	+	1.85671i
$560$	−0.335244	+	1.14501i	−0.0141666	+	0.0483853i
$561$		0			0
$562$	6.33545	+	8.72000i	0.267245	+	0.367831i
$563$	8.60271	+	11.8406i	0.362561	+	0.499022i	0.950860	−	0.309621i	$-0.100202\pi$
$563$	8.60271	+	11.8406i	0.362561	+	0.499022i	−0.588299	+	0.808643i	$0.700202\pi$
$564$		0			0
$565$	1.92442	−	6.57276i	0.0809611	−	0.276518i
$566$	−3.36897	+	2.44770i	−0.141608	+	0.102885i
$567$		0			0
$568$		−	10.1247i		−	0.424822i
$569$	9.65590	−	29.7178i	0.404796	−	1.24583i	−0.516269	−	0.856427i	$-0.672679\pi$
$569$	9.65590	−	29.7178i	0.404796	−	1.24583i	0.921065	−	0.389408i	$-0.127321\pi$
$570$		0			0
$571$	8.10430	+	24.9425i	0.339154	+	1.04381i	0.964639	+	0.263574i	$0.0849012\pi$
$571$	8.10430	+	24.9425i	0.339154	+	1.04381i	−0.625485	+	0.780236i	$0.715099\pi$
$572$	−8.96720	+	2.91362i	−0.374937	+	0.121825i
$573$		0			0
$574$	−4.23729			−0.176861
$575$	11.9358	+	14.5510i	0.497758	+	0.606817i
$576$		0			0
$577$	5.25092	−	7.22727i	0.218599	−	0.300875i	−0.685608	−	0.727971i	$-0.740463\pi$
$577$	5.25092	−	7.22727i	0.218599	−	0.300875i	0.904206	+	0.427096i	$0.140463\pi$
$578$	15.2944	−	4.96944i	0.636162	−	0.206701i
$579$		0			0
$580$	13.2932	+	3.89209i	0.551971	+	0.161610i
$581$	2.69261	−	8.28699i	0.111708	−	0.343802i
$582$		0			0
$583$	−4.41074	−	1.43313i	−0.182674	−	0.0593544i
$584$	11.3077	−	8.21552i	0.467916	−	0.339961i
$585$		0			0
$586$	14.5302	+	10.5568i	0.600237	+	0.436098i
$587$	2.34738	+	3.23089i	0.0968867	+	0.133353i	0.854708	−	0.519109i	$-0.173736\pi$
$587$	2.34738	+	3.23089i	0.0968867	+	0.133353i	−0.757821	+	0.652462i	$0.773736\pi$
$588$		0			0
$589$	−0.402629	−	0.292527i	−0.0165900	−	0.0120534i
$590$	13.3161	−	10.2847i	0.548217	−	0.423414i
$591$		0			0
$592$	3.86406	+	1.25551i	0.158812	+	0.0516011i
$593$			11.2114i			0.460396i	0.973144	+	0.230198i	$0.0739374\pi$
$593$			11.2114i			0.460396i	−0.973144	+	0.230198i	$0.926063\pi$
$594$		0			0
$595$	1.07666	−	0.385090i	0.0441389	−	0.0157872i
$596$	−3.42238	−	10.5330i	−0.140186	−	0.431448i
$597$		0			0
$598$	−14.5443	+	20.0186i	−0.594763	+	0.818620i
$599$	−6.64762			−0.271614			−0.135807	−	0.990735i	$-0.543363\pi$
$599$	−6.64762			−0.271614			−0.135807	+	0.990735i	$0.543363\pi$
$600$		0			0
$601$	−10.7465			−0.438359			−0.219179	−	0.975685i	$-0.570338\pi$
$601$	−10.7465			−0.438359			−0.219179	+	0.975685i	$0.570338\pi$
$602$	−3.56293	+	4.90396i	−0.145214	+	0.199870i
$603$		0			0
$604$	0.504894	+	1.55390i	0.0205438	+	0.0632274i
$605$	11.2744	−	16.5157i	0.458370	−	0.671457i
$606$		0			0
$607$			15.4591i			0.627466i	0.949511	+	0.313733i	$0.101580\pi$
$607$			15.4591i			0.627466i	−0.949511	+	0.313733i	$0.898420\pi$
$608$	0.202470	+	0.0657863i	0.00821122	+	0.00266799i
$609$		0			0
$610$	23.2179	+	15.8497i	0.940066	+	0.641735i
$611$	53.9762	+	39.2160i	2.18364	+	1.58651i
$612$		0			0
$613$	−14.3929	−	19.8101i	−0.581324	−	0.800123i	0.412516	−	0.910950i	$-0.364650\pi$
$613$	−14.3929	−	19.8101i	−0.581324	−	0.800123i	−0.993840	+	0.110827i	$0.964650\pi$
$614$	16.8416	+	12.2362i	0.679673	+	0.493812i
$615$		0			0
$616$	−0.619107	+	0.449808i	−0.0249445	+	0.0181233i
$617$	17.9899	+	5.84526i	0.724244	+	0.235321i	0.647862	−	0.761757i	$-0.275663\pi$
$617$	17.9899	+	5.84526i	0.724244	+	0.235321i	0.0763819	+	0.997079i	$0.475663\pi$
$618$		0			0
$619$	−0.788010	+	2.42524i	−0.0316728	+	0.0974788i	−0.965643	−	0.259872i	$-0.916320\pi$
$619$	−0.788010	+	2.42524i	−0.0316728	+	0.0974788i	0.933970	+	0.357350i	$0.116320\pi$
$620$	3.19525	+	4.13706i	0.128324	+	0.166148i
$621$		0			0
$622$	18.5005	−	6.01118i	0.741803	−	0.241026i
$623$	−1.76322	+	2.42687i	−0.0706420	+	0.0972304i
$624$		0			0
$625$	−21.8065	−	12.2260i	−0.872261	−	0.489040i
$626$	−5.88310			−0.235136
$627$		0			0
$628$	6.32019	−	2.05355i	0.252203	−	0.0819457i
$629$	−1.20330	−	3.70336i	−0.0479785	−	0.147663i
$630$		0			0
$631$	−11.2646	+	34.6688i	−0.448436	+	1.38014i	0.430235	+	0.902717i	$0.358431\pi$
$631$	−11.2646	+	34.6688i	−0.448436	+	1.38014i	−0.878671	+	0.477428i	$0.841569\pi$
$632$		−	15.5279i		−	0.617668i
$633$		0			0
$634$	−8.70586	+	6.32518i	−0.345754	+	0.251205i
$635$	−14.4892	+	0.425125i	−0.574988	+	0.0168706i
$636$		0			0
$637$	25.9483	+	35.7148i	1.02811	+	1.41507i
$638$	5.22215	+	7.18767i	0.206747	+	0.284563i
$639$		0			0
$640$	−1.84679	−	1.26071i	−0.0730006	−	0.0498338i
$641$	−16.4772	+	11.9714i	−0.650809	+	0.472840i	−0.863546	−	0.504269i	$-0.831762\pi$
$641$	−16.4772	+	11.9714i	−0.650809	+	0.472840i	0.212738	+	0.977109i	$0.431762\pi$
$642$		0			0
$643$			11.4218i			0.450433i	0.974309	+	0.225217i	$0.0723090\pi$
$643$			11.4218i			0.450433i	−0.974309	+	0.225217i	$0.927691\pi$
$644$	−0.620606	+	1.91003i	−0.0244553	+	0.0752656i
$645$		0			0
$646$	−0.0630505	−	0.194049i	−0.00248069	−	0.00763477i
$647$	5.60379	−	1.82078i	0.220308	−	0.0715823i	−0.196783	−	0.980447i	$-0.563050\pi$
$647$	5.60379	−	1.82078i	0.220308	−	0.0715823i	0.417091	+	0.908865i	$0.363050\pi$
$648$		0			0
$649$	10.7921			0.423627
$650$	8.30694	−	31.8026i	0.325825	−	1.24740i
$651$		0			0
$652$	−5.94451	+	8.18191i	−0.232805	+	0.320428i
$653$	−16.2691	+	5.28614i	−0.636658	+	0.206863i	−0.609522	−	0.792769i	$-0.708639\pi$
$653$	−16.2691	+	5.28614i	−0.636658	+	0.206863i	−0.0271359	+	0.999632i	$0.508639\pi$
$654$		0			0
$655$	19.9132	−	7.12235i	0.778073	−	0.278293i
$656$	2.45408	−	7.55288i	0.0958157	−	0.294890i
$657$		0			0
$658$	5.15002	+	1.67334i	0.200769	+	0.0652337i
$659$	24.0433	−	17.4685i	0.936593	−	0.680475i	−0.0110052	−	0.999939i	$-0.503503\pi$
$659$	24.0433	−	17.4685i	0.936593	−	0.680475i	0.947598	+	0.319465i	$0.103503\pi$
$660$		0			0
$661$	−37.4604	−	27.2166i	−1.45704	−	1.05860i	−0.984121	−	0.177497i	$-0.943200\pi$
$661$	−37.4604	−	27.2166i	−1.45704	−	1.05860i	−0.472920	−	0.881105i	$-0.656800\pi$
$662$	−0.362718	−	0.499238i	−0.0140974	−	0.0194034i
$663$		0			0
$664$	13.2119	+	9.59902i	0.512722	+	0.372514i
$665$	0.0855388	+	0.239155i	0.00331705	+	0.00927405i
$666$		0			0
$667$	22.1749	+	7.20507i	0.858616	+	0.278981i
$668$			12.7885i			0.494800i
$669$		0			0
$670$	14.8348	+	4.34345i	0.573119	+	0.167802i
$671$	5.57205	+	17.1490i	0.215107	+	0.662030i
$672$		0			0
$673$	−11.5841	+	15.9441i	−0.446534	+	0.614601i	−0.971648	−	0.236430i	$-0.924023\pi$
$673$	−11.5841	+	15.9441i	−0.446534	+	0.614601i	0.525114	+	0.851032i	$0.324023\pi$
$674$	−15.4106			−0.593595
$675$		0			0
$676$	30.2165			1.16217
$677$	14.5638	−	20.0453i	0.559732	−	0.770405i	−0.431560	−	0.902084i	$-0.642037\pi$
$677$	14.5638	−	20.0453i	0.559732	−	0.770405i	0.991292	+	0.131679i	$0.0420368\pi$
$678$		0			0
$679$	−0.917646	−	2.82422i	−0.0352160	−	0.108384i
$680$	0.0628525	+	2.14216i	0.00241028	+	0.0821479i
$681$		0			0
$682$			3.35289i			0.128389i
$683$	−15.7755	−	5.12579i	−0.603635	−	0.196133i	−0.00877377	−	0.999962i	$-0.502793\pi$
$683$	−15.7755	−	5.12579i	−0.603635	−	0.196133i	−0.594861	+	0.803829i	$0.702793\pi$
$684$		0			0
$685$	7.75095	−	26.4729i	0.296149	−	1.01148i
$686$	5.92033	+	4.30137i	0.226039	+	0.164227i
$687$		0			0
$688$	−6.67767	−	9.19103i	−0.254584	−	0.350405i
$689$	17.1973	+	12.4946i	0.655166	+	0.476006i
$690$		0			0
$691$	−34.2128	+	24.8570i	−1.30152	+	0.945606i	−0.999969	−	0.00784530i	$-0.997503\pi$
$691$	−34.2128	+	24.8570i	−1.30152	+	0.945606i	−0.301546	+	0.953452i	$0.597503\pi$
$692$	12.9891	+	4.22041i	0.493771	+	0.160436i
$693$		0			0
$694$	−7.00126	+	21.5477i	−0.265764	+	0.817938i
$695$	0.297678	+	10.1455i	0.0112916	+	0.384842i
$696$		0			0
$697$	−7.23878	+	2.35202i	−0.274188	+	0.0890892i
$698$	−9.96550	+	13.7163i	−0.377200	+	0.519171i
$699$		0			0
$700$	−0.156416	−	2.66321i	−0.00591196	−	0.100660i
$701$	22.7240			0.858273			0.429137	−	0.903240i	$-0.358818\pi$
$701$	22.7240			0.858273			0.429137	+	0.903240i	$0.358818\pi$
$702$		0			0
$703$	0.822615	−	0.267284i	0.0310255	−	0.0100808i
$704$	−0.443209	−	1.36406i	−0.0167041	−	0.0514098i
$705$		0			0
$706$	1.87343	−	5.76583i	0.0705076	−	0.217000i
$707$		−	5.02990i		−	0.189169i
$708$		0			0
$709$	37.5483	−	27.2804i	1.41016	−	1.02454i	0.416855	−	0.908973i	$-0.363132\pi$
$709$	37.5483	−	27.2804i	1.41016	−	1.02454i	0.993300	−	0.115565i	$-0.0368678\pi$
$710$	7.62444	+	21.3170i	0.286140	+	0.800011i
$711$		0			0
$712$	−3.30464	−	4.54845i	−0.123847	−	0.170460i
$713$	5.17206	+	7.11873i	0.193695	+	0.266599i
$714$		0			0
$715$	16.6858	−	12.8873i	0.624015	−	0.481957i
$716$	2.42011	−	1.75831i	0.0904437	−	0.0657112i
$717$		0			0
$718$		−	18.8987i		−	0.705294i
$719$	−8.71631	+	26.8260i	−0.325063	+	1.00044i	0.646349	+	0.763042i	$0.276295\pi$
$719$	−8.71631	+	26.8260i	−0.325063	+	1.00044i	−0.971412	+	0.237400i	$0.923705\pi$
$720$		0			0
$721$	−1.31882	−	4.05891i	−0.0491154	−	0.151162i
$722$	−18.0270	+	5.85732i	−0.670894	+	0.217987i
$723$		0			0
$724$	−7.62285			−0.283301
$725$	−30.9191	+	1.81594i	−1.14831	+	0.0674425i
$726$		0			0
$727$	−0.500553	+	0.688953i	−0.0185645	+	0.0255518i	−0.818198	−	0.574936i	$-0.805027\pi$
$727$	−0.500553	+	0.688953i	−0.0185645	+	0.0255518i	0.799634	+	0.600488i	$0.205027\pi$
$728$	3.33590	−	1.08390i	0.123637	−	0.0401720i
$729$		0			0
$730$	−17.6210	+	25.8127i	−0.652183	+	0.955370i
$731$	−3.36466	+	10.3554i	−0.124447	+	0.383007i
$732$		0			0
$733$	29.2259	+	9.49607i	1.07948	+	0.350745i	0.794174	−	0.607690i	$-0.207904\pi$
$733$	29.2259	+	9.49607i	1.07948	+	0.350745i	0.285309	+	0.958436i	$0.407904\pi$
$734$	20.2645	−	14.7230i	0.747978	−	0.543437i
$735$		0			0
$736$	−3.04515	−	2.21243i	−0.112246	−	0.0815512i
$737$	5.82776	+	8.02122i	0.214668	+	0.295465i
$738$		0			0
$739$	1.67050	+	1.21369i	0.0614502	+	0.0446462i	0.618086	−	0.786110i	$-0.287908\pi$
$739$	1.67050	+	1.21369i	0.0614502	+	0.0446462i	−0.556636	+	0.830756i	$0.687908\pi$
$740$	−9.08103	+	0.266444i	−0.333825	+	0.00979469i
$741$		0			0
$742$	1.64085	+	0.533143i	0.0602373	+	0.0195723i
$743$			37.8972i			1.39031i	0.718858	+	0.695157i	$0.244665\pi$
$743$			37.8972i			1.39031i	−0.718858	+	0.695157i	$0.755335\pi$
$744$		0			0
$745$	15.1376	+	19.5994i	0.554597	+	0.718067i
$746$	3.67589	+	11.3132i	0.134584	+	0.414207i
$747$		0			0
$748$	−0.807974	+	1.11208i	−0.0295424	+	0.0406617i
$749$	−10.0981			−0.368978
$750$		0			0
$751$	−40.6331			−1.48272			−0.741361	−	0.671106i	$-0.765819\pi$
$751$	−40.6331			−1.48272			−0.741361	+	0.671106i	$0.765819\pi$
$752$	−5.96538	+	8.21065i	−0.217535	+	0.299411i
$753$		0			0
$754$	−12.5838	−	38.7290i	−0.458275	−	1.41043i
$755$	−2.23320	−	2.89145i	−0.0812746	−	0.105231i
$756$		0			0
$757$		−	10.0032i		−	0.363572i	−0.983338	−	0.181786i	$-0.941812\pi$
$757$		−	10.0032i		−	0.363572i	0.983338	−	0.181786i	$-0.0581877\pi$
$758$	26.1716	+	8.50366i	0.950594	+	0.308867i
$759$		0			0
$760$	−0.475830	+	0.0139612i	−0.0172602	+	0.000506426i
$761$	−24.4172	−	17.7401i	−0.885121	−	0.643078i	0.0494802	−	0.998775i	$-0.484244\pi$
$761$	−24.4172	−	17.7401i	−0.885121	−	0.643078i	−0.934601	+	0.355697i	$0.884244\pi$
$762$		0			0
$763$	0.832732	+	1.14616i	0.0301469	+	0.0414937i
$764$	6.79610	+	4.93766i	0.245874	+	0.178638i
$765$		0			0
$766$	17.8238	−	12.9497i	0.644000	−	0.467893i
$767$	−47.0448	−	15.2858i	−1.69869	−	0.551938i
$768$		0			0
$769$	−6.53471	+	20.1118i	−0.235648	+	0.725249i	0.761387	+	0.648297i	$0.224519\pi$
$769$	−6.53471	+	20.1118i	−0.235648	+	0.725249i	−0.997035	+	0.0769513i	$0.975481\pi$
$770$	0.964767	−	1.41327i	0.0347678	−	0.0509307i
$771$		0			0
$772$	10.0114	−	3.25290i	0.360319	−	0.117075i
$773$	17.3085	−	23.8231i	0.622544	−	0.856858i	−0.374991	−	0.927028i	$-0.622354\pi$
$773$	17.3085	−	23.8231i	0.622544	−	0.856858i	0.997535	+	0.0701705i	$0.0223543\pi$
$774$		0			0
$775$	−9.84286	−	6.30416i	−0.353566	−	0.226452i
$776$	5.56558			0.199793
$777$		0			0
$778$	16.6332	−	5.40446i	0.596330	−	0.193759i
$779$	−0.522446	−	1.60792i	−0.0187186	−	0.0576099i
$780$		0			0
$781$	−4.48734	+	13.8106i	−0.160570	+	0.494183i
$782$			3.60748i			0.129003i
$783$		0			0
$784$	−5.43280	+	3.94716i	−0.194029	+	0.140970i
$785$	−11.7604	+	9.08310i	−0.419746	+	0.324190i
$786$		0			0
$787$	−3.03811	−	4.18161i	−0.108297	−	0.149058i	0.751428	−	0.659815i	$-0.229365\pi$
$787$	−3.03811	−	4.18161i	−0.108297	−	0.149058i	−0.859725	+	0.510757i	$0.829365\pi$
$788$	6.00014	+	8.25848i	0.213746	+	0.294196i
$789$		0			0
$790$	11.6934	+	32.6932i	0.416033	+	1.16317i
$791$	−1.32210	+	0.960559i	−0.0470083	+	0.0341536i
$792$		0			0
$793$		−	82.6478i		−	2.93491i
$794$	−7.57062	+	23.3000i	−0.268671	+	0.826885i
$795$		0			0
$796$	1.18761	+	3.65508i	0.0420937	+	0.129551i
$797$	3.57413	−	1.16131i	0.126602	−	0.0411356i	−0.245031	−	0.969515i	$-0.578798\pi$
$797$	3.57413	−	1.16131i	0.126602	−	0.0411356i	0.371633	+	0.928380i	$0.378798\pi$
$798$		0			0
$799$	9.72686			0.344111
$800$	4.83769	+	1.26362i	0.171038	+	0.0446757i
$801$		0			0
$802$	0.611913	−	0.842226i	0.0216074	−	0.0297400i
$803$	−19.0655	+	6.19476i	−0.672808	+	0.218608i
$804$		0			0
$805$	−0.131705	−	4.48881i	−0.00464200	−	0.158210i
$806$	4.74899	−	14.6159i	0.167276	−	0.514823i
$807$		0			0
$808$	8.96568	+	2.91313i	0.315412	+	0.102483i
$809$	16.8961	−	12.2757i	0.594034	−	0.431591i	−0.249722	−	0.968317i	$-0.580339\pi$
$809$	16.8961	−	12.2757i	0.594034	−	0.431591i	0.843756	+	0.536727i	$0.180339\pi$
$810$		0			0
$811$	29.5317	+	21.4560i	1.03700	+	0.753423i	0.969697	−	0.244310i	$-0.0785614\pi$
$811$	29.5317	+	21.4560i	1.03700	+	0.753423i	0.0673004	+	0.997733i	$0.478561\pi$
$812$	−1.94270	−	2.67390i	−0.0681755	−	0.0938355i
$813$		0			0
$814$	−4.71434	−	3.42516i	−0.165237	−	0.120052i
$815$	6.35441	−	21.7031i	0.222585	−	0.760227i
$816$		0			0
$817$	−2.30020	−	0.747381i	−0.0804739	−	0.0261476i
$818$			22.2568i			0.778190i
$819$		0			0
$820$	0.520806	+	17.7502i	0.0181873	+	0.619865i
$821$	−10.2662	−	31.5961i	−0.358293	−	1.10271i	−0.954076	−	0.299566i	$-0.903158\pi$
$821$	−10.2662	−	31.5961i	−0.358293	−	1.10271i	0.595783	−	0.803146i	$-0.296842\pi$
$822$		0			0
$823$	−19.2733	+	26.5275i	−0.671827	+	0.924690i	−0.999800	−	0.0199969i	$-0.993634\pi$
$823$	−19.2733	+	26.5275i	−0.671827	+	0.924690i	0.327973	+	0.944687i	$0.393634\pi$
$824$	7.99871			0.278648
$825$		0			0
$826$	−4.01479			−0.139692
$827$	3.05011	−	4.19811i	0.106063	−	0.145983i	−0.752686	−	0.658379i	$-0.771242\pi$
$827$	3.05011	−	4.19811i	0.106063	−	0.145983i	0.858749	+	0.512397i	$0.171242\pi$
$828$		0			0
$829$	1.71758	+	5.28616i	0.0596539	+	0.183596i	0.976443	−	0.215776i	$-0.0692282\pi$
$829$	1.71758	+	5.28616i	0.0596539	+	0.183596i	−0.916789	+	0.399372i	$0.869228\pi$
$830$	−35.0456	−	10.2609i	−1.21645	−	0.356162i
$831$		0			0
$832$			6.57392i			0.227910i
$833$	6.12104	+	1.98885i	0.212082	+	0.0689095i
$834$		0			0
$835$	−9.63042	−	26.9254i	−0.333274	−	0.931792i
$836$	−0.247023	−	0.179472i	−0.00854346	−	0.00620718i
$837$		0			0
$838$	−13.5951	−	18.7121i	−0.469635	−	0.646397i
$839$	−35.1423	−	25.5324i	−1.21325	−	0.881475i	−0.217725	−	0.976010i	$-0.569864\pi$
$839$	−35.1423	−	25.5324i	−1.21325	−	0.881475i	−0.995522	+	0.0945346i	$0.969864\pi$
$840$		0			0
$841$	−7.58178	+	5.50849i	−0.261441	+	0.189948i
$842$	−9.28363	−	3.01643i	−0.319935	−	0.103953i
$843$		0			0
$844$	−1.62209	+	4.99228i	−0.0558347	+	0.171841i
$845$	−63.6192	+	22.7547i	−2.18857	+	0.782785i
$846$		0			0
$847$	−4.53804	+	1.47450i	−0.155929	+	0.0506644i
$848$	−1.90063	+	2.61599i	−0.0652679	+	0.0898336i
$849$		0			0
$850$	−1.74549	−	4.46286i	−0.0598700	−	0.153075i
$851$	−15.2928			−0.524231
$852$		0			0
$853$	−3.17978	+	1.03317i	−0.108874	+	0.0353752i	−0.362947	−	0.931810i	$-0.618229\pi$
$853$	−3.17978	+	1.03317i	−0.108874	+	0.0353752i	0.254074	+	0.967185i	$0.418229\pi$
$854$	−2.07287	−	6.37963i	−0.0709321	−	0.218306i
$855$		0			0
$856$	5.84845	−	17.9997i	0.199896	−	0.615217i
$857$		−	34.5415i		−	1.17991i	−0.807434	−	0.589957i	$-0.799145\pi$
$857$		−	34.5415i		−	1.17991i	0.807434	−	0.589957i	$-0.200855\pi$
$858$		0			0
$859$	−19.2961	+	14.0195i	−0.658375	+	0.478338i	−0.866114	−	0.499847i	$-0.833390\pi$
$859$	−19.2961	+	14.0195i	−0.658375	+	0.478338i	0.207739	+	0.978184i	$0.433390\pi$
$860$	20.9808	+	14.3226i	0.715441	+	0.488395i
$861$		0			0
$862$	−4.99205	−	6.87097i	−0.170030	−	0.234026i
$863$	3.36837	+	4.63616i	0.114661	+	0.157817i	0.862490	−	0.506074i	$-0.168904\pi$
$863$	3.36837	+	4.63616i	0.114661	+	0.157817i	−0.747829	+	0.663891i	$0.768904\pi$
$864$		0			0
$865$	−30.5261	+	0.895658i	−1.03792	+	0.0304533i
$866$	17.8018	−	12.9337i	0.604928	−	0.439506i
$867$		0			0
$868$		−	1.24732i		−	0.0423367i
$869$	−6.88211	+	21.1810i	−0.233460	+	0.718515i
$870$		0			0
$871$	−14.0431	−	43.2203i	−0.475834	−	1.46447i
$872$	−2.52528	+	0.820514i	−0.0855169	+	0.0277861i
$873$		0			0
$874$	−0.801317			−0.0271049
$875$	2.33487	+	5.48945i	0.0789329	+	0.185577i
$876$		0			0
$877$	−29.3000	+	40.3280i	−0.989392	+	1.36178i	−0.0577792	+	0.998329i	$0.518402\pi$
$877$	−29.3000	+	40.3280i	−0.989392	+	1.36178i	−0.931613	+	0.363452i	$0.881598\pi$
$878$	36.4808	−	11.8533i	1.23117	−	0.400031i
$879$		0			0
$880$	1.96036	+	2.53819i	0.0660838	+	0.0855622i
$881$	2.36586	−	7.28138i	0.0797079	−	0.245316i	−0.903260	−	0.429094i	$-0.858833\pi$
$881$	2.36586	−	7.28138i	0.0797079	−	0.245316i	0.982968	+	0.183778i	$0.0588329\pi$
$882$		0			0
$883$	37.0873	+	12.0504i	1.24809	+	0.405528i	0.857235	−	0.514925i	$-0.172180\pi$
$883$	37.0873	+	12.0504i	1.24809	+	0.405528i	0.390852	+	0.920453i	$0.372180\pi$
$884$	5.09724	−	3.70336i	0.171439	−	0.124558i
$885$		0			0
$886$	−10.3132	−	7.49296i	−0.346478	−	0.251731i
$887$	19.1229	+	26.3204i	0.642083	+	0.883752i	0.998725	−	0.0504894i	$-0.0160781\pi$
$887$	19.1229	+	26.3204i	0.642083	+	0.883752i	−0.356641	+	0.934241i	$0.616078\pi$
$888$		0			0
$889$	2.79826	+	2.03305i	0.0938505	+	0.0681864i
$890$	10.3830	+	7.08794i	0.348039	+	0.237588i
$891$		0			0
$892$	−18.3347	−	5.95730i	−0.613891	−	0.199465i
$893$			2.16059i			0.0723015i
$894$		0			0
$895$	−3.77130	+	5.52451i	−0.126061	+	0.184664i
$896$	0.164879	+	0.507445i	0.00550822	+	0.0169525i
$897$		0			0
$898$	−10.6012	+	14.5912i	−0.353765	+	0.486916i
$899$	−14.4810			−0.482969
$900$		0			0
$901$	3.09907			0.103245
$902$	−6.69500	+	9.21488i	−0.222919	+	0.306822i
$903$		0			0
$904$	−0.946466	−	2.91292i	−0.0314790	−	0.0968824i
$905$	16.0495	−	5.74043i	0.533504	−	0.190818i
$906$		0			0
$907$		−	16.5820i		−	0.550595i	−0.961359	−	0.275297i	$-0.911224\pi$
$907$		−	16.5820i		−	0.550595i	0.961359	−	0.275297i	$-0.0887763\pi$
$908$	8.02651	+	2.60797i	0.266369	+	0.0865486i
$909$		0			0
$910$	−6.20733	+	4.79422i	−0.205771	+	0.158927i
$911$	−23.1152	−	16.7942i	−0.765842	−	0.556417i	0.134855	−	0.990865i	$-0.456943\pi$
$911$	−23.1152	−	16.7942i	−0.765842	−	0.556417i	−0.900697	+	0.434449i	$0.856943\pi$
$912$		0			0
$913$	−13.7674	−	18.9492i	−0.455635	−	0.627128i
$914$	17.1103	+	12.4314i	0.565960	+	0.411194i
$915$		0			0
$916$	−4.81825	+	3.50066i	−0.159199	+	0.115665i
$917$	−4.79938	−	1.55941i	−0.158490	−	0.0514964i
$918$		0			0
$919$	0.118310	−	0.364122i	0.00390270	−	0.0120113i	−0.949086	−	0.315016i	$-0.897990\pi$
$919$	0.118310	−	0.364122i	0.00390270	−	0.0120113i	0.952989	+	0.303005i	$0.0979900\pi$
$920$	8.07748	+	2.36499i	0.266307	+	0.0779713i
$921$		0			0
$922$	−30.4419	+	9.89116i	−1.00255	+	0.325748i
$923$	39.1223	−	53.8472i	1.28773	−	1.77240i
$924$		0			0
$925$	18.9190	−	7.39951i	0.622052	−	0.243294i
$926$	−28.7776			−0.945689
$927$		0			0
$928$	5.89130	−	1.91420i	0.193391	−	0.0628367i
$929$	−1.93355	−	5.95087i	−0.0634378	−	0.195242i	0.914314	−	0.405006i	$-0.132730\pi$
$929$	−1.93355	−	5.95087i	−0.0634378	−	0.195242i	−0.977752	+	0.209764i	$0.932730\pi$
$930$		0			0
$931$	−0.441776	+	1.35965i	−0.0144786	+	0.0445606i
$932$			2.09293i			0.0685561i
$933$		0			0
$934$	4.20952	−	3.05840i	0.137740	−	0.100074i
$935$	0.863687	−	2.94988i	0.0282456	−	0.0964713i
$936$		0			0
$937$	−2.89904	−	3.99019i	−0.0947075	−	0.130354i	0.759034	−	0.651052i	$-0.225672\pi$
$937$	−2.89904	−	3.99019i	−0.0947075	−	0.130354i	−0.853741	+	0.520698i	$0.825672\pi$
$938$	−2.16800	−	2.98399i	−0.0707876	−	0.0974307i
$939$		0			0
$940$	6.37672	−	21.7793i	0.207986	−	0.710364i
$941$	24.1174	−	17.5223i	0.786204	−	0.571210i	−0.120631	−	0.992697i	$-0.538492\pi$
$941$	24.1174	−	17.5223i	0.786204	−	0.571210i	0.906834	+	0.421487i	$0.138492\pi$
$942$		0			0
$943$			29.8921i			0.973422i
$944$	2.32521	−	7.15627i	0.0756793	−	0.232917i
$945$		0			0
$946$	5.03518	+	15.4967i	0.163708	+	0.503840i
$947$	25.5953	−	8.31642i	0.831736	−	0.270247i	0.137960	−	0.990438i	$-0.455946\pi$
$947$	25.5953	−	8.31642i	0.831736	−	0.270247i	0.693777	+	0.720190i	$0.255946\pi$
$948$		0			0
$949$	91.8843			2.98269
$950$	0.991321	−	0.387721i	0.0321627	−	0.0125793i
$951$		0			0
$952$	0.300576	−	0.413707i	0.00974172	−	0.0134083i
$953$	35.4113	−	11.5058i	1.14709	−	0.372711i	0.327041	−	0.945010i	$-0.393949\pi$
$953$	35.4113	−	11.5058i	1.14709	−	0.372711i	0.820045	+	0.572300i	$0.193949\pi$
$954$		0			0
$955$	−18.0272	−	5.27813i	−0.583345	−	0.170796i
$956$	−3.05877	+	9.41393i	−0.0989278	+	0.304468i
$957$		0			0
$958$	37.6985	+	12.2490i	1.21798	+	0.395747i
$959$	−5.32497	+	3.86882i	−0.171952	+	0.124931i
$960$		0			0
$961$	20.6583	+	15.0091i	0.666396	+	0.484165i
$962$	15.6993	+	21.6082i	0.506166	+	0.696678i
$963$		0			0
$964$	−17.3588	−	12.6119i	−0.559091	−	0.406203i
$965$	−18.6289	+	14.3880i	−0.599685	+	0.463165i
$966$		0			0
$967$	−15.2973	−	4.97039i	−0.491928	−	0.159837i	0.0525399	−	0.998619i	$-0.483268\pi$
$967$	−15.2973	−	4.97039i	−0.491928	−	0.159837i	−0.544468	+	0.838782i	$0.683268\pi$
$968$		−	8.94292i		−	0.287436i
$969$		0			0
$970$	−11.7180	+	4.19119i	−0.376243	+	0.134571i
$971$	−3.78758	−	11.6570i	−0.121549	−	0.374090i	0.871707	−	0.490027i	$-0.163013\pi$
$971$	−3.78758	−	11.6570i	−0.121549	−	0.374090i	−0.993257	+	0.115937i	$0.963013\pi$
$972$		0			0
$973$	1.42357	−	1.95937i	0.0456375	−	0.0628146i
$974$	−5.44308			−0.174407
$975$		0			0
$976$	12.5721			0.402422
$977$	10.5930	−	14.5800i	0.338899	−	0.466454i	−0.605221	−	0.796058i	$-0.706915\pi$
$977$	10.5930	−	14.5800i	0.338899	−	0.466454i	0.944119	+	0.329604i	$0.106915\pi$
$978$		0			0
$979$	2.49180	+	7.66899i	0.0796384	+	0.245102i
$980$	8.46605	−	12.4017i	0.270438	−	0.396159i
$981$		0			0
$982$			0.873965i			0.0278893i
$983$	−46.9850	−	15.2663i	−1.49859	−	0.486921i	−0.558982	−	0.829180i	$-0.688808\pi$
$983$	−46.9850	−	15.2663i	−1.49859	−	0.486921i	−0.939606	+	0.342259i	$0.888808\pi$
$984$		0			0
$985$	−18.8521	−	12.8694i	−0.600677	−	0.410052i
$986$	−4.80303	−	3.48961i	−0.152960	−	0.111132i
$987$		0			0
$988$	0.822615	+	1.13223i	0.0261709	+	0.0360211i
$989$	34.5951	+	25.1348i	1.10006	+	0.799241i
$990$		0			0
$991$	24.7287	−	17.9665i	0.785533	−	0.570723i	−0.121101	−	0.992640i	$-0.538643\pi$
$991$	24.7287	−	17.9665i	0.785533	−	0.570723i	0.906635	+	0.421917i	$0.138643\pi$
$992$	2.22331	+	0.722398i	0.0705902	+	0.0229362i
$993$		0			0
$994$	1.66934	−	5.13771i	0.0529484	−	0.162958i
$995$	−5.25293	−	6.80125i	−0.166529	−	0.215614i
$996$		0			0
$997$	6.47717	−	2.10456i	0.205134	−	0.0666521i	−0.204648	−	0.978836i	$-0.565605\pi$
$997$	6.47717	−	2.10456i	0.205134	−	0.0666521i	0.409782	+	0.912184i	$0.365605\pi$
$998$	−20.5492	+	28.2836i	−0.650474	+	0.895301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.c.109.2		16
3.2	odd	2		150.2.h.b.109.3	✓	16
15.2	even	4		750.2.g.g.451.3		16
15.8	even	4		750.2.g.f.451.2		16
15.14	odd	2		750.2.h.d.49.2		16
25.14	even	10	inner	450.2.l.c.289.2		16
75.2	even	20		750.2.g.g.301.3		16
75.8	even	20		3750.2.a.v.1.3		8
75.11	odd	10		750.2.h.d.199.1		16
75.14	odd	10		150.2.h.b.139.3	yes	16
75.17	even	20		3750.2.a.u.1.6		8
75.23	even	20		750.2.g.f.301.2		16
75.44	odd	10		3750.2.c.k.1249.6		16
75.56	odd	10		3750.2.c.k.1249.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.3	✓	16	3.2	odd	2
150.2.h.b.139.3	yes	16	75.14	odd	10
450.2.l.c.109.2		16	1.1	even	1	trivial
450.2.l.c.289.2		16	25.14	even	10	inner
750.2.g.f.301.2		16	75.23	even	20
750.2.g.f.451.2		16	15.8	even	4
750.2.g.g.301.3		16	75.2	even	20
750.2.g.g.451.3		16	15.2	even	4
750.2.h.d.49.2		16	15.14	odd	2
750.2.h.d.199.1		16	75.11	odd	10
3750.2.a.u.1.6		8	75.17	even	20
3750.2.a.v.1.3		8	75.8	even	20
3750.2.c.k.1249.6		16	75.44	odd	10
3750.2.c.k.1249.11		16	75.56	odd	10

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(1.36682 + 1.76969i) q^{5} -0.533559i q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(1.36682 + 1.76969i) q^{5} -0.533559i q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.23511 + 0.0655797i) q^{10} +(-1.16034 - 0.843033i) q^{11} +(3.86406 + 5.31842i) q^{13} +(0.431658 + 0.313618i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.911505 + 0.296166i) q^{17} +(-0.0657863 + 0.202470i) q^{19} +(1.26071 - 1.84679i) q^{20} +(1.36406 - 0.443209i) q^{22} +(2.21243 - 3.04515i) q^{23} +(-1.26362 + 4.83769i) q^{25} -6.57392 q^{26} +(-0.507445 + 0.164879i) q^{28} +(1.91420 + 5.89130i) q^{29} +(-0.722398 + 2.22331i) q^{31} -1.00000i q^{32} +(-0.775373 + 0.563341i) q^{34} +(0.944235 - 0.729278i) q^{35} +(-2.38812 - 3.28696i) q^{37} +(-0.125133 - 0.172231i) q^{38} +(0.753056 + 2.10545i) q^{40} +(-6.42486 + 4.66793i) q^{41} +11.3607i q^{43} +(-0.443209 + 1.36406i) q^{44} +(1.16314 + 3.57979i) q^{46} +(9.65219 - 3.13619i) q^{47} +6.71531 q^{49} +(-3.17104 - 3.86581i) q^{50} +(3.86406 - 5.31842i) q^{52} +(3.07528 - 0.999220i) q^{53} +(-0.0940579 - 3.20571i) q^{55} +(0.164879 - 0.507445i) q^{56} +(-5.89130 - 1.91420i) q^{58} +(-6.08749 + 4.42282i) q^{59} +(-10.1710 - 7.38968i) q^{61} +(-1.37408 - 1.89126i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-4.13050 + 14.1075i) q^{65} +(-6.57451 - 2.13619i) q^{67} -0.958413i q^{68} +(0.0349907 + 1.19256i) q^{70} +(-3.12869 - 9.62913i) q^{71} +(8.21552 - 11.3077i) q^{73} +4.06291 q^{74} +0.212889 q^{76} +(-0.449808 + 0.619107i) q^{77} +(-4.79840 - 14.7679i) q^{79} +(-2.14598 - 0.628316i) q^{80} -7.94156i q^{82} +(15.5315 + 5.04650i) q^{83} +(0.721739 + 2.01789i) q^{85} +(-9.19103 - 6.67767i) q^{86} +(-0.843033 - 1.16034i) q^{88} +(-4.54845 - 3.30464i) q^{89} +(2.83769 - 2.06170i) q^{91} +(-3.57979 - 1.16314i) q^{92} +(-3.13619 + 9.65219i) q^{94} +(-0.448227 + 0.160317i) q^{95} +(5.29318 - 1.71986i) q^{97} +(-3.94716 + 5.43280i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 - 4 * q^5	\( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

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