LMFDB - Embedded newform 450.2.h.e.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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, 2]))

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.2
Root			$-0.357358 + 1.86824i$ of defining polynomial
Character	$\chi$	$=$	450.361
Dual form			450.2.h.e.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.02373 - 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.02373 - 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.07822 - 1.95894i) q^{10} +(-3.05361 + 2.21858i) q^{11} +(-2.56969 - 1.86699i) q^{13} +(3.05361 - 2.21858i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.430307 + 1.32435i) q^{17} +(1.20945 + 3.72230i) q^{19} +(-0.279141 - 2.21858i) q^{20} +(-1.16637 + 3.58973i) q^{22} +(0.720859 - 0.523735i) q^{23} +(3.19098 - 3.84937i) q^{25} -3.17632 q^{26} +(1.16637 - 3.58973i) q^{28} +(-0.0152089 + 0.0468081i) q^{29} +(-1.72466 - 5.30795i) q^{31} -1.00000 q^{32} +(1.12656 + 0.818492i) q^{34} +(7.63851 - 3.58973i) q^{35} +(-5.70152 - 4.14240i) q^{37} +(3.16637 + 2.30051i) q^{38} +(-1.52988 - 1.63079i) q^{40} +(-1.20477 - 0.875319i) q^{41} +2.69767 q^{43} +(1.16637 + 3.58973i) q^{44} +(0.275344 - 0.847421i) q^{46} +(-1.16637 + 3.58973i) q^{47} +7.24660 q^{49} +(0.318958 - 4.98982i) q^{50} +(-2.56969 + 1.86699i) q^{52} +(-3.58963 + 11.0477i) q^{53} +(-4.06969 + 7.39396i) q^{55} +(-1.16637 - 3.58973i) q^{56} +(0.0152089 + 0.0468081i) q^{58} +(-0.558282 - 0.405615i) q^{59} +(-8.38168 + 6.08965i) q^{61} +(-4.51521 - 3.28049i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-6.97599 - 1.33437i) q^{65} +(4.73519 + 14.5734i) q^{67} +1.39250 q^{68} +(4.06969 - 7.39396i) q^{70} +(2.06969 - 6.36986i) q^{71} +(-4.18158 + 3.03810i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-11.5257 + 8.37394i) q^{77} +(-0.558282 + 1.71821i) q^{79} +(-2.19625 - 0.420099i) q^{80} -1.48918 q^{82} +(3.08023 + 9.47997i) q^{83} +(2.13035 + 2.27088i) q^{85} +(2.18246 - 1.58565i) q^{86} +(3.05361 + 2.21858i) q^{88} +(11.7390 - 8.52891i) q^{89} +(-9.69922 - 7.04690i) q^{91} +(-0.275344 - 0.847421i) q^{92} +(1.16637 + 3.58973i) q^{94} +(5.98771 + 6.38268i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +(5.86263 - 4.25945i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.02373	−	0.951057i	0.905040	−	0.425325i
$5$	2.02373	−	0.951057i	0.905040	−	0.425325i
$6$		0			0
$7$	3.77447			1.42661			0.713307	−	0.700851i	$-0.247196\pi$
$7$	3.77447			1.42661			0.713307	+	0.700851i	$0.247196\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$		0			0
$10$	1.07822	−	1.95894i	0.340962	−	0.619471i
$11$	−3.05361	+	2.21858i	−0.920698	+	0.668926i	−0.943698	−	0.330810i	$-0.892678\pi$
$11$	−3.05361	+	2.21858i	−0.920698	+	0.668926i	0.0230000	+	0.999735i	$0.492678\pi$
$12$		0			0
$13$	−2.56969	−	1.86699i	−0.712705	−	0.517810i	0.171340	−	0.985212i	$-0.445190\pi$
$13$	−2.56969	−	1.86699i	−0.712705	−	0.517810i	−0.884045	+	0.467402i	$0.845190\pi$
$14$	3.05361	−	2.21858i	0.816111	−	0.592939i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.430307	+	1.32435i	0.104365	+	0.321201i	0.989581	−	0.143979i	$-0.0459896\pi$
$17$	0.430307	+	1.32435i	0.104365	+	0.321201i	−0.885216	+	0.465180i	$0.845990\pi$
$18$		0			0
$19$	1.20945	+	3.72230i	0.277466	+	0.853953i	0.988556	+	0.150852i	$0.0482018\pi$
$19$	1.20945	+	3.72230i	0.277466	+	0.853953i	−0.711090	+	0.703101i	$0.751798\pi$
$20$	−0.279141	−	2.21858i	−0.0624178	−	0.496089i
$21$		0			0
$22$	−1.16637	+	3.58973i	−0.248672	+	0.765333i
$23$	0.720859	−	0.523735i	0.150310	−	0.109206i	−0.510089	−	0.860122i	$-0.670387\pi$
$23$	0.720859	−	0.523735i	0.150310	−	0.109206i	0.660398	+	0.750916i	$0.270387\pi$
$24$		0			0
$25$	3.19098	−	3.84937i	0.638197	−	0.769873i
$26$	−3.17632			−0.622927
$27$		0			0
$28$	1.16637	−	3.58973i	0.220424	−	0.678396i
$29$	−0.0152089	+	0.0468081i	−0.00282422	+	0.00869205i	−0.952459	−	0.304668i	$-0.901455\pi$
$29$	−0.0152089	+	0.0468081i	−0.00282422	+	0.00869205i	0.949634	+	0.313360i	$0.101455\pi$
$30$		0			0
$31$	−1.72466	−	5.30795i	−0.309757	−	0.953335i	−0.977859	−	0.209265i	$-0.932893\pi$
$31$	−1.72466	−	5.30795i	−0.309757	−	0.953335i	0.668102	−	0.744070i	$-0.267107\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.12656	+	0.818492i	0.193203	+	0.140370i
$35$	7.63851	−	3.58973i	1.29114	−	0.606775i
$36$		0			0
$37$	−5.70152	−	4.14240i	−0.937324	−	0.681006i	0.0104512	−	0.999945i	$-0.496673\pi$
$37$	−5.70152	−	4.14240i	−0.937324	−	0.681006i	−0.947775	+	0.318940i	$0.896673\pi$
$38$	3.16637	+	2.30051i	0.513654	+	0.373191i
$39$		0			0
$40$	−1.52988	−	1.63079i	−0.241895	−	0.257851i
$41$	−1.20477	−	0.875319i	−0.188154	−	0.136702i	0.489721	−	0.871879i	$-0.337099\pi$
$41$	−1.20477	−	0.875319i	−0.188154	−	0.136702i	−0.677875	+	0.735178i	$0.737099\pi$
$42$		0			0
$43$	2.69767			0.411391			0.205695	−	0.978616i	$-0.434054\pi$
$43$	2.69767			0.411391			0.205695	+	0.978616i	$0.434054\pi$
$44$	1.16637	+	3.58973i	0.175838	+	0.541172i
$45$		0			0
$46$	0.275344	−	0.847421i	0.0405972	−	0.124945i
$47$	−1.16637	+	3.58973i	−0.170133	+	0.523616i	−0.999378	−	0.0352696i	$-0.988771\pi$
$47$	−1.16637	+	3.58973i	−0.170133	+	0.523616i	0.829245	+	0.558886i	$0.188771\pi$
$48$		0			0
$49$	7.24660			1.03523
$50$	0.318958	−	4.98982i	0.0451075	−	0.705667i
$51$		0			0
$52$	−2.56969	+	1.86699i	−0.356352	+	0.258905i
$53$	−3.58963	+	11.0477i	−0.493073	+	1.51752i	0.326864	+	0.945071i	$0.394008\pi$
$53$	−3.58963	+	11.0477i	−0.493073	+	1.51752i	−0.819938	+	0.572453i	$0.805992\pi$
$54$		0			0
$55$	−4.06969	+	7.39396i	−0.548757	+	0.997001i
$56$	−1.16637	−	3.58973i	−0.155863	−	0.479698i
$57$		0			0
$58$	0.0152089	+	0.0468081i	0.00199702	+	0.00614620i
$59$	−0.558282	−	0.405615i	−0.0726821	−	0.0528066i	0.550851	−	0.834604i	$-0.314303\pi$
$59$	−0.558282	−	0.405615i	−0.0726821	−	0.0528066i	−0.623533	+	0.781797i	$0.714303\pi$
$60$		0			0
$61$	−8.38168	+	6.08965i	−1.07316	+	0.779700i	−0.976478	−	0.215615i	$-0.930824\pi$
$61$	−8.38168	+	6.08965i	−1.07316	+	0.779700i	−0.0966862	+	0.995315i	$0.530824\pi$
$62$	−4.51521	−	3.28049i	−0.573432	−	0.416623i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.97599	−	1.33437i	−0.865265	−	0.165508i
$66$		0			0
$67$	4.73519	+	14.5734i	0.578496	+	1.78043i	0.623955	+	0.781461i	$0.285525\pi$
$67$	4.73519	+	14.5734i	0.578496	+	1.78043i	−0.0454589	+	0.998966i	$0.514475\pi$
$68$	1.39250			0.168866
$69$		0			0
$70$	4.06969	−	7.39396i	0.486421	−	0.883747i
$71$	2.06969	−	6.36986i	0.245627	−	0.755963i	−0.749905	−	0.661545i	$-0.769901\pi$
$71$	2.06969	−	6.36986i	0.245627	−	0.755963i	0.995533	−	0.0944182i	$-0.0300991\pi$
$72$		0			0
$73$	−4.18158	+	3.03810i	−0.489417	+	0.355582i	−0.804960	−	0.593329i	$-0.797813\pi$
$73$	−4.18158	+	3.03810i	−0.489417	+	0.355582i	0.315543	+	0.948911i	$0.397813\pi$
$74$	−7.04746			−0.819251
$75$		0			0
$76$	3.91385			0.448950
$77$	−11.5257	+	8.37394i	−1.31348	+	0.954299i
$78$		0			0
$79$	−0.558282	+	1.71821i	−0.0628116	+	0.193314i	−0.977538	−	0.210760i	$-0.932406\pi$
$79$	−0.558282	+	1.71821i	−0.0628116	+	0.193314i	0.914726	+	0.404074i	$0.132406\pi$
$80$	−2.19625	−	0.420099i	−0.245548	−	0.0469685i
$81$		0			0
$82$	−1.48918			−0.164453
$83$	3.08023	+	9.47997i	0.338099	+	1.04056i	0.965175	+	0.261604i	$0.0842514\pi$
$83$	3.08023	+	9.47997i	0.338099	+	1.04056i	−0.627076	+	0.778958i	$0.715749\pi$
$84$		0			0
$85$	2.13035	+	2.27088i	0.231069	+	0.246311i
$86$	2.18246	−	1.58565i	0.235341	−	0.170985i
$87$		0			0
$88$	3.05361	+	2.21858i	0.325516	+	0.236501i
$89$	11.7390	−	8.52891i	1.24434	−	0.904063i	0.246457	−	0.969154i	$-0.420734\pi$
$89$	11.7390	−	8.52891i	1.24434	−	0.904063i	0.997879	+	0.0650909i	$0.0207337\pi$
$90$		0			0
$91$	−9.69922	−	7.04690i	−1.01675	−	0.738716i
$92$	−0.275344	−	0.847421i	−0.0287066	−	0.0883497i
$93$		0			0
$94$	1.16637	+	3.58973i	0.120302	+	0.370253i
$95$	5.98771	+	6.38268i	0.614326	+	0.654849i
$96$		0			0
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	−0.952461	−	0.304660i	$-0.901457\pi$
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	0.949632	+	0.313367i	$0.101457\pi$
$98$	5.86263	−	4.25945i	0.592215	−	0.430269i
$99$		0			0
$100$	−2.67490	−	4.22433i	−0.267490	−	0.422433i
$101$	−16.3785			−1.62972			−0.814859	−	0.579659i	$-0.803186\pi$
$101$	−16.3785			−1.62972			−0.814859	+	0.579659i	$0.803186\pi$
$102$		0			0
$103$	−0.375822	+	1.15666i	−0.0370308	+	0.113969i	−0.967863	−	0.251477i	$-0.919084\pi$
$103$	−0.375822	+	1.15666i	−0.0370308	+	0.113969i	0.930832	+	0.365446i	$0.119084\pi$
$104$	−0.981536	+	3.02086i	−0.0962475	+	0.296219i
$105$		0			0
$106$	3.58963	+	11.0477i	0.348656	+	1.07305i
$107$	10.8125			1.04528			0.522641	−	0.852553i	$-0.324947\pi$
$107$	10.8125			1.04528			0.522641	+	0.852553i	$0.324947\pi$
$108$		0			0
$109$	−9.23519	−	6.70976i	−0.884571	−	0.642678i	0.0498859	−	0.998755i	$-0.484114\pi$
$109$	−9.23519	−	6.70976i	−0.884571	−	0.642678i	−0.934457	+	0.356077i	$0.884114\pi$
$110$	1.05361	+	8.37394i	0.100458	+	0.798424i
$111$		0			0
$112$	−3.05361	−	2.21858i	−0.288539	−	0.209636i
$113$	−8.43232	−	6.12644i	−0.793246	−	0.576327i	0.115679	−	0.993287i	$-0.463096\pi$
$113$	−8.43232	−	6.12644i	−0.793246	−	0.576327i	−0.908925	+	0.416960i	$0.863096\pi$
$114$		0			0
$115$	0.960724	−	1.74548i	0.0895880	−	0.162767i
$116$	0.0398173	+	0.0289290i	0.00369695	+	0.00268599i
$117$		0			0
$118$	−0.690074			−0.0635265
$119$	1.62418	+	4.99871i	0.148888	+	0.458231i
$120$		0			0
$121$	1.00326	−	3.08770i	0.0912051	−	0.280700i
$122$	−3.20152	+	9.85326i	−0.289852	+	0.892072i
$123$		0			0
$124$	−5.58111			−0.501198
$125$	2.79673	−	10.8249i	0.250147	−	0.968208i
$126$		0			0
$127$	2.87115	−	2.08601i	0.254773	−	0.185104i	−0.453066	−	0.891477i	$-0.649670\pi$
$127$	2.87115	−	2.08601i	0.254773	−	0.185104i	0.707840	+	0.706373i	$0.249670\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	−6.42801	+	3.02086i	−0.563774	+	0.264947i
$131$	−1.25252	−	3.85486i	−0.109433	−	0.336801i	0.881312	−	0.472535i	$-0.156661\pi$
$131$	−1.25252	−	3.85486i	−0.109433	−	0.336801i	−0.990745	+	0.135734i	$0.956661\pi$
$132$		0			0
$133$	4.56502	+	14.0497i	0.395837	+	1.21826i
$134$	12.3969	+	9.00687i	1.07093	+	0.778075i
$135$		0			0
$136$	1.12656	−	0.818492i	0.0966015	−	0.0701851i
$137$	−2.88636	−	2.09706i	−0.246598	−	0.179164i	0.457620	−	0.889148i	$-0.348702\pi$
$137$	−2.88636	−	2.09706i	−0.246598	−	0.179164i	−0.704218	+	0.709984i	$0.748702\pi$
$138$		0			0
$139$	8.04650	−	5.84613i	0.682495	−	0.495862i	−0.191689	−	0.981456i	$-0.561397\pi$
$139$	8.04650	−	5.84613i	0.682495	−	0.495862i	0.874185	+	0.485594i	$0.161397\pi$
$140$	−1.05361	−	8.37394i	−0.0890461	−	0.707727i
$141$		0			0
$142$	−2.06969	−	6.36986i	−0.173685	−	0.534547i
$143$	11.9889			1.00256
$144$		0			0
$145$	0.0137385	+	0.109192i	0.00114092	+	0.00906786i
$146$	−1.59722	+	4.91575i	−0.132187	+	0.406830i
$147$		0			0
$148$	−5.70152	+	4.14240i	−0.468662	+	0.340503i
$149$	19.5103			1.59834			0.799171	−	0.601104i	$-0.205272\pi$
$149$	19.5103			1.59834			0.799171	+	0.601104i	$0.205272\pi$
$150$		0			0
$151$	−18.4324			−1.50001			−0.750003	−	0.661435i	$-0.769948\pi$
$151$	−18.4324			−1.50001			−0.750003	+	0.661435i	$0.769948\pi$
$152$	3.16637	−	2.30051i	0.256827	−	0.186596i
$153$		0			0
$154$	−4.40244	+	13.5493i	−0.354759	+	1.09184i
$155$	−8.53840	−	9.10162i	−0.685821	−	0.731059i
$156$		0			0
$157$	10.1564			0.810572			0.405286	−	0.914190i	$-0.367172\pi$
$157$	10.1564			0.810572			0.405286	+	0.914190i	$0.367172\pi$
$158$	0.558282	+	1.71821i	0.0444145	+	0.136694i
$159$		0			0
$160$	−2.02373	+	0.951057i	−0.159990	+	0.0751876i
$161$	2.72086	−	1.97682i	0.214434	−	0.155795i
$162$		0			0
$163$	15.0481	+	10.9331i	1.17865	+	0.856343i	0.992019	−	0.126086i	$-0.0402416\pi$
$163$	15.0481	+	10.9331i	1.17865	+	0.856343i	0.186636	+	0.982429i	$0.440242\pi$
$164$	−1.20477	+	0.875319i	−0.0940770	+	0.0683510i
$165$		0			0
$166$	8.06414	+	5.85894i	0.625899	+	0.454742i
$167$	−0.671048	−	2.06527i	−0.0519273	−	0.159816i	0.921730	−	0.387832i	$-0.126776\pi$
$167$	−0.671048	−	2.06527i	−0.0519273	−	0.159816i	−0.973657	+	0.228016i	$0.926776\pi$
$168$		0			0
$169$	−0.899554	−	2.76854i	−0.0691965	−	0.212965i
$170$	3.05828	+	0.584988i	0.234560	+	0.0448666i
$171$		0			0
$172$	0.833625	−	2.56564i	0.0635633	−	0.195628i
$173$	−5.17306	+	3.75845i	−0.393300	+	0.285750i	−0.766807	−	0.641878i	$-0.778155\pi$
$173$	−5.17306	+	3.75845i	−0.393300	+	0.285750i	0.373506	+	0.927628i	$0.378155\pi$
$174$		0			0
$175$	12.0443	−	14.5293i	0.910461	−	1.09831i
$176$	3.77447			0.284511
$177$		0			0
$178$	4.48391	−	13.8001i	0.336084	−	1.03436i
$179$	−2.47630	+	7.62127i	−0.185087	+	0.569640i	−0.999950	−	0.0100140i	$-0.996812\pi$
$179$	−2.47630	+	7.62127i	−0.185087	+	0.569640i	0.814862	+	0.579654i	$0.196812\pi$
$180$		0			0
$181$	−3.35682	−	10.3312i	−0.249510	−	0.767913i	−0.994862	−	0.101242i	$-0.967718\pi$
$181$	−3.35682	−	10.3312i	−0.249510	−	0.767913i	0.745352	−	0.666671i	$-0.232282\pi$
$182$	−11.9889			−0.888676
$183$		0			0
$184$	−0.720859	−	0.523735i	−0.0531424	−	0.0386102i
$185$	−15.4780	−	2.96063i	−1.13797	−	0.217670i
$186$		0			0
$187$	−4.25215	−	3.08937i	−0.310948	−	0.225917i
$188$	3.05361	+	2.21858i	0.222707	+	0.161806i
$189$		0			0
$190$	8.59580	+	1.64421i	0.623605	+	0.119283i
$191$	−6.62243	−	4.81147i	−0.479182	−	0.348146i	0.321827	−	0.946798i	$-0.395703\pi$
$191$	−6.62243	−	4.81147i	−0.479182	−	0.348146i	−0.801009	+	0.598652i	$0.795703\pi$
$192$		0			0
$193$	−17.5576			−1.26382			−0.631912	−	0.775040i	$-0.717730\pi$
$193$	−17.5576			−1.26382			−0.631912	+	0.775040i	$0.717730\pi$
$194$	0.0278640	+	0.0857567i	0.00200052	+	0.00615697i
$195$		0			0
$196$	2.23932	−	6.89193i	0.159952	−	0.492281i
$197$	−1.47012	+	4.52458i	−0.104742	+	0.322363i	−0.989670	−	0.143365i	$-0.954208\pi$
$197$	−1.47012	+	4.52458i	−0.104742	+	0.322363i	0.884928	+	0.465728i	$0.154208\pi$
$198$		0			0
$199$	14.5320			1.03015			0.515073	−	0.857146i	$-0.327765\pi$
$199$	14.5320			1.03015			0.515073	+	0.857146i	$0.327765\pi$
$200$	−4.64703	−	1.84529i	−0.328595	−	0.130481i
$201$		0			0
$202$	−13.2505	+	9.62702i	−0.932299	+	0.677355i
$203$	−0.0574054	+	0.176676i	−0.00402907	+	0.0124002i
$204$		0			0
$205$	−3.27062	−	0.625604i	−0.228430	−	0.0436941i
$206$	0.375822	+	1.15666i	0.0261848	+	0.0805884i
$207$		0			0
$208$	0.981536	+	3.02086i	0.0680572	+	0.209459i
$209$	−11.9514	−	8.68318i	−0.826694	−	0.600628i
$210$		0			0
$211$	11.4362	−	8.30886i	0.787298	−	0.572006i	−0.119862	−	0.992791i	$-0.538245\pi$
$211$	11.4362	−	8.30886i	0.787298	−	0.572006i	0.907160	+	0.420785i	$0.138245\pi$
$212$	9.39777	+	6.82788i	0.645441	+	0.468941i
$213$		0			0
$214$	8.74748	−	6.35542i	0.597965	−	0.434447i
$215$	5.45936	−	2.56564i	0.372325	−	0.174975i
$216$		0			0
$217$	−6.50966	−	20.0347i	−0.441904	−	1.36004i
$218$	−11.4153			−0.773143
$219$		0			0
$220$	5.77447	+	6.15537i	0.389315	+	0.414995i
$221$	1.36679	−	4.20655i	0.0919402	−	0.282963i
$222$		0			0
$223$	−3.73139	+	2.71102i	−0.249873	+	0.181543i	−0.705670	−	0.708540i	$-0.749354\pi$
$223$	−3.73139	+	2.71102i	−0.249873	+	0.181543i	0.455798	+	0.890083i	$0.349354\pi$
$224$	−3.77447			−0.252192
$225$		0			0
$226$	−10.4229			−0.693322
$227$	−5.08578	+	3.69503i	−0.337555	+	0.245248i	−0.743630	−	0.668592i	$-0.766897\pi$
$227$	−5.08578	+	3.69503i	−0.337555	+	0.245248i	0.406075	+	0.913840i	$0.366897\pi$
$228$		0			0
$229$	5.48103	−	16.8689i	0.362196	−	1.11473i	−0.589522	−	0.807753i	$-0.700684\pi$
$229$	5.48103	−	16.8689i	0.362196	−	1.11473i	0.951718	−	0.306973i	$-0.0993163\pi$
$230$	−0.248723	−	1.97682i	−0.0164003	−	0.130348i
$231$		0			0
$232$	0.0492169			0.00323125
$233$	−0.792338	−	2.43856i	−0.0519078	−	0.159756i	0.921742	−	0.387803i	$-0.126766\pi$
$233$	−0.792338	−	2.43856i	−0.0519078	−	0.159756i	−0.973650	+	0.228047i	$0.926766\pi$
$234$		0			0
$235$	1.05361	+	8.37394i	0.0687298	+	0.546256i
$236$	−0.558282	+	0.405615i	−0.0363410	+	0.0264033i
$237$		0			0
$238$	4.25215	+	3.08937i	0.275626	+	0.200254i
$239$	7.63851	−	5.54970i	0.494094	−	0.358980i	−0.312662	−	0.949864i	$-0.601221\pi$
$239$	7.63851	−	5.54970i	0.494094	−	0.358980i	0.806757	+	0.590884i	$0.201221\pi$
$240$		0			0
$241$	23.8131	+	17.3012i	1.53394	+	1.11447i	0.953998	+	0.299812i	$0.0969240\pi$
$241$	23.8131	+	17.3012i	1.53394	+	1.11447i	0.579940	+	0.814659i	$0.303076\pi$
$242$	−1.00326	−	3.08770i	−0.0644917	−	0.198485i
$243$		0			0
$244$	3.20152	+	9.85326i	0.204956	+	0.630790i
$245$	14.6652	−	6.89193i	0.936924	−	0.440309i
$246$		0			0
$247$	3.84159	−	11.8232i	0.244434	−	0.752292i
$248$	−4.51521	+	3.28049i	−0.286716	+	0.208311i
$249$		0			0
$250$	−4.10011	−	10.4014i	−0.259314	−	0.657842i
$251$	6.00759			0.379196			0.189598	−	0.981862i	$-0.439282\pi$
$251$	6.00759			0.379196			0.189598	+	0.981862i	$0.439282\pi$
$252$		0			0
$253$	−1.03928	+	3.19856i	−0.0653387	+	0.201092i
$254$	1.09668	−	3.37524i	0.0688119	−	0.211781i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	13.6286			0.850127			0.425063	−	0.905164i	$-0.360252\pi$
$257$	13.6286			0.850127			0.425063	+	0.905164i	$0.360252\pi$
$258$		0			0
$259$	−21.5202	−	15.6353i	−1.33720	−	0.971533i
$260$	−3.42476	+	6.22221i	−0.212394	+	0.385885i
$261$		0			0
$262$	−3.27914	−	2.38244i	−0.202586	−	0.147187i
$263$	−7.41298	−	5.38584i	−0.457104	−	0.332105i	0.335290	−	0.942115i	$-0.391166\pi$
$263$	−7.41298	−	5.38584i	−0.457104	−	0.332105i	−0.792394	+	0.610010i	$0.791166\pi$
$264$		0			0
$265$	3.24258	+	25.7716i	0.199190	+	1.58314i
$266$	11.9514	+	8.68318i	0.732786	+	0.532400i
$267$		0			0
$268$	15.3234			0.936026
$269$	−8.68419	−	26.7272i	−0.529484	−	1.62959i	−0.755274	−	0.655409i	$-0.772496\pi$
$269$	−8.68419	−	26.7272i	−0.529484	−	1.62959i	0.225790	−	0.974176i	$-0.427504\pi$
$270$		0			0
$271$	−2.81162	+	8.65329i	−0.170794	+	0.525650i	−0.999416	−	0.0341581i	$-0.989125\pi$
$271$	−2.81162	+	8.65329i	−0.170794	+	0.525650i	0.828623	+	0.559808i	$0.189125\pi$
$272$	0.430307	−	1.32435i	0.0260912	−	0.0803004i
$273$		0			0
$274$	−3.56773			−0.215535
$275$	−1.20390	+	18.8339i	−0.0725977	+	1.13573i
$276$		0			0
$277$	−15.2006	+	11.0439i	−0.913318	+	0.663564i	−0.941852	−	0.336028i	$-0.890916\pi$
$277$	−15.2006	+	11.0439i	−0.913318	+	0.663564i	0.0285338	+	0.999593i	$0.490916\pi$
$278$	3.07349	−	9.45923i	0.184336	−	0.567327i
$279$		0			0
$280$	−5.77447	−	6.15537i	−0.345090	−	0.367854i
$281$	−2.43554	−	7.49583i	−0.145292	−	0.447164i	0.851756	−	0.523938i	$-0.175538\pi$
$281$	−2.43554	−	7.49583i	−0.145292	−	0.447164i	−0.997048	+	0.0767748i	$0.975538\pi$
$282$		0			0
$283$	−5.65496	−	17.4042i	−0.336153	−	1.03457i	−0.966151	−	0.257975i	$-0.916945\pi$
$283$	−5.65496	−	17.4042i	−0.336153	−	1.03457i	0.629999	−	0.776596i	$-0.283055\pi$
$284$	−5.41853	−	3.93679i	−0.321530	−	0.233606i
$285$		0			0
$286$	9.69922	−	7.04690i	0.573527	−	0.416692i
$287$	−4.54738	−	3.30386i	−0.268423	−	0.195021i
$288$		0			0
$289$	12.1846	−	8.85260i	0.716739	−	0.520741i
$290$	0.0752958	+	0.0802625i	0.00442152	+	0.00471318i
$291$		0			0
$292$	1.59722	+	4.91575i	0.0934704	+	0.287672i
$293$	29.4990			1.72335			0.861675	−	0.507461i	$-0.169416\pi$
$293$	29.4990			1.72335			0.861675	+	0.507461i	$0.169416\pi$
$294$		0			0
$295$	−1.51558	−	0.289899i	−0.0882402	−	0.0168786i
$296$	−2.17779	+	6.70254i	−0.126581	+	0.389577i
$297$		0			0
$298$	15.7841	−	11.4678i	0.914350	−	0.664314i
$299$	−2.83020			−0.163674
$300$		0			0
$301$	10.1823			0.586896
$302$	−14.9121	+	10.8343i	−0.858095	+	0.623443i
$303$		0			0
$304$	1.20945	−	3.72230i	0.0693666	−	0.213488i
$305$	−11.1707	+	20.2953i	−0.639631	+	1.16210i
$306$		0			0
$307$	13.9131			0.794064			0.397032	−	0.917805i	$-0.370040\pi$
$307$	13.9131			0.794064			0.397032	+	0.917805i	$0.370040\pi$
$308$	4.40244	+	13.5493i	0.250852	+	0.772044i
$309$		0			0
$310$	−12.2575	−	2.34462i	−0.696180	−	0.133165i
$311$	21.0050	−	15.2610i	1.19108	−	0.865373i	0.197705	−	0.980262i	$-0.436651\pi$
$311$	21.0050	−	15.2610i	1.19108	−	0.865373i	0.993378	+	0.114889i	$0.0366512\pi$
$312$		0			0
$313$	−7.66454	−	5.56861i	−0.433225	−	0.314757i	0.349712	−	0.936857i	$-0.386279\pi$
$313$	−7.66454	−	5.56861i	−0.433225	−	0.314757i	−0.782937	+	0.622101i	$0.786279\pi$
$314$	8.21673	−	5.96980i	0.463697	−	0.336895i
$315$		0			0
$316$	1.46160	+	1.06192i	0.0822215	+	0.0597374i
$317$	−7.57321	−	23.3079i	−0.425354	−	1.30910i	−0.902655	−	0.430365i	$-0.858385\pi$
$317$	−7.57321	−	23.3079i	−0.425354	−	1.30910i	0.477301	−	0.878740i	$-0.341615\pi$
$318$		0			0
$319$	−0.0574054	−	0.176676i	−0.00321408	−	0.00989194i
$320$	−1.07822	+	1.95894i	−0.0602741	+	0.109508i
$321$		0			0
$322$	1.03928	−	3.19856i	0.0579166	−	0.178249i
$323$	−4.40918	+	3.20346i	−0.245333	+	0.178245i
$324$		0			0
$325$	−15.3866	+	3.93416i	−0.853494	+	0.218228i
$326$	18.6004			1.03018
$327$		0			0
$328$	−0.460183	+	1.41630i	−0.0254093	+	0.0782019i
$329$	−4.40244	+	13.5493i	−0.242715	+	0.746998i
$330$		0			0
$331$	−3.06247	−	9.42530i	−0.168328	−	0.518061i	0.830938	−	0.556365i	$-0.187804\pi$
$331$	−3.06247	−	9.42530i	−0.168328	−	0.518061i	−0.999266	+	0.0383039i	$0.987804\pi$
$332$	9.96783			0.547056
$333$		0			0
$334$	−1.75683	−	1.27641i	−0.0961293	−	0.0698420i
$335$	23.4429	+	24.9893i	1.28082	+	1.36531i
$336$		0			0
$337$	8.03812	+	5.84003i	0.437864	+	0.318127i	0.784786	−	0.619767i	$-0.212773\pi$
$337$	8.03812	+	5.84003i	0.437864	+	0.318127i	−0.346922	+	0.937894i	$0.612773\pi$
$338$	−2.35506	−	1.71105i	−0.128099	−	0.0930690i
$339$		0			0
$340$	2.81805	−	1.32435i	0.152830	−	0.0718228i
$341$	17.0425	+	12.3821i	0.922904	+	0.670529i
$342$		0			0
$343$	0.930796			0.0502583
$344$	−0.833625	−	2.56564i	−0.0449461	−	0.138330i
$345$		0			0
$346$	−1.97593	+	6.08130i	−0.106227	+	0.326933i
$347$	6.06757	−	18.6741i	0.325724	−	1.00248i	−0.645388	−	0.763855i	$-0.723304\pi$
$347$	6.06757	−	18.6741i	0.325724	−	1.00248i	0.971113	−	0.238622i	$-0.0766956\pi$
$348$		0			0
$349$	1.48432			0.0794538			0.0397269	−	0.999211i	$-0.487351\pi$
$349$	1.48432			0.0794538			0.0397269	+	0.999211i	$0.487351\pi$
$350$	1.20390	−	18.8339i	0.0643510	−	1.00671i
$351$		0			0
$352$	3.05361	−	2.21858i	0.162758	−	0.118251i
$353$	−3.17632	+	9.77569i	−0.169058	+	0.520308i	−0.999312	−	0.0370772i	$-0.988195\pi$
$353$	−3.17632	+	9.77569i	−0.169058	+	0.520308i	0.830254	+	0.557385i	$0.188195\pi$
$354$		0			0
$355$	−1.86959	−	14.8593i	−0.0992277	−	0.788649i
$356$	−4.48391	−	13.8001i	−0.237647	−	0.731402i
$357$		0			0
$358$	2.47630	+	7.62127i	0.130877	+	0.402797i
$359$	−8.39154	−	6.09681i	−0.442889	−	0.321777i	0.343893	−	0.939009i	$-0.388254\pi$
$359$	−8.39154	−	6.09681i	−0.442889	−	0.321777i	−0.786782	+	0.617231i	$0.788254\pi$
$360$		0			0
$361$	2.97859	−	2.16408i	0.156768	−	0.113899i
$362$	−8.78826	−	6.38504i	−0.461901	−	0.335590i
$363$		0			0
$364$	−9.69922	+	7.04690i	−0.508377	+	0.369358i
$365$	−5.57300	+	10.1252i	−0.291704	+	0.529978i
$366$		0			0
$367$	8.05741	+	24.7981i	0.420593	+	1.29445i	0.907151	+	0.420804i	$0.138252\pi$
$367$	8.05741	+	24.7981i	0.420593	+	1.29445i	−0.486558	+	0.873648i	$0.661748\pi$
$368$	−0.891031			−0.0464482
$369$		0			0
$370$	−14.2622	+	6.70254i	−0.741455	+	0.348448i
$371$	−13.5489	+	41.6993i	−0.703426	+	2.16492i
$372$		0			0
$373$	−7.65001	+	5.55806i	−0.396102	+	0.287785i	−0.767952	−	0.640508i	$-0.778724\pi$
$373$	−7.65001	+	5.55806i	−0.396102	+	0.287785i	0.371849	+	0.928293i	$0.378724\pi$
$374$	−5.25595			−0.271779
$375$		0			0
$376$	3.77447			0.194653
$377$	0.126472	−	0.0918876i	0.00651366	−	0.00473245i
$378$		0			0
$379$	−10.9163	+	33.5968i	−0.560731	+	1.72575i	0.119576	+	0.992825i	$0.461846\pi$
$379$	−10.9163	+	33.5968i	−0.560731	+	1.72575i	−0.680307	+	0.732927i	$0.738154\pi$
$380$	7.92059	−	3.72230i	0.406318	−	0.190950i
$381$		0			0
$382$	−8.18577			−0.418820
$383$	−9.21407	−	28.3580i	−0.470817	−	1.44902i	−0.851517	−	0.524327i	$-0.824317\pi$
$383$	−9.21407	−	28.3580i	−0.470817	−	1.44902i	0.380700	−	0.924698i	$-0.375683\pi$
$384$		0			0
$385$	−15.3609	+	27.9083i	−0.782865	+	1.42234i
$386$	−14.2044	+	10.3201i	−0.722985	+	0.525280i
$387$		0			0
$388$	0.0729490	+	0.0530006i	0.00370343	+	0.00269070i
$389$	−17.2942	+	12.5649i	−0.876848	+	0.637068i	−0.932416	−	0.361387i	$-0.882303\pi$
$389$	−17.2942	+	12.5649i	−0.876848	+	0.637068i	0.0555675	+	0.998455i	$0.482303\pi$
$390$		0			0
$391$	1.00380	+	0.729301i	0.0507642	+	0.0368824i
$392$	−2.23932	−	6.89193i	−0.113103	−	0.348095i
$393$		0			0
$394$	1.47012	+	4.52458i	0.0740638	+	0.227945i
$395$	0.504306	+	4.00816i	0.0253744	+	0.201673i
$396$		0			0
$397$	6.49555	−	19.9913i	0.326002	−	1.00333i	−0.644984	−	0.764196i	$-0.723136\pi$
$397$	6.49555	−	19.9913i	0.326002	−	1.00333i	0.970986	−	0.239136i	$-0.0768642\pi$
$398$	11.7566	−	8.54169i	0.589307	−	0.428156i
$399$		0			0
$400$	−4.84416	+	1.23859i	−0.242208	+	0.0619295i
$401$	−16.7820			−0.838053			−0.419026	−	0.907974i	$-0.637629\pi$
$401$	−16.7820			−0.838053			−0.419026	+	0.907974i	$0.637629\pi$
$402$		0			0
$403$	−5.47805	+	16.8597i	−0.272881	+	0.839842i
$404$	−5.06122	+	15.5768i	−0.251805	+	0.774977i
$405$		0			0
$406$	0.0574054	+	0.176676i	0.00284898	+	0.00876826i
$407$	26.6004			1.31853
$408$		0			0
$409$	−29.4165	−	21.3723i	−1.45455	−	1.05679i	−0.984741	−	0.174025i	$-0.944323\pi$
$409$	−29.4165	−	21.3723i	−1.45455	−	1.05679i	−0.469809	−	0.882768i	$-0.655677\pi$
$410$	−3.01371	+	1.41630i	−0.148836	+	0.0699459i
$411$		0			0
$412$	0.983915	+	0.714856i	0.0484740	+	0.0352184i
$413$	−2.10722	−	1.53098i	−0.103689	−	0.0753347i
$414$		0			0
$415$	15.2495	+	16.2554i	0.748571	+	0.797948i
$416$	2.56969	+	1.86699i	0.125990	+	0.0915368i
$417$		0			0
$418$	−14.7727			−0.722557
$419$	10.6731	+	32.8484i	0.521415	+	1.60475i	0.771298	+	0.636474i	$0.219608\pi$
$419$	10.6731	+	32.8484i	0.521415	+	1.60475i	−0.249884	+	0.968276i	$0.580392\pi$
$420$		0			0
$421$	3.00798	−	9.25762i	0.146600	−	0.451189i	−0.850613	−	0.525792i	$-0.823769\pi$
$421$	3.00798	−	9.25762i	0.146600	−	0.451189i	0.997213	+	0.0746033i	$0.0237691\pi$
$422$	4.36823	−	13.4440i	0.212642	−	0.654445i
$423$		0			0
$424$	11.6163			0.564136
$425$	6.47100	+	2.56956i	0.313890	+	0.124642i
$426$		0			0
$427$	−31.6364	+	22.9852i	−1.53099	+	1.11233i
$428$	3.34124	−	10.2833i	0.161505	−	0.497061i
$429$		0			0
$430$	2.90867	−	5.28457i	0.140269	−	0.254845i
$431$	0.956560	+	2.94399i	0.0460759	+	0.141807i	0.971448	−	0.237254i	$-0.0762472\pi$
$431$	0.956560	+	2.94399i	0.0460759	+	0.141807i	−0.925372	+	0.379061i	$0.876247\pi$
$432$		0			0
$433$	−5.63542	−	17.3440i	−0.270821	−	0.833501i	−0.990295	−	0.138981i	$-0.955617\pi$
$433$	−5.63542	−	17.3440i	−0.270821	−	0.833501i	0.719474	−	0.694519i	$-0.244383\pi$
$434$	−17.0425	−	12.3821i	−0.818067	−	0.594360i
$435$		0			0
$436$	−9.23519	+	6.70976i	−0.442285	+	0.321339i
$437$	2.82134	+	2.04982i	0.134963	+	0.0980563i
$438$		0			0
$439$	21.4595	−	15.5912i	1.02421	−	0.744129i	0.0570645	−	0.998370i	$-0.481826\pi$
$439$	21.4595	−	15.5912i	1.02421	−	0.744129i	0.967141	+	0.254242i	$0.0818259\pi$
$440$	8.28968	+	1.58565i	0.395195	+	0.0755929i
$441$		0			0
$442$	−1.36679	−	4.20655i	−0.0650115	−	0.200085i
$443$	−35.5267			−1.68793			−0.843963	−	0.536401i	$-0.819783\pi$
$443$	−35.5267			−1.68793			−0.843963	+	0.536401i	$0.819783\pi$
$444$		0			0
$445$	15.6452	−	28.4247i	0.741653	−	1.34746i
$446$	−1.42527	+	4.38652i	−0.0674883	+	0.207708i
$447$		0			0
$448$	−3.05361	+	2.21858i	−0.144269	+	0.104818i
$449$	−16.1841			−0.763776			−0.381888	−	0.924209i	$-0.624726\pi$
$449$	−16.1841			−0.763776			−0.381888	+	0.924209i	$0.624726\pi$
$450$		0			0
$451$	5.62087			0.264676
$452$	−8.43232	+	6.12644i	−0.396623	+	0.288163i
$453$		0			0
$454$	−1.94259	+	5.97869i	−0.0911705	+	0.280594i
$455$	−26.3306	−	5.03652i	−1.23440	−	0.236116i
$456$		0			0
$457$	23.7205			1.10960			0.554799	−	0.831984i	$-0.312795\pi$
$457$	23.7205			1.10960			0.554799	+	0.831984i	$0.312795\pi$
$458$	−5.48103	−	16.8689i	−0.256112	−	0.788230i
$459$		0			0
$460$	−1.36317	−	1.45309i	−0.0635580	−	0.0677504i
$461$	−6.36936	+	4.62761i	−0.296651	+	0.215529i	−0.726147	−	0.687539i	$-0.758691\pi$
$461$	−6.36936	+	4.62761i	−0.296651	+	0.215529i	0.429497	+	0.903068i	$0.358691\pi$
$462$		0			0
$463$	−12.4775	−	9.06543i	−0.579878	−	0.421306i	0.258802	−	0.965930i	$-0.416672\pi$
$463$	−12.4775	−	9.06543i	−0.579878	−	0.421306i	−0.838680	+	0.544624i	$0.816672\pi$
$464$	0.0398173	−	0.0289290i	0.00184847	−	0.00134299i
$465$		0			0
$466$	−2.07437	−	1.50712i	−0.0960932	−	0.0698158i
$467$	5.26481	+	16.2034i	0.243626	+	0.749805i	0.995859	+	0.0909075i	$0.0289768\pi$
$467$	5.26481	+	16.2034i	0.243626	+	0.749805i	−0.752233	+	0.658897i	$0.771023\pi$
$468$		0			0
$469$	17.8728	+	55.0069i	0.825290	+	2.53998i
$470$	5.77447	+	6.15537i	0.266356	+	0.283926i
$471$		0			0
$472$	−0.213245	+	0.656300i	−0.00981538	+	0.0302086i
$473$	−8.23762	+	5.98498i	−0.378766	+	0.275190i
$474$		0			0
$475$	18.1878	+	7.22218i	0.834514	+	0.331376i
$476$	5.25595			0.240906
$477$		0			0
$478$	2.91765	−	8.97961i	0.133450	−	0.410718i
$479$	7.75544	−	23.8688i	0.354355	−	1.09059i	−0.602027	−	0.798476i	$-0.705640\pi$
$479$	7.75544	−	23.8688i	0.354355	−	1.09059i	0.956382	−	0.292118i	$-0.0943598\pi$
$480$		0			0
$481$	6.91734	+	21.2894i	0.315403	+	0.970712i
$482$	29.4346			1.34071
$483$		0			0
$484$	−2.62656	−	1.90831i	−0.119389	−	0.0867412i
$485$	0.0251701	+	0.200049i	0.00114292	+	0.00908375i
$486$		0			0
$487$	11.0735	+	8.04536i	0.501788	+	0.364570i	0.809699	−	0.586845i	$-0.199630\pi$
$487$	11.0735	+	8.04536i	0.501788	+	0.364570i	−0.307912	+	0.951415i	$0.599630\pi$
$488$	8.38168	+	6.08965i	0.379421	+	0.275665i
$489$		0			0
$490$	7.81341	−	14.1957i	0.352974	−	0.641295i
$491$	−2.08733	−	1.51654i	−0.0942001	−	0.0684403i	0.539688	−	0.841865i	$-0.318542\pi$
$491$	−2.08733	−	1.51654i	−0.0942001	−	0.0684403i	−0.633888	+	0.773425i	$0.718542\pi$
$492$		0			0
$493$	−0.0685347			−0.00308665
$494$	−3.84159	−	11.8232i	−0.172841	−	0.531950i
$495$		0			0
$496$	−1.72466	+	5.30795i	−0.0774394	+	0.238334i
$497$	7.81199	−	24.0428i	0.350416	−	1.07847i
$498$		0			0
$499$	−39.0539			−1.74829			−0.874146	−	0.485664i	$-0.838578\pi$
$499$	−39.0539			−1.74829			−0.874146	+	0.485664i	$0.838578\pi$
$500$	−9.43085	−	6.00492i	−0.421760	−	0.268548i
$501$		0			0
$502$	4.86025	−	3.53118i	0.216923	−	0.157604i
$503$	−3.69387	+	11.3686i	−0.164702	+	0.506899i	−0.999014	−	0.0443923i	$-0.985865\pi$
$503$	−3.69387	+	11.3686i	−0.164702	+	0.506899i	0.834313	+	0.551292i	$0.185865\pi$
$504$		0			0
$505$	−33.1456	+	15.5768i	−1.47496	+	0.693160i
$506$	1.03928	+	3.19856i	0.0462014	+	0.142193i
$507$		0			0
$508$	−1.09668	−	3.37524i	−0.0486574	−	0.149752i
$509$	−3.94254	−	2.86442i	−0.174750	−	0.126963i	0.496972	−	0.867767i	$-0.334445\pi$
$509$	−3.94254	−	2.86442i	−0.174750	−	0.126963i	−0.671722	+	0.740803i	$0.734445\pi$
$510$		0			0
$511$	−15.7832	+	11.4672i	−0.698210	+	0.507279i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	11.0257	−	8.01067i	0.486325	−	0.353336i
$515$	0.339487	+	2.69820i	0.0149596	+	0.118897i
$516$		0			0
$517$	−4.40244	−	13.5493i	−0.193619	−	0.595899i
$518$	−26.6004			−1.16876
$519$		0			0
$520$	0.886640	+	7.04690i	0.0388817	+	0.309027i
$521$	2.70131	−	8.31378i	0.118347	−	0.364233i	−0.874284	−	0.485415i	$-0.838668\pi$
$521$	2.70131	−	8.31378i	0.118347	−	0.364233i	0.992630	+	0.121182i	$0.0386684\pi$
$522$		0			0
$523$	17.0534	−	12.3900i	0.745694	−	0.541778i	−0.148795	−	0.988868i	$-0.547540\pi$
$523$	17.0534	−	12.3900i	0.745694	−	0.541778i	0.894489	+	0.447090i	$0.147540\pi$
$524$	−4.05324			−0.177067
$525$		0			0
$526$	−9.16294			−0.399523
$527$	6.28743	−	4.56809i	0.273885	−	0.198989i
$528$		0			0
$529$	−6.86205	+	21.1192i	−0.298350	+	0.918227i
$530$	17.7715	+	18.9437i	0.771943	+	0.822863i
$531$		0			0
$532$	14.7727			0.640478
$533$	1.46169	+	4.49861i	0.0633126	+	0.194856i
$534$		0			0
$535$	21.8816	−	10.2833i	0.946022	−	0.444585i
$536$	12.3969	−	9.00687i	0.535464	−	0.389038i
$537$		0			0
$538$	−22.7355	−	16.5183i	−0.980197	−	0.712155i
$539$	−22.1283	+	16.0771i	−0.953133	+	0.692492i
$540$		0			0
$541$	−26.5406	−	19.2829i	−1.14107	−	0.829036i	−0.153802	−	0.988102i	$-0.549152\pi$
$541$	−26.5406	−	19.2829i	−1.14107	−	0.829036i	−0.987268	+	0.159066i	$0.949152\pi$
$542$	2.81162	+	8.65329i	0.120770	+	0.371690i
$543$		0			0
$544$	−0.430307	−	1.32435i	−0.0184492	−	0.0567809i
$545$	−25.0709	−	4.79557i	−1.07392	−	0.205419i
$546$		0			0
$547$	−1.69044	+	5.20264i	−0.0722781	+	0.222449i	−0.980669	−	0.195672i	$-0.937311\pi$
$547$	−1.69044	+	5.20264i	−0.0722781	+	0.222449i	0.908391	+	0.418121i	$0.137311\pi$
$548$	−2.88636	+	2.09706i	−0.123299	+	0.0895820i
$549$		0			0
$550$	10.0963	+	15.9446i	0.430508	+	0.679879i
$551$	−0.192628			−0.00820623
$552$		0			0
$553$	−2.10722	+	6.48535i	−0.0896080	+	0.275785i
$554$	−5.80613	+	17.8694i	−0.246679	+	0.759199i
$555$		0			0
$556$	−3.07349	−	9.45923i	−0.130345	−	0.401161i
$557$	5.19840			0.220263			0.110132	−	0.993917i	$-0.464873\pi$
$557$	5.19840			0.220263			0.110132	+	0.993917i	$0.464873\pi$
$558$		0			0
$559$	−6.93218	−	5.03652i	−0.293200	−	0.213022i
$560$	−8.28968	−	1.58565i	−0.350303	−	0.0670059i
$561$		0			0
$562$	−6.37633	−	4.63268i	−0.268969	−	0.195418i
$563$	−4.05741	−	2.94788i	−0.170999	−	0.124238i	0.498994	−	0.866605i	$-0.333703\pi$
$563$	−4.05741	−	2.94788i	−0.170999	−	0.124238i	−0.669993	+	0.742367i	$0.733703\pi$
$564$		0			0
$565$	−22.8913	−	4.37866i	−0.963046	−	0.184212i
$566$	−14.8049	−	10.7564i	−0.622296	−	0.452124i
$567$		0			0
$568$	−6.69767			−0.281028
$569$	12.9303	+	39.7952i	0.542064	+	1.66830i	0.727869	+	0.685716i	$0.240511\pi$
$569$	12.9303	+	39.7952i	0.542064	+	1.66830i	−0.185805	+	0.982587i	$0.559489\pi$
$570$		0			0
$571$	−13.7723	+	42.3869i	−0.576355	+	1.77384i	0.0551642	+	0.998477i	$0.482432\pi$
$571$	−13.7723	+	42.3869i	−0.576355	+	1.77384i	−0.631519	+	0.775360i	$0.717568\pi$
$572$	3.70477	−	11.4021i	0.154904	−	0.476747i
$573$		0			0
$574$	−5.62087			−0.234611
$575$	0.284202	−	4.44608i	0.0118520	−	0.185414i
$576$		0			0
$577$	20.3401	−	14.7779i	0.846769	−	0.615213i	−0.0774845	−	0.996994i	$-0.524689\pi$
$577$	20.3401	−	14.7779i	0.846769	−	0.615213i	0.924253	+	0.381780i	$0.124689\pi$
$578$	4.65409	−	14.3238i	0.193584	−	0.595792i
$579$		0			0
$580$	0.108093	+	0.0206760i	0.00448831	+	0.000858524i
$581$	11.6262	+	35.7818i	0.482337	+	1.48448i
$582$		0			0
$583$	−13.5489	−	41.6993i	−0.561140	−	1.72701i
$584$	4.18158	+	3.03810i	0.173035	+	0.125717i
$585$		0			0
$586$	23.8652	−	17.3391i	0.985861	−	0.716270i
$587$	17.2770	+	12.5525i	0.713099	+	0.518097i	0.884172	−	0.467162i	$-0.154723\pi$
$587$	17.2770	+	12.5525i	0.713099	+	0.518097i	−0.171073	+	0.985258i	$0.554723\pi$
$588$		0			0
$589$	17.6719	−	12.8394i	0.728157	−	0.529037i
$590$	−1.39653	+	0.656300i	−0.0574940	+	0.0270194i
$591$		0			0
$592$	2.17779	+	6.70254i	0.0895065	+	0.275473i
$593$	33.4430			1.37334			0.686669	−	0.726970i	$-0.259072\pi$
$593$	33.4430			1.37334			0.686669	+	0.726970i	$0.259072\pi$
$594$		0			0
$595$	8.04095	+	8.57136i	0.329647	+	0.351391i
$596$	6.02900	−	18.5554i	0.246957	−	0.760057i
$597$		0			0
$598$	−2.28968	+	1.66355i	−0.0936318	+	0.0680275i
$599$	−26.3174			−1.07530			−0.537650	−	0.843168i	$-0.680688\pi$
$599$	−26.3174			−1.07530			−0.537650	+	0.843168i	$0.680688\pi$
$600$		0			0
$601$	20.9964			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$601$	20.9964			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$602$	8.23762	−	5.98498i	0.335740	−	0.243930i
$603$		0			0
$604$	−5.69592	+	17.5302i	−0.231764	+	0.713295i
$605$	−0.906260	−	7.20284i	−0.0368447	−	0.292837i
$606$		0			0
$607$	9.32822			0.378621			0.189310	−	0.981917i	$-0.439375\pi$
$607$	9.32822			0.378621			0.189310	+	0.981917i	$0.439375\pi$
$608$	−1.20945	−	3.72230i	−0.0490496	−	0.150959i
$609$		0			0
$610$	2.89199	+	22.9852i	0.117093	+	0.930643i
$611$	9.69922	−	7.04690i	0.392389	−	0.285087i
$612$		0			0
$613$	25.9724	+	18.8700i	1.04902	+	0.762154i	0.972025	−	0.234878i	$-0.0754690\pi$
$613$	25.9724	+	18.8700i	1.04902	+	0.762154i	0.0769902	+	0.997032i	$0.475469\pi$
$614$	11.2560	−	8.17793i	0.454253	−	0.330034i
$615$		0			0
$616$	11.5257	+	8.37394i	0.464385	+	0.337396i
$617$	9.86557	+	30.3631i	0.397173	+	1.22237i	0.927257	+	0.374427i	$0.122160\pi$
$617$	9.86557	+	30.3631i	0.397173	+	1.22237i	−0.530084	+	0.847945i	$0.677840\pi$
$618$		0			0
$619$	−1.40420	−	4.32167i	−0.0564394	−	0.173703i	0.918863	−	0.394577i	$-0.129109\pi$
$619$	−1.40420	−	4.32167i	−0.0564394	−	0.173703i	−0.975302	+	0.220875i	$0.929109\pi$
$620$	−11.2947	+	5.30795i	−0.453605	+	0.213172i
$621$		0			0
$622$	8.02319	−	24.6928i	0.321701	−	0.990093i
$623$	44.3086	−	32.1921i	1.77519	−	1.28975i
$624$		0			0
$625$	−4.63525	−	24.5665i	−0.185410	−	0.982661i
$626$	−9.47389			−0.378653
$627$		0			0
$628$	3.13851	−	9.65934i	0.125240	−	0.385450i
$629$	3.03257	−	9.33329i	0.120916	−	0.372143i
$630$		0			0
$631$	−8.31756	−	25.5988i	−0.331117	−	1.01907i	−0.968603	−	0.248611i	$-0.920026\pi$
$631$	−8.31756	−	25.5988i	−0.331117	−	1.01907i	0.637486	−	0.770462i	$-0.279974\pi$
$632$	1.80664			0.0718642
$633$		0			0
$634$	−19.8269	−	14.4051i	−0.787427	−	0.572100i
$635$	3.82652	−	6.95215i	0.151851	−	0.275888i
$636$		0			0
$637$	−18.6215	−	13.5293i	−0.737813	−	0.536052i
$638$	−0.150289	−	0.109192i	−0.00595001	−	0.00432293i
$639$		0			0
$640$	0.279141	+	2.21858i	0.0110340	+	0.0876969i
$641$	28.9303	+	21.0191i	1.14268	+	0.830205i	0.987490	−	0.157679i	$-0.0504013\pi$
$641$	28.9303	+	21.0191i	1.14268	+	0.830205i	0.155189	+	0.987885i	$0.450401\pi$
$642$		0			0
$643$	28.2255			1.11311			0.556553	−	0.830812i	$-0.312124\pi$
$643$	28.2255			1.11311			0.556553	+	0.830812i	$0.312124\pi$
$644$	−1.03928	−	3.19856i	−0.0409532	−	0.126041i
$645$		0			0
$646$	−1.68416	+	5.18330i	−0.0662623	+	0.203934i
$647$	−0.394848	+	1.21522i	−0.0155231	+	0.0477751i	−0.958518	−	0.285032i	$-0.907996\pi$
$647$	−0.394848	+	1.21522i	−0.0155231	+	0.0477751i	0.942995	+	0.332807i	$0.107996\pi$
$648$		0			0
$649$	2.60466			0.102242
$650$	−10.1356	+	12.2268i	−0.397550	+	0.479575i
$651$		0			0
$652$	15.0481	−	10.9331i	0.589327	−	0.428171i
$653$	8.47040	−	26.0692i	0.331472	−	1.02017i	−0.636961	−	0.770896i	$-0.719809\pi$
$653$	8.47040	−	26.0692i	0.331472	−	1.02017i	0.968434	−	0.249272i	$-0.0801912\pi$
$654$		0			0
$655$	−6.20096	−	6.60999i	−0.242291	−	0.258274i
$656$	0.460183	+	1.41630i	0.0179671	+	0.0552971i
$657$		0			0
$658$	4.40244	+	13.5493i	0.171625	+	0.528208i
$659$	−33.3535	−	24.2327i	−1.29927	−	0.943972i	−0.299318	−	0.954153i	$-0.596759\pi$
$659$	−33.3535	−	24.2327i	−1.29927	−	0.943972i	−0.999948	+	0.0101814i	$0.996759\pi$
$660$		0			0
$661$	21.4653	−	15.5955i	0.834904	−	0.606593i	−0.0860388	−	0.996292i	$-0.527421\pi$
$661$	21.4653	−	15.5955i	0.834904	−	0.606593i	0.920942	+	0.389699i	$0.127421\pi$
$662$	−8.01764	−	5.82516i	−0.311614	−	0.226401i
$663$		0			0
$664$	8.06414	−	5.85894i	0.312949	−	0.227371i
$665$	22.6004	+	24.0912i	0.876407	+	0.934217i
$666$		0			0
$667$	0.0135516	+	0.0417075i	0.000524719	+	0.00161492i
$668$	−2.17156			−0.0840201
$669$		0			0
$670$	33.6540	+	6.43735i	1.30017	+	0.248696i
$671$	12.0840	−	37.1908i	0.466499	−	1.43574i
$672$		0			0
$673$	6.42142	−	4.66543i	0.247527	−	0.179839i	−0.457103	−	0.889414i	$-0.651113\pi$
$673$	6.42142	−	4.66543i	0.247527	−	0.179839i	0.704630	+	0.709575i	$0.251113\pi$
$674$	9.93566			0.382707
$675$		0			0
$676$	−2.91102			−0.111962
$677$	23.8667	−	17.3402i	0.917271	−	0.666436i	−0.0255722	−	0.999673i	$-0.508141\pi$
$677$	23.8667	−	17.3402i	0.917271	−	0.666436i	0.942843	+	0.333237i	$0.108141\pi$
$678$		0			0
$679$	−0.105172	+	0.323686i	−0.00403613	+	0.0124219i
$680$	1.50142	−	2.72783i	0.0575768	−	0.104607i
$681$		0			0
$682$	21.0657			0.806647
$683$	−11.6650	−	35.9012i	−0.446349	−	1.37372i	−0.880997	−	0.473121i	$-0.843127\pi$
$683$	−11.6650	−	35.9012i	−0.446349	−	1.37372i	0.434648	−	0.900600i	$-0.356873\pi$
$684$		0			0
$685$	−7.83564	−	1.49880i	−0.299384	−	0.0572663i
$686$	0.753030	−	0.547108i	0.0287508	−	0.0208887i
$687$		0			0
$688$	−2.18246	−	1.58565i	−0.0832055	−	0.0604523i
$689$	29.8503	−	21.6875i	1.13721	−	0.826228i
$690$		0			0
$691$	−14.2843	−	10.3782i	−0.543401	−	0.394804i	0.281945	−	0.959430i	$-0.409020\pi$
$691$	−14.2843	−	10.3782i	−0.543401	−	0.394804i	−0.825347	+	0.564626i	$0.809020\pi$
$692$	1.97593	+	6.08130i	0.0751137	+	0.231176i
$693$		0			0
$694$	−6.06757	−	18.6741i	−0.230322	−	0.708858i
$695$	10.7240	−	19.4837i	0.406783	−	0.739058i
$696$		0			0
$697$	0.640805	−	1.97219i	0.0242722	−	0.0747022i
$698$	1.20084	−	0.872461i	0.0454524	−	0.0330231i
$699$		0			0
$700$	−10.0963	−	15.9446i	−0.381605	−	0.602648i
$701$	16.8372			0.635931			0.317965	−	0.948102i	$-0.397000\pi$
$701$	16.8372			0.635931			0.317965	+	0.948102i	$0.397000\pi$
$702$		0			0
$703$	8.52354	−	26.2328i	0.321471	−	0.989387i
$704$	1.16637	−	3.58973i	0.0439594	−	0.135293i
$705$		0			0
$706$	3.17632	+	9.77569i	0.119542	+	0.367913i
$707$	−61.8200			−2.32498
$708$		0			0
$709$	23.1615	+	16.8278i	0.869849	+	0.631982i	0.930546	−	0.366174i	$-0.119333\pi$
$709$	23.1615	+	16.8278i	0.869849	+	0.631982i	−0.0606978	+	0.998156i	$0.519333\pi$
$710$	−10.2466	−	10.9225i	−0.384548	−	0.409914i
$711$		0			0
$712$	−11.7390	−	8.52891i	−0.439939	−	0.319635i
$713$	−4.02319	−	2.92302i	−0.150670	−	0.109468i
$714$		0			0
$715$	24.2623	−	11.4021i	0.907359	−	0.426415i
$716$	6.48304	+	4.71020i	0.242283	+	0.176029i
$717$		0			0
$718$	−10.3725			−0.387099
$719$	2.54857	+	7.84368i	0.0950455	+	0.292520i	0.987266	−	0.159081i	$-0.0508531\pi$
$719$	2.54857	+	7.84368i	0.0950455	+	0.292520i	−0.892220	+	0.451601i	$0.850853\pi$
$720$		0			0
$721$	−1.41853	+	4.36578i	−0.0528287	+	0.162590i
$722$	1.13772	−	3.50155i	0.0423416	−	0.130314i
$723$		0			0
$724$	−10.8629			−0.403716
$725$	0.131650	+	0.207908i	0.00488937	+	0.00772152i
$726$		0			0
$727$	1.71013	−	1.24248i	0.0634251	−	0.0460810i	−0.555621	−	0.831436i	$-0.687519\pi$
$727$	1.71013	−	1.24248i	0.0634251	−	0.0460810i	0.619046	+	0.785355i	$0.287519\pi$
$728$	−3.70477	+	11.4021i	−0.137308	+	0.422591i
$729$		0			0
$730$	1.44280	+	11.4672i	0.0534005	+	0.424420i
$731$	1.16082	+	3.57265i	0.0429346	+	0.132139i
$732$		0			0
$733$	13.9537	+	42.9451i	0.515393	+	1.58622i	0.782567	+	0.622567i	$0.213910\pi$
$733$	13.9537	+	42.9451i	0.515393	+	1.58622i	−0.267174	+	0.963648i	$0.586090\pi$
$734$	21.0946	+	15.3261i	0.778614	+	0.565697i
$735$		0			0
$736$	−0.720859	+	0.523735i	−0.0265712	+	0.0193051i
$737$	−46.7917	−	33.9961i	−1.72359	−	1.25226i
$738$		0			0
$739$	−24.2478	+	17.6171i	−0.891969	+	0.648054i	−0.936391	−	0.350959i	$-0.885856\pi$
$739$	−24.2478	+	17.6171i	−0.891969	+	0.648054i	0.0444213	+	0.999013i	$0.485856\pi$
$740$	−7.59869	+	13.8056i	−0.279334	+	0.507503i
$741$		0			0
$742$	13.5489	+	41.6993i	0.497397	+	1.53083i
$743$	−17.6562			−0.647741			−0.323871	−	0.946101i	$-0.604984\pi$
$743$	−17.6562			−0.647741			−0.323871	+	0.946101i	$0.604984\pi$
$744$		0			0
$745$	39.4835	−	18.5554i	1.44656	−	0.679816i
$746$	−2.92204	+	8.99312i	−0.106984	+	0.329262i
$747$		0			0
$748$	−4.25215	+	3.08937i	−0.155474	+	0.112959i
$749$	40.8113			1.49121
$750$		0			0
$751$	30.1342			1.09961			0.549806	−	0.835293i	$-0.314702\pi$
$751$	30.1342			1.09961			0.549806	+	0.835293i	$0.314702\pi$
$752$	3.05361	−	2.21858i	0.111354	−	0.0809031i
$753$		0			0
$754$	0.0483082	−	0.148677i	0.00175928	−	0.00541451i
$755$	−37.3022	+	17.5302i	−1.35757	+	0.637990i
$756$		0			0
$757$	−4.90706			−0.178350			−0.0891750	−	0.996016i	$-0.528423\pi$
$757$	−4.90706			−0.178350			−0.0891750	+	0.996016i	$0.528423\pi$
$758$	10.9163	+	33.5968i	0.396497	+	1.22029i
$759$		0			0
$760$	4.21998	−	7.66701i	0.153075	−	0.278112i
$761$	10.7466	−	7.80786i	0.389564	−	0.283035i	−0.375713	−	0.926736i	$-0.622602\pi$
$761$	10.7466	−	7.80786i	0.389564	−	0.283035i	0.765277	+	0.643701i	$0.222602\pi$
$762$		0			0
$763$	−34.8579	−	25.3258i	−1.26194	−	0.916854i
$764$	−6.62243	+	4.81147i	−0.239591	+	0.174073i
$765$		0			0
$766$	−24.1227	−	17.5262i	−0.871590	−	0.633247i
$767$	0.677332	+	2.08461i	0.0244571	+	0.0752711i
$768$		0			0
$769$	−8.83716	−	27.1980i	−0.318676	−	0.980784i	−0.974215	−	0.225623i	$-0.927558\pi$
$769$	−8.83716	−	27.1980i	−0.318676	−	0.980784i	0.655539	−	0.755162i	$-0.272442\pi$
$770$	3.97681	+	31.6072i	0.143314	+	1.13904i
$771$		0			0
$772$	−5.42560	+	16.6983i	−0.195272	+	0.600984i
$773$	−36.4564	+	26.4871i	−1.31124	+	0.952675i	−0.311247	+	0.950329i	$0.600747\pi$
$773$	−36.4564	+	26.4871i	−1.31124	+	0.952675i	−0.999997	+	0.00234562i	$0.999253\pi$
$774$		0			0
$775$	−25.9356	−	10.2987i	−0.931634	−	0.369941i
$776$	0.0901699			0.00323691
$777$		0			0
$778$	−6.60578	+	20.3305i	−0.236829	+	0.728884i
$779$	1.80109	−	5.54318i	0.0645307	−	0.198605i
$780$		0			0
$781$	7.81199	+	24.0428i	0.279535	+	0.860320i
$782$	1.24076			0.0443695
$783$		0			0
$784$	−5.86263	−	4.25945i	−0.209379	−	0.152123i
$785$	20.5539	−	9.65934i	0.733600	−	0.344757i
$786$		0			0
$787$	−20.8458	−	15.1454i	−0.743074	−	0.539875i	0.150598	−	0.988595i	$-0.451880\pi$
$787$	−20.8458	−	15.1454i	−0.743074	−	0.539875i	−0.893672	+	0.448720i	$0.851880\pi$
$788$	3.84883	+	2.79634i	0.137109	+	0.0996156i
$789$		0			0
$790$	2.76393	+	2.94625i	0.0983363	+	0.104823i
$791$	−31.8275	−	23.1240i	−1.13166	−	0.822196i
$792$		0			0
$793$	32.9077			1.16859
$794$	−6.49555	−	19.9913i	−0.230519	−	0.709463i
$795$		0			0
$796$	4.49063	−	13.8207i	0.159166	−	0.489863i
$797$	−15.5882	+	47.9757i	−0.552164	+	1.69939i	0.151154	+	0.988510i	$0.451701\pi$
$797$	−15.5882	+	47.9757i	−0.552164	+	1.69939i	−0.703318	+	0.710875i	$0.748299\pi$
$798$		0			0
$799$	−5.25595			−0.185942
$800$	−3.19098	+	3.84937i	−0.112818	+	0.136096i
$801$		0			0
$802$	−13.5769	+	9.86421i	−0.479418	+	0.348317i
$803$	6.02866	−	18.5543i	0.212747	−	0.654768i
$804$		0			0
$805$	3.62622	−	6.58824i	0.127808	−	0.232205i
$806$	5.47805	+	16.8597i	0.192956	+	0.593858i
$807$		0			0
$808$	5.06122	+	15.5768i	0.178053	+	0.547991i
$809$	−2.92626	−	2.12605i	−0.102882	−	0.0747480i	0.535155	−	0.844754i	$-0.320253\pi$
$809$	−2.92626	−	2.12605i	−0.102882	−	0.0747480i	−0.638037	+	0.770006i	$0.720253\pi$
$810$		0			0
$811$	−40.8026	+	29.6448i	−1.43277	+	1.04097i	−0.443280	+	0.896383i	$0.646185\pi$
$811$	−40.8026	+	29.6448i	−1.43277	+	1.04097i	−0.989492	+	0.144586i	$0.953815\pi$
$812$	0.150289	+	0.109192i	0.00527412	+	0.00383187i
$813$		0			0
$814$	21.5202	−	15.6353i	0.754282	−	0.548018i
$815$	40.8512	+	7.81402i	1.43095	+	0.273713i
$816$		0			0
$817$	3.26269	+	10.0415i	0.114147	+	0.351308i
$818$	−36.3607			−1.27132
$819$		0			0
$820$	−1.60566	+	2.91722i	−0.0560721	+	0.101874i
$821$	3.48714	−	10.7323i	0.121702	−	0.374560i	−0.871584	−	0.490246i	$-0.836907\pi$
$821$	3.48714	−	10.7323i	0.121702	−	0.374560i	0.993286	+	0.115686i	$0.0369068\pi$
$822$		0			0
$823$	−0.871148	+	0.632926i	−0.0303663	+	0.0220624i	−0.602865	−	0.797843i	$-0.705974\pi$
$823$	−0.871148	+	0.632926i	−0.0303663	+	0.0220624i	0.572499	+	0.819906i	$0.305974\pi$
$824$	1.21619			0.0423678
$825$		0			0
$826$	−2.60466			−0.0906278
$827$	−23.7689	+	17.2691i	−0.826526	+	0.600506i	−0.918574	−	0.395248i	$-0.870659\pi$
$827$	−23.7689	+	17.2691i	−0.826526	+	0.600506i	0.0920482	+	0.995755i	$0.470659\pi$
$828$		0			0
$829$	6.51402	−	20.0481i	0.226241	−	0.696299i	−0.771922	−	0.635717i	$-0.780704\pi$
$829$	6.51402	−	20.0481i	0.226241	−	0.696299i	0.998163	−	0.0605816i	$-0.0192955\pi$
$830$	21.8919	+	4.18748i	0.759877	+	0.145349i
$831$		0			0
$832$	3.17632			0.110119
$833$	3.11826	+	9.59702i	0.108041	+	0.332517i
$834$		0			0
$835$	−3.32221	−	3.54136i	−0.114970	−	0.122554i
$836$	−11.9514	+	8.68318i	−0.413347	+	0.300314i
$837$		0			0
$838$	27.9425	+	20.3014i	0.965258	+	0.701301i
$839$	−2.76181	+	2.00657i	−0.0953483	+	0.0692746i	−0.634438	−	0.772974i	$-0.718768\pi$
$839$	−2.76181	+	2.00657i	−0.0953483	+	0.0692746i	0.539090	+	0.842248i	$0.318768\pi$
$840$		0			0
$841$	23.4595	+	17.0443i	0.808949	+	0.587736i
$842$	−3.00798	−	9.25762i	−0.103662	−	0.319038i
$843$		0			0
$844$	−4.36823	−	13.4440i	−0.150361	−	0.462762i
$845$	−4.45350	−	4.74726i	−0.153205	−	0.163311i
$846$		0			0
$847$	3.78676	−	11.6544i	0.130114	−	0.400451i
$848$	9.39777	−	6.82788i	0.322721	−	0.234470i
$849$		0			0
$850$	6.74550	−	1.72474i	0.231369	−	0.0591581i
$851$	−6.27951			−0.215259
$852$		0			0
$853$	−12.5449	+	38.6094i	−0.429531	+	1.32196i	0.469058	+	0.883167i	$0.344594\pi$
$853$	−12.5449	+	38.6094i	−0.429531	+	1.32196i	−0.898589	+	0.438792i	$0.855406\pi$
$854$	−12.0840	+	37.1908i	−0.413507	+	1.27264i
$855$		0			0
$856$	−3.34124	−	10.2833i	−0.114201	−	0.351475i
$857$	43.0463			1.47043			0.735216	−	0.677833i	$-0.237081\pi$
$857$	43.0463			1.47043			0.735216	+	0.677833i	$0.237081\pi$
$858$		0			0
$859$	−6.17691	−	4.48779i	−0.210753	−	0.153121i	0.477401	−	0.878685i	$-0.341579\pi$
$859$	−6.17691	−	4.48779i	−0.210753	−	0.153121i	−0.688155	+	0.725564i	$0.741579\pi$
$860$	−0.753030	−	5.98498i	−0.0256781	−	0.204086i
$861$		0			0
$862$	2.50431	+	1.81949i	0.0852970	+	0.0619719i
$863$	5.23799	+	3.80562i	0.178303	+	0.129545i	0.673357	−	0.739317i	$-0.264852\pi$
$863$	5.23799	+	3.80562i	0.178303	+	0.129545i	−0.495054	+	0.868862i	$0.664852\pi$
$864$		0			0
$865$	−6.89439	+	12.5260i	−0.234416	+	0.425896i
$866$	−14.7537	−	10.7192i	−0.501351	−	0.364253i
$867$		0			0
$868$	−21.0657			−0.715016
$869$	−2.10722	−	6.48535i	−0.0714824	−	0.220000i
$870$		0			0
$871$	15.0405	−	46.2898i	0.509627	−	1.56847i
$872$	−3.52753	+	10.8566i	−0.119457	+	0.367652i
$873$		0			0
$874$	3.48736			0.117962
$875$	10.5562	−	40.8582i	0.356863	−	1.38126i
$876$		0			0
$877$	6.36784	−	4.62651i	0.215027	−	0.156226i	−0.475058	−	0.879954i	$-0.657573\pi$
$877$	6.36784	−	4.62651i	0.215027	−	0.156226i	0.690085	+	0.723728i	$0.257573\pi$
$878$	8.19679	−	25.2271i	0.276628	−	0.851374i
$879$		0			0
$880$	7.63851	−	3.58973i	0.257494	−	0.121010i
$881$	−5.95327	−	18.3223i	−0.200571	−	0.617293i	−0.999866	−	0.0163551i	$-0.994794\pi$
$881$	−5.95327	−	18.3223i	−0.200571	−	0.617293i	0.799295	−	0.600938i	$-0.205206\pi$
$882$		0			0
$883$	1.93876	+	5.96688i	0.0652444	+	0.200802i	0.978364	−	0.206889i	$-0.0663341\pi$
$883$	1.93876	+	5.96688i	0.0652444	+	0.200802i	−0.913120	+	0.407691i	$0.866334\pi$
$884$	−3.57830	−	2.59979i	−0.120351	−	0.0874403i
$885$		0			0
$886$	−28.7417	+	20.8821i	−0.965597	+	0.701548i
$887$	18.8281	+	13.6794i	0.632185	+	0.459309i	0.857156	−	0.515056i	$-0.172229\pi$
$887$	18.8281	+	13.6794i	0.632185	+	0.459309i	−0.224972	+	0.974365i	$0.572229\pi$
$888$		0			0
$889$	10.8371	−	7.87358i	0.363463	−	0.264071i
$890$	−4.05040	−	32.1921i	−0.135770	−	1.07908i
$891$		0			0
$892$	1.42527	+	4.38652i	0.0477214	+	0.146871i
$893$	−14.7727			−0.494350
$894$		0			0
$895$	2.23689	+	17.7785i	0.0747709	+	0.594270i
$896$	−1.16637	+	3.58973i	−0.0389658	+	0.119925i
$897$		0			0
$898$	−13.0932	+	9.51279i	−0.436927	+	0.317446i
$899$	0.274685			0.00916126
$900$		0			0
$901$	−16.1757			−0.538890
$902$	4.54738	−	3.30386i	0.151411	−	0.110007i
$903$		0			0
$904$	−3.22086	+	9.91279i	−0.107124	+	0.329694i
$905$	−16.6189	−	17.7151i	−0.552430	−	0.588870i
$906$		0			0
$907$	−17.6544			−0.586206			−0.293103	−	0.956081i	$-0.594688\pi$
$907$	−17.6544			−0.586206			−0.293103	+	0.956081i	$0.594688\pi$
$908$	1.94259	+	5.97869i	0.0644673	+	0.198410i
$909$		0			0
$910$	−24.2623	+	11.4021i	−0.804288	+	0.377977i
$911$	−28.2767	+	20.5442i	−0.936847	+	0.680659i	−0.947660	−	0.319282i	$-0.896558\pi$
$911$	−28.2767	+	20.5442i	−0.936847	+	0.680659i	0.0108124	+	0.999942i	$0.496558\pi$
$912$		0			0
$913$	−30.4378	−	22.1144i	−1.00735	−	0.731879i
$914$	19.1903	−	13.9426i	0.634758	−	0.461179i
$915$		0			0
$916$	−14.3495	−	10.4255i	−0.474121	−	0.344469i
$917$	−4.72760	−	14.5500i	−0.156119	−	0.480485i
$918$		0			0
$919$	11.2243	+	34.5449i	0.370256	+	1.13953i	0.946624	+	0.322340i	$0.104469\pi$
$919$	11.2243	+	34.5449i	0.370256	+	1.13953i	−0.576368	+	0.817190i	$0.695531\pi$
$920$	−1.95693	−	0.374321i	−0.0645180	−	0.0123410i
$921$		0			0
$922$	−2.43288	+	7.48764i	−0.0801226	+	0.246592i
$923$	−17.2110	+	12.5045i	−0.566505	+	0.411590i
$924$		0			0
$925$	−34.1390	+	8.72892i	−1.12249	+	0.287005i
$926$	−15.4230			−0.506832
$927$		0			0
$928$	0.0152089	−	0.0468081i	0.000499256	−	0.00153655i
$929$	−5.88811	+	18.1217i	−0.193183	+	0.594555i	0.806810	+	0.590810i	$0.201192\pi$
$929$	−5.88811	+	18.1217i	−0.193183	+	0.594555i	−0.999993	+	0.00374449i	$0.998808\pi$
$930$		0			0
$931$	8.76439	+	26.9740i	0.287241	+	0.884037i
$932$	−2.56406			−0.0839885
$933$		0			0
$934$	13.7834	+	10.0143i	0.451008	+	0.327677i
$935$	−11.5434	−	2.20802i	−0.377509	−	0.0722100i
$936$		0			0
$937$	−48.1590	−	34.9896i	−1.57329	−	1.14306i	−0.923920	−	0.382586i	$-0.875034\pi$
$937$	−48.1590	−	34.9896i	−1.57329	−	1.14306i	−0.649367	−	0.760475i	$-0.724966\pi$
$938$	46.7917	+	33.9961i	1.52780	+	1.11001i
$939$		0			0
$940$	8.28968	+	1.58565i	0.270379	+	0.0517182i
$941$	12.2598	+	8.90727i	0.399658	+	0.290369i	0.769402	−	0.638765i	$-0.220554\pi$
$941$	12.2598	+	8.90727i	0.399658	+	0.290369i	−0.369744	+	0.929134i	$0.620554\pi$
$942$		0			0
$943$	−1.32691			−0.0432101
$944$	0.213245	+	0.656300i	0.00694052	+	0.0213607i
$945$		0			0
$946$	−3.14649	+	9.68391i	−0.102301	+	0.314851i
$947$	−0.778999	+	2.39751i	−0.0253141	+	0.0779087i	−0.962915	−	0.269803i	$-0.913041\pi$
$947$	−0.778999	+	2.39751i	−0.0253141	+	0.0779087i	0.937601	+	0.347712i	$0.113041\pi$
$948$		0			0
$949$	16.4175			0.532934
$950$	18.9593	−	4.84766i	0.615122	−	0.157279i
$951$		0			0
$952$	4.25215	−	3.08937i	0.137813	−	0.100127i
$953$	−9.69336	+	29.8331i	−0.313999	+	0.966389i	0.662166	+	0.749357i	$0.269637\pi$
$953$	−9.69336	+	29.8331i	−0.313999	+	0.966389i	−0.976165	+	0.217032i	$0.930363\pi$
$954$		0			0
$955$	−17.9780	−	3.43883i	−0.581754	−	0.111278i
$956$	−2.91765	−	8.97961i	−0.0943636	−	0.290421i
$957$		0			0
$958$	−7.75544	−	23.8688i	−0.250567	−	0.771166i
$959$	−10.8945	−	7.91529i	−0.351800	−	0.255598i
$960$		0			0
$961$	−0.120328	+	0.0874237i	−0.00388156	+	0.00282012i
$962$	18.1098	+	13.1576i	0.583884	+	0.424217i
$963$		0			0
$964$	23.8131	−	17.3012i	0.766969	−	0.557236i
$965$	−35.5319	+	16.6983i	−1.14381	+	0.537537i
$966$		0			0
$967$	15.1746	+	46.7027i	0.487983	+	1.50186i	0.827613	+	0.561299i	$0.189698\pi$
$967$	15.1746	+	46.7027i	0.487983	+	1.50186i	−0.339630	+	0.940559i	$0.610302\pi$
$968$	−3.24660			−0.104350
$969$		0			0
$970$	0.137949	+	0.147048i	0.00442927	+	0.00472144i
$971$	−7.72049	+	23.7612i	−0.247762	+	0.762534i	0.747407	+	0.664366i	$0.231298\pi$
$971$	−7.72049	+	23.7612i	−0.247762	+	0.762534i	−0.995170	+	0.0981683i	$0.968702\pi$
$972$		0			0
$973$	30.3713	−	22.0660i	0.973658	−	0.707404i
$974$	13.6876			0.438579
$975$		0			0
$976$	10.3603			0.331626
$977$	12.6095	−	9.16131i	0.403412	−	0.293096i	−0.367517	−	0.930017i	$-0.619792\pi$
$977$	12.6095	−	9.16131i	0.403412	−	0.293096i	0.770929	+	0.636921i	$0.219792\pi$
$978$		0			0
$979$	−16.9244	+	52.0879i	−0.540906	+	1.66474i
$980$	−2.02282	−	16.0771i	−0.0646167	−	0.513565i
$981$		0			0
$982$	−2.58009			−0.0823339
$983$	4.18993	+	12.8953i	0.133638	+	0.411296i	0.995376	−	0.0960585i	$-0.0306236\pi$
$983$	4.18993	+	12.8953i	0.133638	+	0.411296i	−0.861738	+	0.507354i	$0.830624\pi$
$984$		0			0
$985$	1.32799	+	10.5547i	0.0423133	+	0.336301i
$986$	−0.0554457	+	0.0402837i	−0.00176575	+	0.00128289i
$987$		0			0
$988$	−10.0574	−	7.30713i	−0.319969	−	0.232471i
$989$	1.94464	−	1.41286i	0.0618359	−	0.0449264i
$990$		0			0
$991$	−25.1120	−	18.2449i	−0.797709	−	0.579570i	0.112532	−	0.993648i	$-0.464104\pi$
$991$	−25.1120	−	18.2449i	−0.797709	−	0.579570i	−0.910241	+	0.414079i	$0.864104\pi$
$992$	1.72466	+	5.30795i	0.0547579	+	0.168527i
$993$		0			0
$994$	−7.81199	−	24.0428i	−0.247781	−	0.762592i
$995$	29.4089	−	13.8207i	0.932324	−	0.438147i
$996$		0			0
$997$	0.478723	−	1.47336i	0.0151613	−	0.0466617i	−0.943190	−	0.332255i	$-0.892191\pi$
$997$	0.478723	−	1.47336i	0.0151613	−	0.0466617i	0.958351	+	0.285593i	$0.0921906\pi$
$998$	−31.5952	+	22.9553i	−1.00013	+	0.726637i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.e.361.2		8
3.2	odd	2		50.2.d.b.11.1	✓	8
12.11	even	2		400.2.u.d.161.2		8
15.2	even	4		250.2.e.c.199.2		16
15.8	even	4		250.2.e.c.199.3		16
15.14	odd	2		250.2.d.d.51.2		8
25.16	even	5	inner	450.2.h.e.91.2		8
75.29	odd	10		1250.2.a.f.1.4		4
75.38	even	20		250.2.e.c.49.2		16
75.41	odd	10		50.2.d.b.41.1	yes	8
75.47	even	20		1250.2.b.e.1249.8		8
75.53	even	20		1250.2.b.e.1249.1		8
75.59	odd	10		250.2.d.d.201.2		8
75.62	even	20		250.2.e.c.49.3		16
75.71	odd	10		1250.2.a.l.1.1		4
300.71	even	10		10000.2.a.t.1.4		4
300.179	even	10		10000.2.a.x.1.1		4
300.191	even	10		400.2.u.d.241.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.1	✓	8	3.2	odd	2
50.2.d.b.41.1	yes	8	75.41	odd	10
250.2.d.d.51.2		8	15.14	odd	2
250.2.d.d.201.2		8	75.59	odd	10
250.2.e.c.49.2		16	75.38	even	20
250.2.e.c.49.3		16	75.62	even	20
250.2.e.c.199.2		16	15.2	even	4
250.2.e.c.199.3		16	15.8	even	4
400.2.u.d.161.2		8	12.11	even	2
400.2.u.d.241.2		8	300.191	even	10
450.2.h.e.91.2		8	25.16	even	5	inner
450.2.h.e.361.2		8	1.1	even	1	trivial
1250.2.a.f.1.4		4	75.29	odd	10
1250.2.a.l.1.1		4	75.71	odd	10
1250.2.b.e.1249.1		8	75.53	even	20
1250.2.b.e.1249.8		8	75.47	even	20
10000.2.a.t.1.4		4	300.71	even	10
10000.2.a.x.1.1		4	300.179	even	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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.02373 - 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.02373 - 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.07822 - 1.95894i) q^{10} +(-3.05361 + 2.21858i) q^{11} +(-2.56969 - 1.86699i) q^{13} +(3.05361 - 2.21858i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.430307 + 1.32435i) q^{17} +(1.20945 + 3.72230i) q^{19} +(-0.279141 - 2.21858i) q^{20} +(-1.16637 + 3.58973i) q^{22} +(0.720859 - 0.523735i) q^{23} +(3.19098 - 3.84937i) q^{25} -3.17632 q^{26} +(1.16637 - 3.58973i) q^{28} +(-0.0152089 + 0.0468081i) q^{29} +(-1.72466 - 5.30795i) q^{31} -1.00000 q^{32} +(1.12656 + 0.818492i) q^{34} +(7.63851 - 3.58973i) q^{35} +(-5.70152 - 4.14240i) q^{37} +(3.16637 + 2.30051i) q^{38} +(-1.52988 - 1.63079i) q^{40} +(-1.20477 - 0.875319i) q^{41} +2.69767 q^{43} +(1.16637 + 3.58973i) q^{44} +(0.275344 - 0.847421i) q^{46} +(-1.16637 + 3.58973i) q^{47} +7.24660 q^{49} +(0.318958 - 4.98982i) q^{50} +(-2.56969 + 1.86699i) q^{52} +(-3.58963 + 11.0477i) q^{53} +(-4.06969 + 7.39396i) q^{55} +(-1.16637 - 3.58973i) q^{56} +(0.0152089 + 0.0468081i) q^{58} +(-0.558282 - 0.405615i) q^{59} +(-8.38168 + 6.08965i) q^{61} +(-4.51521 - 3.28049i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-6.97599 - 1.33437i) q^{65} +(4.73519 + 14.5734i) q^{67} +1.39250 q^{68} +(4.06969 - 7.39396i) q^{70} +(2.06969 - 6.36986i) q^{71} +(-4.18158 + 3.03810i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-11.5257 + 8.37394i) q^{77} +(-0.558282 + 1.71821i) q^{79} +(-2.19625 - 0.420099i) q^{80} -1.48918 q^{82} +(3.08023 + 9.47997i) q^{83} +(2.13035 + 2.27088i) q^{85} +(2.18246 - 1.58565i) q^{86} +(3.05361 + 2.21858i) q^{88} +(11.7390 - 8.52891i) q^{89} +(-9.69922 - 7.04690i) q^{91} +(-0.275344 - 0.847421i) q^{92} +(1.16637 + 3.58973i) q^{94} +(5.98771 + 6.38268i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +(5.86263 - 4.25945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

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