LMFDB - Embedded newform 225.2.m.b.154.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, 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("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (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:	$1.79663404548$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			154.3
Root			$-0.536547i$ of defining polynomial
Character	$\chi$	$=$	225.154
Dual form			225.2.m.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.510286 + 0.165802i) q^{2} +(-1.38513 - 1.00636i) q^{4} +(-2.22820 - 0.187439i) q^{5} -2.57318i q^{7} +(-1.17071 - 1.61134i) q^{8} +O(q^{10})$	\(q+(0.510286 + 0.165802i) q^{2} +(-1.38513 - 1.00636i) q^{4} +(-2.22820 - 0.187439i) q^{5} -2.57318i q^{7} +(-1.17071 - 1.61134i) q^{8} +(-1.10594 - 0.465087i) q^{10} +(1.58949 - 4.89194i) q^{11} +(1.40274 - 0.455776i) q^{13} +(0.426639 - 1.31306i) q^{14} +(0.727915 + 2.24029i) q^{16} +(-0.404314 - 0.556490i) q^{17} +(-6.54709 + 4.75674i) q^{19} +(2.89772 + 2.50199i) q^{20} +(1.62219 - 2.23275i) q^{22} +(-0.354506 - 0.115186i) q^{23} +(4.92973 + 0.835300i) q^{25} +0.791365 q^{26} +(-2.58954 + 3.56419i) q^{28} +(-0.0288595 - 0.0209676i) q^{29} +(3.63169 - 2.63858i) q^{31} +5.24733i q^{32} +(-0.114049 - 0.351005i) q^{34} +(-0.482313 + 5.73355i) q^{35} +(1.81590 - 0.590022i) q^{37} +(-4.12957 + 1.34178i) q^{38} +(2.30654 + 3.80982i) q^{40} +(1.59739 + 4.91625i) q^{41} -11.4506i q^{43} +(-7.12469 + 5.17639i) q^{44} +(-0.161802 - 0.117556i) q^{46} +(5.00860 - 6.89374i) q^{47} +0.378747 q^{49} +(2.37708 + 1.24360i) q^{50} +(-2.40165 - 0.780343i) q^{52} +(5.36247 - 7.38080i) q^{53} +(-4.45863 + 10.6023i) q^{55} +(-4.14627 + 3.01244i) q^{56} +(-0.0112501 - 0.0154845i) q^{58} +(-0.0544457 - 0.167567i) q^{59} +(-1.98127 + 6.09772i) q^{61} +(2.29069 - 0.744289i) q^{62} +(0.585811 - 1.80294i) q^{64} +(-3.21100 + 0.752633i) q^{65} +(0.0490435 + 0.0675025i) q^{67} +1.17770i q^{68} +(-1.19675 + 2.84579i) q^{70} +(9.83589 + 7.14619i) q^{71} +(-11.4619 - 3.72421i) q^{73} +1.02446 q^{74} +13.8556 q^{76} +(-12.5878 - 4.09004i) q^{77} +(4.01019 + 2.91357i) q^{79} +(-1.20202 - 5.12825i) q^{80} +2.77354i q^{82} +(5.50356 + 7.57501i) q^{83} +(0.796583 + 1.31575i) q^{85} +(1.89853 - 5.84308i) q^{86} +(-9.74340 + 3.16582i) q^{88} +(-0.00380677 + 0.0117160i) q^{89} +(-1.17279 - 3.60949i) q^{91} +(0.375120 + 0.516308i) q^{92} +(3.69882 - 2.68735i) q^{94} +(15.4798 - 9.37179i) q^{95} +(4.47917 - 6.16504i) q^{97} +(0.193269 + 0.0627970i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 + 30 * q^8	$ 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.510286	+	0.165802i	0.360827	+	0.117240i	0.483820	−	0.875168i	$-0.339249\pi$
$2$	0.510286	+	0.165802i	0.360827	+	0.117240i	−0.122993	+	0.992408i	$0.539249\pi$
$3$		0			0
$3$		0			0
$4$	−1.38513	−	1.00636i	−0.692566	−	0.503179i
$5$	−2.22820	−	0.187439i	−0.996480	−	0.0838251i
$5$	−2.22820	−	0.187439i	−0.996480	−	0.0838251i
$6$		0			0
$7$		−	2.57318i		−	0.972570i	−0.873800	−	0.486285i	$-0.838352\pi$
$7$		−	2.57318i		−	0.972570i	0.873800	−	0.486285i	$-0.161648\pi$
$8$	−1.17071	−	1.61134i	−0.413907	−	0.569695i
$9$		0			0
$10$	−1.10594	−	0.465087i	−0.349729	−	0.147074i
$11$	1.58949	−	4.89194i	0.479248	−	1.47497i	−0.360893	−	0.932607i	$-0.617528\pi$
$11$	1.58949	−	4.89194i	0.479248	−	1.47497i	0.840141	−	0.542368i	$-0.182472\pi$
$12$		0			0
$13$	1.40274	−	0.455776i	0.389049	−	0.126410i	−0.107960	−	0.994155i	$-0.534432\pi$
$13$	1.40274	−	0.455776i	0.389049	−	0.126410i	0.497009	+	0.867746i	$0.334432\pi$
$14$	0.426639	−	1.31306i	0.114024	−	0.350930i
$15$		0			0
$16$	0.727915	+	2.24029i	0.181979	+	0.560073i
$17$	−0.404314	−	0.556490i	−0.0980605	−	0.134969i	0.757167	−	0.653221i	$-0.226583\pi$
$17$	−0.404314	−	0.556490i	−0.0980605	−	0.134969i	−0.855228	+	0.518252i	$0.826583\pi$
$18$		0			0
$19$	−6.54709	+	4.75674i	−1.50201	+	1.09127i	−0.532432	+	0.846473i	$0.678722\pi$
$19$	−6.54709	+	4.75674i	−1.50201	+	1.09127i	−0.969574	+	0.244799i	$0.921278\pi$
$20$	2.89772	+	2.50199i	0.647950	+	0.559462i
$21$		0			0
$22$	1.62219	−	2.23275i	0.345852	−	0.476024i
$23$	−0.354506	−	0.115186i	−0.0739197	−	0.0240180i	0.271824	−	0.962347i	$-0.412373\pi$
$23$	−0.354506	−	0.115186i	−0.0739197	−	0.0240180i	−0.345743	+	0.938329i	$0.612373\pi$
$24$		0			0
$25$	4.92973	+	0.835300i	0.985947	+	0.167060i
$26$	0.791365			0.155200
$27$		0			0
$28$	−2.58954	+	3.56419i	−0.489377	+	0.673569i
$29$	−0.0288595	−	0.0209676i	−0.00535907	−	0.00389359i	0.585102	−	0.810959i	$-0.301054\pi$
$29$	−0.0288595	−	0.0209676i	−0.00535907	−	0.00389359i	−0.590462	+	0.807066i	$0.701054\pi$
$30$		0			0
$31$	3.63169	−	2.63858i	0.652272	−	0.473903i	−0.211773	−	0.977319i	$-0.567924\pi$
$31$	3.63169	−	2.63858i	0.652272	−	0.473903i	0.864044	+	0.503416i	$0.167924\pi$
$32$			5.24733i			0.927606i
$33$		0			0
$34$	−0.114049	−	0.351005i	−0.0195592	−	0.0601969i
$35$	−0.482313	+	5.73355i	−0.0815258	+	0.969148i
$36$		0			0
$37$	1.81590	−	0.590022i	0.298532	−	0.0969991i	−0.155921	−	0.987770i	$-0.549835\pi$
$37$	1.81590	−	0.590022i	0.298532	−	0.0969991i	0.454454	+	0.890770i	$0.349835\pi$
$38$	−4.12957	+	1.34178i	−0.669905	+	0.217665i
$39$		0			0
$40$	2.30654	+	3.80982i	0.364696	+	0.602385i
$41$	1.59739	+	4.91625i	0.249470	+	0.767789i	0.994869	+	0.101171i	$0.0322588\pi$
$41$	1.59739	+	4.91625i	0.249470	+	0.767789i	−0.745399	+	0.666618i	$0.767741\pi$
$42$		0			0
$43$		−	11.4506i		−	1.74620i	−0.487543	−	0.873099i	$-0.662107\pi$
$43$		−	11.4506i		−	1.74620i	0.487543	−	0.873099i	$-0.337893\pi$
$44$	−7.12469	+	5.17639i	−1.07409	+	0.780370i
$45$		0			0
$46$	−0.161802	−	0.117556i	−0.0238564	−	0.0173327i
$47$	5.00860	−	6.89374i	0.730579	−	1.00556i	−0.268527	−	0.963272i	$-0.586537\pi$
$47$	5.00860	−	6.89374i	0.730579	−	1.00556i	0.999106	−	0.0422836i	$-0.0134633\pi$
$48$		0			0
$49$	0.378747			0.0541067
$50$	2.37708	+	1.24360i	0.336170	+	0.175872i
$51$		0			0
$52$	−2.40165	−	0.780343i	−0.333049	−	0.108214i
$53$	5.36247	−	7.38080i	0.736592	−	1.01383i	−0.262216	−	0.965009i	$-0.584453\pi$
$53$	5.36247	−	7.38080i	0.736592	−	1.01383i	0.998807	−	0.0488220i	$-0.0155467\pi$
$54$		0			0
$55$	−4.45863	+	10.6023i	−0.601202	+	1.42961i
$56$	−4.14627	+	3.01244i	−0.554068	+	0.402554i
$57$		0			0
$58$	−0.0112501	−	0.0154845i	−0.00147721	−	0.00203321i
$59$	−0.0544457	−	0.167567i	−0.00708822	−	0.0218153i	0.947450	−	0.319904i	$-0.103651\pi$
$59$	−0.0544457	−	0.167567i	−0.00708822	−	0.0218153i	−0.954538	+	0.298089i	$0.903651\pi$
$60$		0			0
$61$	−1.98127	+	6.09772i	−0.253676	+	0.780733i	0.740412	+	0.672153i	$0.234630\pi$
$61$	−1.98127	+	6.09772i	−0.253676	+	0.780733i	−0.994088	+	0.108580i	$0.965370\pi$
$62$	2.29069	−	0.744289i	0.290918	−	0.0945248i
$63$		0			0
$64$	0.585811	−	1.80294i	0.0732263	−	0.225367i
$65$	−3.21100	+	0.752633i	−0.398276	+	0.0933527i
$66$		0			0
$67$	0.0490435	+	0.0675025i	0.00599161	+	0.00824675i	0.812002	−	0.583654i	$-0.198378\pi$
$67$	0.0490435	+	0.0675025i	0.00599161	+	0.00824675i	−0.806011	+	0.591901i	$0.798378\pi$
$68$			1.17770i			0.142817i
$69$		0			0
$70$	−1.19675	+	2.84579i	−0.143039	+	0.340137i
$71$	9.83589	+	7.14619i	1.16731	+	0.848097i	0.990684	−	0.136182i	$-0.0434831\pi$
$71$	9.83589	+	7.14619i	1.16731	+	0.848097i	0.176622	+	0.984279i	$0.443483\pi$
$72$		0			0
$73$	−11.4619	−	3.72421i	−1.34152	−	0.435886i	−0.451688	−	0.892176i	$-0.649178\pi$
$73$	−11.4619	−	3.72421i	−1.34152	−	0.435886i	−0.889831	+	0.456290i	$0.849178\pi$
$74$	1.02446			0.119091
$75$		0			0
$76$	13.8556			1.58934
$77$	−12.5878	−	4.09004i	−1.43452	−	0.466103i
$78$		0			0
$79$	4.01019	+	2.91357i	0.451182	+	0.327803i	0.790062	−	0.613027i	$-0.210048\pi$
$79$	4.01019	+	2.91357i	0.451182	+	0.327803i	−0.338881	+	0.940829i	$0.610048\pi$
$80$	−1.20202	−	5.12825i	−0.134390	−	0.573356i
$81$		0			0
$82$			2.77354i			0.306287i
$83$	5.50356	+	7.57501i	0.604095	+	0.831465i	0.996075	−	0.0885084i	$-0.0282100\pi$
$83$	5.50356	+	7.57501i	0.604095	+	0.831465i	−0.391981	+	0.919973i	$0.628210\pi$
$84$		0			0
$85$	0.796583	+	1.31575i	0.0864016	+	0.142714i
$86$	1.89853	−	5.84308i	0.204724	−	0.630075i
$87$		0			0
$88$	−9.74340	+	3.16582i	−1.03865	+	0.337478i
$89$	−0.00380677	+	0.0117160i	−0.000403517	+	0.00124190i	−0.951258	−	0.308396i	$-0.900208\pi$
$89$	−0.00380677	+	0.0117160i	−0.000403517	+	0.00124190i	0.950855	+	0.309638i	$0.100208\pi$
$90$		0			0
$91$	−1.17279	−	3.60949i	−0.122942	−	0.378377i
$92$	0.375120	+	0.516308i	0.0391089	+	0.0538288i
$93$		0			0
$94$	3.69882	−	2.68735i	0.381504	−	0.277179i
$95$	15.4798	−	9.37179i	1.58820	−	0.961525i
$96$		0			0
$97$	4.47917	−	6.16504i	0.454790	−	0.625965i	−0.518628	−	0.855000i	$-0.673557\pi$
$97$	4.47917	−	6.16504i	0.454790	−	0.625965i	0.973418	+	0.229035i	$0.0735570\pi$
$98$	0.193269	+	0.0627970i	0.0195231	+	0.00634345i
$99$		0			0
$100$	−5.98772	−	6.11808i	−0.598772	−	0.611808i
$101$	−8.27518			−0.823411			−0.411706	−	0.911317i	$-0.635067\pi$
$101$	−8.27518			−0.823411			−0.411706	+	0.911317i	$0.635067\pi$
$102$		0			0
$103$	6.10475	−	8.40247i	0.601519	−	0.827920i	−0.394328	−	0.918970i	$-0.629022\pi$
$103$	6.10475	−	8.40247i	0.601519	−	0.827920i	0.995846	+	0.0910504i	$0.0290224\pi$
$104$	−2.37660	−	1.72670i	−0.233045	−	0.169317i
$105$		0			0
$106$	3.96015	−	2.87722i	0.384643	−	0.279460i
$107$		−	12.2737i		−	1.18655i	−0.805001	−	0.593274i	$-0.797835\pi$
$107$		−	12.2737i		−	1.18655i	0.805001	−	0.593274i	$-0.202165\pi$
$108$		0			0
$109$	1.30684	+	4.02203i	0.125172	+	0.385241i	0.993932	−	0.109992i	$-0.0350826\pi$
$109$	1.30684	+	4.02203i	0.125172	+	0.385241i	−0.868760	+	0.495233i	$0.835083\pi$
$110$	−4.03306	+	4.67095i	−0.384537	+	0.445357i
$111$		0			0
$112$	5.76467	−	1.87305i	0.544710	−	0.176987i
$113$	−17.4696	+	5.67623i	−1.64340	+	0.533974i	−0.977296	−	0.211880i	$-0.932041\pi$
$113$	−17.4696	+	5.67623i	−1.64340	+	0.533974i	−0.666109	+	0.745855i	$0.732041\pi$
$114$		0			0
$115$	0.768320	+	0.323106i	0.0716462	+	0.0301297i
$116$	0.0188733	+	0.0580859i	0.00175234	+	0.00539314i
$117$		0			0
$118$		−	0.0945341i		−	0.00870257i
$119$	−1.43195	+	1.04037i	−0.131267	+	0.0953707i
$120$		0			0
$121$	−12.5054	−	9.08571i	−1.13685	−	0.825974i
$122$	−2.02203	+	2.78309i	−0.183066	+	0.251969i
$123$		0			0
$124$	−7.68573			−0.690199
$125$	−10.8279	−	2.78524i	−0.968473	−	0.249119i
$126$		0			0
$127$	−0.328591	−	0.106766i	−0.0291577	−	0.00947391i	0.294402	−	0.955682i	$-0.404880\pi$
$127$	−0.328591	−	0.106766i	−0.0291577	−	0.00947391i	−0.323560	+	0.946208i	$0.604880\pi$
$128$	6.76647	−	9.31325i	0.598077	−	0.823182i
$129$		0			0
$130$	−1.76332	−	0.148332i	−0.154653	−	0.0130096i
$131$	−3.69438	+	2.68413i	−0.322780	+	0.234513i	−0.737361	−	0.675499i	$-0.763928\pi$
$131$	−3.69438	+	2.68413i	−0.322780	+	0.234513i	0.414581	+	0.910012i	$0.363928\pi$
$132$		0			0
$133$	12.2400	+	16.8468i	1.06134	+	1.46081i
$134$	0.0138342	+	0.0425771i	0.00119509	+	0.00367810i
$135$		0			0
$136$	−0.423362	+	1.30297i	−0.0363030	+	0.111729i
$137$	4.58174	−	1.48870i	0.391445	−	0.127188i	−0.106680	−	0.994293i	$-0.534022\pi$
$137$	4.58174	−	1.48870i	0.391445	−	0.127188i	0.498125	+	0.867105i	$0.334022\pi$
$138$		0			0
$139$	1.15595	−	3.55766i	0.0980468	−	0.301757i	−0.889989	−	0.455982i	$-0.849288\pi$
$139$	1.15595	−	3.55766i	0.0980468	−	0.301757i	0.988036	+	0.154225i	$0.0492881\pi$
$140$	6.43807	−	7.45635i	0.544116	−	0.630177i
$141$		0			0
$142$	3.83427	+	5.27742i	0.321765	+	0.442871i
$143$		−	7.58655i		−	0.634419i
$144$		0			0
$145$	0.0603745	+	0.0521294i	0.00501383	+	0.00432911i
$146$	−5.23139	−	3.80083i	−0.432953	−	0.314559i
$147$		0			0
$148$	−3.10904	−	1.01019i	−0.255561	−	0.0830369i
$149$	8.64621			0.708325			0.354163	−	0.935184i	$-0.384766\pi$
$149$	8.64621			0.708325			0.354163	+	0.935184i	$0.384766\pi$
$150$		0			0
$151$	−1.24898			−0.101641			−0.0508205	−	0.998708i	$-0.516184\pi$
$151$	−1.24898			−0.101641			−0.0508205	+	0.998708i	$0.516184\pi$
$152$	15.3295	+	4.98084i	1.24338	+	0.404000i
$153$		0			0
$154$	−5.74527	−	4.17418i	−0.462967	−	0.336365i
$155$	−8.58671	+	5.19856i	−0.689701	+	0.417558i
$156$		0			0
$157$		−	3.86574i		−	0.308520i	−0.988030	−	0.154260i	$-0.950701\pi$
$157$		−	3.86574i		−	0.308520i	0.988030	−	0.154260i	$-0.0492993\pi$
$158$	1.56327	+	2.15166i	0.124367	+	0.171176i
$159$		0			0
$160$	0.983552	−	11.6921i	0.0777566	−	0.924341i
$161$	−0.296394	+	0.912208i	−0.0233592	+	0.0718921i
$162$		0			0
$163$	6.63277	−	2.15512i	0.519519	−	0.168802i	−0.0375081	−	0.999296i	$-0.511942\pi$
$163$	6.63277	−	2.15512i	0.519519	−	0.168802i	0.557027	+	0.830494i	$0.311942\pi$
$164$	2.73491	−	8.41719i	0.213561	−	0.657272i
$165$		0			0
$166$	1.55244	+	4.77793i	0.120493	+	0.370839i
$167$	9.38069	+	12.9114i	0.725900	+	0.999115i	0.999307	+	0.0372169i	$0.0118493\pi$
$167$	9.38069	+	12.9114i	0.725900	+	0.999115i	−0.273408	+	0.961898i	$0.588151\pi$
$168$		0			0
$169$	−8.75729	+	6.36254i	−0.673637	+	0.489426i
$170$	0.188331	+	0.803486i	0.0144443	+	0.0616246i
$171$		0			0
$172$	−11.5234	+	15.8606i	−0.878649	+	1.20936i
$173$	7.29774	+	2.37118i	0.554837	+	0.180277i	0.572997	−	0.819558i	$-0.305781\pi$
$173$	7.29774	+	2.37118i	0.554837	+	0.180277i	−0.0181597	+	0.999835i	$0.505781\pi$
$174$		0			0
$175$	2.14938	−	12.6851i	0.162478	−	0.958903i
$176$	12.1164			0.913306
$177$		0			0
$178$	−0.00388509	+	0.00534737i	−0.000291200	+	0.000400802i
$179$	−8.58312	−	6.23600i	−0.641532	−	0.466100i	0.218844	−	0.975760i	$-0.429771\pi$
$179$	−8.58312	−	6.23600i	−0.641532	−	0.466100i	−0.860376	+	0.509659i	$0.829771\pi$
$180$		0			0
$181$	−12.2223	+	8.88005i	−0.908480	+	0.660049i	−0.940630	−	0.339434i	$-0.889764\pi$
$181$	−12.2223	+	8.88005i	−0.908480	+	0.660049i	0.0321503	+	0.999483i	$0.489764\pi$
$182$		−	2.03633i		−	0.150942i
$183$		0			0
$184$	0.229419	+	0.706079i	0.0169130	+	0.0520528i
$185$	−4.15678	+	0.974317i	−0.305613	+	0.0716332i
$186$		0			0
$187$	−3.36497	+	1.09334i	−0.246071	+	0.0799532i
$188$	−13.8751	+	4.50831i	−1.01195	+	0.328802i
$189$		0			0
$190$	9.45300	−	2.21571i	0.685793	−	0.160744i
$191$	−3.78359	−	11.6447i	−0.273771	−	0.842580i	−0.989542	−	0.144245i	$-0.953925\pi$
$191$	−3.78359	−	11.6447i	−0.273771	−	0.842580i	0.715771	−	0.698335i	$-0.246075\pi$
$192$		0			0
$193$			14.2421i			1.02517i	0.858637	+	0.512585i	$0.171312\pi$
$193$			14.2421i			1.02517i	−0.858637	+	0.512585i	$0.828688\pi$
$194$	3.30783	−	2.40328i	0.237489	−	0.172546i
$195$		0			0
$196$	−0.524614	−	0.381154i	−0.0374724	−	0.0272253i
$197$	−10.4325	+	14.3591i	−0.743286	+	1.02304i	0.255137	+	0.966905i	$0.417879\pi$
$197$	−10.4325	+	14.3591i	−0.743286	+	1.02304i	−0.998423	+	0.0561399i	$0.982121\pi$
$198$		0			0
$199$	18.9550			1.34369			0.671843	−	0.740693i	$-0.265503\pi$
$199$	18.9550			1.34369			0.671843	+	0.740693i	$0.265503\pi$
$200$	−4.42532	−	8.92137i	−0.312917	−	0.630836i
$201$		0			0
$202$	−4.22271	−	1.37204i	−0.297109	−	0.0965366i
$203$	−0.0539535	+	0.0742606i	−0.00378679	+	0.00521207i
$204$		0			0
$205$	−2.63780	−	11.2538i	−0.184232	−	0.785998i
$206$	4.50832	−	3.27548i	0.314109	−	0.228214i
$207$		0			0
$208$	2.04214	+	2.81077i	0.141597	+	0.194892i
$209$	12.8632	+	39.5888i	0.889764	+	2.73841i
$210$		0			0
$211$	−3.33022	+	10.2494i	−0.229262	+	0.705596i	0.768569	+	0.639767i	$0.220969\pi$
$211$	−3.33022	+	10.2494i	−0.229262	+	0.705596i	−0.997831	+	0.0658288i	$0.979031\pi$
$212$	−14.8555	+	4.82683i	−1.02028	+	0.331508i
$213$		0			0
$214$	2.03501	−	6.26312i	0.139111	−	0.428138i
$215$	−2.14628	+	25.5142i	−0.146375	+	1.74005i
$216$		0			0
$217$	−6.78954	−	9.34500i	−0.460904	−	0.634380i
$218$			2.26907i			0.153681i
$219$		0			0
$220$	16.8455	−	10.1986i	1.13572	−	0.687588i
$221$	−0.820780	−	0.596332i	−0.0552116	−	0.0401136i
$222$		0			0
$223$	26.2213	+	8.51983i	1.75591	+	0.570530i	0.996763	−	0.0803900i	$-0.0256166\pi$
$223$	26.2213	+	8.51983i	1.75591	+	0.570530i	0.759147	+	0.650920i	$0.225617\pi$
$224$	13.5023			0.902162
$225$		0			0
$226$	−9.85565			−0.655588
$227$	−3.78731	−	1.23057i	−0.251372	−	0.0816758i	0.180620	−	0.983553i	$-0.442189\pi$
$227$	−3.78731	−	1.23057i	−0.251372	−	0.0816758i	−0.431993	+	0.901877i	$0.642189\pi$
$228$		0			0
$229$	9.68373	+	7.03564i	0.639919	+	0.464928i	0.859822	−	0.510593i	$-0.170574\pi$
$229$	9.68373	+	7.03564i	0.639919	+	0.464928i	−0.219903	+	0.975522i	$0.570574\pi$
$230$	0.338492	+	0.292265i	0.0223195	+	0.0192714i
$231$		0			0
$232$			0.0710494i			0.00466462i
$233$	12.4129	+	17.0849i	0.813197	+	1.11927i	0.990822	+	0.135172i	$0.0431587\pi$
$233$	12.4129	+	17.0849i	0.813197	+	1.11927i	−0.177625	+	0.984098i	$0.556841\pi$
$234$		0			0
$235$	−12.4523	+	14.4218i	−0.812299	+	0.940776i
$236$	−0.0932174	+	0.286894i	−0.00606793	+	0.0186752i
$237$		0			0
$238$	−0.903200	+	0.293467i	−0.0585457	+	0.0190227i
$239$	8.09778	−	24.9224i	0.523802	−	1.61210i	−0.242871	−	0.970059i	$-0.578089\pi$
$239$	8.09778	−	24.9224i	0.523802	−	1.61210i	0.766673	−	0.642038i	$-0.221911\pi$
$240$		0			0
$241$	−2.52607	−	7.77443i	−0.162718	−	0.500795i	0.836143	−	0.548512i	$-0.184805\pi$
$241$	−2.52607	−	7.77443i	−0.162718	−	0.500795i	−0.998861	+	0.0477169i	$0.984805\pi$
$242$	−4.87491	−	6.70974i	−0.313371	−	0.431318i
$243$		0			0
$244$	8.88081	−	6.45228i	0.568535	−	0.413065i
$245$	−0.843923	−	0.0709917i	−0.0539162	−	0.00453549i
$246$		0			0
$247$	−7.01583	+	9.65646i	−0.446406	+	0.614426i
$248$	−8.50330	−	2.76289i	−0.539960	−	0.175444i
$249$		0			0
$250$	−5.06351	−	3.21655i	−0.320244	−	0.203432i
$251$	−24.8145			−1.56628			−0.783139	−	0.621847i	$-0.786382\pi$
$251$	−24.8145			−1.56628			−0.783139	+	0.621847i	$0.786382\pi$
$252$		0			0
$253$	−1.12697	+	1.55114i	−0.0708518	+	0.0975191i
$254$	−0.149973	−	0.108962i	−0.00941017	−	0.00683689i
$255$		0			0
$256$	1.92965	−	1.40197i	0.120603	−	0.0876232i
$257$			24.2995i			1.51576i	0.652392	+	0.757882i	$0.273766\pi$
$257$			24.2995i			1.51576i	−0.652392	+	0.757882i	$0.726234\pi$
$258$		0			0
$259$	−1.51823	−	4.67264i	−0.0943384	−	0.290344i
$260$	5.20508	+	2.18892i	0.322805	+	0.135751i
$261$		0			0
$262$	−2.33023	+	0.757137i	−0.143962	+	0.0467761i
$263$	8.10556	−	2.63366i	0.499810	−	0.162398i	−0.0482528	−	0.998835i	$-0.515365\pi$
$263$	8.10556	−	2.63366i	0.499810	−	0.162398i	0.548063	+	0.836437i	$0.315365\pi$
$264$		0			0
$265$	−13.3321	+	15.4408i	−0.818984	+	0.948518i
$266$	3.45264	+	10.6261i	0.211695	+	0.651530i
$267$		0			0
$268$		−	0.142855i		−	0.00872627i
$269$	−2.08979	+	1.51832i	−0.127417	+	0.0925737i	−0.649668	−	0.760218i	$-0.725092\pi$
$269$	−2.08979	+	1.51832i	−0.127417	+	0.0925737i	0.522252	+	0.852791i	$0.325092\pi$
$270$		0			0
$271$	10.9940	+	7.98759i	0.667837	+	0.485212i	0.869300	−	0.494284i	$-0.164570\pi$
$271$	10.9940	+	7.98759i	0.667837	+	0.485212i	−0.201464	+	0.979496i	$0.564570\pi$
$272$	0.952393	−	1.31086i	0.0577473	−	0.0794824i
$273$		0			0
$274$	2.58483			0.156155
$275$	11.9220	−	22.7883i	0.718923	−	1.37418i
$276$		0			0
$277$	−8.69242	−	2.82434i	−0.522277	−	0.169698i	0.0360015	−	0.999352i	$-0.488538\pi$
$277$	−8.69242	−	2.82434i	−0.522277	−	0.169698i	−0.558278	+	0.829654i	$0.688538\pi$
$278$	1.17974	−	1.62377i	0.0707558	−	0.0973870i
$279$		0			0
$280$	9.80335	−	5.93514i	0.585862	−	0.354692i
$281$	8.42195	−	6.11890i	0.502411	−	0.365023i	−0.307526	−	0.951540i	$-0.599501\pi$
$281$	8.42195	−	6.11890i	0.502411	−	0.365023i	0.809937	+	0.586517i	$0.199501\pi$
$282$		0			0
$283$	−2.83069	−	3.89611i	−0.168267	−	0.231600i	0.716553	−	0.697533i	$-0.245719\pi$
$283$	−2.83069	−	3.89611i	−0.168267	−	0.231600i	−0.884820	+	0.465933i	$0.845719\pi$
$284$	−6.43238	−	19.7968i	−0.381692	−	1.17473i
$285$		0			0
$286$	1.25787	−	3.87131i	0.0743791	−	0.228915i
$287$	12.6504	−	4.11036i	0.746729	−	0.242627i
$288$		0			0
$289$	5.10708	−	15.7180i	0.300416	−	0.924586i
$290$	0.0221651	+	0.0366112i	0.00130158	+	0.00214988i
$291$		0			0
$292$	12.1284	+	16.6933i	0.709762	+	0.976904i
$293$		−	24.4506i		−	1.42842i	−0.699932	−	0.714210i	$-0.746786\pi$
$293$		−	24.4506i		−	1.42842i	0.699932	−	0.714210i	$-0.253214\pi$
$294$		0			0
$295$	0.0899073	+	0.383577i	0.00523460	+	0.0223327i
$296$	−3.07661	−	2.23529i	−0.178825	−	0.129924i
$297$		0			0
$298$	4.41205	+	1.43356i	0.255583	+	0.0830439i
$299$	−0.549778			−0.0317945
$300$		0			0
$301$	−29.4644			−1.69830
$302$	−0.637340	−	0.207084i	−0.0366748	−	0.0119164i
$303$		0			0
$304$	−15.4222	−	11.2049i	−0.884524	−	0.642645i
$305$	5.55761	−	13.2156i	0.318228	−	0.756721i
$306$		0			0
$307$			9.51655i			0.543138i	0.962419	+	0.271569i	$0.0875426\pi$
$307$			9.51655i			0.543138i	−0.962419	+	0.271569i	$0.912457\pi$
$308$	13.3198	+	18.3331i	0.758965	+	1.04463i
$309$		0			0
$310$	−5.24361	+	1.22906i	−0.297817	+	0.0698060i
$311$	−7.71967	+	23.7587i	−0.437742	+	1.34723i	0.452508	+	0.891760i	$0.350529\pi$
$311$	−7.71967	+	23.7587i	−0.437742	+	1.34723i	−0.890250	+	0.455471i	$0.849471\pi$
$312$		0			0
$313$	−9.39797	+	3.05359i	−0.531205	+	0.172599i	−0.562324	−	0.826917i	$-0.690093\pi$
$313$	−9.39797	+	3.05359i	−0.531205	+	0.172599i	0.0311197	+	0.999516i	$0.490093\pi$
$314$	0.640948	−	1.97264i	0.0361708	−	0.111322i
$315$		0			0
$316$	−2.62255	−	8.07137i	−0.147530	−	0.454050i
$317$	−14.5365	−	20.0078i	−0.816453	−	1.12375i	−0.990296	−	0.138978i	$-0.955618\pi$
$317$	−14.5365	−	20.0078i	−0.816453	−	1.12375i	0.173842	−	0.984773i	$-0.444382\pi$
$318$		0			0
$319$	−0.148444	+	0.107851i	−0.00831128	+	0.00603850i
$320$	−1.64324	+	3.90750i	−0.0918601	+	0.218436i
$321$		0			0
$322$	−0.302492	+	0.416345i	−0.0168572	+	0.0232020i
$323$	5.29416	+	1.72018i	0.294575	+	0.0957132i
$324$		0			0
$325$	7.29582	−	1.07515i	0.404699	−	0.0596386i
$326$	3.74194			0.207247
$327$		0			0
$328$	6.05167	−	8.32941i	0.334148	−	0.459915i
$329$	−17.7388	−	12.8880i	−0.977974	−	0.710540i
$330$		0			0
$331$	−0.872336	+	0.633789i	−0.0479479	+	0.0348362i	−0.611501	−	0.791244i	$-0.709434\pi$
$331$	−0.872336	+	0.633789i	−0.0479479	+	0.0348362i	0.563553	+	0.826080i	$0.309434\pi$
$332$		−	16.0309i		−	0.879812i
$333$		0			0
$334$	2.64610	+	8.14386i	0.144788	+	0.445612i
$335$	−0.0966260	−	0.159602i	−0.00527924	−	0.00871997i
$336$		0			0
$337$	−13.3727	+	4.34507i	−0.728460	+	0.236691i	−0.649687	−	0.760202i	$-0.725100\pi$
$337$	−13.3727	+	4.34507i	−0.728460	+	0.236691i	−0.0787727	+	0.996893i	$0.525100\pi$
$338$	−5.52365	+	1.79474i	−0.300447	+	0.0976211i
$339$		0			0
$340$	0.220746	−	2.62414i	0.0119716	−	0.142314i
$341$	−7.13524	−	21.9600i	−0.386395	−	1.18920i
$342$		0			0
$343$		−	18.9868i		−	1.02519i
$344$	−18.4508	+	13.4053i	−0.994799	+	0.722764i
$345$		0			0
$346$	3.33079	+	2.41996i	0.179064	+	0.130098i
$347$	−3.34793	+	4.60804i	−0.179726	+	0.247372i	−0.889369	−	0.457189i	$-0.848856\pi$
$347$	−3.34793	+	4.60804i	−0.179726	+	0.247372i	0.709643	+	0.704561i	$0.248856\pi$
$348$		0			0
$349$	28.4950			1.52530			0.762651	−	0.646810i	$-0.223897\pi$
$349$	28.4950			1.52530			0.762651	+	0.646810i	$0.223897\pi$
$350$	3.20001	−	6.11666i	0.171048	−	0.326949i
$351$		0			0
$352$	25.6696	+	8.34056i	1.36820	+	0.444554i
$353$	7.50341	−	10.3276i	0.399366	−	0.549681i	−0.561218	−	0.827668i	$-0.689667\pi$
$353$	7.50341	−	10.3276i	0.399366	−	0.549681i	0.960585	+	0.277987i	$0.0896672\pi$
$354$		0			0
$355$	−20.5768	−	17.7668i	−1.09211	−	0.942962i
$356$	0.0170634	−	0.0123973i	0.000904359	−	0.000657056i
$357$		0			0
$358$	−3.34591	−	4.60524i	−0.176837	−	0.243395i
$359$	−1.39620	−	4.29707i	−0.0736888	−	0.226791i	0.907428	−	0.420208i	$-0.138043\pi$
$359$	−1.39620	−	4.29707i	−0.0736888	−	0.226791i	−0.981117	+	0.193417i	$0.938043\pi$
$360$		0			0
$361$	14.3665	−	44.2156i	0.756132	−	2.32714i
$362$	−7.70923	+	2.50488i	−0.405188	+	0.131654i
$363$		0			0
$364$	−2.00796	+	6.17987i	−0.105246	+	0.323913i
$365$	24.8414	+	10.4467i	1.30026	+	0.546805i
$366$		0			0
$367$	−1.78361	−	2.45493i	−0.0931039	−	0.128146i	0.759924	−	0.650012i	$-0.225236\pi$
$367$	−1.78361	−	2.45493i	−0.0931039	−	0.128146i	−0.853028	+	0.521866i	$0.825236\pi$
$368$		−	0.878043i		−	0.0457711i
$369$		0			0
$370$	−2.28269	−	0.192023i	−0.118672	−	0.00998279i
$371$	−18.9921	−	13.7986i	−0.986022	−	0.716387i
$372$		0			0
$373$	−14.6138	−	4.74831i	−0.756674	−	0.245858i	−0.0948232	−	0.995494i	$-0.530229\pi$
$373$	−14.6138	−	4.74831i	−0.756674	−	0.245858i	−0.661850	+	0.749636i	$0.730229\pi$
$374$	−1.89838			−0.0981626
$375$		0			0
$376$	−16.9718			−0.875252
$377$	−0.0500388	−	0.0162586i	−0.00257713	−	0.000837359i
$378$		0			0
$379$	8.38117	+	6.08927i	0.430512	+	0.312785i	0.781853	−	0.623462i	$-0.214275\pi$
$379$	8.38117	+	6.08927i	0.430512	+	0.312785i	−0.351342	+	0.936247i	$0.614275\pi$
$380$	−30.8730	−	2.59707i	−1.58375	−	0.133227i
$381$		0			0
$382$		−	6.56946i		−	0.336123i
$383$	9.10278	+	12.5289i	0.465130	+	0.640197i	0.975563	−	0.219721i	$-0.0705147\pi$
$383$	9.10278	+	12.5289i	0.465130	+	0.640197i	−0.510432	+	0.859918i	$0.670515\pi$
$384$		0			0
$385$	27.2816	+	11.4729i	1.39040	+	0.584711i
$386$	−2.36137	+	7.26756i	−0.120191	+	0.369909i
$387$		0			0
$388$	−12.4085	+	4.03176i	−0.629945	+	0.204681i
$389$	−6.61139	+	20.3478i	−0.335211	+	1.03167i	0.631407	+	0.775451i	$0.282478\pi$
$389$	−6.61139	+	20.3478i	−0.335211	+	1.03167i	−0.966618	+	0.256221i	$0.917522\pi$
$390$		0			0
$391$	0.0792318	+	0.243850i	0.00400693	+	0.0123320i
$392$	−0.443401	−	0.610289i	−0.0223951	−	0.0308243i
$393$		0			0
$394$	−7.70434	+	5.59753i	−0.388139	+	0.282000i
$395$	−8.38938	−	7.24368i	−0.422116	−	0.364469i
$396$		0			0
$397$	7.34827	−	10.1140i	0.368799	−	0.507608i	−0.583775	−	0.811916i	$-0.698425\pi$
$397$	7.34827	−	10.1140i	0.368799	−	0.507608i	0.952574	+	0.304307i	$0.0984249\pi$
$398$	9.67249	+	3.14278i	0.484838	+	0.157534i
$399$		0			0
$400$	1.71711	+	11.6521i	0.0858555	+	0.582603i
$401$	33.0478			1.65033			0.825164	−	0.564893i	$-0.191083\pi$
$401$	33.0478			1.65033			0.825164	+	0.564893i	$0.191083\pi$
$402$		0			0
$403$	3.89170	−	5.35647i	0.193860	−	0.266825i
$404$	11.4622	+	8.32779i	0.570267	+	0.414323i
$405$		0			0
$406$	−0.0398443	+	0.0289486i	−0.00197744	+	0.00143669i
$407$		−	9.82111i		−	0.486815i
$408$		0			0
$409$	−0.932426	−	2.86971i	−0.0461055	−	0.141898i	0.925354	−	0.379105i	$-0.123768\pi$
$409$	−0.932426	−	2.86971i	−0.0461055	−	0.141898i	−0.971459	+	0.237207i	$0.923768\pi$
$410$	0.519869	−	6.18000i	0.0256745	−	0.305209i
$411$		0			0
$412$	−16.9118	+	5.49497i	−0.833183	+	0.270718i
$413$	−0.431179	+	0.140098i	−0.0212169	+	0.00689379i
$414$		0			0
$415$	−10.8432	−	17.9102i	−0.532271	−	0.879177i
$416$	2.39161	+	7.36062i	0.117258	+	0.360884i
$417$		0			0
$418$			22.3343i			1.09241i
$419$	−5.75511	+	4.18133i	−0.281156	+	0.204272i	−0.719421	−	0.694574i	$-0.755593\pi$
$419$	−5.75511	+	4.18133i	−0.281156	+	0.204272i	0.438266	+	0.898845i	$0.355593\pi$
$420$		0			0
$421$	17.6826	+	12.8472i	0.861798	+	0.626133i	0.928373	−	0.371649i	$-0.121207\pi$
$421$	17.6826	+	12.8472i	0.861798	+	0.626133i	−0.0665758	+	0.997781i	$0.521207\pi$
$422$	−3.39873	+	4.67796i	−0.165448	+	0.227719i
$423$		0			0
$424$	−18.1709			−0.882455
$425$	−1.52832	−	3.08107i	−0.0741345	−	0.149454i
$426$		0			0
$427$	15.6905	+	5.09816i	0.759318	+	0.246717i
$428$	−12.3518	+	17.0008i	−0.597045	+	0.821763i
$429$		0			0
$430$	−5.32552	+	12.6637i	−0.256819	+	0.610697i
$431$	3.23115	−	2.34757i	0.155639	−	0.113078i	−0.507240	−	0.861805i	$-0.669334\pi$
$431$	3.23115	−	2.34757i	0.155639	−	0.113078i	0.662879	+	0.748726i	$0.269334\pi$
$432$		0			0
$433$	14.8071	+	20.3802i	0.711583	+	0.979410i	0.999762	+	0.0218335i	$0.00695037\pi$
$433$	14.8071	+	20.3802i	0.711583	+	0.979410i	−0.288178	+	0.957577i	$0.593050\pi$
$434$	−1.91519	−	5.89435i	−0.0919321	−	0.282938i
$435$		0			0
$436$	2.23746	−	6.88620i	0.107155	−	0.329789i
$437$	2.86890	−	0.932161i	0.137238	−	0.0445913i
$438$		0			0
$439$	0.529997	−	1.63116i	0.0252954	−	0.0778511i	−0.937612	−	0.347684i	$-0.886968\pi$
$439$	0.529997	−	1.63116i	0.0252954	−	0.0778511i	0.962907	+	0.269833i	$0.0869683\pi$
$440$	22.3036	−	5.22779i	1.06328	−	0.249225i
$441$		0			0
$442$	−0.319960	−	0.440387i	−0.0152189	−	0.0209471i
$443$		−	11.7475i		−	0.558140i	−0.960271	−	0.279070i	$-0.909974\pi$
$443$		−	11.7475i		−	0.558140i	0.960271	−	0.279070i	$-0.0900261\pi$
$444$		0			0
$445$	0.0106783	−	0.0253921i	0.000506199	−	0.00120370i
$446$	11.9678	+	8.69510i	0.566691	+	0.411725i
$447$		0			0
$448$	−4.63929	−	1.50740i	−0.219186	−	0.0712178i
$449$	12.8415			0.606030			0.303015	−	0.952986i	$-0.402007\pi$
$449$	12.8415			0.606030			0.303015	+	0.952986i	$0.402007\pi$
$450$		0			0
$451$	26.5890			1.25203
$452$	29.9101	+	9.71837i	1.40685	+	0.457114i
$453$		0			0
$454$	−1.72858	−	1.25589i	−0.0811263	−	0.0589417i
$455$	1.93666	+	8.26249i	0.0907921	+	0.387351i
$456$		0			0
$457$			13.6882i			0.640309i	0.947365	+	0.320155i	$0.103735\pi$
$457$			13.6882i			0.640309i	−0.947365	+	0.320155i	$0.896265\pi$
$458$	3.77495	+	5.19577i	0.176392	+	0.242783i
$459$		0			0
$460$	−0.739065	−	1.22075i	−0.0344591	−	0.0569177i
$461$	−3.00160	+	9.23799i	−0.139799	+	0.430256i	−0.996306	−	0.0858796i	$-0.972630\pi$
$461$	−3.00160	+	9.23799i	−0.139799	+	0.430256i	0.856507	+	0.516136i	$0.172630\pi$
$462$		0			0
$463$	−20.2328	+	6.57403i	−0.940297	+	0.305521i	−0.738767	−	0.673961i	$-0.764592\pi$
$463$	−20.2328	+	6.57403i	−0.940297	+	0.305521i	−0.201531	+	0.979482i	$0.564592\pi$
$464$	0.0259664	−	0.0799163i	0.00120546	−	0.00371002i
$465$		0			0
$466$	3.50143	+	10.7763i	0.162201	+	0.499202i
$467$	8.17106	+	11.2465i	0.378112	+	0.520426i	0.955083	−	0.296338i	$-0.0957656\pi$
$467$	8.17106	+	11.2465i	0.378112	+	0.520426i	−0.576971	+	0.816764i	$0.695766\pi$
$468$		0			0
$469$	0.173696	−	0.126198i	0.00802054	−	0.00582727i
$470$	−8.74541	+	5.29464i	−0.403396	+	0.244224i
$471$		0			0
$472$	−0.206267	+	0.283902i	−0.00949419	+	0.0130676i
$473$	−56.0156	−	18.2006i	−2.57560	−	0.836862i
$474$		0			0
$475$	−36.2487	+	17.9807i	−1.66321	+	0.825010i
$476$	3.03042			0.138899
$477$		0			0
$478$	8.26438	−	11.3749i	0.378004	−	0.520278i
$479$	10.0057	+	7.26958i	0.457173	+	0.332155i	0.792421	−	0.609974i	$-0.208820\pi$
$479$	10.0057	+	7.26958i	0.457173	+	0.332155i	−0.335249	+	0.942130i	$0.608820\pi$
$480$		0			0
$481$	2.27831	−	1.65529i	0.103882	−	0.0754747i
$482$		−	4.38601i		−	0.199777i
$483$		0			0
$484$	8.17817	+	25.1698i	0.371735	+	1.14408i
$485$	−11.1360	+	12.8974i	−0.505661	+	0.585639i
$486$		0			0
$487$	33.5990	−	10.9170i	1.52251	−	0.494695i	0.576026	−	0.817432i	$-0.304603\pi$
$487$	33.5990	−	10.9170i	1.52251	−	0.494695i	0.946489	+	0.322737i	$0.104603\pi$
$488$	12.1450	−	3.94614i	0.549778	−	0.178634i
$489$		0			0
$490$	−0.418872	−	0.176150i	−0.0189227	−	0.00795766i
$491$	6.70374	+	20.6320i	0.302536	+	0.931109i	0.980585	+	0.196093i	$0.0628254\pi$
$491$	6.70374	+	20.6320i	0.302536	+	0.931109i	−0.678050	+	0.735016i	$0.737175\pi$
$492$		0			0
$493$			0.0245375i			0.00110511i
$494$	−5.18114	+	3.76432i	−0.233111	+	0.169365i
$495$		0			0
$496$	8.55475	+	6.21539i	0.384120	+	0.279079i
$497$	18.3884	−	25.3095i	0.824834	−	1.13529i
$498$		0			0
$499$	−38.7869			−1.73634			−0.868171	−	0.496265i	$-0.834704\pi$
$499$	−38.7869			−1.73634			−0.868171	+	0.496265i	$0.834704\pi$
$500$	12.1951	+	14.7546i	0.545380	+	0.659846i
$501$		0			0
$502$	−12.6625	−	4.11430i	−0.565155	−	0.183630i
$503$	3.77337	−	5.19360i	0.168246	−	0.231571i	−0.716565	−	0.697520i	$-0.754287\pi$
$503$	3.77337	−	5.19360i	0.168246	−	0.231571i	0.884812	+	0.465949i	$0.154287\pi$
$504$		0			0
$505$	18.4387	+	1.55109i	0.820513	+	0.0690225i
$506$	−0.832257	+	0.604670i	−0.0369983	+	0.0268809i
$507$		0			0
$508$	0.347697	+	0.478564i	0.0154266	+	0.0212328i
$509$	−2.22343	−	6.84300i	−0.0985516	−	0.303311i	0.889611	−	0.456718i	$-0.150975\pi$
$509$	−2.22343	−	6.84300i	−0.0985516	−	0.303311i	−0.988163	+	0.153408i	$0.950975\pi$
$510$		0			0
$511$	−9.58307	+	29.4937i	−0.423930	+	1.30472i
$512$	−20.6796	+	6.71922i	−0.913919	+	0.296950i
$513$		0			0
$514$	−4.02891	+	12.3997i	−0.177708	+	0.546928i
$515$	−15.1775	+	17.5781i	−0.668802	+	0.774583i
$516$		0			0
$517$	−25.7627	−	35.4593i	−1.13304	−	1.55950i
$518$		−	2.63611i		−	0.115824i
$519$		0			0
$520$	4.97189	+	4.29290i	0.218032	+	0.188256i
$521$	−8.51120	−	6.18375i	−0.372882	−	0.270915i	0.385523	−	0.922698i	$-0.374021\pi$
$521$	−8.51120	−	6.18375i	−0.372882	−	0.270915i	−0.758405	+	0.651783i	$0.774021\pi$
$522$		0			0
$523$	10.7700	+	3.49938i	0.470938	+	0.153017i	0.534865	−	0.844938i	$-0.320362\pi$
$523$	10.7700	+	3.49938i	0.470938	+	0.153017i	−0.0639269	+	0.997955i	$0.520362\pi$
$524$	7.81840			0.341548
$525$		0			0
$526$	4.57282			0.199385
$527$	−2.93669	−	0.954188i	−0.127924	−	0.0415651i
$528$		0			0
$529$	−18.4950	−	13.4374i	−0.804130	−	0.584234i
$530$	−9.36329	+	5.66872i	−0.406715	+	0.246234i
$531$		0			0
$532$		−	35.6529i		−	1.54575i
$533$	4.48142	+	6.16814i	0.194112	+	0.267172i
$534$		0			0
$535$	−2.30057	+	27.3483i	−0.0994624	+	1.18237i
$536$	0.0513540	−	0.158051i	0.00221815	−	0.00682678i
$537$		0			0
$538$	−1.31813	+	0.428287i	−0.0568287	+	0.0184648i
$539$	0.602013	−	1.85281i	0.0259305	−	0.0798060i
$540$		0			0
$541$	5.22898	+	16.0931i	0.224811	+	0.691898i	0.998311	+	0.0581012i	$0.0185046\pi$
$541$	5.22898	+	16.0931i	0.224811	+	0.691898i	−0.773499	+	0.633797i	$0.781495\pi$
$542$	4.28572	+	5.89879i	0.184087	+	0.253375i
$543$		0			0
$544$	2.92009	−	2.12157i	0.125198	−	0.0909614i
$545$	−2.15801	−	9.20684i	−0.0924390	−	0.394378i
$546$		0			0
$547$	25.9429	−	35.7073i	1.10924	−	1.52674i	0.286705	−	0.958019i	$-0.407440\pi$
$547$	25.9429	−	35.7073i	1.10924	−	1.52674i	0.822533	−	0.568717i	$-0.192560\pi$
$548$	−7.84448	−	2.54883i	−0.335100	−	0.108881i
$549$		0			0
$550$	9.86197	−	9.65185i	0.420516	−	0.411556i
$551$	0.288683			0.0122983
$552$		0			0
$553$	7.49715	−	10.3189i	0.318811	−	0.438806i
$554$	−3.96734	−	2.88244i	−0.168556	−	0.122463i
$555$		0			0
$556$	−5.18143	+	3.76453i	−0.219741	+	0.159652i
$557$			17.8472i			0.756210i	0.925763	+	0.378105i	$0.123424\pi$
$557$			17.8472i			0.756210i	−0.925763	+	0.378105i	$0.876576\pi$
$558$		0			0
$559$	−5.21891	−	16.0621i	−0.220736	−	0.679356i
$560$	−13.1959	+	3.09302i	−0.557629	+	0.130704i
$561$		0			0
$562$	5.31213	−	1.72602i	0.224079	−	0.0728076i
$563$	−20.3586	+	6.61490i	−0.858012	+	0.278785i	−0.704798	−	0.709408i	$-0.748962\pi$
$563$	−20.3586	+	6.61490i	−0.858012	+	0.278785i	−0.153214	+	0.988193i	$0.548962\pi$
$564$		0			0
$565$	39.9897	−	9.37328i	1.68238	−	0.394337i
$566$	−0.798480	−	2.45747i	−0.0335626	−	0.103295i
$567$		0			0
$568$		−	24.2151i		−	1.01604i
$569$	21.0929	−	15.3249i	0.884262	−	0.642454i	−0.0501135	−	0.998744i	$-0.515958\pi$
$569$	21.0929	−	15.3249i	0.884262	−	0.642454i	0.934376	+	0.356289i	$0.115958\pi$
$570$		0			0
$571$	7.71705	+	5.60676i	0.322948	+	0.234636i	0.737433	−	0.675421i	$-0.236038\pi$
$571$	7.71705	+	5.60676i	0.322948	+	0.234636i	−0.414484	+	0.910057i	$0.636038\pi$
$572$	−7.63478	+	10.5084i	−0.319226	+	0.439377i
$573$		0			0
$574$	7.13683			0.297885
$575$	−1.65141	−	0.863956i	−0.0688684	−	0.0360295i
$576$		0			0
$577$	−8.65941	−	2.81361i	−0.360496	−	0.117132i	0.123169	−	0.992386i	$-0.460694\pi$
$577$	−8.65941	−	2.81361i	−0.360496	−	0.117132i	−0.483664	+	0.875254i	$0.660694\pi$
$578$	5.21214	−	7.17390i	0.216797	−	0.298395i
$579$		0			0
$580$	−0.0311658	−	0.132964i	−0.00129409	−	0.00552105i
$581$	19.4919	−	14.1617i	0.808658	−	0.587525i
$582$		0			0
$583$	−27.5829	−	37.9646i	−1.14237	−	1.57233i
$584$	7.41761	+	22.8291i	0.306943	+	0.944673i
$585$		0			0
$586$	4.05396	−	12.4768i	0.167468	−	0.515412i
$587$	28.0072	−	9.10008i	1.15598	−	0.375600i	0.332587	−	0.943073i	$-0.392079\pi$
$587$	28.0072	−	9.10008i	1.15598	−	0.375600i	0.823393	+	0.567472i	$0.192079\pi$
$588$		0			0
$589$	−11.2260	+	34.5501i	−0.462559	+	1.42361i
$590$	−0.0177193	+	0.210641i	−0.000729494	+	0.00867194i
$591$		0			0
$592$	2.64364	+	3.63866i	0.108653	+	0.149548i
$593$			33.7757i			1.38700i	0.720456	+	0.693501i	$0.243933\pi$
$593$			33.7757i			1.38700i	−0.720456	+	0.693501i	$0.756067\pi$
$594$		0			0
$595$	3.38567	−	2.04975i	0.138799	−	0.0840316i
$596$	−11.9761	−	8.70118i	−0.490562	−	0.356414i
$597$		0			0
$598$	−0.280544	−	0.0911543i	−0.0114723	−	0.00372758i
$599$	−12.0575			−0.492656			−0.246328	−	0.969187i	$-0.579224\pi$
$599$	−12.0575			−0.492656			−0.246328	+	0.969187i	$0.579224\pi$
$600$		0			0
$601$	0.0653240			0.00266462			0.00133231	−	0.999999i	$-0.499576\pi$
$601$	0.0653240			0.00266462			0.00133231	+	0.999999i	$0.499576\pi$
$602$	−15.0353	−	4.88526i	−0.612793	−	0.199108i
$603$		0			0
$604$	1.73001	+	1.25692i	0.0703930	+	0.0511435i
$605$	26.1615	+	22.5888i	1.06362	+	0.918363i
$606$		0			0
$607$			25.9556i			1.05350i	0.850019	+	0.526752i	$0.176590\pi$
$607$			25.9556i			1.05350i	−0.850019	+	0.526752i	$0.823410\pi$
$608$	−24.9602	−	34.3548i	−1.01227	−	1.39327i
$609$		0			0
$610$	5.02714	−	5.82226i	0.203543	−	0.235736i
$611$	3.88373	−	11.9529i	0.157119	−	0.483563i
$612$		0			0
$613$	−11.9559	+	3.88472i	−0.482896	+	0.156902i	−0.540341	−	0.841446i	$-0.681705\pi$
$613$	−11.9559	+	3.88472i	−0.482896	+	0.156902i	0.0574448	+	0.998349i	$0.481705\pi$
$614$	−1.57786	+	4.85617i	−0.0636774	+	0.195979i
$615$		0			0
$616$	8.14623	+	25.0715i	0.328221	+	1.01016i
$617$	1.09165	+	1.50253i	0.0439483	+	0.0604896i	0.830426	−	0.557130i	$-0.188097\pi$
$617$	1.09165	+	1.50253i	0.0439483	+	0.0604896i	−0.786477	+	0.617619i	$0.788097\pi$
$618$		0			0
$619$	−14.5814	+	10.5940i	−0.586077	+	0.425810i	−0.840910	−	0.541175i	$-0.817980\pi$
$619$	−14.5814	+	10.5940i	−0.586077	+	0.425810i	0.254833	+	0.966985i	$0.417980\pi$
$620$	17.1253	+	1.44060i	0.687770	+	0.0578560i
$621$		0			0
$622$	−7.87848	+	10.8438i	−0.315898	+	0.434797i
$623$	0.0301475	+	0.00979552i	0.00120783	+	0.000392449i
$624$		0			0
$625$	23.6045	+	8.23562i	0.944182	+	0.329425i
$626$	−5.30195			−0.211908
$627$		0			0
$628$	−3.89032	+	5.35456i	−0.155241	+	0.213670i
$629$	−1.06254	−	0.771977i	−0.0423661	−	0.0307807i
$630$		0			0
$631$	−17.3636	+	12.6154i	−0.691233	+	0.502210i	−0.877065	−	0.480371i	$-0.840502\pi$
$631$	−17.3636	+	12.6154i	−0.691233	+	0.502210i	0.185832	+	0.982582i	$0.440502\pi$
$632$		−	9.87272i		−	0.392716i
$633$		0			0
$634$	−4.10046	−	12.6199i	−0.162850	−	0.501201i
$635$	0.712153	+	0.299485i	0.0282609	+	0.0118847i
$636$		0			0
$637$	0.531281	−	0.172624i	0.0210501	−	0.00683960i
$638$	−0.0936310	+	0.0304225i	−0.00370689	+	0.00120444i
$639$		0			0
$640$	−16.8227	+	19.4835i	−0.664975	+	0.770151i
$641$	−12.2648	−	37.7471i	−0.484430	−	1.49092i	−0.832805	−	0.553567i	$-0.813266\pi$
$641$	−12.2648	−	37.7471i	−0.484430	−	1.49092i	0.348374	−	0.937355i	$-0.386734\pi$
$642$		0			0
$643$		−	1.26211i		−	0.0497729i	−0.999690	−	0.0248864i	$-0.992078\pi$
$643$		−	1.26211i		−	0.0497729i	0.999690	−	0.0248864i	$-0.00792242\pi$
$644$	1.32855	−	0.965250i	0.0523523	−	0.0380362i
$645$		0			0
$646$	2.41633	+	1.75557i	0.0950692	+	0.0690718i
$647$	17.0032	−	23.4029i	0.668466	−	0.920064i	−0.331259	−	0.943540i	$-0.607473\pi$
$647$	17.0032	−	23.4029i	0.668466	−	0.920064i	0.999724	+	0.0234758i	$0.00747326\pi$
$648$		0			0
$649$	−0.906266			−0.0355740
$650$	3.90122	+	0.661028i	0.153018	+	0.0259276i
$651$		0			0
$652$	−11.3561	−	3.68982i	−0.444739	−	0.144504i
$653$	10.2743	−	14.1413i	0.402063	−	0.553393i	−0.559197	−	0.829035i	$-0.688890\pi$
$653$	10.2743	−	14.1413i	0.402063	−	0.553393i	0.961260	+	0.275642i	$0.0888904\pi$
$654$		0			0
$655$	8.73493	−	5.28830i	0.341302	−	0.206631i
$656$	−9.85106	+	7.15721i	−0.384619	+	0.279442i
$657$		0			0
$658$	−6.91503	−	9.51772i	−0.269576	−	0.371039i
$659$	3.50406	+	10.7844i	0.136499	+	0.420100i	0.995820	−	0.0913359i	$-0.0291137\pi$
$659$	3.50406	+	10.7844i	0.136499	+	0.420100i	−0.859321	+	0.511436i	$0.829114\pi$
$660$		0			0
$661$	1.43350	−	4.41185i	0.0557565	−	0.171601i	−0.919300	−	0.393557i	$-0.871244\pi$
$661$	1.43350	−	4.41185i	0.0557565	−	0.171601i	0.975057	+	0.221956i	$0.0712443\pi$
$662$	−0.550225	+	0.178779i	−0.0213851	+	0.00694844i
$663$		0			0
$664$	5.76285	−	17.7362i	0.223642	−	0.688299i
$665$	−24.1153	−	39.8324i	−0.935151	−	1.54463i
$666$		0			0
$667$	0.00781569	+	0.0107574i	0.000302625	+	0.000416527i
$668$		−	27.3243i		−	1.05721i
$669$		0			0
$670$	−0.0228446	−	0.0974634i	−0.000882565	−	0.00376534i
$671$	26.6805	+	19.3845i	1.02999	+	0.748330i
$672$		0			0
$673$	−7.16302	−	2.32741i	−0.276114	−	0.0897149i	0.167687	−	0.985840i	$-0.446370\pi$
$673$	−7.16302	−	2.32741i	−0.276114	−	0.0897149i	−0.443801	+	0.896125i	$0.646370\pi$
$674$	−7.54435			−0.290598
$675$		0			0
$676$	18.5330			0.712807
$677$	−30.0707	−	9.77055i	−1.15571	−	0.375513i	−0.332418	−	0.943132i	$-0.607864\pi$
$677$	−30.0707	−	9.77055i	−1.15571	−	0.375513i	−0.823291	+	0.567619i	$0.807864\pi$
$678$		0			0
$679$	−15.8638	−	11.5257i	−0.608795	−	0.442316i
$680$	1.18756	−	2.82393i	0.0455409	−	0.108293i
$681$		0			0
$682$		−	12.3889i		−	0.474397i
$683$	−18.0215	−	24.8045i	−0.689575	−	0.949118i	0.310424	−	0.950598i	$-0.399529\pi$
$683$	−18.0215	−	24.8045i	−0.689575	−	0.949118i	−0.999999	+	0.00148011i	$0.999529\pi$
$684$		0			0
$685$	−10.4881	+	2.45832i	−0.400729	+	0.0939276i
$686$	3.14806	−	9.68873i	0.120193	−	0.369917i
$687$		0			0
$688$	25.6526	−	8.33505i	0.977998	−	0.317771i
$689$	4.15813	−	12.7974i	0.158412	−	0.487542i
$690$		0			0
$691$	−10.7334	−	33.0341i	−0.408318	−	1.25667i	−0.918092	−	0.396366i	$-0.870271\pi$
$691$	−10.7334	−	33.0341i	−0.408318	−	1.25667i	0.509774	−	0.860308i	$-0.329729\pi$
$692$	−7.72208	−	10.6285i	−0.293550	−	0.404036i
$693$		0			0
$694$	−2.47243	+	1.79632i	−0.0938520	+	0.0681875i
$695$	−3.24254	+	7.71050i	−0.122996	+	0.292476i
$696$		0			0
$697$	2.09000	−	2.87663i	0.0791643	−	0.108960i
$698$	14.5406	+	4.72453i	0.550370	+	0.178826i
$699$		0			0
$700$	−15.7429	+	15.4075i	−0.595026	+	0.582348i
$701$	19.5437			0.738154			0.369077	−	0.929399i	$-0.379674\pi$
$701$	19.5437			0.738154			0.369077	+	0.929399i	$0.379674\pi$
$702$		0			0
$703$	−9.08230	+	12.5007i	−0.342545	+	0.471473i
$704$	−7.88873	−	5.73150i	−0.297318	−	0.216014i
$705$		0			0
$706$	5.54122	−	4.02593i	0.208547	−	0.151518i
$707$			21.2935i			0.800825i
$708$		0			0
$709$	7.82140	+	24.0718i	0.293739	+	0.904035i	0.983642	+	0.180133i	$0.0576529\pi$
$709$	7.82140	+	24.0718i	0.293739	+	0.904035i	−0.689904	+	0.723901i	$0.742347\pi$
$710$	−7.55432	−	12.4778i	−0.283508	−	0.468284i
$711$		0			0
$712$	0.0233351	−	0.00758205i	0.000874522	−	0.000284149i
$713$	−1.59139	+	0.517073i	−0.0595979	+	0.0193645i
$714$		0			0
$715$	−1.42201	+	16.9043i	−0.0531802	+	0.632186i
$716$	5.61311	+	17.2754i	0.209772	+	0.645611i
$717$		0			0
$718$		−	2.42423i		−	0.0904715i
$719$	7.43539	−	5.40213i	0.277293	−	0.201465i	−0.440443	−	0.897781i	$-0.645178\pi$
$719$	7.43539	−	5.40213i	0.277293	−	0.201465i	0.717736	+	0.696315i	$0.245178\pi$
$720$		0			0
$721$	−21.6211	−	15.7086i	−0.805210	−	0.585019i
$722$	14.6621	−	20.1806i	0.545666	−	0.751045i
$723$		0			0
$724$	25.8661			0.961305
$725$	−0.124755	−	0.127471i	−0.00463329	−	0.00473416i
$726$		0			0
$727$	−12.4254	−	4.03726i	−0.460833	−	0.149734i	0.0693942	−	0.997589i	$-0.477893\pi$
$727$	−12.4254	−	4.03726i	−0.460833	−	0.149734i	−0.530227	+	0.847856i	$0.677893\pi$
$728$	−4.44312	+	6.11542i	−0.164673	+	0.226653i
$729$		0			0
$730$	10.9442	+	9.44957i	0.405062	+	0.349744i
$731$	−6.37213	+	4.62963i	−0.235682	+	0.171233i
$732$		0			0
$733$	−5.69030	−	7.83202i	−0.210176	−	0.289282i	0.690894	−	0.722956i	$-0.257217\pi$
$733$	−5.69030	−	7.83202i	−0.210176	−	0.289282i	−0.901070	+	0.433674i	$0.857217\pi$
$734$	−0.503121	−	1.54845i	−0.0185705	−	0.0571542i
$735$		0			0
$736$	0.604419	−	1.86021i	0.0222792	−	0.0685683i
$737$	0.408172	−	0.132623i	0.0150352	−	0.00488524i
$738$		0			0
$739$	−2.82260	+	8.68707i	−0.103831	+	0.319559i	−0.989454	−	0.144845i	$-0.953732\pi$
$739$	−2.82260	+	8.68707i	−0.103831	+	0.319559i	0.885623	+	0.464404i	$0.153732\pi$
$740$	6.73820	+	2.83365i	0.247701	+	0.104167i
$741$		0			0
$742$	−7.40359	−	10.1902i	−0.271794	−	0.374093i
$743$		−	6.35760i		−	0.233238i	−0.993177	−	0.116619i	$-0.962794\pi$
$743$		−	6.35760i		−	0.233238i	0.993177	−	0.116619i	$-0.0372056\pi$
$744$		0			0
$745$	−19.2655	−	1.62063i	−0.705832	−	0.0593754i
$746$	−6.66994	−	4.84600i	−0.244204	−	0.177425i
$747$		0			0
$748$	5.76122	+	1.87193i	0.210651	+	0.0684446i
$749$	−31.5825			−1.15400
$750$		0			0
$751$	35.0142			1.27768			0.638842	−	0.769338i	$-0.279414\pi$
$751$	35.0142			1.27768			0.638842	+	0.769338i	$0.279414\pi$
$752$	19.0898	+	6.20266i	0.696134	+	0.226188i
$753$		0			0
$754$	−0.0228384	−	0.0165931i	−0.000831725	−	0.000604284i
$755$	2.78298	+	0.234108i	0.101283	+	0.00852006i
$756$		0			0
$757$			11.5175i			0.418609i	0.977850	+	0.209305i	$0.0671200\pi$
$757$			11.5175i			0.418609i	−0.977850	+	0.209305i	$0.932880\pi$
$758$	3.26718	+	4.49689i	0.118669	+	0.163334i
$759$		0			0
$760$	−33.2235	−	13.9716i	−1.20514	−	0.506804i
$761$	−12.6925	+	39.0635i	−0.460102	+	1.41605i	0.404936	+	0.914345i	$0.367294\pi$
$761$	−12.6925	+	39.0635i	−0.460102	+	1.41605i	−0.865039	+	0.501705i	$0.832706\pi$
$762$		0			0
$763$	10.3494	−	3.36273i	0.374674	−	0.121739i
$764$	−6.47795	+	19.9371i	−0.234364	+	0.721298i
$765$		0			0
$766$	2.56771	+	7.90259i	0.0927750	+	0.285532i
$767$	−0.152746	−	0.210236i	−0.00551533	−	0.00759120i
$768$		0			0
$769$	14.5193	−	10.5489i	0.523578	−	0.380402i	−0.294372	−	0.955691i	$-0.595111\pi$
$769$	14.5193	−	10.5489i	0.523578	−	0.380402i	0.817950	+	0.575289i	$0.195111\pi$
$770$	12.0192	+	10.3778i	0.433141	+	0.373989i
$771$		0			0
$772$	14.3327	−	19.7272i	0.515844	−	0.709998i
$773$	49.4776	+	16.0762i	1.77958	+	0.578222i	0.998908	−	0.0467133i	$-0.0148747\pi$
$773$	49.4776	+	16.0762i	1.77958	+	0.578222i	0.780676	+	0.624935i	$0.214875\pi$
$774$		0			0
$775$	20.1073	−	9.97394i	0.722275	−	0.358275i
$776$	−15.1778			−0.544850
$777$		0			0
$778$	−6.74741	+	9.28701i	−0.241906	+	0.332955i
$779$	−33.8435	−	24.5888i	−1.21257	−	0.880984i
$780$		0			0
$781$	50.5928	−	36.7578i	1.81035	−	1.31530i
$782$			0.137570i			0.00491951i
$783$		0			0
$784$	0.275695	+	0.848502i	0.00984626	+	0.0303037i
$785$	−0.724589	+	8.61364i	−0.0258617	+	0.307434i
$786$		0			0
$787$	11.9113	−	3.87021i	0.424592	−	0.137958i	−0.0889240	−	0.996038i	$-0.528343\pi$
$787$	11.9113	−	3.87021i	0.424592	−	0.137958i	0.513516	+	0.858080i	$0.328343\pi$
$788$	28.9008	−	9.39044i	1.02955	−	0.334521i
$789$		0			0
$790$	−3.07997	−	5.08733i	−0.109580	−	0.180999i
$791$	14.6060	+	44.9525i	0.519328	+	1.59833i
$792$		0			0
$793$			9.45650i			0.335810i
$794$	5.42665	−	3.94269i	0.192585	−	0.139921i
$795$		0			0
$796$	−26.2552	−	19.0755i	−0.930591	−	0.676114i
$797$	−14.7779	+	20.3400i	−0.523460	+	0.720481i	−0.986116	−	0.166057i	$-0.946896\pi$
$797$	−14.7779	+	20.3400i	−0.523460	+	0.720481i	0.462656	+	0.886538i	$0.346896\pi$
$798$		0			0
$799$	−5.86134			−0.207359
$800$	−4.38310	+	25.8679i	−0.154966	+	0.914570i
$801$		0			0
$802$	16.8638	+	5.47939i	0.595483	+	0.193484i
$803$	−36.4372	+	50.1516i	−1.28584	+	1.76981i
$804$		0			0
$805$	0.831409	−	1.97703i	0.0293033	−	0.0696810i
$806$	2.87400	−	2.08808i	0.101232	−	0.0735495i
$807$		0			0
$808$	9.68781	+	13.3341i	0.340816	+	0.469093i
$809$	−1.49157	−	4.59059i	−0.0524409	−	0.161396i	0.921406	−	0.388601i	$-0.127041\pi$
$809$	−1.49157	−	4.59059i	−0.0524409	−	0.161396i	−0.973847	+	0.227204i	$0.927041\pi$
$810$		0			0
$811$	−11.3898	+	35.0543i	−0.399952	+	1.23092i	0.525086	+	0.851049i	$0.324033\pi$
$811$	−11.3898	+	35.0543i	−0.399952	+	1.23092i	−0.925038	+	0.379875i	$0.875967\pi$
$812$	0.149465	−	0.0485643i	0.00524521	−	0.00170427i
$813$		0			0
$814$	1.62836	−	5.01158i	0.0570740	−	0.175656i
$815$	−15.1831	+	3.55879i	−0.531840	+	0.124659i
$816$		0			0
$817$	54.4675	+	74.9680i	1.90558	+	2.62280i
$818$		−	1.61897i		−	0.0566061i
$819$		0			0
$820$	−7.67163	+	18.2425i	−0.267905	+	0.637057i
$821$	11.4772	+	8.33868i	0.400557	+	0.291022i	0.769768	−	0.638324i	$-0.220372\pi$
$821$	11.4772	+	8.33868i	0.400557	+	0.291022i	−0.369211	+	0.929346i	$0.620372\pi$
$822$		0			0
$823$	−24.7212	−	8.03241i	−0.861728	−	0.279992i	−0.155378	−	0.987855i	$-0.549660\pi$
$823$	−24.7212	−	8.03241i	−0.861728	−	0.279992i	−0.706350	+	0.707863i	$0.749660\pi$
$824$	−20.6861			−0.720634
$825$		0			0
$826$	−0.243253			−0.00846386
$827$	−40.8326	−	13.2673i	−1.41989	−	0.461350i	−0.504322	−	0.863516i	$-0.668257\pi$
$827$	−40.8326	−	13.2673i	−1.41989	−	0.461350i	−0.915567	+	0.402166i	$0.868257\pi$
$828$		0			0
$829$	−4.56100	−	3.31376i	−0.158410	−	0.115092i	0.505756	−	0.862676i	$-0.331213\pi$
$829$	−4.56100	−	3.31376i	−0.158410	−	0.115092i	−0.664167	+	0.747585i	$0.731213\pi$
$830$	−2.56358	−	10.9372i	−0.0889832	−	0.379634i
$831$		0			0
$832$		−	2.79605i		−	0.0969355i
$833$	−0.153132	−	0.210769i	−0.00530572	−	0.00730270i
$834$		0			0
$835$	−18.4819	−	30.5275i	−0.639594	−	1.05645i
$836$	22.0233	−	67.7806i	0.761690	−	2.34424i
$837$		0			0
$838$	−3.63003	+	1.17947i	−0.125397	+	0.0407441i
$839$	−7.12687	+	21.9343i	−0.246047	+	0.757255i	0.749416	+	0.662100i	$0.230335\pi$
$839$	−7.12687	+	21.9343i	−0.246047	+	0.757255i	−0.995463	+	0.0951546i	$0.969665\pi$
$840$		0			0
$841$	−8.96110	−	27.5794i	−0.309003	−	0.951015i
$842$	6.89311	+	9.48755i	0.237552	+	0.326963i
$843$		0			0
$844$	14.9273	−	10.8453i	0.513820	−	0.373312i
$845$	20.7056	−	12.5355i	0.712293	−	0.431236i
$846$		0			0
$847$	−23.3792	+	32.1787i	−0.803317	+	1.10567i
$848$	20.4386	+	6.64089i	0.701863	+	0.228049i
$849$		0			0
$850$	−0.269034	−	1.82563i	−0.00922779	−	0.0626185i
$851$	−0.711711			−0.0243971
$852$		0			0
$853$	−22.9504	+	31.5886i	−0.785808	+	1.08157i	0.208809	+	0.977956i	$0.433041\pi$
$853$	−22.9504	+	31.5886i	−0.785808	+	1.08157i	−0.994617	+	0.103616i	$0.966959\pi$
$854$	7.16138	+	5.20305i	0.245057	+	0.178045i
$855$		0			0
$856$	−19.7772	+	14.3690i	−0.675970	+	0.491121i
$857$		−	12.7315i		−	0.434899i	−0.976072	−	0.217450i	$-0.930226\pi$
$857$		−	12.7315i		−	0.434899i	0.976072	−	0.217450i	$-0.0697738\pi$
$858$		0			0
$859$	−4.50752	−	13.8727i	−0.153795	−	0.473331i	0.844242	−	0.535962i	$-0.180051\pi$
$859$	−4.50752	−	13.8727i	−0.153795	−	0.473331i	−0.998037	+	0.0626308i	$0.980051\pi$
$860$	28.6493	−	33.1806i	0.976931	−	1.13145i
$861$		0			0
$862$	2.03805	−	0.662201i	0.0694161	−	0.0225547i
$863$	16.6573	−	5.41229i	0.567021	−	0.184236i	−0.0114567	−	0.999934i	$-0.503647\pi$
$863$	16.6573	−	5.41229i	0.567021	−	0.184236i	0.578478	+	0.815698i	$0.303647\pi$
$864$		0			0
$865$	−15.8164	−	6.65134i	−0.537773	−	0.226152i
$866$	4.17677	+	12.8548i	0.141933	+	0.436824i
$867$		0			0
$868$			19.7768i			0.671267i
$869$	20.6272	−	14.9865i	0.699729	−	0.508383i
$870$		0			0
$871$	0.0995611	+	0.0723353i	0.00337350	+	0.00245099i
$872$	4.95094	−	6.81438i	0.167660	−	0.230764i
$873$		0			0
$874$	1.61851			0.0547470
$875$	−7.16691	+	27.8620i	−0.242286	+	0.941908i
$876$		0			0
$877$	8.66169	+	2.81435i	0.292485	+	0.0950340i	0.451584	−	0.892229i	$-0.350859\pi$
$877$	8.66169	+	2.81435i	0.292485	+	0.0950340i	−0.159100	+	0.987263i	$0.550859\pi$
$878$	0.540900	−	0.744485i	0.0182545	−	0.0251252i
$879$		0			0
$880$	−26.9977	−	2.27108i	−0.910092	−	0.0765579i
$881$	−36.5744	+	26.5728i	−1.23222	+	0.895261i	−0.997055	−	0.0766939i	$-0.975564\pi$
$881$	−36.5744	+	26.5728i	−1.23222	+	0.895261i	−0.235167	+	0.971955i	$0.575564\pi$
$882$		0			0
$883$	−2.49354	−	3.43206i	−0.0839142	−	0.115498i	0.764996	−	0.644035i	$-0.222741\pi$
$883$	−2.49354	−	3.43206i	−0.0839142	−	0.115498i	−0.848910	+	0.528537i	$0.822741\pi$
$884$	0.536766	+	1.65200i	0.0180534	+	0.0555626i
$885$		0			0
$886$	1.94776	−	5.99458i	0.0654362	−	0.201392i
$887$	−12.1607	+	3.95124i	−0.408316	+	0.132670i	−0.505971	−	0.862551i	$-0.668866\pi$
$887$	−12.1607	+	3.95124i	−0.408316	+	0.132670i	0.0976554	+	0.995220i	$0.468866\pi$
$888$		0			0
$889$	−0.274727	+	0.845523i	−0.00921405	+	0.0283579i
$890$	0.00965906	−	0.0111868i	0.000323772	−	0.000374982i
$891$		0			0
$892$	−27.7460	−	38.1891i	−0.929005	−	1.27867i
$893$			68.9586i			2.30761i
$894$		0			0
$895$	17.9560	+	15.5038i	0.600203	+	0.518236i
$896$	−23.9647	−	17.4113i	−0.800603	−	0.581672i
$897$		0			0
$898$	6.55287	+	2.12916i	0.218672	+	0.0710508i
$899$	−0.160134			−0.00534076
$900$		0			0
$901$	−6.27546			−0.209066
$902$	13.5680	+	4.40851i	0.451765	+	0.146787i
$903$		0			0
$904$	29.5981	+	21.5043i	0.984419	+	0.715223i
$905$	28.8983	−	17.4956i	0.960611	−	0.581573i
$906$		0			0
$907$			9.51928i			0.316082i	0.987433	+	0.158041i	$0.0505179\pi$
$907$			9.51928i			0.316082i	−0.987433	+	0.158041i	$0.949482\pi$
$908$	4.00753	+	5.51589i	0.132994	+	0.183051i
$909$		0			0
$910$	−0.381686	+	4.53734i	−0.0126528	+	0.150411i
$911$	12.8107	−	39.4274i	0.424438	−	1.30629i	−0.479093	−	0.877764i	$-0.659034\pi$
$911$	12.8107	−	39.4274i	0.424438	−	1.30629i	0.903531	−	0.428522i	$-0.140966\pi$
$912$		0			0
$913$	45.8043	−	14.8827i	1.51590	−	0.492546i
$914$	−2.26954	+	6.98492i	−0.0750697	+	0.231041i
$915$		0			0
$916$	−6.33287	−	19.4906i	−0.209244	−	0.643987i
$917$	6.90674	+	9.50631i	0.228081	+	0.313926i
$918$		0			0
$919$	12.8372	−	9.32675i	0.423459	−	0.307661i	−0.355569	−	0.934650i	$-0.615713\pi$
$919$	12.8372	−	9.32675i	0.423459	−	0.307661i	0.779028	+	0.626989i	$0.215713\pi$
$920$	−0.378845	−	1.61629i	−0.0124901	−	0.0532874i
$921$		0			0
$922$	−3.06336	+	4.21635i	−0.100886	+	0.138858i
$923$	17.0542	+	5.54125i	0.561346	+	0.182393i
$924$		0			0
$925$	9.44476	−	1.39183i	0.310542	−	0.0457631i
$926$	−11.4145			−0.375104
$927$		0			0
$928$	0.110024	−	0.151435i	0.00361172	−	0.00497110i
$929$	23.7938	+	17.2872i	0.780650	+	0.567175i	0.905174	−	0.425041i	$-0.139740\pi$
$929$	23.7938	+	17.2872i	0.780650	+	0.567175i	−0.124524	+	0.992217i	$0.539740\pi$
$930$		0			0
$931$	−2.47969	+	1.80160i	−0.0812685	+	0.0590451i
$932$		−	36.1567i		−	1.18435i
$933$		0			0
$934$	2.30489	+	7.09372i	0.0754182	+	0.232114i
$935$	7.70275	−	1.80546i	0.251907	−	0.0590449i
$936$		0			0
$937$	−55.2688	+	17.9579i	−1.80555	+	0.586660i	−0.999983	−	0.00583887i	$-0.998141\pi$
$937$	−55.2688	+	17.9579i	−1.80555	+	0.586660i	−0.805571	+	0.592499i	$0.798141\pi$
$938$	0.109559	−	0.0355978i	0.00357722	−	0.00116231i
$939$		0			0
$940$	31.7616	−	7.44466i	1.03595	−	0.242818i
$941$	−10.5779	−	32.5553i	−0.344828	−	1.06127i	−0.961676	−	0.274189i	$-0.911591\pi$
$941$	−10.5779	−	32.5553i	−0.344828	−	1.06127i	0.616848	−	0.787083i	$-0.288409\pi$
$942$		0			0
$943$		−	1.92684i		−	0.0627464i
$944$	0.335766	−	0.243948i	0.0109282	−	0.00793984i
$945$		0			0
$946$	−25.5663	−	18.5750i	−0.831232	−	0.603925i
$947$	−22.3420	+	30.7511i	−0.726016	+	0.999275i	0.273286	+	0.961933i	$0.411889\pi$
$947$	−22.3420	+	30.7511i	−0.726016	+	0.999275i	−0.999303	+	0.0373427i	$0.988111\pi$
$948$		0			0
$949$	−17.7755			−0.577017
$950$	−21.4785	+	3.16518i	−0.696854	+	0.102692i
$951$		0			0
$952$	3.35278	+	1.08939i	0.108664	+	0.0353072i
$953$	9.94235	−	13.6845i	0.322064	−	0.443284i	−0.617032	−	0.786938i	$-0.711665\pi$
$953$	9.94235	−	13.6845i	0.322064	−	0.443284i	0.939096	+	0.343655i	$0.111665\pi$
$954$		0			0
$955$	6.24792	+	26.6559i	0.202178	+	0.862564i
$956$	−36.2973	+	26.3716i	−1.17394	+	0.852917i
$957$		0			0
$958$	3.90047	+	5.36853i	0.126018	+	0.173449i
$959$	−3.83069	−	11.7897i	−0.123699	−	0.380708i
$960$		0			0
$961$	−3.35243	+	10.3177i	−0.108143	+	0.332829i
$962$	1.43704	−	0.466923i	0.0463321	−	0.0150542i
$963$		0			0
$964$	−4.32492	+	13.3107i	−0.139296	+	0.428710i
$965$	2.66952	−	31.7343i	0.0859349	−	1.02156i
$966$		0			0
$967$	13.3924	+	18.4330i	0.430670	+	0.592767i	0.968107	−	0.250537i	$-0.0806073\pi$
$967$	13.3924	+	18.4330i	0.430670	+	0.592767i	−0.537437	+	0.843304i	$0.680607\pi$
$968$			30.7872i			0.989537i
$969$		0			0
$970$	−7.82098	+	4.73497i	−0.251116	+	0.152031i
$971$	35.5849	+	25.8539i	1.14197	+	0.829692i	0.987393	−	0.158288i	$-0.0505976\pi$
$971$	35.5849	+	25.8539i	1.14197	+	0.829692i	0.154580	+	0.987980i	$0.450598\pi$
$972$		0			0
$973$	−9.15450	−	2.97448i	−0.293480	−	0.0953574i
$974$	18.9552			0.607362
$975$		0			0
$976$	−15.1029			−0.483431
$977$	17.7211	+	5.75794i	0.566948	+	0.184213i	0.578445	−	0.815721i	$-0.303660\pi$
$977$	17.7211	+	5.75794i	0.566948	+	0.184213i	−0.0114968	+	0.999934i	$0.503660\pi$
$978$		0			0
$979$	0.0512634	+	0.0372450i	0.00163838	+	0.00119036i
$980$	1.09750	+	0.947621i	0.0350584	+	0.0302706i
$981$		0			0
$982$			11.6397i			0.371438i
$983$	−32.0387	−	44.0975i	−1.02188	−	1.40649i	−0.910880	−	0.412672i	$-0.864595\pi$
$983$	−32.0387	−	44.0975i	−1.02188	−	1.40649i	−0.110998	−	0.993821i	$-0.535405\pi$
$984$		0			0
$985$	25.9371	−	30.0395i	0.826426	−	0.957138i
$986$	−0.00406837	+	0.0125212i	−0.000129563	+	0.000398755i
$987$		0			0
$988$	19.4357	−	6.31504i	0.618332	−	0.200908i
$989$	−1.31895	+	4.05930i	−0.0419401	+	0.129078i
$990$		0			0
$991$	11.1881	+	34.4335i	0.355403	+	1.09382i	0.955776	+	0.294097i	$0.0950188\pi$
$991$	11.1881	+	34.4335i	0.355403	+	1.09382i	−0.600373	+	0.799720i	$0.704981\pi$
$992$	13.8455	+	19.0567i	0.439595	+	0.605051i
$993$		0			0
$994$	13.5797	−	9.86626i	0.430723	−	0.312939i
$995$	−42.2356	−	3.55290i	−1.33896	−	0.112635i
$996$		0			0
$997$	−4.22750	+	5.81865i	−0.133886	+	0.184279i	−0.870696	−	0.491821i	$-0.836331\pi$
$997$	−4.22750	+	5.81865i	−0.133886	+	0.184279i	0.736810	+	0.676100i	$0.236331\pi$
$998$	−19.7924	−	6.43096i	−0.626519	−	0.203568i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.b.154.3		16
3.2	odd	2		75.2.i.a.4.2	✓	16
15.2	even	4		375.2.g.e.226.3		16
15.8	even	4		375.2.g.d.226.2		16
15.14	odd	2		375.2.i.c.274.3		16
25.12	odd	20		5625.2.a.bd.1.3		8
25.13	odd	20		5625.2.a.t.1.6		8
25.19	even	10	inner	225.2.m.b.19.3		16
75.8	even	20		375.2.g.d.151.2		16
75.17	even	20		375.2.g.e.151.3		16
75.38	even	20		1875.2.a.p.1.3		8
75.41	odd	10		1875.2.b.h.1249.7		16
75.44	odd	10		75.2.i.a.19.2	yes	16
75.56	odd	10		375.2.i.c.349.3		16
75.59	odd	10		1875.2.b.h.1249.10		16
75.62	even	20		1875.2.a.m.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.2	✓	16	3.2	odd	2
75.2.i.a.19.2	yes	16	75.44	odd	10
225.2.m.b.19.3		16	25.19	even	10	inner
225.2.m.b.154.3		16	1.1	even	1	trivial
375.2.g.d.151.2		16	75.8	even	20
375.2.g.d.226.2		16	15.8	even	4
375.2.g.e.151.3		16	75.17	even	20
375.2.g.e.226.3		16	15.2	even	4
375.2.i.c.274.3		16	15.14	odd	2
375.2.i.c.349.3		16	75.56	odd	10
1875.2.a.m.1.6		8	75.62	even	20
1875.2.a.p.1.3		8	75.38	even	20
1875.2.b.h.1249.7		16	75.41	odd	10
1875.2.b.h.1249.10		16	75.59	odd	10
5625.2.a.t.1.6		8	25.13	odd	20
5625.2.a.bd.1.3		8	25.12	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.510286 + 0.165802i) q^{2} +(-1.38513 - 1.00636i) q^{4} +(-2.22820 - 0.187439i) q^{5} -2.57318i q^{7} +(-1.17071 - 1.61134i) q^{8} +O(q^{10})\)	\(q+(0.510286 + 0.165802i) q^{2} +(-1.38513 - 1.00636i) q^{4} +(-2.22820 - 0.187439i) q^{5} -2.57318i q^{7} +(-1.17071 - 1.61134i) q^{8} +(-1.10594 - 0.465087i) q^{10} +(1.58949 - 4.89194i) q^{11} +(1.40274 - 0.455776i) q^{13} +(0.426639 - 1.31306i) q^{14} +(0.727915 + 2.24029i) q^{16} +(-0.404314 - 0.556490i) q^{17} +(-6.54709 + 4.75674i) q^{19} +(2.89772 + 2.50199i) q^{20} +(1.62219 - 2.23275i) q^{22} +(-0.354506 - 0.115186i) q^{23} +(4.92973 + 0.835300i) q^{25} +0.791365 q^{26} +(-2.58954 + 3.56419i) q^{28} +(-0.0288595 - 0.0209676i) q^{29} +(3.63169 - 2.63858i) q^{31} +5.24733i q^{32} +(-0.114049 - 0.351005i) q^{34} +(-0.482313 + 5.73355i) q^{35} +(1.81590 - 0.590022i) q^{37} +(-4.12957 + 1.34178i) q^{38} +(2.30654 + 3.80982i) q^{40} +(1.59739 + 4.91625i) q^{41} -11.4506i q^{43} +(-7.12469 + 5.17639i) q^{44} +(-0.161802 - 0.117556i) q^{46} +(5.00860 - 6.89374i) q^{47} +0.378747 q^{49} +(2.37708 + 1.24360i) q^{50} +(-2.40165 - 0.780343i) q^{52} +(5.36247 - 7.38080i) q^{53} +(-4.45863 + 10.6023i) q^{55} +(-4.14627 + 3.01244i) q^{56} +(-0.0112501 - 0.0154845i) q^{58} +(-0.0544457 - 0.167567i) q^{59} +(-1.98127 + 6.09772i) q^{61} +(2.29069 - 0.744289i) q^{62} +(0.585811 - 1.80294i) q^{64} +(-3.21100 + 0.752633i) q^{65} +(0.0490435 + 0.0675025i) q^{67} +1.17770i q^{68} +(-1.19675 + 2.84579i) q^{70} +(9.83589 + 7.14619i) q^{71} +(-11.4619 - 3.72421i) q^{73} +1.02446 q^{74} +13.8556 q^{76} +(-12.5878 - 4.09004i) q^{77} +(4.01019 + 2.91357i) q^{79} +(-1.20202 - 5.12825i) q^{80} +2.77354i q^{82} +(5.50356 + 7.57501i) q^{83} +(0.796583 + 1.31575i) q^{85} +(1.89853 - 5.84308i) q^{86} +(-9.74340 + 3.16582i) q^{88} +(-0.00380677 + 0.0117160i) q^{89} +(-1.17279 - 3.60949i) q^{91} +(0.375120 + 0.516308i) q^{92} +(3.69882 - 2.68735i) q^{94} +(15.4798 - 9.37179i) q^{95} +(4.47917 - 6.16504i) q^{97} +(0.193269 + 0.0627970i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 + 30 * q^8	\( 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

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