LMFDB - Embedded newform 441.2.bb.e.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.e.298.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86275 - 1.27000i) q^{2} +(1.12626 - 2.86965i) q^{4} +(-3.53817 - 1.09138i) q^{5} +(2.24157 - 1.40547i) q^{7} +(-0.543186 - 2.37985i) q^{8} +O(q^{10})$	\(q+(1.86275 - 1.27000i) q^{2} +(1.12626 - 2.86965i) q^{4} +(-3.53817 - 1.09138i) q^{5} +(2.24157 - 1.40547i) q^{7} +(-0.543186 - 2.37985i) q^{8} +(-7.97679 + 2.46051i) q^{10} +(-0.358238 - 4.78035i) q^{11} +(-1.86453 - 0.897913i) q^{13} +(2.39055 - 5.46485i) q^{14} +(0.485391 + 0.450377i) q^{16} +(-0.0216392 - 0.00326158i) q^{17} +(0.163914 - 0.283908i) q^{19} +(-7.11677 + 8.92414i) q^{20} +(-6.73837 - 8.44965i) q^{22} +(6.27046 - 0.945120i) q^{23} +(7.19635 + 4.90639i) q^{25} +(-4.61352 + 0.695376i) q^{26} +(-1.50862 - 8.01545i) q^{28} +(-5.06165 + 6.34711i) q^{29} +(2.24972 + 3.89662i) q^{31} +(6.30373 + 0.950134i) q^{32} +(-0.0444507 + 0.0214063i) q^{34} +(-9.46498 + 2.52638i) q^{35} +(0.777219 + 1.98032i) q^{37} +(-0.0552322 - 0.737022i) q^{38} +(-0.675442 + 9.01315i) q^{40} +(0.897157 + 3.93070i) q^{41} +(0.516511 - 2.26298i) q^{43} +(-14.1214 - 4.35588i) q^{44} +(10.4800 - 9.72403i) q^{46} +(9.98096 - 6.80491i) q^{47} +(3.04931 - 6.30093i) q^{49} +19.6361 q^{50} +(-4.67664 + 4.33929i) q^{52} +(-2.81349 + 7.16866i) q^{53} +(-3.94968 + 17.3047i) q^{55} +(-4.56240 - 4.57119i) q^{56} +(-1.36775 + 18.2514i) q^{58} +(6.22339 - 1.91966i) q^{59} +(1.42752 + 3.63726i) q^{61} +(9.13939 + 4.40130i) q^{62} +(11.7558 - 5.66129i) q^{64} +(5.61708 + 5.21189i) q^{65} +(-6.97774 - 12.0858i) q^{67} +(-0.0337309 + 0.0584236i) q^{68} +(-14.4224 + 16.7266i) q^{70} +(1.61301 + 2.02266i) q^{71} +(3.30820 + 2.25549i) q^{73} +(3.96278 + 2.70178i) q^{74} +(-0.630108 - 0.790130i) q^{76} +(-7.52166 - 10.2120i) q^{77} +(4.50685 - 7.80609i) q^{79} +(-1.22586 - 2.12326i) q^{80} +(6.66318 + 6.18253i) q^{82} +(-15.0519 + 7.24860i) q^{83} +(0.0730035 + 0.0351566i) q^{85} +(-1.91186 - 4.87135i) q^{86} +(-11.1820 + 3.44918i) q^{88} +(0.0773820 - 1.03259i) q^{89} +(-5.44148 + 0.607809i) q^{91} +(4.34998 - 19.0585i) q^{92} +(9.94981 - 25.3517i) q^{94} +(-0.889809 + 0.825622i) q^{95} -12.4078 q^{97} +(-2.32208 - 15.6097i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

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 $

$2$	1.86275	−	1.27000i	1.31716	−	0.898027i	0.318411	−	0.947953i	$-0.396851\pi$
$2$	1.86275	−	1.27000i	1.31716	−	0.898027i	0.998753	+	0.0499252i	$0.0158983\pi$
$3$		0			0
$3$		0			0
$4$	1.12626	−	2.86965i	0.563128	−	1.43483i
$5$	−3.53817	−	1.09138i	−1.58232	−	0.488081i	−0.625856	−	0.779938i	$-0.715250\pi$
$5$	−3.53817	−	1.09138i	−1.58232	−	0.488081i	−0.956462	+	0.291858i	$0.905727\pi$
$6$		0			0
$7$	2.24157	−	1.40547i	0.847235	−	0.531217i
$7$	2.24157	−	1.40547i	0.847235	−	0.531217i
$8$	−0.543186	−	2.37985i	−0.192045	−	0.841405i
$9$		0			0
$10$	−7.97679	+	2.46051i	−2.52248	+	0.778083i
$11$	−0.358238	−	4.78035i	−0.108013	−	1.44133i	−0.743250	−	0.669014i	$-0.766717\pi$
$11$	−0.358238	−	4.78035i	−0.108013	−	1.44133i	0.635237	−	0.772317i	$-0.280902\pi$
$12$		0			0
$13$	−1.86453	−	0.897913i	−0.517129	−	0.249036i	0.157068	−	0.987588i	$-0.449796\pi$
$13$	−1.86453	−	0.897913i	−0.517129	−	0.249036i	−0.674197	+	0.738552i	$0.735510\pi$
$14$	2.39055	−	5.46485i	0.638901	−	1.46054i
$15$		0			0
$16$	0.485391	+	0.450377i	0.121348	+	0.112594i
$17$	−0.0216392	−	0.00326158i	−0.00524828	−	0.000791050i	0.146418	−	0.989223i	$-0.453226\pi$
$17$	−0.0216392	−	0.00326158i	−0.00524828	−	0.000791050i	−0.151666	+	0.988432i	$0.548464\pi$
$18$		0			0
$19$	0.163914	−	0.283908i	0.0376045	−	0.0651330i	−0.846611	−	0.532213i	$-0.821361\pi$
$19$	0.163914	−	0.283908i	0.0376045	−	0.0651330i	0.884215	+	0.467080i	$0.154694\pi$
$20$	−7.11677	+	8.92414i	−1.59136	+	1.99550i
$21$		0			0
$22$	−6.73837	−	8.44965i	−1.43663	−	1.80147i
$23$	6.27046	−	0.945120i	1.30748	−	0.197071i	0.541918	−	0.840431i	$-0.317698\pi$
$23$	6.27046	−	0.945120i	1.30748	−	0.197071i	0.765564	+	0.643360i	$0.222460\pi$
$24$		0			0
$25$	7.19635	+	4.90639i	1.43927	+	0.981277i
$26$	−4.61352	+	0.695376i	−0.904785	+	0.136374i
$27$		0			0
$28$	−1.50862	−	8.01545i	−0.285103	−	1.51478i
$29$	−5.06165	+	6.34711i	−0.939925	+	1.17863i	0.0438164	+	0.999040i	$0.486048\pi$
$29$	−5.06165	+	6.34711i	−0.939925	+	1.17863i	−0.983742	+	0.179589i	$0.942523\pi$
$30$		0			0
$31$	2.24972	+	3.89662i	0.404061	+	0.699854i	0.994212	−	0.107439i	$-0.0342650\pi$
$31$	2.24972	+	3.89662i	0.404061	+	0.699854i	−0.590151	+	0.807293i	$0.700932\pi$
$32$	6.30373	+	0.950134i	1.11435	+	0.167962i
$33$		0			0
$34$	−0.0444507	+	0.0214063i	−0.00762323	+	0.00367115i
$35$	−9.46498	+	2.52638i	−1.59987	+	0.427036i
$36$		0			0
$37$	0.777219	+	1.98032i	0.127774	+	0.325563i	0.980418	−	0.196930i	$-0.0630972\pi$
$37$	0.777219	+	1.98032i	0.127774	+	0.325563i	−0.852643	+	0.522493i	$0.825002\pi$
$38$	−0.0552322	−	0.737022i	−0.00895984	−	0.119561i
$39$		0			0
$40$	−0.675442	+	9.01315i	−0.106797	+	1.42510i
$41$	0.897157	+	3.93070i	0.140112	+	0.613872i	0.995407	+	0.0957309i	$0.0305188\pi$
$41$	0.897157	+	3.93070i	0.140112	+	0.613872i	−0.855295	+	0.518142i	$0.826624\pi$
$42$		0			0
$43$	0.516511	−	2.26298i	0.0787672	−	0.345102i	−0.920153	−	0.391559i	$-0.871936\pi$
$43$	0.516511	−	2.26298i	0.0787672	−	0.345102i	0.998920	+	0.0464571i	$0.0147931\pi$
$44$	−14.1214	−	4.35588i	−2.12888	−	0.656674i
$45$		0			0
$46$	10.4800	−	9.72403i	1.54519	−	1.43373i
$47$	9.98096	−	6.80491i	1.45587	−	0.992597i	0.461446	−	0.887168i	$-0.347331\pi$
$47$	9.98096	−	6.80491i	1.45587	−	0.992597i	0.994427	−	0.105429i	$-0.0336217\pi$
$48$		0			0
$49$	3.04931	−	6.30093i	0.435616	−	0.900133i
$50$	19.6361			2.77697
$51$		0			0
$52$	−4.67664	+	4.33929i	−0.648533	+	0.601751i
$53$	−2.81349	+	7.16866i	−0.386463	+	0.984692i	0.596782	+	0.802403i	$0.296446\pi$
$53$	−2.81349	+	7.16866i	−0.386463	+	0.984692i	−0.983245	+	0.182288i	$0.941650\pi$
$54$		0			0
$55$	−3.94968	+	17.3047i	−0.532575	+	2.33336i
$56$	−4.56240	−	4.57119i	−0.609677	−	0.610851i
$57$		0			0
$58$	−1.36775	+	18.2514i	−0.179595	+	2.39653i
$59$	6.22339	−	1.91966i	0.810216	−	0.249919i	0.138152	−	0.990411i	$-0.455884\pi$
$59$	6.22339	−	1.91966i	0.810216	−	0.249919i	0.672065	+	0.740492i	$0.265408\pi$
$60$		0			0
$61$	1.42752	+	3.63726i	0.182775	+	0.465703i	0.992668	−	0.120875i	$-0.0385699\pi$
$61$	1.42752	+	3.63726i	0.182775	+	0.465703i	−0.809893	+	0.586578i	$0.800475\pi$
$62$	9.13939	+	4.40130i	1.16070	+	0.558965i
$63$		0			0
$64$	11.7558	−	5.66129i	1.46947	−	0.707661i
$65$	5.61708	+	5.21189i	0.696713	+	0.646455i
$66$		0			0
$67$	−6.97774	−	12.0858i	−0.852467	−	1.47652i	−0.878975	−	0.476868i	$-0.841772\pi$
$67$	−6.97774	−	12.0858i	−0.852467	−	1.47652i	0.0265079	−	0.999649i	$-0.491561\pi$
$68$	−0.0337309	+	0.0584236i	−0.00409047	+	0.00708490i
$69$		0			0
$70$	−14.4224	+	16.7266i	−1.72381	+	1.99921i
$71$	1.61301	+	2.02266i	0.191430	+	0.240045i	0.868279	−	0.496077i	$-0.165227\pi$
$71$	1.61301	+	2.02266i	0.191430	+	0.240045i	−0.676849	+	0.736122i	$0.736655\pi$
$72$		0			0
$73$	3.30820	+	2.25549i	0.387195	+	0.263985i	0.741236	−	0.671245i	$-0.234240\pi$
$73$	3.30820	+	2.25549i	0.387195	+	0.263985i	−0.354040	+	0.935230i	$0.615192\pi$
$74$	3.96278	+	2.70178i	0.460664	+	0.314075i
$75$		0			0
$76$	−0.630108	−	0.790130i	−0.0722783	−	0.0906341i
$77$	−7.52166	−	10.2120i	−0.857172	−	1.16377i
$78$		0			0
$79$	4.50685	−	7.80609i	0.507060	−	0.878253i	−0.492907	−	0.870082i	$-0.664066\pi$
$79$	4.50685	−	7.80609i	0.507060	−	0.878253i	0.999967	−	0.00817123i	$-0.00260101\pi$
$80$	−1.22586	−	2.12326i	−0.137056	−	0.237387i
$81$		0			0
$82$	6.66318	+	6.18253i	0.735825	+	0.682746i
$83$	−15.0519	+	7.24860i	−1.65216	+	0.795637i	−0.652887	+	0.757455i	$0.726442\pi$
$83$	−15.0519	+	7.24860i	−1.65216	+	0.795637i	−0.999271	+	0.0381817i	$0.987843\pi$
$84$		0			0
$85$	0.0730035	+	0.0351566i	0.00791834	+	0.00381327i
$86$	−1.91186	−	4.87135i	−0.206162	−	0.525291i
$87$		0			0
$88$	−11.1820	+	3.44918i	−1.19200	+	0.367683i
$89$	0.0773820	−	1.03259i	0.00820247	−	0.109454i	−0.991600	−	0.129345i	$-0.958713\pi$
$89$	0.0773820	−	1.03259i	0.00820247	−	0.109454i	0.999802	+	0.0198903i	$0.00633169\pi$
$90$		0			0
$91$	−5.44148	+	0.607809i	−0.570422	+	0.0637156i
$92$	4.34998	−	19.0585i	0.453516	−	1.98699i
$93$		0			0
$94$	9.94981	−	25.3517i	1.02624	−	2.61483i
$95$	−0.889809	+	0.825622i	−0.0912925	+	0.0847070i
$96$		0			0
$97$	−12.4078			−1.25983			−0.629913	−	0.776666i	$-0.716909\pi$
$97$	−12.4078			−1.25983			−0.629913	+	0.776666i	$0.716909\pi$
$98$	−2.32208	−	15.6097i	−0.234566	−	1.57682i
$99$		0			0
$100$	22.1845	−	15.1252i	2.21845	−	1.51252i
$101$	2.45468	−	2.27761i	0.244250	−	0.226631i	−0.548542	−	0.836123i	$-0.684817\pi$
$101$	2.45468	−	2.27761i	0.244250	−	0.226631i	0.792792	+	0.609492i	$0.208627\pi$
$102$		0			0
$103$	−8.34803	−	2.57503i	−0.822556	−	0.253725i	−0.145220	−	0.989399i	$-0.546389\pi$
$103$	−8.34803	−	2.57503i	−0.822556	−	0.253725i	−0.677335	+	0.735674i	$0.736865\pi$
$104$	−1.12411	+	4.92505i	−0.110228	+	0.482941i
$105$		0			0
$106$	3.86338	+	16.9266i	0.375245	+	1.64405i
$107$	−0.996892	+	13.3026i	−0.0963732	+	1.28601i	0.714020	+	0.700125i	$0.246872\pi$
$107$	−0.996892	+	13.3026i	−0.0963732	+	1.28601i	−0.810394	+	0.585886i	$0.800747\pi$
$108$		0			0
$109$	0.0551431	+	0.735833i	0.00528175	+	0.0704801i	0.999222	−	0.0394434i	$-0.0125585\pi$
$109$	0.0551431	+	0.735833i	0.00528175	+	0.0704801i	−0.993940	+	0.109923i	$0.964939\pi$
$110$	14.6197	+	37.2504i	1.39394	+	3.55169i
$111$		0			0
$112$	1.72103	+	0.327351i	0.162622	+	0.0309318i
$113$	−9.60122	+	4.62371i	−0.903207	+	0.434962i	−0.827046	−	0.562134i	$-0.809981\pi$
$113$	−9.60122	+	4.62371i	−0.903207	+	0.434962i	−0.0761609	+	0.997096i	$0.524266\pi$
$114$		0			0
$115$	−23.2175	−	3.49947i	−2.16504	−	0.326327i
$116$	12.5133	+	21.6736i	1.16183	+	2.01235i
$117$		0			0
$118$	9.15466	−	11.4796i	0.842754	−	1.05678i
$119$	−0.0530899	+	0.0231021i	−0.00486674	+	0.00211777i
$120$		0			0
$121$	−11.8463	+	1.78554i	−1.07694	+	0.162322i
$122$	7.27844	+	4.96236i	0.658959	+	0.449271i
$123$		0			0
$124$	13.7157	−	2.06731i	1.23171	−	0.185650i
$125$	−8.56428	−	10.7393i	−0.766013	−	0.960549i
$126$		0			0
$127$	2.35282	−	2.95035i	0.208779	−	0.261801i	−0.666406	−	0.745589i	$-0.732168\pi$
$127$	2.35282	−	2.95035i	0.208779	−	0.261801i	0.875185	+	0.483788i	$0.160740\pi$
$128$	8.33334	−	14.4338i	0.736570	−	1.27578i
$129$		0			0
$130$	17.0823	+	2.57475i	1.49822	+	0.225820i
$131$	8.41414	+	7.80718i	0.735147	+	0.682117i	0.956058	−	0.293177i	$-0.0947125\pi$
$131$	8.41414	+	7.80718i	0.735147	+	0.682117i	−0.220911	+	0.975294i	$0.570903\pi$
$132$		0			0
$133$	−0.0315978	−	0.866778i	−0.00273987	−	0.0751592i
$134$	−28.3468	−	13.6511i	−2.44879	−	1.17928i
$135$		0			0
$136$	0.00399202	+	0.0532698i	0.000342313	+	0.00456784i
$137$	−0.758721	+	0.234035i	−0.0648219	+	0.0199949i	−0.326997	−	0.945026i	$-0.606037\pi$
$137$	−0.758721	+	0.234035i	−0.0648219	+	0.0199949i	0.262175	+	0.965020i	$0.415560\pi$
$138$		0			0
$139$	1.70857	+	7.48574i	0.144919	+	0.634933i	0.994251	+	0.107073i	$0.0341480\pi$
$139$	1.70857	+	7.48574i	0.144919	+	0.634933i	−0.849332	+	0.527859i	$0.822995\pi$
$140$	−3.41015	+	30.0065i	−0.288210	+	2.53601i
$141$		0			0
$142$	5.57342	+	1.71917i	0.467711	+	0.144270i
$143$	−3.62439	+	9.23480i	−0.303087	+	0.772253i
$144$		0			0
$145$	24.8361	−	16.9330i	2.06253	−	1.40621i
$146$	9.02683			0.747066
$147$		0			0
$148$	6.55818			0.539079
$149$	7.48233	−	5.10137i	0.612977	−	0.417920i	−0.216642	−	0.976251i	$-0.569510\pi$
$149$	7.48233	−	5.10137i	0.612977	−	0.417920i	0.829618	+	0.558331i	$0.188558\pi$
$150$		0			0
$151$	−1.89852	+	4.83736i	−0.154500	+	0.393659i	−0.987076	−	0.160251i	$-0.948770\pi$
$151$	−1.89852	+	4.83736i	−0.154500	+	0.393659i	0.832577	+	0.553910i	$0.186865\pi$
$152$	−0.764696	−	0.235877i	−0.0620250	−	0.0191322i
$153$		0			0
$154$	−26.9803	−	9.46994i	−2.17413	−	0.763110i
$155$	−3.70718	−	16.2422i	−0.297768	−	1.30461i
$156$		0			0
$157$	8.05912	−	2.48591i	0.643188	−	0.198397i	0.0440328	−	0.999030i	$-0.485979\pi$
$157$	8.05912	−	2.48591i	0.643188	−	0.198397i	0.599155	+	0.800633i	$0.295503\pi$
$158$	−1.51861	−	20.2645i	−0.120815	−	1.61216i
$159$		0			0
$160$	−21.2667	−	10.2415i	−1.68128	−	0.809662i
$161$	12.7274	−	10.9315i	1.00306	−	0.861523i
$162$		0			0
$163$	9.60665	+	8.91367i	0.752451	+	0.698173i	0.959984	−	0.280055i	$-0.0903528\pi$
$163$	9.60665	+	8.91367i	0.752451	+	0.698173i	−0.207533	+	0.978228i	$0.566543\pi$
$164$	12.2902	+	1.85245i	0.959701	+	0.144652i
$165$		0			0
$166$	−18.8322	+	32.6183i	−1.46166	+	2.53167i
$167$	11.7524	−	14.7371i	0.909429	−	1.14039i	−0.0802053	−	0.996778i	$-0.525558\pi$
$167$	11.7524	−	14.7371i	0.909429	−	1.14039i	0.989634	−	0.143610i	$-0.0458710\pi$
$168$		0			0
$169$	−5.43512	−	6.81543i	−0.418086	−	0.524264i
$170$	0.180636	−	0.0272266i	0.0138542	−	0.00208818i
$171$		0			0
$172$	−5.91225	−	4.03090i	−0.450805	−	0.307354i
$173$	4.02442	−	0.606583i	0.305971	−	0.0461177i	0.00573772	−	0.999984i	$-0.498174\pi$
$173$	4.02442	−	0.606583i	0.305971	−	0.0461177i	0.300233	+	0.953866i	$0.402936\pi$
$174$		0			0
$175$	23.0269	+	0.883785i	1.74067	+	0.0668079i
$176$	1.97908	−	2.48168i	0.149178	−	0.187064i
$177$		0			0
$178$	−1.16725	−	2.02173i	−0.0874890	−	0.151535i
$179$	−12.1750	−	1.83509i	−0.910003	−	0.137161i	−0.322675	−	0.946510i	$-0.604582\pi$
$179$	−12.1750	−	1.83509i	−0.910003	−	0.137161i	−0.587328	+	0.809349i	$0.699820\pi$
$180$		0			0
$181$	−12.9947	+	6.25792i	−0.965888	+	0.465147i	−0.849229	−	0.528025i	$-0.822933\pi$
$181$	−12.9947	+	6.25792i	−0.965888	+	0.465147i	−0.116659	+	0.993172i	$0.537219\pi$
$182$	−9.36421	+	8.04289i	−0.694122	+	0.596179i
$183$		0			0
$184$	−5.65528	−	14.4094i	−0.416913	−	1.06228i
$185$	−0.588648	−	7.85496i	−0.0432783	−	0.577508i
$186$		0			0
$187$	−0.00783954	+	0.104611i	−0.000573284	+	0.00764994i
$188$	−8.28659	−	36.3059i	−0.604362	−	2.64788i
$189$		0			0
$190$	−0.608951	+	2.66799i	−0.0441780	+	0.193556i
$191$	−8.64098	−	2.66539i	−0.625240	−	0.192861i	−0.0340847	−	0.999419i	$-0.510852\pi$
$191$	−8.64098	−	2.66539i	−0.625240	−	0.192861i	−0.591155	+	0.806558i	$0.701328\pi$
$192$		0			0
$193$	−12.6657	+	11.7520i	−0.911694	+	0.845929i	−0.988516	−	0.151116i	$-0.951713\pi$
$193$	−12.6657	+	11.7520i	−0.911694	+	0.845929i	0.0768219	+	0.997045i	$0.475523\pi$
$194$	−23.1127	+	15.7580i	−1.65940	+	1.13136i
$195$		0			0
$196$	−14.6472	−	15.8469i	−1.04623	−	1.13192i
$197$	11.6326			0.828789			0.414395	−	0.910097i	$-0.363993\pi$
$197$	11.6326			0.828789			0.414395	+	0.910097i	$0.363993\pi$
$198$		0			0
$199$	−2.83651	+	2.63189i	−0.201075	+	0.186570i	−0.774283	−	0.632840i	$-0.781889\pi$
$199$	−2.83651	+	2.63189i	−0.201075	+	0.186570i	0.573208	+	0.819410i	$0.305699\pi$
$200$	7.76752	−	19.7913i	0.549247	−	1.39946i
$201$		0			0
$202$	1.67989	−	7.36007i	0.118197	−	0.517853i
$203$	−2.42540	+	21.3415i	−0.170230	+	1.49788i
$204$		0			0
$205$	1.11560	−	14.8866i	0.0779168	−	1.03973i
$206$	−18.8206	+	5.80538i	−1.31129	+	0.404480i
$207$		0			0
$208$	−0.500629	−	1.27558i	−0.0347124	−	0.0884457i
$209$	−1.41590	−	0.681862i	−0.0979399	−	0.0471654i
$210$		0			0
$211$	−8.67642	+	4.17834i	−0.597309	+	0.287649i	−0.708007	−	0.706205i	$-0.750406\pi$
$211$	−8.67642	+	4.17834i	−0.597309	+	0.287649i	0.110698	+	0.993854i	$0.464691\pi$
$212$	17.4029	+	16.1475i	1.19523	+	1.10901i
$213$		0			0
$214$	15.0374	+	26.0455i	1.02793	+	1.78043i
$215$	−4.29728	+	7.44311i	−0.293072	+	0.507616i
$216$		0			0
$217$	10.5195	+	5.57267i	0.714110	+	0.378297i
$218$	1.03723	+	1.30064i	0.0702500	+	0.0880907i
$219$		0			0
$220$	45.2101	+	30.8237i	3.04806	+	2.07813i
$221$	0.0374184	+	0.0255114i	0.00251703	+	0.00171609i
$222$		0			0
$223$	10.7975	+	13.5396i	0.723055	+	0.906682i	0.998507	−	0.0546330i	$-0.0173989\pi$
$223$	10.7975	+	13.5396i	0.723055	+	0.906682i	−0.275452	+	0.961315i	$0.588827\pi$
$224$	15.4657	−	6.72990i	1.03334	−	0.449660i
$225$		0			0
$226$	−12.0126	+	20.8064i	−0.799065	+	1.38402i
$227$	−3.62070	−	6.27123i	−0.240314	−	0.416236i	0.720490	−	0.693466i	$-0.243917\pi$
$227$	−3.62070	−	6.27123i	−0.240314	−	0.416236i	−0.960804	+	0.277229i	$0.910584\pi$
$228$		0			0
$229$	−5.23032	−	4.85302i	−0.345629	−	0.320697i	0.488187	−	0.872739i	$-0.337658\pi$
$229$	−5.23032	−	4.85302i	−0.345629	−	0.320697i	−0.833816	+	0.552042i	$0.813849\pi$
$230$	−47.6927	+	22.9676i	−3.14476	+	1.51444i
$231$		0			0
$232$	17.8546	+	8.59833i	1.17221	+	0.564508i
$233$	0.934717	+	2.38162i	0.0612353	+	0.156025i	0.958217	−	0.286043i	$-0.0923401\pi$
$233$	0.934717	+	2.38162i	0.0612353	+	0.156025i	−0.896981	+	0.442068i	$0.854245\pi$
$234$		0			0
$235$	−42.7411	+	13.1839i	−2.78812	+	0.860022i
$236$	1.50037	−	20.0210i	0.0976655	−	1.30326i
$237$		0			0
$238$	−0.0695536	+	0.110458i	−0.00450849	+	0.00715992i
$239$	−3.72775	+	16.3324i	−0.241128	+	1.05645i	0.698863	+	0.715255i	$0.253690\pi$
$239$	−3.72775	+	16.3324i	−0.241128	+	1.05645i	−0.939992	+	0.341197i	$0.889168\pi$
$240$		0			0
$241$	3.45268	−	8.79729i	0.222407	−	0.566683i	−0.775500	−	0.631347i	$-0.782502\pi$
$241$	3.45268	−	8.79729i	0.222407	−	0.566683i	0.997907	+	0.0646639i	$0.0205975\pi$
$242$	−19.7991	+	18.3709i	−1.27273	+	1.18092i
$243$		0			0
$244$	12.0454			0.771129
$245$	−17.6657	+	18.9658i	−1.12862	+	1.21168i
$246$		0			0
$247$	−0.560549	+	0.382176i	−0.0356669	+	0.0243173i
$248$	8.05138	−	7.47059i	0.511263	−	0.474383i
$249$		0			0
$250$	−29.5920	−	9.12793i	−1.87156	−	0.577301i
$251$	−0.723551	+	3.17008i	−0.0456701	+	0.200094i	−0.992616	−	0.121299i	$-0.961294\pi$
$251$	−0.723551	+	3.17008i	−0.0456701	+	0.200094i	0.946946	+	0.321393i	$0.104151\pi$
$252$		0			0
$253$	−6.76433	−	29.6365i	−0.425270	−	1.86323i
$254$	0.635777	−	8.48386i	0.0398922	−	0.532325i
$255$		0			0
$256$	−0.857832	−	11.4470i	−0.0536145	−	0.715435i
$257$	−10.1777	−	25.9323i	−0.634867	−	1.61761i	−0.778255	−	0.627948i	$-0.783895\pi$
$257$	−10.1777	−	25.9323i	−0.634867	−	1.61761i	0.143388	−	0.989667i	$-0.454200\pi$
$258$		0			0
$259$	4.52548	+	3.34668i	0.281199	+	0.207953i
$260$	21.2826	−	10.2491i	1.31989	−	0.635625i
$261$		0			0
$262$	25.5886	+	3.85686i	1.58087	+	0.238278i
$263$	10.4279	+	18.0616i	0.643009	+	1.11372i	0.984758	+	0.173933i	$0.0556476\pi$
$263$	10.4279	+	18.0616i	0.643009	+	1.11372i	−0.341748	+	0.939791i	$0.611019\pi$
$264$		0			0
$265$	17.7784	−	22.2934i	1.09212	−	1.36947i
$266$	−1.15967	−	1.57446i	−0.0711038	−	0.0965365i
$267$		0			0
$268$	−42.5408	+	6.41199i	−2.59859	+	0.391675i
$269$	19.3862	+	13.2173i	1.18199	+	0.805871i	0.984663	−	0.174466i	$-0.0558200\pi$
$269$	19.3862	+	13.2173i	1.18199	+	0.805871i	0.197332	+	0.980337i	$0.436772\pi$
$270$		0			0
$271$	5.86053	−	0.883332i	0.356002	−	0.0536586i	0.0313932	−	0.999507i	$-0.490006\pi$
$271$	5.86053	−	0.883332i	0.356002	−	0.0536586i	0.324608	+	0.945848i	$0.394767\pi$
$272$	−0.00903453	−	0.0113289i	−0.000547799	−	0.000686918i
$273$		0			0
$274$	−1.11608	+	1.39953i	−0.0674252	+	0.0845485i
$275$	20.8763	−	36.1587i	1.25889	−	2.18045i
$276$		0			0
$277$	5.49981	+	0.828963i	0.330452	+	0.0498076i	0.312173	−	0.950025i	$-0.398943\pi$
$277$	5.49981	+	0.828963i	0.330452	+	0.0498076i	0.0182788	+	0.999833i	$0.494181\pi$
$278$	12.6896	+	11.7742i	0.761069	+	0.706169i
$279$		0			0
$280$	11.1537	+	21.1530i	0.666558	+	1.26413i
$281$	−24.7189	−	11.9040i	−1.47460	−	0.710132i	−0.487937	−	0.872879i	$-0.662250\pi$
$281$	−24.7189	−	11.9040i	−1.47460	−	0.710132i	−0.986668	+	0.162747i	$0.947965\pi$
$282$		0			0
$283$	0.0214523	+	0.286261i	0.00127521	+	0.0170165i	0.997805	−	0.0662191i	$-0.0210936\pi$
$283$	0.0214523	+	0.286261i	0.00127521	+	0.0170165i	−0.996530	+	0.0832356i	$0.973475\pi$
$284$	7.62098	−	2.35076i	0.452222	−	0.139492i
$285$		0			0
$286$	4.97688	+	21.8051i	0.294289	+	1.28936i
$287$	7.53552	+	7.55003i	0.444808	+	0.445664i
$288$		0			0
$289$	−16.2443	−	5.01070i	−0.955546	−	0.294747i
$290$	24.7586	−	63.0838i	1.45387	−	3.70441i
$291$		0			0
$292$	10.1983	−	6.95312i	0.596813	−	0.406900i
$293$	16.3036			0.952468			0.476234	−	0.879318i	$-0.342001\pi$
$293$	16.3036			0.952468			0.476234	+	0.879318i	$0.342001\pi$
$294$		0			0
$295$	−24.1145			−1.40400
$296$	4.29070	−	2.92535i	0.249392	−	0.170033i
$297$		0			0
$298$	7.45898	−	19.0052i	0.432087	−	1.10094i
$299$	−12.5401	−	3.86812i	−0.725215	−	0.223699i
$300$		0			0
$301$	−2.02276	−	5.79859i	−0.116590	−	0.334225i
$302$	2.60698	+	11.4219i	0.150015	+	0.657258i
$303$		0			0
$304$	0.207428	−	0.0639831i	0.0118968	−	0.00366968i
$305$	−1.08117	−	14.4272i	−0.0619076	−	0.826100i
$306$		0			0
$307$	19.5150	+	9.39793i	1.11378	+	0.536368i	0.897965	−	0.440066i	$-0.145045\pi$
$307$	19.5150	+	9.39793i	1.11378	+	0.536368i	0.215815	+	0.976434i	$0.430759\pi$
$308$	−37.7763	+	10.0832i	−2.15250	+	0.574543i
$309$		0			0
$310$	−27.5332	−	25.5471i	−1.56378	−	1.45098i
$311$	−2.09988	−	0.316506i	−0.119073	−	0.0179474i	0.0892352	−	0.996011i	$-0.471558\pi$
$311$	−2.09988	−	0.316506i	−0.119073	−	0.0179474i	−0.208309	+	0.978063i	$0.566796\pi$
$312$		0			0
$313$	−0.592651	+	1.02650i	−0.0334986	+	0.0580213i	−0.882289	−	0.470709i	$-0.843998\pi$
$313$	−0.592651	+	1.02650i	−0.0334986	+	0.0580213i	0.848790	+	0.528730i	$0.177332\pi$
$314$	11.8550	−	14.8657i	0.669018	−	0.838922i
$315$		0			0
$316$	−17.3249	−	21.7247i	−0.974601	−	1.22211i
$317$	−27.6584	+	4.16883i	−1.55345	+	0.234145i	−0.868962	−	0.494879i	$-0.835212\pi$
$317$	−27.6584	+	4.16883i	−1.55345	+	0.234145i	−0.684488	+	0.729024i	$0.739974\pi$
$318$		0			0
$319$	32.1547	+	21.9227i	1.80032	+	1.22744i
$320$	−47.7726	+	7.20057i	−2.67057	+	0.402524i
$321$		0			0
$322$	9.82490	−	36.5265i	0.547520	−	2.03554i
$323$	−0.00447296	+	0.00560892i	−0.000248882	+	0.000312089i
$324$		0			0
$325$	−9.01233	−	15.6098i	−0.499914	−	0.865877i
$326$	29.2152	+	4.40348i	1.61808	+	0.243886i
$327$		0			0
$328$	8.86717	−	4.27020i	0.489608	−	0.235783i
$329$	12.8090	−	29.2816i	0.706182	−	1.61435i
$330$		0			0
$331$	0.666118	+	1.69724i	0.0366132	+	0.0932888i	0.948011	−	0.318238i	$-0.103091\pi$
$331$	0.666118	+	1.69724i	0.0366132	+	0.0932888i	−0.911398	+	0.411527i	$0.864996\pi$
$332$	3.84870	+	51.3574i	0.211225	+	2.81860i
$333$		0			0
$334$	3.17572	−	42.3771i	0.173768	−	2.31877i
$335$	11.4982	+	50.3770i	0.628215	+	2.75239i
$336$		0			0
$337$	−3.69490	+	16.1884i	−0.201274	+	0.881840i	0.768888	+	0.639384i	$0.220810\pi$
$337$	−3.69490	+	16.1884i	−0.201274	+	0.881840i	−0.970162	+	0.242457i	$0.922047\pi$
$338$	−18.7799	−	5.79283i	−1.02149	−	0.315089i
$339$		0			0
$340$	0.183108	−	0.169899i	0.00993042	−	0.00921408i
$341$	17.8213	−	12.1504i	0.965078	−	0.657979i
$342$		0			0
$343$	−2.02050	−	18.4097i	−0.109097	−	0.994031i
$344$	−5.66613			−0.305497
$345$		0			0
$346$	6.72613	−	6.24094i	0.361599	−	0.335515i
$347$	−4.57409	+	11.6546i	−0.245550	+	0.625652i	−0.999511	−	0.0312676i	$-0.990046\pi$
$347$	−4.57409	+	11.6546i	−0.245550	+	0.625652i	0.753961	+	0.656919i	$0.228141\pi$
$348$		0			0
$349$	5.56413	−	24.3781i	0.297841	−	1.30493i	−0.575493	−	0.817806i	$-0.695190\pi$
$349$	5.56413	−	24.3781i	0.297841	−	1.30493i	0.873335	−	0.487121i	$-0.161953\pi$
$350$	44.0158	−	27.5980i	2.35275	−	1.47517i
$351$		0			0
$352$	2.28374	−	30.4744i	0.121724	−	1.62429i
$353$	−0.927679	+	0.286151i	−0.0493754	+	0.0152303i	−0.319344	−	0.947639i	$-0.603463\pi$
$353$	−0.927679	+	0.286151i	−0.0493754	+	0.0152303i	0.269969	+	0.962869i	$0.412987\pi$
$354$		0			0
$355$	−3.49963	−	8.91691i	−0.185741	−	0.473261i
$356$	−2.87602	−	1.38502i	−0.152429	−	0.0734059i
$357$		0			0
$358$	−25.0096	+	12.0440i	−1.32180	+	0.636544i
$359$	2.40234	+	2.22905i	0.126791	+	0.117645i	0.741020	−	0.671483i	$-0.234342\pi$
$359$	2.40234	+	2.22905i	0.126791	+	0.117645i	−0.614229	+	0.789128i	$0.710533\pi$
$360$		0			0
$361$	9.44626	+	16.3614i	0.497172	+	0.861127i
$362$	−16.2583	+	28.1603i	−0.854519	+	1.48007i
$363$		0			0
$364$	−4.38430	+	16.2997i	−0.229800	+	0.854337i
$365$	−9.24337	−	11.5908i	−0.483820	−	0.606691i
$366$		0			0
$367$	5.35248	+	3.64926i	0.279397	+	0.190490i	0.694908	−	0.719098i	$-0.255445\pi$
$367$	5.35248	+	3.64926i	0.279397	+	0.190490i	−0.415511	+	0.909588i	$0.636397\pi$
$368$	3.46929	+	2.36532i	0.180849	+	0.123301i
$369$		0			0
$370$	−11.0723	−	13.8843i	−0.575623	−	0.721808i
$371$	3.76868	+	20.0234i	0.195660	+	1.03956i
$372$		0			0
$373$	1.79525	−	3.10946i	0.0929545	−	0.161002i	−0.815799	−	0.578336i	$-0.803702\pi$
$373$	1.79525	−	3.10946i	0.0929545	−	0.161002i	0.908753	+	0.417334i	$0.137036\pi$
$374$	0.118254	+	0.204821i	0.00611475	+	0.0105911i
$375$		0			0
$376$	−21.6162	−	20.0569i	−1.11477	−	1.03436i
$377$	15.1368	−	7.28949i	0.779584	−	0.375428i
$378$		0			0
$379$	15.3758	+	7.40459i	0.789801	+	0.380348i	0.784886	−	0.619640i	$-0.212721\pi$
$379$	15.3758	+	7.40459i	0.789801	+	0.380348i	0.00491496	+	0.999988i	$0.498436\pi$
$380$	1.36710	+	3.48330i	0.0701305	+	0.178690i
$381$		0			0
$382$	−19.4811	+	6.00911i	−0.996738	+	0.307453i
$383$	2.55194	−	34.0533i	0.130398	−	1.74004i	−0.422117	−	0.906541i	$-0.638713\pi$
$383$	2.55194	−	34.0533i	0.130398	−	1.74004i	0.552516	−	0.833503i	$-0.313668\pi$
$384$		0			0
$385$	15.4677	+	44.3409i	0.788307	+	2.25982i
$386$	−8.66789	+	37.9765i	−0.441184	+	1.93295i
$387$		0			0
$388$	−13.9744	+	35.6062i	−0.709442	+	1.80763i
$389$	9.32053	−	8.64819i	0.472569	−	0.438480i	−0.407585	−	0.913167i	$-0.633629\pi$
$389$	9.32053	−	8.64819i	0.472569	−	0.438480i	0.880155	+	0.474687i	$0.157439\pi$
$390$		0			0
$391$	−0.138770			−0.00701792
$392$	−16.6516	−	3.83434i	−0.841034	−	0.193663i
$393$		0			0
$394$	21.6687	−	14.7734i	1.09165	−	0.744276i
$395$	−24.4654	+	22.7006i	−1.23099	+	1.14219i
$396$		0			0
$397$	7.24134	+	2.23366i	0.363433	+	0.112104i	0.471093	−	0.882084i	$-0.343860\pi$
$397$	7.24134	+	2.23366i	0.363433	+	0.112104i	−0.107660	+	0.994188i	$0.534336\pi$
$398$	−1.94120	+	8.50494i	−0.0973034	+	0.426314i
$399$		0			0
$400$	1.28332	+	5.62258i	0.0641659	+	0.281129i
$401$	−1.78069	+	23.7616i	−0.0889232	+	1.18660i	0.757044	+	0.653363i	$0.226643\pi$
$401$	−1.78069	+	23.7616i	−0.0889232	+	1.18660i	−0.845968	+	0.533234i	$0.820976\pi$
$402$		0			0
$403$	−0.695848	−	9.28544i	−0.0346626	−	0.462541i
$404$	−3.77135	−	9.60924i	−0.187632	−	0.478078i
$405$		0			0
$406$	22.5859	+	42.8342i	1.12092	+	2.12583i
$407$	9.18821	−	4.42481i	0.455443	−	0.219330i
$408$		0			0
$409$	−20.7441	−	3.12668i	−1.02573	−	0.154604i	−0.385438	−	0.922734i	$-0.625949\pi$
$409$	−20.7441	−	3.12668i	−1.02573	−	0.154604i	−0.640294	+	0.768130i	$0.721188\pi$
$410$	−16.8280	−	29.1469i	−0.831075	−	1.43946i
$411$		0			0
$412$	−16.7914	+	21.0558i	−0.827255	+	1.03734i
$413$	11.2522	−	13.0498i	0.553683	−	0.642141i
$414$		0			0
$415$	61.1671	−	9.21945i	3.00257	−	0.452565i
$416$	−10.9004	−	7.43175i	−0.534435	−	0.364372i
$417$		0			0
$418$	−3.50344	+	0.528058i	−0.171359	+	0.0258282i
$419$	0.986412	+	1.23692i	0.0481894	+	0.0604276i	0.805342	−	0.592810i	$-0.201982\pi$
$419$	0.986412	+	1.23692i	0.0481894	+	0.0604276i	−0.757153	+	0.653238i	$0.773410\pi$
$420$		0			0
$421$	−6.10328	+	7.65327i	−0.297456	+	0.372998i	−0.907990	−	0.418992i	$-0.862383\pi$
$421$	−6.10328	+	7.65327i	−0.297456	+	0.372998i	0.610534	+	0.791990i	$0.290955\pi$
$422$	−10.8555	+	18.8023i	−0.528438	+	0.915281i
$423$		0			0
$424$	18.5886	+	2.80178i	0.902743	+	0.136067i
$425$	−0.139721	−	0.129642i	−0.00677744	−	0.00628855i
$426$		0			0
$427$	8.31195	+	6.14685i	0.402243	+	0.297467i
$428$	37.0511	+	17.8429i	1.79093	+	0.862467i
$429$		0			0
$430$	1.44800	+	19.3222i	0.0698288	+	0.931801i
$431$	1.26985	−	0.391697i	0.0611666	−	0.0188674i	−0.264021	−	0.964517i	$-0.585049\pi$
$431$	1.26985	−	0.391697i	0.0611666	−	0.0188674i	0.325187	+	0.945650i	$0.394573\pi$
$432$		0			0
$433$	7.67157	+	33.6113i	0.368672	+	1.61526i	0.730431	+	0.682986i	$0.239319\pi$
$433$	7.67157	+	33.6113i	0.368672	+	1.61526i	−0.361759	+	0.932272i	$0.617824\pi$
$434$	26.6725	−	2.97929i	1.28032	−	0.143011i
$435$		0			0
$436$	2.17369	+	0.670495i	0.104101	+	0.0321109i
$437$	0.759492	−	1.93515i	0.0363314	−	0.0925710i
$438$		0			0
$439$	−30.2352	+	20.6140i	−1.44305	+	0.983852i	−0.447045	+	0.894511i	$0.647524\pi$
$439$	−30.2352	+	20.6140i	−1.44305	+	0.983852i	−0.996001	+	0.0893410i	$0.971524\pi$
$440$	43.3280			2.06558
$441$		0			0
$442$	0.102101			0.00485644
$443$	30.8451	−	21.0298i	1.46549	−	0.999156i	0.472456	−	0.881354i	$-0.343368\pi$
$443$	30.8451	−	21.0298i	1.46549	−	0.999156i	0.993037	−	0.117802i	$-0.0375849\pi$
$444$		0			0
$445$	−1.40074	+	3.56903i	−0.0664015	+	0.169188i
$446$	37.3085	+	11.5081i	1.76661	+	0.544926i
$447$		0			0
$448$	18.3947	−	29.2126i	0.869068	−	1.38017i
$449$	−6.94861	−	30.4439i	−0.327925	−	1.43674i	−0.823078	−	0.567929i	$-0.807745\pi$
$449$	−6.94861	−	30.4439i	−0.327925	−	1.43674i	0.495152	−	0.868806i	$-0.335112\pi$
$450$		0			0
$451$	18.4687	−	5.69685i	0.869659	−	0.268254i
$452$	2.45500	+	32.7596i	0.115473	+	1.54088i
$453$		0			0
$454$	−14.7089	−	7.08346i	−0.690325	−	0.332443i
$455$	19.9162	+	3.78820i	0.933688	+	0.177594i
$456$		0			0
$457$	29.0460	+	26.9507i	1.35871	+	1.26070i	0.934881	+	0.354961i	$0.115506\pi$
$457$	29.0460	+	26.9507i	1.35871	+	1.26070i	0.423832	+	0.905741i	$0.360685\pi$
$458$	−15.9061	−	2.39746i	−0.743245	−	0.112026i
$459$		0			0
$460$	−36.1910	+	62.6847i	−1.68742	+	2.92269i
$461$	2.46280	−	3.08825i	0.114704	−	0.143834i	−0.721165	−	0.692763i	$-0.756393\pi$
$461$	2.46280	−	3.08825i	0.114704	−	0.143834i	0.835869	+	0.548929i	$0.184964\pi$
$462$		0			0
$463$	6.49136	+	8.13991i	0.301679	+	0.378294i	0.909446	−	0.415822i	$-0.136506\pi$
$463$	6.49136	+	8.13991i	0.301679	+	0.378294i	−0.607767	+	0.794115i	$0.707935\pi$
$464$	−5.31547	+	0.801179i	−0.246765	+	0.0371938i
$465$		0			0
$466$	4.76581	+	3.24927i	0.220772	+	0.150520i
$467$	−10.7676	+	1.62295i	−0.498265	+	0.0751013i	−0.393367	−	0.919382i	$-0.628690\pi$
$467$	−10.7676	+	1.62295i	−0.498265	+	0.0751013i	−0.104898	+	0.994483i	$0.533452\pi$
$468$		0			0
$469$	−32.6274	−	17.2842i	−1.50659	−	0.798112i
$470$	−62.8725	+	78.8396i	−2.90009	+	3.63660i
$471$		0			0
$472$	−7.94897	−	13.7680i	−0.365881	−	0.633725i
$473$	−11.0029	−	1.65842i	−0.505914	−	0.0762542i
$474$		0			0
$475$	2.57255	−	1.23887i	0.118037	−	0.0568434i
$476$	0.00650230	+	0.178368i	0.000298032	+	0.00817550i
$477$		0			0
$478$	13.7983	+	35.1574i	0.631118	+	1.60806i
$479$	2.12251	+	28.3230i	0.0969801	+	1.29411i	0.807263	+	0.590193i	$0.200948\pi$
$479$	2.12251	+	28.3230i	0.0969801	+	1.29411i	−0.710282	+	0.703917i	$0.751433\pi$
$480$		0			0
$481$	0.329004	−	4.39025i	0.0150013	−	0.200178i
$482$	−4.74109	−	20.7721i	−0.215951	−	0.946143i
$483$		0			0
$484$	−8.21808	+	36.0058i	−0.373549	+	1.63663i
$485$	43.9011	+	13.5417i	1.99344	+	0.614896i
$486$		0			0
$487$	−3.16866	+	2.94008i	−0.143586	+	0.133228i	−0.748696	−	0.662914i	$-0.769320\pi$
$487$	−3.16866	+	2.94008i	−0.143586	+	0.133228i	0.605110	+	0.796142i	$0.293129\pi$
$488$	7.88074	−	5.37299i	0.356744	−	0.243224i
$489$		0			0
$490$	−8.82020	+	57.7641i	−0.398456	+	2.60951i
$491$	−26.4830			−1.19516			−0.597581	−	0.801808i	$-0.703872\pi$
$491$	−26.4830			−1.19516			−0.597581	+	0.801808i	$0.703872\pi$
$492$		0			0
$493$	0.130232	−	0.120837i	0.00586534	−	0.00544224i
$494$	−0.558799	+	1.42380i	−0.0251416	+	0.0640596i
$495$		0			0
$496$	−0.662958	+	2.90461i	−0.0297677	+	0.130421i
$497$	6.45847	+	2.26689i	0.289702	+	0.101684i
$498$		0			0
$499$	1.00537	−	13.4157i	0.0450064	−	0.600569i	−0.928415	−	0.371546i	$-0.878828\pi$
$499$	1.00537	−	13.4157i	0.0450064	−	0.600569i	0.973421	−	0.229023i	$-0.0735532\pi$
$500$	−40.4635	+	12.4813i	−1.80958	+	0.558183i
$501$		0			0
$502$	2.67822	+	6.82399i	0.119535	+	0.304570i
$503$	1.54848	+	0.745708i	0.0690432	+	0.0332495i	0.468087	−	0.883683i	$-0.344943\pi$
$503$	1.54848	+	0.745708i	0.0690432	+	0.0332495i	−0.399044	+	0.916932i	$0.630658\pi$
$504$		0			0
$505$	−11.1708	+	5.37958i	−0.497095	+	0.239388i
$506$	−50.2386	−	46.6146i	−2.23338	−	2.07227i
$507$		0			0
$508$	−5.81659	−	10.0746i	−0.258069	−	0.446989i
$509$	6.37648	−	11.0444i	0.282632	−	0.489534i	−0.689400	−	0.724381i	$-0.742126\pi$
$509$	6.37648	−	11.0444i	0.282632	−	0.489534i	0.972032	+	0.234847i	$0.0754590\pi$
$510$		0			0
$511$	10.5856	+	0.406280i	0.468279	+	0.0179728i
$512$	4.64741	+	5.82766i	0.205388	+	0.257549i
$513$		0			0
$514$	−51.8926	−	35.3798i	−2.28889	−	1.56054i
$515$	26.7264	+	18.2218i	1.17771	+	0.802947i
$516$		0			0
$517$	−36.1054	−	45.2748i	−1.58791	−	1.99118i
$518$	12.6801	+	0.486670i	0.557133	+	0.0213830i
$519$		0			0
$520$	9.35241	−	16.1988i	0.410130	−	0.710366i
$521$	−2.76601	−	4.79087i	−0.121181	−	0.209892i	0.799053	−	0.601261i	$-0.205335\pi$
$521$	−2.76601	−	4.79087i	−0.121181	−	0.209892i	−0.920234	+	0.391369i	$0.872002\pi$
$522$		0			0
$523$	−5.87414	−	5.45041i	−0.256858	−	0.238330i	0.541224	−	0.840879i	$-0.317961\pi$
$523$	−5.87414	−	5.45041i	−0.256858	−	0.238330i	−0.798082	+	0.602549i	$0.794152\pi$
$524$	31.8804	−	15.3528i	1.39270	−	0.670689i
$525$		0			0
$526$	42.3627	+	20.4008i	1.84710	+	0.889518i
$527$	−0.0359729	−	0.0916574i	−0.00156700	−	0.00399266i
$528$		0			0
$529$	16.4473	−	5.07332i	0.715100	−	0.220579i
$530$	4.80405	−	64.1056i	0.208674	−	2.78457i
$531$		0			0
$532$	−2.52294	−	0.885538i	−0.109383	−	0.0383930i
$533$	1.85665	−	8.13450i	0.0804203	−	0.352344i
$534$		0			0
$535$	18.0454	−	45.9789i	0.780170	−	1.98784i
$536$	−24.9722	+	23.1709i	−1.07864	+	1.00083i
$537$		0			0
$538$	52.8976			2.28058
$539$	−31.2130	−	12.3196i	−1.34444	−	0.530641i
$540$		0			0
$541$	−13.0547	+	8.90052i	−0.561264	+	0.382663i	−0.810464	−	0.585789i	$-0.800785\pi$
$541$	−13.0547	+	8.90052i	−0.561264	+	0.382663i	0.249200	+	0.968452i	$0.419832\pi$
$542$	9.79487	−	9.08831i	0.420726	−	0.390376i
$543$		0			0
$544$	−0.133309	−	0.0411203i	−0.00571556	−	0.00176302i
$545$	0.607969	−	2.66369i	0.0260425	−	0.114100i
$546$		0			0
$547$	−5.74175	−	25.1562i	−0.245499	−	1.07560i	−0.935925	−	0.352200i	$-0.885434\pi$
$547$	−5.74175	−	25.1562i	−0.245499	−	1.07560i	0.690426	−	0.723403i	$-0.257423\pi$
$548$	−0.182916	+	2.44085i	−0.00781380	+	0.104268i
$549$		0			0
$550$	−7.03441	−	93.8676i	−0.299948	−	4.00253i
$551$	0.972318	+	2.47743i	0.0414222	+	0.105542i
$552$		0			0
$553$	−0.868784	−	23.8322i	−0.0369445	−	1.01345i
$554$	11.2976	−	5.44062i	0.479988	−	0.231150i
$555$		0			0
$556$	23.4058	+	3.52785i	0.992626	+	0.149614i
$557$	−0.770375	−	1.33433i	−0.0326418	−	0.0565373i	0.849243	−	0.528002i	$-0.177059\pi$
$557$	−0.770375	−	1.33433i	−0.0326418	−	0.0565373i	−0.881885	+	0.471465i	$0.843725\pi$
$558$		0			0
$559$	−2.99502	+	3.75563i	−0.126676	+	0.158846i
$560$	−5.73204	−	3.03653i	−0.242223	−	0.128317i
$561$		0			0
$562$	−61.1632	+	9.21887i	−2.58001	+	0.388875i
$563$	−2.77508	−	1.89202i	−0.116956	−	0.0797390i	0.503430	−	0.864036i	$-0.332071\pi$
$563$	−2.77508	−	1.89202i	−0.116956	−	0.0797390i	−0.620385	+	0.784297i	$0.713024\pi$
$564$		0			0
$565$	39.0170	−	5.88087i	1.64146	−	0.247410i
$566$	0.403513	+	0.505990i	0.0169609	+	0.0212683i
$567$		0			0
$568$	3.93746	−	4.93742i	0.165212	−	0.207169i
$569$	−3.50511	+	6.07102i	−0.146942	+	0.254511i	−0.930096	−	0.367317i	$-0.880276\pi$
$569$	−3.50511	+	6.07102i	−0.146942	+	0.254511i	0.783154	+	0.621828i	$0.213610\pi$
$570$		0			0
$571$	−32.4677	−	4.89371i	−1.35873	−	0.204795i	−0.571067	−	0.820903i	$-0.693470\pi$
$571$	−32.4677	−	4.89371i	−1.35873	−	0.204795i	−0.787662	+	0.616108i	$0.788709\pi$
$572$	22.4187	+	20.8015i	0.937372	+	0.869754i
$573$		0			0
$574$	23.6254	+	4.49370i	0.986104	+	0.187563i
$575$	49.7616	+	23.9639i	2.07520	+	0.999364i
$576$		0			0
$577$	3.31726	+	44.2658i	0.138099	+	1.84281i	0.450401	+	0.892826i	$0.351281\pi$
$577$	3.31726	+	44.2658i	0.138099	+	1.84281i	−0.312302	+	0.949983i	$0.601100\pi$
$578$	−36.6227	+	11.2966i	−1.52330	+	0.469876i
$579$		0			0
$580$	−20.6199	−	90.3418i	−0.856196	−	3.75124i
$581$	−23.5522	+	37.4032i	−0.977110	+	1.55175i
$582$		0			0
$583$	35.2766	+	10.8814i	1.46101	+	0.450662i
$584$	3.57077	−	9.09818i	0.147760	−	0.376485i
$585$		0			0
$586$	30.3696	−	20.7057i	1.25456	−	0.855343i
$587$	−35.3282			−1.45815			−0.729075	−	0.684433i	$-0.760050\pi$
$587$	−35.3282			−1.45815			−0.729075	+	0.684433i	$0.760050\pi$
$588$		0			0
$589$	1.47504			0.0607781
$590$	−44.9193	+	30.6255i	−1.84930	+	1.26083i
$591$		0			0
$592$	−0.514636	+	1.31127i	−0.0211514	+	0.0538930i
$593$	9.90355	+	3.05484i	0.406690	+	0.125447i	0.491349	−	0.870963i	$-0.336504\pi$
$593$	9.90355	+	3.05484i	0.406690	+	0.125447i	−0.0846590	+	0.996410i	$0.526980\pi$
$594$		0			0
$595$	0.213054	−	0.0237980i	0.00873438	−	0.000975622i
$596$	−6.21213	−	27.2171i	−0.254459	−	1.11486i
$597$		0			0
$598$	−28.2717	+	8.72066i	−1.15611	+	0.356614i
$599$	−0.373698	−	4.98665i	−0.0152689	−	0.203749i	−0.999621	−	0.0275355i	$-0.991234\pi$
$599$	−0.373698	−	4.98665i	−0.0152689	−	0.203749i	0.984352	−	0.176214i	$-0.0563850\pi$
$600$		0			0
$601$	19.3553	+	9.32102i	0.789519	+	0.380212i	0.784778	−	0.619777i	$-0.212777\pi$
$601$	19.3553	+	9.32102i	0.789519	+	0.380212i	0.00474045	+	0.999989i	$0.498491\pi$
$602$	−11.1321	−	8.23242i	−0.453711	−	0.335529i
$603$		0			0
$604$	11.7433	+	10.8962i	0.477829	+	0.443360i
$605$	43.8630	+	6.61128i	1.78328	+	0.268787i
$606$		0			0
$607$	−8.24891	+	14.2875i	−0.334813	+	0.579913i	−0.983449	−	0.181186i	$-0.942006\pi$
$607$	−8.24891	+	14.2875i	−0.334813	+	0.579913i	0.648636	+	0.761099i	$0.275340\pi$
$608$	1.30302	−	1.63394i	0.0528445	−	0.0662649i
$609$		0			0
$610$	−20.3365	−	25.5012i	−0.823403	−	1.03251i
$611$	−24.7201	+	3.72595i	−1.00007	+	0.150736i
$612$		0			0
$613$	30.0735	+	20.5038i	1.21466	+	0.828140i	0.989266	−	0.146128i	$-0.0466811\pi$
$613$	30.0735	+	20.5038i	1.21466	+	0.828140i	0.225393	+	0.974268i	$0.427633\pi$
$614$	48.2870	−	7.27809i	1.94870	−	0.293720i
$615$		0			0
$616$	−20.2175	+	23.4475i	−0.814585	+	0.944726i
$617$	18.6919	−	23.4390i	0.752509	−	0.943617i	−0.247169	−	0.968972i	$-0.579500\pi$
$617$	18.6919	−	23.4390i	0.752509	−	0.943617i	0.999679	+	0.0253554i	$0.00807173\pi$
$618$		0			0
$619$	−9.50590	−	16.4647i	−0.382074	−	0.661772i	0.609284	−	0.792952i	$-0.291457\pi$
$619$	−9.50590	−	16.4647i	−0.382074	−	0.661772i	−0.991359	+	0.131180i	$0.958123\pi$
$620$	−50.7847	−	7.65457i	−2.03956	−	0.307415i
$621$		0			0
$622$	−4.31352	+	2.07728i	−0.172956	+	0.0832915i
$623$	−1.27782	−	2.42339i	−0.0511947	−	0.0970909i
$624$		0			0
$625$	2.67108	+	6.80580i	0.106843	+	0.272232i
$626$	0.199698	+	2.66479i	0.00798154	+	0.106506i
$627$		0			0
$628$	1.94293	−	25.9266i	0.0775315	−	1.03459i
$629$	−0.0103594	−	0.0453875i	−0.000413057	−	0.00180972i
$630$		0			0
$631$	−1.54989	+	6.79051i	−0.0617001	+	0.270326i	−0.996363	−	0.0852091i	$-0.972844\pi$
$631$	−1.54989	+	6.79051i	−0.0617001	+	0.270326i	0.934663	+	0.355535i	$0.115701\pi$
$632$	−21.0254	−	6.48548i	−0.836345	−	0.257978i
$633$		0			0
$634$	−46.2263	+	42.8917i	−1.83588	+	1.70345i
$635$	−11.5446	+	7.87101i	−0.458135	+	0.312351i
$636$		0			0
$637$	−11.3432	+	9.01028i	−0.449435	+	0.357000i
$638$	87.7382			3.47359
$639$		0			0
$640$	−45.2375	+	41.9743i	−1.78817	+	1.65918i
$641$	10.1060	−	25.7497i	0.399163	−	1.01705i	−0.580116	−	0.814534i	$-0.696993\pi$
$641$	10.1060	−	25.7497i	0.399163	−	1.01705i	0.979279	−	0.202517i	$-0.0649121\pi$
$642$		0			0
$643$	1.14630	−	5.02226i	0.0452056	−	0.198059i	−0.947283	−	0.320399i	$-0.896183\pi$
$643$	1.14630	−	5.02226i	0.0452056	−	0.198059i	0.992488	+	0.122341i	$0.0390400\pi$
$644$	−17.0353	−	48.8348i	−0.671286	−	1.92436i
$645$		0			0
$646$	−0.00120868	+	0.0161287i	−4.75548e−5	+	0.000634575i
$647$	−3.75834	+	1.15929i	−0.147756	+	0.0455766i	−0.367751	−	0.929924i	$-0.619872\pi$
$647$	−3.75834	+	1.15929i	−0.147756	+	0.0455766i	0.219995	+	0.975501i	$0.429396\pi$
$648$		0			0
$649$	−11.4061	−	29.0623i	−0.447729	−	1.14080i
$650$	−36.6122	−	17.6315i	−1.43605	−	0.691565i
$651$		0			0
$652$	36.3987	−	17.5287i	1.42548	−	0.686476i
$653$	19.6060	+	18.1917i	0.767242	+	0.711896i	0.963221	−	0.268712i	$-0.0865979\pi$
$653$	19.6060	+	18.1917i	0.767242	+	0.711896i	−0.195979	+	0.980608i	$0.562788\pi$
$654$		0			0
$655$	−21.2501	−	36.8062i	−0.830309	−	1.43814i
$656$	−1.33483	+	2.31199i	−0.0521162	+	0.0902679i
$657$		0			0
$658$	−13.3278	−	70.8119i	−0.519572	−	2.76053i
$659$	−4.76896	−	5.98008i	−0.185772	−	0.232951i	0.680221	−	0.733007i	$-0.261884\pi$
$659$	−4.76896	−	5.98008i	−0.185772	−	0.232951i	−0.865993	+	0.500057i	$0.833313\pi$
$660$		0			0
$661$	−10.8289	−	7.38300i	−0.421194	−	0.287165i	0.334117	−	0.942532i	$-0.391562\pi$
$661$	−10.8289	−	7.38300i	−0.421194	−	0.287165i	−0.755311	+	0.655366i	$0.772514\pi$
$662$	3.39631	+	2.31557i	0.132002	+	0.0899971i
$663$		0			0
$664$	25.4266	+	31.8839i	0.986742	+	1.23734i
$665$	−0.834187	+	3.10129i	−0.0323484	+	0.120263i
$666$		0			0
$667$	−25.7401	+	44.5832i	−0.996662	+	1.72627i
$668$	−29.0540	−	50.3230i	−1.12413	−	1.94706i
$669$		0			0
$670$	85.3973	+	79.2371i	3.29919	+	3.06120i
$671$	16.8760	−	8.12705i	0.651491	−	0.313741i
$672$		0			0
$673$	−25.0566	−	12.0666i	−0.965860	−	0.465133i	−0.116641	−	0.993174i	$-0.537213\pi$
$673$	−25.0566	−	12.0666i	−0.965860	−	0.465133i	−0.849219	+	0.528041i	$0.822927\pi$
$674$	13.6767	+	34.8476i	0.526805	+	1.34228i
$675$		0			0
$676$	−25.6792	+	7.92100i	−0.987663	+	0.304654i
$677$	−2.35709	+	31.4531i	−0.0905902	+	1.20884i	0.747857	+	0.663860i	$0.231083\pi$
$677$	−2.35709	+	31.4531i	−0.0905902	+	1.20884i	−0.838447	+	0.544983i	$0.816536\pi$
$678$		0			0
$679$	−27.8131	+	17.4388i	−1.06737	+	0.669241i
$680$	0.0440132	−	0.192834i	0.00168783	−	0.00739486i
$681$		0			0
$682$	17.7657	−	45.2662i	0.680283	−	1.73333i
$683$	11.3199	−	10.5034i	0.433145	−	0.401900i	−0.433238	−	0.901279i	$-0.642629\pi$
$683$	11.3199	−	10.5034i	0.433145	−	0.401900i	0.866383	+	0.499380i	$0.166439\pi$
$684$		0			0
$685$	2.93991			0.112328
$686$	−27.1441	−	31.7267i	−1.03637	−	1.21133i
$687$		0			0
$688$	1.26991	−	0.865807i	0.0484147	−	0.0330086i
$689$	11.6827	−	10.8400i	0.445075	−	0.412969i
$690$		0			0
$691$	−39.9794	−	12.3320i	−1.52089	−	0.469132i	−0.581951	−	0.813224i	$-0.697711\pi$
$691$	−39.9794	−	12.3320i	−1.52089	−	0.469132i	−0.938936	+	0.344092i	$0.888187\pi$
$692$	2.79184	−	12.2318i	0.106130	−	0.464985i
$693$		0			0
$694$	6.28097	+	27.5187i	0.238422	+	1.04460i
$695$	2.12458	−	28.3505i	0.0805899	−	1.07540i
$696$		0			0
$697$	−0.00659344	−	0.0879834i	−0.000249744	−	0.00333261i
$698$	−20.5956	−	52.4767i	−0.779555	−	1.98627i
$699$		0			0
$700$	28.4703	−	65.0839i	1.07608	−	2.45994i
$701$	2.04769	−	0.986118i	0.0773403	−	0.0372451i	−0.394814	−	0.918761i	$-0.629191\pi$
$701$	2.04769	−	0.986118i	0.0773403	−	0.0372451i	0.472154	+	0.881516i	$0.343477\pi$
$702$		0			0
$703$	0.689627	+	0.103945i	0.0260098	+	0.00392034i
$704$	−31.2743	−	54.1688i	−1.17870	−	2.04156i
$705$		0			0
$706$	−1.36462	+	1.71118i	−0.0513583	+	0.0644013i
$707$	2.30124	−	8.55541i	0.0865469	−	0.321759i
$708$		0			0
$709$	8.31306	−	1.25299i	0.312203	−	0.0470571i	0.00892831	−	0.999960i	$-0.497158\pi$
$709$	8.31306	−	1.25299i	0.312203	−	0.0470571i	0.303275	+	0.952903i	$0.401920\pi$
$710$	−17.8434	−	12.1655i	−0.669653	−	0.456561i
$711$		0			0
$712$	−2.49945	+	0.376731i	−0.0936707	+	0.0141186i
$713$	17.7896	+	22.3074i	0.666224	+	0.835418i
$714$		0			0
$715$	22.9024	−	28.7187i	0.856502	−	1.07402i
$716$	−18.9782	+	32.8712i	−0.709250	+	1.22846i
$717$		0			0
$718$	7.30587	+	1.10118i	0.272653	+	0.0410958i
$719$	−38.1020	−	35.3535i	−1.42097	−	1.31846i	−0.877959	−	0.478735i	$-0.841095\pi$
$719$	−38.1020	−	35.3535i	−1.42097	−	1.31846i	−0.543007	−	0.839728i	$-0.682714\pi$
$720$		0			0
$721$	−22.3318	+	5.96079i	−0.831681	+	0.221991i
$722$	38.3751	+	18.4805i	1.42817	+	0.687772i
$723$		0			0
$724$	3.32269	+	44.3383i	0.123487	+	1.64782i
$725$	−67.5668	+	20.8416i	−2.50937	+	0.774037i
$726$		0			0
$727$	−8.60693	−	37.7094i	−0.319213	−	1.39857i	−0.838936	−	0.544230i	$-0.816822\pi$
$727$	−8.60693	−	37.7094i	−0.319213	−	1.39857i	0.519722	−	0.854335i	$-0.326035\pi$
$728$	4.40223	+	12.6198i	0.163158	+	0.467720i
$729$		0			0
$730$	−31.9385	−	9.85171i	−1.18210	−	0.364628i
$731$	−0.0185578	+	0.0472845i	−0.000686385	+	0.00174888i
$732$		0			0
$733$	38.2750	−	26.0955i	1.41372	−	0.963858i	0.415185	−	0.909737i	$-0.363717\pi$
$733$	38.2750	−	26.0955i	1.41372	−	0.963858i	0.998534	−	0.0541209i	$-0.0172356\pi$
$734$	14.6049			0.539077
$735$		0			0
$736$	40.4253			1.49010
$737$	−55.2747	+	37.6857i	−2.03607	+	1.38817i
$738$		0			0
$739$	8.10333	−	20.6469i	0.298086	−	0.759510i	−0.700847	−	0.713312i	$-0.747194\pi$
$739$	8.10333	−	20.6469i	0.298086	−	0.759510i	0.998932	−	0.0461979i	$-0.0147105\pi$
$740$	−23.2040	−	7.15748i	−0.852995	−	0.263114i
$741$		0			0
$742$	32.4499	+	32.5123i	1.19127	+	1.19357i
$743$	6.87248	+	30.1103i	0.252127	+	1.10464i	0.929448	+	0.368953i	$0.120284\pi$
$743$	6.87248	+	30.1103i	0.252127	+	1.10464i	−0.677321	+	0.735687i	$0.736859\pi$
$744$		0			0
$745$	−32.0413	+	9.88344i	−1.17390	+	0.362101i
$746$	−0.604922	−	8.07213i	−0.0221478	−	0.295542i
$747$		0			0
$748$	0.291369	+	0.140316i	0.0106535	+	0.00513046i
$749$	16.4618	+	31.2199i	0.601501	+	1.14075i
$750$		0			0
$751$	−22.8660	−	21.2166i	−0.834393	−	0.774203i	0.142078	−	0.989856i	$-0.454622\pi$
$751$	−22.8660	−	21.2166i	−0.834393	−	0.774203i	−0.976470	+	0.215652i	$0.930812\pi$
$752$	7.90944	+	1.19216i	0.288428	+	0.0434735i
$753$		0			0
$754$	18.9384	−	32.8023i	0.689696	−	1.19459i
$755$	11.9967	−	15.0434i	0.436605	−	0.547485i
$756$		0			0
$757$	28.4382	+	35.6604i	1.03361	+	1.29610i	0.954171	+	0.299260i	$0.0967399\pi$
$757$	28.4382	+	35.6604i	1.03361	+	1.29610i	0.0794343	+	0.996840i	$0.474689\pi$
$758$	38.0451	−	5.73438i	1.38186	−	0.208282i
$759$		0			0
$760$	2.44819	+	1.66915i	0.0888052	+	0.0605464i
$761$	21.2366	−	3.20090i	0.769826	−	0.116033i	0.247626	−	0.968856i	$-0.420350\pi$
$761$	21.2366	−	3.20090i	0.769826	−	0.116033i	0.522200	+	0.852823i	$0.325111\pi$
$762$		0			0
$763$	1.15780	+	1.57192i	0.0419151	+	0.0569074i
$764$	−17.3807	+	21.7947i	−0.628811	+	0.788505i
$765$		0			0
$766$	−38.4942	−	66.6739i	−1.39085	−	2.40902i
$767$	−13.3274	−	2.00878i	−0.481225	−	0.0725330i
$768$		0			0
$769$	−31.4834	+	15.1616i	−1.13532	+	0.546742i	−0.904593	−	0.426276i	$-0.859825\pi$
$769$	−31.4834	+	15.1616i	−1.13532	+	0.546742i	−0.230728	+	0.973018i	$0.574111\pi$
$770$	85.1255	+	62.9521i	3.06771	+	2.26863i
$771$		0			0
$772$	19.4594	+	49.5818i	0.700360	+	1.78449i
$773$	−1.74196	−	23.2449i	−0.0626541	−	0.836061i	−0.936681	−	0.350183i	$-0.886119\pi$
$773$	−1.74196	−	23.2449i	−0.0626541	−	0.836061i	0.874027	−	0.485877i	$-0.161500\pi$
$774$		0			0
$775$	−2.92860	+	39.0794i	−0.105198	+	1.40377i
$776$	6.73977	+	29.5288i	0.241943	+	1.06002i
$777$		0			0
$778$	6.37861	−	27.9465i	0.228684	−	1.00193i
$779$	1.26301	+	0.389588i	0.0452522	+	0.0139585i
$780$		0			0
$781$	9.09117	−	8.43537i	0.325308	−	0.301841i
$782$	−0.258495	+	0.176239i	−0.00924375	+	0.00630228i
$783$		0			0
$784$	4.31790	−	1.68507i	0.154211	−	0.0601812i
$785$	−31.2276			−1.11456
$786$		0			0
$787$	9.44322	−	8.76203i	0.336615	−	0.312333i	−0.493695	−	0.869635i	$-0.664354\pi$
$787$	9.44322	−	8.76203i	0.336615	−	0.312333i	0.830310	+	0.557302i	$0.188164\pi$
$788$	13.1013	−	33.3815i	0.466714	−	1.18917i
$789$		0			0
$790$	−16.7432	+	73.3567i	−0.595696	+	2.60991i
$791$	−15.0234	+	23.8586i	−0.534170	+	0.848314i
$792$		0			0
$793$	0.604282	−	8.06358i	0.0214587	−	0.286346i
$794$	16.3256	−	5.03577i	0.579373	−	0.178713i
$795$		0			0
$796$	4.35799	+	11.1040i	0.154465	+	0.393570i
$797$	−42.3029	−	20.3720i	−1.49845	−	0.721614i	−0.508239	−	0.861216i	$-0.669703\pi$
$797$	−42.3029	−	20.3720i	−1.49845	−	0.721614i	−0.990208	+	0.139602i	$0.955418\pi$
$798$		0			0
$799$	−0.238175	+	0.114699i	−0.00842602	+	0.00405776i
$800$	40.7021	+	37.7660i	1.43904	+	1.33523i
$801$		0			0
$802$	26.8603	+	46.5234i	0.948471	+	1.64280i
$803$	9.59692	−	16.6224i	0.338668	−	0.586590i
$804$		0			0
$805$	−56.9621	+	24.7871i	−2.00765	+	0.873631i
$806$	−13.0887	−	16.4127i	−0.461031	−	0.578114i
$807$		0			0
$808$	−6.75373	−	4.60461i	−0.237595	−	0.161990i
$809$	−45.6160	−	31.1005i	−1.60377	−	1.09343i	−0.937644	−	0.347596i	$-0.886998\pi$
$809$	−45.6160	−	31.1005i	−1.60377	−	1.09343i	−0.666128	−	0.745837i	$-0.732050\pi$
$810$		0			0
$811$	18.1788	+	22.7955i	0.638345	+	0.800460i	0.990795	−	0.135371i	$-0.0432226\pi$
$811$	18.1788	+	22.7955i	0.638345	+	0.800460i	−0.352450	+	0.935831i	$0.614651\pi$
$812$	58.5111	+	30.9961i	2.05334	+	1.08775i
$813$		0			0
$814$	11.4958	−	19.9114i	0.402929	−	0.697893i
$815$	−24.2618	−	42.0226i	−0.849853	−	1.47199i
$816$		0			0
$817$	−0.557816	−	0.517577i	−0.0195155	−	0.0181077i
$818$	−42.6121	+	20.5209i	−1.48990	+	0.717496i
$819$		0			0
$820$	−41.4630	−	19.9675i	−1.44795	−	0.697296i
$821$	−12.4326	−	31.6778i	−0.433901	−	1.10556i	−0.965923	−	0.258831i	$-0.916663\pi$
$821$	−12.4326	−	31.6778i	−0.433901	−	1.10556i	0.532021	−	0.846731i	$-0.321433\pi$
$822$		0			0
$823$	31.1541	−	9.60978i	1.08597	−	0.334976i	0.300437	−	0.953802i	$-0.402868\pi$
$823$	31.1541	−	9.60978i	1.08597	−	0.334976i	0.785528	+	0.618826i	$0.212391\pi$
$824$	−1.59365	+	21.2658i	−0.0555175	+	0.740829i
$825$		0			0
$826$	4.38665	−	38.5989i	0.152631	−	1.34303i
$827$	7.44942	−	32.6380i	0.259042	−	1.13494i	−0.663237	−	0.748410i	$-0.730818\pi$
$827$	7.44942	−	32.6380i	0.259042	−	1.13494i	0.922278	−	0.386526i	$-0.126325\pi$
$828$		0			0
$829$	−17.1832	+	43.7820i	−0.596796	+	1.52061i	0.238688	+	0.971096i	$0.423283\pi$
$829$	−17.1832	+	43.7820i	−0.596796	+	1.52061i	−0.835484	+	0.549515i	$0.814813\pi$
$830$	102.230	−	94.8559i	3.54847	−	3.29250i
$831$		0			0
$832$	−27.0024			−0.936141
$833$	−0.0865356	+	0.126401i	−0.00299828	+	0.00437955i
$834$		0			0
$835$	−57.6658	+	39.3159i	−1.99561	+	1.36058i
$836$	−3.55137	+	3.29519i	−0.122827	+	0.113967i
$837$		0			0
$838$	3.40834	+	1.05133i	0.117739	+	0.0363177i
$839$	−6.39676	+	28.0260i	−0.220841	+	0.967566i	0.736006	+	0.676974i	$0.236709\pi$
$839$	−6.39676	+	28.0260i	−0.220841	+	0.967566i	−0.956847	+	0.290592i	$0.906148\pi$
$840$		0			0
$841$	−8.21239	−	35.9808i	−0.283186	−	1.24072i
$842$	−1.64922	+	22.0073i	−0.0568359	+	0.758423i
$843$		0			0
$844$	2.21853	+	29.6042i	0.0763648	+	1.01902i
$845$	11.7922	+	30.0459i	0.405663	+	1.03361i
$846$		0			0
$847$	−24.0449	+	20.6521i	−0.826191	+	0.709613i
$848$	−4.59425	+	2.21247i	−0.157767	+	0.0759766i
$849$		0			0
$850$	−0.424910	−	0.0640449i	−0.0145743	−	0.00219672i
$851$	6.74517	+	11.6830i	0.231221	+	0.400487i
$852$		0			0
$853$	−3.36142	+	4.21509i	−0.115093	+	0.144322i	−0.836041	−	0.548668i	$-0.815135\pi$
$853$	−3.36142	+	4.21509i	−0.115093	+	0.144322i	0.720948	+	0.692989i	$0.243707\pi$
$854$	23.2896	+	0.893867i	0.796954	+	0.0305875i
$855$		0			0
$856$	32.1997	−	4.85333i	1.10056	−	0.165883i
$857$	6.95967	+	4.74502i	0.237738	+	0.162087i	0.676329	−	0.736600i	$-0.263570\pi$
$857$	6.95967	+	4.74502i	0.237738	+	0.162087i	−0.438591	+	0.898687i	$0.644522\pi$
$858$		0			0
$859$	50.0709	−	7.54697i	1.70840	−	0.257499i	0.779118	−	0.626878i	$-0.215667\pi$
$859$	50.0709	−	7.54697i	1.70840	−	0.257499i	0.929279	+	0.369378i	$0.120429\pi$
$860$	16.5193	+	20.7145i	0.563304	+	0.706360i
$861$		0			0
$862$	1.86796	−	2.34235i	0.0636230	−	0.0797807i
$863$	−9.66331	+	16.7373i	−0.328943	+	0.569746i	−0.982302	−	0.187302i	$-0.940026\pi$
$863$	−9.66331	+	16.7373i	−0.328943	+	0.569746i	0.653359	+	0.757048i	$0.273359\pi$
$864$		0			0
$865$	−14.9011	−	2.24598i	−0.506652	−	0.0763656i
$866$	56.9767	+	52.8667i	1.93615	+	1.79648i
$867$		0			0
$868$	27.8392	−	23.9110i	0.944925	−	0.811594i
$869$	−38.9304	−	18.7479i	−1.32062	−	0.635978i
$870$		0			0
$871$	2.15825	+	28.7998i	0.0731294	+	0.975844i
$872$	1.72122	−	0.530927i	0.0582880	−	0.0179795i
$873$		0			0
$874$	−1.04291	−	4.56927i	−0.0352768	−	0.154558i
$875$	−34.2912	−	12.0360i	−1.15925	−	0.406892i
$876$		0			0
$877$	27.3755	+	8.44423i	0.924406	+	0.285141i	0.720184	−	0.693783i	$-0.244057\pi$
$877$	27.3755	+	8.44423i	0.924406	+	0.285141i	0.204222	+	0.978925i	$0.434534\pi$
$878$	−30.1408	+	76.7975i	−1.01720	+	2.59179i
$879$		0			0
$880$	−9.71077	+	6.62069i	−0.327350	+	0.223183i
$881$	−25.9123			−0.873007			−0.436504	−	0.899702i	$-0.643783\pi$
$881$	−25.9123			−0.873007			−0.436504	+	0.899702i	$0.643783\pi$
$882$		0			0
$883$	1.13404			0.0381634			0.0190817	−	0.999818i	$-0.493926\pi$
$883$	1.13404			0.0381634			0.0190817	+	0.999818i	$0.493926\pi$
$884$	0.115352	−	0.0786454i	0.00387969	−	0.00264513i
$885$		0			0
$886$	30.7488	−	78.3466i	1.03303	−	2.63211i
$887$	−1.42431	−	0.439342i	−0.0478238	−	0.0147517i	0.270751	−	0.962649i	$-0.412728\pi$
$887$	−1.42431	−	0.439342i	−0.0478238	−	0.0147517i	−0.318575	+	0.947898i	$0.603204\pi$
$888$		0			0
$889$	1.12741	−	9.92025i	0.0378120	−	0.332714i
$890$	1.92344	+	8.42716i	0.0644740	+	0.282479i
$891$		0			0
$892$	51.0148	−	15.7360i	1.70810	−	0.526880i
$893$	−0.295944	−	3.94910i	−0.00990339	−	0.132152i
$894$		0			0
$895$	41.0745	+	19.7804i	1.37297	+	0.661187i
$896$	−1.60642	−	44.0666i	−0.0536666	−	1.47216i
$897$		0			0
$898$	−51.6073	−	47.8846i	−1.72216	−	1.59793i
$899$	−36.1196	−	5.44415i	−1.20466	−	0.181573i
$900$		0			0
$901$	0.0842629	−	0.145948i	0.00280720	−	0.00486222i
$902$	27.1677	−	34.0672i	0.904585	−	1.13431i
$903$		0			0
$904$	16.2190	+	20.3380i	0.539436	+	0.676431i
$905$	52.8072	−	7.95941i	1.75537	−	0.264580i
$906$		0			0
$907$	−13.8695	−	9.45604i	−0.460528	−	0.313983i	0.310738	−	0.950496i	$-0.399424\pi$
$907$	−13.8695	−	9.45604i	−0.460528	−	0.313983i	−0.771266	+	0.636513i	$0.780376\pi$
$908$	−22.0741	+	3.32713i	−0.732554	+	0.110415i
$909$		0			0
$910$	41.9100	−	18.2372i	1.38930	−	0.604557i
$911$	−15.4696	+	19.3983i	−0.512532	+	0.642694i	−0.969005	−	0.247043i	$-0.920541\pi$
$911$	−15.4696	+	19.3983i	−0.512532	+	0.642694i	0.456473	+	0.889737i	$0.349113\pi$
$912$		0			0
$913$	40.0430	+	69.3566i	1.32523	+	2.29537i
$914$	88.3329	+	13.3140i	2.92179	+	0.440389i
$915$		0			0
$916$	−19.8172	+	9.54344i	−0.654777	+	0.315324i
$917$	29.8337	+	5.67456i	0.985195	+	0.187391i
$918$		0			0
$919$	−14.6453	−	37.3155i	−0.483102	−	1.23092i	−0.939929	−	0.341369i	$-0.889109\pi$
$919$	−14.6453	−	37.3155i	−0.483102	−	1.23092i	0.456827	−	0.889555i	$-0.348986\pi$
$920$	4.28318	+	57.1550i	0.141212	+	1.88435i
$921$		0			0
$922$	0.665494	−	8.88039i	0.0219169	−	0.292460i
$923$	−1.19135	−	5.21966i	−0.0392139	−	0.171807i
$924$		0			0
$925$	−4.12309	+	18.0644i	−0.135566	+	0.593955i
$926$	22.4295	+	6.91858i	0.737079	+	0.227359i
$927$		0			0
$928$	−37.9379	+	35.2012i	−1.24537	+	1.15554i
$929$	−13.9818	+	9.53263i	−0.458728	+	0.312755i	−0.770544	−	0.637387i	$-0.780015\pi$
$929$	−13.9818	+	9.53263i	−0.458728	+	0.312755i	0.311816	+	0.950143i	$0.399063\pi$
$930$		0			0
$931$	−1.28906	−	1.89854i	−0.0422472	−	0.0622220i
$932$	7.88715			0.258352
$933$		0			0
$934$	−17.9962	+	16.6980i	−0.588854	+	0.546376i
$935$	0.141909	−	0.361577i	0.00464091	−	0.0118248i
$936$		0			0
$937$	4.44506	−	19.4751i	0.145214	−	0.636223i	−0.848962	−	0.528454i	$-0.822772\pi$
$937$	4.44506	−	19.4751i	0.145214	−	0.636223i	0.994176	−	0.107769i	$-0.0343708\pi$
$938$	−82.7277	+	9.24061i	−2.70115	+	0.301717i
$939$		0			0
$940$	−10.3042	+	137.500i	−0.336087	+	4.48477i
$941$	−6.99865	+	2.15880i	−0.228150	+	0.0703748i	−0.406722	−	0.913552i	$-0.633328\pi$
$941$	−6.99865	+	2.15880i	−0.228150	+	0.0703748i	0.178573	+	0.983927i	$0.442852\pi$
$942$		0			0
$943$	9.34058	+	23.7994i	0.304171	+	0.775015i
$944$	3.88535	+	1.87109i	0.126457	+	0.0608987i
$945$		0			0
$946$	−22.6019	+	10.8845i	−0.734850	+	0.353885i
$947$	−5.76559	−	5.34968i	−0.187356	−	0.173841i	0.580918	−	0.813962i	$-0.302694\pi$
$947$	−5.76559	−	5.34968i	−0.187356	−	0.173841i	−0.768274	+	0.640121i	$0.778884\pi$
$948$		0			0
$949$	−4.14302	−	7.17591i	−0.134488	−	0.232940i
$950$	3.21864	−	5.57486i	0.104427	−	0.180872i
$951$		0			0
$952$	0.0838174	+	0.113797i	0.00271654	+	0.00368820i
$953$	6.56406	+	8.23107i	0.212631	+	0.266631i	0.876697	−	0.481043i	$-0.159742\pi$
$953$	6.56406	+	8.23107i	0.212631	+	0.266631i	−0.664066	+	0.747674i	$0.731171\pi$
$954$		0			0
$955$	27.6643	+	18.8612i	0.895196	+	0.610335i
$956$	42.6698	+	29.0918i	1.38004	+	0.940895i
$957$		0			0
$958$	39.9240	+	50.0631i	1.28988	+	1.61746i
$959$	−1.37180	+	1.59097i	−0.0442978	+	0.0513749i
$960$		0			0
$961$	5.37755	−	9.31418i	0.173469	−	0.300457i
$962$	−4.96278	−	8.59579i	−0.160007	−	0.277139i
$963$		0			0
$964$	−21.3566	−	19.8160i	−0.687848	−	0.638230i
$965$	57.6392	−	27.7576i	1.85547	−	0.893548i
$966$		0			0
$967$	−22.2317	−	10.7062i	−0.714923	−	0.344289i	0.0408117	−	0.999167i	$-0.487006\pi$
$967$	−22.2317	−	10.7062i	−0.714923	−	0.344289i	−0.755734	+	0.654878i	$0.772720\pi$
$968$	10.6841	+	27.2226i	0.343399	+	0.874967i
$969$		0			0
$970$	98.9747	−	30.5297i	3.17789	−	0.980248i
$971$	−2.13556	+	28.4971i	−0.0685335	+	0.914516i	0.851922	+	0.523669i	$0.175437\pi$
$971$	−2.13556	+	28.4971i	−0.0685335	+	0.914516i	−0.920456	+	0.390847i	$0.872182\pi$
$972$		0			0
$973$	14.3509	+	14.3785i	0.460068	+	0.460954i
$974$	−2.16851	+	9.50085i	−0.0694834	+	0.304427i
$975$		0			0
$976$	−0.945233	+	2.40841i	−0.0302562	+	0.0770915i
$977$	−41.6795	+	38.6729i	−1.33345	+	1.23726i	−0.383996	+	0.923335i	$0.625452\pi$
$977$	−41.6795	+	38.6729i	−1.33345	+	1.23726i	−0.949449	+	0.313921i	$0.898357\pi$
$978$		0			0
$979$	−4.96387			−0.158646
$980$	34.5291	+	72.0547i	1.10299	+	2.30170i
$981$		0			0
$982$	−49.3313	+	33.6335i	−1.57423	+	1.07329i
$983$	−36.4530	+	33.8234i	−1.16267	+	1.07880i	−0.166989	+	0.985959i	$0.553404\pi$
$983$	−36.4530	+	33.8234i	−1.16267	+	1.07880i	−0.995681	+	0.0928411i	$0.970405\pi$
$984$		0			0
$985$	−41.1582	−	12.6956i	−1.31141	−	0.404516i
$986$	0.0891256	−	0.390485i	0.00283834	−	0.0124356i
$987$		0			0
$988$	0.465390	+	2.03901i	0.0148060	+	0.0648694i
$989$	1.09997	−	14.6781i	0.0349771	−	0.466737i
$990$		0			0
$991$	−2.06319	−	27.5313i	−0.0655392	−	0.874560i	−0.928985	−	0.370118i	$-0.879317\pi$
$991$	−2.06319	−	27.5313i	−0.0655392	−	0.874560i	0.863445	−	0.504442i	$-0.168302\pi$
$992$	10.4793	+	26.7008i	0.332718	+	0.847751i
$993$		0			0
$994$	14.9095	−	3.97962i	0.472900	−	0.126226i
$995$	12.9084	−	6.21638i	0.409225	−	0.197073i
$996$		0			0
$997$	−26.9115	−	4.05625i	−0.852295	−	0.128463i	−0.291656	−	0.956523i	$-0.594206\pi$
$997$	−26.9115	−	4.05625i	−0.852295	−	0.128463i	−0.560639	+	0.828060i	$0.689444\pi$
$998$	−15.1652	−	26.2669i	−0.480047	−	0.831465i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.37.5		60
3.2	odd	2		147.2.m.b.37.1	yes	60
49.4	even	21	inner	441.2.bb.e.298.5		60
147.2	odd	42		7203.2.a.n.1.3		30
147.47	even	42		7203.2.a.m.1.3		30
147.53	odd	42		147.2.m.b.4.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.4.1	✓	60	147.53	odd	42
147.2.m.b.37.1	yes	60	3.2	odd	2
441.2.bb.e.37.5		60	1.1	even	1	trivial
441.2.bb.e.298.5		60	49.4	even	21	inner
7203.2.a.m.1.3		30	147.47	even	42
7203.2.a.n.1.3		30	147.2	odd	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86275 - 1.27000i) q^{2} +(1.12626 - 2.86965i) q^{4} +(-3.53817 - 1.09138i) q^{5} +(2.24157 - 1.40547i) q^{7} +(-0.543186 - 2.37985i) q^{8} +O(q^{10})\)	\(q+(1.86275 - 1.27000i) q^{2} +(1.12626 - 2.86965i) q^{4} +(-3.53817 - 1.09138i) q^{5} +(2.24157 - 1.40547i) q^{7} +(-0.543186 - 2.37985i) q^{8} +(-7.97679 + 2.46051i) q^{10} +(-0.358238 - 4.78035i) q^{11} +(-1.86453 - 0.897913i) q^{13} +(2.39055 - 5.46485i) q^{14} +(0.485391 + 0.450377i) q^{16} +(-0.0216392 - 0.00326158i) q^{17} +(0.163914 - 0.283908i) q^{19} +(-7.11677 + 8.92414i) q^{20} +(-6.73837 - 8.44965i) q^{22} +(6.27046 - 0.945120i) q^{23} +(7.19635 + 4.90639i) q^{25} +(-4.61352 + 0.695376i) q^{26} +(-1.50862 - 8.01545i) q^{28} +(-5.06165 + 6.34711i) q^{29} +(2.24972 + 3.89662i) q^{31} +(6.30373 + 0.950134i) q^{32} +(-0.0444507 + 0.0214063i) q^{34} +(-9.46498 + 2.52638i) q^{35} +(0.777219 + 1.98032i) q^{37} +(-0.0552322 - 0.737022i) q^{38} +(-0.675442 + 9.01315i) q^{40} +(0.897157 + 3.93070i) q^{41} +(0.516511 - 2.26298i) q^{43} +(-14.1214 - 4.35588i) q^{44} +(10.4800 - 9.72403i) q^{46} +(9.98096 - 6.80491i) q^{47} +(3.04931 - 6.30093i) q^{49} +19.6361 q^{50} +(-4.67664 + 4.33929i) q^{52} +(-2.81349 + 7.16866i) q^{53} +(-3.94968 + 17.3047i) q^{55} +(-4.56240 - 4.57119i) q^{56} +(-1.36775 + 18.2514i) q^{58} +(6.22339 - 1.91966i) q^{59} +(1.42752 + 3.63726i) q^{61} +(9.13939 + 4.40130i) q^{62} +(11.7558 - 5.66129i) q^{64} +(5.61708 + 5.21189i) q^{65} +(-6.97774 - 12.0858i) q^{67} +(-0.0337309 + 0.0584236i) q^{68} +(-14.4224 + 16.7266i) q^{70} +(1.61301 + 2.02266i) q^{71} +(3.30820 + 2.25549i) q^{73} +(3.96278 + 2.70178i) q^{74} +(-0.630108 - 0.790130i) q^{76} +(-7.52166 - 10.2120i) q^{77} +(4.50685 - 7.80609i) q^{79} +(-1.22586 - 2.12326i) q^{80} +(6.66318 + 6.18253i) q^{82} +(-15.0519 + 7.24860i) q^{83} +(0.0730035 + 0.0351566i) q^{85} +(-1.91186 - 4.87135i) q^{86} +(-11.1820 + 3.44918i) q^{88} +(0.0773820 - 1.03259i) q^{89} +(-5.44148 + 0.607809i) q^{91} +(4.34998 - 19.0585i) q^{92} +(9.94981 - 25.3517i) q^{94} +(-0.889809 + 0.825622i) q^{95} -12.4078 q^{97} +(-2.32208 - 15.6097i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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