LMFDB - Embedded newform 675.2.r.a.46.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.19
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.727367 + 0.807823i) q^{2} +(0.0855417 - 0.813875i) q^{4} +(-0.934297 + 2.03152i) q^{5} +(1.73969 - 3.01324i) q^{7} +(2.47854 - 1.80077i) q^{8} +O(q^{10})$	\(q+(0.727367 + 0.807823i) q^{2} +(0.0855417 - 0.813875i) q^{4} +(-0.934297 + 2.03152i) q^{5} +(1.73969 - 3.01324i) q^{7} +(2.47854 - 1.80077i) q^{8} +(-2.32069 + 0.722917i) q^{10} +(-2.35402 - 2.61440i) q^{11} +(1.45133 - 1.61187i) q^{13} +(3.69956 - 0.786365i) q^{14} +(1.65656 + 0.352114i) q^{16} +(1.54674 - 1.12377i) q^{17} +(-0.970198 + 0.704890i) q^{19} +(1.57349 + 0.934181i) q^{20} +(0.399739 - 3.80326i) q^{22} +(1.96627 - 0.417944i) q^{23} +(-3.25418 - 3.79609i) q^{25} +2.35776 q^{26} +(-2.30358 - 1.67365i) q^{28} +(3.26898 - 1.45544i) q^{29} +(5.79773 + 2.58132i) q^{31} +(-2.14316 - 3.71207i) q^{32} +(2.03286 + 0.432098i) q^{34} +(4.49607 + 6.34948i) q^{35} +(2.46324 + 7.58107i) q^{37} +(-1.27512 - 0.271034i) q^{38} +(1.34261 + 6.71767i) q^{40} +(-1.73464 + 1.92652i) q^{41} +(5.34941 - 9.26545i) q^{43} +(-2.32917 + 1.69224i) q^{44} +(1.76783 + 1.28440i) q^{46} +(-11.9942 + 5.34016i) q^{47} +(-2.55306 - 4.42203i) q^{49} +(0.699589 - 5.38996i) q^{50} +(-1.18771 - 1.31909i) q^{52} +(11.2674 + 8.18624i) q^{53} +(7.51058 - 2.33962i) q^{55} +(-1.11423 - 10.6012i) q^{56} +(3.55349 + 1.58212i) q^{58} +(3.64544 - 4.04867i) q^{59} +(0.353232 + 0.392304i) q^{61} +(2.13183 + 6.56111i) q^{62} +(2.48651 - 7.65270i) q^{64} +(1.91857 + 4.45438i) q^{65} +(-9.83507 - 4.37885i) q^{67} +(-0.782301 - 1.35499i) q^{68} +(-1.85897 + 8.25044i) q^{70} +(-6.38098 - 4.63605i) q^{71} +(-2.75054 + 8.46529i) q^{73} +(-4.33248 + 7.50408i) q^{74} +(0.490700 + 0.849917i) q^{76} +(-11.9731 + 2.54496i) q^{77} +(6.17366 - 2.74869i) q^{79} +(-2.26305 + 3.03637i) q^{80} -2.81801 q^{82} +(-0.372037 - 3.53969i) q^{83} +(0.837858 + 4.19218i) q^{85} +(11.3758 - 2.41801i) q^{86} +(-10.5425 - 2.24087i) q^{88} +(-2.71707 + 8.36227i) q^{89} +(-2.33207 - 7.17736i) q^{91} +(-0.171956 - 1.63605i) q^{92} +(-13.0381 - 5.80493i) q^{94} +(-0.525548 - 2.62956i) q^{95} +(-15.6914 + 6.98627i) q^{97} +(1.71520 - 5.27886i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.727367	+	0.807823i	0.514326	+	0.571217i	0.943233	−	0.332131i	$-0.107768\pi$
$2$	0.727367	+	0.807823i	0.514326	+	0.571217i	−0.428907	+	0.903349i	$0.641101\pi$
$3$		0			0
$3$		0			0
$4$	0.0855417	−	0.813875i	0.0427709	−	0.406938i
$5$	−0.934297	+	2.03152i	−0.417830	+	0.908525i
$5$	−0.934297	+	2.03152i	−0.417830	+	0.908525i
$6$		0			0
$7$	1.73969	−	3.01324i	0.657542	−	1.13890i	−0.323708	−	0.946157i	$-0.604930\pi$
$7$	1.73969	−	3.01324i	0.657542	−	1.13890i	0.981250	−	0.192739i	$-0.0617370\pi$
$8$	2.47854	−	1.80077i	0.876298	−	0.636668i
$9$		0			0
$10$	−2.32069	+	0.722917i	−0.733866	+	0.228607i
$11$	−2.35402	−	2.61440i	−0.709764	−	0.788272i	0.275135	−	0.961406i	$-0.411278\pi$
$11$	−2.35402	−	2.61440i	−0.709764	−	0.788272i	−0.984898	+	0.173133i	$0.944611\pi$
$12$		0			0
$13$	1.45133	−	1.61187i	0.402527	−	0.447052i	−0.507468	−	0.861671i	$-0.669418\pi$
$13$	1.45133	−	1.61187i	0.402527	−	0.447052i	0.909995	+	0.414619i	$0.136085\pi$
$14$	3.69956	−	0.786365i	0.988748	−	0.210165i
$15$		0			0
$16$	1.65656	+	0.352114i	0.414141	+	0.0880284i
$17$	1.54674	−	1.12377i	0.375140	−	0.272555i	−0.384199	−	0.923250i	$-0.625522\pi$
$17$	1.54674	−	1.12377i	0.375140	−	0.272555i	0.759339	+	0.650695i	$0.225522\pi$
$18$		0			0
$19$	−0.970198	+	0.704890i	−0.222579	+	0.161713i	−0.693487	−	0.720469i	$-0.743926\pi$
$19$	−0.970198	+	0.704890i	−0.222579	+	0.161713i	0.470908	+	0.882182i	$0.343926\pi$
$20$	1.57349	+	0.934181i	0.351842	+	0.208889i
$21$		0			0
$22$	0.399739	−	3.80326i	0.0852247	−	0.810859i
$23$	1.96627	−	0.417944i	0.409996	−	0.0871474i	0.00170377	−	0.999999i	$-0.499458\pi$
$23$	1.96627	−	0.417944i	0.409996	−	0.0871474i	0.408293	+	0.912851i	$0.366124\pi$
$24$		0			0
$25$	−3.25418	−	3.79609i	−0.650836	−	0.759219i
$26$	2.35776			0.462394
$27$		0			0
$28$	−2.30358	−	1.67365i	−0.435336	−	0.316290i
$29$	3.26898	−	1.45544i	0.607035	−	0.270269i	−0.0801144	−	0.996786i	$-0.525529\pi$
$29$	3.26898	−	1.45544i	0.607035	−	0.270269i	0.687149	+	0.726516i	$0.258862\pi$
$30$		0			0
$31$	5.79773	+	2.58132i	1.04130	+	0.463618i	0.854866	−	0.518849i	$-0.173639\pi$
$31$	5.79773	+	2.58132i	1.04130	+	0.463618i	0.186437	+	0.982467i	$0.440306\pi$
$32$	−2.14316	−	3.71207i	−0.378862	−	0.656207i
$33$		0			0
$34$	2.03286	+	0.432098i	0.348633	+	0.0741042i
$35$	4.49607	+	6.34948i	0.759975	+	1.07326i
$36$		0			0
$37$	2.46324	+	7.58107i	0.404954	+	1.24632i	0.920934	+	0.389719i	$0.127428\pi$
$37$	2.46324	+	7.58107i	0.404954	+	1.24632i	−0.515980	+	0.856601i	$0.672572\pi$
$38$	−1.27512	−	0.271034i	−0.206851	−	0.0439676i
$39$		0			0
$40$	1.34261	+	6.71767i	0.212285	+	1.06216i
$41$	−1.73464	+	1.92652i	−0.270906	+	0.300871i	−0.863212	−	0.504842i	$-0.831551\pi$
$41$	−1.73464	+	1.92652i	−0.270906	+	0.300871i	0.592306	+	0.805713i	$0.298218\pi$
$42$		0			0
$43$	5.34941	−	9.26545i	0.815778	−	1.41297i	−0.0929908	−	0.995667i	$-0.529643\pi$
$43$	5.34941	−	9.26545i	0.815778	−	1.41297i	0.908768	−	0.417301i	$-0.137024\pi$
$44$	−2.32917	+	1.69224i	−0.351135	+	0.255114i
$45$		0			0
$46$	1.76783	+	1.28440i	0.260652	+	0.189375i
$47$	−11.9942	+	5.34016i	−1.74953	+	0.778942i	−0.757518	+	0.652814i	$0.773588\pi$
$47$	−11.9942	+	5.34016i	−1.74953	+	0.778942i	−0.992014	+	0.126128i	$0.959745\pi$
$48$		0			0
$49$	−2.55306	−	4.42203i	−0.364723	−	0.631718i
$50$	0.699589	−	5.38996i	0.0989369	−	0.762255i
$51$		0			0
$52$	−1.18771	−	1.31909i	−0.164706	−	0.182924i
$53$	11.2674	+	8.18624i	1.54770	+	1.12447i	0.945269	+	0.326293i	$0.105800\pi$
$53$	11.2674	+	8.18624i	1.54770	+	1.12447i	0.602427	+	0.798174i	$0.294200\pi$
$54$		0			0
$55$	7.51058	−	2.33962i	1.01273	−	0.315474i
$56$	−1.11423	−	10.6012i	−0.148896	−	1.41665i
$57$		0			0
$58$	3.55349	+	1.58212i	0.466597	+	0.207742i
$59$	3.64544	−	4.04867i	0.474596	−	0.527092i	−0.457545	−	0.889186i	$-0.651271\pi$
$59$	3.64544	−	4.04867i	0.474596	−	0.527092i	0.932142	+	0.362094i	$0.117938\pi$
$60$		0			0
$61$	0.353232	+	0.392304i	0.0452268	+	0.0502294i	0.765334	−	0.643634i	$-0.222574\pi$
$61$	0.353232	+	0.392304i	0.0452268	+	0.0502294i	−0.720107	+	0.693863i	$0.755907\pi$
$62$	2.13183	+	6.56111i	0.270743	+	0.833262i
$63$		0			0
$64$	2.48651	−	7.65270i	0.310814	−	0.956588i
$65$	1.91857	+	4.45438i	0.237970	+	0.552498i
$66$		0			0
$67$	−9.83507	−	4.37885i	−1.20154	−	0.534962i	−0.294360	−	0.955695i	$-0.595106\pi$
$67$	−9.83507	−	4.37885i	−1.20154	−	0.534962i	−0.907185	+	0.420732i	$0.861773\pi$
$68$	−0.782301	−	1.35499i	−0.0948680	−	0.164316i
$69$		0			0
$70$	−1.85897	+	8.25044i	−0.222189	+	0.986116i
$71$	−6.38098	−	4.63605i	−0.757283	−	0.550198i	0.140793	−	0.990039i	$-0.455035\pi$
$71$	−6.38098	−	4.63605i	−0.757283	−	0.550198i	−0.898076	+	0.439841i	$0.855035\pi$
$72$		0			0
$73$	−2.75054	+	8.46529i	−0.321926	+	0.990787i	0.650883	+	0.759178i	$0.274399\pi$
$73$	−2.75054	+	8.46529i	−0.321926	+	0.990787i	−0.972809	+	0.231609i	$0.925601\pi$
$74$	−4.33248	+	7.50408i	−0.503641	+	0.872332i
$75$		0			0
$76$	0.490700	+	0.849917i	0.0562871	+	0.0974922i
$77$	−11.9731	+	2.54496i	−1.36446	+	0.290025i
$78$		0			0
$79$	6.17366	−	2.74869i	0.694591	−	0.309252i	−0.0289032	−	0.999582i	$-0.509201\pi$
$79$	6.17366	−	2.74869i	0.694591	−	0.309252i	0.723494	+	0.690330i	$0.242535\pi$
$80$	−2.26305	+	3.03637i	−0.253017	+	0.339477i
$81$		0			0
$82$	−2.81801			−0.311197
$83$	−0.372037	−	3.53969i	−0.0408363	−	0.388532i	−0.995782	−	0.0917511i	$-0.970754\pi$
$83$	−0.372037	−	3.53969i	−0.0408363	−	0.388532i	0.954946	−	0.296781i	$-0.0959131\pi$
$84$		0			0
$85$	0.837858	+	4.19218i	0.0908784	+	0.454706i
$86$	11.3758	−	2.41801i	1.22669	−	0.260741i
$87$		0			0
$88$	−10.5425	−	2.24087i	−1.12383	−	0.238878i
$89$	−2.71707	+	8.36227i	−0.288008	+	0.886399i	0.697472	+	0.716612i	$0.254308\pi$
$89$	−2.71707	+	8.36227i	−0.288008	+	0.886399i	−0.985481	+	0.169787i	$0.945692\pi$
$90$		0			0
$91$	−2.33207	−	7.17736i	−0.244467	−	0.752392i
$92$	−0.171956	−	1.63605i	−0.0179277	−	0.170570i
$93$		0			0
$94$	−13.0381	−	5.80493i	−1.34478	−	0.598733i
$95$	−0.525548	−	2.62956i	−0.0539201	−	0.269787i
$96$		0			0
$97$	−15.6914	+	6.98627i	−1.59322	+	0.709348i	−0.995712	−	0.0925124i	$-0.970510\pi$
$97$	−15.6914	+	6.98627i	−1.59322	+	0.709348i	−0.597511	+	0.801861i	$0.703844\pi$
$98$	1.71520	−	5.27886i	0.173262	−	0.533245i
$99$		0			0
$100$	−3.36791	+	2.32377i	−0.336791	+	0.232377i
$101$	−4.67773	+	8.10206i	−0.465451	+	0.806185i	−0.999222	−	0.0394441i	$-0.987441\pi$
$101$	−4.67773	+	8.10206i	−0.465451	+	0.806185i	0.533770	+	0.845629i	$0.320775\pi$
$102$		0			0
$103$	−0.837734	+	7.97051i	−0.0825444	+	0.785358i	0.872444	+	0.488714i	$0.162534\pi$
$103$	−0.837734	+	7.97051i	−0.0825444	+	0.785358i	−0.954988	+	0.296643i	$0.904133\pi$
$104$	0.694592	−	6.60860i	0.0681104	−	0.648027i
$105$		0			0
$106$	1.58250	+	15.0565i	0.153706	+	1.46241i
$107$	−5.04642			−0.487855			−0.243928	−	0.969793i	$-0.578436\pi$
$107$	−5.04642			−0.487855			−0.243928	+	0.969793i	$0.578436\pi$
$108$		0			0
$109$	−1.49707	−	4.60752i	−0.143394	−	0.441320i	0.853407	−	0.521245i	$-0.174532\pi$
$109$	−1.49707	−	4.60752i	−0.143394	−	0.441320i	−0.996801	+	0.0799245i	$0.974532\pi$
$110$	7.35295	+	4.36546i	0.701076	+	0.416230i
$111$		0			0
$112$	3.94291	−	4.37905i	0.372570	−	0.413781i
$113$	−1.47427	+	1.63734i	−0.138688	+	0.154028i	−0.808487	−	0.588514i	$-0.799713\pi$
$113$	−1.47427	+	1.63734i	−0.138688	+	0.154028i	0.669800	+	0.742542i	$0.266380\pi$
$114$		0			0
$115$	−0.988019	+	4.38501i	−0.0921333	+	0.408905i
$116$	−0.904916	−	2.78505i	−0.0840193	−	0.258585i
$117$		0			0
$118$	5.92219			0.545182
$119$	−0.695340	−	6.61572i	−0.0637418	−	0.606462i
$120$		0			0
$121$	−0.143885	+	1.36898i	−0.0130805	+	0.124453i
$122$	−0.0599828	+	0.570699i	−0.00543059	+	0.0516686i
$123$		0			0
$124$	2.59682	−	4.49782i	0.233201	−	0.403916i
$125$	10.7522	−	3.06426i	0.961708	−	0.274076i
$126$		0			0
$127$	−5.91345	+	18.1997i	−0.524734	+	1.61497i	0.240106	+	0.970747i	$0.422818\pi$
$127$	−5.91345	+	18.1997i	−0.524734	+	1.61497i	−0.764841	+	0.644219i	$0.777182\pi$
$128$	0.159129	−	0.0708488i	0.0140652	−	0.00626221i
$129$		0			0
$130$	−2.20285	+	4.78984i	−0.193202	+	0.420097i
$131$	7.04977	+	3.13876i	0.615941	+	0.274235i	0.690898	−	0.722952i	$-0.257215\pi$
$131$	7.04977	+	3.13876i	0.615941	+	0.274235i	−0.0749569	+	0.997187i	$0.523882\pi$
$132$		0			0
$133$	0.436154	+	4.14972i	0.0378193	+	0.359827i
$134$	−3.61637	−	11.1300i	−0.312407	−	0.961488i
$135$		0			0
$136$	1.81001	−	5.57065i	0.155207	−	0.477679i
$137$	6.13544	+	1.30413i	0.524186	+	0.111419i	0.462402	−	0.886670i	$-0.346988\pi$
$137$	6.13544	+	1.30413i	0.524186	+	0.111419i	0.0617840	+	0.998090i	$0.480321\pi$
$138$		0			0
$139$	19.9459	−	4.23963i	1.69179	−	0.359601i	0.741496	−	0.670958i	$-0.234117\pi$
$139$	19.9459	−	4.23963i	1.69179	−	0.359601i	0.950293	+	0.311357i	$0.100783\pi$
$140$	5.55229	−	3.11609i	0.469254	−	0.263358i
$141$		0			0
$142$	−0.896205	−	8.52682i	−0.0752078	−	0.715555i
$143$	−7.63054			−0.638098
$144$		0			0
$145$	−0.0974297	+	8.00083i	−0.00809110	+	0.664433i
$146$	−8.83911	+	3.93543i	−0.731530	+	0.325698i
$147$		0			0
$148$	6.38075	−	1.35627i	0.524495	−	0.111485i
$149$	3.52387	+	6.10353i	0.288687	+	0.500021i	0.973497	−	0.228701i	$-0.0734480\pi$
$149$	3.52387	+	6.10353i	0.288687	+	0.500021i	−0.684810	+	0.728722i	$0.740115\pi$
$150$		0			0
$151$	0.0155849	−	0.0269939i	0.00126828	−	0.00219673i	−0.865391	−	0.501098i	$-0.832930\pi$
$151$	0.0155849	−	0.0269939i	0.00126828	−	0.00219673i	0.866659	+	0.498901i	$0.166263\pi$
$152$	−1.13533	+	3.49420i	−0.0920878	+	0.283417i
$153$		0			0
$154$	−10.7647	−	7.82102i	−0.867445	−	0.630236i
$155$	−10.6608	+	9.36651i	−0.856297	+	0.752337i
$156$		0			0
$157$	−0.694083	−	1.20219i	−0.0553938	−	0.0959450i	0.836999	−	0.547205i	$-0.184308\pi$
$157$	−0.694083	−	1.20219i	−0.0553938	−	0.0959450i	−0.892393	+	0.451260i	$0.850975\pi$
$158$	6.71098	+	2.98792i	0.533897	+	0.237706i
$159$		0			0
$160$	9.54351	−	0.885714i	0.754481	−	0.0700219i
$161$	2.16135	−	6.65194i	0.170338	−	0.524246i
$162$		0			0
$163$	0.385069	+	1.18512i	0.0301609	+	0.0928258i	0.965004	−	0.262236i	$-0.0844598\pi$
$163$	0.385069	+	1.18512i	0.0301609	+	0.0928258i	−0.934843	+	0.355062i	$0.884460\pi$
$164$	1.41956	+	1.57658i	0.110849	+	0.123110i
$165$		0			0
$166$	2.58884	−	2.87520i	0.200933	−	0.223159i
$167$	−0.203316	−	0.0905220i	−0.0157330	−	0.00700480i	0.398855	−	0.917014i	$-0.369408\pi$
$167$	−0.203316	−	0.0905220i	−0.0157330	−	0.00700480i	−0.414588	+	0.910009i	$0.636074\pi$
$168$		0			0
$169$	0.867117	+	8.25007i	0.0667013	+	0.634621i
$170$	−2.77711	+	3.72610i	−0.212995	+	0.285779i
$171$		0			0
$172$	−7.08332	−	5.14634i	−0.540098	−	0.392404i
$173$	−12.7920	−	14.2070i	−0.972561	−	1.08014i	−0.996760	−	0.0804313i	$-0.974370\pi$
$173$	−12.7920	−	14.2070i	−0.972561	−	1.08014i	0.0241991	−	0.999707i	$-0.492296\pi$
$174$		0			0
$175$	−17.0998	+	3.20157i	−1.29262	+	0.242016i
$176$	−2.97902	−	5.15981i	−0.224552	−	0.388935i
$177$		0			0
$178$	−8.73154	+	3.88753i	−0.654457	+	0.291383i
$179$	−15.4208	−	11.2038i	−1.15260	−	0.837415i	−0.163778	−	0.986497i	$-0.552368\pi$
$179$	−15.4208	−	11.2038i	−1.15260	−	0.837415i	−0.988825	+	0.149082i	$0.952368\pi$
$180$		0			0
$181$	9.13951	−	6.64024i	0.679335	−	0.493565i	−0.193802	−	0.981041i	$-0.562082\pi$
$181$	9.13951	−	6.64024i	0.679335	−	0.493565i	0.873137	+	0.487475i	$0.162082\pi$
$182$	4.10177	−	7.10448i	0.304044	−	0.526619i
$183$		0			0
$184$	4.12088	−	4.57670i	0.303795	−	0.337398i
$185$	−17.7025	−	2.07884i	−1.30152	−	0.152840i
$186$		0			0
$187$	−6.57906	−	1.39842i	−0.481109	−	0.102263i
$188$	3.32022	+	10.2186i	0.242152	+	0.745266i
$189$		0			0
$190$	1.74195	−	2.33720i	0.126374	−	0.169559i
$191$	−2.20315	−	0.468294i	−0.159414	−	0.0338845i	0.127513	−	0.991837i	$-0.459301\pi$
$191$	−2.20315	−	0.468294i	−0.159414	−	0.0338845i	−0.286927	+	0.957952i	$0.592634\pi$
$192$		0			0
$193$	7.89562	+	13.6756i	0.568339	+	0.984393i	0.996730	+	0.0807992i	$0.0257472\pi$
$193$	7.89562	+	13.6756i	0.568339	+	0.984393i	−0.428391	+	0.903593i	$0.640919\pi$
$194$	−17.0571	−	7.59431i	−1.22463	−	0.545240i
$195$		0			0
$196$	−3.81737	+	1.69960i	−0.272669	+	0.121400i
$197$	−17.3982	−	12.6405i	−1.23957	−	0.900601i	−0.242001	−	0.970276i	$-0.577804\pi$
$197$	−17.3982	−	12.6405i	−1.23957	−	0.900601i	−0.997570	+	0.0696750i	$0.977804\pi$
$198$		0			0
$199$	−17.1687			−1.21706			−0.608530	−	0.793531i	$-0.708240\pi$
$199$	−17.1687			−1.21706			−0.608530	+	0.793531i	$0.708240\pi$
$200$	−14.9015	−	3.54877i	−1.05370	−	0.250936i
$201$		0			0
$202$	−9.94746	+	2.11440i	−0.699901	+	0.148769i
$203$	1.30143	−	12.3822i	0.0913422	−	0.869063i
$204$		0			0
$205$	−2.29309	−	5.32391i	−0.160157	−	0.371838i
$206$	−7.04810	+	5.12075i	−0.491065	+	0.356779i
$207$		0			0
$208$	2.97179	−	2.15913i	0.206056	−	0.149709i
$209$	4.12673	+	0.877164i	0.285452	+	0.0606747i
$210$		0			0
$211$	13.3645	−	2.84072i	0.920053	−	0.195563i	0.276544	−	0.961001i	$-0.410811\pi$
$211$	13.3645	−	2.84072i	0.920053	−	0.195563i	0.643510	+	0.765438i	$0.277478\pi$
$212$	7.62641	−	8.46999i	0.523784	−	0.581721i
$213$		0			0
$214$	−3.67060	−	4.07661i	−0.250917	−	0.278672i
$215$	13.8250	+	19.5241i	0.942860	+	1.33154i
$216$		0			0
$217$	17.8644	−	12.9792i	1.21271	−	0.881088i
$218$	2.63314	−	4.56073i	0.178339	−	0.308892i
$219$		0			0
$220$	−1.26169	−	6.31281i	−0.0850631	−	0.425609i
$221$	0.433462	−	4.12412i	0.0291578	−	0.277418i
$222$		0			0
$223$	14.6520	+	16.2727i	0.981169	+	1.08970i	0.995959	+	0.0898080i	$0.0286253\pi$
$223$	14.6520	+	16.2727i	0.981169	+	1.08970i	−0.0147900	+	0.999891i	$0.504708\pi$
$224$	−14.9138			−0.996469
$225$		0			0
$226$	−2.39502			−0.159314
$227$	17.3202	+	19.2360i	1.14958	+	1.27674i	0.955248	+	0.295806i	$0.0955880\pi$
$227$	17.3202	+	19.2360i	1.14958	+	1.27674i	0.194334	+	0.980935i	$0.437745\pi$
$228$		0			0
$229$	−2.40196	+	22.8532i	−0.158726	+	1.51018i	0.567872	+	0.823117i	$0.307767\pi$
$229$	−2.40196	+	22.8532i	−0.158726	+	1.51018i	−0.726598	+	0.687063i	$0.758900\pi$
$230$	−4.26097	+	2.39137i	−0.280960	+	0.157682i
$231$		0			0
$232$	5.48140	−	9.49406i	0.359872	−	0.623316i
$233$	7.19284	−	5.22590i	0.471219	−	0.342360i	−0.326697	−	0.945129i	$-0.605936\pi$
$233$	7.19284	−	5.22590i	0.471219	−	0.342360i	0.797916	+	0.602769i	$0.205936\pi$
$234$		0			0
$235$	0.357478	−	29.3558i	0.0233193	−	1.91496i
$236$	−2.98328	−	3.31327i	−0.194195	−	0.215675i
$237$		0			0
$238$	4.83857	−	5.37377i	0.313638	−	0.348330i
$239$	−5.06749	+	1.07713i	−0.327788	+	0.0696736i	−0.368867	−	0.929482i	$-0.620254\pi$
$239$	−5.06749	+	1.07713i	−0.327788	+	0.0696736i	0.0410781	+	0.999156i	$0.486921\pi$
$240$		0			0
$241$	6.41203	+	1.36292i	0.413035	+	0.0877933i	0.409742	−	0.912201i	$-0.365619\pi$
$241$	6.41203	+	1.36292i	0.413035	+	0.0877933i	0.00329255	+	0.999995i	$0.498952\pi$
$242$	−1.21055	+	0.879516i	−0.0778171	+	0.0565374i
$243$		0			0
$244$	0.349503	−	0.253929i	0.0223746	−	0.0162561i
$245$	11.3688	−	1.05511i	0.726324	−	0.0674087i
$246$		0			0
$247$	−0.271890	+	2.58686i	−0.0173000	+	0.164598i
$248$	19.0183	−	4.04246i	1.20766	−	0.256697i
$249$		0			0
$250$	10.2962	+	6.45705i	0.651189	+	0.408380i
$251$	7.14839			0.451202			0.225601	−	0.974220i	$-0.427565\pi$
$251$	7.14839			0.451202			0.225601	+	0.974220i	$0.427565\pi$
$252$		0			0
$253$	−5.72132	−	4.15678i	−0.359696	−	0.261335i
$254$	−19.0034	+	8.46087i	−1.19238	+	0.530882i
$255$		0			0
$256$	−14.5288	−	6.46862i	−0.908048	−	0.404289i
$257$	−2.06283	−	3.57292i	−0.128676	−	0.222873i	0.794488	−	0.607280i	$-0.207739\pi$
$257$	−2.06283	−	3.57292i	−0.128676	−	0.222873i	−0.923164	+	0.384407i	$0.874406\pi$
$258$		0			0
$259$	27.1288	+	5.76641i	1.68570	+	0.358307i
$260$	3.78943	−	1.18044i	0.235010	−	0.0732080i
$261$		0			0
$262$	2.59221	+	7.97800i	0.160147	+	0.492883i
$263$	17.2609	+	3.66892i	1.06435	+	0.226235i	0.706623	−	0.707590i	$-0.250218\pi$
$263$	17.2609	+	3.66892i	1.06435	+	0.226235i	0.357730	+	0.933825i	$0.383551\pi$
$264$		0			0
$265$	−27.1576	+	15.2416i	−1.66828	+	0.936284i
$266$	−3.03500	+	3.37071i	−0.186088	+	0.206671i
$267$		0			0
$268$	−4.40515	+	7.62994i	−0.269087	+	0.466073i
$269$	21.6298	−	15.7150i	1.31879	−	0.958158i	0.318845	−	0.947807i	$-0.396705\pi$
$269$	21.6298	−	15.7150i	1.31879	−	0.958158i	0.999946	−	0.0103508i	$-0.00329481\pi$
$270$		0			0
$271$	17.6749	+	12.8416i	1.07367	+	0.780069i	0.976569	−	0.215205i	$-0.0690419\pi$
$271$	17.6749	+	12.8416i	1.07367	+	0.780069i	0.0971044	+	0.995274i	$0.469042\pi$
$272$	2.95798	−	1.31698i	0.179354	−	0.0798534i
$273$		0			0
$274$	3.40921	+	5.90493i	0.205958	+	0.356730i
$275$	−2.26412	+	17.4438i	−0.136532	+	1.05190i
$276$		0			0
$277$	−9.51723	−	10.5700i	−0.571835	−	0.635087i	0.385968	−	0.922512i	$-0.373867\pi$
$277$	−9.51723	−	10.5700i	−0.571835	−	0.635087i	−0.957803	+	0.287425i	$0.907201\pi$
$278$	17.9329	+	13.0290i	1.07554	+	0.781427i
$279$		0			0
$280$	22.5777	+	7.64110i	1.34927	+	0.456643i
$281$	−0.750893	−	7.14427i	−0.0447945	−	0.426192i	−0.993821	−	0.110995i	$-0.964596\pi$
$281$	−0.750893	−	7.14427i	−0.0447945	−	0.426192i	0.949026	−	0.315197i	$-0.102070\pi$
$282$		0			0
$283$	12.3369	+	5.49275i	0.733353	+	0.326510i	0.739212	−	0.673473i	$-0.235198\pi$
$283$	12.3369	+	5.49275i	0.733353	+	0.326510i	−0.00585864	+	0.999983i	$0.501865\pi$
$284$	−4.31901	+	4.79675i	−0.256286	+	0.284635i
$285$		0			0
$286$	−5.55021	−	6.16413i	−0.328191	−	0.364493i
$287$	2.78730	+	8.57843i	0.164529	+	0.506369i
$288$		0			0
$289$	−4.12374	+	12.6916i	−0.242573	+	0.746564i
$290$	−6.53413	+	5.74084i	−0.383697	+	0.337114i
$291$		0			0
$292$	6.65441	+	2.96273i	0.389420	+	0.173381i
$293$	0.157560	+	0.272902i	0.00920475	+	0.0159431i	0.870591	−	0.492007i	$-0.163737\pi$
$293$	0.157560	+	0.272902i	0.00920475	+	0.0159431i	−0.861386	+	0.507950i	$0.830403\pi$
$294$		0			0
$295$	4.81905	+	11.1885i	0.280576	+	0.651418i
$296$	19.7570	+	14.3543i	1.14835	+	0.834327i
$297$		0			0
$298$	−2.36742	+	7.28617i	−0.137141	+	0.422077i
$299$	2.18005	−	3.77595i	0.126075	−	0.218369i
$300$		0			0
$301$	−18.6127	−	32.2381i	−1.07282	−	1.85817i
$302$	0.0331423	−	0.00704461i	0.00190712	−	0.000405372i
$303$		0			0
$304$	−1.85540	+	0.826076i	−0.106414	+	0.0473787i
$305$	−1.12700	+	0.351071i	−0.0645318	+	0.0201023i
$306$		0			0
$307$	−8.35636			−0.476923			−0.238461	−	0.971152i	$-0.576643\pi$
$307$	−8.35636			−0.476923			−0.238461	+	0.971152i	$0.576643\pi$
$308$	1.04708	+	9.96230i	0.0596629	+	0.567655i
$309$		0			0
$310$	−15.3208	−	1.79915i	−0.870164	−	0.102185i
$311$	19.9820	−	4.24731i	1.13308	−	0.240843i	0.397050	−	0.917797i	$-0.370034\pi$
$311$	19.9820	−	4.24731i	1.13308	−	0.240843i	0.736025	+	0.676954i	$0.236701\pi$
$312$		0			0
$313$	−15.4110	−	3.27572i	−0.871083	−	0.185154i	−0.249378	−	0.968406i	$-0.580226\pi$
$313$	−15.4110	−	3.27572i	−0.871083	−	0.185154i	−0.621705	+	0.783252i	$0.713560\pi$
$314$	0.466301	−	1.43513i	0.0263149	−	0.0809889i
$315$		0			0
$316$	−1.70899	−	5.25972i	−0.0961380	−	0.295882i
$317$	1.33731	+	12.7236i	0.0751108	+	0.714631i	0.965671	+	0.259767i	$0.0836456\pi$
$317$	1.33731	+	12.7236i	0.0751108	+	0.714631i	−0.890561	+	0.454865i	$0.849688\pi$
$318$		0			0
$319$	−11.5004	−	5.12029i	−0.643897	−	0.286681i
$320$	13.2235	+	12.2013i	0.739217	+	0.682074i
$321$		0			0
$322$	6.94568	−	3.09242i	0.387068	−	0.172334i
$323$	−0.708509	+	2.18057i	−0.0394225	+	0.121330i
$324$		0			0
$325$	−10.8417	−	0.264088i	−0.601389	−	0.0146489i
$326$	−0.677282	+	1.17309i	−0.0375112	+	0.0649712i
$327$		0			0
$328$	−0.830181	+	7.89865i	−0.0458391	+	0.436130i
$329$	−4.77505	+	45.4315i	−0.263257	+	2.50472i
$330$		0			0
$331$	−2.62711	−	24.9953i	−0.144399	−	1.37386i	−0.791364	−	0.611345i	$-0.790629\pi$
$331$	−2.62711	−	24.9953i	−0.144399	−	1.37386i	0.646965	−	0.762519i	$-0.276038\pi$
$332$	−2.91269			−0.159855
$333$		0			0
$334$	−0.0747594	−	0.230086i	−0.00409065	−	0.0125897i
$335$	18.0846	−	15.8890i	0.988068	−	0.868110i
$336$		0			0
$337$	12.6373	−	14.0351i	0.688396	−	0.764541i	−0.293088	−	0.956085i	$-0.594683\pi$
$337$	12.6373	−	14.0351i	0.688396	−	0.764541i	0.981484	+	0.191545i	$0.0613497\pi$
$338$	−6.03388	+	6.70131i	−0.328200	+	0.364503i
$339$		0			0
$340$	3.48359	−	0.323305i	0.188924	−	0.0175337i
$341$	−6.89937	−	21.2341i	−0.373622	−	1.14989i
$342$		0			0
$343$	6.58955			0.355802
$344$	−3.42618	−	32.5979i	−0.184727	−	1.75756i
$345$		0			0
$346$	2.17223	−	20.6674i	0.116780	−	1.11109i
$347$	−2.94999	+	28.0672i	−0.158364	+	1.50673i	0.570061	+	0.821603i	$0.306920\pi$
$347$	−2.94999	+	28.0672i	−0.158364	+	1.50673i	−0.728424	+	0.685126i	$0.759747\pi$
$348$		0			0
$349$	10.1548	−	17.5887i	0.543575	−	0.941500i	−0.455120	−	0.890430i	$-0.650404\pi$
$349$	10.1548	−	17.5887i	0.543575	−	0.941500i	0.998695	−	0.0510695i	$-0.0162630\pi$
$350$	−15.0241	−	11.4849i	−0.803074	−	0.613893i
$351$		0			0
$352$	−4.65980	+	14.3414i	−0.248368	+	0.764398i
$353$	−8.23808	+	3.66783i	−0.438469	+	0.195219i	−0.614085	−	0.789240i	$-0.710475\pi$
$353$	−8.23808	+	3.66783i	−0.438469	+	0.195219i	0.175616	+	0.984459i	$0.443808\pi$
$354$		0			0
$355$	15.3800	−	8.63166i	0.816285	−	0.458121i
$356$	6.57342	+	2.92668i	0.348391	+	0.155113i
$357$		0			0
$358$	−2.16584	−	20.6066i	−0.114468	−	1.08909i
$359$	−2.84427	−	8.75376i	−0.150115	−	0.462006i	0.847518	−	0.530766i	$-0.178096\pi$
$359$	−2.84427	−	8.75376i	−0.150115	−	0.462006i	−0.997633	+	0.0687601i	$0.978096\pi$
$360$		0			0
$361$	−5.42691	+	16.7023i	−0.285627	+	0.879069i
$362$	12.0119	+	2.55321i	0.631333	+	0.134194i
$363$		0			0
$364$	−6.04097	+	1.28405i	−0.316633	+	0.0673024i
$365$	−14.6276	−	13.4969i	−0.765645	−	0.706459i
$366$		0			0
$367$	1.99047	+	18.9381i	0.103902	+	0.988558i	0.914947	+	0.403575i	$0.132232\pi$
$367$	1.99047	+	18.9381i	0.103902	+	0.988558i	−0.811045	+	0.584984i	$0.801101\pi$
$368$	3.40442			0.177468
$369$		0			0
$370$	−11.1969	−	15.8126i	−0.582099	−	0.822057i
$371$	44.2689	−	19.7098i	2.29833	−	1.02328i
$372$		0			0
$373$	−4.19359	+	0.891374i	−0.217136	+	0.0461536i	−0.315195	−	0.949027i	$-0.602070\pi$
$373$	−4.19359	+	0.891374i	−0.217136	+	0.0461536i	0.0980592	+	0.995181i	$0.468737\pi$
$374$	−3.65572	−	6.33189i	−0.189033	−	0.327414i
$375$		0			0
$376$	−20.1117	+	34.8346i	−1.03718	+	1.79646i
$377$	2.39840	−	7.38151i	0.123524	−	0.380167i
$378$		0			0
$379$	−7.81297	−	5.67645i	−0.401325	−	0.291580i	0.368755	−	0.929526i	$-0.379784\pi$
$379$	−7.81297	−	5.67645i	−0.401325	−	0.291580i	−0.770081	+	0.637947i	$0.779784\pi$
$380$	−2.18509	+	0.202794i	−0.112093	+	0.0104031i
$381$		0			0
$382$	−1.22420	−	2.12038i	−0.0626355	−	0.108488i
$383$	−8.53168	−	3.79855i	−0.435948	−	0.194097i	0.177015	−	0.984208i	$-0.443356\pi$
$383$	−8.53168	−	3.79855i	−0.435948	−	0.194097i	−0.612963	+	0.790111i	$0.710023\pi$
$384$		0			0
$385$	6.01627	−	26.7014i	0.306618	−	1.36083i
$386$	−5.30447	+	16.3255i	−0.269990	+	0.830944i
$387$		0			0
$388$	4.34368	+	13.3685i	0.220517	+	0.678682i
$389$	17.3886	+	19.3120i	0.881638	+	0.979158i	0.999904	−	0.0138240i	$-0.00440046\pi$
$389$	17.3886	+	19.3120i	0.881638	+	0.979158i	−0.118267	+	0.992982i	$0.537734\pi$
$390$		0			0
$391$	2.57164	−	2.85610i	0.130054	−	0.144439i
$392$	−14.2909	−	6.36272i	−0.721800	−	0.321366i
$393$		0			0
$394$	−2.44357	−	23.2490i	−0.123105	−	1.17127i
$395$	−0.184002	+	15.1100i	−0.00925812	+	0.760268i
$396$		0			0
$397$	10.9374	+	7.94651i	0.548934	+	0.398824i	0.827392	−	0.561624i	$-0.189823\pi$
$397$	10.9374	+	7.94651i	0.548934	+	0.398824i	−0.278458	+	0.960448i	$0.589823\pi$
$398$	−12.4880	−	13.8693i	−0.625966	−	0.695205i
$399$		0			0
$400$	−4.05410	−	7.43431i	−0.202705	−	0.371716i
$401$	−3.70665	−	6.42010i	−0.185101	−	0.320604i	0.758509	−	0.651662i	$-0.225928\pi$
$401$	−3.70665	−	6.42010i	−0.185101	−	0.320604i	−0.943611	+	0.331057i	$0.892595\pi$
$402$		0			0
$403$	12.5752	−	5.59883i	0.626415	−	0.278898i
$404$	6.19393	+	4.50015i	0.308159	+	0.223891i
$405$		0			0
$406$	10.9493	−	7.95511i	0.543403	−	0.394806i
$407$	14.0215	−	24.2859i	0.695018	−	1.20381i
$408$		0			0
$409$	7.17339	−	7.96686i	0.354701	−	0.393936i	−0.539216	−	0.842167i	$-0.681279\pi$
$409$	7.17339	−	7.96686i	0.354701	−	0.393936i	0.893917	+	0.448232i	$0.147946\pi$
$410$	2.63286	−	5.72485i	0.130027	−	0.282730i
$411$		0			0
$412$	6.41534	+	1.36362i	0.316061	+	0.0671809i
$413$	−5.85766	−	18.0280i	−0.288237	−	0.887101i
$414$		0			0
$415$	7.53857	+	2.55132i	0.370054	+	0.125240i
$416$	−9.09382	−	1.93295i	−0.445861	−	0.0947707i
$417$		0			0
$418$	2.29306	+	3.97169i	0.112157	+	0.194262i
$419$	10.9245	+	4.86390i	0.533697	+	0.237617i	0.655846	−	0.754895i	$-0.272312\pi$
$419$	10.9245	+	4.86390i	0.533697	+	0.237617i	−0.122149	+	0.992512i	$0.538979\pi$
$420$		0			0
$421$	−8.07815	+	3.59663i	−0.393705	+	0.175289i	−0.594034	−	0.804440i	$-0.702466\pi$
$421$	−8.07815	+	3.59663i	−0.393705	+	0.175289i	0.200329	+	0.979729i	$0.435799\pi$
$422$	12.0157	+	8.72994i	0.584917	+	0.424967i
$423$		0			0
$424$	42.6683			2.07215
$425$	−9.29933	−	2.21462i	−0.451084	−	0.107425i
$426$		0			0
$427$	1.79662	−	0.381884i	0.0869446	−	0.0184806i
$428$	−0.431679	+	4.10715i	−0.0208660	+	0.198527i
$429$		0			0
$430$	−5.71617	+	25.3694i	−0.275658	+	1.22342i
$431$	2.85794	−	2.07642i	0.137662	−	0.100017i	−0.516823	−	0.856092i	$-0.672885\pi$
$431$	2.85794	−	2.07642i	0.137662	−	0.100017i	0.654485	+	0.756075i	$0.272885\pi$
$432$		0			0
$433$	−2.00164	+	1.45427i	−0.0961924	+	0.0698879i	−0.634842	−	0.772642i	$-0.718935\pi$
$433$	−2.00164	+	1.45427i	−0.0961924	+	0.0698879i	0.538649	+	0.842530i	$0.318935\pi$
$434$	23.4789	+	4.99059i	1.12702	+	0.239556i
$435$		0			0
$436$	−3.87801	+	0.824296i	−0.185723	+	0.0394766i
$437$	−1.61307	+	1.79149i	−0.0771635	+	0.0856988i
$438$		0			0
$439$	−5.56157	−	6.17675i	−0.265439	−	0.294800i	0.595660	−	0.803236i	$-0.296890\pi$
$439$	−5.56157	−	6.17675i	−0.265439	−	0.294800i	−0.861100	+	0.508436i	$0.830224\pi$
$440$	14.4022	−	19.3237i	0.686598	−	0.921219i
$441$		0			0
$442$	3.64685	−	2.64959i	0.173463	−	0.126028i
$443$	−11.6123	+	20.1132i	−0.551719	+	0.955606i	0.446432	+	0.894818i	$0.352695\pi$
$443$	−11.6123	+	20.1132i	−0.551719	+	0.955606i	−0.998151	+	0.0607879i	$0.980639\pi$
$444$		0			0
$445$	−14.4496	−	13.3326i	−0.684977	−	0.632027i
$446$	−2.48807	+	23.6724i	−0.117814	+	1.12092i
$447$		0			0
$448$	−18.7336	−	20.8058i	−0.885081	−	0.982982i
$449$	−18.8212			−0.888227			−0.444114	−	0.895970i	$-0.646481\pi$
$449$	−18.8212			−0.888227			−0.444114	+	0.895970i	$0.646481\pi$
$450$		0			0
$451$	9.12008			0.429448
$452$	1.20648	+	1.33993i	0.0567481	+	0.0630251i
$453$		0			0
$454$	−2.94117	+	27.9833i	−0.138036	+	1.31332i
$455$	16.7598	+	1.96814i	0.785713	+	0.0922678i
$456$		0			0
$457$	−1.31514	+	2.27788i	−0.0615194	+	0.106555i	−0.895145	−	0.445776i	$-0.852928\pi$
$457$	−1.31514	+	2.27788i	−0.0615194	+	0.106555i	0.833625	+	0.552330i	$0.186261\pi$
$458$	−20.2084	+	14.6823i	−0.944278	+	0.686058i
$459$		0			0
$460$	3.48434	+	1.17923i	0.162458	+	0.0549817i
$461$	13.0570	+	14.5013i	0.608126	+	0.675392i	0.966049	−	0.258359i	$-0.0831816\pi$
$461$	13.0570	+	14.5013i	0.608126	+	0.675392i	−0.357923	+	0.933751i	$0.616515\pi$
$462$		0			0
$463$	1.02652	−	1.14007i	0.0477065	−	0.0529834i	−0.718819	−	0.695197i	$-0.755317\pi$
$463$	1.02652	−	1.14007i	0.0477065	−	0.0529834i	0.766526	+	0.642214i	$0.221984\pi$
$464$	5.92776	−	1.25998i	0.275189	−	0.0584933i
$465$		0			0
$466$	9.45344	+	2.00939i	0.437922	+	0.0930833i
$467$	5.25538	−	3.81826i	0.243190	−	0.176688i	−0.459513	−	0.888171i	$-0.651976\pi$
$467$	5.25538	−	3.81826i	0.243190	−	0.176688i	0.702703	+	0.711483i	$0.251976\pi$
$468$		0			0
$469$	−30.3045	+	22.0175i	−1.39933	+	1.01667i
$470$	23.9743	−	21.0637i	1.10585	−	0.971594i
$471$		0			0
$472$	1.74467	−	16.5994i	0.0803049	−	0.764050i
$473$	−36.8163	+	7.82554i	−1.69281	+	0.359819i
$474$		0			0
$475$	5.83302	+	1.38912i	0.267637	+	0.0637373i
$476$	−5.44385			−0.249519
$477$		0			0
$478$	−4.55605	−	3.31017i	−0.208389	−	0.151403i
$479$	−5.00312	+	2.22753i	−0.228598	+	0.101779i	−0.517840	−	0.855478i	$-0.673264\pi$
$479$	−5.00312	+	2.22753i	−0.228598	+	0.101779i	0.289241	+	0.957256i	$0.406597\pi$
$480$		0			0
$481$	15.7947	+	7.03224i	0.720175	+	0.320643i
$482$	3.56290	+	6.17113i	0.162286	+	0.281087i
$483$		0			0
$484$	1.10187	+	0.234209i	0.0500850	+	0.0106459i
$485$	0.467672	−	38.4047i	0.0212359	−	1.74387i
$486$		0			0
$487$	−10.8960	−	33.5344i	−0.493744	−	1.51959i	−0.818905	−	0.573929i	$-0.805419\pi$
$487$	−10.8960	−	33.5344i	−0.493744	−	1.51959i	0.325162	−	0.945658i	$-0.394581\pi$
$488$	1.58195	+	0.336254i	0.0716116	+	0.0152215i
$489$		0			0
$490$	9.12161	+	8.41650i	0.412072	+	0.380219i
$491$	−1.91440	+	2.12616i	−0.0863958	+	0.0959523i	−0.784792	−	0.619759i	$-0.787231\pi$
$491$	−1.91440	+	2.12616i	−0.0863958	+	0.0959523i	0.698397	+	0.715711i	$0.253897\pi$
$492$		0			0
$493$	3.42068	−	5.92480i	0.154060	−	0.266839i
$494$	−2.28749	+	1.66196i	−0.102919	+	0.0747751i
$495$		0			0
$496$	8.69540	+	6.31758i	0.390435	+	0.283668i
$497$	−25.0705	+	11.1621i	−1.12456	+	0.500688i
$498$		0			0
$499$	18.3438	+	31.7725i	0.821183	+	1.42233i	0.904802	+	0.425833i	$0.140019\pi$
$499$	18.3438	+	31.7725i	0.821183	+	1.42233i	−0.0836188	+	0.996498i	$0.526648\pi$
$500$	−1.57416	−	9.01309i	−0.0703987	−	0.403078i
$501$		0			0
$502$	5.19950	+	5.77463i	0.232065	+	0.257734i
$503$	−14.2611	−	10.3613i	−0.635873	−	0.461989i	0.222557	−	0.974920i	$-0.428560\pi$
$503$	−14.2611	−	10.3613i	−0.635873	−	0.461989i	−0.858430	+	0.512931i	$0.828560\pi$
$504$		0			0
$505$	−12.0891	−	17.0726i	−0.537960	−	0.759723i
$506$	−0.803556	−	7.64533i	−0.0357224	−	0.339876i
$507$		0			0
$508$	14.3065	+	6.36965i	0.634747	+	0.282608i
$509$	10.0917	−	11.2080i	0.447306	−	0.496784i	−0.476751	−	0.879038i	$-0.658186\pi$
$509$	10.0917	−	11.2080i	0.447306	−	0.496784i	0.924057	+	0.382255i	$0.124852\pi$
$510$		0			0
$511$	20.7228	+	23.0150i	0.916724	+	1.01812i
$512$	−5.44990	−	16.7731i	−0.240854	−	0.741272i
$513$		0			0
$514$	1.38585	−	4.26522i	0.0611274	−	0.188131i
$515$	−15.4096	−	9.14870i	−0.679028	−	0.403140i
$516$		0			0
$517$	42.1959	+	18.7868i	1.85577	+	0.826243i
$518$	15.0744	+	26.1096i	0.662330	+	1.14719i
$519$		0			0
$520$	12.7766	+	7.58548i	0.560290	+	0.332645i
$521$	−29.3467	−	21.3216i	−1.28570	−	0.934118i	−0.285994	−	0.958231i	$-0.592324\pi$
$521$	−29.3467	−	21.3216i	−1.28570	−	0.934118i	−0.999709	+	0.0241133i	$0.992324\pi$
$522$		0			0
$523$	−2.83321	+	8.71972i	−0.123888	+	0.381287i	−0.993697	−	0.112102i	$-0.964242\pi$
$523$	−2.83321	+	8.71972i	−0.123888	+	0.381287i	0.869809	+	0.493388i	$0.164242\pi$
$524$	3.15761	−	5.46914i	0.137941	−	0.238920i
$525$		0			0
$526$	9.59118	+	16.6124i	0.418195	+	0.724336i
$527$	11.8684	−	2.52271i	0.516996	−	0.109891i
$528$		0			0
$529$	−17.3200	+	7.71136i	−0.753043	+	0.335276i
$530$	−32.0661	−	10.8523i	−1.39286	−	0.471395i
$531$		0			0
$532$	3.41467			0.148045
$533$	0.587747	+	5.59204i	0.0254581	+	0.242218i
$534$		0			0
$535$	4.71485	−	10.2519i	0.203841	−	0.443229i
$536$	−32.2620	+	6.85749i	−1.39350	+	0.296198i
$537$		0			0
$538$	28.4277	+	6.04249i	1.22561	+	0.260510i
$539$	−5.55101	+	17.0843i	−0.239099	+	0.735871i
$540$		0			0
$541$	−4.66886	−	14.3693i	−0.200730	−	0.617784i	−0.999862	−	0.0166277i	$-0.994707\pi$
$541$	−4.66886	−	14.3693i	−0.200730	−	0.617784i	0.799132	−	0.601156i	$-0.205293\pi$
$542$	2.48243	+	23.6187i	0.106629	+	1.01451i
$543$		0			0
$544$	−7.48645	−	3.33318i	−0.320979	−	0.142909i
$545$	10.7590	+	1.26345i	0.460865	+	0.0541202i
$546$		0			0
$547$	−35.3098	+	15.7209i	−1.50974	+	0.672178i	−0.983951	−	0.178439i	$-0.942895\pi$
$547$	−35.3098	+	15.7209i	−1.50974	+	0.672178i	−0.525785	+	0.850617i	$0.676229\pi$
$548$	1.58623	−	4.88193i	0.0677606	−	0.208546i
$549$		0			0
$550$	−15.7384	+	10.8591i	−0.671086	+	0.463032i
$551$	−2.14563	+	3.71634i	−0.0914069	+	0.158321i
$552$		0			0
$553$	2.45782	−	23.3846i	0.104517	−	0.994413i
$554$	1.61613	−	15.3765i	0.0686629	−	0.653284i
$555$		0			0
$556$	−1.74432	−	16.5961i	−0.0739758	−	0.703833i
$557$	16.9105			0.716522			0.358261	−	0.933621i	$-0.383370\pi$
$557$	16.9105			0.716522			0.358261	+	0.933621i	$0.383370\pi$
$558$		0			0
$559$	−7.17092	−	22.0698i	−0.303297	−	0.933453i
$560$	5.21229	+	12.1015i	0.220259	+	0.511380i
$561$		0			0
$562$	5.22514	−	5.80310i	0.220409	−	0.244789i
$563$	15.1527	−	16.8287i	0.638609	−	0.709247i	−0.333770	−	0.942654i	$-0.608321\pi$
$563$	15.1527	−	16.8287i	0.638609	−	0.709247i	0.972379	+	0.233408i	$0.0749877\pi$
$564$		0			0
$565$	−1.94889	−	4.52478i	−0.0819906	−	0.190359i
$566$	4.53630	+	13.9613i	0.190675	+	0.586837i
$567$		0			0
$568$	−24.1640			−1.01390
$569$	−1.87892	−	17.8767i	−0.0787683	−	0.749431i	−0.960613	−	0.277890i	$-0.910365\pi$
$569$	−1.87892	−	17.8767i	−0.0787683	−	0.749431i	0.881844	−	0.471540i	$-0.156302\pi$
$570$		0			0
$571$	1.55774	−	14.8209i	0.0651893	−	0.620235i	−0.912340	−	0.409434i	$-0.865726\pi$
$571$	1.55774	−	14.8209i	0.0651893	−	0.620235i	0.977529	−	0.210801i	$-0.0676071\pi$
$572$	−0.652730	+	6.21031i	−0.0272920	+	0.259666i
$573$		0			0
$574$	−4.90247	+	8.49132i	−0.204625	+	0.354421i
$575$	−7.98516	−	6.10409i	−0.333004	−	0.254558i
$576$		0			0
$577$	−7.48625	+	23.0403i	−0.311657	+	0.959181i	0.665452	+	0.746441i	$0.268239\pi$
$577$	−7.48625	+	23.0403i	−0.311657	+	0.959181i	−0.977109	+	0.212740i	$0.931761\pi$
$578$	−13.2520	+	5.90018i	−0.551212	+	0.245415i
$579$		0			0
$580$	6.50335	+	0.763701i	0.270037	+	0.0317109i
$581$	−11.3132	−	5.03694i	−0.469349	−	0.208968i
$582$		0			0
$583$	−5.12153	−	48.7281i	−0.212112	−	2.01811i
$584$	8.42669	+	25.9347i	0.348699	+	1.07319i
$585$		0			0
$586$	−0.105852	+	0.325780i	−0.00437272	+	0.0134579i
$587$	−9.91962	−	2.10848i	−0.409426	−	0.0870263i	−0.00140582	−	0.999999i	$-0.500447\pi$
$587$	−9.91962	−	2.10848i	−0.409426	−	0.0870263i	−0.408021	+	0.912973i	$0.633781\pi$
$588$		0			0
$589$	−7.44449	+	1.58238i	−0.306745	+	0.0652006i
$590$	−5.53308	+	12.0311i	−0.227793	+	0.495311i
$591$		0			0
$592$	1.41112	+	13.4259i	0.0579965	+	0.551800i
$593$	−28.7337			−1.17995			−0.589975	−	0.807422i	$-0.700862\pi$
$593$	−28.7337			−1.17995			−0.589975	+	0.807422i	$0.700862\pi$
$594$		0			0
$595$	14.0897	+	4.76845i	0.577619	+	0.195487i
$596$	5.26895	−	2.34589i	0.215825	−	0.0960913i
$597$		0			0
$598$	4.63600	−	0.985411i	0.189580	−	0.0402965i
$599$	0.738992	+	1.27997i	0.0301944	+	0.0522982i	0.880728	−	0.473623i	$-0.157054\pi$
$599$	0.738992	+	1.27997i	0.0301944	+	0.0522982i	−0.850533	+	0.525921i	$0.823721\pi$
$600$		0			0
$601$	−9.97465	+	17.2766i	−0.406874	+	0.704727i	−0.994538	−	0.104378i	$-0.966715\pi$
$601$	−9.97465	+	17.2766i	−0.406874	+	0.704727i	0.587663	+	0.809106i	$0.300048\pi$
$602$	12.5044	−	38.4847i	0.509642	−	1.56852i
$603$		0			0
$604$	−0.0206365	−	0.0149933i	−0.000839688	−	0.000610069i
$605$	−2.64668	−	1.57134i	−0.107603	−	0.0638840i
$606$		0			0
$607$	−11.5351	−	19.9793i	−0.468194	−	0.810935i	0.531146	−	0.847281i	$-0.321762\pi$
$607$	−11.5351	−	19.9793i	−0.468194	−	0.810935i	−0.999339	+	0.0363452i	$0.988428\pi$
$608$	4.69589	+	2.09075i	0.190444	+	0.0847910i
$609$		0			0
$610$	−1.10335	−	0.655059i	−0.0446732	−	0.0265225i
$611$	−8.79993	+	27.0834i	−0.356007	+	1.09568i
$612$		0			0
$613$	−7.36834	−	22.6774i	−0.297605	−	0.915932i	−0.982334	−	0.187135i	$-0.940080\pi$
$613$	−7.36834	−	22.6774i	−0.297605	−	0.915932i	0.684730	−	0.728797i	$-0.259920\pi$
$614$	−6.07815	−	6.75047i	−0.245294	−	0.272427i
$615$		0			0
$616$	−25.0929	+	27.8685i	−1.01102	+	1.12286i
$617$	−0.814192	−	0.362502i	−0.0327782	−	0.0145938i	0.390282	−	0.920695i	$-0.372377\pi$
$617$	−0.814192	−	0.362502i	−0.0327782	−	0.0145938i	−0.423060	+	0.906102i	$0.639044\pi$
$618$		0			0
$619$	0.0314900	+	0.299608i	0.00126569	+	0.0120422i	0.995137	−	0.0985054i	$-0.0314062\pi$
$619$	0.0314900	+	0.299608i	0.00126569	+	0.0120422i	−0.993871	+	0.110548i	$0.964740\pi$
$620$	6.71123	+	9.47780i	0.269529	+	0.380638i
$621$		0			0
$622$	17.9653	+	13.0526i	0.720344	+	0.523361i
$623$	20.4706	+	22.7349i	0.820138	+	0.910856i
$624$		0			0
$625$	−3.82065	+	24.7063i	−0.152826	+	0.988253i
$626$	−8.56328	−	14.8320i	−0.342258	−	0.592808i
$627$		0			0
$628$	−1.03780	+	0.462060i	−0.0414129	+	0.0184382i
$629$	12.3294	+	8.95784i	0.491606	+	0.357173i
$630$		0			0
$631$	−11.5670	+	8.40394i	−0.460476	+	0.334556i	−0.793718	−	0.608286i	$-0.791857\pi$
$631$	−11.5670	+	8.40394i	−0.460476	+	0.334556i	0.333242	+	0.942841i	$0.391857\pi$
$632$	10.3519	−	17.9301i	0.411778	−	0.713221i
$633$		0			0
$634$	−9.30574	+	10.3351i	−0.369578	+	0.410458i
$635$	−31.4483	−	29.0173i	−1.24799	−	1.15152i
$636$		0			0
$637$	−10.8331	−	2.30264i	−0.429222	−	0.0912339i
$638$	−4.22870	−	13.0146i	−0.167416	−	0.515253i
$639$		0			0
$640$	−0.00474273	+	0.389468i	−0.000187473	+	0.0153951i
$641$	1.18274	+	0.251398i	0.0467152	+	0.00992963i	0.231210	−	0.972904i	$-0.425732\pi$
$641$	1.18274	+	0.251398i	0.0467152	+	0.00992963i	−0.184495	+	0.982833i	$0.559065\pi$
$642$		0			0
$643$	−12.3127	−	21.3262i	−0.485566	−	0.841025i	0.514297	−	0.857612i	$-0.328053\pi$
$643$	−12.3127	−	21.3262i	−0.485566	−	0.841025i	−0.999862	+	0.0165876i	$0.994720\pi$
$644$	−5.22896	−	2.32808i	−0.206050	−	0.0917394i
$645$		0			0
$646$	−2.27686	+	1.01372i	−0.0895818	+	0.0398844i
$647$	−5.45922	−	3.96635i	−0.214624	−	0.155933i	0.475279	−	0.879835i	$-0.342347\pi$
$647$	−5.45922	−	3.96635i	−0.214624	−	0.155933i	−0.689903	+	0.723901i	$0.742347\pi$
$648$		0			0
$649$	−19.1663			−0.752344
$650$	−7.67256	−	8.95027i	−0.300943	−	0.351058i
$651$		0			0
$652$	0.997480	−	0.212021i	0.0390643	−	0.00830338i
$653$	−0.182163	+	1.73317i	−0.00712860	+	0.0678241i	−0.997508	−	0.0705556i	$-0.977523\pi$
$653$	−0.182163	+	1.73317i	−0.00712860	+	0.0678241i	0.990379	+	0.138380i	$0.0441894\pi$
$654$		0			0
$655$	−12.9630	+	11.3892i	−0.506508	+	0.445015i
$656$	−3.55190	+	2.58061i	−0.138678	+	0.100756i
$657$		0			0
$658$	−40.1739	+	29.1880i	−1.56614	+	1.13787i
$659$	32.0109	+	6.80414i	1.24697	+	0.265051i	0.783685	−	0.621158i	$-0.213338\pi$
$659$	32.0109	+	6.80414i	1.24697	+	0.265051i	0.463284	+	0.886210i	$0.346671\pi$
$660$		0			0
$661$	−43.1830	+	9.17882i	−1.67962	+	0.357015i	−0.946406	−	0.322980i	$-0.895315\pi$
$661$	−43.1830	+	9.17882i	−1.67962	+	0.357015i	−0.733217	+	0.679995i	$0.761982\pi$
$662$	18.2809	−	20.3030i	0.710507	−	0.789098i
$663$		0			0
$664$	−7.29628	−	8.10334i	−0.283150	−	0.314470i
$665$	−8.83776	−	2.99102i	−0.342714	−	0.115987i
$666$		0			0
$667$	5.81942	−	4.22805i	0.225329	−	0.163711i
$668$	−0.0910656	+	0.157730i	−0.00352343	+	0.00610276i
$669$		0			0
$670$	25.9897	+	3.05202i	1.00407	+	0.117910i
$671$	0.194126	−	1.84698i	0.00749415	−	0.0713020i
$672$		0			0
$673$	4.23131	+	4.69934i	0.163105	+	0.181146i	0.819157	−	0.573569i	$-0.194442\pi$
$673$	4.23131	+	4.69934i	0.163105	+	0.181146i	−0.656052	+	0.754715i	$0.727775\pi$
$674$	20.5298			0.790779
$675$		0			0
$676$	6.78870			0.261104
$677$	−33.5415	−	37.2516i	−1.28911	−	1.43170i	−0.844116	−	0.536161i	$-0.819874\pi$
$677$	−33.5415	−	37.2516i	−1.28911	−	1.43170i	−0.444989	−	0.895536i	$-0.646793\pi$
$678$		0			0
$679$	−6.24697	+	59.4359i	−0.239737	+	2.28094i
$680$	9.62582	+	8.88173i	0.369133	+	0.340599i
$681$		0			0
$682$	12.1350	−	21.0185i	0.464674	−	0.804838i
$683$	−15.2867	+	11.1065i	−0.584931	+	0.424977i	−0.840498	−	0.541814i	$-0.817738\pi$
$683$	−15.2867	+	11.1065i	−0.584931	+	0.424977i	0.255568	+	0.966791i	$0.417738\pi$
$684$		0			0
$685$	−8.38169	+	11.2459i	−0.320248	+	0.429682i
$686$	4.79302	+	5.32319i	0.182999	+	0.203240i
$687$		0			0
$688$	12.1241	−	13.4652i	0.462228	−	0.513357i
$689$	29.5479	−	6.28060i	1.12569	−	0.239272i
$690$		0			0
$691$	−27.3183	−	5.80669i	−1.03924	−	0.220897i	−0.343470	−	0.939163i	$-0.611603\pi$
$691$	−27.3183	−	5.80669i	−1.03924	−	0.220897i	−0.695768	+	0.718266i	$0.744936\pi$
$692$	−12.6570	+	9.19584i	−0.481146	+	0.349573i
$693$		0			0
$694$	−24.8191	+	18.0321i	−0.942120	+	0.684490i
$695$	−10.0225	+	44.4816i	−0.380174	+	1.68728i
$696$		0			0
$697$	−0.518077	+	4.92917i	−0.0196236	+	0.186706i
$698$	21.5948	−	4.59012i	0.817376	−	0.173739i
$699$		0			0
$700$	1.14293	+	14.1910i	0.0431988	+	0.536368i
$701$	14.8415			0.560556			0.280278	−	0.959919i	$-0.409573\pi$
$701$	14.8415			0.560556			0.280278	+	0.959919i	$0.409573\pi$
$702$		0			0
$703$	−7.73365	−	5.61882i	−0.291680	−	0.211918i
$704$	−25.8606	+	11.5139i	−0.974657	+	0.433945i
$705$		0			0
$706$	−8.95506	−	3.98705i	−0.337028	−	0.150055i
$707$	16.2756	+	28.1902i	0.612107	+	1.06020i
$708$		0			0
$709$	−1.56454	−	0.332554i	−0.0587577	−	0.0124893i	0.178439	−	0.983951i	$-0.442895\pi$
$709$	−1.56454	−	0.332554i	−0.0587577	−	0.0124893i	−0.237197	+	0.971462i	$0.576229\pi$
$710$	18.1598	+	6.14592i	0.681524	+	0.230652i
$711$		0			0
$712$	8.32414	+	25.6191i	0.311960	+	0.960115i
$713$	12.4788	+	2.65244i	0.467334	+	0.0993348i
$714$		0			0
$715$	7.12919	−	15.5016i	0.266617	−	0.579728i
$716$	−10.4377	+	11.5922i	−0.390073	+	0.433220i
$717$		0			0
$718$	5.00266	−	8.66487i	0.186698	−	0.323370i
$719$	19.6770	−	14.2962i	0.733830	−	0.533159i	−0.156943	−	0.987608i	$-0.550164\pi$
$719$	19.6770	−	14.2962i	0.733830	−	0.533159i	0.890773	+	0.454449i	$0.150164\pi$
$720$		0			0
$721$	22.5596	+	16.3905i	0.840164	+	0.610415i
$722$	−17.4399	+	7.76473i	−0.649045	+	0.288973i
$723$		0			0
$724$	−4.62252	−	8.00644i	−0.171795	−	0.297557i
$725$	−16.1629	−	7.67309i	−0.600273	−	0.284971i
$726$		0			0
$727$	−8.01143	−	8.89759i	−0.297127	−	0.329993i	0.576033	−	0.817426i	$-0.304600\pi$
$727$	−8.01143	−	8.89759i	−0.297127	−	0.329993i	−0.873160	+	0.487433i	$0.837933\pi$
$728$	−18.7049	−	13.5899i	−0.693250	−	0.503675i
$729$		0			0
$730$	0.263443	−	21.6337i	0.00975048	−	0.800700i
$731$	−2.13811	−	20.3428i	−0.0790810	−	0.752406i
$732$		0			0
$733$	−9.53117	−	4.24355i	−0.352042	−	0.156739i	0.223094	−	0.974797i	$-0.428384\pi$
$733$	−9.53117	−	4.24355i	−0.352042	−	0.156739i	−0.575136	+	0.818058i	$0.695051\pi$
$734$	−13.8508	+	15.3829i	−0.511242	+	0.567792i
$735$		0			0
$736$	−5.76548	−	6.40322i	−0.212519	−	0.236026i
$737$	11.7039	+	36.0208i	0.431117	+	1.32684i
$738$		0			0
$739$	9.63830	−	29.6636i	0.354551	−	1.09119i	−0.601719	−	0.798708i	$-0.705517\pi$
$739$	9.63830	−	29.6636i	0.354551	−	1.09119i	0.956270	−	0.292487i	$-0.0944827\pi$
$740$	−3.20622	+	14.2298i	−0.117863	+	0.523098i
$741$		0			0
$742$	48.1217	+	21.4252i	1.76660	+	0.786543i
$743$	−17.4838	−	30.2828i	−0.641418	−	1.11097i	−0.985116	−	0.171889i	$-0.945013\pi$
$743$	−17.4838	−	30.2828i	−0.641418	−	1.11097i	0.343698	−	0.939080i	$-0.388320\pi$
$744$		0			0
$745$	−15.6918	+	1.45633i	−0.574903	+	0.0533556i
$746$	−3.77035	−	2.73932i	−0.138042	−	0.100294i
$747$		0			0
$748$	−1.70093	+	5.23491i	−0.0621920	+	0.191407i
$749$	−8.77921	+	15.2060i	−0.320785	+	0.555617i
$750$		0			0
$751$	−13.7941	−	23.8921i	−0.503354	−	0.871835i	−0.999992	−	0.00387741i	$-0.998766\pi$
$751$	−13.7941	−	23.8921i	−0.503354	−	0.871835i	0.496638	−	0.867958i	$-0.334568\pi$
$752$	−21.7495	+	4.62300i	−0.793122	+	0.168583i
$753$		0			0
$754$	7.70747	−	3.43159i	0.280689	−	0.124971i
$755$	0.0402778	+	0.0568815i	0.00146586	+	0.00207013i
$756$		0			0
$757$	31.2879			1.13718			0.568589	−	0.822622i	$-0.307489\pi$
$757$	31.2879			1.13718			0.568589	+	0.822622i	$0.307489\pi$
$758$	−1.09733	−	10.4404i	−0.0398567	−	0.379211i
$759$		0			0
$760$	−6.03781	−	5.57108i	−0.219015	−	0.202084i
$761$	−18.3181	+	3.89364i	−0.664032	+	0.141144i	−0.527584	−	0.849503i	$-0.676902\pi$
$761$	−18.3181	+	3.89364i	−0.664032	+	0.141144i	−0.136448	+	0.990647i	$0.543569\pi$
$762$		0			0
$763$	−16.4880	−	3.50463i	−0.596905	−	0.126876i
$764$	−0.569594	+	1.75303i	−0.0206072	+	0.0634224i
$765$		0			0
$766$	−3.13711	−	9.65503i	−0.113348	−	0.348850i
$767$	−1.23518	−	11.7520i	−0.0445998	−	0.424338i
$768$		0			0
$769$	−21.3024	−	9.48442i	−0.768183	−	0.342017i	−0.0150511	−	0.999887i	$-0.504791\pi$
$769$	−21.3024	−	9.48442i	−0.768183	−	0.342017i	−0.753132	+	0.657870i	$0.771458\pi$
$770$	25.9460	−	14.5616i	0.935030	−	0.524764i
$771$		0			0
$772$	11.8057	−	5.25622i	0.424895	−	0.189175i
$773$	0.276069	−	0.849654i	0.00992952	−	0.0305599i	−0.945969	−	0.324257i	$-0.894886\pi$
$773$	0.276069	−	0.849654i	0.00992952	−	0.0305599i	0.955899	+	0.293697i	$0.0948857\pi$
$774$		0			0
$775$	−9.06794	−	30.4088i	−0.325730	−	1.09232i
$776$	−26.3112	+	45.5724i	−0.944518	+	1.63595i
$777$		0			0
$778$	−2.95278	+	28.0939i	−0.105862	+	1.00721i
$779$	0.324965	−	3.09183i	0.0116431	−	0.110776i
$780$		0			0
$781$	2.90044	+	27.5958i	0.103786	+	0.987456i
$782$	4.17775			0.149396
$783$		0			0
$784$	−2.67225	−	8.22434i	−0.0954375	−	0.293726i
$785$	3.09075	−	0.286846i	0.110314	−	0.0102380i
$786$		0			0
$787$	21.1943	−	23.5387i	0.755496	−	0.839063i	−0.235651	−	0.971838i	$-0.575722\pi$
$787$	21.1943	−	23.5387i	0.755496	−	0.839063i	0.991146	+	0.132775i	$0.0423887\pi$
$788$	−11.7761	+	13.0787i	−0.419506	+	0.465909i
$789$		0			0
$790$	−12.3401	+	10.8419i	−0.439040	+	0.385738i
$791$	2.36892	+	7.29079i	0.0842292	+	0.259231i
$792$		0			0
$793$	1.14500			0.0406602
$794$	1.53616	+	14.6156i	0.0545161	+	0.518686i
$795$		0			0
$796$	−1.46864	+	13.9732i	−0.0520547	+	0.495267i
$797$	3.55475	−	33.8212i	0.125916	−	1.19801i	−0.730936	−	0.682446i	$-0.760916\pi$
$797$	3.55475	−	33.8212i	0.125916	−	1.19801i	0.856852	−	0.515562i	$-0.172417\pi$
$798$		0			0
$799$	−12.5508	+	21.7386i	−0.444015	+	0.769057i
$800$	−7.11712	+	20.2154i	−0.251628	+	0.714722i
$801$		0			0
$802$	2.49021	−	7.66409i	0.0879325	−	0.270628i
$803$	28.6065	−	12.7364i	1.00950	−	0.449459i
$804$		0			0
$805$	11.4942	+	10.6057i	0.405118	+	0.373802i
$806$	13.6696	+	6.08612i	0.481493	+	0.214374i
$807$		0			0
$808$	2.99598	+	28.5048i	0.105398	+	1.00280i
$809$	9.52295	+	29.3086i	0.334809	+	1.03044i	0.966816	+	0.255474i	$0.0822315\pi$
$809$	9.52295	+	29.3086i	0.334809	+	1.03044i	−0.632007	+	0.774963i	$0.717769\pi$
$810$		0			0
$811$	−2.77389	+	8.53714i	−0.0974043	+	0.299780i	−0.987873	−	0.155265i	$-0.950377\pi$
$811$	−2.77389	+	8.53714i	−0.0974043	+	0.299780i	0.890469	+	0.455045i	$0.150377\pi$
$812$	−9.96627	−	2.11840i	−0.349748	−	0.0743411i
$813$		0			0
$814$	29.8175	−	6.33790i	1.04510	−	0.222143i
$815$	−2.76737	−	0.324978i	−0.0969368	−	0.0113835i
$816$		0			0
$817$	1.34114	+	12.7601i	0.0469204	+	0.446418i
$818$	11.6535			0.407455
$819$		0			0
$820$	−4.52915	+	1.41087i	−0.158165	+	0.0492699i
$821$	−6.37522	+	2.83843i	−0.222497	+	0.0990619i	−0.514958	−	0.857215i	$-0.672192\pi$
$821$	−6.37522	+	2.83843i	−0.222497	+	0.0990619i	0.292461	+	0.956277i	$0.405526\pi$
$822$		0			0
$823$	−29.3991	+	6.24896i	−1.02479	+	0.217825i	−0.689496	−	0.724290i	$-0.742168\pi$
$823$	−29.3991	+	6.24896i	−1.02479	+	0.217825i	−0.335291	+	0.942115i	$0.608835\pi$
$824$	12.2767	+	21.2638i	0.427678	+	0.740761i
$825$		0			0
$826$	10.3028	−	17.8449i	0.358480	−	0.620905i
$827$	2.38874	−	7.35179i	0.0830647	−	0.255647i	−0.900895	−	0.434037i	$-0.857089\pi$
$827$	2.38874	−	7.35179i	0.0830647	−	0.255647i	0.983960	+	0.178390i	$0.0570888\pi$
$828$		0			0
$829$	40.9296	+	29.7371i	1.42155	+	1.03281i	0.991514	+	0.129999i	$0.0414973\pi$
$829$	40.9296	+	29.7371i	1.42155	+	1.03281i	0.430031	+	0.902814i	$0.358503\pi$
$830$	3.42229	+	7.94558i	0.118789	+	0.275795i
$831$		0			0
$832$	−8.72639	−	15.1146i	−0.302533	−	0.524003i
$833$	−8.91829	−	3.97068i	−0.309000	−	0.137576i
$834$		0			0
$835$	0.373855	−	0.328466i	0.0129378	−	0.0113670i
$836$	1.06691	−	3.28361i	0.0368998	−	0.113566i
$837$		0			0
$838$	4.01695	+	12.3629i	0.138763	+	0.427070i
$839$	−2.23739	−	2.48488i	−0.0772434	−	0.0857875i	0.703284	−	0.710909i	$-0.251716\pi$
$839$	−2.23739	−	2.48488i	−0.0772434	−	0.0857875i	−0.780528	+	0.625121i	$0.785049\pi$
$840$		0			0
$841$	−10.8369	+	12.0356i	−0.373685	+	0.415019i
$842$	−8.78122	−	3.90965i	−0.302621	−	0.134736i
$843$		0			0
$844$	−1.16877	−	11.1201i	−0.0402306	−	0.382769i
$845$	−17.5704	−	5.94644i	−0.604438	−	0.204564i
$846$		0			0
$847$	3.87474	+	2.81516i	0.133138	+	0.0967301i
$848$	15.7827	+	17.5284i	0.541979	+	0.601929i
$849$		0			0
$850$	−4.97501	−	9.12306i	−0.170641	−	0.312918i
$851$	8.01186	+	13.8770i	0.274643	+	0.475696i
$852$		0			0
$853$	46.2076	−	20.5729i	1.58212	−	0.704404i	0.587617	−	0.809139i	$-0.300066\pi$
$853$	46.2076	−	20.5729i	1.58212	−	0.704404i	0.994500	+	0.104735i	$0.0333994\pi$
$854$	1.61530	+	1.17358i	0.0552743	+	0.0401592i
$855$		0			0
$856$	−12.5078	+	9.08743i	−0.427507	+	0.310602i
$857$	24.3694	−	42.2090i	0.832443	−	1.44183i	−0.0636526	−	0.997972i	$-0.520275\pi$
$857$	24.3694	−	42.2090i	0.832443	−	1.44183i	0.896096	−	0.443861i	$-0.146392\pi$
$858$		0			0
$859$	34.2741	−	38.0652i	1.16942	−	1.29877i	0.223371	−	0.974734i	$-0.428294\pi$
$859$	34.2741	−	38.0652i	1.16942	−	1.29877i	0.946045	−	0.324034i	$-0.105039\pi$
$860$	17.0728	−	9.58173i	0.582179	−	0.326734i
$861$		0			0
$862$	3.75615	+	0.798395i	0.127935	+	0.0271934i
$863$	3.13109	+	9.63651i	0.106584	+	0.328031i	0.990099	−	0.140372i	$-0.0448298\pi$
$863$	3.13109	+	9.63651i	0.106584	+	0.328031i	−0.883515	+	0.468402i	$0.844830\pi$
$864$		0			0
$865$	40.8134	−	12.7138i	1.38770	−	0.432281i
$866$	−2.63072	−	0.559177i	−0.0893955	−	0.0190016i
$867$		0			0
$868$	−9.03533	−	15.6496i	−0.306679	−	0.531184i
$869$	−21.7191	−	9.66997i	−0.736770	−	0.328031i
$870$		0			0
$871$	−21.3321	+	9.49766i	−0.722811	+	0.321816i
$872$	−12.0076	−	8.72406i	−0.406630	−	0.295434i
$873$		0			0
$874$	−2.62050			−0.0886399
$875$	9.47221	−	37.7299i	0.320219	−	1.27550i
$876$		0			0
$877$	−26.6196	+	5.65817i	−0.898880	+	0.191063i	−0.634104	−	0.773247i	$-0.718631\pi$
$877$	−26.6196	+	5.65817i	−0.898880	+	0.191063i	−0.264775	+	0.964310i	$0.585298\pi$
$878$	0.944418	−	8.98553i	0.0318726	−	0.303247i
$879$		0			0
$880$	13.2656	−	1.23115i	0.447182	−	0.0415021i
$881$	−26.5743	+	19.3074i	−0.895312	+	0.650482i	−0.937257	−	0.348638i	$-0.886644\pi$
$881$	−26.5743	+	19.3074i	−0.895312	+	0.650482i	0.0419459	+	0.999120i	$0.486644\pi$
$882$		0			0
$883$	−28.3821	+	20.6208i	−0.955134	+	0.693946i	−0.952016	−	0.306050i	$-0.900993\pi$
$883$	−28.3821	+	20.6208i	−0.955134	+	0.693946i	−0.00311854	+	0.999995i	$0.500993\pi$
$884$	−3.31944	−	0.705568i	−0.111645	−	0.0237308i
$885$		0			0
$886$	−24.6943	+	5.24894i	−0.829622	+	0.176342i
$887$	9.87336	−	10.9655i	0.331515	−	0.368185i	−0.554225	−	0.832367i	$-0.686985\pi$
$887$	9.87336	−	10.9655i	0.331515	−	0.368185i	0.885740	+	0.464182i	$0.153652\pi$
$888$		0			0
$889$	44.5525	+	49.4806i	1.49424	+	1.65953i
$890$	0.260237	−	21.3704i	0.00872317	−	0.716339i
$891$		0			0
$892$	14.4973	−	10.5329i	0.485405	−	0.352667i
$893$	7.87251	−	13.6356i	0.263444	−	0.456298i
$894$		0			0
$895$	37.1685	−	20.8599i	1.24240	−	0.697271i
$896$	0.0633514	−	0.602749i	0.00211642	−	0.0201364i
$897$		0			0
$898$	−13.6899	−	15.2042i	−0.456839	−	0.507371i
$899$	22.7096			0.757409
$900$		0			0
$901$	26.6273			0.887083
$902$	6.63365	+	7.36741i	0.220876	+	0.245308i
$903$		0			0
$904$	−0.705569	+	6.71304i	−0.0234669	+	0.223272i
$905$	4.95080	+	24.7711i	0.164570	+	0.823419i
$906$		0			0
$907$	−28.4907	+	49.3473i	−0.946018	+	1.63855i	−0.192318	+	0.981333i	$0.561601\pi$
$907$	−28.4907	+	49.3473i	−0.946018	+	1.63855i	−0.753700	+	0.657219i	$0.771733\pi$
$908$	17.1373	−	12.4510i	0.568723	−	0.413201i
$909$		0			0
$910$	10.6006	+	14.9705i	0.351408	+	0.496269i
$911$	16.7345	+	18.5855i	0.554438	+	0.615765i	0.953586	−	0.301121i	$-0.0973608\pi$
$911$	16.7345	+	18.5855i	0.554438	+	0.615765i	−0.399148	+	0.916886i	$0.630694\pi$
$912$		0			0
$913$	−8.37841	+	9.30516i	−0.277285	+	0.307956i
$914$	−2.79671	+	0.594459i	−0.0925070	+	0.0196630i
$915$		0			0
$916$	18.3942	+	3.90980i	0.607760	+	0.129183i
$917$	21.7223	−	15.7821i	0.717332	−	0.521172i
$918$		0			0
$919$	42.0477	−	30.5494i	1.38703	−	1.00773i	0.390841	−	0.920458i	$-0.372184\pi$
$919$	42.0477	−	30.5494i	1.38703	−	1.00773i	0.996184	−	0.0872745i	$-0.0278157\pi$
$920$	5.44754	+	12.6476i	0.179600	+	0.416981i
$921$		0			0
$922$	−2.21723	+	21.0955i	−0.0730206	+	0.694744i
$923$	−16.7336	+	3.55685i	−0.550795	+	0.117075i
$924$		0			0
$925$	20.7626	−	34.0208i	0.682671	−	1.11860i
$926$	1.66763			0.0548017
$927$		0			0
$928$	−12.4087	−	9.01543i	−0.407335	−	0.295946i
$929$	−4.34150	+	1.93296i	−0.142440	+	0.0634184i	−0.476719	−	0.879056i	$-0.658174\pi$
$929$	−4.34150	+	1.93296i	−0.142440	+	0.0634184i	0.334279	+	0.942474i	$0.391507\pi$
$930$		0			0
$931$	5.59401	+	2.49061i	0.183336	+	0.0816266i
$932$	−3.63795	−	6.30111i	−0.119165	−	0.206400i
$933$		0			0
$934$	6.90707	+	1.46814i	0.226006	+	0.0480391i
$935$	8.98773	−	12.0590i	0.293930	−	0.394371i
$936$		0			0
$937$	−1.81033	−	5.57164i	−0.0591410	−	0.182017i	0.917122	−	0.398608i	$-0.130506\pi$
$937$	−1.81033	−	5.57164i	−0.0591410	−	0.182017i	−0.976263	+	0.216590i	$0.930506\pi$
$938$	−39.8288	−	8.46587i	−1.30046	−	0.276420i
$939$		0			0
$940$	−23.8614	−	2.80209i	−0.778272	−	0.0913940i
$941$	23.6391	−	26.2539i	0.770613	−	0.855852i	−0.222266	−	0.974986i	$-0.571345\pi$
$941$	23.6391	−	26.2539i	0.770613	−	0.855852i	0.992878	+	0.119134i	$0.0380119\pi$
$942$		0			0
$943$	−2.60561	+	4.51304i	−0.0848502	+	0.146965i
$944$	7.46450	−	5.42328i	0.242949	−	0.176513i
$945$		0			0
$946$	−33.1006	−	24.0490i	−1.07619	−	0.781900i
$947$	−34.3051	+	15.2736i	−1.11476	+	0.496325i	−0.879640	−	0.475640i	$-0.842217\pi$
$947$	−34.3051	+	15.2736i	−1.11476	+	0.496325i	−0.235125	+	0.971965i	$0.575550\pi$
$948$		0			0
$949$	9.65299	+	16.7195i	0.313349	+	0.542737i
$950$	3.12058	+	5.72245i	0.101245	+	0.185661i
$951$		0			0
$952$	−13.6368	−	15.1452i	−0.441972	−	0.490859i
$953$	−1.17391	−	0.852898i	−0.0380268	−	0.0276281i	0.568609	−	0.822608i	$-0.307482\pi$
$953$	−1.17391	−	0.852898i	−0.0380268	−	0.0276281i	−0.606636	+	0.794979i	$0.707482\pi$
$954$		0			0
$955$	3.00974	−	4.03822i	0.0973930	−	0.130674i
$956$	0.443166	+	4.21644i	0.0143330	+	0.136369i
$957$		0			0
$958$	−5.43856	−	2.42140i	−0.175712	−	0.0782320i
$959$	14.6034	−	16.2187i	0.471569	−	0.523731i
$960$		0			0
$961$	6.20745	+	6.89408i	0.200240	+	0.222390i
$962$	5.80772	+	17.8743i	0.187248	+	0.576291i
$963$		0			0
$964$	1.65774	−	5.10200i	0.0533922	−	0.164324i
$965$	−35.1592	+	3.26306i	−1.13181	+	0.105041i
$966$		0			0
$967$	−43.5396	−	19.3851i	−1.40014	−	0.623383i	−0.438760	−	0.898604i	$-0.644582\pi$
$967$	−43.5396	−	19.3851i	−1.40014	−	0.623383i	−0.961381	+	0.275222i	$0.911249\pi$
$968$	2.10859	+	3.65218i	0.0677725	+	0.117385i
$969$		0			0
$970$	31.3644	−	27.5566i	1.00705	−	0.884788i
$971$	14.0919	+	10.2383i	0.452229	+	0.328564i	0.790475	−	0.612494i	$-0.209834\pi$
$971$	14.0919	+	10.2383i	0.452229	+	0.328564i	−0.338246	+	0.941058i	$0.609834\pi$
$972$		0			0
$973$	21.9247	−	67.4773i	0.702874	−	2.16322i
$974$	19.1645	−	33.1938i	0.614069	−	1.06360i
$975$		0			0
$976$	0.447017	+	0.774255i	0.0143086	+	0.0247833i
$977$	−2.03039	+	0.431574i	−0.0649581	+	0.0138073i	−0.240276	−	0.970705i	$-0.577238\pi$
$977$	−2.03039	+	0.431574i	−0.0649581	+	0.0138073i	0.175318	+	0.984512i	$0.443905\pi$
$978$		0			0
$979$	28.2584	−	12.5814i	0.903141	−	0.402104i
$980$	0.113774	−	9.34301i	0.00363438	−	0.298452i
$981$		0			0
$982$	−3.11004			−0.0992453
$983$	−3.12635	−	29.7452i	−0.0997150	−	0.948724i	−0.923959	−	0.382490i	$-0.875067\pi$
$983$	−3.12635	−	29.7452i	−0.0997150	−	0.948724i	0.824245	−	0.566234i	$-0.191600\pi$
$984$		0			0
$985$	41.9346	−	23.5349i	1.33615	−	0.749883i
$986$	7.27428	−	1.54620i	0.231660	−	0.0492409i
$987$		0			0
$988$	2.08212	+	0.442569i	0.0662412	+	0.0140800i
$989$	6.64596	−	20.4542i	0.211329	−	0.650405i
$990$		0			0
$991$	3.05364	+	9.39812i	0.0970019	+	0.298541i	0.987770	−	0.155916i	$-0.0498331\pi$
$991$	3.05364	+	9.39812i	0.0970019	+	0.298541i	−0.890768	+	0.454458i	$0.849833\pi$
$992$	−2.84347	−	27.0538i	−0.0902801	−	0.858958i
$993$		0			0
$994$	−27.2524	−	12.1336i	−0.864395	−	0.384853i
$995$	16.0407	−	34.8787i	0.508524	−	1.10573i
$996$		0			0
$997$	−14.1343	+	6.29299i	−0.447638	+	0.199301i	−0.618159	−	0.786053i	$-0.712121\pi$
$997$	−14.1343	+	6.29299i	−0.447638	+	0.199301i	0.170522	+	0.985354i	$0.445455\pi$
$998$	−12.3238	+	37.9288i	−0.390104	+	1.20062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.19		224
3.2	odd	2		225.2.q.a.196.10	yes	224
9.4	even	3	inner	675.2.r.a.496.10		224
9.5	odd	6		225.2.q.a.121.19	yes	224
25.6	even	5	inner	675.2.r.a.181.10		224
75.56	odd	10		225.2.q.a.106.19	yes	224
225.31	even	15	inner	675.2.r.a.631.19		224
225.131	odd	30		225.2.q.a.31.10	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.10	✓	224	225.131	odd	30
225.2.q.a.106.19	yes	224	75.56	odd	10
225.2.q.a.121.19	yes	224	9.5	odd	6
225.2.q.a.196.10	yes	224	3.2	odd	2
675.2.r.a.46.19		224	1.1	even	1	trivial
675.2.r.a.181.10		224	25.6	even	5	inner
675.2.r.a.496.10		224	9.4	even	3	inner
675.2.r.a.631.19		224	225.31	even	15	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.727367 + 0.807823i) q^{2} +(0.0855417 - 0.813875i) q^{4} +(-0.934297 + 2.03152i) q^{5} +(1.73969 - 3.01324i) q^{7} +(2.47854 - 1.80077i) q^{8} +O(q^{10})\)	\(q+(0.727367 + 0.807823i) q^{2} +(0.0855417 - 0.813875i) q^{4} +(-0.934297 + 2.03152i) q^{5} +(1.73969 - 3.01324i) q^{7} +(2.47854 - 1.80077i) q^{8} +(-2.32069 + 0.722917i) q^{10} +(-2.35402 - 2.61440i) q^{11} +(1.45133 - 1.61187i) q^{13} +(3.69956 - 0.786365i) q^{14} +(1.65656 + 0.352114i) q^{16} +(1.54674 - 1.12377i) q^{17} +(-0.970198 + 0.704890i) q^{19} +(1.57349 + 0.934181i) q^{20} +(0.399739 - 3.80326i) q^{22} +(1.96627 - 0.417944i) q^{23} +(-3.25418 - 3.79609i) q^{25} +2.35776 q^{26} +(-2.30358 - 1.67365i) q^{28} +(3.26898 - 1.45544i) q^{29} +(5.79773 + 2.58132i) q^{31} +(-2.14316 - 3.71207i) q^{32} +(2.03286 + 0.432098i) q^{34} +(4.49607 + 6.34948i) q^{35} +(2.46324 + 7.58107i) q^{37} +(-1.27512 - 0.271034i) q^{38} +(1.34261 + 6.71767i) q^{40} +(-1.73464 + 1.92652i) q^{41} +(5.34941 - 9.26545i) q^{43} +(-2.32917 + 1.69224i) q^{44} +(1.76783 + 1.28440i) q^{46} +(-11.9942 + 5.34016i) q^{47} +(-2.55306 - 4.42203i) q^{49} +(0.699589 - 5.38996i) q^{50} +(-1.18771 - 1.31909i) q^{52} +(11.2674 + 8.18624i) q^{53} +(7.51058 - 2.33962i) q^{55} +(-1.11423 - 10.6012i) q^{56} +(3.55349 + 1.58212i) q^{58} +(3.64544 - 4.04867i) q^{59} +(0.353232 + 0.392304i) q^{61} +(2.13183 + 6.56111i) q^{62} +(2.48651 - 7.65270i) q^{64} +(1.91857 + 4.45438i) q^{65} +(-9.83507 - 4.37885i) q^{67} +(-0.782301 - 1.35499i) q^{68} +(-1.85897 + 8.25044i) q^{70} +(-6.38098 - 4.63605i) q^{71} +(-2.75054 + 8.46529i) q^{73} +(-4.33248 + 7.50408i) q^{74} +(0.490700 + 0.849917i) q^{76} +(-11.9731 + 2.54496i) q^{77} +(6.17366 - 2.74869i) q^{79} +(-2.26305 + 3.03637i) q^{80} -2.81801 q^{82} +(-0.372037 - 3.53969i) q^{83} +(0.837858 + 4.19218i) q^{85} +(11.3758 - 2.41801i) q^{86} +(-10.5425 - 2.24087i) q^{88} +(-2.71707 + 8.36227i) q^{89} +(-2.33207 - 7.17736i) q^{91} +(-0.171956 - 1.63605i) q^{92} +(-13.0381 - 5.80493i) q^{94} +(-0.525548 - 2.62956i) q^{95} +(-15.6914 + 6.98627i) q^{97} +(1.71520 - 5.27886i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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