LMFDB - Embedded newform 675.2.r.a.631.19

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			631.19
Character	$\chi$	$=$	675.631
Dual form			675.2.r.a.46.19

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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	−0.428907	−	0.903349i	$-0.641101\pi$
$2$	0.727367	−	0.807823i	0.514326	−	0.571217i	0.943233	+	0.332131i	$0.107768\pi$
$3$		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	0.981250	+	0.192739i	$0.0617370\pi$
$7$	1.73969	+	3.01324i	0.657542	+	1.13890i	−0.323708	+	0.946157i	$0.604930\pi$
$8$	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	−0.984898	−	0.173133i	$-0.944611\pi$
$11$	−2.35402	+	2.61440i	−0.709764	+	0.788272i	0.275135	+	0.961406i	$0.411278\pi$
$12$		0			0
$13$	1.45133	+	1.61187i	0.402527	+	0.447052i	0.909995	−	0.414619i	$-0.136085\pi$
$13$	1.45133	+	1.61187i	0.402527	+	0.447052i	−0.507468	+	0.861671i	$0.669418\pi$
$14$	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	0.759339	−	0.650695i	$-0.225522\pi$
$17$	1.54674	+	1.12377i	0.375140	+	0.272555i	−0.384199	+	0.923250i	$0.625522\pi$
$18$		0			0
$19$	−0.970198	−	0.704890i	−0.222579	−	0.161713i	0.470908	−	0.882182i	$-0.343926\pi$
$19$	−0.970198	−	0.704890i	−0.222579	−	0.161713i	−0.693487	+	0.720469i	$0.743926\pi$
$20$	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	0.408293	−	0.912851i	$-0.366124\pi$
$23$	1.96627	+	0.417944i	0.409996	+	0.0871474i	0.00170377	+	0.999999i	$0.499458\pi$
$24$		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	0.687149	−	0.726516i	$-0.258862\pi$
$29$	3.26898	+	1.45544i	0.607035	+	0.270269i	−0.0801144	+	0.996786i	$0.525529\pi$
$30$		0			0
$31$	5.79773	−	2.58132i	1.04130	−	0.463618i	0.186437	−	0.982467i	$-0.440306\pi$
$31$	5.79773	−	2.58132i	1.04130	−	0.463618i	0.854866	+	0.518849i	$0.173639\pi$
$32$	−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	−0.515980	−	0.856601i	$-0.672572\pi$
$37$	2.46324	−	7.58107i	0.404954	−	1.24632i	0.920934	−	0.389719i	$-0.127428\pi$
$38$	−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	0.592306	−	0.805713i	$-0.298218\pi$
$41$	−1.73464	−	1.92652i	−0.270906	−	0.300871i	−0.863212	+	0.504842i	$0.831551\pi$
$42$		0			0
$43$	5.34941	+	9.26545i	0.815778	+	1.41297i	0.908768	+	0.417301i	$0.137024\pi$
$43$	5.34941	+	9.26545i	0.815778	+	1.41297i	−0.0929908	+	0.995667i	$0.529643\pi$
$44$	−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	−0.992014	−	0.126128i	$-0.959745\pi$
$47$	−11.9942	−	5.34016i	−1.74953	−	0.778942i	−0.757518	−	0.652814i	$-0.773588\pi$
$48$		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	0.602427	−	0.798174i	$-0.294200\pi$
$53$	11.2674	−	8.18624i	1.54770	−	1.12447i	0.945269	−	0.326293i	$-0.105800\pi$
$54$		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	0.932142	−	0.362094i	$-0.117938\pi$
$59$	3.64544	+	4.04867i	0.474596	+	0.527092i	−0.457545	+	0.889186i	$0.651271\pi$
$60$		0			0
$61$	0.353232	−	0.392304i	0.0452268	−	0.0502294i	−0.720107	−	0.693863i	$-0.755907\pi$
$61$	0.353232	−	0.392304i	0.0452268	−	0.0502294i	0.765334	+	0.643634i	$0.222574\pi$
$62$	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	−0.907185	−	0.420732i	$-0.861773\pi$
$67$	−9.83507	+	4.37885i	−1.20154	+	0.534962i	−0.294360	+	0.955695i	$0.595106\pi$
$68$	−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	−0.898076	−	0.439841i	$-0.855035\pi$
$71$	−6.38098	+	4.63605i	−0.757283	+	0.550198i	0.140793	+	0.990039i	$0.455035\pi$
$72$		0			0
$73$	−2.75054	−	8.46529i	−0.321926	−	0.990787i	−0.972809	−	0.231609i	$-0.925601\pi$
$73$	−2.75054	−	8.46529i	−0.321926	−	0.990787i	0.650883	−	0.759178i	$-0.274399\pi$
$74$	−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	0.723494	−	0.690330i	$-0.242535\pi$
$79$	6.17366	+	2.74869i	0.694591	+	0.309252i	−0.0289032	+	0.999582i	$0.509201\pi$
$80$	−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	0.954946	+	0.296781i	$0.0959131\pi$
$83$	−0.372037	+	3.53969i	−0.0408363	+	0.388532i	−0.995782	+	0.0917511i	$0.970754\pi$
$84$		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	−0.985481	−	0.169787i	$-0.945692\pi$
$89$	−2.71707	−	8.36227i	−0.288008	−	0.886399i	0.697472	−	0.716612i	$-0.254308\pi$
$90$		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	−0.597511	−	0.801861i	$-0.703844\pi$
$97$	−15.6914	−	6.98627i	−1.59322	−	0.709348i	−0.995712	+	0.0925124i	$0.970510\pi$
$98$	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	0.533770	−	0.845629i	$-0.320775\pi$
$101$	−4.67773	−	8.10206i	−0.465451	−	0.806185i	−0.999222	+	0.0394441i	$0.987441\pi$
$102$		0			0
$103$	−0.837734	−	7.97051i	−0.0825444	−	0.785358i	−0.954988	−	0.296643i	$-0.904133\pi$
$103$	−0.837734	−	7.97051i	−0.0825444	−	0.785358i	0.872444	−	0.488714i	$-0.162534\pi$
$104$	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	−0.996801	−	0.0799245i	$-0.974532\pi$
$109$	−1.49707	+	4.60752i	−0.143394	+	0.441320i	0.853407	+	0.521245i	$0.174532\pi$
$110$	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	0.669800	−	0.742542i	$-0.266380\pi$
$113$	−1.47427	−	1.63734i	−0.138688	−	0.154028i	−0.808487	+	0.588514i	$0.799713\pi$
$114$		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	−0.764841	−	0.644219i	$-0.777182\pi$
$127$	−5.91345	−	18.1997i	−0.524734	−	1.61497i	0.240106	−	0.970747i	$-0.422818\pi$
$128$	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	−0.0749569	−	0.997187i	$-0.523882\pi$
$131$	7.04977	−	3.13876i	0.615941	−	0.274235i	0.690898	+	0.722952i	$0.257215\pi$
$132$		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	0.0617840	−	0.998090i	$-0.480321\pi$
$137$	6.13544	−	1.30413i	0.524186	−	0.111419i	0.462402	+	0.886670i	$0.346988\pi$
$138$		0			0
$139$	19.9459	+	4.23963i	1.69179	+	0.359601i	0.950293	−	0.311357i	$-0.100783\pi$
$139$	19.9459	+	4.23963i	1.69179	+	0.359601i	0.741496	+	0.670958i	$0.234117\pi$
$140$	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	−0.684810	−	0.728722i	$-0.740115\pi$
$149$	3.52387	−	6.10353i	0.288687	−	0.500021i	0.973497	+	0.228701i	$0.0734480\pi$
$150$		0			0
$151$	0.0155849	+	0.0269939i	0.00126828	+	0.00219673i	0.866659	−	0.498901i	$-0.166263\pi$
$151$	0.0155849	+	0.0269939i	0.00126828	+	0.00219673i	−0.865391	+	0.501098i	$0.832930\pi$
$152$	−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	−0.892393	−	0.451260i	$-0.850975\pi$
$157$	−0.694083	+	1.20219i	−0.0553938	+	0.0959450i	0.836999	+	0.547205i	$0.184308\pi$
$158$	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	−0.934843	−	0.355062i	$-0.884460\pi$
$163$	0.385069	−	1.18512i	0.0301609	−	0.0928258i	0.965004	+	0.262236i	$0.0844598\pi$
$164$	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	−0.414588	−	0.910009i	$-0.636074\pi$
$167$	−0.203316	+	0.0905220i	−0.0157330	+	0.00700480i	0.398855	+	0.917014i	$0.369408\pi$
$168$		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	0.0241991	+	0.999707i	$0.492296\pi$
$173$	−12.7920	+	14.2070i	−0.972561	+	1.08014i	−0.996760	+	0.0804313i	$0.974370\pi$
$174$		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	−0.988825	−	0.149082i	$-0.952368\pi$
$179$	−15.4208	+	11.2038i	−1.15260	+	0.837415i	−0.163778	+	0.986497i	$0.552368\pi$
$180$		0			0
$181$	9.13951	+	6.64024i	0.679335	+	0.493565i	0.873137	−	0.487475i	$-0.162082\pi$
$181$	9.13951	+	6.64024i	0.679335	+	0.493565i	−0.193802	+	0.981041i	$0.562082\pi$
$182$	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	−0.286927	−	0.957952i	$-0.592634\pi$
$191$	−2.20315	+	0.468294i	−0.159414	+	0.0338845i	0.127513	+	0.991837i	$0.459301\pi$
$192$		0			0
$193$	7.89562	−	13.6756i	0.568339	−	0.984393i	−0.428391	−	0.903593i	$-0.640919\pi$
$193$	7.89562	−	13.6756i	0.568339	−	0.984393i	0.996730	−	0.0807992i	$-0.0257472\pi$
$194$	−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	−0.997570	−	0.0696750i	$-0.977804\pi$
$197$	−17.3982	+	12.6405i	−1.23957	+	0.900601i	−0.242001	+	0.970276i	$0.577804\pi$
$198$		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	0.643510	−	0.765438i	$-0.277478\pi$
$211$	13.3645	+	2.84072i	0.920053	+	0.195563i	0.276544	+	0.961001i	$0.410811\pi$
$212$	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	−0.0147900	−	0.999891i	$-0.504708\pi$
$223$	14.6520	−	16.2727i	0.981169	−	1.08970i	0.995959	−	0.0898080i	$-0.0286253\pi$
$224$	−14.9138			−0.996469
$225$		0			0
$226$	−2.39502			−0.159314
$227$	17.3202	−	19.2360i	1.14958	−	1.27674i	0.194334	−	0.980935i	$-0.437745\pi$
$227$	17.3202	−	19.2360i	1.14958	−	1.27674i	0.955248	−	0.295806i	$-0.0955880\pi$
$228$		0			0
$229$	−2.40196	−	22.8532i	−0.158726	−	1.51018i	−0.726598	−	0.687063i	$-0.758900\pi$
$229$	−2.40196	−	22.8532i	−0.158726	−	1.51018i	0.567872	−	0.823117i	$-0.307767\pi$
$230$	−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	0.797916	−	0.602769i	$-0.205936\pi$
$233$	7.19284	+	5.22590i	0.471219	+	0.342360i	−0.326697	+	0.945129i	$0.605936\pi$
$234$		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	0.0410781	−	0.999156i	$-0.486921\pi$
$239$	−5.06749	−	1.07713i	−0.327788	−	0.0696736i	−0.368867	+	0.929482i	$0.620254\pi$
$240$		0			0
$241$	6.41203	−	1.36292i	0.413035	−	0.0877933i	0.00329255	−	0.999995i	$-0.498952\pi$
$241$	6.41203	−	1.36292i	0.413035	−	0.0877933i	0.409742	+	0.912201i	$0.365619\pi$
$242$	−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	−0.923164	−	0.384407i	$-0.874406\pi$
$257$	−2.06283	+	3.57292i	−0.128676	+	0.222873i	0.794488	+	0.607280i	$0.207739\pi$
$258$		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	0.357730	−	0.933825i	$-0.383551\pi$
$263$	17.2609	−	3.66892i	1.06435	−	0.226235i	0.706623	+	0.707590i	$0.250218\pi$
$264$		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	0.999946	+	0.0103508i	$0.00329481\pi$
$269$	21.6298	+	15.7150i	1.31879	+	0.958158i	0.318845	+	0.947807i	$0.396705\pi$
$270$		0			0
$271$	17.6749	−	12.8416i	1.07367	−	0.780069i	0.0971044	−	0.995274i	$-0.469042\pi$
$271$	17.6749	−	12.8416i	1.07367	−	0.780069i	0.976569	+	0.215205i	$0.0690419\pi$
$272$	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	−0.957803	−	0.287425i	$-0.907201\pi$
$277$	−9.51723	+	10.5700i	−0.571835	+	0.635087i	0.385968	+	0.922512i	$0.373867\pi$
$278$	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	0.949026	+	0.315197i	$0.102070\pi$
$281$	−0.750893	+	7.14427i	−0.0447945	+	0.426192i	−0.993821	+	0.110995i	$0.964596\pi$
$282$		0			0
$283$	12.3369	−	5.49275i	0.733353	−	0.326510i	−0.00585864	−	0.999983i	$-0.501865\pi$
$283$	12.3369	−	5.49275i	0.733353	−	0.326510i	0.739212	+	0.673473i	$0.235198\pi$
$284$	−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	−0.861386	−	0.507950i	$-0.830403\pi$
$293$	0.157560	−	0.272902i	0.00920475	−	0.0159431i	0.870591	+	0.492007i	$0.163737\pi$
$294$		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	0.736025	−	0.676954i	$-0.236701\pi$
$311$	19.9820	+	4.24731i	1.13308	+	0.240843i	0.397050	+	0.917797i	$0.370034\pi$
$312$		0			0
$313$	−15.4110	+	3.27572i	−0.871083	+	0.185154i	−0.621705	−	0.783252i	$-0.713560\pi$
$313$	−15.4110	+	3.27572i	−0.871083	+	0.185154i	−0.249378	+	0.968406i	$0.580226\pi$
$314$	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	−0.890561	−	0.454865i	$-0.849688\pi$
$317$	1.33731	−	12.7236i	0.0751108	−	0.714631i	0.965671	−	0.259767i	$-0.0836456\pi$
$318$		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	0.646965	+	0.762519i	$0.276038\pi$
$331$	−2.62711	+	24.9953i	−0.144399	+	1.37386i	−0.791364	+	0.611345i	$0.790629\pi$
$332$	−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	0.981484	−	0.191545i	$-0.0613497\pi$
$337$	12.6373	+	14.0351i	0.688396	+	0.764541i	−0.293088	+	0.956085i	$0.594683\pi$
$338$	−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	−0.728424	−	0.685126i	$-0.759747\pi$
$347$	−2.94999	−	28.0672i	−0.158364	−	1.50673i	0.570061	−	0.821603i	$-0.306920\pi$
$348$		0			0
$349$	10.1548	+	17.5887i	0.543575	+	0.941500i	0.998695	+	0.0510695i	$0.0162630\pi$
$349$	10.1548	+	17.5887i	0.543575	+	0.941500i	−0.455120	+	0.890430i	$0.650404\pi$
$350$	−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	0.175616	−	0.984459i	$-0.443808\pi$
$353$	−8.23808	−	3.66783i	−0.438469	−	0.195219i	−0.614085	+	0.789240i	$0.710475\pi$
$354$		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	−0.997633	−	0.0687601i	$-0.978096\pi$
$359$	−2.84427	+	8.75376i	−0.150115	+	0.462006i	0.847518	+	0.530766i	$0.178096\pi$
$360$		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	−0.811045	−	0.584984i	$-0.801101\pi$
$367$	1.99047	−	18.9381i	0.103902	−	0.988558i	0.914947	−	0.403575i	$-0.132232\pi$
$368$	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	0.0980592	−	0.995181i	$-0.468737\pi$
$373$	−4.19359	−	0.891374i	−0.217136	−	0.0461536i	−0.315195	+	0.949027i	$0.602070\pi$
$374$	−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	−0.770081	−	0.637947i	$-0.779784\pi$
$379$	−7.81297	+	5.67645i	−0.401325	+	0.291580i	0.368755	+	0.929526i	$0.379784\pi$
$380$	−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	−0.612963	−	0.790111i	$-0.710023\pi$
$383$	−8.53168	+	3.79855i	−0.435948	+	0.194097i	0.177015	+	0.984208i	$0.443356\pi$
$384$		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	−0.118267	−	0.992982i	$-0.537734\pi$
$389$	17.3886	−	19.3120i	0.881638	−	0.979158i	0.999904	+	0.0138240i	$0.00440046\pi$
$390$		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	−0.278458	−	0.960448i	$-0.589823\pi$
$397$	10.9374	−	7.94651i	0.548934	−	0.398824i	0.827392	+	0.561624i	$0.189823\pi$
$398$	−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	−0.943611	−	0.331057i	$-0.892595\pi$
$401$	−3.70665	+	6.42010i	−0.185101	+	0.320604i	0.758509	+	0.651662i	$0.225928\pi$
$402$		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	0.893917	−	0.448232i	$-0.147946\pi$
$409$	7.17339	+	7.96686i	0.354701	+	0.393936i	−0.539216	+	0.842167i	$0.681279\pi$
$410$	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	−0.122149	−	0.992512i	$-0.538979\pi$
$419$	10.9245	−	4.86390i	0.533697	−	0.237617i	0.655846	+	0.754895i	$0.272312\pi$
$420$		0			0
$421$	−8.07815	−	3.59663i	−0.393705	−	0.175289i	0.200329	−	0.979729i	$-0.435799\pi$
$421$	−8.07815	−	3.59663i	−0.393705	−	0.175289i	−0.594034	+	0.804440i	$0.702466\pi$
$422$	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	0.654485	−	0.756075i	$-0.272885\pi$
$431$	2.85794	+	2.07642i	0.137662	+	0.100017i	−0.516823	+	0.856092i	$0.672885\pi$
$432$		0			0
$433$	−2.00164	−	1.45427i	−0.0961924	−	0.0698879i	0.538649	−	0.842530i	$-0.318935\pi$
$433$	−2.00164	−	1.45427i	−0.0961924	−	0.0698879i	−0.634842	+	0.772642i	$0.718935\pi$
$434$	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	−0.861100	−	0.508436i	$-0.830224\pi$
$439$	−5.56157	+	6.17675i	−0.265439	+	0.294800i	0.595660	+	0.803236i	$0.296890\pi$
$440$	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	−0.998151	−	0.0607879i	$-0.980639\pi$
$443$	−11.6123	−	20.1132i	−0.551719	−	0.955606i	0.446432	−	0.894818i	$-0.352695\pi$
$444$		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	0.833625	−	0.552330i	$-0.186261\pi$
$457$	−1.31514	−	2.27788i	−0.0615194	−	0.106555i	−0.895145	+	0.445776i	$0.852928\pi$
$458$	−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	−0.357923	−	0.933751i	$-0.616515\pi$
$461$	13.0570	−	14.5013i	0.608126	−	0.675392i	0.966049	+	0.258359i	$0.0831816\pi$
$462$		0			0
$463$	1.02652	+	1.14007i	0.0477065	+	0.0529834i	0.766526	−	0.642214i	$-0.221984\pi$
$463$	1.02652	+	1.14007i	0.0477065	+	0.0529834i	−0.718819	+	0.695197i	$0.755317\pi$
$464$	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	0.702703	−	0.711483i	$-0.251976\pi$
$467$	5.25538	+	3.81826i	0.243190	+	0.176688i	−0.459513	+	0.888171i	$0.651976\pi$
$468$		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	0.289241	−	0.957256i	$-0.406597\pi$
$479$	−5.00312	−	2.22753i	−0.228598	−	0.101779i	−0.517840	+	0.855478i	$0.673264\pi$
$480$		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	0.325162	+	0.945658i	$0.394581\pi$
$487$	−10.8960	+	33.5344i	−0.493744	+	1.51959i	−0.818905	+	0.573929i	$0.805419\pi$
$488$	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	0.698397	−	0.715711i	$-0.253897\pi$
$491$	−1.91440	−	2.12616i	−0.0863958	−	0.0959523i	−0.784792	+	0.619759i	$0.787231\pi$
$492$		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	−0.0836188	−	0.996498i	$-0.526648\pi$
$499$	18.3438	−	31.7725i	0.821183	−	1.42233i	0.904802	−	0.425833i	$-0.140019\pi$
$500$	−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	−0.858430	−	0.512931i	$-0.828560\pi$
$503$	−14.2611	+	10.3613i	−0.635873	+	0.461989i	0.222557	+	0.974920i	$0.428560\pi$
$504$		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	0.924057	−	0.382255i	$-0.124852\pi$
$509$	10.0917	+	11.2080i	0.447306	+	0.496784i	−0.476751	+	0.879038i	$0.658186\pi$
$510$		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	−0.999709	−	0.0241133i	$-0.992324\pi$
$521$	−29.3467	+	21.3216i	−1.28570	+	0.934118i	−0.285994	+	0.958231i	$0.592324\pi$
$522$		0			0
$523$	−2.83321	−	8.71972i	−0.123888	−	0.381287i	0.869809	−	0.493388i	$-0.164242\pi$
$523$	−2.83321	−	8.71972i	−0.123888	−	0.381287i	−0.993697	+	0.112102i	$0.964242\pi$
$524$	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	0.799132	+	0.601156i	$0.205293\pi$
$541$	−4.66886	+	14.3693i	−0.200730	+	0.617784i	−0.999862	+	0.0166277i	$0.994707\pi$
$542$	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	−0.525785	−	0.850617i	$-0.676229\pi$
$547$	−35.3098	−	15.7209i	−1.50974	−	0.672178i	−0.983951	+	0.178439i	$0.942895\pi$
$548$	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	0.972379	−	0.233408i	$-0.0749877\pi$
$563$	15.1527	+	16.8287i	0.638609	+	0.709247i	−0.333770	+	0.942654i	$0.608321\pi$
$564$		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	0.881844	+	0.471540i	$0.156302\pi$
$569$	−1.87892	+	17.8767i	−0.0787683	+	0.749431i	−0.960613	+	0.277890i	$0.910365\pi$
$570$		0			0
$571$	1.55774	+	14.8209i	0.0651893	+	0.620235i	0.977529	+	0.210801i	$0.0676071\pi$
$571$	1.55774	+	14.8209i	0.0651893	+	0.620235i	−0.912340	+	0.409434i	$0.865726\pi$
$572$	−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	−0.977109	−	0.212740i	$-0.931761\pi$
$577$	−7.48625	−	23.0403i	−0.311657	−	0.959181i	0.665452	−	0.746441i	$-0.268239\pi$
$578$	−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	−0.408021	−	0.912973i	$-0.633781\pi$
$587$	−9.91962	+	2.10848i	−0.409426	+	0.0870263i	−0.00140582	+	0.999999i	$0.500447\pi$
$588$		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	−0.850533	−	0.525921i	$-0.823721\pi$
$599$	0.738992	−	1.27997i	0.0301944	−	0.0522982i	0.880728	+	0.473623i	$0.157054\pi$
$600$		0			0
$601$	−9.97465	−	17.2766i	−0.406874	−	0.704727i	0.587663	−	0.809106i	$-0.300048\pi$
$601$	−9.97465	−	17.2766i	−0.406874	−	0.704727i	−0.994538	+	0.104378i	$0.966715\pi$
$602$	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	−0.999339	−	0.0363452i	$-0.988428\pi$
$607$	−11.5351	+	19.9793i	−0.468194	+	0.810935i	0.531146	+	0.847281i	$0.321762\pi$
$608$	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	0.684730	+	0.728797i	$0.259920\pi$
$613$	−7.36834	+	22.6774i	−0.297605	+	0.915932i	−0.982334	+	0.187135i	$0.940080\pi$
$614$	−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	−0.423060	−	0.906102i	$-0.639044\pi$
$617$	−0.814192	+	0.362502i	−0.0327782	+	0.0145938i	0.390282	+	0.920695i	$0.372377\pi$
$618$		0			0
$619$	0.0314900	−	0.299608i	0.00126569	−	0.0120422i	−0.993871	−	0.110548i	$-0.964740\pi$
$619$	0.0314900	−	0.299608i	0.00126569	−	0.0120422i	0.995137	+	0.0985054i	$0.0314062\pi$
$620$	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	0.333242	−	0.942841i	$-0.391857\pi$
$631$	−11.5670	−	8.40394i	−0.460476	−	0.334556i	−0.793718	+	0.608286i	$0.791857\pi$
$632$	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	−0.184495	−	0.982833i	$-0.559065\pi$
$641$	1.18274	−	0.251398i	0.0467152	−	0.00992963i	0.231210	+	0.972904i	$0.425732\pi$
$642$		0			0
$643$	−12.3127	+	21.3262i	−0.485566	+	0.841025i	−0.999862	−	0.0165876i	$-0.994720\pi$
$643$	−12.3127	+	21.3262i	−0.485566	+	0.841025i	0.514297	+	0.857612i	$0.328053\pi$
$644$	−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	−0.689903	−	0.723901i	$-0.742347\pi$
$647$	−5.45922	+	3.96635i	−0.214624	+	0.155933i	0.475279	+	0.879835i	$0.342347\pi$
$648$		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	0.990379	−	0.138380i	$-0.0441894\pi$
$653$	−0.182163	−	1.73317i	−0.00712860	−	0.0678241i	−0.997508	+	0.0705556i	$0.977523\pi$
$654$		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	0.463284	−	0.886210i	$-0.346671\pi$
$659$	32.0109	−	6.80414i	1.24697	−	0.265051i	0.783685	+	0.621158i	$0.213338\pi$
$660$		0			0
$661$	−43.1830	−	9.17882i	−1.67962	−	0.357015i	−0.733217	−	0.679995i	$-0.761982\pi$
$661$	−43.1830	−	9.17882i	−1.67962	−	0.357015i	−0.946406	+	0.322980i	$0.895315\pi$
$662$	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	−0.656052	−	0.754715i	$-0.727775\pi$
$673$	4.23131	−	4.69934i	0.163105	−	0.181146i	0.819157	+	0.573569i	$0.194442\pi$
$674$	20.5298			0.790779
$675$		0			0
$676$	6.78870			0.261104
$677$	−33.5415	+	37.2516i	−1.28911	+	1.43170i	−0.444989	+	0.895536i	$0.646793\pi$
$677$	−33.5415	+	37.2516i	−1.28911	+	1.43170i	−0.844116	+	0.536161i	$0.819874\pi$
$678$		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	0.255568	−	0.966791i	$-0.417738\pi$
$683$	−15.2867	−	11.1065i	−0.584931	−	0.424977i	−0.840498	+	0.541814i	$0.817738\pi$
$684$		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	−0.695768	−	0.718266i	$-0.744936\pi$
$691$	−27.3183	+	5.80669i	−1.03924	+	0.220897i	−0.343470	+	0.939163i	$0.611603\pi$
$692$	−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	−0.237197	−	0.971462i	$-0.576229\pi$
$709$	−1.56454	+	0.332554i	−0.0587577	+	0.0124893i	0.178439	+	0.983951i	$0.442895\pi$
$710$	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	0.890773	−	0.454449i	$-0.150164\pi$
$719$	19.6770	+	14.2962i	0.733830	+	0.533159i	−0.156943	+	0.987608i	$0.550164\pi$
$720$		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	−0.873160	−	0.487433i	$-0.837933\pi$
$727$	−8.01143	+	8.89759i	−0.297127	+	0.329993i	0.576033	+	0.817426i	$0.304600\pi$
$728$	−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	−0.575136	−	0.818058i	$-0.695051\pi$
$733$	−9.53117	+	4.24355i	−0.352042	+	0.156739i	0.223094	+	0.974797i	$0.428384\pi$
$734$	−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	0.956270	+	0.292487i	$0.0944827\pi$
$739$	9.63830	+	29.6636i	0.354551	+	1.09119i	−0.601719	+	0.798708i	$0.705517\pi$
$740$	−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	0.343698	+	0.939080i	$0.388320\pi$
$743$	−17.4838	+	30.2828i	−0.641418	+	1.11097i	−0.985116	+	0.171889i	$0.945013\pi$
$744$		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	0.496638	+	0.867958i	$0.334568\pi$
$751$	−13.7941	+	23.8921i	−0.503354	+	0.871835i	−0.999992	+	0.00387741i	$0.998766\pi$
$752$	−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	−0.136448	−	0.990647i	$-0.543569\pi$
$761$	−18.3181	−	3.89364i	−0.664032	−	0.141144i	−0.527584	+	0.849503i	$0.676902\pi$
$762$		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	−0.753132	−	0.657870i	$-0.771458\pi$
$769$	−21.3024	+	9.48442i	−0.768183	+	0.342017i	−0.0150511	+	0.999887i	$0.504791\pi$
$770$	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	0.955899	−	0.293697i	$-0.0948857\pi$
$773$	0.276069	+	0.849654i	0.00992952	+	0.0305599i	−0.945969	+	0.324257i	$0.894886\pi$
$774$		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

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

L-functions

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