LMFDB - Embedded newform 507.2.p.a.25.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.14
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.55177 + 0.967759i) q^{2} +(0.568065 + 0.822984i) q^{3} +(4.07796 + 3.61275i) q^{4} +(1.13985 + 0.138403i) q^{5} +(0.653121 + 2.64982i) q^{6} +(-2.09908 - 3.99947i) q^{7} +(4.37317 + 8.33237i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(2.77471 + 1.45628i) q^{10} +(-3.69763 + 1.40233i) q^{11} +(-0.656695 + 5.40837i) q^{12} +(-1.77792 - 3.13672i) q^{13} +(-1.48586 - 12.2371i) q^{14} +(0.533607 + 1.01670i) q^{15} +(1.78220 + 14.6777i) q^{16} +(0.0575782 - 0.0302194i) q^{17} +(-1.80974 + 2.04278i) q^{18} -6.77205i q^{19} +(4.14826 + 4.68242i) q^{20} +(2.09908 - 3.99947i) q^{21} -10.7926 q^{22} +5.83762 q^{23} +(-4.37317 + 8.33237i) q^{24} +(-3.57460 - 0.881059i) q^{25} +(-1.50126 - 9.72479i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(5.88913 - 23.8932i) q^{28} +(-1.92477 + 5.07519i) q^{29} +(0.377719 + 3.11080i) q^{30} +(1.19832 + 4.86176i) q^{31} +(-5.15270 + 20.9053i) q^{32} +(-3.25458 - 2.24648i) q^{33} +(0.176171 - 0.0213911i) q^{34} +(-1.83911 - 4.84933i) q^{35} +(-4.82405 + 2.53186i) q^{36} +(0.140370 + 0.569504i) q^{37} +(6.55371 - 17.2807i) q^{38} +(1.57149 - 3.24506i) q^{39} +(3.83154 + 10.1030i) q^{40} +(-1.56973 + 1.08350i) q^{41} +(9.22691 - 8.17433i) q^{42} +(8.67740 + 2.13879i) q^{43} +(-20.1450 - 7.64000i) q^{44} +(-0.533607 + 1.01670i) q^{45} +(14.8963 + 5.64941i) q^{46} +(1.84241 + 2.07966i) q^{47} +(-11.0671 + 9.80463i) q^{48} +(-7.61316 + 11.0296i) q^{49} +(-8.26890 - 5.70761i) q^{50} +(0.0575782 + 0.0302194i) q^{51} +(4.08190 - 19.2146i) q^{52} +(-12.6077 + 6.61705i) q^{53} +(-2.70922 - 0.328959i) q^{54} +(-4.40884 + 1.08668i) q^{55} +(24.1454 - 34.9807i) q^{56} +(5.57329 - 3.84696i) q^{57} +(-9.82312 + 11.0880i) q^{58} +(-1.86985 - 0.227041i) q^{59} +(-1.49707 + 6.07387i) q^{60} +(-4.17802 - 2.19279i) q^{61} +(-1.64718 + 13.5658i) q^{62} +(4.48392 - 0.544446i) q^{63} +(-16.5816 + 24.0226i) q^{64} +(-1.59244 - 3.82147i) q^{65} +(-6.13091 - 8.88215i) q^{66} +(-0.00192812 - 0.00217640i) q^{67} +(0.343977 + 0.0847826i) q^{68} +(3.31614 + 4.80426i) q^{69} -14.1542i q^{70} +(10.5026 - 7.24945i) q^{71} +(-9.34165 + 1.13428i) q^{72} +(8.31961 - 3.15521i) q^{73} +(-0.192950 + 1.58909i) q^{74} +(-1.30551 - 3.44233i) q^{75} +(24.4657 - 27.6161i) q^{76} +(13.3702 + 11.8450i) q^{77} +(7.15053 - 6.75982i) q^{78} +(3.12706 - 2.77033i) q^{79} +16.9771i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-5.05415 + 1.24574i) q^{82} +(9.05731 + 6.25181i) q^{83} +(23.0091 - 8.72620i) q^{84} +(0.0698132 - 0.0264767i) q^{85} +(20.0729 + 13.8553i) q^{86} +(-5.27019 + 1.29899i) q^{87} +(-27.8551 - 24.6774i) q^{88} -5.64754i q^{89} +(-2.34557 + 2.07799i) q^{90} +(-8.81320 + 13.6950i) q^{91} +(23.8056 + 21.0899i) q^{92} +(-3.32043 + 3.74799i) q^{93} +(2.68881 + 7.08982i) q^{94} +(0.937274 - 7.71915i) q^{95} +(-20.1318 + 7.63500i) q^{96} +(-5.58631 + 0.678301i) q^{97} +(-30.1010 + 20.7772i) q^{98} -3.95461i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	2.55177	+	0.967759i	1.80437	+	0.684309i	0.995326	+	0.0965669i	$0.0307862\pi$
$2$	2.55177	+	0.967759i	1.80437	+	0.684309i	0.809048	+	0.587742i	$0.199983\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	4.07796	+	3.61275i	2.03898	+	1.80638i
$5$	1.13985	+	0.138403i	0.509758	+	0.0618959i	0.371375	−	0.928483i	$-0.378886\pi$
$5$	1.13985	+	0.138403i	0.509758	+	0.0618959i	0.138383	+	0.990379i	$0.455809\pi$
$6$	0.653121	+	2.64982i	0.266636	+	1.08178i
$7$	−2.09908	−	3.99947i	−0.793379	−	1.51166i	−0.857943	−	0.513745i	$-0.828258\pi$
$7$	−2.09908	−	3.99947i	−0.793379	−	1.51166i	0.0645639	−	0.997914i	$-0.479434\pi$
$8$	4.37317	+	8.33237i	1.54615	+	2.94594i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	2.77471	+	1.45628i	0.877439	+	0.460516i
$11$	−3.69763	+	1.40233i	−1.11488	+	0.422817i	−0.842133	−	0.539270i	$-0.818700\pi$
$11$	−3.69763	+	1.40233i	−1.11488	+	0.422817i	−0.272744	+	0.962087i	$0.587931\pi$
$12$	−0.656695	+	5.40837i	−0.189572	+	1.56126i
$13$	−1.77792	−	3.13672i	−0.493107	−	0.869969i
$13$	−1.77792	−	3.13672i	−0.493107	−	0.869969i
$14$	−1.48586	−	12.2371i	−0.397112	−	3.27051i
$15$	0.533607	+	1.01670i	0.137777	+	0.262512i
$16$	1.78220	+	14.6777i	0.445550	+	3.66944i
$17$	0.0575782	−	0.0302194i	0.0139648	−	0.00732927i	−0.457726	−	0.889093i	$-0.651336\pi$
$17$	0.0575782	−	0.0302194i	0.0139648	−	0.00732927i	0.471691	+	0.881764i	$0.343644\pi$
$18$	−1.80974	+	2.04278i	−0.426560	+	0.481487i
$19$		−	6.77205i		−	1.55361i	−0.629739	−	0.776807i	$-0.716838\pi$
$19$		−	6.77205i		−	1.55361i	0.629739	−	0.776807i	$-0.283162\pi$
$20$	4.14826	+	4.68242i	0.927579	+	1.04702i
$21$	2.09908	−	3.99947i	0.458058	−	0.872756i
$22$	−10.7926			−2.30099
$23$	5.83762			1.21723			0.608614	−	0.793467i	$-0.291726\pi$
$23$	5.83762			1.21723			0.608614	+	0.793467i	$0.291726\pi$
$24$	−4.37317	+	8.33237i	−0.892669	+	1.70084i
$25$	−3.57460	−	0.881059i	−0.714919	−	0.176212i
$26$	−1.50126	−	9.72479i	−0.294422	−	1.90719i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	5.88913	−	23.8932i	1.11294	−	4.51538i
$29$	−1.92477	+	5.07519i	−0.357420	+	0.942439i	0.628884	+	0.777499i	$0.283512\pi$
$29$	−1.92477	+	5.07519i	−0.357420	+	0.942439i	−0.986304	+	0.164940i	$0.947257\pi$
$30$	0.377719	+	3.11080i	0.0689618	+	0.567951i
$31$	1.19832	+	4.86176i	0.215224	+	0.873198i	0.974854	+	0.222843i	$0.0715337\pi$
$31$	1.19832	+	4.86176i	0.215224	+	0.873198i	−0.759630	+	0.650355i	$0.774620\pi$
$32$	−5.15270	+	20.9053i	−0.910878	+	3.69558i
$33$	−3.25458	−	2.24648i	−0.566550	−	0.391062i
$34$	0.176171	−	0.0213911i	0.0302132	−	0.00366854i
$35$	−1.83911	−	4.84933i	−0.310866	−	0.819687i
$36$	−4.82405	+	2.53186i	−0.804008	+	0.421976i
$37$	0.140370	+	0.569504i	0.0230767	+	0.0936258i	0.981351	−	0.192224i	$-0.0615702\pi$
$37$	0.140370	+	0.569504i	0.0230767	+	0.0936258i	−0.958274	+	0.285850i	$0.907724\pi$
$38$	6.55371	−	17.2807i	1.06315	−	2.80330i
$39$	1.57149	−	3.24506i	0.251640	−	0.519625i
$40$	3.83154	+	10.1030i	0.605820	+	1.59742i
$41$	−1.56973	+	1.08350i	−0.245150	+	0.169215i	−0.684304	−	0.729197i	$-0.739894\pi$
$41$	−1.56973	+	1.08350i	−0.245150	+	0.169215i	0.439154	+	0.898412i	$0.355278\pi$
$42$	9.22691	−	8.17433i	1.42374	−	1.26133i
$43$	8.67740	+	2.13879i	1.32329	+	0.326162i	0.836793	−	0.547520i	$-0.184428\pi$
$43$	8.67740	+	2.13879i	1.32329	+	0.326162i	0.486498	+	0.873682i	$0.338274\pi$
$44$	−20.1450	−	7.64000i	−3.03698	−	1.15177i
$45$	−0.533607	+	1.01670i	−0.0795455	+	0.151561i
$46$	14.8963	+	5.64941i	2.19633	+	0.832960i
$47$	1.84241	+	2.07966i	0.268744	+	0.303349i	0.867354	−	0.497691i	$-0.165819\pi$
$47$	1.84241	+	2.07966i	0.268744	+	0.303349i	−0.598610	+	0.801040i	$0.704280\pi$
$48$	−11.0671	+	9.80463i	−1.59740	+	1.41518i
$49$	−7.61316	+	11.0296i	−1.08759	+	1.57565i
$50$	−8.26890	−	5.70761i	−1.16940	−	0.807178i
$51$	0.0575782	+	0.0302194i	0.00806256	+	0.00423156i
$52$	4.08190	−	19.2146i	0.566058	−	2.66458i
$53$	−12.6077	+	6.61705i	−1.73181	+	0.908922i	−0.768780	+	0.639513i	$0.779136\pi$
$53$	−12.6077	+	6.61705i	−1.73181	+	0.908922i	−0.963026	+	0.269409i	$0.913172\pi$
$54$	−2.70922	−	0.328959i	−0.368678	−	0.0447657i
$55$	−4.40884	+	1.08668i	−0.594488	+	0.146528i
$56$	24.1454	−	34.9807i	3.22657	−	4.67449i
$57$	5.57329	−	3.84696i	0.738200	−	0.509542i
$58$	−9.82312	+	11.0880i	−1.28984	+	1.45593i
$59$	−1.86985	−	0.227041i	−0.243434	−	0.0295582i	−0.00208971	−	0.999998i	$-0.500665\pi$
$59$	−1.86985	−	0.227041i	−0.243434	−	0.0295582i	−0.241344	+	0.970440i	$0.577588\pi$
$60$	−1.49707	+	6.07387i	−0.193271	+	0.784133i
$61$	−4.17802	−	2.19279i	−0.534940	−	0.280758i	0.175544	−	0.984472i	$-0.443832\pi$
$61$	−4.17802	−	2.19279i	−0.534940	−	0.280758i	−0.710484	+	0.703713i	$0.751524\pi$
$62$	−1.64718	+	13.5658i	−0.209193	+	1.72286i
$63$	4.48392	−	0.544446i	0.564920	−	0.0685937i
$64$	−16.5816	+	24.0226i	−2.07270	+	3.00282i
$65$	−1.59244	−	3.82147i	−0.197518	−	0.473995i
$66$	−6.13091	−	8.88215i	−0.754662	−	1.09332i
$67$	−0.00192812	−	0.00217640i	−0.000235557	−	0.000265889i	0.748393	−	0.663256i	$-0.230826\pi$
$67$	−0.00192812	−	0.00217640i	−0.000235557	−	0.000265889i	−0.748629	+	0.662990i	$0.769287\pi$
$68$	0.343977	+	0.0847826i	0.0417133	+	0.0102814i
$69$	3.31614	+	4.80426i	0.399217	+	0.578365i
$70$		−	14.1542i		−	1.69175i
$71$	10.5026	−	7.24945i	1.24644	−	0.860352i	0.252211	−	0.967672i	$-0.418842\pi$
$71$	10.5026	−	7.24945i	1.24644	−	0.860352i	0.994224	+	0.107320i	$0.0342270\pi$
$72$	−9.34165	+	1.13428i	−1.10092	+	0.133676i
$73$	8.31961	−	3.15521i	0.973737	−	0.369290i	0.184130	−	0.982902i	$-0.441053\pi$
$73$	8.31961	−	3.15521i	0.973737	−	0.369290i	0.789608	+	0.613612i	$0.210284\pi$
$74$	−0.192950	+	1.58909i	−0.0224300	+	0.184728i
$75$	−1.30551	−	3.44233i	−0.150747	−	0.397487i
$76$	24.4657	−	27.6161i	2.80641	−	3.16779i
$77$	13.3702	+	11.8450i	1.52368	+	1.34986i
$78$	7.15053	−	6.75982i	0.809638	−	0.765399i
$79$	3.12706	−	2.77033i	0.351821	−	0.311687i	−0.468639	−	0.883390i	$-0.655256\pi$
$79$	3.12706	−	2.77033i	0.351821	−	0.311687i	0.820461	+	0.571703i	$0.193717\pi$
$80$			16.9771i			1.89810i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−5.05415	+	1.24574i	−0.558138	+	0.137569i
$83$	9.05731	+	6.25181i	0.994169	+	0.686226i	0.949822	−	0.312791i	$-0.101264\pi$
$83$	9.05731	+	6.25181i	0.994169	+	0.686226i	0.0443473	+	0.999016i	$0.485879\pi$
$84$	23.0091	−	8.72620i	2.51050	−	0.952106i
$85$	0.0698132	−	0.0264767i	0.00757231	−	0.00287180i
$86$	20.0729	+	13.8553i	2.16452	+	1.49406i
$87$	−5.27019	+	1.29899i	−0.565024	+	0.139266i
$88$	−27.8551	−	24.6774i	−2.96936	−	2.63062i
$89$		−	5.64754i		−	0.598638i	−0.954153	−	0.299319i	$-0.903241\pi$
$89$		−	5.64754i		−	0.598638i	0.954153	−	0.299319i	$-0.0967595\pi$
$90$	−2.34557	+	2.07799i	−0.247245	+	0.219040i
$91$	−8.81320	+	13.6950i	−0.923875	+	1.43562i
$92$	23.8056	+	21.0899i	2.48190	+	2.19877i
$93$	−3.32043	+	3.74799i	−0.344313	+	0.388648i
$94$	2.68881	+	7.08982i	0.277330	+	0.731259i
$95$	0.937274	−	7.71915i	0.0961623	−	0.791968i
$96$	−20.1318	+	7.63500i	−2.05470	+	0.779244i
$97$	−5.58631	+	0.678301i	−0.567204	+	0.0688711i	−0.399115	−	0.916901i	$-0.630683\pi$
$97$	−5.58631	+	0.678301i	−0.567204	+	0.0688711i	−0.168089	+	0.985772i	$0.553760\pi$
$98$	−30.1010	+	20.7772i	−3.04066	+	2.09882i
$99$		−	3.95461i		−	0.397454i
$100$	−11.3940	−	16.5071i	−1.13940	−	1.65071i
$101$	6.75474	+	1.66489i	0.672122	+	0.165663i	0.560585	−	0.828097i	$-0.310576\pi$
$101$	6.75474	+	1.66489i	0.672122	+	0.165663i	0.111537	+	0.993760i	$0.464423\pi$
$102$	0.117681	+	0.132835i	0.0116522	+	0.0131526i
$103$	1.47930	+	2.14314i	0.145760	+	0.211169i	0.889063	−	0.457786i	$-0.151357\pi$
$103$	1.47930	+	2.14314i	0.145760	+	0.211169i	−0.743303	+	0.668955i	$0.766742\pi$
$104$	18.3612	−	28.5317i	1.80046	−	2.79776i
$105$	2.94619	−	4.26829i	0.287519	−	0.416543i
$106$	−38.5758	+	4.68395i	−3.74681	+	0.454945i
$107$	1.75235	−	14.4319i	0.169406	−	1.39518i	−0.621581	−	0.783350i	$-0.713509\pi$
$107$	1.75235	−	14.4319i	0.169406	−	1.39518i	0.790987	−	0.611833i	$-0.209567\pi$
$108$	−4.82405	−	2.53186i	−0.464194	−	0.243628i
$109$	1.64245	−	6.66368i	0.157318	−	0.638265i	−0.838337	−	0.545152i	$-0.816472\pi$
$109$	1.64245	−	6.66368i	0.157318	−	0.638265i	0.995656	−	0.0931133i	$-0.0296819\pi$
$110$	−12.3020	−	1.49373i	−1.17295	−	0.142422i
$111$	−0.388953	+	0.439037i	−0.0369178	+	0.0416716i
$112$	54.9622	−	37.9377i	5.19344	−	3.58477i
$113$	−3.18753	+	4.61793i	−0.299857	+	0.434419i	−0.943731	−	0.330713i	$-0.892711\pi$
$113$	−3.18753	+	4.61793i	−0.299857	+	0.434419i	0.643874	+	0.765132i	$0.277326\pi$
$114$	17.9447	−	4.42297i	1.68067	−	0.414249i
$115$	6.65403	+	0.807946i	0.620492	+	0.0753413i
$116$	−26.1845	+	13.7427i	−2.43117	+	1.27598i
$117$	3.56334	−	0.550090i	0.329431	−	0.0508558i
$118$	−4.55171	−	2.38892i	−0.419019	−	0.219918i
$119$	−0.241723	−	0.166849i	−0.0221587	−	0.0152951i
$120$	−6.13800	+	8.89243i	−0.560320	+	0.811764i
$121$	3.47233	−	3.07621i	0.315666	−	0.279656i
$122$	−8.53925	−	9.63882i	−0.773108	−	0.872658i
$123$	−1.78341	−	0.676359i	−0.160805	−	0.0609852i
$124$	−12.6777	+	24.1553i	−1.13849	+	2.16921i
$125$	−9.32063	−	3.53485i	−0.833662	−	0.316166i
$126$	11.9688	+	2.95005i	1.06627	+	0.262811i
$127$	−11.6287	+	10.3021i	−1.03188	+	0.914166i	−0.996364	−	0.0852032i	$-0.972846\pi$
$127$	−11.6287	+	10.3021i	−1.03188	+	0.914166i	−0.0355164	+	0.999369i	$0.511308\pi$
$128$	−30.1211	+	20.7911i	−2.66235	+	1.83769i
$129$	3.16914	+	8.35633i	0.279027	+	0.735734i
$130$	−0.365276	−	11.2926i	−0.0320368	−	0.990428i
$131$	−0.251495	+	0.663137i	−0.0219732	+	0.0579385i	−0.945554	−	0.325465i	$-0.894479\pi$
$131$	−0.251495	+	0.663137i	−0.0219732	+	0.0579385i	0.923581	+	0.383404i	$0.125248\pi$
$132$	−5.15608	−	20.9191i	−0.448779	−	1.82077i
$133$	−27.0846	+	14.2151i	−2.34853	+	1.23261i
$134$	−0.00281389	−	0.00741963i	−0.000243083	−	0.000640958i
$135$	−1.13985	+	0.138403i	−0.0981030	+	0.0119119i
$136$	0.503598	+	0.347609i	0.0431832	+	0.0298072i
$137$	1.23073	−	4.99329i	0.105149	−	0.426605i	−0.894648	−	0.446772i	$-0.852574\pi$
$137$	1.23073	−	4.99329i	0.105149	−	0.426605i	0.999797	+	0.0201667i	$0.00641969\pi$
$138$	3.81267	+	15.4686i	0.324556	+	1.31678i
$139$	−0.643169	−	5.29698i	−0.0545529	−	0.449284i	−0.994234	−	0.107232i	$-0.965801\pi$
$139$	−0.643169	−	5.29698i	−0.0545529	−	0.449284i	0.939681	−	0.342052i	$-0.111122\pi$
$140$	10.0196	−	26.4196i	0.846815	−	2.23287i
$141$	−0.664913	+	2.69766i	−0.0559958	+	0.227184i
$142$	33.8161	−	8.33492i	2.83778	−	0.699451i
$143$	10.9728	+	9.10519i	0.917591	+	0.761414i
$144$	−14.3559	−	3.53841i	−1.19633	−	0.294868i
$145$	−2.89638	+	5.51858i	−0.240531	+	0.458293i
$146$	24.2832			2.00970
$147$	−13.4019			−1.10537
$148$	−1.48505	+	2.82953i	−0.122071	+	0.232586i
$149$	−6.55399	−	7.39793i	−0.536924	−	0.606062i	0.415965	−	0.909380i	$-0.363444\pi$
$149$	−6.55399	−	7.39793i	−0.536924	−	0.606062i	−0.952889	+	0.303319i	$0.901905\pi$
$150$		−	10.0475i		−	0.820372i
$151$	−10.1992	+	11.5126i	−0.830002	+	0.936879i	−0.998810	−	0.0487703i	$-0.984470\pi$
$151$	−10.1992	+	11.5126i	−0.830002	+	0.936879i	0.168808	+	0.985649i	$0.446008\pi$
$152$	56.4272	−	29.6153i	4.57685	−	2.40212i
$153$	0.00783809	+	0.0645525i	0.000633672	+	0.00521876i
$154$	22.6546	+	43.1648i	1.82556	+	3.47832i
$155$	0.693022	+	5.70755i	0.0556649	+	0.458441i
$156$	18.1321	−	7.55579i	1.45173	−	0.604948i
$157$	−0.822422	+	6.77326i	−0.0656364	+	0.540565i	0.922388	+	0.386265i	$0.126235\pi$
$157$	−0.822422	+	6.77326i	−0.0656364	+	0.540565i	−0.988024	+	0.154299i	$0.950688\pi$
$158$	10.6605	−	4.04301i	0.848108	−	0.321645i
$159$	−12.6077	−	6.61705i	−0.999859	−	0.524766i
$160$	−8.76670	+	23.1159i	−0.693069	+	1.82747i
$161$	−12.2537	−	23.3474i	−0.965723	−	1.84003i
$162$	−1.26829	−	2.41652i	−0.0996459	−	0.189859i
$163$	−3.30054	−	13.3908i	−0.258518	−	1.04885i	−0.946392	−	0.323020i	$-0.895302\pi$
$163$	−3.30054	−	13.3908i	−0.258518	−	1.04885i	0.687874	−	0.725830i	$-0.258544\pi$
$164$	−10.3157	−	1.25255i	−0.805521	−	0.0978080i
$165$	−3.39883	−	3.01110i	−0.264599	−	0.234414i
$166$	17.0619	+	24.7185i	1.32426	+	1.91853i
$167$	7.17962	+	2.72287i	0.555576	+	0.210702i	0.616382	−	0.787448i	$-0.288598\pi$
$167$	7.17962	+	2.72287i	0.555576	+	0.210702i	−0.0608060	+	0.998150i	$0.519367\pi$
$168$	42.5047			3.27931
$169$	−6.67799	+	11.1537i	−0.513692	+	0.857975i
$170$	0.203770			0.0156285
$171$	6.33197	+	2.40140i	0.484218	+	0.183640i
$172$	27.6592	+	40.0712i	2.10899	+	3.05540i
$173$	9.19275	+	8.14407i	0.698912	+	0.619182i	0.935873	−	0.352337i	$-0.114613\pi$
$173$	9.19275	+	8.14407i	0.698912	+	0.619182i	−0.236961	+	0.971519i	$0.576151\pi$
$174$	−14.7054	−	1.78556i	−1.11482	−	0.135363i
$175$	3.97961	+	16.1459i	0.300830	+	1.22052i
$176$	−27.1729	−	51.7736i	−2.04823	−	3.90258i
$177$	−0.875345	−	1.66783i	−0.0657950	−	0.125362i
$178$	5.46546	−	14.4112i	0.409654	−	1.08017i
$179$	−0.640006	−	0.335901i	−0.0478363	−	0.0251064i	0.440635	−	0.897686i	$-0.354753\pi$
$179$	−0.640006	−	0.335901i	−0.0478363	−	0.0251064i	−0.488472	+	0.872580i	$0.662445\pi$
$180$	−5.84913	+	2.21828i	−0.435968	+	0.165341i
$181$	2.06381	−	16.9970i	0.153401	−	1.26337i	−0.689094	−	0.724672i	$-0.741991\pi$
$181$	2.06381	−	16.9970i	0.153401	−	1.26337i	0.842496	−	0.538703i	$-0.181086\pi$
$182$	−35.7427	+	26.4174i	−2.64943	+	1.95819i
$183$	−0.568752	−	4.68409i	−0.0420433	−	0.346258i
$184$	25.5289	+	48.6412i	1.88201	+	3.58588i
$185$	0.0811802	+	0.668579i	0.00596848	+	0.0491549i
$186$	−12.1001	+	6.35064i	−0.887224	+	0.465651i
$187$	−0.170525	+	0.192483i	−0.0124701	+	0.0140758i
$188$			15.1369i			1.10398i
$189$	2.99523	+	3.38091i	0.217871	+	0.245925i
$190$	9.86198	−	18.7904i	0.715463	−	1.36320i
$191$	−9.41936			−0.681561			−0.340781	−	0.940143i	$-0.610691\pi$
$191$	−9.41936			−0.681561			−0.340781	+	0.940143i	$0.610691\pi$
$192$	−29.1896			−2.10658
$193$	−6.17271	+	11.7611i	−0.444321	+	0.846584i	0.555564	+	0.831474i	$0.312502\pi$
$193$	−6.17271	+	11.7611i	−0.444321	+	0.846584i	−0.999886	+	0.0151102i	$0.995190\pi$
$194$	−14.9114	−	3.67534i	−1.07058	−	0.263874i
$195$	2.24040	−	3.48139i	0.160438	−	0.249308i
$196$	−70.8933	+	17.4736i	−5.06381	+	1.24812i
$197$	−1.67953	+	6.81411i	−0.119661	+	0.485485i	0.880278	+	0.474458i	$0.157356\pi$
$197$	−1.67953	+	6.81411i	−0.119661	+	0.485485i	−0.999939	+	0.0110265i	$0.996490\pi$
$198$	3.82711	−	10.0913i	0.271981	−	0.717156i
$199$	2.83473	+	23.3461i	0.200949	+	1.65496i	0.648877	+	0.760893i	$0.275239\pi$
$199$	2.83473	+	23.3461i	0.200949	+	1.65496i	−0.447929	+	0.894069i	$0.647838\pi$
$200$	−8.29100	−	33.6379i	−0.586262	−	2.37856i
$201$	0.000695843	−	0.00282315i	4.90810e−5	−	0.000199129i
$202$	15.6253	+	10.7854i	1.09939	+	0.758857i
$203$	24.3383	−	2.95521i	1.70822	−	0.207415i
$204$	0.125626	+	0.331249i	0.00879560	+	0.0231921i
$205$	−1.93922	+	1.01778i	−0.135441	+	0.0710849i
$206$	1.70080	+	6.90040i	0.118500	+	0.480774i
$207$	−2.07005	+	5.45827i	−0.143878	+	0.379376i
$208$	42.8713	−	31.6861i	2.97259	−	2.19704i
$209$	9.49662	+	25.0405i	0.656895	+	1.73209i
$210$	11.6487	−	8.04051i	0.803836	−	0.554848i
$211$	1.07793	−	0.954965i	0.0742079	−	0.0657425i	−0.625203	−	0.780462i	$-0.714984\pi$
$211$	1.07793	−	0.954965i	0.0742079	−	0.0657425i	0.699411	+	0.714719i	$0.253446\pi$
$212$	−75.3196	−	18.5646i	−5.17297	−	1.27502i
$213$	11.9324	+	4.52535i	0.817592	+	0.310072i
$214$	18.4382	−	35.1310i	1.26041	−	2.40151i
$215$	9.59495	+	3.63889i	0.654370	+	0.248170i
$216$	−6.24016	−	7.04368i	−0.424589	−	0.479262i
$217$	16.9291	−	14.9979i	1.14922	−	1.01812i
$218$	10.6400	−	15.4147i	0.720632	−	1.04402i
$219$	7.32277	+	5.05454i	0.494827	+	0.341554i
$220$	−21.9050	−	11.4966i	−1.47683	−	0.775103i
$221$	−0.197159	−	0.126879i	−0.0132624	−	0.00853480i
$222$	−1.41740	+	0.743910i	−0.0951298	+	0.0499279i
$223$	−14.1207	−	1.71457i	−0.945594	−	0.114816i	−0.366809	−	0.930296i	$-0.619550\pi$
$223$	−14.1207	−	1.71457i	−0.945594	−	0.114816i	−0.578785	+	0.815480i	$0.696473\pi$
$224$	94.4263	−	23.2740i	6.30912	−	1.55506i
$225$	2.09137	−	3.02988i	0.139425	−	0.201992i
$226$	−12.6029	+	8.69915i	−0.838332	+	0.578659i
$227$	8.31726	−	9.38824i	0.552036	−	0.623119i	−0.404569	−	0.914507i	$-0.632579\pi$
$227$	8.31726	−	9.38824i	0.552036	−	0.623119i	0.956605	+	0.291388i	$0.0941170\pi$
$228$	36.6258	+	4.44717i	2.42560	+	0.294521i
$229$	5.86630	−	23.8005i	0.387656	−	1.57278i	−0.375661	−	0.926757i	$-0.622584\pi$
$229$	5.86630	−	23.8005i	0.387656	−	1.57278i	0.763317	−	0.646024i	$-0.223570\pi$
$230$	16.1977	+	8.50119i	1.06804	+	0.560552i
$231$	−2.15307	+	17.7322i	−0.141662	+	1.16669i
$232$	−50.7057	+	6.15679i	−3.32899	+	0.404213i
$233$	9.74328	−	14.1156i	0.638303	−	0.924742i	−0.361668	−	0.932307i	$-0.617793\pi$
$233$	9.74328	−	14.1156i	0.638303	−	0.924742i	0.999971	+	0.00756483i	$0.00240798\pi$
$234$	9.62519	+	2.04475i	0.629218	+	0.133670i
$235$	1.81225	+	2.62550i	0.118218	+	0.171269i
$236$	−6.80493	−	7.68118i	−0.442963	−	0.500002i
$237$	4.05631	+	0.999790i	0.263486	+	0.0649434i
$238$	−0.455352	−	0.659691i	−0.0295161	−	0.0427614i
$239$		−	1.88227i		−	0.121754i	−0.998145	−	0.0608770i	$-0.980610\pi$
$239$		−	1.88227i		−	0.121754i	0.998145	−	0.0608770i	$-0.0193897\pi$
$240$	−13.9719	+	9.64412i	−0.901883	+	0.622525i
$241$	3.03114	−	0.368047i	0.195253	−	0.0237080i	−0.0223258	−	0.999751i	$-0.507107\pi$
$241$	3.03114	−	0.368047i	0.195253	−	0.0237080i	0.217579	+	0.976043i	$0.430184\pi$
$242$	11.8376	−	4.48941i	0.760951	−	0.288590i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−9.11576	−	24.0363i	−0.583576	−	1.53876i
$245$	−10.2044	+	11.5184i	−0.651937	+	0.735884i
$246$	−3.89631	−	3.45183i	−0.248419	−	0.220080i
$247$	−21.2420	+	12.0402i	−1.35160	+	0.766097i
$248$	−35.2696	+	31.2461i	−2.23962	+	1.98413i
$249$			11.0055i			0.697443i
$250$	−20.3632	−	18.0402i	−1.28788	−	1.14097i
$251$	1.60372	−	0.395281i	0.101226	−	0.0249499i	−0.188377	−	0.982097i	$-0.560323\pi$
$251$	1.60372	−	0.395281i	0.101226	−	0.0249499i	0.289603	+	0.957147i	$0.406477\pi$
$252$	20.2522	+	13.9791i	1.27577	+	0.880598i
$253$	−21.5853	+	8.18624i	−1.35706	+	0.514664i
$254$	−39.6438	+	15.0349i	−2.48747	+	0.943373i
$255$	0.0614483	+	0.0424147i	0.00384804	+	0.00265611i
$256$	−40.3002	+	9.93310i	−2.51876	+	0.620818i
$257$	−6.43562	−	5.70147i	−0.401443	−	0.355648i	0.438114	−	0.898920i	$-0.355647\pi$
$257$	−6.43562	−	5.70147i	−0.401443	−	0.355648i	−0.839557	+	0.543272i	$0.817185\pi$
$258$			24.3904i			1.51848i
$259$	1.98306	−	1.75684i	0.123222	−	0.109165i
$260$	7.31214	−	21.3369i	0.453480	−	1.32326i
$261$	−4.06285	−	3.59937i	−0.251484	−	0.222796i
$262$	−1.28351	+	1.44879i	−0.0792957	+	0.0895064i
$263$	8.46145	+	22.3110i	0.521755	+	1.37576i	0.894186	+	0.447696i	$0.147755\pi$
$263$	8.46145	+	22.3110i	0.521755	+	1.37576i	−0.372431	+	0.928060i	$0.621476\pi$
$264$	4.48565	−	36.9426i	0.276073	−	2.27366i
$265$	−15.2868	+	5.79752i	−0.939061	+	0.356139i
$266$	−82.8705	+	10.0623i	−5.08112	+	0.616959i
$267$	4.64784	−	3.20817i	0.284443	−	0.196337i
$268$		−	0.0158411i		−	0.000967648i
$269$	−7.71132	−	11.1718i	−0.470168	−	0.681155i	0.514122	−	0.857717i	$-0.328118\pi$
$269$	−7.71132	−	11.1718i	−0.470168	−	0.681155i	−0.984290	+	0.176562i	$0.943502\pi$
$270$	−3.04259	−	0.749931i	−0.185166	−	0.0456393i
$271$	−5.49500	−	6.20257i	−0.333797	−	0.376779i	0.557517	−	0.830166i	$-0.311754\pi$
$271$	−5.49500	−	6.20257i	−0.333797	−	0.376779i	−0.891314	+	0.453386i	$0.850216\pi$
$272$	0.546168	+	0.791261i	0.0331163	+	0.0479772i
$273$	−16.2772	+	0.526510i	−0.985142	+	0.0318659i
$274$	7.97285	−	11.5507i	0.481658	−	0.697802i
$275$	14.4531	−	1.75492i	0.871553	−	0.105826i
$276$	−3.83353	+	31.5720i	−0.230752	+	1.90041i
$277$	7.35248	+	3.85888i	0.441768	+	0.231858i	0.670915	−	0.741534i	$-0.265901\pi$
$277$	7.35248	+	3.85888i	0.441768	+	0.231858i	−0.229147	+	0.973392i	$0.573594\pi$
$278$	3.48498	−	14.1391i	0.209015	−	0.848007i
$279$	−4.97075	−	0.603559i	−0.297591	−	0.0361341i
$280$	32.3637	−	36.5311i	1.93410	−	2.18315i
$281$	9.57806	−	6.61126i	0.571379	−	0.394394i	−0.247049	−	0.969003i	$-0.579461\pi$
$281$	9.57806	−	6.61126i	0.571379	−	0.394394i	0.818428	+	0.574608i	$0.194846\pi$
$282$	−4.30739	+	6.24033i	−0.256501	+	0.371606i
$283$	4.29060	−	1.05754i	0.255050	−	0.0628642i	−0.109718	−	0.993963i	$-0.534995\pi$
$283$	4.29060	−	1.05754i	0.255050	−	0.0628642i	0.364767	+	0.931099i	$0.381148\pi$
$284$	69.0199	+	8.38053i	4.09558	+	0.497293i
$285$	6.88516	−	3.61361i	0.407842	−	0.214052i
$286$	19.1884	+	33.8534i	1.13464	+	2.00179i
$287$	7.62843	+	4.00371i	0.450292	+	0.236331i
$288$	−17.7197	−	12.2310i	−1.04414	−	0.720719i
$289$	−9.65470	+	13.9872i	−0.567923	+	0.822779i
$290$	−12.7315	+	11.2792i	−0.747622	+	0.662335i
$291$	−3.73162	−	4.21213i	−0.218751	−	0.246919i
$292$	45.3260	+	17.1899i	2.65251	+	1.00596i
$293$	−6.30725	+	12.0175i	−0.368474	+	0.702068i	−0.997138	−	0.0756093i	$-0.975910\pi$
$293$	−6.30725	+	12.0175i	−0.368474	+	0.702068i	0.628664	+	0.777677i	$0.283602\pi$
$294$	−34.1987	−	12.9698i	−1.99451	−	0.756416i
$295$	−2.09993	−	0.517587i	−0.122263	−	0.0301351i
$296$	−4.13146	+	3.66015i	−0.240136	+	0.212742i
$297$	3.25458	−	2.24648i	0.188850	−	0.130354i
$298$	−9.56487	−	25.2205i	−0.554078	−	1.46098i
$299$	−10.3788	−	18.3110i	−0.600223	−	1.05895i
$300$	7.11252	−	18.7542i	0.410641	−	1.08277i
$301$	−9.66058	−	39.1945i	−0.556826	−	2.25913i
$302$	−37.1675	+	19.5070i	−2.13875	+	1.12250i
$303$	2.46695	+	6.50481i	0.141722	+	0.373691i
$304$	99.3984	−	12.0691i	5.70089	−	0.692213i
$305$	−4.45884	−	3.07772i	−0.255313	−	0.176230i
$306$	−0.0424703	+	0.172309i	−0.00242786	+	0.00985023i
$307$	1.19098	+	4.83201i	0.0679731	+	0.275778i	0.995087	−	0.0990012i	$-0.0315648\pi$
$307$	1.19098	+	4.83201i	0.0679731	+	0.275778i	−0.927114	+	0.374779i	$0.877719\pi$
$308$	11.7302	+	96.6065i	0.668387	+	5.50467i
$309$	−0.923428	+	2.43488i	−0.0525320	+	0.138515i
$310$	−3.75510	+	15.2350i	−0.213275	+	0.865292i
$311$	−8.87234	+	2.18684i	−0.503104	+	0.124004i	−0.482697	−	0.875788i	$-0.660343\pi$
$311$	−8.87234	+	2.18684i	−0.503104	+	0.124004i	−0.0204077	+	0.999792i	$0.506496\pi$
$312$	33.9114	−	1.09692i	1.91986	−	0.0621006i
$313$	32.5236	+	8.01635i	1.83834	+	0.453111i	0.996273	−	0.0862564i	$-0.0274904\pi$
$313$	32.5236	+	8.01635i	1.83834	+	0.453111i	0.842071	+	0.539367i	$0.181337\pi$
$314$	−8.65351	+	16.4879i	−0.488346	+	0.930466i
$315$	5.18636			0.292218
$316$	22.7605			1.28038
$317$	−0.788631	+	1.50261i	−0.0442939	+	0.0843950i	−0.906597	−	0.421998i	$-0.861329\pi$
$317$	−0.788631	+	1.50261i	−0.0442939	+	0.0843950i	0.862303	+	0.506393i	$0.169021\pi$
$318$	−25.7684	−	29.0865i	−1.44502	−	1.63109i
$319$		−	21.4653i		−	1.20183i
$320$	−22.2254	+	25.0873i	−1.24244	+	1.40242i
$321$	12.8727	−	6.75609i	0.718481	−	0.377088i
$322$	−8.67387	−	71.4358i	−0.483376	−	3.98096i
$323$	−0.204647	−	0.389922i	−0.0113869	−	0.0216959i
$324$	−0.656695	−	5.40837i	−0.0364831	−	0.300465i
$325$	3.59172	+	12.7790i	0.199233	+	0.708849i
$326$	4.53687	−	37.3645i	0.251274	−	2.06943i
$327$	6.41712	−	2.43369i	0.354868	−	0.134584i
$328$	−15.8928	−	8.34120i	−0.877534	−	0.460566i
$329$	4.45014	−	11.7341i	0.245344	−	0.646920i
$330$	−5.75902	−	10.9729i	−0.317024	−	0.604038i
$331$	4.08037	+	7.77450i	0.224278	+	0.427325i	0.971430	−	0.237328i	$-0.0762716\pi$
$331$	4.08037	+	7.77450i	0.224278	+	0.427325i	−0.747152	+	0.664653i	$0.768579\pi$
$332$	14.3491	+	58.2165i	0.787508	+	3.19504i
$333$	−0.582271	−	0.0707005i	−0.0319083	−	0.00387436i
$334$	15.6857	+	13.8963i	0.858281	+	0.760371i
$335$	−0.00189656	−	0.00274763i	−0.000103620	−	0.000150119i
$336$	62.4442	+	23.6820i	3.40661	+	1.29196i
$337$	−19.3089			−1.05182			−0.525911	−	0.850540i	$-0.676276\pi$
$337$	−19.3089			−1.05182			−0.525911	+	0.850540i	$0.676276\pi$
$338$	−27.8348	+	21.9989i	−1.51401	+	1.19658i
$339$	−5.61121			−0.304759
$340$	0.380349	+	0.144247i	0.0206273	+	0.00782291i
$341$	−11.2487	−	16.2966i	−0.609151	−	0.882508i
$342$	13.8338	+	12.2557i	0.748045	+	0.662710i
$343$	28.7057	+	3.48550i	1.54996	+	0.188199i
$344$	20.1265	+	81.6566i	1.08515	+	4.40263i
$345$	3.11499	+	5.93513i	0.167706	+	0.319536i
$346$	15.5763	+	29.6782i	0.837387	+	1.59551i
$347$	8.06571	−	21.2675i	0.432990	−	1.14170i	−0.524035	−	0.851697i	$-0.675574\pi$
$347$	8.06571	−	21.2675i	0.432990	−	1.14170i	0.957025	−	0.290005i	$-0.0936568\pi$
$348$	−26.1845	−	13.7427i	−1.40364	−	0.736686i
$349$	−20.1678	+	7.64864i	−1.07956	+	0.409422i	−0.829327	−	0.558764i	$-0.811276\pi$
$349$	−20.1678	+	7.64864i	−1.07956	+	0.409422i	−0.250231	+	0.968186i	$0.580507\pi$
$350$	−5.47030	+	45.0520i	−0.292400	+	2.40813i
$351$	2.47692	+	2.62009i	0.132208	+	0.139850i
$352$	−10.2633	−	84.5260i	−0.547036	−	4.50525i
$353$	2.33921	+	4.45699i	0.124503	+	0.237222i	0.939728	−	0.341924i	$-0.111079\pi$
$353$	2.33921	+	4.45699i	0.124503	+	0.237222i	−0.815224	+	0.579146i	$0.803386\pi$
$354$	−0.619622	−	5.10305i	−0.0329325	−	0.271224i
$355$	12.9748	−	6.80972i	0.688633	−	0.361422i
$356$	20.4032	−	23.0304i	1.08137	−	1.22061i
$357$		−	0.293715i		−	0.0155451i
$358$	−1.30808	−	1.47651i	−0.0691340	−	0.0780362i
$359$	−12.5615	+	23.9339i	−0.662970	+	1.26318i	0.289099	+	0.957299i	$0.406644\pi$
$359$	−12.5615	+	23.9339i	−0.662970	+	1.26318i	−0.952069	+	0.305884i	$0.901048\pi$
$360$	−10.8051			−0.569479
$361$	−26.8606			−1.41372
$362$	21.7153	−	41.3751i	1.14133	−	2.17463i
$363$	4.50418	+	1.11018i	0.236408	+	0.0582694i
$364$	−85.4165	+	24.0076i	−4.47704	+	1.25834i
$365$	9.91984	−	2.44502i	0.519228	−	0.127978i
$366$	3.08175	−	12.5031i	0.161086	−	0.653550i
$367$	13.3550	−	35.2144i	0.697128	−	1.83817i	0.176710	−	0.984263i	$-0.443455\pi$
$367$	13.3550	−	35.2144i	0.697128	−	1.83817i	0.520418	−	0.853912i	$-0.325776\pi$
$368$	10.4038	+	85.6830i	0.542336	+	4.46654i
$369$	−0.456461	−	1.85193i	−0.0237624	−	0.0964078i
$370$	−0.439870	+	1.78462i	−0.0228678	+	0.0927781i
$371$	52.9294	+	36.5345i	2.74796	+	1.89678i
$372$	−27.0811	+	3.28825i	−1.40409	+	0.170488i
$373$	3.12882	+	8.25002i	0.162004	+	0.427170i	0.991297	−	0.131645i	$-0.0420257\pi$
$373$	3.12882	+	8.25002i	0.162004	+	0.427170i	−0.829293	+	0.558814i	$0.811257\pi$
$374$	−0.621420	+	0.326146i	−0.0321328	+	0.0168646i
$375$	−2.38560	−	9.67875i	−0.123192	−	0.499808i
$376$	−9.27129	+	24.4464i	−0.478130	+	1.26073i
$377$	19.3415	−	2.98584i	0.996139	−	0.153779i
$378$	4.37122	+	11.5260i	0.224831	+	0.592832i
$379$	18.9239	−	13.0622i	0.972057	−	0.670962i	0.0276072	−	0.999619i	$-0.491211\pi$
$379$	18.9239	−	13.0622i	0.972057	−	0.670962i	0.944449	+	0.328657i	$0.106596\pi$
$380$	31.7095	−	28.0922i	1.62667	−	1.44110i
$381$	−15.0843	−	3.71796i	−0.772794	−	0.190477i
$382$	−24.0361	−	9.11567i	−1.22979	−	0.466398i
$383$	−13.1739	+	25.1007i	−0.673153	+	1.28259i	0.273978	+	0.961736i	$0.411661\pi$
$383$	−13.1739	+	25.1007i	−0.673153	+	1.28259i	−0.947130	+	0.320849i	$0.896032\pi$
$384$	−34.2215	−	12.9785i	−1.74636	−	0.662306i
$385$	13.6007	+	15.3520i	0.693155	+	0.782411i
$386$	−27.1333	+	24.0380i	−1.38105	+	1.22350i
$387$	−5.07685	+	7.35509i	−0.258071	+	0.373880i
$388$	−25.2313	−	17.4159i	−1.28092	−	0.884158i
$389$	−19.9497	−	10.4704i	−1.01149	−	0.530872i	−0.124286	−	0.992246i	$-0.539664\pi$
$389$	−19.9497	−	10.4704i	−1.01149	−	0.530872i	−0.887205	+	0.461375i	$0.847356\pi$
$390$	9.08614	−	6.71555i	0.460095	−	0.340055i
$391$	0.336119	−	0.176409i	0.0169983	−	0.00892139i
$392$	−125.196	−	15.2016i	−6.32336	−	0.767795i
$393$	−0.688616	+	0.169729i	−0.0347361	+	0.00856167i
$394$	−10.8802	+	15.7627i	−0.548136	+	0.794111i
$395$	3.94781	−	2.72498i	0.198636	−	0.137109i
$396$	14.2871	−	16.1268i	0.717951	−	0.810400i
$397$	−5.61011	−	0.681190i	−0.281563	−	0.0341880i	−0.0214632	−	0.999770i	$-0.506832\pi$
$397$	−5.61011	−	0.681190i	−0.281563	−	0.0341880i	−0.260100	+	0.965582i	$0.583756\pi$
$398$	−15.3598	+	62.3173i	−0.769919	+	3.12368i
$399$	−27.0846	−	14.2151i	−1.35593	−	0.711645i
$400$	6.56131	−	54.0372i	0.328065	−	2.70186i
$401$	4.57996	−	0.556108i	0.228712	−	0.0277707i	−0.00537804	−	0.999986i	$-0.501712\pi$
$401$	4.57996	−	0.556108i	0.228712	−	0.0277707i	0.234090	+	0.972215i	$0.424789\pi$
$402$	0.00450776	−	0.00653062i	0.000224827	−	0.000325718i
$403$	13.1195	−	12.4026i	0.653527	−	0.617818i
$404$	21.5307	+	31.1926i	1.07119	+	1.55189i
$405$	−0.761415	−	0.859459i	−0.0378350	−	0.0427069i
$406$	64.9658	+	16.0126i	3.22420	+	0.794693i
$407$	−1.31767	−	1.90897i	−0.0653143	−	0.0946241i
$408$			0.611918i			0.0302944i
$409$	31.7030	−	21.8830i	1.56761	−	1.08204i	0.610623	−	0.791922i	$-0.290919\pi$
$409$	31.7030	−	21.8830i	1.56761	−	1.08204i	0.956989	−	0.290123i	$-0.0936962\pi$
$410$	−5.93341	+	0.720446i	−0.293030	+	0.0355803i
$411$	4.80853	−	1.82364i	0.237187	−	0.0899533i
$412$	−1.71010	+	14.0840i	−0.0842507	+	0.693867i
$413$	3.01693	+	7.95499i	0.148453	+	0.391440i
$414$	−10.5646	+	11.9249i	−0.519221	+	0.586079i
$415$	9.45875	+	8.37972i	0.464312	+	0.411344i
$416$	74.7353	−	21.0055i	3.66420	−	1.02988i
$417$	3.99396	−	3.53834i	0.195585	−	0.173273i
$418$			73.0881i			3.57486i
$419$	6.81336	+	6.03611i	0.332855	+	0.294883i	0.812951	−	0.582332i	$-0.197860\pi$
$419$	6.81336	+	6.03611i	0.332855	+	0.294883i	−0.480096	+	0.877216i	$0.659398\pi$
$420$	27.4347	−	6.76206i	1.33868	−	0.329955i
$421$	14.2409	+	9.82981i	0.694061	+	0.479076i	0.862122	−	0.506701i	$-0.169135\pi$
$421$	14.2409	+	9.82981i	0.694061	+	0.479076i	−0.168061	+	0.985777i	$0.553751\pi$
$422$	3.67481	−	1.39367i	0.178887	−	0.0678429i
$423$	−2.59784	+	0.985231i	−0.126311	+	0.0479036i
$424$	−110.272	−	76.1149i	−5.35526	−	3.69647i
$425$	−0.232444	+	0.0572923i	−0.0112752	+	0.00277908i
$426$	26.0692	+	23.0953i	1.26306	+	1.11897i
$427$			21.3127i			1.03139i
$428$	59.2848	−	52.5218i	2.86564	−	2.53874i
$429$	−1.26017	+	14.2028i	−0.0608416	+	0.685716i
$430$	20.9626	+	18.5712i	1.01090	+	0.895583i
$431$	23.3952	−	26.4078i	1.12691	−	1.27202i	0.168788	−	0.985652i	$-0.446015\pi$
$431$	23.3952	−	26.4078i	1.12691	−	1.27202i	0.958121	−	0.286364i	$-0.0924468\pi$
$432$	−5.24303	−	13.8247i	−0.252255	−	0.665142i
$433$	−1.75154	+	14.4252i	−0.0841736	+	0.693232i	0.888143	+	0.459566i	$0.151995\pi$
$433$	−1.75154	+	14.4252i	−0.0841736	+	0.693232i	−0.972317	+	0.233666i	$0.924928\pi$
$434$	57.7135	−	21.8879i	2.77034	−	1.05065i
$435$	−6.18703	+	0.751242i	−0.296646	+	0.0360193i
$436$	30.7721	−	21.2404i	1.47372	−	1.01723i
$437$		−	39.5326i		−	1.89110i
$438$	13.7945	+	19.9847i	0.659124	+	0.954907i
$439$	−19.4337	−	4.78996i	−0.927518	−	0.228613i	−0.253506	−	0.967334i	$-0.581584\pi$
$439$	−19.4337	−	4.78996i	−0.927518	−	0.228613i	−0.674011	+	0.738721i	$0.735430\pi$
$440$	−28.3353	−	31.9839i	−1.35083	−	1.52477i
$441$	−7.61316	−	11.0296i	−0.362532	−	0.525218i
$442$	−0.380317	−	0.514568i	−0.0180898	−	0.0244755i
$443$	7.71138	−	11.1719i	0.366379	−	0.530792i	−0.595828	−	0.803112i	$-0.703176\pi$
$443$	7.71138	−	11.1719i	0.366379	−	0.530792i	0.962206	+	0.272321i	$0.0877912\pi$
$444$	−3.17227	+	0.385183i	−0.150549	+	0.0182800i
$445$	0.781639	−	6.43737i	0.0370532	−	0.305161i
$446$	−34.3736	−	18.0406i	−1.62764	−	0.854249i
$447$	2.36528	−	9.59633i	0.111874	−	0.453891i
$448$	130.884	+	15.8922i	6.18367	+	0.750834i
$449$	−18.6587	+	21.0613i	−0.880559	+	0.993946i	0.119440	+	0.992841i	$0.461890\pi$
$449$	−18.6587	+	21.0613i	−0.880559	+	0.993946i	−0.999999	+	0.00110420i	$0.999649\pi$
$450$	8.26890	−	5.70761i	0.389800	−	0.269059i
$451$	4.28484	−	6.20766i	0.201765	−	0.292307i
$452$	−29.6821	+	7.31597i	−1.39613	+	0.344114i
$453$	−15.2685	−	1.85393i	−0.717376	−	0.0871052i
$454$	30.3093	−	15.9075i	1.42249	−	0.746578i
$455$	−11.9412	+	14.3905i	−0.559812	+	0.674637i
$456$	56.4272	+	29.6153i	2.64245	+	1.38686i
$457$	1.36482	+	0.942070i	0.0638438	+	0.0440682i	0.599559	−	0.800330i	$-0.295343\pi$
$457$	1.36482	+	0.942070i	0.0638438	+	0.0440682i	−0.535715	+	0.844399i	$0.679958\pi$
$458$	38.0026	−	55.0563i	1.77575	−	2.57261i
$459$	−0.0486731	+	0.0431206i	−0.00227187	+	0.00201270i
$460$	24.2159	+	27.3342i	1.12907	+	1.27446i
$461$	12.0870	+	4.58399i	0.562948	+	0.213498i	0.619630	−	0.784894i	$-0.287283\pi$
$461$	12.0870	+	4.58399i	0.562948	+	0.213498i	−0.0566819	+	0.998392i	$0.518052\pi$
$462$	−22.6546	+	43.1648i	−1.05399	+	2.00821i
$463$	−5.61746	−	2.13042i	−0.261066	−	0.0990092i	0.220599	−	0.975364i	$-0.429199\pi$
$463$	−5.61746	−	2.13042i	−0.261066	−	0.0990092i	−0.481665	+	0.876355i	$0.659968\pi$
$464$	−77.9227	−	19.2062i	−3.61747	−	0.891626i
$465$	−4.30354	+	3.81260i	−0.199572	+	0.176805i
$466$	38.5231	−	26.5906i	1.78455	−	1.23178i
$467$	−11.7467	−	30.9735i	−0.543573	−	1.43328i	−0.872352	−	0.488878i	$-0.837406\pi$
$467$	−11.7467	−	30.9735i	−0.543573	−	1.43328i	0.328779	−	0.944407i	$-0.393363\pi$
$468$	16.5185	+	10.6302i	0.763568	+	0.491383i
$469$	−0.00465715	+	0.0122799i	−0.000215047	+	0.000567033i
$470$	2.08360	+	8.45350i	0.0961094	+	0.389931i
$471$	−6.04147	+	3.17081i	−0.278376	+	0.146103i
$472$	−6.28538	−	16.5732i	−0.289308	−	0.762843i
$473$	−35.0851	+	4.26010i	−1.61321	+	0.195880i
$474$	9.38322	+	6.47677i	0.430985	+	0.297488i
$475$	−5.96657	+	24.2073i	−0.273765	+	1.11071i
$476$	−0.382950	−	1.55369i	−0.0175525	−	0.0712133i
$477$	−1.71629	−	14.1349i	−0.0785833	−	0.647192i
$478$	1.82158	−	4.80312i	0.0833174	−	0.219690i
$479$	4.37668	−	17.7569i	0.199976	−	0.811333i	−0.782147	−	0.623093i	$-0.785876\pi$
$479$	4.37668	−	17.7569i	0.199976	−	0.811333i	0.982123	−	0.188240i	$-0.0602782\pi$
$480$	−24.0041	+	5.91647i	−1.09563	+	0.270049i
$481$	1.53681	−	1.45283i	0.0700723	−	0.0662435i
$482$	8.09097	+	1.99424i	0.368533	+	0.0908353i
$483$	12.2537	−	23.3474i	0.557560	−	1.06234i
$484$	25.2736			1.14880
$485$	−6.46146			−0.293400
$486$	1.26829	−	2.41652i	0.0575306	−	0.109615i
$487$	−15.6668	−	17.6842i	−0.709931	−	0.801347i	0.277276	−	0.960790i	$-0.410569\pi$
$487$	−15.6668	−	17.6842i	−0.709931	−	0.801347i	−0.987207	+	0.159443i	$0.949030\pi$
$488$		−	44.4023i		−	2.01000i
$489$	9.14551	−	10.3231i	0.413574	−	0.466829i
$490$	−37.1864	+	19.5169i	−1.67991	+	0.881685i
$491$	−0.403437	−	3.32261i	−0.0182069	−	0.149947i	0.980770	−	0.195166i	$-0.0625246\pi$
$491$	−0.403437	−	3.32261i	−0.0182069	−	0.149947i	−0.998977	+	0.0452189i	$0.985601\pi$
$492$	−4.82916	−	9.20119i	−0.217715	−	0.414822i
$493$	0.0425445	+	0.350386i	0.00191611	+	0.0157806i
$494$	−65.8567	+	10.1666i	−2.96303	+	0.457418i
$495$	0.547332	−	4.50768i	0.0246007	−	0.202605i
$496$	−69.2240	+	26.2532i	−3.10825	+	1.17880i
$497$	−51.0399	−	26.7878i	−2.28945	−	1.20160i
$498$	−10.6506	+	28.0834i	−0.477266	+	1.25845i
$499$	−6.33056	−	12.0619i	−0.283395	−	0.539963i	0.701595	−	0.712576i	$-0.252472\pi$
$499$	−6.33056	−	12.0619i	−0.283395	−	0.539963i	−0.984990	+	0.172612i	$0.944779\pi$
$500$	−25.2386	−	48.0881i	−1.12870	−	2.15057i
$501$	1.83761	+	7.45548i	0.0820984	+	0.333086i
$502$	4.47486	+	0.543346i	0.199723	+	0.0242507i
$503$	7.09762	+	6.28795i	0.316467	+	0.280366i	0.806370	−	0.591412i	$-0.201429\pi$
$503$	7.09762	+	6.28795i	0.316467	+	0.280366i	−0.489902	+	0.871777i	$0.662968\pi$
$504$	24.1454	+	34.9807i	1.07552	+	1.55816i
$505$	7.46899	+	2.83261i	0.332366	+	0.126050i
$506$	−63.0032			−2.80083
$507$	−12.9728	+	0.840129i	−0.576143	+	0.0373114i
$508$	−84.6404			−3.75531
$509$	28.8520	+	10.9421i	1.27884	+	0.485001i	0.898145	−	0.439699i	$-0.144915\pi$
$509$	28.8520	+	10.9421i	1.27884	+	0.485001i	0.380697	+	0.924700i	$0.375684\pi$
$510$	0.115755	+	0.167700i	0.00512571	+	0.00742587i
$511$	−30.0828	−	26.6510i	−1.33078	−	1.17897i
$512$	−39.7836	−	4.83060i	−1.75820	−	0.213485i
$513$	1.62066	+	6.57526i	0.0715538	+	0.290305i
$514$	−10.9046	−	20.7770i	−0.480981	−	0.916433i
$515$	1.38957	+	2.64760i	0.0612317	+	0.116667i
$516$	−17.2658	+	45.5261i	−0.760083	+	2.00417i
$517$	−9.72892	−	5.10613i	−0.427878	−	0.224567i
$518$	6.76053	−	2.56393i	0.297041	−	0.112653i
$519$	−1.48036	+	12.1918i	−0.0649805	+	0.535163i
$520$	24.8779	−	29.9807i	1.09097	−	1.31474i
$521$	−0.589584	−	4.85566i	−0.0258301	−	0.212730i	0.974079	−	0.226208i	$-0.0726329\pi$
$521$	−0.589584	−	4.85566i	−0.0258301	−	0.212730i	−0.999909	+	0.0134776i	$0.995710\pi$
$522$	−6.88415	−	13.1166i	−0.301311	−	0.574100i
$523$	−2.50792	−	20.6546i	−0.109664	−	0.903162i	−0.938882	−	0.344238i	$-0.888137\pi$
$523$	−2.50792	−	20.6546i	−0.109664	−	0.903162i	0.829219	−	0.558924i	$-0.188786\pi$
$524$	−3.42133	+	1.79565i	−0.149462	+	0.0784435i
$525$	−11.0272	+	12.4471i	−0.481264	+	0.543235i
$526$			65.1212i			2.83942i
$527$	0.215916	+	0.243719i	0.00940546	+	0.0106166i
$528$	27.1729	−	51.7736i	1.18255	−	2.25316i
$529$	11.0778			0.481642
$530$	−44.6190			−1.93813
$531$	0.875345	−	1.66783i	0.0379867	−	0.0723777i
$532$	−161.806	−	39.8815i	−7.01516	−	1.72908i
$533$	6.18949	+	2.99740i	0.268097	+	0.129832i
$534$	14.9649	−	3.68853i	0.647597	−	0.159618i
$535$	3.99484	−	16.2077i	0.172712	−	0.700720i
$536$	0.00970257	−	0.0255836i	0.000419087	−	0.00110504i
$537$	−0.0871237	−	0.717528i	−0.00375966	−	0.0309636i
$538$	−8.86594	−	35.9705i	−0.382238	−	1.55080i
$539$	12.6836	−	51.4594i	0.546321	−	2.21651i
$540$	−5.14829	−	3.55361i	−0.221547	−	0.152923i
$541$	31.8555	−	3.86795i	1.36957	−	0.166296i	0.597520	−	0.801854i	$-0.296153\pi$
$541$	31.8555	−	3.86795i	1.36957	−	0.166296i	0.772054	+	0.635558i	$0.219230\pi$
$542$	−8.01938	−	21.1454i	−0.344462	−	0.908271i
$543$	15.1606	−	7.95690i	0.650604	−	0.341463i
$544$	0.335063	+	1.35940i	0.0143657	+	0.0582840i
$545$	2.79443	−	7.36831i	0.119700	−	0.315624i
$546$	−42.0453	−	14.4089i	−1.79937	−	0.616644i
$547$	−8.96945	−	23.6505i	−0.383506	−	1.01122i	−0.978272	−	0.207324i	$-0.933525\pi$
$547$	−8.96945	−	23.6505i	−0.383506	−	1.01122i	0.594766	−	0.803899i	$-0.297245\pi$
$548$	23.0584	−	15.9161i	0.985006	−	0.679901i
$549$	3.53184	−	3.12894i	0.150735	−	0.133540i
$550$	38.5793	+	9.50893i	1.64503	+	0.405462i
$551$	34.3694	+	13.0346i	1.46419	+	0.555293i
$552$	−25.5289	+	48.6412i	−1.08658	+	2.07031i
$553$	−17.6438	−	6.69142i	−0.750291	−	0.284548i
$554$	15.0274	+	16.9624i	0.638453	+	0.720664i
$555$	−0.504114	+	0.446606i	−0.0213984	+	0.0189574i
$556$	16.5139	−	23.9245i	0.700344	−	1.01462i
$557$	22.5403	+	15.5584i	0.955063	+	0.659232i	0.940188	−	0.340657i	$-0.110650\pi$
$557$	22.5403	+	15.5584i	0.955063	+	0.659232i	0.0148750	+	0.999889i	$0.495265\pi$
$558$	−12.1001	−	6.35064i	−0.512239	−	0.268844i
$559$	−8.71896	−	31.0211i	−0.368773	−	1.31205i
$560$	67.8996	−	35.6365i	2.86928	−	1.50592i
$561$	−0.255280	−	0.0309966i	−0.0107779	−	0.00130868i
$562$	30.8391	−	7.60116i	1.30087	−	0.320636i
$563$	−22.3654	+	32.4019i	−0.942591	+	1.36558i	−0.0118382	+	0.999930i	$0.503768\pi$
$563$	−22.3654	+	32.4019i	−0.942591	+	1.36558i	−0.930753	+	0.365649i	$0.880847\pi$
$564$	−12.4575	+	8.59876i	−0.524554	+	0.362073i
$565$	−4.27246	+	4.82260i	−0.179744	+	0.202889i
$566$	11.9721	+	1.45367i	0.503224	+	0.0611025i
$567$	−1.08095	+	4.38560i	−0.0453957	+	0.184178i
$568$	106.335	+	55.8089i	4.46172	+	2.34169i
$569$	−5.44178	+	44.8171i	−0.228131	+	1.87883i	0.206822	+	0.978378i	$0.433688\pi$
$569$	−5.44178	+	44.8171i	−0.228131	+	1.87883i	−0.434954	+	0.900453i	$0.643235\pi$
$570$	21.0665	−	2.55793i	0.882377	−	0.107140i
$571$	13.5553	−	19.6382i	0.567271	−	0.821834i	−0.429421	−	0.903104i	$-0.641282\pi$
$571$	13.5553	−	19.6382i	0.567271	−	0.821834i	0.996692	+	0.0812703i	$0.0258977\pi$
$572$	11.8518	+	76.7726i	0.495547	+	3.21002i
$573$	−5.35081	−	7.75198i	−0.223533	−	0.323844i
$574$	15.5914	+	17.5990i	0.650771	+	0.734569i
$575$	−20.8671	−	5.14328i	−0.870219	−	0.214490i
$576$	−16.5816	−	24.0226i	−0.690899	−	1.00094i
$577$			35.9730i			1.49757i	0.662811	+	0.748787i	$0.269363\pi$
$577$			35.9730i			1.49757i	−0.662811	+	0.748787i	$0.730637\pi$
$578$	−38.1729	+	26.3488i	−1.58778	+	1.09597i
$579$	−13.1857	+	1.60103i	−0.547979	+	0.0665367i
$580$	−31.7486	+	12.0406i	−1.31829	+	0.499961i
$581$	5.99188	−	49.3476i	0.248585	−	2.04728i
$582$	−5.44591	−	14.3597i	−0.225740	−	0.595229i
$583$	37.3395	−	42.1476i	1.54644	−	1.74557i
$584$	62.6735	+	55.5239i	2.59345	+	2.29759i
$585$	4.13782	−	0.133844i	0.171078	−	0.00553377i
$586$	−27.7247	+	24.5619i	−1.14530	+	1.01464i
$587$		−	40.0096i		−	1.65137i	−0.564130	−	0.825686i	$-0.690788\pi$
$587$		−	40.0096i		−	1.65137i	0.564130	−	0.825686i	$-0.309212\pi$
$588$	−54.6525	−	48.4179i	−2.25383	−	1.99672i
$589$	32.9241	−	8.11506i	1.35661	−	0.334375i
$590$	−4.85765	−	3.35299i	−0.199986	−	0.138041i
$591$	−6.56198	+	2.48863i	−0.269924	+	0.102369i
$592$	−8.10886	+	3.07528i	−0.333272	+	0.126393i
$593$	−17.1912	−	11.8662i	−0.705959	−	0.487288i	0.160183	−	0.987087i	$-0.448792\pi$
$593$	−17.1912	−	11.8662i	−0.705959	−	0.487288i	−0.866141	+	0.499799i	$0.833407\pi$
$594$	10.4790	−	2.58284i	0.429959	−	0.105975i
$595$	−0.252436	−	0.223639i	−0.0103489	−	0.00916831i
$596$		−	53.8464i		−	2.20563i
$597$	−17.6032	+	15.5950i	−0.720450	+	0.638263i
$598$	−8.76379	−	56.7696i	−0.358378	−	2.32148i
$599$	15.9283	+	14.1112i	0.650812	+	0.576569i	0.922586	−	0.385792i	$-0.126072\pi$
$599$	15.9283	+	14.1112i	0.650812	+	0.576569i	−0.271774	+	0.962361i	$0.587610\pi$
$600$	22.9736	−	25.9319i	0.937894	−	1.05866i
$601$	0.871117	+	2.29695i	0.0355336	+	0.0936944i	0.951609	−	0.307312i	$-0.0994296\pi$
$601$	0.871117	+	2.29695i	0.0355336	+	0.0936944i	−0.916075	+	0.401007i	$0.868660\pi$
$602$	13.2793	−	109.365i	0.541222	−	4.45737i
$603$	0.00271869	−	0.00103106i	0.000110714	−	4.19881e-5i
$604$	−83.1841	+	10.1004i	−3.38471	+	0.410979i
$605$	4.38370	−	3.02585i	0.178223	−	0.123018i
$606$			18.9862i			0.771262i
$607$	−1.85781	−	2.69150i	−0.0754060	−	0.109244i	0.783466	−	0.621434i	$-0.213450\pi$
$607$	−1.85781	−	2.69150i	−0.0754060	−	0.109244i	−0.858872	+	0.512190i	$0.828834\pi$
$608$	141.572	+	34.8944i	5.74150	+	1.41515i
$609$	16.2578	+	18.3513i	0.658801	+	0.743632i
$610$	−8.39946	−	12.1687i	−0.340084	−	0.492697i
$611$	3.24763	−	9.47660i	0.131385	−	0.383382i
$612$	−0.201249	+	0.291559i	−0.00813501	+	0.0117856i
$613$	−27.6705	+	3.35981i	−1.11760	+	0.135701i	−0.658427	−	0.752645i	$-0.728778\pi$
$613$	−27.6705	+	3.35981i	−1.11760	+	0.135701i	−0.459175	+	0.888346i	$0.651855\pi$
$614$	−1.63711	+	13.4828i	−0.0660682	+	0.544121i
$615$	−1.93922	−	1.01778i	−0.0781968	−	0.0410409i
$616$	−40.2265	+	163.205i	−1.62077	+	6.57574i
$617$	−37.6313	−	4.56926i	−1.51498	−	0.183952i	−0.679581	−	0.733600i	$-0.737839\pi$
$617$	−37.6313	−	4.56926i	−1.51498	−	0.183952i	−0.835396	+	0.549648i	$0.814762\pi$
$618$	−4.71276	+	5.31960i	−0.189575	+	0.213986i
$619$	23.2820	−	16.0704i	0.935784	−	0.645925i	0.000566682	−	1.00000i	$-0.499820\pi$
$619$	23.2820	−	16.0704i	0.935784	−	0.645925i	0.935217	+	0.354075i	$0.115204\pi$
$620$	−17.7939	+	25.7789i	−0.714619	+	1.03530i
$621$	−5.66799	+	1.39703i	−0.227448	+	0.0560610i
$622$	−24.7565	−	3.00598i	−0.992646	−	0.120529i
$623$	−22.5872	+	11.8547i	−0.904936	+	0.474947i
$624$	50.4309	+	17.2826i	2.01885	+	0.691859i
$625$	6.16445	+	3.23535i	0.246578	+	0.129414i
$626$	75.2349	+	51.9309i	3.00699	+	2.07558i
$627$	−15.2133	+	22.0402i	−0.607559	+	0.880201i
$628$	−27.8239	+	24.6498i	−1.11030	+	0.983636i
$629$	0.0252923	+	0.0285491i	0.00100847	+	0.00113833i
$630$	13.2344	+	5.01915i	0.527272	+	0.199968i
$631$	10.4133	−	19.8408i	0.414546	−	0.789851i	−0.585233	−	0.810865i	$-0.698997\pi$
$631$	10.4133	−	19.8408i	0.414546	−	0.789851i	0.999779	+	0.0210138i	$0.00668941\pi$
$632$	36.7586	+	13.9407i	1.46218	+	0.554531i
$633$	1.39826	+	0.344639i	0.0555757	+	0.0136982i
$634$	−3.46657	+	3.07111i	−0.137675	+	0.121969i
$635$	−14.6809	+	10.1335i	−0.582592	+	0.402135i
$636$	−27.5080	−	72.5327i	−1.09076	−	2.87611i
$637$	48.1322	+	4.27063i	1.90707	+	0.169209i
$638$	20.7733	−	54.7746i	0.822421	−	2.16855i
$639$	3.05407	+	12.3908i	0.120817	+	0.490174i
$640$	−37.2112	+	19.5300i	−1.47090	+	0.771989i
$641$	10.3807	+	27.3716i	0.410012	+	1.08111i	0.967931	+	0.251217i	$0.0808307\pi$
$641$	10.3807	+	27.3716i	0.410012	+	1.08111i	−0.557919	+	0.829895i	$0.688400\pi$
$642$	39.3863	−	4.78237i	1.55445	−	0.188745i
$643$	15.0755	+	10.4058i	0.594518	+	0.410366i	0.826974	−	0.562241i	$-0.190061\pi$
$643$	15.0755	+	10.4058i	0.594518	+	0.410366i	−0.232456	+	0.972607i	$0.574676\pi$
$644$	34.3785	−	139.479i	1.35470	−	5.49624i
$645$	2.45581	+	9.96362i	0.0966974	+	0.392317i
$646$	−0.144861	−	1.19304i	−0.00569950	−	0.0469396i
$647$	8.39643	−	22.1396i	0.330098	−	0.870396i	−0.662513	−	0.749051i	$-0.730510\pi$
$647$	8.39643	−	22.1396i	0.330098	−	0.870396i	0.992610	−	0.121345i	$-0.0387208\pi$
$648$	2.25202	−	9.13682i	0.0884678	−	0.358928i
$649$	7.23240	−	1.78263i	0.283897	−	0.0699742i
$650$	−3.20171	+	36.0849i	−0.125581	+	1.41537i
$651$	21.9598	+	5.41261i	0.860674	+	0.212137i
$652$	34.9183	−	66.5313i	1.36751	−	2.60557i
$653$	−34.5084			−1.35042			−0.675209	−	0.737627i	$-0.735946\pi$
$653$	−34.5084			−1.35042			−0.675209	+	0.737627i	$0.735946\pi$
$654$	18.7303			0.732411
$655$	−0.378447	+	0.721071i	−0.0147872	+	0.0281746i
$656$	−18.7009	−	21.1090i	−0.730149	−	0.824168i
$657$			8.89783i			0.347137i
$658$	22.7115	−	25.6360i	0.885386	−	0.999394i
$659$	−17.5306	+	9.20077i	−0.682895	+	0.358411i	−0.770228	−	0.637768i	$-0.779858\pi$
$659$	−17.5306	+	9.20077i	−0.682895	+	0.358411i	0.0873333	+	0.996179i	$0.472165\pi$
$660$	−2.98192	−	24.5583i	−0.116071	−	0.955930i
$661$	−11.1502	−	21.2449i	−0.433692	−	0.826331i	−0.999998	−	0.00213590i	$-0.999320\pi$
$661$	−11.1502	−	21.2449i	−0.433692	−	0.826331i	0.566306	−	0.824195i	$-0.308372\pi$
$662$	2.88833	+	23.7876i	0.112258	+	0.924530i
$663$	−0.00757988	−	0.234334i	−0.000294378	−	0.00910079i
$664$	−12.4833	+	102.809i	−0.484446	+	3.98977i
$665$	−32.8399	+	12.4545i	−1.27348	+	0.482966i
$666$	−1.41740	−	0.743910i	−0.0549232	−	0.0288259i
$667$	−11.2360	+	29.6270i	−0.435061	+	1.14716i
$668$	19.4411	+	37.0420i	0.752199	+	1.43320i
$669$	−6.61043	−	12.5951i	−0.255574	−	0.486955i
$670$	−0.00218053	−	0.00884674i	−8.42411e−5	−	0.000341780i
$671$	18.5238	+	2.24919i	0.715102	+	0.0868291i
$672$	72.7944	+	64.4902i	2.80810	+	2.48776i
$673$	27.4892	+	39.8249i	1.05963	+	1.53514i	0.826699	+	0.562644i	$0.190216\pi$
$673$	27.4892	+	39.8249i	1.05963	+	1.53514i	0.232930	+	0.972493i	$0.425169\pi$
$674$	−49.2719	−	18.6864i	−1.89788	−	0.719772i
$675$	3.68158			0.141704
$676$	−67.5281	+	21.3583i	−2.59723	+	0.821471i
$677$	−33.3655			−1.28234			−0.641169	−	0.767400i	$-0.721550\pi$
$677$	−33.3655			−1.28234			−0.641169	+	0.767400i	$0.721550\pi$
$678$	−14.3185	−	5.43030i	−0.549899	−	0.208549i
$679$	14.4390	+	20.9185i	0.554118	+	0.802778i
$680$	0.525918	+	0.465923i	0.0201680	+	0.0178673i
$681$	12.4511	+	1.51184i	0.477128	+	0.0579338i
$682$	−12.9330	−	52.4711i	−0.495229	−	2.00922i
$683$	7.55102	+	14.3873i	0.288932	+	0.550514i	0.986051	−	0.166441i	$-0.0532276\pi$
$683$	7.55102	+	14.3873i	0.288932	+	0.550514i	−0.697120	+	0.716955i	$0.745535\pi$
$684$	17.1458	+	32.6687i	0.655588	+	1.24912i
$685$	2.09395	−	5.52128i	0.0800055	−	0.210957i
$686$	69.8773	+	36.6744i	2.66793	+	1.40024i
$687$	22.9199	−	8.69236i	0.874448	−	0.331634i
$688$	−15.9277	+	131.176i	−0.607238	+	5.00105i
$689$	43.1714	+	27.7823i	1.64470	+	1.05842i
$690$	2.20498	+	18.1596i	0.0839422	+	0.691326i
$691$	−4.44544	−	8.47007i	−0.169112	−	0.322217i	0.786120	−	0.618074i	$-0.212087\pi$
$691$	−4.44544	−	8.47007i	−0.169112	−	0.322217i	−0.955232	+	0.295858i	$0.904395\pi$
$692$	8.06513	+	66.4223i	0.306590	+	2.52500i
$693$	−15.8164	+	8.30107i	−0.600814	+	0.315332i
$694$	41.1637	−	46.4642i	1.56255	−	1.76376i
$695$		−	6.12680i		−	0.232403i
$696$	−33.8711	−	38.2325i	−1.28388	−	1.44920i
$697$	−0.0576392	+	0.109822i	−0.00218324	+	0.00415982i
$698$	−58.8656			−2.22810
$699$	17.1517			0.648737
$700$	−42.1026	+	80.2197i	−1.59133	+	3.03202i
$701$	37.7294	+	9.29946i	1.42502	+	0.351236i	0.875084	−	0.483971i	$-0.160806\pi$
$701$	37.7294	+	9.29946i	1.42502	+	0.351236i	0.549936	+	0.835207i	$0.314652\pi$
$702$	3.78493	+	9.08293i	0.142853	+	0.342813i
$703$	3.85671	−	0.950593i	0.145458	−	0.0358523i
$704$	27.6251	−	112.079i	1.04116	−	4.22415i
$705$	−1.13127	+	2.98291i	−0.0426060	+	0.112343i
$706$	1.65583	+	13.6370i	0.0623181	+	0.513235i
$707$	−7.52007	−	30.5101i	−0.282821	−	1.14745i
$708$	2.45584	−	9.96375i	0.0922963	−	0.374461i
$709$	10.9492	+	7.55771i	0.411207	+	0.283836i	0.755655	−	0.654970i	$-0.227319\pi$
$709$	10.9492	+	7.55771i	0.411207	+	0.283836i	−0.344448	+	0.938805i	$0.611934\pi$
$710$	39.6990	−	4.82033i	1.48988	−	0.180904i
$711$	1.48143	+	3.90622i	0.0555581	+	0.146495i
$712$	47.0574	−	24.6976i	1.76355	−	0.925583i
$713$	6.99531	+	28.3811i	0.261976	+	1.06288i
$714$	0.284246	−	0.749495i	0.0106376	−	0.0280491i
$715$	11.2472	+	11.8973i	0.420621	+	0.444932i
$716$	−1.39639	−	3.68197i	−0.0521855	−	0.137602i
$717$	1.54908	−	1.06925i	0.0578514	−	0.0399319i
$718$	−55.2163	+	48.9174i	−2.06065	+	1.82558i
$719$	35.3642	+	8.71650i	1.31886	+	0.325071i	0.835086	−	0.550120i	$-0.185418\pi$
$719$	35.3642	+	8.71650i	1.31886	+	0.325071i	0.483778	+	0.875191i	$0.339264\pi$
$720$	−15.8739	−	6.02018i	−0.591586	−	0.224359i
$721$	5.46624	−	10.4150i	0.203573	−	0.387876i
$722$	−68.5422	−	25.9946i	−2.55088	−	0.967420i
$723$	2.02478	+	2.28551i	0.0753025	+	0.0849989i
$724$	69.8220	−	61.8569i	2.59491	−	2.29889i
$725$	11.3518	−	16.4459i	0.421595	−	0.610786i
$726$	10.4192	+	7.19189i	0.386694	+	0.266916i
$727$	31.0850	+	16.3147i	1.15288	+	0.605078i	0.929197	−	0.369584i	$-0.120500\pi$
$727$	31.0850	+	16.3147i	1.15288	+	0.605078i	0.223682	+	0.974662i	$0.428192\pi$
$728$	−152.653	−	13.5445i	−5.65771	−	0.501992i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	27.6794	+	3.36088i	1.02446	+	0.124392i
$731$	0.564262	−	0.139078i	0.0208700	−	0.00514399i
$732$	14.6031	−	21.1563i	0.539747	−	0.781959i
$733$	−2.86583	+	1.97814i	−0.105852	+	0.0730642i	−0.619815	−	0.784748i	$-0.712792\pi$
$733$	−2.86583	+	1.97814i	−0.105852	+	0.0730642i	0.513963	+	0.857812i	$0.328177\pi$
$734$	68.1580	−	76.9345i	2.51576	−	2.83971i
$735$	−15.2762	−	1.85487i	−0.563473	−	0.0684180i
$736$	−30.0795	+	122.037i	−1.10875	+	4.49836i
$737$	0.0101815	+	0.00534366i	0.000375040	+	0.000196836i
$738$	0.627443	−	5.16746i	0.0230965	−	0.190217i
$739$	−7.35110	+	0.892585i	−0.270415	+	0.0328343i	−0.254621	−	0.967041i	$-0.581951\pi$
$739$	−7.35110	+	0.892585i	−0.270415	+	0.0328343i	−0.0157938	+	0.999875i	$0.505028\pi$
$740$	−2.08436	+	3.01972i	−0.0766227	+	0.111007i
$741$	−21.9757	−	10.6422i	−0.807297	−	0.390952i
$742$	99.7071	+	144.451i	3.66036	+	5.30295i
$743$	−8.47474	−	9.56600i	−0.310908	−	0.350943i	0.572198	−	0.820115i	$-0.306091\pi$
$743$	−8.47474	−	9.56600i	−0.310908	−	0.350943i	−0.883107	+	0.469173i	$0.844552\pi$
$744$	−45.7504	−	11.2765i	−1.67729	−	0.413416i
$745$	−6.44670	−	9.33965i	−0.236189	−	0.342178i
$746$			24.0801i			0.881635i
$747$	−9.05731	+	6.25181i	−0.331390	+	0.228742i
$748$	−1.39079	+	0.168873i	−0.0508524	+	0.00617459i
$749$	−61.3982	+	23.2853i	−2.24344	+	0.850825i
$750$	3.27920	−	27.0066i	0.119739	−	0.986143i
$751$	−17.4875	−	46.1107i	−0.638127	−	1.68260i	−0.727067	−	0.686566i	$-0.759117\pi$
$751$	−17.4875	−	46.1107i	−0.638127	−	1.68260i	0.0889403	−	0.996037i	$-0.471652\pi$
$752$	−27.2411	+	30.7489i	−0.993381	+	1.12130i
$753$	1.23633	+	1.09529i	0.0450542	+	0.0399145i
$754$	52.2447	+	11.0987i	1.90264	+	0.404193i
$755$	−13.2190	+	11.7110i	−0.481089	+	0.426208i
$756$			24.6082i			0.894992i
$757$	−16.9380	−	15.0058i	−0.615623	−	0.545394i	0.296645	−	0.954988i	$-0.404132\pi$
$757$	−16.9380	−	15.0058i	−0.615623	−	0.545394i	−0.912268	+	0.409593i	$0.865671\pi$
$758$	60.9306	−	15.0181i	2.21310	−	0.545480i
$759$	−18.9990	−	13.1141i	−0.689621	−	0.476011i
$760$	68.4177	−	25.9474i	2.48177	−	0.941211i
$761$	2.38666	−	0.905142i	0.0865165	−	0.0328114i	−0.310967	−	0.950421i	$-0.600653\pi$
$761$	2.38666	−	0.905142i	0.0865165	−	0.0328114i	0.397483	+	0.917609i	$0.369884\pi$
$762$	−34.8937	−	24.0854i	−1.26407	−	0.872521i
$763$	−30.0989	+	7.41870i	−1.08965	+	0.268575i
$764$	−38.4118	−	34.0298i	−1.38969	−	1.23116i
$765$			0.0746652i			0.00269953i
$766$	−57.9081	+	51.3021i	−2.09230	+	1.85362i
$767$	2.61228	+	6.26885i	0.0943241	+	0.226355i
$768$	−31.0679	−	27.5237i	−1.12107	−	0.993177i
$769$	10.3385	−	11.6697i	0.372814	−	0.420820i	−0.531921	−	0.846794i	$-0.678530\pi$
$769$	10.3385	−	11.6697i	0.372814	−	0.420820i	0.904736	+	0.425973i	$0.140068\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.55177 + 0.967759i) q^{2} +(0.568065 + 0.822984i) q^{3} +(4.07796 + 3.61275i) q^{4} +(1.13985 + 0.138403i) q^{5} +(0.653121 + 2.64982i) q^{6} +(-2.09908 - 3.99947i) q^{7} +(4.37317 + 8.33237i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(2.77471 + 1.45628i) q^{10} +(-3.69763 + 1.40233i) q^{11} +(-0.656695 + 5.40837i) q^{12} +(-1.77792 - 3.13672i) q^{13} +(-1.48586 - 12.2371i) q^{14} +(0.533607 + 1.01670i) q^{15} +(1.78220 + 14.6777i) q^{16} +(0.0575782 - 0.0302194i) q^{17} +(-1.80974 + 2.04278i) q^{18} -6.77205i q^{19} +(4.14826 + 4.68242i) q^{20} +(2.09908 - 3.99947i) q^{21} -10.7926 q^{22} +5.83762 q^{23} +(-4.37317 + 8.33237i) q^{24} +(-3.57460 - 0.881059i) q^{25} +(-1.50126 - 9.72479i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(5.88913 - 23.8932i) q^{28} +(-1.92477 + 5.07519i) q^{29} +(0.377719 + 3.11080i) q^{30} +(1.19832 + 4.86176i) q^{31} +(-5.15270 + 20.9053i) q^{32} +(-3.25458 - 2.24648i) q^{33} +(0.176171 - 0.0213911i) q^{34} +(-1.83911 - 4.84933i) q^{35} +(-4.82405 + 2.53186i) q^{36} +(0.140370 + 0.569504i) q^{37} +(6.55371 - 17.2807i) q^{38} +(1.57149 - 3.24506i) q^{39} +(3.83154 + 10.1030i) q^{40} +(-1.56973 + 1.08350i) q^{41} +(9.22691 - 8.17433i) q^{42} +(8.67740 + 2.13879i) q^{43} +(-20.1450 - 7.64000i) q^{44} +(-0.533607 + 1.01670i) q^{45} +(14.8963 + 5.64941i) q^{46} +(1.84241 + 2.07966i) q^{47} +(-11.0671 + 9.80463i) q^{48} +(-7.61316 + 11.0296i) q^{49} +(-8.26890 - 5.70761i) q^{50} +(0.0575782 + 0.0302194i) q^{51} +(4.08190 - 19.2146i) q^{52} +(-12.6077 + 6.61705i) q^{53} +(-2.70922 - 0.328959i) q^{54} +(-4.40884 + 1.08668i) q^{55} +(24.1454 - 34.9807i) q^{56} +(5.57329 - 3.84696i) q^{57} +(-9.82312 + 11.0880i) q^{58} +(-1.86985 - 0.227041i) q^{59} +(-1.49707 + 6.07387i) q^{60} +(-4.17802 - 2.19279i) q^{61} +(-1.64718 + 13.5658i) q^{62} +(4.48392 - 0.544446i) q^{63} +(-16.5816 + 24.0226i) q^{64} +(-1.59244 - 3.82147i) q^{65} +(-6.13091 - 8.88215i) q^{66} +(-0.00192812 - 0.00217640i) q^{67} +(0.343977 + 0.0847826i) q^{68} +(3.31614 + 4.80426i) q^{69} -14.1542i q^{70} +(10.5026 - 7.24945i) q^{71} +(-9.34165 + 1.13428i) q^{72} +(8.31961 - 3.15521i) q^{73} +(-0.192950 + 1.58909i) q^{74} +(-1.30551 - 3.44233i) q^{75} +(24.4657 - 27.6161i) q^{76} +(13.3702 + 11.8450i) q^{77} +(7.15053 - 6.75982i) q^{78} +(3.12706 - 2.77033i) q^{79} +16.9771i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-5.05415 + 1.24574i) q^{82} +(9.05731 + 6.25181i) q^{83} +(23.0091 - 8.72620i) q^{84} +(0.0698132 - 0.0264767i) q^{85} +(20.0729 + 13.8553i) q^{86} +(-5.27019 + 1.29899i) q^{87} +(-27.8551 - 24.6774i) q^{88} -5.64754i q^{89} +(-2.34557 + 2.07799i) q^{90} +(-8.81320 + 13.6950i) q^{91} +(23.8056 + 21.0899i) q^{92} +(-3.32043 + 3.74799i) q^{93} +(2.68881 + 7.08982i) q^{94} +(0.937274 - 7.71915i) q^{95} +(-20.1318 + 7.63500i) q^{96} +(-5.58631 + 0.678301i) q^{97} +(-30.1010 + 20.7772i) q^{98} -3.95461i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

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