LMFDB - Embedded newform 570.2.v.c.83.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.8
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.681821 + 1.59221i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.65405 - 1.50470i) q^{5} +(-1.36148 - 1.07068i) q^{6} +(0.292109 - 0.292109i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.07024 - 2.17120i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.681821 + 1.59221i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.65405 - 1.50470i) q^{5} +(-1.36148 - 1.07068i) q^{6} +(0.292109 - 0.292109i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.07024 - 2.17120i) q^{9} +(1.02533 + 1.98714i) q^{10} +2.54723i q^{11} +(1.38658 - 1.03798i) q^{12} +(-6.57813 + 1.76261i) q^{13} +(0.206552 + 0.357759i) q^{14} +(1.26802 + 3.65953i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.85004 + 6.90445i) q^{17} +(2.63304 - 1.43775i) q^{18} +(0.0773896 + 4.35821i) q^{19} +(-2.18480 + 0.476080i) q^{20} +(0.265932 + 0.664264i) q^{21} +(-2.46044 - 0.659273i) q^{22} +(1.56757 + 5.85024i) q^{23} +(0.643739 + 1.60798i) q^{24} +(0.471774 - 4.97769i) q^{25} -6.81019i q^{26} +(4.86853 - 1.81588i) q^{27} +(-0.399029 + 0.106919i) q^{28} +(0.463033 - 0.801997i) q^{29} +(-3.86302 + 0.277659i) q^{30} -4.40762 q^{31} +(-0.965926 + 0.258819i) q^{32} +(-4.05572 - 1.73676i) q^{33} +(-6.19036 - 3.57401i) q^{34} +(0.0436278 - 0.922699i) q^{35} +(0.707280 + 2.91543i) q^{36} +(-6.76926 + 6.76926i) q^{37} +(-4.22974 - 1.05324i) q^{38} +(1.67868 - 11.6755i) q^{39} +(0.105610 - 2.23357i) q^{40} +(5.12340 - 2.95800i) q^{41} +(-0.710458 + 0.0849461i) q^{42} +(0.372550 - 1.39037i) q^{43} +(1.27362 - 2.20597i) q^{44} +(-6.69128 - 0.476193i) q^{45} -6.05662 q^{46} +(7.99255 - 2.14160i) q^{47} +(-1.71980 + 0.205628i) q^{48} +6.82934i q^{49} +(4.68598 + 1.74402i) q^{50} +(-9.73191 - 7.65325i) q^{51} +(6.57813 + 1.76261i) q^{52} +(0.141129 + 0.526700i) q^{53} +(0.493935 + 5.17262i) q^{54} +(3.83281 + 4.21326i) q^{55} -0.413105i q^{56} +(-6.99194 - 2.84830i) q^{57} +(0.654828 + 0.654828i) q^{58} +(-4.43602 - 7.68341i) q^{59} +(0.731625 - 3.80325i) q^{60} +(6.24536 - 10.8173i) q^{61} +(1.14077 - 4.25743i) q^{62} +(-1.23896 - 0.0294913i) q^{63} -1.00000i q^{64} +(-8.22839 + 12.8135i) q^{65} +(2.72728 - 3.46802i) q^{66} +(0.609779 + 2.27573i) q^{67} +(5.05441 - 5.05441i) q^{68} +(-10.3836 - 1.49293i) q^{69} +(0.879967 + 0.280953i) q^{70} +(4.55290 - 2.62862i) q^{71} +(-2.99915 - 0.0713894i) q^{72} +(-0.580021 + 2.16467i) q^{73} +(-4.78659 - 8.29061i) q^{74} +(7.60385 + 4.14506i) q^{75} +(2.11208 - 3.81302i) q^{76} +(0.744070 + 0.744070i) q^{77} +(10.8432 + 4.64333i) q^{78} +(0.314359 - 0.181495i) q^{79} +(2.13013 + 0.680102i) q^{80} +(-0.428215 + 8.98981i) q^{81} +(1.53117 + 5.71441i) q^{82} +(6.72563 - 6.72563i) q^{83} +(0.101828 - 0.708235i) q^{84} +(7.32904 + 14.2041i) q^{85} +(1.24658 + 0.719711i) q^{86} +(0.961239 + 1.28406i) q^{87} +(1.80117 + 1.80117i) q^{88} +(-5.26392 + 9.11738i) q^{89} +(2.19180 - 6.34003i) q^{90} +(-1.40666 + 2.43641i) q^{91} +(1.56757 - 5.85024i) q^{92} +(3.00521 - 7.01783i) q^{93} +8.27449i q^{94} +(6.68579 + 7.09226i) q^{95} +(0.246495 - 1.71442i) q^{96} +(5.90862 + 1.58321i) q^{97} +(-6.59664 - 1.76756i) q^{98} +(5.53055 - 5.27338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) $ 144 * q - 4 * q^3 + 8 * q^6	$ 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) $ 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.681821	+	1.59221i	−0.393650	+	0.919261i
$3$	−0.681821	+	1.59221i	−0.393650	+	0.919261i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	1.65405	−	1.50470i	0.739714	−	0.672921i
$5$	1.65405	−	1.50470i	0.739714	−	0.672921i
$6$	−1.36148	−	1.07068i	−0.555824	−	0.437104i
$7$	0.292109	−	0.292109i	0.110407	−	0.110407i	−0.649745	−	0.760152i	$-0.725124\pi$
$7$	0.292109	−	0.292109i	0.110407	−	0.110407i	0.760152	+	0.649745i	$0.225124\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.07024	−	2.17120i	−0.690080	−	0.723733i
$10$	1.02533	+	1.98714i	0.324236	+	0.628387i
$11$			2.54723i			0.768020i	0.923329	+	0.384010i	$0.125457\pi$
$11$			2.54723i			0.768020i	−0.923329	+	0.384010i	$0.874543\pi$
$12$	1.38658	−	1.03798i	0.400270	−	0.299639i
$13$	−6.57813	+	1.76261i	−1.82445	+	0.488859i	−0.997320	−	0.0731576i	$-0.976692\pi$
$13$	−6.57813	+	1.76261i	−1.82445	+	0.488859i	−0.827126	+	0.562017i	$0.810026\pi$
$14$	0.206552	+	0.357759i	0.0552034	+	0.0956152i
$15$	1.26802	+	3.65953i	0.327401	+	0.944885i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.85004	+	6.90445i	−0.448701	+	1.67457i	0.257274	+	0.966338i	$0.417176\pi$
$17$	−1.85004	+	6.90445i	−0.448701	+	1.67457i	−0.705975	+	0.708236i	$0.749491\pi$
$18$	2.63304	−	1.43775i	0.620612	−	0.338881i
$19$	0.0773896	+	4.35821i	0.0177544	+	0.999842i
$19$	0.0773896	+	4.35821i	0.0177544	+	0.999842i
$20$	−2.18480	+	0.476080i	−0.488536	+	0.106455i
$21$	0.265932	+	0.664264i	0.0580311	+	0.144954i
$22$	−2.46044	−	0.659273i	−0.524567	−	0.140557i
$23$	1.56757	+	5.85024i	0.326860	+	1.21986i	0.912428	+	0.409236i	$0.134205\pi$
$23$	1.56757	+	5.85024i	0.326860	+	1.21986i	−0.585568	+	0.810623i	$0.699128\pi$
$24$	0.643739	+	1.60798i	0.131403	+	0.328228i
$25$	0.471774	−	4.97769i	0.0943547	−	0.995539i
$26$		−	6.81019i		−	1.33559i
$27$	4.86853	−	1.81588i	0.936949	−	0.349466i
$28$	−0.399029	+	0.106919i	−0.0754093	+	0.0202059i
$29$	0.463033	−	0.801997i	0.0859831	−	0.148927i	−0.819827	−	0.572612i	$-0.805930\pi$
$29$	0.463033	−	0.801997i	0.0859831	−	0.148927i	0.905810	+	0.423685i	$0.139264\pi$
$30$	−3.86302	+	0.277659i	−0.705287	+	0.0506933i
$31$	−4.40762			−0.791631			−0.395816	−	0.918330i	$-0.629538\pi$
$31$	−4.40762			−0.791631			−0.395816	+	0.918330i	$0.629538\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−4.05572	−	1.73676i	−0.706010	−	0.302331i
$34$	−6.19036	−	3.57401i	−1.06164	−	0.612937i
$35$	0.0436278	−	0.922699i	0.00737445	−	0.155965i
$36$	0.707280	+	2.91543i	0.117880	+	0.485906i
$37$	−6.76926	+	6.76926i	−1.11286	+	1.11286i	−0.120097	+	0.992762i	$0.538321\pi$
$37$	−6.76926	+	6.76926i	−1.11286	+	1.11286i	−0.992762	+	0.120097i	$0.961679\pi$
$38$	−4.22974	−	1.05324i	−0.686154	−	0.170857i
$39$	1.67868	−	11.6755i	0.268804	−	1.86958i
$40$	0.105610	−	2.23357i	0.0166983	−	0.353159i
$41$	5.12340	−	2.95800i	0.800141	−	0.461961i	−0.0433798	−	0.999059i	$-0.513813\pi$
$41$	5.12340	−	2.95800i	0.800141	−	0.461961i	0.843520	+	0.537097i	$0.180479\pi$
$42$	−0.710458	+	0.0849461i	−0.109626	+	0.0131075i
$43$	0.372550	−	1.39037i	0.0568133	−	0.212030i	−0.931684	−	0.363270i	$-0.881660\pi$
$43$	0.372550	−	1.39037i	0.0568133	−	0.212030i	0.988497	+	0.151240i	$0.0483268\pi$
$44$	1.27362	−	2.20597i	0.192005	−	0.332562i
$45$	−6.69128	−	0.476193i	−0.997477	−	0.0709866i
$46$	−6.05662			−0.892999
$47$	7.99255	−	2.14160i	1.16583	−	0.312384i	0.376540	−	0.926401i	$-0.377114\pi$
$47$	7.99255	−	2.14160i	1.16583	−	0.312384i	0.789293	+	0.614017i	$0.210447\pi$
$48$	−1.71980	+	0.205628i	−0.248232	+	0.0296799i
$49$			6.82934i			0.975621i
$50$	4.68598	+	1.74402i	0.662697	+	0.246642i
$51$	−9.73191	−	7.65325i	−1.36274	−	1.07167i
$52$	6.57813	+	1.76261i	0.912223	+	0.244429i
$53$	0.141129	+	0.526700i	0.0193856	+	0.0723479i	0.974941	−	0.222464i	$-0.0714098\pi$
$53$	0.141129	+	0.526700i	0.0193856	+	0.0723479i	−0.955555	+	0.294811i	$0.904743\pi$
$54$	0.493935	+	5.17262i	0.0672161	+	0.703905i
$55$	3.83281	+	4.21326i	0.516817	+	0.568115i
$56$		−	0.413105i		−	0.0552034i
$57$	−6.99194	−	2.84830i	−0.926105	−	0.377267i
$58$	0.654828	+	0.654828i	0.0859831	+	0.0859831i
$59$	−4.43602	−	7.68341i	−0.577520	−	1.00029i	−0.995763	−	0.0919593i	$-0.970687\pi$
$59$	−4.43602	−	7.68341i	−0.577520	−	1.00029i	0.418242	−	0.908336i	$-0.362646\pi$
$60$	0.731625	−	3.80325i	0.0944524	−	0.490998i
$61$	6.24536	−	10.8173i	0.799637	−	1.38501i	−0.120216	−	0.992748i	$-0.538359\pi$
$61$	6.24536	−	10.8173i	0.799637	−	1.38501i	0.919853	−	0.392264i	$-0.128308\pi$
$62$	1.14077	−	4.25743i	0.144879	−	0.540694i
$63$	−1.23896	−	0.0294913i	−0.156095	−	0.00371556i
$64$		−	1.00000i		−	0.125000i
$65$	−8.22839	+	12.8135i	−1.02061	+	1.58932i
$66$	2.72728	−	3.46802i	0.335705	−	0.426884i
$67$	0.609779	+	2.27573i	0.0744964	+	0.278024i	0.993119	−	0.117113i	$-0.0373638\pi$
$67$	0.609779	+	2.27573i	0.0744964	+	0.278024i	−0.918622	+	0.395137i	$0.870697\pi$
$68$	5.05441	−	5.05441i	0.612937	−	0.612937i
$69$	−10.3836	−	1.49293i	−1.25004	−	0.179727i
$70$	0.879967	+	0.280953i	0.105176	+	0.0335804i
$71$	4.55290	−	2.62862i	0.540329	−	0.311959i	−0.204883	−	0.978786i	$-0.565681\pi$
$71$	4.55290	−	2.62862i	0.540329	−	0.311959i	0.745212	+	0.666827i	$0.232348\pi$
$72$	−2.99915	−	0.0713894i	−0.353453	−	0.00841333i
$73$	−0.580021	+	2.16467i	−0.0678863	+	0.253355i	−0.991526	−	0.129906i	$-0.958532\pi$
$73$	−0.580021	+	2.16467i	−0.0678863	+	0.253355i	0.923640	+	0.383261i	$0.125199\pi$
$74$	−4.78659	−	8.29061i	−0.556430	−	0.963764i
$75$	7.60385	+	4.14506i	0.878017	+	0.478630i
$76$	2.11208	−	3.81302i	0.242273	−	0.437383i
$77$	0.744070	+	0.744070i	0.0847947	+	0.0847947i
$78$	10.8432	+	4.64333i	1.22775	+	0.525754i
$79$	0.314359	−	0.181495i	0.0353681	−	0.0204198i	−0.482212	−	0.876055i	$-0.660166\pi$
$79$	0.314359	−	0.181495i	0.0353681	−	0.0204198i	0.517580	+	0.855635i	$0.326833\pi$
$80$	2.13013	+	0.680102i	0.238156	+	0.0760377i
$81$	−0.428215	+	8.98981i	−0.0475795	+	0.998867i
$82$	1.53117	+	5.71441i	0.169090	+	0.631051i
$83$	6.72563	−	6.72563i	0.738234	−	0.738234i	−0.234002	−	0.972236i	$-0.575182\pi$
$83$	6.72563	−	6.72563i	0.738234	−	0.738234i	0.972236	+	0.234002i	$0.0751823\pi$
$84$	0.101828	−	0.708235i	0.0111104	−	0.0772748i
$85$	7.32904	+	14.2041i	0.794946	+	1.54065i
$86$	1.24658	+	0.719711i	0.134422	+	0.0776084i
$87$	0.961239	+	1.28406i	0.103056	+	0.137666i
$88$	1.80117	+	1.80117i	0.192005	+	0.192005i
$89$	−5.26392	+	9.11738i	−0.557975	+	0.966440i	0.439691	+	0.898149i	$0.355088\pi$
$89$	−5.26392	+	9.11738i	−0.557975	+	0.966440i	−0.997665	+	0.0682911i	$0.978245\pi$
$90$	2.19180	−	6.34003i	0.231036	−	0.668298i
$91$	−1.40666	+	2.43641i	−0.147458	+	0.255405i
$92$	1.56757	−	5.85024i	0.163430	−	0.609930i
$93$	3.00521	−	7.01783i	0.311625	−	0.727715i
$94$			8.27449i			0.853449i
$95$	6.68579	+	7.09226i	0.685948	+	0.727650i
$96$	0.246495	−	1.71442i	0.0251578	−	0.174977i
$97$	5.90862	+	1.58321i	0.599930	+	0.160751i	0.545987	−	0.837793i	$-0.316155\pi$
$97$	5.90862	+	1.58321i	0.599930	+	0.160751i	0.0539423	+	0.998544i	$0.482821\pi$
$98$	−6.59664	−	1.76756i	−0.666361	−	0.178551i
$99$	5.53055	−	5.27338i	0.555841	−	0.529995i
$100$	−2.89741	+	4.07492i	−0.289741	+	0.407492i
$101$	−15.7819	−	9.11166i	−1.57035	−	0.906644i	−0.996125	−	0.0879494i	$-0.971969\pi$
$101$	−15.7819	−	9.11166i	−1.57035	−	0.906644i	−0.574229	−	0.818695i	$-0.694698\pi$
$102$	9.91127	−	7.41949i	0.981362	−	0.734639i
$103$	−2.01726	−	2.01726i	−0.198766	−	0.198766i	0.600705	−	0.799471i	$-0.294887\pi$
$103$	−2.01726	−	2.01726i	−0.198766	−	0.198766i	−0.799471	+	0.600705i	$0.794887\pi$
$104$	−3.40509	+	5.89779i	−0.333897	+	0.578326i
$105$	1.43938	+	0.698580i	0.140469	+	0.0681745i
$106$	−0.545280			−0.0529623
$107$	13.1745	+	13.1745i	1.27362	+	1.27362i	0.944173	+	0.329451i	$0.106864\pi$
$107$	13.1745	+	13.1745i	1.27362	+	1.27362i	0.329451	+	0.944173i	$0.393136\pi$
$108$	−5.12421	−	0.861669i	−0.493077	−	0.0829141i
$109$	−7.66525	+	4.42554i	−0.734198	+	0.423890i	−0.819956	−	0.572426i	$-0.806002\pi$
$109$	−7.66525	+	4.42554i	−0.734198	+	0.423890i	0.0857579	+	0.996316i	$0.472669\pi$
$110$	−5.06170	+	2.61174i	−0.482614	+	0.249020i
$111$	−6.16263	−	15.3935i	−0.584931	−	1.46108i
$112$	0.399029	+	0.106919i	0.0377046	+	0.0101029i
$113$	0.158281	−	0.158281i	0.0148899	−	0.0148899i	−0.699623	−	0.714513i	$-0.746649\pi$
$113$	0.158281	−	0.158281i	0.0148899	−	0.0148899i	0.714513	+	0.699623i	$0.246649\pi$
$114$	4.56089	−	6.01650i	0.427167	−	0.563497i
$115$	11.3957	+	7.31789i	1.06265	+	0.682397i
$116$	−0.801997	+	0.463033i	−0.0744636	+	0.0429916i
$117$	17.4453	+	10.6334i	1.61282	+	0.983061i
$118$	8.56973	−	2.29625i	0.788908	−	0.211387i
$119$	1.47644	+	2.55727i	0.135345	+	0.234424i
$120$	3.48430	+	1.69105i	0.318072	+	0.154371i
$121$	4.51160			0.410146
$122$	8.83228	+	8.83228i	0.799637	+	0.799637i
$123$	1.21650	+	10.1743i	0.109688	+	0.917389i
$124$	3.81711	+	2.20381i	0.342786	+	0.197908i
$125$	−6.70958	−	8.94324i	−0.600123	−	0.799908i
$126$	0.349154	−	1.18911i	0.0311051	−	0.105935i
$127$	0.553196	+	2.06455i	0.0490882	+	0.183200i	0.986117	−	0.166053i	$-0.0531022\pi$
$127$	0.553196	+	2.06455i	0.0490882	+	0.183200i	−0.937029	+	0.349252i	$0.886436\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	1.95975	+	1.54116i	0.172546	+	0.135692i
$130$	−10.2473	−	11.2644i	−0.898745	−	0.987953i
$131$	10.6998	−	6.17754i	0.934847	−	0.539734i	0.0465057	−	0.998918i	$-0.485191\pi$
$131$	10.6998	−	6.17754i	0.934847	−	0.539734i	0.888341	+	0.459184i	$0.151858\pi$
$132$	2.64398	+	3.53194i	0.230129	+	0.307416i
$133$	1.29568	+	1.25047i	0.112350	+	0.108429i
$134$	−2.35601			−0.203528
$135$	5.32045	−	10.3292i	0.457912	−	0.888998i
$136$	3.57401	+	6.19036i	0.306468	+	0.530819i
$137$	0.0701820	−	0.0188052i	0.00599605	−	0.00160664i	−0.255820	−	0.966724i	$-0.582345\pi$
$137$	0.0701820	−	0.0188052i	0.00599605	−	0.00160664i	0.261816	+	0.965118i	$0.415679\pi$
$138$	4.12953	−	9.64338i	0.351529	−	0.820899i
$139$	10.7975	+	6.23396i	0.915835	+	0.528758i	0.882304	−	0.470680i	$-0.155991\pi$
$139$	10.7975	+	6.23396i	0.915835	+	0.528758i	0.0335310	+	0.999438i	$0.489325\pi$
$140$	−0.499132	+	0.777267i	−0.0421844	+	0.0656911i
$141$	−2.03963	+	14.1860i	−0.171767	+	1.19467i
$142$	1.36067	+	5.07810i	0.114185	+	0.426144i
$143$	−4.48977	−	16.7560i	−0.375453	−	1.40121i
$144$	0.845194	−	2.87848i	0.0704328	−	0.239873i
$145$	−0.440882	−	2.02327i	−0.0366132	−	0.168023i
$146$	−1.94079	−	1.12051i	−0.160621	−	0.0927344i
$147$	−10.8737	−	4.65639i	−0.896850	−	0.384053i
$148$	9.24698	−	2.47772i	0.760097	−	0.203667i
$149$	7.83108	+	13.5638i	0.641547	+	1.11119i	0.985087	+	0.172054i	$0.0550404\pi$
$149$	7.83108	+	13.5638i	0.641547	+	1.11119i	−0.343540	+	0.939138i	$0.611626\pi$
$150$	−5.97184	+	6.27193i	−0.487599	+	0.512101i
$151$	−20.2682			−1.64940			−0.824700	−	0.565571i	$-0.808656\pi$
$151$	−20.2682			−1.64940			−0.824700	+	0.565571i	$0.808656\pi$
$152$	3.13644	+	3.02700i	0.254399	+	0.245522i
$153$	18.8210	−	10.2771i	1.52158	−	0.830851i
$154$	−0.911296	+	0.526137i	−0.0734343	+	0.0423973i
$155$	−7.29042	+	6.63213i	−0.585581	+	0.532705i
$156$	−7.29154	+	9.27196i	−0.583791	+	0.742351i
$157$	−11.3689	−	3.04629i	−0.907337	−	0.243120i	−0.225173	−	0.974319i	$-0.572295\pi$
$157$	−11.3689	−	3.04629i	−0.907337	−	0.243120i	−0.682165	+	0.731199i	$0.738961\pi$
$158$	0.0939488	+	0.350622i	0.00747416	+	0.0278940i
$159$	−0.934840	−	0.134409i	−0.0741377	−	0.0106593i
$160$	−1.20825	+	1.88153i	−0.0955203	+	0.148748i
$161$	2.16681	+	1.25101i	0.170769	+	0.0985933i
$162$	−8.57266	−	2.74036i	−0.673532	−	0.215303i
$163$	−11.2602	−	11.2602i	−0.881964	−	0.881964i	0.111770	−	0.993734i	$-0.464348\pi$
$163$	−11.2602	−	11.2602i	−0.881964	−	0.881964i	−0.993734	+	0.111770i	$0.964348\pi$
$164$	−5.91599			−0.461961
$165$	−9.32167	+	3.22994i	−0.725691	+	0.251451i
$166$	4.75574	+	8.23718i	0.369117	+	0.639329i
$167$	1.60871	−	0.431052i	0.124485	−	0.0333558i	−0.196038	−	0.980596i	$-0.562808\pi$
$167$	1.60871	−	0.431052i	0.124485	−	0.0333558i	0.320524	+	0.947240i	$0.396141\pi$
$168$	0.657748	+	0.281664i	0.0507463	+	0.0217308i
$169$	28.9067	−	16.6893i	2.22360	−	1.28379i
$170$	−15.6170	+	3.40303i	−1.19777	+	0.261000i
$171$	9.30233	−	9.19057i	0.711367	−	0.702821i
$172$	−1.01782	+	1.01782i	−0.0776084	+	0.0776084i
$173$	−8.65121	−	2.31808i	−0.657739	−	0.176241i	−0.0855138	−	0.996337i	$-0.527253\pi$
$173$	−8.65121	−	2.31808i	−0.657739	−	0.176241i	−0.572226	+	0.820096i	$0.693920\pi$
$174$	−1.48910	+	0.596145i	−0.112888	+	0.0451937i
$175$	−1.31622	−	1.59184i	−0.0994969	−	0.120332i
$176$	−2.20597	+	1.27362i	−0.166281	+	0.0960025i
$177$	15.2581	−	1.82434i	1.14687	−	0.137126i
$178$	−7.44431	−	7.44431i	−0.557975	−	0.557975i
$179$	−7.96524			−0.595350			−0.297675	−	0.954667i	$-0.596211\pi$
$179$	−7.96524			−0.595350			−0.297675	+	0.954667i	$0.596211\pi$
$180$	5.55672	+	3.75804i	0.414174	+	0.280107i
$181$	7.60308	−	13.1689i	0.565133	−	0.978839i	−0.431905	−	0.901919i	$-0.642158\pi$
$181$	7.60308	−	13.1689i	0.565133	−	0.978839i	0.997037	−	0.0769193i	$-0.0245084\pi$
$182$	−1.98932	−	1.98932i	−0.147458	−	0.147458i
$183$	12.9651	+	17.3194i	0.958410	+	1.28028i
$184$	5.24518	+	3.02831i	0.386680	+	0.223250i
$185$	−1.01102	+	21.3824i	−0.0743316	+	1.57206i
$186$	6.00090	+	4.71915i	0.440007	+	0.346025i
$187$	−17.5872	−	4.71249i	−1.28611	−	0.344611i
$188$	−7.99255	−	2.14160i	−0.582916	−	0.156192i
$189$	0.891708	−	1.95258i	0.0648622	−	0.142029i
$190$	−8.58101	+	4.62237i	−0.622532	+	0.335342i
$191$		−	1.70680i		−	0.123500i	−0.998092	−	0.0617498i	$-0.980332\pi$
$191$		−	1.70680i		−	0.123500i	0.998092	−	0.0617498i	$-0.0196681\pi$
$192$	1.59221	+	0.681821i	0.114908	+	0.0492062i
$193$	1.45094	−	5.41497i	0.104441	−	0.389778i	−0.893840	−	0.448385i	$-0.851999\pi$
$193$	1.45094	−	5.41497i	0.104441	−	0.389778i	0.998281	+	0.0586071i	$0.0186659\pi$
$194$	−3.05853	+	5.29753i	−0.219589	+	0.380340i
$195$	−14.7915	−	21.8378i	−1.05924	−	1.56384i
$196$	3.41467	−	5.91439i	0.243905	−	0.422456i
$197$	−3.47329	−	3.47329i	−0.247462	−	0.247462i	0.572466	−	0.819928i	$-0.305987\pi$
$197$	−3.47329	−	3.47329i	−0.247462	−	0.247462i	−0.819928	+	0.572466i	$0.805987\pi$
$198$	3.66229	+	6.70696i	0.260267	+	0.476643i
$199$	10.0492	+	5.80193i	0.712371	+	0.411288i	0.811938	−	0.583743i	$-0.198412\pi$
$199$	10.0492	+	5.80193i	0.712371	+	0.411288i	−0.0995671	+	0.995031i	$0.531746\pi$
$200$	−3.18617	−	3.85335i	−0.225296	−	0.272473i
$201$	−4.03919	−	0.580745i	−0.284902	−	0.0409626i
$202$	12.8858	−	12.8858i	0.906644	−	0.906644i
$203$	−0.0990145	−	0.369527i	−0.00694945	−	0.0259357i
$204$	4.60146	+	11.4939i	0.322166	+	0.804731i
$205$	4.02348	−	12.6018i	0.281012	−	0.880151i
$206$	2.47063	−	1.42642i	0.172137	−	0.0993832i
$207$	9.45680	−	15.5149i	0.657293	−	1.07836i
$208$	−4.81553	−	4.81553i	−0.333897	−	0.333897i
$209$	−11.1014	+	0.197129i	−0.767899	+	0.0136357i
$210$	−1.04732	+	1.20953i	−0.0722717	+	0.0834655i
$211$	5.65215	+	9.78982i	0.389110	+	0.673959i	0.992330	−	0.123616i	$-0.0394492\pi$
$211$	5.65215	+	9.78982i	0.389110	+	0.673959i	−0.603220	+	0.797575i	$0.706116\pi$
$212$	0.141129	−	0.526700i	0.00969278	−	0.0361739i
$213$	1.08104	+	9.04140i	0.0740714	+	0.619506i
$214$	−16.1354	+	9.31575i	−1.10299	+	0.636812i
$215$	−1.47588	−	2.86032i	−0.100654	−	0.195073i
$216$	2.15855	−	4.72659i	0.146871	−	0.321604i
$217$	−1.28750	+	1.28750i	−0.0874015	+	0.0874015i
$218$	−2.29083	−	8.54948i	−0.155154	−	0.579044i
$219$	−3.05113	−	2.39943i	−0.206176	−	0.162138i
$220$	−1.21269	−	5.56519i	−0.0817594	−	0.375205i
$221$		−	48.6793i		−	3.27452i
$222$	16.4640	−	1.96852i	1.10499	−	0.132118i
$223$	−2.31820	+	8.65163i	−0.155238	+	0.579356i	0.843847	+	0.536584i	$0.180286\pi$
$223$	−2.31820	+	8.65163i	−0.155238	+	0.579356i	−0.999085	+	0.0427720i	$0.986381\pi$
$224$	−0.206552	+	0.357759i	−0.0138009	+	0.0239038i
$225$	−11.7842	+	9.28070i	−0.785617	+	0.618714i
$226$	0.111922	+	0.193854i	0.00744493	+	0.0128950i
$227$	16.4074	+	16.4074i	1.08900	+	1.08900i	0.995632	+	0.0933636i	$0.0297619\pi$
$227$	16.4074	+	16.4074i	1.08900	+	1.08900i	0.0933636	+	0.995632i	$0.470238\pi$
$228$	4.63104	+	5.96267i	0.306698	+	0.394887i
$229$		−	10.1159i		−	0.668480i	−0.942488	−	0.334240i	$-0.891520\pi$
$229$		−	10.1159i		−	0.668480i	0.942488	−	0.334240i	$-0.108480\pi$
$230$	−10.0180	+	9.11337i	−0.660564	+	0.600918i
$231$	−1.69204	+	0.677390i	−0.111328	+	0.0445690i
$232$	−0.239684	−	0.894512i	−0.0157360	−	0.0587276i
$233$	4.21966	+	1.13066i	0.276439	+	0.0740717i	0.394375	−	0.918950i	$-0.370961\pi$
$233$	4.21966	+	1.13066i	0.276439	+	0.0740717i	−0.117936	+	0.993021i	$0.537628\pi$
$234$	−14.7863	+	14.0987i	−0.966609	+	0.921662i
$235$	9.99763	−	15.5687i	0.652174	−	1.01559i
$236$			8.87204i			0.577520i
$237$	0.0746411	+	0.624271i	0.00484846	+	0.0405508i
$238$	−2.85226	+	0.764261i	−0.184885	+	0.0495397i
$239$	7.21223			0.466520			0.233260	−	0.972414i	$-0.425061\pi$
$239$	7.21223			0.466520			0.233260	+	0.972414i	$0.425061\pi$
$240$	−2.53523	+	2.92790i	−0.163649	+	0.188995i
$241$	−4.97215	+	8.61201i	−0.320284	+	0.554749i	−0.980547	−	0.196286i	$-0.937112\pi$
$241$	−4.97215	+	8.61201i	−0.320284	+	0.554749i	0.660262	+	0.751035i	$0.270445\pi$
$242$	−1.16769	+	4.35787i	−0.0750618	+	0.280135i
$243$	−14.0217	−	6.81125i	−0.899490	−	0.436942i
$244$	−10.8173	+	6.24536i	−0.692506	+	0.399818i
$245$	10.2761	+	11.2961i	0.656516	+	0.721681i
$246$	−10.1425	−	1.45827i	−0.646662	−	0.0929756i
$247$	−8.19089	−	28.5325i	−0.521174	−	1.81548i
$248$	−3.11666	+	3.11666i	−0.197908	+	0.197908i
$249$	6.12291	+	15.2943i	0.388024	+	0.969235i
$250$	10.3751	−	4.16628i	0.656177	−	0.263499i
$251$	11.0582	+	6.38445i	0.697987	+	0.402983i	0.806597	−	0.591101i	$-0.201307\pi$
$251$	11.0582	+	6.38445i	0.697987	+	0.402983i	−0.108610	+	0.994084i	$0.534640\pi$
$252$	1.05823	+	0.645022i	0.0666621	+	0.0406326i
$253$	−14.9019	+	3.99296i	−0.936877	+	0.251035i
$254$	−2.13738			−0.134111
$255$	−27.6129	+	1.98471i	−1.72919	+	0.124287i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.58486	+	1.22851i	−0.285996	+	0.0766324i	−0.398965	−	0.916966i	$-0.630631\pi$
$257$	−4.58486	+	1.22851i	−0.285996	+	0.0766324i	0.112969	+	0.993598i	$0.463964\pi$
$258$	−1.99587	+	1.49409i	−0.124257	+	0.0930180i
$259$			3.95472i			0.245735i
$260$	13.5328	−	6.98266i	0.839266	−	0.433046i
$261$	−2.69989	+	0.654989i	−0.167119	+	0.0405428i
$262$	3.19773	+	11.9341i	0.197556	+	0.737291i
$263$	16.4620	+	4.41098i	1.01509	+	0.271993i	0.727755	−	0.685837i	$-0.240564\pi$
$263$	16.4620	+	4.41098i	1.01509	+	0.271993i	0.287336	+	0.957830i	$0.407230\pi$
$264$	−4.09590	+	1.63975i	−0.252085	+	0.100920i
$265$	1.02596	+	0.658833i	0.0630242	+	0.0404718i
$266$	−1.54321	+	0.927886i	−0.0946200	+	0.0568923i
$267$	−10.9277	−	14.5977i	−0.668764	−	0.893363i
$268$	0.609779	−	2.27573i	0.0372482	−	0.139012i
$269$	−3.50446	−	6.06990i	−0.213671	−	0.370088i	0.739190	−	0.673497i	$-0.235209\pi$
$269$	−3.50446	−	6.06990i	−0.213671	−	0.370088i	−0.952860	+	0.303409i	$0.901875\pi$
$270$	8.60022	+	7.81256i	0.523393	+	0.475457i
$271$	12.0932	+	20.9460i	0.734608	+	1.27238i	0.954895	+	0.296943i	$0.0959670\pi$
$271$	12.0932	+	20.9460i	0.734608	+	1.27238i	−0.220288	+	0.975435i	$0.570700\pi$
$272$	−6.90445	+	1.85004i	−0.418644	+	0.112175i
$273$	−2.92017	−	3.90089i	−0.176737	−	0.236092i
$274$			0.0726577i			0.00438941i
$275$	12.6793	+	1.20172i	0.764593	+	0.0724663i
$276$	8.24599	+	6.48471i	0.496350	+	0.390334i
$277$	−16.2202	+	16.2202i	−0.974576	+	0.974576i	−0.999685	−	0.0251086i	$-0.992007\pi$
$277$	−16.2202	+	16.2202i	−0.974576	+	0.974576i	0.0251086	+	0.999685i	$0.492007\pi$
$278$	−8.81615	+	8.81615i	−0.528758	+	0.528758i
$279$	9.12482	+	9.56981i	0.546289	+	0.572930i
$280$	−0.621597	−	0.683297i	−0.0371476	−	0.0408348i
$281$	19.4786	+	11.2459i	1.16199	+	0.670877i	0.951781	−	0.306779i	$-0.0992511\pi$
$281$	19.4786	+	11.2459i	1.16199	+	0.670877i	0.210212	+	0.977656i	$0.432584\pi$
$282$	−13.1747	−	5.64173i	−0.784542	−	0.335960i
$283$	−5.20482	+	19.4246i	−0.309394	+	1.15467i	0.619702	+	0.784837i	$0.287253\pi$
$283$	−5.20482	+	19.4246i	−0.309394	+	1.15467i	−0.929096	+	0.369838i	$0.879413\pi$
$284$	−5.25723			−0.311959
$285$	−15.8509	+	5.80951i	−0.938924	+	0.344126i
$286$	17.3471			1.02576
$287$	0.632534	−	2.36065i	0.0373373	−	0.139345i
$288$	2.56165	+	1.56140i	0.150946	+	0.0920064i
$289$	−29.5263	−	17.0470i	−1.73684	−	1.00277i
$290$	2.06844	+	0.0978015i	0.121463	+	0.00574310i
$291$	−6.54942	+	8.32828i	−0.383934	+	0.488212i
$292$	1.58465	−	1.58465i	0.0927344	−	0.0927344i
$293$	15.0112	−	15.0112i	0.876962	−	0.876962i	−0.116257	−	0.993219i	$-0.537090\pi$
$293$	15.0112	−	15.0112i	0.876962	−	0.876962i	0.993219	+	0.116257i	$0.0370896\pi$
$294$	7.31206	−	9.29805i	0.426448	−	0.542273i
$295$	−18.8986	−	6.03389i	−1.10032	−	0.351307i
$296$			9.57318i			0.556430i
$297$	4.62547	+	12.4013i	0.268397	+	0.719595i
$298$	−15.1285	+	4.05367i	−0.876370	+	0.234823i
$299$	−20.6233	−	35.7207i	−1.19268	−	2.06578i
$300$	−4.51260	−	7.39165i	−0.260535	−	0.426757i
$301$	−0.297316	−	0.514966i	−0.0171370	−	0.0296822i
$302$	5.24579	−	19.5775i	0.301861	−	1.12656i
$303$	25.2680	−	18.9154i	1.45161	−	1.08666i
$304$	−3.73563	+	2.24613i	−0.214253	+	0.128824i
$305$	−5.94659	−	27.2897i	−0.340500	−	1.56261i
$306$	5.05565	+	20.8396i	0.289012	+	1.19132i
$307$	−0.992285	−	0.265882i	−0.0566327	−	0.0151747i	0.230391	−	0.973098i	$-0.425999\pi$
$307$	−0.992285	−	0.265882i	−0.0566327	−	0.0151747i	−0.287024	+	0.957923i	$0.592666\pi$
$308$	−0.272349	−	1.01642i	−0.0155185	−	0.0579158i
$309$	4.58730	−	1.83648i	0.260962	−	0.104474i
$310$	−4.51924	−	8.75853i	−0.256676	−	0.497451i
$311$			7.36319i			0.417528i	0.977966	+	0.208764i	$0.0669441\pi$
$311$			7.36319i			0.417528i	−0.977966	+	0.208764i	$0.933056\pi$
$312$	−7.06884	−	9.44285i	−0.400194	−	0.534596i
$313$	9.99351	−	2.67775i	0.564866	−	0.151355i	0.0349252	−	0.999390i	$-0.488881\pi$
$313$	9.99351	−	2.67775i	0.564866	−	0.151355i	0.529941	+	0.848034i	$0.322214\pi$
$314$	5.88498	−	10.1931i	0.332109	−	0.575229i
$315$	−2.09368	+	1.81548i	−0.117966	+	0.102291i
$316$	−0.362990			−0.0204198
$317$	−10.0129	+	2.68295i	−0.562381	+	0.150690i	−0.528800	−	0.848746i	$-0.677358\pi$
$317$	−10.0129	+	2.68295i	−0.562381	+	0.150690i	−0.0335812	+	0.999436i	$0.510691\pi$
$318$	0.371784	−	0.868199i	0.0208486	−	0.0486862i
$319$	2.04287	+	1.17945i	0.114379	+	0.0660367i
$320$	−1.50470	−	1.65405i	−0.0841151	−	0.0924643i
$321$	−29.9591	+	11.9938i	−1.67215	+	0.669430i
$322$	−1.76919	+	1.76919i	−0.0985933	+	0.0985933i
$323$	−30.2342	−	7.52854i	−1.68228	−	0.418899i
$324$	4.86575	−	7.57129i	0.270319	−	0.420627i
$325$	5.67032	+	33.5755i	0.314533	+	1.86243i
$326$	13.7908	−	7.96214i	0.763803	−	0.440982i
$327$	−1.82003	−	15.2221i	−0.100648	−	0.841783i
$328$	1.53117	−	5.71441i	0.0845448	−	0.315525i
$329$	1.70912	−	2.96028i	0.0942266	−	0.163205i
$330$	−0.707261	−	9.84001i	−0.0389335	−	0.541675i
$331$	−4.35634			−0.239446			−0.119723	−	0.992807i	$-0.538201\pi$
$331$	−4.35634			−0.239446			−0.119723	+	0.992807i	$0.538201\pi$
$332$	−9.18738	+	2.46175i	−0.504223	+	0.135106i
$333$	28.7114	+	0.683424i	1.57337	+	0.0374514i
$334$			1.66546i			0.0911297i
$335$	4.43289	+	2.84664i	0.242194	+	0.155528i
$336$	−0.442304	+	0.562436i	−0.0241296	+	0.0306834i
$337$	21.0370	+	5.63685i	1.14596	+	0.307059i	0.781345	−	0.624100i	$-0.214534\pi$
$337$	21.0370	+	5.63685i	1.14596	+	0.307059i	0.364615	+	0.931158i	$0.381201\pi$
$338$	8.63903	+	32.2413i	0.469901	+	1.75369i
$339$	0.144097	+	0.359936i	0.00782627	+	0.0195491i
$340$	0.754899	−	15.9656i	0.0409401	−	0.865856i
$341$		−	11.2272i		−	0.607988i
$342$	6.46979	+	11.3641i	0.349846	+	0.614498i
$343$	4.03968	+	4.03968i	0.218122	+	0.218122i
$344$	−0.719711	−	1.24658i	−0.0388042	−	0.0672108i
$345$	−19.4214	+	13.1548i	−1.04561	+	0.708229i
$346$	4.47820	−	7.75646i	0.240749	−	0.416990i
$347$	−5.55281	+	20.7234i	−0.298091	+	1.11249i	0.640641	+	0.767840i	$0.278669\pi$
$347$	−5.55281	+	20.7234i	−0.298091	+	1.11249i	−0.938732	+	0.344649i	$0.887998\pi$
$348$	−0.190426	−	1.59265i	−0.0102079	−	0.0853750i
$349$		−	11.4986i		−	0.615504i	−0.951467	−	0.307752i	$-0.900423\pi$
$349$		−	11.4986i		−	0.615504i	0.951467	−	0.307752i	$-0.0995767\pi$
$350$	1.87826	−	0.859373i	0.100397	−	0.0459354i
$351$	−28.8252	+	20.5264i	−1.53857	+	1.09562i
$352$	−0.659273	−	2.46044i	−0.0351393	−	0.131142i
$353$	−12.0701	+	12.0701i	−0.642427	+	0.642427i	−0.951151	−	0.308725i	$-0.900098\pi$
$353$	−12.0701	+	12.0701i	−0.642427	+	0.642427i	0.308725	+	0.951151i	$0.400098\pi$
$354$	−2.18692	+	15.2104i	−0.116233	+	0.808424i
$355$	3.57546	−	11.1986i	0.189765	−	0.594360i
$356$	9.11738	−	5.26392i	0.483220	−	0.278987i
$357$	−5.07836	+	0.607196i	−0.268775	+	0.0321362i
$358$	2.06156	−	7.69383i	0.108957	−	0.406632i
$359$	6.02651	+	10.4382i	0.318067	+	0.550908i	0.980085	−	0.198580i	$-0.0636329\pi$
$359$	6.02651	+	10.4382i	0.318067	+	0.550908i	−0.662018	+	0.749488i	$0.730300\pi$
$360$	−5.06817	+	4.39473i	−0.267116	+	0.231623i
$361$	−18.9880	+	0.674560i	−0.999370	+	0.0355032i
$362$	10.7524	+	10.7524i	0.565133	+	0.565133i
$363$	−3.07611	+	7.18340i	−0.161454	+	0.377031i
$364$	2.43641	−	1.40666i	0.127702	−	0.0737290i
$365$	2.29778	+	4.45323i	0.120272	+	0.233093i
$366$	−20.0848	+	8.04077i	−1.04985	+	0.420298i
$367$	−8.51491	−	31.7781i	−0.444475	−	1.65880i	−0.717320	−	0.696744i	$-0.754632\pi$
$367$	−8.51491	−	31.7781i	−0.444475	−	1.65880i	0.272846	−	0.962058i	$-0.412035\pi$
$368$	−4.28267	+	4.28267i	−0.223250	+	0.223250i
$369$	−17.0291	−	5.00016i	−0.886498	−	0.260298i
$370$	−20.3921	−	6.51074i	−1.06014	−	0.338477i
$371$	0.195079	+	0.112629i	0.0101280	+	0.00584740i
$372$	−6.11150	+	4.57502i	−0.316867	+	0.237204i
$373$	−10.7738	−	10.7738i	−0.557847	−	0.557847i	0.370847	−	0.928694i	$-0.379067\pi$
$373$	−10.7738	−	10.7738i	−0.557847	−	0.557847i	−0.928694	+	0.370847i	$0.879067\pi$
$374$	9.10383	−	15.7683i	0.470748	−	0.815359i
$375$	18.8142	−	4.58535i	0.971562	−	0.236786i
$376$	4.13725	−	7.16592i	0.213362	−	0.369554i
$377$	−1.63229	+	6.09179i	−0.0840672	+	0.313743i
$378$	1.65525	+	1.36669i	0.0851370	+	0.0702948i
$379$		−	17.3597i		−	0.891706i	−0.895106	−	0.445853i	$-0.852900\pi$
$379$		−	17.3597i		−	0.891706i	0.895106	−	0.445853i	$-0.147100\pi$
$380$	−2.24394	−	9.48497i	−0.115112	−	0.486569i
$381$	−3.66438	−	0.526855i	−0.187732	−	0.0269916i
$382$	1.64864	+	0.441752i	0.0843518	+	0.0226020i
$383$	−11.0020	−	2.94798i	−0.562176	−	0.150635i	−0.0334703	−	0.999440i	$-0.510656\pi$
$383$	−11.0020	−	2.94798i	−0.562176	−	0.150635i	−0.528706	+	0.848805i	$0.677323\pi$
$384$	−1.07068	+	1.36148i	−0.0546380	+	0.0694780i
$385$	2.35033	+	0.111130i	0.119784	+	0.00566372i
$386$	4.85493	+	2.80300i	0.247110	+	0.142669i
$387$	−3.79005	+	2.06953i	−0.192659	+	0.105200i
$388$	−4.32541	−	4.32541i	−0.219589	−	0.219589i
$389$	−5.96445	+	10.3307i	−0.302410	+	0.523789i	−0.976681	−	0.214695i	$-0.931124\pi$
$389$	−5.96445	+	10.3307i	−0.302410	+	0.523789i	0.674272	+	0.738484i	$0.264458\pi$
$390$	24.9220	−	8.63545i	1.26198	−	0.437273i
$391$	−43.2928			−2.18941
$392$	4.82908	+	4.82908i	0.243905	+	0.243905i
$393$	2.54056	+	21.2483i	0.128154	+	1.07183i
$394$	4.25390	−	2.45599i	0.214308	−	0.123731i
$395$	0.246870	−	0.773217i	0.0124214	−	0.0389048i
$396$	−7.42629	+	1.80161i	−0.373185	+	0.0905342i
$397$	2.78471	+	0.746161i	0.139761	+	0.0374487i	0.328021	−	0.944670i	$-0.393618\pi$
$397$	2.78471	+	0.746161i	0.139761	+	0.0374487i	−0.188261	+	0.982119i	$0.560285\pi$
$398$	−8.20517	+	8.20517i	−0.411288	+	0.411288i
$399$	−2.87442	+	1.21039i	−0.143901	+	0.0605955i
$400$	4.54670	−	2.08028i	0.227335	−	0.104014i
$401$	−5.98795	+	3.45714i	−0.299024	+	0.172641i	−0.642004	−	0.766701i	$-0.721897\pi$
$401$	−5.98795	+	3.45714i	−0.299024	+	0.172641i	0.342980	+	0.939343i	$0.388564\pi$
$402$	1.60637	−	3.75125i	0.0801187	−	0.187095i
$403$	28.9939	−	7.76889i	1.44429	−	0.386996i
$404$	9.11166	+	15.7819i	0.453322	+	0.785177i
$405$	12.8186	+	15.5139i	0.636964	+	0.770894i
$406$	0.382562			0.0189863
$407$	−17.2429	−	17.2429i	−0.854698	−	0.854698i
$408$	−12.2932	+	1.46983i	−0.608602	+	0.0727677i
$409$	13.1410	+	7.58699i	0.649783	+	0.375152i	0.788373	−	0.615198i	$-0.210924\pi$
$409$	13.1410	+	7.58699i	0.649783	+	0.375152i	−0.138590	+	0.990350i	$0.544257\pi$
$410$	11.1311	+	7.14798i	0.549725	+	0.353014i
$411$	−0.0179098	+	0.124566i	−0.000883425	+	0.00614438i
$412$	0.738368	+	2.75563i	0.0363768	+	0.135760i
$413$	−3.54020	−	0.948593i	−0.174202	−	0.0466772i
$414$	12.5386	+	13.1501i	0.616241	+	0.646293i
$415$	1.00450	−	21.2446i	0.0493091	−	1.04286i
$416$	5.89779	−	3.40509i	0.289163	−	0.166948i
$417$	−17.2877	+	12.9415i	−0.846584	+	0.633746i
$418$	2.68284	−	10.7741i	0.131222	−	0.526980i
$419$	19.2618			0.941000			0.470500	−	0.882400i	$-0.344074\pi$
$419$	19.2618			0.941000			0.470500	+	0.882400i	$0.344074\pi$
$420$	−0.897250	−	1.32468i	−0.0437813	−	0.0646377i
$421$	6.23858	+	10.8055i	0.304050	+	0.526629i	0.977049	−	0.213013i	$-0.0683278\pi$
$421$	6.23858	+	10.8055i	0.304050	+	0.526629i	−0.673000	+	0.739643i	$0.734994\pi$
$422$	−10.9191	+	2.92577i	−0.531535	+	0.142424i
$423$	−21.1963	−	12.9198i	−1.03060	−	0.628182i
$424$	0.472227	+	0.272640i	0.0229334	+	0.0132406i
$425$	33.4954	+	12.4663i	1.62477	+	0.604703i
$426$	−9.01311	−	1.29588i	−0.436687	−	0.0627858i
$427$	−1.33550	−	4.98416i	−0.0646294	−	0.241200i
$428$	−4.82219	−	17.9967i	−0.233089	−	0.869901i
$429$	29.7403	+	4.27599i	1.43588	+	0.206447i
$430$	3.14485	−	0.685280i	0.151658	−	0.0330471i
$431$	28.7914	+	16.6227i	1.38683	+	0.800688i	0.992957	−	0.118476i	$-0.0378008\pi$
$431$	28.7914	+	16.6227i	1.38683	+	0.800688i	0.393875	+	0.919164i	$0.371134\pi$
$432$	4.00686	+	3.30833i	0.192780	+	0.159172i
$433$	−7.55951	+	2.02556i	−0.363287	+	0.0973424i	−0.435845	−	0.900022i	$-0.643550\pi$
$433$	−7.55951	+	2.02556i	−0.363287	+	0.0973424i	0.0725582	+	0.997364i	$0.476884\pi$
$434$	−0.910403	−	1.57686i	−0.0437008	−	0.0756919i
$435$	3.52206	+	0.677533i	0.168870	+	0.0324852i
$436$	8.85107			0.423890
$437$	−25.3753	+	7.28454i	−1.21386	+	0.348467i
$438$	3.10736	−	2.32614i	0.148475	−	0.111147i
$439$	19.1872	−	11.0777i	0.915753	−	0.528710i	0.0334754	−	0.999440i	$-0.489342\pi$
$439$	19.1872	−	11.0777i	0.915753	−	0.528710i	0.882278	+	0.470729i	$0.156009\pi$
$440$	5.68943	+	0.269012i	0.271233	+	0.0128247i
$441$	14.8279	−	14.1384i	0.706089	−	0.673256i
$442$	47.0206	+	12.5991i	2.23654	+	0.599279i
$443$	0.558225	+	2.08332i	0.0265221	+	0.0989817i	0.977918	−	0.208988i	$-0.0670170\pi$
$443$	0.558225	+	2.08332i	0.0265221	+	0.0989817i	−0.951396	+	0.307970i	$0.900350\pi$
$444$	−2.35974	+	16.4125i	−0.111989	+	0.778901i
$445$	5.01210	+	23.0012i	0.237596	+	1.09036i
$446$	−7.75684	−	4.47841i	−0.367297	−	0.212059i
$447$	−26.9358	+	3.22059i	−1.27402	+	0.152328i
$448$	−0.292109	−	0.292109i	−0.0138009	−	0.0138009i
$449$	12.7789			0.603073			0.301536	−	0.953455i	$-0.402501\pi$
$449$	12.7789			0.603073			0.301536	+	0.953455i	$0.402501\pi$
$450$	−5.91448	−	13.7847i	−0.278811	−	0.649819i
$451$	7.53471	+	13.0505i	0.354795	+	0.614524i
$452$	−0.216216	+	0.0579350i	−0.0101700	+	0.00272503i
$453$	13.8193	−	32.2711i	0.649285	−	1.51623i
$454$	−20.0948	+	11.6018i	−0.943098	+	0.544498i
$455$	1.33937	+	6.14654i	0.0627904	+	0.288154i
$456$	−6.95810	+	2.92999i	−0.325843	+	0.137209i
$457$	26.5768	−	26.5768i	1.24321	−	1.24321i	0.284550	−	0.958661i	$-0.408156\pi$
$457$	26.5768	−	26.5768i	1.24321	−	1.24321i	0.958661	−	0.284550i	$-0.0918443\pi$
$458$	9.77124	+	2.61820i	0.456580	+	0.122340i
$459$	3.53065	+	36.9740i	0.164797	+	1.72580i
$460$	−6.21000	−	12.0353i	−0.289543	−	0.561150i
$461$	−8.64977	+	4.99395i	−0.402860	+	0.232591i	−0.687717	−	0.725979i	$-0.741387\pi$
$461$	−8.64977	+	4.99395i	−0.402860	+	0.232591i	0.284857	+	0.958570i	$0.408054\pi$
$462$	−0.216378	−	1.80970i	−0.0100668	−	0.0841950i
$463$	21.1954	+	21.1954i	0.985032	+	0.985032i	0.999890	−	0.0148572i	$-0.00472937\pi$
$463$	21.1954	+	21.1954i	0.985032	+	0.985032i	−0.0148572	+	0.999890i	$0.504729\pi$
$464$	0.926067			0.0429916
$465$	−5.58895	−	16.1298i	−0.259181	−	0.748001i
$466$	−2.18426	+	3.78325i	−0.101184	+	0.175256i
$467$	−8.41676	−	8.41676i	−0.389481	−	0.389481i	0.485021	−	0.874502i	$-0.338812\pi$
$467$	−8.41676	−	8.41676i	−0.389481	−	0.389481i	−0.874502	+	0.485021i	$0.838812\pi$
$468$	−9.79135	−	17.9315i	−0.452605	−	0.828882i
$469$	0.842883	+	0.486639i	0.0389207	+	0.0224709i
$470$	12.4506	+	13.6864i	0.574304	+	0.631308i
$471$	12.6019	−	16.0246i	0.580664	−	0.738375i
$472$	−8.56973	−	2.29625i	−0.394454	−	0.105694i
$473$	3.54161	+	0.948971i	0.162843	+	0.0436337i
$474$	−0.622318	−	0.0894754i	−0.0285840	−	0.00410974i
$475$	21.7304	+	1.67087i	0.997057	+	0.0766647i
$476$		−	2.95288i		−	0.135345i
$477$	0.851401	−	1.39682i	0.0389830	−	0.0639558i
$478$	−1.86666	+	6.96648i	−0.0853791	+	0.318639i
$479$	16.6108	−	28.7708i	0.758967	−	1.31457i	−0.184410	−	0.982849i	$-0.559038\pi$
$479$	16.6108	−	28.7708i	0.758967	−	1.31457i	0.943378	−	0.331720i	$-0.107629\pi$
$480$	−2.17197	−	3.20664i	−0.0991363	−	0.146363i
$481$	32.5976	−	56.4606i	1.48632	−	2.57438i
$482$	−7.03168	−	7.03168i	−0.320284	−	0.320284i
$483$	−3.46924	+	2.59704i	−0.157856	+	0.118170i
$484$	−3.90716	−	2.25580i	−0.177598	−	0.102536i
$485$	12.1554	−	6.27197i	0.551949	−	0.284796i
$486$	10.2082	−	11.7810i	0.463055	−	0.534397i
$487$	8.35415	−	8.35415i	0.378563	−	0.378563i	−0.492021	−	0.870584i	$-0.663742\pi$
$487$	8.35415	−	8.35415i	0.378563	−	0.378563i	0.870584	+	0.492021i	$0.163742\pi$
$488$	−3.23284	−	12.0651i	−0.146344	−	0.546162i
$489$	25.6059	−	10.2511i	1.15794	−	0.463570i
$490$	−13.5708	+	7.00230i	−0.613068	+	0.316332i
$491$	−8.74570	+	5.04933i	−0.394688	+	0.227873i	−0.684189	−	0.729304i	$-0.739844\pi$
$491$	−8.74570	+	5.04933i	−0.394688	+	0.227873i	0.289501	+	0.957178i	$0.406511\pi$
$492$	4.03365	−	9.41948i	0.181851	−	0.424663i
$493$	4.68072	+	4.68072i	0.210809	+	0.210809i
$494$	29.6802	−	0.527037i	1.33538	−	0.0237125i
$495$	1.21297	−	17.0443i	0.0545191	−	0.766082i
$496$	−2.20381	−	3.81711i	−0.0989539	−	0.171393i
$497$	0.562100	−	2.09779i	0.0252136	−	0.0940986i
$498$	−16.3579	+	1.95583i	−0.733013	+	0.0876429i
$499$	5.14690	−	2.97157i	0.230407	−	0.133026i	−0.380353	−	0.924841i	$-0.624197\pi$
$499$	5.14690	−	2.97157i	0.230407	−	0.133026i	0.610760	+	0.791816i	$0.290864\pi$
$500$	1.33905	+	11.0999i	0.0598841	+	0.496401i
$501$	−0.410527	+	2.85529i	−0.0183410	+	0.127565i
$502$	−9.02898	+	9.02898i	−0.402983	+	0.402983i
$503$	7.68929	+	28.6968i	0.342848	+	1.27953i	0.895106	+	0.445854i	$0.147100\pi$
$503$	7.68929	+	28.6968i	0.342848	+	1.27953i	−0.552257	+	0.833674i	$0.686233\pi$
$504$	−0.896933	+	0.855226i	−0.0399526	+	0.0380948i
$505$	−39.8143	+	8.67576i	−1.77171	+	0.386066i
$506$		−	15.4276i		−	0.685841i
$507$	6.86360	+	57.4046i	0.304823	+	2.54943i
$508$	0.553196	−	2.06455i	0.0245441	−	0.0915998i
$509$	1.18263	−	2.04837i	0.0524191	−	0.0907925i	−0.838625	−	0.544709i	$-0.816640\pi$
$509$	1.18263	−	2.04837i	0.0524191	−	0.0907925i	0.891044	+	0.453916i	$0.149974\pi$
$510$	5.22966	−	27.1857i	0.231573	−	1.20380i
$511$	0.462890	+	0.801749i	0.0204770	+	0.0354673i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	8.29075	+	21.0776i	0.366046	+	0.930597i
$514$		−	4.74660i		−	0.209364i
$515$	−6.37201	−	0.301287i	−0.280784	−	0.0132763i
$516$	−0.926612	−	2.31456i	−0.0407918	−	0.101893i
$517$	5.45515	+	20.3589i	0.239917	+	0.895383i
$518$	−3.81997	−	1.02356i	−0.167840	−	0.0449726i
$519$	9.58945	−	12.1940i	0.420930	−	0.535257i
$520$	3.24219	+	14.8789i	0.142180	+	0.652482i
$521$			0.841012i			0.0368454i	0.999830	+	0.0184227i	$0.00586446\pi$
$521$			0.841012i			0.0368454i	−0.999830	+	0.0184227i	$0.994136\pi$
$522$	0.0661114	−	2.77741i	0.00289362	−	0.121564i
$523$	−6.87435	+	1.84198i	−0.300594	+	0.0805440i	−0.405964	−	0.913889i	$-0.633064\pi$
$523$	−6.87435	+	1.84198i	−0.300594	+	0.0805440i	0.105370	+	0.994433i	$0.466397\pi$
$524$	−12.3551			−0.539734
$525$	3.43196	−	1.01034i	0.149783	−	0.0440950i
$526$	−8.52136	+	14.7594i	−0.371549	+	0.643542i
$527$	8.15427	−	30.4322i	0.355206	−	1.32565i
$528$	−0.523784	−	4.38074i	−0.0227948	−	0.190647i
$529$	−11.8495	+	6.84130i	−0.515195	+	0.297448i
$530$	−0.901922	+	0.820482i	−0.0391770	+	0.0356395i
$531$	−7.49859	+	25.5380i	−0.325411	+	1.10825i
$532$	−0.496858	−	1.73078i	−0.0215415	−	0.0750387i
$533$	−28.4886	+	28.4886i	−1.23398	+	1.23398i
$534$	16.9286	−	6.77719i	0.732570	−	0.293277i
$535$	41.6148	+	1.96767i	1.79917	+	0.0850696i
$536$	2.04036	+	1.17800i	0.0881302	+	0.0508820i
$537$	5.43087	−	12.6823i	0.234359	−	0.547282i
$538$	6.77009	−	1.81404i	0.291879	−	0.0782088i
$539$	−17.3959			−0.749296
$540$	−9.77226	+	6.28514i	−0.420531	+	0.270469i
$541$	−7.28852	+	12.6241i	−0.313358	+	0.542752i	−0.979087	−	0.203442i	$-0.934787\pi$
$541$	−7.28852	+	12.6241i	−0.313358	+	0.542752i	0.665729	+	0.746193i	$0.268121\pi$
$542$	−23.3622	+	6.25988i	−1.00349	+	0.268885i
$543$	15.7837	+	21.0845i	0.677343	+	0.904824i
$544$		−	7.14801i		−	0.306468i
$545$	−6.01963	+	18.8540i	−0.257853	+	0.807615i
$546$	4.52376	−	1.81104i	0.193599	−	0.0775055i
$547$	0.930670	+	3.47331i	0.0397926	+	0.148508i	0.982964	−	0.183799i	$-0.0588396\pi$
$547$	0.930670	+	3.47331i	0.0397926	+	0.148508i	−0.943171	+	0.332307i	$0.892173\pi$
$548$	−0.0701820	−	0.0188052i	−0.00299802	−	0.000803318i
$549$	−36.4159	+	8.83444i	−1.55419	+	0.377045i
$550$	−4.44243	+	11.9363i	−0.189426	+	0.508965i
$551$	3.53111	+	1.95593i	0.150430	+	0.0833255i
$552$	−8.39797	+	6.28665i	−0.357441	+	0.267578i
$553$	0.0388107	−	0.144843i	0.00165040	−	0.00615937i
$554$	−11.4694	−	19.8656i	−0.487288	−	0.844008i
$555$	−33.3558	−	16.1887i	−1.41588	−	0.687173i
$556$	−6.23396	−	10.7975i	−0.264379	−	0.457917i
$557$	24.9666	−	6.68978i	1.05787	−	0.283455i	0.312369	−	0.949961i	$-0.398878\pi$
$557$	24.9666	−	6.68978i	1.05787	−	0.283455i	0.745500	+	0.666506i	$0.232211\pi$
$558$	−11.6054	+	6.33705i	−0.491296	+	0.268269i
$559$			9.80273i			0.414611i
$560$	0.820895	−	0.423567i	0.0346891	−	0.0178990i
$561$	19.4946	−	24.7894i	0.823063	−	1.04661i
$562$	−15.9042	+	15.9042i	−0.670877	+	0.670877i
$563$	−25.4396	+	25.4396i	−1.07215	+	1.07215i	−0.0749639	+	0.997186i	$0.523884\pi$
$563$	−25.4396	+	25.4396i	−1.07215	+	1.07215i	−0.997186	+	0.0749639i	$0.976116\pi$
$564$	8.85935	−	11.2656i	0.373046	−	0.474367i
$565$	0.0236401	−	0.499971i	0.000994544	−	0.0210339i
$566$	−17.4157	−	10.0549i	−0.732034	−	0.422640i
$567$	2.50092	+	2.75109i	0.105029	+	0.115535i
$568$	1.36067	−	5.07810i	0.0570925	−	0.213072i
$569$	−3.28202			−0.137590			−0.0687948	−	0.997631i	$-0.521915\pi$
$569$	−3.28202			−0.137590			−0.0687948	+	0.997631i	$0.521915\pi$
$570$	−1.50905	−	16.8144i	−0.0632072	−	0.704276i
$571$	8.22090			0.344034			0.172017	−	0.985094i	$-0.444972\pi$
$571$	8.22090			0.344034			0.172017	+	0.985094i	$0.444972\pi$
$572$	−4.48977	+	16.7560i	−0.187727	+	0.700606i
$573$	2.71757	+	1.16373i	0.113528	+	0.0486156i
$574$	2.11650	+	1.22196i	0.0883410	+	0.0510037i
$575$	29.8602	−	5.04288i	1.24526	−	0.210303i
$576$	−2.17120	+	2.07024i	−0.0904666	+	0.0862600i
$577$	−18.5100	+	18.5100i	−0.770580	+	0.770580i	−0.978208	−	0.207628i	$-0.933426\pi$
$577$	−18.5100	+	18.5100i	−0.770580	+	0.770580i	0.207628	+	0.978208i	$0.433426\pi$
$578$	24.1081	−	24.1081i	1.00277	−	1.00277i
$579$	7.63247	+	6.00223i	0.317195	+	0.249444i
$580$	−0.629820	+	1.97264i	−0.0261518	+	0.0819096i
$581$		−	3.92924i		−	0.163012i
$582$	−6.34938	−	8.48177i	−0.263190	−	0.351581i
$583$	−1.34163	+	0.359488i	−0.0555646	+	0.0148885i
$584$	1.12051	+	1.94079i	0.0463672	+	0.0803104i
$585$	44.8555	−	8.66163i	1.85455	−	0.358114i
$586$	10.6145	+	18.3849i	0.438481	+	0.759472i
$587$	−0.126400	+	0.471730i	−0.00521708	+	0.0194704i	−0.968485	−	0.249071i	$-0.919875\pi$
$587$	−0.126400	+	0.471730i	−0.00521708	+	0.0194704i	0.963268	+	0.268541i	$0.0865415\pi$
$588$	7.08872	+	9.46942i	0.292334	+	0.390512i
$589$	−0.341103	−	19.2093i	−0.0140549	−	0.791506i
$590$	10.7196	−	16.6930i	0.441319	−	0.687239i
$591$	7.89836	−	3.16203i	0.324895	−	0.130069i
$592$	−9.24698	−	2.47772i	−0.380048	−	0.101834i
$593$	−0.731460	−	2.72985i	−0.0300375	−	0.112101i	0.949279	−	0.314434i	$-0.101815\pi$
$593$	−0.731460	−	2.72985i	−0.0300375	−	0.112101i	−0.979317	+	0.202332i	$0.935148\pi$
$594$	−13.1759	+	1.25817i	−0.540613	+	0.0516233i
$595$	6.29002	+	2.00826i	0.257866	+	0.0823306i
$596$		−	15.6622i		−	0.641547i
$597$	−16.0896	+	12.0446i	−0.658505	+	0.492952i
$598$	39.8412	−	10.6754i	1.62923	−	0.436551i
$599$	4.70662	−	8.15210i	0.192307	−	0.333086i	−0.753707	−	0.657210i	$-0.771736\pi$
$599$	4.70662	−	8.15210i	0.192307	−	0.333086i	0.946014	+	0.324125i	$0.105070\pi$
$600$	8.30773	−	2.44573i	0.339162	−	0.0998467i
$601$	11.2360			0.458325			0.229163	−	0.973388i	$-0.426401\pi$
$601$	11.2360			0.458325			0.229163	+	0.973388i	$0.426401\pi$
$602$	0.574370	−	0.153902i	0.0234096	−	0.00627258i
$603$	3.67867	−	6.03525i	0.149807	−	0.245774i
$604$	17.5527	+	10.1341i	0.714211	+	0.412350i
$605$	7.46242	−	6.78859i	0.303391	−	0.275996i
$606$	11.7311	+	29.3027i	0.476542	+	1.19034i
$607$	3.00918	−	3.00918i	0.122139	−	0.122139i	−0.643395	−	0.765534i	$-0.722475\pi$
$607$	3.00918	−	3.00918i	0.122139	−	0.122139i	0.765534	+	0.643395i	$0.222475\pi$
$608$	−1.20274	−	4.18968i	−0.0487776	−	0.169914i
$609$	0.655873	+	0.0942999i	0.0265773	+	0.00382123i
$610$	27.8989	+	1.31914i	1.12960	+	0.0534104i
$611$	−48.8013	+	28.1754i	−1.97429	+	1.13986i
$612$	−21.4380	−	0.510293i	−0.866578	−	0.0206274i
$613$	−3.74763	+	13.9863i	−0.151365	+	0.564903i	0.848024	+	0.529958i	$0.177792\pi$
$613$	−3.74763	+	13.9863i	−0.151365	+	0.564903i	−0.999389	+	0.0349448i	$0.988874\pi$
$614$	0.513644	−	0.889658i	0.0207290	−	0.0359037i
$615$	17.3214	+	14.9984i	0.698468	+	0.604794i
$616$	1.05227			0.0423973
$617$	−11.6982	+	3.13453i	−0.470953	+	0.126191i	−0.486487	−	0.873688i	$-0.661722\pi$
$617$	−11.6982	+	3.13453i	−0.470953	+	0.126191i	0.0155339	+	0.999879i	$0.495055\pi$
$618$	0.586624	+	4.90631i	0.0235975	+	0.197361i
$619$			13.8933i			0.558421i	0.960230	+	0.279210i	$0.0900727\pi$
$619$			13.8933i			0.558421i	−0.960230	+	0.279210i	$0.909927\pi$
$620$	9.62976	−	2.09838i	0.386740	−	0.0842729i
$621$	18.2551	+	25.6356i	0.732551	+	1.02872i
$622$	−7.11230	−	1.90573i	−0.285177	−	0.0764130i
$623$	1.12563	+	4.20091i	0.0450974	+	0.168306i
$624$	10.9506	−	4.38398i	0.438377	−	0.175500i
$625$	−24.5549	−	4.69669i	−0.982194	−	0.187868i
$626$			10.3460i			0.413511i
$627$	7.25529	−	17.8101i	0.289748	−	0.711267i
$628$	8.32262	+	8.32262i	0.332109	+	0.332109i
$629$	−34.2146	−	59.2614i	−1.36422	−	2.36291i
$630$	−1.21174	−	2.49223i	−0.0482768	−	0.0992927i
$631$	−7.22868	+	12.5204i	−0.287769	+	0.498431i	−0.973277	−	0.229634i	$-0.926247\pi$
$631$	−7.22868	+	12.5204i	−0.287769	+	0.498431i	0.685508	+	0.728065i	$0.259580\pi$
$632$	0.0939488	−	0.350622i	0.00373708	−	0.0139470i
$633$	−19.4412	+	2.32449i	−0.772717	+	0.0923901i
$634$		−	10.3661i		−	0.411692i
$635$	4.02154	+	2.58249i	0.159590	+	0.102483i
$636$	0.742391	+	0.583822i	0.0294377	+	0.0231500i
$637$	−12.0374	−	44.9243i	−0.476941	−	1.77997i
$638$	−1.66800	+	1.66800i	−0.0660367	+	0.0660367i
$639$	−15.1328	−	4.44338i	−0.598646	−	0.175777i
$640$	1.98714	−	1.02533i	0.0785484	−	0.0405296i
$641$	23.3328	−	13.4712i	0.921590	−	0.532080i	0.0374482	−	0.999299i	$-0.488077\pi$
$641$	23.3328	−	13.4712i	0.921590	−	0.532080i	0.884142	+	0.467218i	$0.154744\pi$
$642$	−3.83117	−	32.0425i	−0.151204	−	1.26462i
$643$	2.81960	−	10.5229i	0.111194	−	0.414982i	−0.887780	−	0.460268i	$-0.847753\pi$
$643$	2.81960	−	10.5229i	0.111194	−	0.414982i	0.998974	+	0.0452859i	$0.0144199\pi$
$644$	−1.25101	−	2.16681i	−0.0492966	−	0.0853843i
$645$	5.56051	−	0.399668i	0.218945	−	0.0157369i
$646$	15.0972	−	27.2555i	0.593992	−	1.07235i
$647$	−19.0924	−	19.0924i	−0.750601	−	0.750601i	0.223990	−	0.974591i	$-0.428092\pi$
$647$	−19.0924	−	19.0924i	−0.750601	−	0.750601i	−0.974591	+	0.223990i	$0.928092\pi$
$648$	6.05396	+	6.65955i	0.237822	+	0.261612i
$649$	19.5714	−	11.2996i	0.768246	−	0.443547i
$650$	−33.8990	−	3.21287i	−1.32963	−	0.126019i
$651$	−1.17212	−	2.92782i	−0.0459392	−	0.114750i
$652$	4.12150	+	15.3817i	0.161411	+	0.602392i
$653$	2.63960	−	2.63960i	0.103295	−	0.103295i	−0.653570	−	0.756866i	$-0.726730\pi$
$653$	2.63960	−	2.63960i	0.103295	−	0.103295i	0.756866	+	0.653570i	$0.226730\pi$
$654$	15.1745	+	2.18175i	0.593369	+	0.0853132i
$655$	8.40272	−	26.3179i	0.328321	−	1.02833i
$656$	5.12340	+	2.95800i	0.200035	+	0.115490i
$657$	5.90071	−	3.22204i	0.230209	−	0.125704i
$658$	2.41706	+	2.41706i	0.0942266	+	0.0942266i
$659$	−2.80893	+	4.86521i	−0.109420	+	0.189522i	−0.915536	−	0.402237i	$-0.868233\pi$
$659$	−2.80893	+	4.86521i	−0.109420	+	0.189522i	0.806115	+	0.591759i	$0.201566\pi$
$660$	9.68777	+	1.86362i	0.377096	+	0.0725413i
$661$	3.34370	−	5.79146i	0.130055	−	0.225262i	−0.793643	−	0.608384i	$-0.791818\pi$
$661$	3.34370	−	5.79146i	0.130055	−	0.225262i	0.923698	+	0.383123i	$0.125151\pi$
$662$	1.12750	−	4.20790i	0.0438216	−	0.163545i
$663$	77.5075	+	33.1906i	3.01014	+	1.28902i
$664$		−	9.51148i		−	0.369117i
$665$	4.02470	+	0.118732i	0.156071	+	0.00460423i
$666$	−8.09119	+	27.5562i	−0.313527	+	1.06778i
$667$	5.41771	+	1.45167i	0.209775	+	0.0562090i
$668$	−1.60871	−	0.431052i	−0.0622427	−	0.0166779i
$669$	−12.1946	−	9.58991i	−0.471470	−	0.370768i
$670$	−3.89696	+	3.54508i	−0.150553	+	0.136958i
$671$	27.5542	+	15.9084i	1.06372	+	0.614137i
$672$	−0.428795	−	0.572802i	−0.0165411	−	0.0220963i
$673$	−11.0331	−	11.0331i	−0.425293	−	0.425293i	0.461728	−	0.887021i	$-0.347229\pi$
$673$	−11.0331	−	11.0331i	−0.425293	−	0.425293i	−0.887021	+	0.461728i	$0.847229\pi$
$674$	−10.8896	+	18.8613i	−0.419450	+	0.726509i
$675$	−6.74204	−	25.0907i	−0.259501	−	0.965743i
$676$	−33.3786			−1.28379
$677$	−16.9744	−	16.9744i	−0.652377	−	0.652377i	0.301188	−	0.953565i	$-0.402617\pi$
$677$	−16.9744	−	16.9744i	−0.652377	−	0.652377i	−0.953565	+	0.301188i	$0.902617\pi$
$678$	−0.384967	+	0.0460286i	−0.0147846	+	0.00176772i
$679$	2.18843	−	1.26349i	0.0839843	−	0.0484884i
$680$	15.2262	+	4.86138i	0.583898	+	0.186425i
$681$	−37.3108	+	14.9370i	−1.42975	+	0.572388i
$682$	10.8447	+	2.90582i	0.415264	+	0.111270i
$683$	−13.7480	+	13.7480i	−0.526052	+	0.526052i	−0.919393	−	0.393341i	$-0.871319\pi$
$683$	−13.7480	+	13.7480i	−0.526052	+	0.526052i	0.393341	+	0.919393i	$0.371319\pi$
$684$	−12.6513	+	3.30810i	−0.483736	+	0.126488i
$685$	0.0877885	−	0.136707i	0.00335422	−	0.00522332i
$686$	−4.94757	+	2.85648i	−0.188899	+	0.109061i
$687$	16.1067	+	6.89726i	0.614507	+	0.263147i
$688$	1.39037	−	0.372550i	0.0530075	−	0.0142033i
$689$	−1.85673	−	3.21595i	−0.0707358	−	0.122518i
$690$	−7.67991	−	22.1643i	−0.292369	−	0.843782i
$691$	−0.383551			−0.0145910			−0.00729549	−	0.999973i	$-0.502322\pi$
$691$	−0.383551			−0.0145910			−0.00729549	+	0.999973i	$0.502322\pi$
$692$	6.33313	+	6.33313i	0.240749	+	0.240749i
$693$	0.0751213	−	3.15593i	0.00285362	−	0.119884i
$694$	−18.5801	−	10.7272i	−0.705290	−	0.407199i
$695$	27.2399	−	5.93573i	1.03327	−	0.225155i
$696$	1.58767	+	0.228271i	0.0601804	+	0.00865260i
$697$	10.9448	+	40.8467i	0.414565	+	1.54718i
$698$	11.1068	+	2.97605i	0.420397	+	0.112645i
$699$	−4.67729	+	5.94767i	−0.176911	+	0.224962i
$700$	0.343961	+	2.03668i	0.0130005	+	0.0769794i
$701$	−33.3597	+	19.2602i	−1.25998	+	0.727448i	−0.973070	−	0.230510i	$-0.925961\pi$
$701$	−33.3597	+	19.2602i	−1.25998	+	0.727448i	−0.286908	+	0.957958i	$0.592627\pi$
$702$	−12.3665	−	33.1556i	−0.466742	−	1.25138i
$703$	−30.0257	−	28.9780i	−1.13244	−	1.09293i
$704$	2.54723			0.0960025
$705$	17.9719	+	26.5333i	0.676862	+	0.999303i
$706$	−8.53485	−	14.7828i	−0.321213	−	0.556358i
$707$	−7.27163	+	1.94843i	−0.273478	+	0.0732781i
$708$	−14.1261	−	6.04914i	−0.530892	−	0.227341i
$709$	32.0785	+	18.5205i	1.20473	+	0.695553i	0.961604	−	0.274441i	$-0.0884928\pi$
$709$	32.0785	+	18.5205i	1.20473	+	0.695553i	0.243129	+	0.969994i	$0.421826\pi$
$710$	9.89162	+	6.35204i	0.371226	+	0.238388i
$711$	−1.04486	−	0.306797i	−0.0391853	−	0.0115058i
$712$	2.72481	+	10.1691i	0.102116	+	0.381104i
$713$	−6.90924	−	25.7856i	−0.258753	−	0.965679i
$714$	0.727871	−	5.06248i	0.0272399	−	0.189458i
$715$	−32.6391	−	20.9596i	−1.22063	−	0.783845i
$716$	6.89810	+	3.98262i	0.257794	+	0.148837i
$717$	−4.91745	+	11.4833i	−0.183645	+	0.428854i
$718$	−11.6423	+	3.11955i	−0.434488	+	0.116421i
$719$	3.65614	+	6.33262i	0.136351	+	0.236167i	0.926113	−	0.377247i	$-0.123129\pi$
$719$	3.65614	+	6.33262i	0.136351	+	0.236167i	−0.789762	+	0.613414i	$0.789796\pi$
$720$	−2.93325	−	6.03292i	−0.109316	−	0.224833i
$721$	−1.17852			−0.0438904
$722$	4.26289	−	18.5156i	0.158648	−	0.689080i
$723$	−10.3220	−	13.7885i	−0.383879	−	0.512801i
$724$	−13.1689	+	7.60308i	−0.489419	+	0.282566i
$725$	−3.77365	−	2.68320i	−0.140150	−	0.0996515i
$726$	−6.14247	−	4.83049i	−0.227969	−	0.179276i
$727$	−32.0467	−	8.58688i	−1.18855	−	0.318470i	−0.390234	−	0.920716i	$-0.627606\pi$
$727$	−32.0467	−	8.58688i	−1.18855	−	0.318470i	−0.798311	+	0.602246i	$0.794273\pi$
$728$	0.728141	+	2.71746i	0.0269867	+	0.100716i
$729$	20.4052	−	17.6813i	0.755747	−	0.654863i
$730$	−4.89620	+	1.06691i	−0.181216	+	0.0394881i
$731$	8.91053	+	5.14450i	0.329568	+	0.190276i
$732$	−2.56845	−	21.4816i	−0.0949326	−	0.793982i
$733$	−10.2472	−	10.2472i	−0.378489	−	0.378489i	0.492068	−	0.870557i	$-0.336241\pi$
$733$	−10.2472	−	10.2472i	−0.378489	−	0.378489i	−0.870557	+	0.492068i	$0.836241\pi$
$734$	32.8991			1.21433
$735$	−24.9922	+	8.65975i	−0.921850	+	0.319420i
$736$	−3.02831	−	5.24518i	−0.111625	−	0.193340i
$737$	−5.79681	+	1.55325i	−0.213528	+	0.0572147i
$738$	9.23723	−	15.1547i	0.340027	−	0.557851i
$739$	−37.4070	+	21.5969i	−1.37604	+	0.794457i	−0.991680	−	0.128727i	$-0.958911\pi$
$739$	−37.4070	+	21.5969i	−1.37604	+	0.794457i	−0.384359	+	0.923184i	$0.625578\pi$
$740$	11.5668	−	18.0122i	0.425203	−	0.662141i
$741$	51.0143	+	6.41248i	1.87406	+	0.235568i
$742$	−0.159281	+	0.159281i	−0.00584740	+	0.00584740i
$743$	32.9710	+	8.83455i	1.20959	+	0.324108i	0.806600	−	0.591097i	$-0.201305\pi$
$743$	32.9710	+	8.83455i	1.20959	+	0.324108i	0.402988	+	0.915205i	$0.367972\pi$
$744$	−2.83736	−	7.08736i	−0.104022	−	0.259835i
$745$	33.3625	+	10.6519i	1.22231	+	0.390254i
$746$	13.1952	−	7.61823i	0.483109	−	0.278923i
$747$	−28.5263	−	0.679019i	−1.04372	−	0.0248440i
$748$	12.8748	+	12.8748i	0.470748	+	0.470748i
$749$	7.69676			0.281234
$750$	−0.440370	+	19.3599i	−0.0160800	+	0.706924i
$751$	9.18864	−	15.9152i	0.335298	−	0.580754i	−0.648244	−	0.761433i	$-0.724496\pi$
$751$	9.18864	−	15.9152i	0.335298	−	0.580754i	0.983542	+	0.180679i	$0.0578295\pi$
$752$	5.85095	+	5.85095i	0.213362	+	0.213362i
$753$	−17.7051	+	13.2539i	−0.645209	+	0.482998i
$754$	−5.46175	−	3.15334i	−0.198905	−	0.114838i
$755$	−33.5246	+	30.4974i	−1.22008	+	1.10992i
$756$	−1.74853	+	1.24513i	−0.0635934	+	0.0452848i
$757$	−8.43210	−	2.25937i	−0.306470	−	0.0821184i	0.102307	−	0.994753i	$-0.467378\pi$
$757$	−8.43210	−	2.25937i	−0.306470	−	0.0821184i	−0.408776	+	0.912635i	$0.634044\pi$
$758$	16.7681	+	4.49301i	0.609046	+	0.163193i
$759$	3.80284	−	26.4494i	0.138034	−	0.960054i
$760$	9.74256	+	0.287414i	0.353400	+	0.0104256i
$761$			3.82185i			0.138542i	0.997598	+	0.0692710i	$0.0220673\pi$
$761$			3.82185i			0.138542i	−0.997598	+	0.0692710i	$0.977933\pi$
$762$	1.45731	−	3.40316i	0.0527929	−	0.123283i
$763$	−0.946351	+	3.53183i	−0.0342602	+	0.127861i
$764$	−0.853399	+	1.47813i	−0.0308749	+	0.0534769i
$765$	15.6670	−	45.3186i	0.566441	−	1.63850i
$766$	5.69506	−	9.86413i	0.205771	−	0.356405i
$767$	42.7236	+	42.7236i	1.54266	+	1.54266i
$768$	−1.03798	−	1.38658i	−0.0374549	−	0.0500338i
$769$	−33.4927	−	19.3370i	−1.20778	−	0.697310i	−0.245503	−	0.969396i	$-0.578953\pi$
$769$	−33.4927	−	19.3370i	−1.20778	−	0.697310i	−0.962273	+	0.272086i	$0.912287\pi$
$770$	−0.715654	+	2.24148i	−0.0257904	+	0.0807774i
$771$	1.17002	−	8.13767i	0.0421371	−	0.293071i
$772$	−3.96404	+	3.96404i	−0.142669	+	0.142669i
$773$	−9.56914	−	35.7125i	−0.344178	−	1.28449i	−0.893569	−	0.448925i	$-0.851807\pi$
$773$	−9.56914	−	35.7125i	−0.344178	−	1.28449i	0.549391	−	0.835565i	$-0.314860\pi$
$774$	−1.01807	−	4.19654i	−0.0365939	−	0.150841i
$775$	−2.07940	+	21.9398i	−0.0746941	+	0.788099i
$776$	5.29753	−	3.05853i	0.190170	−	0.109795i
$777$	−6.29674	−	2.69641i	−0.225894	−	0.0967333i
$778$	−8.43501	−	8.43501i	−0.302410	−	0.302410i
$779$	13.2881	+	22.0999i	0.476095	+	0.791813i
$780$	1.89091	+	26.3079i	0.0677053	+	0.941973i
$781$	6.69570	+	11.5973i	0.239591	+	0.414984i
$782$	11.2050	−	41.8176i	0.400690	−	1.49539i
$783$	0.797963	−	4.74536i	0.0285169	−	0.169585i
$784$	−5.91439	+	3.41467i	−0.211228	+	0.121953i
$785$	−23.3885	+	12.0680i	−0.834771	+	0.430727i
$786$	−21.1818	−	3.04547i	−0.755530	−	0.108628i
$787$	−10.7827	+	10.7827i	−0.384361	+	0.384361i	−0.872671	−	0.488309i	$-0.837614\pi$
$787$	−10.7827	+	10.7827i	−0.384361	+	0.384361i	0.488309	+	0.872671i	$0.337614\pi$
$788$	1.27131	+	4.74461i	0.0452887	+	0.169020i
$789$	−18.2473	+	23.2034i	−0.649622	+	0.826063i
$790$	0.682975	+	0.438582i	0.0242992	+	0.0156040i
$791$		−	0.0924709i		−	0.00328789i
$792$	0.181846	−	7.63954i	0.00646160	−	0.271459i
$793$	−22.0162	+	82.1657i	−0.781819	+	2.91779i
$794$	−1.44147	+	2.49670i	−0.0511559	+	0.0886047i
$795$	−1.74852	+	1.18433i	−0.0620136	+	0.0420039i
$796$	−5.80193	−	10.0492i	−0.205644	−	0.356186i
$797$	−6.65870	−	6.65870i	−0.235863	−	0.235863i	0.579272	−	0.815135i	$-0.303337\pi$
$797$	−6.65870	−	6.65870i	−0.235863	−	0.235863i	−0.815135	+	0.579272i	$0.803337\pi$
$798$	−0.425195	−	3.08975i	−0.0150517	−	0.109376i
$799$			59.1462i			2.09244i
$800$	0.832624	+	4.93019i	0.0294377	+	0.174308i
$801$	30.6932	−	7.44614i	1.08449	−	0.263096i
$802$	−1.78955	−	6.67869i	−0.0631912	−	0.235833i
$803$	−5.51391	−	1.47745i	−0.194582	−	0.0521380i
$804$	3.20767	+	2.52253i	0.113126	+	0.0889629i
$805$	5.46640	−	1.19116i	0.192665	−	0.0419829i
$806$			30.0167i			1.05729i
$807$	12.0539	−	1.44123i	0.424319	−	0.0507338i
$808$	−17.6024	+	4.71654i	−0.619250	+	0.165927i
$809$	−44.5341			−1.56574			−0.782868	−	0.622188i	$-0.786244\pi$
$809$	−44.5341			−1.56574			−0.782868	+	0.622188i	$0.786244\pi$
$810$	−18.3030	+	8.36656i	−0.643103	+	0.293971i
$811$	−8.73632	+	15.1318i	−0.306774	+	0.531348i	−0.977655	−	0.210217i	$-0.932583\pi$
$811$	−8.73632	+	15.1318i	−0.306774	+	0.531348i	0.670881	+	0.741565i	$0.265916\pi$
$812$	−0.0990145	+	0.369527i	−0.00347473	+	0.0129679i
$813$	−41.5957	+	4.97340i	−1.45882	+	0.174425i
$814$	21.1181	−	12.1926i	0.740190	−	0.427349i
$815$	−35.5680	−	1.68176i	−1.24589	−	0.0589094i
$816$	1.76195	−	12.2547i	0.0616807	−	0.429000i
$817$	6.08838	+	1.51605i	0.213005	+	0.0530399i
$818$	−10.7296	+	10.7296i	−0.375152	+	0.375152i
$819$	8.20205	−	1.98981i	0.286603	−	0.0695294i
$820$	−9.78536	+	8.90178i	−0.341719	+	0.310863i
$821$	38.1383	+	22.0192i	1.33104	+	0.768474i	0.985458	−	0.169916i	$-0.0543498\pi$
$821$	38.1383	+	22.0192i	1.33104	+	0.768474i	0.345577	+	0.938390i	$0.387683\pi$
$822$	−0.115686	−	0.0495396i	−0.00403501	−	0.00172789i
$823$	12.4841	−	3.34511i	0.435169	−	0.116603i	−0.0345828	−	0.999402i	$-0.511010\pi$
$823$	12.4841	−	3.34511i	0.435169	−	0.116603i	0.469751	+	0.882799i	$0.344344\pi$
$824$	−2.85283			−0.0993832
$825$	−10.5584	+	19.3688i	−0.367597	+	0.674334i
$826$	1.83254	−	3.17405i	0.0637622	−	0.110439i
$827$	−17.1617	+	4.59845i	−0.596769	+	0.159904i	−0.544545	−	0.838732i	$-0.683298\pi$
$827$	−17.1617	+	4.59845i	−0.596769	+	0.159904i	−0.0522240	+	0.998635i	$0.516631\pi$
$828$	−15.9473	+	8.70790i	−0.554206	+	0.302620i
$829$		−	2.75949i		−	0.0958412i	−0.998851	−	0.0479206i	$-0.984741\pi$
$829$		−	2.75949i		−	0.0958412i	0.998851	−	0.0479206i	$-0.0152594\pi$
$830$	20.2607	+	6.46878i	0.703259	+	0.224534i
$831$	−14.7666	−	36.8851i	−0.512248	−	1.27953i
$832$	1.76261	+	6.57813i	0.0611074	+	0.228056i
$833$	−47.1529	−	12.6346i	−1.63375	−	0.437762i
$834$	−8.02609	−	20.0482i	−0.277921	−	0.694211i
$835$	2.01228	−	3.13360i	0.0696379	−	0.108443i
$836$	9.71265	+	5.37997i	0.335919	+	0.186070i
$837$	−21.4586	+	8.00369i	−0.741718	+	0.276648i
$838$	−4.98532	+	18.6055i	−0.172215	+	0.642715i
$839$	21.9486	+	38.0160i	0.757749	+	1.31246i	0.943996	+	0.329956i	$0.107034\pi$
$839$	21.9486	+	38.0160i	0.757749	+	1.31246i	−0.186248	+	0.982503i	$0.559633\pi$
$840$	1.51177	−	0.523825i	0.0521609	−	0.0180737i
$841$	14.0712	+	24.3720i	0.485214	+	0.840415i
$842$	−12.0520	+	3.22932i	−0.415339	+	0.111290i
$843$	−31.1868	+	23.3461i	−1.07413	+	0.804084i
$844$		−	11.3043i		−	0.389110i
$845$	22.7009	−	71.1009i	0.780934	−	2.44595i
$846$	17.9656	−	17.1302i	0.617669	−	0.588948i
$847$	1.31788	−	1.31788i	0.0452829	−	0.0452829i
$848$	−0.385571	+	0.385571i	−0.0132406	+	0.0132406i
$849$	−27.3793	−	21.5313i	−0.939654	−	0.738951i
$850$	−20.7108	+	29.1276i	−0.710373	+	0.999068i
$851$	−50.2131	−	28.9905i	−1.72128	−	0.993783i
$852$	3.58449	−	8.37060i	0.122803	−	0.286772i
$853$	11.4832	−	42.8560i	0.393178	−	1.46736i	−0.431683	−	0.902026i	$-0.642080\pi$
$853$	11.4832	−	42.8560i	0.393178	−	1.46736i	0.824861	−	0.565336i	$-0.191253\pi$
$854$	5.15998			0.176571
$855$	1.55751	−	29.1989i	0.0532658	−	0.998580i
$856$	18.6315			0.636812
$857$	8.72533	−	32.5634i	0.298052	−	1.11234i	−0.640712	−	0.767782i	$-0.721361\pi$
$857$	8.72533	−	32.5634i	0.298052	−	1.11234i	0.938763	−	0.344563i	$-0.111973\pi$
$858$	−11.8276	+	27.6202i	−0.403789	+	0.942939i
$859$	−34.1614	−	19.7231i	−1.16557	−	0.672943i	−0.212939	−	0.977065i	$-0.568304\pi$
$859$	−34.1614	−	19.7231i	−1.16557	−	0.672943i	−0.952633	+	0.304122i	$0.901637\pi$
$860$	−0.152017	+	3.21505i	−0.00518373	+	0.109632i
$861$	3.32736	+	2.61667i	0.113396	+	0.0891757i
$862$	−23.5081	+	23.5081i	−0.800688	+	0.800688i
$863$	13.9249	−	13.9249i	0.474007	−	0.474007i	−0.429201	−	0.903209i	$-0.641205\pi$
$863$	13.9249	−	13.9249i	0.474007	−	0.474007i	0.903209	+	0.429201i	$0.141205\pi$
$864$	−4.23266	+	3.01407i	−0.143998	+	0.102541i
$865$	−17.7976	+	9.18322i	−0.605135	+	0.312239i
$866$		−	7.82618i		−	0.265944i
$867$	47.2741	−	35.3890i	1.60551	−	1.20187i
$868$	1.75876	−	0.471259i	0.0596964	−	0.0159956i
$869$	0.462310	+	0.800745i	0.0156828	+	0.0271634i
$870$	−1.56602	+	3.22669i	−0.0530932	+	0.109395i
$871$	−8.02242	−	13.8952i	−0.271829	−	0.470822i
$872$	−2.29083	+	8.54948i	−0.0775772	+	0.289522i
$873$	−8.79480	−	16.1064i	−0.297659	−	0.545120i
$874$	−0.468719	−	26.3960i	−0.0158547	−	0.892859i
$875$	−4.57233	−	0.652471i	−0.154573	−	0.0220575i
$876$	1.44264	+	3.60353i	0.0487422	+	0.121752i
$877$	−9.27180	−	2.48437i	−0.313086	−	0.0838912i	0.0988543	−	0.995102i	$-0.468482\pi$
$877$	−9.27180	−	2.48437i	−0.313086	−	0.0838912i	−0.411941	+	0.911211i	$0.635149\pi$
$878$	5.73425	+	21.4005i	0.193521	+	0.722232i
$879$	13.6659	+	34.1358i	0.460941	+	1.15137i
$880$	−1.73238	+	5.42594i	−0.0583985	+	0.182909i
$881$		−	28.2274i		−	0.951006i	−0.879714	−	0.475503i	$-0.842266\pi$
$881$		−	28.2274i		−	0.951006i	0.879714	−	0.475503i	$-0.157734\pi$
$882$	9.81889	+	17.9819i	0.330619	+	0.605482i
$883$	−44.8901	+	12.0283i	−1.51067	+	0.404784i	−0.916659	−	0.399671i	$-0.869124\pi$
$883$	−44.8901	+	12.0283i	−1.51067	+	0.404784i	−0.594014	+	0.804454i	$0.702458\pi$
$884$	−24.3396	+	42.1575i	−0.818631	+	1.41791i
$885$	22.4927	−	25.9764i	0.756083	−	0.873189i
$886$	−2.15681			−0.0724596
$887$	−39.6409	+	10.6218i	−1.33101	+	0.356643i	−0.853092	−	0.521760i	$-0.825276\pi$
$887$	−39.6409	+	10.6218i	−1.33101	+	0.356643i	−0.477919	+	0.878404i	$0.658609\pi$
$888$	−15.2425	−	6.52719i	−0.511504	−	0.219038i
$889$	0.764669	+	0.441482i	0.0256462	+	0.0148068i
$890$	−23.5147	−	1.11184i	−0.788215	−	0.0372690i
$891$	−22.8991	−	1.09076i	−0.767150	−	0.0365420i
$892$	6.33343	−	6.33343i	0.212059	−	0.212059i
$893$	9.95207	+	34.6675i	0.333033	+	1.16010i
$894$	3.86065	−	26.8515i	0.129120	−	0.898050i
$895$	−13.1749	+	11.9853i	−0.440389	+	0.400623i
$896$	0.357759	−	0.206552i	0.0119519	−	0.00690043i
$897$	70.9361	−	8.48149i	2.36849	−	0.283189i
$898$	−3.30742	+	12.3435i	−0.110370	+	0.411906i
$899$	−2.04087	+	3.53490i	−0.0680669	+	0.117895i
$900$	14.8458	−	2.14520i	0.494860	−	0.0715067i
$901$	−3.89767			−0.129850
$902$	−14.5559	+	3.90025i	−0.484660	+	0.129864i
$903$	1.02265	−	0.122273i	0.0340316	−	0.00406900i
$904$		−	0.223844i		−	0.00744493i
$905$	−7.23935	−	33.2224i	−0.240644	−	1.10435i
$906$	27.5948	+	21.7007i	0.916775	+	0.720959i
$907$	25.6405	+	6.87034i	0.851378	+	0.228126i	0.658018	−	0.753002i	$-0.271395\pi$
$907$	25.6405	+	6.87034i	0.851378	+	0.228126i	0.193360	+	0.981128i	$0.438062\pi$
$908$	−6.00552	−	22.4129i	−0.199300	−	0.743798i
$909$	12.8890	+	53.1289i	0.427501	+	1.76217i
$910$	−6.28375	−	0.297114i	−0.208304	−	0.00984922i
$911$		−	22.3060i		−	0.739031i	−0.929225	−	0.369515i	$-0.879524\pi$
$911$		−	22.3060i		−	0.739031i	0.929225	−	0.369515i	$-0.120476\pi$
$912$	−1.02927	−	7.47935i	−0.0340824	−	0.247666i
$913$	17.1318	+	17.1318i	0.566978	+	0.566978i
$914$	18.7927	+	32.5498i	0.621606	+	1.07665i
$915$	47.5054	+	9.13853i	1.57048	+	0.302110i
$916$	−5.05797	+	8.76066i	−0.167120	+	0.289460i
$917$	1.32100	−	4.93003i	0.0436232	−	0.162804i
$918$	−36.6279	−	6.15922i	−1.20890	−	0.203284i
$919$			48.0377i			1.58462i	0.610120	+	0.792309i	$0.291121\pi$
$919$			48.0377i			1.58462i	−0.610120	+	0.792309i	$0.708879\pi$
$920$	13.2325	−	2.88343i	0.436262	−	0.0950640i
$921$	1.09990	−	1.39864i	0.0362429	−	0.0460867i
$922$	−2.58506	−	9.64757i	−0.0851344	−	0.317726i
$923$	−25.3164	+	25.3164i	−0.833298	+	0.833298i
$924$	1.80404	+	0.259381i	0.0593486	+	0.00853300i
$925$	30.5017	+	36.8888i	1.00289	+	1.21290i
$926$	−25.9589	+	14.9874i	−0.853063	+	0.492516i
$927$	−0.203662	+	8.55608i	−0.00668915	+	0.281019i
$928$	−0.239684	+	0.894512i	−0.00786800	+	0.0293638i
$929$	9.20781	+	15.9484i	0.302099	+	0.523250i	0.976611	−	0.215013i	$-0.0689795\pi$
$929$	9.20781	+	15.9484i	0.302099	+	0.523250i	−0.674513	+	0.738263i	$0.735646\pi$
$930$	17.0267	−	1.22381i	0.558327	−	0.0401304i
$931$	−29.7637	+	0.528520i	−0.975467	+	0.0173215i
$932$	−3.08901	−	3.08901i	−0.101184	−	0.101184i
$933$	−11.7237	−	5.02038i	−0.383817	−	0.164360i
$934$	10.3084	−	5.95155i	0.337301	−	0.194741i
$935$	−36.1811	+	18.6688i	−1.18325	+	0.610534i
$936$	19.8546	−	4.81671i	0.648969	−	0.157439i
$937$	−7.20876	−	26.9034i	−0.235500	−	0.878897i	−0.977923	−	0.208966i	$-0.932990\pi$
$937$	−7.20876	−	26.9034i	−0.235500	−	0.878897i	0.742423	−	0.669931i	$-0.233676\pi$
$938$	−0.688211	+	0.688211i	−0.0224709	+	0.0224709i
$939$	−2.55025	+	17.7375i	−0.0832243	+	0.578840i
$940$	−16.4425	+	8.48405i	−0.536296	+	0.276719i
$941$	40.4134	+	23.3327i	1.31744	+	0.760624i	0.983316	−	0.181905i	$-0.0582263\pi$
$941$	40.4134	+	23.3327i	1.31744	+	0.760624i	0.334124	+	0.942529i	$0.391560\pi$
$942$	12.2170	+	16.3200i	0.398051	+	0.531733i
$943$	25.3363	+	25.3363i	0.825062	+	0.825062i
$944$	4.43602	−	7.68341i	0.144380	−	0.250074i
$945$	−1.46311	−	4.57141i	−0.0475948	−	0.148708i
$946$	−1.83327	+	3.17532i	−0.0596048	+	0.103239i
$947$	−0.949140	+	3.54224i	−0.0308429	+	0.115107i	−0.979631	−	0.200806i	$-0.935644\pi$
$947$	−0.949140	+	3.54224i	−0.0308429	+	0.115107i	0.948788	+	0.315913i	$0.102311\pi$
$948$	0.247494	−	0.577955i	0.00803825	−	0.0187711i
$949$		−	15.2618i		−	0.495420i
$950$	−7.23816	+	20.5575i	−0.234837	+	0.666972i
$951$	2.55520	−	17.7719i	0.0828582	−	0.576294i
$952$	2.85226	+	0.764261i	0.0924423	+	0.0247698i
$953$	23.5632	+	6.31375i	0.763288	+	0.204522i	0.619404	−	0.785072i	$-0.287374\pi$
$953$	23.5632	+	6.31375i	0.763288	+	0.204522i	0.143884	+	0.989595i	$0.454041\pi$
$954$	1.12886	+	1.18391i	0.0365482	+	0.0383306i
$955$	−2.56821	−	2.82313i	−0.0831055	−	0.0913544i
$956$	−6.24597	−	3.60611i	−0.202009	−	0.116630i
$957$	−3.27081	+	2.44850i	−0.105730	+	0.0791488i
$958$	23.4912	+	23.4912i	0.758967	+	0.758967i
$959$	0.0150076	−	0.0259940i	0.000484621	−	0.000839389i
$960$	3.65953	−	1.26802i	0.118111	−	0.0409252i
$961$	−11.5729			−0.373320
$962$	46.0999	+	46.0999i	1.48632	+	1.48632i
$963$	1.33009	−	55.8787i	0.0428616	−	1.80067i
$964$	8.61201	−	4.97215i	0.277374	−	0.160142i
$965$	−5.74797	−	11.1399i	−0.185034	−	0.358605i
$966$	−1.61065	−	4.02319i	−0.0518217	−	0.129444i
$967$	9.50338	+	2.54642i	0.305608	+	0.0818875i	0.408364	−	0.912819i	$-0.366099\pi$
$967$	9.50338	+	2.54642i	0.305608	+	0.0818875i	−0.102756	+	0.994707i	$0.532766\pi$
$968$	3.19018	−	3.19018i	0.102536	−	0.102536i
$969$	32.6013	−	43.0060i	1.04731	−	1.38155i
$970$	2.91221	+	13.3645i	0.0935054	+	0.429109i
$971$	22.5732	−	13.0326i	0.724408	−	0.418237i	−0.0919651	−	0.995762i	$-0.529315\pi$
$971$	22.5732	−	13.0326i	0.724408	−	0.418237i	0.816373	+	0.577525i	$0.195981\pi$
$972$	8.73749	+	12.9095i	0.280255	+	0.414074i
$973$	4.97506	−	1.33306i	0.159493	−	0.0427360i
$974$	5.90728	+	10.2317i	0.189281	+	0.327845i
$975$	−57.3252	−	13.8642i	−1.83588	−	0.444008i
$976$	12.4907			0.399818
$977$	−34.1008	−	34.1008i	−1.09098	−	1.09098i	−0.995424	−	0.0955569i	$-0.969537\pi$
$977$	−34.1008	−	34.1008i	−1.09098	−	1.09098i	−0.0955569	−	0.995424i	$-0.530463\pi$
$978$	3.27448	+	27.3866i	0.104706	+	0.875726i
$979$	−23.2241	−	13.4084i	−0.742245	−	0.428536i
$980$	−3.25131	−	14.9207i	−0.103859	−	0.476626i
$981$	25.4776	+	7.48088i	0.813438	+	0.238846i
$982$	−2.61373	−	9.75456i	−0.0834074	−	0.311281i
$983$	−11.1509	−	2.98787i	−0.355658	−	0.0952984i	0.0765659	−	0.997065i	$-0.475604\pi$
$983$	−11.1509	−	2.98787i	−0.355658	−	0.0952984i	−0.432224	+	0.901766i	$0.642271\pi$
$984$	8.05453	+	6.33415i	0.256769	+	0.201925i
$985$	−10.9713	−	0.518752i	−0.349573	−	0.0165288i
$986$	−5.73269	+	3.30977i	−0.182566	+	0.105404i
$987$	3.54806	+	4.73964i	0.112936	+	0.150865i
$988$	−7.17273	+	28.8053i	−0.228195	+	0.916419i
$989$	8.71802			0.277217
$990$	16.1495	+	5.58302i	0.513266	+	0.177440i
$991$	6.08282	+	10.5358i	0.193227	+	0.334679i	0.946318	−	0.323237i	$-0.104771\pi$
$991$	6.08282	+	10.5358i	0.193227	+	0.334679i	−0.753091	+	0.657917i	$0.771438\pi$
$992$	4.25743	−	1.14077i	0.135174	−	0.0362196i
$993$	2.97024	−	6.93619i	0.0942578	−	0.220113i
$994$	1.88082	+	1.08589i	0.0596561	+	0.0344425i
$995$	25.3521	−	5.52436i	0.803715	−	0.175134i
$996$	2.34454	−	16.3067i	0.0742895	−	0.516697i
$997$	−2.07770	−	7.75409i	−0.0658015	−	0.245575i	0.925189	−	0.379507i	$-0.123906\pi$
$997$	−2.07770	−	7.75409i	−0.0658015	−	0.245575i	−0.990991	+	0.133932i	$0.957240\pi$
$998$	1.53820	+	5.74062i	0.0486907	+	0.181716i
$999$	−20.6642	+	45.2485i	−0.653786	+	1.43160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.c.83.8	✓	144
3.2	odd	2	inner	570.2.v.c.83.26	yes	144
5.2	odd	4	inner	570.2.v.c.197.17	yes	144
15.2	even	4	inner	570.2.v.c.197.36	yes	144
19.11	even	3	inner	570.2.v.c.353.36	yes	144
57.11	odd	6	inner	570.2.v.c.353.17	yes	144
95.87	odd	12	inner	570.2.v.c.467.26	yes	144
285.182	even	12	inner	570.2.v.c.467.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.c.83.8	✓	144	1.1	even	1	trivial
570.2.v.c.83.26	yes	144	3.2	odd	2	inner
570.2.v.c.197.17	yes	144	5.2	odd	4	inner
570.2.v.c.197.36	yes	144	15.2	even	4	inner
570.2.v.c.353.17	yes	144	57.11	odd	6	inner
570.2.v.c.353.36	yes	144	19.11	even	3	inner
570.2.v.c.467.8	yes	144	285.182	even	12	inner
570.2.v.c.467.26	yes	144	95.87	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.681821 + 1.59221i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.65405 - 1.50470i) q^{5} +(-1.36148 - 1.07068i) q^{6} +(0.292109 - 0.292109i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.07024 - 2.17120i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.681821 + 1.59221i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.65405 - 1.50470i) q^{5} +(-1.36148 - 1.07068i) q^{6} +(0.292109 - 0.292109i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.07024 - 2.17120i) q^{9} +(1.02533 + 1.98714i) q^{10} +2.54723i q^{11} +(1.38658 - 1.03798i) q^{12} +(-6.57813 + 1.76261i) q^{13} +(0.206552 + 0.357759i) q^{14} +(1.26802 + 3.65953i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.85004 + 6.90445i) q^{17} +(2.63304 - 1.43775i) q^{18} +(0.0773896 + 4.35821i) q^{19} +(-2.18480 + 0.476080i) q^{20} +(0.265932 + 0.664264i) q^{21} +(-2.46044 - 0.659273i) q^{22} +(1.56757 + 5.85024i) q^{23} +(0.643739 + 1.60798i) q^{24} +(0.471774 - 4.97769i) q^{25} -6.81019i q^{26} +(4.86853 - 1.81588i) q^{27} +(-0.399029 + 0.106919i) q^{28} +(0.463033 - 0.801997i) q^{29} +(-3.86302 + 0.277659i) q^{30} -4.40762 q^{31} +(-0.965926 + 0.258819i) q^{32} +(-4.05572 - 1.73676i) q^{33} +(-6.19036 - 3.57401i) q^{34} +(0.0436278 - 0.922699i) q^{35} +(0.707280 + 2.91543i) q^{36} +(-6.76926 + 6.76926i) q^{37} +(-4.22974 - 1.05324i) q^{38} +(1.67868 - 11.6755i) q^{39} +(0.105610 - 2.23357i) q^{40} +(5.12340 - 2.95800i) q^{41} +(-0.710458 + 0.0849461i) q^{42} +(0.372550 - 1.39037i) q^{43} +(1.27362 - 2.20597i) q^{44} +(-6.69128 - 0.476193i) q^{45} -6.05662 q^{46} +(7.99255 - 2.14160i) q^{47} +(-1.71980 + 0.205628i) q^{48} +6.82934i q^{49} +(4.68598 + 1.74402i) q^{50} +(-9.73191 - 7.65325i) q^{51} +(6.57813 + 1.76261i) q^{52} +(0.141129 + 0.526700i) q^{53} +(0.493935 + 5.17262i) q^{54} +(3.83281 + 4.21326i) q^{55} -0.413105i q^{56} +(-6.99194 - 2.84830i) q^{57} +(0.654828 + 0.654828i) q^{58} +(-4.43602 - 7.68341i) q^{59} +(0.731625 - 3.80325i) q^{60} +(6.24536 - 10.8173i) q^{61} +(1.14077 - 4.25743i) q^{62} +(-1.23896 - 0.0294913i) q^{63} -1.00000i q^{64} +(-8.22839 + 12.8135i) q^{65} +(2.72728 - 3.46802i) q^{66} +(0.609779 + 2.27573i) q^{67} +(5.05441 - 5.05441i) q^{68} +(-10.3836 - 1.49293i) q^{69} +(0.879967 + 0.280953i) q^{70} +(4.55290 - 2.62862i) q^{71} +(-2.99915 - 0.0713894i) q^{72} +(-0.580021 + 2.16467i) q^{73} +(-4.78659 - 8.29061i) q^{74} +(7.60385 + 4.14506i) q^{75} +(2.11208 - 3.81302i) q^{76} +(0.744070 + 0.744070i) q^{77} +(10.8432 + 4.64333i) q^{78} +(0.314359 - 0.181495i) q^{79} +(2.13013 + 0.680102i) q^{80} +(-0.428215 + 8.98981i) q^{81} +(1.53117 + 5.71441i) q^{82} +(6.72563 - 6.72563i) q^{83} +(0.101828 - 0.708235i) q^{84} +(7.32904 + 14.2041i) q^{85} +(1.24658 + 0.719711i) q^{86} +(0.961239 + 1.28406i) q^{87} +(1.80117 + 1.80117i) q^{88} +(-5.26392 + 9.11738i) q^{89} +(2.19180 - 6.34003i) q^{90} +(-1.40666 + 2.43641i) q^{91} +(1.56757 - 5.85024i) q^{92} +(3.00521 - 7.01783i) q^{93} +8.27449i q^{94} +(6.68579 + 7.09226i) q^{95} +(0.246495 - 1.71442i) q^{96} +(5.90862 + 1.58321i) q^{97} +(-6.59664 - 1.76756i) q^{98} +(5.53055 - 5.27338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) \) 144 * q - 4 * q^3 + 8 * q^6	\( 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) \) 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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