LMFDB - Embedded newform 560.2.cp.a.221.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(221,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 0, 8]))

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

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

chi := DirichletCharacter("560.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			221.11
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19222 + 0.760664i) q^{2} +(-0.450503 + 0.120712i) q^{3} +(0.842782 - 1.81376i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.445278 - 0.486597i) q^{6} +(2.07294 + 1.64406i) q^{7} +(0.374878 + 2.80347i) q^{8} +(-2.40969 + 1.39124i) q^{9} +O(q^{10})$	\(q+(-1.19222 + 0.760664i) q^{2} +(-0.450503 + 0.120712i) q^{3} +(0.842782 - 1.81376i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.445278 - 0.486597i) q^{6} +(2.07294 + 1.64406i) q^{7} +(0.374878 + 2.80347i) q^{8} +(-2.40969 + 1.39124i) q^{9} +(-1.34847 + 0.426175i) q^{10} +(-0.323244 - 1.20636i) q^{11} +(-0.160734 + 0.918838i) q^{12} +(1.23263 + 1.23263i) q^{13} +(-3.72198 - 0.383271i) q^{14} -0.466395 q^{15} +(-2.57944 - 3.05720i) q^{16} +(1.55977 - 2.70159i) q^{17} +(1.81462 - 3.49163i) q^{18} +(-1.58134 + 5.90166i) q^{19} +(1.28350 - 1.53383i) q^{20} +(-1.13232 - 0.490425i) q^{21} +(1.30302 + 1.19237i) q^{22} +(3.66316 - 2.11493i) q^{23} +(-0.507297 - 1.21772i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.40719 - 0.531952i) q^{26} +(1.90701 - 1.90701i) q^{27} +(4.72896 - 2.37423i) q^{28} +(3.80964 + 3.80964i) q^{29} +(0.556046 - 0.354770i) q^{30} +(-4.59589 + 7.96031i) q^{31} +(5.40076 + 1.68278i) q^{32} +(0.291245 + 0.504452i) q^{33} +(0.195418 + 4.40735i) q^{34} +(1.57679 + 2.12455i) q^{35} +(0.492522 + 5.54311i) q^{36} +(3.30794 + 0.886360i) q^{37} +(-2.60386 - 8.23895i) q^{38} +(-0.704098 - 0.406511i) q^{39} +(-0.363488 + 2.80497i) q^{40} -7.11538i q^{41} +(1.72303 - 0.276622i) q^{42} +(-7.58075 + 7.58075i) q^{43} +(-2.46048 - 0.430415i) q^{44} +(-2.68766 + 0.720158i) q^{45} +(-2.75855 + 5.30790i) q^{46} +(2.11545 + 3.66407i) q^{47} +(1.53109 + 1.06591i) q^{48} +(1.59415 + 6.81606i) q^{49} +(-1.41283 + 0.0626435i) q^{50} +(-0.376565 + 1.40536i) q^{51} +(3.27454 - 1.19686i) q^{52} +(0.467566 + 1.74498i) q^{53} +(-0.822984 + 3.72417i) q^{54} -1.24892i q^{55} +(-3.83197 + 6.42775i) q^{56} -2.84960i q^{57} +(-7.43979 - 1.64408i) q^{58} +(2.20962 + 8.24641i) q^{59} +(-0.393069 + 0.845928i) q^{60} +(1.07271 - 4.00341i) q^{61} +(-0.575805 - 12.9864i) q^{62} +(-7.28242 - 1.07773i) q^{63} +(-7.71893 + 2.10192i) q^{64} +(0.871603 + 1.50966i) q^{65} +(-0.730947 - 0.379878i) q^{66} +(-7.21849 + 1.93419i) q^{67} +(-3.58549 - 5.10589i) q^{68} +(-1.39497 + 1.39497i) q^{69} +(-3.49595 - 1.33353i) q^{70} +2.26299i q^{71} +(-4.80364 - 6.23397i) q^{72} +(2.83312 + 1.63570i) q^{73} +(-4.61802 + 1.45949i) q^{74} +(-0.450503 - 0.120712i) q^{75} +(9.37145 + 7.84198i) q^{76} +(1.31327 - 3.03215i) q^{77} +(1.14866 - 0.0509306i) q^{78} +(-0.627678 - 1.08717i) q^{79} +(-1.70028 - 3.62064i) q^{80} +(3.54480 - 6.13977i) q^{81} +(5.41241 + 8.48310i) q^{82} +(3.33449 + 3.33449i) q^{83} +(-1.84381 + 1.64044i) q^{84} +(2.20584 - 2.20584i) q^{85} +(3.27153 - 14.8043i) q^{86} +(-2.17612 - 1.25639i) q^{87} +(3.26083 - 1.35845i) q^{88} +(2.25962 - 1.30459i) q^{89} +(2.65649 - 2.90300i) q^{90} +(0.528653 + 4.58169i) q^{91} +(-0.748721 - 8.42651i) q^{92} +(1.10956 - 4.14092i) q^{93} +(-5.30921 - 2.75923i) q^{94} +(-3.05492 + 5.29128i) q^{95} +(-2.63619 - 0.106161i) q^{96} +8.90510 q^{97} +(-7.08531 - 6.91364i) q^{98} +(2.45726 + 2.45726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4}+O(q^{10}) $ 256 * q + 4 * q^4	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46} + 80 q^{47} - 160 q^{48} - 8 q^{50} - 40 q^{51} + 24 q^{52} - 16 q^{53} - 116 q^{54} - 96 q^{56} - 8 q^{58} + 16 q^{59} - 28 q^{60} + 88 q^{62} - 56 q^{64} - 16 q^{66} - 40 q^{67} - 20 q^{68} - 16 q^{70} + 76 q^{72} + 52 q^{74} - 48 q^{78} + 128 q^{81} - 80 q^{83} - 68 q^{84} + 52 q^{86} + 20 q^{88} - 72 q^{90} - 32 q^{91} - 112 q^{92} + 120 q^{94} + 140 q^{96} + 24 q^{98} - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.19222	+	0.760664i	−0.843028	+	0.537870i
$2$	−1.19222	+	0.760664i	−0.843028	+	0.537870i
$3$	−0.450503	+	0.120712i	−0.260098	+	0.0696931i	−0.386512	−	0.922285i	$-0.626320\pi$
$3$	−0.450503	+	0.120712i	−0.260098	+	0.0696931i	0.126413	+	0.991978i	$0.459653\pi$
$4$	0.842782	−	1.81376i	0.421391	−	0.906879i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	0.445278	−	0.486597i	0.181784	−	0.198652i
$7$	2.07294	+	1.64406i	0.783497	+	0.621395i
$7$	2.07294	+	1.64406i	0.783497	+	0.621395i
$8$	0.374878	+	2.80347i	0.132539	+	0.991178i
$9$	−2.40969	+	1.39124i	−0.803231	+	0.463746i
$10$	−1.34847	+	0.426175i	−0.426424	+	0.134768i
$11$	−0.323244	−	1.20636i	−0.0974618	−	0.363732i	0.899919	−	0.436056i	$-0.143625\pi$
$11$	−0.323244	−	1.20636i	−0.0974618	−	0.363732i	−0.997381	+	0.0723238i	$0.976958\pi$
$12$	−0.160734	+	0.918838i	−0.0463998	+	0.265246i
$13$	1.23263	+	1.23263i	0.341871	+	0.341871i	0.857070	−	0.515200i	$-0.172282\pi$
$13$	1.23263	+	1.23263i	0.341871	+	0.341871i	−0.515200	+	0.857070i	$0.672282\pi$
$14$	−3.72198	−	0.383271i	−0.994740	−	0.102433i
$15$	−0.466395			−0.120423
$16$	−2.57944	−	3.05720i	−0.644859	−	0.764301i
$17$	1.55977	−	2.70159i	0.378299	−	0.655233i	−0.612516	−	0.790458i	$-0.709843\pi$
$17$	1.55977	−	2.70159i	0.378299	−	0.655233i	0.990815	+	0.135226i	$0.0431759\pi$
$18$	1.81462	−	3.49163i	0.427711	−	0.822985i
$19$	−1.58134	+	5.90166i	−0.362785	+	1.35393i	0.507613	+	0.861585i	$0.330528\pi$
$19$	−1.58134	+	5.90166i	−0.362785	+	1.35393i	−0.870399	+	0.492348i	$0.836139\pi$
$20$	1.28350	−	1.53383i	0.286999	−	0.342974i
$21$	−1.13232	−	0.490425i	−0.247093	−	0.107019i
$22$	1.30302	+	1.19237i	0.277804	+	0.254215i
$23$	3.66316	−	2.11493i	0.763822	−	0.440993i	−0.0668442	−	0.997763i	$-0.521293\pi$
$23$	3.66316	−	2.11493i	0.763822	−	0.440993i	0.830666	+	0.556770i	$0.187960\pi$
$24$	−0.507297	−	1.21772i	−0.103551	−	0.248566i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−2.40719	−	0.531952i	−0.472089	−	0.104324i
$27$	1.90701	−	1.90701i	0.367004	−	0.367004i
$28$	4.72896	−	2.37423i	0.893689	−	0.448687i
$29$	3.80964	+	3.80964i	0.707432	+	0.707432i	0.965995	−	0.258562i	$-0.0832488\pi$
$29$	3.80964	+	3.80964i	0.707432	+	0.707432i	−0.258562	+	0.965995i	$0.583249\pi$
$30$	0.556046	−	0.354770i	0.101520	−	0.0647718i
$31$	−4.59589	+	7.96031i	−0.825445	+	1.42971i	0.0761330	+	0.997098i	$0.475743\pi$
$31$	−4.59589	+	7.96031i	−0.825445	+	1.42971i	−0.901578	+	0.432616i	$0.857591\pi$
$32$	5.40076	+	1.68278i	0.954729	+	0.297476i
$33$	0.291245	+	0.504452i	0.0506993	+	0.0878137i
$34$	0.195418	+	4.40735i	0.0335140	+	0.755855i
$35$	1.57679	+	2.12455i	0.266526	+	0.359115i
$36$	0.492522	+	5.54311i	0.0820871	+	0.923852i
$37$	3.30794	+	0.886360i	0.543822	+	0.145717i	0.520264	−	0.854006i	$-0.325834\pi$
$37$	3.30794	+	0.886360i	0.543822	+	0.145717i	0.0235587	+	0.999722i	$0.492500\pi$
$38$	−2.60386	−	8.23895i	−0.422402	−	1.33653i
$39$	−0.704098	−	0.406511i	−0.112746	−	0.0650939i
$40$	−0.363488	+	2.80497i	−0.0574726	+	0.443505i
$41$		−	7.11538i		−	1.11123i	−0.831438	−	0.555617i	$-0.812482\pi$
$41$		−	7.11538i		−	1.11123i	0.831438	−	0.555617i	$-0.187518\pi$
$42$	1.72303	−	0.276622i	0.265869	−	0.0426838i
$43$	−7.58075	+	7.58075i	−1.15605	+	1.15605i	−0.170738	+	0.985317i	$0.554615\pi$
$43$	−7.58075	+	7.58075i	−1.15605	+	1.15605i	−0.985317	+	0.170738i	$0.945385\pi$
$44$	−2.46048	−	0.430415i	−0.370931	−	0.0648875i
$45$	−2.68766	+	0.720158i	−0.400653	+	0.107355i
$46$	−2.75855	+	5.30790i	−0.406726	+	0.782607i
$47$	2.11545	+	3.66407i	0.308570	+	0.534459i	0.978050	−	0.208371i	$-0.0668162\pi$
$47$	2.11545	+	3.66407i	0.308570	+	0.534459i	−0.669480	+	0.742830i	$0.733483\pi$
$48$	1.53109	+	1.06591i	0.220993	+	0.153851i
$49$	1.59415	+	6.81606i	0.227736	+	0.973723i
$50$	−1.41283	+	0.0626435i	−0.199804	+	0.00885913i
$51$	−0.376565	+	1.40536i	−0.0527296	+	0.196790i
$52$	3.27454	−	1.19686i	0.454097	−	0.165974i
$53$	0.467566	+	1.74498i	0.0642251	+	0.239691i	0.990575	−	0.136973i	$-0.0437375\pi$
$53$	0.467566	+	1.74498i	0.0642251	+	0.239691i	−0.926350	+	0.376665i	$0.877071\pi$
$54$	−0.822984	+	3.72417i	−0.111994	+	0.506795i
$55$		−	1.24892i		−	0.168404i
$56$	−3.83197	+	6.42775i	−0.512069	+	0.858944i
$57$		−	2.84960i		−	0.377439i
$58$	−7.43979	−	1.64408i	−0.976892	−	0.215878i
$59$	2.20962	+	8.24641i	0.287668	+	1.07359i	0.946868	+	0.321623i	$0.104229\pi$
$59$	2.20962	+	8.24641i	0.287668	+	1.07359i	−0.659200	+	0.751968i	$0.729105\pi$
$60$	−0.393069	+	0.845928i	−0.0507451	+	0.109209i
$61$	1.07271	−	4.00341i	0.137346	−	0.512584i	−0.862631	−	0.505834i	$-0.831185\pi$
$61$	1.07271	−	4.00341i	0.137346	−	0.512584i	0.999977	−	0.00674971i	$-0.00214852\pi$
$62$	−0.575805	−	12.9864i	−0.0731273	−	1.64927i
$63$	−7.28242	−	1.07773i	−0.917499	−	0.135781i
$64$	−7.71893	+	2.10192i	−0.964867	+	0.262740i
$65$	0.871603	+	1.50966i	0.108109	+	0.187250i
$66$	−0.730947	−	0.379878i	−0.0899733	−	0.0467598i
$67$	−7.21849	+	1.93419i	−0.881879	+	0.236299i	−0.671218	−	0.741260i	$-0.734228\pi$
$67$	−7.21849	+	1.93419i	−0.881879	+	0.236299i	−0.210661	+	0.977559i	$0.567562\pi$
$68$	−3.58549	−	5.10589i	−0.434805	−	0.619180i
$69$	−1.39497	+	1.39497i	−0.167935	+	0.167935i
$70$	−3.49595	−	1.33353i	−0.417847	−	0.159387i
$71$			2.26299i			0.268567i	0.990943	+	0.134284i	$0.0428733\pi$
$71$			2.26299i			0.268567i	−0.990943	+	0.134284i	$0.957127\pi$
$72$	−4.80364	−	6.23397i	−0.566114	−	0.734681i
$73$	2.83312	+	1.63570i	0.331592	+	0.191445i	0.656548	−	0.754285i	$-0.272016\pi$
$73$	2.83312	+	1.63570i	0.331592	+	0.191445i	−0.324956	+	0.945729i	$0.605349\pi$
$74$	−4.61802	+	1.45949i	−0.536834	+	0.169663i
$75$	−0.450503	−	0.120712i	−0.0520196	−	0.0139386i
$76$	9.37145	+	7.84198i	1.07498	+	0.899537i
$77$	1.31327	−	3.03215i	0.149661	−	0.345546i
$78$	1.14866	−	0.0509306i	0.130060	−	0.00576676i
$79$	−0.627678	−	1.08717i	−0.0706193	−	0.122316i	0.828554	−	0.559910i	$-0.189164\pi$
$79$	−0.627678	−	1.08717i	−0.0706193	−	0.122316i	−0.899173	+	0.437594i	$0.855831\pi$
$80$	−1.70028	−	3.62064i	−0.190097	−	0.404800i
$81$	3.54480	−	6.13977i	0.393866	−	0.682197i
$82$	5.41241	+	8.48310i	0.597700	+	0.936802i
$83$	3.33449	+	3.33449i	0.366008	+	0.366008i	0.866019	−	0.500011i	$-0.166671\pi$
$83$	3.33449	+	3.33449i	0.366008	+	0.366008i	−0.500011	+	0.866019i	$0.666671\pi$
$84$	−1.84381	+	1.64044i	−0.201177	+	0.178987i
$85$	2.20584	−	2.20584i	0.239257	−	0.239257i
$86$	3.27153	−	14.8043i	0.352778	−	1.59639i
$87$	−2.17612	−	1.25639i	−0.233305	−	0.134699i
$88$	3.26083	−	1.35845i	0.347606	−	0.144811i
$89$	2.25962	−	1.30459i	0.239519	−	0.138286i	−0.375437	−	0.926848i	$-0.622507\pi$
$89$	2.25962	−	1.30459i	0.239519	−	0.138286i	0.614956	+	0.788562i	$0.289174\pi$
$90$	2.65649	−	2.90300i	0.280019	−	0.306003i
$91$	0.528653	+	4.58169i	0.0554179	+	0.480292i
$92$	−0.748721	−	8.42651i	−0.0780596	−	0.878525i
$93$	1.10956	−	4.14092i	0.115056	−	0.429394i
$94$	−5.30921	−	2.75923i	−0.547603	−	0.284593i
$95$	−3.05492	+	5.29128i	−0.313428	+	0.542874i
$96$	−2.63619	−	0.106161i	−0.269055	−	0.0108350i
$97$	8.90510			0.904176			0.452088	−	0.891973i	$-0.350679\pi$
$97$	8.90510			0.904176			0.452088	+	0.891973i	$0.350679\pi$
$98$	−7.08531	−	6.91364i	−0.715724	−	0.698383i
$99$	2.45726	+	2.45726i	0.246964	+	0.246964i
$100$	1.63675	−	1.14937i	0.163675	−	0.114937i
$101$	−2.89317	−	10.7975i	−0.287881	−	1.07439i	−0.946708	−	0.322093i	$-0.895614\pi$
$101$	−2.89317	−	10.7975i	−0.287881	−	1.07439i	0.658827	−	0.752295i	$-0.271053\pi$
$102$	−0.620057	−	1.96194i	−0.0613948	−	0.194261i
$103$	12.2408	−	7.06723i	1.20612	−	0.696355i	0.244212	−	0.969722i	$-0.421471\pi$
$103$	12.2408	−	7.06723i	1.20612	−	0.696355i	0.961910	+	0.273367i	$0.0881373\pi$
$104$	−2.99357	+	3.91774i	−0.293543	+	0.384166i
$105$	−0.966809	−	0.766781i	−0.0943509	−	0.0748301i
$106$	−1.88478	−	1.72474i	−0.183066	−	0.167522i
$107$	3.38837	+	0.907910i	0.327566	+	0.0877710i	0.418854	−	0.908054i	$-0.362432\pi$
$107$	3.38837	+	0.907910i	0.327566	+	0.0877710i	−0.0912884	+	0.995824i	$0.529099\pi$
$108$	−1.85166	−	5.06605i	−0.178176	−	0.487481i
$109$	−18.8170	+	5.04200i	−1.80234	+	0.482936i	−0.994340	−	0.106245i	$-0.966117\pi$
$109$	−18.8170	+	5.04200i	−1.80234	+	0.482936i	−0.808001	+	0.589181i	$0.799451\pi$
$110$	0.950008	+	1.48899i	0.0905797	+	0.141970i
$111$	−1.59723			−0.151603
$112$	−0.320796	−	10.5781i	−0.0303124	−	0.999540i
$113$	15.1657			1.42667			0.713334	−	0.700825i	$-0.247184\pi$
$113$	15.1657			1.42667			0.713334	+	0.700825i	$0.247184\pi$
$114$	2.16759	+	3.39736i	0.203013	+	0.318192i
$115$	4.08573	−	1.09477i	0.380996	−	0.102088i
$116$	10.1205	−	3.69907i	0.939661	−	0.343450i
$117$	−4.68515	−	1.25538i	−0.433142	−	0.116060i
$118$	−8.90710	−	8.15077i	−0.819965	−	0.750339i
$119$	7.67487	−	3.03589i	0.703554	−	0.278300i
$120$	−0.174841	−	1.30753i	−0.0159607	−	0.119360i
$121$	8.17545	−	4.72010i	0.743223	−	0.429100i
$122$	1.76634	+	5.58892i	0.159917	+	0.505997i
$123$	0.858911	+	3.20550i	0.0774454	+	0.289030i
$124$	10.5647	+	15.0446i	0.948742	+	1.35105i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	9.50204	−	4.25459i	0.846509	−	0.379029i
$127$	3.18169			0.282329			0.141164	−	0.989986i	$-0.454915\pi$
$127$	3.18169			0.282329			0.141164	+	0.989986i	$0.454915\pi$
$128$	7.60382	−	8.37746i	0.672089	−	0.740470i
$129$	2.50007	−	4.33024i	0.220119	−	0.381257i
$130$	−2.18749	−	1.13685i	−0.191855	−	0.0997085i
$131$	1.23059	−	4.59262i	0.107517	−	0.401259i	−0.891101	−	0.453804i	$-0.850067\pi$
$131$	1.23059	−	4.59262i	0.107517	−	0.401259i	0.998619	+	0.0525447i	$0.0167332\pi$
$132$	1.16041	−	0.103106i	0.101001	−	0.00897421i
$133$	−12.9807	+	9.63395i	−1.12557	+	0.835369i
$134$	7.13477	−	7.79682i	0.616350	−	0.673543i
$135$	2.33560	−	1.34846i	0.201017	−	0.116057i
$136$	8.15857	+	3.36000i	0.699591	+	0.288117i
$137$	−4.24657	−	2.45176i	−0.362809	−	0.209468i	0.307503	−	0.951547i	$-0.400506\pi$
$137$	−4.24657	−	2.45176i	−0.362809	−	0.209468i	−0.670312	+	0.742079i	$0.733840\pi$
$138$	0.602010	−	2.72421i	0.0512465	−	0.231901i
$139$	1.05524	−	1.05524i	0.0895041	−	0.0895041i	−0.660937	−	0.750441i	$-0.729841\pi$
$139$	1.05524	−	1.05524i	0.0895041	−	0.0895041i	0.750441	+	0.660937i	$0.229841\pi$
$140$	5.18232	−	1.06938i	0.437986	−	0.0903794i
$141$	−1.39531	−	1.39531i	−0.117507	−	0.117507i
$142$	−1.72137	−	2.69798i	−0.144454	−	0.226409i
$143$	1.08856	−	1.88544i	0.0910301	−	0.157669i
$144$	10.4690	+	3.77832i	0.872413	+	0.314860i
$145$	2.69382	+	4.66584i	0.223710	+	0.387477i
$146$	−4.62193	+	0.204933i	−0.382514	+	0.0169603i
$147$	−1.54095	−	2.87822i	−0.127095	−	0.237392i
$148$	4.39552	−	5.25280i	0.361309	−	0.431777i
$149$	−21.9082	−	5.87029i	−1.79479	−	0.480913i	−0.801647	−	0.597797i	$-0.796043\pi$
$149$	−21.9082	−	5.87029i	−1.79479	−	0.480913i	−0.993146	+	0.116884i	$0.962709\pi$
$150$	0.628921	−	0.198766i	0.0513512	−	0.0162292i
$151$	−12.3743	−	7.14429i	−1.00700	−	0.581394i	−0.0966912	−	0.995314i	$-0.530826\pi$
$151$	−12.3743	−	7.14429i	−1.00700	−	0.581394i	−0.910313	+	0.413920i	$0.864159\pi$
$152$	−17.1379	−	2.22086i	−1.39007	−	0.180135i
$153$			8.68002i			0.701738i
$154$	0.740743	+	4.61395i	0.0596908	+	0.371803i
$155$	−6.49956	+	6.49956i	−0.522058	+	0.522058i
$156$	−1.33071	+	0.934464i	−0.106542	+	0.0748170i
$157$	6.60385	−	1.76950i	0.527045	−	0.141221i	0.0145215	−	0.999895i	$-0.495377\pi$
$157$	6.60385	−	1.76950i	0.527045	−	0.141221i	0.512523	+	0.858673i	$0.328711\pi$
$158$	1.57530	+	0.818695i	0.125324	+	0.0651319i
$159$	−0.421280	−	0.729678i	−0.0334097	−	0.0578672i
$160$	4.78120	+	3.02326i	0.377987	+	0.239010i
$161$	11.0706	+	1.63833i	0.872484	+	0.129119i
$162$	0.444117	+	10.0164i	0.0348931	+	0.786960i
$163$	2.27289	−	8.48255i	0.178027	−	0.664405i	−0.817990	−	0.575233i	$-0.804911\pi$
$163$	2.27289	−	8.48255i	0.178027	−	0.664405i	0.996016	−	0.0891716i	$-0.0284220\pi$
$164$	−12.9056	−	5.99671i	−1.00776	−	0.468264i
$165$	0.150760	+	0.562643i	0.0117366	+	0.0438017i
$166$	−6.51188	−	1.43903i	−0.505420	−	0.111690i
$167$		−	24.1332i		−	1.86749i	−0.357944	−	0.933743i	$-0.616522\pi$
$167$		−	24.1332i		−	1.86749i	0.357944	−	0.933743i	$-0.383478\pi$
$168$	0.950410	−	3.35829i	0.0733257	−	0.259098i
$169$		−	9.96123i		−	0.766249i
$170$	−0.951947	+	4.30775i	−0.0730110	+	0.330390i
$171$	−4.40005	−	16.4212i	−0.336480	−	1.25576i
$172$	7.36073	+	20.1386i	0.561251	+	1.53555i
$173$	3.16981	−	11.8299i	0.240996	−	0.899411i	−0.734357	−	0.678763i	$-0.762516\pi$
$173$	3.16981	−	11.8299i	0.240996	−	0.899411i	0.975354	−	0.220648i	$-0.0708171\pi$
$174$	3.55011	−	0.157409i	0.269133	−	0.0119331i
$175$	0.973189	+	2.46026i	0.0735662	+	0.185979i
$176$	−2.85431	+	4.09997i	−0.215152	+	0.309047i
$177$	−1.99088	−	3.44831i	−0.149644	−	0.259191i
$178$	−1.70161	+	3.27417i	−0.127541	+	0.245409i
$179$	−15.7485	+	4.21979i	−1.17710	+	0.315402i	−0.793774	−	0.608213i	$-0.791887\pi$
$179$	−15.7485	+	4.21979i	−1.17710	+	0.315402i	−0.383322	+	0.923615i	$0.625220\pi$
$180$	−0.958923	+	5.48171i	−0.0714739	+	0.408583i
$181$	17.3039	−	17.3039i	1.28619	−	1.28619i	0.349108	−	0.937083i	$-0.386485\pi$
$181$	17.3039	−	17.3039i	1.28619	−	1.28619i	0.937083	−	0.349108i	$-0.113515\pi$
$182$	−4.11540	−	5.06026i	−0.305053	−	0.375091i
$183$			1.93304i			0.142894i
$184$	7.30238	+	9.47674i	0.538339	+	0.698635i
$185$	2.96582	+	1.71232i	0.218051	+	0.125892i
$186$	1.82701	+	5.78090i	0.133963	+	0.423876i
$187$	−3.76329	−	1.00837i	−0.275199	−	0.0737394i
$188$	8.42860	−	0.748906i	0.614719	−	0.0546196i
$189$	7.08835	−	0.817881i	0.515602	−	0.0594921i
$190$	−0.382742	−	8.63214i	−0.0277670	−	0.626241i
$191$	−12.9895	−	22.4985i	−0.939887	−	1.62793i	−0.765679	−	0.643223i	$-0.777597\pi$
$191$	−12.9895	−	22.4985i	−0.939887	−	1.62793i	−0.174208	−	0.984709i	$-0.555736\pi$
$192$	3.22368	−	1.87869i	0.232649	−	0.135583i
$193$	−0.620168	+	1.07416i	−0.0446407	+	0.0773199i	−0.887482	−	0.460842i	$-0.847548\pi$
$193$	−0.620168	+	1.07416i	−0.0446407	+	0.0773199i	0.842842	+	0.538162i	$0.180881\pi$
$194$	−10.6169	+	6.77379i	−0.762246	+	0.486330i
$195$	−0.574894	−	0.574894i	−0.0411690	−	0.0411690i
$196$	13.7062	+	2.85305i	0.979015	+	0.203789i
$197$	−12.3942	+	12.3942i	−0.883049	+	0.883049i	−0.993843	−	0.110794i	$-0.964660\pi$
$197$	−12.3942	+	12.3942i	−0.883049	+	0.883049i	0.110794	+	0.993843i	$0.464660\pi$
$198$	−4.79874	−	1.06045i	−0.341032	−	0.0753628i
$199$	−6.71638	−	3.87770i	−0.476112	−	0.274883i	0.242683	−	0.970106i	$-0.421973\pi$
$199$	−6.71638	−	3.87770i	−0.476112	−	0.274883i	−0.718795	+	0.695222i	$0.755306\pi$
$200$	−1.07708	+	2.61532i	−0.0761613	+	0.184931i
$201$	3.01847	−	1.74272i	0.212907	−	0.122922i
$202$	11.6625	+	10.6722i	0.820574	+	0.750896i
$203$	1.63388	+	14.1604i	0.114676	+	0.993866i
$204$	2.23162	+	1.86741i	0.156245	+	0.130745i
$205$	1.84159	−	6.87292i	0.128623	−	0.480026i
$206$	−9.21796	+	17.7368i	−0.642245	+	1.23578i
$207$	−5.88474	+	10.1927i	−0.409017	+	0.708439i
$208$	0.588911	−	6.94791i	0.0408336	−	0.481751i
$209$	7.63071			0.527827
$210$	1.73591	+	0.178756i	0.119789	+	0.0123353i
$211$	19.0920	+	19.0920i	1.31435	+	1.31435i	0.918178	+	0.396167i	$0.129660\pi$
$211$	19.0920	+	19.0920i	1.31435	+	1.31435i	0.396167	+	0.918178i	$0.370340\pi$
$212$	3.55903	+	0.622585i	0.244435	+	0.0427593i
$213$	−0.273170	−	1.01948i	−0.0187173	−	0.0698538i
$214$	−4.73030	+	1.49498i	−0.323356	+	0.102195i
$215$	−9.28449	+	5.36040i	−0.633197	+	0.365576i
$216$	6.06115	+	4.63136i	0.412409	+	0.315124i
$217$	−22.6142	+	8.94533i	−1.53515	+	0.607249i
$218$	18.5988	−	20.3246i	1.25967	−	1.37655i
$219$	−1.47378	−	0.394898i	−0.0995889	−	0.0266848i
$220$	−2.26524	−	1.05257i	−0.152722	−	0.0709641i
$221$	5.25269	−	1.40745i	0.353334	−	0.0946756i
$222$	1.90425	−	1.21496i	0.127805	−	0.0815426i
$223$	1.35416			0.0906813			0.0453406	−	0.998972i	$-0.485563\pi$
$223$	1.35416			0.0906813			0.0453406	+	0.998972i	$0.485563\pi$
$224$	8.42887	+	12.3675i	0.563177	+	0.826336i
$225$	−2.78248			−0.185498
$226$	−18.0808	+	11.5360i	−1.20272	+	0.767362i
$227$	11.3610	−	3.04417i	0.754057	−	0.202049i	0.138740	−	0.990329i	$-0.455695\pi$
$227$	11.3610	−	3.04417i	0.754057	−	0.202049i	0.615317	+	0.788280i	$0.289028\pi$
$228$	−5.16849	−	2.40159i	−0.342292	−	0.159049i
$229$	2.42789	+	0.650551i	0.160439	+	0.0429896i	0.338145	−	0.941094i	$-0.390201\pi$
$229$	2.42789	+	0.650551i	0.160439	+	0.0429896i	−0.177705	+	0.984084i	$0.556867\pi$
$230$	−4.03834	+	4.41307i	−0.266280	+	0.290989i
$231$	−0.225614	+	1.52452i	−0.0148443	+	0.100306i
$232$	−9.25208	+	12.1084i	−0.607428	+	0.794954i
$233$	−0.780664	+	0.450717i	−0.0511430	+	0.0295274i	−0.525353	−	0.850884i	$-0.676067\pi$
$233$	−0.780664	+	0.450717i	−0.0511430	+	0.0295274i	0.474210	+	0.880412i	$0.342734\pi$
$234$	6.54066	−	2.06713i	0.427576	−	0.135133i
$235$	1.09504	+	4.08674i	0.0714324	+	0.266589i
$236$	16.8192	+	2.94221i	1.09484	+	0.191522i
$237$	0.414006	+	0.414006i	0.0268925	+	0.0268925i
$238$	−6.84085	+	9.45745i	−0.443427	+	0.613036i
$239$	−7.01137			−0.453528			−0.226764	−	0.973950i	$-0.572815\pi$
$239$	−7.01137			−0.453528			−0.226764	+	0.973950i	$0.572815\pi$
$240$	1.20304	+	1.42587i	0.0776558	+	0.0920393i
$241$	0.423683	−	0.733841i	0.0272918	−	0.0472708i	−0.852057	−	0.523449i	$-0.824645\pi$
$241$	0.423683	−	0.733841i	0.0272918	−	0.0472708i	0.879349	+	0.476178i	$0.157978\pi$
$242$	−6.15654	+	11.8462i	−0.395757	+	0.761501i
$243$	−2.94984	+	11.0090i	−0.189232	+	0.706225i
$244$	−6.35715	−	5.31963i	−0.406975	−	0.340555i
$245$	−0.224295	+	6.99641i	−0.0143297	+	0.446984i
$246$	−3.46232	−	3.16832i	−0.220749	−	0.202005i
$247$	−9.22379	+	5.32536i	−0.586896	+	0.338844i
$248$	−24.0394	−	9.90030i	−1.52650	−	0.628670i
$249$	−1.90471	−	1.09969i	−0.120706	−	0.0696898i
$250$	−1.38090	−	0.305157i	−0.0873357	−	0.0192998i
$251$	−11.3975	+	11.3975i	−0.719403	+	0.719403i	−0.968483	−	0.249080i	$-0.919872\pi$
$251$	−11.3975	+	11.3975i	−0.719403	+	0.719403i	0.249080	+	0.968483i	$0.419872\pi$
$252$	−8.09223	+	12.3003i	−0.509762	+	0.774844i
$253$	−3.73547	−	3.73547i	−0.234847	−	0.234847i
$254$	−3.79327	+	2.42019i	−0.238011	+	0.151856i
$255$	−0.727467	+	1.26001i	−0.0455558	+	0.0789049i
$256$	−2.69300	+	15.7717i	−0.168313	+	0.985734i
$257$	−11.8133	−	20.4612i	−0.736891	−	1.27633i	−0.953889	−	0.300161i	$-0.902960\pi$
$257$	−11.8133	−	20.4612i	−0.736891	−	1.27633i	0.216998	−	0.976172i	$-0.430374\pi$
$258$	0.313226	+	7.06432i	0.0195006	+	0.439805i
$259$	5.39993	+	7.27582i	0.335536	+	0.452097i
$260$	3.47273	−	0.308562i	0.215370	−	0.0191362i
$261$	−14.4802	−	3.87995i	−0.896301	−	0.240163i
$262$	2.02631	+	6.41149i	0.125186	+	0.396103i
$263$	16.3732	+	9.45306i	1.00961	+	0.582901i	0.911079	−	0.412233i	$-0.135251\pi$
$263$	16.3732	+	9.45306i	1.00961	+	0.582901i	0.0985352	+	0.995134i	$0.468584\pi$
$264$	−1.30504	+	1.00561i	−0.0803194	+	0.0618908i
$265$			1.80654i			0.110975i
$266$	8.14765	−	21.3597i	0.499565	−	1.30965i
$267$	−0.860486	+	0.860486i	−0.0526609	+	0.0526609i
$268$	−2.57546	+	14.7227i	−0.157321	+	0.899332i
$269$	17.9130	−	4.79978i	1.09218	−	0.292648i	0.332601	−	0.943068i	$-0.392074\pi$
$269$	17.9130	−	4.79978i	1.09218	−	0.292648i	0.759575	+	0.650420i	$0.225407\pi$
$270$	−1.75883	+	3.38427i	−0.107039	+	0.205960i
$271$	−0.374243	−	0.648207i	−0.0227336	−	0.0393758i	0.854435	−	0.519559i	$-0.173904\pi$
$271$	−0.374243	−	0.648207i	−0.0227336	−	0.0393758i	−0.877168	+	0.480183i	$0.840570\pi$
$272$	−12.2826	+	2.20007i	−0.744745	+	0.133399i
$273$	−0.791225	−	2.00025i	−0.0478871	−	0.121061i
$274$	6.92781	−	0.307173i	0.418525	−	0.0185570i
$275$	0.323244	−	1.20636i	0.0194924	−	0.0727465i
$276$	1.35448	+	3.70579i	0.0815303	+	0.223063i
$277$	3.40625	+	12.7123i	0.204661	+	0.763807i	0.989552	+	0.144173i	$0.0460522\pi$
$277$	3.40625	+	12.7123i	0.204661	+	0.763807i	−0.784891	+	0.619634i	$0.787281\pi$
$278$	−0.455395	+	2.06076i	−0.0273128	+	0.123596i
$279$		−	25.5759i		−	1.53119i
$280$	−5.36503	+	5.21694i	−0.320622	+	0.311772i
$281$		−	10.3017i		−	0.614549i	−0.951621	−	0.307275i	$-0.900583\pi$
$281$		−	10.3017i		−	0.614549i	0.951621	−	0.307275i	$-0.0994170\pi$
$282$	2.72489	+	0.602158i	0.162265	+	0.0358580i
$283$	−3.67907	−	13.7305i	−0.218698	−	0.816191i	−0.984832	−	0.173511i	$-0.944489\pi$
$283$	−3.67907	−	13.7305i	−0.218698	−	0.816191i	0.766134	−	0.642681i	$-0.222178\pi$
$284$	4.10451	+	1.90720i	0.243558	+	0.113172i
$285$	0.737531	−	2.75250i	0.0436876	−	0.163044i
$286$	0.136383	+	3.07590i	0.00806448	+	0.181882i
$287$	11.6981	−	14.7497i	0.690516	−	0.870649i
$288$	−15.3553	+	3.45876i	−0.904822	+	0.203810i
$289$	3.63426	+	6.29473i	0.213780	+	0.370278i
$290$	−6.76076	−	3.51362i	−0.397006	−	0.206327i
$291$	−4.01178	+	1.07495i	−0.235175	+	0.0630149i
$292$	5.35448	−	3.76006i	0.313347	−	0.220041i
$293$	−20.4080	+	20.4080i	−1.19225	+	1.19225i	−0.215812	+	0.976435i	$0.569240\pi$
$293$	−20.4080	+	20.4080i	−1.19225	+	1.19225i	−0.976435	+	0.215812i	$0.930760\pi$
$294$	4.02651	+	2.25934i	0.234831	+	0.131767i
$295$			8.53731i			0.497062i
$296$	−1.24481	+	9.60601i	−0.0723534	+	0.558338i
$297$	−2.91698	−	1.68412i	−0.169260	−	0.0977225i
$298$	30.5848	−	9.66611i	1.77173	−	0.559943i
$299$	7.12226	+	1.90840i	0.411891	+	0.110366i
$300$	−0.598618	+	0.715370i	−0.0345612	+	0.0413019i
$301$	−28.1776	+	3.25124i	−1.62413	+	0.187399i
$302$	20.1873	−	0.895087i	1.16165	−	0.0515065i
$303$	2.60677	+	4.51505i	0.149755	+	0.259383i
$304$	22.1215	−	10.3885i	1.26876	−	0.595819i
$305$	2.07232	−	3.58936i	0.118660	−	0.205526i
$306$	−6.60257	−	10.3485i	−0.377444	−	0.591584i
$307$	10.3474	+	10.3474i	0.590555	+	0.590555i	0.937781	−	0.347227i	$-0.112877\pi$
$307$	10.3474	+	10.3474i	0.590555	+	0.590555i	−0.347227	+	0.937781i	$0.612877\pi$
$308$	−4.39279	−	4.93739i	−0.250303	−	0.281334i
$309$	−4.66142	+	4.66142i	−0.265179	+	0.265179i
$310$	2.80493	−	12.6929i	0.159310	−	0.720908i
$311$	12.1434	+	7.01098i	0.688588	+	0.397556i	0.803083	−	0.595867i	$-0.203192\pi$
$311$	12.1434	+	7.01098i	0.688588	+	0.397556i	−0.114495	+	0.993424i	$0.536525\pi$
$312$	0.875693	−	2.12631i	0.0495764	−	0.120379i
$313$	25.5865	−	14.7724i	1.44623	−	0.834983i	0.447978	−	0.894044i	$-0.352144\pi$
$313$	25.5865	−	14.7724i	1.44623	−	0.834983i	0.998254	+	0.0590616i	$0.0188109\pi$
$314$	−6.52726	+	7.13294i	−0.368355	+	0.402535i
$315$	−6.75535	−	2.92583i	−0.380621	−	0.164852i
$316$	−2.50086	+	0.222209i	−0.140684	+	0.0125002i
$317$	−2.70202	+	10.0841i	−0.151761	+	0.566378i	0.847600	+	0.530635i	$0.178046\pi$
$317$	−2.70202	+	10.0841i	−0.151761	+	0.566378i	−0.999361	+	0.0357431i	$0.988620\pi$
$318$	1.05730	+	0.549485i	0.0592903	+	0.0308136i
$319$	3.36437	−	5.82726i	0.188368	−	0.326264i
$320$	−7.99993	+	0.0324919i	−0.447210	+	0.00181635i
$321$	−1.63607			−0.0913163
$322$	−14.4448	+	6.46773i	−0.804977	+	0.360432i
$323$	13.4773	+	13.4773i	0.749900	+	0.749900i
$324$	−8.14857	−	11.6039i	−0.452698	−	0.644661i
$325$	0.451175	+	1.68381i	0.0250267	+	0.0934008i
$326$	3.74258	+	11.8420i	0.207282	+	0.655867i
$327$	7.86849	−	4.54287i	0.435128	−	0.251222i
$328$	19.9478	−	2.66740i	1.10143	−	0.147282i
$329$	−1.63874	+	11.0733i	−0.0903466	+	0.610492i
$330$	−0.607721	−	0.556117i	−0.0334539	−	0.0306132i
$331$	−20.6215	−	5.52552i	−1.13346	−	0.303710i	−0.357142	−	0.934050i	$-0.616249\pi$
$331$	−20.6215	−	5.52552i	−1.13346	−	0.303710i	−0.776319	+	0.630340i	$0.782916\pi$
$332$	8.85822	−	3.23772i	0.486158	−	0.177693i
$333$	−9.20427	+	2.46628i	−0.504391	+	0.135151i
$334$	18.3573	+	28.7722i	1.00447	+	1.57434i
$335$	−7.47313			−0.408301
$336$	1.42143	+	4.72676i	0.0775453	+	0.257866i
$337$	7.38944			0.402528			0.201264	−	0.979537i	$-0.435495\pi$
$337$	7.38944			0.402528			0.201264	+	0.979537i	$0.435495\pi$
$338$	7.57715	+	11.8760i	0.412143	+	0.645969i
$339$	−6.83219	+	1.83068i	−0.371074	+	0.0994289i
$340$	−2.14182	−	5.85991i	−0.116157	−	0.317798i
$341$	11.0886	+	2.97119i	0.600483	+	0.160899i
$342$	17.7368	+	16.2308i	0.959099	+	0.877659i
$343$	−7.90142	+	16.7502i	−0.426637	+	0.904423i
$344$	−24.0943	−	18.4106i	−1.29908	−	0.992632i
$345$	−1.70848	+	0.986393i	−0.0919816	+	0.0531056i
$346$	5.21946	+	16.5150i	0.280600	+	0.887853i
$347$	−7.15391	−	26.6988i	−0.384042	−	1.43326i	−0.839671	−	0.543095i	$-0.817252\pi$
$347$	−7.15391	−	26.6988i	−0.384042	−	1.43326i	0.455629	−	0.890170i	$-0.349414\pi$
$348$	−4.11278	+	2.88810i	−0.220468	+	0.154819i
$349$	0.943208	+	0.943208i	0.0504888	+	0.0504888i	0.731900	−	0.681412i	$-0.238634\pi$
$349$	0.943208	+	0.943208i	0.0504888	+	0.0504888i	−0.681412	+	0.731900i	$0.738634\pi$
$350$	−3.03169	−	2.19291i	−0.162051	−	0.117216i
$351$	4.70128			0.250936
$352$	0.284278	−	7.05924i	0.0151521	−	0.376259i
$353$	−4.29150	+	7.43310i	−0.228414	+	0.395624i	−0.957338	−	0.288970i	$-0.906687\pi$
$353$	−4.29150	+	7.43310i	−0.228414	+	0.395624i	0.728924	+	0.684594i	$0.240021\pi$
$354$	4.99657	+	2.59675i	0.265565	+	0.138016i
$355$	−0.585704	+	2.18588i	−0.0310859	+	0.116014i
$356$	−0.461848	−	5.19789i	−0.0244779	−	0.275487i
$357$	−3.09109	+	2.29413i	−0.163598	+	0.121418i
$358$	15.5658	−	17.0102i	0.822679	−	0.899018i
$359$	3.17739	−	1.83447i	0.167696	−	0.0968195i	−0.413803	−	0.910367i	$-0.635800\pi$
$359$	3.17739	−	1.83447i	0.167696	−	0.0968195i	0.581499	+	0.813547i	$0.302466\pi$
$360$	−3.02649	−	7.26483i	−0.159510	−	0.382890i
$361$	−15.8744	−	9.16509i	−0.835495	−	0.482373i
$362$	−7.46763	+	33.7926i	−0.392490	+	1.77610i
$363$	−3.11330	+	3.11330i	−0.163406	+	0.163406i
$364$	8.75562	+	2.90252i	0.458919	+	0.152133i
$365$	2.31324	+	2.31324i	0.121080	+	0.121080i
$366$	−1.47039	−	2.30461i	−0.0768586	−	0.120464i
$367$	−5.57346	+	9.65351i	−0.290932	+	0.503909i	−0.974030	−	0.226417i	$-0.927299\pi$
$367$	−5.57346	+	9.65351i	−0.290932	+	0.503909i	0.683098	+	0.730327i	$0.260632\pi$
$368$	−15.9147	−	5.74371i	−0.829609	−	0.299412i
$369$	9.89918	+	17.1459i	0.515331	+	0.892579i
$370$	−4.83841	+	0.214531i	−0.251537	+	0.0111529i
$371$	−1.89961	+	4.38594i	−0.0986229	+	0.227707i
$372$	−6.57552	−	5.50236i	−0.340925	−	0.285284i
$373$	−1.95270	−	0.523224i	−0.101107	−	0.0270915i	0.207911	−	0.978148i	$-0.433334\pi$
$373$	−1.95270	−	0.523224i	−0.101107	−	0.0270915i	−0.309018	+	0.951056i	$0.600000\pi$
$374$	5.25370	−	1.66040i	0.271663	−	0.0858571i
$375$	−0.403910	−	0.233198i	−0.0208578	−	0.0120423i
$376$	−9.47909	+	7.30419i	−0.488847	+	0.376685i
$377$			9.39177i			0.483701i
$378$	−7.82875	+	6.36694i	−0.402667	+	0.327480i
$379$	9.38741	−	9.38741i	0.482199	−	0.482199i	−0.423634	−	0.905833i	$-0.639246\pi$
$379$	9.38741	−	9.38741i	0.482199	−	0.482199i	0.905833	+	0.423634i	$0.139246\pi$
$380$	7.02247	+	10.0003i	0.360245	+	0.513004i
$381$	−1.43336	+	0.384068i	−0.0734333	+	0.0196764i
$382$	32.6001	+	16.9425i	1.66797	+	0.866854i
$383$	−13.2963	−	23.0299i	−0.679409	−	1.17677i	−0.975159	−	0.221505i	$-0.928903\pi$
$383$	−13.2963	−	23.0299i	−0.679409	−	1.17677i	0.295750	−	0.955265i	$-0.404430\pi$
$384$	−2.41429	+	4.69195i	−0.123203	+	0.239435i
$385$	2.05330	−	2.58893i	0.104646	−	0.131944i
$386$	−0.0776990	−	1.75238i	−0.00395478	−	0.0891937i
$387$	7.72067	−	28.8139i	0.392464	−	1.46469i
$388$	7.50506	−	16.1517i	0.381012	−	0.819979i
$389$	−3.73629	−	13.9440i	−0.189437	−	0.706990i	−0.993637	−	0.112630i	$-0.964072\pi$
$389$	−3.73629	−	13.9440i	−0.189437	−	0.706990i	0.804200	−	0.594359i	$-0.202594\pi$
$390$	1.12270	+	0.248100i	0.0568502	+	0.0125630i
$391$		−	13.1952i		−	0.667308i
$392$	−18.5110	+	7.02435i	−0.934949	+	0.354783i
$393$			2.21754i			0.111860i
$394$	5.34880	−	24.2044i	0.269469	−	1.21940i
$395$	−0.324910	−	1.21258i	−0.0163480	−	0.0610116i
$396$	6.52781	−	2.38594i	0.328035	−	0.119898i
$397$	6.38514	−	23.8297i	0.320461	−	1.19598i	−0.598335	−	0.801246i	$-0.704171\pi$
$397$	6.38514	−	23.8297i	0.320461	−	1.19598i	0.918797	−	0.394731i	$-0.129162\pi$
$398$	10.9570	−	0.485826i	0.549227	−	0.0243523i
$399$	4.68491	−	5.90705i	0.234539	−	0.295722i
$400$	−0.705256	−	3.93734i	−0.0352628	−	0.196867i
$401$	15.8268	+	27.4128i	0.790351	+	1.36893i	0.925749	+	0.378138i	$0.123435\pi$
$401$	15.8268	+	27.4128i	0.790351	+	1.36893i	−0.135398	+	0.990791i	$0.543231\pi$
$402$	−2.27307	+	4.37375i	−0.113370	+	0.218143i
$403$	−15.4772	+	4.14710i	−0.770973	+	0.206582i
$404$	−22.0223	−	3.85239i	−1.09565	−	0.191664i
$405$	5.01310	−	5.01310i	0.249103	−	0.249103i
$406$	−12.7193	−	15.6395i	−0.631246	−	0.776176i
$407$		−	4.27709i		−	0.212008i
$408$	−4.08105	−	0.528852i	−0.202042	−	0.0261821i
$409$	23.3489	+	13.4805i	1.15453	+	0.666567i	0.949986	−	0.312291i	$-0.101096\pi$
$409$	23.3489	+	13.4805i	1.15453	+	0.666567i	0.204541	+	0.978858i	$0.434430\pi$
$410$	3.03240	+	9.59488i	0.149759	+	0.473857i
$411$	2.20905	+	0.591913i	0.108964	+	0.0291969i
$412$	−2.50192	−	28.1580i	−0.123261	−	1.38724i
$413$	−8.97717	+	20.7270i	−0.441738	+	1.01991i
$414$	−0.737281	−	16.6282i	−0.0362354	−	0.817232i
$415$	2.35784	+	4.08390i	0.115742	+	0.200471i
$416$	4.58291	+	8.73140i	0.224696	+	0.428092i
$417$	−0.348008	+	0.602768i	−0.0170420	+	0.0295177i
$418$	−9.09749	+	5.80440i	−0.444973	+	0.283902i
$419$	20.4105	+	20.4105i	0.997116	+	0.997116i	0.999996	−	0.00287947i	$-0.000916564\pi$
$419$	20.4105	+	20.4105i	0.997116	+	0.997116i	−0.00287947	+	0.999996i	$0.500917\pi$
$420$	−2.20556	+	1.10733i	−0.107620	+	0.0540321i
$421$	10.2151	−	10.2151i	0.497855	−	0.497855i	−0.412915	−	0.910770i	$-0.635489\pi$
$421$	10.2151	−	10.2151i	0.497855	−	0.497855i	0.910770	+	0.412915i	$0.135489\pi$
$422$	−37.2844	−	8.23928i	−1.81498	−	0.401082i
$423$	−10.1952	−	5.88619i	−0.495707	−	0.286196i
$424$	−4.71672	+	1.96496i	−0.229064	+	0.0954270i
$425$	2.70159	−	1.55977i	0.131047	−	0.0756597i
$426$	1.10116	+	1.00766i	0.0533515	+	0.0488212i
$427$	8.80549	−	6.53522i	0.426128	−	0.316262i
$428$	4.50238	−	5.38051i	0.217631	−	0.260077i
$429$	−0.262805	+	0.980802i	−0.0126883	+	0.0473536i
$430$	6.99170	−	13.4532i	0.337170	−	0.648769i
$431$	7.38631	−	12.7935i	0.355786	−	0.616240i	−0.631466	−	0.775404i	$-0.717546\pi$
$431$	7.38631	−	12.7935i	0.355786	−	0.616240i	0.987252	+	0.159164i	$0.0508798\pi$
$432$	−10.7491	−	0.911106i	−0.517168	−	0.0438356i
$433$	−20.9602			−1.00728			−0.503642	−	0.863913i	$-0.668007\pi$
$433$	−20.9602			−1.00728			−0.503642	+	0.863913i	$0.668007\pi$
$434$	20.1567	−	27.8666i	0.967554	−	1.33764i
$435$	−1.77680	−	1.77680i	−0.0851909	−	0.0851909i
$436$	−6.71365	+	38.3788i	−0.321526	+	1.83801i
$437$	6.68886	+	24.9632i	0.319971	+	1.19415i
$438$	2.05746	−	0.650245i	0.0983091	−	0.0310699i
$439$	20.6155	−	11.9024i	0.983924	−	0.568069i	0.0804713	−	0.996757i	$-0.474357\pi$
$439$	20.6155	−	11.9024i	0.983924	−	0.568069i	0.903452	+	0.428688i	$0.141024\pi$
$440$	3.50132	−	0.468192i	0.166919	−	0.0223202i
$441$	−13.3242	−	14.2068i	−0.634485	−	0.676513i
$442$	−5.19177	+	5.67352i	−0.246947	+	0.269862i
$443$	35.2525	+	9.44588i	1.67490	+	0.448787i	0.966424	−	0.256951i	$-0.0827180\pi$
$443$	35.2525	+	9.44588i	1.67490	+	0.448787i	0.708472	+	0.705739i	$0.249385\pi$
$444$	−1.34612	+	2.89699i	−0.0638840	+	0.137485i
$445$	2.52028	−	0.675306i	0.119473	−	0.0320126i
$446$	−1.61446	+	1.03006i	−0.0764468	+	0.0487748i
$447$	10.5783			0.500339
$448$	−19.4566	−	8.33322i	−0.919236	−	0.393708i
$449$	−32.8650			−1.55100			−0.775498	−	0.631350i	$-0.782501\pi$
$449$	−32.8650			−1.55100			−0.775498	+	0.631350i	$0.782501\pi$
$450$	3.31733	−	2.11653i	0.156380	−	0.0997741i
$451$	−8.58373	+	2.30000i	−0.404192	+	0.108303i
$452$	12.7814	−	27.5069i	0.601185	−	1.29381i
$453$	6.43705	+	1.72480i	0.302439	+	0.0810383i
$454$	−11.2292	+	12.2712i	−0.527014	+	0.575917i
$455$	−0.675189	+	4.56240i	−0.0316533	+	0.213889i
$456$	7.98879	−	1.06825i	0.374109	−	0.0500255i
$457$	−32.6490	+	18.8499i	−1.52725	+	0.881760i	−0.527778	+	0.849382i	$0.676975\pi$
$457$	−32.6490	+	18.8499i	−1.52725	+	0.881760i	−0.999476	+	0.0323780i	$0.989692\pi$
$458$	−3.38943	+	1.07121i	−0.158378	+	0.0500542i
$459$	−2.17748	−	8.12645i	−0.101636	−	0.379310i
$460$	1.45773	−	8.33317i	0.0679672	−	0.388536i
$461$	−4.45270	−	4.45270i	−0.207383	−	0.207383i	0.595771	−	0.803154i	$-0.296846\pi$
$461$	−4.45270	−	4.45270i	−0.207383	−	0.207383i	−0.803154	+	0.595771i	$0.796846\pi$
$462$	−0.890666	−	1.98918i	−0.0414375	−	0.0925451i
$463$	12.0300			0.559084			0.279542	−	0.960133i	$-0.409817\pi$
$463$	12.0300			0.559084			0.279542	+	0.960133i	$0.409817\pi$
$464$	1.82012	−	21.4736i	0.0844969	−	0.996886i
$465$	2.14350	−	3.71265i	0.0994024	−	0.172170i
$466$	0.587881	−	1.13118i	0.0272330	−	0.0524008i
$467$	3.55437	−	13.2651i	0.164477	−	0.613836i	−0.833630	−	0.552324i	$-0.813741\pi$
$467$	3.55437	−	13.2651i	0.164477	−	0.613836i	0.998106	−	0.0615118i	$-0.0195922\pi$
$468$	−6.22552	+	7.43972i	−0.287775	+	0.343901i
$469$	−18.1434	−	7.85816i	−0.837785	−	0.362856i
$470$	−4.41416	−	4.03934i	−0.203610	−	0.186321i
$471$	−2.76146	+	1.59433i	−0.127241	+	0.0734628i
$472$	−22.2903	+	9.28601i	−1.02599	+	0.427423i
$473$	11.5956	+	6.69471i	0.533166	+	0.307823i
$474$	−0.808505	−	0.178667i	−0.0371359	−	0.00820645i
$475$	−4.32031	+	4.32031i	−0.198229	+	0.198229i
$476$	0.961867	−	16.4790i	0.0440871	−	0.755312i
$477$	−3.55437	−	3.55437i	−0.162743	−	0.162743i
$478$	8.35911	−	5.33330i	0.382337	−	0.243939i
$479$	15.4266	−	26.7196i	0.704859	−	1.22085i	−0.261884	−	0.965099i	$-0.584344\pi$
$479$	15.4266	−	26.7196i	0.704859	−	1.22085i	0.966743	−	0.255751i	$-0.0823229\pi$
$480$	−2.51889	−	0.784840i	−0.114971	−	0.0358229i
$481$	2.98492	+	5.17003i	0.136101	+	0.235733i
$482$	0.0530820	+	1.19718i	0.00241782	+	0.0545301i
$483$	−5.18510	+	0.598276i	−0.235930	+	0.0272225i
$484$	−1.67100	−	18.8063i	−0.0759544	−	0.854832i
$485$	8.60167	+	2.30481i	0.390582	+	0.104656i
$486$	−4.85725	−	15.3689i	−0.220329	−	0.697150i
$487$	−14.0115	−	8.08952i	−0.634920	−	0.366571i	0.147735	−	0.989027i	$-0.452802\pi$
$487$	−14.0115	−	8.08952i	−0.634920	−	0.366571i	−0.782655	+	0.622456i	$0.786135\pi$
$488$	11.6256	+	1.50653i	0.526265	+	0.0681972i
$489$			4.09578i			0.185218i
$490$	−5.05450	−	8.51188i	−0.228339	−	0.384527i
$491$	−13.9530	+	13.9530i	−0.629689	+	0.629689i	−0.947990	−	0.318300i	$-0.896888\pi$
$491$	−13.9530	+	13.9530i	−0.629689	+	0.629689i	0.318300	+	0.947990i	$0.396888\pi$
$492$	6.53788	+	1.14368i	0.294750	+	0.0515611i
$493$	16.2342	−	4.34995i	0.731153	−	0.195912i
$494$	6.94599	−	13.3652i	0.312515	−	0.601329i
$495$	1.73754	+	3.00952i	0.0780968	+	0.135268i
$496$	36.1911	−	6.48255i	1.62503	−	0.291075i
$497$	−3.72048	+	4.69103i	−0.166886	+	0.210422i
$498$	3.10733	−	0.137777i	0.139243	−	0.00617391i
$499$	6.70565	−	25.0258i	0.300186	−	1.12031i	−0.636824	−	0.771009i	$-0.719752\pi$
$499$	6.70565	−	25.0258i	0.300186	−	1.12031i	0.937011	−	0.349301i	$-0.113581\pi$
$500$	1.87846	−	0.686584i	0.0840072	−	0.0307050i
$501$	2.91317	+	10.8721i	0.130151	+	0.485730i
$502$	4.91867	−	22.2580i	0.219531	−	0.993422i
$503$		−	16.5689i		−	0.738773i	−0.929276	−	0.369386i	$-0.879568\pi$
$503$		−	16.5689i		−	0.738773i	0.929276	−	0.369386i	$-0.120432\pi$
$504$	0.291357	−	20.8201i	0.0129781	−	0.927401i
$505$		−	11.1784i		−	0.497431i
$506$	7.29494	+	1.61207i	0.324300	+	0.0716652i
$507$	1.20244	+	4.48757i	0.0534023	+	0.199300i
$508$	2.68147	−	5.77081i	0.118971	−	0.256038i
$509$	−6.59685	+	24.6198i	−0.292400	+	1.09125i	0.650860	+	0.759198i	$0.274408\pi$
$509$	−6.59685	+	24.6198i	−0.292400	+	1.09125i	−0.943260	+	0.332054i	$0.892258\pi$
$510$	−0.0911422	−	2.05557i	−0.00403585	−	0.0910221i
$511$	3.18370	+	8.04853i	0.140839	+	0.356046i
$512$	−8.78633	−	20.8519i	−0.388305	−	0.921531i
$513$	8.23888	+	14.2702i	0.363755	+	0.630043i
$514$	29.6481	+	15.4083i	1.30772	+	0.679632i
$515$	13.6528	−	3.65827i	0.601616	−	0.161203i
$516$	−5.74700	−	8.18397i	−0.252998	−	0.360279i
$517$	3.73639	−	3.73639i	0.164326	−	0.164326i
$518$	−11.9724	−	4.56685i	−0.526035	−	0.200656i
$519$			5.71204i			0.250731i
$520$	−3.90555	+	3.00945i	−0.171270	+	0.131973i
$521$	35.2372	+	20.3442i	1.54377	+	0.891295i	0.998596	+	0.0529716i	$0.0168693\pi$
$521$	35.2372	+	20.3442i	1.54377	+	0.891295i	0.545173	+	0.838324i	$0.316464\pi$
$522$	20.2149	−	6.38878i	0.884783	−	0.279630i
$523$	8.61533	+	2.30847i	0.376722	+	0.100942i	0.442211	−	0.896911i	$-0.354194\pi$
$523$	8.61533	+	2.30847i	0.376722	+	0.100942i	−0.0654891	+	0.997853i	$0.520861\pi$
$524$	−7.29279	−	6.10257i	−0.318587	−	0.266592i
$525$	−0.735408	−	0.990882i	−0.0320958	−	0.0432456i
$526$	−26.7111	+	1.18435i	−1.16466	+	0.0516399i
$527$	14.3370	+	24.8324i	0.624530	+	1.08172i
$528$	0.790963	−	2.19160i	0.0344222	−	0.0953771i
$529$	−2.55416	+	4.42393i	−0.111050	+	0.192345i
$530$	−1.37417	−	2.15379i	−0.0596899	−	0.0935546i
$531$	−16.7972	−	16.7972i	−0.728937	−	0.728937i
$532$	6.53377	+	31.6631i	0.283275	+	1.37277i
$533$	8.77064	−	8.77064i	0.379899	−	0.379899i
$534$	0.371349	−	1.68043i	0.0160698	−	0.0727193i
$535$	3.03793	+	1.75395i	0.131341	+	0.0758298i
$536$	−8.12850	−	19.5118i	−0.351098	−	0.842780i
$537$	6.58536	−	3.80206i	0.284179	−	0.164071i
$538$	−17.7053	+	19.3482i	−0.763328	+	0.834159i
$539$	7.70735	−	4.12638i	0.331979	−	0.177736i
$540$	−0.477378	−	5.37267i	−0.0205431	−	0.231203i
$541$	2.81676	−	10.5123i	0.121102	−	0.451958i	−0.878569	−	0.477615i	$-0.841501\pi$
$541$	2.81676	−	10.5123i	0.121102	−	0.451958i	0.999671	+	0.0256574i	$0.00816789\pi$
$542$	0.939247	+	0.488133i	0.0403441	+	0.0209671i
$543$	−5.70668	+	9.88426i	−0.244897	+	0.424174i
$544$	12.9701	−	11.9659i	0.556089	−	0.513035i
$545$	−19.4808			−0.834465
$546$	2.46483	+	1.78289i	0.105485	+	0.0763005i
$547$	−10.6250	−	10.6250i	−0.454294	−	0.454294i	0.442483	−	0.896777i	$-0.354098\pi$
$547$	−10.6250	−	10.6250i	−0.454294	−	0.454294i	−0.896777	+	0.442483i	$0.854098\pi$
$548$	−8.02583	+	5.63595i	−0.342846	+	0.240756i
$549$	2.98479	+	11.1394i	0.127388	+	0.475417i
$550$	0.532259	+	1.68413i	0.0226956	+	0.0718117i
$551$	−28.5075	+	16.4588i	−1.21446	+	0.701170i
$552$	−4.43370	−	3.38782i	−0.188711	−	0.144195i
$553$	0.486232	−	3.28558i	0.0206767	−	0.139717i
$554$	−13.7308	−	12.5648i	−0.583364	−	0.533829i
$555$	−1.54281	−	0.413394i	−0.0654886	−	0.0175476i
$556$	−1.02461	−	2.80328i	−0.0434532	−	0.118886i
$557$	−8.59765	+	2.30373i	−0.364294	+	0.0976123i	−0.436323	−	0.899790i	$-0.643719\pi$
$557$	−8.59765	+	2.30373i	−0.364294	+	0.0976123i	0.0720286	+	0.997403i	$0.477053\pi$
$558$	19.4546	+	30.4921i	0.823581	+	1.29083i
$559$	−18.6886			−0.790442
$560$	2.42796	−	10.3007i	0.102600	−	0.435285i
$561$	1.81710			0.0767179
$562$	7.83614	+	12.2819i	0.330548	+	0.518082i
$563$	−21.5129	+	5.76435i	−0.906659	+	0.242939i	−0.681874	−	0.731470i	$-0.738835\pi$
$563$	−21.5129	+	5.76435i	−0.906659	+	0.242939i	−0.224785	+	0.974408i	$0.572168\pi$
$564$	−3.70671	+	1.35482i	−0.156081	+	0.0570481i
$565$	14.6489	+	3.92517i	0.616285	+	0.165133i
$566$	14.8305	+	13.5712i	0.623373	+	0.570441i
$567$	17.4423	−	6.89952i	0.732507	−	0.289752i
$568$	−6.34422	+	0.848343i	−0.266198	+	0.0355957i
$569$	29.2554	−	16.8906i	1.22645	−	0.708090i	0.260163	−	0.965565i	$-0.416224\pi$
$569$	29.2554	−	16.8906i	1.22645	−	0.708090i	0.966285	+	0.257474i	$0.0828902\pi$
$570$	1.21443	+	3.84261i	0.0508669	+	0.160949i
$571$	−2.17214	−	8.10652i	−0.0909011	−	0.339247i	0.905465	−	0.424421i	$-0.139522\pi$
$571$	−2.17214	−	8.10652i	−0.0909011	−	0.339247i	−0.996366	+	0.0851734i	$0.972856\pi$
$572$	−2.50232	−	3.56341i	−0.104627	−	0.148994i
$573$	8.56764	+	8.56764i	0.357918	+	0.357918i
$574$	−2.72712	+	26.4833i	−0.113828	+	1.10539i
$575$	4.22986			0.176397
$576$	15.6760	−	15.8039i	0.653167	−	0.658494i
$577$	−19.2193	+	33.2888i	−0.800111	+	1.38583i	0.119432	+	0.992842i	$0.461893\pi$
$577$	−19.2193	+	33.2888i	−0.800111	+	1.38583i	−0.919543	+	0.392990i	$0.871441\pi$
$578$	−9.12102	−	4.74026i	−0.379384	−	0.197169i
$579$	0.149723	−	0.558776i	0.00622230	−	0.0232219i
$580$	10.7330	−	0.953660i	0.445664	−	0.0395986i
$581$	1.43010	+	12.3943i	0.0593306	+	0.514202i
$582$	3.96525	−	4.33320i	0.164365	−	0.179617i
$583$	1.95394	−	1.12811i	0.0809240	−	0.0467215i
$584$	−3.52358	+	8.55578i	−0.145807	+	0.354041i
$585$	−4.20059	−	2.42521i	−0.173673	−	0.100270i
$586$	8.80721	−	39.8544i	0.363823	−	1.64637i
$587$	11.9589	−	11.9589i	0.493598	−	0.493598i	−0.415840	−	0.909438i	$-0.636512\pi$
$587$	11.9589	−	11.9589i	0.493598	−	0.493598i	0.909438	+	0.415840i	$0.136512\pi$
$588$	−6.51909	+	0.369196i	−0.268843	+	0.0152254i
$589$	−39.7113	−	39.7113i	−1.63628	−	1.63628i
$590$	−6.49402	−	10.1784i	−0.267355	−	0.419037i
$591$	4.08749	−	7.07975i	0.168137	−	0.291222i
$592$	−5.82285	−	12.3994i	−0.239317	−	0.509611i
$593$	1.68846	+	2.92450i	0.0693367	+	0.120095i	0.898609	−	0.438749i	$-0.144578\pi$
$593$	1.68846	+	2.92450i	0.0693367	+	0.120095i	−0.829273	+	0.558844i	$0.811245\pi$
$594$	4.75873	−	0.210998i	0.195253	−	0.00865736i
$595$	8.19910	−	0.946044i	0.336131	−	0.0387840i
$596$	−29.1112	+	34.7889i	−1.19244	+	1.42501i
$597$	3.49384	+	0.936171i	0.142993	+	0.0383149i
$598$	−9.94296	+	3.14241i	−0.406598	+	0.128503i
$599$	−3.84522	−	2.22004i	−0.157111	−	0.0907083i	0.419383	−	0.907809i	$-0.362246\pi$
$599$	−3.84522	−	2.22004i	−0.157111	−	0.0907083i	−0.576494	+	0.817101i	$0.695580\pi$
$600$	0.169529	−	1.30823i	0.00692100	−	0.0534081i
$601$		−	45.0884i		−	1.83919i	−0.392862	−	0.919597i	$-0.628515\pi$
$601$		−	45.0884i		−	1.83919i	0.392862	−	0.919597i	$-0.371485\pi$
$602$	31.1209	−	25.3099i	1.26839	−	1.03155i
$603$	14.7034	−	14.7034i	0.598770	−	0.598770i
$604$	−23.3868	+	16.4229i	−0.951597	+	0.668237i
$605$	9.11853	−	2.44330i	0.370721	−	0.0993344i
$606$	−6.54228	−	3.40007i	−0.265762	−	0.138118i
$607$	22.5465	+	39.0517i	0.915134	+	1.58506i	0.806704	+	0.590955i	$0.201249\pi$
$607$	22.5465	+	39.0517i	0.915134	+	1.58506i	0.108430	+	0.994104i	$0.465418\pi$
$608$	−18.4716	+	29.2124i	−0.749124	+	1.18472i
$609$	−2.44540	−	6.18208i	−0.0990927	−	0.250511i
$610$	0.259634	+	5.85564i	0.0105123	+	0.237088i
$611$	−1.90888	+	7.12402i	−0.0772249	+	0.288207i
$612$	15.7435	+	7.31536i	0.636391	+	0.295706i
$613$	1.67997	+	6.26974i	0.0678534	+	0.253233i	0.991518	−	0.129970i	$-0.0414880\pi$
$613$	1.67997	+	6.26974i	0.0678534	+	0.253233i	−0.923665	+	0.383202i	$0.874821\pi$
$614$	−20.2072	−	4.46548i	−0.815496	−	0.180212i
$615$			3.31858i			0.133818i
$616$	8.99287	+	2.54502i	0.362333	+	0.102542i
$617$			29.2448i			1.17735i	0.808369	+	0.588676i	$0.200351\pi$
$617$			29.2448i			1.17735i	−0.808369	+	0.588676i	$0.799649\pi$
$618$	2.01167	−	9.10322i	0.0809213	−	0.366185i
$619$	−1.15901	−	4.32550i	−0.0465847	−	0.173856i	0.938714	−	0.344697i	$-0.112018\pi$
$619$	−1.15901	−	4.32550i	−0.0465847	−	0.173856i	−0.985299	+	0.170841i	$0.945352\pi$
$620$	6.31092	+	17.2664i	0.253453	+	0.693433i
$621$	2.95250	−	11.0189i	0.118480	−	0.442172i
$622$	−19.8106	+	0.878385i	−0.794333	+	0.0352200i
$623$	6.82887	+	1.01060i	0.273593	+	0.0404890i
$624$	0.573389	+	3.20114i	0.0229539	+	0.128148i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−19.2679	+	37.0746i	−0.770101	+	1.48180i
$627$	−3.43766	+	0.921118i	−0.137287	+	0.0367859i
$628$	2.35617	−	13.4691i	0.0940213	−	0.537475i
$629$	7.55420	−	7.55420i	0.301206	−	0.301206i
$630$	10.2794	−	1.65031i	0.409543	−	0.0657498i
$631$			40.2497i			1.60232i	0.598453	+	0.801158i	$0.295782\pi$
$631$			40.2497i			1.60232i	−0.598453	+	0.801158i	$0.704218\pi$
$632$	2.81255	−	2.16724i	0.111877	−	0.0862080i
$633$	−10.9056	−	6.29637i	−0.433460	−	0.250258i
$634$	−4.44918	−	14.0778i	−0.176700	−	0.559100i
$635$	3.07327	+	0.823481i	0.121959	+	0.0326788i
$636$	−1.67851	+	0.149140i	−0.0665571	+	0.00591380i
$637$	−6.43670	+	10.3667i	−0.255031	+	0.410744i
$638$	0.421512	+	9.50653i	0.0166878	+	0.376367i
$639$	−3.14835	−	5.45311i	−0.124547	−	0.215722i
$640$	9.51297	−	6.12400i	0.376033	−	0.242072i
$641$	12.0907	−	20.9417i	0.477555	−	0.827149i	−0.522114	−	0.852876i	$-0.674857\pi$
$641$	12.0907	−	20.9417i	0.477555	−	0.827149i	0.999669	+	0.0257265i	$0.00818989\pi$
$642$	1.95055	−	1.24450i	0.0769822	−	0.0491163i
$643$	−3.10495	−	3.10495i	−0.122447	−	0.122447i	0.643228	−	0.765675i	$-0.277595\pi$
$643$	−3.10495	−	3.10495i	−0.122447	−	0.122447i	−0.765675	+	0.643228i	$0.777595\pi$
$644$	12.3016	−	18.6986i	0.484752	−	0.736828i
$645$	3.53563	−	3.53563i	0.139215	−	0.139215i
$646$	−26.3197	−	5.81625i	−1.03553	−	0.228837i
$647$	−35.8726	−	20.7111i	−1.41030	−	0.814236i	−0.414881	−	0.909876i	$-0.636177\pi$
$647$	−35.8726	−	20.7111i	−1.41030	−	0.814236i	−0.995416	+	0.0956400i	$0.969510\pi$
$648$	18.5416	+	7.63609i	0.728381	+	0.299974i
$649$	9.23393	−	5.33121i	0.362463	−	0.209268i
$650$	−1.81871	−	1.66428i	−0.0713357	−	0.0652784i
$651$	9.10796	−	6.75970i	0.356969	−	0.264934i
$652$	−13.4697	−	11.2714i	−0.527516	−	0.441423i
$653$	−9.31728	+	34.7725i	−0.364613	+	1.36075i	0.503331	+	0.864094i	$0.332108\pi$
$653$	−9.31728	+	34.7725i	−0.364613	+	1.36075i	−0.867944	+	0.496661i	$0.834559\pi$
$654$	−5.92538	+	11.4014i	−0.231701	+	0.445829i
$655$	2.37732	−	4.11763i	0.0928895	−	0.160889i
$656$	−21.7532	+	18.3537i	−0.849318	+	0.716590i
$657$	−9.10262			−0.355127
$658$	−6.46933	−	14.4484i	−0.252201	−	0.563256i
$659$	14.2006	+	14.2006i	0.553175	+	0.553175i	0.927356	−	0.374181i	$-0.122076\pi$
$659$	14.2006	+	14.2006i	0.553175	+	0.553175i	−0.374181	+	0.927356i	$0.622076\pi$
$660$	1.14756	+	0.200743i	0.0446685	+	0.00781393i
$661$	8.05927	+	30.0776i	0.313469	+	1.16988i	0.925406	+	0.378977i	$0.123724\pi$
$661$	8.05927	+	30.0776i	0.313469	+	1.16988i	−0.611937	+	0.790907i	$0.709609\pi$
$662$	28.7885	−	9.09840i	1.11890	−	0.353619i
$663$	−2.19646	+	1.26813i	−0.0853033	+	0.0492499i
$664$	−8.09814	+	10.5982i	−0.314269	+	0.411290i
$665$	−15.0318	+	5.94603i	−0.582909	+	0.230577i
$666$	9.09751	−	9.94170i	0.352522	−	0.385233i
$667$	22.0124	+	5.89822i	0.852325	+	0.228380i
$668$	−43.7719	−	20.3391i	−1.69358	−	0.786942i
$669$	−0.610054	+	0.163463i	−0.0235860	+	0.00631986i
$670$	8.90962	−	5.68454i	0.344209	−	0.219613i
$671$	−5.17631			−0.199829
$672$	−5.29013	−	4.55412i	−0.204071	−	0.175679i
$673$	−39.1372			−1.50863			−0.754313	−	0.656515i	$-0.772030\pi$
$673$	−39.1372			−1.50863			−0.754313	+	0.656515i	$0.772030\pi$
$674$	−8.80984	+	5.62088i	−0.339343	+	0.216508i
$675$	2.60502	−	0.698014i	0.100267	−	0.0268666i
$676$	−18.0673	−	8.39515i	−0.694895	−	0.322890i
$677$	11.9359	+	3.19823i	0.458735	+	0.122918i	0.480784	−	0.876839i	$-0.340352\pi$
$677$	11.9359	+	3.19823i	0.458735	+	0.122918i	−0.0220485	+	0.999757i	$0.507019\pi$
$678$	6.75295	−	7.37957i	0.259345	−	0.283411i
$679$	18.4597	+	14.6405i	0.708420	+	0.561851i
$680$	7.01094	+	5.35710i	0.268857	+	0.205435i
$681$	−4.75070	+	2.74282i	−0.182047	+	0.105105i
$682$	−15.4802	+	4.89240i	−0.592766	+	0.187340i
$683$	−3.04910	−	11.3794i	−0.116671	−	0.435421i	0.882736	−	0.469870i	$-0.155699\pi$
$683$	−3.04910	−	11.3794i	−0.116671	−	0.435421i	−0.999406	+	0.0344487i	$0.989032\pi$
$684$	−33.4924	−	5.85887i	−1.28061	−	0.224019i
$685$	−3.46731	−	3.46731i	−0.132479	−	0.132479i
$686$	−3.32099	−	25.9802i	−0.126796	−	0.991929i
$687$	−1.17230			−0.0447261
$688$	42.7300	+	3.62183i	1.62907	+	0.138081i
$689$	−1.57458	+	2.72725i	−0.0599868	+	0.103900i
$690$	1.28658	−	2.47558i	0.0489791	−	0.0942436i
$691$	−6.05702	+	22.6051i	−0.230420	+	0.859939i	0.749740	+	0.661732i	$0.230178\pi$
$691$	−6.05702	+	22.6051i	−0.230420	+	0.859939i	−0.980160	+	0.198207i	$0.936488\pi$
$692$	−18.7851	−	15.7193i	−0.714103	−	0.597558i
$693$	1.05387	+	9.13362i	0.0400333	+	0.346958i
$694$	28.8378	+	26.3891i	1.09467	+	1.00172i
$695$	1.29240	−	0.746165i	0.0490234	−	0.0283037i
$696$	2.70646	−	6.57170i	0.102588	−	0.249100i
$697$	−19.2228	−	11.0983i	−0.728117	−	0.420379i
$698$	−1.84198	−	0.407049i	−0.0697199	−	0.0154070i
$699$	0.297285	−	0.297285i	0.0112443	−	0.0112443i
$700$	5.28251	+	0.308337i	0.199660	+	0.0116540i
$701$	14.2281	+	14.2281i	0.537390	+	0.537390i	0.922761	−	0.385372i	$-0.125927\pi$
$701$	14.2281	+	14.2281i	0.537390	+	0.537390i	−0.385372	+	0.922761i	$0.625927\pi$
$702$	−5.60497	+	3.57610i	−0.211546	+	0.134971i
$703$	−10.4620	+	18.1207i	−0.394581	+	0.683435i
$704$	5.03078	+	8.63241i	0.189605	+	0.325346i
$705$	−0.986637	−	1.70890i	−0.0371589	−	0.0643611i
$706$	−0.537670	−	12.1263i	−0.0202355	−	0.456379i
$707$	11.7543	−	27.1390i	0.442065	−	1.02067i
$708$	−7.93228	+	0.704807i	−0.298113	+	0.0264883i
$709$	−44.7577	−	11.9928i	−1.68091	−	0.450399i	−0.712892	−	0.701273i	$-0.752615\pi$
$709$	−44.7577	−	11.9928i	−1.68091	−	0.450399i	−0.968020	+	0.250874i	$0.919282\pi$
$710$	−0.964428	−	3.05157i	−0.0361944	−	0.114523i
$711$	3.02502	+	1.74650i	0.113447	+	0.0654988i
$712$	4.50447	+	5.84572i	0.168812	+	0.219078i
$713$			38.8799i			1.45606i
$714$	1.94020	−	5.08639i	0.0726101	−	0.190353i
$715$	1.53946	−	1.53946i	0.0575725	−	0.0575725i
$716$	−5.61885	+	32.1203i	−0.209986	+	1.20039i
$717$	3.15865	−	0.846357i	0.117962	−	0.0316078i
$718$	−2.39274	+	4.60402i	−0.0892963	+	0.171820i
$719$	−12.7442	−	22.0736i	−0.475279	−	0.823207i	0.524320	−	0.851521i	$-0.324319\pi$
$719$	−12.7442	−	22.0736i	−0.475279	−	0.823207i	−0.999599	+	0.0283142i	$0.990986\pi$
$720$	9.13433	+	6.35914i	0.340417	+	0.236991i
$721$	36.9934	+	5.47465i	1.37770	+	0.203886i
$722$	25.8973	−	1.14827i	0.963800	−	0.0427341i
$723$	−0.102287	+	0.381741i	−0.00380410	+	0.0141971i
$724$	−16.8017	−	45.9686i	−0.624430	−	1.70841i
$725$	1.39442	+	5.20406i	0.0517876	+	0.193274i
$726$	1.34357	−	6.07991i	0.0498644	−	0.225647i
$727$			4.26612i			0.158222i	0.996866	+	0.0791109i	$0.0252081\pi$
$727$			4.26612i			0.158222i	−0.996866	+	0.0791109i	$0.974792\pi$
$728$	−12.6465	+	3.19964i	−0.468709	+	0.118586i
$729$			15.9531i			0.590857i
$730$	−4.51748	−	0.998294i	−0.167200	−	0.0369485i
$731$	8.65591	+	32.3043i	0.320151	+	1.19482i
$732$	3.50606	+	1.62913i	0.129588	+	0.0602143i
$733$	−1.63628	+	6.10669i	−0.0604375	+	0.225556i	−0.989538	−	0.144271i	$-0.953916\pi$
$733$	−1.63628	+	6.10669i	−0.0604375	+	0.225556i	0.929101	+	0.369827i	$0.120583\pi$
$734$	−0.698282	−	15.7486i	−0.0257741	−	0.581293i
$735$	−0.743504	−	3.17898i	−0.0274246	−	0.117258i
$736$	23.3428	−	5.25793i	0.860428	−	0.193810i
$737$	4.66667	+	8.08291i	0.171899	+	0.297738i
$738$	−24.8443	−	12.9117i	−0.914530	−	0.475287i
$739$	−29.4189	+	7.88278i	−1.08219	+	0.289973i	−0.755494	−	0.655156i	$-0.772603\pi$
$739$	−29.4189	+	7.88278i	−1.08219	+	0.289973i	−0.326699	+	0.945129i	$0.605936\pi$
$740$	5.60527	−	3.93617i	0.206054	−	0.144697i
$741$	3.51251	−	3.51251i	0.129035	−	0.129035i
$742$	−1.07147	−	6.67397i	−0.0393349	−	0.245009i
$743$			27.4086i			1.00553i	0.864425	+	0.502763i	$0.167683\pi$
$743$			27.4086i			1.00553i	−0.864425	+	0.502763i	$0.832317\pi$
$744$	12.0249	+	1.55827i	0.440855	+	0.0571291i
$745$	−19.6424	−	11.3405i	−0.719641	−	0.415485i
$746$	2.72604	−	0.861547i	0.0998075	−	0.0315435i
$747$	−12.6742	−	3.39604i	−0.463724	−	0.124255i
$748$	−5.00057	+	5.97586i	−0.182839	+	0.218499i
$749$	5.53122	+	7.45271i	0.202106	+	0.272316i
$750$	0.658935	−	0.0292166i	0.0240609	−	0.00106684i
$751$	13.2890	+	23.0173i	0.484924	+	0.839913i	0.999850	−	0.0173217i	$-0.00551395\pi$
$751$	13.2890	+	23.0173i	0.484924	+	0.839913i	−0.514926	+	0.857235i	$0.672181\pi$
$752$	5.74513	−	15.9186i	0.209503	−	0.580492i
$753$	3.75879	−	6.51042i	0.136978	−	0.237253i
$754$	−7.14398	−	11.1971i	−0.260168	−	0.407773i
$755$	−10.1036	−	10.1036i	−0.367706	−	0.367706i
$756$	4.49049	−	13.5458i	0.163318	−	0.492658i
$757$	22.5403	−	22.5403i	0.819243	−	0.819243i	−0.166756	−	0.985998i	$-0.553329\pi$
$757$	22.5403	−	22.5403i	0.819243	−	0.819243i	0.985998	+	0.166756i	$0.0533291\pi$
$758$	−4.05121	+	18.3325i	−0.147146	+	0.665868i
$759$	2.13376	+	1.23193i	0.0774505	+	0.0447161i
$760$	−15.9792	−	6.58081i	−0.579626	−	0.238711i
$761$	−9.34590	+	5.39586i	−0.338789	+	0.195600i	−0.659736	−	0.751497i	$-0.729332\pi$
$761$	−9.34590	+	5.39586i	−0.338789	+	0.195600i	0.320948	+	0.947097i	$0.395999\pi$
$762$	1.41674	−	1.54820i	0.0513229	−	0.0560853i
$763$	−47.2958	−	20.4845i	−1.71222	−	0.741587i
$764$	−51.7541	+	4.59851i	−1.87240	+	0.166368i
$765$	−2.24655	+	8.38425i	−0.0812243	+	0.303133i
$766$	33.3701	+	17.3427i	1.20571	+	0.626616i
$767$	−7.44115	+	12.8884i	−0.268684	+	0.465375i
$768$	−0.690632	−	7.43030i	−0.0249210	−	0.268118i
$769$	−26.1120			−0.941624			−0.470812	−	0.882234i	$-0.656039\pi$
$769$	−26.1120			−0.941624			−0.470812	+	0.882234i	$0.656039\pi$
$770$	−0.478675	+	4.64845i	−0.0172502	+	0.167519i
$771$	7.79182	+	7.79182i	0.280616	+	0.280616i
$772$	1.42561	+	2.03012i	0.0513087	+	0.0730656i
$773$	−9.39580	−	35.0656i	−0.337943	−	1.26122i	−0.900643	−	0.434560i	$-0.856904\pi$
$773$	−9.39580	−	35.0656i	−0.337943	−	1.26122i	0.562699	−	0.826662i	$-0.309763\pi$
$774$	12.7130	+	40.2254i	0.456958	+	1.44587i
$775$	−7.96031	+	4.59589i	−0.285943	+	0.165089i
$776$	3.33833	+	24.9652i	0.119839	+	0.896200i
$777$	−3.31097	−	2.62594i	−0.118780	−	0.0942052i
$778$	15.0612	+	13.7823i	0.539970	+	0.494119i
$779$	41.9925	+	11.2519i	1.50454	+	0.403140i
$780$	−1.52723	+	0.558209i	−0.0546836	+	0.0199871i
$781$	2.72999	−	0.731497i	0.0976866	−	0.0261750i
$782$	10.0371	+	15.7316i	0.358925	+	0.562559i
$783$	14.5300			0.519261
$784$	16.7261	−	22.4552i	0.597360	−	0.801973i
$785$	6.83681			0.244016
$786$	−1.68680	−	2.64380i	−0.0601662	−	0.0943011i
$787$	39.0231	−	10.4562i	1.39103	−	0.372724i	0.515912	−	0.856642i	$-0.327453\pi$
$787$	39.0231	−	10.4562i	1.39103	−	0.372724i	0.875113	+	0.483918i	$0.160787\pi$
$788$	12.0345	+	32.9256i	0.428710	+	1.17293i
$789$	−8.51727	−	2.28220i	−0.303223	−	0.0812483i
$790$	1.30973	+	1.19852i	0.0465981	+	0.0426413i
$791$	31.4375	+	24.9332i	1.11779	+	0.886524i
$792$	−5.96769	+	7.81003i	−0.212053	+	0.277517i
$793$	6.25699	−	3.61247i	0.222192	−	0.128283i
$794$	10.5139	+	33.2672i	0.373123	+	1.18061i
$795$	−0.218070	−	0.813850i	−0.00773416	−	0.0288643i
$796$	−12.6937	+	8.91383i	−0.449915	+	0.315942i
$797$	21.9467	+	21.9467i	0.777391	+	0.777391i	0.979386	−	0.201996i	$-0.0647427\pi$
$797$	21.9467	+	21.9467i	0.777391	+	0.777391i	−0.201996	+	0.979386i	$0.564743\pi$
$798$	−1.09217	+	10.6062i	−0.0386624	+	0.375454i
$799$	13.1984			0.466927
$800$	3.83581	+	4.15771i	0.135616	+	0.146997i
$801$	−3.62999	+	6.28733i	−0.128259	+	0.222152i
$802$	−39.7209	−	20.6432i	−1.40259	−	0.728938i
$803$	1.05746	−	3.94651i	0.0373171	−	0.139269i
$804$	−0.616952	−	6.94351i	−0.0217582	−	0.244879i
$805$	10.2693	+	4.44778i	0.361946	+	0.156764i
$806$	15.2977	−	16.7172i	0.538837	−	0.588837i
$807$	−7.49048	+	4.32463i	−0.263677	+	0.152234i
$808$	29.1858	−	12.1587i	1.02675	−	0.427740i
$809$	31.3035	+	18.0731i	1.10057	+	0.635416i	0.936371	−	0.351011i	$-0.114162\pi$
$809$	31.3035	+	18.0731i	1.10057	+	0.635416i	0.164201	+	0.986427i	$0.447495\pi$
$810$	−2.16344	+	9.79001i	−0.0760156	+	0.343986i
$811$	−7.28087	+	7.28087i	−0.255666	+	0.255666i	−0.823289	−	0.567623i	$-0.807863\pi$
$811$	−7.28087	+	7.28087i	−0.255666	+	0.255666i	0.567623	+	0.823289i	$0.307863\pi$
$812$	27.0606	+	8.97067i	0.949640	+	0.314809i
$813$	0.246844	+	0.246844i	0.00865719	+	0.00865719i
$814$	3.25343	+	5.09924i	0.114033	+	0.178728i
$815$	4.39089	−	7.60525i	0.153806	−	0.266400i
$816$	5.26780	−	2.47380i	0.184410	−	0.0866003i
$817$	−32.7512	−	56.7268i	−1.14582	−	1.98462i
$818$	−38.0911	+	1.68893i	−1.33182	+	0.0590520i
$819$	−7.64811	−	10.3050i	−0.267247	−	0.360086i
$820$	−10.9138	−	9.13258i	−0.381125	−	0.318924i
$821$	−2.23549	−	0.598999i	−0.0780193	−	0.0209052i	0.219598	−	0.975590i	$-0.429525\pi$
$821$	−2.23549	−	0.598999i	−0.0780193	−	0.0209052i	−0.297618	+	0.954685i	$0.596192\pi$
$822$	−3.08392	+	0.974653i	−0.107564	+	0.0339949i
$823$	12.8674	+	7.42901i	0.448530	+	0.258959i	0.707209	−	0.707004i	$-0.249954\pi$
$823$	12.8674	+	7.42901i	0.448530	+	0.258959i	−0.258679	+	0.965963i	$0.583287\pi$
$824$	24.4016	+	31.6674i	0.850070	+	1.10319i
$825$			0.582491i			0.0202797i
$826$	−5.06354	−	31.5398i	−0.176183	−	1.09741i
$827$	10.4703	−	10.4703i	0.364089	−	0.364089i	−0.501227	−	0.865316i	$-0.667118\pi$
$827$	10.4703	−	10.4703i	0.364089	−	0.364089i	0.865316	+	0.501227i	$0.167118\pi$
$828$	13.5275	+	19.2637i	0.470112	+	0.669459i
$829$	26.1738	−	7.01325i	0.909054	−	0.243580i	0.226153	−	0.974092i	$-0.427385\pi$
$829$	26.1738	−	7.01325i	0.909054	−	0.243580i	0.682901	+	0.730511i	$0.260718\pi$
$830$	−5.91755	−	3.07539i	−0.205401	−	0.106748i
$831$	−3.06905	−	5.31575i	−0.106464	−	0.184401i
$832$	−12.1055	−	6.92371i	−0.419683	−	0.240037i
$833$	20.9007	+	6.32471i	0.724167	+	0.219138i
$834$	−0.0436009	−	0.983349i	−0.00150978	−	0.0340506i
$835$	6.24614	−	23.3109i	0.216157	−	0.806708i
$836$	6.43102	−	13.8403i	0.222421	−	0.478675i
$837$	6.41599	+	23.9448i	0.221769	+	0.827653i
$838$	−39.8593	−	8.80829i	−1.37692	−	0.304277i
$839$			4.57635i			0.157993i	0.996875	+	0.0789966i	$0.0251716\pi$
$839$			4.57635i			0.157993i	−0.996875	+	0.0789966i	$0.974828\pi$
$840$	1.78721	−	2.99787i	0.0616648	−	0.103436i
$841$			0.0266983i			0.000920632i
$842$	−4.40841	+	19.9490i	−0.151924	+	0.687486i
$843$	1.24354	+	4.64096i	0.0428298	+	0.159843i
$844$	50.7186	−	18.5379i	1.74581	−	0.638099i
$845$	2.57816	−	9.62181i	0.0886913	−	0.331000i
$846$	16.6323	−	0.737463i	0.571831	−	0.0253545i
$847$	24.7073	+	3.65644i	0.848954	+	0.125637i
$848$	4.12870	−	5.93051i	0.141780	−	0.203655i
$849$	3.31486	+	5.74151i	0.113766	+	0.197048i
$850$	−2.03444	+	3.91459i	−0.0697807	+	0.134269i
$851$	13.9921	−	3.74918i	0.479644	−	0.128520i
$852$	−2.07932	−	0.363738i	−0.0712362	−	0.0124615i
$853$	29.7217	−	29.7217i	1.01765	−	1.01765i	0.0178097	−	0.999841i	$-0.494331\pi$
$853$	29.7217	−	29.7217i	1.01765	−	1.01765i	0.999841	−	0.0178097i	$-0.00566931\pi$
$854$	−5.52699	+	14.4894i	−0.189130	+	0.495819i
$855$		−	17.0005i		−	0.581404i
$856$	−1.27508	+	9.83955i	−0.0435813	+	0.336309i
$857$	11.4429	+	6.60656i	0.390882	+	0.225676i	0.682542	−	0.730846i	$-0.260874\pi$
$857$	11.4429	+	6.60656i	0.390882	+	0.225676i	−0.291660	+	0.956522i	$0.594208\pi$
$858$	−0.432738	−	1.36924i	−0.0147734	−	0.0467450i
$859$	−35.7695	−	9.58442i	−1.22044	−	0.327016i	−0.409590	−	0.912270i	$-0.634328\pi$
$859$	−35.7695	−	9.58442i	−1.22044	−	0.327016i	−0.810850	+	0.585254i	$0.800995\pi$
$860$	1.89768	+	21.3575i	0.0647102	+	0.728284i
$861$	−3.48956	+	8.05690i	−0.118924	+	0.274579i
$862$	0.925409	+	20.8711i	0.0315196	+	0.710874i
$863$	−2.63376	−	4.56181i	−0.0896543	−	0.155286i	0.817711	−	0.575629i	$-0.195243\pi$
$863$	−2.63376	−	4.56181i	−0.0896543	−	0.155286i	−0.907365	+	0.420344i	$0.861910\pi$
$864$	13.5084	−	7.09023i	0.459565	−	0.241215i
$865$	6.12361	−	10.6064i	0.208209	−	0.360628i
$866$	24.9892	−	15.9437i	0.849168	−	0.541788i
$867$	−2.39710	−	2.39710i	−0.0814097	−	0.0814097i
$868$	−2.83416	+	48.5556i	−0.0961978	+	1.64809i
$869$	−1.10863	+	1.10863i	−0.0376077	+	0.0376077i
$870$	3.46988	+	0.766790i	0.117640	+	0.0259966i
$871$	−11.2819	−	6.51360i	−0.382272	−	0.220705i
$872$	−21.1892	−	50.8628i	−0.717556	−	1.72243i
$873$	−21.4586	+	12.3891i	−0.726263	+	0.419308i
$874$	−26.9632	−	24.6736i	−0.912042	−	0.834598i
$875$	0.303265	+	2.62831i	0.0102522	+	0.0888532i
$876$	−1.95833	+	2.34027i	−0.0661657	+	0.0790703i
$877$	1.60881	−	6.00415i	0.0543256	−	0.202746i	−0.933429	−	0.358763i	$-0.883199\pi$
$877$	1.60881	−	6.00415i	0.0543256	−	0.202746i	0.987754	+	0.156017i	$0.0498654\pi$
$878$	−15.5245	+	29.8717i	−0.523928	+	1.00812i
$879$	6.73037	−	11.6573i	0.227010	−	0.393193i
$880$	−3.81820	+	3.22151i	−0.128712	+	0.108597i
$881$	−43.4652			−1.46438			−0.732189	−	0.681101i	$-0.761501\pi$
$881$	−43.4652			−1.46438			−0.732189	+	0.681101i	$0.761501\pi$
$882$	26.6919	+	6.80241i	0.898764	+	0.229049i
$883$	23.6683	+	23.6683i	0.796503	+	0.796503i	0.982542	−	0.186039i	$-0.0595651\pi$
$883$	23.6683	+	23.6683i	0.796503	+	0.796503i	−0.186039	+	0.982542i	$0.559565\pi$
$884$	1.87409	−	10.7133i	0.0630325	−	0.360327i
$885$	−1.03056	−	3.84609i	−0.0346418	−	0.129285i
$886$	−49.2139	+	15.5537i	−1.65337	+	0.522537i
$887$	11.2322	−	6.48494i	0.377142	−	0.217743i	−0.299432	−	0.954118i	$-0.596797\pi$
$887$	11.2322	−	6.48494i	0.377142	−	0.217743i	0.676574	+	0.736375i	$0.263464\pi$
$888$	−0.598767	−	4.47780i	−0.0200933	−	0.150265i
$889$	6.59544	+	5.23087i	0.221204	+	0.175438i
$890$	−2.49105	+	2.72220i	−0.0835000	+	0.0912482i
$891$	−8.55263	−	2.29167i	−0.286524	−	0.0767739i
$892$	1.14126	−	2.45612i	0.0382123	−	0.0822370i
$893$	−24.9693	+	6.69051i	−0.835567	+	0.223889i
$894$	−12.6117	+	8.04656i	−0.421799	+	0.269117i
$895$	−16.3040			−0.544983
$896$	29.5353	−	4.86485i	0.986705	−	0.162523i
$897$	−3.43897			−0.114824
$898$	39.1824	−	24.9992i	1.30753	−	0.834235i
$899$	−47.8346	+	12.8172i	−1.59537	+	0.427479i
$900$	−2.34502	+	5.04674i	−0.0781673	+	0.168225i
$901$	5.44352	+	1.45859i	0.181350	+	0.0485925i
$902$	8.48418	−	9.27145i	0.282492	−	0.308705i
$903$	12.3017	−	4.86607i	0.409373	−	0.161933i
$904$	5.68528	+	42.5166i	0.189089	+	1.41408i
$905$	21.1929	−	12.2357i	0.704475	−	0.406729i
$906$	−8.98639	+	2.84009i	−0.298553	+	0.0943555i
$907$	−0.285501	−	1.06550i	−0.00947990	−	0.0353795i	0.961024	−	0.276465i	$-0.0891631\pi$
$907$	−0.285501	−	1.06550i	−0.00947990	−	0.0353795i	−0.970504	+	0.241086i	$0.922496\pi$
$908$	4.05346	−	23.1717i	0.134519	−	0.768980i
$909$	21.9935	+	21.9935i	0.729479	+	0.729479i
$910$	−2.66548	−	5.95298i	−0.0883597	−	0.197339i
$911$	−23.0712			−0.764382			−0.382191	−	0.924083i	$-0.624830\pi$
$911$	−23.0712			−0.764382			−0.382191	+	0.924083i	$0.624830\pi$
$912$	−8.71182	+	7.35037i	−0.288477	+	0.243395i
$913$	2.94476	−	5.10047i	0.0974573	−	0.168801i
$914$	24.5863	−	47.3081i	0.813244	−	1.56481i
$915$	−0.500307	+	1.86717i	−0.0165396	+	0.0617267i
$916$	3.22612	−	3.85533i	0.106594	−	0.127384i
$917$	10.1015	−	7.49707i	0.333580	−	0.247575i
$918$	8.77753	+	8.03220i	0.289702	+	0.265102i
$919$	−28.1800	+	16.2697i	−0.929573	+	0.536689i	−0.886676	−	0.462390i	$-0.846992\pi$
$919$	−28.1800	+	16.2697i	−0.929573	+	0.536689i	−0.0428964	+	0.999080i	$0.513659\pi$
$920$	4.60080	+	11.0438i	0.151684	+	0.364104i
$921$	−5.91057	−	3.41247i	−0.194760	−	0.112445i
$922$	8.69560	+	1.92159i	0.286374	+	0.0632843i
$923$	−2.78943	+	2.78943i	−0.0918152	+	0.0918152i
$924$	2.57497	+	1.69405i	0.0847103	+	0.0557301i
$925$	2.42158	+	2.42158i	0.0796211	+	0.0796211i
$926$	−14.3425	+	9.15082i	−0.471323	+	0.300715i
$927$	−19.6644	+	34.0597i	−0.645863	+	1.11867i
$928$	14.1642	+	26.9857i	0.464962	+	0.885850i
$929$	−15.6818	−	27.1617i	−0.514504	−	0.891148i	−0.999858	−	0.0168299i	$-0.994643\pi$
$929$	−15.6818	−	27.1617i	−0.514504	−	0.891148i	0.485354	−	0.874318i	$-0.338691\pi$
$930$	0.268553	+	6.05678i	0.00880619	+	0.198610i
$931$	−42.7469	−	1.37041i	−1.40097	−	0.0449134i
$932$	0.159562	+	1.79579i	0.00522661	+	0.0588231i
$933$	−6.31694	−	1.69262i	−0.206807	−	0.0554139i
$934$	5.85268	+	18.5186i	0.191506	+	0.605948i
$935$	−3.37407	−	1.94802i	−0.110344	−	0.0637071i
$936$	1.76307	−	13.6053i	0.0576279	−	0.444704i
$937$			47.0197i			1.53607i	0.640410	+	0.768033i	$0.278764\pi$
$937$			47.0197i			1.53607i	−0.640410	+	0.768033i	$0.721236\pi$
$938$	27.6084	−	4.43237i	0.901445	−	0.144722i
$939$	−9.74359	+	9.74359i	−0.317970	+	0.317970i
$940$	8.33523	+	1.45809i	0.271865	+	0.0475578i
$941$	18.2900	−	4.90080i	0.596238	−	0.159762i	0.0519356	−	0.998650i	$-0.483461\pi$
$941$	18.2900	−	4.90080i	0.596238	−	0.159762i	0.544303	+	0.838889i	$0.316794\pi$
$942$	2.07952	−	4.00133i	0.0677544	−	0.130370i
$943$	−15.0485	−	26.0648i	−0.490047	−	0.848786i
$944$	19.5114	−	28.0264i	0.635042	−	0.912180i
$945$	7.05850	+	1.04459i	0.229613	+	0.0339804i
$946$	−18.9169	+	0.838761i	−0.615042	+	0.0272705i
$947$	12.5608	−	46.8775i	0.408171	−	1.52331i	−0.389962	−	0.920831i	$-0.627512\pi$
$947$	12.5608	−	46.8775i	0.408171	−	1.52331i	0.798132	−	0.602482i	$-0.205822\pi$
$948$	1.09982	−	0.401990i	0.0357206	−	0.0130560i
$949$	1.47598	+	5.50842i	0.0479122	+	0.178811i
$950$	1.86446	−	8.43707i	0.0604911	−	0.273735i
$951$		−	4.86908i		−	0.157891i
$952$	11.3882	+	20.3782i	0.369093	+	0.660462i
$953$		−	43.9007i		−	1.42208i	−0.703149	−	0.711042i	$-0.748223\pi$
$953$		−	43.9007i		−	1.42208i	0.703149	−	0.711042i	$-0.251777\pi$
$954$	6.94128	+	1.53392i	0.224732	+	0.0496623i
$955$	−6.72386	−	25.0938i	−0.217579	−	0.812016i
$956$	−5.90906	+	12.7169i	−0.191113	+	0.411295i
$957$	−0.812239	+	3.03132i	−0.0262560	+	0.0979886i
$958$	1.93275	+	43.5901i	0.0624443	+	1.40833i
$959$	−4.77205	−	12.0640i	−0.154097	−	0.389565i
$960$	3.60007	−	0.980326i	0.116192	−	0.0316399i
$961$	−26.7443	−	46.3225i	−0.862720	−	1.49428i
$962$	−7.49134	−	3.89330i	−0.241530	−	0.125525i
$963$	−9.42805	+	2.52624i	−0.303815	+	0.0814069i
$964$	−0.973937	−	1.38693i	−0.0313684	−	0.0446699i
$965$	−0.877050	+	0.877050i	−0.0282332	+	0.0282332i
$966$	5.72669	−	4.65739i	0.184253	−	0.149849i
$967$			47.1575i			1.51648i	0.651974	+	0.758241i	$0.273941\pi$
$967$			47.1575i			1.51648i	−0.651974	+	0.758241i	$0.726059\pi$
$968$	16.2975	+	21.1502i	0.523821	+	0.679793i
$969$	−7.69847	−	4.44471i	−0.247310	−	0.142785i
$970$	−12.0083	+	3.79513i	−0.385563	+	0.121854i
$971$	10.8615	+	2.91032i	0.348561	+	0.0933966i	0.428852	−	0.903375i	$-0.358918\pi$
$971$	10.8615	+	2.91032i	0.348561	+	0.0933966i	−0.0802908	+	0.996771i	$0.525585\pi$
$972$	17.4815	+	14.6284i	0.560720	+	0.469208i
$973$	3.92231	−	0.452572i	0.125744	−	0.0145088i
$974$	22.8582	−	1.01351i	0.732422	−	0.0324750i
$975$	−0.406511	−	0.704098i	−0.0130188	−	0.0225492i
$976$	−15.0062	+	7.04705i	−0.480337	+	0.225570i
$977$	27.6146	−	47.8300i	0.883471	−	1.53022i	0.0360141	−	0.999351i	$-0.488534\pi$
$977$	27.6146	−	47.8300i	0.883471	−	1.53022i	0.847457	−	0.530865i	$-0.178133\pi$
$978$	−3.11551	−	4.88308i	−0.0996231	−	0.156144i
$979$	−2.30422	−	2.30422i	−0.0736432	−	0.0736432i
$980$	12.5008	+	6.30326i	0.399322	+	0.201350i
$981$	38.3286	−	38.3286i	1.22374	−	1.22374i
$982$	6.02151	−	27.2486i	0.192154	−	0.869537i
$983$	−43.0347	−	24.8461i	−1.37259	−	0.792468i	−0.381341	−	0.924435i	$-0.624537\pi$
$983$	−43.0347	−	24.8461i	−1.37259	−	0.792468i	−0.991254	+	0.131967i	$0.957871\pi$
$984$	−8.66455	+	3.60961i	−0.276216	+	0.115070i
$985$	−15.1797	+	8.76401i	−0.483666	+	0.279245i
$986$	−16.0459	+	17.5349i	−0.511007	+	0.558425i
$987$	−0.598424	−	5.18638i	−0.0190481	−	0.165084i
$988$	1.88527	+	21.2178i	0.0599784	+	0.675029i
$989$	−11.7368	+	43.8023i	−0.373208	+	1.39283i
$990$	−4.36077	−	2.26632i	−0.138594	−	0.0720284i
$991$	26.5894	−	46.0542i	0.844639	−	1.46296i	−0.0412944	−	0.999147i	$-0.513148\pi$
$991$	26.5894	−	46.0542i	0.844639	−	1.46296i	0.885934	−	0.463811i	$-0.153519\pi$
$992$	−38.2167	+	35.2579i	−1.21338	+	1.11944i
$993$	9.95706			0.315978
$994$	0.867336	−	8.42278i	0.0275102	−	0.267154i
$995$	−5.48390	−	5.48390i	−0.173851	−	0.173851i
$996$	−3.59983	+	2.52789i	−0.114065	+	0.0800994i
$997$	−1.00208	−	3.73982i	−0.0317362	−	0.118441i	0.948241	−	0.317553i	$-0.102861\pi$
$997$	−1.00208	−	3.73982i	−0.0317362	−	0.118441i	−0.979977	+	0.199112i	$0.936194\pi$
$998$	11.0416	+	34.9371i	0.349516	+	1.10591i
$999$	7.99858	−	4.61798i	0.253064	−	0.146106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.221.11	✓	256
7.2	even	3	inner	560.2.cp.a.541.55	yes	256
16.5	even	4	inner	560.2.cp.a.501.55	yes	256
112.37	even	12	inner	560.2.cp.a.261.11	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.11	✓	256	1.1	even	1	trivial
560.2.cp.a.261.11	yes	256	112.37	even	12	inner
560.2.cp.a.501.55	yes	256	16.5	even	4	inner
560.2.cp.a.541.55	yes	256	7.2	even	3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19222 + 0.760664i) q^{2} +(-0.450503 + 0.120712i) q^{3} +(0.842782 - 1.81376i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.445278 - 0.486597i) q^{6} +(2.07294 + 1.64406i) q^{7} +(0.374878 + 2.80347i) q^{8} +(-2.40969 + 1.39124i) q^{9} +O(q^{10})\)	\(q+(-1.19222 + 0.760664i) q^{2} +(-0.450503 + 0.120712i) q^{3} +(0.842782 - 1.81376i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.445278 - 0.486597i) q^{6} +(2.07294 + 1.64406i) q^{7} +(0.374878 + 2.80347i) q^{8} +(-2.40969 + 1.39124i) q^{9} +(-1.34847 + 0.426175i) q^{10} +(-0.323244 - 1.20636i) q^{11} +(-0.160734 + 0.918838i) q^{12} +(1.23263 + 1.23263i) q^{13} +(-3.72198 - 0.383271i) q^{14} -0.466395 q^{15} +(-2.57944 - 3.05720i) q^{16} +(1.55977 - 2.70159i) q^{17} +(1.81462 - 3.49163i) q^{18} +(-1.58134 + 5.90166i) q^{19} +(1.28350 - 1.53383i) q^{20} +(-1.13232 - 0.490425i) q^{21} +(1.30302 + 1.19237i) q^{22} +(3.66316 - 2.11493i) q^{23} +(-0.507297 - 1.21772i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.40719 - 0.531952i) q^{26} +(1.90701 - 1.90701i) q^{27} +(4.72896 - 2.37423i) q^{28} +(3.80964 + 3.80964i) q^{29} +(0.556046 - 0.354770i) q^{30} +(-4.59589 + 7.96031i) q^{31} +(5.40076 + 1.68278i) q^{32} +(0.291245 + 0.504452i) q^{33} +(0.195418 + 4.40735i) q^{34} +(1.57679 + 2.12455i) q^{35} +(0.492522 + 5.54311i) q^{36} +(3.30794 + 0.886360i) q^{37} +(-2.60386 - 8.23895i) q^{38} +(-0.704098 - 0.406511i) q^{39} +(-0.363488 + 2.80497i) q^{40} -7.11538i q^{41} +(1.72303 - 0.276622i) q^{42} +(-7.58075 + 7.58075i) q^{43} +(-2.46048 - 0.430415i) q^{44} +(-2.68766 + 0.720158i) q^{45} +(-2.75855 + 5.30790i) q^{46} +(2.11545 + 3.66407i) q^{47} +(1.53109 + 1.06591i) q^{48} +(1.59415 + 6.81606i) q^{49} +(-1.41283 + 0.0626435i) q^{50} +(-0.376565 + 1.40536i) q^{51} +(3.27454 - 1.19686i) q^{52} +(0.467566 + 1.74498i) q^{53} +(-0.822984 + 3.72417i) q^{54} -1.24892i q^{55} +(-3.83197 + 6.42775i) q^{56} -2.84960i q^{57} +(-7.43979 - 1.64408i) q^{58} +(2.20962 + 8.24641i) q^{59} +(-0.393069 + 0.845928i) q^{60} +(1.07271 - 4.00341i) q^{61} +(-0.575805 - 12.9864i) q^{62} +(-7.28242 - 1.07773i) q^{63} +(-7.71893 + 2.10192i) q^{64} +(0.871603 + 1.50966i) q^{65} +(-0.730947 - 0.379878i) q^{66} +(-7.21849 + 1.93419i) q^{67} +(-3.58549 - 5.10589i) q^{68} +(-1.39497 + 1.39497i) q^{69} +(-3.49595 - 1.33353i) q^{70} +2.26299i q^{71} +(-4.80364 - 6.23397i) q^{72} +(2.83312 + 1.63570i) q^{73} +(-4.61802 + 1.45949i) q^{74} +(-0.450503 - 0.120712i) q^{75} +(9.37145 + 7.84198i) q^{76} +(1.31327 - 3.03215i) q^{77} +(1.14866 - 0.0509306i) q^{78} +(-0.627678 - 1.08717i) q^{79} +(-1.70028 - 3.62064i) q^{80} +(3.54480 - 6.13977i) q^{81} +(5.41241 + 8.48310i) q^{82} +(3.33449 + 3.33449i) q^{83} +(-1.84381 + 1.64044i) q^{84} +(2.20584 - 2.20584i) q^{85} +(3.27153 - 14.8043i) q^{86} +(-2.17612 - 1.25639i) q^{87} +(3.26083 - 1.35845i) q^{88} +(2.25962 - 1.30459i) q^{89} +(2.65649 - 2.90300i) q^{90} +(0.528653 + 4.58169i) q^{91} +(-0.748721 - 8.42651i) q^{92} +(1.10956 - 4.14092i) q^{93} +(-5.30921 - 2.75923i) q^{94} +(-3.05492 + 5.29128i) q^{95} +(-2.63619 - 0.106161i) q^{96} +8.90510 q^{97} +(-7.08531 - 6.91364i) q^{98} +(2.45726 + 2.45726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4}+O(q^{10}) \) 256 * q + 4 * q^4	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46} + 80 q^{47} - 160 q^{48} - 8 q^{50} - 40 q^{51} + 24 q^{52} - 16 q^{53} - 116 q^{54} - 96 q^{56} - 8 q^{58} + 16 q^{59} - 28 q^{60} + 88 q^{62} - 56 q^{64} - 16 q^{66} - 40 q^{67} - 20 q^{68} - 16 q^{70} + 76 q^{72} + 52 q^{74} - 48 q^{78} + 128 q^{81} - 80 q^{83} - 68 q^{84} + 52 q^{86} + 20 q^{88} - 72 q^{90} - 32 q^{91} - 112 q^{92} + 120 q^{94} + 140 q^{96} + 24 q^{98} - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more