LMFDB - Embedded newform 640.2.bm.a.341.64

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			341.64
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.64

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41028 - 0.105369i) q^{2} +(1.19231 - 1.45283i) q^{3} +(1.97779 - 0.297201i) q^{4} +(0.956940 - 0.290285i) q^{5} +(1.52841 - 2.17454i) q^{6} +(-0.768791 - 0.152922i) q^{7} +(2.75793 - 0.627535i) q^{8} +(-0.103851 - 0.522093i) q^{9} +O(q^{10})$	\(q+(1.41028 - 0.105369i) q^{2} +(1.19231 - 1.45283i) q^{3} +(1.97779 - 0.297201i) q^{4} +(0.956940 - 0.290285i) q^{5} +(1.52841 - 2.17454i) q^{6} +(-0.768791 - 0.152922i) q^{7} +(2.75793 - 0.627535i) q^{8} +(-0.103851 - 0.522093i) q^{9} +(1.31897 - 0.510215i) q^{10} +(-1.03956 - 0.102387i) q^{11} +(1.92636 - 3.22776i) q^{12} +(0.221009 - 0.728568i) q^{13} +(-1.10033 - 0.134656i) q^{14} +(0.719233 - 1.73638i) q^{15} +(3.82334 - 1.17560i) q^{16} +(-0.120025 - 0.289767i) q^{17} +(-0.201471 - 0.725356i) q^{18} +(-5.96337 + 3.18749i) q^{19} +(1.80636 - 0.858527i) q^{20} +(-1.13881 + 0.934594i) q^{21} +(-1.47686 - 0.0348580i) q^{22} +(-1.63281 + 2.44367i) q^{23} +(2.37660 - 4.75503i) q^{24} +(0.831470 - 0.555570i) q^{25} +(0.234916 - 1.05077i) q^{26} +(4.09024 + 2.18628i) q^{27} +(-1.56596 - 0.0739632i) q^{28} +(0.0102075 + 0.103638i) q^{29} +(0.831361 - 2.52458i) q^{30} +(-1.57773 - 1.57773i) q^{31} +(5.26812 - 2.06080i) q^{32} +(-1.38822 + 1.38822i) q^{33} +(-0.199802 - 0.396006i) q^{34} +(-0.780078 + 0.0768310i) q^{35} +(-0.360562 - 1.00173i) q^{36} +(0.615613 - 1.15173i) q^{37} +(-8.07417 + 5.12361i) q^{38} +(-0.794976 - 1.18977i) q^{39} +(2.45701 - 1.40110i) q^{40} +(2.68883 + 1.79662i) q^{41} +(-1.50756 + 1.43804i) q^{42} +(0.906064 + 1.10404i) q^{43} +(-2.08646 + 0.106456i) q^{44} +(-0.250934 - 0.469465i) q^{45} +(-2.04524 + 3.61832i) q^{46} +(-11.3613 + 4.70600i) q^{47} +(2.85065 - 6.95636i) q^{48} +(-5.89950 - 2.44365i) q^{49} +(1.11407 - 0.871122i) q^{50} +(-0.564090 - 0.171115i) q^{51} +(0.220579 - 1.50664i) q^{52} +(0.787917 - 7.99985i) q^{53} +(5.99876 + 2.65228i) q^{54} +(-1.02452 + 0.203789i) q^{55} +(-2.21624 + 0.0606947i) q^{56} +(-2.47929 + 12.4642i) q^{57} +(0.0253157 + 0.145084i) q^{58} +(0.598811 + 1.97401i) q^{59} +(0.906442 - 3.64796i) q^{60} +(3.68122 + 3.02110i) q^{61} +(-2.39130 - 2.05881i) q^{62} +0.417261i q^{63} +(7.21240 - 3.46140i) q^{64} -0.761351i q^{65} +(-1.81151 + 2.10406i) q^{66} +(7.91857 + 6.49860i) q^{67} +(-0.323504 - 0.537427i) q^{68} +(1.60343 + 5.28581i) q^{69} +(-1.09203 + 0.190550i) q^{70} +(1.42020 - 7.13984i) q^{71} +(-0.614045 - 1.37473i) q^{72} +(0.892647 - 0.177559i) q^{73} +(0.746831 - 1.68913i) q^{74} +(0.184218 - 1.87040i) q^{75} +(-10.8470 + 8.07651i) q^{76} +(0.783545 + 0.237686i) q^{77} +(-1.24651 - 1.59414i) q^{78} +(-13.5062 - 5.59446i) q^{79} +(3.31745 - 2.23484i) q^{80} +(9.52852 - 3.94684i) q^{81} +(3.98131 + 2.25042i) q^{82} +(2.59224 + 4.84974i) q^{83} +(-1.97456 + 2.18689i) q^{84} +(-0.198972 - 0.242448i) q^{85} +(1.39414 + 1.46154i) q^{86} +(0.162739 + 0.108739i) q^{87} +(-2.93128 + 0.369981i) q^{88} +(5.32126 + 7.96383i) q^{89} +(-0.403356 - 0.635638i) q^{90} +(-0.281323 + 0.526319i) q^{91} +(-2.50310 + 5.31836i) q^{92} +(-4.17333 + 0.411037i) q^{93} +(-15.5268 + 7.83393i) q^{94} +(-4.78131 + 4.78131i) q^{95} +(3.28724 - 10.1108i) q^{96} +(9.97976 + 9.97976i) q^{97} +(-8.57745 - 2.82462i) q^{98} +(0.0545030 + 0.553378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

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 $

$2$	1.41028	−	0.105369i	0.997220	−	0.0745072i
$2$	1.41028	−	0.105369i	0.997220	−	0.0745072i
$3$	1.19231	−	1.45283i	0.688380	−	0.838793i	−0.305157	−	0.952302i	$-0.598709\pi$
$3$	1.19231	−	1.45283i	0.688380	−	0.838793i	0.993537	+	0.113509i	$0.0362090\pi$
$4$	1.97779	−	0.297201i	0.988897	−	0.148600i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$6$	1.52841	−	2.17454i	0.623970	−	0.887751i
$7$	−0.768791	−	0.152922i	−0.290576	−	0.0577991i	0.0476501	−	0.998864i	$-0.484827\pi$
$7$	−0.768791	−	0.152922i	−0.290576	−	0.0577991i	−0.338226	+	0.941065i	$0.609827\pi$
$8$	2.75793	−	0.627535i	0.975077	−	0.221867i
$9$	−0.103851	−	0.522093i	−0.0346169	−	0.174031i
$10$	1.31897	−	0.510215i	0.417095	−	0.161344i
$11$	−1.03956	−	0.102387i	−0.313438	−	0.0308710i	−0.0599250	−	0.998203i	$-0.519086\pi$
$11$	−1.03956	−	0.102387i	−0.313438	−	0.0308710i	−0.253513	+	0.967332i	$0.581586\pi$
$12$	1.92636	−	3.22776i	0.556092	−	0.931774i
$13$	0.221009	−	0.728568i	0.0612967	−	0.202068i	−0.920943	−	0.389696i	$-0.872580\pi$
$13$	0.221009	−	0.728568i	0.0612967	−	0.202068i	0.982240	+	0.187628i	$0.0600800\pi$
$14$	−1.10033	−	0.134656i	−0.294074	−	0.0359884i
$15$	0.719233	−	1.73638i	0.185705	−	0.448332i
$16$	3.82334	−	1.17560i	0.955836	−	0.293901i
$17$	−0.120025	−	0.289767i	−0.0291104	−	0.0702787i	0.908656	−	0.417546i	$-0.137110\pi$
$17$	−0.120025	−	0.289767i	−0.0291104	−	0.0702787i	−0.937766	+	0.347267i	$0.887110\pi$
$18$	−0.201471	−	0.725356i	−0.0474872	−	0.170968i
$19$	−5.96337	+	3.18749i	−1.36809	+	0.731260i	−0.981585	−	0.191027i	$-0.938818\pi$
$19$	−5.96337	+	3.18749i	−1.36809	+	0.731260i	−0.386506	+	0.922287i	$0.626318\pi$
$20$	1.80636	−	0.858527i	0.403914	−	0.191972i
$21$	−1.13881	+	0.934594i	−0.248508	+	0.203945i
$22$	−1.47686	−	0.0348580i	−0.314867	−	0.00743175i
$23$	−1.63281	+	2.44367i	−0.340464	+	0.509541i	−0.961708	−	0.274077i	$-0.911628\pi$
$23$	−1.63281	+	2.44367i	−0.340464	+	0.509541i	0.621243	+	0.783618i	$0.286628\pi$
$24$	2.37660	−	4.75503i	0.485122	−	0.970617i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	0.234916	−	1.05077i	0.0460708	−	0.206074i
$27$	4.09024	+	2.18628i	0.787167	+	0.420749i
$28$	−1.56596	−	0.0739632i	−0.295938	−	0.0139777i
$29$	0.0102075	+	0.103638i	0.00189548	+	0.0192451i	0.996086	−	0.0883900i	$-0.0281722\pi$
$29$	0.0102075	+	0.103638i	0.00189548	+	0.0192451i	−0.994190	+	0.107635i	$0.965672\pi$
$30$	0.831361	−	2.52458i	0.151785	−	0.460922i
$31$	−1.57773	−	1.57773i	−0.283370	−	0.283370i	0.551082	−	0.834451i	$-0.314215\pi$
$31$	−1.57773	−	1.57773i	−0.283370	−	0.283370i	−0.834451	+	0.551082i	$0.814215\pi$
$32$	5.26812	−	2.06080i	0.931281	−	0.364301i
$33$	−1.38822	+	1.38822i	−0.241659	+	0.241659i
$34$	−0.199802	−	0.396006i	−0.0342658	−	0.0679145i
$35$	−0.780078	+	0.0768310i	−0.131857	+	0.0129868i
$36$	−0.360562	−	1.00173i	−0.0600936	−	0.166955i
$37$	0.615613	−	1.15173i	0.101206	−	0.189343i	−0.826222	−	0.563345i	$-0.809514\pi$
$37$	0.615613	−	1.15173i	0.101206	−	0.189343i	0.927428	+	0.374001i	$0.122014\pi$
$38$	−8.07417	+	5.12361i	−1.30980	+	0.831160i
$39$	−0.794976	−	1.18977i	−0.127298	−	0.190515i
$40$	2.45701	−	1.40110i	0.388488	−	0.221533i
$41$	2.68883	+	1.79662i	0.419924	+	0.280584i	0.747527	−	0.664231i	$-0.231241\pi$
$41$	2.68883	+	1.79662i	0.419924	+	0.280584i	−0.327603	+	0.944815i	$0.606241\pi$
$42$	−1.50756	+	1.43804i	−0.232622	+	0.221894i
$43$	0.906064	+	1.10404i	0.138173	+	0.168365i	0.837500	−	0.546438i	$-0.184017\pi$
$43$	0.906064	+	1.10404i	0.138173	+	0.168365i	−0.699326	+	0.714803i	$0.746517\pi$
$44$	−2.08646	+	0.106456i	−0.314546	+	0.0160488i
$45$	−0.250934	−	0.469465i	−0.0374071	−	0.0699837i
$46$	−2.04524	+	3.61832i	−0.301554	+	0.533492i
$47$	−11.3613	+	4.70600i	−1.65722	+	0.686441i	−0.997860	−	0.0653894i	$-0.979171\pi$
$47$	−11.3613	+	4.70600i	−1.65722	+	0.686441i	−0.659356	+	0.751831i	$0.729171\pi$
$48$	2.85065	−	6.95636i	0.411456	−	1.00406i
$49$	−5.89950	−	2.44365i	−0.842786	−	0.349093i
$50$	1.11407	−	0.871122i	0.157553	−	0.123195i
$51$	−0.564090	−	0.171115i	−0.0789883	−	0.0239608i
$52$	0.220579	−	1.50664i	0.0305888	−	0.208934i
$53$	0.787917	−	7.99985i	0.108229	−	1.09886i	−0.775655	−	0.631157i	$-0.782580\pi$
$53$	0.787917	−	7.99985i	0.108229	−	1.09886i	0.883884	−	0.467707i	$-0.154920\pi$
$54$	5.99876	+	2.65228i	0.816328	+	0.360930i
$55$	−1.02452	+	0.203789i	−0.138146	+	0.0274789i
$56$	−2.21624	+	0.0606947i	−0.296157	+	0.00811067i
$57$	−2.47929	+	12.4642i	−0.328390	+	1.65093i
$58$	0.0253157	+	0.145084i	0.00332411	+	0.0190504i
$59$	0.598811	+	1.97401i	0.0779585	+	0.256995i	0.987253	−	0.159158i	$-0.0508780\pi$
$59$	0.598811	+	1.97401i	0.0779585	+	0.256995i	−0.909295	+	0.416153i	$0.863378\pi$
$60$	0.906442	−	3.64796i	0.117021	−	0.470950i
$61$	3.68122	+	3.02110i	0.471331	+	0.386812i	0.839859	−	0.542805i	$-0.182638\pi$
$61$	3.68122	+	3.02110i	0.471331	+	0.386812i	−0.368527	+	0.929617i	$0.620138\pi$
$62$	−2.39130	−	2.05881i	−0.303695	−	0.261469i
$63$			0.417261i			0.0525700i
$64$	7.21240	−	3.46140i	0.901550	−	0.432675i
$65$		−	0.761351i		−	0.0944340i
$66$	−1.81151	+	2.10406i	−0.222982	+	0.258992i
$67$	7.91857	+	6.49860i	0.967407	+	0.793930i	0.978550	−	0.206008i	$-0.0660472\pi$
$67$	7.91857	+	6.49860i	0.967407	+	0.793930i	−0.0111435	+	0.999938i	$0.503547\pi$
$68$	−0.323504	−	0.537427i	−0.0392306	−	0.0651726i
$69$	1.60343	+	5.28581i	0.193031	+	0.636337i
$70$	−1.09203	+	0.190550i	−0.130523	+	0.0227750i
$71$	1.42020	−	7.13984i	0.168547	−	0.847343i	−0.800284	−	0.599621i	$-0.795318\pi$
$71$	1.42020	−	7.13984i	0.168547	−	0.847343i	0.968831	−	0.247722i	$-0.0796820\pi$
$72$	−0.614045	−	1.37473i	−0.0723659	−	0.162013i
$73$	0.892647	−	0.177559i	0.104476	−	0.0207817i	−0.142575	−	0.989784i	$-0.545538\pi$
$73$	0.892647	−	0.177559i	0.104476	−	0.0207817i	0.247052	+	0.969002i	$0.420538\pi$
$74$	0.746831	−	1.68913i	0.0868174	−	0.196358i
$75$	0.184218	−	1.87040i	0.0212717	−	0.215975i
$76$	−10.8470	+	8.07651i	−1.24424	+	0.926439i
$77$	0.783545	+	0.237686i	0.0892932	+	0.0270868i
$78$	−1.24651	−	1.59414i	−0.141139	−	0.180501i
$79$	−13.5062	−	5.59446i	−1.51957	−	0.629426i	−0.542063	−	0.840338i	$-0.682357\pi$
$79$	−13.5062	−	5.59446i	−1.51957	−	0.629426i	−0.977505	+	0.210912i	$0.932357\pi$
$80$	3.31745	−	2.23484i	0.370902	−	0.249863i
$81$	9.52852	−	3.94684i	1.05872	−	0.438538i
$82$	3.98131	+	2.25042i	0.439663	+	0.248517i
$83$	2.59224	+	4.84974i	0.284535	+	0.532328i	0.983066	−	0.183252i	$-0.0586625\pi$
$83$	2.59224	+	4.84974i	0.284535	+	0.532328i	−0.698531	+	0.715580i	$0.746162\pi$
$84$	−1.97456	+	2.18689i	−0.215442	+	0.238609i
$85$	−0.198972	−	0.242448i	−0.0215815	−	0.0262972i
$86$	1.39414	+	1.46154i	0.150334	+	0.157602i
$87$	0.162739	+	0.108739i	0.0174475	+	0.0116580i
$88$	−2.93128	+	0.369981i	−0.312476	+	0.0394401i
$89$	5.32126	+	7.96383i	0.564052	+	0.844164i	0.998398	−	0.0565823i	$-0.0180203\pi$
$89$	5.32126	+	7.96383i	0.564052	+	0.844164i	−0.434346	+	0.900746i	$0.643020\pi$
$90$	−0.403356	−	0.635638i	−0.0425174	−	0.0670021i
$91$	−0.281323	+	0.526319i	−0.0294907	+	0.0551732i
$92$	−2.50310	+	5.31836i	−0.260966	+	0.554477i
$93$	−4.17333	+	0.411037i	−0.432754	+	0.0426226i
$94$	−15.5268	+	7.83393i	−1.60146	+	0.808008i
$95$	−4.78131	+	4.78131i	−0.490552	+	0.490552i
$96$	3.28724	−	10.1108i	0.335502	−	1.03193i
$97$	9.97976	+	9.97976i	1.01329	+	1.01329i	0.999910	+	0.0133804i	$0.00425925\pi$
$97$	9.97976	+	9.97976i	1.01329	+	1.01329i	0.0133804	+	0.999910i	$0.495741\pi$
$98$	−8.57745	−	2.82462i	−0.866454	−	0.285329i
$99$	0.0545030	+	0.553378i	0.00547776	+	0.0556166i
$100$	1.47936	−	1.34592i	0.147936	−	0.134592i
$101$	−4.42414	−	2.36475i	−0.440218	−	0.235302i	0.236370	−	0.971663i	$-0.424042\pi$
$101$	−4.42414	−	2.36475i	−0.440218	−	0.235302i	−0.676588	+	0.736362i	$0.736542\pi$
$102$	−0.813556	−	0.181882i	−0.0805540	−	0.0180090i
$103$	9.90538	−	6.61857i	0.976006	−	0.652147i	0.0381872	−	0.999271i	$-0.487842\pi$
$103$	9.90538	−	6.61857i	0.976006	−	0.652147i	0.937819	+	0.347124i	$0.112842\pi$
$104$	0.152325	−	2.14803i	0.0149367	−	0.210632i
$105$	−0.818471	+	1.22493i	−0.0798746	+	0.119541i
$106$	0.268248	−	11.3651i	0.0260545	−	1.10387i
$107$	−7.18685	+	5.89810i	−0.694779	+	0.570191i	−0.914113	−	0.405459i	$-0.867112\pi$
$107$	−7.18685	+	5.89810i	−0.694779	+	0.570191i	0.219334	+	0.975650i	$0.429612\pi$
$108$	8.73941	+	3.10839i	0.840950	+	0.299105i
$109$	3.55615	−	1.90080i	0.340618	−	0.182064i	−0.292215	−	0.956353i	$-0.594392\pi$
$109$	3.55615	−	1.90080i	0.340618	−	0.182064i	0.632832	+	0.774289i	$0.281892\pi$
$110$	−1.42338	+	0.395352i	−0.135714	+	0.0376953i
$111$	−0.939271	−	2.26760i	−0.0891517	−	0.215231i
$112$	−3.11913	+	0.319120i	−0.294730	+	0.0301540i
$113$	3.36004	−	8.11186i	0.316086	−	0.763100i	−0.683368	−	0.730074i	$-0.739486\pi$
$113$	3.36004	−	8.11186i	0.316086	−	0.763100i	0.999455	−	0.0330258i	$-0.0105143\pi$
$114$	−2.18316	+	17.8393i	−0.204471	+	1.67081i
$115$	−0.853141	+	2.81243i	−0.0795558	+	0.262260i
$116$	0.0509896	+	0.201941i	0.00473426	+	0.0187498i
$117$	−0.403332	−	0.0397247i	−0.0372880	−	0.00367255i
$118$	1.05249	+	2.72082i	0.0968898	+	0.250472i
$119$	0.0479626	+	0.241124i	0.00439673	+	0.0221038i
$120$	0.893956	−	5.24017i	0.0816067	−	0.478360i
$121$	−9.71844	−	1.93312i	−0.883495	−	0.175738i
$122$	5.50989	+	3.87271i	0.498842	+	0.350619i
$123$	5.81609	−	1.76429i	0.524419	−	0.159081i
$124$	−3.58934	−	2.65153i	−0.322332	−	0.238115i
$125$	0.634393	−	0.773010i	0.0567419	−	0.0691402i
$126$	0.0439664	+	0.588456i	0.00391684	+	0.0524238i
$127$	−9.71600			−0.862155			−0.431078	−	0.902315i	$-0.641866\pi$
$127$	−9.71600			−0.862155			−0.431078	+	0.902315i	$0.641866\pi$
$128$	9.80680	−	5.64152i	0.866807	−	0.498645i
$129$	2.68430			0.236339
$130$	−0.0802229	−	1.07372i	−0.00703602	−	0.0941715i
$131$	−1.20419	+	1.46731i	−0.105211	+	0.128200i	−0.822954	−	0.568109i	$-0.807675\pi$
$131$	−1.20419	+	1.46731i	−0.105211	+	0.128200i	0.717743	+	0.696308i	$0.245175\pi$
$132$	−2.33304	+	3.15820i	−0.203065	+	0.274886i
$133$	5.07202	−	1.53858i	0.439800	−	0.133412i
$134$	11.8522	+	8.33049i	1.02387	+	0.719645i
$135$	4.54876	+	0.904804i	0.391495	+	0.0778731i
$136$	−0.512861	−	0.723837i	−0.0439774	−	0.0620685i
$137$	0.902456	+	4.53695i	0.0771020	+	0.387618i	0.999997	+	0.00256555i	$0.000816641\pi$
$137$	0.902456	+	4.53695i	0.0771020	+	0.387618i	−0.922895	+	0.385052i	$0.874183\pi$
$138$	2.81826	+	7.28554i	0.239906	+	0.620186i
$139$	0.582965	+	0.0574171i	0.0494465	+	0.00487005i	0.122710	−	0.992443i	$-0.460841\pi$
$139$	0.582965	+	0.0574171i	0.0494465	+	0.00487005i	−0.0732637	+	0.997313i	$0.523341\pi$
$140$	−1.52000	+	0.383795i	−0.128463	+	0.0324366i
$141$	−6.70914	+	22.1171i	−0.565012	+	1.86259i
$142$	1.25057	−	10.2188i	0.104945	−	0.857546i
$143$	−0.304347	+	0.734759i	−0.0254508	+	0.0614436i
$144$	−1.01083	−	1.87405i	−0.0842359	−	0.156171i
$145$	0.0398525	+	0.0962124i	0.00330957	+	0.00799001i
$146$	1.24018	−	0.344465i	0.102638	−	0.0285081i
$147$	−10.5842	+	5.65740i	−0.872974	+	0.466614i
$148$	0.875261	−	2.46085i	0.0719460	−	0.202280i
$149$	−4.81666	+	3.95293i	−0.394596	+	0.323837i	−0.810680	−	0.585490i	$-0.800902\pi$
$149$	−4.81666	+	3.95293i	−0.394596	+	0.323837i	0.416084	+	0.909326i	$0.363402\pi$
$150$	0.0627174	−	2.65720i	0.00512085	−	0.216959i
$151$	3.26816	−	4.89115i	0.265959	−	0.398036i	−0.674321	−	0.738439i	$-0.735563\pi$
$151$	3.26816	−	4.89115i	0.265959	−	0.398036i	0.940280	+	0.340403i	$0.110563\pi$
$152$	−14.4463	+	12.5331i	−1.17175	+	1.01657i
$153$	−0.138820	+	0.0927568i	−0.0112230	+	0.00749894i
$154$	1.13006	+	0.252643i	0.0910632	+	0.0203585i
$155$	−1.96779	−	1.05181i	−0.158057	−	0.0844831i
$156$	−1.92590	−	2.11685i	−0.154195	−	0.169483i
$157$	2.18532	+	22.1880i	0.174408	+	1.77079i	0.541589	+	0.840643i	$0.317823\pi$
$157$	2.18532	+	22.1880i	0.174408	+	1.77079i	−0.367182	+	0.930149i	$0.619677\pi$
$158$	−19.6371	−	6.46663i	−1.56224	−	0.514457i
$159$	−10.6830	−	10.6830i	−0.847217	−	0.847217i
$160$	4.44306	−	3.50131i	0.351255	−	0.276803i
$161$	1.62898	−	1.62898i	0.128382	−	0.128382i
$162$	13.0220	−	6.57018i	1.02311	−	0.516202i
$163$	6.79355	−	0.669107i	0.532112	−	0.0524085i	0.171607	−	0.985166i	$-0.445104\pi$
$163$	6.79355	−	0.669107i	0.532112	−	0.0524085i	0.360506	+	0.932757i	$0.382604\pi$
$164$	5.85190	+	2.75422i	0.456957	+	0.215068i
$165$	−0.925468	+	1.73143i	−0.0720476	+	0.134791i
$166$	4.16680	+	6.56636i	0.323407	+	0.509648i
$167$	−11.3357	−	16.9651i	−0.877182	−	1.31279i	−0.948967	−	0.315375i	$-0.897870\pi$
$167$	−11.3357	−	16.9651i	−0.877182	−	1.31279i	0.0717856	−	0.997420i	$-0.477130\pi$
$168$	−2.55426	+	3.29219i	−0.197065	+	0.253998i
$169$	10.3271	+	6.90037i	0.794395	+	0.530798i
$170$	−0.306153	−	0.320955i	−0.0234809	−	0.0246161i
$171$	2.28346	+	2.78241i	0.174621	+	0.212776i
$172$	2.12013	+	1.91429i	0.161658	+	0.145963i
$173$	−3.67465	−	6.87478i	−0.279378	−	0.522680i	0.702621	−	0.711564i	$-0.252013\pi$
$173$	−3.67465	−	6.87478i	−0.279378	−	0.522680i	−0.981999	+	0.188884i	$0.939513\pi$
$174$	0.240966	+	0.136205i	0.0182676	+	0.0103257i
$175$	−0.724185	+	0.299967i	−0.0547433	+	0.0226754i
$176$	−4.09495	+	0.830644i	−0.308668	+	0.0626122i
$177$	3.58188	+	1.48366i	0.269230	+	0.111519i
$178$	8.34362	+	10.6706i	0.625381	+	0.799792i
$179$	−9.77000	−	2.96370i	−0.730244	−	0.221517i	−0.0967982	−	0.995304i	$-0.530860\pi$
$179$	−9.77000	−	2.96370i	−0.730244	−	0.221517i	−0.633446	+	0.773787i	$0.718360\pi$
$180$	−0.635822	−	0.853928i	−0.0473914	−	0.0636480i
$181$	0.437380	−	4.44080i	0.0325102	−	0.330082i	−0.965149	−	0.261701i	$-0.915717\pi$
$181$	0.437380	−	4.44080i	0.0325102	−	0.330082i	0.997659	−	0.0683810i	$-0.0217834\pi$
$182$	−0.341288	+	0.771901i	−0.0252979	+	0.0572171i
$183$	8.77829	−	1.74611i	0.648910	−	0.129076i
$184$	−2.96969	+	7.76414i	−0.218929	+	0.572380i
$185$	0.254775	−	1.28084i	0.0187314	−	0.0941693i
$186$	−5.84227	+	1.01942i	−0.428376	+	0.0747474i
$187$	0.0951046	+	0.313518i	0.00695474	+	0.0229267i
$188$	−21.0717	+	12.6841i	−1.53681	+	0.925083i
$189$	−2.81021	−	2.30628i	−0.204413	−	0.167757i
$190$	−6.23920	+	7.24680i	−0.452639	+	0.525738i
$191$		−	18.1980i		−	1.31676i	−0.752686	−	0.658380i	$-0.771242\pi$
$191$		−	18.1980i		−	1.31676i	0.752686	−	0.658380i	$-0.228758\pi$
$192$	3.57057	−	14.6055i	0.257684	−	1.05406i
$193$		−	7.98240i		−	0.574586i	−0.957843	−	0.287293i	$-0.907245\pi$
$193$		−	7.98240i		−	0.574586i	0.957843	−	0.287293i	$-0.0927553\pi$
$194$	15.1258	+	13.0227i	1.08597	+	0.934977i
$195$	−1.10612	−	0.907765i	−0.0792106	−	0.0650064i
$196$	−12.3943	−	3.07971i	−0.885304	−	0.219979i
$197$	1.44483	+	4.76297i	0.102940	+	0.339347i	0.993248	−	0.116011i	$-0.0370109\pi$
$197$	1.44483	+	4.76297i	0.102940	+	0.339347i	−0.890308	+	0.455359i	$0.849511\pi$
$198$	0.135174	+	0.774676i	0.00960637	+	0.0550539i
$199$	0.333241	−	1.67532i	0.0236228	−	0.118760i	−0.967175	−	0.254112i	$-0.918217\pi$
$199$	0.333241	−	1.67532i	0.0236228	−	0.118760i	0.990798	+	0.135352i	$0.0432167\pi$
$200$	1.94450	−	2.05400i	0.137497	−	0.145240i
$201$	18.8827	−	3.75601i	1.33189	−	0.264929i
$202$	−6.48846	−	2.86880i	−0.456526	−	0.201848i
$203$	0.00800115	−	0.0812370i	0.000561570	−	0.00570172i
$204$	−1.16651	−	0.170782i	−0.0816719	−	0.0119571i
$205$	3.09458	+	0.938730i	0.216135	+	0.0655637i
$206$	13.2720	−	10.3778i	0.924704	−	0.723054i
$207$	1.44539	+	0.598701i	0.100462	+	0.0416126i
$208$	−0.0115149	−	3.04538i	−0.000798414	−	0.211159i
$209$	6.52562	−	2.70300i	0.451387	−	0.186970i
$210$	−1.02521	+	1.81374i	−0.0707459	+	0.125160i
$211$	−9.38469	−	17.5575i	−0.646069	−	1.20871i	−0.965327	−	0.261042i	$-0.915934\pi$
$211$	−9.38469	−	17.5575i	−0.646069	−	1.20871i	0.319259	−	0.947668i	$-0.396566\pi$
$212$	−0.819223	−	16.0562i	−0.0562645	−	1.10275i
$213$	−8.67967	−	10.5762i	−0.594721	−	0.724670i
$214$	−9.51401	+	9.07526i	−0.650365	+	0.620372i
$215$	1.18754	+	0.793486i	0.0809893	+	0.0541153i
$216$	12.6526	+	3.46284i	0.860898	+	0.235616i
$217$	0.971678	+	1.45422i	0.0659618	+	0.0987188i
$218$	4.81490	−	3.05538i	0.326106	−	0.206936i
$219$	0.806348	−	1.50857i	0.0544879	−	0.101940i
$220$	−1.96571	+	0.707539i	−0.132528	+	0.0477023i
$221$	−0.237641	+	0.0234056i	−0.0159855	+	0.00157443i
$222$	−1.56357	−	3.09899i	−0.104940	−	0.207990i
$223$	−6.60764	+	6.60764i	−0.442480	+	0.442480i	−0.892845	−	0.450365i	$-0.851294\pi$
$223$	−6.60764	+	6.60764i	−0.442480	+	0.442480i	0.450365	+	0.892845i	$0.351294\pi$
$224$	−4.36523	+	0.778709i	−0.291664	+	0.0520297i
$225$	−0.376408	−	0.376408i	−0.0250939	−	0.0250939i
$226$	3.88387	−	11.7941i	0.258351	−	0.784529i
$227$	−0.0845950	−	0.858908i	−0.00561477	−	0.0570077i	0.991969	−	0.126481i	$-0.0403682\pi$
$227$	−0.0845950	−	0.858908i	−0.00561477	−	0.0570077i	−0.997584	+	0.0694731i	$0.977868\pi$
$228$	−1.19915	+	25.3886i	−0.0794157	+	1.68140i
$229$	10.8608	+	5.80522i	0.717702	+	0.383620i	0.789460	−	0.613802i	$-0.210361\pi$
$229$	10.8608	+	5.80522i	0.717702	+	0.383620i	−0.0717575	+	0.997422i	$0.522861\pi$
$230$	−0.906827	+	4.05621i	−0.0597944	+	0.267459i
$231$	1.27954	−	0.854964i	0.0841878	−	0.0562525i
$232$	0.0931881	+	0.279422i	0.00611810	+	0.0183449i
$233$	−2.34614	+	3.51124i	−0.153700	+	0.230029i	−0.900327	−	0.435215i	$-0.856672\pi$
$233$	−2.34614	+	3.51124i	−0.153700	+	0.230029i	0.746626	+	0.665244i	$0.231672\pi$
$234$	−0.572997	−	0.0135243i	−0.0374580	−	0.000884114i
$235$	−9.50601	+	7.80138i	−0.620103	+	0.508906i
$236$	1.77100	+	3.72623i	0.115282	+	0.242557i
$237$	−24.2314	+	12.9519i	−1.57400	+	0.841319i
$238$	0.0930480	+	0.335000i	0.00603140	+	0.0217148i
$239$	−7.39560	−	17.8545i	−0.478381	−	1.15491i	−0.960368	−	0.278736i	$-0.910085\pi$
$239$	−7.39560	−	17.8545i	−0.478381	−	1.15491i	0.481986	−	0.876179i	$-0.339915\pi$
$240$	0.708578	−	7.48432i	0.0457385	−	0.483111i
$241$	6.45367	−	15.5805i	0.415718	−	1.00363i	−0.567857	−	0.823127i	$-0.692227\pi$
$241$	6.45367	−	15.5805i	0.415718	−	1.00363i	0.983574	−	0.180504i	$-0.0577727\pi$
$242$	−13.9094	−	1.70222i	−0.894133	−	0.109423i
$243$	1.58793	−	5.23470i	0.101866	−	0.335806i
$244$	8.17856	+	4.88105i	0.523579	+	0.312477i
$245$	−6.35483	−	0.625896i	−0.405995	−	0.0399870i
$246$	8.01643	−	3.10099i	0.511109	−	0.197712i
$247$	1.00434	+	5.04918i	0.0639049	+	0.321272i
$248$	−5.34137	−	3.36120i	−0.339178	−	0.213437i
$249$	10.1366	+	2.01630i	0.642381	+	0.127778i
$250$	0.813222	−	1.15701i	0.0514327	−	0.0731757i
$251$	−8.44285	+	2.56111i	−0.532908	+	0.161656i	−0.545259	−	0.838268i	$-0.683569\pi$
$251$	−8.44285	+	2.56111i	−0.532908	+	0.161656i	0.0123507	+	0.999924i	$0.496069\pi$
$252$	0.124010	+	0.825257i	0.00781191	+	0.0519863i
$253$	1.94760	−	2.37316i	0.122445	−	0.149199i
$254$	−13.7023	+	1.02377i	−0.859759	+	0.0642368i
$255$	−0.589472			−0.0369142
$256$	13.2359	−	8.98947i	0.827245	−	0.561842i
$257$	−20.0768			−1.25236			−0.626178	−	0.779680i	$-0.715382\pi$
$257$	−20.0768			−1.25236			−0.626178	+	0.779680i	$0.715382\pi$
$258$	3.78562	−	0.282842i	0.235682	−	0.0176090i
$259$	−0.649403	+	0.791299i	−0.0403519	+	0.0491689i
$260$	−0.226274	−	1.50580i	−0.0140329	−	0.0933855i
$261$	0.0530487	−	0.0160921i	0.00328363	−	0.000996078i
$262$	−1.54364	+	2.19621i	−0.0953664	+	0.135682i
$263$	2.71793	+	0.540630i	0.167595	+	0.0333366i	0.278174	−	0.960531i	$-0.410271\pi$
$263$	2.71793	+	0.540630i	0.167595	+	0.0333366i	−0.110580	+	0.993867i	$0.535271\pi$
$264$	−2.95747	+	4.69979i	−0.182020	+	0.289252i
$265$	−1.56825	−	7.88410i	−0.0963366	−	0.484317i
$266$	6.99086	−	2.70427i	0.428637	−	0.165809i
$267$	17.9147	+	1.76444i	1.09636	+	0.107982i
$268$	17.5927	+	10.4995i	1.07464	+	0.641359i
$269$	2.09767	−	6.91508i	0.127897	−	0.421620i	−0.869483	−	0.493963i	$-0.835548\pi$
$269$	2.09767	−	6.91508i	0.127897	−	0.421620i	0.997380	+	0.0723435i	$0.0230478\pi$
$270$	6.51037	+	0.796731i	0.396209	+	0.0484875i
$271$	7.03926	−	16.9943i	0.427605	−	1.03233i	−0.552440	−	0.833553i	$-0.686303\pi$
$271$	7.03926	−	16.9943i	0.427605	−	1.03233i	0.980045	−	0.198777i	$-0.0636968\pi$
$272$	−0.799549	−	0.966775i	−0.0484798	−	0.0586194i
$273$	0.429229	+	1.03625i	0.0259781	+	0.0627167i
$274$	1.75077	+	6.30329i	0.105768	+	0.380796i
$275$	−0.921243	+	0.492415i	−0.0555531	+	0.0296937i
$276$	4.74221	+	9.97771i	0.285447	+	0.600587i
$277$	4.82621	−	3.96077i	0.289979	−	0.237980i	−0.478145	−	0.878281i	$-0.658691\pi$
$277$	4.82621	−	3.96077i	0.289979	−	0.237980i	0.768124	+	0.640301i	$0.221191\pi$
$278$	0.828196	+	0.0195477i	0.0496719	+	0.00117240i
$279$	−0.659875	+	0.987573i	−0.0395057	+	0.0591244i
$280$	−2.10319	+	0.701421i	−0.125690	+	0.0419179i
$281$	13.7846	−	9.21055i	0.822318	−	0.549455i	−0.0717311	−	0.997424i	$-0.522852\pi$
$281$	13.7846	−	9.21055i	0.822318	−	0.549455i	0.894049	+	0.447969i	$0.147852\pi$
$282$	−7.13133	+	31.8983i	−0.424664	+	1.89951i
$283$	8.06800	+	4.31244i	0.479593	+	0.256348i	0.693433	−	0.720521i	$-0.256097\pi$
$283$	8.06800	+	4.31244i	0.479593	+	0.256348i	−0.213840	+	0.976869i	$0.568597\pi$
$284$	0.686904	−	14.5432i	0.0407603	−	0.862981i
$285$	1.24564	+	12.6472i	0.0737856	+	0.749158i
$286$	−0.351795	+	1.06829i	−0.0208020	+	0.0631691i
$287$	−1.79240	−	1.79240i	−0.105802	−	0.105802i
$288$	−1.62302	−	2.53643i	−0.0956376	−	0.149461i
$289$	11.9513	−	11.9513i	0.703015	−	0.703015i
$290$	0.0663411	+	0.131488i	0.00389568	+	0.00772121i
$291$	26.3979	−	2.59996i	1.54747	−	0.152413i
$292$	1.71270	−	0.616470i	0.100228	−	0.0360762i
$293$	0.309723	−	0.579451i	0.0180942	−	0.0338519i	−0.872712	−	0.488236i	$-0.837641\pi$
$293$	0.309723	−	0.579451i	0.0180942	−	0.0338519i	0.890806	+	0.454384i	$0.150141\pi$
$294$	−14.3307	+	9.09378i	−0.835781	+	0.530360i
$295$	1.14605	+	1.71519i	0.0667257	+	0.0998621i
$296$	0.975068	−	3.56272i	0.0566747	−	0.207079i
$297$	−4.02819	−	2.69155i	−0.233739	−	0.156180i
$298$	−6.37633	+	6.08228i	−0.369371	+	0.352337i
$299$	1.41952	+	1.72969i	0.0820927	+	0.100030i
$300$	−0.191538	−	3.75401i	−0.0110584	−	0.216738i
$301$	−0.527741	−	0.987335i	−0.0304185	−	0.0569090i
$302$	4.09365	−	7.24226i	0.235563	−	0.416746i
$303$	−8.71053	+	3.60802i	−0.500407	+	0.207275i
$304$	−19.0528	+	19.1974i	−1.09275	+	1.10105i
$305$	4.39968	+	1.82241i	0.251925	+	0.104351i
$306$	−0.186002	+	0.145441i	−0.0106330	+	0.00831429i
$307$	10.1204	+	3.06999i	0.577602	+	0.175214i	0.565550	−	0.824714i	$-0.308664\pi$
$307$	10.1204	+	3.06999i	0.577602	+	0.175214i	0.0120513	+	0.999927i	$0.496164\pi$
$308$	1.62033	+	0.237223i	0.0923269	+	0.0135171i
$309$	2.19461	−	22.2822i	0.124847	−	1.26759i
$310$	−2.88597	−	1.27600i	−0.163912	−	0.0724719i
$311$	8.39505	−	1.66988i	0.476040	−	0.0946902i	0.0487616	−	0.998810i	$-0.484473\pi$
$311$	8.39505	−	1.66988i	0.476040	−	0.0946902i	0.427278	+	0.904120i	$0.359473\pi$
$312$	−2.93911	−	2.78242i	−0.166394	−	0.157523i
$313$	−3.44610	+	17.3247i	−0.194785	+	0.979250i	0.752435	+	0.658666i	$0.228879\pi$
$313$	−3.44610	+	17.3247i	−0.194785	+	0.979250i	−0.947220	+	0.320584i	$0.896121\pi$
$314$	5.41985	+	31.0610i	0.305860	+	1.75288i
$315$	0.121125	+	0.399294i	0.00682459	+	0.0224977i
$316$	−28.3752	−	7.05064i	−1.59623	−	0.396629i
$317$	−16.0081	−	13.1375i	−0.899107	−	0.737878i	0.0665271	−	0.997785i	$-0.478808\pi$
$317$	−16.0081	−	13.1375i	−0.899107	−	0.737878i	−0.965634	+	0.259907i	$0.916308\pi$
$318$	−16.1917	−	13.9404i	−0.907986	−	0.781739i
$319$		−	0.108783i		−	0.00609067i
$320$	5.89704	−	5.40600i	0.329655	−	0.302205i
$321$			17.4736i			0.975283i
$322$	2.12568	−	2.46897i	0.118459	−	0.137590i
$323$	1.63938	+	1.34541i	0.0912177	+	0.0748604i
$324$	17.6725	−	10.6379i	0.981803	−	0.590996i
$325$	−0.221009	−	0.728568i	−0.0122593	−	0.0404137i
$326$	9.51033	−	1.65946i	0.526728	−	0.0919090i
$327$	1.47848	−	7.43284i	0.0817603	−	0.411037i
$328$	8.54305	+	3.26762i	0.471711	+	0.180424i
$329$	9.45412	−	1.88054i	0.521222	−	0.103678i
$330$	−1.12273	+	2.53932i	−0.0618044	+	0.139785i
$331$	0.192171	−	1.95115i	0.0105627	−	0.107245i	−0.988458	−	0.151497i	$-0.951591\pi$
$331$	0.192171	−	1.95115i	0.0105627	−	0.107245i	0.999020	+	0.0442524i	$0.0140906\pi$
$332$	6.56826	+	8.82137i	0.360480	+	0.484136i
$333$	−0.665242	−	0.201799i	−0.0364550	−	0.0110585i
$334$	−17.7741	−	22.7311i	−0.972556	−	1.24379i
$335$	9.46404	+	3.92013i	0.517076	+	0.214180i
$336$	−3.25533	+	4.91206i	−0.177593	+	0.267975i
$337$	25.1346	−	10.4111i	1.36917	−	0.567128i	0.427606	−	0.903965i	$-0.359357\pi$
$337$	25.1346	−	10.4111i	1.36917	−	0.567128i	0.941563	+	0.336837i	$0.109357\pi$
$338$	15.2913	+	8.64332i	0.831736	+	0.470134i
$339$	−7.77896	−	14.5534i	−0.422495	−	0.790433i
$340$	−0.465581	−	0.420378i	−0.0252497	−	0.0227982i
$341$	1.47860	+	1.80169i	0.0800709	+	0.0975667i
$342$	3.51351	+	3.68338i	0.189989	+	0.199174i
$343$	8.72404	+	5.82922i	0.471054	+	0.314748i
$344$	3.19169	+	2.47629i	0.172084	+	0.133513i
$345$	3.06878	+	4.59275i	0.165218	+	0.247266i
$346$	−5.90668	−	9.30819i	−0.317545	−	0.500411i
$347$	−14.3278	+	26.8055i	−0.769158	+	1.43899i	0.125431	+	0.992102i	$0.459969\pi$
$347$	−14.3278	+	26.8055i	−0.769158	+	1.43899i	−0.894589	+	0.446890i	$0.852531\pi$
$348$	0.354182	+	0.166697i	0.0189862	+	0.00893590i
$349$	1.91147	−	0.188263i	0.102319	−	0.0100775i	−0.0467282	−	0.998908i	$-0.514879\pi$
$349$	1.91147	−	0.188263i	0.102319	−	0.0100775i	0.149047	+	0.988830i	$0.452379\pi$
$350$	−0.989698	+	0.499345i	−0.0529016	+	0.0266911i
$351$	2.49683	−	2.49683i	0.133271	−	0.133271i
$352$	−5.68751	+	1.60292i	−0.303145	+	0.0854362i
$353$	−12.4638	−	12.4638i	−0.663380	−	0.663380i	0.292795	−	0.956175i	$-0.405415\pi$
$353$	−12.4638	−	12.4638i	−0.663380	−	0.663380i	−0.956175	+	0.292795i	$0.905415\pi$
$354$	5.20779	+	1.71496i	0.276791	+	0.0911493i
$355$	−0.713537	−	7.24466i	−0.0378706	−	0.384507i
$356$	12.8912	+	14.1693i	0.683233	+	0.750973i
$357$	0.407500	+	0.217813i	0.0215672	+	0.0115279i
$358$	−14.0907	−	3.15020i	−0.744719	−	0.166493i
$359$	19.1609	−	12.8029i	1.01128	−	0.675713i	0.0646037	−	0.997911i	$-0.479422\pi$
$359$	19.1609	−	12.8029i	1.01128	−	0.675713i	0.946672	+	0.322198i	$0.104422\pi$
$360$	−0.986667	−	1.13728i	−0.0520019	−	0.0599401i
$361$	14.8459	−	22.2184i	0.781361	−	1.16939i
$362$	0.148907	−	6.30887i	0.00782637	−	0.331587i
$363$	−14.3959	+	11.8144i	−0.755588	+	0.620095i
$364$	−0.399978	+	1.12456i	−0.0209645	+	0.0589430i
$365$	0.802667	−	0.429035i	0.0420135	−	0.0224567i
$366$	12.1959	−	3.38747i	0.637489	−	0.177066i
$367$	4.38409	+	10.5841i	0.228847	+	0.552487i	0.996038	−	0.0889331i	$-0.0283457\pi$
$367$	4.38409	+	10.5841i	0.228847	+	0.552487i	−0.767190	+	0.641420i	$0.778346\pi$
$368$	−3.37000	+	11.2625i	−0.175674	+	0.587100i
$369$	0.658764	−	1.59040i	0.0342939	−	0.0827927i
$370$	0.224344	−	1.83319i	0.0116631	−	0.0953032i
$371$	−1.82910	+	6.02972i	−0.0949620	+	0.313048i
$372$	−8.13183	+	2.05326i	−0.421616	+	0.106457i
$373$	−22.5007	−	2.21613i	−1.16504	−	0.114747i	−0.503051	−	0.864257i	$-0.667789\pi$
$373$	−22.5007	−	2.21613i	−1.16504	−	0.114747i	−0.661993	+	0.749510i	$0.730289\pi$
$374$	0.167160	+	0.432128i	0.00864362	+	0.0223448i
$375$	−0.366662	−	1.84333i	−0.0189343	−	0.0951894i
$376$	−28.3805	+	20.1085i	−1.46361	+	1.03702i
$377$	0.0777633	+	0.0154681i	0.00400501	+	0.000796647i
$378$	−4.20620	−	2.95639i	−0.216343	−	0.152061i
$379$	28.2731	−	8.57657i	1.45229	−	0.440549i	0.537085	−	0.843528i	$-0.319525\pi$
$379$	28.2731	−	8.57657i	1.45229	−	0.440549i	0.915209	+	0.402980i	$0.132025\pi$
$380$	−8.03544	+	10.8775i	−0.412209	+	0.558002i
$381$	−11.5845	+	14.1157i	−0.593490	+	0.723170i
$382$	−1.91751	−	25.6643i	−0.0981082	−	1.31310i
$383$	28.0851			1.43508			0.717540	−	0.696517i	$-0.245268\pi$
$383$	28.0851			1.43508			0.717540	+	0.696517i	$0.245268\pi$
$384$	3.49655	−	20.9741i	0.178432	−	1.07033i
$385$	0.818802			0.0417300
$386$	−0.841099	−	11.2574i	−0.0428108	−	0.572989i
$387$	0.482317	−	0.587705i	0.0245175	−	0.0298747i
$388$	22.7039	+	16.7719i	1.15262	+	0.851465i
$389$	15.2878	−	4.63751i	0.775124	−	0.235131i	0.122150	−	0.992512i	$-0.461021\pi$
$389$	15.2878	−	4.63751i	0.775124	−	0.235131i	0.652974	+	0.757380i	$0.273521\pi$
$390$	−1.65559	−	1.16366i	−0.0838339	−	0.0589240i
$391$	0.904074	+	0.179831i	0.0457210	+	0.00909447i
$392$	−17.8039	−	3.03729i	−0.899234	−	0.153406i
$393$	0.695989	+	3.49898i	0.0351080	+	0.176500i
$394$	2.53949	+	6.56489i	0.127938	+	0.330734i
$395$	−14.5486	−	1.43292i	−0.732021	−	0.0720978i
$396$	0.272260	+	1.07827i	0.0136816	+	0.0541851i
$397$	−4.87285	+	16.0636i	−0.244561	+	0.806210i	0.745614	+	0.666378i	$0.232156\pi$
$397$	−4.87285	+	16.0636i	−0.244561	+	0.806210i	−0.990175	+	0.139832i	$0.955344\pi$
$398$	0.293438	−	2.39778i	0.0147087	−	0.120190i
$399$	3.81211	−	9.20326i	0.190844	−	0.460739i
$400$	2.52586	−	3.10161i	0.126293	−	0.155081i
$401$	−12.9298	−	31.2152i	−0.645681	−	1.55881i	−0.818905	−	0.573930i	$-0.805418\pi$
$401$	−12.9298	−	31.2152i	−0.645681	−	1.55881i	0.173223	−	0.984883i	$-0.444582\pi$
$402$	26.2342	−	7.28670i	1.30845	−	0.363427i
$403$	−1.49818	+	0.800794i	−0.0746296	+	0.0398904i
$404$	−9.45284	−	3.36214i	−0.470297	−	0.167273i
$405$	7.97252	−	6.54288i	0.396158	−	0.325118i
$406$	0.00272400	−	0.115410i	0.000135190	−	0.00572771i
$407$	−0.757887	+	1.13426i	−0.0375671	+	0.0562231i
$408$	−1.66310	−	0.117937i	−0.0823358	−	0.00583874i
$409$	13.0954	−	8.75005i	0.647525	−	0.432662i	−0.187959	−	0.982177i	$-0.560187\pi$
$409$	13.0954	−	8.75005i	0.647525	−	0.432662i	0.835484	+	0.549515i	$0.185187\pi$
$410$	4.46314	+	0.997801i	0.220419	+	0.0492779i
$411$	7.66744	+	4.09833i	0.378207	+	0.202156i
$412$	17.6238	−	16.0341i	0.868261	−	0.789941i
$413$	−0.158490	−	1.60918i	−0.00779878	−	0.0791823i
$414$	2.10150	+	0.692038i	0.103283	+	0.0340118i
$415$	3.88842	+	3.88842i	0.190875	+	0.190875i
$416$	−0.337129	−	4.29364i	−0.0165291	−	0.210513i
$417$	0.778492	−	0.778492i	0.0381229	−	0.0381229i
$418$	8.91816	−	4.49959i	0.436201	−	0.220082i
$419$	12.9669	−	1.27713i	0.633475	−	0.0623919i	0.223817	−	0.974631i	$-0.428148\pi$
$419$	12.9669	−	1.27713i	0.633475	−	0.0623919i	0.409658	+	0.912239i	$0.365648\pi$
$420$	−1.25472	+	2.66591i	−0.0612240	+	0.130083i
$421$	−12.1590	+	22.7479i	−0.592593	+	1.10866i	0.389634	+	0.920970i	$0.372601\pi$
$421$	−12.1590	+	22.7479i	−0.592593	+	1.10866i	−0.982227	+	0.187694i	$0.939899\pi$
$422$	−15.0851	−	23.7722i	−0.734331	−	1.15721i
$423$	3.63685	+	5.44293i	0.176830	+	0.264644i
$424$	−2.84717	−	22.5575i	−0.138271	−	1.09549i
$425$	−0.260783	−	0.174250i	−0.0126498	−	0.00845235i
$426$	−13.3552	−	14.0009i	−0.647061	−	0.678344i
$427$	−2.36809	−	2.88553i	−0.114600	−	0.139641i
$428$	−12.4612	+	13.8012i	−0.602335	+	0.667104i
$429$	0.704606	+	1.31822i	0.0340187	+	0.0636445i
$430$	1.75837	+	0.993910i	0.0847961	+	0.0479306i
$431$	−27.7570	+	11.4973i	−1.33701	+	0.553806i	−0.932646	−	0.360793i	$-0.882506\pi$
$431$	−27.7570	+	11.4973i	−1.33701	+	0.553806i	−0.404361	+	0.914600i	$0.632506\pi$
$432$	18.2086	+	3.55039i	0.876061	+	0.170818i
$433$	−31.2134	−	12.9290i	−1.50002	−	0.621329i	−0.526550	−	0.850144i	$-0.676515\pi$
$433$	−31.2134	−	12.9290i	−1.50002	−	0.621329i	−0.973470	+	0.228816i	$0.926515\pi$
$434$	1.52357	+	1.94847i	0.0731337	+	0.0935298i
$435$	0.187297	+	0.0568159i	0.00898020	+	0.00272411i
$436$	6.46842	−	4.81629i	0.309781	−	0.230659i
$437$	1.94787	−	19.7771i	0.0931794	−	0.946066i
$438$	0.978222	−	2.21248i	0.0467412	−	0.105716i
$439$	−4.80621	+	0.956014i	−0.229388	+	0.0456280i	−0.308446	−	0.951242i	$-0.599809\pi$
$439$	−4.80621	+	0.956014i	−0.229388	+	0.0456280i	0.0790579	+	0.996870i	$0.474809\pi$
$440$	−2.69766	+	1.20496i	−0.128606	+	0.0574440i
$441$	−0.663146	+	3.33386i	−0.0315784	+	0.158755i
$442$	−0.332675	+	0.0580486i	−0.0158237	+	0.00276109i
$443$	−2.25825	−	7.44444i	−0.107293	−	0.353696i	0.886811	−	0.462133i	$-0.152916\pi$
$443$	−2.25825	−	7.44444i	−0.107293	−	0.353696i	−0.994103	+	0.108437i	$0.965416\pi$
$444$	−2.53162	−	4.20570i	−0.120145	−	0.199594i
$445$	7.40390	+	6.07623i	0.350979	+	0.288041i
$446$	−8.62240	+	10.0149i	−0.408282	+	0.474218i
$447$			11.7109i			0.553907i
$448$	−6.07415	+	1.55816i	−0.286977	+	0.0736161i
$449$		−	26.9471i		−	1.27171i	−0.771808	−	0.635855i	$-0.780648\pi$
$449$		−	26.9471i		−	1.27171i	0.771808	−	0.635855i	$-0.219352\pi$
$450$	−0.570503	−	0.491180i	−0.0268938	−	0.0231544i
$451$	−2.61124	−	2.14299i	−0.122958	−	0.100909i
$452$	4.23462	−	17.0422i	0.199180	−	0.801598i
$453$	−3.20936	−	10.5798i	−0.150789	−	0.497085i
$454$	−0.209805	−	1.20239i	−0.00984665	−	0.0564309i
$455$	−0.116427	+	0.585320i	−0.00545820	+	0.0274402i
$456$	0.984030	+	35.9314i	0.0460814	+	1.68264i
$457$	5.41367	−	1.07685i	0.253241	−	0.0503727i	−0.0668373	−	0.997764i	$-0.521291\pi$
$457$	5.41367	−	1.07685i	0.253241	−	0.0503727i	0.320078	+	0.947391i	$0.396291\pi$
$458$	15.9285	+	7.04261i	0.744290	+	0.329080i
$459$	0.142578	−	1.44762i	0.00665499	−	0.0675693i
$460$	−0.851482	+	5.81596i	−0.0397006	+	0.271171i
$461$	−21.0793	−	6.39432i	−0.981759	−	0.297813i	−0.241697	−	0.970352i	$-0.577704\pi$
$461$	−21.0793	−	6.39432i	−0.981759	−	0.297813i	−0.740062	+	0.672539i	$0.765204\pi$
$462$	1.71443	−	1.34057i	0.0797626	−	0.0623688i
$463$	14.4972	+	6.00495i	0.673743	+	0.279074i	0.693209	−	0.720737i	$-0.256196\pi$
$463$	14.4972	+	6.00495i	0.673743	+	0.279074i	−0.0194655	+	0.999811i	$0.506196\pi$
$464$	0.160864	+	0.384244i	0.00746792	+	0.0178381i
$465$	−3.87431	+	1.60479i	−0.179667	+	0.0744204i
$466$	−2.93874	+	5.19905i	−0.136134	+	0.240841i
$467$	3.93889	+	7.36915i	0.182270	+	0.341004i	0.956418	−	0.292001i	$-0.0943212\pi$
$467$	3.93889	+	7.36915i	0.182270	+	0.341004i	−0.774148	+	0.633005i	$0.781821\pi$
$468$	−0.809513	+	0.0413031i	−0.0374198	+	0.00190924i
$469$	−5.09394	−	6.20699i	−0.235216	−	0.286612i
$470$	−12.5841	+	12.0038i	−0.580463	+	0.553693i
$471$	34.8410	+	23.2800i	1.60539	+	1.07269i
$472$	2.89024	+	5.06843i	0.133034	+	0.233293i
$473$	−0.828865	−	1.24048i	−0.0381113	−	0.0570375i
$474$	−32.8084	+	20.8192i	−1.50694	+	0.956255i
$475$	−3.18749	+	5.96337i	−0.146252	+	0.273618i
$476$	0.166523	+	0.462640i	0.00763255	+	0.0212051i
$477$	−4.25849	+	0.419425i	−0.194983	+	0.0192041i
$478$	−12.3112	−	24.4007i	−0.563101	−	1.11606i
$479$	−18.2342	+	18.2342i	−0.833140	+	0.833140i	−0.987945	−	0.154805i	$-0.950525\pi$
$479$	−18.2342	+	18.2342i	−0.833140	+	0.833140i	0.154805	+	0.987945i	$0.450525\pi$
$480$	0.210679	−	10.6297i	0.00961615	−	0.485176i
$481$	−0.703058	−	0.703058i	−0.0320567	−	0.0320567i
$482$	7.45979	−	22.6530i	0.339784	−	1.03182i
$483$	−0.424388	−	4.30888i	−0.0193103	−	0.196061i
$484$	−19.7956	−	0.934985i	−0.899800	−	0.0424993i
$485$	12.4470	+	6.65306i	0.565189	+	0.302100i
$486$	1.68785	−	7.54972i	0.0765625	−	0.342462i
$487$	29.8499	−	19.9450i	1.35263	−	0.903796i	0.353131	−	0.935574i	$-0.385117\pi$
$487$	29.8499	−	19.9450i	1.35263	−	0.903796i	0.999495	+	0.0317778i	$0.0101169\pi$
$488$	12.0484	+	6.02189i	0.545405	+	0.272598i
$489$	7.12791	−	10.6677i	0.322335	−	0.482409i
$490$	−9.02805	−	0.213087i	−0.407846	−	0.00962631i
$491$	−26.7759	+	21.9744i	−1.20838	+	0.991692i	−0.208474	+	0.978028i	$0.566850\pi$
$491$	−26.7759	+	21.9744i	−1.20838	+	0.991692i	−0.999907	+	0.0136646i	$0.995650\pi$
$492$	10.9787	−	5.21795i	0.494958	−	0.235244i
$493$	0.0288057	−	0.0153970i	0.00129734	−	0.000693445i
$494$	1.94844	+	7.01494i	0.0876643	+	0.315617i
$495$	0.212793	+	0.513728i	0.00956435	+	0.0230904i
$496$	−7.88701	−	4.17743i	−0.354137	−	0.187572i
$497$	−2.18368	+	5.27186i	−0.0979513	+	0.236475i
$498$	14.5079	+	1.77546i	0.650116	+	0.0795604i
$499$	−1.08121	+	3.56428i	−0.0484017	+	0.159559i	−0.977810	−	0.209495i	$-0.932818\pi$
$499$	−1.08121	+	3.56428i	−0.0484017	+	0.159559i	0.929408	+	0.369054i	$0.120318\pi$
$500$	1.02496	−	1.71740i	0.0458376	−	0.0768044i
$501$	−38.1630	−	3.75873i	−1.70500	−	0.167928i
$502$	−11.6369	+	4.50151i	−0.519382	+	0.200912i
$503$	8.30655	+	41.7599i	0.370371	+	1.86198i	0.493726	+	0.869618i	$0.335635\pi$
$503$	8.30655	+	41.7599i	0.370371	+	1.86198i	−0.123355	+	0.992363i	$0.539365\pi$
$504$	0.261846	+	1.15078i	0.0116636	+	0.0512597i
$505$	−4.92009	−	0.978666i	−0.218941	−	0.0435501i
$506$	2.49661	−	3.55204i	0.110988	−	0.157907i
$507$	22.3382	−	6.77623i	0.992075	−	0.300943i
$508$	−19.2162	+	2.88760i	−0.852583	+	0.128117i
$509$	8.07159	−	9.83526i	0.357767	−	0.435940i	−0.562759	−	0.826621i	$-0.690260\pi$
$509$	8.07159	−	9.83526i	0.357767	−	0.435940i	0.920526	+	0.390680i	$0.127760\pi$
$510$	−0.831322	+	0.0621122i	−0.0368116	+	0.00275037i
$511$	−0.713411			−0.0315595
$512$	17.7192	−	14.0724i	0.783084	−	0.621916i
$513$	−31.3603			−1.38459
$514$	−28.3140	+	2.11548i	−1.24888	+	0.0933096i
$515$	7.55759	−	9.20895i	0.333027	−	0.405795i
$516$	5.30899	−	0.797774i	0.233715	−	0.0351201i
$517$	12.2926	−	3.72891i	0.540626	−	0.163997i
$518$	−0.832463	+	1.18438i	−0.0365763	+	0.0520388i
$519$	−14.3692	−	2.85822i	−0.630739	−	0.125462i
$520$	−0.477775	−	2.09976i	−0.0209518	−	0.0920804i
$521$	−4.17139	−	20.9710i	−0.182752	−	0.918755i	−0.957928	−	0.287010i	$-0.907339\pi$
$521$	−4.17139	−	20.9710i	−0.182752	−	0.918755i	0.775176	−	0.631746i	$-0.217661\pi$
$522$	0.0731180	−	0.0282841i	0.00320029	−	0.00123796i
$523$	27.5765	+	2.71605i	1.20584	+	0.118765i	0.680900	−	0.732376i	$-0.261589\pi$
$523$	27.5765	+	2.71605i	1.20584	+	0.118765i	0.524937	+	0.851141i	$0.324089\pi$
$524$	−1.94556	+	3.25993i	−0.0849921	+	0.142411i
$525$	−0.427650	+	1.40977i	−0.0186642	+	0.0615275i
$526$	3.89001	+	0.476055i	0.169613	+	0.0207570i
$527$	−0.267807	+	0.646543i	−0.0116659	+	0.0281639i
$528$	−3.67566	+	6.93966i	−0.159962	+	0.302010i
$529$	5.49625	+	13.2691i	0.238967	+	0.576918i
$530$	−3.04241	−	10.9536i	−0.132154	−	0.475793i
$531$	0.968431	−	0.517637i	0.0420263	−	0.0224635i
$532$	9.57415	−	4.55040i	0.415092	−	0.197285i
$533$	1.90321	−	1.56192i	0.0824372	−	0.0676544i
$534$	25.4507	+	0.600708i	1.10136	+	0.0259952i
$535$	−5.16526	+	7.73036i	−0.223314	+	0.334213i
$536$	25.9170	+	12.9535i	1.11944	+	0.559507i
$537$	−15.9546	+	10.6605i	−0.688492	+	0.460036i
$538$	2.22967	−	9.97324i	0.0961277	−	0.429977i
$539$	5.88267	+	3.14435i	0.253384	+	0.135437i
$540$	9.26541	+	0.437623i	0.398720	+	0.0188323i
$541$	2.18097	+	22.1438i	0.0937673	+	0.952035i	0.920840	+	0.389940i	$0.127504\pi$
$541$	2.18097	+	22.1438i	0.0937673	+	0.952035i	−0.827073	+	0.562095i	$0.809996\pi$
$542$	8.13668	−	24.7085i	0.349500	−	1.06132i
$543$	−5.93024	−	5.93024i	−0.254491	−	0.254491i
$544$	−1.22946	−	1.27918i	−0.0527126	−	0.0548443i
$545$	2.85125	−	2.85125i	0.122134	−	0.122134i
$546$	0.714523	+	1.41618i	0.0305788	+	0.0606068i
$547$	36.6738	−	3.61205i	1.56806	−	0.154440i	0.723659	−	0.690158i	$-0.242459\pi$
$547$	36.6738	−	3.61205i	1.56806	−	0.154440i	0.844397	+	0.535717i	$0.179959\pi$
$548$	3.13326	+	8.70495i	0.133846	+	0.371857i
$549$	1.19500	−	2.23568i	0.0510011	−	0.0954164i
$550$	−1.24733	+	0.791515i	−0.0531863	+	0.0337503i
$551$	−0.391216	−	0.585496i	−0.0166664	−	0.0249430i
$552$	7.73920	+	13.5717i	0.329402	+	0.577650i
$553$	9.52794	+	6.36637i	0.405169	+	0.270725i
$554$	6.38898	−	6.09434i	0.271442	−	0.258924i
$555$	−1.55708	−	1.89730i	−0.0660942	−	0.0805360i
$556$	1.17005	−	0.0596984i	0.0496212	−	0.00253178i
$557$	−11.7479	−	21.9787i	−0.497773	−	0.931268i	−0.997866	−	0.0652960i	$-0.979201\pi$
$557$	−11.7479	−	21.9787i	−0.497773	−	0.931268i	0.500093	−	0.865972i	$-0.333299\pi$
$558$	−0.826550	+	1.46229i	−0.0349907	+	0.0619035i
$559$	1.00462	−	0.416126i	0.0424908	−	0.0176003i
$560$	−2.89218	+	1.21081i	−0.122217	+	0.0511662i
$561$	0.568883	+	0.235639i	0.0240183	+	0.00994869i
$562$	18.4696	−	14.4420i	0.779094	−	0.609197i
$563$	−28.1140	−	8.52830i	−1.18487	−	0.359425i	−0.364466	−	0.931217i	$-0.618749\pi$
$563$	−28.1140	−	8.52830i	−1.18487	−	0.359425i	−0.820399	+	0.571791i	$0.806249\pi$
$564$	−6.69610	+	45.7370i	−0.281957	+	1.92587i
$565$	0.860611	−	8.73793i	0.0362062	−	0.367608i
$566$	11.8326	+	5.23164i	0.497360	+	0.219902i
$567$	−7.92900	+	1.57718i	−0.332987	+	0.0662352i
$568$	−0.563678	−	20.5824i	−0.0236514	−	0.863620i
$569$	−6.62588	+	33.3106i	−0.277772	+	1.39645i	0.549896	+	0.835233i	$0.314667\pi$
$569$	−6.62588	+	33.3106i	−0.277772	+	1.39645i	−0.827668	+	0.561219i	$0.810333\pi$
$570$	3.08934	+	17.7049i	0.129398	+	0.741578i
$571$	5.00099	+	16.4860i	0.209285	+	0.689919i	0.997244	+	0.0741919i	$0.0236377\pi$
$571$	5.00099	+	16.4860i	0.209285	+	0.689919i	−0.787959	+	0.615727i	$0.788862\pi$
$572$	−0.383565	+	1.54365i	−0.0160377	+	0.0645434i
$573$	−26.4386	−	21.6976i	−1.10449	−	0.906431i
$574$	−2.71666	−	2.33893i	−0.113391	−	0.0976251i
$575$			2.93898i			0.122564i
$576$	−2.55619	−	3.40607i	−0.106508	−	0.141920i
$577$			17.3991i			0.724333i	0.932113	+	0.362166i	$0.117963\pi$
$577$			17.3991i			0.724333i	−0.932113	+	0.362166i	$0.882037\pi$
$578$	15.5954	−	18.1139i	0.648681	−	0.753441i
$579$	−11.5971	−	9.51749i	−0.481959	−	0.395533i
$580$	0.107414	+	0.178444i	0.00446014	+	0.00740949i
$581$	−1.25126	−	4.12484i	−0.0519109	−	0.171127i
$582$	36.9545	−	6.44820i	1.53181	−	0.267287i
$583$	−1.63817	+	8.23563i	−0.0678460	+	0.341085i
$584$	2.35044	−	1.04986i	0.0972618	−	0.0434436i
$585$	−0.397496	+	0.0790668i	−0.0164344	+	0.00326901i
$586$	0.375741	−	0.849825i	0.0155217	−	0.0351059i
$587$	−2.53489	+	25.7372i	−0.104626	+	1.06229i	0.789280	+	0.614034i	$0.210454\pi$
$587$	−2.53489	+	25.7372i	−0.104626	+	1.06229i	−0.893906	+	0.448255i	$0.852046\pi$
$588$	−19.2521	+	14.3348i	−0.793943	+	0.591158i
$589$	14.4376	+	4.37961i	0.594892	+	0.180458i
$590$	1.79699	+	2.29814i	0.0739807	+	0.0946130i
$591$	8.64248	+	3.57983i	0.355504	+	0.147255i
$592$	0.999721	−	5.12718i	0.0410883	−	0.210726i
$593$	−1.88512	+	0.780842i	−0.0774126	+	0.0320653i	−0.421054	−	0.907036i	$-0.638340\pi$
$593$	−1.88512	+	0.780842i	−0.0774126	+	0.0320653i	0.343641	+	0.939101i	$0.388340\pi$
$594$	−5.96449	−	3.37140i	−0.244726	−	0.138330i
$595$	0.115892	+	0.216819i	0.00475111	+	0.00888871i
$596$	−8.35155	+	9.24960i	−0.342093	+	0.378878i
$597$	−2.03663	−	2.48164i	−0.0833536	−	0.101567i
$598$	2.18417	+	2.28977i	0.0893175	+	0.0936357i
$599$	−12.9931	−	8.68173i	−0.530885	−	0.354726i	0.261056	−	0.965324i	$-0.415929\pi$
$599$	−12.9931	−	8.68173i	−0.530885	−	0.354726i	−0.791941	+	0.610598i	$0.790929\pi$
$600$	−0.665679	−	5.27403i	−0.0271762	−	0.215312i
$601$	7.86714	+	11.7740i	0.320908	+	0.480272i	0.956492	−	0.291760i	$-0.0942407\pi$
$601$	7.86714	+	11.7740i	0.320908	+	0.480272i	−0.635584	+	0.772032i	$0.719241\pi$
$602$	−0.848299	−	1.33681i	−0.0345741	−	0.0544844i
$603$	2.57052	−	4.80911i	0.104680	−	0.195842i
$604$	5.01010	−	10.6450i	0.203858	−	0.433138i
$605$	−9.86112	+	0.971236i	−0.400912	+	0.0394864i
$606$	−11.9041	+	6.00615i	−0.483572	+	0.243983i
$607$	−25.9388	+	25.9388i	−1.05282	+	1.05282i	−0.0543001	+	0.998525i	$0.517293\pi$
$607$	−25.9388	+	25.9388i	−1.05282	+	1.05282i	−0.998525	+	0.0543001i	$0.982707\pi$
$608$	−24.8470	+	29.0814i	−1.00768	+	1.17940i
$609$	−0.108484	−	0.108484i	−0.00439599	−	0.00439599i
$610$	6.39682	+	2.10652i	0.259000	+	0.0852905i
$611$	0.917698	+	9.31754i	0.0371261	+	0.376947i
$612$	−0.246991	+	0.224711i	−0.00998401	+	0.00908342i
$613$	30.6782	+	16.3978i	1.23908	+	0.662302i	0.955030	−	0.296508i	$-0.0958220\pi$
$613$	30.6782	+	16.3978i	1.23908	+	0.662302i	0.284049	+	0.958810i	$0.408322\pi$
$614$	14.5961	+	3.26317i	0.589051	+	0.131691i
$615$	5.05351	−	3.37665i	0.203777	−	0.136159i
$616$	2.31012	+	0.163819i	0.0930774	+	0.00660047i
$617$	0.547638	−	0.819599i	0.0220471	−	0.0329958i	−0.820282	−	0.571959i	$-0.806184\pi$
$617$	0.547638	−	0.819599i	0.0220471	−	0.0329958i	0.842329	+	0.538963i	$0.181184\pi$
$618$	0.747158	−	31.6555i	0.0300551	−	1.27337i
$619$	−31.8154	+	26.1102i	−1.27877	+	1.04946i	−0.282853	+	0.959163i	$0.591281\pi$
$619$	−31.8154	+	26.1102i	−1.27877	+	1.04946i	−0.995915	+	0.0902947i	$0.971219\pi$
$620$	−4.20448	−	1.49543i	−0.168856	−	0.0600578i
$621$	−12.0211	+	6.42543i	−0.482391	+	0.257844i
$622$	11.6634	−	3.23958i	0.467661	−	0.129895i
$623$	−2.87309	−	6.93626i	−0.115108	−	0.277895i
$624$	−4.43816	−	3.61431i	−0.177669	−	0.144688i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	−3.03448	+	24.7958i	−0.121282	+	0.991041i
$627$	3.85355	−	12.7034i	0.153896	−	0.507327i
$628$	10.9164	+	43.2338i	0.435612	+	1.72521i
$629$	−0.407622	−	0.0401473i	−0.0162530	−	0.00160078i
$630$	0.212893	+	0.550355i	0.00848186	+	0.0219267i
$631$	5.58094	+	28.0573i	0.222174	+	1.11694i	0.917343	+	0.398097i	$0.130329\pi$
$631$	5.58094	+	28.0573i	0.222174	+	1.11694i	−0.695170	+	0.718846i	$0.744671\pi$
$632$	−40.7600	−	6.95352i	−1.62134	−	0.276596i
$633$	−36.6976	−	7.29960i	−1.45860	−	0.290133i
$634$	−23.9603	−	16.8409i	−0.951585	−	0.668837i
$635$	−9.29763	+	2.82040i	−0.368965	+	0.111924i
$636$	−24.3038	−	17.9538i	−0.963708	−	0.711914i
$637$	−3.08421	+	3.75812i	−0.122201	+	0.148902i
$638$	−0.0114624	−	0.153415i	−0.000453799	−	0.00607374i
$639$	−3.87515			−0.153298
$640$	7.74687	−	8.24536i	0.306222	−	0.325927i
$641$	−45.3401			−1.79083			−0.895414	−	0.445235i	$-0.853120\pi$
$641$	−45.3401			−1.79083			−0.895414	+	0.445235i	$0.853120\pi$
$642$	1.84118	+	24.6428i	0.0726657	+	0.972573i
$643$	−1.00964	+	1.23024i	−0.0398161	+	0.0485161i	−0.792538	−	0.609823i	$-0.791241\pi$
$643$	−1.00964	+	1.23024i	−0.0398161	+	0.0485161i	0.752722	+	0.658339i	$0.228741\pi$
$644$	2.73766	−	3.70592i	0.107879	−	0.146034i
$645$	2.56871	−	0.779210i	0.101143	−	0.0306814i
$646$	2.45376	+	1.72466i	0.0965418	+	0.0678560i
$647$	−36.3505	−	7.23057i	−1.42909	−	0.284263i	−0.580906	−	0.813971i	$-0.697302\pi$
$647$	−36.3505	−	7.23057i	−1.42909	−	0.284263i	−0.848180	+	0.529708i	$0.822302\pi$
$648$	23.8022	−	16.8646i	0.935041	−	0.662505i
$649$	−0.420384	−	2.11341i	−0.0165015	−	0.0829586i
$650$	−0.388453	−	1.00420i	−0.0152364	−	0.0393879i
$651$	3.27128	+	0.322192i	0.128211	+	0.0126277i
$652$	13.2374	−	3.34240i	0.518416	−	0.130899i
$653$	−10.0425	+	33.1055i	−0.392992	+	1.29552i	0.507877	+	0.861429i	$0.330430\pi$
$653$	−10.0425	+	33.1055i	−0.392992	+	1.29552i	−0.900869	+	0.434091i	$0.857070\pi$
$654$	1.30189	−	10.6382i	0.0509079	−	0.415986i
$655$	−0.726401	+	1.75369i	−0.0283828	+	0.0685222i
$656$	12.3924	+	3.70809i	0.483843	+	0.144777i
$657$	−0.185404	−	0.447605i	−0.00723330	−	0.0174627i
$658$	13.1348	−	3.64827i	0.512049	−	0.142224i
$659$	−22.8935	+	12.2368i	−0.891802	+	0.476678i	−0.852607	−	0.522553i	$-0.824980\pi$
$659$	−22.8935	+	12.2368i	−0.891802	+	0.476678i	−0.0391957	+	0.999232i	$0.512480\pi$
$660$	−1.31580	+	3.69946i	−0.0512176	+	0.144001i
$661$	−20.6489	+	16.9461i	−0.803148	+	0.659127i	−0.943647	−	0.330954i	$-0.892629\pi$
$661$	−20.6489	+	16.9461i	−0.803148	+	0.659127i	0.140499	+	0.990081i	$0.455129\pi$
$662$	0.0654250	−	2.77192i	0.00254281	−	0.107734i
$663$	−0.249337	+	0.373160i	−0.00968346	+	0.0144923i
$664$	10.1926	+	11.7485i	0.395550	+	0.455932i
$665$	4.40699	−	2.94466i	0.170896	−	0.114189i
$666$	−0.959443	−	0.214498i	−0.0371777	−	0.00831161i
$667$	−0.269925	−	0.144278i	−0.0104515	−	0.00558645i
$668$	−27.4617	−	30.1844i	−1.06252	−	1.16787i
$669$	1.72145	+	17.4781i	0.0665549	+	0.675744i
$670$	13.7600	+	4.53128i	0.531596	+	0.175059i
$671$	−3.51751	−	3.51751i	−0.135792	−	0.135792i
$672$	−4.07336	+	7.27040i	−0.157133	+	0.280462i
$673$	−34.3309	+	34.3309i	−1.32336	+	1.32336i	−0.412323	+	0.911038i	$0.635282\pi$
$673$	−34.3309	+	34.3309i	−1.32336	+	1.32336i	−0.911038	+	0.412323i	$0.864718\pi$
$674$	34.3499	−	17.3310i	1.32311	−	0.667565i
$675$	4.61554	−	0.454591i	0.177652	−	0.0174972i
$676$	22.4758	+	10.5783i	0.864452	+	0.406857i
$677$	6.71088	−	12.5552i	0.257920	−	0.482534i	−0.719318	−	0.694681i	$-0.755546\pi$
$677$	6.71088	−	12.5552i	0.257920	−	0.482534i	0.977238	+	0.212147i	$0.0680455\pi$
$678$	−12.5040	−	19.7048i	−0.480214	−	0.756757i
$679$	−6.14622	−	9.19847i	−0.235870	−	0.353005i
$680$	−0.700896	−	0.543793i	−0.0268781	−	0.0208535i
$681$	−1.34871	−	0.901181i	−0.0516828	−	0.0345333i
$682$	2.27509	+	2.38509i	0.0871178	+	0.0913297i
$683$	1.61419	+	1.96690i	0.0617653	+	0.0752612i	0.802977	−	0.596011i	$-0.203248\pi$
$683$	1.61419	+	1.96690i	0.0617653	+	0.0752612i	−0.741211	+	0.671272i	$0.765748\pi$
$684$	5.34316	+	4.82439i	0.204301	+	0.184465i
$685$	2.18060	+	4.07962i	0.0833166	+	0.155874i
$686$	12.9176	+	7.30160i	0.493196	+	0.278776i
$687$	21.3834	−	8.85731i	0.815829	−	0.337928i
$688$	4.76211	+	3.15596i	0.181554	+	0.120320i
$689$	−5.65430	−	2.34209i	−0.215412	−	0.0892264i
$690$	4.81178	+	6.15373i	0.183181	+	0.234268i
$691$	21.8575	+	6.63039i	0.831497	+	0.252232i	0.677206	−	0.735793i	$-0.263191\pi$
$691$	21.8575	+	6.63039i	0.831497	+	0.252232i	0.154291	+	0.988025i	$0.450691\pi$
$692$	−9.31089	−	12.5048i	−0.353947	−	0.475361i
$693$	0.0427223	−	0.433767i	0.00162289	−	0.0164774i
$694$	−17.3818	+	39.3130i	−0.659804	+	1.49230i
$695$	0.574530	−	0.114281i	0.0217932	−	0.00433493i
$696$	0.517062	+	0.197770i	0.0195992	+	0.00749645i
$697$	0.197872	−	0.994772i	0.00749495	−	0.0376797i
$698$	2.67588	−	0.466915i	0.101283	−	0.0176730i
$699$	2.30392	+	7.59502i	0.0871424	+	0.287270i
$700$	−1.34314	+	0.808502i	−0.0507659	+	0.0305585i
$701$	−1.76333	−	1.44713i	−0.0666000	−	0.0546572i	0.600504	−	0.799621i	$-0.294966\pi$
$701$	−1.76333	−	1.44713i	−0.0666000	−	0.0546572i	−0.667104	+	0.744964i	$0.732466\pi$
$702$	3.25815	−	3.78432i	0.122971	−	0.142830i
$703$			8.83045i			0.333047i
$704$	−7.85210	+	2.85987i	−0.295937	+	0.107785i
$705$			23.1123i			0.870459i
$706$	−18.8908	−	16.2642i	−0.710963	−	0.612110i
$707$	3.03962	+	2.49455i	0.114316	+	0.0938171i
$708$	7.52517	+	1.86984i	0.282813	+	0.0702730i
$709$	12.2403	+	40.3509i	0.459695	+	1.51541i	0.814328	+	0.580405i	$0.197106\pi$
$709$	12.2403	+	40.3509i	0.459695	+	1.51541i	−0.354633	+	0.935006i	$0.615394\pi$
$710$	−1.76965	−	10.1418i	−0.0664139	−	0.380616i
$711$	−1.51820	+	7.63249i	−0.0569368	+	0.286241i
$712$	19.6733	+	18.6244i	0.737287	+	0.697980i
$713$	6.43161	−	1.27933i	0.240866	−	0.0479112i
$714$	0.597641	+	0.264240i	0.0223661	+	0.00988894i
$715$	−0.0779528	+	0.791468i	−0.00291527	+	0.0295992i
$716$	−20.2039	−	2.95794i	−0.755054	−	0.110543i
$717$	−34.7575	−	10.5436i	−1.29804	−	0.393757i
$718$	25.6733	−	20.0747i	0.958120	−	0.749182i
$719$	6.54744	+	2.71204i	0.244178	+	0.101142i	0.501416	−	0.865206i	$-0.332812\pi$
$719$	6.54744	+	2.71204i	0.244178	+	0.101142i	−0.257238	+	0.966348i	$0.582812\pi$
$720$	−1.51131	−	1.49993i	−0.0563233	−	0.0558990i
$721$	−8.62729	+	3.57354i	−0.321297	+	0.133086i
$722$	18.5957	−	32.8985i	0.692061	−	1.22436i
$723$	−14.9411	−	27.9529i	−0.555667	−	1.03958i
$724$	−0.454759	−	8.91297i	−0.0169010	−	0.331248i
$725$	0.0660655	+	0.0805010i	0.00245361	+	0.00298973i
$726$	−19.0574	+	18.1785i	−0.707286	+	0.674668i
$727$	−17.3808	−	11.6135i	−0.644618	−	0.430720i	0.189822	−	0.981818i	$-0.439209\pi$
$727$	−17.3808	−	11.6135i	−0.644618	−	0.430720i	−0.834440	+	0.551099i	$0.814209\pi$
$728$	−0.445587	+	1.62809i	−0.0165146	+	0.0603412i
$729$	11.4779	+	17.1780i	0.425109	+	0.636221i
$730$	1.08678	−	0.689637i	0.0402236	−	0.0255246i
$731$	0.211164	−	0.395060i	0.00781018	−	0.0146118i
$732$	16.8427	−	6.06236i	0.622524	−	0.224071i
$733$	39.9244	−	3.93221i	1.47464	−	0.145240i	0.671490	−	0.741014i	$-0.265655\pi$
$733$	39.9244	−	3.93221i	1.47464	−	0.145240i	0.803152	+	0.595774i	$0.203155\pi$
$734$	7.29804	+	14.4647i	0.269376	+	0.533900i
$735$	−8.48624	+	8.48624i	−0.313020	+	0.313020i
$736$	−3.56593	+	16.2385i	−0.131442	+	0.598558i
$737$	−7.56643	−	7.56643i	−0.278713	−	0.278713i
$738$	0.761464	−	2.31232i	0.0280299	−	0.0851177i
$739$	−2.57342	−	26.1284i	−0.0946648	−	0.961148i	−0.918792	−	0.394743i	$-0.870834\pi$
$739$	−2.57342	−	26.1284i	−0.0946648	−	0.961148i	0.824127	−	0.566405i	$-0.191666\pi$
$740$	0.123226	−	2.60896i	0.00452988	−	0.0959072i
$741$	8.53310	+	4.56104i	0.313471	+	0.167554i
$742$	−1.94420	+	8.69635i	−0.0713737	+	0.319253i
$743$	20.9217	−	13.9794i	0.767543	−	0.512856i	−0.109080	−	0.994033i	$-0.534791\pi$
$743$	20.9217	−	13.9794i	0.767543	−	0.512856i	0.876624	+	0.481177i	$0.159791\pi$
$744$	−11.2518	+	3.75253i	−0.412512	+	0.137574i
$745$	−3.46178	+	5.18092i	−0.126830	+	0.189814i
$746$	−31.9659	−	0.754485i	−1.17035	−	0.0276237i
$747$	2.26281	−	1.85704i	0.0827918	−	0.0679454i
$748$	0.281275	+	0.591809i	0.0102844	+	0.0216387i
$749$	6.42713	−	3.43537i	0.234842	−	0.125526i
$750$	−0.711328	−	2.56099i	−0.0259740	−	0.0935140i
$751$	1.06759	+	2.57738i	0.0389568	+	0.0940499i	0.942160	−	0.335162i	$-0.108791\pi$
$751$	1.06759	+	2.57738i	0.0389568	+	0.0940499i	−0.903204	+	0.429212i	$0.858791\pi$
$752$	−37.9058	+	31.3491i	−1.38228	+	1.14318i
$753$	−6.34562	+	15.3197i	−0.231247	+	0.558280i
$754$	0.111298	+	0.0136205i	0.00405324	+	0.000496030i
$755$	1.70761	−	5.62923i	0.0621463	−	0.204869i
$756$	−6.24344	−	3.72615i	−0.227072	−	0.135519i
$757$	38.2975	+	3.77197i	1.39195	+	0.137095i	0.766034	−	0.642800i	$-0.222227\pi$
$757$	38.2975	+	3.77197i	1.39195	+	0.137095i	0.625911	+	0.779894i	$0.284727\pi$
$758$	38.9694	−	15.0745i	1.41543	−	0.547530i
$759$	−1.12566	−	5.65907i	−0.0408589	−	0.205411i
$760$	−10.1861	+	16.1870i	−0.369488	+	0.587163i
$761$	−15.1387	−	3.01128i	−0.548779	−	0.109159i	−0.0870894	−	0.996201i	$-0.527757\pi$
$761$	−15.1387	−	3.01128i	−0.548779	−	0.109159i	−0.461690	+	0.887042i	$0.652757\pi$
$762$	−14.8500	+	21.1278i	−0.537959	+	0.765379i
$763$	−3.02461	+	0.917507i	−0.109498	+	0.0332160i
$764$	−5.40845	−	35.9919i	−0.195671	−	1.30214i
$765$	−0.105917	+	0.129060i	−0.00382943	+	0.00466618i
$766$	39.6079	−	2.95930i	1.43109	−	0.106924i
$767$	1.57055			0.0567091
$768$	2.72110	−	29.9478i	0.0981892	−	1.08065i
$769$	−47.8398			−1.72515			−0.862574	−	0.505931i	$-0.831149\pi$
$769$	−47.8398			−1.72515			−0.862574	+	0.505931i	$0.831149\pi$
$770$	1.15474	−	0.0862765i	0.0416140	−	0.00310919i
$771$	−23.9377	+	29.1682i	−0.862097	+	1.05047i
$772$	−2.37237	−	15.7876i	−0.0853836	−	0.568206i
$773$	−2.73332	+	0.829144i	−0.0983107	+	0.0298222i	−0.339057	−	0.940766i	$-0.610108\pi$
$773$	−2.73332	+	0.829144i	−0.0983107	+	0.0298222i	0.240746	+	0.970588i	$0.422608\pi$
$774$	0.618277	−	0.879651i	0.0222235	−	0.0316184i
$775$	−2.18838	−	0.435296i	−0.0786090	−	0.0156363i
$776$	33.7862	+	21.2609i	1.21285	+	0.763220i
$777$	0.375337	+	1.88695i	0.0134651	+	0.0676938i
$778$	21.0715	−	8.15107i	0.755450	−	0.292230i
$779$	−21.7612	−	2.14329i	−0.779674	−	0.0767912i
$780$	−2.45746	−	1.46664i	−0.0879911	−	0.0525140i
$781$	−2.20741	+	7.27686i	−0.0789874	+	0.260386i
$782$	1.29395	+	0.158352i	0.0462715	+	0.00566264i
$783$	−0.184831	+	0.446221i	−0.00660531	+	0.0159466i
$784$	−25.4286	−	2.40745i	−0.908164	−	0.0859805i
$785$	8.53205	+	20.5982i	0.304522	+	0.735181i
$786$	1.35023	+	4.86121i	0.0481610	+	0.173394i
$787$	2.63599	−	1.40897i	0.0939629	−	0.0502242i	−0.423746	−	0.905781i	$-0.639285\pi$
$787$	2.63599	−	1.40897i	0.0939629	−	0.0502242i	0.517709	+	0.855557i	$0.326785\pi$
$788$	4.27314	+	8.99077i	0.152224	+	0.320283i
$789$	4.02605	−	3.30410i	0.143331	−	0.117629i
$790$	−20.6687	−	0.487839i	−0.735358	−	0.0173565i
$791$	−3.82365	+	5.72250i	−0.135953	+	0.203469i
$792$	0.497580	+	1.49198i	0.0176807	+	0.0530151i
$793$	3.01465	−	2.01433i	0.107053	−	0.0715308i
$794$	−5.17948	+	23.1677i	−0.183813	+	0.822191i
$795$	−13.3241	−	7.12189i	−0.472557	−	0.252587i
$796$	0.161178	−	3.41247i	0.00571279	−	0.120952i
$797$	−0.687880	−	6.98417i	−0.0243660	−	0.247392i	−0.999650	−	0.0264389i	$-0.991583\pi$
$797$	−0.687880	−	6.98417i	−0.0243660	−	0.247392i	0.975284	−	0.220953i	$-0.0709167\pi$
$798$	4.40642	−	13.3809i	0.155986	−	0.473678i
$799$	2.72729	+	2.72729i	0.0964845	+	0.0964845i
$800$	3.23537	−	4.64030i	0.114388	−	0.164059i
$801$	3.60524	−	3.60524i	0.127385	−	0.127385i
$802$	−21.5237	−	42.6598i	−0.760029	−	1.50637i
$803$	−0.946137	+	0.0931864i	−0.0333885	+	0.00328848i
$804$	36.2299	−	13.0406i	1.27773	−	0.459906i
$805$	1.08597	−	2.03171i	0.0382754	−	0.0716082i
$806$	−2.02848	+	1.28721i	−0.0714501	+	0.0453399i
$807$	−7.54538	−	11.2925i	−0.265610	−	0.397513i
$808$	−13.6854	−	3.74552i	−0.481452	−	0.131767i
$809$	2.91228	+	1.94592i	0.102390	+	0.0684150i	0.605711	−	0.795685i	$-0.292889\pi$
$809$	2.91228	+	1.94592i	0.102390	+	0.0684150i	−0.503321	+	0.864100i	$0.667889\pi$
$810$	10.5541	−	10.0674i	0.370833	−	0.353731i
$811$	33.5234	+	40.8484i	1.17717	+	1.43438i	0.876996	+	0.480497i	$0.159544\pi$
$811$	33.5234	+	40.8484i	1.17717	+	1.43438i	0.300171	+	0.953885i	$0.402956\pi$
$812$	−0.00831906	−	0.163048i	−0.000291942	−	0.00572186i
$813$	−16.2969	−	30.4893i	−0.571556	−	1.06931i
$814$	−0.949320	+	1.67948i	−0.0332736	+	0.0588659i
$815$	6.30680	−	2.61236i	0.220917	−	0.0915070i
$816$	−2.35787	+	0.00891535i	−0.0825420	+	0.000312100i
$817$	−8.92231	−	3.69574i	−0.312152	−	0.129298i
$818$	17.5462	−	13.7199i	0.613489	−	0.479705i
$819$	0.304003	+	0.0922183i	0.0106227	+	0.00322237i
$820$	6.39943	+	0.936904i	0.223478	+	0.0327181i
$821$	2.09870	−	21.3085i	0.0732452	−	0.743671i	−0.886487	−	0.462754i	$-0.846861\pi$
$821$	2.09870	−	21.3085i	0.0732452	−	0.743671i	0.959732	−	0.280917i	$-0.0906386\pi$
$822$	11.2451	+	4.97189i	0.392218	+	0.173415i
$823$	41.1089	−	8.17706i	1.43297	−	0.285034i	0.583257	−	0.812288i	$-0.301778\pi$
$823$	41.1089	−	8.17706i	1.43297	−	0.285034i	0.849708	+	0.527253i	$0.176778\pi$
$824$	23.1650	−	24.4695i	0.806991	−	0.852437i
$825$	−0.383010	+	1.92552i	−0.0133347	+	0.0670381i
$826$	−0.393073	−	2.25269i	−0.0136768	−	0.0783812i
$827$	7.22459	+	23.8163i	0.251223	+	0.828173i	0.988321	+	0.152386i	$0.0486958\pi$
$827$	7.22459	+	23.8163i	0.251223	+	0.828173i	−0.737098	+	0.675786i	$0.763804\pi$
$828$	3.03662	+	0.754536i	0.105530	+	0.0262220i
$829$	−37.2335	−	30.5567i	−1.29317	−	1.06128i	−0.994259	−	0.106999i	$-0.965876\pi$
$829$	−37.2335	−	30.5567i	−1.29317	−	1.06128i	−0.298913	−	0.954280i	$-0.596624\pi$
$830$	5.89350	+	5.07406i	0.204566	+	0.176123i
$831$		−	11.7341i		−	0.407053i
$832$	−0.927864	−	6.01972i	−0.0321679	−	0.208696i
$833$			2.00278i			0.0693922i
$834$	1.01586	−	1.17992i	0.0351765	−	0.0408574i
$835$	−15.7723	−	12.9440i	−0.545822	−	0.447944i
$836$	12.1030	−	7.28540i	0.418591	−	0.251971i
$837$	−3.00394	−	9.90268i	−0.103832	−	0.342287i
$838$	18.1524	−	3.16743i	0.627066	−	0.109417i
$839$	−9.95144	+	50.0293i	−0.343562	+	1.72720i	0.293121	+	0.956075i	$0.405306\pi$
$839$	−9.95144	+	50.0293i	−0.343562	+	1.72720i	−0.636682	+	0.771126i	$0.719694\pi$
$840$	−1.48860	+	3.89189i	−0.0513617	+	0.134283i
$841$	28.4321	−	5.65550i	0.980418	−	0.195017i
$842$	−14.7507	+	33.3621i	−0.508343	+	1.14973i
$843$	3.05407	−	31.0085i	0.105188	−	1.06799i
$844$	−23.7791	−	31.9360i	−0.818510	−	1.09928i
$845$	11.8855	+	3.60544i	0.408875	+	0.124031i
$846$	5.70250	+	7.29286i	0.196056	+	0.250734i
$847$	7.17583	+	2.97233i	0.246565	+	0.102130i
$848$	−6.39218	−	31.5125i	−0.219508	−	1.08214i
$849$	15.8848	−	6.57970i	0.545165	−	0.225815i
$850$	−0.386138	−	0.218263i	−0.0132444	−	0.00748635i
$851$	1.80927	+	3.38491i	0.0620211	+	0.116033i
$852$	−20.3099	−	18.3380i	−0.695804	−	0.628248i
$853$	28.3616	+	34.5587i	0.971083	+	1.18327i	0.983050	+	0.183340i	$0.0586908\pi$
$853$	28.3616	+	34.5587i	0.971083	+	1.18327i	−0.0119666	+	0.999928i	$0.503809\pi$
$854$	−3.64373	−	3.81989i	−0.124686	−	0.130714i
$855$	2.99283	+	1.99974i	0.102353	+	0.0683898i
$856$	−16.1196	+	20.7766i	−0.550956	+	0.710128i
$857$	13.9658	+	20.9012i	0.477061	+	0.713973i	0.989465	−	0.144772i	$-0.0462448\pi$
$857$	13.9658	+	20.9012i	0.477061	+	0.713973i	−0.512404	+	0.858745i	$0.671245\pi$
$858$	1.13259	+	1.78483i	0.0386661	+	0.0609329i
$859$	14.3890	−	26.9200i	0.490947	−	0.918497i	−0.507438	−	0.861688i	$-0.669407\pi$
$859$	14.3890	−	26.9200i	0.490947	−	0.918497i	0.998385	−	0.0568089i	$-0.0180926\pi$
$860$	2.58453	+	1.21642i	0.0881316	+	0.0414794i
$861$	−4.74116	+	0.466963i	−0.161578	+	0.0159141i
$862$	−37.9337	+	19.1392i	−1.29203	+	0.651884i
$863$	7.58435	−	7.58435i	0.258174	−	0.258174i	−0.566137	−	0.824311i	$-0.691563\pi$
$863$	7.58435	−	7.58435i	0.258174	−	0.258174i	0.824311	+	0.566137i	$0.191563\pi$
$864$	26.0533	+	3.08844i	0.886353	+	0.105071i
$865$	−5.51206	−	5.51206i	−0.187416	−	0.187416i
$866$	−45.3820	−	14.9446i	−1.54214	−	0.507839i
$867$	−3.11358	−	31.6128i	−0.105743	−	1.07363i
$868$	2.35397	+	2.58736i	0.0798991	+	0.0878208i
$869$	13.4677	+	7.19863i	0.456860	+	0.244197i
$870$	0.270128	+	0.0603912i	0.00915821	+	0.00204745i
$871$	6.48474	−	4.33296i	0.219727	−	0.146817i
$872$	8.61482	−	7.47390i	0.291735	−	0.253098i
$873$	4.17395	−	6.24676i	0.141267	−	0.211421i
$874$	0.663157	−	28.0965i	0.0224316	−	0.950379i
$875$	−0.605926	+	0.497271i	−0.0204840	+	0.0168108i
$876$	1.14644	−	3.22329i	0.0387347	−	0.108905i
$877$	−7.06573	+	3.77671i	−0.238593	+	0.127531i	−0.586361	−	0.810050i	$-0.699440\pi$
$877$	−7.06573	+	3.77671i	−0.238593	+	0.127531i	0.347768	+	0.937581i	$0.386940\pi$
$878$	−6.67737	+	1.85468i	−0.225350	+	0.0625923i
$879$	−0.472560	−	1.14086i	−0.0159390	−	0.0384802i
$880$	−3.67750	+	1.98358i	−0.123968	+	0.0668664i
$881$	−18.2124	+	43.9686i	−0.613591	+	1.48134i	0.245438	+	0.969412i	$0.421068\pi$
$881$	−18.2124	+	43.9686i	−0.613591	+	1.48134i	−0.859029	+	0.511927i	$0.828932\pi$
$882$	−0.583938	+	4.77156i	−0.0196622	+	0.160667i
$883$	16.9013	−	55.7163i	0.568776	−	1.87500i	0.0924843	−	0.995714i	$-0.470519\pi$
$883$	16.9013	−	55.7163i	0.568776	−	1.87500i	0.476291	−	0.879288i	$-0.341981\pi$
$884$	−0.463049	+	0.116919i	−0.0155740	+	0.00393240i
$885$	3.85833	+	0.380012i	0.129696	+	0.0127740i
$886$	−3.96918	−	10.2608i	−0.133347	−	0.344719i
$887$	−2.91498	−	14.6546i	−0.0978755	−	0.492053i	−0.998364	−	0.0571740i	$-0.981791\pi$
$887$	−2.91498	−	14.6546i	−0.0978755	−	0.492053i	0.900489	−	0.434879i	$-0.143209\pi$
$888$	−4.01345	−	5.66447i	−0.134682	−	0.190087i
$889$	7.46957	+	1.48579i	0.250521	+	0.0498318i
$890$	11.0818	+	7.78906i	0.371464	+	0.261090i
$891$	−10.3095	+	3.12737i	−0.345383	+	0.104771i
$892$	−11.1048	+	15.0323i	−0.371815	+	0.503320i
$893$	52.7513	−	64.2776i	1.76525	−	2.15097i
$894$	1.23397	+	16.5157i	0.0412701	+	0.552367i
$895$	−10.2096			−0.341270
$896$	−8.40209	+	2.83747i	−0.280694	+	0.0947934i
$897$	4.20544			0.140416
$898$	−2.83939	−	38.0030i	−0.0947516	−	1.26818i
$899$	0.147409	−	0.179618i	0.00491636	−	0.00599060i
$900$	−0.856326	−	0.632589i	−0.0285442	−	0.0210863i
$901$	−2.41266	+	0.731873i	−0.0803774	+	0.0243822i
$902$	−3.90839	−	2.74707i	−0.130135	−	0.0914675i
$903$	−2.06366	−	0.410488i	−0.0686744	−	0.0136602i
$904$	4.17630	−	24.4805i	0.138902	−	0.814210i
$905$	−0.870548	−	4.37654i	−0.0289380	−	0.145481i
$906$	−5.64090	−	14.5824i	−0.187406	−	0.484468i
$907$	12.1175	+	1.19347i	0.402356	+	0.0396286i	0.297172	−	0.954824i	$-0.403957\pi$
$907$	12.1175	+	1.19347i	0.402356	+	0.0396286i	0.105185	+	0.994453i	$0.466457\pi$
$908$	−0.422579	−	1.67360i	−0.0140238	−	0.0555404i
$909$	−0.775170	+	2.55539i	−0.0257108	+	0.0847570i
$910$	−0.102521	+	0.837734i	−0.00339853	+	0.0277706i
$911$	21.3369	−	51.5119i	0.706924	−	1.70667i	−0.000623185	−	1.00000i	$-0.500198\pi$
$911$	21.3369	−	51.5119i	0.706924	−	1.70667i	0.707547	−	0.706666i	$-0.249802\pi$
$912$	5.17382	+	50.5697i	0.171322	+	1.67453i
$913$	−2.19823	−	5.30699i	−0.0727507	−	0.175636i
$914$	7.52134	−	2.08909i	0.248784	−	0.0691010i
$915$	7.89343	−	4.21913i	0.260949	−	0.139480i
$916$	23.2058	+	8.25370i	0.766740	+	0.272710i
$917$	1.15016	−	0.943908i	0.0379815	−	0.0311706i
$918$	0.0485411	−	2.05658i	0.00160209	−	0.0678773i
$919$	−9.39850	+	14.0659i	−0.310028	+	0.463990i	−0.953463	−	0.301511i	$-0.902509\pi$
$919$	−9.39850	+	14.0659i	−0.310028	+	0.463990i	0.643435	+	0.765501i	$0.277509\pi$
$920$	−0.588008	+	8.29187i	−0.0193860	+	0.273375i
$921$	16.5268	−	11.0429i	0.544577	−	0.363875i
$922$	−30.4015	−	6.79670i	−1.00122	−	0.223837i
$923$	−4.88798	−	2.61268i	−0.160890	−	0.0859974i
$924$	2.27658	−	2.07122i	0.0748940	−	0.0681383i
$925$	−0.128004	−	1.29965i	−0.00420874	−	0.0427321i
$926$	21.0779	+	6.94111i	0.692663	+	0.228099i
$927$	−4.48419	−	4.48419i	−0.147280	−	0.147280i
$928$	0.267351	+	0.524943i	0.00877623	+	0.0172321i
$929$	28.8575	−	28.8575i	0.946785	−	0.946785i	−0.0518692	−	0.998654i	$-0.516518\pi$
$929$	28.8575	−	28.8575i	0.946785	−	0.946785i	0.998654	+	0.0518692i	$0.0165179\pi$
$930$	−5.29478	+	2.67144i	−0.173623	+	0.0876001i
$931$	42.9700	−	4.23218i	1.40829	−	0.138704i
$932$	−3.59663	+	7.64178i	−0.117812	+	0.250315i
$933$	7.58343	−	14.1876i	0.248271	−	0.464481i
$934$	6.33143	+	9.97755i	0.207171	+	0.326475i
$935$	0.182019	+	0.272411i	0.00595266	+	0.00890878i
$936$	−1.13729	+	0.143547i	−0.0371735	+	0.00469197i
$937$	−44.5483	−	29.7662i	−1.45533	−	0.972421i	−0.996473	−	0.0839110i	$-0.973259\pi$
$937$	−44.5483	−	29.7662i	−1.45533	−	0.972421i	−0.458857	−	0.888510i	$-0.651741\pi$
$938$	−7.83792	−	8.21686i	−0.255917	−	0.268290i
$939$	21.0611	+	25.6630i	0.687302	+	0.837480i
$940$	−16.4824	+	18.2547i	−0.537595	+	0.595403i
$941$	13.5167	+	25.2880i	0.440632	+	0.824365i	0.999990	−	0.00456143i	$-0.00145195\pi$
$941$	13.5167	+	25.2880i	0.440632	+	0.824365i	−0.559357	+	0.828927i	$0.688952\pi$
$942$	51.5886	+	29.1602i	1.68085	+	0.950091i
$943$	−8.78069	+	3.63708i	−0.285938	+	0.118440i
$944$	4.61012	+	6.84337i	0.150047	+	0.222733i
$945$	−3.35868	−	1.39121i	−0.109258	−	0.0452561i
$946$	−1.29964	−	1.66210i	−0.0422550	−	0.0540394i
$947$	−15.1410	−	4.59297i	−0.492016	−	0.149252i	0.0345202	−	0.999404i	$-0.489010\pi$
$947$	−15.1410	−	4.59297i	−0.492016	−	0.149252i	−0.526537	+	0.850152i	$0.676510\pi$
$948$	−44.0754	+	32.8179i	−1.43150	+	1.06588i
$949$	0.0679192	−	0.689596i	0.00220475	−	0.0223852i
$950$	−3.86690	+	8.74590i	−0.125459	+	0.283754i
$951$	−38.1733	+	7.59314i	−1.23785	+	0.246224i
$952$	0.283592	+	0.634907i	0.00919127	+	0.0205775i
$953$	−11.8067	+	59.3562i	−0.382456	+	1.92273i	0.00297042	+	0.999996i	$0.499054\pi$
$953$	−11.8067	+	59.3562i	−0.382456	+	1.92273i	−0.385426	+	0.922739i	$0.625946\pi$
$954$	−5.96148	+	1.04022i	−0.193010	+	0.0336784i
$955$	−5.28260	−	17.4144i	−0.170941	−	0.563516i
$956$	−19.9334	−	33.1147i	−0.644691	−	1.07100i
$957$	−0.158043	−	0.129703i	−0.00510881	−	0.00419269i
$958$	−23.7940	+	27.6366i	−0.768749	+	0.892899i
$959$		−	3.62597i		−	0.117089i
$960$	−0.822922	−	15.0130i	−0.0265597	−	0.484544i
$961$		−	26.0215i		−	0.839403i
$962$	−1.06559	−	0.917430i	−0.0343560	−	0.0295791i
$963$	3.82571	+	3.13968i	0.123282	+	0.101175i
$964$	8.13349	−	32.7331i	0.261962	−	1.05426i
$965$	−2.31717	−	7.63868i	−0.0745923	−	0.245898i
$966$	−1.05253	−	6.03203i	−0.0338646	−	0.194077i
$967$	8.89751	−	44.7308i	0.286125	−	1.43845i	−0.523764	−	0.851863i	$-0.675473\pi$
$967$	8.89751	−	44.7308i	0.286125	−	1.43845i	0.809889	−	0.586583i	$-0.199527\pi$
$968$	−28.0159	+	0.767254i	−0.900466	+	0.0246605i
$969$	3.90930	−	0.777608i	0.125585	−	0.0249804i
$970$	18.2548	+	8.07117i	0.586127	+	0.259150i
$971$	−3.02456	+	30.7089i	−0.0970629	+	0.985496i	0.816103	+	0.577907i	$0.196130\pi$
$971$	−3.02456	+	30.7089i	−0.0970629	+	0.985496i	−0.913165	+	0.407589i	$0.866370\pi$
$972$	1.58484	−	10.8251i	0.0508338	−	0.347215i
$973$	−0.439398	−	0.133290i	−0.0140865	−	0.00427308i
$974$	39.9951	−	31.2734i	1.28153	−	1.00206i
$975$	−1.32200	−	0.547589i	−0.0423378	−	0.0175369i
$976$	17.6262	+	7.22304i	0.564200	+	0.231204i
$977$	53.2855	−	22.0716i	1.70475	−	0.706132i	0.704760	−	0.709446i	$-0.251055\pi$
$977$	53.2855	−	22.0716i	1.70475	−	0.706132i	0.999995	+	0.00331378i	$0.00105481\pi$
$978$	8.92833	−	15.7955i	0.285496	−	0.505084i
$979$	−4.71636	−	8.82368i	−0.150735	−	0.282006i
$980$	−12.7546	+	0.650765i	−0.407429	+	0.0207879i
$981$	−1.36170	−	1.65924i	−0.0434759	−	0.0529755i
$982$	−35.4462	+	33.8115i	−1.13113	+	1.07897i
$983$	26.2038	+	17.5088i	0.835773	+	0.558445i	0.898191	−	0.439605i	$-0.144881\pi$
$983$	26.2038	+	17.5088i	0.835773	+	0.558445i	−0.0624188	+	0.998050i	$0.519881\pi$
$984$	14.9332	−	8.51561i	0.476054	−	0.271468i
$985$	2.76523	+	4.13846i	0.0881077	+	0.131862i
$986$	0.0390018	−	0.0247493i	0.00124207	−	0.000788179i
$987$	8.54011	−	15.9774i	0.271835	−	0.508567i
$988$	3.48701	+	9.68775i	0.110936	+	0.308208i
$989$	−4.17735	+	0.411433i	−0.132832	+	0.0130828i
$990$	0.354230	+	0.702080i	0.0112582	+	0.0223136i
$991$	−12.3833	+	12.3833i	−0.393369	+	0.393369i	−0.875886	−	0.482517i	$-0.839723\pi$
$991$	−12.3833	+	12.3833i	−0.393369	+	0.393369i	0.482517	+	0.875886i	$0.339723\pi$
$992$	−11.5631	−	5.06031i	−0.367128	−	0.160665i
$993$	−2.60556	−	2.60556i	−0.0826849	−	0.0826849i
$994$	−2.52411	+	7.66491i	−0.0800599	+	0.243116i
$995$	−0.167427	−	1.69991i	−0.00530779	−	0.0538909i
$996$	20.6474	+	0.975215i	0.654237	+	0.0309009i
$997$	5.27815	+	2.82123i	0.167161	+	0.0893493i	0.552855	−	0.833277i	$-0.313538\pi$
$997$	5.27815	+	2.82123i	0.167161	+	0.0893493i	−0.385695	+	0.922626i	$0.626038\pi$
$998$	−1.14925	+	5.14057i	−0.0363789	+	0.162722i
$999$	5.03601	−	3.36495i	0.159332	−	0.106462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.64	✓	1024
128.125	even	32	inner	640.2.bm.a.381.64	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.64	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.64	yes	1024	128.125	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41028 - 0.105369i) q^{2} +(1.19231 - 1.45283i) q^{3} +(1.97779 - 0.297201i) q^{4} +(0.956940 - 0.290285i) q^{5} +(1.52841 - 2.17454i) q^{6} +(-0.768791 - 0.152922i) q^{7} +(2.75793 - 0.627535i) q^{8} +(-0.103851 - 0.522093i) q^{9} +O(q^{10})\)	\(q+(1.41028 - 0.105369i) q^{2} +(1.19231 - 1.45283i) q^{3} +(1.97779 - 0.297201i) q^{4} +(0.956940 - 0.290285i) q^{5} +(1.52841 - 2.17454i) q^{6} +(-0.768791 - 0.152922i) q^{7} +(2.75793 - 0.627535i) q^{8} +(-0.103851 - 0.522093i) q^{9} +(1.31897 - 0.510215i) q^{10} +(-1.03956 - 0.102387i) q^{11} +(1.92636 - 3.22776i) q^{12} +(0.221009 - 0.728568i) q^{13} +(-1.10033 - 0.134656i) q^{14} +(0.719233 - 1.73638i) q^{15} +(3.82334 - 1.17560i) q^{16} +(-0.120025 - 0.289767i) q^{17} +(-0.201471 - 0.725356i) q^{18} +(-5.96337 + 3.18749i) q^{19} +(1.80636 - 0.858527i) q^{20} +(-1.13881 + 0.934594i) q^{21} +(-1.47686 - 0.0348580i) q^{22} +(-1.63281 + 2.44367i) q^{23} +(2.37660 - 4.75503i) q^{24} +(0.831470 - 0.555570i) q^{25} +(0.234916 - 1.05077i) q^{26} +(4.09024 + 2.18628i) q^{27} +(-1.56596 - 0.0739632i) q^{28} +(0.0102075 + 0.103638i) q^{29} +(0.831361 - 2.52458i) q^{30} +(-1.57773 - 1.57773i) q^{31} +(5.26812 - 2.06080i) q^{32} +(-1.38822 + 1.38822i) q^{33} +(-0.199802 - 0.396006i) q^{34} +(-0.780078 + 0.0768310i) q^{35} +(-0.360562 - 1.00173i) q^{36} +(0.615613 - 1.15173i) q^{37} +(-8.07417 + 5.12361i) q^{38} +(-0.794976 - 1.18977i) q^{39} +(2.45701 - 1.40110i) q^{40} +(2.68883 + 1.79662i) q^{41} +(-1.50756 + 1.43804i) q^{42} +(0.906064 + 1.10404i) q^{43} +(-2.08646 + 0.106456i) q^{44} +(-0.250934 - 0.469465i) q^{45} +(-2.04524 + 3.61832i) q^{46} +(-11.3613 + 4.70600i) q^{47} +(2.85065 - 6.95636i) q^{48} +(-5.89950 - 2.44365i) q^{49} +(1.11407 - 0.871122i) q^{50} +(-0.564090 - 0.171115i) q^{51} +(0.220579 - 1.50664i) q^{52} +(0.787917 - 7.99985i) q^{53} +(5.99876 + 2.65228i) q^{54} +(-1.02452 + 0.203789i) q^{55} +(-2.21624 + 0.0606947i) q^{56} +(-2.47929 + 12.4642i) q^{57} +(0.0253157 + 0.145084i) q^{58} +(0.598811 + 1.97401i) q^{59} +(0.906442 - 3.64796i) q^{60} +(3.68122 + 3.02110i) q^{61} +(-2.39130 - 2.05881i) q^{62} +0.417261i q^{63} +(7.21240 - 3.46140i) q^{64} -0.761351i q^{65} +(-1.81151 + 2.10406i) q^{66} +(7.91857 + 6.49860i) q^{67} +(-0.323504 - 0.537427i) q^{68} +(1.60343 + 5.28581i) q^{69} +(-1.09203 + 0.190550i) q^{70} +(1.42020 - 7.13984i) q^{71} +(-0.614045 - 1.37473i) q^{72} +(0.892647 - 0.177559i) q^{73} +(0.746831 - 1.68913i) q^{74} +(0.184218 - 1.87040i) q^{75} +(-10.8470 + 8.07651i) q^{76} +(0.783545 + 0.237686i) q^{77} +(-1.24651 - 1.59414i) q^{78} +(-13.5062 - 5.59446i) q^{79} +(3.31745 - 2.23484i) q^{80} +(9.52852 - 3.94684i) q^{81} +(3.98131 + 2.25042i) q^{82} +(2.59224 + 4.84974i) q^{83} +(-1.97456 + 2.18689i) q^{84} +(-0.198972 - 0.242448i) q^{85} +(1.39414 + 1.46154i) q^{86} +(0.162739 + 0.108739i) q^{87} +(-2.93128 + 0.369981i) q^{88} +(5.32126 + 7.96383i) q^{89} +(-0.403356 - 0.635638i) q^{90} +(-0.281323 + 0.526319i) q^{91} +(-2.50310 + 5.31836i) q^{92} +(-4.17333 + 0.411037i) q^{93} +(-15.5268 + 7.83393i) q^{94} +(-4.78131 + 4.78131i) q^{95} +(3.28724 - 10.1108i) q^{96} +(9.97976 + 9.97976i) q^{97} +(-8.57745 - 2.82462i) q^{98} +(0.0545030 + 0.553378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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