LMFDB - Embedded newform 640.2.bm.a.101.2

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			101.2
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40746 + 0.138072i) q^{2} +(-2.92329 + 1.56253i) q^{3} +(1.96187 - 0.388660i) q^{4} +(0.634393 + 0.773010i) q^{5} +(3.89867 - 2.60282i) q^{6} +(0.184506 - 0.123283i) q^{7} +(-2.70759 + 0.817901i) q^{8} +(4.43742 - 6.64107i) q^{9} +(-0.999612 - 1.00039i) q^{10} +(-3.53980 + 1.07379i) q^{11} +(-5.12783 + 4.20166i) q^{12} +(3.73398 + 3.06440i) q^{13} +(-0.242663 + 0.198991i) q^{14} +(-3.06237 - 1.26848i) q^{15} +(3.69789 - 1.52500i) q^{16} +(-5.90887 + 2.44753i) q^{17} +(-5.32854 + 9.95971i) q^{18} +(0.659567 + 6.69670i) q^{19} +(1.54504 + 1.26998i) q^{20} +(-0.346732 + 0.648690i) q^{21} +(4.83386 - 2.00006i) q^{22} +(2.02927 - 0.403647i) q^{23} +(6.63708 - 6.62166i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-5.67852 - 3.79745i) q^{26} +(-1.62031 + 16.4512i) q^{27} +(0.314063 - 0.313576i) q^{28} +(1.28760 - 4.24464i) q^{29} +(4.48530 + 1.36250i) q^{30} +(-4.20161 - 4.20161i) q^{31} +(-4.99406 + 2.65695i) q^{32} +(8.67005 - 8.67005i) q^{33} +(7.97855 - 4.26065i) q^{34} +(0.212349 + 0.0644153i) q^{35} +(6.12454 - 14.7536i) q^{36} +(-1.40048 - 0.137935i) q^{37} +(-1.85294 - 9.33425i) q^{38} +(-15.7037 - 3.12367i) q^{39} +(-2.34992 - 1.57412i) q^{40} +(0.467852 + 2.35205i) q^{41} +(0.398445 - 0.960878i) q^{42} +(-2.63414 - 1.40798i) q^{43} +(-6.52730 + 3.48241i) q^{44} +(7.94869 - 0.782878i) q^{45} +(-2.80038 + 0.848300i) q^{46} +(-0.976066 - 2.35643i) q^{47} +(-8.42714 + 10.2361i) q^{48} +(-2.65994 + 6.42166i) q^{49} +(0.139163 - 1.40735i) q^{50} +(13.4490 - 16.3877i) q^{51} +(8.51660 + 4.56071i) q^{52} +(-3.80337 - 12.5380i) q^{53} +(0.00906249 - 23.3781i) q^{54} +(-3.07568 - 2.05510i) q^{55} +(-0.398734 + 0.484708i) q^{56} +(-12.3919 - 18.5458i) q^{57} +(-1.22618 + 6.15193i) q^{58} +(-4.17140 + 3.42338i) q^{59} +(-6.50099 - 1.29837i) q^{60} +(1.37213 + 2.56707i) q^{61} +(6.49370 + 5.33346i) q^{62} -1.77238i q^{63} +(6.66208 - 4.42908i) q^{64} +4.83044i q^{65} +(-11.0056 + 13.3998i) q^{66} +(-3.92948 - 7.35153i) q^{67} +(-10.6412 + 7.09829i) q^{68} +(-5.30144 + 4.35078i) q^{69} +(-0.307766 - 0.0613425i) q^{70} +(-4.33755 - 6.49160i) q^{71} +(-6.58298 + 21.6107i) q^{72} +(-3.68245 - 2.46053i) q^{73} +(1.99016 + 0.000771483i) q^{74} +(-0.962203 - 3.17196i) q^{75} +(3.89672 + 12.8817i) q^{76} +(-0.520736 + 0.634519i) q^{77} +(22.5336 + 2.22819i) q^{78} +(4.70266 - 11.3532i) q^{79} +(3.52476 + 1.89105i) q^{80} +(-11.7993 - 28.4861i) q^{81} +(-0.983234 - 3.24582i) q^{82} +(4.68744 - 0.461672i) q^{83} +(-0.428124 + 1.40741i) q^{84} +(-5.64052 - 3.01492i) q^{85} +(3.90184 + 1.61797i) q^{86} +(2.86837 + 14.4202i) q^{87} +(8.70608 - 5.80258i) q^{88} +(3.08319 + 0.613284i) q^{89} +(-11.0793 + 2.19936i) q^{90} +(1.06673 + 0.105064i) q^{91} +(3.82429 - 1.58060i) q^{92} +(18.8477 + 5.71738i) q^{93} +(1.69913 + 3.18181i) q^{94} +(-4.75819 + 4.75819i) q^{95} +(10.4475 - 15.5704i) q^{96} +(-10.1661 - 10.1661i) q^{97} +(2.85710 - 9.40548i) q^{98} +(-8.57650 + 28.2729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−1.40746	+	0.138072i	−0.995223	+	0.0976314i
$2$	−1.40746	+	0.138072i	−0.995223	+	0.0976314i
$3$	−2.92329	+	1.56253i	−1.68776	+	0.902129i	−0.706930	+	0.707283i	$0.749920\pi$
$3$	−2.92329	+	1.56253i	−1.68776	+	0.902129i	−0.980834	+	0.194845i	$0.937580\pi$
$4$	1.96187	−	0.388660i	0.980936	−	0.194330i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	3.89867	−	2.60282i	1.59162	−	1.06260i
$7$	0.184506	−	0.123283i	0.0697368	−	0.0465967i	−0.520213	−	0.854037i	$-0.674147\pi$
$7$	0.184506	−	0.123283i	0.0697368	−	0.0465967i	0.589950	+	0.807440i	$0.299147\pi$
$8$	−2.70759	+	0.817901i	−0.957277	+	0.289172i
$9$	4.43742	−	6.64107i	1.47914	−	2.21369i
$10$	−0.999612	−	1.00039i	−0.316105	−	0.316350i
$11$	−3.53980	+	1.07379i	−1.06729	+	0.323759i	−0.774602	−	0.632449i	$-0.782050\pi$
$11$	−3.53980	+	1.07379i	−1.06729	+	0.323759i	−0.292688	+	0.956208i	$0.594550\pi$
$12$	−5.12783	+	4.20166i	−1.48028	+	1.21291i
$13$	3.73398	+	3.06440i	1.03562	+	0.849911i	0.988838	−	0.148994i	$-0.0476036\pi$
$13$	3.73398	+	3.06440i	1.03562	+	0.849911i	0.0467814	+	0.998905i	$0.485104\pi$
$14$	−0.242663	+	0.198991i	−0.0648544	+	0.0531826i
$15$	−3.06237	−	1.26848i	−0.790701	−	0.327519i
$16$	3.69789	−	1.52500i	0.924472	−	0.381250i
$17$	−5.90887	+	2.44753i	−1.43311	+	0.593614i	−0.958118	−	0.286375i	$-0.907550\pi$
$17$	−5.90887	+	2.44753i	−1.43311	+	0.593614i	−0.474994	+	0.879989i	$0.657550\pi$
$18$	−5.32854	+	9.95971i	−1.25595	+	2.34753i
$19$	0.659567	+	6.69670i	0.151315	+	1.53633i	0.708363	+	0.705848i	$0.249434\pi$
$19$	0.659567	+	6.69670i	0.151315	+	1.53633i	−0.557048	+	0.830480i	$0.688066\pi$
$20$	1.54504	+	1.26998i	0.345481	+	0.283977i
$21$	−0.346732	+	0.648690i	−0.0756631	+	0.141556i
$22$	4.83386	−	2.00006i	1.03058	−	0.426413i
$23$	2.02927	−	0.403647i	0.423132	−	0.0841662i	0.0210686	−	0.999778i	$-0.493293\pi$
$23$	2.02927	−	0.403647i	0.423132	−	0.0841662i	0.402063	+	0.915612i	$0.368293\pi$
$24$	6.63708	−	6.62166i	1.35479	−	1.35164i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−5.67852	−	3.79745i	−1.11365	−	0.744742i
$27$	−1.62031	+	16.4512i	−0.311828	+	3.16604i
$28$	0.314063	−	0.313576i	0.0593523	−	0.0592603i
$29$	1.28760	−	4.24464i	0.239101	−	0.788210i	−0.752468	−	0.658629i	$-0.771137\pi$
$29$	1.28760	−	4.24464i	0.239101	−	0.788210i	0.991569	−	0.129581i	$-0.0413633\pi$
$30$	4.48530	+	1.36250i	0.818900	+	0.248757i
$31$	−4.20161	−	4.20161i	−0.754631	−	0.754631i	0.220709	−	0.975340i	$-0.429163\pi$
$31$	−4.20161	−	4.20161i	−0.754631	−	0.754631i	−0.975340	+	0.220709i	$0.929163\pi$
$32$	−4.99406	+	2.65695i	−0.882833	+	0.469686i
$33$	8.67005	−	8.67005i	1.50926	−	1.50926i
$34$	7.97855	−	4.26065i	1.36831	−	0.730695i
$35$	0.212349	+	0.0644153i	0.0358935	+	0.0108882i
$36$	6.12454	−	14.7536i	1.02076	−	2.45893i
$37$	−1.40048	−	0.137935i	−0.230238	−	0.0226764i	−0.0177598	−	0.999842i	$-0.505653\pi$
$37$	−1.40048	−	0.137935i	−0.230238	−	0.0226764i	−0.212478	+	0.977166i	$0.568153\pi$
$38$	−1.85294	−	9.33425i	−0.300586	−	1.51422i
$39$	−15.7037	−	3.12367i	−2.51461	−	0.500187i
$40$	−2.34992	−	1.57412i	−0.371555	−	0.248891i
$41$	0.467852	+	2.35205i	0.0730663	+	0.367329i	0.999968	−	0.00797469i	$-0.00253845\pi$
$41$	0.467852	+	2.35205i	0.0730663	+	0.367329i	−0.926902	+	0.375304i	$0.877538\pi$
$42$	0.398445	−	0.960878i	0.0614814	−	0.148267i
$43$	−2.63414	−	1.40798i	−0.401702	−	0.214714i	0.258158	−	0.966103i	$-0.416884\pi$
$43$	−2.63414	−	1.40798i	−0.401702	−	0.214714i	−0.659860	+	0.751389i	$0.729384\pi$
$44$	−6.52730	+	3.48241i	−0.984028	+	0.524993i
$45$	7.94869	−	0.782878i	1.18492	−	0.116705i
$46$	−2.80038	+	0.848300i	−0.412893	+	0.125075i
$47$	−0.976066	−	2.35643i	−0.142374	−	0.343721i	0.836567	−	0.547865i	$-0.184559\pi$
$47$	−0.976066	−	2.35643i	−0.142374	−	0.343721i	−0.978941	+	0.204143i	$0.934559\pi$
$48$	−8.42714	+	10.2361i	−1.21635	+	1.47745i
$49$	−2.65994	+	6.42166i	−0.379991	+	0.917381i
$50$	0.139163	−	1.40735i	0.0196806	−	0.199029i
$51$	13.4490	−	16.3877i	1.88324	−	2.29473i
$52$	8.51660	+	4.56071i	1.18104	+	0.632457i
$53$	−3.80337	−	12.5380i	−0.522434	−	1.72223i	−0.678606	−	0.734503i	$-0.737415\pi$
$53$	−3.80337	−	12.5380i	−0.522434	−	1.72223i	0.156172	−	0.987730i	$-0.450085\pi$
$54$	0.00906249	−	23.3781i	0.00123325	−	3.18136i
$55$	−3.07568	−	2.05510i	−0.414724	−	0.277110i
$56$	−0.398734	+	0.484708i	−0.0532831	+	0.0647719i
$57$	−12.3919	−	18.5458i	−1.64135	−	2.45645i
$58$	−1.22618	+	6.15193i	−0.161005	+	0.807789i
$59$	−4.17140	+	3.42338i	−0.543070	+	0.445686i	−0.865501	−	0.500907i	$-0.833000\pi$
$59$	−4.17140	+	3.42338i	−0.543070	+	0.445686i	0.322431	+	0.946593i	$0.395500\pi$
$60$	−6.50099	−	1.29837i	−0.839274	−	0.167619i
$61$	1.37213	+	2.56707i	0.175683	+	0.328680i	0.954316	−	0.298800i	$-0.0965864\pi$
$61$	1.37213	+	2.56707i	0.175683	+	0.328680i	−0.778633	+	0.627480i	$0.784086\pi$
$62$	6.49370	+	5.33346i	0.824701	+	0.677350i
$63$		−	1.77238i		−	0.223299i
$64$	6.66208	−	4.42908i	0.832760	−	0.553635i
$65$			4.83044i			0.599142i
$66$	−11.0056	+	13.3998i	−1.35470	+	1.64940i
$67$	−3.92948	−	7.35153i	−0.480062	−	0.898133i	−0.999060	−	0.0433570i	$-0.986195\pi$
$67$	−3.92948	−	7.35153i	−0.480062	−	0.898133i	0.518998	−	0.854776i	$-0.326305\pi$
$68$	−10.6412	+	7.09829i	−1.29043	+	0.860794i
$69$	−5.30144	+	4.35078i	−0.638218	+	0.523772i
$70$	−0.307766	−	0.0613425i	−0.0367850	−	0.00733183i
$71$	−4.33755	−	6.49160i	−0.514772	−	0.770411i	0.479471	−	0.877558i	$-0.340829\pi$
$71$	−4.33755	−	6.49160i	−0.514772	−	0.770411i	−0.994243	+	0.107147i	$0.965829\pi$
$72$	−6.58298	+	21.6107i	−0.775812	+	2.54684i
$73$	−3.68245	−	2.46053i	−0.430998	−	0.287984i	0.321087	−	0.947050i	$-0.395952\pi$
$73$	−3.68245	−	2.46053i	−0.430998	−	0.287984i	−0.752085	+	0.659066i	$0.770952\pi$
$74$	1.99016		0.000771483i	0.231352		8.96831e-5i
$75$	−0.962203	−	3.17196i	−0.111106	−	0.366266i
$76$	3.89672	+	12.8817i	0.446985	+	1.47763i
$77$	−0.520736	+	0.634519i	−0.0593434	+	0.0723101i
$78$	22.5336	+	2.22819i	2.55143	+	0.252293i
$79$	4.70266	−	11.3532i	0.529090	−	1.27734i	−0.403030	−	0.915187i	$-0.632043\pi$
$79$	4.70266	−	11.3532i	0.529090	−	1.27734i	0.932120	−	0.362150i	$-0.117957\pi$
$80$	3.52476	+	1.89105i	0.394080	+	0.211426i
$81$	−11.7993	−	28.4861i	−1.31104	−	3.16512i
$82$	−0.983234	−	3.24582i	−0.108580	−	0.358441i
$83$	4.68744	−	0.461672i	0.514513	−	0.0506751i	0.162571	−	0.986697i	$-0.448021\pi$
$83$	4.68744	−	0.461672i	0.514513	−	0.0506751i	0.351942	+	0.936022i	$0.385521\pi$
$84$	−0.428124	+	1.40741i	−0.0467122	+	0.153561i
$85$	−5.64052	−	3.01492i	−0.611800	−	0.327014i
$86$	3.90184	+	1.61797i	0.420746	+	0.174470i
$87$	2.86837	+	14.4202i	0.307521	+	1.54601i
$88$	8.70608	−	5.80258i	0.928071	−	0.618557i
$89$	3.08319	+	0.613284i	0.326817	+	0.0650080i	0.355772	−	0.934573i	$-0.384218\pi$
$89$	3.08319	+	0.613284i	0.326817	+	0.0650080i	−0.0289550	+	0.999581i	$0.509218\pi$
$90$	−11.0793	+	2.19936i	−1.16787	+	0.231832i
$91$	1.06673	+	0.105064i	0.111824	+	0.0110137i
$92$	3.82429	−	1.58060i	0.398709	−	0.164789i
$93$	18.8477	+	5.71738i	1.95441	+	0.592864i
$94$	1.69913	+	3.18181i	0.175252	+	0.328179i
$95$	−4.75819	+	4.75819i	−0.488180	+	0.488180i
$96$	10.4475	−	15.5704i	1.06630	−	1.58915i
$97$	−10.1661	−	10.1661i	−1.03221	−	1.03221i	−0.999464	−	0.0327433i	$-0.989576\pi$
$97$	−10.1661	−	10.1661i	−1.03221	−	1.03221i	−0.0327433	−	0.999464i	$-0.510424\pi$
$98$	2.85710	−	9.40548i	0.288611	−	0.950097i
$99$	−8.57650	+	28.2729i	−0.861971	+	2.84154i
$100$	−0.00155059	+	2.00000i	−0.000155059	+	0.200000i
$101$	0.704610	−	7.15402i	0.0701113	−	0.711852i	−0.894304	−	0.447460i	$-0.852329\pi$
$101$	0.704610	−	7.15402i	0.0701113	−	0.711852i	0.964415	−	0.264392i	$-0.0851713\pi$
$102$	−16.6662	+	24.9219i	−1.65020	+	2.46763i
$103$	−1.82983	+	9.19917i	−0.180298	+	0.906421i	0.779644	+	0.626223i	$0.215400\pi$
$103$	−1.82983	+	9.19917i	−0.180298	+	0.906421i	−0.959942	+	0.280198i	$0.909600\pi$
$104$	−12.6165	−	5.24310i	−1.23715	−	0.514129i
$105$	−0.721409	+	0.143497i	−0.0704023	+	0.0140039i
$106$	7.08423	+	17.1216i	0.688082	+	1.66300i
$107$	0.151796	−	0.283990i	0.0146747	−	0.0274544i	−0.874477	−	0.485067i	$-0.838795\pi$
$107$	0.151796	−	0.283990i	0.0146747	−	0.0274544i	0.889152	+	0.457612i	$0.151295\pi$
$108$	3.21510	+	32.9050i	0.309373	+	3.16628i
$109$	1.37956	+	14.0070i	0.132138	+	1.34162i	0.801191	+	0.598408i	$0.204200\pi$
$109$	1.37956	+	14.0070i	0.132138	+	1.34162i	−0.669053	+	0.743215i	$0.733300\pi$
$110$	4.61263	+	2.46780i	0.439797	+	0.235296i
$111$	4.30955	−	1.78507i	0.409044	−	0.169432i
$112$	0.494277	−	0.737260i	0.0467047	−	0.0696645i
$113$	1.90389	+	0.788619i	0.179103	+	0.0741870i	0.470433	−	0.882436i	$-0.344098\pi$
$113$	1.90389	+	0.788619i	0.179103	+	0.0741870i	−0.291330	+	0.956623i	$0.594098\pi$
$114$	20.0018	+	24.3915i	1.87334	+	2.28447i
$115$	1.59938	+	1.31258i	0.149143	+	0.122398i
$116$	0.876382	−	8.82789i	0.0813700	−	0.819649i
$117$	36.9201	−	11.1996i	3.41327	−	1.03540i
$118$	5.39840	−	5.39421i	0.496963	−	0.496578i
$119$	−0.788484	+	1.18005i	−0.0722802	+	0.108175i
$120$	9.32913	+	0.929795i	0.851629	+	0.0848783i
$121$	2.23101	−	1.49071i	0.202819	−	0.135520i
$122$	−2.28565	−	3.42359i	−0.206933	−	0.309958i
$123$	−5.04283	−	6.14470i	−0.454697	−	0.554049i
$124$	−9.87601	−	6.61002i	−0.886892	−	0.593597i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	0.244715	+	2.49455i	0.0218010	+	0.222232i
$127$	17.5296			1.55550			0.777749	−	0.628575i	$-0.216362\pi$
$127$	17.5296			1.55550			0.777749	+	0.628575i	$0.216362\pi$
$128$	−8.76506	+	7.15358i	−0.774729	+	0.632293i
$129$	9.90036			0.871678
$130$	−0.666946	−	6.79864i	−0.0584951	−	0.596280i
$131$	−12.8115	+	6.84789i	−1.11935	+	0.598303i	−0.923985	−	0.382428i	$-0.875088\pi$
$131$	−12.8115	+	6.84789i	−1.11935	+	0.598303i	−0.195361	+	0.980731i	$0.562588\pi$
$132$	13.6398	−	20.3792i	1.18720	−	1.77378i
$133$	0.947285	+	1.15427i	0.0821400	+	0.100088i
$134$	6.54561	+	9.80442i	0.565454	+	0.846973i
$135$	−13.7449	+	9.18405i	−1.18297	+	0.790437i
$136$	13.9969	−	11.4598i	1.20023	−	0.982668i
$137$	−8.96414	+	13.4158i	−0.765859	+	1.14619i	0.219487	+	0.975616i	$0.429562\pi$
$137$	−8.96414	+	13.4158i	−0.765859	+	1.14619i	−0.985345	+	0.170573i	$0.945438\pi$
$138$	6.86083	−	6.85551i	0.584032	−	0.583580i
$139$	−11.7300	+	3.55826i	−0.994927	+	0.301808i	−0.745442	−	0.666571i	$-0.767761\pi$
$139$	−11.7300	+	3.55826i	−0.994927	+	0.301808i	−0.249485	+	0.968379i	$0.580261\pi$
$140$	0.441637	+	0.0438432i	0.0373251	+	0.00370543i
$141$	6.53533	+	5.36341i	0.550374	+	0.451680i
$142$	7.00122	+	8.53776i	0.587529	+	0.716473i
$143$	−16.5081	−	6.83786i	−1.38047	−	0.571811i
$144$	6.28144	−	31.3250i	0.523454	−	2.61042i
$145$	4.09800	−	1.69745i	0.340320	−	0.140965i
$146$	5.52262	+	2.95466i	0.457055	+	0.244529i
$147$	−2.25827	−	22.9286i	−0.186259	−	1.89112i
$148$	−2.80118	+	0.273699i	−0.230255	+	0.0224979i
$149$	−8.18136	+	15.3062i	−0.670243	+	1.25394i	0.285117	+	0.958493i	$0.407967\pi$
$149$	−8.18136	+	15.3062i	−0.670243	+	1.25394i	−0.955360	+	0.295444i	$0.904533\pi$
$150$	1.79222	+	4.33154i	0.146334	+	0.353669i
$151$	−4.45623	+	0.886400i	−0.362643	+	0.0721342i	−0.373049	−	0.927812i	$-0.621688\pi$
$151$	−4.45623	+	0.886400i	−0.362643	+	0.0721342i	0.0104058	+	0.999946i	$0.496688\pi$
$152$	−7.26307	−	17.5924i	−0.589113	−	1.42694i
$153$	−9.96590	+	50.1020i	−0.805695	+	4.05050i
$154$	0.645305	−	0.964957i	0.0520001	−	0.0777584i
$155$	0.582415	−	5.91335i	0.0467807	−	0.474972i
$156$	−32.0228	−	0.0248271i	−2.56387	−	0.00198776i
$157$	1.95031	−	6.42931i	0.155652	−	0.513115i	−0.844082	−	0.536215i	$-0.819854\pi$
$157$	1.95031	−	6.42931i	0.155652	−	0.513115i	0.999733	+	0.0231002i	$0.00735368\pi$
$158$	−5.05123	+	16.6285i	−0.401854	+	1.32289i
$159$	30.7095	+	30.7095i	2.43542	+	2.43542i
$160$	−5.22205	−	2.17491i	−0.412839	−	0.171942i
$161$	0.324650	−	0.324650i	0.0255860	−	0.0255860i
$162$	20.5402	+	38.4638i	1.61379	+	3.02200i
$163$	−14.1399	−	4.28930i	−1.10752	−	0.335964i	−0.317019	−	0.948419i	$-0.602682\pi$
$163$	−14.1399	−	4.28930i	−1.10752	−	0.335964i	−0.790505	+	0.612455i	$0.790182\pi$
$164$	1.83201	+	4.43259i	0.143056	+	0.346127i
$165$	12.2023	+	1.20182i	0.949945	+	0.0935614i
$166$	−6.53362	+	1.29699i	−0.507108	+	0.100666i
$167$	5.83864	+	1.16138i	0.451807	+	0.0898700i	0.415748	−	0.909480i	$-0.363520\pi$
$167$	5.83864	+	1.16138i	0.451807	+	0.0898700i	0.0360587	+	0.999350i	$0.488520\pi$
$168$	0.408244	−	2.03998i	0.0314967	−	0.157388i
$169$	2.01589	+	10.1346i	0.155069	+	0.779583i
$170$	8.35506	+	3.46457i	0.640804	+	0.265721i
$171$	47.4000	+	25.3359i	3.62477	+	1.93748i
$172$	−5.71506	−	1.73848i	−0.435769	−	0.132558i
$173$	−24.1565	+	2.37921i	−1.83659	+	0.180888i	−0.956072	−	0.293132i	$-0.905303\pi$
$173$	−24.1565	+	2.37921i	−1.83659	+	0.180888i	−0.880514	+	0.474020i	$0.842803\pi$
$174$	−6.02813	−	19.8998i	−0.456991	−	1.50860i
$175$	0.0849189	+	0.205012i	0.00641927	+	0.0154975i
$176$	−11.4523	+	9.36895i	−0.863247	+	0.706211i
$177$	6.84509	−	16.5255i	0.514508	−	1.24213i
$178$	−4.42413	−	0.437470i	−0.331603	−	0.0327898i
$179$	−3.04073	+	3.70514i	−0.227275	+	0.276935i	−0.874145	−	0.485665i	$-0.838578\pi$
$179$	−3.04073	+	3.70514i	−0.227275	+	0.276935i	0.646870	+	0.762600i	$0.276078\pi$
$180$	15.2900	−	4.62524i	1.13965	−	0.344745i
$181$	−4.70272	−	15.5028i	−0.349550	−	1.15231i	−0.938829	−	0.344383i	$-0.888088\pi$
$181$	−4.70272	−	15.5028i	−0.349550	−	1.15231i	0.589279	−	0.807930i	$-0.299412\pi$
$182$	−1.51589		0.000587630i	−0.112365		4.35580e-5i
$183$	−8.02227	−	5.36031i	−0.593023	−	0.396245i
$184$	−5.16428	+	2.75265i	−0.380716	+	0.202928i
$185$	−0.781831	−	1.17009i	−0.0574813	−	0.0860269i
$186$	−27.3167	−	5.44464i	−2.00296	−	0.399220i
$187$	18.2881	−	15.0087i	1.33736	−	1.09754i
$188$	−2.83077	−	4.24366i	−0.206455	−	0.309501i
$189$	1.72921	+	3.23512i	0.125781	+	0.235320i
$190$	6.03998	−	7.35393i	0.438186	−	0.533510i
$191$			8.07419i			0.584228i	0.956384	+	0.292114i	$0.0943586\pi$
$191$			8.07419i			0.584228i	−0.956384	+	0.292114i	$0.905641\pi$
$192$	−12.5546	+	23.3572i	−0.906052	+	1.68566i
$193$		−	25.9589i		−	1.86856i	−0.356534	−	0.934282i	$-0.616042\pi$
$193$		−	25.9589i		−	1.86856i	0.356534	−	0.934282i	$-0.383958\pi$
$194$	15.7119	+	12.9047i	1.12805	+	0.926500i
$195$	−7.54772	−	14.1208i	−0.540503	−	1.01121i
$196$	−2.72262	+	13.6323i	−0.194473	+	0.973735i
$197$	−4.99559	+	4.09977i	−0.355921	+	0.292097i	−0.795313	−	0.606198i	$-0.792694\pi$
$197$	−4.99559	+	4.09977i	−0.355921	+	0.292097i	0.439393	+	0.898295i	$0.355194\pi$
$198$	8.16737	−	40.9771i	0.580430	−	2.91212i
$199$	−6.50017	−	9.72819i	−0.460785	−	0.689613i	0.526212	−	0.850353i	$-0.323612\pi$
$199$	−6.50017	−	9.72819i	−0.460785	−	0.689613i	−0.986997	+	0.160740i	$0.948612\pi$
$200$	−0.273961	−	2.81513i	−0.0193719	−	0.199060i
$201$	22.9740	+	15.3507i	1.62046	+	1.08276i
$202$	−0.00394093	+	10.1663i	−0.000277283	+	0.715296i
$203$	−0.285723	−	0.941903i	−0.0200538	−	0.0661086i
$204$	20.0160	−	37.3776i	1.40140	−	2.61695i
$205$	−1.52136	+	1.85378i	−0.106256	+	0.129474i
$206$	1.30526	−	13.2001i	0.0909419	−	0.919694i
$207$	6.32408	−	15.2677i	0.439554	−	1.06118i
$208$	18.4810	+	5.63747i	1.28143	+	0.390888i
$209$	−9.52557	−	22.9968i	−0.658897	−	1.59072i
$210$	0.995539	−	0.301572i	0.0686987	−	0.0208105i
$211$	21.1181	−	2.07995i	1.45383	−	0.143190i	0.659970	−	0.751292i	$-0.270569\pi$
$211$	21.1181	−	2.07995i	1.45383	−	0.143190i	0.793859	+	0.608102i	$0.208069\pi$
$212$	−12.3348	−	23.1198i	−0.847155	−	1.58788i
$213$	22.8233	+	12.1993i	1.56382	+	0.835881i
$214$	−0.174435	+	0.420663i	−0.0119241	+	0.0287559i
$215$	−0.582699	−	2.92942i	−0.0397397	−	0.199785i
$216$	−9.06836	−	45.8685i	−0.617024	−	3.12095i
$217$	−1.29321	−	0.257236i	−0.0877888	−	0.0174623i
$218$	−3.87564	−	19.5237i	−0.262492	−	1.32231i
$219$	14.6095	+	1.43891i	0.987221	+	0.0972328i
$220$	−6.83282	−	2.83645i	−0.460668	−	0.191234i
$221$	−29.5638	−	8.96808i	−1.98868	−	0.603259i
$222$	−5.81904	+	3.10744i	−0.390548	+	0.208558i
$223$	8.88681	−	8.88681i	0.595105	−	0.595105i	−0.343901	−	0.939006i	$-0.611749\pi$
$223$	8.88681	−	8.88681i	0.595105	−	0.595105i	0.939006	+	0.343901i	$0.111749\pi$
$224$	−0.593879	+	1.10591i	−0.0396802	+	0.0738915i
$225$	5.64777	+	5.64777i	0.376518	+	0.376518i
$226$	−2.78854	−	0.847074i	−0.185491	−	0.0563465i
$227$	1.27653	−	4.20817i	0.0847266	−	0.279306i	−0.904332	−	0.426830i	$-0.859630\pi$
$227$	1.27653	−	4.20817i	0.0847266	−	0.279306i	0.989058	+	0.147524i	$0.0471303\pi$
$228$	−31.5194	−	31.5683i	−2.08742	−	2.09066i
$229$	−2.19866	+	22.3234i	−0.145292	+	1.47517i	0.595455	+	0.803388i	$0.296972\pi$
$229$	−2.19866	+	22.3234i	−0.145292	+	1.47517i	−0.740747	+	0.671784i	$0.765528\pi$
$230$	−2.43229	−	1.62657i	−0.160380	−	0.107253i
$231$	0.530808	−	2.66855i	0.0349246	−	0.175578i
$232$	−0.0145902	+	12.5459i	−0.000957891	+	0.823677i
$233$	7.18900	−	1.42998i	0.470967	−	0.0936812i	0.0460999	−	0.998937i	$-0.485321\pi$
$233$	7.18900	−	1.42998i	0.470967	−	0.0936812i	0.424867	+	0.905256i	$0.360321\pi$
$234$	−50.4172	+	20.8606i	−3.29587	+	1.36370i
$235$	1.20234	−	2.24941i	0.0784318	−	0.146736i
$236$	−6.85323	+	8.33749i	−0.446107	+	0.542725i
$237$	3.99253	+	40.5368i	0.259343	+	2.63315i
$238$	0.946826	−	1.76974i	0.0613736	−	0.114715i
$239$	−5.50946	+	2.28209i	−0.356377	+	0.147616i	−0.553687	−	0.832725i	$-0.686780\pi$
$239$	−5.50946	+	2.28209i	−0.356377	+	0.147616i	0.197310	+	0.980341i	$0.436780\pi$
$240$	−13.2587	−	0.0205589i	−0.855848	−	0.00132707i
$241$	−16.5086	−	6.83809i	−1.06341	−	0.440480i	−0.218751	−	0.975781i	$-0.570198\pi$
$241$	−16.5086	−	6.83809i	−1.06341	−	0.440480i	−0.844662	+	0.535301i	$0.820198\pi$
$242$	−2.93423	+	2.40616i	−0.188619	+	0.154674i
$243$	40.6678	+	33.3752i	2.60884	+	2.14102i
$244$	3.68966	+	4.50298i	0.236206	+	0.288274i
$245$	−6.65146	+	2.01770i	−0.424946	+	0.128906i
$246$	7.94598	+	7.95214i	0.506617	+	0.507010i
$247$	−18.0585	+	27.0265i	−1.14904	+	1.71966i
$248$	14.8127	+	7.93972i	0.940608	+	0.504173i
$249$	−12.9814	+	8.67388i	−0.822661	+	0.549685i
$250$	1.17618	−	0.785239i	0.0743882	−	0.0496629i
$251$	2.59218	+	3.15858i	0.163617	+	0.199368i	0.848365	−	0.529412i	$-0.177588\pi$
$251$	2.59218	+	3.15858i	0.163617	+	0.199368i	−0.684748	+	0.728780i	$0.740088\pi$
$252$	−0.688853	−	3.47718i	−0.0433936	−	0.219042i
$253$	−6.74978	+	3.60783i	−0.424355	+	0.226822i
$254$	−24.6721	+	2.42034i	−1.54807	+	0.151865i
$255$	21.1998			1.32758
$256$	11.3487	−	11.2786i	0.709296	−	0.704911i
$257$	−0.377487			−0.0235470			−0.0117735	−	0.999931i	$-0.503748\pi$
$257$	−0.377487			−0.0235470			−0.0117735	+	0.999931i	$0.503748\pi$
$258$	−13.9343	+	1.36696i	−0.867514	+	0.0851031i
$259$	−0.275403	+	0.147206i	−0.0171127	+	0.00914693i
$260$	1.87740	+	9.47670i	0.116431	+	0.587720i
$261$	−22.4754	−	27.3863i	−1.39119	−	1.69517i
$262$	17.0862	−	11.4070i	1.05559	−	0.704728i
$263$	10.0076	−	6.68689i	0.617098	−	0.412332i	−0.207352	−	0.978266i	$-0.566485\pi$
$263$	10.0076	−	6.68689i	0.617098	−	0.412332i	0.824450	+	0.565935i	$0.191485\pi$
$264$	−16.3837	+	30.5662i	−1.00835	+	1.88122i
$265$	7.27920	−	10.8941i	0.447158	−	0.669219i
$266$	−1.49264	−	1.49379i	−0.0915193	−	0.0915903i
$267$	−9.97133	+	3.02477i	−0.610236	+	0.185113i
$268$	−10.5664	−	12.8955i	−0.645444	−	0.787721i
$269$	13.1804	+	10.8169i	0.803626	+	0.659519i	0.943766	−	0.330613i	$-0.107255\pi$
$269$	13.1804	+	10.8169i	0.803626	+	0.659519i	−0.140141	+	0.990132i	$0.544755\pi$
$270$	18.0773	−	14.8239i	1.10015	−	0.902156i
$271$	−2.12711	−	0.881076i	−0.129212	−	0.0535215i	0.317140	−	0.948379i	$-0.397277\pi$
$271$	−2.12711	−	0.881076i	−0.129212	−	0.0535215i	−0.446353	+	0.894857i	$0.647277\pi$
$272$	−18.1178	+	18.0617i	−1.09856	+	1.09515i
$273$	−3.28253	+	1.35967i	−0.198668	+	0.0822910i
$274$	10.7643	−	20.1198i	0.650296	−	1.21548i
$275$	−0.362574	−	3.68127i	−0.0218640	−	0.221989i
$276$	−8.70977	+	10.5961i	−0.524267	+	0.637812i
$277$	−14.1340	+	26.4429i	−0.849231	+	1.58880i	−0.0415817	+	0.999135i	$0.513240\pi$
$277$	−14.1340	+	26.4429i	−0.849231	+	1.58880i	−0.807649	+	0.589664i	$0.799260\pi$
$278$	16.0182	−	6.62768i	0.960708	−	0.397502i
$279$	−46.5475	+	9.25887i	−2.78672	+	0.554314i
$280$	−0.627639		0.000729909i	−0.0375086		4.36204e-5i
$281$	−1.00422	+	5.04858i	−0.0599070	+	0.301173i	−0.999110	−	0.0421906i	$-0.986566\pi$
$281$	−1.00422	+	5.04858i	−0.0599070	+	0.301173i	0.939203	+	0.343364i	$0.111566\pi$
$282$	−9.93874	−	6.64642i	−0.591843	−	0.395789i
$283$	0.274536	−	2.78741i	0.0163195	−	0.165695i	−0.983571	−	0.180524i	$-0.942221\pi$
$283$	0.274536	−	2.78741i	0.0163195	−	0.165695i	0.999890	+	0.0148296i	$0.00472058\pi$
$284$	−11.0327	−	11.0499i	−0.654673	−	0.655689i
$285$	6.47476	−	21.3444i	0.383532	−	1.26433i
$286$	24.1785	+	7.34470i	1.42970	+	0.434301i
$287$	0.376290	+	0.376290i	0.0222117	+	0.0222117i
$288$	−4.51577	+	44.9559i	−0.266094	+	2.64905i
$289$	16.9035	−	16.9035i	0.994323	−	0.994323i
$290$	−5.53339	+	2.95490i	−0.324932	+	0.173518i
$291$	45.6032	+	13.8336i	2.67331	+	0.810938i
$292$	−8.18081	−	3.39603i	−0.478745	−	0.198738i
$293$	0.985520	+	0.0970653i	0.0575747	+	0.00567061i	0.126763	−	0.991933i	$-0.459541\pi$
$293$	0.985520	+	0.0970653i	0.0575747	+	0.00567061i	−0.0691888	+	0.997604i	$0.522041\pi$
$294$	6.34422	+	31.9593i	0.370002	+	1.86390i
$295$	−5.29262	−	1.05277i	−0.308148	−	0.0612945i
$296$	3.90475	−	0.771983i	0.226959	−	0.0448706i
$297$	−11.9296	−	59.9740i	−0.692224	−	3.48004i
$298$	9.40155	−	22.6725i	0.544617	−	1.31338i
$299$	8.81418	+	4.71128i	0.509737	+	0.272460i
$300$	−3.12053	−	5.84901i	−0.180164	−	0.337693i
$301$	−0.659595	+	0.0649644i	−0.0380184	+	0.00374449i
$302$	6.14957	−	1.86285i	0.353868	−	0.107195i
$303$	9.11861	+	22.0143i	0.523851	+	1.26469i
$304$	12.6515	+	23.7578i	0.725612	+	1.36260i
$305$	−1.11390	+	2.68920i	−0.0637820	+	0.153983i
$306$	7.10892	−	71.8924i	0.406390	−	4.10982i
$307$	−16.5217	+	20.1317i	−0.942942	+	1.14898i	0.0457401	+	0.998953i	$0.485435\pi$
$307$	−16.5217	+	20.1317i	−0.942942	+	1.14898i	−0.988682	+	0.150025i	$0.952065\pi$
$308$	−0.775006	+	1.44723i	−0.0441601	+	0.0824638i
$309$	−9.02488	−	29.7510i	−0.513408	−	1.69248i
$310$	−0.00325749	+	8.40321i	−0.000185013	+	0.477270i
$311$	4.71084	+	3.14769i	0.267127	+	0.178489i	0.681919	−	0.731428i	$-0.261146\pi$
$311$	4.71084	+	3.14769i	0.267127	+	0.178489i	−0.414792	+	0.909916i	$0.636146\pi$
$312$	45.0741	−	4.38649i	2.55182	−	0.248336i
$313$	14.4106	+	21.5670i	0.814535	+	1.21904i	0.972801	+	0.231641i	$0.0744095\pi$
$313$	14.4106	+	21.5670i	0.814535	+	1.21904i	−0.158267	+	0.987396i	$0.550591\pi$
$314$	−1.85727	+	9.31826i	−0.104812	+	0.525860i
$315$	1.37007	−	1.12439i	0.0771946	−	0.0633520i
$316$	4.81347	−	24.1013i	0.270779	−	1.35580i
$317$	8.52797	+	15.9547i	0.478978	+	0.896106i	0.999117	+	0.0420235i	$0.0133804\pi$
$317$	8.52797	+	15.9547i	0.478978	+	0.896106i	−0.520138	+	0.854082i	$0.674120\pi$
$318$	−47.4624	−	38.9822i	−2.66156	−	2.18601i
$319$			16.4078i			0.918660i
$320$	7.65010	+	2.34008i	0.427654	+	0.130814i
$321$			1.06737i			0.0595749i
$322$	−0.412106	+	0.501756i	−0.0229658	+	0.0279618i
$323$	−20.2877	−	37.9556i	−1.12884	−	2.11191i
$324$	−34.2202	−	51.3002i	−1.90112	−	2.85001i
$325$	−3.73398	+	3.06440i	−0.207124	+	0.169982i
$326$	20.4936	+	4.08468i	1.13503	+	0.226230i
$327$	−25.9192	−	38.7908i	−1.43333	−	2.14514i
$328$	−3.19050	−	5.98574i	−0.176166	−	0.330507i
$329$	−0.470599	−	0.314444i	−0.0259450	−	0.0173359i
$330$	−17.3401	−	0.00672185i	−0.954541	−	0.000370026i
$331$	−4.98867	−	16.4454i	−0.274202	−	0.903923i	−0.980585	−	0.196094i	$-0.937174\pi$
$331$	−4.98867	−	16.4454i	−0.274202	−	0.903923i	0.706383	−	0.707830i	$-0.250326\pi$
$332$	9.01672	−	2.72756i	0.494857	−	0.149694i
$333$	−7.13057	+	8.68863i	−0.390753	+	0.476134i
$334$	−8.37798	−	0.828439i	−0.458423	−	0.0453302i
$335$	3.18998	−	7.70129i	0.174287	−	0.420766i
$336$	−0.292923	+	2.92755i	−0.0159802	+	0.159711i
$337$	10.5300	+	25.4217i	0.573606	+	1.38481i	0.898465	+	0.439045i	$0.144683\pi$
$337$	10.5300	+	25.4217i	0.573606	+	1.38481i	−0.324859	+	0.945762i	$0.605317\pi$
$338$	−4.23658	−	13.9857i	−0.230440	−	0.760720i
$339$	−6.79789	+	0.669533i	−0.369210	+	0.0363641i
$340$	−12.2378	−	3.72264i	−0.663685	−	0.201889i
$341$	19.3845	+	10.3612i	1.04973	+	0.561092i
$342$	−70.2117	−	29.1145i	−3.79661	−	1.57433i
$343$	0.603947	+	3.03624i	0.0326100	+	0.163942i
$344$	8.28374	+	1.65776i	0.446629	+	0.0893802i
$345$	−6.72639	−	1.33796i	−0.362137	−	0.0720335i
$346$	33.6708	−	6.68397i	1.81015	−	0.359332i
$347$	30.3160	+	2.98586i	1.62745	+	0.160289i	0.870152	−	0.492784i	$-0.164021\pi$
$347$	30.3160	+	2.98586i	1.62745	+	0.160289i	0.757295	+	0.653073i	$0.226521\pi$
$348$	11.2319	+	27.1759i	0.602095	+	1.45678i
$349$	8.54227	+	2.59127i	0.457257	+	0.138708i	0.510507	−	0.859874i	$-0.329458\pi$
$349$	8.54227	+	2.59127i	0.457257	+	0.138708i	−0.0532494	+	0.998581i	$0.516958\pi$
$350$	−0.147826	−	0.276821i	−0.00790164	−	0.0147967i
$351$	−56.4633	+	56.4633i	−3.01379	+	3.01379i
$352$	14.8250	−	14.7676i	0.790174	−	0.787117i
$353$	−2.62044	−	2.62044i	−0.139472	−	0.139472i	0.633924	−	0.773396i	$-0.281443\pi$
$353$	−2.62044	−	2.62044i	−0.139472	−	0.139472i	−0.773396	+	0.633924i	$0.781443\pi$
$354$	−7.35246	+	24.2040i	−0.390779	+	1.28643i
$355$	2.26636	−	7.47120i	0.120286	−	0.396530i
$356$	6.28718	+	0.00487442i	0.333220	+	0.000258344i
$357$	0.461104	−	4.68166i	0.0244042	−	0.247780i
$358$	3.76813	−	5.63467i	0.199152	−	0.297802i
$359$	0.319391	−	1.60569i	0.0168568	−	0.0847450i	−0.971441	−	0.237281i	$-0.923744\pi$
$359$	0.319391	−	1.60569i	0.0168568	−	0.0847450i	0.988298	+	0.152536i	$0.0487439\pi$
$360$	−20.8815	+	8.62095i	−1.10055	+	0.454364i
$361$	−25.7758	+	5.12713i	−1.35662	+	0.269849i
$362$	8.75937	+	21.1702i	0.460382	+	1.11268i
$363$	−4.19261	+	7.84383i	−0.220055	+	0.411694i
$364$	2.13363	−	0.208474i	0.111832	−	0.0109270i
$365$	−0.434103	−	4.40752i	−0.0227220	−	0.230700i
$366$	12.0311	+	6.43676i	0.628876	+	0.336455i
$367$	20.4103	−	8.45421i	1.06541	−	0.441306i	0.220040	−	0.975491i	$-0.429381\pi$
$367$	20.4103	−	8.45421i	1.06541	−	0.441306i	0.845368	+	0.534185i	$0.179381\pi$
$368$	6.88845	−	4.58728i	0.359085	−	0.239128i
$369$	17.6962	+	7.33001i	0.921228	+	0.381585i
$370$	1.26195	+	1.53891i	0.0656057	+	0.0800039i
$371$	−2.24748	−	1.84446i	−0.116683	−	0.0957594i
$372$	39.1988	+	3.89144i	2.03237	+	0.201762i
$373$	8.57767	−	2.60201i	0.444135	−	0.134727i	−0.0602928	−	0.998181i	$-0.519203\pi$
$373$	8.57767	−	2.60201i	0.444135	−	0.134727i	0.504428	+	0.863454i	$0.331703\pi$
$374$	−23.6674	+	23.6491i	−1.22381	+	1.22287i
$375$	1.84154	−	2.75606i	0.0950968	−	0.142322i
$376$	4.57012	+	5.58193i	0.235686	+	0.287866i
$377$	17.8151	−	11.9037i	0.917526	−	0.613071i
$378$	−2.88046	−	4.31453i	−0.148155	−	0.221916i
$379$	−10.5734	−	12.8838i	−0.543120	−	0.661794i	0.427047	−	0.904229i	$-0.359554\pi$
$379$	−10.5734	−	12.8838i	−0.543120	−	0.661794i	−0.970168	+	0.242435i	$0.922054\pi$
$380$	−7.48565	+	11.1843i	−0.384006	+	0.573742i
$381$	−51.2441	+	27.3905i	−2.62531	+	1.40326i
$382$	−1.11482	−	11.3641i	−0.0570389	−	0.581437i
$383$	0.532837			0.0272267			0.0136134	−	0.999907i	$-0.495667\pi$
$383$	0.532837			0.0272267			0.0136134	+	0.999907i	$0.495667\pi$
$384$	14.4451	−	34.6077i	0.737150	−	1.76607i
$385$	−0.820841			−0.0418339
$386$	3.58419	+	36.5361i	0.182431	+	1.85964i
$387$	−21.0392	+	11.2457i	−1.06948	+	0.571652i
$388$	−23.8957	−	15.9934i	−1.21312	−	0.811941i
$389$	3.32395	+	4.05025i	0.168531	+	0.205356i	0.850426	−	0.526094i	$-0.176344\pi$
$389$	3.32395	+	4.05025i	0.168531	+	0.205356i	−0.681895	+	0.731450i	$0.738844\pi$
$390$	12.5728	+	18.8323i	0.636647	+	0.953610i
$391$	−11.0027	+	7.35180i	−0.556433	+	0.371797i
$392$	1.94974	−	19.5628i	0.0984768	−	0.988070i
$393$	26.7517	−	40.0368i	1.34945	−	2.01959i
$394$	6.46502	−	6.46001i	0.325703	−	0.325450i
$395$	11.7595	−	3.56720i	0.591684	−	0.179485i
$396$	−5.83745	+	58.8012i	−0.293343	+	2.95487i
$397$	−10.0478	−	8.24599i	−0.504283	−	0.413855i	0.347555	−	0.937660i	$-0.387012\pi$
$397$	−10.0478	−	8.24599i	−0.504283	−	0.413855i	−0.851838	+	0.523805i	$0.824512\pi$
$398$	10.4919	+	12.7945i	0.525911	+	0.641331i
$399$	−4.57278	−	1.89411i	−0.228925	−	0.0948239i
$400$	0.774277	+	3.92435i	0.0387139	+	0.196217i
$401$	23.4842	−	9.72747i	1.17274	−	0.485767i	0.290645	−	0.956831i	$-0.406130\pi$
$401$	23.4842	−	9.72747i	1.17274	−	0.485767i	0.882099	+	0.471064i	$0.156130\pi$
$402$	−34.4545	−	18.4335i	−1.71843	−	0.919378i
$403$	−2.81332	−	28.5641i	−0.140141	−	1.42288i
$404$	−1.39813	−	14.3091i	−0.0695594	−	0.711906i
$405$	14.5346	−	27.1924i	0.722232	−	1.35120i
$406$	0.532193	+	1.28624i	0.0264123	+	0.0638349i
$407$	5.10554	−	1.01556i	0.253072	−	0.0503392i
$408$	−23.0109	+	55.3710i	−1.13921	+	2.74127i
$409$	−4.82058	+	24.2347i	−0.238362	+	1.19833i	0.657312	+	0.753618i	$0.271693\pi$
$409$	−4.82058	+	24.2347i	−0.238362	+	1.19833i	−0.895675	+	0.444710i	$0.853307\pi$
$410$	1.88529	−	2.81917i	0.0931080	−	0.139229i
$411$	5.24221	−	53.2251i	0.258579	−	2.62540i
$412$	−0.0145436	+	18.7588i	−0.000716512	+	0.924179i
$413$	−0.347605	+	1.14590i	−0.0171045	+	0.0563860i
$414$	−6.79284	+	22.3618i	−0.333850	+	1.09902i
$415$	3.33056	+	3.33056i	0.163491	+	0.163491i
$416$	−26.7897	−	5.38279i	−1.31347	−	0.263913i
$417$	28.7304	−	28.7304i	1.40693	−	1.40693i
$418$	16.5820	+	31.0517i	0.811053	+	1.51879i
$419$	11.4884	+	3.48495i	0.561243	+	0.170251i	0.558144	−	0.829744i	$-0.311514\pi$
$419$	11.4884	+	3.48495i	0.561243	+	0.170251i	0.00309873	+	0.999995i	$0.499014\pi$
$420$	−1.35954	+	0.561906i	−0.0663388	+	0.0274182i
$421$	−25.3135	−	2.49316i	−1.23370	−	0.121509i	−0.539935	−	0.841706i	$-0.681551\pi$
$421$	−25.3135	−	2.49316i	−1.23370	−	0.121509i	−0.693769	+	0.720197i	$0.744051\pi$
$422$	−29.4356	+	5.84325i	−1.43290	+	0.284445i
$423$	−19.9805	−	3.97436i	−0.971483	−	0.193240i
$424$	20.5528	+	30.8371i	0.998135	+	1.49758i
$425$	−1.24774	−	6.27282i	−0.0605244	−	0.304277i
$426$	−33.8071	−	14.0187i	−1.63796	−	0.679210i
$427$	0.569643	+	0.304481i	0.0275670	+	0.0147349i
$428$	0.187429	−	0.616149i	0.00905970	−	0.0297827i
$429$	58.9423	−	5.80531i	2.84576	−	0.280283i
$430$	1.22459	+	4.04259i	0.0590552	+	0.194951i
$431$	0.00193775	+	0.00467815i	9.33383e−5	+	0.000225338i	0.923926	−	0.382571i	$-0.124961\pi$
$431$	0.00193775	+	0.00467815i	9.33383e−5	+	0.000225338i	−0.923833	+	0.382796i	$0.874961\pi$
$432$	19.0965	+	63.3058i	0.918779	+	3.04580i
$433$	−8.02724	+	19.3795i	−0.385765	+	0.931318i	0.605062	+	0.796178i	$0.293148\pi$
$433$	−8.02724	+	19.3795i	−0.385765	+	0.931318i	−0.990827	+	0.135140i	$0.956852\pi$
$434$	1.85566	+	0.183492i	0.0890743	+	0.00880792i
$435$	−9.32733	+	11.3654i	−0.447211	+	0.544929i
$436$	8.15047	+	26.9437i	0.390337	+	1.29037i
$437$	4.04154	+	13.3232i	0.193333	+	0.637334i
$438$	−20.7610	−	0.00804795i	−0.991998	−	0.000384546i
$439$	−18.6780	−	12.4803i	−0.891453	−	0.595650i	0.0232707	−	0.999729i	$-0.492592\pi$
$439$	−18.6780	−	12.4803i	−0.891453	−	0.595650i	−0.914724	+	0.404079i	$0.867592\pi$
$440$	10.0085	+	3.04877i	0.477138	+	0.145344i
$441$	30.8435	+	46.1605i	1.46874	+	2.19812i
$442$	42.8480	+	8.54027i	2.03807	+	0.406219i
$443$	−17.4438	+	14.3158i	−0.828780	+	0.680162i	−0.949927	−	0.312472i	$-0.898843\pi$
$443$	−17.4438	+	14.3158i	−0.828780	+	0.680162i	0.121147	+	0.992635i	$0.461343\pi$
$444$	7.76100	−	5.17703i	0.368321	−	0.245691i
$445$	1.48188	+	2.77240i	0.0702477	+	0.131424i
$446$	−11.2808	+	13.7348i	−0.534161	+	0.650362i
$447$		−	57.5283i		−	2.72099i
$448$	0.683164	−	1.63852i	0.0322765	−	0.0774126i
$449$			0.960321i			0.0453203i	0.999743	+	0.0226602i	$0.00721357\pi$
$449$			0.960321i			0.0453203i	−0.999743	+	0.0226602i	$0.992786\pi$
$450$	−8.72879	−	7.16920i	−0.411479	−	0.337959i
$451$	−4.18171	−	7.82343i	−0.196909	−	0.368391i
$452$	4.04170	+	0.807203i	0.190106	+	0.0379676i
$453$	11.6418	−	9.55422i	0.546982	−	0.448896i
$454$	−1.21564	+	6.09907i	−0.0570528	+	0.286244i
$455$	0.595512	+	0.891247i	0.0279180	+	0.0417823i
$456$	48.7209	+	40.0791i	2.28156	+	1.87688i
$457$	−2.12356	−	1.41892i	−0.0993360	−	0.0663742i	0.504910	−	0.863172i	$-0.331526\pi$
$457$	−2.12356	−	1.41892i	−0.0993360	−	0.0663742i	−0.604246	+	0.796798i	$0.706526\pi$
$458$	0.0122973	−	31.7228i	0.000574614	−	1.48231i
$459$	−30.6908	−	101.174i	−1.43252	−	4.72240i
$460$	3.64792	+	1.95349i	0.170085	+	0.0910820i
$461$	10.8564	−	13.2285i	0.505632	−	0.616114i	−0.456159	−	0.889898i	$-0.650775\pi$
$461$	10.8564	−	13.2285i	0.505632	−	0.616114i	0.961791	+	0.273784i	$0.0882753\pi$
$462$	−0.378638	+	3.82916i	−0.0176158	+	0.178149i
$463$	−1.36382	+	3.29256i	−0.0633822	+	0.153018i	−0.952397	−	0.304860i	$-0.901390\pi$
$463$	−1.36382	+	3.29256i	−0.0633822	+	0.153018i	0.889015	+	0.457878i	$0.151390\pi$
$464$	−1.71169	−	17.6598i	−0.0794634	−	0.819836i
$465$	7.53724	+	18.1965i	0.349531	+	0.843843i
$466$	−9.92078	+	3.00524i	−0.459571	+	0.139215i
$467$	3.08374	−	0.303722i	0.142698	−	0.0140546i	−0.0264157	−	0.999651i	$-0.508409\pi$
$467$	3.08374	−	0.303722i	0.142698	−	0.0140546i	0.169114	+	0.985596i	$0.445909\pi$
$468$	68.0798	−	36.3216i	3.14699	−	1.67896i
$469$	−1.63133	−	0.871966i	−0.0753280	−	0.0402637i
$470$	−1.38166	+	3.33196i	−0.0637311	+	0.153692i
$471$	4.34468	+	21.8422i	0.200192	+	1.00643i
$472$	8.49446	−	12.6809i	0.390989	−	0.583686i
$473$	10.8362	+	2.15545i	0.498248	+	0.0991078i
$474$	−11.2163	−	56.5026i	−0.515182	−	2.59525i
$475$	−6.69670	−	0.659567i	−0.307266	−	0.0302630i
$476$	−1.08827	+	2.62156i	−0.0498807	+	0.120159i
$477$	−100.143	−	30.3781i	−4.58524	−	1.39092i
$478$	7.43923	−	3.97265i	0.340263	−	0.181705i
$479$	−0.737759	+	0.737759i	−0.0337090	+	0.0337090i	−0.723760	−	0.690051i	$-0.757588\pi$
$479$	−0.737759	+	0.737759i	−0.0337090	+	0.0337090i	0.690051	+	0.723760i	$0.257588\pi$
$480$	18.6639	−	1.80172i	0.851888	−	0.0822368i
$481$	−4.80668	−	4.80668i	−0.219166	−	0.219166i
$482$	24.1793	+	7.34495i	1.10134	+	0.334553i
$483$	−0.441771	+	1.45632i	−0.0201013	+	0.0662650i
$484$	3.79758	−	3.79170i	0.172617	−	0.172350i
$485$	1.40919	−	14.3078i	0.0639881	−	0.649682i
$486$	−61.8464	−	41.3591i	−2.80541	−	1.87609i
$487$	−8.05759	+	40.5083i	−0.365124	+	1.83560i	0.163240	+	0.986586i	$0.447805\pi$
$487$	−8.05759	+	40.5083i	−0.365124	+	1.83560i	−0.528364	+	0.849018i	$0.677195\pi$
$488$	−5.81477	−	5.82831i	−0.263222	−	0.263835i
$489$	48.0373	−	9.55522i	2.17232	−	0.432102i
$490$	9.08306	−	3.75820i	0.410331	−	0.169778i
$491$	−12.6679	+	23.7000i	−0.571694	+	1.06956i	0.415433	+	0.909624i	$0.363630\pi$
$491$	−12.6679	+	23.7000i	−0.571694	+	1.06956i	−0.987127	+	0.159940i	$0.948870\pi$
$492$	−12.2816	−	10.0952i	−0.553697	−	0.455126i
$493$	2.78066	+	28.2325i	0.125234	+	1.27153i
$494$	21.6850	−	40.5320i	0.975656	−	1.82362i
$495$	−27.2961	+	11.3064i	−1.22687	+	0.508186i
$496$	−21.9445	−	9.12961i	−0.985338	−	0.409931i
$497$	−1.60061	−	0.662995i	−0.0717972	−	0.0297394i
$498$	17.0731	−	14.0005i	0.765065	−	0.627376i
$499$	−8.82490	−	7.24241i	−0.395057	−	0.324215i	0.415804	−	0.909454i	$-0.363500\pi$
$499$	−8.82490	−	7.24241i	−0.395057	−	0.324215i	−0.810860	+	0.585240i	$0.801000\pi$
$500$	−1.54700	+	1.26759i	−0.0691841	+	0.0566882i
$501$	−18.8827	+	5.72801i	−0.843618	+	0.255909i
$502$	−4.08449	−	4.08766i	−0.182300	−	0.182441i
$503$	−2.13553	+	3.19604i	−0.0952184	+	0.142504i	−0.876020	−	0.482274i	$-0.839811\pi$
$503$	−2.13553	+	3.19604i	−0.0952184	+	0.142504i	0.780802	+	0.624779i	$0.214811\pi$
$504$	1.44963	+	4.79888i	0.0645717	+	0.213759i
$505$	5.97713	−	3.99379i	0.265979	−	0.177721i
$506$	9.00189	−	6.00982i	0.400183	−	0.267169i
$507$	−21.7287	−	26.4765i	−0.965004	−	1.17586i
$508$	34.3908	−	6.81304i	1.52584	−	0.302280i
$509$	10.5281	−	5.62741i	0.466652	−	0.249431i	−0.221274	−	0.975212i	$-0.571022\pi$
$509$	10.5281	−	5.62741i	0.466652	−	0.249431i	0.687926	+	0.725781i	$0.258522\pi$
$510$	−29.8378	+	2.92709i	−1.32124	+	0.129614i
$511$	−0.982778			−0.0434755
$512$	−14.4156	+	17.4410i	−0.637086	+	0.770792i
$513$	−111.238			−4.91127
$514$	0.531297	−	0.0521202i	0.0234345	−	0.00229893i
$515$	−8.27189	+	4.42142i	−0.364503	+	0.194831i
$516$	19.4232	−	3.84787i	0.855061	−	0.169393i
$517$	5.98539	+	7.29322i	0.263237	+	0.320755i
$518$	0.367293	−	0.245211i	0.0161379	−	0.0107740i
$519$	66.8990	−	44.7005i	2.93654	−	1.96213i
$520$	−3.95082	−	13.0788i	−0.173255	−	0.573545i
$521$	6.57994	−	9.84757i	0.288272	−	0.431430i	−0.658864	−	0.752262i	$-0.728963\pi$
$521$	6.57994	−	9.84757i	0.288272	−	0.431430i	0.947136	+	0.320832i	$0.103963\pi$
$522$	35.4144	+	35.4419i	1.55005	+	1.55125i
$523$	35.8887	−	10.8867i	1.56930	−	0.476043i	0.618485	−	0.785796i	$-0.287747\pi$
$523$	35.8887	−	10.8867i	1.56930	−	0.476043i	0.950817	+	0.309754i	$0.100247\pi$
$524$	−22.4730	+	18.4140i	−0.981740	+	0.804420i
$525$	−0.568582	−	0.466623i	−0.0248149	−	0.0203651i
$526$	−13.1621	+	10.7933i	−0.573893	+	0.470610i
$527$	35.1103	+	14.5432i	1.52943	+	0.633510i
$528$	18.8390	−	45.2827i	0.819863	−	1.97068i
$529$	−17.2942	+	7.16350i	−0.751923	+	0.311457i
$530$	−8.74100	+	16.3380i	−0.379685	+	0.709679i
$531$	4.22465	+	42.8936i	0.183334	+	1.86142i
$532$	2.30707	+	1.89636i	0.100024	+	0.0822176i
$533$	−5.46067	+	10.2162i	−0.236528	+	0.442513i
$534$	13.6166	−	5.63399i	0.589247	−	0.243807i
$535$	0.315826	−	0.0628216i	0.0136543	−	0.00271601i
$536$	16.6522	+	16.6910i	0.719267	+	0.720942i
$537$	3.09955	−	15.5825i	0.133755	−	0.672433i
$538$	−20.0444	−	13.4045i	−0.864176	−	0.577909i
$539$	2.52016	−	25.5876i	0.108551	−	1.10214i
$540$	−23.3963	+	23.3600i	−1.00681	+	1.00525i
$541$	4.36000	−	14.3730i	0.187451	−	0.617943i	−0.811963	−	0.583709i	$-0.801601\pi$
$541$	4.36000	−	14.3730i	0.187451	−	0.617943i	0.999414	−	0.0342342i	$-0.0108992\pi$
$542$	3.11546	+	0.946384i	0.133821	+	0.0406507i
$543$	37.9710	+	37.9710i	1.62949	+	1.62949i
$544$	23.0063	−	27.9227i	0.986386	−	1.19718i
$545$	−9.95234	+	9.95234i	−0.426311	+	0.426311i
$546$	4.43230	−	2.36690i	0.189685	−	0.101294i
$547$	−30.1519	−	9.14649i	−1.28920	−	0.391076i	−0.430055	−	0.902803i	$-0.641506\pi$
$547$	−30.1519	−	9.14649i	−1.28920	−	0.391076i	−0.859148	+	0.511727i	$0.829006\pi$
$548$	−12.3723	+	29.8041i	−0.528520	+	1.27317i
$549$	23.1368	+	2.27878i	0.987456	+	0.0972559i
$550$	1.01859	+	5.13117i	0.0434326	+	0.218794i
$551$	29.2744	+	5.82303i	1.24713	+	0.248069i
$552$	10.7956	−	16.1162i	0.459492	−	0.685950i
$553$	−0.531991	−	2.67450i	−0.0226226	−	0.113731i
$554$	16.2420	−	39.1687i	0.690057	−	1.66412i
$555$	4.11383	+	2.19889i	0.174622	+	0.0933376i
$556$	−21.6298	+	11.5398i	−0.917310	+	0.489398i
$557$	12.8813	−	1.26870i	0.545797	−	0.0537563i	0.178639	−	0.983915i	$-0.442831\pi$
$557$	12.8813	−	1.26870i	0.545797	−	0.0537563i	0.367159	+	0.930158i	$0.380331\pi$
$558$	64.2352	−	19.4583i	2.71929	−	0.823737i
$559$	−5.52121	−	13.3294i	−0.233522	−	0.563773i
$560$	0.883475	−	0.0856317i	0.0373336	−	0.00361860i
$561$	−30.0100	+	72.4504i	−1.26702	+	3.05886i
$562$	0.716338	−	7.24431i	0.0302169	−	0.305583i
$563$	1.99703	−	2.43338i	0.0841646	−	0.102555i	−0.729226	−	0.684273i	$-0.760119\pi$
$563$	1.99703	−	2.43338i	0.0841646	−	0.102555i	0.813390	+	0.581719i	$0.197619\pi$
$564$	14.9060	+	7.98230i	0.627657	+	0.336116i
$565$	0.598207	+	1.97203i	0.0251668	+	0.0829637i
$566$	−0.00153550	+	3.96107i	−6.45420e−5	+	0.166496i
$567$	−5.68891	−	3.80121i	−0.238912	−	0.159636i
$568$	17.0538	+	14.0289i	0.715561	+	0.588640i
$569$	−13.1284	−	19.6481i	−0.550373	−	0.823691i	0.447119	−	0.894475i	$-0.352450\pi$
$569$	−13.1284	−	19.6481i	−0.550373	−	0.823691i	−0.997492	+	0.0707834i	$0.977450\pi$
$570$	−6.16589	+	30.9354i	−0.258261	+	1.29574i
$571$	18.4172	−	15.1146i	0.770736	−	0.632526i	−0.164571	−	0.986365i	$-0.552624\pi$
$571$	18.4172	−	15.1146i	0.770736	−	0.632526i	0.935306	+	0.353839i	$0.115124\pi$
$572$	−35.0443	−	6.99899i	−1.46528	−	0.292643i
$573$	−12.6162	−	23.6032i	−0.527048	−	0.986038i
$574$	−0.581568	−	0.477658i	−0.0242742	−	0.0199370i
$575$			2.06902i			0.0862843i
$576$	0.148618	−	63.8970i	0.00619240	−	2.66238i
$577$			36.3454i			1.51308i	0.653948	+	0.756539i	$0.273111\pi$
$577$			36.3454i			1.51308i	−0.653948	+	0.756539i	$0.726889\pi$
$578$	−21.4571	+	26.1248i	−0.892496	+	1.08665i
$579$	40.5617	+	75.8856i	1.68569	+	3.15370i
$580$	7.38002	−	4.92290i	0.306439	−	0.204412i
$581$	0.807945	−	0.663064i	0.0335192	−	0.0275085i
$582$	−66.0946	−	13.1737i	−2.73971	−	0.546066i
$583$	26.9264	+	40.2982i	1.11518	+	1.66898i
$584$	11.9830	+	3.65024i	0.495861	+	0.151048i
$585$	32.0793	+	21.4347i	1.32632	+	0.886216i
$586$	−1.40048		0.000542893i	−0.0578533		2.24267e-5i
$587$	12.5590	+	41.4014i	0.518364	+	1.70882i	0.690135	+	0.723680i	$0.257551\pi$
$587$	12.5590	+	41.4014i	0.518364	+	1.70882i	−0.171771	+	0.985137i	$0.554949\pi$
$588$	−13.3419	−	44.1054i	−0.550210	−	1.81888i
$589$	25.3656	−	30.9081i	1.04517	−	1.27355i
$590$	7.59449	+	0.750965i	0.312660	+	0.0309167i
$591$	8.19754	−	19.7906i	0.337202	−	0.814077i
$592$	−5.38918	+	1.62567i	−0.221494	+	0.0668145i
$593$	4.12308	+	9.95401i	0.169315	+	0.408762i	0.985647	−	0.168821i	$-0.0539960\pi$
$593$	4.12308	+	9.95401i	0.169315	+	0.408762i	−0.816332	+	0.577583i	$0.803996\pi$
$594$	25.0711	+	82.7637i	1.02868	+	3.39584i
$595$	−1.41240	+	0.139109i	−0.0579028	+	0.00570292i
$596$	−10.1019	+	33.2087i	−0.413788	+	1.36028i
$597$	34.2025	+	18.2816i	1.39982	+	0.748217i
$598$	−13.0561	−	5.41394i	−0.533903	−	0.221392i
$599$	8.66880	+	43.5810i	0.354198	+	1.78067i	0.588489	+	0.808505i	$0.299723\pi$
$599$	8.66880	+	43.5810i	0.354198	+	1.78067i	−0.234291	+	0.972166i	$0.575277\pi$
$600$	5.19960	+	7.80137i	0.212273	+	0.318490i
$601$	22.0505	+	4.38612i	0.899459	+	0.178913i	0.623101	−	0.782141i	$-0.285873\pi$
$601$	22.0505	+	4.38612i	0.899459	+	0.178913i	0.276358	+	0.961055i	$0.410873\pi$
$602$	0.919381	−	0.182506i	0.0374712	−	0.00743838i
$603$	−66.2588	−	6.52592i	−2.69827	−	0.265756i
$604$	−8.39805	+	3.47096i	−0.341712	+	0.141231i
$605$	2.56768	+	0.778896i	0.104391	+	0.0316666i
$606$	−15.8736	−	29.7251i	−0.644821	−	1.20750i
$607$	22.9514	−	22.9514i	0.931569	−	0.931569i	−0.0662354	−	0.997804i	$-0.521099\pi$
$607$	22.9514	−	22.9514i	0.931569	−	0.931569i	0.997804	+	0.0662354i	$0.0210988\pi$
$608$	−21.0867	−	31.6913i	−0.855179	−	1.28525i
$609$	2.30701	+	2.30701i	0.0934846	+	0.0934846i
$610$	1.19647	−	3.93874i	0.0484437	−	0.159475i
$611$	3.57644	−	11.7899i	0.144687	−	0.476969i
$612$	−0.0792097	+	102.167i	−0.00320186	+	4.12986i
$613$	−0.686690	+	6.97208i	−0.0277352	+	0.281600i	0.971307	+	0.237831i	$0.0764365\pi$
$613$	−0.686690	+	6.97208i	−0.0277352	+	0.281600i	−0.999042	+	0.0437687i	$0.986064\pi$
$614$	20.4739	−	30.6157i	0.826261	−	1.23555i
$615$	1.55078	−	7.79632i	0.0625337	−	0.314378i
$616$	0.890966	−	2.14393i	0.0358980	−	0.0863812i
$617$	19.6639	−	3.91138i	0.791637	−	0.157466i	0.217321	−	0.976100i	$-0.430268\pi$
$617$	19.6639	−	3.91138i	0.791637	−	0.157466i	0.574316	+	0.818634i	$0.305268\pi$
$618$	16.8099	+	40.6272i	0.676194	+	1.63427i
$619$	−4.68495	+	8.76493i	−0.188304	+	0.352292i	−0.958303	−	0.285752i	$-0.907756\pi$
$619$	−4.68495	+	8.76493i	−0.188304	+	0.352292i	0.769999	+	0.638045i	$0.220256\pi$
$620$	−1.15566	−	11.8276i	−0.0464124	−	0.475008i
$621$	3.35245	+	34.0380i	0.134529	+	1.36590i
$622$	−7.06492	−	3.77980i	−0.283277	−	0.151556i
$623$	0.644475	−	0.266950i	0.0258203	−	0.0106951i
$624$	−62.8342	+	12.3973i	−2.51538	+	0.496287i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−23.2601	−	28.3649i	−0.929660	−	1.13369i
$627$	63.7792	+	52.3422i	2.54710	+	2.09035i
$628$	1.32745	−	13.3715i	0.0529708	−	0.533581i
$629$	8.61287	−	2.61268i	0.343417	−	0.104175i
$630$	−1.77307	+	1.77169i	−0.0706407	+	0.0705859i
$631$	−7.23559	+	10.8288i	−0.288044	+	0.431089i	−0.947068	−	0.321034i	$-0.895970\pi$
$631$	−7.23559	+	10.8288i	−0.288044	+	0.431089i	0.659024	+	0.752122i	$0.270970\pi$
$632$	−3.44705	+	34.5861i	−0.137116	+	1.37576i
$633$	−58.4844	+	39.0780i	−2.32455	+	1.55321i
$634$	−14.2056	−	21.2781i	−0.564178	−	0.845061i
$635$	11.1206	+	13.5505i	0.441309	+	0.537737i
$636$	72.1836	+	48.3125i	2.86227	+	1.91572i
$637$	−29.6107	+	15.8272i	−1.17322	+	0.627098i
$638$	−2.26545	−	23.0933i	−0.0896901	−	0.914272i
$639$	−62.3587			−2.46687
$640$	−11.0903	−	2.23730i	−0.438382	−	0.0884369i
$641$	6.72231			0.265515			0.132758	−	0.991149i	$-0.457617\pi$
$641$	6.72231			0.265515			0.132758	+	0.991149i	$0.457617\pi$
$642$	−0.147374	−	1.50228i	−0.00581638	−	0.0592903i
$643$	−36.3028	+	19.4042i	−1.43164	+	0.765228i	−0.991177	−	0.132543i	$-0.957686\pi$
$643$	−36.3028	+	19.4042i	−1.43164	+	0.765228i	−0.440464	+	0.897770i	$0.645186\pi$
$644$	0.510744	−	0.763101i	0.0201261	−	0.0300704i
$645$	6.28072	+	7.65308i	0.247303	+	0.301340i
$646$	33.7947	+	50.6197i	1.32963	+	1.99161i
$647$	9.63626	−	6.43874i	0.378840	−	0.253133i	−0.351541	−	0.936172i	$-0.614342\pi$
$647$	9.63626	−	6.43874i	0.378840	−	0.253133i	0.730382	+	0.683039i	$0.239342\pi$
$648$	55.2465	+	67.4780i	2.17029	+	2.65078i
$649$	11.0900	−	16.5973i	0.435319	−	0.651501i
$650$	4.83231	−	4.82857i	0.189539	−	0.189392i
$651$	4.18237	−	1.26871i	0.163920	−	0.0497246i
$652$	−29.4078	−	2.91944i	−1.15170	−	0.114334i
$653$	−38.2641	−	31.4026i	−1.49739	−	1.22888i	−0.906556	−	0.422085i	$-0.861298\pi$
$653$	−38.2641	−	31.4026i	−1.49739	−	1.22888i	−0.590835	−	0.806792i	$-0.701202\pi$
$654$	41.8361	+	51.0177i	1.63592	+	1.99495i
$655$	−13.4210	−	5.55917i	−0.524403	−	0.217215i
$656$	5.31695	+	7.98415i	0.207592	+	0.311729i
$657$	−32.6812	+	13.5370i	−1.27501	+	0.528128i
$658$	0.705764	+	0.377590i	0.0275135	+	0.0147200i
$659$	−0.562038	−	5.70647i	−0.0218939	−	0.222292i	−0.999906	−	0.0137423i	$-0.995626\pi$
$659$	−0.562038	−	5.70647i	−0.0218939	−	0.222292i	0.978012	−	0.208550i	$-0.0668744\pi$
$660$	24.4064	−	2.38471i	0.950017	−	0.0928249i
$661$	−21.5073	+	40.2374i	−0.836538	+	1.56505i	−0.0115297	+	0.999934i	$0.503670\pi$
$661$	−21.5073	+	40.2374i	−0.836538	+	1.56505i	−0.825009	+	0.565120i	$0.808830\pi$
$662$	9.29199	+	22.4575i	0.361143	+	0.872834i
$663$	100.437	−	19.9781i	3.90063	−	0.775884i
$664$	−12.3141	+	5.08388i	−0.477878	+	0.197293i
$665$	−0.291312	+	1.46452i	−0.0112966	+	0.0567917i
$666$	8.83632	−	13.2134i	0.342401	−	0.512009i
$667$	0.899547	−	9.13326i	0.0348306	−	0.353641i
$668$	11.9060	+	0.00923071i	0.460659	+	0.000357147i
$669$	−12.0928	+	39.8647i	−0.467535	+	1.54126i
$670$	−3.42643	+	11.2797i	−0.132375	+	0.435772i
$671$	−7.61355	−	7.61355i	−0.293918	−	0.293918i
$672$	0.00806473	−	4.16085i	0.000311104	−	0.160508i
$673$	−7.53653	+	7.53653i	−0.290512	+	0.290512i	−0.837282	−	0.546771i	$-0.815857\pi$
$673$	−7.53653	+	7.53653i	−0.290512	+	0.290512i	0.546771	+	0.837282i	$0.315857\pi$
$674$	−18.3305	−	34.3260i	−0.706066	−	1.32219i
$675$	−15.8190	−	4.79865i	−0.608875	−	0.184700i
$676$	7.89383	+	19.0993i	0.303609	+	0.734587i
$677$	−23.9592	−	2.35978i	−0.920828	−	0.0906936i	−0.373517	−	0.927623i	$-0.621848\pi$
$677$	−23.9592	−	2.35978i	−0.920828	−	0.0906936i	−0.547310	+	0.836930i	$0.684348\pi$
$678$	9.47529	−	1.88093i	0.363896	−	0.0722368i
$679$	−3.12901	−	0.622398i	−0.120080	−	0.0238855i
$680$	17.7381	+	3.54978i	0.680225	+	0.136128i
$681$	2.84372	+	14.2963i	0.108972	+	0.547837i
$682$	−28.7134	−	11.9065i	−1.09949	−	0.455925i
$683$	0.167986	+	0.0897905i	0.00642781	+	0.00343574i	0.474608	−	0.880198i	$-0.342590\pi$
$683$	0.167986	+	0.0897905i	0.00642781	+	0.00343574i	−0.468180	+	0.883633i	$0.655090\pi$
$684$	102.840	+	31.2832i	3.93218	+	1.19614i
$685$	−16.0573	+	1.58151i	−0.613519	+	0.0604264i
$686$	−1.26925	−	4.19000i	−0.0484601	−	0.159975i
$687$	−28.4537	−	68.6933i	−1.08558	−	2.62081i
$688$	−11.8879	−	1.18947i	−0.453222	−	0.0453482i
$689$	24.2198	−	58.4718i	0.922702	−	2.22760i
$690$	9.65184	+	0.954402i	0.367439	+	0.0363335i
$691$	14.3496	−	17.4850i	0.545883	−	0.665160i	−0.424866	−	0.905256i	$-0.639679\pi$
$691$	14.3496	−	17.4850i	0.545883	−	0.665160i	0.970749	+	0.240096i	$0.0771789\pi$
$692$	−46.4673	+	14.0564i	−1.76642	+	0.534343i
$693$	1.90316	+	6.27387i	0.0722950	+	0.238325i
$694$	−43.0807	−	0.0167001i	−1.63532	−	0.000633929i
$695$	−10.1920	−	6.81009i	−0.386605	−	0.258321i
$696$	−19.5607	−	36.6981i	−0.741446	−	1.39104i
$697$	−8.52121	−	12.7529i	−0.322764	−	0.483050i
$698$	−12.3807	−	2.46766i	−0.468615	−	0.0934022i
$699$	−18.7812	+	15.4133i	−0.710369	+	0.582985i
$700$	0.246280	+	0.369204i	0.00930852	+	0.0139546i
$701$	0.330872	+	0.619018i	0.0124969	+	0.0233800i	0.888092	−	0.459665i	$-0.152031\pi$
$701$	0.330872	+	0.619018i	0.0124969	+	0.0233800i	−0.875595	+	0.483045i	$0.839531\pi$
$702$	71.6738	−	87.2657i	2.70515	−	3.29363i
$703$		−	9.46958i		−	0.357152i
$704$	−18.8265	+	22.8317i	−0.709552	+	0.860503i
$705$			8.45439i			0.318411i
$706$	4.04996	+	3.32635i	0.152422	+	0.125189i
$707$	−0.751966	−	1.40683i	−0.0282806	−	0.0529093i
$708$	7.00639	−	35.0813i	0.263316	−	1.31844i
$709$	2.05440	−	1.68601i	0.0771548	−	0.0633193i	−0.595025	−	0.803707i	$-0.702858\pi$
$709$	2.05440	−	1.68601i	0.0771548	−	0.0633193i	0.672180	+	0.740388i	$0.265358\pi$
$710$	−2.15825	+	10.8283i	−0.0809977	+	0.406379i
$711$	−54.5299	−	81.6097i	−2.04503	−	3.06060i
$712$	−8.84961	+	0.861220i	−0.331653	+	0.0322756i
$713$	−10.2222	−	6.83022i	−0.382823	−	0.255794i
$714$	−0.00257899	+	6.65291i	−9.65161e−5	+	0.248979i
$715$	−5.18686	−	17.0988i	−0.193978	−	0.639459i
$716$	−4.52549	+	8.45083i	−0.169126	+	0.315822i
$717$	12.5399	−	15.2799i	0.468312	−	0.570639i
$718$	−0.227830	+	2.30404i	−0.00850253	+	0.0859859i
$719$	−5.73724	+	13.8509i	−0.213963	+	0.516552i	−0.994025	−	0.109150i	$-0.965187\pi$
$719$	−5.73724	+	13.8509i	−0.213963	+	0.516552i	0.780063	+	0.625702i	$0.215187\pi$
$720$	28.1995	−	15.0168i	1.05093	−	0.559642i
$721$	0.796488	+	1.92289i	0.0296628	+	0.0716123i
$722$	35.5705	−	10.7751i	1.32380	−	0.401009i
$723$	58.9442	−	5.80550i	2.19216	−	0.215909i
$724$	−15.2514	−	28.5867i	−0.566815	−	1.06242i
$725$	3.91189	+	2.09095i	0.145284	+	0.0776558i
$726$	4.81791	−	11.6187i	0.178810	−	0.431212i
$727$	−3.46917	−	17.4407i	−0.128665	−	0.646840i	−0.990258	−	0.139242i	$-0.955533\pi$
$727$	−3.46917	−	17.4407i	−0.128665	−	0.646840i	0.861594	−	0.507598i	$-0.169467\pi$
$728$	−2.97420	+	0.588011i	−0.110231	+	0.0217931i
$729$	−80.3117	−	15.9750i	−2.97451	−	0.591666i
$730$	1.21953	+	6.14346i	0.0451370	+	0.227380i
$731$	19.0108	+	1.87240i	0.703141	+	0.0692533i
$732$	−17.8220	−	7.39831i	−0.658720	−	0.273449i
$733$	44.7256	+	13.5674i	1.65198	+	0.501122i	0.972565	−	0.232632i	$-0.0747339\pi$
$733$	44.7256	+	13.5674i	1.65198	+	0.501122i	0.679414	+	0.733755i	$0.262234\pi$
$734$	−27.5593	+	14.7170i	−1.01723	+	0.543215i
$735$	16.2915	−	16.2915i	0.600919	−	0.600919i
$736$	−9.06182	+	7.40750i	−0.334023	+	0.273044i
$737$	21.8035	+	21.8035i	0.803144	+	0.803144i
$738$	−25.9187	−	7.87333i	−0.954082	−	0.289821i
$739$	4.27624	−	14.0969i	0.157304	−	0.518562i	−0.842493	−	0.538707i	$-0.818913\pi$
$739$	4.27624	−	14.0969i	0.157304	−	0.518562i	0.999797	+	0.0201453i	$0.00641289\pi$
$740$	−1.98862	−	1.99171i	−0.0731031	−	0.0732166i
$741$	10.5606	−	107.223i	0.387953	−	3.93895i
$742$	3.41789	+	2.28568i	0.125475	+	0.0839100i
$743$	−0.406350	+	2.04286i	−0.0149075	+	0.0749452i	−0.987523	−	0.157475i	$-0.949665\pi$
$743$	−0.406350	+	2.04286i	−0.0149075	+	0.0749452i	0.972615	+	0.232420i	$0.0746645\pi$
$744$	−55.7080	−	0.0647853i	−2.04235	−	0.00237514i
$745$	−17.0221	+	3.38590i	−0.623641	+	0.124050i
$746$	−11.7134	+	4.84655i	−0.428860	+	0.177445i
$747$	17.7341	−	33.1782i	0.648858	−	1.21393i
$748$	30.0457	−	36.5529i	1.09858	−	1.33651i
$749$	−0.00700391	−	0.0711118i	−0.000255917	−	0.00259837i
$750$	−2.21136	+	4.13330i	−0.0807474	+	0.150927i
$751$	−32.1049	+	13.2983i	−1.17152	+	0.485261i	−0.881696	−	0.471818i	$-0.843598\pi$
$751$	−32.1049	+	13.2983i	−1.17152	+	0.485261i	−0.289827	+	0.957079i	$0.593598\pi$
$752$	−7.20295	−	7.22532i	−0.262664	−	0.263480i
$753$	−12.5131	−	5.18309i	−0.456002	−	0.188882i
$754$	−23.4305	+	19.2137i	−0.853288	+	0.699722i
$755$	−3.51220	−	2.88239i	−0.127822	−	0.104901i
$756$	4.64984	+	5.67481i	0.169113	+	0.206391i
$757$	9.44875	−	2.86625i	0.343420	−	0.104175i	−0.113863	−	0.993496i	$-0.536322\pi$
$757$	9.44875	−	2.86625i	0.343420	−	0.104175i	0.457283	+	0.889321i	$0.348822\pi$
$758$	16.6605	+	16.6734i	0.605137	+	0.605607i
$759$	14.0942	−	21.0935i	0.511588	−	0.765646i
$760$	8.99150	−	16.7750i	0.326156	−	0.608492i
$761$	14.2697	−	9.53473i	0.517277	−	0.345634i	−0.269369	−	0.963037i	$-0.586815\pi$
$761$	14.2697	−	9.53473i	0.517277	−	0.345634i	0.786647	+	0.617403i	$0.211815\pi$
$762$	68.3420	−	45.6263i	2.47577	−	1.65287i
$763$	1.98136	+	2.41429i	0.0717301	+	0.0874033i
$764$	3.13811	+	15.8405i	0.113533	+	0.573090i
$765$	−45.0517	+	24.0806i	−1.62885	+	0.870636i
$766$	−0.749946	+	0.0735697i	−0.0270966	+	0.00265818i
$767$	−26.0665			−0.941208
$768$	−15.5526	+	50.7033i	−0.561205	+	1.82960i
$769$	−48.4093			−1.74568			−0.872842	−	0.488003i	$-0.837726\pi$
$769$	−48.4093			−1.74568			−0.872842	+	0.488003i	$0.837726\pi$
$770$	1.15530	−	0.113335i	0.0416341	−	0.00408430i
$771$	1.10351	−	0.589836i	0.0397418	−	0.0212424i
$772$	−10.0892	−	50.9281i	−0.363118	−	1.83294i
$773$	−31.3606	−	38.2130i	−1.12796	−	1.37443i	−0.917935	−	0.396732i	$-0.870144\pi$
$773$	−31.3606	−	38.2130i	−1.12796	−	1.37443i	−0.210028	−	0.977695i	$-0.567356\pi$
$774$	28.0591	−	18.7328i	1.00856	−	0.673336i
$775$	4.94057	−	3.30118i	0.177470	−	0.118582i
$776$	35.8403	+	19.2107i	1.28659	+	0.689623i
$777$	0.575069	−	0.860652i	0.0206305	−	0.0308757i
$778$	−5.23754	−	5.24161i	−0.187775	−	0.187921i
$779$	−15.4424	+	4.68440i	−0.553282	+	0.167836i
$780$	−20.2958	−	24.7697i	−0.726708	−	0.886897i
$781$	22.3247	+	18.3214i	0.798839	+	0.655590i
$782$	14.4708	−	11.8665i	0.517476	−	0.424346i
$783$	67.7434	+	28.0602i	2.42095	+	1.00279i
$784$	−0.0431111	+	27.8030i	−0.00153968	+	0.992964i
$785$	6.20719	−	2.57110i	0.221544	−	0.0917665i
$786$	−32.1240	+	60.0437i	−1.14582	+	2.14169i
$787$	−3.71919	−	37.7616i	−0.132575	−	1.34605i	−0.799381	−	0.600824i	$-0.794839\pi$
$787$	−3.71919	−	37.7616i	−0.132575	−	1.34605i	0.666807	−	0.745231i	$-0.267661\pi$
$788$	−8.20729	+	9.98482i	−0.292373	+	0.355694i
$789$	−18.8068	+	35.1850i	−0.669539	+	1.25262i
$790$	−16.0584	+	6.64433i	−0.571334	+	0.236395i
$791$	0.448504	−	0.0892130i	0.0159470	−	0.00317205i
$792$	0.0971828	−	83.5662i	0.00345324	−	2.96940i
$793$	−2.74303	+	13.7901i	−0.0974079	+	0.489702i
$794$	15.2803	+	10.2186i	0.542279	+	0.362644i
$795$	−4.25686	+	43.2206i	−0.150975	+	1.53288i
$796$	−16.5335	−	16.5591i	−0.586013	−	0.586922i
$797$	−11.9860	+	39.5127i	−0.424567	+	1.39961i	0.440409	+	0.897797i	$0.354834\pi$
$797$	−11.9860	+	39.5127i	−0.424567	+	1.39961i	−0.864976	+	0.501813i	$0.832666\pi$
$798$	6.69751	+	2.03450i	0.237089	+	0.0720206i
$799$	11.5349	+	11.5349i	0.408075	+	0.408075i
$800$	−1.63160	−	5.41644i	−0.0576859	−	0.191500i
$801$	17.7543	−	17.7543i	0.627316	−	0.627316i
$802$	−31.7099	+	16.9335i	−1.11972	+	0.597943i
$803$	15.6772	+	4.75564i	0.553237	+	0.167823i
$804$	51.0383	+	21.1871i	1.79998	+	0.747213i
$805$	0.456914	+	0.0450021i	0.0161041	+	0.00158612i
$806$	7.90351	+	39.8143i	0.278389	+	1.40240i
$807$	−55.4321	−	11.0261i	−1.95130	−	0.388138i
$808$	3.94349	+	19.9465i	0.138731	+	0.701714i
$809$	−0.788691	−	3.96502i	−0.0277289	−	0.139403i	0.964441	−	0.264298i	$-0.0851403\pi$
$809$	−0.788691	−	3.96502i	−0.0277289	−	0.139403i	−0.992170	+	0.124896i	$0.960140\pi$
$810$	−16.7024	+	40.2789i	−0.586862	+	1.41526i
$811$	−22.5254	−	12.0401i	−0.790974	−	0.422784i	0.0258543	−	0.999666i	$-0.491769\pi$
$811$	−22.5254	−	12.0401i	−0.790974	−	0.422784i	−0.816828	+	0.576882i	$0.804269\pi$
$812$	−0.926632	−	1.73684i	−0.0325184	−	0.0609513i
$813$	7.59486	−	0.748029i	0.266363	−	0.0262345i
$814$	−7.04561	+	2.13428i	−0.246949	+	0.0748065i
$815$	−5.65460	−	13.6514i	−0.198072	−	0.478188i
$816$	24.7417	−	81.1095i	0.866133	−	2.83940i
$817$	7.69140	−	18.5687i	0.269088	−	0.649636i
$818$	3.43864	−	34.7749i	0.120229	−	1.21588i
$819$	5.43128	−	6.61803i	0.189784	−	0.231253i
$820$	−2.26422	+	4.22817i	−0.0790701	+	0.147654i
$821$	6.01806	+	19.8389i	0.210032	+	0.692382i	0.997141	+	0.0755681i	$0.0240770\pi$
$821$	6.01806	+	19.8389i	0.210032	+	0.692382i	−0.787109	+	0.616814i	$0.788423\pi$
$822$	−0.0293201	+	75.6358i	−0.00102265	+	2.63810i
$823$	−1.43366	−	0.957943i	−0.0499743	−	0.0333918i	0.530332	−	0.847790i	$-0.322067\pi$
$823$	−1.43366	−	0.957943i	−0.0499743	−	0.0333918i	−0.580306	+	0.814398i	$0.697067\pi$
$824$	−2.56959	−	26.4042i	−0.0895158	−	0.919834i
$825$	6.81201	+	10.1949i	0.237164	+	0.354941i
$826$	0.331023	−	1.66080i	0.0115178	−	0.0577866i
$827$	−25.5071	+	20.9332i	−0.886970	+	0.727917i	−0.963089	−	0.269182i	$-0.913247\pi$
$827$	−25.5071	+	20.9332i	−0.886970	+	0.727917i	0.0761199	+	0.997099i	$0.475747\pi$
$828$	6.47310	−	32.4111i	0.224956	−	1.12637i
$829$	−0.358648	−	0.670983i	−0.0124564	−	0.0233042i	0.875616	−	0.483008i	$-0.160456\pi$
$829$	−0.358648	−	0.670983i	−0.0124564	−	0.0233042i	−0.888072	+	0.459703i	$0.847956\pi$
$830$	−5.14747	−	4.22776i	−0.178671	−	0.146748i
$831$		−	99.3852i		−	3.44763i
$832$	38.4485	+	3.87716i	1.33296	+	0.134416i
$833$		−	44.4551i		−	1.54028i
$834$	−36.4699	+	44.4036i	−1.26285	+	1.53757i
$835$	2.80624	+	5.25010i	0.0971138	+	0.181687i
$836$	−27.6259	−	41.4145i	−0.955460	−	1.43235i
$837$	75.9295	−	62.3137i	2.62451	−	2.15388i
$838$	−16.6505	−	3.31871i	−0.575183	−	0.114643i
$839$	−0.324572	−	0.485756i	−0.0112055	−	0.0167701i	0.825825	−	0.563927i	$-0.190710\pi$
$839$	−0.324572	−	0.485756i	−0.0112055	−	0.0167701i	−0.837030	+	0.547157i	$0.815710\pi$
$840$	1.83591	−	0.978572i	0.0633450	−	0.0337639i
$841$	7.75353	+	5.18075i	0.267363	+	0.178646i
$842$	35.9719	+	0.0139444i	1.23967	+	0.000480557i
$843$	−4.95293	−	16.3276i	−0.170588	−	0.562353i
$844$	40.6226	−	12.2883i	1.39829	−	0.422982i
$845$	−6.55527	+	7.98762i	−0.225508	+	0.274782i
$846$	28.6704	+	2.83501i	0.985709	+	0.0974696i
$847$	0.227856	−	0.550093i	0.00782922	−	0.0189014i
$848$	−33.1850	−	40.5641i	−1.13958	−	1.39298i
$849$	3.55288	+	8.57740i	0.121934	+	0.294376i
$850$	2.62224	+	8.65645i	0.0899422	+	0.296914i
$851$	−2.89763	+	0.285392i	−0.0993295	+	0.00978311i
$852$	49.5177	+	15.0630i	1.69645	+	0.516049i
$853$	−33.5594	−	17.9379i	−1.14905	−	0.614181i	−0.216880	−	0.976198i	$-0.569588\pi$
$853$	−33.5594	−	17.9379i	−1.14905	−	0.614181i	−0.932171	+	0.362017i	$0.882088\pi$
$854$	−0.843789	−	0.349892i	−0.0288739	−	0.0119731i
$855$	10.4854	+	52.7136i	0.358593	+	1.80277i
$856$	−0.178725	+	0.893082i	−0.00610870	+	0.0305249i
$857$	−19.7690	−	3.93230i	−0.675297	−	0.134325i	−0.154483	−	0.987995i	$-0.549371\pi$
$857$	−19.7690	−	3.93230i	−0.675297	−	0.134325i	−0.520813	+	0.853671i	$0.674371\pi$
$858$	−82.1572	+	16.3090i	−2.80480	+	0.556779i
$859$	−31.7856	−	3.13061i	−1.08451	−	0.106815i	−0.460067	−	0.887884i	$-0.652175\pi$
$859$	−31.7856	−	3.13061i	−1.08451	−	0.106815i	−0.624445	+	0.781069i	$0.714675\pi$
$860$	−2.28173	−	5.52069i	−0.0778064	−	0.188254i
$861$	−1.68797	−	0.512041i	−0.0575260	−	0.0174503i
$862$	−0.00337322	−	0.00631675i	−0.000114892	−	0.000215149i
$863$	4.30942	−	4.30942i	0.146694	−	0.146694i	−0.629945	−	0.776640i	$-0.716923\pi$
$863$	4.30942	−	4.30942i	0.146694	−	0.146694i	0.776640	+	0.629945i	$0.216923\pi$
$864$	−35.6182	−	86.4636i	−1.21176	−	2.94155i
$865$	−17.1639	−	17.1639i	−0.583590	−	0.583590i
$866$	8.62224	−	28.3841i	0.292996	−	0.964531i
$867$	−23.0016	+	75.8262i	−0.781176	+	2.57519i
$868$	−2.63709	−	0.00204453i	−0.0895087	−	6.93957e-5i
$869$	−4.45553	+	45.2378i	−0.151144	+	1.53459i
$870$	11.5586	−	17.2841i	0.391873	−	0.585987i
$871$	7.85544	−	39.4919i	0.266171	−	1.33813i
$872$	−15.1916	−	36.7967i	−0.514452	−	1.24609i
$873$	−112.625	+	22.4024i	−3.81177	+	0.758208i
$874$	−7.52785	−	18.1938i	−0.254633	−	0.615414i
$875$	−0.104605	+	0.195702i	−0.00353629	+	0.00661593i
$876$	29.2213	−	2.85517i	0.987297	−	0.0964674i
$877$	−1.58260	−	16.0684i	−0.0534407	−	0.542593i	−0.984212	−	0.176992i	$-0.943363\pi$
$877$	−1.58260	−	16.0684i	−0.0534407	−	0.542593i	0.930772	−	0.365601i	$-0.119137\pi$
$878$	28.0117	+	14.9865i	0.945349	+	0.505771i
$879$	−3.03263	+	1.25616i	−0.102288	+	0.0423691i
$880$	−14.5075	−	2.90912i	−0.489049	−	0.0980664i
$881$	34.6964	+	14.3717i	1.16895	+	0.484196i	0.880846	−	0.473403i	$-0.156975\pi$
$881$	34.6964	+	14.3717i	1.16895	+	0.484196i	0.288106	+	0.957599i	$0.406975\pi$
$882$	−49.7843	−	60.7103i	−1.67632	−	2.04422i
$883$	25.4116	+	20.8547i	0.855167	+	0.701818i	0.956089	−	0.293077i	$-0.0946791\pi$
$883$	25.4116	+	20.8547i	0.855167	+	0.701818i	−0.100922	+	0.994894i	$0.532179\pi$
$884$	−61.4860	−	6.10397i	−2.06800	−	0.205299i
$885$	17.1169	−	5.19234i	0.575377	−	0.174539i
$886$	22.5748	−	22.5573i	0.758416	−	0.757828i
$887$	27.8910	−	41.7419i	0.936489	−	1.40156i	0.0207490	−	0.999785i	$-0.493395\pi$
$887$	27.8910	−	41.7419i	0.936489	−	1.40156i	0.915740	−	0.401771i	$-0.131605\pi$
$888$	−10.2085	+	8.35803i	−0.342574	+	0.280477i
$889$	3.23432	−	2.16110i	0.108476	−	0.0724810i
$890$	−2.46847	−	3.69743i	−0.0827433	−	0.123938i
$891$	72.3553	+	88.1652i	2.42399	+	2.95364i
$892$	13.9808	−	20.8887i	0.468113	−	0.699406i
$893$	15.1365	−	8.09065i	0.506525	−	0.270743i
$894$	7.94302	+	80.9686i	0.265654	+	2.70799i
$895$	−4.79314			−0.160217
$896$	−0.735292	+	2.40047i	−0.0245644	+	0.0801939i
$897$	−33.1280			−1.10611
$898$	−0.132593	−	1.35161i	−0.00442469	−	0.0451038i
$899$	−23.2443	+	12.4243i	−0.775241	+	0.414375i
$900$	13.2753	+	8.88514i	0.442509	+	0.296171i
$901$	53.1609	+	64.7768i	1.77105	+	2.15803i
$902$	6.96577	+	10.4338i	0.231935	+	0.347406i
$903$	1.82668	−	1.22055i	0.0607881	−	0.0406173i
$904$	−5.79998	−	0.578059i	−0.192904	−	0.0192260i
$905$	9.00044	−	13.4701i	0.299185	−	0.447762i
$906$	−15.0662	+	15.0546i	−0.500542	+	0.500154i
$907$	−24.8582	+	7.54065i	−0.825403	+	0.250383i	−0.674603	−	0.738181i	$-0.735685\pi$
$907$	−24.8582	+	7.54065i	−0.825403	+	0.250383i	−0.150800	+	0.988564i	$0.548185\pi$
$908$	0.868851	−	8.75203i	0.0288338	−	0.290446i
$909$	−44.3837	−	36.4248i	−1.47212	−	1.20813i
$910$	−0.961213	−	1.17217i	−0.0318639	−	0.0388570i
$911$	42.1499	+	17.4591i	1.39649	+	0.578445i	0.948838	−	0.315764i	$-0.102261\pi$
$911$	42.1499	+	17.4591i	1.39649	+	0.578445i	0.447651	+	0.894208i	$0.352261\pi$
$912$	−74.1063	−	49.6826i	−2.45391	−	1.64516i
$913$	−16.0969	+	6.66754i	−0.532728	+	0.220663i
$914$	3.18473	+	1.70386i	0.105342	+	0.0563588i
$915$	−0.945699	−	9.60184i	−0.0312638	−	0.317427i
$916$	4.36271	+	44.6502i	0.144148	+	1.47528i
$917$	−1.51957	+	2.84292i	−0.0501808	+	0.0938816i
$918$	57.1652	+	138.161i	1.88673	+	4.55998i
$919$	42.3150	−	8.41698i	1.39584	−	0.277650i	0.560853	−	0.827916i	$-0.310473\pi$
$919$	42.3150	−	8.41698i	1.39584	−	0.277650i	0.834990	+	0.550265i	$0.185473\pi$
$920$	−5.40401	−	2.24578i	−0.178165	−	0.0740413i
$921$	16.8412	−	84.6666i	0.554938	−	2.78986i
$922$	−13.4534	+	20.1176i	−0.443064	+	0.662537i
$923$	3.69653	−	37.5315i	0.121673	−	1.23536i
$924$	0.00421890	−	5.44166i	0.000138792	−	0.179017i
$925$	0.408506	−	1.34666i	0.0134316	−	0.0442780i
$926$	1.46491	−	4.82244i	0.0481400	−	0.158475i
$927$	52.9727	+	52.9727i	1.73985	+	1.73985i
$928$	4.84745	+	24.6191i	0.159125	+	0.808161i
$929$	10.2177	−	10.2177i	0.335233	−	0.335233i	−0.519336	−	0.854570i	$-0.673821\pi$
$929$	10.2177	−	10.2177i	0.335233	−	0.335233i	0.854570	+	0.519336i	$0.173821\pi$
$930$	−13.1208	−	24.5701i	−0.430247	−	0.805686i
$931$	−44.7584	−	13.5773i	−1.46690	−	0.444978i
$932$	13.5481	−	5.59952i	0.443784	−	0.183418i
$933$	−18.6895	−	1.84076i	−0.611868	−	0.0602637i
$934$	−4.29830	+	0.853252i	−0.140645	+	0.0279193i
$935$	23.2037	+	4.61550i	0.758842	+	0.150943i
$936$	−90.8044	+	60.5209i	−2.96803	+	1.97819i
$937$	−0.114707	−	0.576673i	−0.00374733	−	0.0188391i	0.978866	−	0.204501i	$-0.0655571\pi$
$937$	−0.114707	−	0.576673i	−0.00374733	−	0.0188391i	−0.982614	+	0.185662i	$0.940557\pi$
$938$	2.41643	+	1.00201i	0.0788991	+	0.0327169i
$939$	−75.8255	−	40.5296i	−2.47447	−	1.32263i
$940$	1.48458	−	4.88036i	0.0484215	−	0.159180i
$941$	−31.2951	+	3.08230i	−1.02019	+	0.100480i	−0.594258	−	0.804274i	$-0.702554\pi$
$941$	−31.2951	+	3.08230i	−1.02019	+	0.100480i	−0.425934	+	0.904754i	$0.640054\pi$
$942$	−9.13073	−	30.1421i	−0.297495	−	0.982081i
$943$	1.89880	+	4.58410i	0.0618333	+	0.149279i
$944$	−10.2047	+	19.0207i	−0.332135	+	0.619070i
$945$	−1.40378	+	3.38903i	−0.0456650	+	0.110245i
$946$	−15.5491	−	1.53754i	−0.505544	−	0.0499896i
$947$	−33.4099	+	40.7101i	−1.08568	+	1.32290i	−0.142804	+	0.989751i	$0.545612\pi$
$947$	−33.4099	+	40.7101i	−1.08568	+	1.32290i	−0.942874	+	0.333151i	$0.891888\pi$
$948$	23.5879	+	77.9764i	0.766098	+	2.53255i
$949$	−6.21013	−	20.4721i	−0.201590	−	0.664552i
$950$	9.51639	+	0.00368901i	0.308752	+	0.000119687i
$951$	−49.8595	−	33.3151i	−1.61681	−	1.08031i
$952$	1.16973	−	3.83999i	0.0379111	−	0.124455i
$953$	−0.597954	−	0.894902i	−0.0193696	−	0.0289887i	0.821658	−	0.569980i	$-0.193049\pi$
$953$	−0.597954	−	0.894902i	−0.0193696	−	0.0289887i	−0.841028	+	0.540991i	$0.818049\pi$
$954$	145.142	+	28.9290i	4.69914	+	0.936610i
$955$	−6.24143	+	5.12221i	−0.201968	+	0.165751i
$956$	−9.92189	+	6.61848i	−0.320897	+	0.214057i
$957$	−25.6377	−	47.9648i	−0.828750	−	1.55048i
$958$	0.936500	−	1.14023i	0.0302569	−	0.0368391i
$959$			3.58043i			0.115618i
$960$	−26.0199	+	5.11280i	−0.839790	+	0.165015i
$961$			4.30697i			0.138935i
$962$	7.42887	+	6.10153i	0.239516	+	0.196721i
$963$	−1.21242	−	2.26827i	−0.0390696	−	0.0730940i
$964$	−35.0455	−	6.99923i	−1.12874	−	0.225430i
$965$	20.0665	−	16.4682i	0.645964	−	0.530129i
$966$	0.420697	−	2.11071i	0.0135357	−	0.0679110i
$967$	5.83757	+	8.73654i	0.187724	+	0.280948i	0.913379	−	0.407110i	$-0.133463\pi$
$967$	5.83757	+	8.73654i	0.187724	+	0.280948i	−0.725656	+	0.688058i	$0.758463\pi$
$968$	−4.82141	+	5.86099i	−0.154966	+	0.188379i
$969$	118.614	+	79.2552i	3.81042	+	2.54604i
$970$	−0.00788171	+	20.3321i	−0.000253066	+	0.652825i
$971$	−13.2651	−	43.7292i	−0.425698	−	1.40334i	−0.863537	−	0.504285i	$-0.831756\pi$
$971$	−13.2651	−	43.7292i	−0.425698	−	1.40334i	0.437839	−	0.899053i	$-0.355744\pi$
$972$	92.7566	+	49.6719i	2.97517	+	1.59323i
$973$	−1.72559	+	2.10264i	−0.0553198	+	0.0674074i
$974$	5.74768	−	58.1262i	0.184168	−	1.86248i
$975$	6.12729	−	14.7926i	0.196230	−	0.473742i
$976$	8.98877	+	7.40025i	0.287723	+	0.236876i
$977$	−12.2191	−	29.4996i	−0.390924	−	0.943775i	−0.989739	−	0.142887i	$-0.954361\pi$
$977$	−12.2191	−	29.4996i	−0.390924	−	0.943775i	0.598815	−	0.800888i	$-0.295639\pi$
$978$	−66.2912	+	20.0811i	−2.11976	+	0.642124i
$979$	−11.5724	+	1.13978i	−0.369856	+	0.0364276i
$980$	−12.2651	+	6.54362i	−0.391795	+	0.209028i
$981$	99.1429	+	52.9930i	3.16539	+	1.69194i
$982$	14.5572	−	35.1058i	0.464540	−	1.12027i
$983$	1.09287	+	5.49424i	0.0348572	+	0.175239i	0.994292	−	0.106691i	$-0.0340255\pi$
$983$	1.09287	+	5.49424i	0.0348572	+	0.175239i	−0.959435	+	0.281930i	$0.909025\pi$
$984$	18.6797	+	12.5128i	0.595486	+	0.398894i
$985$	−6.33834	−	1.26077i	−0.201956	−	0.0401716i
$986$	−7.81176	−	39.3521i	−0.248777	−	1.25323i
$987$	1.86703	+	0.183886i	0.0594282	+	0.00585316i
$988$	−24.9244	+	60.0412i	−0.792952	+	1.91016i
$989$	−5.91370	−	1.79390i	−0.188045	−	0.0570427i
$990$	36.8571	−	19.6821i	1.17139	−	0.625540i
$991$	−38.8395	+	38.8395i	−1.23378	+	1.23378i	−0.271276	+	0.962502i	$0.587446\pi$
$991$	−38.8395	+	38.8395i	−1.23378	+	1.23378i	−0.962502	+	0.271276i	$0.912554\pi$
$992$	32.1465	+	9.81962i	1.02065	+	0.311773i
$993$	40.2799	+	40.2799i	1.27824	+	1.27824i
$994$	2.34433	+	0.712138i	0.0743577	+	0.0225876i
$995$	3.39633	−	11.1962i	0.107671	−	0.354943i
$996$	−22.0966	+	22.0624i	−0.700158	+	0.699073i
$997$	−3.68868	+	37.4518i	−0.116822	+	1.18611i	0.740762	+	0.671767i	$0.234464\pi$
$997$	−3.68868	+	37.4518i	−0.116822	+	1.18611i	−0.857584	+	0.514344i	$0.828036\pi$
$998$	13.4206	+	8.97491i	0.424823	+	0.284096i
$999$	4.53842	−	22.8162i	0.143589	−	0.721872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.2	✓	1024
128.109	even	32	inner	640.2.bm.a.621.2	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.2	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.2	yes	1024	128.109	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+(-1.40746 + 0.138072i) q^{2} +(-2.92329 + 1.56253i) q^{3} +(1.96187 - 0.388660i) q^{4} +(0.634393 + 0.773010i) q^{5} +(3.89867 - 2.60282i) q^{6} +(0.184506 - 0.123283i) q^{7} +(-2.70759 + 0.817901i) q^{8} +(4.43742 - 6.64107i) q^{9} +(-0.999612 - 1.00039i) q^{10} +(-3.53980 + 1.07379i) q^{11} +(-5.12783 + 4.20166i) q^{12} +(3.73398 + 3.06440i) q^{13} +(-0.242663 + 0.198991i) q^{14} +(-3.06237 - 1.26848i) q^{15} +(3.69789 - 1.52500i) q^{16} +(-5.90887 + 2.44753i) q^{17} +(-5.32854 + 9.95971i) q^{18} +(0.659567 + 6.69670i) q^{19} +(1.54504 + 1.26998i) q^{20} +(-0.346732 + 0.648690i) q^{21} +(4.83386 - 2.00006i) q^{22} +(2.02927 - 0.403647i) q^{23} +(6.63708 - 6.62166i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-5.67852 - 3.79745i) q^{26} +(-1.62031 + 16.4512i) q^{27} +(0.314063 - 0.313576i) q^{28} +(1.28760 - 4.24464i) q^{29} +(4.48530 + 1.36250i) q^{30} +(-4.20161 - 4.20161i) q^{31} +(-4.99406 + 2.65695i) q^{32} +(8.67005 - 8.67005i) q^{33} +(7.97855 - 4.26065i) q^{34} +(0.212349 + 0.0644153i) q^{35} +(6.12454 - 14.7536i) q^{36} +(-1.40048 - 0.137935i) q^{37} +(-1.85294 - 9.33425i) q^{38} +(-15.7037 - 3.12367i) q^{39} +(-2.34992 - 1.57412i) q^{40} +(0.467852 + 2.35205i) q^{41} +(0.398445 - 0.960878i) q^{42} +(-2.63414 - 1.40798i) q^{43} +(-6.52730 + 3.48241i) q^{44} +(7.94869 - 0.782878i) q^{45} +(-2.80038 + 0.848300i) q^{46} +(-0.976066 - 2.35643i) q^{47} +(-8.42714 + 10.2361i) q^{48} +(-2.65994 + 6.42166i) q^{49} +(0.139163 - 1.40735i) q^{50} +(13.4490 - 16.3877i) q^{51} +(8.51660 + 4.56071i) q^{52} +(-3.80337 - 12.5380i) q^{53} +(0.00906249 - 23.3781i) q^{54} +(-3.07568 - 2.05510i) q^{55} +(-0.398734 + 0.484708i) q^{56} +(-12.3919 - 18.5458i) q^{57} +(-1.22618 + 6.15193i) q^{58} +(-4.17140 + 3.42338i) q^{59} +(-6.50099 - 1.29837i) q^{60} +(1.37213 + 2.56707i) q^{61} +(6.49370 + 5.33346i) q^{62} -1.77238i q^{63} +(6.66208 - 4.42908i) q^{64} +4.83044i q^{65} +(-11.0056 + 13.3998i) q^{66} +(-3.92948 - 7.35153i) q^{67} +(-10.6412 + 7.09829i) q^{68} +(-5.30144 + 4.35078i) q^{69} +(-0.307766 - 0.0613425i) q^{70} +(-4.33755 - 6.49160i) q^{71} +(-6.58298 + 21.6107i) q^{72} +(-3.68245 - 2.46053i) q^{73} +(1.99016 + 0.000771483i) q^{74} +(-0.962203 - 3.17196i) q^{75} +(3.89672 + 12.8817i) q^{76} +(-0.520736 + 0.634519i) q^{77} +(22.5336 + 2.22819i) q^{78} +(4.70266 - 11.3532i) q^{79} +(3.52476 + 1.89105i) q^{80} +(-11.7993 - 28.4861i) q^{81} +(-0.983234 - 3.24582i) q^{82} +(4.68744 - 0.461672i) q^{83} +(-0.428124 + 1.40741i) q^{84} +(-5.64052 - 3.01492i) q^{85} +(3.90184 + 1.61797i) q^{86} +(2.86837 + 14.4202i) q^{87} +(8.70608 - 5.80258i) q^{88} +(3.08319 + 0.613284i) q^{89} +(-11.0793 + 2.19936i) q^{90} +(1.06673 + 0.105064i) q^{91} +(3.82429 - 1.58060i) q^{92} +(18.8477 + 5.71738i) q^{93} +(1.69913 + 3.18181i) q^{94} +(-4.75819 + 4.75819i) q^{95} +(10.4475 - 15.5704i) q^{96} +(-10.1661 - 10.1661i) q^{97} +(2.85710 - 9.40548i) q^{98} +(-8.57650 + 28.2729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 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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