LMFDB - Embedded newform 366.3.s.a.85.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [366,3,Mod(37,366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(366, base_ring=CyclotomicField(20))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("366.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 366 = 2 \cdot 3 \cdot 61 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	366.s (of order $20$, degree $8$, 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:	$9.97277767559$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			85.9
Character	$\chi$	$=$	366.85
Dual form			366.3.s.a.211.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26007 + 0.642040i) q^{2} +(1.64728 - 0.535233i) q^{3} +(1.17557 + 1.61803i) q^{4} +(2.50035 + 3.44144i) q^{5} +(2.41933 + 0.383185i) q^{6} +(1.92026 + 3.76873i) q^{7} +(0.442463 + 2.79360i) q^{8} +(2.42705 - 1.76336i) q^{9} +(0.941088 + 5.94179i) q^{10} +(-4.11800 - 4.11800i) q^{11} +(2.80252 + 2.03615i) q^{12} +9.59247 q^{13} +5.98176i q^{14} +(5.96075 + 4.33074i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(19.5106 + 3.09018i) q^{17} +(4.19041 - 0.663695i) q^{18} +(-34.2100 + 11.1155i) q^{19} +(-2.62903 + 8.09131i) q^{20} +(5.18035 + 5.18035i) q^{21} +(-2.54507 - 7.83291i) q^{22} +(-4.72283 + 29.8188i) q^{23} +(2.22409 + 4.36502i) q^{24} +(2.13367 - 6.56677i) q^{25} +(12.0872 + 6.15874i) q^{26} +(3.05422 - 4.20378i) q^{27} +(-3.84052 + 7.53745i) q^{28} +(-32.2372 - 32.2372i) q^{29} +(4.73048 + 9.28409i) q^{30} +(48.0335 - 24.4743i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-8.98759 - 4.57940i) q^{33} +(22.6008 + 16.4204i) q^{34} +(-8.16852 + 16.0316i) q^{35} +(5.70634 + 1.85410i) q^{36} +(3.55937 - 1.81359i) q^{37} +(-50.2437 - 7.95782i) q^{38} +(15.8015 - 5.13421i) q^{39} +(-8.50771 + 8.50771i) q^{40} +(52.4859 + 17.0537i) q^{41} +(3.20163 + 9.85362i) q^{42} +(3.86382 + 24.3952i) q^{43} +(1.82207 - 11.5041i) q^{44} +(12.1370 + 3.94354i) q^{45} +(-25.0959 + 34.5416i) q^{46} +15.6593 q^{47} +6.92820i q^{48} +(18.2856 - 25.1679i) q^{49} +(6.90471 - 6.90471i) q^{50} +(33.7934 - 5.35235i) q^{51} +(11.2766 + 15.5209i) q^{52} +(-55.2792 + 8.75537i) q^{53} +(6.54753 - 3.33614i) q^{54} +(3.87540 - 24.4683i) q^{55} +(-9.67869 + 7.03198i) q^{56} +(-50.4040 + 36.6206i) q^{57} +(-19.9237 - 61.3188i) q^{58} +(19.2973 - 37.8731i) q^{59} +14.7358i q^{60} +(-30.8721 - 52.6110i) q^{61} +76.2391 q^{62} +(11.3062 + 5.76079i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(23.9846 + 33.0119i) q^{65} +(-8.38486 - 11.5408i) q^{66} +(-113.524 - 17.9804i) q^{67} +(17.9361 + 35.2016i) q^{68} +(8.18018 + 51.6476i) q^{69} +(-20.5859 + 14.9565i) q^{70} +(1.92156 + 12.1322i) q^{71} +(6.00000 + 6.00000i) q^{72} +(-109.538 - 79.5838i) q^{73} +5.64947 q^{74} -11.9593i q^{75} +(-58.2015 - 42.2859i) q^{76} +(7.61198 - 23.4273i) q^{77} +(23.2074 + 3.67569i) q^{78} +(120.282 - 19.0507i) q^{79} +(-16.1826 + 5.25805i) q^{80} +(2.78115 - 8.55951i) q^{81} +(55.1869 + 55.1869i) q^{82} +(-3.53681 - 10.8852i) q^{83} +(-2.29212 + 14.4719i) q^{84} +(38.1488 + 74.8712i) q^{85} +(-10.7940 + 33.2205i) q^{86} +(-70.3580 - 35.8492i) q^{87} +(9.68200 - 13.3261i) q^{88} +(2.39220 - 4.69496i) q^{89} +(12.7616 + 12.7616i) q^{90} +(18.4201 + 36.1514i) q^{91} +(-53.7998 + 27.4124i) q^{92} +(66.0250 - 66.0250i) q^{93} +(19.7318 + 10.0539i) q^{94} +(-123.790 - 89.9390i) q^{95} +(-4.44818 + 8.73005i) q^{96} +(-124.133 - 40.3333i) q^{97} +(39.2000 - 19.9734i) q^{98} +(-17.2561 - 2.73310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 20 q^{2} - 40 q^{5} + 20 q^{7} + 40 q^{8} + 60 q^{9} + 60 q^{10} + 20 q^{11} - 32 q^{13} + 80 q^{16} + 80 q^{17} + 60 q^{18} - 100 q^{19} - 40 q^{20} + 12 q^{21} - 60 q^{22} + 56 q^{23} + 144 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) $ 80 * q - 20 * q^2 - 40 * q^5 + 20 * q^7 + 40 * q^8 + 60 * q^9 + 60 * q^10 + 20 * q^11 - 32 * q^13 + 80 * q^16 + 80 * q^17 + 60 * q^18 - 100 * q^19 - 40 * q^20 + 12 * q^21 - 60 * q^22 + 56 * q^23 + 144 * q^25 + 48 * q^26 - 40 * q^28 - 4 * q^29 - 68 * q^31 - 320 * q^32 + 12 * q^33 + 20 * q^34 + 12 * q^35 + 100 * q^37 + 148 * q^38 + 120 * q^39 + 280 * q^41 - 36 * q^42 - 260 * q^43 + 40 * q^44 - 40 * q^46 + 392 * q^47 + 20 * q^49 - 416 * q^50 + 96 * q^51 + 40 * q^52 - 504 * q^53 + 188 * q^55 + 72 * q^57 + 92 * q^58 + 108 * q^59 + 236 * q^61 - 136 * q^62 - 60 * q^63 + 120 * q^65 - 180 * q^66 - 600 * q^67 - 280 * q^68 - 360 * q^69 - 96 * q^70 + 424 * q^71 + 480 * q^72 - 324 * q^73 - 560 * q^74 + 136 * q^76 - 548 * q^77 + 48 * q^78 - 252 * q^79 - 180 * q^81 + 136 * q^82 - 312 * q^83 + 24 * q^84 + 992 * q^85 - 340 * q^86 - 108 * q^87 + 1128 * q^89 - 416 * q^91 + 48 * q^92 + 36 * q^93 - 88 * q^94 - 132 * q^95 - 260 * q^97 - 4 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/366\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.26007	+	0.642040i	0.630037	+	0.321020i
$2$	1.26007	+	0.642040i	0.630037	+	0.321020i
$3$	1.64728	−	0.535233i	0.549093	−	0.178411i
$3$	1.64728	−	0.535233i	0.549093	−	0.178411i
$4$	1.17557	+	1.61803i	0.293893	+	0.404508i
$5$	2.50035	+	3.44144i	0.500071	+	0.688288i	0.982206	−	0.187809i	$-0.0601385\pi$
$5$	2.50035	+	3.44144i	0.500071	+	0.688288i	−0.482135	+	0.876097i	$0.660139\pi$
$6$	2.41933	+	0.383185i	0.403222	+	0.0638641i
$7$	1.92026	+	3.76873i	0.274323	+	0.538390i	0.986530	−	0.163580i	$-0.0523042\pi$
$7$	1.92026	+	3.76873i	0.274323	+	0.538390i	−0.712207	+	0.701970i	$0.752304\pi$
$8$	0.442463	+	2.79360i	0.0553079	+	0.349201i
$9$	2.42705	−	1.76336i	0.269672	−	0.195928i
$10$	0.941088	+	5.94179i	0.0941088	+	0.594179i
$11$	−4.11800	−	4.11800i	−0.374364	−	0.374364i	0.494700	−	0.869064i	$-0.335278\pi$
$11$	−4.11800	−	4.11800i	−0.374364	−	0.374364i	−0.869064	+	0.494700i	$0.835278\pi$
$12$	2.80252	+	2.03615i	0.233543	+	0.169679i
$13$	9.59247			0.737882			0.368941	−	0.929453i	$-0.379720\pi$
$13$	9.59247			0.737882			0.368941	+	0.929453i	$0.379720\pi$
$14$			5.98176i			0.427268i
$15$	5.96075	+	4.33074i	0.397383	+	0.288716i
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	19.5106	+	3.09018i	1.14768	+	0.181775i	0.701165	−	0.712999i	$-0.252664\pi$
$17$	19.5106	+	3.09018i	1.14768	+	0.181775i	0.446519	+	0.894774i	$0.352664\pi$
$18$	4.19041	−	0.663695i	0.232800	−	0.0368720i
$19$	−34.2100	+	11.1155i	−1.80053	+	0.585026i	−0.999900	−	0.0141391i	$-0.995499\pi$
$19$	−34.2100	+	11.1155i	−1.80053	+	0.585026i	−0.800625	+	0.599165i	$0.795499\pi$
$20$	−2.62903	+	8.09131i	−0.131451	+	0.404566i
$21$	5.18035	+	5.18035i	0.246683	+	0.246683i
$22$	−2.54507	−	7.83291i	−0.115685	−	0.356041i
$23$	−4.72283	+	29.8188i	−0.205340	+	1.29647i	0.642528	+	0.766262i	$0.277886\pi$
$23$	−4.72283	+	29.8188i	−0.205340	+	1.29647i	−0.847869	+	0.530206i	$0.822114\pi$
$24$	2.22409	+	4.36502i	0.0926704	+	0.181876i
$25$	2.13367	−	6.56677i	0.0853470	−	0.262671i
$26$	12.0872	+	6.15874i	0.464893	+	0.236875i
$27$	3.05422	−	4.20378i	0.113119	−	0.155695i
$28$	−3.84052	+	7.53745i	−0.137162	+	0.269195i
$29$	−32.2372	−	32.2372i	−1.11163	−	1.11163i	−0.992931	−	0.118696i	$-0.962129\pi$
$29$	−32.2372	−	32.2372i	−1.11163	−	1.11163i	−0.118696	−	0.992931i	$-0.537871\pi$
$30$	4.73048	+	9.28409i	0.157683	+	0.309470i
$31$	48.0335	−	24.4743i	1.54947	−	0.789493i	0.550495	−	0.834838i	$-0.314439\pi$
$31$	48.0335	−	24.4743i	1.54947	−	0.789493i	0.998971	+	0.0453459i	$0.0144390\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−8.98759	−	4.57940i	−0.272351	−	0.138770i
$34$	22.6008	+	16.4204i	0.664729	+	0.482954i
$35$	−8.16852	+	16.0316i	−0.233386	+	0.458046i
$36$	5.70634	+	1.85410i	0.158509	+	0.0515028i
$37$	3.55937	−	1.81359i	0.0961993	−	0.0490160i	−0.405229	−	0.914215i	$-0.632808\pi$
$37$	3.55937	−	1.81359i	0.0961993	−	0.0490160i	0.501428	+	0.865199i	$0.332808\pi$
$38$	−50.2437	−	7.95782i	−1.32220	−	0.209416i
$39$	15.8015	−	5.13421i	0.405166	−	0.131646i
$40$	−8.50771	+	8.50771i	−0.212693	+	0.212693i
$41$	52.4859	+	17.0537i	1.28014	+	0.415944i	0.868631	−	0.495460i	$-0.165000\pi$
$41$	52.4859	+	17.0537i	1.28014	+	0.415944i	0.411513	+	0.911404i	$0.365000\pi$
$42$	3.20163	+	9.85362i	0.0762294	+	0.234610i
$43$	3.86382	+	24.3952i	0.0898564	+	0.567331i	0.991005	+	0.133822i	$0.0427249\pi$
$43$	3.86382	+	24.3952i	0.0898564	+	0.567331i	−0.901149	+	0.433509i	$0.857275\pi$
$44$	1.82207	−	11.5041i	0.0414106	−	0.261456i
$45$	12.1370	+	3.94354i	0.269710	+	0.0876342i
$46$	−25.0959	+	34.5416i	−0.545564	+	0.750904i
$47$	15.6593			0.333176			0.166588	−	0.986027i	$-0.446725\pi$
$47$	15.6593			0.333176			0.166588	+	0.986027i	$0.446725\pi$
$48$			6.92820i			0.144338i
$49$	18.2856	−	25.1679i	0.373175	−	0.513632i
$50$	6.90471	−	6.90471i	0.138094	−	0.138094i
$51$	33.7934	−	5.35235i	0.662615	−	0.104948i
$52$	11.2766	+	15.5209i	0.216858	+	0.298480i
$53$	−55.2792	+	8.75537i	−1.04300	+	0.165196i	−0.654353	−	0.756189i	$-0.727059\pi$
$53$	−55.2792	+	8.75537i	−1.04300	+	0.165196i	−0.388651	+	0.921385i	$0.627059\pi$
$54$	6.54753	−	3.33614i	0.121251	−	0.0617803i
$55$	3.87540	−	24.4683i	0.0704618	−	0.444879i
$56$	−9.67869	+	7.03198i	−0.172834	+	0.125571i
$57$	−50.4040	+	36.6206i	−0.884280	+	0.642467i
$58$	−19.9237	−	61.3188i	−0.343512	−	1.05722i
$59$	19.2973	−	37.8731i	0.327073	−	0.641917i	−0.667654	−	0.744472i	$-0.732701\pi$
$59$	19.2973	−	37.8731i	0.327073	−	0.641917i	0.994727	+	0.102554i	$0.0327015\pi$
$60$			14.7358i			0.245596i
$61$	−30.8721	−	52.6110i	−0.506100	−	0.862475i
$61$	−30.8721	−	52.6110i	−0.506100	−	0.862475i
$62$	76.2391			1.22966
$63$	11.3062	+	5.76079i	0.179463	+	0.0914411i
$64$	−7.60845	+	2.47214i	−0.118882	+	0.0386271i
$65$	23.9846	+	33.0119i	0.368993	+	0.507876i
$66$	−8.38486	−	11.5408i	−0.127043	−	0.174860i
$67$	−113.524	−	17.9804i	−1.69438	−	0.268364i	−0.766773	−	0.641918i	$-0.778139\pi$
$67$	−113.524	−	17.9804i	−1.69438	−	0.268364i	−0.927608	+	0.373555i	$0.878139\pi$
$68$	17.9361	+	35.2016i	0.263766	+	0.517670i
$69$	8.18018	+	51.6476i	0.118553	+	0.748516i
$70$	−20.5859	+	14.9565i	−0.294084	+	0.213664i
$71$	1.92156	+	12.1322i	0.0270642	+	0.170877i	0.997518	−	0.0704097i	$-0.0224307\pi$
$71$	1.92156	+	12.1322i	0.0270642	+	0.170877i	−0.970454	+	0.241286i	$0.922431\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	−109.538	−	79.5838i	−1.50052	−	1.09019i	−0.970175	−	0.242406i	$-0.922063\pi$
$73$	−109.538	−	79.5838i	−1.50052	−	1.09019i	−0.530342	−	0.847784i	$-0.677937\pi$
$74$	5.64947			0.0763442
$75$		−	11.9593i		−	0.159458i
$76$	−58.2015	−	42.2859i	−0.765809	−	0.556393i
$77$	7.61198	−	23.4273i	0.0988569	−	0.304250i
$78$	23.2074	+	3.67569i	0.297530	+	0.0471242i
$79$	120.282	−	19.0507i	1.52255	−	0.241149i	0.661609	−	0.749849i	$-0.269874\pi$
$79$	120.282	−	19.0507i	1.52255	−	0.241149i	0.860943	+	0.508701i	$0.169874\pi$
$80$	−16.1826	+	5.25805i	−0.202283	+	0.0657257i
$81$	2.78115	−	8.55951i	0.0343352	−	0.105673i
$82$	55.1869	+	55.1869i	0.673011	+	0.673011i
$83$	−3.53681	−	10.8852i	−0.0426122	−	0.131147i	0.927487	−	0.373855i	$-0.121964\pi$
$83$	−3.53681	−	10.8852i	−0.0426122	−	0.131147i	−0.970099	+	0.242708i	$0.921964\pi$
$84$	−2.29212	+	14.4719i	−0.0272871	+	0.172284i
$85$	38.1488	+	74.8712i	0.448809	+	0.880837i
$86$	−10.7940	+	33.2205i	−0.125512	+	0.386285i
$87$	−70.3580	−	35.8492i	−0.808713	−	0.412060i
$88$	9.68200	−	13.3261i	0.110023	−	0.151433i
$89$	2.39220	−	4.69496i	0.0268787	−	0.0527523i	−0.877177	−	0.480168i	$-0.840576\pi$
$89$	2.39220	−	4.69496i	0.0268787	−	0.0527523i	0.904055	+	0.427415i	$0.140576\pi$
$90$	12.7616	+	12.7616i	0.141795	+	0.141795i
$91$	18.4201	+	36.1514i	0.202418	+	0.397268i
$92$	−53.7998	+	27.4124i	−0.584780	+	0.297961i
$93$	66.0250	−	66.0250i	0.709947	−	0.709947i
$94$	19.7318	+	10.0539i	0.209913	+	0.106956i
$95$	−123.790	−	89.9390i	−1.30306	−	0.946726i
$96$	−4.44818	+	8.73005i	−0.0463352	+	0.0909380i
$97$	−124.133	−	40.3333i	−1.27972	−	0.415807i	−0.411241	−	0.911527i	$-0.634904\pi$
$97$	−124.133	−	40.3333i	−1.27972	−	0.415807i	−0.868483	+	0.495719i	$0.834904\pi$
$98$	39.2000	−	19.9734i	0.400000	−	0.203810i
$99$	−17.2561	−	2.73310i	−0.174304	−	0.0276071i
$100$	13.1335	−	4.26735i	0.131335	−	0.0426735i
$101$	68.3594	−	68.3594i	0.676826	−	0.676826i	−0.282455	−	0.959281i	$-0.591149\pi$
$101$	68.3594	−	68.3594i	0.676826	−	0.676826i	0.959281	+	0.282455i	$0.0911486\pi$
$102$	46.0186	+	14.9523i	0.451162	+	0.146592i
$103$	−9.65656	−	29.7198i	−0.0937530	−	0.288542i	0.893174	−	0.449712i	$-0.148473\pi$
$103$	−9.65656	−	29.7198i	−0.0937530	−	0.288542i	−0.986927	+	0.161170i	$0.948473\pi$
$104$	4.24432	+	26.7976i	0.0408107	+	0.257669i
$105$	−4.87517	+	30.7806i	−0.0464302	+	0.293149i
$106$	−75.2772	−	24.4590i	−0.710162	−	0.230746i
$107$	−97.9662	+	134.839i	−0.915572	+	1.26018i	0.0496559	+	0.998766i	$0.484188\pi$
$107$	−97.9662	+	134.839i	−0.915572	+	1.26018i	−0.965228	+	0.261410i	$0.915812\pi$
$108$	10.3923			0.0962250
$109$		−	171.032i		−	1.56910i	−0.620063	−	0.784552i	$-0.712893\pi$
$109$		−	171.032i		−	1.56910i	0.620063	−	0.784552i	$-0.287107\pi$
$110$	20.5929	−	28.3437i	0.187208	−	0.257670i
$111$	4.89258	−	4.89258i	0.0440773	−	0.0440773i
$112$	−16.7107	+	2.64671i	−0.149202	+	0.0236313i
$113$	31.7469	+	43.6959i	0.280946	+	0.386690i	0.926047	−	0.377408i	$-0.123185\pi$
$113$	31.7469	+	43.6959i	0.280946	+	0.386690i	−0.645101	+	0.764098i	$0.723185\pi$
$114$	−87.0246	+	13.7833i	−0.763374	+	0.120907i
$115$	−114.428	+	58.3041i	−0.995029	+	0.506992i
$116$	14.2638	−	90.0579i	0.122964	−	0.776361i
$117$	23.2814	−	16.9149i	0.198986	−	0.144572i
$118$	48.6321	−	35.3333i	0.412136	−	0.299435i
$119$	25.8195	+	79.4641i	0.216970	+	0.667766i
$120$	−9.46096	+	18.5682i	−0.0788413	+	0.154735i
$121$		−	87.0841i		−	0.719703i
$122$	−5.12279	−	86.1148i	−0.0419901	−	0.705859i
$123$	95.5866			0.777127
$124$	96.0669	+	48.9485i	0.774733	+	0.394746i
$125$	129.076	−	41.9392i	1.03260	−	0.335513i
$126$	10.5480	+	14.5180i	0.0837140	+	0.115222i
$127$	11.0538	+	15.2143i	0.0870381	+	0.119798i	0.850316	−	0.526273i	$-0.176411\pi$
$127$	11.0538	+	15.2143i	0.0870381	+	0.119798i	−0.763277	+	0.646071i	$0.776411\pi$
$128$	−11.1744	−	1.76985i	−0.0873001	−	0.0138270i
$129$	19.4219	+	38.1177i	0.150558	+	0.295486i
$130$	9.02735	+	56.9965i	0.0694412	+	0.438434i
$131$	1.43179	−	1.04025i	0.0109297	−	0.00794087i	−0.582307	−	0.812969i	$-0.697850\pi$
$131$	1.43179	−	1.04025i	0.0109297	−	0.00794087i	0.593237	+	0.805028i	$0.297850\pi$
$132$	−3.15591	−	19.9256i	−0.0239084	−	0.150952i
$133$	−107.583	−	107.583i	−0.808898	−	0.808898i
$134$	−131.504	−	95.5432i	−0.981373	−	0.713009i
$135$	22.1037			0.163731
$136$			55.8722i			0.410825i
$137$	191.547	+	139.167i	1.39815	+	1.01582i	0.994915	+	0.100721i	$0.0321151\pi$
$137$	191.547	+	139.167i	1.39815	+	1.01582i	0.403237	+	0.915095i	$0.367885\pi$
$138$	−22.8522	+	70.3318i	−0.165596	+	0.509651i
$139$	−40.4960	−	6.41394i	−0.291338	−	0.0461435i	0.00905459	−	0.999959i	$-0.497118\pi$
$139$	−40.4960	−	6.41394i	−0.291338	−	0.0461435i	−0.300393	+	0.953816i	$0.597118\pi$
$140$	−35.5424	+	5.62936i	−0.253874	+	0.0402097i
$141$	25.7951	−	8.38135i	0.182944	−	0.0594422i
$142$	−5.36808	+	16.5212i	−0.0378034	+	0.116347i
$143$	−39.5018	−	39.5018i	−0.276236	−	0.276236i
$144$	3.70820	+	11.4127i	0.0257514	+	0.0792547i
$145$	30.3380	−	191.547i	0.209228	−	1.32101i
$146$	−86.9297	−	170.609i	−0.595409	−	1.16856i
$147$	16.6507	−	51.2457i	0.113270	−	0.348610i
$148$	7.11875	+	3.62718i	0.0480996	+	0.0245080i
$149$	−67.1790	+	92.4640i	−0.450866	+	0.620564i	−0.972583	−	0.232555i	$-0.925292\pi$
$149$	−67.1790	+	92.4640i	−0.450866	+	0.620564i	0.521717	+	0.853118i	$0.325292\pi$
$150$	7.67835	−	15.0696i	0.0511890	−	0.100464i
$151$	−194.038	−	194.038i	−1.28502	−	1.28502i	−0.937775	−	0.347245i	$-0.887117\pi$
$151$	−194.038	−	194.038i	−1.28502	−	1.28502i	−0.347245	−	0.937775i	$-0.612883\pi$
$152$	−46.1890	−	90.6510i	−0.303875	−	0.596388i
$153$	52.8023	−	26.9041i	0.345113	−	0.175844i
$154$	24.6329	−	24.6329i	0.159954	−	0.159954i
$155$	204.327	+	104.110i	1.31824	+	0.671677i
$156$	26.8831	+	19.5317i	0.172327	+	0.125203i
$157$	72.0668	−	141.439i	0.459024	−	0.900886i	−0.539249	−	0.842146i	$-0.681292\pi$
$157$	72.0668	−	141.439i	0.459024	−	0.900886i	0.998273	−	0.0587396i	$-0.0187082\pi$
$158$	163.795	+	53.2202i	1.03668	+	0.336837i
$159$	−86.3741	+	44.0098i	−0.543233	+	0.276791i
$160$	−23.7672	−	3.76435i	−0.148545	−	0.0235272i
$161$	−121.448	+	39.4608i	−0.754335	+	0.245098i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	101.269	+	32.9042i	0.621280	+	0.201866i	0.602708	−	0.797962i	$-0.294088\pi$
$163$	101.269	+	32.9042i	0.621280	+	0.201866i	0.0185712	+	0.999828i	$0.494088\pi$
$164$	34.1074	+	104.972i	0.207972	+	0.640072i
$165$	−6.71239	−	42.3804i	−0.0406812	−	0.256851i
$166$	2.53208	−	15.9869i	0.0152535	−	0.0963066i
$167$	171.962	+	55.8738i	1.02971	+	0.334574i	0.774676	−	0.632358i	$-0.217913\pi$
$167$	171.962	+	55.8738i	1.02971	+	0.334574i	0.255036	+	0.966932i	$0.417913\pi$
$168$	−12.1797	+	16.7640i	−0.0724985	+	0.0997856i
$169$	−76.9846			−0.455530
$170$			118.836i			0.699037i
$171$	−63.4288	+	87.3022i	−0.370929	+	0.510539i
$172$	−34.9301	+	34.9301i	−0.203082	+	0.203082i
$173$	−141.655	+	22.4360i	−0.818816	+	0.129688i	−0.551770	−	0.833996i	$-0.686047\pi$
$173$	−141.655	+	22.4360i	−0.818816	+	0.129688i	−0.267046	+	0.963684i	$0.586047\pi$
$174$	−65.6397	−	90.3452i	−0.377239	−	0.519226i
$175$	28.8456	−	4.56869i	0.164832	−	0.0261068i
$176$	20.7559	−	10.5757i	0.117931	−	0.0600891i
$177$	11.5171	−	72.7161i	0.0650684	−	0.410826i
$178$	6.02870	−	4.38011i	0.0338691	−	0.0246073i
$179$	99.9710	−	72.6332i	0.558497	−	0.405772i	−0.272411	−	0.962181i	$-0.587821\pi$
$179$	99.9710	−	72.6332i	0.558497	−	0.405772i	0.830909	+	0.556409i	$0.187821\pi$
$180$	7.88708	+	24.2739i	0.0438171	+	0.134855i
$181$	−117.363	+	230.337i	−0.648413	+	1.27258i	0.299513	+	0.954092i	$0.403176\pi$
$181$	−117.363	+	230.337i	−0.648413	+	1.27258i	−0.947926	+	0.318490i	$0.896824\pi$
$182$			57.3798i			0.315274i
$183$	−79.0141	−	70.1411i	−0.431771	−	0.383285i
$184$	−85.3915			−0.464084
$185$	15.1411	+	7.71475i	0.0818436	+	0.0417014i
$186$	125.587	−	40.8057i	0.675199	−	0.219386i
$187$	−67.6194	−	93.0701i	−0.361601	−	0.497701i
$188$	18.4086	+	25.3372i	0.0979178	+	0.134772i
$189$	21.7078	+	3.43818i	0.114856	+	0.0181914i
$190$	−98.2406	−	192.808i	−0.517056	−	1.01478i
$191$	−14.8920	−	94.0244i	−0.0779686	−	0.492275i	−0.995512	−	0.0946382i	$-0.969831\pi$
$191$	−14.8920	−	94.0244i	−0.0779686	−	0.492275i	0.917543	−	0.397636i	$-0.130169\pi$
$192$	−11.2101	+	8.14459i	−0.0583858	+	0.0424197i
$193$	19.6004	+	123.752i	0.101556	+	0.641202i	0.984986	+	0.172637i	$0.0552287\pi$
$193$	19.6004	+	123.752i	0.101556	+	0.641202i	−0.883429	+	0.468565i	$0.844771\pi$
$194$	−130.521	−	130.521i	−0.672790	−	0.672790i
$195$	57.1783	+	41.5425i	0.293222	+	0.213038i
$196$	62.2186			0.317442
$197$		−	7.03627i		−	0.0357171i	−0.999841	−	0.0178585i	$-0.994315\pi$
$197$		−	7.03627i		−	0.0357171i	0.999841	−	0.0178585i	$-0.00568485\pi$
$198$	−19.9892	−	14.5230i	−0.100956	−	0.0733485i
$199$	−66.7682	+	205.491i	−0.335519	+	1.03262i	0.630947	+	0.775826i	$0.282666\pi$
$199$	−66.7682	+	205.491i	−0.335519	+	1.03262i	−0.966466	+	0.256795i	$0.917334\pi$
$200$	19.2890	+	3.05508i	0.0964452	+	0.0152754i
$201$	−196.629	+	31.1429i	−0.978252	+	0.154940i
$202$	130.027	−	42.2485i	0.643700	−	0.209151i
$203$	59.5893	−	183.397i	0.293543	−	0.903433i
$204$	48.3868	+	48.3868i	0.237190	+	0.237190i
$205$	72.5440	+	223.267i	0.353873	+	1.08911i
$206$	6.91333	−	43.6491i	0.0335599	−	0.211889i
$207$	41.1185	+	80.6997i	0.198640	+	0.389854i
$208$	−11.8569	+	36.4919i	−0.0570045	+	0.175442i
$209$	186.650	+	95.1031i	0.893064	+	0.455039i
$210$	−25.9054	+	35.6558i	−0.123359	+	0.169789i
$211$	−13.1247	+	25.7586i	−0.0622021	+	0.122079i	−0.920014	−	0.391885i	$-0.871823\pi$
$211$	−13.1247	+	25.7586i	−0.0622021	+	0.122079i	0.857812	+	0.513963i	$0.171823\pi$
$212$	−79.1511	−	79.1511i	−0.373354	−	0.373354i
$213$	9.65892	+	18.9567i	0.0453471	+	0.0889986i
$214$	−210.017	+	107.009i	−0.981386	+	0.500041i
$215$	−74.2938	+	74.2938i	−0.345553	+	0.345553i
$216$	13.0951	+	6.67227i	0.0606253	+	0.0308901i
$217$	184.474	+	134.028i	0.850109	+	0.617640i
$218$	109.810	−	215.513i	0.503713	−	0.988593i
$219$	−223.035	−	72.4685i	−1.01842	−	0.330906i
$220$	44.1464	−	22.4937i	0.200665	−	0.102244i
$221$	187.155	+	29.6424i	0.846855	+	0.134129i
$222$	9.30625	−	3.02378i	0.0419200	−	0.0136206i
$223$	−174.987	+	174.987i	−0.784697	+	0.784697i	−0.980619	−	0.195922i	$-0.937230\pi$
$223$	−174.987	+	174.987i	−0.784697	+	0.784697i	0.195922	+	0.980619i	$0.437230\pi$
$224$	−22.7560	−	7.39386i	−0.101589	−	0.0330083i
$225$	−6.40102	−	19.7003i	−0.0284490	−	0.0875570i
$226$	11.9490	+	75.4429i	0.0528716	+	0.333818i
$227$	−60.3611	+	381.105i	−0.265908	+	1.67888i	0.387498	+	0.921870i	$0.373339\pi$
$227$	−60.3611	+	381.105i	−0.265908	+	1.67888i	−0.653406	+	0.757007i	$0.726661\pi$
$228$	−118.507	−	38.5052i	−0.519767	−	0.168883i
$229$	124.479	−	171.330i	0.543575	−	0.748167i	−0.445548	−	0.895258i	$-0.646991\pi$
$229$	124.479	−	171.330i	0.543575	−	0.748167i	0.989123	+	0.147091i	$0.0469910\pi$
$230$	−181.622			−0.789659
$231$		−	42.6654i		−	0.184699i
$232$	75.7942	−	104.322i	0.326699	−	0.449663i
$233$	−27.7990	+	27.7990i	−0.119309	+	0.119309i	−0.764240	−	0.644931i	$-0.776886\pi$
$233$	−27.7990	+	27.7990i	−0.119309	+	0.119309i	0.644931	+	0.764240i	$0.276886\pi$
$234$	40.1963	−	6.36648i	0.171779	−	0.0272072i
$235$	39.1537	+	53.8904i	0.166611	+	0.229321i
$236$	83.9654	−	13.2988i	0.355785	−	0.0563509i
$237$	187.941	−	95.7606i	0.792999	−	0.404053i
$238$	−18.4847	+	116.708i	−0.0776668	+	0.490369i
$239$	−319.443	+	232.089i	−1.33658	+	0.971083i	−0.337019	+	0.941498i	$0.609419\pi$
$239$	−319.443	+	232.089i	−1.33658	+	0.971083i	−0.999562	+	0.0295852i	$0.990581\pi$
$240$	−23.8430	+	17.3230i	−0.0993459	+	0.0721790i
$241$	89.0047	+	273.928i	0.369314	+	1.13663i	0.947235	+	0.320539i	$0.103864\pi$
$241$	89.0047	+	273.928i	0.369314	+	1.13663i	−0.577921	+	0.816093i	$0.696136\pi$
$242$	55.9114	−	109.732i	0.231039	−	0.453440i
$243$		−	15.5885i		−	0.0641500i
$244$	48.8340	−	111.800i	0.200139	−	0.458197i
$245$	132.334			0.540141
$246$	120.446	+	61.3704i	0.489618	+	0.249473i
$247$	−328.158	+	106.625i	−1.32858	+	0.431680i
$248$	89.6245	+	123.358i	0.361389	+	0.497409i
$249$	−11.6522	−	16.0379i	−0.0467961	−	0.0644092i
$250$	189.571	+	30.0251i	0.758285	+	0.120101i
$251$	112.718	+	221.222i	0.449076	+	0.881361i	0.998937	+	0.0461045i	$0.0146807\pi$
$251$	112.718	+	221.222i	0.449076	+	0.881361i	−0.549861	+	0.835256i	$0.685319\pi$
$252$	3.97006	+	25.0660i	0.0157542	+	0.0994682i
$253$	142.242	−	103.345i	0.562223	−	0.408479i
$254$	4.16046	+	26.2681i	0.0163798	+	0.103418i
$255$	102.915	+	102.915i	0.403589	+	0.403589i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	262.122			1.01993			0.509966	−	0.860195i	$-0.329658\pi$
$257$	262.122			1.01993			0.509966	+	0.860195i	$0.329658\pi$
$258$			60.5007i			0.234499i
$259$	13.6699	+	9.93173i	0.0527794	+	0.0383465i
$260$	−25.2189	+	77.6157i	−0.0969956	+	0.298522i
$261$	−135.087	−	21.3957i	−0.517574	−	0.0819757i
$262$	2.47204	−	0.391533i	0.00943527	−	0.00149440i
$263$	−337.563	+	109.681i	−1.28351	+	0.417038i	−0.869815	−	0.493378i	$-0.835762\pi$
$263$	−337.563	+	109.681i	−1.28351	+	0.417038i	−0.413695	+	0.910416i	$0.635762\pi$
$264$	8.81636	−	27.1340i	0.0333953	−	0.102780i
$265$	−168.349	−	168.349i	−0.635278	−	0.635278i
$266$	−66.4902	−	204.636i	−0.249963	−	0.769308i
$267$	1.42772	−	9.01429i	0.00534728	−	0.0337614i
$268$	−104.362	−	204.822i	−0.389411	−	0.764262i
$269$	58.0304	−	178.599i	0.215727	−	0.663938i	−0.783375	−	0.621550i	$-0.786503\pi$
$269$	58.0304	−	178.599i	0.215727	−	0.663938i	0.999101	−	0.0423883i	$-0.0134967\pi$
$270$	27.8523	+	14.1914i	0.103157	+	0.0525609i
$271$	181.214	−	249.420i	0.668688	−	0.920370i	−0.331042	−	0.943616i	$-0.607400\pi$
$271$	181.214	−	249.420i	0.668688	−	0.920370i	0.999730	+	0.0232459i	$0.00740005\pi$
$272$	−35.8722	+	70.4031i	−0.131883	+	0.258835i
$273$	49.6924	+	49.6924i	0.182023	+	0.182023i
$274$	152.012	+	298.341i	0.554790	+	1.08884i
$275$	−35.8285	+	18.2555i	−0.130285	+	0.0663837i
$276$	−73.9512	+	73.9512i	−0.267939	+	0.267939i
$277$	328.665	+	167.463i	1.18652	+	0.604560i	0.931982	−	0.362504i	$-0.118078\pi$
$277$	328.665	+	167.463i	1.18652	+	0.604560i	0.254533	+	0.967064i	$0.418078\pi$
$278$	−46.9100	−	34.0821i	−0.168741	−	0.122597i
$279$	73.4228	−	144.100i	0.263164	−	0.516489i
$280$	−48.4003	−	15.7262i	−0.172858	−	0.0561650i
$281$	274.072	−	139.646i	0.975344	−	0.496962i	0.107719	−	0.994181i	$-0.465645\pi$
$281$	274.072	−	139.646i	0.975344	−	0.496962i	0.867625	+	0.497219i	$0.165645\pi$
$282$	37.8849	+	6.00038i	0.134344	+	0.0212780i
$283$	48.9866	−	15.9167i	0.173097	−	0.0562428i	−0.221186	−	0.975232i	$-0.570993\pi$
$283$	48.9866	−	15.9167i	0.173097	−	0.0562428i	0.394283	+	0.918989i	$0.370993\pi$
$284$	−17.3715	+	17.3715i	−0.0611671	+	0.0611671i
$285$	−252.056	−	81.8978i	−0.884405	−	0.287361i
$286$	−24.4135	−	75.1369i	−0.0853617	−	0.262716i
$287$	36.5159	+	230.553i	0.127233	+	0.803319i
$288$	−2.65478	+	16.7616i	−0.00921799	+	0.0582001i
$289$	96.2597	+	31.2767i	0.333079	+	0.108224i
$290$	161.209	−	221.885i	0.555892	−	0.765120i
$291$	−226.070			−0.776871
$292$		−	270.792i		−	0.927371i
$293$	−144.072	+	198.298i	−0.491712	+	0.676784i	−0.980703	−	0.195505i	$-0.937365\pi$
$293$	−144.072	+	198.298i	−0.491712	+	0.676784i	0.488990	+	0.872289i	$0.337365\pi$
$294$	53.8829	−	53.8829i	0.183275	−	0.183275i
$295$	178.588	−	28.2856i	0.605384	−	0.0958834i
$296$	6.64135	+	9.14103i	0.0224370	+	0.0308819i
$297$	−29.8884	+	4.73386i	−0.100635	+	0.0159389i
$298$	−144.016	+	73.3798i	−0.483275	+	0.246241i
$299$	−45.3036	+	286.036i	−0.151517	+	0.956641i
$300$	19.3506	−	14.0590i	0.0645019	−	0.0468634i
$301$	−84.5194	+	61.4069i	−0.280795	+	0.204010i
$302$	−119.922	−	369.082i	−0.397093	−	1.22213i
$303$	76.0188	−	149.195i	0.250887	−	0.492394i
$304$		−	143.882i		−	0.473296i
$305$	103.866	−	237.791i	0.340546	−	0.779641i
$306$	83.8084			0.273884
$307$	149.405	+	76.1258i	0.486662	+	0.247967i	0.680064	−	0.733153i	$-0.261952\pi$
$307$	149.405	+	76.1258i	0.486662	+	0.247967i	−0.193402	+	0.981120i	$0.561952\pi$
$308$	46.8545	−	15.2240i	0.152125	−	0.0494284i
$309$	−31.8141	−	43.7883i	−0.102958	−	0.141710i
$310$	190.625	+	262.372i	0.614919	+	0.846363i
$311$	448.327	+	71.0080i	1.44157	+	0.228322i	0.827736	−	0.561117i	$-0.189628\pi$
$311$	448.327	+	71.0080i	1.44157	+	0.228322i	0.613829	+	0.789439i	$0.289628\pi$
$312$	21.3345	+	41.8713i	0.0683799	+	0.134203i
$313$	83.2993	+	525.931i	0.266132	+	1.68029i	0.652376	+	0.757895i	$0.273772\pi$
$313$	83.2993	+	525.931i	0.266132	+	1.68029i	−0.386244	+	0.922397i	$0.626228\pi$
$314$	181.619	−	131.954i	0.578404	−	0.420235i
$315$	8.44404	+	53.3136i	0.0268065	+	0.169249i
$316$	172.224	+	172.224i	0.545013	+	0.545013i
$317$	166.912	+	121.269i	0.526537	+	0.382551i	0.819061	−	0.573707i	$-0.194495\pi$
$317$	166.912	+	121.269i	0.526537	+	0.382551i	−0.292524	+	0.956258i	$0.594495\pi$
$318$	−137.094			−0.431112
$319$			265.506i			0.832306i
$320$	−27.5315	−	20.0028i	−0.0860360	−	0.0625088i
$321$	−89.2073	+	274.552i	−0.277904	+	0.855302i
$322$	−178.369	−	28.2508i	−0.553940	−	0.0877354i
$323$	−701.807	+	111.155i	−2.17278	+	0.344134i
$324$	17.1190	−	5.56231i	0.0528365	−	0.0171676i
$325$	20.4672	−	62.9916i	0.0629760	−	0.193820i
$326$	106.480	+	106.480i	0.326626	+	0.326626i
$327$	−91.5422	−	281.738i	−0.279946	−	0.861584i
$328$	−24.4182	+	154.170i	−0.0744457	+	0.470032i
$329$	30.0699	+	59.0154i	0.0913978	+	0.179378i
$330$	18.7518	−	57.7120i	0.0568235	−	0.174885i
$331$	318.782	+	162.427i	0.963086	+	0.490717i	0.863520	−	0.504314i	$-0.168255\pi$
$331$	318.782	+	162.427i	0.963086	+	0.490717i	0.0995660	+	0.995031i	$0.468255\pi$
$332$	13.4548	−	18.5190i	0.0405266	−	0.0557800i
$333$	5.44077	−	10.6781i	0.0163387	−	0.0320664i
$334$	180.811	+	180.811i	0.541352	+	0.541352i
$335$	−221.971	−	435.642i	−0.662599	−	1.30042i
$336$	−26.1105	+	13.3040i	−0.0777098	+	0.0395951i
$337$	29.0806	−	29.0806i	0.0862925	−	0.0862925i	−0.662643	−	0.748935i	$-0.730565\pi$
$337$	29.0806	−	29.0806i	0.0862925	−	0.0862925i	0.748935	+	0.662643i	$0.230565\pi$
$338$	−97.0062	−	49.4271i	−0.287001	−	0.146234i
$339$	75.6835	+	54.9873i	0.223255	+	0.162204i
$340$	−76.2975	+	149.742i	−0.224405	+	0.440419i
$341$	−298.587	−	97.0168i	−0.875622	−	0.284507i
$342$	−135.976	+	69.2835i	−0.397592	+	0.202583i
$343$	334.670	+	53.0065i	0.975714	+	0.154538i
$344$	−66.4410	+	21.5880i	−0.193142	+	0.0627558i
$345$	−157.289	+	157.289i	−0.455910	+	0.455910i
$346$	−192.901	−	62.6772i	−0.557517	−	0.181148i
$347$	3.45463	+	10.6323i	0.00995572	+	0.0306405i	0.955911	−	0.293657i	$-0.0948722\pi$
$347$	3.45463	+	10.6323i	0.00995572	+	0.0306405i	−0.945955	+	0.324297i	$0.894872\pi$
$348$	−24.7056	−	155.985i	−0.0709931	−	0.448233i
$349$	−26.1534	+	165.126i	−0.0749380	+	0.473140i	0.921469	+	0.388451i	$0.126990\pi$
$349$	−26.1534	+	165.126i	−0.0749380	+	0.473140i	−0.996407	+	0.0846889i	$0.973010\pi$
$350$	39.2808	+	12.7631i	0.112231	+	0.0364661i
$351$	29.2975	−	40.3246i	0.0834687	−	0.114885i
$352$	32.9440			0.0935910
$353$		−	375.993i		−	1.06514i	−0.846387	−	0.532569i	$-0.821227\pi$
$353$		−	375.993i		−	1.06514i	0.846387	−	0.532569i	$-0.178773\pi$
$354$	61.1990	−	84.2333i	0.172879	−	0.237947i
$355$	−36.9478	+	36.9478i	−0.104078	+	0.104078i
$356$	10.4088	−	1.64859i	0.0292382	−	0.00463088i
$357$	85.0637	+	117.080i	0.238274	+	0.327956i
$358$	172.604	−	27.3378i	0.482135	−	0.0763626i
$359$	−476.882	+	242.983i	−1.32836	+	0.676834i	−0.966805	−	0.255517i	$-0.917754\pi$
$359$	−476.882	+	242.983i	−1.32836	+	0.676834i	−0.361556	+	0.932350i	$0.617754\pi$
$360$	−5.64653	+	35.6508i	−0.0156848	+	0.0990299i
$361$	754.713	−	548.331i	2.09062	−	1.51892i
$362$	−295.771	+	214.890i	−0.817048	+	0.593620i
$363$	−46.6103	−	143.452i	−0.128403	−	0.395184i
$364$	−36.8401	+	72.3028i	−0.101209	+	0.198634i
$365$		−	575.955i		−	1.57796i
$366$	−54.5301	−	139.113i	−0.148989	−	0.380091i
$367$	−252.842			−0.688943			−0.344472	−	0.938797i	$-0.611942\pi$
$367$	−252.842			−0.688943			−0.344472	+	0.938797i	$0.611942\pi$
$368$	−107.600	−	54.8247i	−0.292390	−	0.148980i
$369$	157.458	−	51.1611i	0.426715	−	0.138648i
$370$	14.1257	+	19.4423i	0.0381775	+	0.0525468i
$371$	−139.147	−	191.520i	−0.375060	−	0.516225i
$372$	184.448	+	29.2137i	0.495827	+	0.0785314i
$373$	−169.610	−	332.877i	−0.454717	−	0.892433i	−0.998581	−	0.0532592i	$-0.983039\pi$
$373$	−169.610	−	332.877i	−0.454717	−	0.892433i	0.543863	−	0.839174i	$-0.316961\pi$
$374$	−25.4507	−	160.690i	−0.0680501	−	0.429651i
$375$	190.176	−	138.171i	0.507136	−	0.368456i
$376$	6.92865	+	43.7458i	0.0184273	+	0.116345i
$377$	−309.234	−	309.234i	−0.820250	−	0.820250i
$378$	25.1460	+	18.2696i	0.0665237	+	0.0483323i
$379$	−83.1643			−0.219431			−0.109715	−	0.993963i	$-0.534994\pi$
$379$	−83.1643			−0.219431			−0.109715	+	0.993963i	$0.534994\pi$
$380$		−	306.027i		−	0.805333i
$381$	26.3519	+	19.1458i	0.0691652	+	0.0502514i
$382$	41.6024	−	128.039i	0.108907	−	0.335181i
$383$	−304.630	−	48.2487i	−0.795380	−	0.125976i	−0.254497	−	0.967074i	$-0.581910\pi$
$383$	−304.630	−	48.2487i	−0.795380	−	0.125976i	−0.540883	+	0.841098i	$0.681910\pi$
$384$	−19.3547	+	3.06548i	−0.0504028	+	0.00798301i
$385$	99.6562	−	32.3803i	0.258847	−	0.0841046i
$386$	−54.7557	+	168.521i	−0.141854	+	0.436582i
$387$	52.3952	+	52.3952i	0.135388	+	0.135388i
$388$	−80.6666	−	248.266i	−0.207904	−	0.639862i
$389$	−58.0715	+	366.649i	−0.149284	+	0.942542i	0.793362	+	0.608750i	$0.208329\pi$
$389$	−58.0715	+	366.649i	−0.149284	+	0.942542i	−0.942647	+	0.333793i	$0.891671\pi$
$390$	45.3770	+	89.0573i	0.116351	+	0.228352i
$391$	−184.291	+	567.188i	−0.471332	+	1.45061i
$392$	78.4000	+	39.9468i	0.200000	+	0.101905i
$393$	1.80177	−	2.47993i	0.00458466	−	0.00631025i
$394$	4.51756	−	8.86621i	0.0114659	−	0.0225031i
$395$	366.309	+	366.309i	0.927363	+	0.927363i
$396$	−15.8635	−	31.1339i	−0.0400594	−	0.0786210i
$397$	−5.59690	+	2.85176i	−0.0140980	+	0.00718328i	−0.461025	−	0.887387i	$-0.652518\pi$
$397$	−5.59690	+	2.85176i	−0.0140980	+	0.00718328i	0.446927	+	0.894570i	$0.352518\pi$
$398$	−216.066	+	216.066i	−0.542881	+	0.542881i
$399$	−234.802	−	119.638i	−0.588476	−	0.299844i
$400$	22.3441	+	16.2340i	0.0558603	+	0.0405849i
$401$	−33.6718	+	66.0846i	−0.0839695	+	0.164799i	−0.929173	−	0.369645i	$-0.879479\pi$
$401$	−33.6718	+	66.0846i	−0.0839695	+	0.164799i	0.845203	+	0.534445i	$0.179479\pi$
$402$	−267.761	−	87.0010i	−0.666073	−	0.216420i
$403$	460.759	−	234.769i	1.14332	−	0.582552i
$404$	190.969	+	30.2466i	0.472696	+	0.0748677i
$405$	36.4109	−	11.8306i	0.0899035	−	0.0292114i
$406$	192.835	−	192.835i	0.474963	−	0.474963i
$407$	−22.1259	−	7.18913i	−0.0543633	−	0.0176637i
$408$	29.9047	+	92.0371i	0.0732958	+	0.225581i
$409$	−5.30693	−	33.5066i	−0.0129754	−	0.0819233i	0.980351	−	0.197262i	$-0.0632048\pi$
$409$	−5.30693	−	33.5066i	−0.0129754	−	0.0819233i	−0.993326	+	0.115338i	$0.963205\pi$
$410$	−51.9357	+	327.909i	−0.126673	+	0.799779i
$411$	390.018	+	126.724i	0.948948	+	0.308332i
$412$	36.7357	−	50.5624i	0.0891644	−	0.122724i
$413$	179.789			0.435325
$414$			128.087i			0.309390i
$415$	28.6174	−	39.3885i	0.0689577	−	0.0949121i
$416$	−38.3699	+	38.3699i	−0.0922353	+	0.0922353i
$417$	−70.1412	+	11.1093i	−0.168204	+	0.0266409i
$418$	174.133	+	239.674i	0.416587	+	0.573382i
$419$	−233.914	+	37.0484i	−0.558268	+	0.0884209i	−0.429191	−	0.903214i	$-0.641201\pi$
$419$	−233.914	+	37.0484i	−0.558268	+	0.0884209i	−0.129077	+	0.991635i	$0.541201\pi$
$420$	−55.5352	+	28.2966i	−0.132227	+	0.0673728i
$421$	−31.1243	+	196.511i	−0.0739294	+	0.466772i	0.922754	+	0.385390i	$0.125933\pi$
$421$	−31.1243	+	196.511i	−0.0739294	+	0.466772i	−0.996683	+	0.0813814i	$0.974067\pi$
$422$	−33.0761	+	24.0312i	−0.0783793	+	0.0569459i
$423$	38.0058	−	27.6128i	0.0898482	−	0.0652786i
$424$	−48.9181	−	150.554i	−0.115373	−	0.355081i
$425$	61.9218	−	121.528i	0.145698	−	0.285949i
$426$			30.0883i			0.0706297i
$427$	138.994	−	217.375i	0.325513	−	0.509076i
$428$	−333.340			−0.778832
$429$	−86.2131	−	43.9278i	−0.200963	−	0.102396i
$430$	−141.315	+	45.9161i	−0.328640	+	0.106782i
$431$	−260.968	−	359.191i	−0.605494	−	0.833391i	0.390704	−	0.920517i	$-0.372232\pi$
$431$	−260.968	−	359.191i	−0.605494	−	0.833391i	−0.996197	+	0.0871259i	$0.972232\pi$
$432$	12.2169	+	16.8151i	0.0282798	+	0.0389238i
$433$	−129.991	−	20.5885i	−0.300210	−	0.0475486i	0.00451236	−	0.999990i	$-0.498564\pi$
$433$	−129.991	−	20.5885i	−0.300210	−	0.0475486i	−0.304722	+	0.952441i	$0.598564\pi$
$434$	146.399	+	287.324i	0.337325	+	0.662038i
$435$	−52.5470	−	331.769i	−0.120798	−	0.762687i
$436$	276.736	−	201.061i	0.634716	−	0.461148i
$437$	−169.883	−	1072.60i	−0.388747	−	2.45445i
$438$	−234.513	−	234.513i	−0.535418	−	0.535418i
$439$	−269.464	−	195.777i	−0.613813	−	0.445961i	0.236942	−	0.971524i	$-0.423855\pi$
$439$	−269.464	−	195.777i	−0.613813	−	0.445961i	−0.850755	+	0.525563i	$0.823855\pi$
$440$	70.0695			0.159249
$441$		−	93.3279i		−	0.211628i
$442$	216.797	+	157.513i	0.490492	+	0.356363i
$443$	99.5056	−	306.247i	0.224618	−	0.691302i	−0.773713	−	0.633537i	$-0.781603\pi$
$443$	99.5056	−	306.247i	0.224618	−	0.691302i	0.998330	−	0.0577652i	$-0.0183975\pi$
$444$	13.6679	+	2.16479i	0.0307837	+	0.00487565i
$445$	22.1388	−	3.50644i	0.0497500	−	0.00787963i
$446$	−332.846	+	108.148i	−0.746291	+	0.242485i
$447$	−61.1727	+	188.270i	−0.136852	+	0.421186i
$448$	−23.9270	−	23.9270i	−0.0534085	−	0.0534085i
$449$	−141.975	−	436.954i	−0.316202	−	0.973170i	−0.975257	−	0.221075i	$-0.929043\pi$
$449$	−141.975	−	436.954i	−0.316202	−	0.973170i	0.659055	−	0.752095i	$-0.270957\pi$
$450$	4.58263	−	28.9336i	0.0101836	−	0.0642968i
$451$	−145.910	−	286.364i	−0.323525	−	0.634954i
$452$	−33.3807	+	102.735i	−0.0738511	+	0.227290i
$453$	−423.490	−	215.779i	−0.934856	−	0.476333i
$454$	−320.744	+	441.466i	−0.706485	+	0.972393i
$455$	−78.3562	+	153.783i	−0.172212	+	0.337984i
$456$	−124.605	−	124.605i	−0.273258	−	0.273258i
$457$	172.240	+	338.040i	0.376892	+	0.739693i	0.999067	−	0.0431854i	$-0.0137506\pi$
$457$	172.240	+	338.040i	0.376892	+	0.739693i	−0.622175	+	0.782878i	$0.713751\pi$
$458$	266.853	−	135.969i	0.582649	−	0.296874i
$459$	72.5802	−	72.5802i	0.158127	−	0.158127i
$460$	−228.857	−	116.608i	−0.497514	−	0.253496i
$461$	−148.801	−	108.110i	−0.322779	−	0.234513i	0.414581	−	0.910012i	$-0.363928\pi$
$461$	−148.801	−	108.110i	−0.322779	−	0.234513i	−0.737360	+	0.675500i	$0.763928\pi$
$462$	27.3929	−	53.7616i	0.0592919	−	0.116367i
$463$	−220.564	−	71.6655i	−0.476379	−	0.154785i	0.0609790	−	0.998139i	$-0.480578\pi$
$463$	−220.564	−	71.6655i	−0.476379	−	0.154785i	−0.537358	+	0.843354i	$0.680578\pi$
$464$	162.485	−	82.7902i	0.350183	−	0.178427i
$465$	392.307	+	62.1353i	0.843671	+	0.133624i
$466$	−52.8769	+	17.1807i	−0.113470	+	0.0368685i
$467$	−334.310	+	334.310i	−0.715866	+	0.715866i	−0.967756	−	0.251890i	$-0.918948\pi$
$467$	−334.310	+	334.310i	−0.715866	+	0.715866i	0.251890	+	0.967756i	$0.418948\pi$
$468$	54.7379	+	17.7854i	0.116961	+	0.0380030i
$469$	−150.232	−	462.366i	−0.320324	−	0.985856i
$470$	14.7367	+	93.0441i	0.0313547	+	0.197966i
$471$	43.0112	−	271.562i	0.0913189	−	0.576565i
$472$	114.341	+	37.1516i	0.242248	+	0.0787110i
$473$	84.5484	−	116.371i	0.178749	−	0.246027i
$474$	298.301			0.629327
$475$			248.366i			0.522876i
$476$	−98.2231	+	135.192i	−0.206351	+	0.284018i
$477$	−118.727	+	118.727i	−0.248903	+	0.248903i
$478$	−551.532	+	87.3541i	−1.15383	+	0.182749i
$479$	5.08696	+	7.00159i	0.0106199	+	0.0146171i	0.814294	−	0.580453i	$-0.197124\pi$
$479$	5.08696	+	7.00159i	0.0106199	+	0.0146171i	−0.803674	+	0.595070i	$0.797124\pi$
$480$	−41.1660	+	6.52005i	−0.0857624	+	0.0135834i
$481$	34.1432	−	17.3968i	0.0709837	−	0.0361680i
$482$	−63.7203	+	402.314i	−0.132200	+	0.834677i
$483$	−178.938	+	130.006i	−0.370471	+	0.269163i
$484$	140.905	−	102.374i	0.291126	−	0.211516i
$485$	−171.572	−	528.045i	−0.353757	−	1.08875i
$486$	10.0084	−	19.6426i	0.0205934	−	0.0404169i
$487$			550.499i			1.13039i	0.824958	+	0.565194i	$0.191199\pi$
$487$			550.499i			1.13039i	−0.824958	+	0.565194i	$0.808801\pi$
$488$	133.314	−	109.523i	0.273185	−	0.224432i
$489$	184.429			0.377155
$490$	166.751	+	84.9639i	0.340308	+	0.173396i
$491$	−456.789	+	148.420i	−0.930325	+	0.302281i	−0.734695	−	0.678397i	$-0.762675\pi$
$491$	−456.789	+	148.420i	−0.930325	+	0.302281i	−0.195629	+	0.980678i	$0.562675\pi$
$492$	112.369	+	154.662i	0.228392	+	0.314354i
$493$	−529.349	−	728.586i	−1.07373	−	1.47786i
$494$	−481.961	−	76.3351i	−0.975629	−	0.154525i
$495$	−33.7406	−	66.2196i	−0.0681627	−	0.133777i
$496$	33.7330	+	212.982i	0.0680101	+	0.429399i
$497$	−42.0332	+	30.5389i	−0.0845739	+	0.0614465i
$498$	−4.38568	−	27.6901i	−0.00880659	−	0.0556026i
$499$	−145.387	−	145.387i	−0.291357	−	0.291357i	0.546259	−	0.837616i	$-0.316051\pi$
$499$	−145.387	−	145.387i	−0.291357	−	0.291357i	−0.837616	+	0.546259i	$0.816051\pi$
$500$	219.596	+	159.546i	0.439193	+	0.319092i
$501$	313.175			0.625099
$502$			351.125i			0.699452i
$503$	−214.748	−	156.023i	−0.426934	−	0.310186i	0.353488	−	0.935439i	$-0.384996\pi$
$503$	−214.748	−	156.023i	−0.426934	−	0.310186i	−0.780422	+	0.625253i	$0.784996\pi$
$504$	−11.0908	+	34.1339i	−0.0220055	+	0.0677261i
$505$	406.178	+	64.3322i	0.804312	+	0.127391i
$506$	245.587	−	38.8972i	0.485351	−	0.0768720i
$507$	−126.815	+	41.2047i	−0.250128	+	0.0812716i
$508$	−11.6227	+	35.7710i	−0.0228793	+	0.0704153i
$509$	147.490	+	147.490i	0.289765	+	0.289765i	0.836987	−	0.547222i	$-0.184315\pi$
$509$	147.490	+	147.490i	0.289765	+	0.289765i	−0.547222	+	0.836987i	$0.684315\pi$
$510$	63.6051	+	195.756i	0.124716	+	0.383836i
$511$	89.5885	−	565.640i	0.175320	−	1.10693i
$512$	−10.2726	−	20.1612i	−0.0200637	−	0.0393773i
$513$	−57.7578	+	177.760i	−0.112588	+	0.346511i
$514$	330.294	+	168.293i	0.642595	+	0.327418i
$515$	78.1342	−	107.543i	0.151717	−	0.208820i
$516$	−38.8439	+	76.2354i	−0.0752788	+	0.147743i
$517$	−64.4848	−	64.4848i	−0.124729	−	0.124729i
$518$	10.8485	+	21.2913i	0.0209430	+	0.0411029i
$519$	−221.337	+	112.777i	−0.426468	+	0.217296i
$520$	−81.6099	+	81.6099i	−0.156942	+	0.156942i
$521$	−776.120	−	395.453i	−1.48967	−	0.759027i	−0.495685	−	0.868502i	$-0.665083\pi$
$521$	−776.120	−	395.453i	−1.48967	−	0.759027i	−0.993990	+	0.109475i	$0.965083\pi$
$522$	−156.483	−	113.691i	−0.299775	−	0.217799i
$523$	86.6773	−	170.114i	0.165731	−	0.325265i	−0.793173	−	0.608996i	$-0.791572\pi$
$523$	86.6773	−	170.114i	0.165731	−	0.325265i	0.958904	+	0.283731i	$0.0915724\pi$
$524$	3.36633	+	1.09379i	0.00642430	+	0.00208738i
$525$	45.0714	−	22.9650i	0.0858503	−	0.0437429i
$526$	−495.774	−	78.5228i	−0.942536	−	0.149283i
$527$	1012.79	−	329.076i	1.92181	−	0.624433i
$528$	28.5304	−	28.5304i	0.0540348	−	0.0540348i
$529$	−363.745	−	118.188i	−0.687609	−	0.223418i
$530$	−104.045	−	320.218i	−0.196312	−	0.604185i
$531$	−19.9482	−	125.948i	−0.0375673	−	0.237190i
$532$	47.6017	−	300.545i	0.0894769	−	0.564935i
$533$	503.469	+	163.587i	0.944595	+	0.306918i
$534$	7.58657	−	10.4420i	0.0142071	−	0.0195543i
$535$	−708.990			−1.32522
$536$		−	325.096i		−	0.606522i
$537$	125.804	−	173.155i	0.234273	−	0.322449i
$538$	187.790	−	187.790i	0.349053	−	0.349053i
$539$	−178.942	+	28.3416i	−0.331988	+	0.0525818i
$540$	25.9844	+	35.7645i	0.0481193	+	0.0662306i
$541$	−322.172	+	51.0271i	−0.595512	+	0.0943199i	−0.446913	−	0.894578i	$-0.647477\pi$
$541$	−322.172	+	51.0271i	−0.595512	+	0.0943199i	−0.148600	+	0.988897i	$0.547477\pi$
$542$	388.481	−	197.941i	0.716755	−	0.365205i
$543$	−70.0449	+	442.246i	−0.128996	+	0.814449i
$544$	−90.4032	+	65.6818i	−0.166182	+	0.120739i
$545$	588.598	−	427.641i	1.08000	−	0.784663i
$546$	30.7116	+	94.5205i	0.0562483	+	0.173114i
$547$	416.952	−	818.315i	0.762253	−	1.49601i	−0.103006	−	0.994681i	$-0.532846\pi$
$547$	416.952	−	818.315i	0.762253	−	1.49601i	0.865259	−	0.501325i	$-0.167154\pi$
$548$			473.530i			0.864105i
$549$	−167.700	−	73.2510i	−0.305464	−	0.133426i
$550$	−56.8673			−0.103395
$551$	1461.17	+	744.501i	2.65184	+	1.35118i
$552$	−140.664	+	45.7044i	−0.254825	+	0.0827978i
$553$	302.769	+	416.726i	0.547503	+	0.753573i
$554$	306.624	+	422.032i	0.553473	+	0.761790i
$555$	29.0707	+	4.60435i	0.0523797	+	0.00829613i
$556$	−37.2280	−	73.0640i	−0.0669568	−	0.131410i
$557$	90.3858	+	570.673i	0.162272	+	1.02455i	0.925591	+	0.378525i	$0.123569\pi$
$557$	90.3858	+	570.673i	0.162272	+	1.02455i	−0.763318	+	0.646022i	$0.776431\pi$
$558$	185.036	−	134.437i	0.331606	−	0.240926i
$559$	37.0636	+	234.010i	0.0663034	+	0.418623i
$560$	−50.8911	−	50.8911i	−0.0908769	−	0.0908769i
$561$	−161.202	−	117.120i	−0.287348	−	0.208770i
$562$	435.009			0.774037
$563$			410.800i			0.729662i	0.931074	+	0.364831i	$0.118873\pi$
$563$			410.800i			0.729662i	−0.931074	+	0.364831i	$0.881127\pi$
$564$	43.8853	+	31.8846i	0.0778109	+	0.0565329i
$565$	−70.9984	+	218.510i	−0.125661	+	0.386744i
$566$	71.9458	+	11.3951i	0.127113	+	0.0201327i
$567$	37.5990	−	5.95510i	0.0663122	−	0.0105028i
$568$	−33.0425	+	10.7362i	−0.0581734	+	0.0189017i
$569$	186.938	−	575.336i	0.328538	−	1.01114i	−0.641280	−	0.767307i	$-0.721596\pi$
$569$	186.938	−	575.336i	0.328538	−	1.01114i	0.969818	−	0.243829i	$-0.0784036\pi$
$570$	−265.027	−	265.027i	−0.464959	−	0.464959i
$571$	−289.351	−	890.530i	−0.506744	−	1.55960i	−0.797819	−	0.602897i	$-0.794013\pi$
$571$	−289.351	−	890.530i	−0.506744	−	1.55960i	0.291076	−	0.956700i	$-0.405987\pi$
$572$	17.4781	−	110.352i	0.0305561	−	0.192924i
$573$	−74.8563	−	146.914i	−0.130639	−	0.256394i
$574$	−102.011	+	313.958i	−0.177720	+	0.546965i
$575$	185.736	+	94.6373i	0.323019	+	0.164587i
$576$	−14.1068	+	19.4164i	−0.0244911	+	0.0337090i
$577$	−205.985	+	404.269i	−0.356994	+	0.700640i	−0.997746	−	0.0671082i	$-0.978623\pi$
$577$	−205.985	+	404.269i	−0.356994	+	0.700640i	0.640752	+	0.767748i	$0.278623\pi$
$578$	101.213	+	101.213i	0.175110	+	0.175110i
$579$	98.5234	+	193.363i	0.170161	+	0.333960i
$580$	345.594	−	176.089i	0.595851	−	0.303601i
$581$	34.2317	−	34.2317i	0.0589185	−	0.0589185i
$582$	−284.864	−	145.146i	−0.489458	−	0.249391i
$583$	263.694	+	191.585i	0.452306	+	0.328620i
$584$	173.859	−	341.218i	0.297704	−	0.584278i
$585$	116.424	+	37.8283i	0.199015	+	0.0646637i
$586$	−308.856	+	157.370i	−0.527058	+	0.268549i
$587$	151.050	+	23.9240i	0.257325	+	0.0407563i	0.283764	−	0.958894i	$-0.408417\pi$
$587$	151.050	+	23.9240i	0.257325	+	0.0407563i	−0.0264389	+	0.999650i	$0.508417\pi$
$588$	102.491	−	33.3014i	0.174305	−	0.0566351i
$589$	−1371.18	+	1371.18i	−2.32798	+	2.32798i
$590$	243.195	+	79.0188i	0.412195	+	0.133930i
$591$	−3.76604	−	11.5907i	−0.00637232	−	0.0196120i
$592$	2.49968	+	15.7824i	0.00422244	+	0.0266594i
$593$	−127.951	+	807.850i	−0.215769	+	1.36231i	0.607347	+	0.794437i	$0.292234\pi$
$593$	−127.951	+	807.850i	−0.215769	+	1.36231i	−0.823116	+	0.567874i	$0.807766\pi$
$594$	−40.7010	−	13.2245i	−0.0685201	−	0.0222635i
$595$	−208.913	+	287.545i	−0.351115	+	0.483268i
$596$	−228.584			−0.383529
$597$			374.238i			0.626865i
$598$	−240.732	+	331.339i	−0.402562	+	0.554079i
$599$	306.466	−	306.466i	0.511629	−	0.511629i	−0.403396	−	0.915025i	$-0.632170\pi$
$599$	306.466	−	306.466i	0.511629	−	0.511629i	0.915025	+	0.403396i	$0.132170\pi$
$600$	33.4096	−	5.29156i	0.0556827	−	0.00881927i
$601$	393.054	+	540.992i	0.653999	+	0.900153i	0.999264	−	0.0383523i	$-0.0122109\pi$
$601$	393.054	+	540.992i	0.653999	+	0.900153i	−0.345265	+	0.938505i	$0.612211\pi$
$602$	−145.926	+	23.1125i	−0.242403	+	0.0383928i
$603$	−307.233	+	156.543i	−0.509508	+	0.259607i
$604$	85.8547	−	542.065i	0.142144	−	0.897459i
$605$	299.695	−	217.741i	0.495363	−	0.359903i
$606$	191.578	−	139.190i	0.316136	−	0.229686i
$607$	−83.2245	−	256.139i	−0.137108	−	0.421975i	0.858804	−	0.512304i	$-0.171208\pi$
$607$	−83.2245	−	256.139i	−0.137108	−	0.421975i	−0.995912	+	0.0903295i	$0.971208\pi$
$608$	92.3779	−	181.302i	0.151937	−	0.298194i
$609$		−	334.000i		−	0.548440i
$610$	283.550	−	232.947i	0.464836	−	0.381881i
$611$	150.211			0.245844
$612$	105.605	+	53.8083i	0.172557	+	0.0879220i
$613$	355.626	−	115.550i	0.580140	−	0.188499i	−0.00422319	−	0.999991i	$-0.501344\pi$
$613$	355.626	−	115.550i	0.580140	−	0.188499i	0.584363	+	0.811492i	$0.301344\pi$
$614$	139.386	+	191.848i	0.227013	+	0.312456i
$615$	239.000	+	328.956i	0.388618	+	0.534887i
$616$	68.8145	+	10.8992i	0.111712	+	0.0176934i
$617$	−8.65912	−	16.9945i	−0.0140342	−	0.0275437i	0.883883	−	0.467708i	$-0.154920\pi$
$617$	−8.65912	−	16.9945i	−0.0140342	−	0.0275437i	−0.897917	+	0.440164i	$0.854920\pi$
$618$	−11.9742	−	75.6024i	−0.0193758	−	0.122334i
$619$	−46.4531	+	33.7501i	−0.0750454	+	0.0545237i	−0.624675	−	0.780885i	$-0.714769\pi$
$619$	−46.4531	+	33.7501i	−0.0750454	+	0.0545237i	0.549630	+	0.835408i	$0.314769\pi$
$620$	71.7477	+	452.997i	0.115722	+	0.730641i
$621$	110.927	+	110.927i	0.178626	+	0.178626i
$622$	519.335	+	377.319i	0.834944	+	0.606622i
$623$	22.2877			0.0357747
$624$			66.4586i			0.106504i
$625$	327.415	+	237.881i	0.523864	+	0.380609i
$626$	−232.705	+	716.194i	−0.371734	+	1.14408i
$627$	358.367	+	56.7598i	0.571559	+	0.0905261i
$628$	313.573	−	49.6651i	0.499320	−	0.0790845i
$629$	75.0499	−	24.3852i	0.119316	−	0.0387682i
$630$	−23.5893	+	72.6004i	−0.0374433	+	0.115239i
$631$	−57.6442	−	57.6442i	−0.0913537	−	0.0913537i	0.659953	−	0.751307i	$-0.270576\pi$
$631$	−57.6442	−	57.6442i	−0.0913537	−	0.0913537i	−0.751307	+	0.659953i	$0.770576\pi$
$632$	106.440	+	327.590i	0.168418	+	0.518339i
$633$	−7.83311	+	49.4563i	−0.0123746	+	0.0781300i
$634$	132.462	+	259.972i	0.208931	+	0.410050i
$635$	−24.7206	+	76.0822i	−0.0389301	+	0.119815i
$636$	−172.748	−	88.0196i	−0.271617	−	0.138396i
$637$	175.404	−	241.423i	0.275359	−	0.379000i
$638$	−170.465	+	334.556i	−0.267187	+	0.524383i
$639$	26.0572	+	26.0572i	0.0407781	+	0.0407781i
$640$	−21.8491	−	42.8814i	−0.0341393	−	0.0670021i
$641$	1084.64	−	552.651i	1.69210	−	0.862170i	0.703669	−	0.710528i	$-0.251544\pi$
$641$	1084.64	−	552.651i	1.69210	−	0.862170i	0.988436	−	0.151642i	$-0.0484560\pi$
$642$	−288.681	+	288.681i	−0.449659	+	0.449659i
$643$	208.595	+	106.284i	0.324409	+	0.165295i	0.608609	−	0.793470i	$-0.291728\pi$
$643$	208.595	+	106.284i	0.324409	+	0.165295i	−0.284200	+	0.958765i	$0.591728\pi$
$644$	−206.619	−	150.118i	−0.320838	−	0.233102i
$645$	−82.6181	+	162.147i	−0.128090	+	0.251391i
$646$	−955.694	−	310.524i	−1.47940	−	0.480687i
$647$	−1043.96	+	531.925i	−1.61354	+	0.822141i	−0.614084	+	0.789240i	$0.710475\pi$
$647$	−1043.96	+	531.925i	−1.61354	+	0.822141i	−0.999459	+	0.0329007i	$0.989525\pi$
$648$	25.1424	+	3.98217i	0.0388001	+	0.00614533i
$649$	−235.428	+	76.4952i	−0.362755	+	0.117866i
$650$	66.2333	−	66.2333i	0.101897	−	0.101897i
$651$	375.616	+	122.045i	0.576983	+	0.187473i
$652$	65.8083	+	202.537i	0.100933	+	0.310640i
$653$	159.895	+	1009.54i	0.244863	+	1.54600i	0.737246	+	0.675625i	$0.236126\pi$
$653$	159.895	+	1009.54i	0.244863	+	1.54600i	−0.492383	+	0.870379i	$0.663874\pi$
$654$	65.5370	−	413.784i	0.100209	−	0.632697i
$655$	7.15994	+	2.32641i	0.0109312	+	0.00355177i
$656$	−129.752	+	178.589i	−0.197793	+	0.272239i
$657$	−406.188			−0.618247
$658$			93.6698i			0.142355i
$659$	398.101	−	547.939i	0.604098	−	0.831470i	−0.391978	−	0.919975i	$-0.628209\pi$
$659$	398.101	−	547.939i	0.604098	−	0.831470i	0.996076	+	0.0885050i	$0.0282089\pi$
$660$	60.6820	−	60.6820i	0.0919424	−	0.0919424i
$661$	−576.762	+	91.3501i	−0.872559	+	0.138200i	−0.576626	−	0.817009i	$-0.695631\pi$
$661$	−576.762	+	91.3501i	−0.872559	+	0.138200i	−0.295934	+	0.955208i	$0.595631\pi$
$662$	297.403	+	409.341i	0.449250	+	0.618340i
$663$	324.162	−	51.3422i	0.488932	−	0.0774392i
$664$	28.8440	−	14.6967i	0.0434397	−	0.0221336i
$665$	101.245	−	639.239i	0.152249	−	0.961261i
$666$	13.7115	−	9.96202i	0.0205879	−	0.0149580i
$667$	1113.52	−	809.022i	1.66945	−	1.21293i
$668$	111.748	+	343.924i	0.167287	+	0.514856i
$669$	−194.594	+	381.912i	−0.290873	+	0.570870i
$670$		−	691.455i		−	1.03202i
$671$	−89.5207	+	343.783i	−0.133414	+	0.512345i
$672$	−41.4428			−0.0616709
$673$	29.5790	+	15.0712i	0.0439509	+	0.0223941i	0.475828	−	0.879538i	$-0.342149\pi$
$673$	29.5790	+	15.0712i	0.0439509	+	0.0223941i	−0.431877	+	0.901933i	$0.642149\pi$
$674$	55.3146	−	17.9728i	0.0820691	−	0.0266659i
$675$	−21.0885	−	29.0259i	−0.0312423	−	0.0430013i
$676$	−90.5008	−	124.564i	−0.133877	−	0.184266i
$677$	−741.439	−	117.432i	−1.09518	−	0.173460i	−0.417401	−	0.908722i	$-0.637059\pi$
$677$	−741.439	−	117.432i	−1.09518	−	0.173460i	−0.677782	+	0.735262i	$0.737059\pi$
$678$	60.0628	+	117.880i	0.0885882	+	0.173864i
$679$	−86.3630	−	545.275i	−0.127191	−	0.803055i
$680$	−192.281	+	139.700i	−0.282766	+	0.205442i
$681$	104.549	+	660.094i	0.153522	+	0.969300i
$682$	−313.953	−	313.953i	−0.460341	−	0.460341i
$683$	−54.0498	−	39.2695i	−0.0791359	−	0.0574956i	0.547514	−	0.836797i	$-0.315574\pi$
$683$	−54.0498	−	39.2695i	−0.0791359	−	0.0574956i	−0.626650	+	0.779301i	$0.715574\pi$
$684$	−215.823			−0.315531
$685$			1007.16i			1.47031i
$686$	387.676	+	281.663i	0.565126	+	0.410588i
$687$	113.349	−	348.854i	0.164992	−	0.507793i
$688$	−97.5809	−	15.4553i	−0.141833	−	0.0224641i
$689$	−530.264	+	83.9856i	−0.769614	+	0.121895i
$690$	−299.181	+	97.2099i	−0.433596	+	0.140884i
$691$	−104.873	+	322.767i	−0.151770	+	0.467101i	−0.997819	−	0.0660039i	$-0.978975\pi$
$691$	−104.873	+	322.767i	−0.151770	+	0.467101i	0.846049	+	0.533105i	$0.178975\pi$
$692$	−202.828	−	202.828i	−0.293104	−	0.293104i
$693$	−22.8359	−	70.2818i	−0.0329523	−	0.101417i
$694$	−2.47324	+	15.6155i	−0.00356375	+	0.0225007i
$695$	−79.1812	−	155.402i	−0.113930	−	0.223600i
$696$	69.0176	−	212.414i	0.0991633	−	0.305193i
$697$	971.333	+	494.919i	1.39359	+	0.710070i
$698$	−138.972	+	191.279i	−0.199101	+	0.274039i
$699$	−30.9137	+	60.6716i	−0.0442257	+	0.0867978i
$700$	41.3023	+	41.3023i	0.0590033	+	0.0590033i
$701$	494.422	+	970.358i	0.705310	+	1.38425i	0.913776	+	0.406219i	$0.133153\pi$
$701$	494.422	+	970.358i	0.705310	+	1.38425i	−0.208466	+	0.978030i	$0.566847\pi$
$702$	62.8070	−	32.0018i	0.0894687	−	0.0455866i
$703$	−101.607	+	101.607i	−0.144534	+	0.144534i
$704$	41.5119	+	21.1514i	0.0589657	+	0.0300445i
$705$	93.3409	+	67.8161i	0.132398	+	0.0961931i
$706$	241.403	−	473.779i	0.341930	−	0.671076i
$707$	388.896	+	126.360i	0.550065	+	0.178727i
$708$	131.196	−	66.8479i	0.185306	−	0.0944179i
$709$	−158.695	−	25.1349i	−0.223830	−	0.0354512i	0.0435121	−	0.999053i	$-0.486145\pi$
$709$	−158.695	−	25.1349i	−0.223830	−	0.0354512i	−0.267342	+	0.963602i	$0.586145\pi$
$710$	−70.2790	+	22.8350i	−0.0989845	+	0.0321620i
$711$	258.336	−	258.336i	0.363342	−	0.363342i
$712$	14.1743	+	4.60552i	0.0199078	+	0.00646842i
$713$	502.939	+	1547.89i	0.705384	+	2.17095i
$714$	32.0164	+	202.144i	0.0448409	+	0.283115i
$715$	37.1747	−	234.712i	0.0519925	−	0.328268i
$716$	235.046	+	76.3711i	0.328276	+	0.106663i
$717$	−401.990	+	553.291i	−0.560655	+	0.771676i
$718$	−756.911			−1.05419
$719$		−	276.430i		−	0.384464i	−0.981350	−	0.192232i	$-0.938427\pi$
$719$		−	276.430i		−	0.384464i	0.981350	−	0.192232i	$-0.0615726\pi$
$720$	−30.0042	+	41.2973i	−0.0416726	+	0.0573574i
$721$	93.4628	−	93.4628i	0.129629	−	0.129629i
$722$	1303.04	−	206.382i	1.80477	−	0.285848i
$723$	293.231	+	403.598i	0.405575	+	0.558226i
$724$	−510.662	+	80.8809i	−0.705334	+	0.111714i
$725$	−280.478	+	142.911i	−0.386866	+	0.197118i
$726$	33.3693	−	210.685i	0.0459632	−	0.290200i
$727$	247.558	−	179.861i	0.340520	−	0.247402i	−0.404361	−	0.914599i	$-0.632506\pi$
$727$	247.558	−	179.861i	0.340520	−	0.247402i	0.744881	+	0.667197i	$0.232506\pi$
$728$	−92.8425	+	67.4540i	−0.127531	+	0.0926566i
$729$	−8.34346	−	25.6785i	−0.0114451	−	0.0352243i
$730$	369.786	−	725.746i	0.506556	−	0.994173i
$731$			487.906i			0.667450i
$732$	20.6041	−	210.303i	0.0281477	−	0.287300i
$733$	−184.154			−0.251233			−0.125616	−	0.992079i	$-0.540091\pi$
$733$	−184.154			−0.251233			−0.125616	+	0.992079i	$0.540091\pi$
$734$	−318.600	−	162.335i	−0.434059	−	0.221164i
$735$	217.992	−	70.8298i	0.296587	−	0.0963670i
$736$	−100.384	−	138.166i	−0.136391	−	0.187726i
$737$	393.447	+	541.533i	0.533849	+	0.734781i
$738$	231.256	+	36.6273i	0.313355	+	0.0496305i
$739$	629.515	+	1235.49i	0.851847	+	1.67184i	0.734349	+	0.678772i	$0.237487\pi$
$739$	629.515	+	1235.49i	0.851847	+	1.67184i	0.117498	+	0.993073i	$0.462513\pi$
$740$	5.31665	+	33.5680i	0.00718466	+	0.0453621i
$741$	−483.499	+	351.282i	−0.652495	+	0.474065i
$742$	−52.3725	−	330.667i	−0.0705828	−	0.445643i
$743$	−280.977	−	280.977i	−0.378165	−	0.378165i	0.492275	−	0.870440i	$-0.336166\pi$
$743$	−280.977	−	280.977i	−0.378165	−	0.378165i	−0.870440	+	0.492275i	$0.836166\pi$
$744$	213.661	+	155.234i	0.287179	+	0.208648i
$745$	−486.181			−0.652591
$746$		−	528.346i		−	0.708239i
$747$	−27.7785	−	20.1822i	−0.0371867	−	0.0270177i
$748$	71.0992	−	218.821i	0.0950525	−	0.292541i
$749$	−696.292	−	110.282i	−0.929628	−	0.147239i
$750$	328.347	−	52.0051i	0.437796	−	0.0693401i
$751$	−147.497	+	47.9248i	−0.196401	+	0.0638146i	−0.405566	−	0.914066i	$-0.632926\pi$
$751$	−147.497	+	47.9248i	−0.196401	+	0.0638146i	0.209165	+	0.977880i	$0.432926\pi$
$752$	−19.3559	+	59.5713i	−0.0257392	+	0.0792172i
$753$	304.083	+	304.083i	0.403829	+	0.403829i
$754$	−191.117	−	588.198i	−0.253471	−	0.780104i
$755$	182.607	−	1152.93i	0.241863	−	1.52706i
$756$	19.9559	+	39.1658i	0.0263968	+	0.0518066i
$757$	204.821	−	630.373i	0.270569	−	0.832726i	−0.719789	−	0.694193i	$-0.755761\pi$
$757$	204.821	−	630.373i	0.270569	−	0.832726i	0.990358	−	0.138533i	$-0.0442386\pi$
$758$	−104.793	−	53.3948i	−0.138249	−	0.0704416i
$759$	178.999	−	246.371i	0.235835	−	0.324599i
$760$	196.481	−	385.616i	0.258528	−	0.507390i
$761$	−688.655	−	688.655i	−0.904934	−	0.904934i	0.0909241	−	0.995858i	$-0.471018\pi$
$761$	−688.655	−	688.655i	−0.904934	−	0.904934i	−0.995858	+	0.0909241i	$0.971018\pi$
$762$	20.9130	+	41.0441i	0.0274449	+	0.0538636i
$763$	644.574	−	328.427i	0.844789	−	0.430442i
$764$	134.628	−	134.628i	0.176215	−	0.176215i
$765$	224.614	+	114.446i	0.293612	+	0.149603i
$766$	−352.879	−	256.382i	−0.460678	−	0.334702i
$767$	185.109	−	363.297i	0.241342	−	0.473659i
$768$	−26.3565	−	8.56373i	−0.0343183	−	0.0111507i
$769$	−738.501	+	376.285i	−0.960340	+	0.489318i	−0.862596	−	0.505894i	$-0.831163\pi$
$769$	−738.501	+	376.285i	−0.960340	+	0.489318i	−0.0977443	+	0.995212i	$0.531163\pi$
$770$	146.364	+	23.1817i	0.190083	+	0.0301061i
$771$	431.789	−	140.297i	0.560037	−	0.181967i
$772$	−177.193	+	177.193i	−0.229525	+	0.229525i
$773$	−949.921	−	308.648i	−1.22888	−	0.399286i	−0.378569	−	0.925573i	$-0.623584\pi$
$773$	−949.921	−	308.648i	−1.22888	−	0.399286i	−0.850307	+	0.526287i	$0.823584\pi$
$774$	32.3820	+	99.6615i	0.0418372	+	0.128762i
$775$	−58.2292	−	367.645i	−0.0751345	−	0.474381i
$776$	57.7509	−	364.625i	0.0744213	−	0.469878i
$777$	27.8339	+	9.04377i	0.0358222	+	0.0116393i
$778$	−308.577	+	424.720i	−0.396629	+	0.545913i
$779$	−1985.10			−2.54827
$780$			141.353i			0.181221i
$781$	42.0476	−	57.8736i	0.0538382	−	0.0741019i
$782$	−596.377	+	596.377i	−0.762630	+	0.762630i
$783$	−233.977	+	37.0584i	−0.298822	+	0.0473287i
$784$	73.1423	+	100.672i	0.0932938	+	0.128408i
$785$	666.947	−	105.634i	0.849614	−	0.134566i
$786$	3.86258	−	1.96808i	0.00491422	−	0.00250392i
$787$	197.455	−	1246.68i	0.250896	−	1.58409i	−0.464630	−	0.885505i	$-0.653812\pi$
$787$	197.455	−	1246.68i	0.250896	−	1.58409i	0.715525	−	0.698587i	$-0.246188\pi$
$788$	11.3849	−	8.27163i	0.0144479	−	0.0104970i
$789$	−497.355	+	361.350i	−0.630362	+	0.457985i
$790$	226.391	+	696.760i	0.286571	+	0.881975i
$791$	−103.716	+	203.553i	−0.131119	+	0.257336i
$792$		−	49.4160i		−	0.0623940i
$793$	−296.140	−	504.669i	−0.373442	−	0.636405i
$794$	−8.88345			−0.0111882
$795$	−367.423	−	187.211i	−0.462167	−	0.235486i
$796$	−410.983	+	133.536i	−0.516310	+	0.167759i
$797$	−220.815	−	303.926i	−0.277058	−	0.381337i	0.647699	−	0.761896i	$-0.275731\pi$
$797$	−220.815	−	303.926i	−0.277058	−	0.381337i	−0.924757	+	0.380559i	$0.875731\pi$
$798$	−219.056	−	301.504i	−0.274506	−	0.377825i
$799$	305.522	+	48.3899i	0.382380	+	0.0605631i
$800$	17.7324	+	34.8018i	0.0221655	+	0.0435022i
$801$	−2.47289	−	15.6132i	−0.00308725	−	0.0194921i
$802$	−84.8578	+	61.6528i	−0.105808	+	0.0768738i
$803$	123.350	+	778.803i	0.153612	+	0.969867i
$804$	−281.541	−	281.541i	−0.350175	−	0.350175i
$805$	−439.465	−	319.290i	−0.545919	−	0.396633i
$806$	731.321			0.907347
$807$		−	325.263i		−	0.403052i
$808$	221.216	+	160.723i	0.273782	+	0.198914i
$809$	−150.405	+	462.899i	−0.185915	+	0.572186i	−0.999963	−	0.00861094i	$-0.997259\pi$
$809$	−150.405	+	462.899i	−0.185915	+	0.572186i	0.814048	+	0.580797i	$0.197259\pi$
$810$	53.4762	+	8.46979i	0.0660199	+	0.0104565i
$811$	−439.996	+	69.6885i	−0.542535	+	0.0859290i	−0.421686	−	0.906742i	$-0.638562\pi$
$811$	−439.996	+	69.6885i	−0.542535	+	0.0859290i	−0.120849	+	0.992671i	$0.538562\pi$
$812$	366.794	−	119.179i	0.451717	−	0.146772i
$813$	165.013	−	507.857i	0.202968	−	0.624670i
$814$	−23.2645	−	23.2645i	−0.0285805	−	0.0285805i
$815$	139.969	+	430.782i	0.171742	+	0.528567i
$816$	−21.4094	+	135.174i	−0.0262370	+	0.165654i
$817$	−403.346	−	791.612i	−0.493692	−	0.968925i
$818$	14.8255	−	45.6281i	0.0181240	−	0.0557800i
$819$	108.454	+	55.2602i	0.132423	+	0.0674727i
$820$	−275.974	+	379.845i	−0.336553	+	0.463226i
$821$	489.367	−	960.436i	0.596062	−	1.16984i	−0.374102	−	0.927387i	$-0.622049\pi$
$821$	489.367	−	960.436i	0.596062	−	1.16984i	0.970164	−	0.242449i	$-0.0779509\pi$
$822$	410.089	+	410.089i	0.498892	+	0.498892i
$823$	−526.600	−	1033.51i	−0.639854	−	1.25578i	−0.952101	−	0.305783i	$-0.901082\pi$
$823$	−526.600	−	1033.51i	−0.639854	−	1.25578i	0.312247	−	0.950001i	$-0.398918\pi$
$824$	78.7528	−	40.1265i	0.0955737	−	0.0486972i
$825$	−49.2485	+	49.2485i	−0.0596951	+	0.0596951i
$826$	226.548	+	115.432i	0.274271	+	0.139748i
$827$	398.780	+	289.731i	0.482201	+	0.350339i	0.802177	−	0.597086i	$-0.203675\pi$
$827$	398.780	+	289.731i	0.482201	+	0.350339i	−0.319976	+	0.947426i	$0.603675\pi$
$828$	−82.2371	+	161.399i	−0.0993202	+	0.194927i
$829$	−217.805	−	70.7692i	−0.262732	−	0.0853669i	0.174689	−	0.984624i	$-0.444108\pi$
$829$	−217.805	−	70.7692i	−0.262732	−	0.0853669i	−0.437421	+	0.899257i	$0.644108\pi$
$830$	61.3490	−	31.2589i	0.0739145	−	0.0376613i
$831$	631.034	+	99.9460i	0.759367	+	0.120272i
$832$	−72.9838	+	23.7139i	−0.0877210	+	0.0285023i
$833$	434.536	−	434.536i	0.521652	−	0.521652i
$834$	−95.5156	−	31.0349i	−0.114527	−	0.0372121i
$835$	237.679	+	731.501i	0.284646	+	0.876049i
$836$	65.5406	+	413.807i	0.0783979	+	0.494985i
$837$	43.8205	−	276.672i	0.0523542	−	0.330552i
$838$	−318.536	−	103.498i	−0.380114	−	0.123507i
$839$	314.243	−	432.519i	0.374545	−	0.515517i	−0.579584	−	0.814912i	$-0.696785\pi$
$839$	314.243	−	432.519i	0.374545	−	0.515517i	0.954129	+	0.299395i	$0.0967850\pi$
$840$	−88.1459			−0.104936
$841$			1237.47i			1.47143i
$842$	−165.387	+	227.635i	−0.196421	+	0.270351i
$843$	376.729	−	376.729i	0.446891	−	0.446891i
$844$	−57.1072	+	9.04489i	−0.0676626	+	0.0107167i
$845$	−192.489	−	264.938i	−0.227797	−	0.313536i
$846$	65.6186	−	10.3930i	0.0775634	−	0.0122848i
$847$	328.196	−	167.224i	0.387481	−	0.197431i
$848$	35.0215	−	221.117i	0.0412989	−	0.260751i
$849$	72.1754	−	52.4385i	0.0850122	−	0.0617650i
$850$	156.052	−	113.378i	0.183591	−	0.133386i
$851$	37.2687	+	114.701i	0.0437941	+	0.134784i
$852$	−19.3178	+	37.9134i	−0.0226735	+	0.0444993i
$853$		−	685.217i		−	0.803302i	−0.915793	−	0.401651i	$-0.868436\pi$
$853$		−	685.217i		−	0.803302i	0.915793	−	0.401651i	$-0.131564\pi$
$854$	314.706	−	184.669i	0.368508	−	0.216240i
$855$	−459.040			−0.536889
$856$	−420.033	−	214.018i	−0.490693	−	0.250020i
$857$	986.510	−	320.537i	1.15112	−	0.374022i	0.329555	−	0.944136i	$-0.393101\pi$
$857$	986.510	−	320.537i	1.15112	−	0.374022i	0.821565	+	0.570115i	$0.193101\pi$
$858$	−80.4315	−	110.704i	−0.0937430	−	0.129026i
$859$	235.098	+	323.585i	0.273689	+	0.376700i	0.923631	−	0.383284i	$-0.125207\pi$
$859$	235.098	+	323.585i	0.273689	+	0.376700i	−0.649942	+	0.759984i	$0.725207\pi$
$860$	−207.548	−	32.8723i	−0.241334	−	0.0382236i
$861$	183.551	+	360.240i	0.213184	+	0.418397i
$862$	−98.2236	−	620.159i	−0.113948	−	0.719442i
$863$	−319.932	+	232.444i	−0.370721	+	0.269344i	−0.757510	−	0.652824i	$-0.773584\pi$
$863$	−319.932	+	232.444i	−0.370721	+	0.269344i	0.386789	+	0.922168i	$0.373584\pi$
$864$	4.59822	+	29.0320i	0.00532201	+	0.0336018i
$865$	−431.400	−	431.400i	−0.498728	−	0.498728i
$866$	−150.579	−	109.402i	−0.173879	−	0.126331i
$867$	175.307			0.202199
$868$			456.044i			0.525396i
$869$	−573.771	−	416.869i	−0.660266	−	0.479711i
$870$	146.796	−	451.790i	0.168730	−	0.519299i
$871$	−1088.97	−	172.476i	−1.25025	−	0.198021i
$872$	477.797	−	75.6756i	0.547932	−	0.0867839i
$873$	−372.400	+	121.000i	−0.426574	+	0.138602i
$874$	474.585	−	1460.62i	0.543003	−	1.67119i
$875$	405.916	+	405.916i	0.463904	+	0.463904i
$876$	−144.937	−	446.070i	−0.165453	−	0.509212i
$877$	−201.587	+	1272.77i	−0.229860	+	1.45128i	0.555127	+	0.831765i	$0.312669\pi$
$877$	−201.587	+	1272.77i	−0.229860	+	1.45128i	−0.784987	+	0.619512i	$0.787331\pi$
$878$	−213.848	−	419.700i	−0.243562	−	0.478018i
$879$	−131.191	+	403.763i	−0.149250	+	0.459344i
$880$	88.2928	+	44.9874i	0.100333	+	0.0511221i
$881$	658.753	−	906.695i	0.747733	−	1.02917i	−0.250403	−	0.968142i	$-0.580563\pi$
$881$	658.753	−	906.695i	0.747733	−	1.02917i	0.998136	−	0.0610245i	$-0.0194368\pi$
$882$	59.9202	−	117.600i	0.0679367	−	0.133333i
$883$	−608.801	−	608.801i	−0.689469	−	0.689469i	0.272645	−	0.962115i	$-0.412101\pi$
$883$	−608.801	−	608.801i	−0.689469	−	0.689469i	−0.962115	+	0.272645i	$0.912101\pi$
$884$	172.051	+	337.670i	0.194628	+	0.381980i
$885$	279.045	−	142.181i	0.315305	−	0.160656i
$886$	322.007	−	322.007i	0.363439	−	0.363439i
$887$	−71.3897	−	36.3749i	−0.0804845	−	0.0410089i	0.413285	−	0.910602i	$-0.364381\pi$
$887$	−71.3897	−	36.3749i	−0.0804845	−	0.0410089i	−0.493769	+	0.869593i	$0.664381\pi$
$888$	15.8327	+	11.5032i	0.0178297	+	0.0129540i
$889$	−36.1123	+	70.8743i	−0.0406212	+	0.0797236i
$890$	30.1478	+	9.79560i	0.0338739	+	0.0110063i
$891$	−46.7009	+	23.7953i	−0.0524140	+	0.0267063i
$892$	−488.846	−	77.4255i	−0.548033	−	0.0867999i
$893$	−535.703	+	174.060i	−0.599891	+	0.194916i
$894$	−197.959	+	197.959i	−0.221431	+	0.221431i
$895$	499.926	+	162.436i	0.558576	+	0.181492i
$896$	−14.7877	−	45.5119i	−0.0165041	−	0.0507945i
$897$	78.4681	+	495.428i	0.0874784	+	0.552317i
$898$	101.643	−	641.747i	0.113188	−	0.714640i
$899$	−2337.44	−	759.482i	−2.60005	−	0.844807i
$900$	24.3509	−	33.5162i	0.0270566	−	0.0372402i
$901$	−1105.59			−1.22707
$902$		−	454.520i		−	0.503902i
$903$	−106.360	+	146.392i	−0.117785	+	0.162117i
$904$	−108.022	+	108.022i	−0.119494	+	0.119494i
$905$	−1086.14	+	172.028i	−1.20016	+	0.190086i
$906$	−395.090	−	543.795i	−0.436082	−	0.600215i
$907$	−54.4694	+	8.62711i	−0.0600545	+	0.00951170i	−0.186389	−	0.982476i	$-0.559679\pi$
$907$	−54.4694	+	8.62711i	−0.0600545	+	0.00951170i	0.126335	+	0.991988i	$0.459679\pi$
$908$	−687.600	+	350.350i	−0.757269	+	0.385848i
$909$	45.3698	−	286.454i	0.0499118	−	0.315131i
$910$	−197.469	+	143.470i	−0.216999	+	0.157659i
$911$	1354.32	−	983.968i	1.48663	−	1.08010i	0.511280	−	0.859414i	$-0.329171\pi$
$911$	1354.32	−	983.968i	1.48663	−	1.08010i	0.975346	−	0.220683i	$-0.0708286\pi$
$912$	−77.0104	−	237.014i	−0.0844413	−	0.259883i
$913$	−30.2606	+	59.3898i	−0.0331441	+	0.0650490i
$914$			536.540i			0.587024i
$915$	43.8235	−	447.300i	0.0478945	−	0.488852i
$916$	423.552			0.462393
$917$	6.66984	+	3.39845i	0.00727354	+	0.00370605i
$918$	138.056	−	44.8570i	0.150387	−	0.0488638i
$919$	−545.308	−	750.552i	−0.593371	−	0.816705i	0.401710	−	0.915767i	$-0.368416\pi$
$919$	−545.308	−	750.552i	−0.593371	−	0.816705i	−0.995081	+	0.0990615i	$0.968416\pi$
$920$	−213.509	−	293.870i	−0.232075	−	0.319424i
$921$	286.857	+	45.4337i	0.311463	+	0.0493308i
$922$	−118.089	−	231.763i	−0.128079	−	0.251370i
$923$	18.4325	+	116.378i	0.0199702	+	0.126087i
$924$	69.0341	−	50.1562i	0.0747122	−	0.0542816i
$925$	−4.31490	−	27.2432i	−0.00466476	−	0.0294521i
$926$	−231.914	−	231.914i	−0.250447	−	0.250447i
$927$	−75.8436	−	55.1036i	−0.0818162	−	0.0594429i
$928$	257.897			0.277907
$929$			672.255i			0.723633i	0.932249	+	0.361817i	$0.117843\pi$
$929$			672.255i			0.723633i	−0.932249	+	0.361817i	$0.882157\pi$
$930$	454.442	+	330.172i	0.488648	+	0.355023i
$931$	−345.795	+	1064.25i	−0.371423	+	1.14312i
$932$	−77.6594	−	12.3000i	−0.0833256	−	0.0131975i
$933$	776.525	−	122.989i	0.832288	−	0.131822i
$934$	−635.895	+	206.615i	−0.680829	+	0.221215i
$935$	151.223	−	465.416i	0.161736	−	0.497772i
$936$	57.5548	+	57.5548i	0.0614902	+	0.0614902i
$937$	471.380	+	1450.76i	0.503073	+	1.54830i	0.803986	+	0.594649i	$0.202709\pi$
$937$	471.380	+	1450.76i	0.503073	+	1.54830i	−0.300912	+	0.953652i	$0.597291\pi$
$938$	107.554	−	679.070i	0.114663	−	0.723956i
$939$	418.713	+	821.771i	0.445914	+	0.875155i
$940$	−41.1686	+	126.704i	−0.0437964	+	0.134791i
$941$	−525.308	−	267.658i	−0.558244	−	0.284440i	0.152017	−	0.988378i	$-0.451423\pi$
$941$	−525.308	−	267.658i	−0.558244	−	0.284440i	−0.710261	+	0.703938i	$0.751423\pi$
$942$	228.551	−	314.573i	0.242623	−	0.333942i
$943$	−756.402	+	1484.52i	−0.802123	+	1.57426i
$944$	120.225	+	120.225i	0.127357	+	0.127357i
$945$	42.4449	+	83.3027i	0.0449152	+	0.0881510i
$946$	181.252	−	92.3524i	0.191598	−	0.0976241i
$947$	−95.7504	+	95.7504i	−0.101109	+	0.101109i	−0.755852	−	0.654743i	$-0.772777\pi$
$947$	−95.7504	+	95.7504i	−0.101109	+	0.101109i	0.654743	+	0.755852i	$0.272777\pi$
$948$	375.881	+	191.521i	0.396499	+	0.202027i
$949$	−1050.74	−	763.405i	−1.10720	−	0.804431i
$950$	−159.461	+	312.960i	−0.167854	+	0.329431i
$951$	339.858	+	110.426i	0.357369	+	0.116116i
$952$	−210.567	+	107.289i	−0.221184	+	0.112699i
$953$	736.573	+	116.662i	0.772899	+	0.122415i	0.530413	−	0.847740i	$-0.322037\pi$
$953$	736.573	+	116.662i	0.772899	+	0.122415i	0.242487	+	0.970155i	$0.422037\pi$
$954$	−225.831	+	73.3771i	−0.236721	+	0.0769152i
$955$	286.344	−	286.344i	0.299837	−	0.299837i
$956$	−751.055	−	244.033i	−0.785623	−	0.255264i
$957$	142.107	+	437.361i	0.148493	+	0.457013i
$958$	1.91464	+	12.0885i	0.00199858	+	0.0126185i
$959$	−156.662	+	989.125i	−0.163360	+	1.03141i
$960$	−56.0583	−	18.2144i	−0.0583940	−	0.0189734i
$961$	1143.36	−	1573.70i	1.18976	−	1.63757i
$962$	54.1923			0.0563330
$963$			500.010i			0.519221i
$964$	−338.594	+	466.035i	−0.351238	+	0.483438i
$965$	−376.877	+	376.877i	−0.390546	+	0.390546i
$966$	−308.944	+	48.9318i	−0.319817	+	0.0506541i
$967$	−266.918	−	367.382i	−0.276027	−	0.379919i	0.648386	−	0.761312i	$-0.275444\pi$
$967$	−266.918	−	367.382i	−0.276027	−	0.379919i	−0.924413	+	0.381393i	$0.875444\pi$
$968$	243.279	−	38.5315i	0.251321	−	0.0398053i
$969$	−1096.58	+	558.734i	−1.13166	+	0.576609i
$970$	122.832	−	775.531i	0.126631	−	0.799517i
$971$	859.314	−	624.328i	0.884978	−	0.642974i	−0.0495857	−	0.998770i	$-0.515790\pi$
$971$	859.314	−	624.328i	0.884978	−	0.642974i	0.934564	+	0.355796i	$0.115790\pi$
$972$	25.2227	−	18.3253i	0.0259492	−	0.0188532i
$973$	−53.5906	−	164.935i	−0.0550777	−	0.169512i
$974$	−353.442	+	693.670i	−0.362877	+	0.712186i
$975$		−	114.719i		−	0.117661i
$976$	238.304	−	52.4137i	0.244164	−	0.0537026i
$977$	999.258			1.02278			0.511391	−	0.859348i	$-0.329130\pi$
$977$	999.258			1.02278			0.511391	+	0.859348i	$0.329130\pi$
$978$	232.394	+	118.411i	0.237622	+	0.121074i
$979$	−29.1849	+	9.48276i	−0.0298110	+	0.00968617i
$980$	155.568	+	214.122i	0.158743	+	0.218491i
$981$	−301.591	−	415.104i	−0.307432	−	0.423144i
$982$	−670.880	−	106.257i	−0.683177	−	0.108205i
$983$	274.892	+	539.506i	0.279646	+	0.548836i	0.987518	−	0.157504i	$-0.0503448\pi$
$983$	274.892	+	539.506i	0.279646	+	0.548836i	−0.707872	+	0.706340i	$0.750345\pi$
$984$	42.2936	+	267.031i	0.0429813	+	0.271373i
$985$	24.2149	−	17.5932i	0.0245837	−	0.0178611i
$986$	−199.237	−	1257.93i	−0.202066	−	1.27580i
$987$	81.1205	+	81.1205i	0.0821889	+	0.0821889i
$988$	−558.296	−	405.626i	−0.565077	−	0.410552i
$989$	−745.684			−0.753978
$990$		−	105.104i		−	0.106166i
$991$	1415.84	+	1028.67i	1.42870	+	1.03801i	0.990257	+	0.139249i	$0.0444690\pi$
$991$	1415.84	+	1028.67i	1.42870	+	1.03801i	0.438440	+	0.898760i	$0.355531\pi$
$992$	−94.2368	+	290.031i	−0.0949967	+	0.292370i
$993$	612.059	+	96.9405i	0.616373	+	0.0976239i
$994$	−72.5722	+	11.4943i	−0.0730102	+	0.0115637i
$995$	−874.131	+	284.022i	−0.878523	+	0.285450i
$996$	12.2519	−	37.7074i	0.0123011	−	0.0378588i
$997$	1264.72	+	1264.72i	1.26853	+	1.26853i	0.946849	+	0.321680i	$0.104247\pi$
$997$	1264.72	+	1264.72i	1.26853	+	1.26853i	0.321680	+	0.946849i	$0.395753\pi$
$998$	−89.8541	−	276.543i	−0.0900342	−	0.277097i
$999$	3.24718	−	20.5019i	0.00325043	−	0.0205224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	366.3.s.a.85.9	✓	80
61.28	odd	20	inner	366.3.s.a.211.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.3.s.a.85.9	✓	80	1.1	even	1	trivial
366.3.s.a.211.9	yes	80	61.28	odd	20	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:	\( N \)	\(=\)	\( 366 = 2 \cdot 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	366.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26007 + 0.642040i) q^{2} +(1.64728 - 0.535233i) q^{3} +(1.17557 + 1.61803i) q^{4} +(2.50035 + 3.44144i) q^{5} +(2.41933 + 0.383185i) q^{6} +(1.92026 + 3.76873i) q^{7} +(0.442463 + 2.79360i) q^{8} +(2.42705 - 1.76336i) q^{9} +(0.941088 + 5.94179i) q^{10} +(-4.11800 - 4.11800i) q^{11} +(2.80252 + 2.03615i) q^{12} +9.59247 q^{13} +5.98176i q^{14} +(5.96075 + 4.33074i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(19.5106 + 3.09018i) q^{17} +(4.19041 - 0.663695i) q^{18} +(-34.2100 + 11.1155i) q^{19} +(-2.62903 + 8.09131i) q^{20} +(5.18035 + 5.18035i) q^{21} +(-2.54507 - 7.83291i) q^{22} +(-4.72283 + 29.8188i) q^{23} +(2.22409 + 4.36502i) q^{24} +(2.13367 - 6.56677i) q^{25} +(12.0872 + 6.15874i) q^{26} +(3.05422 - 4.20378i) q^{27} +(-3.84052 + 7.53745i) q^{28} +(-32.2372 - 32.2372i) q^{29} +(4.73048 + 9.28409i) q^{30} +(48.0335 - 24.4743i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-8.98759 - 4.57940i) q^{33} +(22.6008 + 16.4204i) q^{34} +(-8.16852 + 16.0316i) q^{35} +(5.70634 + 1.85410i) q^{36} +(3.55937 - 1.81359i) q^{37} +(-50.2437 - 7.95782i) q^{38} +(15.8015 - 5.13421i) q^{39} +(-8.50771 + 8.50771i) q^{40} +(52.4859 + 17.0537i) q^{41} +(3.20163 + 9.85362i) q^{42} +(3.86382 + 24.3952i) q^{43} +(1.82207 - 11.5041i) q^{44} +(12.1370 + 3.94354i) q^{45} +(-25.0959 + 34.5416i) q^{46} +15.6593 q^{47} +6.92820i q^{48} +(18.2856 - 25.1679i) q^{49} +(6.90471 - 6.90471i) q^{50} +(33.7934 - 5.35235i) q^{51} +(11.2766 + 15.5209i) q^{52} +(-55.2792 + 8.75537i) q^{53} +(6.54753 - 3.33614i) q^{54} +(3.87540 - 24.4683i) q^{55} +(-9.67869 + 7.03198i) q^{56} +(-50.4040 + 36.6206i) q^{57} +(-19.9237 - 61.3188i) q^{58} +(19.2973 - 37.8731i) q^{59} +14.7358i q^{60} +(-30.8721 - 52.6110i) q^{61} +76.2391 q^{62} +(11.3062 + 5.76079i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(23.9846 + 33.0119i) q^{65} +(-8.38486 - 11.5408i) q^{66} +(-113.524 - 17.9804i) q^{67} +(17.9361 + 35.2016i) q^{68} +(8.18018 + 51.6476i) q^{69} +(-20.5859 + 14.9565i) q^{70} +(1.92156 + 12.1322i) q^{71} +(6.00000 + 6.00000i) q^{72} +(-109.538 - 79.5838i) q^{73} +5.64947 q^{74} -11.9593i q^{75} +(-58.2015 - 42.2859i) q^{76} +(7.61198 - 23.4273i) q^{77} +(23.2074 + 3.67569i) q^{78} +(120.282 - 19.0507i) q^{79} +(-16.1826 + 5.25805i) q^{80} +(2.78115 - 8.55951i) q^{81} +(55.1869 + 55.1869i) q^{82} +(-3.53681 - 10.8852i) q^{83} +(-2.29212 + 14.4719i) q^{84} +(38.1488 + 74.8712i) q^{85} +(-10.7940 + 33.2205i) q^{86} +(-70.3580 - 35.8492i) q^{87} +(9.68200 - 13.3261i) q^{88} +(2.39220 - 4.69496i) q^{89} +(12.7616 + 12.7616i) q^{90} +(18.4201 + 36.1514i) q^{91} +(-53.7998 + 27.4124i) q^{92} +(66.0250 - 66.0250i) q^{93} +(19.7318 + 10.0539i) q^{94} +(-123.790 - 89.9390i) q^{95} +(-4.44818 + 8.73005i) q^{96} +(-124.133 - 40.3333i) q^{97} +(39.2000 - 19.9734i) q^{98} +(-17.2561 - 2.73310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 20 q^{2} - 40 q^{5} + 20 q^{7} + 40 q^{8} + 60 q^{9} + 60 q^{10} + 20 q^{11} - 32 q^{13} + 80 q^{16} + 80 q^{17} + 60 q^{18} - 100 q^{19} - 40 q^{20} + 12 q^{21} - 60 q^{22} + 56 q^{23} + 144 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 80 * q - 20 * q^2 - 40 * q^5 + 20 * q^7 + 40 * q^8 + 60 * q^9 + 60 * q^10 + 20 * q^11 - 32 * q^13 + 80 * q^16 + 80 * q^17 + 60 * q^18 - 100 * q^19 - 40 * q^20 + 12 * q^21 - 60 * q^22 + 56 * q^23 + 144 * q^25 + 48 * q^26 - 40 * q^28 - 4 * q^29 - 68 * q^31 - 320 * q^32 + 12 * q^33 + 20 * q^34 + 12 * q^35 + 100 * q^37 + 148 * q^38 + 120 * q^39 + 280 * q^41 - 36 * q^42 - 260 * q^43 + 40 * q^44 - 40 * q^46 + 392 * q^47 + 20 * q^49 - 416 * q^50 + 96 * q^51 + 40 * q^52 - 504 * q^53 + 188 * q^55 + 72 * q^57 + 92 * q^58 + 108 * q^59 + 236 * q^61 - 136 * q^62 - 60 * q^63 + 120 * q^65 - 180 * q^66 - 600 * q^67 - 280 * q^68 - 360 * q^69 - 96 * q^70 + 424 * q^71 + 480 * q^72 - 324 * q^73 - 560 * q^74 + 136 * q^76 - 548 * q^77 + 48 * q^78 - 252 * q^79 - 180 * q^81 + 136 * q^82 - 312 * q^83 + 24 * q^84 + 992 * q^85 - 340 * q^86 - 108 * q^87 + 1128 * q^89 - 416 * q^91 + 48 * q^92 + 36 * q^93 - 88 * q^94 - 132 * q^95 - 260 * q^97 - 4 * q^98 - 60 * q^99

Introduction

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