LMFDB - Embedded newform 220.3.c.a.111.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(111,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.111"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			111.11
Character	$\chi$	$=$	220.111
Dual form			220.3.c.a.111.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12341 - 1.65468i) q^{2} -0.776243i q^{3} +(-1.47591 + 3.71775i) q^{4} -2.23607 q^{5} +(-1.28443 + 0.872037i) q^{6} -8.96218i q^{7} +(7.80973 - 1.73439i) q^{8} +8.39745 q^{9} +(2.51201 + 3.69997i) q^{10} -3.31662i q^{11} +(2.88588 + 1.14567i) q^{12} -19.7795 q^{13} +(-14.8295 + 10.0682i) q^{14} +1.73573i q^{15} +(-11.6434 - 10.9742i) q^{16} -29.4276 q^{17} +(-9.43375 - 13.8951i) q^{18} +25.2569i q^{19} +(3.30024 - 8.31315i) q^{20} -6.95683 q^{21} +(-5.48794 + 3.72592i) q^{22} -18.0350i q^{23} +(-1.34631 - 6.06225i) q^{24} +5.00000 q^{25} +(22.2205 + 32.7287i) q^{26} -13.5046i q^{27} +(33.3192 + 13.2274i) q^{28} -24.0636 q^{29} +(2.87208 - 1.94993i) q^{30} -17.2747i q^{31} +(-5.07844 + 31.5945i) q^{32} -2.57451 q^{33} +(33.0592 + 48.6932i) q^{34} +20.0401i q^{35} +(-12.3939 + 31.2196i) q^{36} -34.7399 q^{37} +(41.7921 - 28.3738i) q^{38} +15.3537i q^{39} +(-17.4631 + 3.87822i) q^{40} -17.3790 q^{41} +(7.81536 + 11.5113i) q^{42} +13.3441i q^{43} +(12.3304 + 4.89505i) q^{44} -18.7773 q^{45} +(-29.8421 + 20.2606i) q^{46} -50.2496i q^{47} +(-8.51861 + 9.03808i) q^{48} -31.3207 q^{49} +(-5.61704 - 8.27339i) q^{50} +22.8430i q^{51} +(29.1929 - 73.5354i) q^{52} +102.407 q^{53} +(-22.3458 + 15.1712i) q^{54} +7.41620i q^{55} +(-15.5439 - 69.9922i) q^{56} +19.6055 q^{57} +(27.0332 + 39.8175i) q^{58} -101.330i q^{59} +(-6.45302 - 2.56179i) q^{60} -35.9361 q^{61} +(-28.5841 + 19.4066i) q^{62} -75.2595i q^{63} +(57.9838 - 27.0903i) q^{64} +44.2284 q^{65} +(2.89222 + 4.25998i) q^{66} +110.089i q^{67} +(43.4326 - 109.405i) q^{68} -13.9995 q^{69} +(33.1598 - 22.5131i) q^{70} -42.1766i q^{71} +(65.5818 - 14.5645i) q^{72} +6.36787 q^{73} +(39.0271 + 57.4834i) q^{74} -3.88122i q^{75} +(-93.8990 - 37.2770i) q^{76} -29.7242 q^{77} +(25.4055 - 17.2485i) q^{78} +5.11241i q^{79} +(26.0354 + 24.5390i) q^{80} +65.0941 q^{81} +(19.5237 + 28.7566i) q^{82} -69.3381i q^{83} +(10.2677 - 25.8638i) q^{84} +65.8021 q^{85} +(22.0801 - 14.9908i) q^{86} +18.6792i q^{87} +(-5.75233 - 25.9019i) q^{88} -80.3175 q^{89} +(21.0945 + 31.0703i) q^{90} +177.268i q^{91} +(67.0496 + 26.6181i) q^{92} -13.4094 q^{93} +(-83.1469 + 56.4508i) q^{94} -56.4762i q^{95} +(24.5250 + 3.94210i) q^{96} -0.308392 q^{97} +(35.1859 + 51.8257i) q^{98} -27.8512i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} + 36 q^{8} - 120 q^{9} + 20 q^{10} - 80 q^{12} + 32 q^{13} - 56 q^{14} + 40 q^{16} + 16 q^{18} - 20 q^{20} - 80 q^{21} + 104 q^{24} + 200 q^{25} + 100 q^{26} + 60 q^{28} - 48 q^{29} - 280 q^{32}+ \cdots + 680 q^{98}+O(q^{100}) $ 40 * q - 4 * q^4 + 36 * q^8 - 120 * q^9 + 20 * q^10 - 80 * q^12 + 32 * q^13 - 56 * q^14 + 40 * q^16 + 16 * q^18 - 20 * q^20 - 80 * q^21 + 104 * q^24 + 200 * q^25 + 100 * q^26 + 60 * q^28 - 48 * q^29 - 280 * q^32 + 8 * q^34 + 160 * q^36 + 160 * q^37 - 200 * q^38 - 80 * q^40 - 120 * q^42 + 44 * q^44 + 80 * q^45 + 120 * q^46 - 16 * q^48 - 376 * q^49 - 36 * q^52 + 296 * q^54 - 40 * q^56 + 288 * q^57 + 96 * q^58 + 60 * q^60 - 160 * q^61 - 16 * q^62 + 500 * q^64 - 220 * q^66 + 116 * q^68 - 304 * q^69 - 60 * q^70 - 380 * q^72 - 480 * q^73 - 320 * q^74 - 480 * q^76 + 744 * q^78 - 80 * q^80 + 280 * q^81 - 480 * q^82 + 16 * q^84 + 320 * q^85 - 460 * q^86 + 224 * q^89 - 60 * q^90 + 24 * q^92 + 480 * q^93 + 432 * q^94 + 424 * q^96 + 720 * q^97 + 680 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.12341	−	1.65468i	−0.561704	−	0.827339i
$2$	−1.12341	−	1.65468i	−0.561704	−	0.827339i
$3$		−	0.776243i		−	0.258748i	−0.991596	−	0.129374i	$-0.958703\pi$
$3$		−	0.776243i		−	0.258748i	0.991596	−	0.129374i	$-0.0412967\pi$
$4$	−1.47591	+	3.71775i	−0.368978	+	0.929438i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	−1.28443	+	0.872037i	−0.214072	+	0.145340i
$7$		−	8.96218i		−	1.28031i	−0.768245	−	0.640156i	$-0.778870\pi$
$7$		−	8.96218i		−	1.28031i	0.768245	−	0.640156i	$-0.221130\pi$
$8$	7.80973	−	1.73439i	0.976216	−	0.216799i
$9$	8.39745			0.933050
$10$	2.51201	+	3.69997i	0.251201	+	0.369997i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	2.88588	+	1.14567i	0.240490	+	0.0954722i
$13$	−19.7795			−1.52150			−0.760751	−	0.649044i	$-0.775169\pi$
$13$	−19.7795			−1.52150			−0.760751	+	0.649044i	$0.775169\pi$
$14$	−14.8295	+	10.0682i	−1.05925	+	0.719156i
$15$			1.73573i			0.115716i
$16$	−11.6434	−	10.9742i	−0.727710	−	0.685885i
$17$	−29.4276			−1.73104			−0.865518	−	0.500878i	$-0.833011\pi$
$17$	−29.4276			−1.73104			−0.865518	+	0.500878i	$0.833011\pi$
$18$	−9.43375	−	13.8951i	−0.524097	−	0.771948i
$19$			25.2569i			1.32931i	0.747150	+	0.664656i	$0.231422\pi$
$19$			25.2569i			1.32931i	−0.747150	+	0.664656i	$0.768578\pi$
$20$	3.30024	−	8.31315i	0.165012	−	0.415657i
$21$	−6.95683			−0.331278
$22$	−5.48794	+	3.72592i	−0.249452	+	0.169360i
$23$		−	18.0350i		−	0.784130i	−0.919937	−	0.392065i	$-0.871761\pi$
$23$		−	18.0350i		−	0.784130i	0.919937	−	0.392065i	$-0.128239\pi$
$24$	−1.34631	−	6.06225i	−0.0560962	−	0.252594i
$25$	5.00000			0.200000
$26$	22.2205	+	32.7287i	0.854633	+	1.25880i
$27$		−	13.5046i		−	0.500172i
$28$	33.3192	+	13.2274i	1.18997	+	0.472407i
$29$	−24.0636			−0.829779			−0.414889	−	0.909872i	$-0.636180\pi$
$29$	−24.0636			−0.829779			−0.414889	+	0.909872i	$0.636180\pi$
$30$	2.87208	−	1.94993i	0.0957359	−	0.0649978i
$31$		−	17.2747i		−	0.557250i	−0.960400	−	0.278625i	$-0.910121\pi$
$31$		−	17.2747i		−	0.557250i	0.960400	−	0.278625i	$-0.0898787\pi$
$32$	−5.07844	+	31.5945i	−0.158701	+	0.987327i
$33$	−2.57451			−0.0780154
$34$	33.0592	+	48.6932i	0.972329	+	1.43215i
$35$			20.0401i			0.572573i
$36$	−12.3939	+	31.2196i	−0.344275	+	0.867212i
$37$	−34.7399			−0.938917			−0.469459	−	0.882955i	$-0.655551\pi$
$37$	−34.7399			−0.938917			−0.469459	+	0.882955i	$0.655551\pi$
$38$	41.7921	−	28.3738i	1.09979	−	0.746679i
$39$			15.3537i			0.393685i
$40$	−17.4631	+	3.87822i	−0.436577	+	0.0969554i
$41$	−17.3790			−0.423878			−0.211939	−	0.977283i	$-0.567978\pi$
$41$	−17.3790			−0.423878			−0.211939	+	0.977283i	$0.567978\pi$
$42$	7.81536	+	11.5113i	0.186080	+	0.274079i
$43$			13.3441i			0.310328i	0.987889	+	0.155164i	$0.0495905\pi$
$43$			13.3441i			0.310328i	−0.987889	+	0.155164i	$0.950409\pi$
$44$	12.3304	+	4.89505i	0.280236	+	0.111251i
$45$	−18.7773			−0.417272
$46$	−29.8421	+	20.2606i	−0.648741	+	0.440449i
$47$		−	50.2496i		−	1.06914i	−0.845124	−	0.534571i	$-0.820473\pi$
$47$		−	50.2496i		−	1.06914i	0.845124	−	0.534571i	$-0.179527\pi$
$48$	−8.51861	+	9.03808i	−0.177471	+	0.188293i
$49$	−31.3207			−0.639198
$50$	−5.61704	−	8.27339i	−0.112341	−	0.165468i
$51$			22.8430i			0.447902i
$52$	29.1929	−	73.5354i	0.561401	−	1.41414i
$53$	102.407			1.93221			0.966107	−	0.258143i	$-0.0831105\pi$
$53$	102.407			1.93221			0.966107	+	0.258143i	$0.0831105\pi$
$54$	−22.3458	+	15.1712i	−0.413812	+	0.280949i
$55$			7.41620i			0.134840i
$56$	−15.5439	−	69.9922i	−0.277570	−	1.24986i
$57$	19.6055			0.343956
$58$	27.0332	+	39.8175i	0.466090	+	0.686508i
$59$		−	101.330i		−	1.71746i	−0.512424	−	0.858732i	$-0.671253\pi$
$59$		−	101.330i		−	1.71746i	0.512424	−	0.858732i	$-0.328747\pi$
$60$	−6.45302	−	2.56179i	−0.107550	−	0.0426965i
$61$	−35.9361			−0.589116			−0.294558	−	0.955634i	$-0.595172\pi$
$61$	−35.9361			−0.589116			−0.294558	+	0.955634i	$0.595172\pi$
$62$	−28.5841	+	19.4066i	−0.461034	+	0.313009i
$63$		−	75.2595i		−	1.19459i
$64$	57.9838	−	27.0903i	0.905996	−	0.423285i
$65$	44.2284			0.680436
$66$	2.89222	+	4.25998i	0.0438215	+	0.0645451i
$67$			110.089i			1.64311i	0.570127	+	0.821557i	$0.306894\pi$
$67$			110.089i			1.64311i	−0.570127	+	0.821557i	$0.693106\pi$
$68$	43.4326	−	109.405i	0.638714	−	1.60889i
$69$	−13.9995			−0.202892
$70$	33.1598	−	22.5131i	0.473712	−	0.321616i
$71$		−	42.1766i		−	0.594037i	−0.954872	−	0.297018i	$-0.904008\pi$
$71$		−	42.1766i		−	0.594037i	0.954872	−	0.297018i	$-0.0959923\pi$
$72$	65.5818	−	14.5645i	0.910858	−	0.202284i
$73$	6.36787			0.0872312			0.0436156	−	0.999048i	$-0.486112\pi$
$73$	6.36787			0.0872312			0.0436156	+	0.999048i	$0.486112\pi$
$74$	39.0271	+	57.4834i	0.527393	+	0.776802i
$75$		−	3.88122i		−	0.0517495i
$76$	−93.8990	−	37.2770i	−1.23551	−	0.490487i
$77$	−29.7242			−0.386029
$78$	25.4055	−	17.2485i	0.325711	−	0.221134i
$79$			5.11241i			0.0647140i	0.999476	+	0.0323570i	$0.0103014\pi$
$79$			5.11241i			0.0647140i	−0.999476	+	0.0323570i	$0.989699\pi$
$80$	26.0354	+	24.5390i	0.325442	+	0.306737i
$81$	65.0941			0.803631
$82$	19.5237	+	28.7566i	0.238094	+	0.350690i
$83$		−	69.3381i		−	0.835399i	−0.908585	−	0.417699i	$-0.862837\pi$
$83$		−	69.3381i		−	0.835399i	0.908585	−	0.417699i	$-0.137163\pi$
$84$	10.2677	−	25.8638i	0.122234	−	0.307902i
$85$	65.8021			0.774143
$86$	22.0801	−	14.9908i	0.256746	−	0.174312i
$87$			18.6792i			0.214703i
$88$	−5.75233	−	25.9019i	−0.0653673	−	0.294340i
$89$	−80.3175			−0.902444			−0.451222	−	0.892412i	$-0.649012\pi$
$89$	−80.3175			−0.902444			−0.451222	+	0.892412i	$0.649012\pi$
$90$	21.0945	+	31.0703i	0.234383	+	0.345226i
$91$			177.268i			1.94800i
$92$	67.0496	+	26.6181i	0.728800	+	0.289327i
$93$	−13.4094			−0.144187
$94$	−83.1469	+	56.4508i	−0.884542	+	0.600540i
$95$		−	56.4762i		−	0.594486i
$96$	24.5250	+	3.94210i	0.255469	+	0.0410636i
$97$	−0.308392			−0.00317930			−0.00158965	−	0.999999i	$-0.500506\pi$
$97$	−0.308392			−0.00317930			−0.00158965	+	0.999999i	$0.500506\pi$
$98$	35.1859	+	51.8257i	0.359040	+	0.528833i
$99$		−	27.8512i		−	0.281325i
$100$	−7.37956	+	18.5888i	−0.0737956	+	0.185888i
$101$	99.5383			0.985528			0.492764	−	0.870163i	$-0.335987\pi$
$101$	99.5383			0.985528			0.492764	+	0.870163i	$0.335987\pi$
$102$	37.7978	−	25.6620i	0.370566	−	0.251588i
$103$		−	102.708i		−	0.997167i	−0.866842	−	0.498584i	$-0.833854\pi$
$103$		−	102.708i		−	0.997167i	0.866842	−	0.498584i	$-0.166146\pi$
$104$	−154.473	+	34.3054i	−1.48532	+	0.329860i
$105$	15.5560			0.148152
$106$	−115.045	−	169.451i	−1.08533	−	1.59859i
$107$		−	163.212i		−	1.52534i	−0.646785	−	0.762672i	$-0.723887\pi$
$107$		−	163.212i		−	1.52534i	0.646785	−	0.762672i	$-0.276113\pi$
$108$	50.2069	+	19.9317i	0.464879	+	0.184553i
$109$	67.7048			0.621145			0.310572	−	0.950550i	$-0.399479\pi$
$109$	67.7048			0.621145			0.310572	+	0.950550i	$0.399479\pi$
$110$	12.2714	−	8.33141i	0.111558	−	0.0757401i
$111$			26.9666i			0.242943i
$112$	−98.3524	+	104.350i	−0.878146	+	0.931696i
$113$	153.570			1.35903			0.679515	−	0.733661i	$-0.262190\pi$
$113$	153.570			1.35903			0.679515	+	0.733661i	$0.262190\pi$
$114$	−22.0250	−	32.4408i	−0.193202	−	0.284568i
$115$			40.3275i			0.350674i
$116$	35.5157	−	89.4625i	0.306170	−	0.771228i
$117$	−166.098			−1.41964
$118$	−167.669	+	113.835i	−1.42092	+	0.964706i
$119$			263.736i			2.21627i
$120$	3.01044	+	13.5556i	0.0250870	+	0.112963i
$121$	−11.0000			−0.0909091
$122$	40.3708	+	59.4626i	0.330908	+	0.487398i
$123$			13.4903i			0.109677i
$124$	64.2232	+	25.4960i	0.517929	+	0.205613i
$125$	−11.1803			−0.0894427
$126$	−124.530	+	84.5470i	−0.988334	+	0.671008i
$127$			156.653i			1.23349i	0.787163	+	0.616745i	$0.211549\pi$
$127$			156.653i			1.23349i	−0.787163	+	0.616745i	$0.788451\pi$
$128$	−109.965	−	65.5110i	−0.859102	−	0.511805i
$129$	10.3583			0.0802965
$130$	−49.6865	−	73.1837i	−0.382204	−	0.562951i
$131$			140.157i			1.06990i	0.844883	+	0.534951i	$0.179670\pi$
$131$			140.157i			1.06990i	−0.844883	+	0.534951i	$0.820330\pi$
$132$	3.79975	−	9.57138i	0.0287860	−	0.0725105i
$133$	226.357			1.70193
$134$	182.161	−	123.674i	1.35941	−	0.922943i
$135$			30.1973i			0.223684i
$136$	−229.822	+	51.0390i	−1.68987	+	0.375287i
$137$	−79.0249			−0.576824			−0.288412	−	0.957506i	$-0.593127\pi$
$137$	−79.0249			−0.576824			−0.288412	+	0.957506i	$0.593127\pi$
$138$	15.7272	+	23.1647i	0.113965	+	0.167860i
$139$		−	163.928i		−	1.17934i	−0.807646	−	0.589668i	$-0.799259\pi$
$139$		−	163.928i		−	1.17934i	0.807646	−	0.589668i	$-0.200741\pi$
$140$	−74.5039	−	29.5774i	−0.532171	−	0.211267i
$141$	−39.0059			−0.276638
$142$	−69.7887	+	47.3815i	−0.491470	+	0.333673i
$143$			65.6013i			0.458750i
$144$	−97.7745	−	92.1549i	−0.678990	−	0.639964i
$145$	53.8078			0.371088
$146$	−7.15372	−	10.5368i	−0.0489981	−	0.0721697i
$147$			24.3125i			0.165391i
$148$	51.2731	−	129.154i	0.346440	−	0.872665i
$149$	−37.5534			−0.252036			−0.126018	−	0.992028i	$-0.540220\pi$
$149$	−37.5534			−0.252036			−0.126018	+	0.992028i	$0.540220\pi$
$150$	−6.42216	+	4.36019i	−0.0428144	+	0.0290679i
$151$			17.4858i			0.115800i	0.998322	+	0.0579001i	$0.0184405\pi$
$151$			17.4858i			0.115800i	−0.998322	+	0.0579001i	$0.981560\pi$
$152$	43.8054	+	197.250i	0.288193	+	1.29770i
$153$	−247.117			−1.61514
$154$	33.3924	+	49.1839i	0.216834	+	0.319376i
$155$			38.6275i			0.249210i
$156$	−57.0813	−	22.6608i	−0.365906	−	0.145261i
$157$	−94.0151			−0.598823			−0.299411	−	0.954124i	$-0.596790\pi$
$157$	−94.0151			−0.598823			−0.299411	+	0.954124i	$0.596790\pi$
$158$	8.45938	−	5.74332i	0.0535404	−	0.0363501i
$159$		−	79.4930i		−	0.499956i
$160$	11.3557	−	70.6473i	0.0709734	−	0.441546i
$161$	−161.633			−1.00393
$162$	−73.1272	−	107.710i	−0.451403	−	0.664875i
$163$			288.246i			1.76838i	0.467124	+	0.884192i	$0.345290\pi$
$163$			288.246i			1.76838i	−0.467124	+	0.884192i	$0.654710\pi$
$164$	25.6499	−	64.6108i	0.156402	−	0.393968i
$165$	5.75677			0.0348895
$166$	−114.732	+	77.8949i	−0.691157	+	0.469246i
$167$		−	222.687i		−	1.33345i	−0.745303	−	0.666726i	$-0.767695\pi$
$167$		−	222.687i		−	1.33345i	0.745303	−	0.666726i	$-0.232305\pi$
$168$	−54.3310	+	12.0659i	−0.323399	+	0.0718207i
$169$	222.230			1.31497
$170$	−73.9226	−	108.881i	−0.434839	−	0.640478i
$171$			212.094i			1.24031i
$172$	−49.6100	−	19.6947i	−0.288430	−	0.114504i
$173$	127.800			0.738730			0.369365	−	0.929284i	$-0.379575\pi$
$173$	127.800			0.738730			0.369365	+	0.929284i	$0.379575\pi$
$174$	30.9080	−	20.9843i	0.177632	−	0.120600i
$175$		−	44.8109i		−	0.256062i
$176$	−36.3972	+	38.6167i	−0.206802	+	0.219413i
$177$	−78.6570			−0.444390
$178$	90.2293	+	132.900i	0.506906	+	0.746627i
$179$		−	3.29210i		−	0.0183916i	−0.999958	−	0.00919581i	$-0.997073\pi$
$179$		−	3.29210i		−	0.0183916i	0.999958	−	0.00919581i	$-0.00292716\pi$
$180$	27.7136	−	69.8092i	0.153964	−	0.387829i
$181$	171.199			0.945849			0.472925	−	0.881103i	$-0.343198\pi$
$181$	171.199			0.945849			0.472925	+	0.881103i	$0.343198\pi$
$182$	293.321	−	199.144i	1.61165	−	1.09420i
$183$			27.8951i			0.152432i
$184$	−31.2797	−	140.848i	−0.169999	−	0.765481i
$185$	77.6808			0.419896
$186$	15.0642	+	22.1882i	0.0809905	+	0.119292i
$187$			97.6004i			0.521927i
$188$	186.816	+	74.1641i	0.993700	+	0.394490i
$189$	−121.031			−0.640376
$190$	−93.4499	+	63.4458i	−0.491841	+	0.333925i
$191$			69.8698i			0.365810i	0.983131	+	0.182905i	$0.0585501\pi$
$191$			69.8698i			0.365810i	−0.983131	+	0.182905i	$0.941450\pi$
$192$	−21.0286	−	45.0095i	−0.109524	−	0.234425i
$193$	−175.289			−0.908231			−0.454116	−	0.890943i	$-0.650045\pi$
$193$	−175.289			−0.908231			−0.454116	+	0.890943i	$0.650045\pi$
$194$	0.346450	+	0.510289i	0.00178582	+	0.00263035i
$195$		−	34.3320i		−	0.176061i
$196$	46.2266	−	116.443i	0.235850	−	0.594095i
$197$	264.570			1.34300			0.671498	−	0.741006i	$-0.265651\pi$
$197$	264.570			1.34300			0.671498	+	0.741006i	$0.265651\pi$
$198$	−46.0847	+	31.2882i	−0.232751	+	0.158021i
$199$		−	206.409i		−	1.03723i	−0.855008	−	0.518615i	$-0.826448\pi$
$199$		−	206.409i		−	1.03723i	0.855008	−	0.518615i	$-0.173552\pi$
$200$	39.0487	−	8.67196i	0.195243	−	0.0433598i
$201$	85.4555			0.425152
$202$	−111.822	−	164.704i	−0.553575	−	0.815365i
$203$			215.662i			1.06238i
$204$	−84.9246	−	33.7142i	−0.416297	−	0.165266i
$205$	38.8606			0.189564
$206$	−169.949	+	115.383i	−0.824995	+	0.560113i
$207$		−	151.448i		−	0.731632i
$208$	230.300	+	217.064i	1.10721	+	1.04357i
$209$	83.7677			0.400803
$210$	−17.4757	−	25.7401i	−0.0832175	−	0.122572i
$211$		−	214.896i		−	1.01846i	−0.860629	−	0.509232i	$-0.829930\pi$
$211$		−	214.896i		−	1.01846i	0.860629	−	0.509232i	$-0.170070\pi$
$212$	−151.144	+	380.725i	−0.712944	+	1.79587i
$213$	−32.7393			−0.153706
$214$	−270.063	+	183.353i	−1.26198	+	0.856791i
$215$		−	29.8383i		−	0.138783i
$216$	−23.4223	−	105.468i	−0.108437	−	0.488276i
$217$	−154.819			−0.713454
$218$	−76.0600	−	112.030i	−0.348899	−	0.513897i
$219$		−	4.94302i		−	0.0225709i
$220$	−27.5716	−	10.9457i	−0.125325	−	0.0497530i
$221$	582.064			2.63378
$222$	44.6211	−	30.2945i	0.200996	−	0.136462i
$223$		−	178.398i		−	0.799990i	−0.916517	−	0.399995i	$-0.869012\pi$
$223$		−	178.398i		−	0.799990i	0.916517	−	0.399995i	$-0.130988\pi$
$224$	283.155	+	45.5139i	1.26409	+	0.203187i
$225$	41.9872			0.186610
$226$	−172.522	−	254.110i	−0.763372	−	1.12438i
$227$		−	64.8609i		−	0.285731i	−0.989742	−	0.142865i	$-0.954368\pi$
$227$		−	64.8609i		−	0.285731i	0.989742	−	0.142865i	$-0.0456316\pi$
$228$	−28.9360	+	72.8884i	−0.126912	+	0.319686i
$229$	−429.620			−1.87607			−0.938035	−	0.346539i	$-0.887357\pi$
$229$	−429.620			−1.87607			−0.938035	+	0.346539i	$0.887357\pi$
$230$	66.7289	−	45.3042i	0.290126	−	0.196975i
$231$			23.0732i			0.0998840i
$232$	−187.930	+	41.7357i	−0.810044	+	0.179895i
$233$	−381.685			−1.63813			−0.819067	−	0.573698i	$-0.805508\pi$
$233$	−381.685			−1.63813			−0.819067	+	0.573698i	$0.805508\pi$
$234$	186.595	+	274.838i	0.797415	+	1.17452i
$235$			112.362i			0.478134i
$236$	376.721	+	149.555i	1.59628	+	0.633707i
$237$	3.96847			0.0167446
$238$	436.397	−	296.283i	1.83360	−	1.24488i
$239$		−	327.279i		−	1.36937i	−0.728840	−	0.684684i	$-0.759940\pi$
$239$		−	327.279i		−	1.36937i	0.728840	−	0.684684i	$-0.240060\pi$
$240$	19.0482	−	20.2098i	0.0793675	−	0.0842074i
$241$	327.019			1.35692			0.678462	−	0.734636i	$-0.262647\pi$
$241$	327.019			1.35692			0.678462	+	0.734636i	$0.262647\pi$
$242$	12.3575	+	18.2014i	0.0510640	+	0.0752126i
$243$		−	172.071i		−	0.708110i
$244$	53.0385	−	133.601i	0.217371	−	0.547546i
$245$	70.0353			0.285858
$246$	22.3221	−	15.1551i	0.0907403	−	0.0616062i
$247$		−	499.570i		−	2.02255i
$248$	−29.9612	−	134.911i	−0.120811	−	0.543997i
$249$	−53.8232			−0.216157
$250$	12.5601	+	18.4999i	0.0502403	+	0.0739994i
$251$			97.4725i			0.388337i	0.980968	+	0.194168i	$0.0622008\pi$
$251$			97.4725i			0.388337i	−0.980968	+	0.194168i	$0.937799\pi$
$252$	279.796	+	111.076i	1.11030	+	0.440779i
$253$	−59.8153			−0.236424
$254$	259.211	−	175.985i	1.02051	−	0.692856i
$255$		−	51.0785i		−	0.200308i
$256$	15.1359	+	255.552i	0.0591246	+	0.998251i
$257$	−101.720			−0.395798			−0.197899	−	0.980222i	$-0.563412\pi$
$257$	−101.720			−0.395798			−0.197899	+	0.980222i	$0.563412\pi$
$258$	−11.6365	−	17.1396i	−0.0451029	−	0.0664324i
$259$			311.346i			1.20211i
$260$	−65.2772	+	164.430i	−0.251066	+	0.632424i
$261$	−202.073			−0.774225
$262$	231.915	−	157.454i	0.885172	−	0.600968i
$263$			196.098i			0.745622i	0.927907	+	0.372811i	$0.121606\pi$
$263$			196.098i			0.745622i	−0.927907	+	0.372811i	$0.878394\pi$
$264$	−20.1062	+	4.46520i	−0.0761599	+	0.0169136i
$265$	−228.990			−0.864112
$266$	−254.291	−	374.548i	−0.955982	−	1.40808i
$267$			62.3459i			0.233505i
$268$	−409.282	−	162.481i	−1.52717	−	0.606273i
$269$	−164.379			−0.611075			−0.305537	−	0.952180i	$-0.598836\pi$
$269$	−164.379			−0.611075			−0.305537	+	0.952180i	$0.598836\pi$
$270$	49.9668	−	33.9239i	0.185062	−	0.125644i
$271$			3.63640i			0.0134185i	0.999977	+	0.00670923i	$0.00213563\pi$
$271$			3.63640i			0.0134185i	−0.999977	+	0.00670923i	$0.997864\pi$
$272$	342.636	+	322.943i	1.25969	+	1.18729i
$273$	137.603			0.504040
$274$	88.7772	+	130.761i	0.324004	+	0.477229i
$275$		−	16.5831i		−	0.0603023i
$276$	20.6621	−	52.0468i	0.0748627	−	0.188575i
$277$	−142.363			−0.513945			−0.256972	−	0.966419i	$-0.582725\pi$
$277$	−142.363			−0.513945			−0.256972	+	0.966419i	$0.582725\pi$
$278$	−271.247	+	184.158i	−0.975710	+	0.662437i
$279$		−	145.064i		−	0.519942i
$280$	34.7573	+	156.507i	0.124133	+	0.558955i
$281$	162.559			0.578503			0.289252	−	0.957253i	$-0.406594\pi$
$281$	162.559			0.578503			0.289252	+	0.957253i	$0.406594\pi$
$282$	43.8195	+	64.5422i	0.155388	+	0.228873i
$283$			247.166i			0.873379i	0.899612	+	0.436689i	$0.143849\pi$
$283$			247.166i			0.873379i	−0.899612	+	0.436689i	$0.856151\pi$
$284$	156.802	+	62.2490i	0.552121	+	0.219187i
$285$	−43.8393			−0.153822
$286$	108.549	−	73.6969i	0.379542	−	0.257682i
$287$			155.754i			0.542696i
$288$	−42.6459	+	265.313i	−0.148076	+	0.921225i
$289$	576.984			1.99649
$290$	−60.4481	−	89.0346i	−0.208442	−	0.307016i
$291$			0.239387i			0.000822636i
$292$	−9.39843	+	23.6742i	−0.0321864	+	0.0810760i
$293$	−204.069			−0.696481			−0.348241	−	0.937405i	$-0.613221\pi$
$293$	−204.069			−0.696481			−0.348241	+	0.937405i	$0.613221\pi$
$294$	40.2293	−	27.3128i	0.136834	−	0.0929008i
$295$			226.582i			0.768074i
$296$	−271.309	+	60.2526i	−0.916586	+	0.203556i
$297$	−44.7899			−0.150808
$298$	42.1878	+	62.1388i	0.141570	+	0.208519i
$299$			356.724i			1.19306i
$300$	14.4294	+	5.72833i	0.0480980	+	0.0190944i
$301$	119.592			0.397316
$302$	28.9334	−	19.6437i	0.0958059	−	0.0650454i
$303$		−	77.2660i		−	0.255003i
$304$	277.173	−	294.076i	0.911754	−	0.967354i
$305$	80.3555			0.263461
$306$	277.613	+	408.899i	0.907231	+	1.33627i
$307$		−	171.874i		−	0.559849i	−0.960022	−	0.279924i	$-0.909691\pi$
$307$		−	171.874i		−	0.559849i	0.960022	−	0.279924i	$-0.0903094\pi$
$308$	43.8703	−	110.507i	0.142436	−	0.358790i
$309$	−79.7266			−0.258015
$310$	63.9161	−	43.3944i	0.206181	−	0.139982i
$311$		−	312.906i		−	1.00613i	−0.864249	−	0.503064i	$-0.832206\pi$
$311$		−	312.906i		−	1.00613i	0.864249	−	0.503064i	$-0.167794\pi$
$312$	26.6294	+	119.908i	0.0853505	+	0.384322i
$313$	394.718			1.26108			0.630540	−	0.776157i	$-0.282833\pi$
$313$	394.718			1.26108			0.630540	+	0.776157i	$0.282833\pi$
$314$	105.617	+	155.565i	0.336361	+	0.495429i
$315$			168.285i			0.534239i
$316$	−19.0067	−	7.54547i	−0.0601477	−	0.0238781i
$317$	−283.839			−0.895393			−0.447696	−	0.894186i	$-0.647755\pi$
$317$	−283.839			−0.895393			−0.447696	+	0.894186i	$0.647755\pi$
$318$	−131.535	+	89.3030i	−0.413633	+	0.280827i
$319$			79.8099i			0.250188i
$320$	−129.656	+	60.5757i	−0.405174	+	0.189299i
$321$	−126.692			−0.394679
$322$	181.580	+	267.450i	0.563912	+	0.830591i
$323$		−	743.251i		−	2.30109i
$324$	−96.0732	+	242.004i	−0.296522	+	0.746925i
$325$	−98.8976			−0.304300
$326$	476.955	−	323.818i	1.46305	−	0.993307i
$327$		−	52.5554i		−	0.160720i
$328$	−135.725	+	30.1420i	−0.413796	+	0.0918962i
$329$	−450.346			−1.36883
$330$	−6.46720	−	9.52560i	−0.0195976	−	0.0288655i
$331$			249.870i			0.754896i	0.926031	+	0.377448i	$0.123198\pi$
$331$			249.870i			0.754896i	−0.926031	+	0.377448i	$0.876802\pi$
$332$	257.782	+	102.337i	0.776451	+	0.308244i
$333$	−291.727			−0.876056
$334$	−368.474	+	250.168i	−1.10322	+	0.749005i
$335$		−	246.166i		−	0.734823i
$336$	81.0010	+	76.3454i	0.241074	+	0.227218i
$337$	117.027			0.347261			0.173631	−	0.984811i	$-0.444450\pi$
$337$	117.027			0.347261			0.173631	+	0.984811i	$0.444450\pi$
$338$	−249.655	−	367.719i	−0.738623	−	1.08792i
$339$		−	119.208i		−	0.351646i
$340$	−97.1182	+	244.636i	−0.285642	+	0.719518i
$341$	−57.2939			−0.168017
$342$	350.947	−	238.268i	1.02616	−	0.696689i
$343$		−	158.445i		−	0.461939i
$344$	23.1439	+	104.214i	0.0672787	+	0.302947i
$345$	31.3039			0.0907360
$346$	−143.572	−	211.468i	−0.414948	−	0.611180i
$347$			96.6160i			0.278432i	0.990262	+	0.139216i	$0.0444583\pi$
$347$			96.6160i			0.278432i	−0.990262	+	0.139216i	$0.955542\pi$
$348$	−69.4446	−	27.5689i	−0.199554	−	0.0792209i
$349$	−106.013			−0.303763			−0.151882	−	0.988399i	$-0.548533\pi$
$349$	−106.013			−0.303763			−0.151882	+	0.988399i	$0.548533\pi$
$350$	−74.1476	+	50.3409i	−0.211850	+	0.143831i
$351$			267.116i			0.761013i
$352$	104.787	+	16.8433i	0.297690	+	0.0478502i
$353$	−367.318			−1.04056			−0.520280	−	0.853996i	$-0.674172\pi$
$353$	−367.318			−1.04056			−0.520280	+	0.853996i	$0.674172\pi$
$354$	88.3639	+	130.152i	0.249616	+	0.367661i
$355$			94.3098i			0.265661i
$356$	118.542	−	298.601i	0.332982	−	0.838766i
$357$	204.723			0.573454
$358$	−5.44736	+	3.69837i	−0.0152161	+	0.0103306i
$359$		−	272.137i		−	0.758043i	−0.925388	−	0.379021i	$-0.876261\pi$
$359$		−	272.137i		−	0.758043i	0.925388	−	0.379021i	$-0.123739\pi$
$360$	−146.645	+	32.5671i	−0.407348	+	0.0904642i
$361$	−276.912			−0.767070
$362$	−192.326	−	283.279i	−0.531287	−	0.782538i
$363$			8.53868i			0.0235225i
$364$	−659.038	−	261.632i	−1.81054	−	0.718768i
$365$	−14.2390			−0.0390110
$366$	46.1574	−	31.3376i	0.126113	−	0.0856218i
$367$		−	171.225i		−	0.466554i	−0.972410	−	0.233277i	$-0.925055\pi$
$367$		−	171.225i		−	0.466554i	0.972410	−	0.233277i	$-0.0749448\pi$
$368$	−197.919	+	209.988i	−0.537823	+	0.570620i
$369$	−145.939			−0.395499
$370$	−87.2672	−	128.537i	−0.235857	−	0.347397i
$371$		−	917.793i		−	2.47384i
$372$	19.7911	−	49.8529i	0.0532019	−	0.134013i
$373$	175.084			0.469395			0.234697	−	0.972068i	$-0.424590\pi$
$373$	175.084			0.469395			0.234697	+	0.972068i	$0.424590\pi$
$374$	161.497	−	109.645i	0.431810	−	0.293168i
$375$			8.67866i			0.0231431i
$376$	−87.1525	−	392.436i	−0.231789	−	1.04371i
$377$	475.966			1.26251
$378$	135.967	+	200.267i	0.359702	+	0.529808i
$379$		−	203.464i		−	0.536845i	−0.963301	−	0.268423i	$-0.913498\pi$
$379$		−	203.464i		−	0.536845i	0.963301	−	0.268423i	$-0.0865024\pi$
$380$	209.965	+	83.3539i	0.552538	+	0.219352i
$381$	121.601			0.319163
$382$	115.612	−	78.4922i	0.302649	−	0.205477i
$383$			187.471i			0.489480i	0.969589	+	0.244740i	$0.0787027\pi$
$383$			187.471i			0.489480i	−0.969589	+	0.244740i	$0.921297\pi$
$384$	−50.8525	+	85.3596i	−0.132428	+	0.222291i
$385$	66.4653			0.172637
$386$	196.921	+	290.046i	0.510157	+	0.751415i
$387$			112.056i			0.289551i
$388$	0.455159	−	1.14652i	0.00117309	−	0.00295496i
$389$	−563.938			−1.44971			−0.724857	−	0.688900i	$-0.758094\pi$
$389$	−563.938			−1.44971			−0.724857	+	0.688900i	$0.758094\pi$
$390$	−56.8083	+	38.5688i	−0.145662	+	0.0988943i
$391$			530.727i			1.35736i
$392$	−244.606	+	54.3224i	−0.623996	+	0.138578i
$393$	108.796			0.276835
$394$	−297.220	−	437.778i	−0.754366	−	1.11111i
$395$		−	11.4317i		−	0.0289410i
$396$	103.544	+	41.1059i	0.261474	+	0.103803i
$397$	−591.425			−1.48974			−0.744868	−	0.667212i	$-0.767488\pi$
$397$	−591.425			−1.48974			−0.744868	+	0.667212i	$0.767488\pi$
$398$	−341.540	+	231.881i	−0.858141	+	0.582616i
$399$		−	175.708i		−	0.440371i
$400$	−58.2168	−	54.8708i	−0.145542	−	0.137177i
$401$	98.2867			0.245104			0.122552	−	0.992462i	$-0.460892\pi$
$401$	98.2867			0.245104			0.122552	+	0.992462i	$0.460892\pi$
$402$	−96.0014	−	141.401i	−0.238809	−	0.351745i
$403$			341.686i			0.847857i
$404$	−146.910	+	370.059i	−0.363638	+	0.915987i
$405$	−145.555			−0.359395
$406$	356.851	−	242.277i	0.878944	−	0.596740i
$407$			115.219i			0.283094i
$408$	39.6187	+	178.398i	0.0971046	+	0.437249i
$409$	567.793			1.38825			0.694124	−	0.719856i	$-0.255792\pi$
$409$	567.793			1.38825			0.694124	+	0.719856i	$0.255792\pi$
$410$	−43.6563	−	64.3017i	−0.106479	−	0.156834i
$411$			61.3426i			0.149252i
$412$	381.844	+	151.588i	0.926805	+	0.367933i
$413$	−908.142			−2.19889
$414$	−250.597	+	170.138i	−0.605308	+	0.410961i
$415$			155.045i			0.373602i
$416$	100.449	−	624.923i	0.241464	−	1.50222i
$417$	−127.248			−0.305150
$418$	−94.1053	−	138.609i	−0.225132	−	0.331599i
$419$			633.656i			1.51231i	0.654395	+	0.756153i	$0.272924\pi$
$419$			633.656i			1.51231i	−0.654395	+	0.756153i	$0.727076\pi$
$420$	−22.9592	+	57.8332i	−0.0546648	+	0.137698i
$421$	18.8891			0.0448673			0.0224336	−	0.999748i	$-0.492859\pi$
$421$	18.8891			0.0448673			0.0224336	+	0.999748i	$0.492859\pi$
$422$	−355.583	+	241.415i	−0.842614	+	0.572075i
$423$		−	421.969i		−	0.997562i
$424$	799.774	−	177.614i	1.88626	−	0.418902i
$425$	−147.138			−0.346207
$426$	36.7796	+	54.1730i	0.0863371	+	0.127167i
$427$			322.065i			0.754252i
$428$	606.781	+	240.886i	1.41771	+	0.562819i
$429$	50.9225			0.118701
$430$	−49.3727	+	33.5205i	−0.114820	+	0.0779547i
$431$		−	93.7507i		−	0.217519i	−0.994068	−	0.108760i	$-0.965312\pi$
$431$		−	93.7507i		−	0.217519i	0.994068	−	0.108760i	$-0.0346878\pi$
$432$	−148.202	+	157.240i	−0.343060	+	0.363980i
$433$	−307.113			−0.709267			−0.354633	−	0.935005i	$-0.615394\pi$
$433$	−307.113			−0.709267			−0.354633	+	0.935005i	$0.615394\pi$
$434$	173.925	+	256.176i	0.400750	+	0.590268i
$435$		−	41.7680i		−	0.0960183i
$436$	−99.9263	+	251.710i	−0.229189	+	0.577316i
$437$	455.508			1.04235
$438$	−8.17910	+	5.55302i	−0.0186737	+	0.0126781i
$439$			299.883i			0.683105i	0.939863	+	0.341553i	$0.110953\pi$
$439$			299.883i			0.683105i	−0.939863	+	0.341553i	$0.889047\pi$
$440$	12.8626	+	57.9185i	0.0292332	+	0.131633i
$441$	−263.014			−0.596404
$442$	−653.895	−	963.129i	−1.47940	−	2.17902i
$443$			310.362i			0.700591i	0.936639	+	0.350296i	$0.113919\pi$
$443$			310.362i			0.700591i	−0.936639	+	0.350296i	$0.886081\pi$
$444$	−100.255	−	39.8004i	−0.225800	−	0.0896405i
$445$	179.595			0.403585
$446$	−295.191	+	200.413i	−0.661862	+	0.449357i
$447$			29.1506i			0.0652139i
$448$	−242.788	−	519.661i	−0.541937	−	1.15996i
$449$	−385.474			−0.858516			−0.429258	−	0.903182i	$-0.641225\pi$
$449$	−385.474			−0.858516			−0.429258	+	0.903182i	$0.641225\pi$
$450$	−47.1688	−	69.4753i	−0.104819	−	0.154390i
$451$			57.6396i			0.127804i
$452$	−226.657	+	570.937i	−0.501453	+	1.26313i
$453$	13.5733			0.0299630
$454$	−107.324	+	72.8652i	−0.236396	+	0.160496i
$455$		−	396.383i		−	0.871171i
$456$	153.114	−	34.0036i	0.335776	−	0.0745694i
$457$	133.668			0.292490			0.146245	−	0.989248i	$-0.453281\pi$
$457$	133.668			0.292490			0.146245	+	0.989248i	$0.453281\pi$
$458$	482.638	+	710.883i	1.05380	+	1.55215i
$459$			397.410i			0.865816i
$460$	−149.928	−	59.5198i	−0.325929	−	0.129391i
$461$	305.812			0.663367			0.331683	−	0.943391i	$-0.392383\pi$
$461$	305.812			0.663367			0.331683	+	0.943391i	$0.392383\pi$
$462$	38.1787	−	25.9206i	0.0826379	−	0.0561052i
$463$		−	469.769i		−	1.01462i	−0.861763	−	0.507310i	$-0.830640\pi$
$463$		−	469.769i		−	1.01462i	0.861763	−	0.507310i	$-0.169360\pi$
$464$	280.181	+	264.078i	0.603839	+	0.569133i
$465$	29.9843			0.0644825
$466$	428.788	+	631.566i	0.920146	+	1.35529i
$467$			586.447i			1.25577i	0.778304	+	0.627887i	$0.216080\pi$
$467$			586.447i			1.25577i	−0.778304	+	0.627887i	$0.783920\pi$
$468$	245.145	−	617.510i	0.523815	−	1.31946i
$469$	986.634			2.10370
$470$	185.922	−	126.228i	0.395579	−	0.268570i
$471$			72.9786i			0.154944i
$472$	−175.747	−	791.363i	−0.372344	−	1.67662i
$473$	44.2573			0.0935673
$474$	−4.45821	−	6.56654i	−0.00940551	−	0.0138535i
$475$			126.285i			0.265862i
$476$	−980.504	−	389.251i	−2.05988	−	0.817754i
$477$	859.960			1.80285
$478$	−541.541	+	367.667i	−1.13293	+	0.769179i
$479$			229.662i			0.479462i	0.970839	+	0.239731i	$0.0770593\pi$
$479$			229.662i			0.479462i	−0.970839	+	0.239731i	$0.922941\pi$
$480$	−54.8395	−	8.81481i	−0.114249	−	0.0183642i
$481$	687.139			1.42856
$482$	−367.375	−	541.110i	−0.762189	−	1.12263i
$483$			125.466i			0.259765i
$484$	16.2350	−	40.8953i	0.0335435	−	0.0844944i
$485$	0.689585			0.00142182
$486$	−284.721	+	193.305i	−0.585847	+	0.397748i
$487$		−	425.112i		−	0.872920i	−0.899724	−	0.436460i	$-0.856232\pi$
$487$		−	425.112i		−	0.872920i	0.899724	−	0.436460i	$-0.143768\pi$
$488$	−280.651	+	62.3272i	−0.575104	+	0.127720i
$489$	223.749			0.457565
$490$	−78.6781	−	115.886i	−0.160568	−	0.236502i
$491$			137.887i			0.280829i	0.990093	+	0.140415i	$0.0448435\pi$
$491$			137.887i			0.280829i	−0.990093	+	0.140415i	$0.955156\pi$
$492$	−50.1537	−	19.9105i	−0.101938	−	0.0404686i
$493$	708.134			1.43638
$494$	−826.627	+	561.221i	−1.67333	+	1.13607i
$495$			62.2771i			0.125812i
$496$	−189.576	+	201.136i	−0.382209	+	0.405517i
$497$	−377.995			−0.760553
$498$	60.4654	+	89.0600i	0.121416	+	0.178835i
$499$			124.713i			0.249926i	0.992161	+	0.124963i	$0.0398813\pi$
$499$			124.713i			0.249926i	−0.992161	+	0.124963i	$0.960119\pi$
$500$	16.5012	−	41.5657i	0.0330024	−	0.0831315i
$501$	−172.859			−0.345028
$502$	161.286	−	109.501i	0.321286	−	0.218130i
$503$		−	183.840i		−	0.365487i	−0.983161	−	0.182744i	$-0.941502\pi$
$503$		−	183.840i		−	0.365487i	0.983161	−	0.182744i	$-0.0584978\pi$
$504$	−130.529	−	587.756i	−0.258987	−	1.16618i
$505$	−222.574			−0.440742
$506$	67.1969	+	98.9750i	0.132800	+	0.195603i
$507$		−	172.504i		−	0.340245i
$508$	−582.398	−	231.207i	−1.14645	−	0.455131i
$509$	693.777			1.36302			0.681510	−	0.731809i	$-0.261324\pi$
$509$	693.777			1.36302			0.681510	+	0.731809i	$0.261324\pi$
$510$	−84.5184	+	57.3819i	−0.165722	+	0.112514i
$511$		−	57.0701i		−	0.111683i
$512$	405.853	−	312.134i	0.792681	−	0.609637i
$513$	341.086			0.664885
$514$	114.273	+	168.314i	0.222321	+	0.327459i
$515$			229.663i			0.445947i
$516$	−15.2879	+	38.5094i	−0.0296277	+	0.0746307i
$517$	−166.659			−0.322358
$518$	515.176	−	349.768i	0.994549	−	0.675228i
$519$		−	99.2042i		−	0.191145i
$520$	345.412	−	76.7093i	0.664253	−	0.147518i
$521$	−18.1905			−0.0349145			−0.0174572	−	0.999848i	$-0.505557\pi$
$521$	−18.1905			−0.0349145			−0.0174572	+	0.999848i	$0.505557\pi$
$522$	227.010	+	334.365i	0.434885	+	0.640546i
$523$			841.844i			1.60964i	0.593516	+	0.804822i	$0.297739\pi$
$523$			841.844i			1.60964i	−0.593516	+	0.804822i	$0.702261\pi$
$524$	−521.070	−	206.860i	−0.994408	−	0.394771i
$525$	−34.7842			−0.0662556
$526$	324.480	−	220.298i	0.616881	−	0.418818i
$527$			508.355i			0.964620i
$528$	29.9759	+	28.2530i	0.0567726	+	0.0535095i
$529$	203.739			0.385140
$530$	257.249	+	378.904i	0.485375	+	0.714913i
$531$		−	850.917i		−	1.60248i
$532$	−334.083	+	841.540i	−0.627976	+	1.58184i
$533$	343.748			0.644931
$534$	103.162	−	70.0398i	0.193188	−	0.131161i
$535$			364.953i			0.682155i
$536$	190.937	+	859.762i	0.356225	+	1.60403i
$537$	−2.55547			−0.00475879
$538$	184.665	+	271.994i	0.343243	+	0.505566i
$539$			103.879i			0.192726i
$540$	−112.266	−	44.5686i	−0.207900	−	0.0825344i
$541$	55.5711			0.102719			0.0513596	−	0.998680i	$-0.483645\pi$
$541$	55.5711			0.102719			0.0513596	+	0.998680i	$0.483645\pi$
$542$	6.01707	−	4.08516i	0.0111016	−	0.00753719i
$543$		−	132.892i		−	0.244736i
$544$	149.446	−	929.749i	0.274718	−	1.70910i
$545$	−151.392			−0.277784
$546$	−154.584	−	227.688i	−0.283121	−	0.417012i
$547$		−	123.468i		−	0.225718i	−0.993611	−	0.112859i	$-0.963999\pi$
$547$		−	123.468i		−	0.225718i	0.993611	−	0.112859i	$-0.0360009\pi$
$548$	116.634	−	293.795i	0.212836	−	0.536122i
$549$	−301.771			−0.549674
$550$	−27.4397	+	18.6296i	−0.0498904	+	0.0338720i
$551$		−	607.772i		−	1.10303i
$552$	−109.333	+	24.2807i	−0.198066	+	0.0439867i
$553$	45.8183			0.0828541
$554$	159.931	+	235.564i	0.288685	+	0.425206i
$555$		−	60.2992i		−	0.108647i
$556$	609.442	+	241.943i	1.09612	+	0.435149i
$557$	−121.134			−0.217476			−0.108738	−	0.994070i	$-0.534681\pi$
$557$	−121.134			−0.217476			−0.108738	+	0.994070i	$0.534681\pi$
$558$	−240.034	+	162.966i	−0.430168	+	0.292053i
$559$		−	263.940i		−	0.472164i
$560$	219.923	−	233.334i	0.392719	−	0.416667i
$561$	75.7616			0.135047
$562$	−182.620	−	268.983i	−0.324947	−	0.478618i
$563$			505.558i			0.897972i	0.893539	+	0.448986i	$0.148215\pi$
$563$			505.558i			0.897972i	−0.893539	+	0.448986i	$0.851785\pi$
$564$	57.5693	−	145.014i	0.102073	−	0.257118i
$565$	−343.394			−0.607777
$566$	408.980	−	277.668i	0.722580	−	0.490580i
$567$		−	583.385i		−	1.02890i
$568$	−73.1508	−	329.388i	−0.128787	−	0.579909i
$569$	−30.8456			−0.0542101			−0.0271051	−	0.999633i	$-0.508629\pi$
$569$	−30.8456			−0.0542101			−0.0271051	+	0.999633i	$0.508629\pi$
$570$	49.2493	+	72.5398i	0.0864024	+	0.127263i
$571$		−	963.464i		−	1.68733i	−0.536872	−	0.843664i	$-0.680394\pi$
$571$		−	963.464i		−	1.68733i	0.536872	−	0.843664i	$-0.319606\pi$
$572$	−243.889	−	96.8217i	−0.426380	−	0.169269i
$573$	54.2359			0.0946526
$574$	257.722	−	174.975i	0.448993	−	0.304834i
$575$		−	90.1750i		−	0.156826i
$576$	486.916	−	227.489i	0.845340	−	0.394946i
$577$	60.2083			0.104347			0.0521736	−	0.998638i	$-0.483385\pi$
$577$	60.2083			0.104347			0.0521736	+	0.998638i	$0.483385\pi$
$578$	−648.189	−	954.723i	−1.12143	−	1.65177i
$579$			136.067i			0.235003i
$580$	−79.4156	+	200.044i	−0.136923	+	0.344904i
$581$	−621.421			−1.06957
$582$	0.396108	−	0.268929i	0.000680598	−	0.000462077i
$583$		−	339.647i		−	0.582584i
$584$	49.7314	−	11.0444i	0.0851565	−	0.0189116i
$585$	371.405			0.634881
$586$	229.253	+	337.668i	0.391216	+	0.576226i
$587$		−	152.298i		−	0.259451i	−0.991550	−	0.129725i	$-0.958590\pi$
$587$		−	152.298i		−	0.259451i	0.991550	−	0.129725i	$-0.0414096\pi$
$588$	−90.3878	−	35.8831i	−0.153721	−	0.0610257i
$589$	436.307			0.740759
$590$	374.920	−	254.544i	0.635457	−	0.431430i
$591$		−	205.371i		−	0.347497i
$592$	404.490	+	381.241i	0.683260	+	0.643989i
$593$	911.536			1.53716			0.768580	−	0.639754i	$-0.220964\pi$
$593$	911.536			1.53716			0.768580	+	0.639754i	$0.220964\pi$
$594$	50.3172	+	74.1127i	0.0847092	+	0.124769i
$595$		−	589.731i		−	0.991144i
$596$	55.4256	−	139.614i	0.0929959	−	0.234252i
$597$	−160.224			−0.268381
$598$	590.262	−	400.746i	0.987061	−	0.670144i
$599$		−	331.186i		−	0.552899i	−0.961028	−	0.276449i	$-0.910842\pi$
$599$		−	331.186i		−	0.552899i	0.961028	−	0.276449i	$-0.0891578\pi$
$600$	−6.73155	−	30.3112i	−0.0112192	−	0.0505187i
$601$	−323.427			−0.538148			−0.269074	−	0.963119i	$-0.586718\pi$
$601$	−323.427			−0.538148			−0.269074	+	0.963119i	$0.586718\pi$
$602$	−134.351	−	197.886i	−0.223174	−	0.328715i
$603$			924.463i			1.53311i
$604$	−65.0080	−	25.8075i	−0.107629	−	0.0427277i
$605$	24.5967			0.0406558
$606$	−127.850	+	86.8011i	−0.210974	+	0.143236i
$607$			961.071i			1.58331i	0.610967	+	0.791656i	$0.290781\pi$
$607$			961.071i			1.58331i	−0.610967	+	0.791656i	$0.709219\pi$
$608$	−797.979	−	128.266i	−1.31246	−	0.210963i
$609$	167.406			0.274887
$610$	−90.2719	−	132.962i	−0.147987	−	0.217971i
$611$			993.914i			1.62670i
$612$	364.723	−	918.719i	0.595952	−	1.50118i
$613$	−240.586			−0.392474			−0.196237	−	0.980557i	$-0.562872\pi$
$613$	−240.586			−0.392474			−0.196237	+	0.980557i	$0.562872\pi$
$614$	−284.395	+	193.084i	−0.463184	+	0.314469i
$615$		−	30.1653i		−	0.0490492i
$616$	−232.138	+	51.5534i	−0.376847	+	0.0836906i
$617$	1015.49			1.64586			0.822928	−	0.568146i	$-0.192339\pi$
$617$	1015.49			1.64586			0.822928	+	0.568146i	$0.192339\pi$
$618$	89.5654	+	131.922i	0.144928	+	0.213466i
$619$		−	361.927i		−	0.584696i	−0.956312	−	0.292348i	$-0.905563\pi$
$619$		−	361.927i		−	0.584696i	0.956312	−	0.292348i	$-0.0944366\pi$
$620$	−143.608	−	57.0108i	−0.231625	−	0.0919529i
$621$	−243.556			−0.392200
$622$	−517.758	+	351.520i	−0.832408	+	0.565145i
$623$			719.820i			1.15541i
$624$	168.494	−	178.769i	0.270023	−	0.286489i
$625$	25.0000			0.0400000
$626$	−443.429	−	653.131i	−0.708353	−	1.04334i
$627$		−	65.0241i		−	0.103707i
$628$	138.758	−	349.525i	0.220952	−	0.556568i
$629$	1022.31			1.62530
$630$	278.458	−	189.053i	0.441996	−	0.300084i
$631$			1193.98i			1.89221i	0.323861	+	0.946105i	$0.395019\pi$
$631$			1193.98i			1.89221i	−0.323861	+	0.946105i	$0.604981\pi$
$632$	8.86692	+	39.9265i	0.0140299	+	0.0631749i
$633$	−166.811			−0.263525
$634$	318.867	+	469.663i	0.502945	+	0.740793i
$635$		−	350.287i		−	0.551634i
$636$	295.535	+	117.325i	0.464678	+	0.184473i
$637$	619.509			0.972542
$638$	132.060	−	89.6590i	0.206990	−	0.140531i
$639$		−	354.176i		−	0.554266i
$640$	245.889	+	146.487i	0.384202	+	0.228886i
$641$	−1043.78			−1.62837			−0.814183	−	0.580608i	$-0.802815\pi$
$641$	−1043.78			−1.62837			−0.814183	+	0.580608i	$0.802815\pi$
$642$	142.327	+	209.634i	0.221693	+	0.326533i
$643$		−	129.076i		−	0.200740i	−0.994950	−	0.100370i	$-0.967997\pi$
$643$		−	129.076i		−	0.200740i	0.994950	−	0.100370i	$-0.0320026\pi$
$644$	238.556	−	600.911i	0.370429	−	0.933092i
$645$	−23.1618			−0.0359097
$646$	−1229.84	+	834.974i	−1.90378	+	1.29253i
$647$			19.3335i			0.0298817i	0.999888	+	0.0149409i	$0.00475600\pi$
$647$			19.3335i			0.0298817i	−0.999888	+	0.0149409i	$0.995244\pi$
$648$	508.368	−	112.899i	0.784518	−	0.174226i
$649$	−336.075			−0.517835
$650$	111.102	+	163.644i	0.170927	+	0.251759i
$651$			120.178i			0.184605i
$652$	−1071.63	−	425.427i	−1.64360	−	0.652495i
$653$	399.417			0.611665			0.305833	−	0.952085i	$-0.401065\pi$
$653$	399.417			0.611665			0.305833	+	0.952085i	$0.401065\pi$
$654$	−86.9622	+	59.0411i	−0.132970	+	0.0902769i
$655$		−	313.401i		−	0.478475i
$656$	202.350	+	190.720i	0.308460	+	0.290731i
$657$	53.4739			0.0813910
$658$	505.922	+	745.178i	0.768879	+	1.13249i
$659$		−	1302.83i		−	1.97698i	−0.151275	−	0.988492i	$-0.548338\pi$
$659$		−	1302.83i		−	1.97698i	0.151275	−	0.988492i	$-0.451662\pi$
$660$	−8.49649	+	21.4023i	−0.0128735	+	0.0324277i
$661$	−33.5288			−0.0507244			−0.0253622	−	0.999678i	$-0.508074\pi$
$661$	−33.5288			−0.0507244			−0.0253622	+	0.999678i	$0.508074\pi$
$662$	413.455	−	280.706i	0.624554	−	0.424028i
$663$		−	451.823i		−	0.681483i
$664$	−120.259	−	541.512i	−0.181114	−	0.815530i
$665$	−506.150			−0.761128
$666$	327.728	+	482.713i	0.492084	+	0.724795i
$667$			433.987i			0.650655i
$668$	827.893	+	328.666i	1.23936	+	0.492015i
$669$	−138.480			−0.206996
$670$	−407.325	+	276.544i	−0.607947	+	0.412753i
$671$			119.186i			0.177625i
$672$	35.3299	−	219.797i	0.0525742	−	0.327079i
$673$	−376.344			−0.559204			−0.279602	−	0.960116i	$-0.590202\pi$
$673$	−376.344			−0.559204			−0.279602	+	0.960116i	$0.590202\pi$
$674$	−131.469	−	193.642i	−0.195058	−	0.287303i
$675$		−	67.5232i		−	0.100034i
$676$	−327.992	+	826.195i	−0.485195	+	1.22218i
$677$	−153.217			−0.226317			−0.113159	−	0.993577i	$-0.536097\pi$
$677$	−153.217			−0.226317			−0.113159	+	0.993577i	$0.536097\pi$
$678$	−197.251	+	133.919i	−0.290930	+	0.197521i
$679$			2.76386i			0.00407049i
$680$	513.897	−	114.127i	0.755731	−	0.167833i
$681$	−50.3478			−0.0739322
$682$	64.3643	+	94.8028i	0.0943759	+	0.139007i
$683$			945.926i			1.38496i	0.721438	+	0.692479i	$0.243481\pi$
$683$			945.926i			1.38496i	−0.721438	+	0.692479i	$0.756519\pi$
$684$	−788.512	−	313.032i	−1.15279	−	0.457649i
$685$	176.705			0.257964
$686$	−262.175	+	177.998i	−0.382180	+	0.259473i
$687$			333.490i			0.485429i
$688$	146.440	−	155.370i	0.212849	−	0.225829i
$689$	−2025.57			−2.93987
$690$	−35.1671	−	51.7979i	−0.0509667	−	0.0750694i
$691$		−	419.271i		−	0.606760i	−0.952870	−	0.303380i	$-0.901885\pi$
$691$		−	419.271i		−	0.606760i	0.952870	−	0.303380i	$-0.0981152\pi$
$692$	−188.622	+	475.130i	−0.272575	+	0.686604i
$693$	−249.607			−0.360184
$694$	159.868	−	108.539i	0.230358	−	0.156396i
$695$			366.553i			0.527415i
$696$	32.3970	+	145.879i	0.0465475	+	0.209597i
$697$	511.422			0.733748
$698$	119.096	+	175.418i	0.170625	+	0.251315i
$699$			296.281i			0.423864i
$700$	166.596	+	66.1370i	0.237994	+	0.0944814i
$701$	−193.554			−0.276112			−0.138056	−	0.990424i	$-0.544085\pi$
$701$	−193.554			−0.276112			−0.138056	+	0.990424i	$0.544085\pi$
$702$	441.990	−	300.080i	0.629615	−	0.427464i
$703$		−	877.424i		−	1.24811i
$704$	−89.8482	−	192.310i	−0.127625	−	0.273168i
$705$	87.2199			0.123716
$706$	412.647	+	607.792i	0.584487	+	0.860896i
$707$		−	892.081i		−	1.26178i
$708$	116.091	−	292.427i	0.163970	−	0.413033i
$709$	86.2823			0.121696			0.0608479	−	0.998147i	$-0.480620\pi$
$709$	86.2823			0.121696			0.0608479	+	0.998147i	$0.480620\pi$
$710$	156.052	−	105.948i	0.219792	−	0.149223i
$711$			42.9312i			0.0603814i
$712$	−627.258	+	139.302i	−0.880980	+	0.195649i
$713$	−311.550			−0.436956
$714$	−229.987	−	338.750i	−0.322111	−	0.474440i
$715$		−	146.689i		−	0.205159i
$716$	12.2392	+	4.85885i	0.0170939	+	0.00678610i
$717$	−254.048			−0.354321
$718$	−450.300	+	305.721i	−0.627158	+	0.425795i
$719$			371.428i			0.516590i	0.966066	+	0.258295i	$0.0831607\pi$
$719$			371.428i			0.516590i	−0.966066	+	0.258295i	$0.916839\pi$
$720$	218.631	+	206.065i	0.303653	+	0.286201i
$721$	−920.490			−1.27669
$722$	311.085	+	458.200i	0.430866	+	0.634626i
$723$		−	253.846i		−	0.351101i
$724$	−252.674	+	636.475i	−0.348998	+	0.879109i
$725$	−120.318			−0.165956
$726$	14.1287	−	9.59241i	0.0194611	−	0.0132127i
$727$			1216.91i			1.67388i	0.547294	+	0.836940i	$0.315658\pi$
$727$			1216.91i			1.67388i	−0.547294	+	0.836940i	$0.684342\pi$
$728$	307.452	+	1384.41i	0.422324	+	1.90167i
$729$	452.278			0.620409
$730$	15.9962	+	23.5609i	0.0219126	+	0.0322753i
$731$		−	392.685i		−	0.537188i
$732$	−103.707	−	41.1707i	−0.141676	−	0.0562442i
$733$	261.836			0.357212			0.178606	−	0.983921i	$-0.442841\pi$
$733$	261.836			0.357212			0.178606	+	0.983921i	$0.442841\pi$
$734$	−283.322	+	192.356i	−0.385998	+	0.262065i
$735$		−	54.3644i		−	0.0739652i
$736$	569.806	+	91.5896i	0.774193	+	0.124442i
$737$	365.123			0.495417
$738$	163.949	+	241.482i	0.222153	+	0.327212i
$739$		−	706.893i		−	0.956553i	−0.878209	−	0.478276i	$-0.841262\pi$
$739$		−	706.893i		−	0.956553i	0.878209	−	0.478276i	$-0.158738\pi$
$740$	−114.650	+	288.798i	−0.154933	+	0.390268i
$741$	−387.788			−0.523330
$742$	−1518.65	+	1031.06i	−2.04670	+	1.38956i
$743$		−	1385.33i		−	1.86451i	−0.361798	−	0.932256i	$-0.617837\pi$
$743$		−	1385.33i		−	1.86451i	0.361798	−	0.932256i	$-0.382163\pi$
$744$	−104.724	+	23.2572i	−0.140758	+	0.0312596i
$745$	83.9720			0.112714
$746$	−196.691	−	289.708i	−0.263661	−	0.388348i
$747$		−	582.263i		−	0.779468i
$748$	−362.854	−	144.050i	−0.485099	−	0.192580i
$749$	−1462.73			−1.95292
$750$	14.3604	−	9.74967i	0.0191472	−	0.0129996i
$751$			1069.54i			1.42416i	0.702100	+	0.712078i	$0.252246\pi$
$751$			1069.54i			1.42416i	−0.702100	+	0.712078i	$0.747754\pi$
$752$	−551.447	+	585.075i	−0.733307	+	0.778025i
$753$	75.6624			0.100481
$754$	−534.704	−	787.571i	−0.709157	−	1.04452i
$755$		−	39.0995i		−	0.0517874i
$756$	178.631	−	449.964i	0.236285	−	0.595190i
$757$	−98.2980			−0.129852			−0.0649260	−	0.997890i	$-0.520681\pi$
$757$	−98.2980			−0.129852			−0.0649260	+	0.997890i	$0.520681\pi$
$758$	−336.668	+	228.573i	−0.444153	+	0.301548i
$759$			46.4312i			0.0611742i
$760$	−97.9518	−	441.064i	−0.128884	−	0.580347i
$761$	−1247.24			−1.63895			−0.819477	−	0.573113i	$-0.805736\pi$
$761$	−1247.24			−1.63895			−0.819477	+	0.573113i	$0.805736\pi$
$762$	−136.607	−	201.210i	−0.179275	−	0.264056i
$763$		−	606.783i		−	0.795259i
$764$	−259.759	−	103.122i	−0.339998	−	0.134976i
$765$	552.570			0.722314
$766$	310.204	−	210.606i	0.404966	−	0.274943i
$767$			2004.27i			2.61313i
$768$	198.371	−	11.7491i	0.258295	−	0.0152984i
$769$	−592.727			−0.770776			−0.385388	−	0.922755i	$-0.625932\pi$
$769$	−592.727			−0.770776			−0.385388	+	0.922755i	$0.625932\pi$
$770$	−74.6676	−	109.979i	−0.0969709	−	0.142829i
$771$			78.9596i			0.102412i
$772$	258.711	−	651.680i	0.335117	−	0.844145i
$773$	−509.305			−0.658868			−0.329434	−	0.944179i	$-0.606858\pi$
$773$	−509.305			−0.658868			−0.329434	+	0.944179i	$0.606858\pi$
$774$	185.417	−	125.885i	0.239557	−	0.162642i
$775$		−	86.3737i		−	0.111450i
$776$	−2.40846	+	0.534872i	−0.00310368	+	0.000689268i
$777$	241.680			0.311042
$778$	633.532	+	933.136i	0.814309	+	1.19940i
$779$		−	438.940i		−	0.563466i
$780$	127.638	+	50.6710i	0.163638	+	0.0649628i
$781$	−139.884			−0.179109
$782$	878.181	−	596.222i	1.12299	−	0.762433i
$783$			324.970i			0.415032i
$784$	364.679	+	343.718i	0.465151	+	0.438416i
$785$	210.224			0.267802
$786$	−122.222	−	180.022i	−0.155499	−	0.229036i
$787$			589.916i			0.749576i	0.927111	+	0.374788i	$0.122284\pi$
$787$			589.916i			0.749576i	−0.927111	+	0.374788i	$0.877716\pi$
$788$	−390.482	+	983.607i	−0.495536	+	1.24823i
$789$	152.220			0.192928
$790$	−18.9158	+	12.8424i	−0.0239440	+	0.0162563i
$791$		−	1376.33i		−	1.73998i
$792$	−48.3048	−	217.510i	−0.0609910	−	0.274634i
$793$	710.798			0.896341
$794$	664.412	+	978.618i	0.836790	+	1.23252i
$795$			177.752i			0.223587i
$796$	767.377	+	304.642i	0.964042	+	0.382716i
$797$	−998.779			−1.25317			−0.626587	−	0.779352i	$-0.715549\pi$
$797$	−998.779			−1.25317			−0.626587	+	0.779352i	$0.715549\pi$
$798$	−290.740	+	197.392i	−0.364336	+	0.247358i
$799$			1478.73i			1.85072i
$800$	−25.3922	+	157.972i	−0.0317403	+	0.197465i
$801$	−674.462			−0.842025
$802$	−110.416	−	162.633i	−0.137676	−	0.202784i
$803$		−	21.1199i		−	0.0263012i
$804$	−126.125	+	317.703i	−0.156872	+	0.395152i
$805$	361.422			0.448972
$806$	565.381	−	383.853i	0.701465	−	0.476244i
$807$			127.598i			0.158114i
$808$	777.368	−	172.638i	0.962089	−	0.213661i
$809$	456.441			0.564204			0.282102	−	0.959384i	$-0.408968\pi$
$809$	456.441			0.564204			0.282102	+	0.959384i	$0.408968\pi$
$810$	163.517	+	240.846i	0.201873	+	0.297341i
$811$		−	280.408i		−	0.345755i	−0.984943	−	0.172878i	$-0.944693\pi$
$811$		−	280.408i		−	0.345755i	0.984943	−	0.172878i	$-0.0553065\pi$
$812$	−801.779	−	318.299i	−0.987412	−	0.391993i
$813$	2.82273			0.00347199
$814$	190.651	−	129.438i	0.234215	−	0.159015i
$815$		−	644.539i		−	0.790845i
$816$	250.682	−	265.969i	0.307209	−	0.325943i
$817$	−337.030			−0.412522
$818$	−637.863	−	939.514i	−0.779784	−	1.14855i
$819$			1488.60i			1.81758i
$820$	−57.3548	+	144.474i	−0.0699449	+	0.176188i
$821$	−1193.42			−1.45361			−0.726806	−	0.686843i	$-0.758996\pi$
$821$	−1193.42			−1.45361			−0.726806	+	0.686843i	$0.758996\pi$
$822$	101.502	−	68.9127i	0.123482	−	0.0838354i
$823$		−	279.060i		−	0.339076i	−0.985524	−	0.169538i	$-0.945772\pi$
$823$		−	279.060i		−	0.339076i	0.985524	−	0.169538i	$-0.0542276\pi$
$824$	−178.136	−	802.124i	−0.216185	−	0.973451i
$825$	−12.8725			−0.0156031
$826$	1020.21	+	1502.68i	1.23512	+	1.81923i
$827$		−	548.515i		−	0.663259i	−0.943410	−	0.331630i	$-0.892402\pi$
$827$		−	548.515i		−	0.663259i	0.943410	−	0.331630i	$-0.107598\pi$
$828$	563.046	+	223.524i	0.680007	+	0.269956i
$829$	938.125			1.13163			0.565817	−	0.824531i	$-0.308561\pi$
$829$	938.125			1.13163			0.565817	+	0.824531i	$0.308561\pi$
$830$	256.549	−	174.178i	0.309095	−	0.209853i
$831$			110.508i			0.132982i
$832$	−1146.89	+	535.833i	−1.37848	+	0.644030i
$833$	921.694			1.10648
$834$	142.951	+	210.554i	0.171404	+	0.252463i
$835$			497.942i			0.596338i
$836$	−123.634	+	311.428i	−0.147887	+	0.372521i
$837$	−233.289			−0.278721
$838$	1048.50	−	711.854i	1.25119	−	0.849468i
$839$		−	288.310i		−	0.343635i	−0.985129	−	0.171818i	$-0.945036\pi$
$839$		−	288.310i		−	0.343635i	0.985129	−	0.171818i	$-0.0549640\pi$
$840$	121.488	−	26.9801i	0.144628	−	0.0321192i
$841$	−261.944			−0.311467
$842$	−21.2202	−	31.2554i	−0.0252021	−	0.0371204i
$843$		−	126.186i		−	0.149686i
$844$	798.929	+	317.167i	0.946599	+	0.375791i
$845$	−496.921			−0.588072
$846$	−698.222	+	474.043i	−0.825321	+	0.560334i
$847$			98.5840i			0.116392i
$848$	−1192.37	−	1123.83i	−1.40609	−	1.32528i
$849$	191.861			0.225985
$850$	165.296	+	243.466i	0.194466	+	0.286431i
$851$			626.534i			0.736233i
$852$	48.3204	−	121.717i	0.0567140	−	0.142860i
$853$	158.467			0.185776			0.0928880	−	0.995677i	$-0.470390\pi$
$853$	158.467			0.185776			0.0928880	+	0.995677i	$0.470390\pi$
$854$	532.914	−	361.811i	0.624021	−	0.423666i
$855$		−	474.256i		−	0.554685i
$856$	−283.073	−	1274.64i	−0.330693	−	1.48907i
$857$	−996.532			−1.16281			−0.581407	−	0.813613i	$-0.697498\pi$
$857$	−996.532			−1.16281			−0.581407	+	0.813613i	$0.697498\pi$
$858$	−57.2068	−	84.2604i	−0.0666745	−	0.0982056i
$859$		−	329.312i		−	0.383367i	−0.981457	−	0.191683i	$-0.938605\pi$
$859$		−	329.312i		−	0.383367i	0.981457	−	0.191683i	$-0.0613947\pi$
$860$	110.931	+	44.0387i	0.128990	+	0.0512078i
$861$	120.903			0.140421
$862$	−155.127	+	105.320i	−0.179962	+	0.122181i
$863$		−	84.8837i		−	0.0983588i	−0.998790	−	0.0491794i	$-0.984339\pi$
$863$		−	84.8837i		−	0.0983588i	0.998790	−	0.0491794i	$-0.0156606\pi$
$864$	426.672	+	68.5826i	0.493833	+	0.0793780i
$865$	−285.770			−0.330370
$866$	345.012	+	508.172i	0.398398	+	0.586804i
$867$		−	447.880i		−	0.516586i
$868$	228.500	−	575.580i	0.263249	−	0.663111i
$869$	16.9559			0.0195120
$870$	−69.1125	+	46.9224i	−0.0794396	+	0.0539338i
$871$		−	2177.50i		−	2.50000i
$872$	528.756	−	117.427i	0.606372	−	0.134663i
$873$	−2.58970			−0.00296644
$874$	−511.721	−	753.719i	−0.585494	−	0.862379i
$875$			100.200i			0.114515i
$876$	18.3769	+	7.29546i	0.0209782	+	0.00832815i
$877$	−526.192			−0.599991			−0.299995	−	0.953941i	$-0.596985\pi$
$877$	−526.192			−0.599991			−0.299995	+	0.953941i	$0.596985\pi$
$878$	496.210	−	336.891i	0.565159	−	0.383703i
$879$			158.407i			0.180213i
$880$	81.3865	−	86.3495i	0.0924847	−	0.0981244i
$881$	1332.36			1.51233			0.756163	−	0.654383i	$-0.227071\pi$
$881$	1332.36			1.51233			0.756163	+	0.654383i	$0.227071\pi$
$882$	295.472	+	435.203i	0.335002	+	0.493428i
$883$		−	1475.76i		−	1.67130i	−0.549262	−	0.835650i	$-0.685091\pi$
$883$		−	1475.76i		−	1.67130i	0.549262	−	0.835650i	$-0.314909\pi$
$884$	−859.076	+	2163.97i	−0.971805	+	2.44793i
$885$	175.882			0.198737
$886$	513.549	−	348.663i	0.579626	−	0.393525i
$887$		−	1434.14i		−	1.61684i	−0.588607	−	0.808420i	$-0.700323\pi$
$887$		−	1434.14i		−	1.61684i	0.588607	−	0.808420i	$-0.299677\pi$
$888$	46.7707	+	210.602i	0.0526697	+	0.237165i
$889$	1403.96			1.57925
$890$	−201.759	−	297.172i	−0.226695	−	0.333902i
$891$		−	215.893i		−	0.242304i
$892$	663.239	+	263.299i	0.743541	+	0.295179i
$893$	1269.15			1.42122
$894$	48.2348	−	32.7480i	0.0539539	−	0.0366309i
$895$			7.36136i			0.00822498i
$896$	−587.122	+	985.527i	−0.655270	+	1.09992i
$897$	276.904			0.308700
$898$	433.044	+	637.835i	0.482232	+	0.710284i
$899$			415.692i			0.462394i
$900$	−61.9695	+	156.098i	−0.0688550	+	0.173442i
$901$	−3013.60			−3.34473
$902$	95.3749	−	64.7527i	0.105737	−	0.0717879i
$903$		−	92.8326i		−	0.102805i
$904$	1199.34	−	266.351i	1.32671	−	0.294636i
$905$	−382.812			−0.422997
$906$	−15.2483	−	22.4594i	−0.0168303	−	0.0247896i
$907$		−	1366.09i		−	1.50616i	−0.657928	−	0.753080i	$-0.728567\pi$
$907$		−	1366.09i		−	1.50616i	0.657928	−	0.753080i	$-0.271433\pi$
$908$	241.137	+	95.7290i	0.265569	+	0.105428i
$909$	835.868			0.919547
$910$	−655.885	+	445.299i	−0.720753	+	0.489340i
$911$			577.916i			0.634375i	0.948363	+	0.317188i	$0.102739\pi$
$911$			577.916i			0.634375i	−0.948363	+	0.317188i	$0.897261\pi$
$912$	−228.274	−	215.154i	−0.250301	−	0.235914i
$913$	−229.968			−0.251882
$914$	−150.163	−	221.177i	−0.164293	−	0.241988i
$915$		−	62.3754i		−	0.0681698i
$916$	634.082	−	1597.22i	0.692229	−	1.74369i
$917$	1256.11			1.36981
$918$	657.585	−	446.453i	0.716323	−	0.486332i
$919$			1304.76i			1.41976i	0.704321	+	0.709881i	$0.251251\pi$
$919$			1304.76i			1.41976i	−0.704321	+	0.709881i	$0.748749\pi$
$920$	69.9436	+	314.947i	0.0760257	+	0.342333i
$921$	−133.416			−0.144860
$922$	−343.551	−	506.020i	−0.372615	−	0.548829i
$923$			834.234i			0.903829i
$924$	−85.7805	−	34.0540i	−0.0928360	−	0.0368550i
$925$	−173.700			−0.187783
$926$	−777.317	+	527.742i	−0.839435	+	0.569916i
$927$		−	862.487i		−	0.930407i
$928$	122.205	−	760.276i	0.131687	−	0.819263i
$929$	−335.256			−0.360879			−0.180439	−	0.983586i	$-0.557752\pi$
$929$	−335.256			−0.360879			−0.180439	+	0.983586i	$0.557752\pi$
$930$	−33.6846	−	49.6144i	−0.0362200	−	0.0533488i
$931$		−	791.065i		−	0.849694i
$932$	563.334	−	1419.01i	0.604436	−	1.52254i
$933$	−242.891			−0.260333
$934$	970.380	−	658.818i	1.03895	−	0.705373i
$935$		−	218.241i		−	0.233413i
$936$	−1297.18	+	288.078i	−1.38587	+	0.307776i
$937$	−227.848			−0.243168			−0.121584	−	0.992581i	$-0.538797\pi$
$937$	−227.848			−0.243168			−0.121584	+	0.992581i	$0.538797\pi$
$938$	−1108.39	−	1632.56i	−1.18165	−	1.74047i
$939$		−	306.397i		−	0.326302i
$940$	−417.733	−	165.836i	−0.444396	−	0.176421i
$941$	427.841			0.454667			0.227333	−	0.973817i	$-0.426999\pi$
$941$	427.841			0.454667			0.227333	+	0.973817i	$0.426999\pi$
$942$	120.756	−	81.9847i	0.128191	−	0.0870326i
$943$			313.430i			0.332375i
$944$	−1112.02	+	1179.83i	−1.17798	+	1.24982i
$945$	270.634			0.286385
$946$	−49.7190	−	73.2316i	−0.0525571	−	0.0774118i
$947$		−	554.025i		−	0.585032i	−0.956261	−	0.292516i	$-0.905508\pi$
$947$		−	554.025i		−	0.585032i	0.956261	−	0.292516i	$-0.0944924\pi$
$948$	−5.85712	+	14.7538i	−0.00617839	+	0.0155631i
$949$	−125.954			−0.132722
$950$	208.960	−	141.869i	0.219958	−	0.149336i
$951$			220.328i			0.231681i
$952$	457.421	+	2059.70i	0.480484	+	2.16356i
$953$	1060.57			1.11287			0.556436	−	0.830891i	$-0.312169\pi$
$953$	1060.57			1.11287			0.556436	+	0.830891i	$0.312169\pi$
$954$	−966.085	−	1422.96i	−1.01267	−	1.49157i
$955$		−	156.234i		−	0.163595i
$956$	1216.74	+	483.035i	1.27274	+	0.505267i
$957$	61.9519			0.0647355
$958$	380.017	−	258.004i	0.396678	−	0.269316i
$959$			708.236i			0.738515i
$960$	47.0214	+	100.644i	0.0489807	+	0.104838i
$961$	662.583			0.689472
$962$	−771.937	−	1136.99i	−0.802430	−	1.18191i
$963$		−	1370.56i		−	1.42322i
$964$	−482.651	+	1215.77i	−0.500675	+	1.26118i
$965$	391.957			0.406173
$966$	207.606	−	140.950i	0.214913	−	0.145911i
$967$			754.326i			0.780068i	0.920800	+	0.390034i	$0.127537\pi$
$967$			754.326i			0.780068i	−0.920800	+	0.390034i	$0.872463\pi$
$968$	−85.9070	+	19.0783i	−0.0887469	+	0.0197090i
$969$	−576.944			−0.595401
$970$	−0.774685	−	1.14104i	−0.000798644	−	0.00117633i
$971$		−	71.2361i		−	0.0733637i	−0.999327	−	0.0366818i	$-0.988321\pi$
$971$		−	71.2361i		−	0.0733637i	0.999327	−	0.0366818i	$-0.0116788\pi$
$972$	639.716	+	253.961i	0.658144	+	0.261277i
$973$	−1469.15			−1.50992
$974$	−703.423	+	477.574i	−0.722201	+	0.490323i
$975$			76.7686i			0.0787371i
$976$	418.417	+	394.368i	0.428705	+	0.404065i
$977$	678.412			0.694383			0.347191	−	0.937794i	$-0.387135\pi$
$977$	678.412			0.694383			0.347191	+	0.937794i	$0.387135\pi$
$978$	−251.362	−	370.233i	−0.257016	−	0.378561i
$979$			266.383i			0.272097i
$980$	−103.366	+	260.374i	−0.105475	+	0.265688i
$981$	568.547			0.579559
$982$	228.159	−	154.903i	0.232341	−	0.157743i
$983$		−	234.489i		−	0.238545i	−0.992862	−	0.119272i	$-0.961944\pi$
$983$		−	234.489i		−	0.238545i	0.992862	−	0.119272i	$-0.0380561\pi$
$984$	23.3975	+	105.356i	0.0237779	+	0.107069i
$985$	−591.597			−0.600606
$986$	−795.523	−	1171.73i	−0.806818	−	1.18837i
$987$			349.578i			0.354183i
$988$	1857.28	+	737.322i	1.87984	+	0.746277i
$989$	240.660			0.243337
$990$	103.049	−	69.9626i	0.104089	−	0.0706693i
$991$			384.777i			0.388271i	0.980975	+	0.194136i	$0.0621902\pi$
$991$			384.777i			0.388271i	−0.980975	+	0.194136i	$0.937810\pi$
$992$	545.786	+	87.7288i	0.550188	+	0.0884363i
$993$	193.960			0.195328
$994$	424.642	+	625.459i	0.427205	+	0.629234i
$995$			461.544i			0.463864i
$996$	79.4384	−	200.101i	0.0797574	−	0.200905i
$997$	1012.38			1.01543			0.507715	−	0.861525i	$-0.330490\pi$
$997$	1012.38			1.01543			0.507715	+	0.861525i	$0.330490\pi$
$998$	206.360	−	140.104i	0.206774	−	0.140384i
$999$			469.151i			0.469620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.c.a.111.11	✓	40
4.3	odd	2	inner	220.3.c.a.111.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.c.a.111.11	✓	40	1.1	even	1	trivial
220.3.c.a.111.12	yes	40	4.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12341 - 1.65468i) q^{2} -0.776243i q^{3} +(-1.47591 + 3.71775i) q^{4} -2.23607 q^{5} +(-1.28443 + 0.872037i) q^{6} -8.96218i q^{7} +(7.80973 - 1.73439i) q^{8} +8.39745 q^{9} +(2.51201 + 3.69997i) q^{10} -3.31662i q^{11} +(2.88588 + 1.14567i) q^{12} -19.7795 q^{13} +(-14.8295 + 10.0682i) q^{14} +1.73573i q^{15} +(-11.6434 - 10.9742i) q^{16} -29.4276 q^{17} +(-9.43375 - 13.8951i) q^{18} +25.2569i q^{19} +(3.30024 - 8.31315i) q^{20} -6.95683 q^{21} +(-5.48794 + 3.72592i) q^{22} -18.0350i q^{23} +(-1.34631 - 6.06225i) q^{24} +5.00000 q^{25} +(22.2205 + 32.7287i) q^{26} -13.5046i q^{27} +(33.3192 + 13.2274i) q^{28} -24.0636 q^{29} +(2.87208 - 1.94993i) q^{30} -17.2747i q^{31} +(-5.07844 + 31.5945i) q^{32} -2.57451 q^{33} +(33.0592 + 48.6932i) q^{34} +20.0401i q^{35} +(-12.3939 + 31.2196i) q^{36} -34.7399 q^{37} +(41.7921 - 28.3738i) q^{38} +15.3537i q^{39} +(-17.4631 + 3.87822i) q^{40} -17.3790 q^{41} +(7.81536 + 11.5113i) q^{42} +13.3441i q^{43} +(12.3304 + 4.89505i) q^{44} -18.7773 q^{45} +(-29.8421 + 20.2606i) q^{46} -50.2496i q^{47} +(-8.51861 + 9.03808i) q^{48} -31.3207 q^{49} +(-5.61704 - 8.27339i) q^{50} +22.8430i q^{51} +(29.1929 - 73.5354i) q^{52} +102.407 q^{53} +(-22.3458 + 15.1712i) q^{54} +7.41620i q^{55} +(-15.5439 - 69.9922i) q^{56} +19.6055 q^{57} +(27.0332 + 39.8175i) q^{58} -101.330i q^{59} +(-6.45302 - 2.56179i) q^{60} -35.9361 q^{61} +(-28.5841 + 19.4066i) q^{62} -75.2595i q^{63} +(57.9838 - 27.0903i) q^{64} +44.2284 q^{65} +(2.89222 + 4.25998i) q^{66} +110.089i q^{67} +(43.4326 - 109.405i) q^{68} -13.9995 q^{69} +(33.1598 - 22.5131i) q^{70} -42.1766i q^{71} +(65.5818 - 14.5645i) q^{72} +6.36787 q^{73} +(39.0271 + 57.4834i) q^{74} -3.88122i q^{75} +(-93.8990 - 37.2770i) q^{76} -29.7242 q^{77} +(25.4055 - 17.2485i) q^{78} +5.11241i q^{79} +(26.0354 + 24.5390i) q^{80} +65.0941 q^{81} +(19.5237 + 28.7566i) q^{82} -69.3381i q^{83} +(10.2677 - 25.8638i) q^{84} +65.8021 q^{85} +(22.0801 - 14.9908i) q^{86} +18.6792i q^{87} +(-5.75233 - 25.9019i) q^{88} -80.3175 q^{89} +(21.0945 + 31.0703i) q^{90} +177.268i q^{91} +(67.0496 + 26.6181i) q^{92} -13.4094 q^{93} +(-83.1469 + 56.4508i) q^{94} -56.4762i q^{95} +(24.5250 + 3.94210i) q^{96} -0.308392 q^{97} +(35.1859 + 51.8257i) q^{98} -27.8512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} + 36 q^{8} - 120 q^{9} + 20 q^{10} - 80 q^{12} + 32 q^{13} - 56 q^{14} + 40 q^{16} + 16 q^{18} - 20 q^{20} - 80 q^{21} + 104 q^{24} + 200 q^{25} + 100 q^{26} + 60 q^{28} - 48 q^{29} - 280 q^{32}+ \cdots + 680 q^{98}+O(q^{100}) \) 40 * q - 4 * q^4 + 36 * q^8 - 120 * q^9 + 20 * q^10 - 80 * q^12 + 32 * q^13 - 56 * q^14 + 40 * q^16 + 16 * q^18 - 20 * q^20 - 80 * q^21 + 104 * q^24 + 200 * q^25 + 100 * q^26 + 60 * q^28 - 48 * q^29 - 280 * q^32 + 8 * q^34 + 160 * q^36 + 160 * q^37 - 200 * q^38 - 80 * q^40 - 120 * q^42 + 44 * q^44 + 80 * q^45 + 120 * q^46 - 16 * q^48 - 376 * q^49 - 36 * q^52 + 296 * q^54 - 40 * q^56 + 288 * q^57 + 96 * q^58 + 60 * q^60 - 160 * q^61 - 16 * q^62 + 500 * q^64 - 220 * q^66 + 116 * q^68 - 304 * q^69 - 60 * q^70 - 380 * q^72 - 480 * q^73 - 320 * q^74 - 480 * q^76 + 744 * q^78 - 80 * q^80 + 280 * q^81 - 480 * q^82 + 16 * q^84 + 320 * q^85 - 460 * q^86 + 224 * q^89 - 60 * q^90 + 24 * q^92 + 480 * q^93 + 432 * q^94 + 424 * q^96 + 720 * q^97 + 680 * q^98

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