LMFDB - Embedded newform 220.3.c.a.111.23

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			111.23
Character	$\chi$	$=$	220.111
Dual form			220.3.c.a.111.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00238754 - 2.00000i) q^{2} -5.13249i q^{3} +(-3.99999 + 0.00955014i) q^{4} -2.23607 q^{5} +(-10.2650 + 0.0122540i) q^{6} +6.37838i q^{7} +(0.0286504 + 7.99995i) q^{8} -17.3424 q^{9} +(0.00533870 + 4.47213i) q^{10} -3.31662i q^{11} +(0.0490160 + 20.5299i) q^{12} -1.30510 q^{13} +(12.7568 - 0.0152286i) q^{14} +11.4766i q^{15} +(15.9998 - 0.0764009i) q^{16} -24.9568 q^{17} +(0.0414057 + 34.6848i) q^{18} -29.5076i q^{19} +(8.94425 - 0.0213548i) q^{20} +32.7370 q^{21} +(-6.63324 + 0.00791857i) q^{22} -4.05241i q^{23} +(41.0596 - 0.147048i) q^{24} +5.00000 q^{25} +(0.00311597 + 2.61019i) q^{26} +42.8174i q^{27} +(-0.0609144 - 25.5135i) q^{28} -6.14231 q^{29} +(22.9532 - 0.0274008i) q^{30} +16.6988i q^{31} +(-0.191002 - 31.9994i) q^{32} -17.0225 q^{33} +(0.0595853 + 49.9136i) q^{34} -14.2625i q^{35} +(69.3695 - 0.165623i) q^{36} -11.3744 q^{37} +(-59.0151 + 0.0704504i) q^{38} +6.69839i q^{39} +(-0.0640642 - 17.8884i) q^{40} -46.1717 q^{41} +(-0.0781607 - 65.4739i) q^{42} -51.0071i q^{43} +(0.0316742 + 13.2665i) q^{44} +38.7788 q^{45} +(-8.10481 + 0.00967527i) q^{46} +74.9308i q^{47} +(-0.392127 - 82.1189i) q^{48} +8.31626 q^{49} +(-0.0119377 - 9.99999i) q^{50} +128.090i q^{51} +(5.22037 - 0.0124639i) q^{52} -52.6013 q^{53} +(85.6347 - 0.102228i) q^{54} +7.41620i q^{55} +(-51.0267 + 0.182743i) q^{56} -151.447 q^{57} +(0.0146650 + 12.2846i) q^{58} -11.6650i q^{59} +(-0.109603 - 45.9062i) q^{60} +62.5903 q^{61} +(33.3975 - 0.0398689i) q^{62} -110.617i q^{63} +(-63.9984 + 0.458403i) q^{64} +2.91828 q^{65} +(0.0406419 + 34.0450i) q^{66} +49.7495i q^{67} +(99.8269 - 0.238341i) q^{68} -20.7989 q^{69} +(-28.5250 + 0.0340522i) q^{70} -132.219i q^{71} +(-0.496867 - 138.738i) q^{72} -113.628 q^{73} +(0.0271567 + 22.7487i) q^{74} -25.6624i q^{75} +(0.281802 + 118.030i) q^{76} +21.1547 q^{77} +(13.3968 - 0.0159927i) q^{78} -144.683i q^{79} +(-35.7767 + 0.170838i) q^{80} +63.6778 q^{81} +(0.110237 + 92.3433i) q^{82} -67.6918i q^{83} +(-130.947 + 0.312643i) q^{84} +55.8051 q^{85} +(-102.014 + 0.121781i) q^{86} +31.5253i q^{87} +(26.5328 - 0.0950226i) q^{88} +155.770 q^{89} +(-0.0925859 - 77.5576i) q^{90} -8.32440i q^{91} +(0.0387011 + 16.2096i) q^{92} +85.7061 q^{93} +(149.861 - 0.178900i) q^{94} +65.9809i q^{95} +(-164.237 + 0.980315i) q^{96} +163.943 q^{97} +(-0.0198554 - 16.6325i) q^{98} +57.5183i 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 $

$2$	−0.00238754	−	2.00000i	−0.00119377	−	0.999999i
$2$	−0.00238754	−	2.00000i	−0.00119377	−	0.999999i
$3$		−	5.13249i		−	1.71083i	−0.517944	−	0.855414i	$-0.673302\pi$
$3$		−	5.13249i		−	1.71083i	0.517944	−	0.855414i	$-0.326698\pi$
$4$	−3.99999	+	0.00955014i	−0.999997	+	0.00238754i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	−10.2650	+	0.0122540i	−1.71083	+	0.00204233i
$7$			6.37838i			0.911197i	0.890185	+	0.455599i	$0.150575\pi$
$7$			6.37838i			0.911197i	−0.890185	+	0.455599i	$0.849425\pi$
$8$	0.0286504	+	7.99995i	0.00358130	+	0.999994i
$9$	−17.3424			−1.92694
$10$	0.00533870	+	4.47213i	0.000533870	+	0.447213i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	0.0490160	+	20.5299i	0.00408467	+	1.71082i
$13$	−1.30510			−0.100392			−0.0501960	−	0.998739i	$-0.515985\pi$
$13$	−1.30510			−0.100392			−0.0501960	+	0.998739i	$0.515985\pi$
$14$	12.7568	−	0.0152286i	0.911197	−	0.00108776i
$15$			11.4766i			0.765106i
$16$	15.9998	−	0.0764009i	0.999989	−	0.00477506i
$17$	−24.9568			−1.46805			−0.734024	−	0.679124i	$-0.762360\pi$
$17$	−24.9568			−1.46805			−0.734024	+	0.679124i	$0.762360\pi$
$18$	0.0414057	+	34.6848i	0.00230032	+	1.92693i
$19$		−	29.5076i		−	1.55303i	−0.630099	−	0.776515i	$-0.716986\pi$
$19$		−	29.5076i		−	1.55303i	0.630099	−	0.776515i	$-0.283014\pi$
$20$	8.94425	−	0.0213548i	0.447212	−	0.00106774i
$21$	32.7370			1.55890
$22$	−6.63324	+	0.00791857i	−0.301511	+	0.000359935i
$23$		−	4.05241i		−	0.176192i	−0.996112	−	0.0880958i	$-0.971922\pi$
$23$		−	4.05241i		−	0.176192i	0.996112	−	0.0880958i	$-0.0280782\pi$
$24$	41.0596	−	0.147048i	1.71082	−	0.00612699i
$25$	5.00000			0.200000
$26$	0.00311597	+	2.61019i	0.000119845	+	0.100392i
$27$			42.8174i			1.58583i
$28$	−0.0609144	−	25.5135i	−0.00217552	−	0.911195i
$29$	−6.14231			−0.211804			−0.105902	−	0.994377i	$-0.533773\pi$
$29$	−6.14231			−0.211804			−0.105902	+	0.994377i	$0.533773\pi$
$30$	22.9532	−	0.0274008i	0.765105	−	0.000913360i
$31$			16.6988i			0.538669i	0.963047	+	0.269335i	$0.0868038\pi$
$31$			16.6988i			0.538669i	−0.963047	+	0.269335i	$0.913196\pi$
$32$	−0.191002	−	31.9994i	−0.00596881	−	0.999982i
$33$	−17.0225			−0.515834
$34$	0.0595853	+	49.9136i	0.00175251	+	1.46805i
$35$		−	14.2625i		−	0.407500i
$36$	69.3695	−	0.165623i	1.92693	−	0.00460063i
$37$	−11.3744			−0.307415			−0.153708	−	0.988116i	$-0.549121\pi$
$37$	−11.3744			−0.307415			−0.153708	+	0.988116i	$0.549121\pi$
$38$	−59.0151	+	0.0704504i	−1.55303	+	0.00185396i
$39$			6.69839i			0.171754i
$40$	−0.0640642	−	17.8884i	−0.00160161	−	0.447211i
$41$	−46.1717			−1.12614			−0.563069	−	0.826410i	$-0.690380\pi$
$41$	−46.1717			−1.12614			−0.563069	+	0.826410i	$0.690380\pi$
$42$	−0.0781607	−	65.4739i	−0.00186097	−	1.55890i
$43$		−	51.0071i		−	1.18621i	−0.805124	−	0.593106i	$-0.797901\pi$
$43$		−	51.0071i		−	1.18621i	0.805124	−	0.593106i	$-0.202099\pi$
$44$	0.0316742	+	13.2665i	0.000719869	+	0.301510i
$45$	38.7788			0.861752
$46$	−8.10481	+	0.00967527i	−0.176191	+	0.000210332i
$47$			74.9308i			1.59427i	0.603800	+	0.797136i	$0.293653\pi$
$47$			74.9308i			1.59427i	−0.603800	+	0.797136i	$0.706347\pi$
$48$	−0.392127	−	82.1189i	−0.00816931	−	1.71081i
$49$	8.31626			0.169720
$50$	−0.0119377	−	9.99999i	−0.000238754	−	0.200000i
$51$			128.090i			2.51158i
$52$	5.22037	−	0.0124639i	0.100392	−	0.000239689i
$53$	−52.6013			−0.992478			−0.496239	−	0.868186i	$-0.665286\pi$
$53$	−52.6013			−0.992478			−0.496239	+	0.868186i	$0.665286\pi$
$54$	85.6347	−	0.102228i	1.58583	−	0.00189311i
$55$			7.41620i			0.134840i
$56$	−51.0267	+	0.182743i	−0.911191	+	0.00326327i
$57$	−151.447			−2.65697
$58$	0.0146650	+	12.2846i	0.000252845	+	0.211804i
$59$		−	11.6650i		−	0.197712i	−0.995102	−	0.0988560i	$-0.968482\pi$
$59$		−	11.6650i		−	0.197712i	0.995102	−	0.0988560i	$-0.0315183\pi$
$60$	−0.109603	−	45.9062i	−0.00182672	−	0.765104i
$61$	62.5903			1.02607			0.513035	−	0.858368i	$-0.328521\pi$
$61$	62.5903			1.02607			0.513035	+	0.858368i	$0.328521\pi$
$62$	33.3975	−	0.0398689i	0.538669	−	0.000643047i
$63$		−	110.617i		−	1.75582i
$64$	−63.9984	+	0.458403i	−0.999974	+	0.00716255i
$65$	2.91828			0.0448967
$66$	0.0406419	+	34.0450i	0.000615787	+	0.515834i
$67$			49.7495i			0.742529i	0.928527	+	0.371265i	$0.121076\pi$
$67$			49.7495i			0.742529i	−0.928527	+	0.371265i	$0.878924\pi$
$68$	99.8269	−	0.238341i	1.46804	−	0.00350502i
$69$	−20.7989			−0.301434
$70$	−28.5250	+	0.0340522i	−0.407500	+	0.000486461i
$71$		−	132.219i		−	1.86224i	−0.364708	−	0.931122i	$-0.618831\pi$
$71$		−	132.219i		−	1.86224i	0.364708	−	0.931122i	$-0.381169\pi$
$72$	−0.496867	−	138.738i	−0.00690093	−	1.92692i
$73$	−113.628			−1.55655			−0.778277	−	0.627921i	$-0.783906\pi$
$73$	−113.628			−1.55655			−0.778277	+	0.627921i	$0.783906\pi$
$74$	0.0271567	+	22.7487i	0.000366982	+	0.307415i
$75$		−	25.6624i		−	0.342166i
$76$	0.281802	+	118.030i	0.00370792	+	1.55303i
$77$	21.1547			0.274736
$78$	13.3968	−	0.0159927i	0.171753	−	0.000205034i
$79$		−	144.683i		−	1.83143i	−0.401824	−	0.915717i	$-0.631624\pi$
$79$		−	144.683i		−	1.83143i	0.401824	−	0.915717i	$-0.368376\pi$
$80$	−35.7767	+	0.170838i	−0.447208	+	0.00213547i
$81$	63.6778			0.786145
$82$	0.110237	+	92.3433i	0.00134435	+	1.12614i
$83$		−	67.6918i		−	0.815564i	−0.913079	−	0.407782i	$-0.866302\pi$
$83$		−	67.6918i		−	0.815564i	0.913079	−	0.407782i	$-0.133698\pi$
$84$	−130.947	+	0.312643i	−1.55890	+	0.00372194i
$85$	55.8051			0.656531
$86$	−102.014	+	0.121781i	−1.18621	+	0.00141606i
$87$			31.5253i			0.362360i
$88$	26.5328	−	0.0950226i	0.301509	−	0.00107980i
$89$	155.770			1.75022			0.875111	−	0.483922i	$-0.160788\pi$
$89$	155.770			1.75022			0.875111	+	0.483922i	$0.160788\pi$
$90$	−0.0925859	−	77.5576i	−0.00102873	−	0.861751i
$91$		−	8.32440i		−	0.0914769i
$92$	0.0387011	+	16.2096i	0.000420664	+	0.176191i
$93$	85.7061			0.921571
$94$	149.861	−	0.178900i	1.59427	−	0.00190319i
$95$			65.9809i			0.694536i
$96$	−164.237	+	0.980315i	−1.71080	+	0.0102116i
$97$	163.943			1.69014			0.845069	−	0.534658i	$-0.179560\pi$
$97$	163.943			1.69014			0.845069	+	0.534658i	$0.179560\pi$
$98$	−0.0198554	−	16.6325i	−0.000202606	−	0.169719i
$99$			57.5183i			0.580993i
$100$	−19.9999	+	0.0477507i	−0.199999	+	0.000477507i
$101$	−147.497			−1.46036			−0.730181	−	0.683253i	$-0.760564\pi$
$101$	−147.497			−1.46036			−0.730181	+	0.683253i	$0.760564\pi$
$102$	256.181	−	0.305821i	2.51158	−	0.00299824i
$103$		−	95.6826i		−	0.928958i	−0.885584	−	0.464479i	$-0.846242\pi$
$103$		−	95.6826i		−	0.928958i	0.885584	−	0.464479i	$-0.153758\pi$
$104$	−0.0373915	−	10.4407i	−0.000359534	−	0.100391i
$105$	−73.2021			−0.697162
$106$	0.125588	+	105.203i	0.00118479	+	0.992477i
$107$		−	57.9162i		−	0.541273i	−0.962682	−	0.270637i	$-0.912766\pi$
$107$		−	57.9162i		−	0.541273i	0.962682	−	0.270637i	$-0.0872342\pi$
$108$	−0.408912	−	171.269i	−0.00378622	−	1.58582i
$109$	89.1432			0.817827			0.408914	−	0.912573i	$-0.365908\pi$
$109$	89.1432			0.817827			0.408914	+	0.912573i	$0.365908\pi$
$110$	14.8324	−	0.0177065i	0.134840	−	0.000160968i
$111$			58.3787i			0.525935i
$112$	0.487314	+	102.053i	0.00435102	+	0.911187i
$113$	−112.390			−0.994599			−0.497299	−	0.867579i	$-0.665675\pi$
$113$	−112.390			−0.994599			−0.497299	+	0.867579i	$0.665675\pi$
$114$	0.361586	+	302.894i	0.00317181	+	2.65697i
$115$			9.06146i			0.0787953i
$116$	24.5692	−	0.0586600i	0.211803	−	0.000505689i
$117$	22.6335			0.193449
$118$	−23.3300	+	0.0278506i	−0.197712	+	0.000236022i
$119$		−	159.184i		−	1.33768i
$120$	−91.8121	+	0.328809i	−0.765101	+	0.00274007i
$121$	−11.0000			−0.0909091
$122$	−0.149437	−	125.181i	−0.00122489	−	1.02607i
$123$			236.975i			1.92663i
$124$	−0.159475	−	66.7948i	−0.00128609	−	0.538668i
$125$	−11.1803			−0.0894427
$126$	−221.233	+	0.264101i	−1.75582	+	0.00209604i
$127$		−	18.1115i		−	0.142610i	−0.997455	−	0.0713050i	$-0.977284\pi$
$127$		−	18.1115i		−	0.142610i	0.997455	−	0.0713050i	$-0.0227164\pi$
$128$	1.06960	+	127.996i	0.00835629	+	0.999965i
$129$	−261.794			−2.02941
$130$	−0.00696751	−	5.83656i	−5.35962e−5	−	0.0448966i
$131$		−	137.311i		−	1.04818i	−0.851664	−	0.524088i	$-0.824406\pi$
$131$		−	137.311i		−	1.04818i	0.851664	−	0.524088i	$-0.175594\pi$
$132$	68.0899	−	0.162568i	0.515833	−	0.00123157i
$133$	188.211			1.41512
$134$	99.4989	−	0.118779i	0.742529	−	0.000886408i
$135$		−	95.7425i		−	0.709204i
$136$	−0.715022	−	199.653i	−0.00525752	−	1.46804i
$137$	−93.7355			−0.684201			−0.342100	−	0.939663i	$-0.611138\pi$
$137$	−93.7355			−0.684201			−0.342100	+	0.939663i	$0.611138\pi$
$138$	0.0496582	+	41.5978i	0.000359842	+	0.301433i
$139$			235.100i			1.69137i	0.533684	+	0.845684i	$0.320807\pi$
$139$			235.100i			1.69137i	−0.533684	+	0.845684i	$0.679193\pi$
$140$	0.136209	+	57.0498i	0.000972920	+	0.407499i
$141$	384.581			2.72753
$142$	−264.438	+	0.315679i	−1.86224	+	0.00222309i
$143$			4.32851i			0.0302693i
$144$	−277.476	+	1.32498i	−1.92691	+	0.00920123i
$145$	13.7346			0.0947216
$146$	0.271292	+	227.257i	0.00185817	+	1.55655i
$147$		−	42.6831i		−	0.290361i
$148$	45.4973	−	0.108627i	0.307414	−	0.000733964i
$149$	4.77550			0.0320503			0.0160252	−	0.999872i	$-0.494899\pi$
$149$	4.77550			0.0320503			0.0160252	+	0.999872i	$0.494899\pi$
$150$	−51.3248	+	0.0612700i	−0.342166	+	0.000408467i
$151$			209.061i			1.38451i	0.721654	+	0.692253i	$0.243382\pi$
$151$			209.061i			1.38451i	−0.721654	+	0.692253i	$0.756618\pi$
$152$	236.059	−	0.845404i	1.55302	−	0.00556187i
$153$	432.811			2.82883
$154$	−0.0505076	−	42.3094i	−0.000327972	−	0.274736i
$155$		−	37.3395i		−	0.240900i
$156$	−0.0639706	−	26.7935i	−0.000410068	−	0.171753i
$157$	−35.9558			−0.229018			−0.114509	−	0.993422i	$-0.536529\pi$
$157$	−35.9558			−0.229018			−0.114509	+	0.993422i	$0.536529\pi$
$158$	−289.366	+	0.345437i	−1.83143	+	0.00218631i
$159$			269.976i			1.69796i
$160$	0.427093	+	71.5529i	0.00266933	+	0.447206i
$161$	25.8478			0.160545
$162$	−0.152033	−	127.355i	−0.000938476	−	0.786145i
$163$			170.575i			1.04647i	0.852187	+	0.523237i	$0.175276\pi$
$163$			170.575i			1.04647i	−0.852187	+	0.523237i	$0.824724\pi$
$164$	184.686	−	0.440946i	1.12613	−	0.00268870i
$165$	38.0635			0.230688
$166$	−135.383	+	0.161617i	−0.815563	+	0.000973594i
$167$			96.8359i			0.579856i	0.957049	+	0.289928i	$0.0936313\pi$
$167$			96.8359i			0.579856i	−0.957049	+	0.289928i	$0.906369\pi$
$168$	0.937927	+	261.894i	0.00558290	+	1.55889i
$169$	−167.297			−0.989921
$170$	−0.133237	−	111.610i	−0.000783746	−	0.656530i
$171$			511.733i			2.99259i
$172$	0.487126	+	204.028i	0.00283213	+	1.18621i
$173$	72.3360			0.418127			0.209064	−	0.977902i	$-0.432958\pi$
$173$	72.3360			0.418127			0.209064	+	0.977902i	$0.432958\pi$
$174$	63.0506	−	0.0752679i	0.362360	−	0.000432574i
$175$			31.8919i			0.182239i
$176$	−0.253393	−	53.0654i	−0.00143973	−	0.301508i
$177$	−59.8705			−0.338251
$178$	−0.371906	−	311.539i	−0.00208936	−	1.75022i
$179$		−	234.477i		−	1.30993i	−0.755661	−	0.654963i	$-0.772684\pi$
$179$		−	234.477i		−	1.30993i	0.755661	−	0.654963i	$-0.227316\pi$
$180$	−155.115	+	0.370343i	−0.861749	+	0.00205746i
$181$	301.119			1.66364			0.831821	−	0.555044i	$-0.187299\pi$
$181$	301.119			1.66364			0.831821	+	0.555044i	$0.187299\pi$
$182$	−16.6488	+	0.0198748i	−0.0914768	+	0.000109202i
$183$		−	321.244i		−	1.75543i
$184$	32.4190	−	0.116103i	0.176190	−	0.000630995i
$185$	25.4338			0.137480
$186$	−0.204627	−	171.412i	−0.00110014	−	0.921570i
$187$			82.7724i			0.442633i
$188$	−0.715599	−	299.722i	−0.00380638	−	1.59427i
$189$	−273.105			−1.44500
$190$	131.962	−	0.157532i	0.694536	−	0.000829116i
$191$		−	270.501i		−	1.41624i	−0.706094	−	0.708118i	$-0.749544\pi$
$191$		−	270.501i		−	1.41624i	0.706094	−	0.708118i	$-0.250456\pi$
$192$	2.35275	+	328.471i	0.0122539	+	1.71079i
$193$	82.1894			0.425852			0.212926	−	0.977068i	$-0.431701\pi$
$193$	82.1894			0.425852			0.212926	+	0.977068i	$0.431701\pi$
$194$	−0.391421	−	327.886i	−0.00201763	−	1.69014i
$195$		−	14.9780i		−	0.0768105i
$196$	−33.2649	+	0.0794215i	−0.169719	+	0.000405211i
$197$	−33.7745			−0.171444			−0.0857220	−	0.996319i	$-0.527320\pi$
$197$	−33.7745			−0.171444			−0.0857220	+	0.996319i	$0.527320\pi$
$198$	115.037	−	0.137327i	0.580993	−	0.000693571i
$199$		−	93.9901i		−	0.472312i	−0.971715	−	0.236156i	$-0.924112\pi$
$199$		−	93.9901i		−	0.472312i	0.971715	−	0.236156i	$-0.0758877\pi$
$200$	0.143252	+	39.9997i	0.000716260	+	0.199999i
$201$	255.338			1.27034
$202$	0.352154	+	294.993i	0.00174334	+	1.46036i
$203$		−	39.1780i		−	0.192995i
$204$	−1.22328	−	512.360i	−0.00599648	−	2.51157i
$205$	103.243			0.503624
$206$	−191.365	+	0.228446i	−0.928957	+	0.00110896i
$207$			70.2785i			0.339510i
$208$	−20.8813	+	0.0997105i	−0.100391	+	0.000479378i
$209$	−97.8656			−0.468256
$210$	0.174773	+	146.404i	0.000832251	+	0.697162i
$211$		−	152.131i		−	0.720998i	−0.932760	−	0.360499i	$-0.882606\pi$
$211$		−	152.131i		−	0.720998i	0.932760	−	0.360499i	$-0.117394\pi$
$212$	210.405	−	0.502350i	0.992475	−	0.00236958i
$213$	−678.614			−3.18598
$214$	−115.832	+	0.138277i	−0.541273	+	0.000646155i
$215$			114.055i			0.530490i
$216$	−342.537	+	1.22673i	−1.58582	+	0.00567933i
$217$	−106.511			−0.490834
$218$	−0.212833	−	178.286i	−0.000976296	−	0.817827i
$219$			583.196i			2.66300i
$220$	−0.0708258	−	29.6647i	−0.000321935	−	0.134840i
$221$	32.5710			0.147380
$222$	116.757	−	0.139381i	0.525934	−	0.000627844i
$223$		−	102.083i		−	0.457770i	−0.973453	−	0.228885i	$-0.926492\pi$
$223$		−	102.083i		−	0.457770i	0.973453	−	0.228885i	$-0.0735079\pi$
$224$	204.105	−	1.21828i	0.911181	−	0.00543876i
$225$	−86.7121			−0.385387
$226$	0.268334	+	224.779i	0.00118732	+	0.994598i
$227$		−	266.438i		−	1.17373i	−0.809683	−	0.586867i	$-0.800361\pi$
$227$		−	266.438i		−	1.17373i	0.809683	−	0.586867i	$-0.199639\pi$
$228$	605.787	−	1.44634i	2.65696	−	0.00634361i
$229$	145.674			0.636131			0.318066	−	0.948069i	$-0.396967\pi$
$229$	145.674			0.636131			0.318066	+	0.948069i	$0.396967\pi$
$230$	18.1229	−	0.0216346i	0.0787952	−	9.40633e-5i
$231$		−	108.576i		−	0.470027i
$232$	−0.175980	−	49.1382i	−0.000758533	−	0.211803i
$233$	89.3191			0.383344			0.191672	−	0.981459i	$-0.438609\pi$
$233$	89.3191			0.383344			0.191672	+	0.981459i	$0.438609\pi$
$234$	−0.0540384	−	45.2670i	−0.000230933	−	0.193449i
$235$		−	167.550i		−	0.712980i
$236$	0.111403	+	46.6599i	0.000472045	+	0.197711i
$237$	−742.585			−3.13327
$238$	−318.368	+	0.380058i	−1.33768	+	0.00159688i
$239$		−	43.5101i		−	0.182051i	−0.995849	−	0.0910253i	$-0.970986\pi$
$239$		−	43.5101i		−	0.182051i	0.995849	−	0.0910253i	$-0.0290144\pi$
$240$	0.876822	+	183.623i	0.00365343	+	0.765097i
$241$	62.7643			0.260433			0.130216	−	0.991486i	$-0.458433\pi$
$241$	62.7643			0.260433			0.130216	+	0.991486i	$0.458433\pi$
$242$	0.0262629	+	22.0000i	0.000108524	+	0.0909090i
$243$			58.5309i			0.240868i
$244$	−250.360	+	0.597746i	−1.02607	+	0.00244978i
$245$	−18.5957			−0.0759009
$246$	473.951	−	0.565788i	1.92663	−	0.00229995i
$247$			38.5102i			0.155912i
$248$	−133.589	+	0.478426i	−0.538666	+	0.00192914i
$249$	−347.427			−1.39529
$250$	0.0266935	+	22.3607i	0.000106774	+	0.0894427i
$251$			297.853i			1.18666i	0.804958	+	0.593332i	$0.202188\pi$
$251$			297.853i			1.18666i	−0.804958	+	0.593332i	$0.797812\pi$
$252$	1.05640	+	442.465i	0.00419208	+	1.75581i
$253$	−13.4403			−0.0531238
$254$	−36.2229	+	0.0432418i	−0.142610	+	0.000170243i
$255$		−	286.419i		−	1.12321i
$256$	255.988	−	2.44480i	0.999954	−	0.00955001i
$257$	333.576			1.29796			0.648980	−	0.760806i	$-0.275196\pi$
$257$	333.576			1.29796			0.648980	+	0.760806i	$0.275196\pi$
$258$	0.625042	+	523.587i	0.00242264	+	2.02941i
$259$		−	72.5500i		−	0.280116i
$260$	−11.6731	+	0.0278700i	−0.0448965	+	0.000107192i
$261$	106.523			0.408132
$262$	−274.622	+	0.327835i	−1.04818	+	0.00125128i
$263$		−	296.022i		−	1.12556i	−0.826608	−	0.562779i	$-0.809732\pi$
$263$		−	296.022i		−	1.12556i	0.826608	−	0.562779i	$-0.190268\pi$
$264$	−0.487702	−	136.179i	−0.00184736	−	0.515831i
$265$	117.620			0.443850
$266$	−0.449360	−	376.421i	−0.00168932	−	1.41512i
$267$		−	799.486i		−	2.99433i
$268$	−0.475115	−	198.997i	−0.00177282	−	0.742527i
$269$	352.997			1.31225			0.656127	−	0.754650i	$-0.272193\pi$
$269$	352.997			1.31225			0.656127	+	0.754650i	$0.272193\pi$
$270$	−191.485	+	0.228589i	−0.709204	+	0.000846626i
$271$		−	34.7106i		−	0.128083i	−0.997947	−	0.0640417i	$-0.979601\pi$
$271$		−	34.7106i		−	0.128083i	0.997947	−	0.0640417i	$-0.0203991\pi$
$272$	−399.304	+	1.90672i	−1.46803	+	0.00701001i
$273$	−42.7249			−0.156501
$274$	0.223797	+	187.471i	0.000816778	+	0.684201i
$275$		−	16.5831i		−	0.0603023i
$276$	83.1955	−	0.198633i	0.301433	−	0.000719684i
$277$	−381.424			−1.37698			−0.688492	−	0.725244i	$-0.741727\pi$
$277$	−381.424			−1.37698			−0.688492	+	0.725244i	$0.741727\pi$
$278$	470.200	−	0.561310i	1.69137	−	0.00201910i
$279$		−	289.597i		−	1.03798i
$280$	114.099	−	0.408626i	0.407497	−	0.00145938i
$281$	−27.0493			−0.0962610			−0.0481305	−	0.998841i	$-0.515326\pi$
$281$	−27.0493			−0.0962610			−0.0481305	+	0.998841i	$0.515326\pi$
$282$	−0.918202	−	769.162i	−0.00325604	−	2.72752i
$283$			140.593i			0.496794i	0.968658	+	0.248397i	$0.0799037\pi$
$283$			140.593i			0.496794i	−0.968658	+	0.248397i	$0.920096\pi$
$284$	1.26271	+	528.876i	0.00444617	+	1.86224i
$285$	338.646			1.18823
$286$	8.65702	−	0.0103345i	0.0302693	−	3.61346e-5i
$287$		−	294.500i		−	1.02613i
$288$	3.31244	+	554.948i	0.0115015	+	1.92690i
$289$	333.842			1.15516
$290$	−0.0327919	−	27.4692i	−0.000113076	−	0.0947215i
$291$		−	841.437i		−	2.89154i
$292$	454.512	−	1.08517i	1.55655	−	0.00371633i
$293$	−268.061			−0.914885			−0.457443	−	0.889239i	$-0.651235\pi$
$293$	−268.061			−0.914885			−0.457443	+	0.889239i	$0.651235\pi$
$294$	−85.3661	+	0.101907i	−0.290361	+	0.000346624i
$295$			26.0838i			0.0884195i
$296$	−0.325880	−	90.9943i	−0.00110095	−	0.307413i
$297$	142.009			0.478145
$298$	−0.0114017	−	9.55099i	−3.82607e−5	−	0.0320503i
$299$			5.28878i			0.0176882i
$300$	0.245080	+	102.649i	0.000816933	+	0.342165i
$301$	325.343			1.08087
$302$	418.121	−	0.499140i	1.38451	−	0.00165278i
$303$			757.025i			2.49843i
$304$	−2.25441	−	472.116i	−0.00741581	−	1.55301i
$305$	−139.956			−0.458873
$306$	−1.03335	−	865.622i	−0.00337697	−	2.82883i
$307$		−	135.295i		−	0.440700i	−0.975421	−	0.220350i	$-0.929280\pi$
$307$		−	135.295i		−	0.440700i	0.975421	−	0.220350i	$-0.0707199\pi$
$308$	−84.6185	+	0.202030i	−0.274736	+	0.000655943i
$309$	−491.090			−1.58929
$310$	−74.6790	+	0.0891496i	−0.240900	+	0.000287579i
$311$			384.401i			1.23602i	0.786172	+	0.618008i	$0.212060\pi$
$311$			384.401i			1.23602i	−0.786172	+	0.618008i	$0.787940\pi$
$312$	−53.5868	+	0.191911i	−0.171752	+	0.000615101i
$313$	−181.077			−0.578520			−0.289260	−	0.957251i	$-0.593409\pi$
$313$	−181.077			−0.578520			−0.289260	+	0.957251i	$0.593409\pi$
$314$	0.0858458	+	71.9115i	0.000273394	+	0.229018i
$315$			247.346i			0.785226i
$316$	1.38175	+	578.731i	0.00437261	+	1.83143i
$317$	−89.3877			−0.281980			−0.140990	−	0.990011i	$-0.545029\pi$
$317$	−89.3877			−0.281980			−0.140990	+	0.990011i	$0.545029\pi$
$318$	539.951	−	0.644577i	1.69796	−	0.00202697i
$319$			20.3717i			0.0638613i
$320$	143.105	−	1.02502i	0.447202	−	0.00320319i
$321$	−297.254			−0.926026
$322$	−0.0617126	−	51.6956i	−0.000191654	−	0.160545i
$323$			736.415i			2.27992i
$324$	−254.710	+	0.608132i	−0.786143	+	0.00187695i
$325$	−6.52548			−0.0200784
$326$	341.150	−	0.407255i	1.04647	−	0.00124925i
$327$		−	457.526i		−	1.39916i
$328$	−1.32284	−	369.371i	−0.00403304	−	1.12613i
$329$	−477.937			−1.45270
$330$	−0.0908781	−	76.1270i	−0.000275388	−	0.230688i
$331$		−	328.048i		−	0.991082i	−0.868585	−	0.495541i	$-0.834970\pi$
$331$		−	328.048i		−	0.991082i	0.868585	−	0.495541i	$-0.165030\pi$
$332$	0.646466	+	270.766i	0.00194719	+	0.815561i
$333$	197.259			0.592369
$334$	193.672	−	0.231199i	0.579855	−	0.000692214i
$335$		−	111.243i		−	0.332069i
$336$	523.785	−	2.50113i	1.55888	−	0.00744385i
$337$	−45.2017			−0.134130			−0.0670649	−	0.997749i	$-0.521363\pi$
$337$	−45.2017			−0.134130			−0.0670649	+	0.997749i	$0.521363\pi$
$338$	0.399427	+	334.593i	0.00118174	+	0.989921i
$339$			576.838i			1.70159i
$340$	−223.220	+	0.532947i	−0.656529	+	0.00156749i
$341$	55.3835			0.162415
$342$	1023.46	−	1.22178i	2.99259	−	0.00357246i
$343$			365.585i			1.06585i
$344$	408.055	−	1.46137i	1.18621	−	0.00424818i
$345$	46.5078			0.134805
$346$	−0.172705	−	144.672i	−0.000499147	−	0.418127i
$347$			41.0192i			0.118211i	0.998252	+	0.0591054i	$0.0188248\pi$
$347$			41.0192i			0.118211i	−0.998252	+	0.0591054i	$0.981175\pi$
$348$	−0.301072	−	126.101i	−0.000865148	−	0.362359i
$349$	435.974			1.24921			0.624605	−	0.780941i	$-0.285260\pi$
$349$	435.974			1.24921			0.624605	+	0.780941i	$0.285260\pi$
$350$	63.7838	−	0.0761431i	0.182239	−	0.000217552i
$351$		−	55.8808i		−	0.159204i
$352$	−106.130	+	0.633482i	−0.301506	+	0.00179966i
$353$	272.935			0.773186			0.386593	−	0.922250i	$-0.373652\pi$
$353$	272.935			0.773186			0.386593	+	0.922250i	$0.373652\pi$
$354$	0.142943	+	119.741i	0.000403794	+	0.338251i
$355$			295.651i			0.832821i
$356$	−623.077	+	1.48762i	−1.75022	+	0.00417872i
$357$	−817.010			−2.28854
$358$	−468.953	+	0.559822i	−1.30992	+	0.00156375i
$359$			374.700i			1.04373i	0.853027	+	0.521867i	$0.174764\pi$
$359$			374.700i			1.04373i	−0.853027	+	0.521867i	$0.825236\pi$
$360$	1.11103	+	310.229i	0.00308619	+	0.861746i
$361$	−509.697			−1.41190
$362$	−0.718933	−	602.238i	−0.00198600	−	1.66364i
$363$			56.4574i			0.155530i
$364$	0.0794992	+	33.2975i	0.000218404	+	0.0914766i
$365$	254.081			0.696112
$366$	−642.487	+	0.766982i	−1.75543	+	0.00209558i
$367$			232.694i			0.634044i	0.948418	+	0.317022i	$0.102683\pi$
$367$			232.694i			0.634044i	−0.948418	+	0.317022i	$0.897317\pi$
$368$	−0.309608	−	64.8378i	−0.000841325	−	0.176190i
$369$	800.728			2.17000
$370$	−0.0607242	−	50.8676i	−0.000164120	−	0.137480i
$371$		−	335.511i		−	0.904343i
$372$	−342.823	+	0.818506i	−0.921569	+	0.00220028i
$373$	−520.658			−1.39587			−0.697934	−	0.716163i	$-0.745897\pi$
$373$	−520.658			−1.39587			−0.697934	+	0.716163i	$0.745897\pi$
$374$	165.545	−	0.197622i	0.442633	−	0.000528401i
$375$			57.3829i			0.153021i
$376$	−599.442	+	2.14680i	−1.59426	+	0.00570956i
$377$	8.01631			0.0212634
$378$	0.652050	+	546.211i	0.00172500	+	1.44500i
$379$			377.772i			0.996759i	0.866959	+	0.498380i	$0.166071\pi$
$379$			377.772i			0.996759i	−0.866959	+	0.498380i	$0.833929\pi$
$380$	−0.630127	−	263.923i	−0.00165823	−	0.694534i
$381$	−92.9568			−0.243981
$382$	−541.002	+	0.645832i	−1.41624	+	0.00169066i
$383$			527.501i			1.37729i	0.725100	+	0.688644i	$0.241793\pi$
$383$			527.501i			1.37729i	−0.725100	+	0.688644i	$0.758207\pi$
$384$	656.935	−	5.48973i	1.71077	−	0.0142962i
$385$	−47.3033			−0.122866
$386$	−0.196230	−	164.379i	−0.000508369	−	0.425852i
$387$			884.587i			2.28576i
$388$	−655.771	+	1.56568i	−1.69013	+	0.00403526i
$389$	−576.120			−1.48103			−0.740514	−	0.672040i	$-0.765418\pi$
$389$	−576.120			−1.48103			−0.740514	+	0.672040i	$0.765418\pi$
$390$	−29.9561	+	0.0357607i	−0.0768105	+	9.16940e-5i
$391$			101.135i			0.258658i
$392$	0.238264	+	66.5296i	0.000607817	+	0.169718i
$393$	−704.748			−1.79325
$394$	0.0806378	+	67.5489i	0.000204665	+	0.171444i
$395$			323.522i			0.819042i
$396$	−0.549308	−	230.073i	−0.00138714	−	0.580991i
$397$	−19.3195			−0.0486638			−0.0243319	−	0.999704i	$-0.507746\pi$
$397$	−19.3195			−0.0486638			−0.0243319	+	0.999704i	$0.507746\pi$
$398$	−187.980	+	0.224405i	−0.472312	+	0.000563832i
$399$		−	965.988i		−	2.42102i
$400$	79.9991	−	0.382005i	0.199998	−	0.000955012i
$401$	−204.104			−0.508987			−0.254494	−	0.967074i	$-0.581909\pi$
$401$	−204.104			−0.508987			−0.254494	+	0.967074i	$0.581909\pi$
$402$	−0.609630	−	510.677i	−0.00151649	−	1.27034i
$403$		−	21.7935i		−	0.0540781i
$404$	589.985	−	1.40861i	1.46036	−	0.00348667i
$405$	−142.388			−0.351575
$406$	−78.3560	+	0.0935390i	−0.192995	+	0.000230392i
$407$			37.7245i			0.0926891i
$408$	−1024.72	+	3.66984i	−2.51156	+	0.00899471i
$409$	381.984			0.933947			0.466973	−	0.884271i	$-0.345344\pi$
$409$	381.984			0.933947			0.466973	+	0.884271i	$0.345344\pi$
$410$	−0.246496	−	206.486i	−0.000601211	−	0.503624i
$411$			481.096i			1.17055i
$412$	0.913783	+	382.729i	0.00221792	+	0.928955i
$413$	74.4039			0.180155
$414$	140.557	−	0.167793i	0.339510	−	0.000405296i
$415$			151.363i			0.364731i
$416$	0.249276	+	41.7623i	0.000599221	+	0.100390i
$417$	1206.65			2.89364
$418$	0.233658	+	195.731i	0.000558990	+	0.468256i
$419$			159.870i			0.381551i	0.981634	+	0.190775i	$0.0611002\pi$
$419$			159.870i			0.381551i	−0.981634	+	0.190775i	$0.938900\pi$
$420$	292.807	−	0.699090i	0.697160	−	0.00166450i
$421$	245.508			0.583154			0.291577	−	0.956547i	$-0.405820\pi$
$421$	245.508			0.583154			0.291577	+	0.956547i	$0.405820\pi$
$422$	−304.261	+	0.363217i	−0.720997	+	0.000860705i
$423$		−	1299.48i		−	3.07206i
$424$	−1.50705	−	420.808i	−0.00355436	−	0.992472i
$425$	−124.784			−0.293609
$426$	1.62022	+	1357.23i	0.00380332	+	3.18598i
$427$			399.225i			0.934953i
$428$	0.553108	+	231.664i	0.00129231	+	0.541272i
$429$	22.2160			0.0517856
$430$	228.111	−	0.272312i	0.530490	−	0.000633283i
$431$		−	478.856i		−	1.11103i	−0.831505	−	0.555517i	$-0.812520\pi$
$431$		−	478.856i		−	1.11103i	0.831505	−	0.555517i	$-0.187480\pi$
$432$	3.27129	+	685.070i	0.00757242	+	1.58581i
$433$	−5.18978			−0.0119856			−0.00599282	−	0.999982i	$-0.501908\pi$
$433$	−5.18978			−0.0119856			−0.00599282	+	0.999982i	$0.501908\pi$
$434$	0.254299	+	213.022i	0.000585942	+	0.490834i
$435$		−	70.4928i		−	0.162052i
$436$	−356.572	+	0.851330i	−0.817825	+	0.00195259i
$437$	−119.577			−0.273631
$438$	1166.39	−	1.39240i	2.66300	−	0.00317900i
$439$		−	550.310i		−	1.25355i	−0.779199	−	0.626777i	$-0.784374\pi$
$439$		−	550.310i		−	1.25355i	0.779199	−	0.626777i	$-0.215626\pi$
$440$	−59.3292	+	0.212477i	−0.134839	+	0.000482902i
$441$	−144.224			−0.327039
$442$	−0.0777645	−	65.1420i	−0.000175938	−	0.147380i
$443$			220.435i			0.497597i	0.968555	+	0.248798i	$0.0800357\pi$
$443$			220.435i			0.497597i	−0.968555	+	0.248798i	$0.919964\pi$
$444$	−0.557525	−	233.514i	−0.00125569	−	0.525933i
$445$	−348.312			−0.782723
$446$	−204.165	+	0.243726i	−0.457770	+	0.000546471i
$447$		−	24.5102i		−	0.0548326i
$448$	−2.92387	−	408.206i	−0.00652650	−	0.911174i
$449$	40.9818			0.0912734			0.0456367	−	0.998958i	$-0.485468\pi$
$449$	40.9818			0.0912734			0.0456367	+	0.998958i	$0.485468\pi$
$450$	0.207028	+	173.424i	0.000460063	+	0.385387i
$451$			153.134i			0.339543i
$452$	449.557	−	1.07334i	0.994596	−	0.00237464i
$453$	1073.00			2.36865
$454$	−532.875	+	0.636130i	−1.17373	+	0.00140117i
$455$			18.6139i			0.0409097i
$456$	−4.33902	−	1211.57i	−0.00951540	−	2.65695i
$457$	726.983			1.59077			0.795386	−	0.606103i	$-0.207268\pi$
$457$	726.983			1.59077			0.795386	+	0.606103i	$0.207268\pi$
$458$	−0.347802	−	291.348i	−0.000759393	−	0.636131i
$459$		−	1068.58i		−	2.32807i
$460$	−0.0865382	−	36.2457i	−0.000188127	−	0.0787951i
$461$	−829.567			−1.79949			−0.899747	−	0.436411i	$-0.856249\pi$
$461$	−829.567			−1.79949			−0.899747	+	0.436411i	$0.856249\pi$
$462$	−217.152	+	0.259230i	−0.470026	+	0.000561103i
$463$		−	225.710i		−	0.487494i	−0.969839	−	0.243747i	$-0.921623\pi$
$463$		−	225.710i		−	0.487494i	0.969839	−	0.243747i	$-0.0783766\pi$
$464$	−98.2759	+	0.469278i	−0.211801	+	0.00101138i
$465$	−191.645			−0.412139
$466$	−0.213253	−	178.638i	−0.000457624	−	0.383344i
$467$			599.596i			1.28393i	0.766733	+	0.641966i	$0.221881\pi$
$467$			599.596i			1.28393i	−0.766733	+	0.641966i	$0.778119\pi$
$468$	−90.5338	+	0.216153i	−0.193448	+	0.000461866i
$469$	−317.321			−0.676591
$470$	−335.100	+	0.400033i	−0.712979	+	0.000851133i
$471$			184.543i			0.391810i
$472$	93.3195	−	0.334207i	0.197711	−	0.000708066i
$473$	−169.172			−0.357657
$474$	1.77295	+	1485.17i	0.00374040	+	3.13327i
$475$		−	147.538i		−	0.310606i
$476$	1.52023	+	636.734i	0.00319376	+	1.33768i
$477$	912.235			1.91244
$478$	−87.0201	+	0.103882i	−0.182050	+	0.000217326i
$479$			365.422i			0.762885i	0.924392	+	0.381443i	$0.124573\pi$
$479$			365.422i			0.762885i	−0.924392	+	0.381443i	$0.875427\pi$
$480$	367.244	−	2.19205i	0.765092	−	0.00456677i
$481$	14.8446			0.0308620
$482$	−0.149852	−	125.528i	−0.000310896	−	0.260433i
$483$		−	132.663i		−	0.274666i
$484$	43.9999	−	0.105052i	0.0909088	−	0.000217049i
$485$	−366.588			−0.755852
$486$	117.062	−	0.139745i	0.240868	−	0.000287541i
$487$		−	167.861i		−	0.344684i	−0.985037	−	0.172342i	$-0.944867\pi$
$487$		−	167.861i		−	0.344684i	0.985037	−	0.172342i	$-0.0551334\pi$
$488$	1.79324	+	500.719i	0.00367467	+	1.02606i
$489$	875.476			1.79034
$490$	0.0443980	+	37.1914i	9.06081e−5	+	0.0759008i
$491$		−	158.546i		−	0.322904i	−0.986881	−	0.161452i	$-0.948382\pi$
$491$		−	158.546i		−	0.322904i	0.986881	−	0.161452i	$-0.0516177\pi$
$492$	−2.26315	−	947.899i	−0.00459990	−	1.92662i
$493$	153.293			0.310938
$494$	77.0204	−	0.0919446i	0.155912	−	0.000186123i
$495$		−	128.615i		−	0.259828i
$496$	1.27580	+	267.177i	0.00257218	+	0.538663i
$497$	843.345			1.69687
$498$	0.829495	+	694.854i	0.00166565	+	1.39529i
$499$		−	515.469i		−	1.03300i	−0.856286	−	0.516502i	$-0.827234\pi$
$499$		−	515.469i		−	1.03300i	0.856286	−	0.516502i	$-0.172766\pi$
$500$	44.7212	−	0.106774i	0.0894425	−	0.000213548i
$501$	497.009			0.992034
$502$	595.705	−	0.711134i	1.18666	−	0.00141660i
$503$			2.02994i			0.00403567i	0.999998	+	0.00201783i	$0.000642297\pi$
$503$			2.02994i			0.00403567i	−0.999998	+	0.00201783i	$0.999358\pi$
$504$	884.927	−	3.16921i	1.75581	−	0.00628811i
$505$	329.812			0.653094
$506$	0.0320893	+	26.8806i	6.34175e−5	+	0.0531237i
$507$			858.648i			1.69359i
$508$	0.172967	+	72.4456i	0.000340486	+	0.142610i
$509$	39.9749			0.0785362			0.0392681	−	0.999229i	$-0.487497\pi$
$509$	39.9749			0.0785362			0.0392681	+	0.999229i	$0.487497\pi$
$510$	−572.838	+	0.683836i	−1.12321	+	0.00134086i
$511$		−	724.765i		−	1.41833i
$512$	−5.50078	−	511.970i	−0.0107437	−	0.999942i
$513$	1263.44			2.46284
$514$	−0.796424	−	667.151i	−0.00154946	−	1.29796i
$515$			213.953i			0.415442i
$516$	1047.17	−	2.50017i	2.02940	−	0.00484528i
$517$	248.517			0.480691
$518$	−145.100	+	0.173216i	−0.280116	+	0.000334393i
$519$		−	371.264i		−	0.715344i
$520$	0.0836100	+	23.3461i	0.000160788	+	0.0448964i
$521$	−304.099			−0.583684			−0.291842	−	0.956467i	$-0.594268\pi$
$521$	−304.099			−0.583684			−0.291842	+	0.956467i	$0.594268\pi$
$522$	−0.254327	−	213.045i	−0.000487216	−	0.408132i
$523$		−	2.59953i		−	0.00497042i	−0.999997	−	0.00248521i	$-0.999209\pi$
$523$		−	2.59953i		−	0.00497042i	0.999997	−	0.00248521i	$-0.000791068\pi$
$524$	1.31134	+	549.243i	0.00250256	+	1.04817i
$525$	163.685			0.311781
$526$	−592.043	+	0.706763i	−1.12556	+	0.00134366i
$527$		−	416.747i		−	0.790792i
$528$	−272.357	+	1.30054i	−0.515828	+	0.00246314i
$529$	512.578			0.968957
$530$	−0.280823	−	235.240i	−0.000529854	−	0.443849i
$531$			202.300i			0.380978i
$532$	−752.840	+	1.79744i	−1.41511	+	0.00337864i
$533$	60.2584			0.113055
$534$	−1598.97	+	1.90880i	−2.99433	+	0.00357454i
$535$			129.505i			0.242065i
$536$	−397.993	+	1.42534i	−0.742525	+	0.00265922i
$537$	−1203.45			−2.24106
$538$	−0.842792	−	705.993i	−0.00156653	−	1.31225i
$539$		−	27.5819i		−	0.0511724i
$540$	0.914355	+	382.969i	0.00169325	+	0.709202i
$541$	152.962			0.282739			0.141370	−	0.989957i	$-0.454849\pi$
$541$	152.962			0.282739			0.141370	+	0.989957i	$0.454849\pi$
$542$	−69.4212	+	0.0828729i	−0.128083	+	0.000152902i
$543$		−	1545.49i		−	2.84621i
$544$	4.76680	+	798.604i	0.00876250	+	1.46802i
$545$	−199.330			−0.365743
$546$	0.102007	+	85.4497i	0.000186826	+	0.156501i
$547$		−	0.691126i		−	0.00126348i	−1.00000		0.000631742i	$-0.999799\pi$
$547$		−	0.691126i		−	0.00126348i	1.00000		0.000631742i	$-0.000201090\pi$
$548$	374.941	−	0.895188i	0.684199	−	0.00163355i
$549$	−1085.47			−1.97717
$550$	−33.1662	+	0.0395928i	−0.0603022	+	7.19870e-5i
$551$			181.245i			0.328938i
$552$	−0.595897	−	166.390i	−0.00107952	−	0.301432i
$553$	922.845			1.66880
$554$	0.910665	+	762.848i	0.00164380	+	1.37698i
$555$		−	130.539i		−	0.235205i
$556$	−2.24524	−	940.398i	−0.00403820	−	1.69136i
$557$	480.644			0.862915			0.431457	−	0.902133i	$-0.358000\pi$
$557$	480.644			0.862915			0.431457	+	0.902133i	$0.358000\pi$
$558$	−579.193	+	0.691423i	−1.03798	+	0.00123911i
$559$			66.5692i			0.119086i
$560$	−1.08967	−	228.197i	−0.00194584	−	0.407495i
$561$	424.828			0.757269
$562$	0.0645813	+	54.0987i	0.000114913	+	0.0962610i
$563$			285.102i			0.506398i	0.967414	+	0.253199i	$0.0814828\pi$
$563$			285.102i			0.506398i	−0.967414	+	0.253199i	$0.918517\pi$
$564$	−1538.32	+	3.67280i	−2.72752	+	0.00651207i
$565$	251.311			0.444798
$566$	281.185	−	0.335670i	0.496794	−	0.000593057i
$567$			406.161i			0.716334i
$568$	1057.75	−	3.78814i	1.86223	−	0.00666925i
$569$	−41.7674			−0.0734048			−0.0367024	−	0.999326i	$-0.511685\pi$
$569$	−41.7674			−0.0734048			−0.0367024	+	0.999326i	$0.511685\pi$
$570$	−0.808531	−	677.292i	−0.00141847	−	1.18823i
$571$			107.128i			0.187615i	0.995590	+	0.0938077i	$0.0299039\pi$
$571$			107.128i			0.187615i	−0.995590	+	0.0938077i	$0.970096\pi$
$572$	−0.0413379	−	17.3140i	−7.22691e−5	−	0.0302692i
$573$	−1388.34			−2.42294
$574$	−589.001	+	0.703131i	−1.02613	+	0.00122497i
$575$		−	20.2620i		−	0.0352383i
$576$	1109.89	−	7.94982i	1.92689	−	0.0138018i
$577$	−888.703			−1.54021			−0.770107	−	0.637915i	$-0.779797\pi$
$577$	−888.703			−1.54021			−0.770107	+	0.637915i	$0.779797\pi$
$578$	−0.797061	−	667.684i	−0.00137900	−	1.15516i
$579$		−	421.836i		−	0.728560i
$580$	−54.9384	+	0.131168i	−0.0947213	+	0.000226151i
$581$	431.764			0.743139
$582$	−1682.87	+	2.00896i	−2.89153	+	0.00345182i
$583$			174.459i			0.299243i
$584$	−3.25550	−	909.022i	−0.00557448	−	1.55654i
$585$	−50.6101			−0.0865130
$586$	0.640007	+	536.122i	0.00109216	+	0.914885i
$587$		−	491.247i		−	0.836878i	−0.908245	−	0.418439i	$-0.862577\pi$
$587$		−	491.247i		−	0.836878i	0.908245	−	0.418439i	$-0.137423\pi$
$588$	0.407630	+	170.732i	0.000693248	+	0.290360i
$589$	492.740			0.836570
$590$	52.1675	−	0.0622759i	0.0884194	−	0.000105552i
$591$			173.347i			0.293311i
$592$	−181.988	+	0.869011i	−0.307412	+	0.00146792i
$593$	−181.008			−0.305242			−0.152621	−	0.988285i	$-0.548771\pi$
$593$	−181.008			−0.305242			−0.152621	+	0.988285i	$0.548771\pi$
$594$	−0.339052	−	284.018i	−0.000570795	−	0.478145i
$595$			355.946i			0.598229i
$596$	−19.1019	+	0.0456067i	−0.0320502	+	7.65213e-5i
$597$	−482.403			−0.808046
$598$	10.5776	−	0.0126272i	0.0176882	−	2.11157e-5i
$599$		−	199.402i		−	0.332891i	−0.986051	−	0.166446i	$-0.946771\pi$
$599$		−	199.402i		−	0.332891i	0.986051	−	0.166446i	$-0.0532290\pi$
$600$	205.298	−	0.735239i	0.342164	−	0.00122540i
$601$	−1026.83			−1.70854			−0.854269	−	0.519831i	$-0.825995\pi$
$601$	−1026.83			−1.70854			−0.854269	+	0.519831i	$0.825995\pi$
$602$	−0.776769	−	650.686i	−0.00129031	−	1.08087i
$603$		−	862.776i		−	1.43081i
$604$	−1.99656	−	836.240i	−0.00330556	−	1.38450i
$605$	24.5967			0.0406558
$606$	1514.05	−	1.80742i	2.49843	−	0.00298255i
$607$			383.203i			0.631307i	0.948875	+	0.315653i	$0.102224\pi$
$607$			383.203i			0.631307i	−0.948875	+	0.315653i	$0.897776\pi$
$608$	−944.226	+	5.63600i	−1.55300	+	0.00926974i
$609$	−201.081			−0.330182
$610$	0.334151	+	279.912i	0.000547788	+	0.458872i
$611$		−	97.7918i		−	0.160052i
$612$	−1731.24	+	4.13341i	−2.82882	+	0.00675394i
$613$	10.7520			0.0175399			0.00876996	−	0.999962i	$-0.497208\pi$
$613$	10.7520			0.0175399			0.00876996	+	0.999962i	$0.497208\pi$
$614$	−270.589	+	0.323021i	−0.440699	+	0.000526093i
$615$		−	529.893i		−	0.861615i
$616$	0.606090	+	169.236i	0.000983913	+	0.274735i
$617$	−680.199			−1.10243			−0.551215	−	0.834363i	$-0.685835\pi$
$617$	−680.199			−1.10243			−0.551215	+	0.834363i	$0.685835\pi$
$618$	1.17250	+	982.179i	0.00189724	+	1.58929i
$619$		−	724.567i		−	1.17055i	−0.810837	−	0.585273i	$-0.800988\pi$
$619$		−	724.567i		−	1.17055i	0.810837	−	0.585273i	$-0.199012\pi$
$620$	0.356598	+	149.358i	0.000575158	+	0.240900i
$621$	173.513			0.279410
$622$	768.801	−	0.917771i	1.23601	−	0.00147552i
$623$			993.559i			1.59480i
$624$	0.511763	+	107.173i	0.000820133	+	0.171752i
$625$	25.0000			0.0400000
$626$	0.432328	+	362.153i	0.000690619	+	0.578520i
$627$			502.294i			0.801106i
$628$	143.823	−	0.343383i	0.229017	−	0.000546788i
$629$	283.868			0.451300
$630$	494.692	−	0.590548i	0.785225	−	0.000937378i
$631$		−	223.588i		−	0.354338i	−0.984180	−	0.177169i	$-0.943306\pi$
$631$		−	223.588i		−	0.354338i	0.984180	−	0.177169i	$-0.0566940\pi$
$632$	1157.46	−	4.14523i	1.83142	−	0.00655891i
$633$	−780.808			−1.23350
$634$	0.213416	+	178.775i	0.000336619	+	0.281980i
$635$			40.4985i			0.0637771i
$636$	−2.57831	−	1079.90i	−0.00405394	−	1.69796i
$637$	−10.8535			−0.0170385
$638$	40.7435	−	0.0486383i	0.0638612	−	7.62356e-5i
$639$			2293.00i			3.58842i
$640$	−2.39171	−	286.207i	−0.00373704	−	0.447198i
$641$	−822.060			−1.28246			−0.641232	−	0.767347i	$-0.721576\pi$
$641$	−822.060			−1.28246			−0.641232	+	0.767347i	$0.721576\pi$
$642$	0.709706	+	594.508i	0.00110546	+	0.926025i
$643$			365.290i			0.568103i	0.958809	+	0.284051i	$0.0916786\pi$
$643$			365.290i			0.568103i	−0.958809	+	0.284051i	$0.908321\pi$
$644$	−103.391	+	0.246850i	−0.160545	+	0.000383308i
$645$	585.388			0.907578
$646$	1472.83	−	1.75822i	2.27992	−	0.00272170i
$647$			304.263i			0.470267i	0.971963	+	0.235133i	$0.0755527\pi$
$647$			304.263i			0.470267i	−0.971963	+	0.235133i	$0.924447\pi$
$648$	1.82439	+	509.419i	0.00281542	+	0.786140i
$649$	−38.6885			−0.0596124
$650$	0.0155798	+	13.0509i	2.39690e−5	+	0.0200784i
$651$			546.666i			0.839733i
$652$	−1.62902	−	682.299i	−0.00249849	−	1.04647i
$653$	339.553			0.519990			0.259995	−	0.965610i	$-0.416279\pi$
$653$	339.553			0.519990			0.259995	+	0.965610i	$0.416279\pi$
$654$	−915.052	+	1.09236i	−1.39916	+	0.00167028i
$655$			307.037i			0.468759i
$656$	−738.738	+	3.52756i	−1.12613	+	0.00537737i
$657$	1970.59			2.99938
$658$	1.14109	+	955.873i	0.00173418	+	1.45269i
$659$		−	400.301i		−	0.607437i	−0.952762	−	0.303718i	$-0.901772\pi$
$659$		−	400.301i		−	0.607437i	0.952762	−	0.303718i	$-0.0982282\pi$
$660$	−152.254	+	0.363512i	−0.230687	+	0.000550776i
$661$	602.700			0.911800			0.455900	−	0.890031i	$-0.349318\pi$
$661$	602.700			0.911800			0.455900	+	0.890031i	$0.349318\pi$
$662$	−656.096	+	0.783227i	−0.991081	+	0.00118312i
$663$		−	167.170i		−	0.252142i
$664$	541.531	−	1.93940i	0.815558	−	0.00292078i
$665$	−420.852			−0.632860
$666$	−0.470963	−	394.517i	−0.000707152	−	0.592369i
$667$			24.8912i			0.0373181i
$668$	−0.924797	−	387.343i	−0.00138443	−	0.579854i
$669$	−523.938			−0.783166
$670$	−222.486	+	0.265597i	−0.332069	+	0.000396414i
$671$		−	207.589i		−	0.309372i
$672$	−6.25282	−	1047.56i	−0.00930479	−	1.55887i
$673$	−384.662			−0.571564			−0.285782	−	0.958295i	$-0.592253\pi$
$673$	−384.662			−0.571564			−0.285782	+	0.958295i	$0.592253\pi$
$674$	0.107921	+	90.4034i	0.000160120	+	0.134130i
$675$			214.087i			0.317166i
$676$	669.185	−	1.59771i	0.989919	−	0.00236347i
$677$	−662.457			−0.978519			−0.489259	−	0.872138i	$-0.662733\pi$
$677$	−662.457			−0.978519			−0.489259	+	0.872138i	$0.662733\pi$
$678$	1153.68	−	1.37722i	1.70159	−	0.00203130i
$679$			1045.69i			1.54005i
$680$	1.59884	+	446.438i	0.00235123	+	0.656527i
$681$	−1367.49			−2.00806
$682$	−0.132230	−	110.767i	−0.000193886	−	0.162415i
$683$		−	484.228i		−	0.708972i	−0.935061	−	0.354486i	$-0.884656\pi$
$683$		−	484.228i		−	0.708972i	0.935061	−	0.354486i	$-0.115344\pi$
$684$	−4.88712	−	2046.93i	−0.00714491	−	2.99258i
$685$	209.599			0.305984
$686$	731.169	−	0.872848i	1.06584	−	0.00127237i
$687$		−	747.670i		−	1.08831i
$688$	−3.89699	−	816.105i	−0.00566423	−	1.18620i
$689$	68.6498			0.0996369
$690$	−0.111039	−	93.0156i	−0.000160926	−	0.134805i
$691$		−	479.038i		−	0.693254i	−0.938003	−	0.346627i	$-0.887327\pi$
$691$		−	479.038i		−	0.693254i	0.938003	−	0.346627i	$-0.112673\pi$
$692$	−289.343	+	0.690819i	−0.418126	+	0.000998294i
$693$	−366.874			−0.529399
$694$	82.0383	−	0.0979348i	0.118211	−	0.000141116i
$695$		−	525.700i		−	0.756403i
$696$	−252.201	+	0.903213i	−0.362358	+	0.00129772i
$697$	1152.30			1.65322
$698$	−1.04090	−	871.948i	−0.00149127	−	1.24921i
$699$		−	458.429i		−	0.655836i
$700$	−0.304572	−	127.567i	−0.000435103	−	0.182239i
$701$	792.976			1.13121			0.565603	−	0.824678i	$-0.308643\pi$
$701$	792.976			1.13121			0.565603	+	0.824678i	$0.308643\pi$
$702$	−111.761	+	0.133417i	−0.159204	+	0.000190053i
$703$			335.630i			0.477425i
$704$	1.52035	+	212.259i	0.00215959	+	0.301504i
$705$	−859.950			−1.21979
$706$	−0.651642	−	545.869i	−0.000923005	−	0.773185i
$707$		−	940.790i		−	1.33068i
$708$	239.481	−	0.571772i	0.338250	−	0.000807587i
$709$	744.553			1.05015			0.525073	−	0.851057i	$-0.324038\pi$
$709$	744.553			1.05015			0.525073	+	0.851057i	$0.324038\pi$
$710$	591.302	−	0.705879i	0.832820	−	0.000994195i
$711$			2509.16i			3.52906i
$712$	4.46286	+	1246.15i	0.00626807	+	1.75021i
$713$	67.6701			0.0949090
$714$	1.95064	+	1634.02i	0.00273199	+	2.28854i
$715$		−	9.67885i		−	0.0135369i
$716$	2.23929	+	937.904i	0.00312749	+	1.30992i
$717$	−223.315			−0.311457
$718$	749.400	−	0.894611i	1.04373	−	0.00124598i
$719$			588.807i			0.818925i	0.912327	+	0.409463i	$0.134284\pi$
$719$			588.807i			0.818925i	−0.912327	+	0.409463i	$0.865716\pi$
$720$	620.454	−	2.96274i	0.861742	−	0.00411491i
$721$	610.300			0.846464
$722$	1.21692	+	1019.39i	0.00168549	+	1.41190i
$723$		−	322.137i		−	0.445556i
$724$	−1204.47	+	2.87573i	−1.66364	+	0.00397200i
$725$	−30.7116			−0.0423608
$726$	112.915	−	0.134794i	0.155530	−	0.000185667i
$727$			276.147i			0.379845i	0.981799	+	0.189922i	$0.0608237\pi$
$727$			276.147i			0.379845i	−0.981799	+	0.189922i	$0.939176\pi$
$728$	66.5948	−	0.238497i	0.0914763	−	0.000327606i
$729$	873.509			1.19823
$730$	−0.606628	−	508.161i	−0.000830997	−	0.696111i
$731$			1272.98i			1.74142i
$732$	3.06792	+	1284.97i	0.00419115	+	1.75543i
$733$	162.942			0.222295			0.111148	−	0.993804i	$-0.464547\pi$
$733$	162.942			0.222295			0.111148	+	0.993804i	$0.464547\pi$
$734$	465.388	−	0.555566i	0.634043	−	0.000756902i
$735$			95.4423i			0.129853i
$736$	−129.675	+	0.774017i	−0.176188	+	0.00105165i
$737$	165.000			0.223881
$738$	−1.91177	−	1601.46i	−0.00259047	−	2.16999i
$739$		−	0.493572i		−	0.000667892i	−1.00000		0.000333946i	$-0.999894\pi$
$739$		−	0.493572i		−	0.000667892i	1.00000		0.000333946i	$-0.000106298\pi$
$740$	−101.735	+	0.242897i	−0.137480	+	0.000328239i
$741$	197.653			0.266738
$742$	−671.022	+	0.801046i	−0.904343	+	0.00107958i
$743$		−	318.193i		−	0.428255i	−0.976806	−	0.214127i	$-0.931309\pi$
$743$		−	318.193i		−	0.428255i	0.976806	−	0.214127i	$-0.0686907\pi$
$744$	2.45551	+	685.645i	0.00330042	+	0.921565i
$745$	−10.6783			−0.0143333
$746$	1.24309	+	1041.32i	0.00166634	+	1.39587i
$747$			1173.94i			1.57154i
$748$	−0.790488	−	331.089i	−0.00105680	−	0.442632i
$749$	369.412			0.493207
$750$	114.766	−	0.137004i	0.153021	−	0.000182672i
$751$			339.166i			0.451619i	0.974172	+	0.225809i	$0.0725026\pi$
$751$			339.166i			0.451619i	−0.974172	+	0.225809i	$0.927497\pi$
$752$	5.72478	+	1198.88i	0.00761274	+	1.59425i
$753$	1528.72			2.03018
$754$	−0.0191392	−	16.0326i	−2.53836e−5	−	0.0212634i
$755$		−	467.474i		−	0.619170i
$756$	1092.42	−	2.60820i	1.44500	−	0.00344999i
$757$	1206.26			1.59347			0.796734	−	0.604330i	$-0.206559\pi$
$757$	1206.26			1.59347			0.796734	+	0.604330i	$0.206559\pi$
$758$	755.543	−	0.901944i	0.996759	−	0.00118990i
$759$			68.9822i			0.0908857i
$760$	−527.844	+	1.89038i	−0.694532	+	0.00248734i
$761$	60.5213			0.0795286			0.0397643	−	0.999209i	$-0.487339\pi$
$761$	60.5213			0.0795286			0.0397643	+	0.999209i	$0.487339\pi$
$762$	0.221938	+	185.914i	0.000291257	+	0.243981i
$763$			568.589i			0.745202i
$764$	2.58333	+	1082.00i	0.00338132	+	1.41623i
$765$	−967.796			−1.26509
$766$	1055.00	−	1.25943i	1.37729	−	0.00164416i
$767$			15.2240i			0.0198487i
$768$	−12.5479	−	1313.86i	−0.0163384	−	1.71075i
$769$	−1493.51			−1.94214			−0.971071	−	0.238790i	$-0.923249\pi$
$769$	−1493.51			−1.94214			−0.971071	+	0.238790i	$0.923249\pi$
$770$	0.112938	+	94.6066i	0.000146673	+	0.122866i
$771$		−	1712.07i		−	2.22059i
$772$	−328.757	+	0.784921i	−0.425851	+	0.00101674i
$773$	426.859			0.552210			0.276105	−	0.961127i	$-0.410956\pi$
$773$	426.859			0.552210			0.276105	+	0.961127i	$0.410956\pi$
$774$	1769.17	−	2.11199i	2.28575	−	0.00272866i
$775$			83.4938i			0.107734i
$776$	4.69704	+	1311.54i	0.00605289	+	1.69013i
$777$	−372.362			−0.479230
$778$	1.37551	+	1152.24i	0.00176801	+	1.48103i
$779$			1362.41i			1.74893i
$780$	0.143043	+	59.9120i	0.000183388	+	0.0768103i
$781$	−438.522			−0.561488
$782$	202.270	−	0.241464i	0.258657	−	0.000308777i
$783$		−	262.998i		−	0.335885i
$784$	133.059	−	0.635370i	0.169718	−	0.000810421i
$785$	80.3996			0.102420
$786$	1.68261	+	1409.49i	0.00214073	+	1.79325i
$787$		−	623.589i		−	0.792362i	−0.918172	−	0.396181i	$-0.870335\pi$
$787$		−	623.589i		−	0.792362i	0.918172	−	0.396181i	$-0.129665\pi$
$788$	135.098	−	0.322551i	0.171444	−	0.000409329i
$789$	−1519.33			−1.92564
$790$	647.043	−	0.772420i	0.819042	−	0.000977747i
$791$		−	716.864i		−	0.906275i
$792$	−460.143	+	1.64792i	−0.580989	+	0.00208071i
$793$	−81.6863			−0.103009
$794$	0.0461261	+	38.6390i	5.80933e−5	+	0.0486638i
$795$		−	603.684i		−	0.759351i
$796$	0.897619	+	375.959i	0.00112766	+	0.472311i
$797$	−387.527			−0.486233			−0.243116	−	0.969997i	$-0.578170\pi$
$797$	−387.527			−0.486233			−0.243116	+	0.969997i	$0.578170\pi$
$798$	−1931.97	+	2.30633i	−2.42102	+	0.00289014i
$799$		−	1870.03i		−	2.34047i
$800$	−0.955010	−	159.997i	−0.00119376	−	0.199996i
$801$	−2701.42			−3.37256
$802$	0.487306	+	408.207i	0.000607613	+	0.508987i
$803$			376.863i			0.469319i
$804$	−1021.35	+	2.43852i	−1.27034	+	0.00303298i
$805$	−57.7974			−0.0717980
$806$	−43.5869	+	0.0520327i	−0.0540781	+	6.45567e-5i
$807$		−	1811.75i		−	2.24504i
$808$	−4.22584	−	1179.97i	−0.00523000	−	1.46035i
$809$	−898.317			−1.11040			−0.555202	−	0.831715i	$-0.687359\pi$
$809$	−898.317			−1.11040			−0.555202	+	0.831715i	$0.687359\pi$
$810$	0.339956	+	284.775i	0.000419699	+	0.351575i
$811$		−	1016.64i		−	1.25357i	−0.779193	−	0.626784i	$-0.784371\pi$
$811$		−	1016.64i		−	1.25357i	0.779193	−	0.626784i	$-0.215629\pi$
$812$	0.374156	+	156.712i	0.000460783	+	0.192995i
$813$	−178.152			−0.219129
$814$	75.4489	−	0.0900686i	0.0926891	−	0.000110649i
$815$		−	381.418i		−	0.467998i
$816$	9.78623	+	2049.42i	0.0119929	+	2.51155i
$817$	−1505.10			−1.84222
$818$	−0.912001	−	763.968i	−0.00111492	−	0.933946i
$819$			144.365i			0.176270i
$820$	−412.971	+	0.985985i	−0.503623	+	0.00120242i
$821$	21.7430			0.0264835			0.0132418	−	0.999912i	$-0.495785\pi$
$821$	21.7430			0.0264835			0.0132418	+	0.999912i	$0.495785\pi$
$822$	962.192	−	1.14864i	1.17055	−	0.00139737i
$823$		−	993.092i		−	1.20667i	−0.797487	−	0.603337i	$-0.793838\pi$
$823$		−	993.092i		−	1.20667i	0.797487	−	0.603337i	$-0.206162\pi$
$824$	765.456	−	2.74135i	0.928952	−	0.00332688i
$825$	−85.1127			−0.103167
$826$	−0.177642	−	148.808i	−0.000215063	−	0.180155i
$827$		−	467.919i		−	0.565803i	−0.959149	−	0.282901i	$-0.908703\pi$
$827$		−	467.919i		−	0.565803i	0.959149	−	0.282901i	$-0.0912969\pi$
$828$	−0.671170	−	281.113i	−0.000810592	−	0.339509i
$829$	−649.343			−0.783284			−0.391642	−	0.920118i	$-0.628093\pi$
$829$	−649.343			−0.783284			−0.391642	+	0.920118i	$0.628093\pi$
$830$	302.727	−	0.361386i	0.364731	−	0.000435405i
$831$			1957.66i			2.35578i
$832$	83.5240	−	0.598260i	0.100389	−	0.000719063i
$833$	−207.547			−0.249156
$834$	−2.88092	−	2413.29i	−0.00345434	−	2.89364i
$835$		−	216.532i		−	0.259319i
$836$	391.461	−	0.934630i	0.468255	−	0.00111798i
$837$	−714.997			−0.854237
$838$	319.740	−	0.381695i	0.381551	−	0.000455484i
$839$			1254.79i			1.49558i	0.663936	+	0.747789i	$0.268885\pi$
$839$			1254.79i			1.49558i	−0.663936	+	0.747789i	$0.731115\pi$
$840$	−2.09727	−	585.613i	−0.00249675	−	0.697158i
$841$	−803.272			−0.955139
$842$	−0.586159	−	491.015i	−0.000696151	−	0.583154i
$843$			138.830i			0.164686i
$844$	1.45287	+	608.520i	0.00172141	+	0.720996i
$845$	374.087			0.442706
$846$	−2598.96	+	3.10256i	−3.07206	+	0.00366733i
$847$		−	70.1622i		−	0.0828361i
$848$	−841.612	+	4.01879i	−0.992467	+	0.00473914i
$849$	721.590			0.849929
$850$	0.297927	+	249.568i	0.000350502	+	0.293609i
$851$			46.0935i			0.0541640i
$852$	2714.45	−	6.48086i	3.18597	−	0.00760664i
$853$	−114.174			−0.133850			−0.0669248	−	0.997758i	$-0.521319\pi$
$853$	−114.174			−0.133850			−0.0669248	+	0.997758i	$0.521319\pi$
$854$	798.449	−	0.953164i	0.934952	−	0.00111612i
$855$		−	1144.27i		−	1.33833i
$856$	463.327	−	1.65932i	0.541270	−	0.00193846i
$857$	1292.55			1.50823			0.754116	−	0.656742i	$-0.228066\pi$
$857$	1292.55			1.50823			0.754116	+	0.656742i	$0.228066\pi$
$858$	−0.0530416	−	44.4320i	−6.18201e−5	−	0.0517856i
$859$		−	649.789i		−	0.756449i	−0.925714	−	0.378224i	$-0.876535\pi$
$859$		−	649.789i		−	0.756449i	0.925714	−	0.378224i	$-0.123465\pi$
$860$	−1.08925	−	456.221i	−0.00126656	−	0.530489i
$861$	−1511.52			−1.75554
$862$	−957.711	+	1.14329i	−1.11103	+	0.00132632i
$863$			1062.65i			1.23135i	0.788001	+	0.615674i	$0.211116\pi$
$863$			1062.65i			1.23135i	−0.788001	+	0.615674i	$0.788884\pi$
$864$	1370.13	−	8.17820i	1.58580	−	0.00946551i
$865$	−161.748			−0.186992
$866$	0.0123908	+	10.3796i	1.43081e−5	+	0.0119856i
$867$		−	1713.44i		−	1.97629i
$868$	426.043	−	1.01720i	0.490833	−	0.00117188i
$869$	−479.860			−0.552198
$870$	−140.986	+	0.168304i	−0.162052	+	0.000193453i
$871$		−	64.9278i		−	0.0745440i
$872$	2.55399	+	713.141i	0.00292888	+	0.817822i
$873$	−2843.17			−3.25679
$874$	0.285494	+	239.153i	0.000326652	+	0.273631i
$875$		−	71.3125i		−	0.0815000i
$876$	−5.56961	−	2332.78i	−0.00635800	−	2.66299i
$877$	1573.73			1.79445			0.897223	−	0.441579i	$-0.145581\pi$
$877$	1573.73			1.79445			0.897223	+	0.441579i	$0.145581\pi$
$878$	−1100.62	+	1.31389i	−1.25355	+	0.00149645i
$879$			1375.82i			1.56521i
$880$	0.566604	+	118.658i	0.000643869	+	0.134838i
$881$	163.682			0.185791			0.0928955	−	0.995676i	$-0.470388\pi$
$881$	163.682			0.185791			0.0928955	+	0.995676i	$0.470388\pi$
$882$	0.344340	+	288.448i	0.000390409	+	0.327038i
$883$		−	178.832i		−	0.202528i	−0.994860	−	0.101264i	$-0.967711\pi$
$883$		−	178.832i		−	0.202528i	0.994860	−	0.101264i	$-0.0322887\pi$
$884$	−130.284	+	0.311058i	−0.147380	+	0.000351875i
$885$	133.875			0.151271
$886$	440.870	−	0.526298i	0.497596	−	0.000594015i
$887$			130.641i			0.147284i	0.997285	+	0.0736420i	$0.0234622\pi$
$887$			130.641i			0.147284i	−0.997285	+	0.0736420i	$0.976538\pi$
$888$	−467.027	+	1.67257i	−0.525931	+	0.00188353i
$889$	115.522			0.129946
$890$	0.831607	+	696.623i	0.000934390	+	0.782722i
$891$		−	211.195i		−	0.237032i
$892$	0.974904	+	408.330i	0.00109294	+	0.457769i
$893$	2211.03			2.47595
$894$	−49.0203	+	0.0585190i	−0.0548326	+	6.54575e-5i
$895$			524.306i			0.585817i
$896$	−816.404	+	6.82235i	−0.911165	+	0.00761422i
$897$	27.1446			0.0302615
$898$	−0.0978455	−	81.9634i	−0.000108959	−	0.0912733i
$899$		−	102.569i		−	0.114092i
$900$	346.847	−	0.828113i	0.385386	−	0.000920126i
$901$	1312.76			1.45700
$902$	306.268	−	0.365613i	0.339543	−	0.000405336i
$903$		−	1669.82i		−	1.84919i
$904$	−3.22001	−	899.111i	−0.00356195	−	0.994592i
$905$	−673.323			−0.744003
$906$	−2.56183	−	2146.00i	−0.00282763	−	2.36865i
$907$		−	93.5147i		−	0.103103i	−0.998670	−	0.0515516i	$-0.983583\pi$
$907$		−	93.5147i		−	0.103103i	0.998670	−	0.0515516i	$-0.0164167\pi$
$908$	2.54452	+	1065.75i	0.00280233	+	1.17373i
$909$	2557.95			2.81402
$910$	37.2278	−	0.0444414i	0.0409097	−	4.88367e-5i
$911$			848.400i			0.931285i	0.884973	+	0.465642i	$0.154177\pi$
$911$			848.400i			0.931285i	−0.884973	+	0.465642i	$0.845823\pi$
$912$	−2423.13	+	11.5707i	−2.65694	+	0.0126872i
$913$	−224.508			−0.245902
$914$	−1.73570	−	1453.96i	−0.00189901	−	1.59077i
$915$			718.323i			0.785053i
$916$	−582.694	+	1.39121i	−0.636129	+	0.00151879i
$917$	875.823			0.955096
$918$	−2137.17	+	2.55129i	−2.32807	+	0.00277918i
$919$			941.220i			1.02418i	0.858932	+	0.512089i	$0.171128\pi$
$919$			941.220i			1.02418i	−0.858932	+	0.512089i	$0.828872\pi$
$920$	−72.4912	+	0.259614i	−0.0787948	+	0.000282189i
$921$	−694.399			−0.753961
$922$	1.98062	+	1659.13i	0.00214818	+	1.79949i
$923$			172.559i			0.186954i
$924$	1.03692	+	434.304i	0.00112221	+	0.470025i
$925$	−56.8718			−0.0614830
$926$	−451.419	+	0.538890i	−0.487494	+	0.000581955i
$927$			1659.37i			1.79004i
$928$	1.17319	+	196.551i	0.00126422	+	0.211800i
$929$	−1466.34			−1.57841			−0.789203	−	0.614132i	$-0.789506\pi$
$929$	−1466.34			−1.57841			−0.789203	+	0.614132i	$0.789506\pi$
$930$	0.457559	+	383.289i	0.000491999	+	0.412139i
$931$		−	245.393i		−	0.263580i
$932$	−357.275	+	0.853010i	−0.383343	+	0.000915247i
$933$	1972.93			2.11461
$934$	1199.19	−	1.43156i	1.28393	−	0.00153272i
$935$		−	185.085i		−	0.197951i
$936$	0.648459	+	181.067i	0.000692798	+	0.193448i
$937$	−1489.88			−1.59006			−0.795028	−	0.606573i	$-0.792544\pi$
$937$	−1489.88			−1.59006			−0.795028	+	0.606573i	$0.792544\pi$
$938$	0.757616	+	634.642i	0.000807693	+	0.676590i
$939$			929.374i			0.989749i
$940$	1.60013	+	670.199i	0.00170226	+	0.712978i
$941$	−523.545			−0.556371			−0.278186	−	0.960527i	$-0.589733\pi$
$941$	−523.545			−0.556371			−0.278186	+	0.960527i	$0.589733\pi$
$942$	369.085	−	0.440602i	0.391810	−	0.000467731i
$943$			187.106i			0.198416i
$944$	−0.891218	−	186.638i	−0.000944086	−	0.197710i
$945$	610.682			0.646225
$946$	0.403903	+	338.343i	0.000426959	+	0.357656i
$947$		−	1739.49i		−	1.83685i	−0.395598	−	0.918424i	$-0.629463\pi$
$947$		−	1739.49i		−	1.83685i	0.395598	−	0.918424i	$-0.370537\pi$
$948$	2970.33	−	7.09179i	3.13326	−	0.00748079i
$949$	148.296			0.156266
$950$	−295.076	+	0.352252i	−0.310606	+	0.000370792i
$951$			458.781i			0.482420i
$952$	1273.46	−	4.56068i	1.33767	−	0.00479064i
$953$	620.763			0.651377			0.325689	−	0.945477i	$-0.394404\pi$
$953$	620.763			0.651377			0.325689	+	0.945477i	$0.394404\pi$
$954$	−2.17799	−	1824.47i	−0.00228301	−	1.91244i
$955$			604.859i			0.633360i
$956$	0.415527	+	174.040i	0.000434652	+	0.182050i
$957$	104.558			0.109256
$958$	730.844	−	0.872459i	0.762885	−	0.000910709i
$959$		−	597.881i		−	0.623442i
$960$	−5.26091	−	734.483i	−0.00548011	−	0.765086i
$961$	682.152			0.709835
$962$	−0.0354421	−	29.6892i	−3.68421e−5	−	0.0308620i
$963$			1004.41i			1.04300i
$964$	−251.056	+	0.599408i	−0.260432	+	0.000621792i
$965$	−183.781			−0.190447
$966$	−265.327	+	0.316739i	−0.274665	+	0.000327887i
$967$			482.969i			0.499451i	0.968317	+	0.249725i	$0.0803403\pi$
$967$			482.969i			0.499451i	−0.968317	+	0.249725i	$0.919660\pi$
$968$	−0.315154	−	87.9994i	−0.000325573	−	0.0909085i
$969$	3779.64			3.90056
$970$	0.875243	+	733.176i	0.000902313	+	0.755852i
$971$		−	255.772i		−	0.263411i	−0.991289	−	0.131705i	$-0.957955\pi$
$971$		−	255.772i		−	0.263411i	0.991289	−	0.131705i	$-0.0420453\pi$
$972$	−0.558979	−	234.123i	−0.000575081	−	0.240867i
$973$	−1499.56			−1.54117
$974$	−335.722	+	0.400775i	−0.344684	+	0.000411473i
$975$			33.4919i			0.0343507i
$976$	1001.43	−	4.78196i	1.02606	−	0.00489955i
$977$	1559.94			1.59666			0.798330	−	0.602221i	$-0.205717\pi$
$977$	1559.94			1.59666			0.798330	+	0.602221i	$0.205717\pi$
$978$	−2.09023	−	1750.95i	−0.00213725	−	1.79034i
$979$		−	516.630i		−	0.527712i
$980$	74.3827	−	0.177592i	0.0759007	−	0.000181216i
$981$	−1545.96			−1.57590
$982$	−317.092	+	0.378534i	−0.322904	+	0.000385473i
$983$		−	1310.90i		−	1.33357i	−0.745248	−	0.666787i	$-0.767669\pi$
$983$		−	1310.90i		−	1.33357i	0.745248	−	0.666787i	$-0.232331\pi$
$984$	−1895.79	+	6.78944i	−1.92662	+	0.00689984i
$985$	75.5220			0.0766721
$986$	−0.365992	−	306.585i	−0.000371188	−	0.310938i
$987$			2453.01i			2.48531i
$988$	−0.367778	−	154.040i	−0.000372245	−	0.155911i
$989$	−206.702			−0.209001
$990$	−257.229	+	0.307073i	−0.259828	+	0.000310174i
$991$		−	1148.23i		−	1.15865i	−0.815095	−	0.579327i	$-0.803315\pi$
$991$		−	1148.23i		−	1.15865i	0.815095	−	0.579327i	$-0.196685\pi$
$992$	534.350	−	3.18949i	0.538660	−	0.00321521i
$993$	−1683.70			−1.69557
$994$	−2.01352	−	1686.69i	−0.00202567	−	1.69687i
$995$			210.168i			0.211224i
$996$	1389.70	−	3.31798i	1.39529	−	0.00333130i
$997$	249.320			0.250070			0.125035	−	0.992152i	$-0.460096\pi$
$997$	249.320			0.250070			0.125035	+	0.992152i	$0.460096\pi$
$998$	−1030.94	+	1.23070i	−1.03300	+	0.00123317i
$999$		−	487.020i		−	0.487508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.c.a.111.23	✓	40
4.3	odd	2	inner	220.3.c.a.111.24	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.c.a.111.23	✓	40	1.1	even	1	trivial
220.3.c.a.111.24	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+(-0.00238754 - 2.00000i) q^{2} -5.13249i q^{3} +(-3.99999 + 0.00955014i) q^{4} -2.23607 q^{5} +(-10.2650 + 0.0122540i) q^{6} +6.37838i q^{7} +(0.0286504 + 7.99995i) q^{8} -17.3424 q^{9} +(0.00533870 + 4.47213i) q^{10} -3.31662i q^{11} +(0.0490160 + 20.5299i) q^{12} -1.30510 q^{13} +(12.7568 - 0.0152286i) q^{14} +11.4766i q^{15} +(15.9998 - 0.0764009i) q^{16} -24.9568 q^{17} +(0.0414057 + 34.6848i) q^{18} -29.5076i q^{19} +(8.94425 - 0.0213548i) q^{20} +32.7370 q^{21} +(-6.63324 + 0.00791857i) q^{22} -4.05241i q^{23} +(41.0596 - 0.147048i) q^{24} +5.00000 q^{25} +(0.00311597 + 2.61019i) q^{26} +42.8174i q^{27} +(-0.0609144 - 25.5135i) q^{28} -6.14231 q^{29} +(22.9532 - 0.0274008i) q^{30} +16.6988i q^{31} +(-0.191002 - 31.9994i) q^{32} -17.0225 q^{33} +(0.0595853 + 49.9136i) q^{34} -14.2625i q^{35} +(69.3695 - 0.165623i) q^{36} -11.3744 q^{37} +(-59.0151 + 0.0704504i) q^{38} +6.69839i q^{39} +(-0.0640642 - 17.8884i) q^{40} -46.1717 q^{41} +(-0.0781607 - 65.4739i) q^{42} -51.0071i q^{43} +(0.0316742 + 13.2665i) q^{44} +38.7788 q^{45} +(-8.10481 + 0.00967527i) q^{46} +74.9308i q^{47} +(-0.392127 - 82.1189i) q^{48} +8.31626 q^{49} +(-0.0119377 - 9.99999i) q^{50} +128.090i q^{51} +(5.22037 - 0.0124639i) q^{52} -52.6013 q^{53} +(85.6347 - 0.102228i) q^{54} +7.41620i q^{55} +(-51.0267 + 0.182743i) q^{56} -151.447 q^{57} +(0.0146650 + 12.2846i) q^{58} -11.6650i q^{59} +(-0.109603 - 45.9062i) q^{60} +62.5903 q^{61} +(33.3975 - 0.0398689i) q^{62} -110.617i q^{63} +(-63.9984 + 0.458403i) q^{64} +2.91828 q^{65} +(0.0406419 + 34.0450i) q^{66} +49.7495i q^{67} +(99.8269 - 0.238341i) q^{68} -20.7989 q^{69} +(-28.5250 + 0.0340522i) q^{70} -132.219i q^{71} +(-0.496867 - 138.738i) q^{72} -113.628 q^{73} +(0.0271567 + 22.7487i) q^{74} -25.6624i q^{75} +(0.281802 + 118.030i) q^{76} +21.1547 q^{77} +(13.3968 - 0.0159927i) q^{78} -144.683i q^{79} +(-35.7767 + 0.170838i) q^{80} +63.6778 q^{81} +(0.110237 + 92.3433i) q^{82} -67.6918i q^{83} +(-130.947 + 0.312643i) q^{84} +55.8051 q^{85} +(-102.014 + 0.121781i) q^{86} +31.5253i q^{87} +(26.5328 - 0.0950226i) q^{88} +155.770 q^{89} +(-0.0925859 - 77.5576i) q^{90} -8.32440i q^{91} +(0.0387011 + 16.2096i) q^{92} +85.7061 q^{93} +(149.861 - 0.178900i) q^{94} +65.9809i q^{95} +(-164.237 + 0.980315i) q^{96} +163.943 q^{97} +(-0.0198554 - 16.6325i) q^{98} +57.5183i 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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