LMFDB - Embedded newform 880.2.w.a.221.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.221"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			221.13
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.820740 - 1.15169i) q^{2} +(-0.928026 - 0.928026i) q^{3} +(-0.652771 + 1.89047i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.307128 + 1.83047i) q^{6} +0.454189i q^{7} +(2.71299 - 0.799799i) q^{8} -1.27753i q^{9} +(1.39472 + 0.234015i) q^{10} +(0.707107 - 0.707107i) q^{11} +(2.36020 - 1.14862i) q^{12} +(1.69624 + 1.69624i) q^{13} +(0.523084 - 0.372771i) q^{14} +1.31243 q^{15} +(-3.14778 - 2.46809i) q^{16} -5.02242 q^{17} +(-1.47132 + 1.04852i) q^{18} +(-5.00428 - 5.00428i) q^{19} +(-0.875188 - 1.79835i) q^{20} +(0.421499 - 0.421499i) q^{21} +(-1.39472 - 0.234015i) q^{22} +3.74454i q^{23} +(-3.25996 - 1.77549i) q^{24} -1.00000i q^{25} +(0.561367 - 3.34571i) q^{26} +(-3.96966 + 3.96966i) q^{27} +(-0.858632 - 0.296481i) q^{28} +(3.90492 + 3.90492i) q^{29} +(-1.07716 - 1.51151i) q^{30} -0.907497 q^{31} +(-0.258963 + 5.65092i) q^{32} -1.31243 q^{33} +(4.12210 + 5.78426i) q^{34} +(-0.321160 - 0.321160i) q^{35} +(2.41514 + 0.833937i) q^{36} +(-2.75378 + 2.75378i) q^{37} +(-1.65616 + 9.87059i) q^{38} -3.14831i q^{39} +(-1.35283 + 2.48392i) q^{40} +5.92805i q^{41} +(-0.831377 - 0.139494i) q^{42} +(-1.64187 + 1.64187i) q^{43} +(0.875188 + 1.79835i) q^{44} +(0.903353 + 0.903353i) q^{45} +(4.31255 - 3.07330i) q^{46} +2.91136 q^{47} +(0.630768 + 5.21168i) q^{48} +6.79371 q^{49} +(-1.15169 + 0.820740i) q^{50} +(4.66094 + 4.66094i) q^{51} +(-4.31395 + 2.09944i) q^{52} +(-8.18387 + 8.18387i) q^{53} +(7.82988 + 1.31375i) q^{54} +1.00000i q^{55} +(0.363260 + 1.23221i) q^{56} +9.28822i q^{57} +(1.29233 - 7.70218i) q^{58} +(-4.18163 + 4.18163i) q^{59} +(-0.856714 + 2.48111i) q^{60} +(-2.75880 - 2.75880i) q^{61} +(0.744819 + 1.04515i) q^{62} +0.580242 q^{63} +(6.72064 - 4.33970i) q^{64} -2.39885 q^{65} +(1.07716 + 1.51151i) q^{66} +(-11.5020 - 11.5020i) q^{67} +(3.27849 - 9.49476i) q^{68} +(3.47504 - 3.47504i) q^{69} +(-0.106287 + 0.633465i) q^{70} -9.03904i q^{71} +(-1.02177 - 3.46594i) q^{72} +14.5363i q^{73} +(5.43164 + 0.911359i) q^{74} +(-0.928026 + 0.928026i) q^{75} +(12.7271 - 6.19382i) q^{76} +(0.321160 + 0.321160i) q^{77} +(-3.62587 + 2.58394i) q^{78} +6.29965 q^{79} +(3.97102 - 0.480612i) q^{80} +3.53530 q^{81} +(6.82726 - 4.86539i) q^{82} +(6.58447 + 6.58447i) q^{83} +(0.521691 + 1.07198i) q^{84} +(3.55139 - 3.55139i) q^{85} +(3.23848 + 0.543374i) q^{86} -7.24774i q^{87} +(1.35283 - 2.48392i) q^{88} +16.3014i q^{89} +(0.298963 - 1.78180i) q^{90} +(-0.770413 + 0.770413i) q^{91} +(-7.07896 - 2.44433i) q^{92} +(0.842181 + 0.842181i) q^{93} +(-2.38947 - 3.35298i) q^{94} +7.07713 q^{95} +(5.48453 - 5.00388i) q^{96} -0.511104 q^{97} +(-5.57587 - 7.82424i) q^{98} +(-0.903353 - 0.903353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.820740	−	1.15169i	−0.580351	−	0.814366i
$2$	−0.820740	−	1.15169i	−0.580351	−	0.814366i
$3$	−0.928026	−	0.928026i	−0.535796	−	0.535796i	0.386495	−	0.922291i	$-0.373686\pi$
$3$	−0.928026	−	0.928026i	−0.535796	−	0.535796i	−0.922291	+	0.386495i	$0.873686\pi$
$4$	−0.652771	+	1.89047i	−0.326385	+	0.945237i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.307128	+	1.83047i	−0.125385	+	0.747284i
$7$			0.454189i			0.171667i	0.996309	+	0.0858337i	$0.0273554\pi$
$7$			0.454189i			0.171667i	−0.996309	+	0.0858337i	$0.972645\pi$
$8$	2.71299	−	0.799799i	0.959187	−	0.282772i
$9$		−	1.27753i		−	0.425845i
$10$	1.39472	+	0.234015i	0.441048	+	0.0740022i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	2.36020	−	1.14862i	0.681330	−	0.331578i
$13$	1.69624	+	1.69624i	0.470452	+	0.470452i	0.902061	−	0.431609i	$-0.142054\pi$
$13$	1.69624	+	1.69624i	0.470452	+	0.470452i	−0.431609	+	0.902061i	$0.642054\pi$
$14$	0.523084	−	0.372771i	0.139800	−	0.0996273i
$15$	1.31243			0.338867
$16$	−3.14778	−	2.46809i	−0.786945	−	0.617023i
$17$	−5.02242			−1.21812			−0.609058	−	0.793126i	$-0.708452\pi$
$17$	−5.02242			−1.21812			−0.609058	+	0.793126i	$0.708452\pi$
$18$	−1.47132	+	1.04852i	−0.346794	+	0.247139i
$19$	−5.00428	−	5.00428i	−1.14806	−	1.14806i	−0.986933	−	0.161128i	$-0.948487\pi$
$19$	−5.00428	−	5.00428i	−1.14806	−	1.14806i	−0.161128	−	0.986933i	$-0.551513\pi$
$20$	−0.875188	−	1.79835i	−0.195698	−	0.402122i
$21$	0.421499	−	0.421499i	0.0919787	−	0.0919787i
$22$	−1.39472	−	0.234015i	−0.297355	−	0.0498923i
$23$			3.74454i			0.780791i	0.920647	+	0.390396i	$0.127662\pi$
$23$			3.74454i			0.780791i	−0.920647	+	0.390396i	$0.872338\pi$
$24$	−3.25996	−	1.77549i	−0.665437	−	0.362421i
$25$		−	1.00000i		−	0.200000i
$26$	0.561367	−	3.34571i	0.110093	−	0.656148i
$27$	−3.96966	+	3.96966i	−0.763962	+	0.763962i
$28$	−0.858632	−	0.296481i	−0.162266	−	0.0560297i
$29$	3.90492	+	3.90492i	0.725125	+	0.725125i	0.969645	−	0.244519i	$-0.0786301\pi$
$29$	3.90492	+	3.90492i	0.725125	+	0.725125i	−0.244519	+	0.969645i	$0.578630\pi$
$30$	−1.07716	−	1.51151i	−0.196662	−	0.275962i
$31$	−0.907497			−0.162991			−0.0814957	−	0.996674i	$-0.525970\pi$
$31$	−0.907497			−0.162991			−0.0814957	+	0.996674i	$0.525970\pi$
$32$	−0.258963	+	5.65092i	−0.0457786	+	0.998952i
$33$	−1.31243			−0.228464
$34$	4.12210	+	5.78426i	0.706935	+	0.991993i
$35$	−0.321160	−	0.321160i	−0.0542860	−	0.0542860i
$36$	2.41514	+	0.833937i	0.402524	+	0.138990i
$37$	−2.75378	+	2.75378i	−0.452719	+	0.452719i	−0.896256	−	0.443537i	$-0.853724\pi$
$37$	−2.75378	+	2.75378i	−0.452719	+	0.452719i	0.443537	+	0.896256i	$0.353724\pi$
$38$	−1.65616	+	9.87059i	−0.268664	+	1.60122i
$39$		−	3.14831i		−	0.504133i
$40$	−1.35283	+	2.48392i	−0.213901	+	0.392742i
$41$			5.92805i			0.925806i	0.886409	+	0.462903i	$0.153192\pi$
$41$			5.92805i			0.925806i	−0.886409	+	0.462903i	$0.846808\pi$
$42$	−0.831377	−	0.139494i	−0.128284	−	0.0215244i
$43$	−1.64187	+	1.64187i	−0.250383	+	0.250383i	−0.821128	−	0.570745i	$-0.806655\pi$
$43$	−1.64187	+	1.64187i	−0.250383	+	0.250383i	0.570745	+	0.821128i	$0.306655\pi$
$44$	0.875188	+	1.79835i	0.131940	+	0.271111i
$45$	0.903353	+	0.903353i	0.134664	+	0.134664i
$46$	4.31255	−	3.07330i	0.635850	−	0.453133i
$47$	2.91136			0.424666			0.212333	−	0.977197i	$-0.431894\pi$
$47$	2.91136			0.424666			0.212333	+	0.977197i	$0.431894\pi$
$48$	0.630768	+	5.21168i	0.0910435	+	0.752241i
$49$	6.79371			0.970530
$50$	−1.15169	+	0.820740i	−0.162873	+	0.116070i
$51$	4.66094	+	4.66094i	0.652662	+	0.652662i
$52$	−4.31395	+	2.09944i	−0.598238	+	0.291140i
$53$	−8.18387	+	8.18387i	−1.12414	+	1.12414i	−0.133029	+	0.991112i	$0.542470\pi$
$53$	−8.18387	+	8.18387i	−1.12414	+	1.12414i	−0.991112	+	0.133029i	$0.957530\pi$
$54$	7.82988	+	1.31375i	1.06551	+	0.178779i
$55$			1.00000i			0.134840i
$56$	0.363260	+	1.23221i	0.0485427	+	0.164661i
$57$			9.28822i			1.23025i
$58$	1.29233	−	7.70218i	0.169691	−	1.01135i
$59$	−4.18163	+	4.18163i	−0.544402	+	0.544402i	−0.924816	−	0.380415i	$-0.875781\pi$
$59$	−4.18163	+	4.18163i	−0.544402	+	0.544402i	0.380415	+	0.924816i	$0.375781\pi$
$60$	−0.856714	+	2.48111i	−0.110601	+	0.320310i
$61$	−2.75880	−	2.75880i	−0.353228	−	0.353228i	0.508081	−	0.861309i	$-0.330355\pi$
$61$	−2.75880	−	2.75880i	−0.353228	−	0.353228i	−0.861309	+	0.508081i	$0.830355\pi$
$62$	0.744819	+	1.04515i	0.0945922	+	0.132735i
$63$	0.580242			0.0731036
$64$	6.72064	−	4.33970i	0.840080	−	0.542462i
$65$	−2.39885			−0.297540
$66$	1.07716	+	1.51151i	0.132589	+	0.186054i
$67$	−11.5020	−	11.5020i	−1.40519	−	1.40519i	−0.782349	−	0.622840i	$-0.785979\pi$
$67$	−11.5020	−	11.5020i	−1.40519	−	1.40519i	−0.622840	−	0.782349i	$-0.714021\pi$
$68$	3.27849	−	9.49476i	0.397575	−	1.15141i
$69$	3.47504	−	3.47504i	0.418345	−	0.418345i
$70$	−0.106287	+	0.633465i	−0.0127038	+	0.0757136i
$71$		−	9.03904i		−	1.07274i	−0.843984	−	0.536368i	$-0.819796\pi$
$71$		−	9.03904i		−	1.07274i	0.843984	−	0.536368i	$-0.180204\pi$
$72$	−1.02177	−	3.46594i	−0.120417	−	0.408465i
$73$			14.5363i			1.70135i	0.525693	+	0.850674i	$0.323806\pi$
$73$			14.5363i			1.70135i	−0.525693	+	0.850674i	$0.676194\pi$
$74$	5.43164	+	0.911359i	0.631415	+	0.105943i
$75$	−0.928026	+	0.928026i	−0.107159	+	0.107159i
$76$	12.7271	−	6.19382i	1.45990	−	0.710479i
$77$	0.321160	+	0.321160i	0.0365996	+	0.0365996i
$78$	−3.62587	+	2.58394i	−0.410549	+	0.292574i
$79$	6.29965			0.708766			0.354383	−	0.935100i	$-0.384691\pi$
$79$	6.29965			0.708766			0.354383	+	0.935100i	$0.384691\pi$
$80$	3.97102	−	0.480612i	0.443974	−	0.0537340i
$81$	3.53530			0.392811
$82$	6.82726	−	4.86539i	0.753945	−	0.537292i
$83$	6.58447	+	6.58447i	0.722740	+	0.722740i	0.969162	−	0.246423i	$-0.0792551\pi$
$83$	6.58447	+	6.58447i	0.722740	+	0.722740i	−0.246423	+	0.969162i	$0.579255\pi$
$84$	0.521691	+	1.07198i	0.0569211	+	0.116962i
$85$	3.55139	−	3.55139i	0.385202	−	0.385202i
$86$	3.23848	+	0.543374i	0.349214	+	0.0585935i
$87$		−	7.24774i		−	0.777039i
$88$	1.35283	−	2.48392i	0.144212	−	0.264787i
$89$			16.3014i			1.72795i	0.503535	+	0.863975i	$0.332032\pi$
$89$			16.3014i			1.72795i	−0.503535	+	0.863975i	$0.667968\pi$
$90$	0.298963	−	1.78180i	0.0315134	−	0.187818i
$91$	−0.770413	+	0.770413i	−0.0807613	+	0.0807613i
$92$	−7.07896	−	2.44433i	−0.738033	−	0.254839i
$93$	0.842181	+	0.842181i	0.0873301	+	0.0873301i
$94$	−2.38947	−	3.35298i	−0.246455	−	0.345834i
$95$	7.07713			0.726098
$96$	5.48453	−	5.00388i	0.559763	−	0.510707i
$97$	−0.511104			−0.0518947			−0.0259474	−	0.999663i	$-0.508260\pi$
$97$	−0.511104			−0.0518947			−0.0259474	+	0.999663i	$0.508260\pi$
$98$	−5.57587	−	7.82424i	−0.563248	−	0.790367i
$99$	−0.903353	−	0.903353i	−0.0907904	−	0.0907904i
$100$	1.89047	+	0.652771i	0.189047	+	0.0652771i
$101$	−7.56974	+	7.56974i	−0.753218	+	0.753218i	−0.975078	−	0.221861i	$-0.928787\pi$
$101$	−7.56974	+	7.56974i	−0.753218	+	0.753218i	0.221861	+	0.975078i	$0.428787\pi$
$102$	1.54253	−	9.19337i	0.152733	−	0.910279i
$103$			11.1719i			1.10080i	0.834900	+	0.550401i	$0.185525\pi$
$103$			11.1719i			1.10080i	−0.834900	+	0.550401i	$0.814475\pi$
$104$	5.95853	+	3.24523i	0.584282	+	0.318221i
$105$			0.596090i			0.0581724i
$106$	16.1421	+	2.70844i	1.56786	+	0.263066i
$107$	−9.37542	+	9.37542i	−0.906356	+	0.906356i	−0.995976	−	0.0896198i	$-0.971435\pi$
$107$	−9.37542	+	9.37542i	−0.906356	+	0.906356i	0.0896198	+	0.995976i	$0.471435\pi$
$108$	−4.91326	−	10.0958i	−0.472779	−	0.971471i
$109$	−2.49283	−	2.49283i	−0.238770	−	0.238770i	0.577571	−	0.816341i	$-0.304001\pi$
$109$	−2.49283	−	2.49283i	−0.238770	−	0.238770i	−0.816341	+	0.577571i	$0.804001\pi$
$110$	1.15169	−	0.820740i	0.109809	−	0.0782545i
$111$	5.11117			0.485131
$112$	1.12098	−	1.42969i	0.105923	−	0.135093i
$113$	13.0610			1.22867			0.614336	−	0.789045i	$-0.289424\pi$
$113$	13.0610			1.22867			0.614336	+	0.789045i	$0.289424\pi$
$114$	10.6971	−	7.62321i	1.00188	−	0.713979i
$115$	−2.64779	−	2.64779i	−0.246908	−	0.246908i
$116$	−9.93117	+	4.83313i	−0.922086	+	0.448745i
$117$	2.16700	−	2.16700i	0.200340	−	0.200340i
$118$	8.24796	+	1.38390i	0.759286	+	0.127398i
$119$		−	2.28113i		−	0.209111i
$120$	3.56060	−	1.04968i	0.325037	−	0.0958221i
$121$		−	1.00000i		−	0.0909091i
$122$	−0.913020	+	5.44154i	−0.0826609	+	0.492654i
$123$	5.50139	−	5.50139i	0.496043	−	0.496043i
$124$	0.592388	−	1.71560i	0.0531980	−	0.154065i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.476228	−	0.668258i	−0.0424258	−	0.0595331i
$127$	−17.2492			−1.53062			−0.765310	−	0.643662i	$-0.777414\pi$
$127$	−17.2492			−1.53062			−0.765310	+	0.643662i	$0.777414\pi$
$128$	−10.5139	−	4.17832i	−0.929304	−	0.369315i
$129$	3.04740			0.268309
$130$	1.96883	+	2.76272i	0.172678	+	0.242307i
$131$	−6.75979	−	6.75979i	−0.590605	−	0.590605i	0.347190	−	0.937795i	$-0.387136\pi$
$131$	−6.75979	−	6.75979i	−0.590605	−	0.590605i	−0.937795	+	0.347190i	$0.887136\pi$
$132$	0.856714	−	2.48111i	0.0745674	−	0.215953i
$133$	2.27289	−	2.27289i	0.197085	−	0.197085i
$134$	−3.80655	+	22.6868i	−0.328836	+	1.95984i
$135$		−	5.61395i		−	0.483172i
$136$	−13.6258	+	4.01693i	−1.16840	+	0.344449i
$137$		−	11.9178i		−	1.01821i	−0.860706	−	0.509103i	$-0.829977\pi$
$137$		−	11.9178i		−	1.01821i	0.860706	−	0.509103i	$-0.170023\pi$
$138$	−6.85426	−	1.15006i	−0.583473	−	0.0978992i
$139$	0.303240	−	0.303240i	0.0257205	−	0.0257205i	−0.694130	−	0.719850i	$-0.744211\pi$
$139$	0.303240	−	0.303240i	0.0257205	−	0.0257205i	0.719850	+	0.694130i	$0.244211\pi$
$140$	0.816789	−	0.397501i	0.0690312	−	0.0335949i
$141$	−2.70182	−	2.70182i	−0.227534	−	0.227534i
$142$	−10.4102	+	7.41870i	−0.873601	+	0.622564i
$143$	2.39885			0.200602
$144$	−3.15307	+	4.02140i	−0.262756	+	0.335116i
$145$	−5.52239			−0.458610
$146$	16.7413	−	11.9305i	1.38552	−	0.987379i
$147$	−6.30474	−	6.30474i	−0.520006	−	0.520006i
$148$	−3.40837	−	7.00355i	−0.280166	−	0.575688i
$149$	−15.3850	+	15.3850i	−1.26039	+	1.26039i	−0.309484	+	0.950904i	$0.600156\pi$
$149$	−15.3850	+	15.3850i	−1.26039	+	1.26039i	−0.950904	+	0.309484i	$0.899844\pi$
$150$	1.83047	+	0.307128i	0.149457	+	0.0250769i
$151$		−	18.4666i		−	1.50279i	−0.659854	−	0.751394i	$-0.729382\pi$
$151$		−	18.4666i		−	1.50279i	0.659854	−	0.751394i	$-0.270618\pi$
$152$	−17.5790	−	9.57416i	−1.42585	−	0.776567i
$153$			6.41632i			0.518729i
$154$	0.106287	−	0.633465i	0.00856487	−	0.0510461i
$155$	0.641697	−	0.641697i	0.0515424	−	0.0515424i
$156$	5.95180	+	2.05513i	0.476525	+	0.164542i
$157$	6.21339	+	6.21339i	0.495883	+	0.495883i	0.910154	−	0.414271i	$-0.135963\pi$
$157$	6.21339	+	6.21339i	0.495883	+	0.495883i	−0.414271	+	0.910154i	$0.635963\pi$
$158$	−5.17037	−	7.25523i	−0.411333	−	0.577195i
$159$	15.1897			1.20462
$160$	−3.81269	−	4.17892i	−0.301420	−	0.330373i
$161$	−1.70073			−0.134036
$162$	−2.90157	−	4.07157i	−0.227968	−	0.319892i
$163$	−2.55397	−	2.55397i	−0.200042	−	0.200042i	0.599976	−	0.800018i	$-0.295177\pi$
$163$	−2.55397	−	2.55397i	−0.200042	−	0.200042i	−0.800018	+	0.599976i	$0.795177\pi$
$164$	−11.2068	−	3.86966i	−0.875106	−	0.302170i
$165$	0.928026	−	0.928026i	0.0722467	−	0.0722467i
$166$	2.17912	−	12.9874i	0.169132	−	1.00802i
$167$			4.05865i			0.314068i	0.987593	+	0.157034i	$0.0501932\pi$
$167$			4.05865i			0.314068i	−0.987593	+	0.157034i	$0.949807\pi$
$168$	0.806409	−	1.48064i	0.0622158	−	0.114234i
$169$		−	7.24554i		−	0.557349i
$170$	−7.00486	−	1.17532i	−0.537248	−	0.0901433i
$171$	−6.39315	+	6.39315i	−0.488896	+	0.488896i
$172$	−2.03215	−	4.17568i	−0.154950	−	0.318393i
$173$	−4.23452	−	4.23452i	−0.321945	−	0.321945i	0.527568	−	0.849513i	$-0.323104\pi$
$173$	−4.23452	−	4.23452i	−0.321945	−	0.321945i	−0.849513	+	0.527568i	$0.823104\pi$
$174$	−8.34713	+	5.94851i	−0.632795	+	0.450955i
$175$	0.454189			0.0343335
$176$	−3.97102	+	0.480612i	−0.299327	+	0.0362275i
$177$	7.76132			0.583377
$178$	18.7742	−	13.3792i	1.40718	−	1.00282i
$179$	−0.352206	−	0.352206i	−0.0263251	−	0.0263251i	0.693822	−	0.720147i	$-0.255926\pi$
$179$	−0.352206	−	0.352206i	−0.0263251	−	0.0263251i	−0.720147	+	0.693822i	$0.755926\pi$
$180$	−2.29745	+	1.11808i	−0.171242	+	0.0833370i
$181$	−10.3576	+	10.3576i	−0.769877	+	0.769877i	−0.978085	−	0.208207i	$-0.933237\pi$
$181$	−10.3576	+	10.3576i	−0.769877	+	0.769877i	0.208207	+	0.978085i	$0.433237\pi$
$182$	1.51959	+	0.254967i	0.112639	+	0.0188994i
$183$			5.12048i			0.378517i
$184$	2.99488	+	10.1589i	0.220786	+	0.748925i
$185$		−	3.89444i		−	0.286325i
$186$	0.278718	−	1.66114i	0.0204366	−	0.121801i
$187$	−3.55139	+	3.55139i	−0.259703	+	0.259703i
$188$	−1.90045	+	5.50385i	−0.138605	+	0.401410i
$189$	−1.80298	−	1.80298i	−0.131147	−	0.131147i
$190$	−5.80848	−	8.15064i	−0.421392	−	0.591310i
$191$	23.1351			1.67399			0.836997	−	0.547207i	$-0.184309\pi$
$191$	23.1351			1.67399			0.836997	+	0.547207i	$0.184309\pi$
$192$	−10.2643	−	2.20958i	−0.740761	−	0.159463i
$193$	−10.4021			−0.748757			−0.374378	−	0.927276i	$-0.622144\pi$
$193$	−10.4021			−0.748757			−0.374378	+	0.927276i	$0.622144\pi$
$194$	0.419483	+	0.588632i	0.0301172	+	0.0422613i
$195$	2.22619	+	2.22619i	0.159421	+	0.159421i
$196$	−4.43474	+	12.8433i	−0.316767	+	0.917381i
$197$	−4.76688	+	4.76688i	−0.339626	+	0.339626i	−0.856227	−	0.516600i	$-0.827197\pi$
$197$	−4.76688	+	4.76688i	−0.339626	+	0.339626i	0.516600	+	0.856227i	$0.327197\pi$
$198$	−0.298963	+	1.78180i	−0.0212464	+	0.126627i
$199$		−	12.2243i		−	0.866558i	−0.901260	−	0.433279i	$-0.857356\pi$
$199$		−	12.2243i		−	0.866558i	0.901260	−	0.433279i	$-0.142644\pi$
$200$	−0.799799	−	2.71299i	−0.0565543	−	0.191837i
$201$			21.3483i			1.50579i
$202$	14.9308	+	2.50519i	1.05053	+	0.176265i
$203$	−1.77357	+	1.77357i	−0.124480	+	0.124480i
$204$	−11.8539	+	5.76886i	−0.829940	+	0.403901i
$205$	−4.19176	−	4.19176i	−0.292765	−	0.292765i
$206$	12.8666	−	9.16924i	0.896456	−	0.638852i
$207$	4.78378			0.332496
$208$	−1.15291	−	9.52587i	−0.0799402	−	0.660500i
$209$	−7.07713			−0.489535
$210$	0.686510	−	0.489235i	0.0473737	−	0.0337604i
$211$	−0.535279	−	0.535279i	−0.0368501	−	0.0368501i	0.688442	−	0.725292i	$-0.258295\pi$
$211$	−0.535279	−	0.535279i	−0.0368501	−	0.0368501i	−0.725292	+	0.688442i	$0.758295\pi$
$212$	−10.1292	−	20.8136i	−0.695676	−	1.42948i
$213$	−8.38847	+	8.38847i	−0.574768	+	0.574768i
$214$	18.4923	+	3.10278i	1.26411	+	0.212101i
$215$		−	2.32196i		−	0.158356i
$216$	−7.59473	+	13.9446i	−0.516756	+	0.948810i
$217$		−	0.412175i		−	0.0279803i
$218$	−0.824996	+	4.91692i	−0.0558758	+	0.333016i
$219$	13.4901	−	13.4901i	0.911576	−	0.911576i
$220$	−1.89047	−	0.652771i	−0.127456	−	0.0440098i
$221$	−8.51923	−	8.51923i	−0.573066	−	0.573066i
$222$	−4.19494	−	5.88647i	−0.281546	−	0.395074i
$223$	18.4911			1.23825			0.619127	−	0.785291i	$-0.287487\pi$
$223$	18.4911			1.23825			0.619127	+	0.785291i	$0.287487\pi$
$224$	−2.56659	−	0.117618i	−0.171487	−	0.00785869i
$225$	−1.27753			−0.0851690
$226$	−10.7197	−	15.0422i	−0.713061	−	1.00059i
$227$	−10.2982	−	10.2982i	−0.683514	−	0.683514i	0.277276	−	0.960790i	$-0.410568\pi$
$227$	−10.2982	−	10.2982i	−0.683514	−	0.683514i	−0.960790	+	0.277276i	$0.910568\pi$
$228$	−17.5591	−	6.06308i	−1.16288	−	0.401537i
$229$	12.8375	−	12.8375i	0.848324	−	0.848324i	−0.141600	−	0.989924i	$-0.545225\pi$
$229$	12.8375	−	12.8375i	0.848324	−	0.848324i	0.989924	+	0.141600i	$0.0452246\pi$
$230$	−0.876281	+	5.22258i	−0.0577803	+	0.344367i
$231$		−	0.596090i		−	0.0392198i
$232$	13.7172	+	7.47086i	0.900576	+	0.490486i
$233$		−	1.38063i		−	0.0904482i	−0.998977	−	0.0452241i	$-0.985600\pi$
$233$		−	1.38063i		−	0.0904482i	0.998977	−	0.0452241i	$-0.0144002\pi$
$234$	−4.27426	−	0.717166i	−0.279417	−	0.0468826i
$235$	−2.05864	+	2.05864i	−0.134291	+	0.134291i
$236$	−5.17561	−	10.6349i	−0.336904	−	0.692273i
$237$	−5.84624	−	5.84624i	−0.379754	−	0.379754i
$238$	−2.62715	+	1.87221i	−0.170293	+	0.121358i
$239$	−21.2733			−1.37605			−0.688027	−	0.725686i	$-0.741523\pi$
$239$	−21.2733			−1.37605			−0.688027	+	0.725686i	$0.741523\pi$
$240$	−4.13123	−	3.23919i	−0.266670	−	0.209089i
$241$	16.5142			1.06377			0.531887	−	0.846816i	$-0.321483\pi$
$241$	16.5142			1.06377			0.531887	+	0.846816i	$0.321483\pi$
$242$	−1.15169	+	0.820740i	−0.0740333	+	0.0527592i
$243$	8.62814	+	8.62814i	0.553495	+	0.553495i
$244$	7.01631	−	3.41458i	0.449173	−	0.218596i
$245$	−4.80388	+	4.80388i	−0.306909	+	0.306909i
$246$	−10.8511	−	1.82067i	−0.691840	−	0.116082i
$247$		−	16.9769i		−	1.08022i
$248$	−2.46203	+	0.725815i	−0.156339	+	0.0460893i
$249$		−	12.2211i		−	0.774483i
$250$	0.234015	−	1.39472i	0.0148004	−	0.0882097i
$251$	−1.81985	+	1.81985i	−0.114868	+	0.114868i	−0.762204	−	0.647336i	$-0.775883\pi$
$251$	−1.81985	+	1.81985i	−0.114868	+	0.114868i	0.647336	+	0.762204i	$0.275883\pi$
$252$	−0.378765	+	1.09693i	−0.0238600	+	0.0691002i
$253$	2.64779	+	2.64779i	0.166465	+	0.166465i
$254$	14.1571	+	19.8657i	0.888297	+	1.24649i
$255$	−6.59156			−0.412780
$256$	3.81704	+	15.5380i	0.238565	+	0.971127i
$257$	−17.5934			−1.09745			−0.548724	−	0.836004i	$-0.684886\pi$
$257$	−17.5934			−1.09745			−0.548724	+	0.836004i	$0.684886\pi$
$258$	−2.50113	−	3.50966i	−0.155713	−	0.218502i
$259$	−1.25074	−	1.25074i	−0.0777171	−	0.0777171i
$260$	1.56590	−	4.53495i	0.0971128	−	0.281246i
$261$	4.98867	−	4.98867i	0.308791	−	0.308791i
$262$	−2.23714	+	13.3332i	−0.138211	+	0.823727i
$263$		−	20.7559i		−	1.27987i	−0.768431	−	0.639933i	$-0.778962\pi$
$263$		−	20.7559i		−	1.27987i	0.768431	−	0.639933i	$-0.221038\pi$
$264$	−3.56060	+	1.04968i	−0.219140	+	0.0646032i
$265$		−	11.5737i		−	0.710969i
$266$	−4.48311	−	0.752208i	−0.274877	−	0.0461209i
$267$	15.1282	−	15.1282i	0.925829	−	0.925829i
$268$	29.2523	−	14.2360i	1.78687	−	0.869603i
$269$	−14.3643	−	14.3643i	−0.875809	−	0.875809i	0.117289	−	0.993098i	$-0.462580\pi$
$269$	−14.3643	−	14.3643i	−0.875809	−	0.875809i	−0.993098	+	0.117289i	$0.962580\pi$
$270$	−6.46552	+	4.60760i	−0.393479	+	0.280409i
$271$	−13.6663			−0.830170			−0.415085	−	0.909783i	$-0.636248\pi$
$271$	−13.6663			−0.830170			−0.415085	+	0.909783i	$0.636248\pi$
$272$	15.8095	+	12.3958i	0.958591	+	0.751606i
$273$	1.42993			0.0865432
$274$	−13.7256	+	9.78141i	−0.829192	+	0.590917i
$275$	−0.707107	−	0.707107i	−0.0426401	−	0.0426401i
$276$	4.30106	+	8.83786i	0.258893	+	0.531977i
$277$	2.94540	−	2.94540i	0.176972	−	0.176972i	−0.613062	−	0.790034i	$-0.710063\pi$
$277$	2.94540	−	2.94540i	0.176972	−	0.176972i	0.790034	+	0.613062i	$0.210063\pi$
$278$	−0.598119	−	0.100357i	−0.0358728	−	0.00601899i
$279$			1.15936i			0.0694090i
$280$	−1.12817	−	0.614441i	−0.0674209	−	0.0367199i
$281$			3.42392i			0.204254i	0.994771	+	0.102127i	$0.0325648\pi$
$281$			3.42392i			0.204254i	−0.994771	+	0.102127i	$0.967435\pi$
$282$	−0.894162	+	5.32915i	−0.0532466	+	0.317346i
$283$	−2.62336	+	2.62336i	−0.155943	+	0.155943i	−0.780766	−	0.624824i	$-0.785171\pi$
$283$	−2.62336	+	2.62336i	−0.155943	+	0.155943i	0.624824	+	0.780766i	$0.285171\pi$
$284$	17.0881	+	5.90042i	1.01399	+	0.350126i
$285$	−6.56776	−	6.56776i	−0.389041	−	0.389041i
$286$	−1.96883	−	2.76272i	−0.116419	−	0.163363i
$287$	−2.69245			−0.158931
$288$	7.21925	+	0.330834i	0.425398	+	0.0194946i
$289$	8.22473			0.483807
$290$	4.53245	+	6.36007i	0.266155	+	0.373476i
$291$	0.474318	+	0.474318i	0.0278050	+	0.0278050i
$292$	−27.4805	−	9.48889i	−1.60818	−	0.555295i
$293$	17.7813	−	17.7813i	1.03879	−	1.03879i	0.0395778	−	0.999216i	$-0.487399\pi$
$293$	17.7813	−	17.7813i	1.03879	−	1.03879i	0.999216	−	0.0395778i	$-0.0126013\pi$
$294$	−2.08654	+	12.4357i	−0.121690	+	0.725262i
$295$		−	5.91371i		−	0.344310i
$296$	−5.26852	+	9.67346i	−0.306226	+	0.562259i
$297$			5.61395i			0.325755i
$298$	30.3458	+	5.09164i	1.75789	+	0.294951i
$299$	−6.35164	+	6.35164i	−0.367325	+	0.367325i
$300$	−1.14862	−	2.36020i	−0.0663156	−	0.136266i
$301$	−0.745720	−	0.745720i	−0.0429826	−	0.0429826i
$302$	−21.2677	+	15.1563i	−1.22382	+	0.872145i
$303$	14.0498			0.807142
$304$	3.40135	+	28.1034i	0.195081	+	1.61184i
$305$	3.90153			0.223401
$306$	7.38960	−	5.26613i	0.422435	−	0.301045i
$307$	−10.2010	−	10.2010i	−0.582201	−	0.582201i	0.353306	−	0.935508i	$-0.385057\pi$
$307$	−10.2010	−	10.2010i	−0.582201	−	0.582201i	−0.935508	+	0.353306i	$0.885057\pi$
$308$	−0.816789	+	0.397501i	−0.0465409	+	0.0226497i
$309$	10.3678	−	10.3678i	0.589806	−	0.589806i
$310$	−1.26570	−	0.212368i	−0.0718871	−	0.0120617i
$311$			16.2144i			0.919435i	0.888065	+	0.459718i	$0.152049\pi$
$311$			16.2144i			0.919435i	−0.888065	+	0.459718i	$0.847951\pi$
$312$	−2.51802	−	8.54134i	−0.142555	−	0.483558i
$313$		−	17.1100i		−	0.967112i	−0.875313	−	0.483556i	$-0.839345\pi$
$313$		−	17.1100i		−	0.967112i	0.875313	−	0.483556i	$-0.160655\pi$
$314$	2.05631	−	12.2555i	0.116044	−	0.691616i
$315$	−0.410293	+	0.410293i	−0.0231174	+	0.0231174i
$316$	−4.11223	+	11.9093i	−0.231331	+	0.669951i
$317$	11.8823	+	11.8823i	0.667374	+	0.667374i	0.957107	−	0.289733i	$-0.0935666\pi$
$317$	11.8823	+	11.8823i	0.667374	+	0.667374i	−0.289733	+	0.957107i	$0.593567\pi$
$318$	−12.4668	−	17.4938i	−0.699103	−	0.981003i
$319$	5.52239			0.309195
$320$	−1.68358	+	7.82084i	−0.0941152	+	0.437198i
$321$	17.4013			0.971244
$322$	1.39586	+	1.95871i	0.0777881	+	0.109155i
$323$	25.1336	+	25.1336i	1.39847	+	1.39847i
$324$	−2.30774	+	6.68340i	−0.128208	+	0.371300i
$325$	1.69624	−	1.69624i	0.0940904	−	0.0940904i
$326$	−0.845230	+	5.03752i	−0.0468130	+	0.279002i
$327$			4.62682i			0.255864i
$328$	4.74125	+	16.0827i	0.261792	+	0.888021i
$329$			1.32231i			0.0729012i
$330$	−1.83047	−	0.307128i	−0.100764	−	0.0169069i
$331$	8.21887	−	8.21887i	0.451750	−	0.451750i	−0.444185	−	0.895935i	$-0.646507\pi$
$331$	8.21887	−	8.21887i	0.451750	−	0.451750i	0.895935	+	0.444185i	$0.146507\pi$
$332$	−16.7459	+	8.14962i	−0.919052	+	0.447269i
$333$	3.51805	+	3.51805i	0.192788	+	0.192788i
$334$	4.67430	−	3.33110i	0.255766	−	0.182270i
$335$	16.2662			0.888720
$336$	−2.36709	+	0.286488i	−0.129135	+	0.0156292i
$337$	12.4465			0.678004			0.339002	−	0.940786i	$-0.389911\pi$
$337$	12.4465			0.678004			0.339002	+	0.940786i	$0.389911\pi$
$338$	−8.34460	+	5.94671i	−0.453887	+	0.323458i
$339$	−12.1209	−	12.1209i	−0.658318	−	0.658318i
$340$	4.39556	+	9.03205i	0.238383	+	0.489832i
$341$	−0.641697	+	0.641697i	−0.0347499	+	0.0347499i
$342$	12.6100	+	2.11580i	0.681872	+	0.114409i
$343$			6.26495i			0.338276i
$344$	−3.14122	+	5.76755i	−0.169363	+	0.310966i
$345$			4.91444i			0.264585i
$346$	−1.40141	+	8.35229i	−0.0753401	+	0.449022i
$347$	−11.4171	+	11.4171i	−0.612901	+	0.612901i	−0.943701	−	0.330800i	$-0.892682\pi$
$347$	−11.4171	+	11.4171i	−0.612901	+	0.612901i	0.330800	+	0.943701i	$0.392682\pi$
$348$	13.7017	+	4.73111i	0.734486	+	0.253614i
$349$	−19.7743	−	19.7743i	−1.05849	−	1.05849i	−0.998179	−	0.0603149i	$-0.980790\pi$
$349$	−19.7743	−	19.7743i	−1.05849	−	1.05849i	−0.0603149	−	0.998179i	$-0.519210\pi$
$350$	−0.372771	−	0.523084i	−0.0199255	−	0.0279600i
$351$	−13.4670			−0.718816
$352$	3.81269	+	4.17892i	0.203217	+	0.222737i
$353$	−19.3850			−1.03176			−0.515881	−	0.856660i	$-0.672535\pi$
$353$	−19.3850			−1.03176			−0.515881	+	0.856660i	$0.672535\pi$
$354$	−6.37003	−	8.93862i	−0.338563	−	0.475082i
$355$	6.39157	+	6.39157i	0.339229	+	0.339229i
$356$	−30.8174	−	10.6411i	−1.63332	−	0.563978i
$357$	−2.11695	+	2.11695i	−0.112041	+	0.112041i
$358$	−0.116562	+	0.694701i	−0.00616048	+	0.0367161i
$359$		−	2.92587i		−	0.154422i	−0.997015	−	0.0772108i	$-0.975399\pi$
$359$		−	2.92587i		−	0.154422i	0.997015	−	0.0772108i	$-0.0246015\pi$
$360$	3.17329	+	1.72829i	0.167247	+	0.0910888i
$361$			31.0857i			1.63609i
$362$	20.4297	+	3.42784i	1.07376	+	0.180163i
$363$	−0.928026	+	0.928026i	−0.0487087	+	0.0487087i
$364$	−0.953543	−	1.95935i	−0.0499792	−	0.102698i
$365$	−10.2787	−	10.2787i	−0.538014	−	0.538014i
$366$	5.89720	−	4.20258i	0.308251	−	0.219673i
$367$	23.4950			1.22643			0.613216	−	0.789916i	$-0.289876\pi$
$367$	23.4950			1.22643			0.613216	+	0.789916i	$0.289876\pi$
$368$	9.24188	−	11.7870i	0.481766	−	0.614440i
$369$	7.57329			0.394250
$370$	−4.48518	+	3.19632i	−0.233173	+	0.166169i
$371$	−3.71702	−	3.71702i	−0.192978	−	0.192978i
$372$	−2.14187	+	1.04237i	−0.111051	+	0.0540444i
$373$	16.4560	−	16.4560i	0.852062	−	0.852062i	−0.138325	−	0.990387i	$-0.544172\pi$
$373$	16.4560	−	16.4560i	0.852062	−	0.852062i	0.990387	+	0.138325i	$0.0441719\pi$
$374$	7.00486	+	1.17532i	0.362213	+	0.0607746i
$375$		−	1.31243i		−	0.0677735i
$376$	7.89850	−	2.32850i	0.407334	−	0.120083i
$377$			13.2474i			0.682274i
$378$	−0.596692	+	3.55624i	−0.0306905	+	0.182913i
$379$	13.0999	−	13.0999i	0.672897	−	0.672897i	−0.285486	−	0.958383i	$-0.592155\pi$
$379$	13.0999	−	13.0999i	0.672897	−	0.672897i	0.958383	+	0.285486i	$0.0921550\pi$
$380$	−4.61974	+	13.3791i	−0.236988	+	0.686334i
$381$	16.0077	+	16.0077i	0.820100	+	0.820100i
$382$	−18.9879	−	26.6444i	−0.971505	−	1.36325i
$383$	−13.7992			−0.705105			−0.352553	−	0.935792i	$-0.614686\pi$
$383$	−13.7992			−0.705105			−0.352553	+	0.935792i	$0.614686\pi$
$384$	5.87956	+	13.6347i	0.300040	+	0.695795i
$385$	−0.454189			−0.0231476
$386$	8.53739	+	11.9799i	0.434542	+	0.609762i
$387$	2.09755	+	2.09755i	0.106624	+	0.106624i
$388$	0.333634	−	0.966228i	0.0169377	−	0.0490528i
$389$	24.0290	−	24.0290i	1.21832	−	1.21832i	0.250100	−	0.968220i	$-0.419537\pi$
$389$	24.0290	−	24.0290i	1.21832	−	1.21832i	0.968220	−	0.250100i	$-0.0804634\pi$
$390$	0.736753	−	4.39100i	0.0373070	−	0.222347i
$391$		−	18.8067i		−	0.951095i
$392$	18.4313	−	5.43361i	0.930920	−	0.274439i
$393$			12.5465i			0.632888i
$394$	9.40233	+	1.57759i	0.473683	+	0.0794778i
$395$	−4.45452	+	4.45452i	−0.224131	+	0.224131i
$396$	2.29745	−	1.11808i	0.115451	−	0.0561858i
$397$	−2.16678	−	2.16678i	−0.108748	−	0.108748i	0.650639	−	0.759387i	$-0.274501\pi$
$397$	−2.16678	−	2.16678i	−0.108748	−	0.108748i	−0.759387	+	0.650639i	$0.774501\pi$
$398$	−14.0786	+	10.0330i	−0.705696	+	0.502908i
$399$	−4.21861			−0.211194
$400$	−2.46809	+	3.14778i	−0.123405	+	0.157389i
$401$	−0.773436			−0.0386236			−0.0193118	−	0.999814i	$-0.506148\pi$
$401$	−0.773436			−0.0386236			−0.0193118	+	0.999814i	$0.506148\pi$
$402$	24.5865	−	17.5214i	1.22627	−	0.873887i
$403$	−1.53933	−	1.53933i	−0.0766796	−	0.0766796i
$404$	−9.36909	−	19.2517i	−0.466130	−	0.957808i
$405$	−2.49984	+	2.49984i	−0.124218	+	0.124218i
$406$	3.49824	+	0.586960i	0.173615	+	0.0291303i
$407$			3.89444i			0.193040i
$408$	16.3729	+	8.91727i	0.810580	+	0.441471i
$409$			31.5893i			1.56199i	0.624538	+	0.780994i	$0.285287\pi$
$409$			31.5893i			1.56199i	−0.624538	+	0.780994i	$0.714713\pi$
$410$	−1.38726	+	8.26795i	−0.0685117	+	0.408325i
$411$	−11.0600	+	11.0600i	−0.545551	+	0.545551i
$412$	−21.1202	−	7.29271i	−1.04052	−	0.359286i
$413$	−1.89925	−	1.89925i	−0.0934559	−	0.0934559i
$414$	−3.92624	−	5.50943i	−0.192964	−	0.270774i
$415$	−9.31185			−0.457101
$416$	−10.0246	+	9.14606i	−0.491496	+	0.448422i
$417$	−0.562829			−0.0275619
$418$	5.80848	+	8.15064i	0.284102	+	0.398661i
$419$	18.9633	+	18.9633i	0.926420	+	0.926420i	0.997473	−	0.0710526i	$-0.0226358\pi$
$419$	18.9633	+	18.9633i	0.926420	+	0.926420i	−0.0710526	+	0.997473i	$0.522636\pi$
$420$	−1.12689	−	0.389110i	−0.0549867	−	0.0189866i
$421$	−7.22822	+	7.22822i	−0.352282	+	0.352282i	−0.860958	−	0.508676i	$-0.830135\pi$
$421$	−7.22822	+	7.22822i	−0.352282	+	0.352282i	0.508676	+	0.860958i	$0.330135\pi$
$422$	−0.177149	+	1.05580i	−0.00862350	+	0.0513955i
$423$		−	3.71937i		−	0.180842i
$424$	−15.6573	+	28.7482i	−0.760387	+	1.39614i
$425$			5.02242i			0.243623i
$426$	16.5456	+	2.77615i	0.801639	+	0.134505i
$427$	1.25302	−	1.25302i	0.0606378	−	0.0606378i
$428$	−11.6040	−	23.8440i	−0.560900	−	1.15254i
$429$	−2.22619	−	2.22619i	−0.107482	−	0.107482i
$430$	−2.67417	+	1.90572i	−0.128960	+	0.0919022i
$431$	18.8166			0.906363			0.453181	−	0.891418i	$-0.350289\pi$
$431$	18.8166			0.906363			0.453181	+	0.891418i	$0.350289\pi$
$432$	22.2931	−	2.69813i	1.07258	−	0.129814i
$433$	11.8666			0.570271			0.285136	−	0.958487i	$-0.407961\pi$
$433$	11.8666			0.570271			0.285136	+	0.958487i	$0.407961\pi$
$434$	−0.474697	+	0.338289i	−0.0227862	+	0.0162384i
$435$	5.12492	+	5.12492i	0.245721	+	0.245721i
$436$	6.33987	−	3.08538i	0.303625	−	0.147763i
$437$	18.7388	−	18.7388i	0.896397	−	0.896397i
$438$	−26.6082	−	4.46452i	−1.27139	−	0.213323i
$439$		−	2.33769i		−	0.111572i	−0.998443	−	0.0557858i	$-0.982234\pi$
$439$		−	2.33769i		−	0.111572i	0.998443	−	0.0557858i	$-0.0177664\pi$
$440$	0.799799	+	2.71299i	0.0381289	+	0.129337i
$441$		−	8.67920i		−	0.413295i
$442$	−2.81942	+	16.8036i	−0.134106	+	0.799265i
$443$	−21.7373	+	21.7373i	−1.03277	+	1.03277i	−0.0333275	+	0.999444i	$0.510610\pi$
$443$	−21.7373	+	21.7373i	−1.03277	+	1.03277i	−0.999444	+	0.0333275i	$0.989390\pi$
$444$	−3.33642	+	9.66253i	−0.158340	+	0.458563i
$445$	−11.5269	−	11.5269i	−0.546426	−	0.546426i
$446$	−15.1764	−	21.2959i	−0.718622	−	1.00839i
$447$	28.5554			1.35062
$448$	1.97104	+	3.05244i	0.0931230	+	0.144214i
$449$	21.3050			1.00545			0.502723	−	0.864447i	$-0.332331\pi$
$449$	21.3050			1.00545			0.502723	+	0.864447i	$0.332331\pi$
$450$	1.04852	+	1.47132i	0.0494279	+	0.0693587i
$451$	4.19176	+	4.19176i	0.197382	+	0.197382i
$452$	−8.52582	+	24.6914i	−0.401021	+	1.16139i
$453$	−17.1375	+	17.1375i	−0.805188	+	0.805188i
$454$	−3.40816	+	20.3124i	−0.159953	+	0.953309i
$455$		−	1.08953i		−	0.0510779i
$456$	7.42871	+	25.1988i	0.347881	+	1.18004i
$457$		−	11.2058i		−	0.524185i	−0.965043	−	0.262093i	$-0.915587\pi$
$457$		−	11.2058i		−	0.524185i	0.965043	−	0.262093i	$-0.0844126\pi$
$458$	−25.3210	−	4.24854i	−1.18317	−	0.198521i
$459$	19.9373	−	19.9373i	0.930595	−	0.930595i
$460$	6.73398	−	3.27718i	0.313974	−	0.152799i
$461$	−7.25592	−	7.25592i	−0.337942	−	0.337942i	0.517650	−	0.855592i	$-0.326807\pi$
$461$	−7.25592	−	7.25592i	−0.337942	−	0.337942i	−0.855592	+	0.517650i	$0.826807\pi$
$462$	−0.686510	+	0.489235i	−0.0319393	+	0.0227613i
$463$	12.5166			0.581698			0.290849	−	0.956769i	$-0.406062\pi$
$463$	12.5166			0.581698			0.290849	+	0.956769i	$0.406062\pi$
$464$	−2.65413	−	21.9295i	−0.123215	−	1.01805i
$465$	−1.19102			−0.0552324
$466$	−1.59006	+	1.13314i	−0.0736580	+	0.0524917i
$467$	2.64800	+	2.64800i	0.122535	+	0.122535i	0.765715	−	0.643180i	$-0.222385\pi$
$467$	2.64800	+	2.64800i	0.122535	+	0.122535i	−0.643180	+	0.765715i	$0.722385\pi$
$468$	2.68211	+	5.51122i	0.123980	+	0.254756i
$469$	5.22407	−	5.22407i	0.241225	−	0.241225i
$470$	4.06053	+	0.681304i	0.187298	+	0.0314262i
$471$		−	11.5324i		−	0.531384i
$472$	−8.00026	+	14.6892i	−0.368242	+	0.676124i
$473$			2.32196i			0.106764i
$474$	−1.93480	+	11.5313i	−0.0888683	+	0.529650i
$475$	−5.00428	+	5.00428i	−0.229612	+	0.229612i
$476$	4.31241	+	1.48905i	0.197659	+	0.0682507i
$477$	10.4552	+	10.4552i	0.478710	+	0.478710i
$478$	17.4598	+	24.5002i	0.798594	+	1.12061i
$479$	−27.3409			−1.24924			−0.624620	−	0.780929i	$-0.714746\pi$
$479$	−27.3409			−1.24924			−0.624620	+	0.780929i	$0.714746\pi$
$480$	−0.339870	+	7.41643i	−0.0155129	+	0.338512i
$481$	−9.34215			−0.425966
$482$	−13.5539	−	19.0192i	−0.617362	−	0.866301i
$483$	1.57832	+	1.57832i	0.0718162	+	0.0718162i
$484$	1.89047	+	0.652771i	0.0859306	+	0.0296714i
$485$	0.361405	−	0.361405i	0.0164106	−	0.0164106i
$486$	2.85546	−	17.0184i	0.129526	−	0.771970i
$487$		−	4.44679i		−	0.201503i	−0.994912	−	0.100752i	$-0.967875\pi$
$487$		−	4.44679i		−	0.201503i	0.994912	−	0.100752i	$-0.0321247\pi$
$488$	−9.69109	−	5.27812i	−0.438695	−	0.238929i
$489$			4.74030i			0.214364i
$490$	9.47531	+	1.58983i	0.428051	+	0.0718214i
$491$	−12.5327	+	12.5327i	−0.565591	+	0.565591i	−0.930890	−	0.365299i	$-0.880967\pi$
$491$	−12.5327	+	12.5327i	−0.565591	+	0.565591i	0.365299	+	0.930890i	$0.380967\pi$
$492$	6.80908	+	13.9914i	0.306977	+	0.630780i
$493$	−19.6122	−	19.6122i	−0.883287	−	0.883287i
$494$	−19.5521	+	13.9337i	−0.879692	+	0.626905i
$495$	1.27753			0.0574209
$496$	2.85660	+	2.23979i	0.128265	+	0.100569i
$497$	4.10543			0.184154
$498$	−14.0749	+	10.0304i	−0.630713	+	0.449472i
$499$	−24.2554	−	24.2554i	−1.08582	−	1.08582i	−0.995954	−	0.0898672i	$-0.971356\pi$
$499$	−24.2554	−	24.2554i	−1.08582	−	1.08582i	−0.0898672	−	0.995954i	$-0.528644\pi$
$500$	−1.79835	+	0.875188i	−0.0804245	+	0.0391396i
$501$	3.76654	−	3.76654i	0.168276	−	0.168276i
$502$	3.58953	+	0.602276i	0.160208	+	0.0268809i
$503$			37.6186i			1.67733i	0.544647	+	0.838665i	$0.316664\pi$
$503$			37.6186i			1.67733i	−0.544647	+	0.838665i	$0.683336\pi$
$504$	1.57419	−	0.464077i	0.0701201	−	0.0206716i
$505$		−	10.7052i		−	0.476377i
$506$	0.876281	−	5.22258i	0.0389555	−	0.232172i
$507$	−6.72405	+	6.72405i	−0.298626	+	0.298626i
$508$	11.2598	−	32.6092i	0.499572	−	1.44680i
$509$	18.6045	+	18.6045i	0.824631	+	0.824631i	0.986768	−	0.162138i	$-0.0518388\pi$
$509$	18.6045	+	18.6045i	0.824631	+	0.824631i	−0.162138	+	0.986768i	$0.551839\pi$
$510$	5.40996	+	7.59143i	0.239557	+	0.336154i
$511$	−6.60224			−0.292066
$512$	14.7622	−	17.1487i	0.652401	−	0.757874i
$513$	39.7307			1.75415
$514$	14.4396	+	20.2621i	0.636904	+	0.893724i
$515$	−7.89974	−	7.89974i	−0.348104	−	0.348104i
$516$	−1.98926	+	5.76103i	−0.0875721	+	0.253615i
$517$	2.05864	−	2.05864i	0.0905391	−	0.0905391i
$518$	−0.413929	+	2.46699i	−0.0181870	+	0.108393i
$519$			7.85950i			0.344994i
$520$	−6.50805	+	1.91859i	−0.285397	+	0.0841359i
$521$		−	19.2499i		−	0.843355i	−0.906746	−	0.421677i	$-0.861441\pi$
$521$		−	19.2499i		−	0.843355i	0.906746	−	0.421677i	$-0.138559\pi$
$522$	−9.83979	−	1.65099i	−0.430676	−	0.0722619i
$523$	−15.5301	+	15.5301i	−0.679084	+	0.679084i	−0.959793	−	0.280709i	$-0.909430\pi$
$523$	−15.5301	+	15.5301i	−0.679084	+	0.679084i	0.280709	+	0.959793i	$0.409430\pi$
$524$	17.1918	−	8.36660i	0.751027	−	0.365497i
$525$	−0.421499	−	0.421499i	−0.0183957	−	0.0183957i
$526$	−23.9044	+	17.0352i	−1.04228	+	0.742771i
$527$	4.55783			0.198542
$528$	4.13123	+	3.23919i	0.179789	+	0.140968i
$529$	8.97839			0.390365
$530$	−13.3293	+	9.49904i	−0.578990	+	0.412612i
$531$	5.34217	+	5.34217i	0.231831	+	0.231831i
$532$	2.81316	+	5.78052i	0.121966	+	0.250617i
$533$	−10.0554	+	10.0554i	−0.435547	+	0.435547i
$534$	−29.8392	−	5.00663i	−1.29127	−	0.216658i
$535$		−	13.2588i		−	0.573230i
$536$	−40.4040	−	22.0055i	−1.74519	−	0.950492i
$537$			0.653713i			0.0282098i
$538$	−4.75385	+	28.3326i	−0.204953	+	1.22151i
$539$	4.80388	−	4.80388i	0.206918	−	0.206918i
$540$	10.6130	+	3.66463i	0.456712	+	0.157700i
$541$	14.1657	+	14.1657i	0.609031	+	0.609031i	0.942693	−	0.333662i	$-0.108284\pi$
$541$	14.1657	+	14.1657i	0.609031	+	0.609031i	−0.333662	+	0.942693i	$0.608284\pi$
$542$	11.2165	+	15.7393i	0.481790	+	0.676062i
$543$	19.2243			0.824995
$544$	1.30062	−	28.3813i	0.0557637	−	1.21684i
$545$	3.52539			0.151011
$546$	−1.17360	−	1.64683i	−0.0502254	−	0.0704779i
$547$	5.21958	+	5.21958i	0.223173	+	0.223173i	0.809833	−	0.586660i	$-0.199558\pi$
$547$	5.21958	+	5.21958i	0.223173	+	0.223173i	−0.586660	+	0.809833i	$0.699558\pi$
$548$	22.5303	+	7.77959i	0.962445	+	0.332327i
$549$	−3.52446	+	3.52446i	−0.150420	+	0.150420i
$550$	−0.234015	+	1.39472i	−0.00997845	+	0.0594710i
$551$		−	39.0827i		−	1.66498i
$552$	6.64841	−	12.2071i	0.282975	−	0.519567i
$553$			2.86123i			0.121672i
$554$	−5.80959	−	0.974775i	−0.246826	−	0.0414142i
$555$	−3.61414	+	3.61414i	−0.153412	+	0.153412i
$556$	0.375321	+	0.771214i	0.0159172	+	0.0327067i
$557$	21.7128	+	21.7128i	0.920000	+	0.920000i	0.997029	−	0.0770293i	$-0.0245435\pi$
$557$	21.7128	+	21.7128i	0.920000	+	0.920000i	−0.0770293	+	0.997029i	$0.524543\pi$
$558$	1.33522	−	0.951532i	0.0565244	−	0.0402816i
$559$	−5.57002			−0.235587
$560$	0.218289	+	1.80359i	0.00922438	+	0.0762158i
$561$	6.59156			0.278296
$562$	3.94329	−	2.81015i	0.166337	−	0.118539i
$563$	12.7314	+	12.7314i	0.536565	+	0.536565i	0.922518	−	0.385953i	$-0.126127\pi$
$563$	12.7314	+	12.7314i	0.536565	+	0.536565i	−0.385953	+	0.922518i	$0.626127\pi$
$564$	6.87139	−	3.34405i	0.289338	−	0.140810i
$565$	−9.23549	+	9.23549i	−0.388540	+	0.388540i
$566$	5.17439	+	0.868195i	0.217496	+	0.0364930i
$567$			1.60570i			0.0674329i
$568$	−7.22942	−	24.5228i	−0.303340	−	1.02896i
$569$			6.24485i			0.261798i	0.991396	+	0.130899i	$0.0417863\pi$
$569$			6.24485i			0.261798i	−0.991396	+	0.130899i	$0.958214\pi$
$570$	−2.17359	+	12.9544i	−0.0910415	+	0.542602i
$571$	−14.8963	+	14.8963i	−0.623390	+	0.623390i	−0.946397	−	0.323007i	$-0.895306\pi$
$571$	−14.8963	+	14.8963i	−0.623390	+	0.623390i	0.323007	+	0.946397i	$0.395306\pi$
$572$	−1.56590	+	4.53495i	−0.0654734	+	0.189616i
$573$	−21.4700	−	21.4700i	−0.896920	−	0.896920i
$574$	2.20981	+	3.10087i	0.0922355	+	0.129428i
$575$	3.74454			0.156158
$576$	−5.54411	−	8.58585i	−0.231005	−	0.357744i
$577$	−34.3799			−1.43125			−0.715627	−	0.698483i	$-0.753859\pi$
$577$	−34.3799			−1.43125			−0.715627	+	0.698483i	$0.753859\pi$
$578$	−6.75036	−	9.47232i	−0.280778	−	0.393997i
$579$	9.65339	+	9.65339i	0.401181	+	0.401181i
$580$	3.60486	−	10.4399i	0.149684	−	0.433495i
$581$	−2.99060	+	2.99060i	−0.124071	+	0.124071i
$582$	0.156974	−	0.935558i	0.00650680	−	0.0387801i
$583$			11.5737i			0.479335i
$584$	11.6261	+	39.4369i	0.481093	+	1.63191i
$585$			3.06461i			0.126706i
$586$	−35.0723	−	5.88468i	−1.44882	−	0.243094i
$587$	27.5457	−	27.5457i	1.13693	−	1.13693i	0.147934	−	0.988997i	$-0.452738\pi$
$587$	27.5457	−	27.5457i	1.13693	−	1.13693i	0.988997	−	0.147934i	$-0.0472624\pi$
$588$	16.0345	−	7.80340i	0.661252	−	0.321807i
$589$	4.54137	+	4.54137i	0.187124	+	0.187124i
$590$	−6.81075	+	4.85362i	−0.280394	+	0.199821i
$591$	8.84758			0.363941
$592$	15.4649	−	1.87171i	0.635603	−	0.0769269i
$593$	−35.7603			−1.46850			−0.734250	−	0.678879i	$-0.762466\pi$
$593$	−35.7603			−1.46850			−0.734250	+	0.678879i	$0.762466\pi$
$594$	6.46552	−	4.60760i	0.265284	−	0.189052i
$595$	1.61300	+	1.61300i	0.0661266	+	0.0661266i
$596$	−19.0421	−	39.1278i	−0.779993	−	1.60274i
$597$	−11.3445	+	11.3445i	−0.464299	+	0.464299i
$598$	12.5282	+	2.10206i	0.512315	+	0.0859598i
$599$			3.63349i			0.148460i	0.997241	+	0.0742302i	$0.0236499\pi$
$599$			3.63349i			0.148460i	−0.997241	+	0.0742302i	$0.976350\pi$
$600$	−1.77549	+	3.25996i	−0.0724842	+	0.133087i
$601$			24.0797i			0.982232i	0.871094	+	0.491116i	$0.163411\pi$
$601$			24.0797i			0.982232i	−0.871094	+	0.491116i	$0.836589\pi$
$602$	−0.246795	+	1.47088i	−0.0100586	+	0.0599486i
$603$	−14.6942	+	14.6942i	−0.598393	+	0.598393i
$604$	34.9106	+	12.0544i	1.42049	+	0.490488i
$605$	0.707107	+	0.707107i	0.0287480	+	0.0287480i
$606$	−11.5313	−	16.1810i	−0.468426	−	0.657310i
$607$	−35.7604			−1.45147			−0.725735	−	0.687974i	$-0.758500\pi$
$607$	−35.7604			−1.45147			−0.725735	+	0.687974i	$0.758500\pi$
$608$	29.5748	−	26.9829i	1.19941	−	1.09430i
$609$	3.29184			0.133392
$610$	−3.20215	−	4.49335i	−0.129651	−	0.181930i
$611$	4.93837	+	4.93837i	0.199785	+	0.199785i
$612$	−12.1299	−	4.18839i	−0.490321	−	0.169305i
$613$	11.0611	−	11.0611i	0.446755	−	0.446755i	−0.447519	−	0.894274i	$-0.647692\pi$
$613$	11.0611	−	11.0611i	0.446755	−	0.446755i	0.894274	+	0.447519i	$0.147692\pi$
$614$	−3.37600	+	20.1207i	−0.136244	+	0.812006i
$615$			7.78013i			0.313725i
$616$	1.12817	+	0.614441i	0.0454552	+	0.0247565i
$617$		−	10.3895i		−	0.418265i	−0.977887	−	0.209133i	$-0.932936\pi$
$617$		−	10.3895i		−	0.418265i	0.977887	−	0.209133i	$-0.0670640\pi$
$618$	−20.4498	−	3.43121i	−0.822612	−	0.138024i
$619$	−11.0692	+	11.0692i	−0.444907	+	0.444907i	−0.893657	−	0.448750i	$-0.851869\pi$
$619$	−11.0692	+	11.0692i	−0.444907	+	0.444907i	0.448750	+	0.893657i	$0.351869\pi$
$620$	0.794231	+	1.63199i	0.0318971	+	0.0655424i
$621$	−14.8646	−	14.8646i	−0.596495	−	0.596495i
$622$	18.6740	−	13.3078i	0.748757	−	0.533595i
$623$	−7.40394			−0.296632
$624$	−7.77032	+	9.91019i	−0.311062	+	0.396725i
$625$	−1.00000			−0.0400000
$626$	−19.7053	+	14.0428i	−0.787583	+	0.561264i
$627$	6.56776	+	6.56776i	0.262291	+	0.262291i
$628$	−15.8022	+	7.69033i	−0.630575	+	0.306878i
$629$	13.8307	−	13.8307i	0.551465	−	0.551465i
$630$	0.809274	+	0.135786i	0.0322422	+	0.00540983i
$631$			36.7114i			1.46146i	0.682667	+	0.730729i	$0.260820\pi$
$631$			36.7114i			1.46146i	−0.682667	+	0.730729i	$0.739180\pi$
$632$	17.0909	−	5.03845i	0.679839	−	0.200419i
$633$			0.993506i			0.0394883i
$634$	3.93241	−	23.4369i	0.156176	−	0.930798i
$635$	12.1970	−	12.1970i	0.484024	−	0.484024i
$636$	−9.91539	+	28.7157i	−0.393171	+	1.13865i
$637$	11.5238	+	11.5238i	0.456588	+	0.456588i
$638$	−4.53245	−	6.36007i	−0.179441	−	0.251798i
$639$	−11.5477			−0.456819
$640$	10.3890	−	4.47992i	0.410659	−	0.177084i
$641$	41.1262			1.62439			0.812194	−	0.583387i	$-0.198273\pi$
$641$	41.1262			1.62439			0.812194	+	0.583387i	$0.198273\pi$
$642$	−14.2819	−	20.0408i	−0.563663	−	0.790949i
$643$	13.3711	+	13.3711i	0.527305	+	0.527305i	0.919768	−	0.392463i	$-0.128377\pi$
$643$	13.3711	+	13.3711i	0.527305	+	0.527305i	−0.392463	+	0.919768i	$0.628377\pi$
$644$	1.11019	−	3.21519i	0.0437475	−	0.126696i
$645$	−2.15484	+	2.15484i	−0.0848467	+	0.0848467i
$646$	8.31792	−	49.5743i	0.327264	−	1.95047i
$647$		−	7.67070i		−	0.301566i	−0.988567	−	0.150783i	$-0.951820\pi$
$647$		−	7.67070i		−	0.301566i	0.988567	−	0.150783i	$-0.0481795\pi$
$648$	9.59124	−	2.82753i	0.376780	−	0.111076i
$649$			5.91371i			0.232134i
$650$	−3.34571	−	0.561367i	−0.131230	−	0.0220186i
$651$	−0.382509	+	0.382509i	−0.0149917	+	0.0149917i
$652$	6.49536	−	3.16105i	0.254378	−	0.123796i
$653$	−29.7807	−	29.7807i	−1.16541	−	1.16541i	−0.983273	−	0.182136i	$-0.941699\pi$
$653$	−29.7807	−	29.7807i	−1.16541	−	1.16541i	−0.182136	−	0.983273i	$-0.558301\pi$
$654$	5.32865	−	3.79742i	0.208367	−	0.148491i
$655$	9.55978			0.373532
$656$	14.6310	−	18.6602i	0.571243	−	0.728558i
$657$	18.5707			0.724510
$658$	1.52289	−	1.08527i	0.0593683	−	0.0423083i
$659$	−32.5013	−	32.5013i	−1.26607	−	1.26607i	−0.948100	−	0.317972i	$-0.896998\pi$
$659$	−32.5013	−	32.5013i	−1.26607	−	1.26607i	−0.317972	−	0.948100i	$-0.603002\pi$
$660$	1.14862	+	2.36020i	0.0447100	+	0.0918706i
$661$	7.27185	−	7.27185i	0.282842	−	0.282842i	−0.551399	−	0.834241i	$-0.685906\pi$
$661$	7.27185	−	7.27185i	0.282842	−	0.282842i	0.834241	+	0.551399i	$0.185906\pi$
$662$	−16.2111	−	2.72002i	−0.630063	−	0.105716i
$663$			15.8121i			0.614093i
$664$	23.1299	+	12.5974i	0.897613	+	0.488873i
$665$			3.21435i			0.124647i
$666$	1.16429	−	6.93911i	0.0451154	−	0.268885i
$667$	−14.6221	+	14.6221i	−0.566172	+	0.566172i
$668$	−7.67277	−	2.64937i	−0.296868	−	0.102507i
$669$	−17.1602	−	17.1602i	−0.663452	−	0.663452i
$670$	−13.3504	−	18.7336i	−0.515769	−	0.723744i
$671$	−3.90153			−0.150617
$672$	2.27271	+	2.49101i	0.0876716	+	0.0960929i
$673$	−18.2470			−0.703371			−0.351686	−	0.936118i	$-0.614391\pi$
$673$	−18.2470			−0.703371			−0.351686	+	0.936118i	$0.614391\pi$
$674$	−10.2153	−	14.3345i	−0.393481	−	0.552144i
$675$	3.96966	+	3.96966i	0.152792	+	0.152792i
$676$	13.6975	+	4.72968i	0.526827	+	0.181911i
$677$	20.8326	−	20.8326i	0.800662	−	0.800662i	−0.182537	−	0.983199i	$-0.558431\pi$
$677$	20.8326	−	20.8326i	0.800662	−	0.800662i	0.983199	+	0.182537i	$0.0584308\pi$
$678$	−4.01139	+	23.9076i	−0.154057	+	0.918167i
$679$		−	0.232138i		−	0.00890863i
$680$	6.79449	−	12.4753i	0.260557	−	0.478405i
$681$			19.1140i			0.732448i
$682$	1.26570	+	0.212368i	0.0484662	+	0.00813201i
$683$	16.9267	−	16.9267i	0.647683	−	0.647683i	−0.304749	−	0.952433i	$-0.598573\pi$
$683$	16.9267	−	16.9267i	0.647683	−	0.647683i	0.952433	+	0.304749i	$0.0985726\pi$
$684$	−7.91281	−	16.2593i	−0.302554	−	0.621691i
$685$	8.42715	+	8.42715i	0.321985	+	0.321985i
$686$	7.21527	−	5.14190i	0.275480	−	0.196319i
$687$	−23.8270			−0.909058
$688$	9.22055	−	1.11596i	0.351530	−	0.0425456i
$689$	−27.7636			−1.05771
$690$	5.65990	−	4.03348i	0.215469	−	0.153552i
$691$	0.172548	+	0.172548i	0.00656404	+	0.00656404i	0.710381	−	0.703817i	$-0.248523\pi$
$691$	0.172548	+	0.172548i	0.00656404	+	0.00656404i	−0.703817	+	0.710381i	$0.748523\pi$
$692$	10.7694	−	5.24108i	0.409392	−	0.199236i
$693$	0.410293	−	0.410293i	0.0155857	−	0.0155857i
$694$	22.5194	+	3.77846i	0.854824	+	0.143428i
$695$			0.428846i			0.0162671i
$696$	−5.79673	−	19.6630i	−0.219725	−	0.745326i
$697$		−	29.7732i		−	1.12774i
$698$	−6.54426	+	39.0034i	−0.247704	+	1.47630i
$699$	−1.28126	+	1.28126i	−0.0484618	+	0.0484618i
$700$	−0.296481	+	0.858632i	−0.0112059	+	0.0324533i
$701$	−15.5559	−	15.5559i	−0.587538	−	0.587538i	0.349426	−	0.936964i	$-0.386377\pi$
$701$	−15.5559	−	15.5559i	−0.587538	−	0.587538i	−0.936964	+	0.349426i	$0.886377\pi$
$702$	11.0529	+	15.5098i	0.417165	+	0.585379i
$703$	27.5614			1.03950
$704$	1.68358	−	7.82084i	0.0634524	−	0.294759i
$705$	3.82095			0.143905
$706$	15.9101	+	22.3255i	0.598784	+	0.840232i
$707$	−3.43809	−	3.43809i	−0.129303	−	0.129303i
$708$	−5.06636	+	14.6726i	−0.190406	+	0.551429i
$709$	22.4989	−	22.4989i	0.844963	−	0.844963i	−0.144536	−	0.989500i	$-0.546169\pi$
$709$	22.4989	−	22.4989i	0.844963	−	0.844963i	0.989500	+	0.144536i	$0.0461690\pi$
$710$	2.11528	−	12.6069i	0.0793849	−	0.473129i
$711$		−	8.04802i		−	0.301824i
$712$	13.0379	+	44.2257i	0.488615	+	1.65743i
$713$		−	3.39816i		−	0.127262i
$714$	4.17553	+	0.700599i	0.156265	+	0.0262193i
$715$	−1.69624	+	1.69624i	−0.0634358	+	0.0634358i
$716$	0.895746	−	0.435926i	0.0334756	−	0.0162913i
$717$	19.7421	+	19.7421i	0.737284	+	0.737284i
$718$	−3.36969	+	2.40138i	−0.125756	+	0.0896188i
$719$	34.1219			1.27253			0.636265	−	0.771470i	$-0.280478\pi$
$719$	34.1219			1.27253			0.636265	+	0.771470i	$0.280478\pi$
$720$	−0.613998	−	5.07312i	−0.0228824	−	0.189064i
$721$	−5.07416			−0.188972
$722$	35.8011	−	25.5133i	1.33238	−	0.949507i
$723$	−15.3256	−	15.3256i	−0.569966	−	0.569966i
$724$	−12.8197	−	26.3420i	−0.476440	−	0.978993i
$725$	3.90492	−	3.90492i	0.145025	−	0.145025i
$726$	1.83047	+	0.307128i	0.0679349	+	0.0113986i
$727$			12.8599i			0.476949i	0.971149	+	0.238474i	$0.0766473\pi$
$727$			12.8599i			0.476949i	−0.971149	+	0.238474i	$0.923353\pi$
$728$	−1.47395	+	2.70630i	−0.0546282	+	0.100302i
$729$		−	26.6202i		−	0.985933i
$730$	−3.40173	+	20.2741i	−0.125904	+	0.750377i
$731$	8.24618	−	8.24618i	0.304996	−	0.304996i
$732$	−9.68013	−	3.34250i	−0.357788	−	0.123542i
$733$	−14.0410	−	14.0410i	−0.518618	−	0.518618i	0.398535	−	0.917153i	$-0.369519\pi$
$733$	−14.0410	−	14.0410i	−0.518618	−	0.518618i	−0.917153	+	0.398535i	$0.869519\pi$
$734$	−19.2833	−	27.0590i	−0.711761	−	0.998765i
$735$	8.91625			0.328881
$736$	−21.1601	−	0.969698i	−0.779973	−	0.0357435i
$737$	−16.2662			−0.599175
$738$	−6.21570	−	8.72206i	−0.228803	−	0.321064i
$739$	−0.778891	−	0.778891i	−0.0286520	−	0.0286520i	0.692636	−	0.721288i	$-0.256449\pi$
$739$	−0.778891	−	0.778891i	−0.0286520	−	0.0286520i	−0.721288	+	0.692636i	$0.756449\pi$
$740$	7.36233	+	2.54218i	0.270645	+	0.0934523i
$741$	−15.7550	+	15.7550i	−0.578776	+	0.578776i
$742$	−1.23014	+	7.33157i	−0.0451599	+	0.269150i
$743$			19.6788i			0.721944i	0.932577	+	0.360972i	$0.117555\pi$
$743$			19.6788i			0.721944i	−0.932577	+	0.360972i	$0.882445\pi$
$744$	2.95841	+	1.61125i	0.108460	+	0.0590715i
$745$		−	21.7577i		−	0.797140i
$746$	−32.4584	−	5.44609i	−1.18839	−	0.199396i
$747$	8.41189	−	8.41189i	0.307775	−	0.307775i
$748$	−4.39556	−	9.03205i	−0.160718	−	0.330244i
$749$	−4.25821	−	4.25821i	−0.155592	−	0.155592i
$750$	−1.51151	+	1.07716i	−0.0551924	+	0.0393324i
$751$	−31.0413			−1.13271			−0.566357	−	0.824160i	$-0.691648\pi$
$751$	−31.0413			−1.13271			−0.566357	+	0.824160i	$0.691648\pi$
$752$	−9.16433	−	7.18551i	−0.334189	−	0.262029i
$753$	3.37774			0.123092
$754$	15.2568	−	10.8726i	0.555621	−	0.395958i
$755$	13.0578	+	13.0578i	0.475223	+	0.475223i
$756$	4.58541	−	2.23155i	0.166770	−	0.0811607i
$757$	10.3912	−	10.3912i	0.377675	−	0.377675i	−0.492588	−	0.870263i	$-0.663949\pi$
$757$	10.3912	−	10.3912i	0.377675	−	0.377675i	0.870263	+	0.492588i	$0.163949\pi$
$758$	−25.8386	−	4.33539i	−0.938501	−	0.157468i
$759$		−	4.91444i		−	0.178383i
$760$	19.2002	−	5.66028i	0.696464	−	0.205320i
$761$			20.2454i			0.733897i	0.930241	+	0.366948i	$0.119597\pi$
$761$			20.2454i			0.733897i	−0.930241	+	0.366948i	$0.880403\pi$
$762$	5.29772	−	31.5741i	0.191916	−	1.14381i
$763$	1.13221	−	1.13221i	0.0409889	−	0.0409889i
$764$	−15.1019	+	43.7362i	−0.546368	+	1.58232i
$765$	−4.53702	−	4.53702i	−0.164036	−	0.164036i
$766$	11.3255	+	15.8924i	0.409209	+	0.574214i
$767$	−14.1861			−0.512230
$768$	10.8774	−	17.9620i	0.392504	−	0.648148i
$769$	−52.8361			−1.90532			−0.952659	−	0.304040i	$-0.901664\pi$
$769$	−52.8361			−1.90532			−0.952659	+	0.304040i	$0.901664\pi$
$770$	0.372771	+	0.523084i	0.0134337	+	0.0188506i
$771$	16.3272	+	16.3272i	0.588008	+	0.588008i
$772$	6.79016	−	19.6648i	0.244383	−	0.707753i
$773$	−17.9112	+	17.9112i	−0.644221	+	0.644221i	−0.951590	−	0.307370i	$-0.900551\pi$
$773$	−17.9112	+	17.9112i	−0.644221	+	0.644221i	0.307370	+	0.951590i	$0.400551\pi$
$774$	0.694179	−	4.13726i	0.0249518	−	0.148711i
$775$			0.907497i			0.0325983i
$776$	−1.38662	+	0.408780i	−0.0497768	+	0.0146744i
$777$			2.32144i			0.0832811i
$778$	−47.3955	−	7.95235i	−1.69921	−	0.285106i
$779$	29.6656	−	29.6656i	1.06288	−	1.06288i
$780$	−5.66175	+	2.75536i	−0.202723	+	0.0986578i
$781$	−6.39157	−	6.39157i	−0.228708	−	0.228708i
$782$	−21.6594	+	15.4354i	−0.774540	+	0.551969i
$783$	−31.0024			−1.10794
$784$	−21.3851	−	16.7675i	−0.763754	−	0.598840i
$785$	−8.78706			−0.313624
$786$	14.4497	−	10.2974i	0.515403	−	0.367297i
$787$	−8.11455	−	8.11455i	−0.289252	−	0.289252i	0.547532	−	0.836785i	$-0.315567\pi$
$787$	−8.11455	−	8.11455i	−0.289252	−	0.289252i	−0.836785	+	0.547532i	$0.815567\pi$
$788$	−5.89998	−	12.1233i	−0.210178	−	0.431876i
$789$	−19.2621	+	19.2621i	−0.685747	+	0.685747i
$790$	8.78623	+	1.47422i	0.312600	+	0.0524502i
$791$			5.93214i			0.210923i
$792$	−3.17329	−	1.72829i	−0.112758	−	0.0614121i
$793$		−	9.35918i		−	0.332354i
$794$	−0.717091	+	4.27382i	−0.0254486	+	0.151672i
$795$	−10.7407	+	10.7407i	−0.380935	+	0.380935i
$796$	23.1097	+	7.97967i	0.819103	+	0.282832i
$797$	−12.0758	−	12.0758i	−0.427746	−	0.427746i	0.460114	−	0.887860i	$-0.347808\pi$
$797$	−12.0758	−	12.0758i	−0.427746	−	0.427746i	−0.887860	+	0.460114i	$0.847808\pi$
$798$	3.46238	+	4.85852i	0.122567	+	0.171990i
$799$	−14.6221			−0.517292
$800$	5.65092	+	0.258963i	0.199790	+	0.00915572i
$801$	20.8257			0.735838
$802$	0.634790	+	0.890757i	0.0224152	+	0.0314537i
$803$	10.2787	+	10.2787i	0.362729	+	0.362729i
$804$	−40.3583	−	13.9355i	−1.42333	−	0.491468i
$805$	1.20260	−	1.20260i	0.0423860	−	0.0423860i
$806$	−0.509439	+	3.03622i	−0.0179442	+	0.106946i
$807$			26.6610i			0.938510i
$808$	−14.4824	+	26.5909i	−0.509488	+	0.935465i
$809$		−	9.68982i		−	0.340676i	−0.985386	−	0.170338i	$-0.945514\pi$
$809$		−	9.68982i		−	0.340676i	0.985386	−	0.170338i	$-0.0544859\pi$
$810$	4.93075	+	0.827316i	0.173249	+	0.0290689i
$811$	−30.7246	+	30.7246i	−1.07889	+	1.07889i	−0.0822783	+	0.996609i	$0.526220\pi$
$811$	−30.7246	+	30.7246i	−1.07889	+	1.07889i	−0.996609	+	0.0822783i	$0.973780\pi$
$812$	−2.19515	−	4.51063i	−0.0770348	−	0.158292i
$813$	12.6827	+	12.6827i	0.444802	+	0.444802i
$814$	4.48518	−	3.19632i	0.157205	−	0.112031i
$815$	3.61186			0.126518
$816$	−3.16798	−	26.1752i	−0.110902	−	0.916317i
$817$	16.4328			0.574911
$818$	36.3810	−	25.9266i	1.27203	−	0.906501i
$819$	0.984230	+	0.984230i	0.0343918	+	0.0343918i
$820$	10.6607	−	5.18816i	0.372287	−	0.181178i
$821$	−26.4623	+	26.4623i	−0.923542	+	0.923542i	−0.997278	−	0.0737359i	$-0.976508\pi$
$821$	−26.4623	+	26.4623i	−0.923542	+	0.923542i	0.0737359	+	0.997278i	$0.476508\pi$
$822$	21.8151	+	3.66029i	0.760889	+	0.127667i
$823$		−	6.48749i		−	0.226140i	−0.993587	−	0.113070i	$-0.963932\pi$
$823$		−	6.48749i		−	0.226140i	0.993587	−	0.113070i	$-0.0360684\pi$
$824$	8.93529	+	30.3093i	0.311276	+	1.05588i
$825$			1.31243i			0.0456929i
$826$	−0.628552	+	3.74613i	−0.0218701	+	0.130345i
$827$	−14.3758	+	14.3758i	−0.499897	+	0.499897i	−0.911406	−	0.411509i	$-0.865002\pi$
$827$	−14.3758	+	14.3758i	−0.499897	+	0.499897i	0.411509	+	0.911406i	$0.365002\pi$
$828$	−3.12272	+	9.04362i	−0.108522	+	0.314287i
$829$	−22.1397	−	22.1397i	−0.768943	−	0.768943i	0.208977	−	0.977921i	$-0.432987\pi$
$829$	−22.1397	−	22.1397i	−0.768943	−	0.768943i	−0.977921	+	0.208977i	$0.932987\pi$
$830$	7.64261	+	10.7244i	0.265279	+	0.372248i
$831$	−5.46682			−0.189642
$832$	18.7610	+	4.03866i	0.650420	+	0.140015i
$833$	−34.1209			−1.18222
$834$	0.461937	+	0.648204i	0.0159956	+	0.0224455i
$835$	−2.86990	−	2.86990i	−0.0993170	−	0.0993170i
$836$	4.61974	−	13.3791i	0.159777	−	0.462727i
$837$	3.60246	−	3.60246i	0.124519	−	0.124519i
$838$	6.27588	−	37.4038i	0.216797	−	1.29209i
$839$			25.6088i			0.884114i	0.896987	+	0.442057i	$0.145751\pi$
$839$			25.6088i			0.884114i	−0.896987	+	0.442057i	$0.854249\pi$
$840$	0.476752	+	1.61719i	0.0164495	+	0.0557983i
$841$			1.49681i			0.0516140i
$842$	14.2571	+	2.39216i	0.491334	+	0.0824394i
$843$	3.17749	−	3.17749i	0.109438	−	0.109438i
$844$	1.36134	−	0.662516i	0.0468594	−	0.0228047i
$845$	5.12337	+	5.12337i	0.176249	+	0.176249i
$846$	−4.28355	+	3.05263i	−0.147271	+	0.104952i
$847$	0.454189			0.0156061
$848$	45.9596	−	5.56248i	1.57826	−	0.191016i
$849$	4.86909			0.167107
$850$	5.78426	−	4.12210i	0.198399	−	0.141387i
$851$	−10.3117	−	10.3117i	−0.353479	−	0.353479i
$852$	−10.3824	−	21.3339i	−0.355696	−	0.730888i
$853$	8.00247	−	8.00247i	0.273999	−	0.273999i	−0.556709	−	0.830708i	$-0.687936\pi$
$853$	8.00247	−	8.00247i	0.273999	−	0.273999i	0.830708	+	0.556709i	$0.187936\pi$
$854$	−2.47149	−	0.414683i	−0.0845725	−	0.0141902i
$855$		−	9.04127i		−	0.309205i
$856$	−17.9370	+	32.9339i	−0.613073	+	1.12566i
$857$			27.8203i			0.950324i	0.879898	+	0.475162i	$0.157611\pi$
$857$			27.8203i			0.950324i	−0.879898	+	0.475162i	$0.842389\pi$
$858$	−0.736753	+	4.39100i	−0.0251523	+	0.149906i
$859$	0.841849	−	0.841849i	0.0287235	−	0.0287235i	−0.692599	−	0.721323i	$-0.743534\pi$
$859$	0.841849	−	0.841849i	0.0287235	−	0.0287235i	0.721323	+	0.692599i	$0.243534\pi$
$860$	4.38960	+	1.51571i	0.149684	+	0.0516852i
$861$	2.49867	+	2.49867i	0.0851544	+	0.0851544i
$862$	−15.4435	−	21.6708i	−0.526009	−	0.738112i
$863$	−32.4604			−1.10497			−0.552483	−	0.833524i	$-0.686319\pi$
$863$	−32.4604			−1.10497			−0.552483	+	0.833524i	$0.686319\pi$
$864$	−21.4043	−	23.4603i	−0.728188	−	0.798134i
$865$	5.98852			0.203616
$866$	−9.73938	−	13.6666i	−0.330957	−	0.464410i
$867$	−7.63276	−	7.63276i	−0.259222	−	0.259222i
$868$	0.779206	+	0.269056i	0.0264480	+	0.00913236i
$869$	4.45452	−	4.45452i	0.151109	−	0.151109i
$870$	1.69608	−	10.1085i	0.0575026	−	0.342712i
$871$		−	39.0202i		−	1.32215i
$872$	−8.75678	−	4.76926i	−0.296542	−	0.161507i
$873$			0.652953i			0.0220991i
$874$	−36.9609	−	6.20155i	−1.25022	−	0.209771i
$875$	−0.321160	+	0.321160i	−0.0108572	+	0.0108572i
$876$	16.6967	+	34.3086i	0.564130	+	1.15918i
$877$	33.9328	+	33.9328i	1.14583	+	1.14583i	0.987365	+	0.158464i	$0.0506542\pi$
$877$	33.9328	+	33.9328i	1.14583	+	1.14583i	0.158464	+	0.987365i	$0.449346\pi$
$878$	−2.69229	+	1.91863i	−0.0908602	+	0.0647507i
$879$	−33.0030			−1.11316
$880$	2.46809	−	3.14778i	0.0831994	−	0.106112i
$881$	57.7416			1.94536			0.972682	−	0.232143i	$-0.0745737\pi$
$881$	57.7416			1.94536			0.972682	+	0.232143i	$0.0745737\pi$
$882$	−9.99573	+	7.12337i	−0.336574	+	0.239856i
$883$	−23.0370	−	23.0370i	−0.775257	−	0.775257i	0.203763	−	0.979020i	$-0.434683\pi$
$883$	−23.0370	−	23.0370i	−0.775257	−	0.775257i	−0.979020	+	0.203763i	$0.934683\pi$
$884$	21.6665	−	10.5443i	0.728723	−	0.354642i
$885$	−5.48808	+	5.48808i	−0.184480	+	0.184480i
$886$	42.8753	+	7.19393i	1.44043	+	0.241685i
$887$		−	29.3168i		−	0.984362i	−0.870493	−	0.492181i	$-0.836200\pi$
$887$		−	29.3168i		−	0.984362i	0.870493	−	0.492181i	$-0.163800\pi$
$888$	13.8666	−	4.08791i	0.465331	−	0.137181i
$889$		−	7.83440i		−	0.262757i
$890$	−3.81479	+	22.7359i	−0.127872	+	0.762109i
$891$	2.49984	−	2.49984i	0.0837477	−	0.0837477i
$892$	−12.0704	+	34.9569i	−0.404148	+	1.17044i
$893$	−14.5693	−	14.5693i	−0.487543	−	0.487543i
$894$	−23.4366	−	32.8869i	−0.783836	−	1.09990i
$895$	0.498094			0.0166495
$896$	1.89775	−	4.77529i	0.0633993	−	0.159531i
$897$	11.7890			0.393623
$898$	−17.4859	−	24.5368i	−0.583512	−	0.818802i
$899$	−3.54370	−	3.54370i	−0.118189	−	0.118189i
$900$	0.833937	−	2.41514i	0.0277979	−	0.0805048i
$901$	41.1029	−	41.1029i	1.36933	−	1.36933i
$902$	1.38726	−	8.26795i	0.0461905	−	0.275293i
$903$			1.38410i			0.0460598i
$904$	35.4343	−	10.4461i	1.17853	−	0.347434i
$905$		−	14.6479i		−	0.486913i
$906$	33.8024	+	5.67161i	1.12301	+	0.188427i
$907$	−27.1029	+	27.1029i	−0.899936	+	0.899936i	−0.995430	−	0.0954936i	$-0.969557\pi$
$907$	−27.1029	+	27.1029i	−0.899936	+	0.899936i	0.0954936	+	0.995430i	$0.469557\pi$
$908$	26.1908	−	12.7461i	0.869171	−	0.422993i
$909$	9.67061	+	9.67061i	0.320754	+	0.320754i
$910$	−1.25480	+	0.894220i	−0.0415961	+	0.0296431i
$911$	28.7942			0.953994			0.476997	−	0.878905i	$-0.341725\pi$
$911$	28.7942			0.953994			0.476997	+	0.878905i	$0.341725\pi$
$912$	22.9242	−	29.2373i	0.759095	−	0.968142i
$913$	9.31185			0.308177
$914$	−12.9056	+	9.19705i	−0.426879	+	0.304212i
$915$	−3.62073	−	3.62073i	−0.119698	−	0.119698i
$916$	15.8890	+	32.6488i	0.524987	+	1.07875i
$917$	3.07022	−	3.07022i	0.101388	−	0.101388i
$918$	−39.3250	−	6.59822i	−1.29792	−	0.217774i
$919$			21.1685i			0.698285i	0.937070	+	0.349142i	$0.113527\pi$
$919$			21.1685i			0.698285i	−0.937070	+	0.349142i	$0.886473\pi$
$920$	−9.30114	−	5.06574i	−0.306649	−	0.167012i
$921$			18.9336i			0.623883i
$922$	−2.40133	+	14.3118i	−0.0790836	+	0.471333i
$923$	15.3324	−	15.3324i	0.504671	−	0.504671i
$924$	1.12689	+	0.389110i	0.0370720	+	0.0128008i
$925$	2.75378	+	2.75378i	0.0905438	+	0.0905438i
$926$	−10.2729	−	14.4153i	−0.337589	−	0.473715i
$927$	14.2725			0.468771
$928$	−23.0776	+	21.0552i	−0.757561	+	0.691170i
$929$	−11.1111			−0.364545			−0.182272	−	0.983248i	$-0.558345\pi$
$929$	−11.1111			−0.364545			−0.182272	+	0.983248i	$0.558345\pi$
$930$	0.977521	+	1.37169i	0.0320542	+	0.0449794i
$931$	−33.9977	−	33.9977i	−1.11423	−	1.11423i
$932$	2.61005	+	0.901236i	0.0854949	+	0.0295210i
$933$	15.0474	−	15.0474i	0.492630	−	0.492630i
$934$	0.876351	−	5.22300i	0.0286751	−	0.170902i
$935$		−	5.02242i		−	0.164251i
$936$	4.14590	−	7.61223i	0.135513	−	0.248814i
$937$			15.3123i			0.500230i	0.968216	+	0.250115i	$0.0804684\pi$
$937$			15.3123i			0.500230i	−0.968216	+	0.250115i	$0.919532\pi$
$938$	−10.3041	−	1.72889i	−0.336441	−	0.0564504i
$939$	−15.8785	+	15.8785i	−0.518175	+	0.518175i
$940$	−2.54799	−	5.23563i	−0.0831062	−	0.170768i
$941$	−25.6305	−	25.6305i	−0.835530	−	0.835530i	0.152737	−	0.988267i	$-0.451191\pi$
$941$	−25.6305	−	25.6305i	−0.835530	−	0.835530i	−0.988267	+	0.152737i	$0.951191\pi$
$942$	−13.2817	+	9.46509i	−0.432741	+	0.308389i
$943$	−22.1978			−0.722861
$944$	23.4835	−	2.84220i	0.764322	−	0.0925058i
$945$	2.54980			0.0829449
$946$	2.67417	−	1.90572i	0.0869448	−	0.0619605i
$947$	41.5553	+	41.5553i	1.35037	+	1.35037i	0.885250	+	0.465115i	$0.153987\pi$
$947$	41.5553	+	41.5553i	1.35037	+	1.35037i	0.465115	+	0.885250i	$0.346013\pi$
$948$	14.8684	−	7.23590i	0.482904	−	0.235011i
$949$	−24.6571	+	24.6571i	−0.800403	+	0.800403i
$950$	9.87059	+	1.65616i	0.320244	+	0.0537328i
$951$		−	22.0541i		−	0.715153i
$952$	−1.82444	−	6.18868i	−0.0591306	−	0.200576i
$953$		−	26.0458i		−	0.843705i	−0.906664	−	0.421853i	$-0.861380\pi$
$953$		−	26.0458i		−	0.843705i	0.906664	−	0.421853i	$-0.138620\pi$
$954$	3.46012	−	20.6221i	0.112025	−	0.667665i
$955$	−16.3590	+	16.3590i	−0.529364	+	0.529364i
$956$	13.8866	−	40.2165i	0.449124	−	1.30070i
$957$	−5.12492	−	5.12492i	−0.165665	−	0.165665i
$958$	22.4398	+	31.4882i	0.724997	+	1.01734i
$959$	5.41293			0.174793
$960$	8.82036	−	5.69554i	0.284676	−	0.183823i
$961$	−30.1764			−0.973434
$962$	7.66748	+	10.7592i	0.247210	+	0.346892i
$963$	11.9774	+	11.9774i	0.385967	+	0.385967i
$964$	−10.7800	+	31.2197i	−0.347200	+	1.00552i
$965$	7.35537	−	7.35537i	0.236778	−	0.236778i
$966$	0.522343	−	3.11313i	0.0168061	−	0.100163i
$967$			30.0505i			0.966358i	0.875522	+	0.483179i	$0.160518\pi$
$967$			30.0505i			0.966358i	−0.875522	+	0.483179i	$0.839482\pi$
$968$	−0.799799	−	2.71299i	−0.0257065	−	0.0871988i
$969$		−	46.6493i		−	1.49859i
$970$	−0.712845	−	0.119606i	−0.0228881	−	0.00384032i
$971$	−25.8874	+	25.8874i	−0.830768	+	0.830768i	−0.987622	−	0.156854i	$-0.949865\pi$
$971$	−25.8874	+	25.8874i	−0.830768	+	0.830768i	0.156854	+	0.987622i	$0.449865\pi$
$972$	−21.9435	+	10.6791i	−0.703837	+	0.342531i
$973$	0.137728	+	0.137728i	0.00441537	+	0.00441537i
$974$	−5.12131	+	3.64966i	−0.164097	+	0.116943i
$975$	−3.14831			−0.100827
$976$	1.87512	+	15.4931i	0.0600213	+	0.495921i
$977$	−55.1436			−1.76420			−0.882101	−	0.471061i	$-0.843871\pi$
$977$	−55.1436			−1.76420			−0.882101	+	0.471061i	$0.843871\pi$
$978$	5.45935	−	3.89055i	0.174571	−	0.124406i
$979$	11.5269	+	11.5269i	0.368400	+	0.368400i
$980$	−5.94577	−	12.2174i	−0.189931	−	0.390272i
$981$	−3.18467	+	3.18467i	−0.101679	+	0.101679i
$982$	24.7198	+	4.14766i	0.788839	+	0.132357i
$983$			39.1650i			1.24917i	0.780957	+	0.624585i	$0.214732\pi$
$983$			39.1650i			1.24917i	−0.780957	+	0.624585i	$0.785268\pi$
$984$	10.5252	−	19.3252i	0.335531	−	0.616065i
$985$		−	6.74139i		−	0.214798i
$986$	−6.49060	+	38.6836i	−0.206703	+	1.23194i
$987$	1.22714	−	1.22714i	0.0390602	−	0.0390602i
$988$	32.0944	+	11.0820i	1.02106	+	0.352567i
$989$	−6.14806	−	6.14806i	−0.195497	−	0.195497i
$990$	−1.04852	−	1.47132i	−0.0333243	−	0.0467617i
$991$	−32.1343			−1.02078			−0.510390	−	0.859943i	$-0.670499\pi$
$991$	−32.1343			−1.02078			−0.510390	+	0.859943i	$0.670499\pi$
$992$	0.235008	−	5.12820i	0.00746151	−	0.162820i
$993$	−15.2547			−0.484092
$994$	−3.36949	−	4.72818i	−0.106874	−	0.149969i
$995$	8.64389	+	8.64389i	0.274030	+	0.274030i
$996$	23.1037	+	7.97760i	0.732069	+	0.252780i
$997$	12.0934	−	12.0934i	0.383001	−	0.383001i	−0.489181	−	0.872182i	$-0.662704\pi$
$997$	12.0934	−	12.0934i	0.383001	−	0.383001i	0.872182	+	0.489181i	$0.162704\pi$
$998$	−8.02727	+	47.8420i	−0.254099	+	1.51441i
$999$		−	21.8632i		−	0.691721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.13	✓	72
16.5	even	4	inner	880.2.w.a.661.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.13	✓	72	1.1	even	1	trivial
880.2.w.a.661.13	yes	72	16.5	even	4	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.820740 - 1.15169i) q^{2} +(-0.928026 - 0.928026i) q^{3} +(-0.652771 + 1.89047i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.307128 + 1.83047i) q^{6} +0.454189i q^{7} +(2.71299 - 0.799799i) q^{8} -1.27753i q^{9} +(1.39472 + 0.234015i) q^{10} +(0.707107 - 0.707107i) q^{11} +(2.36020 - 1.14862i) q^{12} +(1.69624 + 1.69624i) q^{13} +(0.523084 - 0.372771i) q^{14} +1.31243 q^{15} +(-3.14778 - 2.46809i) q^{16} -5.02242 q^{17} +(-1.47132 + 1.04852i) q^{18} +(-5.00428 - 5.00428i) q^{19} +(-0.875188 - 1.79835i) q^{20} +(0.421499 - 0.421499i) q^{21} +(-1.39472 - 0.234015i) q^{22} +3.74454i q^{23} +(-3.25996 - 1.77549i) q^{24} -1.00000i q^{25} +(0.561367 - 3.34571i) q^{26} +(-3.96966 + 3.96966i) q^{27} +(-0.858632 - 0.296481i) q^{28} +(3.90492 + 3.90492i) q^{29} +(-1.07716 - 1.51151i) q^{30} -0.907497 q^{31} +(-0.258963 + 5.65092i) q^{32} -1.31243 q^{33} +(4.12210 + 5.78426i) q^{34} +(-0.321160 - 0.321160i) q^{35} +(2.41514 + 0.833937i) q^{36} +(-2.75378 + 2.75378i) q^{37} +(-1.65616 + 9.87059i) q^{38} -3.14831i q^{39} +(-1.35283 + 2.48392i) q^{40} +5.92805i q^{41} +(-0.831377 - 0.139494i) q^{42} +(-1.64187 + 1.64187i) q^{43} +(0.875188 + 1.79835i) q^{44} +(0.903353 + 0.903353i) q^{45} +(4.31255 - 3.07330i) q^{46} +2.91136 q^{47} +(0.630768 + 5.21168i) q^{48} +6.79371 q^{49} +(-1.15169 + 0.820740i) q^{50} +(4.66094 + 4.66094i) q^{51} +(-4.31395 + 2.09944i) q^{52} +(-8.18387 + 8.18387i) q^{53} +(7.82988 + 1.31375i) q^{54} +1.00000i q^{55} +(0.363260 + 1.23221i) q^{56} +9.28822i q^{57} +(1.29233 - 7.70218i) q^{58} +(-4.18163 + 4.18163i) q^{59} +(-0.856714 + 2.48111i) q^{60} +(-2.75880 - 2.75880i) q^{61} +(0.744819 + 1.04515i) q^{62} +0.580242 q^{63} +(6.72064 - 4.33970i) q^{64} -2.39885 q^{65} +(1.07716 + 1.51151i) q^{66} +(-11.5020 - 11.5020i) q^{67} +(3.27849 - 9.49476i) q^{68} +(3.47504 - 3.47504i) q^{69} +(-0.106287 + 0.633465i) q^{70} -9.03904i q^{71} +(-1.02177 - 3.46594i) q^{72} +14.5363i q^{73} +(5.43164 + 0.911359i) q^{74} +(-0.928026 + 0.928026i) q^{75} +(12.7271 - 6.19382i) q^{76} +(0.321160 + 0.321160i) q^{77} +(-3.62587 + 2.58394i) q^{78} +6.29965 q^{79} +(3.97102 - 0.480612i) q^{80} +3.53530 q^{81} +(6.82726 - 4.86539i) q^{82} +(6.58447 + 6.58447i) q^{83} +(0.521691 + 1.07198i) q^{84} +(3.55139 - 3.55139i) q^{85} +(3.23848 + 0.543374i) q^{86} -7.24774i q^{87} +(1.35283 - 2.48392i) q^{88} +16.3014i q^{89} +(0.298963 - 1.78180i) q^{90} +(-0.770413 + 0.770413i) q^{91} +(-7.07896 - 2.44433i) q^{92} +(0.842181 + 0.842181i) q^{93} +(-2.38947 - 3.35298i) q^{94} +7.07713 q^{95} +(5.48453 - 5.00388i) q^{96} -0.511104 q^{97} +(-5.57587 - 7.82424i) q^{98} +(-0.903353 - 0.903353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more