LMFDB - Embedded newform 273.2.cc.a.50.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.13
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.397883 - 0.106613i) q^{2} +(-1.64214 + 0.550805i) q^{3} +(-1.58511 - 0.915161i) q^{4} +(0.406846 - 0.406846i) q^{5} +(0.712102 - 0.0440836i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.11566 + 1.11566i) q^{8} +(2.39323 - 1.80899i) q^{9} +O(q^{10})$	\(q+(-0.397883 - 0.106613i) q^{2} +(-1.64214 + 0.550805i) q^{3} +(-1.58511 - 0.915161i) q^{4} +(0.406846 - 0.406846i) q^{5} +(0.712102 - 0.0440836i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.11566 + 1.11566i) q^{8} +(2.39323 - 1.80899i) q^{9} +(-0.205252 + 0.118502i) q^{10} +(-1.45913 + 5.44555i) q^{11} +(3.10704 + 0.629737i) q^{12} +(2.33812 + 2.74467i) q^{13} +0.411919i q^{14} +(-0.444005 + 0.892190i) q^{15} +(1.50536 + 2.60736i) q^{16} +(-1.33392 + 2.31041i) q^{17} +(-1.14509 + 0.464620i) q^{18} +(-2.54803 + 0.682741i) q^{19} +(-1.01722 + 0.272564i) q^{20} +(0.957053 + 1.44362i) q^{21} +(1.16113 - 2.01113i) q^{22} +(0.162226 + 0.280984i) q^{23} +(-2.44658 - 1.21756i) q^{24} +4.66895i q^{25} +(-0.637683 - 1.34133i) q^{26} +(-2.93361 + 4.28882i) q^{27} +(-0.473722 + 1.76796i) q^{28} +(6.22607 - 3.59462i) q^{29} +(0.271781 - 0.307651i) q^{30} +(2.80802 + 2.80802i) q^{31} +(-1.13770 - 4.24596i) q^{32} +(-0.603341 - 9.74603i) q^{33} +(0.777063 - 0.777063i) q^{34} +(-0.498283 - 0.287684i) q^{35} +(-5.44904 + 0.677256i) q^{36} +(9.63888 + 2.58273i) q^{37} +1.08661 q^{38} +(-5.35129 - 3.21927i) q^{39} +0.907806 q^{40} +(-11.6992 - 3.13480i) q^{41} +(-0.226887 - 0.676428i) q^{42} +(-1.38932 - 0.802124i) q^{43} +(7.29643 - 7.29643i) q^{44} +(0.237694 - 1.70966i) q^{45} +(-0.0345908 - 0.129094i) q^{46} +(1.21422 + 1.21422i) q^{47} +(-3.90816 - 3.45249i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.497769 - 1.85770i) q^{50} +(0.917889 - 4.52874i) q^{51} +(-1.19436 - 6.49034i) q^{52} +3.50253i q^{53} +(1.62448 - 1.39369i) q^{54} +(1.62186 + 2.80914i) q^{55} +(0.788892 - 1.36640i) q^{56} +(3.80815 - 2.52462i) q^{57} +(-2.86048 + 0.766464i) q^{58} +(-3.42446 + 0.917582i) q^{59} +(1.52029 - 1.00788i) q^{60} +(-4.29464 + 7.43854i) q^{61} +(-0.817894 - 1.41663i) q^{62} +(-2.36677 - 1.84348i) q^{63} -4.21076i q^{64} +(2.06791 + 0.165402i) q^{65} +(-0.798990 + 3.94211i) q^{66} +(-0.739592 + 2.76019i) q^{67} +(4.22880 - 2.44150i) q^{68} +(-0.421166 - 0.372060i) q^{69} +(0.167588 + 0.167588i) q^{70} +(0.226337 + 0.844700i) q^{71} +(4.68826 + 0.651809i) q^{72} +(6.61183 - 6.61183i) q^{73} +(-3.55980 - 2.05525i) q^{74} +(-2.57168 - 7.66706i) q^{75} +(4.66371 + 1.24964i) q^{76} +5.63765 q^{77} +(1.78597 + 1.85141i) q^{78} -12.4455 q^{79} +(1.67325 + 0.448345i) q^{80} +(2.45509 - 8.65867i) q^{81} +(4.32073 + 2.49457i) q^{82} +(-7.36965 + 7.36965i) q^{83} +(-0.195881 - 3.16415i) q^{84} +(0.397284 + 1.48268i) q^{85} +(0.467271 + 0.467271i) q^{86} +(-8.24412 + 9.33221i) q^{87} +(-7.70328 + 4.44749i) q^{88} +(-1.00365 + 3.74568i) q^{89} +(-0.276846 + 0.654904i) q^{90} +(2.04599 - 2.96882i) q^{91} -0.593853i q^{92} +(-6.15782 - 3.06448i) q^{93} +(-0.353667 - 0.612569i) q^{94} +(-0.758884 + 1.31443i) q^{95} +(4.20696 + 6.34580i) q^{96} +(-9.95292 + 2.66688i) q^{97} +(0.397883 - 0.106613i) q^{98} +(6.35893 + 15.6720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.397883	−	0.106613i	−0.281346	−	0.0753865i	0.115387	−	0.993321i	$-0.463189\pi$
$2$	−0.397883	−	0.106613i	−0.281346	−	0.0753865i	−0.396733	+	0.917934i	$0.629856\pi$
$3$	−1.64214	+	0.550805i	−0.948088	+	0.318007i
$3$	−1.64214	+	0.550805i	−0.948088	+	0.318007i
$4$	−1.58511	−	0.915161i	−0.792553	−	0.457581i
$5$	0.406846	−	0.406846i	0.181947	−	0.181947i	−0.610257	−	0.792204i	$-0.708934\pi$
$5$	0.406846	−	0.406846i	0.181947	−	0.181947i	0.792204	+	0.610257i	$0.208934\pi$
$6$	0.712102	−	0.0440836i	0.290714	−	0.0179971i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	1.11566	+	1.11566i	0.394446	+	0.394446i
$9$	2.39323	−	1.80899i	0.797743	−	0.602998i
$10$	−0.205252	+	0.118502i	−0.0649065	+	0.0374738i
$11$	−1.45913	+	5.44555i	−0.439944	+	1.64189i	0.289006	+	0.957327i	$0.406675\pi$
$11$	−1.45913	+	5.44555i	−0.439944	+	1.64189i	−0.728950	+	0.684567i	$0.759991\pi$
$12$	3.10704	+	0.629737i	0.896924	+	0.181789i
$13$	2.33812	+	2.74467i	0.648478	+	0.761234i
$13$	2.33812	+	2.74467i	0.648478	+	0.761234i
$14$			0.411919i			0.110090i
$15$	−0.444005	+	0.892190i	−0.114641	+	0.230363i
$16$	1.50536	+	2.60736i	0.376341	+	0.651841i
$17$	−1.33392	+	2.31041i	−0.323523	+	0.560357i	−0.981212	−	0.192931i	$-0.938200\pi$
$17$	−1.33392	+	2.31041i	−0.323523	+	0.560357i	0.657690	+	0.753289i	$0.271534\pi$
$18$	−1.14509	+	0.464620i	−0.269900	+	0.109512i
$19$	−2.54803	+	0.682741i	−0.584557	+	0.156632i	−0.538964	−	0.842329i	$-0.681184\pi$
$19$	−2.54803	+	0.682741i	−0.584557	+	0.156632i	−0.0455927	+	0.998960i	$0.514518\pi$
$20$	−1.01722	+	0.272564i	−0.227458	+	0.0609473i
$21$	0.957053	+	1.44362i	0.208846	+	0.315025i
$22$	1.16113	−	2.01113i	0.247553	−	0.428775i
$23$	0.162226	+	0.280984i	0.0338266	+	0.0585893i	0.882443	−	0.470419i	$-0.155897\pi$
$23$	0.162226	+	0.280984i	0.0338266	+	0.0585893i	−0.848617	+	0.529009i	$0.822564\pi$
$24$	−2.44658	−	1.21756i	−0.499406	−	0.248533i
$25$			4.66895i			0.933790i
$26$	−0.637683	−	1.34133i	−0.125060	−	0.263057i
$27$	−2.93361	+	4.28882i	−0.564573	+	0.825383i
$28$	−0.473722	+	1.76796i	−0.0895251	+	0.334112i
$29$	6.22607	−	3.59462i	1.15615	−	0.667505i	0.205773	−	0.978600i	$-0.434029\pi$
$29$	6.22607	−	3.59462i	1.15615	−	0.667505i	0.950379	+	0.311095i	$0.100696\pi$
$30$	0.271781	−	0.307651i	0.0496202	−	0.0561692i
$31$	2.80802	+	2.80802i	0.504335	+	0.504335i	0.912782	−	0.408447i	$-0.133930\pi$
$31$	2.80802	+	2.80802i	0.504335	+	0.504335i	−0.408447	+	0.912782i	$0.633930\pi$
$32$	−1.13770	−	4.24596i	−0.201119	−	0.750587i
$33$	−0.603341	−	9.74603i	−0.105028	−	1.69657i
$34$	0.777063	−	0.777063i	0.133265	−	0.133265i
$35$	−0.498283	−	0.287684i	−0.0842252	−	0.0486274i
$36$	−5.44904	+	0.677256i	−0.908174	+	0.112876i
$37$	9.63888	+	2.58273i	1.58462	+	0.424598i	0.940353	−	0.340200i	$-0.110495\pi$
$37$	9.63888	+	2.58273i	1.58462	+	0.424598i	0.644270	+	0.764799i	$0.277162\pi$
$38$	1.08661			0.176271
$39$	−5.35129	−	3.21927i	−0.856892	−	0.515496i
$40$	0.907806			0.143537
$41$	−11.6992	−	3.13480i	−1.82711	−	0.489574i	−0.829494	−	0.558516i	$-0.811371\pi$
$41$	−11.6992	−	3.13480i	−1.82711	−	0.489574i	−0.997621	+	0.0689419i	$0.978038\pi$
$42$	−0.226887	−	0.676428i	−0.0350094	−	0.104375i
$43$	−1.38932	−	0.802124i	−0.211869	−	0.122323i	0.390311	−	0.920683i	$-0.372368\pi$
$43$	−1.38932	−	0.802124i	−0.211869	−	0.122323i	−0.602180	+	0.798360i	$0.705701\pi$
$44$	7.29643	−	7.29643i	1.09998	−	1.09998i
$45$	0.237694	−	1.70966i	0.0354333	−	0.254861i
$46$	−0.0345908	−	0.129094i	−0.00510013	−	0.0190339i
$47$	1.21422	+	1.21422i	0.177112	+	0.177112i	0.790096	−	0.612984i	$-0.210031\pi$
$47$	1.21422	+	1.21422i	0.177112	+	0.177112i	−0.612984	+	0.790096i	$0.710031\pi$
$48$	−3.90816	−	3.45249i	−0.564094	−	0.498324i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.497769	−	1.85770i	0.0703952	−	0.262718i
$51$	0.917889	−	4.52874i	0.128530	−	0.634151i
$52$	−1.19436	−	6.49034i	−0.165627	−	0.900049i
$53$			3.50253i			0.481110i	0.970636	+	0.240555i	$0.0773294\pi$
$53$			3.50253i			0.481110i	−0.970636	+	0.240555i	$0.922671\pi$
$54$	1.62448	−	1.39369i	0.221063	−	0.189657i
$55$	1.62186	+	2.80914i	0.218691	+	0.378785i
$56$	0.788892	−	1.36640i	0.105420	−	0.182593i
$57$	3.80815	−	2.52462i	0.504402	−	0.334394i
$58$	−2.86048	+	0.766464i	−0.375600	+	0.100642i
$59$	−3.42446	+	0.917582i	−0.445827	+	0.119459i	−0.474746	−	0.880123i	$-0.657460\pi$
$59$	−3.42446	+	0.917582i	−0.445827	+	0.119459i	0.0289190	+	0.999582i	$0.490794\pi$
$60$	1.52029	−	1.00788i	0.196269	−	0.130117i
$61$	−4.29464	+	7.43854i	−0.549873	+	0.952407i	0.448410	+	0.893828i	$0.351990\pi$
$61$	−4.29464	+	7.43854i	−0.549873	+	0.952407i	−0.998283	+	0.0585794i	$0.981343\pi$
$62$	−0.817894	−	1.41663i	−0.103873	−	0.179913i
$63$	−2.36677	−	1.84348i	−0.298185	−	0.232257i
$64$		−	4.21076i		−	0.526345i
$65$	2.06791	+	0.165402i	0.256493	+	0.0205156i
$66$	−0.798990	+	3.94211i	−0.0983489	+	0.485240i
$67$	−0.739592	+	2.76019i	−0.0903555	+	0.337211i	−0.996274	−	0.0862399i	$-0.972515\pi$
$67$	−0.739592	+	2.76019i	−0.0903555	+	0.337211i	0.905919	+	0.423451i	$0.139182\pi$
$68$	4.22880	−	2.44150i	0.512817	−	0.296075i
$69$	−0.421166	−	0.372060i	−0.0507024	−	0.0447908i
$70$	0.167588	+	0.167588i	0.0200306	+	0.0200306i
$71$	0.226337	+	0.844700i	0.0268612	+	0.100247i	0.978055	−	0.208347i	$-0.0668082\pi$
$71$	0.226337	+	0.844700i	0.0268612	+	0.100247i	−0.951194	+	0.308594i	$0.900142\pi$
$72$	4.68826	+	0.651809i	0.552516	+	0.0768164i
$73$	6.61183	−	6.61183i	0.773857	−	0.773857i	−0.204922	−	0.978778i	$-0.565694\pi$
$73$	6.61183	−	6.61183i	0.773857	−	0.773857i	0.978778	+	0.204922i	$0.0656940\pi$
$74$	−3.55980	−	2.05525i	−0.413818	−	0.238918i
$75$	−2.57168	−	7.66706i	−0.296952	−	0.885316i
$76$	4.66371	+	1.24964i	0.534964	+	0.143343i
$77$	5.63765			0.642469
$78$	1.78597	+	1.85141i	0.202222	+	0.209631i
$79$	−12.4455			−1.40022			−0.700112	−	0.714033i	$-0.746867\pi$
$79$	−12.4455			−1.40022			−0.700112	+	0.714033i	$0.746867\pi$
$80$	1.67325	+	0.448345i	0.187075	+	0.0501265i
$81$	2.45509	−	8.65867i	0.272787	−	0.962074i
$82$	4.32073	+	2.49457i	0.477144	+	0.275479i
$83$	−7.36965	+	7.36965i	−0.808924	+	0.808924i	−0.984471	−	0.175547i	$-0.943831\pi$
$83$	−7.36965	+	7.36965i	−0.808924	+	0.808924i	0.175547	+	0.984471i	$0.443831\pi$
$84$	−0.195881	−	3.16415i	−0.0213724	−	0.345238i
$85$	0.397284	+	1.48268i	0.0430915	+	0.160819i
$86$	0.467271	+	0.467271i	0.0503871	+	0.0503871i
$87$	−8.24412	+	9.33221i	−0.883863	+	1.00052i
$88$	−7.70328	+	4.44749i	−0.821173	+	0.474104i
$89$	−1.00365	+	3.74568i	−0.106387	+	0.397041i	−0.998499	−	0.0547731i	$-0.982556\pi$
$89$	−1.00365	+	3.74568i	−0.106387	+	0.397041i	0.892112	+	0.451815i	$0.149223\pi$
$90$	−0.276846	+	0.654904i	−0.0291821	+	0.0690329i
$91$	2.04599	−	2.96882i	0.214478	−	0.311217i
$92$		−	0.593853i		−	0.0619135i
$93$	−6.15782	−	3.06448i	−0.638536	−	0.317772i
$94$	−0.353667	−	0.612569i	−0.0364780	−	0.0631817i
$95$	−0.758884	+	1.31443i	−0.0778598	+	0.134857i
$96$	4.20696	+	6.34580i	0.429371	+	0.647666i
$97$	−9.95292	+	2.66688i	−1.01057	+	0.270780i	−0.725866	−	0.687836i	$-0.758561\pi$
$97$	−9.95292	+	2.66688i	−1.01057	+	0.270780i	−0.284700	+	0.958617i	$0.591894\pi$
$98$	0.397883	−	0.106613i	0.0401923	−	0.0107695i
$99$	6.35893	+	15.6720i	0.639096	+	1.57510i
$100$	4.27284	−	7.40078i	0.427284	−	0.740078i
$101$	−5.47672	−	9.48595i	−0.544954	−	0.943888i	−0.998610	−	0.0527107i	$-0.983214\pi$
$101$	−5.47672	−	9.48595i	−0.544954	−	0.943888i	0.453656	−	0.891177i	$-0.350119\pi$
$102$	−0.848034	+	1.70405i	−0.0839679	+	0.168726i
$103$			6.93888i			0.683708i	0.939753	+	0.341854i	$0.111055\pi$
$103$			6.93888i			0.683708i	−0.939753	+	0.341854i	$0.888945\pi$
$104$	−0.453568	+	5.67067i	−0.0444760	+	0.556055i
$105$	0.976706	+	0.197960i	0.0953168	+	0.0193189i
$106$	0.373414	−	1.39360i	0.0362692	−	0.135358i
$107$	16.9915	−	9.81003i	1.64263	−	0.948371i	0.662733	−	0.748856i	$-0.269397\pi$
$107$	16.9915	−	9.81003i	1.64263	−	0.948371i	0.979895	−	0.199515i	$-0.0639368\pi$
$108$	8.57504	−	4.11350i	0.825133	−	0.395822i
$109$	3.53854	+	3.53854i	0.338931	+	0.338931i	0.855965	−	0.517034i	$-0.172964\pi$
$109$	3.53854	+	3.53854i	0.338931	+	0.338931i	−0.517034	+	0.855965i	$0.672964\pi$
$110$	−0.345821	−	1.29062i	−0.0329728	−	0.123056i
$111$	−17.2509	+	1.06794i	−1.63739	+	0.101365i
$112$	2.12890	−	2.12890i	0.201163	−	0.201163i
$113$	0.482425	+	0.278528i	0.0453827	+	0.0262017i	0.522520	−	0.852627i	$-0.324992\pi$
$113$	0.482425	+	0.278528i	0.0453827	+	0.0262017i	−0.477137	+	0.878829i	$0.658325\pi$
$114$	−1.78436	+	0.598508i	−0.167120	+	0.0560554i
$115$	0.180319	+	0.0483163i	0.0168148	+	0.00450551i
$116$	−13.1586			−1.22175
$117$	10.5607	+	2.33897i	0.976341	+	0.216238i
$118$	1.46036			0.134437
$119$	2.57693	+	0.690487i	0.236227	+	0.0632968i
$120$	−1.49074	+	0.500024i	−0.136085	+	0.0456457i
$121$	−17.9987	−	10.3915i	−1.63624	−	0.944684i
$122$	2.50181	−	2.50181i	0.226503	−	0.226503i
$123$	20.9384	−	1.29622i	1.88795	−	0.116876i
$124$	−1.88122	−	7.02079i	−0.168938	−	0.630486i
$125$	3.93378	+	3.93378i	0.351848	+	0.351848i
$126$	0.745159	+	0.985817i	0.0663841	+	0.0878236i
$127$	15.7022	−	9.06568i	1.39335	−	0.804449i	0.399662	−	0.916662i	$-0.369127\pi$
$127$	15.7022	−	9.06568i	1.39335	−	0.804449i	0.993684	+	0.112214i	$0.0357941\pi$
$128$	−2.72432	+	10.1673i	−0.240798	+	0.898672i
$129$	2.72327	+	0.551954i	0.239770	+	0.0485968i
$130$	−0.805154	−	0.286276i	−0.0706167	−	0.0251081i
$131$			17.3500i			1.51587i	0.652328	+	0.757937i	$0.273793\pi$
$131$			17.3500i			1.51587i	−0.652328	+	0.757937i	$0.726207\pi$
$132$	−7.96283	+	16.0006i	−0.693075	+	1.39268i
$133$	1.31896	+	2.28450i	0.114368	+	0.198091i
$134$	0.588543	−	1.01939i	0.0508423	−	0.0880615i
$135$	0.551362	+	2.93842i	0.0474537	+	0.252899i
$136$	−4.06584	+	1.08944i	−0.348643	+	0.0934186i
$137$	12.3317	−	3.30426i	1.05357	−	0.282302i	0.309841	−	0.950788i	$-0.399724\pi$
$137$	12.3317	−	3.30426i	1.05357	−	0.282302i	0.743725	+	0.668486i	$0.233057\pi$
$138$	0.127909	+	0.192938i	0.0108883	+	0.0164240i
$139$	6.14111	−	10.6367i	0.520882	−	0.902194i	−0.478823	−	0.877911i	$-0.658937\pi$
$139$	6.14111	−	10.6367i	0.520882	−	0.902194i	0.999705	−	0.0242825i	$-0.00773012\pi$
$140$	0.526554	+	0.912018i	0.0445019	+	0.0770796i
$141$	−2.66271	−	1.32512i	−0.224241	−	0.111595i
$142$		−	0.360223i		−	0.0302292i
$143$	−18.3578	+	8.72752i	−1.53516	+	0.729832i
$144$	8.31938	+	3.51683i	0.693282	+	0.293069i
$145$	1.07059	−	3.99551i	0.0889080	−	0.331809i
$146$	−3.33564	+	1.92584i	−0.276060	+	0.159383i
$147$	1.14673	−	1.29808i	0.0945807	−	0.107064i
$148$	−12.9150	−	12.9150i	−1.06161	−	1.06161i
$149$	2.18873	+	8.16845i	0.179308	+	0.669185i	0.995778	+	0.0917975i	$0.0292613\pi$
$149$	2.18873	+	8.16845i	0.179308	+	0.669185i	−0.816470	+	0.577388i	$0.804072\pi$
$150$	0.205824	+	3.32477i	0.0168055	+	0.271466i
$151$	−6.10296	+	6.10296i	−0.496651	+	0.496651i	−0.910394	−	0.413742i	$-0.864221\pi$
$151$	−6.10296	+	6.10296i	−0.496651	+	0.496651i	0.413742	+	0.910394i	$0.364221\pi$
$152$	−3.60444	−	2.08103i	−0.292359	−	0.168793i
$153$	0.987153	+	7.94239i	0.0798065	+	0.642105i
$154$	−2.24313	−	0.601044i	−0.180756	−	0.0484335i
$155$	2.28486			0.183525
$156$	5.53621	+	10.0002i	0.443251	+	0.800655i
$157$	13.9996			1.11729			0.558645	−	0.829407i	$-0.311322\pi$
$157$	13.9996			1.11729			0.558645	+	0.829407i	$0.311322\pi$
$158$	4.95184	+	1.32684i	0.393948	+	0.105558i
$159$	−1.92921	−	5.75164i	−0.152996	−	0.456135i
$160$	−2.19032	−	1.26458i	−0.173160	−	0.0999741i
$161$	0.229423	−	0.229423i	0.0180811	−	0.0180811i
$162$	−1.89996	+	3.18340i	−0.149275	+	0.250111i
$163$	4.64141	+	17.3220i	0.363543	+	1.35676i	0.869385	+	0.494135i	$0.164515\pi$
$163$	4.64141	+	17.3220i	0.363543	+	1.35676i	−0.505842	+	0.862626i	$0.668818\pi$
$164$	15.6757	+	15.6757i	1.22407	+	1.22407i
$165$	−4.21060	−	3.71967i	−0.327795	−	0.289576i
$166$	3.71796	−	2.14656i	0.288570	−	0.166606i
$167$	−2.71398	+	10.1287i	−0.210014	+	0.783783i	0.777849	+	0.628452i	$0.216311\pi$
$167$	−2.71398	+	10.1287i	−0.210014	+	0.783783i	−0.987862	+	0.155331i	$0.950356\pi$
$168$	−0.542849	+	2.67834i	−0.0418817	+	0.206639i
$169$	−2.06639	+	12.8347i	−0.158953	+	0.987286i
$170$		−	0.632290i		−	0.0484945i
$171$	−4.86293	+	6.24332i	−0.371878	+	0.477438i
$172$	1.46815	+	2.54290i	0.111945	+	0.193895i
$173$	10.4146	−	18.0386i	0.791808	−	1.37145i	−0.133039	−	0.991111i	$-0.542473\pi$
$173$	10.4146	−	18.0386i	0.791808	−	1.37145i	0.924846	−	0.380341i	$-0.124193\pi$
$174$	4.27513	−	2.83420i	0.324097	−	0.214861i
$175$	4.50986	−	1.20841i	0.340913	−	0.0913475i
$176$	−16.3950	+	4.39304i	−1.23582	+	0.331138i
$177$	5.11803	−	3.39301i	0.384695	−	0.255034i
$178$	0.798673	−	1.38334i	0.0598631	−	0.103686i
$179$	−5.16559	−	8.94707i	−0.386095	−	0.668735i	0.605826	−	0.795597i	$-0.292843\pi$
$179$	−5.16559	−	8.94707i	−0.386095	−	0.668735i	−0.991920	+	0.126862i	$0.959510\pi$
$180$	−1.94138	+	2.49246i	−0.144702	+	0.185777i
$181$		−	11.1179i		−	0.826383i	−0.910644	−	0.413192i	$-0.864414\pi$
$181$		−	11.1179i		−	0.826383i	0.910644	−	0.413192i	$-0.135586\pi$
$182$	−1.13058	+	0.963117i	−0.0838042	+	0.0713910i
$183$	2.95521	−	14.5806i	0.218455	−	1.07783i
$184$	−0.132494	+	0.494473i	−0.00976757	+	0.0364531i
$185$	4.97232	−	2.87077i	0.365572	−	0.211063i
$186$	2.12338	+	1.87581i	0.155694	+	0.137541i
$187$	−10.6351	−	10.6351i	−0.777716	−	0.777716i
$188$	−0.813460	−	3.03587i	−0.0593276	−	0.221414i
$189$	4.90195	+	1.72362i	0.356565	+	0.125375i
$190$	0.442082	−	0.442082i	0.0320720	−	0.0320720i
$191$	−14.6651	−	8.46689i	−1.06113	−	0.612643i	−0.135384	−	0.990793i	$-0.543227\pi$
$191$	−14.6651	−	8.46689i	−1.06113	−	0.612643i	−0.925744	+	0.378150i	$0.876560\pi$
$192$	2.31931	+	6.91464i	0.167381	+	0.499021i
$193$	−6.33384	−	1.69715i	−0.455920	−	0.122163i	0.0235481	−	0.999723i	$-0.492504\pi$
$193$	−6.33384	−	1.69715i	−0.455920	−	0.122163i	−0.479468	+	0.877559i	$0.659170\pi$
$194$	4.24442			0.304732
$195$	−3.48690	+	0.867403i	−0.249702	+	0.0621160i
$196$	1.83032			0.130737
$197$	8.61621	+	2.30871i	0.613880	+	0.164489i	0.552344	−	0.833616i	$-0.313733\pi$
$197$	8.61621	+	2.30871i	0.613880	+	0.164489i	0.0615358	+	0.998105i	$0.480400\pi$
$198$	−0.859281	−	6.91357i	−0.0610664	−	0.491326i
$199$	−4.27939	−	2.47071i	−0.303358	−	0.175144i	0.340592	−	0.940211i	$-0.389372\pi$
$199$	−4.27939	−	2.47071i	−0.303358	−	0.175144i	−0.643950	+	0.765067i	$0.722706\pi$
$200$	−5.20897	+	5.20897i	−0.368330	+	0.368330i
$201$	−0.305817	−	4.93999i	−0.0215706	−	0.348440i
$202$	1.16777	+	4.35819i	0.0821643	+	0.306641i
$203$	−5.08356	−	5.08356i	−0.356796	−	0.356796i
$204$	−5.59948	+	6.33852i	−0.392042	+	0.443785i
$205$	−6.03518	+	3.48441i	−0.421515	+	0.243362i
$206$	0.739771	−	2.76086i	0.0515423	−	0.192359i
$207$	0.896544	+	0.378993i	0.0623141	+	0.0263419i
$208$	−3.63663	+	10.2281i	−0.252155	+	0.709188i
$209$		−	14.8716i		−	1.02869i
$210$	−0.367510	−	0.182894i	−0.0253606	−	0.0126209i
$211$	−3.59401	−	6.22501i	−0.247422	−	0.428547i	0.715388	−	0.698728i	$-0.246250\pi$
$211$	−3.59401	−	6.22501i	−0.247422	−	0.428547i	−0.962810	+	0.270180i	$0.912917\pi$
$212$	3.20538	−	5.55189i	0.220147	−	0.381305i
$213$	−0.836941	−	1.26245i	−0.0573462	−	0.0865014i
$214$	−7.80650	+	2.09174i	−0.533641	+	0.142989i
$215$	−0.891581	+	0.238898i	−0.0608053	+	0.0162927i
$216$	−8.05778	+	1.51195i	−0.548263	+	0.102876i
$217$	1.98557	−	3.43910i	0.134789	−	0.233462i
$218$	−1.03067	−	1.78518i	−0.0698060	−	0.120908i
$219$	−7.21571	+	14.4994i	−0.487592	+	0.979777i
$220$		−	5.93705i		−	0.400276i
$221$	−9.46017	+	1.74086i	−0.636360	+	0.117103i
$222$	6.97772	+	1.41425i	0.468314	+	0.0949183i
$223$	3.16192	−	11.8005i	0.211738	−	0.790218i	−0.775551	−	0.631285i	$-0.782528\pi$
$223$	3.16192	−	11.8005i	0.211738	−	0.790218i	0.987289	−	0.158933i	$-0.0508053\pi$
$224$	−3.80683	+	2.19787i	−0.254354	+	0.146851i
$225$	8.44610	+	11.1739i	0.563074	+	0.744925i
$226$	−0.162254	−	0.162254i	−0.0107930	−	0.0107930i
$227$	−2.53646	−	9.46621i	−0.168351	−	0.628295i	−0.997589	−	0.0693990i	$-0.977892\pi$
$227$	−2.53646	−	9.46621i	−0.168351	−	0.628295i	0.829238	−	0.558896i	$-0.188775\pi$
$228$	−8.34675	+	0.516717i	−0.552777	+	0.0342204i
$229$	−6.62544	+	6.62544i	−0.437821	+	0.437821i	−0.891278	−	0.453457i	$-0.850191\pi$
$229$	−6.62544	+	6.62544i	−0.437821	+	0.437821i	0.453457	+	0.891278i	$0.350191\pi$
$230$	−0.0665947	−	0.0384485i	−0.00439113	−	0.00253522i
$231$	−9.25779	+	3.10524i	−0.609118	+	0.204310i
$232$	10.9566	+	2.93580i	0.719334	+	0.192745i
$233$	6.70148			0.439029			0.219514	−	0.975609i	$-0.429553\pi$
$233$	6.70148			0.439029			0.219514	+	0.975609i	$0.429553\pi$
$234$	−3.95258	−	2.05655i	−0.258388	−	0.134441i
$235$	0.988001			0.0644501
$236$	6.26787	+	1.67947i	0.408004	+	0.109324i
$237$	20.4372	−	6.85502i	1.32754	−	0.445281i
$238$	−0.951704	−	0.549466i	−0.0616898	−	0.0356166i
$239$	11.5154	−	11.5154i	0.744870	−	0.744870i	−0.228641	−	0.973511i	$-0.573428\pi$
$239$	11.5154	−	11.5154i	0.744870	−	0.744870i	0.973511	+	0.228641i	$0.0734282\pi$
$240$	−2.99465	+	0.185388i	−0.193304	+	0.0119667i
$241$	1.79899	+	6.71394i	0.115883	+	0.432483i	0.999351	−	0.0360086i	$-0.0114644\pi$
$241$	1.79899	+	6.71394i	0.115883	+	0.432483i	−0.883468	+	0.468491i	$0.844798\pi$
$242$	6.05350	+	6.05350i	0.389134	+	0.389134i
$243$	0.737648	+	15.5710i	0.0473202	+	0.998880i
$244$	13.6149	−	7.86058i	0.871606	−	0.503222i
$245$	−0.148916	+	0.555762i	−0.00951390	+	0.0355064i
$246$	−8.46925	−	1.71655i	−0.539979	−	0.109443i
$247$	−7.83149	−	5.39715i	−0.498306	−	0.343412i
$248$			6.26559i			0.397866i
$249$	8.04274	−	16.1612i	0.509688	−	1.02418i
$250$	−1.14579	−	1.98458i	−0.0724664	−	0.125516i
$251$	9.75718	−	16.8999i	0.615868	−	1.06671i	−0.374364	−	0.927282i	$-0.622139\pi$
$251$	9.75718	−	16.8999i	0.615868	−	1.06671i	0.990232	−	0.139432i	$-0.0445278\pi$
$252$	2.06449	+	5.08808i	0.130051	+	0.320519i
$253$	−1.76682	+	0.473419i	−0.111079	+	0.0297636i
$254$	−7.21417	+	1.93303i	−0.452657	+	0.121289i
$255$	−1.46906	−	2.21594i	−0.0919963	−	0.138768i
$256$	−2.04283	+	3.53829i	−0.127677	+	0.221143i
$257$	−11.1708	−	19.3484i	−0.696816	−	1.20692i	−0.969565	−	0.244835i	$-0.921266\pi$
$257$	−11.1708	−	19.3484i	−0.696816	−	1.20692i	0.272749	−	0.962085i	$-0.412067\pi$
$258$	−1.02470	−	0.509948i	−0.0637949	−	0.0317480i
$259$		−	9.97891i		−	0.620059i
$260$	−3.12649	−	2.15465i	−0.193897	−	0.133626i
$261$	8.39776	−	19.8657i	0.519808	−	1.22965i
$262$	1.84972	−	6.90327i	0.114276	−	0.426485i
$263$	2.62922	−	1.51798i	0.162125	−	0.0936027i	−0.416742	−	0.909025i	$-0.636828\pi$
$263$	2.62922	−	1.51798i	0.162125	−	0.0936027i	0.578867	+	0.815422i	$0.303495\pi$
$264$	10.2001	−	11.5464i	0.627776	−	0.710632i
$265$	1.42499	+	1.42499i	0.0875366	+	0.0875366i
$266$	−0.281234	−	1.04958i	−0.0172436	−	0.0643539i
$267$	−0.415004	−	6.70374i	−0.0253978	−	0.410262i
$268$	3.69835	−	3.69835i	0.225913	−	0.225913i
$269$	−1.84545	−	1.06547i	−0.112519	−	0.0649630i	0.442684	−	0.896678i	$-0.354026\pi$
$269$	−1.84545	−	1.06547i	−0.112519	−	0.0649630i	−0.555203	+	0.831715i	$0.687360\pi$
$270$	0.0938943	−	1.22793i	0.00571423	−	0.0747294i
$271$	20.7155	+	5.55071i	1.25838	+	0.337181i	0.825568	−	0.564303i	$-0.190855\pi$
$271$	20.7155	+	5.55071i	1.25838	+	0.337181i	0.432811	+	0.901485i	$0.357522\pi$
$272$	−8.03212			−0.487019
$273$	−1.72456	+	6.00216i	−0.104375	+	0.363267i
$274$	−5.25884			−0.317698
$275$	−25.4250	−	6.81261i	−1.53319	−	0.410816i
$276$	0.327097	+	0.975189i	0.0196889	+	0.0586995i
$277$	−21.8121	−	12.5932i	−1.31056	−	0.756655i	−0.328375	−	0.944547i	$-0.606501\pi$
$277$	−21.8121	−	12.5932i	−1.31056	−	0.756655i	−0.982190	+	0.187893i	$0.939834\pi$
$278$	−3.57745	+	3.57745i	−0.214561	+	0.214561i
$279$	11.7999	+	1.64054i	0.706442	+	0.0982167i
$280$	−0.234957	−	0.876873i	−0.0140414	−	0.0524032i
$281$	11.7407	+	11.7407i	0.700392	+	0.700392i	0.964495	−	0.264102i	$-0.0850757\pi$
$281$	11.7407	+	11.7407i	0.700392	+	0.700392i	−0.264102	+	0.964495i	$0.585076\pi$
$282$	0.918175	+	0.811121i	0.0546765	+	0.0483015i
$283$	−5.19348	+	2.99846i	−0.308721	+	0.178240i	−0.646354	−	0.763038i	$-0.723707\pi$
$283$	−5.19348	+	2.99846i	−0.308721	+	0.178240i	0.337633	+	0.941278i	$0.390374\pi$
$284$	0.414269	−	1.54607i	0.0245824	−	0.0917426i
$285$	0.522200	−	2.57646i	0.0309324	−	0.152617i
$286$	8.23474	−	1.51536i	0.486931	−	0.0896051i
$287$			12.1119i			0.714946i
$288$	−10.4037	−	8.10346i	−0.613044	−	0.477501i
$289$	4.94133	+	8.55863i	0.290666	+	0.503449i
$290$	−0.851943	+	1.47561i	−0.0500278	+	0.0866508i
$291$	14.8751	−	9.86149i	0.871996	−	0.578091i
$292$	−16.5314	+	4.42956i	−0.967424	+	0.259221i
$293$	29.2869	−	7.84741i	1.71096	−	0.458451i	0.735301	−	0.677741i	$-0.237041\pi$
$293$	29.2869	−	7.84741i	1.71096	−	0.458451i	0.975660	+	0.219290i	$0.0703742\pi$
$294$	−0.594657	+	0.394228i	−0.0346811	+	0.0229919i
$295$	−1.01992	+	1.76655i	−0.0593818	+	0.102852i
$296$	7.87228	+	13.6352i	0.457567	+	0.792529i
$297$	−19.0744	−	22.2330i	−1.10681	−	1.29009i
$298$		−	3.48344i		−	0.201790i
$299$	−0.391904	+	1.10223i	−0.0226644	+	0.0637438i
$300$	−2.94021	+	14.5066i	−0.169753	+	0.837539i
$301$	−0.415210	+	1.54958i	−0.0239323	+	0.0893166i
$302$	3.07892	−	1.77761i	0.177172	−	0.102290i
$303$	14.2184	+	12.5606i	0.816827	+	0.721590i
$304$	−5.61586	−	5.61586i	−0.322092	−	0.322092i
$305$	1.27908	+	4.77360i	0.0732401	+	0.273336i
$306$	0.453987	−	3.26539i	0.0259527	−	0.186670i
$307$	0.516426	−	0.516426i	0.0294740	−	0.0294740i	−0.692216	−	0.721690i	$-0.743366\pi$
$307$	0.516426	−	0.516426i	0.0294740	−	0.0294740i	0.721690	+	0.692216i	$0.243366\pi$
$308$	−8.93627	−	5.15936i	−0.509191	−	0.293982i
$309$	−3.82197	−	11.3946i	−0.217424	−	0.648215i
$310$	−0.909109	−	0.243595i	−0.0516339	−	0.0138353i
$311$	−14.8541			−0.842298			−0.421149	−	0.906992i	$-0.638373\pi$
$311$	−14.8541			−0.842298			−0.421149	+	0.906992i	$0.638373\pi$
$312$	−2.37861	−	9.56184i	−0.134662	−	0.541333i
$313$	−21.8659			−1.23593			−0.617967	−	0.786204i	$-0.712044\pi$
$313$	−21.8659			−1.23593			−0.617967	+	0.786204i	$0.712044\pi$
$314$	−5.57021	−	1.49253i	−0.314345	−	0.0842285i
$315$	−1.71292	+	0.212898i	−0.0965123	+	0.0119954i
$316$	19.7274	+	11.3896i	1.10975	+	0.640715i
$317$	−6.82047	+	6.82047i	−0.383076	+	0.383076i	−0.872209	−	0.489133i	$-0.837313\pi$
$317$	−6.82047	+	6.82047i	−0.383076	+	0.383076i	0.489133	+	0.872209i	$0.337313\pi$
$318$	0.154404	+	2.49416i	0.00865857	+	0.139866i
$319$	10.4900	+	39.1494i	0.587330	+	2.19194i
$320$	−1.71313	−	1.71313i	−0.0957670	−	0.0957670i
$321$	−22.4989	+	25.4684i	−1.25577	+	1.42151i
$322$	−0.115743	+	0.0668242i	−0.00645010	+	0.00372397i
$323$	1.82144	−	6.79771i	0.101348	−	0.378235i
$324$	−11.8156	+	11.4781i	−0.656425	+	0.637673i
$325$	−12.8147	+	10.9166i	−0.710833	+	0.605542i
$326$		−	7.38696i		−	0.409126i
$327$	−7.75981	−	3.86172i	−0.429119	−	0.213554i
$328$	−9.55502	−	16.5498i	−0.527587	−	0.913808i
$329$	0.858583	−	1.48711i	0.0473352	−	0.0819870i
$330$	1.27877	+	1.92890i	0.0703938	+	0.106182i
$331$	22.8466	−	6.12173i	1.25576	−	0.336481i	0.431203	−	0.902255i	$-0.358089\pi$
$331$	22.8466	−	6.12173i	1.25576	−	0.336481i	0.824560	+	0.565774i	$0.191422\pi$
$332$	18.4261	−	4.93726i	1.01126	−	0.270967i
$333$	27.7402	−	11.2556i	1.52015	−	0.616804i
$334$	2.15969	−	3.74070i	0.118173	−	0.204682i
$335$	0.822075	+	1.42388i	0.0449147	+	0.0777946i
$336$	−2.32334	+	4.66856i	−0.126749	+	0.254691i
$337$		−	6.32237i		−	0.344401i	−0.985062	−	0.172201i	$-0.944912\pi$
$337$		−	6.32237i		−	0.344401i	0.985062	−	0.172201i	$-0.0550878\pi$
$338$	2.19052	−	4.88642i	0.119149	−	0.265786i
$339$	−0.945623	−	0.191660i	−0.0513592	−	0.0104095i
$340$	0.727157	−	2.71379i	0.0394356	−	0.147176i
$341$	−19.3885	+	11.1939i	−1.04994	+	0.606185i
$342$	2.60050	−	1.96566i	0.140619	−	0.106291i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−0.655112	−	2.44491i	−0.0353213	−	0.131821i
$345$	−0.322721	+	0.0199785i	−0.0173747	+	0.00107560i
$346$	−6.06694	+	6.06694i	−0.326161	+	0.326161i
$347$	15.2579	+	8.80917i	0.819089	+	0.472901i	0.850102	−	0.526618i	$-0.176540\pi$
$347$	15.2579	+	8.80917i	0.819089	+	0.472901i	−0.0310133	+	0.999519i	$0.509873\pi$
$348$	21.6083	−	7.24784i	1.15833	−	0.388525i
$349$	3.21888	+	0.862495i	0.172302	+	0.0461683i	0.343939	−	0.938992i	$-0.388239\pi$
$349$	3.21888	+	0.862495i	0.172302	+	0.0461683i	−0.171636	+	0.985160i	$0.554905\pi$
$350$	−1.92323			−0.102801
$351$	−18.6305	+	1.97599i	−0.994422	+	0.105471i
$352$	24.7816			1.32087
$353$	12.4896	+	3.34659i	0.664756	+	0.178121i	0.575392	−	0.817878i	$-0.304850\pi$
$353$	12.4896	+	3.34659i	0.664756	+	0.178121i	0.0893647	+	0.995999i	$0.471516\pi$
$354$	−2.39812	+	0.804375i	−0.127458	+	0.0427521i
$355$	0.435747	+	0.251579i	0.0231271	+	0.0133524i
$356$	5.01880	−	5.01880i	0.265996	−	0.265996i
$357$	−4.61200	+	0.285512i	−0.244093	+	0.0151109i
$358$	1.10143	+	4.11061i	0.0582126	+	0.217252i
$359$	−15.8906	−	15.8906i	−0.838672	−	0.838672i	0.150013	−	0.988684i	$-0.452069\pi$
$359$	−15.8906	−	15.8906i	−0.838672	−	0.838672i	−0.988684	+	0.150013i	$0.952069\pi$
$360$	2.17259	−	1.64221i	0.114505	−	0.0865523i
$361$	−10.4282	+	6.02072i	−0.548852	+	0.316880i
$362$	−1.18530	+	4.42361i	−0.0622981	+	0.232500i
$363$	35.2800	+	7.15057i	1.85172	+	0.375308i
$364$	−5.96007	+	2.83348i	−0.312392	+	0.148515i
$365$		−	5.38000i		−	0.281602i
$366$	−2.73031	+	5.48632i	−0.142715	+	0.286775i
$367$	1.22219	+	2.11690i	0.0637979	+	0.110501i	0.896160	−	0.443731i	$-0.146345\pi$
$367$	1.22219	+	2.11690i	0.0637979	+	0.110501i	−0.832362	+	0.554232i	$0.813012\pi$
$368$	−0.488419	+	0.845967i	−0.0254606	+	0.0440991i
$369$	−33.6698	+	13.6616i	−1.75278	+	0.711192i
$370$	−2.28446	+	0.612120i	−0.118764	+	0.0318226i
$371$	3.38319	−	0.906522i	0.175646	−	0.0470643i
$372$	6.95630	+	10.4929i	0.360667	+	0.544033i
$373$	−7.25664	+	12.5689i	−0.375735	+	0.650792i	−0.990437	−	0.137968i	$-0.955943\pi$
$373$	−7.25664	+	12.5689i	−0.375735	+	0.650792i	0.614702	+	0.788760i	$0.289276\pi$
$374$	3.09770	+	5.36537i	0.160178	+	0.277437i
$375$	−8.62654	−	4.29306i	−0.445473	−	0.221693i
$376$			2.70932i			0.139722i
$377$	24.4233	+	8.68382i	1.25787	+	0.447240i
$378$	−1.76665	−	1.20841i	−0.0908665	−	0.0621539i
$379$	−3.25658	+	12.1537i	−0.167279	+	0.624294i	0.830459	+	0.557079i	$0.188078\pi$
$379$	−3.25658	+	12.1537i	−0.167279	+	0.624294i	−0.997739	+	0.0672149i	$0.978589\pi$
$380$	2.40582	−	1.38900i	0.123416	−	0.0712543i
$381$	−20.7918	+	23.5359i	−1.06519	+	1.20578i
$382$	4.93232	+	4.93232i	0.252359	+	0.252359i
$383$	3.50152	+	13.0679i	0.178919	+	0.667737i	0.995851	+	0.0910016i	$0.0290068\pi$
$383$	3.50152	+	13.0679i	0.178919	+	0.667737i	−0.816931	+	0.576735i	$0.804327\pi$
$384$	−1.12649	−	18.1967i	−0.0574860	−	0.928596i
$385$	2.29366	−	2.29366i	0.116896	−	0.116896i
$386$	2.33919	+	1.35053i	0.119062	+	0.0687404i
$387$	−4.77600	+	0.593604i	−0.242778	+	0.0301746i
$388$	18.2171	+	4.88124i	0.924831	+	0.247808i
$389$	20.6213			1.04554			0.522771	−	0.852473i	$-0.324898\pi$
$389$	20.6213			1.04554			0.522771	+	0.852473i	$0.324898\pi$
$390$	1.47986	+	0.0266219i	0.0749354	+	0.00134805i
$391$	−0.865587			−0.0437746
$392$	−1.52402	−	0.408360i	−0.0769747	−	0.0206253i
$393$	−9.55644	−	28.4910i	−0.482059	−	1.43718i
$394$	−3.18211	−	1.83719i	−0.160312	−	0.0925565i
$395$	−5.06339	+	5.06339i	−0.254767	+	0.254767i
$396$	4.26283	−	30.6612i	0.214215	−	1.54078i
$397$	−3.97373	−	14.8302i	−0.199436	−	0.744304i	−0.991074	−	0.133314i	$-0.957438\pi$
$397$	−3.97373	−	14.8302i	−0.199436	−	0.744304i	0.791638	−	0.610990i	$-0.209229\pi$
$398$	1.43929	+	1.43929i	0.0721451	+	0.0721451i
$399$	−3.42422	−	3.02497i	−0.171425	−	0.151438i
$400$	−12.1737	+	7.02847i	−0.608683	+	0.351423i
$401$	−4.54418	+	16.9591i	−0.226925	+	0.846897i	0.754699	+	0.656072i	$0.227783\pi$
$401$	−4.54418	+	16.9591i	−0.226925	+	0.846897i	−0.981624	+	0.190825i	$0.938884\pi$
$402$	−0.404985	+	1.99814i	−0.0201988	+	0.0996583i
$403$	−1.14159	+	14.2726i	−0.0568666	+	0.710966i
$404$			20.0483i			0.997441i
$405$	−2.52391	−	4.52159i	−0.125414	−	0.224680i
$406$	1.48069	+	2.56464i	0.0734856	+	0.127281i
$407$	−28.1288	+	48.7205i	−1.39429	+	2.41498i
$408$	6.07660	−	4.02849i	0.300836	−	0.199440i
$409$	5.48725	−	1.47030i	0.271327	−	0.0727018i	−0.120590	−	0.992702i	$-0.538479\pi$
$409$	5.48725	−	1.47030i	0.271327	−	0.0727018i	0.391917	+	0.920001i	$0.371812\pi$
$410$	2.77278	−	0.742964i	0.136938	−	0.0366924i
$411$	−18.4303	+	12.2184i	−0.909099	+	0.602689i
$412$	6.35019	−	10.9989i	0.312851	−	0.541875i
$413$	1.77263	+	3.07029i	0.0872256	+	0.151079i
$414$	−0.316315	−	0.246378i	−0.0155460	−	0.0121088i
$415$			5.99663i			0.294363i
$416$	8.99367	−	13.0502i	0.440951	−	0.639838i
$417$	−4.22579	+	20.8495i	−0.206938	+	1.02100i
$418$	−1.58550	+	5.91717i	−0.0775493	+	0.289418i
$419$	8.55895	−	4.94151i	0.418132	−	0.241409i	−0.276146	−	0.961116i	$-0.589057\pi$
$419$	8.55895	−	4.94151i	0.418132	−	0.241409i	0.694278	+	0.719707i	$0.255724\pi$
$420$	−1.36702	−	1.20763i	−0.0667036	−	0.0589264i
$421$	6.13424	+	6.13424i	0.298965	+	0.298965i	0.840608	−	0.541644i	$-0.182198\pi$
$421$	6.13424	+	6.13424i	0.298965	+	0.298965i	−0.541644	+	0.840608i	$0.682198\pi$
$422$	0.766334	+	2.86000i	0.0373045	+	0.139222i
$423$	5.10242	+	0.709390i	0.248088	+	0.0344917i
$424$	−3.90764	+	3.90764i	−0.189772	+	0.189772i
$425$	−10.7872	−	6.22800i	−0.523256	−	0.302102i
$426$	0.198412	+	0.591535i	0.00961311	+	0.0286600i
$427$	8.29661	+	2.22307i	0.401501	+	0.107582i
$428$	−35.9110			−1.73583
$429$	25.3389	−	24.4434i	1.22337	−	1.18014i
$430$	0.380215			0.0183356
$431$	−0.530721	−	0.142206i	−0.0255639	−	0.00684983i	0.246014	−	0.969266i	$-0.420879\pi$
$431$	−0.530721	−	0.142206i	−0.0255639	−	0.00684983i	−0.271578	+	0.962416i	$0.587546\pi$
$432$	−15.5987	−	1.19276i	−0.750491	−	0.0573867i
$433$	25.7768	+	14.8822i	1.23875	+	0.715195i	0.968839	−	0.247690i	$-0.0796714\pi$
$433$	25.7768	+	14.8822i	1.23875	+	0.715195i	0.269914	+	0.962884i	$0.413005\pi$
$434$	−1.15668	+	1.15668i	−0.0555222	+	0.0555222i
$435$	0.442684	+	7.15087i	0.0212251	+	0.342858i
$436$	−2.37063	−	8.84730i	−0.113532	−	0.423709i
$437$	−0.605197	−	0.605197i	−0.0289505	−	0.0289505i
$438$	4.41683	−	4.99977i	0.211044	−	0.238898i
$439$	25.4871	−	14.7150i	1.21643	−	0.702309i	0.252281	−	0.967654i	$-0.418819\pi$
$439$	25.4871	−	14.7150i	1.21643	−	0.702309i	0.964153	+	0.265345i	$0.0854859\pi$
$440$	−1.32461	+	4.94350i	−0.0631481	+	0.235672i
$441$	−1.16810	+	2.76325i	−0.0556238	+	0.131583i
$442$	3.94964	+	0.315912i	0.187865	+	0.0150264i
$443$		−	1.30384i		−	0.0619475i	−0.999520	−	0.0309738i	$-0.990139\pi$
$443$		−	1.30384i		−	0.0619475i	0.999520	−	0.0309738i	$-0.00986083\pi$
$444$	28.3219	+	14.0946i	1.34410	+	0.668900i
$445$	1.11558	+	1.93225i	0.0528838	+	0.0915974i
$446$	−2.51616	+	4.35811i	−0.119143	+	0.206362i
$447$	−8.09341	−	12.2082i	−0.382805	−	0.577426i
$448$	−4.06728	+	1.08982i	−0.192161	+	0.0514894i
$449$	−30.9059	+	8.28120i	−1.45854	+	0.390814i	−0.898985	−	0.437980i	$-0.855694\pi$
$449$	−30.9059	+	8.28120i	−1.45854	+	0.390814i	−0.559553	+	0.828794i	$0.689027\pi$
$450$	−2.16929	−	5.34636i	−0.102261	−	0.252030i
$451$	34.1414	−	59.1347i	1.60766	−	2.78454i
$452$	−0.509797	−	0.882993i	−0.0239788	−	0.0415325i
$453$	6.66035	−	13.3834i	0.312931	−	0.628808i
$454$			4.03687i			0.189460i
$455$	−0.375449	−	2.04026i	−0.0176013	−	0.0956489i
$456$	7.06523	+	1.43199i	0.330860	+	0.0670589i
$457$	−2.45001	+	9.14358i	−0.114607	+	0.427718i	−0.999257	−	0.0385365i	$-0.987730\pi$
$457$	−2.45001	+	9.14358i	−0.114607	+	0.427718i	0.884650	+	0.466255i	$0.154397\pi$
$458$	3.34251	−	1.92980i	0.156185	−	0.0901735i
$459$	−5.99575	−	12.4988i	−0.279858	−	0.583393i
$460$	−0.241607	−	0.241607i	−0.0112650	−	0.0112650i
$461$	1.62057	+	6.04806i	0.0754776	+	0.281686i	0.993341	−	0.115210i	$-0.0367540\pi$
$461$	1.62057	+	6.04806i	0.0754776	+	0.281686i	−0.917864	+	0.396896i	$0.870087\pi$
$462$	4.01458	−	0.248528i	0.186775	−	0.0115626i
$463$	14.6085	−	14.6085i	0.678915	−	0.678915i	−0.280840	−	0.959755i	$-0.590613\pi$
$463$	14.6085	−	14.6085i	0.678915	−	0.678915i	0.959755	+	0.280840i	$0.0906129\pi$
$464$	18.7450	+	10.8224i	0.870214	+	0.502418i
$465$	−3.75206	+	1.25851i	−0.173998	+	0.0583621i
$466$	−2.66641	−	0.714462i	−0.123519	−	0.0330968i
$467$	33.8720			1.56741			0.783704	−	0.621135i	$-0.213328\pi$
$467$	33.8720			1.56741			0.783704	+	0.621135i	$0.213328\pi$
$468$	−14.5994	−	13.3723i	−0.674855	−	0.618135i
$469$	2.85756			0.131950
$470$	−0.393109	−	0.105333i	−0.0181328	−	0.00485867i
$471$	−22.9893	+	7.71104i	−1.05929	+	0.355306i
$472$	−4.84425	−	2.79683i	−0.222975	−	0.128735i
$473$	6.39520	−	6.39520i	0.294052	−	0.294052i
$474$	−8.86244	+	0.548641i	−0.407065	+	0.0251999i
$475$	−3.18769	−	11.8966i	−0.146261	−	0.545854i
$476$	−3.45280	−	3.45280i	−0.158259	−	0.158259i
$477$	6.33606	+	8.38236i	0.290108	+	0.383802i
$478$	−5.80948	+	3.35410i	−0.265719	+	0.153413i
$479$	−0.618999	+	2.31013i	−0.0282828	+	0.105553i	−0.978624	−	0.205656i	$-0.934067\pi$
$479$	−0.618999	+	2.31013i	−0.0282828	+	0.105553i	0.950342	+	0.311209i	$0.100734\pi$
$480$	4.29335	+	0.870180i	0.195964	+	0.0397181i
$481$	15.4481	+	32.4943i	0.704374	+	1.48161i
$482$		−	2.86316i		−	0.130413i
$483$	−0.250377	+	0.503111i	−0.0113925	+	0.0228923i
$484$	19.0198	+	32.9433i	0.864538	+	1.49742i
$485$	−2.96430	+	5.13432i	−0.134602	+	0.233137i
$486$	1.36657	−	6.27408i	0.0619887	−	0.284598i
$487$	−3.66693	+	0.982552i	−0.166165	+	0.0445237i	−0.340942	−	0.940084i	$-0.610746\pi$
$487$	−3.66693	+	0.982552i	−0.166165	+	0.0445237i	0.174778	+	0.984608i	$0.444079\pi$
$488$	−13.0903	+	3.50752i	−0.592568	+	0.158778i
$489$	−17.1629	−	25.8885i	−0.776131	−	1.17072i
$490$	0.118502	−	0.205252i	0.00535340	−	0.00927236i
$491$	−3.51843	−	6.09410i	−0.158784	−	0.275023i	0.775646	−	0.631168i	$-0.217424\pi$
$491$	−3.51843	−	6.09410i	−0.158784	−	0.275023i	−0.934431	+	0.356145i	$0.884091\pi$
$492$	−34.3759	−	17.1074i	−1.54978	−	0.771260i
$493$			19.1797i			0.863811i
$494$	2.54062	+	2.98237i	0.114308	+	0.134183i
$495$	8.96320	+	3.78899i	0.402866	+	0.170302i
$496$	−3.09444	+	11.5486i	−0.138944	+	0.518548i
$497$	0.757338	−	0.437249i	0.0339712	−	0.0196133i
$498$	−4.92306	+	5.57282i	−0.220608	+	0.249724i
$499$	−1.23434	−	1.23434i	−0.0552565	−	0.0552565i	0.678939	−	0.734195i	$-0.262440\pi$
$499$	−1.23434	−	1.23434i	−0.0552565	−	0.0552565i	−0.734195	+	0.678939i	$0.762440\pi$
$500$	−2.63541	−	9.83549i	−0.117859	−	0.439857i
$501$	−1.12221	−	18.1276i	−0.0501368	−	0.809881i
$502$	−5.68397	+	5.68397i	−0.253688	+	0.253688i
$503$	24.4458	+	14.1138i	1.08998	+	0.629302i	0.933572	−	0.358390i	$-0.116674\pi$
$503$	24.4458	+	14.1138i	1.08998	+	0.629302i	0.156411	+	0.987692i	$0.450008\pi$
$504$	−0.583812	−	4.69721i	−0.0260050	−	0.209230i
$505$	−6.08751	−	1.63114i	−0.270891	−	0.0725849i
$506$	0.753462			0.0334955
$507$	−3.67613	−	22.2145i	−0.163263	−	0.986583i
$508$	−33.1862			−1.47240
$509$	−20.6255	−	5.52660i	−0.914211	−	0.244962i	−0.229102	−	0.973402i	$-0.573579\pi$
$509$	−20.6255	−	5.52660i	−0.914211	−	0.244962i	−0.685109	+	0.728440i	$0.740246\pi$
$510$	0.348268	+	1.03831i	0.0154216	+	0.0459770i
$511$	−8.09781	−	4.67527i	−0.358226	−	0.206822i
$512$	16.0760	−	16.0760i	0.710466	−	0.710466i
$513$	4.54675	−	12.9309i	0.200744	−	0.570914i
$514$	2.38190	+	8.88936i	0.105061	+	0.392093i
$515$	2.82306	+	2.82306i	0.124399	+	0.124399i
$516$	−3.81154	−	3.36713i	−0.167794	−	0.148230i
$517$	−8.38380	+	4.84039i	−0.368719	+	0.212880i
$518$	−1.06388	+	3.97044i	−0.0467441	+	0.174451i
$519$	−7.16645	+	35.3583i	−0.314572	+	1.55206i
$520$	2.12256	+	2.49162i	0.0930803	+	0.109265i
$521$		−	14.1163i		−	0.618446i	−0.950990	−	0.309223i	$-0.899931\pi$
$521$		−	14.1163i		−	0.618446i	0.950990	−	0.309223i	$-0.100069\pi$
$522$	−5.45926	+	7.00892i	−0.238945	+	0.306772i
$523$	10.1325	+	17.5501i	0.443065	+	0.767412i	0.997915	−	0.0645388i	$-0.0205576\pi$
$523$	10.1325	+	17.5501i	0.443065	+	0.767412i	−0.554850	+	0.831950i	$0.687224\pi$
$524$	15.8780	−	27.5015i	0.693634	−	1.20141i
$525$	−6.74021	+	4.46843i	−0.294167	+	0.195018i
$526$	−1.20796	+	0.323672i	−0.0526695	+	0.0141128i
$527$	−10.2333	+	2.74202i	−0.445771	+	0.119444i
$528$	24.5032	−	16.2444i	1.06637	−	0.706949i
$529$	11.4474	−	19.8274i	0.497712	−	0.862062i
$530$	−0.415059	−	0.718903i	−0.0180290	−	0.0312272i
$531$	−6.53563	+	8.39082i	−0.283622	+	0.364130i
$532$		−	4.82823i		−	0.209330i
$533$	−18.7502	−	39.4401i	−0.812163	−	1.70834i
$534$	−0.549580	+	2.71155i	−0.0237826	+	0.117340i
$535$	2.92174	−	10.9041i	0.126318	−	0.471425i
$536$	−3.90458	+	2.25431i	−0.168652	+	0.0973713i
$537$	13.4107	+	11.8471i	0.578714	+	0.511239i
$538$	0.620682	+	0.620682i	0.0267595	+	0.0267595i
$539$	−1.45913	−	5.44555i	−0.0628492	−	0.234556i
$540$	1.81516	−	5.16229i	0.0781120	−	0.222149i
$541$	−12.3244	+	12.3244i	−0.529868	+	0.529868i	−0.920533	−	0.390665i	$-0.872245\pi$
$541$	−12.3244	+	12.3244i	−0.529868	+	0.529868i	0.390665	+	0.920533i	$0.372245\pi$
$542$	−7.65059	−	4.41707i	−0.328621	−	0.189729i
$543$	6.12376	+	18.2570i	0.262796	+	0.783484i
$544$	11.3275	+	3.03520i	0.485664	+	0.130133i
$545$	2.87928			0.123335
$546$	1.32608	−	2.20430i	0.0567510	−	0.0943353i
$547$	−34.6992			−1.48363			−0.741816	−	0.670603i	$-0.766035\pi$
$547$	−34.6992			−1.48363			−0.741816	+	0.670603i	$0.766035\pi$
$548$	−22.5709	−	6.04786i	−0.964183	−	0.258352i
$549$	3.17821	+	25.5711i	0.135643	+	1.09135i
$550$	9.38988	+	5.42125i	0.400386	+	0.231163i
$551$	−13.4100	+	13.4100i	−0.571284	+	0.571284i
$552$	−0.0547853	−	0.884971i	−0.00233182	−	0.0376669i
$553$	3.22112	+	12.0214i	0.136976	+	0.511202i
$554$	7.33609	+	7.33609i	0.311681	+	0.311681i
$555$	−6.58400	+	7.45297i	−0.279475	+	0.316361i
$556$	−19.4686	+	11.2402i	−0.825653	+	0.476691i
$557$	10.4368	−	38.9506i	0.442220	−	1.65039i	−0.280953	−	0.959721i	$-0.590651\pi$
$557$	10.4368	−	38.9506i	0.442220	−	1.65039i	0.723173	−	0.690666i	$-0.242683\pi$
$558$	−4.52009	−	1.91076i	−0.191351	−	0.0808891i
$559$	−1.04683	−	5.68868i	−0.0442763	−	0.240606i
$560$		−	1.73227i		−	0.0732019i
$561$	23.3222	+	11.6064i	0.984663	+	0.490024i
$562$	−3.41973	−	5.92314i	−0.144253	−	0.249853i
$563$	−1.02113	+	1.76865i	−0.0430356	+	0.0745399i	−0.886741	−	0.462267i	$-0.847036\pi$
$563$	−1.02113	+	1.76865i	−0.0430356	+	0.0745399i	0.843705	+	0.536807i	$0.180370\pi$
$564$	3.00799	+	4.53726i	0.126659	+	0.191053i
$565$	0.309591	−	0.0829547i	0.0130246	−	0.00348993i
$566$	2.38607	−	0.639347i	0.100294	−	0.0268738i
$567$	−8.99906	−	0.130402i	−0.377925	−	0.00547636i
$568$	−0.689884	+	1.19491i	−0.0289469	+	0.0501375i
$569$	7.93831	+	13.7496i	0.332791	+	0.576411i	0.983058	−	0.183295i	$-0.0586762\pi$
$569$	7.93831	+	13.7496i	0.332791	+	0.576411i	−0.650267	+	0.759706i	$0.725343\pi$
$570$	−0.482458	+	0.969459i	−0.0202079	+	0.0406062i
$571$		−	29.4823i		−	1.23380i	−0.787043	−	0.616898i	$-0.788389\pi$
$571$		−	29.4823i		−	1.23380i	0.787043	−	0.616898i	$-0.211611\pi$
$572$	37.0862	+	2.96634i	1.55065	+	0.124029i
$573$	28.7457	+	5.82620i	1.20087	+	0.243393i
$574$	1.29129	−	4.81914i	0.0538972	−	0.201147i
$575$	−1.31190	+	0.757428i	−0.0547101	+	0.0315869i
$576$	−7.61724	−	10.0773i	−0.317385	−	0.419888i
$577$	0.322874	+	0.322874i	0.0134414	+	0.0134414i	0.713796	−	0.700354i	$-0.246975\pi$
$577$	0.322874	+	0.322874i	0.0134414	+	0.0134414i	−0.700354	+	0.713796i	$0.746975\pi$
$578$	−1.05362	−	3.93215i	−0.0438246	−	0.163556i
$579$	11.3358	−	0.701760i	0.471101	−	0.0291642i
$580$	−5.35354	+	5.35354i	−0.222294	+	0.222294i
$581$	9.02594	+	5.21113i	0.374459	+	0.216194i
$582$	−6.96993	+	2.33785i	−0.288913	+	0.0969069i
$583$	−19.0732	−	5.11065i	−0.789932	−	0.211662i
$584$	14.7531			0.610489
$585$	5.24820	−	3.34500i	0.216986	−	0.138299i
$586$	−12.4894			−0.515933
$587$	12.2031	+	3.26980i	0.503674	+	0.134959i	0.501705	−	0.865039i	$-0.332706\pi$
$587$	12.2031	+	3.26980i	0.503674	+	0.134959i	0.00196931	+	0.999998i	$0.499373\pi$
$588$	−3.00564	+	1.00815i	−0.123951	+	0.0415754i
$589$	−9.07205	−	5.23775i	−0.373807	−	0.215818i
$590$	0.594144	−	0.594144i	0.0244605	−	0.0244605i
$591$	−15.4207	+	0.954636i	−0.634321	+	0.0392685i
$592$	7.77589	+	29.0200i	0.319587	+	1.19272i
$593$	−25.2016	−	25.2016i	−1.03490	−	1.03490i	−0.999368	−	0.0355363i	$-0.988686\pi$
$593$	−25.2016	−	25.2016i	−1.03490	−	1.03490i	−0.0355363	−	0.999368i	$-0.511314\pi$
$594$	5.21908	+	10.8797i	0.214142	+	0.446401i
$595$	1.32934	−	0.767493i	0.0544975	−	0.0314641i
$596$	4.00608	−	14.9509i	0.164095	−	0.612413i
$597$	8.38823	+	1.70013i	0.343307	+	0.0695818i
$598$	0.273444	−	0.396778i	0.0111820	−	0.0162255i
$599$		−	33.3266i		−	1.36169i	−0.732429	−	0.680843i	$-0.761613\pi$
$599$		−	33.3266i		−	1.36169i	0.732429	−	0.680843i	$-0.238387\pi$
$600$	5.68472	−	11.4230i	0.232078	−	0.466341i
$601$	−7.37774	−	12.7786i	−0.300944	−	0.521251i	0.675406	−	0.737446i	$-0.263969\pi$
$601$	−7.37774	−	12.7786i	−0.300944	−	0.521251i	−0.976350	+	0.216195i	$0.930635\pi$
$602$	0.330410	−	0.572288i	0.0134665	−	0.0233247i
$603$	3.22316	+	7.94369i	0.131257	+	0.323492i
$604$	15.2590	−	4.08864i	0.620881	−	0.166364i
$605$	−11.5504	+	3.09493i	−0.469592	+	0.125827i
$606$	−4.31816	−	6.51353i	−0.175413	−	0.264594i
$607$	−1.94899	+	3.37574i	−0.0791069	+	0.137017i	−0.902865	−	0.429924i	$-0.858540\pi$
$607$	−1.94899	+	3.37574i	−0.0791069	+	0.137017i	0.823758	+	0.566942i	$0.191874\pi$
$608$	5.79779	+	10.0421i	0.235131	+	0.407259i
$609$	11.1480	+	5.54786i	0.451738	+	0.224811i
$610$		−	2.03570i		−	0.0824232i
$611$	−0.493637	+	6.17162i	−0.0199704	+	0.249677i
$612$	5.70383	−	13.4929i	0.230564	−	0.545420i
$613$	1.96958	−	7.35058i	0.0795507	−	0.296887i	−0.914676	−	0.404188i	$-0.867554\pi$
$613$	1.96958	−	7.35058i	0.0795507	−	0.296887i	0.994227	+	0.107301i	$0.0342208\pi$
$614$	−0.260535	+	0.150420i	−0.0105143	+	0.00607046i
$615$	7.99136	−	9.04608i	0.322243	−	0.364773i
$616$	6.28971	+	6.28971i	0.253419	+	0.253419i
$617$	9.14113	+	34.1152i	0.368008	+	1.37342i	0.863297	+	0.504696i	$0.168395\pi$
$617$	9.14113	+	34.1152i	0.368008	+	1.37342i	−0.495289	+	0.868728i	$0.664938\pi$
$618$	0.305891	+	4.94119i	0.0123047	+	0.198764i
$619$	−2.55502	+	2.55502i	−0.102695	+	0.102695i	−0.756587	−	0.653892i	$-0.773135\pi$
$619$	−2.55502	+	2.55502i	−0.102695	+	0.102695i	0.653892	+	0.756587i	$0.273135\pi$
$620$	−3.62175	−	2.09102i	−0.145453	−	0.0839773i
$621$	−1.68100	−	0.128539i	−0.0674562	−	0.00515808i
$622$	5.91019	+	1.58363i	0.236977	+	0.0634978i
$623$	3.87781			0.155361
$624$	0.338184	−	18.7989i	0.0135382	−	0.752560i
$625$	−20.1439			−0.805755
$626$	8.70009	+	2.33118i	0.347725	+	0.0931727i
$627$	8.19135	+	24.4212i	0.327131	+	0.975289i
$628$	−22.1908	−	12.8119i	−0.885511	−	0.511250i
$629$	−18.8247	+	18.8247i	−0.750588	+	0.750588i
$630$	0.704241	+	0.0979107i	0.0280576	+	0.00390086i
$631$	−10.4662	−	39.0602i	−0.416651	−	1.55496i	−0.781506	−	0.623898i	$-0.785548\pi$
$631$	−10.4662	−	39.0602i	−0.416651	−	1.55496i	0.364855	−	0.931064i	$-0.381119\pi$
$632$	−13.8849	−	13.8849i	−0.552313	−	0.552313i
$633$	9.33063	+	8.24272i	0.370859	+	0.327619i
$634$	3.44090	−	1.98660i	0.136656	−	0.0788981i
$635$	2.70005	−	10.0767i	0.107148	−	0.399883i
$636$	−2.20567	+	10.8825i	−0.0874607	+	0.431519i
$637$	−3.39720	−	1.20789i	−0.134602	−	0.0478584i
$638$		−	16.6953i		−	0.660972i
$639$	2.06973	+	1.61212i	0.0818774	+	0.0637744i
$640$	3.02815	+	5.24492i	0.119698	+	0.207324i
$641$	−22.7590	+	39.4197i	−0.898926	+	1.55699i	−0.0700562	+	0.997543i	$0.522318\pi$
$641$	−22.7590	+	39.4197i	−0.898926	+	1.55699i	−0.828870	+	0.559442i	$0.811015\pi$
$642$	11.6672	−	7.73479i	0.460468	−	0.305268i
$643$	−36.4711	+	9.77239i	−1.43828	+	0.385386i	−0.891930	−	0.452173i	$-0.850649\pi$
$643$	−36.4711	+	9.77239i	−1.43828	+	0.385386i	−0.546348	+	0.837558i	$0.683982\pi$
$644$	−0.573618	+	0.153701i	−0.0226037	+	0.00605665i
$645$	1.33251	−	0.883391i	0.0524676	−	0.0347835i
$646$	−1.44944	+	2.51051i	−0.0570276	+	0.0987746i
$647$	−12.5677	−	21.7680i	−0.494089	−	0.855787i	0.505888	−	0.862599i	$-0.331165\pi$
$647$	−12.5677	−	21.7680i	−0.494089	−	0.855787i	−0.999977	+	0.00681216i	$0.997832\pi$
$648$	12.3992	−	6.92110i	0.487086	−	0.271886i
$649$		−	19.9870i		−	0.784557i
$650$	6.26261	−	2.97731i	0.245640	−	0.116780i
$651$	−1.36630	+	6.74114i	−0.0535495	+	0.264206i
$652$	8.49528	−	31.7048i	0.332701	−	1.24166i
$653$	−8.96367	+	5.17518i	−0.350776	+	0.202520i	−0.665027	−	0.746819i	$-0.731580\pi$
$653$	−8.96367	+	5.17518i	−0.350776	+	0.202520i	0.314251	+	0.949340i	$0.398247\pi$
$654$	2.67579	+	2.36381i	0.104632	+	0.0924323i
$655$	7.05877	+	7.05877i	0.275809	+	0.275809i
$656$	−9.43803	−	35.2232i	−0.368493	−	1.37524i
$657$	3.86287	−	27.7844i	0.150705	−	1.08397i
$658$	−0.500160	+	0.500160i	−0.0194983	+	0.0194983i
$659$	30.5019	+	17.6103i	1.18818	+	0.685998i	0.957893	−	0.287124i	$-0.0926992\pi$
$659$	30.5019	+	17.6103i	1.18818	+	0.685998i	0.230290	+	0.973122i	$0.426033\pi$
$660$	3.27016	+	9.74945i	0.127291	+	0.379497i
$661$	39.3089	+	10.5328i	1.52894	+	0.409678i	0.922673	−	0.385583i	$-0.126000\pi$
$661$	39.3089	+	10.5328i	1.52894	+	0.409678i	0.606267	+	0.795261i	$0.292666\pi$
$662$	−9.74295			−0.378670
$663$	14.5760	−	8.06944i	0.566086	−	0.313391i
$664$	−16.4441			−0.638154
$665$	1.46605	+	0.392827i	0.0568510	+	0.0152332i
$666$	−12.2374	+	1.52097i	−0.474188	+	0.0589363i
$667$	2.02007	+	1.16629i	0.0782173	+	0.0451588i
$668$	13.5713	−	13.5713i	0.525091	−	0.525091i
$669$	1.30744	+	21.1196i	0.0505484	+	0.816530i
$670$	−0.175287	−	0.654180i	−0.00677193	−	0.0252732i
$671$	−34.2405	−	34.2405i	−1.32184	−	1.32184i
$672$	5.04073	−	5.70602i	0.194450	−	0.220115i
$673$	18.3276	−	10.5814i	0.706476	−	0.407884i	−0.103279	−	0.994652i	$-0.532933\pi$
$673$	18.3276	−	10.5814i	0.706476	−	0.407884i	0.809755	+	0.586768i	$0.199600\pi$
$674$	−0.674044	+	2.51557i	−0.0259632	+	0.0968960i
$675$	−20.0243	−	13.6969i	−0.770735	−	0.527193i
$676$	15.0213	−	18.4533i	0.577742	−	0.709743i
$677$		−	0.807509i		−	0.0310351i	−0.999880	−	0.0155176i	$-0.995060\pi$
$677$		−	0.807509i		−	0.0310351i	0.999880	−	0.0155176i	$-0.00493959\pi$
$678$	0.355814	+	0.177073i	0.0136650	+	0.00680046i
$679$	5.15201	+	8.92354i	0.197716	+	0.342454i
$680$	−1.21094	+	2.09741i	−0.0464373	+	0.0804318i
$681$	9.37926	+	14.1477i	0.359414	+	0.542142i
$682$	8.90776	−	2.38683i	0.341096	−	0.0913963i
$683$	−0.145007	+	0.0388544i	−0.00554852	+	0.00148672i	−0.261592	−	0.965178i	$-0.584248\pi$
$683$	−0.145007	+	0.0388544i	−0.00554852	+	0.00148672i	0.256044	+	0.966665i	$0.417581\pi$
$684$	13.4219	−	5.44595i	0.513199	−	0.208231i
$685$	3.67277	−	6.36142i	0.140329	−	0.243057i
$686$	−0.205960	−	0.356733i	−0.00786358	−	0.0136201i
$687$	7.23055	−	14.5292i	0.275863	−	0.554323i
$688$		−	4.82995i		−	0.184140i
$689$	−9.61329	+	8.18934i	−0.366237	+	0.311989i
$690$	0.130535	+	0.0264570i	0.00496939	+	0.00100720i
$691$	5.09012	−	18.9966i	0.193637	−	0.722665i	−0.798978	−	0.601360i	$-0.794626\pi$
$691$	5.09012	−	18.9966i	0.193637	−	0.722665i	0.992615	−	0.121304i	$-0.0387077\pi$
$692$	−33.0165	+	19.0621i	−1.25510	+	0.724632i
$693$	13.4922	−	10.1985i	0.512525	−	0.387408i
$694$	−5.13171	−	5.13171i	−0.194797	−	0.194797i
$695$	−1.82902	−	6.82599i	−0.0693786	−	0.258925i
$696$	−19.6092	+	1.21394i	−0.743286	+	0.0460141i
$697$	22.8485	−	22.8485i	0.865449	−	0.865449i
$698$	−1.18878	−	0.686345i	−0.0449962	−	0.0259786i
$699$	−11.0048	+	3.69121i	−0.416238	+	0.139614i
$700$	−8.25450	−	2.21179i	−0.311991	−	0.0835977i
$701$	−32.3695			−1.22258			−0.611290	−	0.791407i	$-0.709349\pi$
$701$	−32.3695			−1.22258			−0.611290	+	0.791407i	$0.709349\pi$
$702$	7.62343	+	1.20003i	0.287728	+	0.0452922i
$703$	−26.3235			−0.992808
$704$	22.9299	+	6.14405i	0.864203	+	0.231562i
$705$	−1.62243	+	0.544196i	−0.0611044	+	0.0204956i
$706$	−4.61263	−	2.66310i	−0.173599	−	0.100227i
$707$	−7.74525	+	7.74525i	−0.291290	+	0.291290i
$708$	−11.2178	+	0.694451i	−0.421590	+	0.0260991i
$709$	−4.21162	−	15.7180i	−0.158171	−	0.590301i	−0.998813	−	0.0487101i	$-0.984489\pi$
$709$	−4.21162	−	15.7180i	−0.158171	−	0.590301i	0.840642	−	0.541591i	$-0.182178\pi$
$710$	−0.146555	−	0.146555i	−0.00550012	−	0.00550012i
$711$	−29.7848	+	22.5138i	−1.11702	+	0.844332i
$712$	−5.29865	+	3.05918i	−0.198575	+	0.114647i
$713$	−0.333475	+	1.24454i	−0.0124887	+	0.0466085i
$714$	1.86548	+	0.378096i	0.0698137	+	0.0141499i
$715$	−3.91806	+	11.0196i	−0.146527	+	0.412109i
$716$			18.9094i			0.706678i
$717$	−12.5671	+	25.2526i	−0.469328	+	0.943076i
$718$	4.62846	+	8.01672i	0.172732	+	0.299181i
$719$	20.8549	−	36.1218i	0.777757	−	1.34712i	−0.155474	−	0.987840i	$-0.549691\pi$
$719$	20.8549	−	36.1218i	0.777757	−	1.34712i	0.933232	−	0.359275i	$-0.116976\pi$
$720$	4.81552	−	1.95390i	0.179464	−	0.0728176i
$721$	6.70244	−	1.79591i	0.249612	−	0.0668833i
$722$	4.79109	−	1.28377i	0.178306	−	0.0477769i
$723$	−6.65227	−	10.0343i	−0.247400	−	0.373180i
$724$	−10.1746	+	17.6230i	−0.378137	+	0.654953i
$725$	16.7831	+	29.0692i	0.623309	+	1.07960i
$726$	−13.2750	−	6.60638i	−0.492680	−	0.245186i
$727$		−	25.0055i		−	0.927403i	−0.885992	−	0.463701i	$-0.846521\pi$
$727$		−	25.0055i		−	0.927403i	0.885992	−	0.463701i	$-0.153479\pi$
$728$	5.59484	−	1.02956i	0.207359	−	0.0381582i
$729$	−9.78790	−	25.1634i	−0.362515	−	0.931978i
$730$	−0.573576	+	2.14061i	−0.0212290	+	0.0792277i
$731$	3.70648	−	2.13994i	0.137089	−	0.0791484i
$732$	−18.0279	+	20.4073i	−0.666331	+	0.754276i
$733$	8.08802	+	8.08802i	0.298738	+	0.298738i	0.840519	−	0.541782i	$-0.182250\pi$
$733$	8.08802	+	8.08802i	0.298738	+	0.298738i	−0.541782	+	0.840519i	$0.682250\pi$
$734$	−0.260602	−	0.972579i	−0.00961899	−	0.0358986i
$735$	−0.0615759	−	0.994662i	−0.00227126	−	0.0366886i
$736$	1.00848	−	1.00848i	0.0371732	−	0.0371732i
$737$	−13.9516	−	8.05497i	−0.513914	−	0.296708i
$738$	14.8531	−	1.84608i	0.546752	−	0.0679553i
$739$	−17.9629	−	4.81315i	−0.660777	−	0.177055i	−0.0871803	−	0.996193i	$-0.527786\pi$
$739$	−17.9629	−	4.81315i	−0.660777	−	0.177055i	−0.573597	+	0.819138i	$0.694452\pi$
$740$	−10.5089			−0.386314
$741$	15.8331	+	4.54924i	0.581645	+	0.167120i
$742$	−1.44276			−0.0529654
$743$	42.7404	+	11.4523i	1.56799	+	0.420143i	0.935183	−	0.354164i	$-0.115235\pi$
$743$	42.7404	+	11.4523i	1.56799	+	0.420143i	0.632810	+	0.774307i	$0.281901\pi$
$744$	−3.45112	−	10.2890i	−0.126524	−	0.377212i
$745$	4.21378	+	2.43283i	0.154381	+	0.0891319i
$746$	4.22730	−	4.22730i	0.154772	−	0.154772i
$747$	−4.30561	+	30.9689i	−0.157534	+	1.13309i
$748$	7.12493	+	26.5906i	0.260513	+	0.972249i
$749$	−13.8735	−	13.8735i	−0.506926	−	0.506926i
$750$	2.97467	+	2.62784i	0.108619	+	0.0959550i
$751$	0.695327	−	0.401448i	0.0253729	−	0.0146490i	−0.487260	−	0.873257i	$-0.662004\pi$
$751$	0.695327	−	0.401448i	0.0253729	−	0.0146490i	0.512633	+	0.858608i	$0.328670\pi$
$752$	−1.33807	+	4.99375i	−0.0487945	+	0.182103i
$753$	−6.71407	+	33.1263i	−0.244674	+	1.20719i
$754$	−8.79184	−	6.05898i	−0.320180	−	0.220655i
$755$			4.96593i			0.180729i
$756$	−6.19272	−	7.21820i	−0.225227	−	0.262523i
$757$	1.54085	+	2.66884i	0.0560033	+	0.0970005i	0.892668	−	0.450715i	$-0.148831\pi$
$757$	1.54085	+	2.66884i	0.0560033	+	0.0970005i	−0.836665	+	0.547716i	$0.815498\pi$
$758$	2.59148	−	4.48857i	0.0941266	−	0.163032i
$759$	2.64061	−	1.75059i	0.0958479	−	0.0635425i
$760$	−2.31311	+	0.619796i	−0.0839054	+	0.0224824i
$761$	27.9537	−	7.49017i	1.01332	−	0.271519i	0.286305	−	0.958139i	$-0.407573\pi$
$761$	27.9537	−	7.49017i	1.01332	−	0.271519i	0.727016	+	0.686620i	$0.240906\pi$
$762$	10.7819	−	7.14790i	0.390588	−	0.258941i
$763$	2.50213	−	4.33381i	0.0905830	−	0.156894i
$764$	15.4971	+	26.8418i	0.560667	+	0.971104i
$765$	3.63295	+	2.82971i	0.131350	+	0.102309i
$766$		−	5.57279i		−	0.201353i
$767$	−10.5253	−	7.25359i	−0.380045	−	0.261912i
$768$	1.40570	−	6.93556i	0.0507240	−	0.250265i
$769$	−1.58174	+	5.90312i	−0.0570389	+	0.212872i	−0.988563	−	0.150807i	$-0.951813\pi$
$769$	−1.58174	+	5.90312i	−0.0570389	+	0.212872i	0.931524	+	0.363679i	$0.118479\pi$
$770$	−1.15714	+	0.668075i	−0.0417004	+	0.0240758i
$771$	29.0012	+	25.6198i	1.04445	+	0.922675i
$772$	8.48665	+	8.48665i	0.305441	+	0.305441i
$773$	13.5350	+	50.5134i	0.486821	+	1.81684i	0.571717	+	0.820451i	$0.306278\pi$
$773$	13.5350	+	50.5134i	0.486821	+	1.81684i	−0.0848956	+	0.996390i	$0.527056\pi$
$774$	1.96358	+	0.272996i	0.0705793	+	0.00981264i
$775$	−13.1105	+	13.1105i	−0.470943	+	0.470943i
$776$	−14.0794	−	8.12876i	−0.505422	−	0.291805i
$777$	5.49643	+	16.3867i	0.197183	+	0.587871i
$778$	−8.20487	−	2.19849i	−0.294159	−	0.0788197i
$779$	31.9502			1.14474
$780$	6.32092	+	1.81615i	0.226325	+	0.0650286i
$781$	−4.93011			−0.176413
$782$	0.344403	+	0.0922824i	0.0123158	+	0.00330001i
$783$	−2.84816	+	37.2477i	−0.101785	+	1.33112i
$784$	−2.60736	−	1.50536i	−0.0931202	−	0.0537630i
$785$	5.69569	−	5.69569i	0.203288	−	0.203288i
$786$	0.764850	+	12.3549i	0.0272813	+	0.440686i
$787$	−6.31848	−	23.5809i	−0.225230	−	0.840568i	−0.982312	−	0.187249i	$-0.940043\pi$
$787$	−6.31848	−	23.5809i	−0.225230	−	0.840568i	0.757083	−	0.653319i	$-0.226624\pi$
$788$	−11.5448	−	11.5448i	−0.411265	−	0.411265i
$789$	−3.48143	+	3.94092i	−0.123942	+	0.140300i
$790$	2.55446	−	1.47482i	0.0908836	−	0.0524717i
$791$	0.144177	−	0.538075i	0.00512634	−	0.0191318i
$792$	−10.3902	+	24.5791i	−0.369201	+	0.873379i
$793$	−30.4577	+	5.60484i	−1.08158	+	0.199034i
$794$			6.32432i			0.224442i
$795$	−3.12493	−	1.55514i	−0.110830	−	0.0551552i
$796$	4.52219	+	7.83267i	0.160285	+	0.277622i
$797$	−13.3775	+	23.1706i	−0.473857	+	0.820744i	−0.999552	−	0.0299292i	$-0.990472\pi$
$797$	−13.3775	+	23.1706i	−0.473857	+	0.820744i	0.525695	+	0.850673i	$0.323805\pi$
$798$	1.03994	+	1.56865i	0.0368135	+	0.0555296i
$799$	−4.42502	+	1.18568i	−0.156546	+	0.0419463i
$800$	19.8242	−	5.31188i	0.700891	−	0.187803i
$801$	4.37394	+	10.7799i	0.154546	+	0.380888i
$802$	3.61611	−	6.26328i	0.127689	−	0.221164i
$803$	26.3575	+	45.6526i	0.930137	+	1.61104i
$804$	−4.03613	+	8.11028i	−0.142343	+	0.286027i
$805$		−	0.186680i		−	0.00657959i
$806$	1.97585	−	5.55711i	0.0695965	−	0.195741i
$807$	3.61735	+	0.733168i	0.127337	+	0.0258087i
$808$	4.47295	−	16.6933i	0.157358	−	0.587267i
$809$	−30.4847	+	17.6003i	−1.07178	+	0.618795i	−0.928668	−	0.370911i	$-0.879046\pi$
$809$	−30.4847	+	17.6003i	−1.07178	+	0.618795i	−0.143116	+	0.989706i	$0.545712\pi$
$810$	0.522162	+	2.06815i	0.0183469	+	0.0726672i
$811$	27.1865	+	27.1865i	0.954647	+	0.954647i	0.999015	−	0.0443687i	$-0.0141276\pi$
$811$	27.1865	+	27.1865i	0.954647	+	0.954647i	−0.0443687	+	0.999015i	$0.514128\pi$
$812$	3.40571	+	12.7103i	0.119517	+	0.446043i
$813$	−37.0751	+	2.29518i	−1.30028	+	0.0804956i
$814$	16.3862	−	16.3862i	0.574335	−	0.574335i
$815$	8.93572	+	5.15904i	0.313005	+	0.180713i
$816$	13.1898	−	4.42413i	0.461737	−	0.154875i
$817$	4.08767	+	1.09529i	0.143009	+	0.0383192i
$818$	−2.34004			−0.0818175
$819$	−0.474049	−	10.8063i	−0.0165646	−	0.377601i
$820$	12.7552			0.445431
$821$	42.4393	+	11.3716i	1.48114	+	0.396871i	0.906736	−	0.421699i	$-0.138566\pi$
$821$	42.4393	+	11.3716i	1.48114	+	0.396871i	0.574407	+	0.818570i	$0.305233\pi$
$822$	8.63574	−	2.89660i	0.301206	−	0.101030i
$823$	−14.7567	−	8.51981i	−0.514388	−	0.296982i	0.220248	−	0.975444i	$-0.429313\pi$
$823$	−14.7567	−	8.51981i	−0.514388	−	0.296982i	−0.734635	+	0.678462i	$0.762647\pi$
$824$	−7.74144	+	7.74144i	−0.269686	+	0.269686i
$825$	45.5038	−	2.81697i	1.58424	−	0.0980744i
$826$	−0.377970	−	1.41060i	−0.0131513	−	0.0490812i
$827$	29.3156	+	29.3156i	1.01940	+	1.01940i	0.999808	+	0.0195947i	$0.00623758\pi$
$827$	29.3156	+	29.3156i	1.01940	+	1.01940i	0.0195947	+	0.999808i	$0.493762\pi$
$828$	−1.07428	−	1.42123i	−0.0373337	−	0.0493911i
$829$	−12.6686	+	7.31423i	−0.439999	+	0.254034i	−0.703597	−	0.710599i	$-0.748424\pi$
$829$	−12.6686	+	7.31423i	−0.439999	+	0.254034i	0.263598	+	0.964633i	$0.415091\pi$
$830$	0.639316	−	2.38596i	0.0221910	−	0.0828179i
$831$	42.7549	+	8.66561i	1.48315	+	0.300607i
$832$	11.5571	−	9.84526i	0.400671	−	0.341323i
$833$		−	2.66784i		−	0.0924350i
$834$	3.90419	−	7.84514i	0.135191	−	0.271655i
$835$	3.01665	+	5.22500i	0.104396	+	0.180819i
$836$	−13.6099	+	23.5731i	−0.470709	+	0.815291i
$837$	−20.2807	+	3.80545i	−0.701003	+	0.131536i
$838$	−3.93229	+	1.05365i	−0.135839	+	0.0363979i
$839$	−25.3595	+	6.79507i	−0.875508	+	0.234592i	−0.668468	−	0.743741i	$-0.733050\pi$
$839$	−25.3595	+	6.79507i	−0.875508	+	0.234592i	−0.207040	+	0.978332i	$0.566383\pi$
$840$	0.868818	+	1.31053i	0.0299771	+	0.0452176i
$841$	11.3426	−	19.6460i	0.391125	−	0.677448i
$842$	−1.78673	−	3.09470i	−0.0615746	−	0.106650i
$843$	−25.7467	−	12.8130i	−0.886763	−	0.441304i
$844$			13.1564i			0.452862i
$845$	4.38106	+	6.06246i	0.150713	+	0.208555i
$846$	−1.95454	−	0.826236i	−0.0671984	−	0.0284066i
$847$	−5.37905	+	20.0749i	−0.184826	+	0.689781i
$848$	−9.13238	+	5.27258i	−0.313607	+	0.181061i
$849$	6.87685	−	7.78448i	0.236013	−	0.267163i
$850$	3.62807	+	3.62807i	0.124442	+	0.124442i
$851$	0.837975	+	3.12736i	0.0287254	+	0.107205i
$852$	0.171298	+	2.76705i	0.00586856	+	0.0947975i
$853$	−35.2462	+	35.2462i	−1.20681	+	1.20681i	−0.234753	+	0.972055i	$0.575428\pi$
$853$	−35.2462	+	35.2462i	−1.20681	+	1.20681i	−0.972055	+	0.234753i	$0.924572\pi$
$854$	−3.06408	−	1.76905i	−0.104851	−	0.0605355i
$855$	0.561605	+	4.51854i	0.0192065	+	0.154531i
$856$	29.9014	+	8.01206i	1.02201	+	0.273846i
$857$	−29.3826			−1.00369			−0.501845	−	0.864957i	$-0.667345\pi$
$857$	−29.3826			−1.00369			−0.501845	+	0.864957i	$0.667345\pi$
$858$	−12.6879	+	7.02416i	−0.433158	+	0.239801i
$859$	42.8906			1.46341			0.731704	−	0.681622i	$-0.238725\pi$
$859$	42.8906			1.46341			0.731704	+	0.681622i	$0.238725\pi$
$860$	1.63188	+	0.437261i	0.0556467	+	0.0149105i
$861$	−6.67132	−	19.8895i	−0.227358	−	0.677832i
$862$	0.196004	+	0.113163i	0.00667592	+	0.00385435i
$863$	−29.0260	+	29.0260i	−0.988055	+	0.988055i	−0.999929	−	0.0118744i	$-0.996220\pi$
$863$	−29.0260	+	29.0260i	−0.988055	+	0.988055i	0.0118744	+	0.999929i	$0.496220\pi$
$864$	21.5477	+	7.57659i	0.733068	+	0.257761i
$865$	−3.10180	−	11.5761i	−0.105465	−	0.393599i
$866$	−8.66952	−	8.66952i	−0.294602	−	0.294602i
$867$	−12.8285	−	11.3327i	−0.435678	−	0.384880i
$868$	−6.29467	+	3.63423i	−0.213655	+	0.123354i
$869$	18.1596	−	67.7724i	0.616021	−	2.29902i
$870$	0.586235	−	2.89241i	0.0198752	−	0.0980618i
$871$	−9.30507	+	4.42373i	−0.315290	+	0.149892i
$872$			7.89563i			0.267380i
$873$	−18.9952	+	24.3872i	−0.642892	+	0.825382i
$874$	0.176276	+	0.305319i	0.00596263	+	0.0103276i
$875$	2.78160	−	4.81787i	0.0940353	−	0.162874i
$876$	24.7069	−	16.3795i	0.834770	−	0.553412i
$877$	−11.4420	+	3.06587i	−0.386368	+	0.103527i	−0.446774	−	0.894647i	$-0.647427\pi$
$877$	−11.4420	+	3.06587i	−0.386368	+	0.103527i	0.0604059	+	0.998174i	$0.480760\pi$
$878$	−11.7097	+	3.13761i	−0.395184	+	0.105889i
$879$	−43.7708	+	29.0179i	−1.47635	+	0.978749i
$880$	−4.88297	+	8.45756i	−0.164605	+	0.285104i
$881$	−5.71996	−	9.90726i	−0.192710	−	0.333784i	0.753437	−	0.657520i	$-0.228394\pi$
$881$	−5.71996	−	9.90726i	−0.192710	−	0.333784i	−0.946147	+	0.323736i	$0.895061\pi$
$882$	0.759365	−	0.974917i	0.0255691	−	0.0328272i
$883$		−	13.5582i		−	0.456271i	−0.973629	−	0.228135i	$-0.926737\pi$
$883$		−	13.5582i		−	0.456271i	0.973629	−	0.228135i	$-0.0732629\pi$
$884$	16.5885	+	5.89813i	0.557933	+	0.198376i
$885$	0.701820	−	3.46268i	0.0235914	−	0.116397i
$886$	−0.139006	+	0.518778i	−0.00467000	+	0.0174287i
$887$	−13.3781	+	7.72384i	−0.449192	+	0.259341i	−0.707489	−	0.706725i	$-0.750172\pi$
$887$	−13.3781	+	7.72384i	−0.449192	+	0.259341i	0.258297	+	0.966066i	$0.416839\pi$
$888$	−20.4377	−	18.0548i	−0.685844	−	0.605878i
$889$	−12.8208	−	12.8208i	−0.429996	−	0.429996i
$890$	−0.237871	−	0.887745i	−0.00797344	−	0.0297573i
$891$	43.5689	+	26.0034i	1.45961	+	0.871147i
$892$	−15.8113	+	15.8113i	−0.529402	+	0.529402i
$893$	−3.92286	−	2.26486i	−0.131274	−	0.0757908i
$894$	1.91869	+	5.72028i	0.0641707	+	0.191315i
$895$	−5.74169	−	1.53848i	−0.191923	−	0.0514257i
$896$	10.5260			0.351648
$897$	0.0364447	−	2.02588i	0.00121685	−	0.0676422i
$898$	13.1798			0.439816
$899$	27.5767	+	7.38915i	0.919733	+	0.246442i
$900$	−3.16208	−	25.4413i	−0.105403	−	0.848044i
$901$	−8.09230	−	4.67209i	−0.269594	−	0.155650i
$902$	−19.8888	+	19.8888i	−0.662225	+	0.662225i
$903$	−0.171687	−	2.77333i	−0.00571338	−	0.0922907i
$904$	0.227480	+	0.848966i	0.00756587	+	0.0282362i
$905$	−4.52326	−	4.52326i	−0.150358	−	0.150358i
$906$	−4.07689	+	4.61497i	−0.135445	+	0.153322i
$907$	41.1650	−	23.7666i	1.36686	−	0.789157i	0.376335	−	0.926484i	$-0.377184\pi$
$907$	41.1650	−	23.7666i	1.36686	−	0.789157i	0.990526	+	0.137327i	$0.0438510\pi$
$908$	−4.64255	+	17.3262i	−0.154068	+	0.574991i
$909$	−30.2671	−	12.7947i	−1.00390	−	0.424374i
$910$	−0.0681323	+	0.851813i	−0.00225856	+	0.0282373i
$911$		−	29.6438i		−	0.982144i	−0.871119	−	0.491072i	$-0.836605\pi$
$911$		−	29.6438i		−	0.982144i	0.871119	−	0.491072i	$-0.163395\pi$
$912$	12.3152	+	6.12877i	0.407799	+	0.202944i
$913$	−29.3785	−	50.8851i	−0.972286	−	1.68405i
$914$	1.94964	−	3.37688i	0.0644884	−	0.111697i
$915$	−4.72975	−	7.13438i	−0.156361	−	0.235855i
$916$	16.5654	−	4.43867i	0.547335	−	0.146658i
$917$	16.7588	−	4.49050i	0.553424	−	0.148289i
$918$	1.05308	+	5.61228i	0.0347569	+	0.185233i
$919$	19.1394	−	33.1504i	0.631350	−	1.09353i	−0.355926	−	0.934514i	$-0.615834\pi$
$919$	19.1394	−	33.1504i	0.631350	−	1.09353i	0.987276	−	0.159016i	$-0.0508322\pi$
$920$	0.147270	+	0.255079i	0.00485535	+	0.00840971i
$921$	−0.563593	+	1.13249i	−0.0185710	+	0.0373169i
$922$		−	2.57920i		−	0.0849413i
$923$	−1.78922	+	2.59623i	−0.0588928	+	0.0854559i
$924$	17.5164	+	3.55023i	0.576246	+	0.116794i
$925$	−12.0586	+	45.0035i	−0.396486	+	1.47971i
$926$	−7.36994	+	4.25503i	−0.242191	+	0.139829i
$927$	12.5524	+	16.6063i	0.412274	+	0.545423i
$928$	−22.3460	−	22.3460i	−0.733545	−	0.733545i
$929$	−1.84237	−	6.87582i	−0.0604463	−	0.225588i	0.929094	−	0.369843i	$-0.120588\pi$
$929$	−1.84237	−	6.87582i	−0.0604463	−	0.225588i	−0.989541	+	0.144254i	$0.953922\pi$
$930$	1.62706	−	0.100725i	0.0533532	−	0.00330290i
$931$	1.86528	−	1.86528i	0.0611322	−	0.0611322i
$932$	−10.6226	−	6.13294i	−0.347954	−	0.200891i
$933$	24.3924	−	8.18170i	0.798573	−	0.267857i
$934$	−13.4771	−	3.61118i	−0.440984	−	0.118161i
$935$	−8.65371			−0.283006
$936$	9.17271	+	14.3917i	0.299819	+	0.470408i
$937$	30.6391			1.00093			0.500467	−	0.865755i	$-0.333162\pi$
$937$	30.6391			1.00093			0.500467	+	0.865755i	$0.333162\pi$
$938$	−1.13698	−	0.304652i	−0.0371236	−	0.00994724i
$939$	35.9068	−	12.0438i	1.17177	−	0.393036i
$940$	−1.56609	−	0.904181i	−0.0510801	−	0.0294911i
$941$	16.3571	−	16.3571i	0.533225	−	0.533225i	−0.388306	−	0.921531i	$-0.626939\pi$
$941$	16.3571	−	16.3571i	0.533225	−	0.533225i	0.921531	+	0.388306i	$0.126939\pi$
$942$	9.96914	−	0.617153i	0.324812	−	0.0201079i
$943$	−1.01710	−	3.79585i	−0.0331212	−	0.123610i
$944$	−7.54753	−	7.54753i	−0.245651	−	0.245651i
$945$	2.69559	−	1.29309i	0.0876875	−	0.0420643i
$946$	−3.22636	+	1.86274i	−0.104898	+	0.0605628i
$947$	9.56210	−	35.6863i	0.310727	−	1.15965i	−0.617176	−	0.786825i	$-0.711723\pi$
$947$	9.56210	−	35.6863i	0.310727	−	1.15965i	0.927903	−	0.372822i	$-0.121610\pi$
$948$	−38.6685	−	7.83736i	−1.25589	−	0.254546i
$949$	33.6065	+	2.68802i	1.09091	+	0.0872568i
$950$			5.07331i			0.164600i
$951$	7.44340	−	14.9569i	0.241369	−	0.485010i
$952$	2.10463	+	3.64533i	0.0682116	+	0.118146i
$953$	−15.1949	+	26.3183i	−0.492211	+	0.852534i	−0.999960	−	0.00897085i	$-0.997144\pi$
$953$	−15.1949	+	26.3183i	−0.492211	+	0.852534i	0.507749	+	0.861505i	$0.330478\pi$
$954$	−1.62735	−	4.01071i	−0.0526874	−	0.129851i
$955$	−9.41116	+	2.52171i	−0.304538	+	0.0816007i
$956$	−28.7916	+	7.71468i	−0.931187	+	0.249511i
$957$	−38.7897	−	58.5107i	−1.25389	−	1.89138i
$958$	0.492579	−	0.853171i	0.0159145	−	0.0275647i
$959$	−6.38334	−	11.0563i	−0.206129	−	0.357026i
$960$	3.75680	+	1.86960i	0.121250	+	0.0603410i
$961$		−	15.2301i		−	0.491293i
$962$	−2.68226	−	14.5759i	−0.0864795	−	0.469946i
$963$	22.9182	−	54.2151i	0.738528	−	1.74706i
$964$	3.29274	−	12.2887i	0.106052	−	0.395792i
$965$	−3.26738	+	1.88642i	−0.105181	+	0.0607261i
$966$	0.153259	−	0.173486i	0.00493102	−	0.00558183i
$967$	−18.7943	−	18.7943i	−0.604383	−	0.604383i	0.337089	−	0.941473i	$-0.390558\pi$
$967$	−18.7943	−	18.7943i	−0.604383	−	0.604383i	−0.941473	+	0.337089i	$0.890558\pi$
$968$	−8.48698	−	31.6738i	−0.272782	−	1.01804i
$969$	0.753155	+	12.1660i	0.0241948	+	0.390829i
$970$	1.72683	−	1.72683i	0.0554451	−	0.0554451i
$971$	30.1922	+	17.4315i	0.968913	+	0.559402i	0.898905	−	0.438144i	$-0.144364\pi$
$971$	30.1922	+	17.4315i	0.968913	+	0.559402i	0.0700085	+	0.997546i	$0.477697\pi$
$972$	13.0807	−	25.3567i	0.419564	−	0.813318i
$973$	−11.8637	−	3.17887i	−0.380333	−	0.101910i
$974$	1.56377			0.0501063
$975$	15.0306	−	24.9849i	0.481365	−	0.800158i
$976$	−25.8600			−0.827758
$977$	−13.7948	−	3.69631i	−0.441336	−	0.118255i	0.0313069	−	0.999510i	$-0.490033\pi$
$977$	−13.7948	−	3.69631i	−0.441336	−	0.118255i	−0.472642	+	0.881254i	$0.656700\pi$
$978$	4.06877	+	12.1304i	0.130105	+	0.387887i
$979$	−18.9328	−	10.9309i	−0.605096	−	0.349352i
$980$	0.744660	−	0.744660i	0.0237873	−	0.0237873i
$981$	14.8697	+	2.06734i	0.474754	+	0.0660051i
$982$	0.750217	+	2.79985i	0.0239404	+	0.0893468i
$983$	−2.71409	−	2.71409i	−0.0865661	−	0.0865661i	0.662498	−	0.749064i	$-0.269496\pi$
$983$	−2.71409	−	2.71409i	−0.0865661	−	0.0865661i	−0.749064	+	0.662498i	$0.769496\pi$
$984$	24.8063	+	21.9140i	0.790797	+	0.698594i
$985$	4.44476	−	2.56619i	0.141622	−	0.0817655i
$986$	2.04480	−	7.63129i	0.0651197	−	0.243030i
$987$	−0.590804	+	2.91495i	−0.0188055	+	0.0927838i
$988$	7.47447	+	15.7221i	0.237795	+	0.500187i
$989$		−	0.520503i		−	0.0165510i
$990$	−3.16236	−	2.46317i	−0.100506	−	0.0782845i
$991$	−1.25003	−	2.16511i	−0.0397084	−	0.0687769i	0.845488	−	0.533994i	$-0.179310\pi$
$991$	−1.25003	−	2.16511i	−0.0397084	−	0.0687769i	−0.885197	+	0.465217i	$0.845976\pi$
$992$	8.72805	−	15.1174i	0.277116	−	0.479979i
$993$	−34.1454	+	22.6368i	−1.08357	+	0.718356i
$994$	−0.347948	+	0.0932325i	−0.0110363	+	0.00295715i
$995$	−2.74625	+	0.735856i	−0.0870621	+	0.0233282i
$996$	−27.5387	+	18.2568i	−0.872597	+	0.578490i
$997$	−18.2299	+	31.5751i	−0.577347	+	0.999994i	0.418436	+	0.908246i	$0.362579\pi$
$997$	−18.2299	+	31.5751i	−0.577347	+	0.999994i	−0.995782	+	0.0917474i	$0.970755\pi$
$998$	0.359526	+	0.622718i	0.0113806	+	0.0197118i
$999$	−39.3536	+	33.7627i	−1.24509	+	1.06820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.13	✓	112
3.2	odd	2	inner	273.2.cc.a.50.16	yes	112
13.6	odd	12	inner	273.2.cc.a.71.16	yes	112
39.32	even	12	inner	273.2.cc.a.71.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.13	✓	112	1.1	even	1	trivial
273.2.cc.a.50.16	yes	112	3.2	odd	2	inner
273.2.cc.a.71.13	yes	112	39.32	even	12	inner
273.2.cc.a.71.16	yes	112	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.397883 - 0.106613i) q^{2} +(-1.64214 + 0.550805i) q^{3} +(-1.58511 - 0.915161i) q^{4} +(0.406846 - 0.406846i) q^{5} +(0.712102 - 0.0440836i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.11566 + 1.11566i) q^{8} +(2.39323 - 1.80899i) q^{9} +O(q^{10})\)	\(q+(-0.397883 - 0.106613i) q^{2} +(-1.64214 + 0.550805i) q^{3} +(-1.58511 - 0.915161i) q^{4} +(0.406846 - 0.406846i) q^{5} +(0.712102 - 0.0440836i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.11566 + 1.11566i) q^{8} +(2.39323 - 1.80899i) q^{9} +(-0.205252 + 0.118502i) q^{10} +(-1.45913 + 5.44555i) q^{11} +(3.10704 + 0.629737i) q^{12} +(2.33812 + 2.74467i) q^{13} +0.411919i q^{14} +(-0.444005 + 0.892190i) q^{15} +(1.50536 + 2.60736i) q^{16} +(-1.33392 + 2.31041i) q^{17} +(-1.14509 + 0.464620i) q^{18} +(-2.54803 + 0.682741i) q^{19} +(-1.01722 + 0.272564i) q^{20} +(0.957053 + 1.44362i) q^{21} +(1.16113 - 2.01113i) q^{22} +(0.162226 + 0.280984i) q^{23} +(-2.44658 - 1.21756i) q^{24} +4.66895i q^{25} +(-0.637683 - 1.34133i) q^{26} +(-2.93361 + 4.28882i) q^{27} +(-0.473722 + 1.76796i) q^{28} +(6.22607 - 3.59462i) q^{29} +(0.271781 - 0.307651i) q^{30} +(2.80802 + 2.80802i) q^{31} +(-1.13770 - 4.24596i) q^{32} +(-0.603341 - 9.74603i) q^{33} +(0.777063 - 0.777063i) q^{34} +(-0.498283 - 0.287684i) q^{35} +(-5.44904 + 0.677256i) q^{36} +(9.63888 + 2.58273i) q^{37} +1.08661 q^{38} +(-5.35129 - 3.21927i) q^{39} +0.907806 q^{40} +(-11.6992 - 3.13480i) q^{41} +(-0.226887 - 0.676428i) q^{42} +(-1.38932 - 0.802124i) q^{43} +(7.29643 - 7.29643i) q^{44} +(0.237694 - 1.70966i) q^{45} +(-0.0345908 - 0.129094i) q^{46} +(1.21422 + 1.21422i) q^{47} +(-3.90816 - 3.45249i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.497769 - 1.85770i) q^{50} +(0.917889 - 4.52874i) q^{51} +(-1.19436 - 6.49034i) q^{52} +3.50253i q^{53} +(1.62448 - 1.39369i) q^{54} +(1.62186 + 2.80914i) q^{55} +(0.788892 - 1.36640i) q^{56} +(3.80815 - 2.52462i) q^{57} +(-2.86048 + 0.766464i) q^{58} +(-3.42446 + 0.917582i) q^{59} +(1.52029 - 1.00788i) q^{60} +(-4.29464 + 7.43854i) q^{61} +(-0.817894 - 1.41663i) q^{62} +(-2.36677 - 1.84348i) q^{63} -4.21076i q^{64} +(2.06791 + 0.165402i) q^{65} +(-0.798990 + 3.94211i) q^{66} +(-0.739592 + 2.76019i) q^{67} +(4.22880 - 2.44150i) q^{68} +(-0.421166 - 0.372060i) q^{69} +(0.167588 + 0.167588i) q^{70} +(0.226337 + 0.844700i) q^{71} +(4.68826 + 0.651809i) q^{72} +(6.61183 - 6.61183i) q^{73} +(-3.55980 - 2.05525i) q^{74} +(-2.57168 - 7.66706i) q^{75} +(4.66371 + 1.24964i) q^{76} +5.63765 q^{77} +(1.78597 + 1.85141i) q^{78} -12.4455 q^{79} +(1.67325 + 0.448345i) q^{80} +(2.45509 - 8.65867i) q^{81} +(4.32073 + 2.49457i) q^{82} +(-7.36965 + 7.36965i) q^{83} +(-0.195881 - 3.16415i) q^{84} +(0.397284 + 1.48268i) q^{85} +(0.467271 + 0.467271i) q^{86} +(-8.24412 + 9.33221i) q^{87} +(-7.70328 + 4.44749i) q^{88} +(-1.00365 + 3.74568i) q^{89} +(-0.276846 + 0.654904i) q^{90} +(2.04599 - 2.96882i) q^{91} -0.593853i q^{92} +(-6.15782 - 3.06448i) q^{93} +(-0.353667 - 0.612569i) q^{94} +(-0.758884 + 1.31443i) q^{95} +(4.20696 + 6.34580i) q^{96} +(-9.95292 + 2.66688i) q^{97} +(0.397883 - 0.106613i) q^{98} +(6.35893 + 15.6720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

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