LMFDB - Embedded newform 354.2.e.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	354.121
Dual form			354.2.e.b.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(1.82294 + 1.09682i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(-0.192354 + 3.54777i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})$	\(q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(1.82294 + 1.09682i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(-0.192354 + 3.54777i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(-2.11500 - 0.230020i) q^{10} +(0.389551 - 2.37615i) q^{11} +(0.856857 - 0.515554i) q^{12} +(-3.04455 + 2.31441i) q^{13} +(-1.31509 - 3.30063i) q^{14} +(1.37729 + 1.62148i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(-0.0145950 - 0.269188i) q^{17} +(-0.976621 - 0.214970i) q^{18} +(-1.55591 + 1.47384i) q^{19} +(2.01610 - 0.679304i) q^{20} +(-1.31509 + 3.30063i) q^{21} +(0.644175 + 2.32011i) q^{22} +(7.94654 - 1.74916i) q^{23} +(-0.561187 + 0.827689i) q^{24} +(-0.221970 - 0.418679i) q^{25} +(1.79137 - 3.37887i) q^{26} +(0.561187 + 0.827689i) q^{27} +(2.57945 + 2.44338i) q^{28} +(-1.95486 - 0.904416i) q^{29} +(-1.93084 - 0.893301i) q^{30} +(2.08407 + 1.97414i) q^{31} +(0.561187 + 0.827689i) q^{32} +(1.12787 - 2.12739i) q^{33} +(0.126275 + 0.238180i) q^{34} +(-4.24193 + 6.25638i) q^{35} +(0.976621 - 0.214970i) q^{36} +(0.314922 + 1.13425i) q^{37} +(0.793259 - 1.99093i) q^{38} +(-3.62417 + 1.22113i) q^{39} +(-1.54453 + 1.46306i) q^{40} +(-5.57339 - 1.22680i) q^{41} +(-0.192354 - 3.54777i) q^{42} +(1.77439 + 10.8233i) q^{43} +(-1.55882 - 1.83519i) q^{44} +(0.787457 + 1.97637i) q^{45} +(-6.47763 + 4.92416i) q^{46} +(7.10345 - 4.27401i) q^{47} +(0.161782 - 0.986827i) q^{48} +(-5.59069 - 0.608024i) q^{49} +(0.377253 + 0.286780i) q^{50} +(0.0721212 - 0.259757i) q^{51} +(-0.207047 + 3.81876i) q^{52} +(-0.282076 + 0.0306777i) q^{53} +(-0.856857 - 0.515554i) q^{54} +(3.31635 - 3.90431i) q^{55} +(-3.36699 - 1.13447i) q^{56} +(-1.94506 + 0.899882i) q^{57} +2.15394 q^{58} +(-2.66736 - 7.20314i) q^{59} +2.12747 q^{60} +(9.80821 - 4.53776i) q^{61} +(-2.72037 - 0.916600i) q^{62} +(-2.30015 + 2.70795i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(-8.08852 + 0.879680i) q^{65} +(-0.130360 + 2.40434i) q^{66} +(2.21678 - 7.98413i) q^{67} +(-0.214613 - 0.163145i) q^{68} +(8.08907 + 0.879740i) q^{69} +(1.22289 - 7.45927i) q^{70} +(2.33240 - 1.40336i) q^{71} +(-0.796093 + 0.605174i) q^{72} +(-4.10476 - 10.3022i) q^{73} +(-0.762073 - 0.897182i) q^{74} +(-0.0766653 - 0.467638i) q^{75} +(0.116027 + 2.14000i) q^{76} +(8.35511 + 1.83910i) q^{77} +(2.77647 - 2.63002i) q^{78} +(-2.68765 + 0.905576i) q^{79} +(0.787457 - 1.97637i) q^{80} +(0.267528 + 0.963550i) q^{81} +(5.57339 - 1.22680i) q^{82} +(8.51914 - 12.5648i) q^{83} +(1.66425 + 3.13910i) q^{84} +(0.268646 - 0.506721i) q^{85} +(-6.15499 - 9.07792i) q^{86} +(-1.56375 - 1.48126i) q^{87} +(2.18533 + 1.01104i) q^{88} +(-7.84611 - 3.63000i) q^{89} +(-1.54453 - 1.46306i) q^{90} +(-7.62535 - 11.2466i) q^{91} +(3.81133 - 7.18893i) q^{92} +(1.34463 + 2.53625i) q^{93} +(-4.65231 + 6.86164i) q^{94} +(-4.45287 + 0.980151i) q^{95} +(0.267528 + 0.963550i) q^{96} +(1.37817 - 3.45896i) q^{97} +(5.32928 - 1.79564i) q^{98} +(1.74811 - 1.65589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{25}{29}\right)$	$1$

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 $

$2$	−0.907575	+	0.419889i	−0.641753	+	0.296906i
$2$	−0.907575	+	0.419889i	−0.641753	+	0.296906i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$4$	0.647386	−	0.762162i	0.323693	−	0.381081i
$5$	1.82294	+	1.09682i	0.815242	+	0.490515i	0.861101	−	0.508433i	$-0.169775\pi$
$5$	1.82294	+	1.09682i	0.815242	+	0.490515i	−0.0458596	+	0.998948i	$0.514603\pi$
$6$	−0.994138	+	0.108119i	−0.405855	+	0.0441394i
$7$	−0.192354	+	3.54777i	−0.0727031	+	1.34093i	0.703612	+	0.710585i	$0.251570\pi$
$7$	−0.192354	+	3.54777i	−0.0727031	+	1.34093i	−0.776315	+	0.630345i	$0.782913\pi$
$8$	−0.267528	+	0.963550i	−0.0945856	+	0.340666i
$9$	0.796093	+	0.605174i	0.265364	+	0.201725i
$10$	−2.11500	−	0.230020i	−0.668821	−	0.0727386i
$11$	0.389551	−	2.37615i	0.117454	−	0.716437i	−0.860787	−	0.508965i	$-0.830028\pi$
$11$	0.389551	−	2.37615i	0.117454	−	0.716437i	0.978241	−	0.207472i	$-0.0665236\pi$
$12$	0.856857	−	0.515554i	0.247353	−	0.148828i
$13$	−3.04455	+	2.31441i	−0.844407	+	0.641901i	−0.935259	−	0.353963i	$-0.884834\pi$
$13$	−3.04455	+	2.31441i	−0.844407	+	0.641901i	0.0908525	+	0.995864i	$0.471041\pi$
$14$	−1.31509	−	3.30063i	−0.351473	−	0.882132i
$15$	1.37729	+	1.62148i	0.355616	+	0.418663i
$16$	−0.161782	−	0.986827i	−0.0404455	−	0.246707i
$17$	−0.0145950	−	0.269188i	−0.00353980	−	0.0652877i	0.996230	−	0.0867538i	$-0.0276494\pi$
$17$	−0.0145950	−	0.269188i	−0.00353980	−	0.0652877i	−0.999770	+	0.0214661i	$0.993167\pi$
$18$	−0.976621	−	0.214970i	−0.230192	−	0.0506690i
$19$	−1.55591	+	1.47384i	−0.356951	+	0.338122i	−0.845070	−	0.534655i	$-0.820442\pi$
$19$	−1.55591	+	1.47384i	−0.356951	+	0.338122i	0.488120	+	0.872777i	$0.337683\pi$
$20$	2.01610	−	0.679304i	0.450814	−	0.151897i
$21$	−1.31509	+	3.30063i	−0.286977	+	0.720257i
$22$	0.644175	+	2.32011i	0.137338	+	0.494649i
$23$	7.94654	−	1.74916i	1.65697	−	0.364726i	0.714659	−	0.699473i	$-0.246582\pi$
$23$	7.94654	−	1.74916i	1.65697	−	0.364726i	0.942308	+	0.334747i	$0.108651\pi$
$24$	−0.561187	+	0.827689i	−0.114552	+	0.168951i
$25$	−0.221970	−	0.418679i	−0.0443939	−	0.0837358i
$26$	1.79137	−	3.37887i	0.351316	−	0.662652i
$27$	0.561187	+	0.827689i	0.108001	+	0.159289i
$28$	2.57945	+	2.44338i	0.487470	+	0.461756i
$29$	−1.95486	−	0.904416i	−0.363009	−	0.167946i	0.229902	−	0.973214i	$-0.426159\pi$
$29$	−1.95486	−	0.904416i	−0.363009	−	0.167946i	−0.592911	+	0.805268i	$0.702021\pi$
$30$	−1.93084	−	0.893301i	−0.352521	−	0.163094i
$31$	2.08407	+	1.97414i	0.374311	+	0.354566i	0.851611	−	0.524174i	$-0.175626\pi$
$31$	2.08407	+	1.97414i	0.374311	+	0.354566i	−0.477300	+	0.878740i	$0.658385\pi$
$32$	0.561187	+	0.827689i	0.0992048	+	0.146316i
$33$	1.12787	−	2.12739i	0.196337	−	0.370330i
$34$	0.126275	+	0.238180i	0.0216560	+	0.0408476i
$35$	−4.24193	+	6.25638i	−0.717017	+	1.05752i
$36$	0.976621	−	0.214970i	0.162770	−	0.0358284i
$37$	0.314922	+	1.13425i	0.0517728	+	0.186469i	0.984915	−	0.173039i	$-0.0553585\pi$
$37$	0.314922	+	1.13425i	0.0517728	+	0.186469i	−0.933142	+	0.359507i	$0.882945\pi$
$38$	0.793259	−	1.99093i	0.128684	−	0.322971i
$39$	−3.62417	+	1.22113i	−0.580332	+	0.195537i
$40$	−1.54453	+	1.46306i	−0.244212	+	0.231330i
$41$	−5.57339	−	1.22680i	−0.870417	−	0.191593i	−0.242763	−	0.970086i	$-0.578054\pi$
$41$	−5.57339	−	1.22680i	−0.870417	−	0.191593i	−0.627654	+	0.778492i	$0.715985\pi$
$42$	−0.192354	−	3.54777i	−0.0296809	−	0.547432i
$43$	1.77439	+	10.8233i	0.270592	+	1.65054i	0.676366	+	0.736566i	$0.263554\pi$
$43$	1.77439	+	10.8233i	0.270592	+	1.65054i	−0.405773	+	0.913974i	$0.632998\pi$
$44$	−1.55882	−	1.83519i	−0.235002	−	0.276665i
$45$	0.787457	+	1.97637i	0.117387	+	0.294620i
$46$	−6.47763	+	4.92416i	−0.955074	+	0.726028i
$47$	7.10345	−	4.27401i	1.03614	−	0.623428i	0.107426	−	0.994213i	$-0.465739\pi$
$47$	7.10345	−	4.27401i	1.03614	−	0.623428i	0.928719	+	0.370785i	$0.120911\pi$
$48$	0.161782	−	0.986827i	0.0233512	−	0.142436i
$49$	−5.59069	−	0.608024i	−0.798670	−	0.0868606i
$50$	0.377253	+	0.286780i	0.0533516	+	0.0405568i
$51$	0.0721212	−	0.259757i	0.0100990	−	0.0363733i
$52$	−0.207047	+	3.81876i	−0.0287123	+	0.529567i
$53$	−0.282076	+	0.0306777i	−0.0387462	+	0.00421390i	−0.127472	−	0.991842i	$-0.540686\pi$
$53$	−0.282076	+	0.0306777i	−0.0387462	+	0.00421390i	0.0887254	+	0.996056i	$0.471721\pi$
$54$	−0.856857	−	0.515554i	−0.116603	−	0.0701580i
$55$	3.31635	−	3.90431i	0.447177	−	0.526457i
$56$	−3.36699	−	1.13447i	−0.449933	−	0.151600i
$57$	−1.94506	+	0.899882i	−0.257630	+	0.119192i
$58$	2.15394			0.282826
$59$	−2.66736	−	7.20314i	−0.347261	−	0.937769i
$59$	−2.66736	−	7.20314i	−0.347261	−	0.937769i
$60$	2.12747			0.274655
$61$	9.80821	−	4.53776i	1.25581	−	0.581001i	0.324729	−	0.945807i	$-0.394727\pi$
$61$	9.80821	−	4.53776i	1.25581	−	0.581001i	0.931083	+	0.364807i	$0.118865\pi$
$62$	−2.72037	−	0.916600i	−0.345488	−	0.116408i
$63$	−2.30015	+	2.70795i	−0.289792	+	0.341169i
$64$	−0.856857	−	0.515554i	−0.107107	−	0.0644442i
$65$	−8.08852	+	0.879680i	−1.00326	+	0.109111i
$66$	−0.130360	+	2.40434i	−0.0160462	+	0.295954i
$67$	2.21678	−	7.98413i	0.270823	−	0.975416i	−0.695594	−	0.718436i	$-0.744859\pi$
$67$	2.21678	−	7.98413i	0.270823	−	0.975416i	0.966417	−	0.256981i	$-0.0827277\pi$
$68$	−0.214613	−	0.163145i	−0.0260257	−	0.0197842i
$69$	8.08907	+	0.879740i	0.973810	+	0.105908i
$70$	1.22289	−	7.45927i	0.146163	−	0.891554i
$71$	2.33240	−	1.40336i	0.276805	−	0.166548i	−0.370381	−	0.928880i	$-0.620773\pi$
$71$	2.33240	−	1.40336i	0.276805	−	0.166548i	0.647187	+	0.762331i	$0.275945\pi$
$72$	−0.796093	+	0.605174i	−0.0938205	+	0.0713205i
$73$	−4.10476	−	10.3022i	−0.480426	−	1.20578i	−0.946982	−	0.321287i	$-0.895885\pi$
$73$	−4.10476	−	10.3022i	−0.480426	−	1.20578i	0.466556	−	0.884492i	$-0.345495\pi$
$74$	−0.762073	−	0.897182i	−0.0885892	−	0.104295i
$75$	−0.0766653	−	0.467638i	−0.00885255	−	0.0539981i
$76$	0.116027	+	2.14000i	0.0133093	+	0.245475i
$77$	8.35511	+	1.83910i	0.952153	+	0.209585i
$78$	2.77647	−	2.63002i	0.314374	−	0.297791i
$79$	−2.68765	+	0.905576i	−0.302385	+	0.101885i	−0.466404	−	0.884572i	$-0.654451\pi$
$79$	−2.68765	+	0.905576i	−0.302385	+	0.101885i	0.164019	+	0.986457i	$0.447554\pi$
$80$	0.787457	−	1.97637i	0.0880404	−	0.220965i
$81$	0.267528	+	0.963550i	0.0297254	+	0.107061i
$82$	5.57339	−	1.22680i	0.615478	−	0.135477i
$83$	8.51914	−	12.5648i	0.935097	−	1.37916i	0.00978744	−	0.999952i	$-0.496885\pi$
$83$	8.51914	−	12.5648i	0.935097	−	1.37916i	0.925310	−	0.379213i	$-0.123805\pi$
$84$	1.66425	+	3.13910i	0.181584	+	0.342504i
$85$	0.268646	−	0.506721i	0.0291388	−	0.0549616i
$86$	−6.15499	−	9.07792i	−0.663709	−	0.978898i
$87$	−1.56375	−	1.48126i	−0.167652	−	0.158808i
$88$	2.18533	+	1.01104i	0.232957	+	0.107777i
$89$	−7.84611	−	3.63000i	−0.831686	−	0.384779i	−0.0426231	−	0.999091i	$-0.513571\pi$
$89$	−7.84611	−	3.63000i	−0.831686	−	0.384779i	−0.789063	+	0.614312i	$0.789434\pi$
$90$	−1.54453	−	1.46306i	−0.162808	−	0.154220i
$91$	−7.62535	−	11.2466i	−0.799354	−	1.17896i
$92$	3.81133	−	7.18893i	0.397359	−	0.749498i
$93$	1.34463	+	2.53625i	0.139432	+	0.262997i
$94$	−4.65231	+	6.86164i	−0.479849	+	0.707725i
$95$	−4.45287	+	0.980151i	−0.456855	+	0.100561i
$96$	0.267528	+	0.963550i	0.0273045	+	0.0983419i
$97$	1.37817	−	3.45896i	0.139932	−	0.351204i	−0.842263	−	0.539067i	$-0.818777\pi$
$97$	1.37817	−	3.45896i	0.139932	−	0.351204i	0.982195	+	0.187863i	$0.0601562\pi$
$98$	5.32928	−	1.79564i	0.538338	−	0.181387i
$99$	1.74811	−	1.65589i	0.175691	−	0.166424i
$100$	−0.462801	−	0.101870i	−0.0462801	−	0.0101870i
$101$	0.206072	+	3.80077i	0.0205049	+	0.378190i	0.990718	+	0.135936i	$0.0434041\pi$
$101$	0.206072	+	3.80077i	0.0205049	+	0.378190i	−0.970213	+	0.242255i	$0.922113\pi$
$102$	0.0436137	+	0.266032i	0.00431840	+	0.0263411i
$103$	−3.56263	−	4.19425i	−0.351036	−	0.413272i	0.558098	−	0.829775i	$-0.311531\pi$
$103$	−3.56263	−	4.19425i	−0.351036	−	0.413272i	−0.909134	+	0.416503i	$0.863255\pi$
$104$	−1.41554	−	3.55275i	−0.138806	−	0.348376i
$105$	−6.01755	+	4.57442i	−0.587252	+	0.446418i
$106$	0.243124	−	0.146283i	0.0236143	−	0.0142083i
$107$	−2.62690	+	16.0234i	−0.253952	+	1.54904i	0.484534	+	0.874772i	$0.338989\pi$
$107$	−2.62690	+	16.0234i	−0.253952	+	1.54904i	−0.738486	+	0.674268i	$0.764459\pi$
$108$	0.994138	+	0.108119i	0.0956610	+	0.0104038i
$109$	−15.6005	−	11.8592i	−1.49426	−	1.13590i	−0.956093	−	0.293063i	$-0.905325\pi$
$109$	−15.6005	−	11.8592i	−1.49426	−	1.13590i	−0.538163	−	0.842841i	$-0.680881\pi$
$110$	−1.37046	+	4.93595i	−0.130668	+	0.470625i
$111$	−0.0637298	+	1.17543i	−0.00604897	+	0.111567i
$112$	3.53215	−	0.384145i	0.333757	−	0.0362983i
$113$	0.959327	+	0.577208i	0.0902459	+	0.0542992i	0.559961	−	0.828519i	$-0.310816\pi$
$113$	0.959327	+	0.577208i	0.0902459	+	0.0542992i	−0.469716	+	0.882818i	$0.655644\pi$
$114$	1.38744	−	1.63342i	0.129946	−	0.152984i
$115$	16.4046	+	5.52734i	1.52973	+	0.515427i
$116$	−1.95486	+	0.904416i	−0.181505	+	0.0839729i
$117$	−3.82437			−0.353563
$118$	5.44535	+	5.41739i	0.501285	+	0.498712i
$119$	0.957824			0.0878036
$120$	−1.93084	+	0.893301i	−0.176261	+	0.0815468i
$121$	4.92983	+	1.66105i	0.448166	+	0.151005i
$122$	−6.99633	+	8.23672i	−0.633418	+	0.745717i
$123$	−4.88992	−	2.94217i	−0.440909	−	0.265286i
$124$	2.85381	−	0.310371i	0.256280	−	0.0278721i
$125$	0.630475	−	11.6284i	0.0563914	−	1.04008i
$126$	0.950522	−	3.42347i	0.0846793	−	0.304987i
$127$	−1.81299	−	1.37820i	−0.160877	−	0.122296i	0.521638	−	0.853167i	$-0.325321\pi$
$127$	−1.81299	−	1.37820i	−0.160877	−	0.122296i	−0.682516	+	0.730871i	$0.739114\pi$
$128$	0.994138	+	0.108119i	0.0878702	+	0.00955646i
$129$	−1.77439	+	10.8233i	−0.156227	+	0.952940i
$130$	6.97158	−	4.19466i	0.611448	−	0.367896i
$131$	8.58644	−	6.52724i	0.750201	−	0.570288i	−0.158687	−	0.987329i	$-0.550726\pi$
$131$	8.58644	−	6.52724i	0.750201	−	0.570288i	0.908888	+	0.417041i	$0.136933\pi$
$132$	−0.891246	−	2.23686i	−0.0775730	−	0.194694i
$133$	−4.92955	−	5.80351i	−0.427446	−	0.503229i
$134$	1.34055	+	8.17700i	0.115806	+	0.706385i
$135$	0.115179	+	2.12435i	0.00991301	+	0.182835i
$136$	0.263281	+	0.0579525i	0.0225761	+	0.00496938i
$137$	−6.19468	+	5.86792i	−0.529248	+	0.501330i	−0.905012	−	0.425385i	$-0.860139\pi$
$137$	−6.19468	+	5.86792i	−0.529248	+	0.501330i	0.375765	+	0.926715i	$0.377380\pi$
$138$	−7.71084	+	2.59808i	−0.656390	+	0.221164i
$139$	−1.21497	+	3.04934i	−0.103052	+	0.258642i	−0.971458	−	0.237213i	$-0.923766\pi$
$139$	−1.21497	+	3.04934i	−0.103052	+	0.258642i	0.868405	+	0.495855i	$0.165145\pi$
$140$	2.02221	+	7.28333i	0.170908	+	0.615554i
$141$	8.09630	−	1.78213i	0.681832	−	0.150083i
$142$	−1.52758	+	2.25301i	−0.128191	+	0.189068i
$143$	4.31338	+	8.13591i	0.360703	+	0.680359i
$144$	0.468408	−	0.883512i	0.0390340	−	0.0736260i
$145$	−2.57161	−	3.79283i	−0.213560	−	0.314978i
$146$	8.05115	+	7.62646i	0.666318	+	0.631170i
$147$	−5.10389	−	2.36131i	−0.420962	−	0.194758i
$148$	1.06836	+	0.494274i	0.0878183	+	0.0406291i
$149$	3.61555	+	3.42483i	0.296197	+	0.280573i	0.821337	−	0.570443i	$-0.193228\pi$
$149$	3.61555	+	3.42483i	0.296197	+	0.280573i	−0.525140	+	0.851016i	$0.675987\pi$
$150$	0.265936	+	0.392226i	0.0217135	+	0.0320251i
$151$	10.2176	−	19.2724i	0.831495	−	1.56837i	0.00874516	−	0.999962i	$-0.497216\pi$
$151$	10.2176	−	19.2724i	0.831495	−	1.56837i	0.822750	−	0.568404i	$-0.192439\pi$
$152$	−1.00387	−	1.89349i	−0.0814243	−	0.153583i
$153$	0.151287	−	0.223131i	0.0122308	−	0.0180391i
$154$	−8.35511	+	1.83910i	−0.673274	+	0.148199i
$155$	1.63385	+	5.88459i	0.131234	+	0.472662i
$156$	−1.41554	+	3.55275i	−0.113334	+	0.284448i
$157$	−22.2886	+	7.50990i	−1.77882	+	0.599355i	−0.999624	−	0.0274206i	$-0.991271\pi$
$157$	−22.2886	+	7.50990i	−1.77882	+	0.599355i	−0.779200	+	0.626776i	$0.784374\pi$
$158$	2.05901	−	1.95039i	0.163806	−	0.155165i
$159$	−0.277106	−	0.0609957i	−0.0219759	−	0.00483727i
$160$	0.115179	+	2.12435i	0.00910568	+	0.167944i
$161$	4.67708	+	28.5289i	0.368606	+	2.24839i
$162$	−0.647386	−	0.762162i	−0.0508635	−	0.0598811i
$163$	3.22339	+	8.09010i	0.252475	+	0.633665i	0.999516	−	0.0311132i	$-0.00990522\pi$
$163$	3.22339	+	8.09010i	0.252475	+	0.633665i	−0.747041	+	0.664779i	$0.768526\pi$
$164$	−4.54315	+	3.45361i	−0.354761	+	0.269682i
$165$	4.38940	−	2.64102i	0.341714	−	0.205603i
$166$	−2.45594	+	14.9806i	−0.190618	+	1.16272i
$167$	−4.33615	−	0.471585i	−0.335542	−	0.0364923i	−0.0612025	−	0.998125i	$-0.519494\pi$
$167$	−4.33615	−	0.471585i	−0.335542	−	0.0364923i	−0.274339	+	0.961633i	$0.588459\pi$
$168$	−2.82850	−	2.15017i	−0.218224	−	0.165889i
$169$	0.434944	−	1.56653i	0.0334572	−	0.120502i
$170$	−0.0310503	+	0.572689i	−0.00238145	+	0.0439232i
$171$	−2.13058	+	0.231715i	−0.162930	+	0.0177197i
$172$	9.39784	+	5.65449i	0.716578	+	0.431151i
$173$	12.8060	−	15.0764i	0.973622	−	1.14624i	−0.0156095	−	0.999878i	$-0.504969\pi$
$173$	12.8060	−	15.0764i	0.973622	−	1.14624i	0.989232	−	0.146358i	$-0.0467553\pi$
$174$	2.04119	+	0.687757i	0.154742	+	0.0521387i
$175$	1.52807	−	0.706962i	0.115511	−	0.0534413i
$176$	−2.40787			−0.181500
$177$	−0.227760	−	7.67777i	−0.0171195	−	0.577096i
$178$	8.64513			0.647980
$179$	−18.2963	+	8.46478i	−1.36753	+	0.632687i	−0.959870	−	0.280446i	$-0.909518\pi$
$179$	−18.2963	+	8.46478i	−1.36753	+	0.632687i	−0.407661	+	0.913133i	$0.633656\pi$
$180$	2.01610	+	0.679304i	0.150271	+	0.0506323i
$181$	−4.94300	+	5.81934i	−0.367410	+	0.432548i	−0.914538	−	0.404501i	$-0.867445\pi$
$181$	−4.94300	+	5.81934i	−0.367410	+	0.432548i	0.547128	+	0.837049i	$0.315721\pi$
$182$	11.6429	+	7.00529i	0.863028	+	0.519267i
$183$	10.7437	−	1.16845i	0.794196	−	0.0863741i
$184$	−0.440516	+	8.12484i	−0.0324753	+	0.598971i
$185$	−0.669986	+	2.41307i	−0.0492584	+	0.177413i
$186$	−2.28530	−	1.73724i	−0.167566	−	0.127381i
$187$	−0.645318	−	0.0701825i	−0.0471903	−	0.00513226i
$188$	1.34119	−	8.18091i	0.0978165	−	0.596654i
$189$	−3.04440	+	1.83175i	−0.221447	+	0.133240i
$190$	3.62976	−	2.75927i	0.263331	−	0.200179i
$191$	−0.417938	−	1.04895i	−0.0302410	−	0.0758991i	0.913081	−	0.407779i	$-0.133697\pi$
$191$	−0.417938	−	1.04895i	−0.0302410	−	0.0758991i	−0.943322	+	0.331880i	$0.892317\pi$
$192$	−0.647386	−	0.762162i	−0.0467211	−	0.0550043i
$193$	0.0755638	+	0.460919i	0.00543920	+	0.0331777i	0.989407	−	0.145170i	$-0.0463730\pi$
$193$	0.0755638	+	0.460919i	0.00543920	+	0.0331777i	−0.983967	+	0.178348i	$0.942925\pi$
$194$	0.201581	+	3.71794i	0.0144727	+	0.266933i
$195$	−7.94600	−	1.74905i	−0.569025	−	0.125252i
$196$	−4.08275	+	3.86739i	−0.291625	+	0.276242i
$197$	−16.5781	+	5.58583i	−1.18114	+	0.397974i	−0.840287	−	0.542142i	$-0.817614\pi$
$197$	−16.5781	+	5.58583i	−1.18114	+	0.397974i	−0.340857	+	0.940115i	$0.610717\pi$
$198$	−0.891246	+	2.23686i	−0.0633381	+	0.158967i
$199$	7.13070	+	25.6824i	0.505482	+	1.82058i	0.568653	+	0.822578i	$0.307465\pi$
$199$	7.13070	+	25.6824i	0.505482	+	1.82058i	−0.0631713	+	0.998003i	$0.520121\pi$
$200$	0.462801	−	0.101870i	0.0327250	−	0.00720332i
$201$	4.65008	−	6.85836i	0.327992	−	0.483752i
$202$	−1.78293	−	3.36296i	−0.125446	−	0.236617i
$203$	3.58469	−	6.76143i	0.251596	−	0.474560i
$204$	−0.151287	−	0.223131i	−0.0105922	−	0.0156223i
$205$	−8.81435	−	8.34940i	−0.615621	−	0.583147i
$206$	4.99447	+	2.31069i	0.347981	+	0.160993i
$207$	7.38473	+	3.41654i	0.513274	+	0.237466i
$208$	2.77647	+	2.63002i	0.192514	+	0.182359i
$209$	2.89596	+	4.27122i	0.200318	+	0.295447i
$210$	3.54063	−	6.67833i	0.244327	−	0.460849i
$211$	10.6701	+	20.1259i	0.734557	+	1.38552i	0.915618	+	0.402049i	$0.131702\pi$
$211$	10.6701	+	20.1259i	0.734557	+	1.38552i	−0.181061	+	0.983472i	$0.557953\pi$
$212$	−0.159231	+	0.234848i	−0.0109360	+	0.0161294i
$213$	2.65841	−	0.585159i	0.182151	−	0.0400945i
$214$	−4.34394	−	15.6455i	−0.296946	−	1.06950i
$215$	−8.63667	+	21.6764i	−0.589016	+	1.47832i
$216$	−0.947653	+	0.319302i	−0.0644796	+	0.0217257i
$217$	−7.40467	+	7.01407i	−0.502662	+	0.476146i
$218$	19.1382	+	4.21263i	1.29620	+	0.285315i
$219$	−0.600390	−	11.0735i	−0.0405706	−	0.748281i
$220$	−0.828757	−	5.05519i	−0.0558748	−	0.340821i
$221$	0.667446	+	0.785778i	0.0448973	+	0.0528572i
$222$	−0.435709	−	1.09355i	−0.0292429	−	0.0733942i
$223$	20.4937	−	15.5789i	1.37236	−	1.04324i	0.379343	−	0.925256i	$-0.376150\pi$
$223$	20.4937	−	15.5789i	1.37236	−	1.04324i	0.993016	−	0.117984i	$-0.0376431\pi$
$224$	−3.04440	+	1.83175i	−0.203412	+	0.122389i
$225$	0.0766653	−	0.467638i	0.00511102	−	0.0311758i
$226$	−1.11303	−	0.121049i	−0.0740373	−	0.00805205i
$227$	22.8444	+	17.3659i	1.51624	+	1.15261i	0.942798	+	0.333365i	$0.108184\pi$
$227$	22.8444	+	17.3659i	1.51624	+	1.15261i	0.573439	+	0.819248i	$0.305609\pi$
$228$	−0.573351	+	2.06503i	−0.0379711	+	0.136760i
$229$	−0.899704	+	16.5941i	−0.0594541	+	1.09657i	0.804811	+	0.593531i	$0.202267\pi$
$229$	−0.899704	+	16.5941i	−0.0594541	+	1.09657i	−0.864265	+	0.503036i	$0.832216\pi$
$230$	−17.2092	+	1.87162i	−1.13474	+	0.123411i
$231$	7.33052	+	4.41063i	0.482313	+	0.290198i
$232$	1.39443	−	1.64165i	0.0915489	−	0.107780i
$233$	−15.6976	−	5.28914i	−1.02838	−	0.346503i	−0.245980	−	0.969275i	$-0.579110\pi$
$233$	−15.6976	−	5.28914i	−1.02838	−	0.346503i	−0.782403	+	0.622772i	$0.786006\pi$
$234$	3.47090	−	1.60581i	0.226900	−	0.104975i
$235$	17.6370			1.15051
$236$	−7.21677	−	2.63025i	−0.469772	−	0.171215i
$237$	−2.83611			−0.184225
$238$	−0.869298	+	0.402180i	−0.0563482	+	0.0260695i
$239$	−11.1434	−	3.75465i	−0.720808	−	0.242868i	−0.0650953	−	0.997879i	$-0.520735\pi$
$239$	−11.1434	−	3.75465i	−0.720808	−	0.242868i	−0.655713	+	0.755011i	$0.727632\pi$
$240$	1.37729	−	1.62148i	0.0889039	−	0.104666i
$241$	−13.9058	−	8.36683i	−0.895750	−	0.538955i	−0.00835511	−	0.999965i	$-0.502660\pi$
$241$	−13.9058	−	8.36683i	−0.895750	−	0.538955i	−0.887395	+	0.461010i	$0.847487\pi$
$242$	−5.17165	+	0.562450i	−0.332446	+	0.0361557i
$243$	−0.0541389	+	0.998533i	−0.00347301	+	0.0640559i
$244$	2.89119	−	10.4131i	0.185089	−	0.666632i
$245$	−9.52458	−	7.24040i	−0.608503	−	0.462572i
$246$	5.67336	+	0.617015i	0.361720	+	0.0393394i
$247$	1.32599	−	8.08819i	0.0843709	−	0.514639i
$248$	−2.45973	+	1.47997i	−0.156193	+	0.0939782i
$249$	12.0851	−	9.18689i	0.765865	−	0.582195i
$250$	4.31045	+	10.8184i	0.272617	+	0.684216i
$251$	−11.1824	−	13.1650i	−0.705828	−	0.830965i	0.286043	−	0.958217i	$-0.407660\pi$
$251$	−11.1824	−	13.1650i	−0.705828	−	0.830965i	−0.991870	+	0.127252i	$0.959384\pi$
$252$	0.574808	+	3.50617i	0.0362095	+	0.220868i
$253$	−1.06071	−	19.5636i	−0.0666861	−	1.22995i
$254$	2.22412	+	0.489566i	0.139554	+	0.0307181i
$255$	0.416380	−	0.394416i	0.0260747	−	0.0246993i
$256$	−0.947653	+	0.319302i	−0.0592283	+	0.0199563i
$257$	−1.48995	+	3.73948i	−0.0929402	+	0.233262i	−0.968096	−	0.250578i	$-0.919379\pi$
$257$	−1.48995	+	3.73948i	−0.0929402	+	0.233262i	0.875156	+	0.483841i	$0.160759\pi$
$258$	−2.93420	−	10.5680i	−0.182675	−	0.657936i
$259$	−4.08462	+	0.899093i	−0.253806	+	0.0558669i
$260$	−4.56594	+	6.73426i	−0.283168	+	0.417641i
$261$	−1.00892	−	1.90303i	−0.0624508	−	0.117795i
$262$	−5.05212	+	9.52932i	−0.312121	+	0.588723i
$263$	−4.19956	−	6.19389i	−0.258956	−	0.381931i	0.675880	−	0.737012i	$-0.263764\pi$
$263$	−4.19956	−	6.19389i	−0.258956	−	0.381931i	−0.934836	+	0.355080i	$0.884453\pi$
$264$	1.74811	+	1.65589i	0.107588	+	0.101913i
$265$	−0.547855	−	0.253465i	−0.0336545	−	0.0155702i
$266$	6.91077	+	3.19726i	0.423727	+	0.196037i
$267$	−6.27633	−	5.94525i	−0.384105	−	0.363844i
$268$	−4.65008	−	6.85836i	−0.284049	−	0.418941i
$269$	7.40785	−	13.9727i	0.451665	−	0.851930i	−0.548214	−	0.836338i	$-0.684692\pi$
$269$	7.40785	−	13.9727i	0.451665	−	0.851930i	0.999878	−	0.0155918i	$-0.00496324\pi$
$270$	−0.996524	−	1.87964i	−0.0606465	−	0.114391i
$271$	7.86161	−	11.5950i	0.477559	−	0.704346i	−0.510249	−	0.860027i	$-0.670447\pi$
$271$	7.86161	−	11.5950i	0.477559	−	0.704346i	0.987807	+	0.155680i	$0.0497570\pi$
$272$	−0.263281	+	0.0579525i	−0.0159637	+	0.00351388i
$273$	−3.63515	−	13.0926i	−0.220009	−	0.792401i
$274$	3.15827	−	7.92666i	0.190798	−	0.478867i
$275$	−1.08131	+	0.364337i	−0.0652057	+	0.0219704i
$276$	5.90726	−	5.59565i	0.355575	−	0.336819i
$277$	1.12364	+	0.247332i	0.0675131	+	0.0148607i	0.248599	−	0.968607i	$-0.420030\pi$
$277$	1.12364	+	0.247332i	0.0675131	+	0.0148607i	−0.181085	+	0.983467i	$0.557961\pi$
$278$	−0.177710	−	3.27766i	−0.0106583	−	0.196581i
$279$	0.464418	+	2.83283i	0.0278040	+	0.169597i
$280$	−4.89349	−	5.76107i	−0.292442	−	0.344290i
$281$	−4.95293	−	12.4309i	−0.295467	−	0.741566i	−0.999507	−	0.0314053i	$-0.990002\pi$
$281$	−4.95293	−	12.4309i	−0.295467	−	0.741566i	0.704040	−	0.710160i	$-0.251378\pi$
$282$	−6.59971	+	5.01697i	−0.393007	+	0.298756i
$283$	−8.17089	+	4.91626i	−0.485709	+	0.292242i	−0.737268	−	0.675601i	$-0.763884\pi$
$283$	−8.17089	+	4.91626i	−0.485709	+	0.292242i	0.251559	+	0.967842i	$0.419057\pi$
$284$	0.440378	−	2.68619i	0.0261316	−	0.159396i
$285$	−4.53274	−	0.492965i	−0.268496	−	0.0292007i
$286$	−7.33090	−	5.57281i	−0.433485	−	0.329527i
$287$	5.42445	−	19.5371i	0.320195	−	1.15324i
$288$	−0.0541389	+	0.998533i	−0.00319017	+	0.0588391i
$289$	16.8281	−	1.83017i	0.989888	−	0.107657i
$290$	3.92650	+	2.36249i	0.230572	+	0.138730i
$291$	2.41048	−	2.83784i	0.141305	−	0.166357i
$292$	−10.5093	−	3.54099i	−0.615010	−	0.207221i
$293$	5.02973	−	2.32700i	0.293840	−	0.135945i	−0.267431	−	0.963577i	$-0.586175\pi$
$293$	5.02973	−	2.32700i	0.293840	−	0.135945i	0.561271	+	0.827632i	$0.310313\pi$
$294$	5.62366			0.327978
$295$	3.03815	−	16.0565i	0.176888	−	0.934845i
$296$	−1.17715			−0.0684207
$297$	2.18533	−	1.01104i	0.126806	−	0.0586665i
$298$	−4.71943	−	1.59016i	−0.273389	−	0.0921156i
$299$	−20.1454	+	23.7170i	−1.16504	+	1.37159i
$300$	−0.406048	−	0.244311i	−0.0234432	−	0.0141053i
$301$	−38.7399	+	4.21322i	−2.23293	+	0.242846i
$302$	−1.18095	+	21.7814i	−0.0679562	+	1.25338i
$303$	−1.01831	+	3.66761i	−0.0585002	+	0.210699i
$304$	1.70614	+	1.29697i	0.0978539	+	0.0743866i
$305$	22.8569	+	2.48583i	1.30878	+	0.142338i
$306$	−0.0436137	+	0.266032i	−0.00249323	+	0.0152080i
$307$	15.0183	−	9.03621i	0.857140	−	0.515724i	−0.0178639	−	0.999840i	$-0.505687\pi$
$307$	15.0183	−	9.03621i	0.857140	−	0.515724i	0.875003	+	0.484117i	$0.160859\pi$
$308$	6.81068	−	5.17734i	0.388074	−	0.295006i
$309$	−2.03690	−	5.11225i	−0.115875	−	0.290826i
$310$	−3.95372	−	4.65468i	−0.224556	−	0.264368i
$311$	−0.245523	−	1.49762i	−0.0139223	−	0.0849223i	0.978951	−	0.204093i	$-0.0654246\pi$
$311$	−0.245523	−	1.49762i	−0.0139223	−	0.0849223i	−0.992874	+	0.119171i	$0.961976\pi$
$312$	−0.207047	−	3.81876i	−0.0117217	−	0.216195i
$313$	11.8308	+	2.60417i	0.668719	+	0.147196i	0.536339	−	0.844003i	$-0.319807\pi$
$313$	11.8308	+	2.60417i	0.668719	+	0.147196i	0.132380	+	0.991199i	$0.457738\pi$
$314$	17.0753	−	16.1745i	0.963612	−	0.912782i
$315$	−7.16317	+	2.41355i	−0.403599	+	0.135988i
$316$	−1.04975	+	2.63468i	−0.0590533	+	0.148213i
$317$	6.75037	+	24.3127i	0.379139	+	1.36553i	0.869465	+	0.493995i	$0.164464\pi$
$317$	6.75037	+	24.3127i	0.379139	+	1.36553i	−0.490326	+	0.871539i	$0.663122\pi$
$318$	0.277106	−	0.0609957i	0.0155393	−	0.00342047i
$319$	−2.91055	+	4.29274i	−0.162960	+	0.240347i
$320$	−0.996524	−	1.87964i	−0.0557074	−	0.105075i
$321$	−7.60569	+	14.3459i	−0.424508	+	0.800707i
$322$	−16.2238	−	23.9283i	−0.904116	−	1.33347i
$323$	0.419448	+	0.397322i	0.0233387	+	0.0221076i
$324$	0.907575	+	0.419889i	0.0504209	+	0.0233272i
$325$	1.64479	+	0.760962i	0.0912367	+	0.0422106i
$326$	−6.32241	−	5.98891i	−0.350166	−	0.331695i
$327$	−10.9972	−	16.2197i	−0.608146	−	0.896949i
$328$	2.67312	−	5.04204i	0.147598	−	0.278400i
$329$	13.7968	+	26.0235i	0.760642	+	1.43472i
$330$	−2.87478	+	4.23998i	−0.158251	+	0.233403i
$331$	−22.7679	+	5.01160i	−1.25144	+	0.275463i	−0.790772	−	0.612111i	$-0.790321\pi$
$331$	−22.7679	+	5.01160i	−1.25144	+	0.275463i	−0.460667	+	0.887573i	$0.652390\pi$
$332$	−4.06123	−	14.6272i	−0.222889	−	0.802774i
$333$	−0.435709	+	1.09355i	−0.0238767	+	0.0599261i
$334$	4.13340	−	1.39270i	0.226170	−	0.0762054i
$335$	12.7982	−	12.1231i	0.699242	−	0.662358i
$336$	3.46991	+	0.763785i	0.189299	+	0.0416679i
$337$	0.311779	+	5.75042i	0.0169837	+	0.313245i	0.994665	+	0.103154i	$0.0328934\pi$
$337$	0.311779	+	5.75042i	0.0169837	+	0.313245i	−0.977682	+	0.210091i	$0.932624\pi$
$338$	0.263023	+	1.60437i	0.0143066	+	0.0872662i
$339$	0.724806	+	0.853308i	0.0393661	+	0.0463453i
$340$	−0.212285	−	0.532796i	−0.0115128	−	0.0288949i
$341$	5.50271	−	4.18305i	0.297989	−	0.226525i
$342$	1.83637	−	1.10491i	0.0992994	−	0.0597465i
$343$	−0.791133	+	4.82570i	−0.0427171	+	0.260563i
$344$	−10.9035	−	1.18583i	−0.587877	−	0.0639355i
$345$	13.7809	+	10.4760i	0.741941	+	0.564009i
$346$	−5.29200	+	19.0601i	−0.284500	+	1.02468i
$347$	0.154297	−	2.84585i	0.00828312	−	0.152773i	−0.991466	−	0.130367i	$-0.958385\pi$
$347$	0.154297	−	2.84585i	0.00828312	−	0.152773i	0.999749	−	0.0224063i	$-0.00713274\pi$
$348$	−2.14131	+	0.232882i	−0.114786	+	0.0124838i
$349$	5.54508	+	3.33636i	0.296821	+	0.178591i	0.656172	−	0.754611i	$-0.272174\pi$
$349$	5.54508	+	3.33636i	0.296821	+	0.178591i	−0.359351	+	0.933202i	$0.617002\pi$
$350$	−1.09000	+	1.28324i	−0.0582627	+	0.0685922i
$351$	−3.62417	−	1.22113i	−0.193444	−	0.0651789i
$352$	2.18533	−	1.01104i	0.116478	−	0.0538886i
$353$	7.57191			0.403012			0.201506	−	0.979487i	$-0.435416\pi$
$353$	7.57191			0.403012			0.201506	+	0.979487i	$0.435416\pi$
$354$	3.43052	+	6.87252i	0.182330	+	0.365270i
$355$	5.79107			0.307358
$356$	−7.84611	+	3.63000i	−0.415843	+	0.192389i
$357$	0.907685	+	0.305835i	0.0480398	+	0.0161865i
$358$	13.0510	−	15.3648i	0.689768	−	0.812057i
$359$	15.4648	+	9.30489i	0.816203	+	0.491093i	0.861426	−	0.507884i	$-0.169572\pi$
$359$	15.4648	+	9.30489i	0.816203	+	0.491093i	−0.0452225	+	0.998977i	$0.514400\pi$
$360$	−2.11500	+	0.230020i	−0.111470	+	0.0121231i
$361$	−0.779976	+	14.3858i	−0.0410514	+	0.757148i
$362$	2.04266	−	7.35700i	0.107360	−	0.386676i
$363$	4.14139	+	3.14820i	0.217367	+	0.165238i
$364$	−13.5082	−	1.46911i	−0.708024	−	0.0770023i
$365$	3.81696	−	23.2824i	0.199789	−	1.21866i
$366$	−9.26009	+	5.57161i	−0.484033	+	0.291233i
$367$	10.9061	−	8.29058i	0.569292	−	0.432765i	−0.280521	−	0.959848i	$-0.590507\pi$
$367$	10.9061	−	8.29058i	0.569292	−	0.432765i	0.849814	+	0.527083i	$0.176714\pi$
$368$	−3.01173	−	7.55887i	−0.156997	−	0.394033i
$369$	−3.69451	−	4.34951i	−0.192329	−	0.226427i
$370$	−0.405160	−	2.47137i	−0.0210633	−	0.128480i
$371$	−0.0545786	−	1.00664i	−0.00283358	−	0.0522623i
$372$	2.80353	+	0.617103i	0.145356	+	0.0319953i
$373$	0.200667	−	0.190082i	0.0103901	−	0.00984207i	−0.682487	−	0.730898i	$-0.739102\pi$
$373$	0.200667	−	0.190082i	0.0103901	−	0.00984207i	0.692877	+	0.721056i	$0.256343\pi$
$374$	0.615143	−	0.207266i	0.0318083	−	0.0107175i
$375$	4.31045	−	10.8184i	0.222590	−	0.558660i
$376$	2.21784	+	7.98795i	0.114377	+	0.411947i
$377$	8.04487	−	1.77081i	0.414332	−	0.0912014i
$378$	1.99389	−	2.94076i	0.102554	−	0.151256i
$379$	−12.1310	−	22.8815i	−0.623127	−	1.17534i	−0.971288	−	0.237908i	$-0.923538\pi$
$379$	−12.1310	−	22.8815i	−0.623127	−	1.17534i	0.348160	−	0.937435i	$-0.386807\pi$
$380$	−2.13569	+	4.02834i	−0.109559	+	0.206650i
$381$	−1.27803	−	1.88495i	−0.0654753	−	0.0965688i
$382$	0.819752	+	0.776510i	0.0419421	+	0.0397297i
$383$	12.9293	+	5.98173i	0.660657	+	0.305652i	0.721418	−	0.692500i	$-0.243491\pi$
$383$	12.9293	+	5.98173i	0.660657	+	0.305652i	−0.0607613	+	0.998152i	$0.519353\pi$
$384$	0.907575	+	0.419889i	0.0463145	+	0.0214274i
$385$	13.2137	+	12.5167i	0.673431	+	0.637908i
$386$	−0.262115	−	0.386590i	−0.0133413	−	0.0196769i
$387$	−5.13741	+	9.69018i	−0.261149	+	0.492580i
$388$	−1.74407	−	3.28967i	−0.0885420	−	0.167008i
$389$	−3.59174	+	5.29741i	−0.182108	+	0.268590i	−0.907776	−	0.419456i	$-0.862221\pi$
$389$	−3.59174	+	5.29741i	−0.182108	+	0.268590i	0.725667	+	0.688046i	$0.241531\pi$
$390$	7.94600	−	1.74905i	0.402361	−	0.0885664i
$391$	−0.586834	−	2.11358i	−0.0296774	−	0.106889i
$392$	2.08153	−	5.22425i	0.105133	−	0.263864i
$393$	10.2211	−	3.44390i	0.515588	−	0.173722i
$394$	12.7005	−	12.0305i	0.639841	−	0.606090i
$395$	−5.89268	−	1.29708i	−0.296493	−	0.0652630i
$396$	−0.130360	−	2.40434i	−0.00655082	−	0.120823i
$397$	5.71932	+	34.8863i	0.287044	+	1.75089i	0.598956	+	0.800782i	$0.295582\pi$
$397$	5.71932	+	34.8863i	0.287044	+	1.75089i	−0.311912	+	0.950111i	$0.600969\pi$
$398$	−17.2554	−	20.3147i	−0.864936	−	1.01828i
$399$	−2.81843	−	7.07373i	−0.141098	−	0.354130i
$400$	−0.377253	+	0.286780i	−0.0188626	+	0.0143390i
$401$	−20.1812	+	12.1426i	−1.00780	+	0.606374i	−0.920882	−	0.389841i	$-0.872530\pi$
$401$	−20.1812	+	12.1426i	−1.00780	+	0.606374i	−0.0869194	+	0.996215i	$0.527702\pi$
$402$	−1.34055	+	8.17700i	−0.0668606	+	0.407832i
$403$	−10.9140	−	1.18697i	−0.543667	−	0.0591273i
$404$	3.03021	+	2.30350i	0.150759	+	0.114604i
$405$	−0.569158	+	2.04992i	−0.0282817	+	0.101861i
$406$	−0.414320	+	7.64168i	−0.0205624	+	0.379250i
$407$	2.81782	−	0.306457i	0.139674	−	0.0151905i
$408$	0.230994	+	0.138985i	0.0114359	+	0.00688077i
$409$	−8.18139	+	9.63188i	−0.404544	+	0.476266i	−0.926277	−	0.376843i	$-0.877010\pi$
$409$	−8.18139	+	9.63188i	−0.404544	+	0.476266i	0.521734	+	0.853109i	$0.325286\pi$
$410$	11.5055	+	3.87666i	0.568217	+	0.191454i
$411$	−7.74405	+	3.58278i	−0.381986	+	0.176725i
$412$	−5.50309			−0.271118
$413$	26.0681	−	8.07762i	1.28273	−	0.397474i
$414$	−8.13677			−0.399900
$415$	29.3112	−	13.5608i	1.43883	−	0.665674i
$416$	−3.62417	−	1.22113i	−0.177690	−	0.0598706i
$417$	−2.12503	+	2.50178i	−0.104063	+	0.122513i
$418$	−4.42174	−	2.66047i	−0.216274	−	0.130128i
$419$	−27.4539	+	2.98579i	−1.34121	+	0.145865i	−0.750421	−	0.660960i	$-0.770149\pi$
$419$	−27.4539	+	2.98579i	−1.34121	+	0.145865i	−0.590790	+	0.806826i	$0.701184\pi$
$420$	−0.409228	+	7.54776i	−0.0199683	+	0.368293i
$421$	−5.36325	+	19.3167i	−0.261389	+	0.941437i	0.710051	+	0.704150i	$0.248672\pi$
$421$	−5.36325	+	19.3167i	−0.261389	+	0.941437i	−0.971440	+	0.237287i	$0.923742\pi$
$422$	−18.1345	−	13.7855i	−0.882774	−	0.671067i
$423$	8.24153	+	0.896320i	0.400717	+	0.0435806i
$424$	0.0459040	−	0.280002i	0.00222929	−	0.0135981i
$425$	−0.109464	+	0.0658621i	−0.00530977	+	0.00319478i
$426$	−2.16700	+	1.64731i	−0.104992	+	0.0798125i
$427$	14.2123	+	35.6701i	0.687780	+	1.72620i
$428$	10.5118	+	12.3755i	0.508107	+	0.598190i
$429$	1.48979	+	9.08729i	0.0719275	+	0.438738i
$430$	−1.26326	−	23.2994i	−0.0609197	−	1.12360i
$431$	−33.6048	−	7.39698i	−1.61869	−	0.356300i	−0.689032	−	0.724730i	$-0.741964\pi$
$431$	−33.6048	−	7.39698i	−1.61869	−	0.356300i	−0.929655	+	0.368430i	$0.879895\pi$
$432$	0.725995	−	0.687699i	0.0349295	−	0.0330870i
$433$	8.38771	−	2.82615i	0.403087	−	0.135816i	−0.110453	−	0.993881i	$-0.535230\pi$
$433$	8.38771	−	2.82615i	0.403087	−	0.135816i	0.513540	+	0.858065i	$0.328334\pi$
$434$	3.77516	−	9.47494i	0.181214	−	0.454812i
$435$	−1.22593	−	4.41541i	−0.0587790	−	0.211703i
$436$	−19.1382	+	4.21263i	−0.916552	+	0.201748i
$437$	−9.78613	+	14.4335i	−0.468134	+	0.690446i
$438$	5.19456	+	9.79798i	0.248206	+	0.468166i
$439$	−17.7994	+	33.5732i	−0.849519	+	1.60236i	−0.0523317	+	0.998630i	$0.516665\pi$
$439$	−17.7994	+	33.5732i	−0.849519	+	1.60236i	−0.797187	+	0.603733i	$0.793680\pi$
$440$	2.87478	+	4.23998i	0.137050	+	0.202133i
$441$	−4.08275	−	3.86739i	−0.194417	−	0.184161i
$442$	−0.935698	−	0.432900i	−0.0445066	−	0.0205909i
$443$	2.60507	+	1.20523i	0.123770	+	0.0572623i	0.480797	−	0.876832i	$-0.340347\pi$
$443$	2.60507	+	1.20523i	0.123770	+	0.0572623i	−0.357027	+	0.934094i	$0.616209\pi$
$444$	0.854608	+	0.809528i	0.0405579	+	0.0384185i
$445$	−10.3215	−	15.2231i	−0.489286	−	0.721642i
$446$	−12.0582	+	22.7441i	−0.570970	+	1.07696i
$447$	2.33273	+	4.40000i	0.110334	+	0.208113i
$448$	1.99389	−	2.94076i	0.0942022	−	0.138938i
$449$	−9.15314	+	2.01476i	−0.431963	+	0.0950823i	−0.425629	−	0.904898i	$-0.639947\pi$
$449$	−9.15314	+	2.01476i	−0.431963	+	0.0950823i	−0.00633396	+	0.999980i	$0.502016\pi$
$450$	0.126776	+	0.456607i	0.00597630	+	0.0215247i
$451$	−5.08617	+	12.7653i	−0.239499	+	0.601096i
$452$	1.06098	−	0.357486i	0.0499044	−	0.0168147i
$453$	15.8364	−	15.0011i	0.744060	−	0.704811i
$454$	−28.0248	−	6.16872i	−1.31527	−	0.289512i
$455$	−1.56504	−	28.8654i	−0.0733701	−	1.35323i
$456$	−0.346722	−	2.11491i	−0.0162367	−	0.0990397i
$457$	−24.6391	−	29.0074i	−1.15257	−	1.35691i	−0.923547	−	0.383486i	$-0.874723\pi$
$457$	−24.6391	−	29.0074i	−1.15257	−	1.35691i	−0.229021	−	0.973421i	$-0.573553\pi$
$458$	−6.15112	−	15.4381i	−0.287423	−	0.721377i
$459$	0.214613	−	0.163145i	0.0100173	−	0.00761495i
$460$	14.8328	−	8.92461i	0.691583	−	0.416112i
$461$	5.81085	−	35.4446i	0.270638	−	1.65082i	−0.405537	−	0.914079i	$-0.632915\pi$
$461$	5.81085	−	35.4446i	0.270638	−	1.65082i	0.676175	−	0.736741i	$-0.263636\pi$
$462$	−8.50498	−	0.924972i	−0.395687	−	0.0430336i
$463$	5.96012	+	4.53077i	0.276990	+	0.210563i	0.734441	−	0.678672i	$-0.237444\pi$
$463$	5.96012	+	4.53077i	0.276990	+	0.210563i	−0.457451	+	0.889235i	$0.651237\pi$
$464$	−0.576240	+	2.07543i	−0.0267513	+	0.0963494i
$465$	−0.330637	+	6.09824i	−0.0153329	+	0.282799i
$466$	16.4676	−	1.79096i	0.762847	−	0.0829646i
$467$	−29.2092	−	17.5746i	−1.35164	−	0.813256i	−0.358884	−	0.933382i	$-0.616843\pi$
$467$	−29.2092	−	17.5746i	−1.35164	−	0.813256i	−0.992759	+	0.120126i	$0.961670\pi$
$468$	−2.47584	+	2.91479i	−0.114446	+	0.134736i
$469$	27.8994	+	9.40041i	1.28828	+	0.434071i
$470$	−16.0069	+	7.40557i	−0.738342	+	0.341594i
$471$	−23.5198			−1.08373
$472$	7.65418	−	0.643092i	0.352312	−	0.0296007i
$473$	26.4091			1.21429
$474$	2.57399	−	1.19085i	0.118227	−	0.0546977i
$475$	0.962430	+	0.324280i	0.0441593	+	0.0148790i
$476$	0.620082	−	0.730017i	0.0284214	−	0.0334603i
$477$	−0.243124	−	0.146283i	−0.0111319	−	0.00669784i
$478$	11.6900	−	1.27137i	0.534690	−	0.0581510i
$479$	1.19123	−	21.9709i	0.0544287	−	1.00388i	−0.835993	−	0.548741i	$-0.815107\pi$
$479$	1.19123	−	21.9709i	0.0544287	−	1.00388i	0.890421	−	0.455137i	$-0.150410\pi$
$480$	−0.569158	+	2.04992i	−0.0259784	+	0.0935657i
$481$	−3.58391	−	2.72441i	−0.163412	−	0.124223i
$482$	16.1337	+	1.75464i	0.734869	+	0.0799218i
$483$	−4.67708	+	28.5289i	−0.212815	+	1.29811i
$484$	4.45749	−	2.68198i	0.202613	−	0.121908i
$485$	6.30619	−	4.79384i	0.286349	−	0.217677i
$486$	−0.370138	−	0.928977i	−0.0167898	−	0.0421392i
$487$	−8.69699	−	10.2389i	−0.394098	−	0.463968i	0.528950	−	0.848653i	$-0.322586\pi$
$487$	−8.69699	−	10.2389i	−0.394098	−	0.463968i	−0.923048	+	0.384685i	$0.874310\pi$
$488$	1.74838	+	10.6647i	0.0791457	+	0.482767i
$489$	0.471475	+	8.69584i	0.0213208	+	0.393239i
$490$	11.6844	+	2.57194i	0.527849	+	0.116188i
$491$	−10.8171	+	10.2465i	−0.488169	+	0.462418i	−0.891752	−	0.452525i	$-0.850523\pi$
$491$	−10.8171	+	10.2465i	−0.488169	+	0.462418i	0.403583	+	0.914943i	$0.367765\pi$
$492$	−5.40808	+	1.82219i	−0.243815	+	0.0821508i
$493$	−0.214927	+	0.539426i	−0.00967982	+	0.0242945i
$494$	2.19271	+	7.89742i	0.0986545	+	0.355322i
$495$	5.00291	−	1.10122i	0.224864	−	0.0494963i
$496$	1.61097	−	2.37600i	0.0723346	−	0.106686i
$497$	4.53015	+	8.54477i	0.203205	+	0.383285i
$498$	−7.11071	+	13.4122i	−0.318638	+	0.601016i
$499$	16.8688	+	24.8796i	0.755150	+	1.11376i	0.989908	+	0.141710i	$0.0452599\pi$
$499$	16.8688	+	24.8796i	0.755150	+	1.11376i	−0.234758	+	0.972054i	$0.575430\pi$
$500$	−8.45458	−	8.00861i	−0.378100	−	0.358156i
$501$	−3.95859	−	1.83144i	−0.176857	−	0.0818227i
$502$	15.6767	+	7.25282i	0.699686	+	0.323709i
$503$	21.6486	+	20.5066i	0.965263	+	0.914346i	0.996366	−	0.0851702i	$-0.0271434\pi$
$503$	21.6486	+	20.5066i	0.965263	+	0.914346i	−0.0311031	+	0.999516i	$0.509902\pi$
$504$	−1.99389	−	2.94076i	−0.0888147	−	0.130992i
$505$	−3.79312	+	7.15458i	−0.168792	+	0.318375i
$506$	9.17721	+	17.3100i	0.407977	+	0.769526i
$507$	0.912371	−	1.34565i	0.0405198	−	0.0597623i
$508$	−2.22412	+	0.489566i	−0.0986794	+	0.0217210i
$509$	−0.777413	−	2.79999i	−0.0344582	−	0.124107i	0.944321	−	0.329027i	$-0.106721\pi$
$509$	−0.777413	−	2.79999i	−0.0344582	−	0.124107i	−0.978779	+	0.204919i	$0.934307\pi$
$510$	−0.212285	+	0.532796i	−0.00940015	+	0.0235926i
$511$	37.3393	−	12.5811i	1.65179	−	0.556554i
$512$	0.725995	−	0.687699i	0.0320848	−	0.0303923i
$513$	−2.09304	−	0.460712i	−0.0924099	−	0.0203409i
$514$	−0.217929	−	4.01947i	−0.00961246	−	0.177291i
$515$	−1.89409	−	11.5534i	−0.0834635	−	0.509105i
$516$	7.10040	+	8.35924i	0.312578	+	0.367995i
$517$	−7.38854	−	18.5438i	−0.324948	−	0.815557i
$518$	3.32958	−	2.53108i	0.146293	−	0.111209i
$519$	16.9496	−	10.1982i	0.744003	−	0.447652i
$520$	1.31629	−	8.02904i	0.0577233	−	0.352097i
$521$	27.3421	+	2.97363i	1.19788	+	0.130277i	0.685234	−	0.728323i	$-0.259700\pi$
$521$	27.3421	+	2.97363i	1.19788	+	0.130277i	0.512645	+	0.858601i	$0.328666\pi$
$522$	1.71474	+	1.30351i	0.0750520	+	0.0570531i
$523$	−10.5944	+	38.1577i	−0.463262	+	1.66852i	0.250488	+	0.968120i	$0.419409\pi$
$523$	−10.5944	+	38.1577i	−0.463262	+	1.66852i	−0.713751	+	0.700400i	$0.753005\pi$
$524$	0.583927	−	10.7699i	0.0255090	−	0.470486i
$525$	1.67382	−	0.182039i	0.0730514	−	0.00794481i
$526$	6.41216	+	3.85807i	0.279584	+	0.168220i
$527$	0.500998	−	0.589820i	0.0218238	−	0.0256930i
$528$	−2.28183	−	0.768838i	−0.0993039	−	0.0334594i
$529$	39.2136	−	18.1422i	1.70494	−	0.788789i
$530$	0.603647			0.0262208
$531$	2.23569	−	7.34859i	0.0970205	−	0.318901i
$532$	−7.61454			−0.330132
$533$	19.8078	−	9.16405i	0.857970	−	0.396939i
$534$	8.19259	+	2.76040i	0.354528	+	0.119454i
$535$	−22.3635	+	26.3284i	−0.966860	+	1.13828i
$536$	7.10005	+	4.27196i	0.306676	+	0.184521i
$537$	−20.0414	+	2.17963i	−0.864849	+	0.0940580i
$538$	−0.856204	+	15.7918i	−0.0369136	+	0.680831i
$539$	−3.62262	+	13.0475i	−0.156037	+	0.561995i
$540$	1.69366	+	1.28749i	0.0728836	+	0.0554047i
$541$	18.9497	+	2.06090i	0.814710	+	0.0886051i	0.505981	−	0.862545i	$-0.331131\pi$
$541$	18.9497	+	2.06090i	0.814710	+	0.0886051i	0.308730	+	0.951150i	$0.400096\pi$
$542$	−2.26639	+	13.8243i	−0.0973496	+	0.593806i
$543$	−6.54237	+	3.93641i	−0.280760	+	0.168928i
$544$	0.214613	−	0.163145i	0.00920148	−	0.00699478i
$545$	−15.4313	−	38.7295i	−0.661002	−	1.65899i
$546$	8.79662	+	10.3562i	0.376460	+	0.443204i
$547$	5.16652	+	31.5144i	0.220904	+	1.34746i	0.831504	+	0.555518i	$0.187480\pi$
$547$	5.16652	+	31.5144i	0.220904	+	1.34746i	−0.610600	+	0.791939i	$0.709072\pi$
$548$	0.461950	+	8.52016i	0.0197335	+	0.363963i
$549$	10.5544	+	2.32319i	0.450450	+	0.0991515i
$550$	0.828393	−	0.784696i	0.0353228	−	0.0334595i
$551$	4.37456	−	1.47396i	0.186362	−	0.0627928i
$552$	−3.01173	+	7.55887i	−0.128188	+	0.321727i
$553$	−2.69579	−	9.70936i	−0.114637	−	0.412884i
$554$	−1.12364	+	0.247332i	−0.0477389	+	0.0105081i
$555$	−1.40541	+	2.07283i	−0.0596564	+	0.0879867i
$556$	1.53754	+	2.90010i	0.0652061	+	0.122992i
$557$	−2.44100	+	4.60421i	−0.103428	+	0.195087i	−0.929825	−	0.368002i	$-0.880042\pi$
$557$	−2.44100	+	4.60421i	−0.103428	+	0.195087i	0.826397	+	0.563088i	$0.190387\pi$
$558$	−1.61097	−	2.37600i	−0.0681977	−	0.100584i
$559$	−30.4518	−	28.8455i	−1.28797	−	1.22003i
$560$	6.86022	+	3.17388i	0.289897	+	0.134121i
$561$	−0.589128	−	0.272560i	−0.0248730	−	0.0115075i
$562$	9.71476	+	9.20231i	0.409792	+	0.388176i
$563$	−14.5987	−	21.5315i	−0.615263	−	0.907445i	0.384615	−	0.923077i	$-0.374334\pi$
$563$	−14.5987	−	21.5315i	−0.615263	−	0.907445i	−0.999878	+	0.0156323i	$0.995024\pi$
$564$	3.88316	−	7.32442i	0.163511	−	0.308414i
$565$	1.11570	+	2.10443i	0.0469377	+	0.0885339i
$566$	5.35142	−	7.89275i	0.224937	−	0.331757i
$567$	−3.46991	+	0.763785i	−0.145723	+	0.0320760i
$568$	0.728224	+	2.62283i	0.0305556	+	0.110051i
$569$	−13.2350	+	33.2174i	−0.554841	+	1.39255i	0.337560	+	0.941304i	$0.390398\pi$
$569$	−13.2350	+	33.2174i	−0.554841	+	1.39255i	−0.892401	+	0.451243i	$0.850981\pi$
$570$	4.32079	−	1.45585i	0.180978	−	0.0609786i
$571$	−31.0202	+	29.3839i	−1.29816	+	1.22968i	−0.341013	+	0.940059i	$0.610770\pi$
$571$	−31.0202	+	29.3839i	−1.29816	+	1.22968i	−0.957142	+	0.289619i	$0.906471\pi$
$572$	8.99331	+	1.97958i	0.376029	+	0.0827702i
$573$	−0.0611305	−	1.12749i	−0.00255376	−	0.0471014i
$574$	3.28032	+	20.0091i	0.136918	+	0.835162i
$575$	−2.49623	−	2.93879i	−0.104100	−	0.122556i
$576$	−0.370138	−	0.928977i	−0.0154224	−	0.0387074i
$577$	23.2645	−	17.6852i	0.968515	−	0.736246i	0.00392268	−	0.999992i	$-0.498751\pi$
$577$	23.2645	−	17.6852i	0.968515	−	0.736246i	0.964592	+	0.263747i	$0.0849583\pi$
$578$	−14.5043	+	8.72695i	−0.603299	+	0.362993i
$579$	−0.0755638	+	0.460919i	−0.00314033	+	0.0191551i
$580$	−4.55558	−	0.495449i	−0.189160	−	0.0205724i
$581$	42.9383	+	32.6408i	1.78138	+	1.35417i
$582$	−0.996116	+	3.58769i	−0.0412903	+	0.148714i
$583$	−0.0369882	+	0.682208i	−0.00153190	+	0.0282542i
$584$	11.0248	−	1.19902i	0.456209	−	0.0496158i
$585$	−6.97158	−	4.19466i	−0.288239	−	0.173428i
$586$	−3.58778	+	4.22386i	−0.148210	+	0.174486i
$587$	−39.6542	−	13.3610i	−1.63670	−	0.551469i	−0.657342	−	0.753592i	$-0.728319\pi$
$587$	−39.6542	−	13.3610i	−1.63670	−	0.551469i	−0.979360	+	0.202123i	$0.935216\pi$
$588$	−5.10389	+	2.36131i	−0.210481	+	0.0973789i
$589$	−6.15220			−0.253497
$590$	3.98460	+	15.8482i	0.164043	+	0.652458i
$591$	−17.4939			−0.719603
$592$	1.06836	−	0.494274i	0.0439091	−	0.0203145i
$593$	3.97684	+	1.33995i	0.163309	+	0.0550252i	0.399769	−	0.916616i	$-0.369090\pi$
$593$	3.97684	+	1.33995i	0.163309	+	0.0550252i	−0.236459	+	0.971641i	$0.575987\pi$
$594$	−1.55882	+	1.83519i	−0.0639594	+	0.0752988i
$595$	1.74605	+	1.05056i	0.0715812	+	0.0430690i
$596$	4.95093	−	0.538446i	0.202798	−	0.0220556i
$597$	−1.44302	+	26.6149i	−0.0590588	+	1.08928i
$598$	8.32495	−	29.9837i	0.340432	−	1.22613i
$599$	−15.5486	−	11.8198i	−0.635301	−	0.482943i	0.237262	−	0.971446i	$-0.423750\pi$
$599$	−15.5486	−	11.8198i	−0.635301	−	0.482943i	−0.872562	+	0.488503i	$0.837543\pi$
$600$	0.471102	+	0.0512355i	0.0192327	+	0.00209168i
$601$	6.34599	−	38.7088i	0.258858	−	1.57897i	−0.462637	−	0.886548i	$-0.653097\pi$
$601$	6.34599	−	38.7088i	0.258858	−	1.57897i	0.721496	−	0.692419i	$-0.243455\pi$
$602$	33.3903	−	20.0903i	1.36089	−	0.818819i
$603$	6.59655	−	5.01457i	0.268632	−	0.204209i
$604$	−8.07397	−	20.2641i	−0.328525	−	0.824536i
$605$	7.16487	+	8.43514i	0.291294	+	0.342937i
$606$	−0.615799	−	3.75621i	−0.0250151	−	0.152585i
$607$	0.292911	+	5.40242i	0.0118889	+	0.219277i	0.998440	+	0.0558272i	$0.0177796\pi$
$607$	0.292911	+	5.40242i	0.0118889	+	0.219277i	−0.986552	+	0.163450i	$0.947738\pi$
$608$	−2.09304	−	0.460712i	−0.0848839	−	0.0186844i
$609$	5.55597	−	5.26290i	0.225139	−	0.213263i
$610$	−21.7881	+	7.34126i	−0.882174	+	0.297239i
$611$	−11.7350	+	29.4527i	−0.474749	+	1.19153i
$612$	−0.0721212	−	0.259757i	−0.00291533	−	0.0105001i
$613$	−25.3194	+	5.57322i	−1.02264	+	0.225100i	−0.694472	−	0.719519i	$-0.744362\pi$
$613$	−25.3194	+	5.57322i	−1.02264	+	0.225100i	−0.328168	+	0.944620i	$0.606431\pi$
$614$	−9.83603	+	14.5071i	−0.396950	+	0.585457i
$615$	−5.68697	−	10.7268i	−0.229321	−	0.432545i
$616$	−4.00729	+	7.55856i	−0.161458	+	0.304543i
$617$	−18.9174	−	27.9011i	−0.761586	−	1.12326i	−0.988776	−	0.149405i	$-0.952264\pi$
$617$	−18.9174	−	27.9011i	−0.761586	−	1.12326i	0.227190	−	0.973850i	$-0.427046\pi$
$618$	3.99522	+	3.78447i	0.160711	+	0.152234i
$619$	−11.3617	−	5.25647i	−0.456664	−	0.211275i	0.178051	−	0.984021i	$-0.443021\pi$
$619$	−11.3617	−	5.25647i	−0.456664	−	0.211275i	−0.634716	+	0.772746i	$0.718883\pi$
$620$	5.54274	+	2.56435i	0.222602	+	0.102987i
$621$	5.90726	+	5.59565i	0.237050	+	0.224546i
$622$	0.851665	+	1.25611i	0.0341487	+	0.0503655i
$623$	14.3876	−	27.1379i	0.576428	−	1.08726i
$624$	1.79137	+	3.37887i	0.0717120	+	0.135263i
$625$	12.5740	−	18.5452i	0.502959	−	0.741809i
$626$	−11.8308	+	2.60417i	−0.472856	+	0.104083i
$627$	1.38056	+	4.97232i	0.0551342	+	0.198575i
$628$	−8.70557	+	21.8493i	−0.347390	+	0.871883i
$629$	0.300729	−	0.101327i	0.0119909	−	0.00404019i
$630$	5.48769	−	5.19822i	0.218635	−	0.207102i
$631$	0.373848	+	0.0822902i	0.0148827	+	0.00327592i	0.222406	−	0.974954i	$-0.428609\pi$
$631$	0.373848	+	0.0822902i	0.0148827	+	0.00327592i	−0.207523	+	0.978230i	$0.566540\pi$
$632$	−0.153544	−	2.83196i	−0.00610766	−	0.112649i
$633$	3.68529	+	22.4793i	0.146477	+	0.893472i
$634$	−16.3351	−	19.2312i	−0.648749	−	0.763767i
$635$	−1.79333	−	4.50091i	−0.0711660	−	0.178613i
$636$	−0.225883	+	0.171712i	−0.00895685	+	0.00680882i
$637$	18.4284	−	11.0880i	0.730159	−	0.439322i
$638$	0.839069	−	5.11810i	0.0332191	−	0.202627i
$639$	2.70609	+	0.294305i	0.107051	+	0.0116425i
$640$	1.69366	+	1.28749i	0.0669479	+	0.0508925i
$641$	5.76497	−	20.7636i	0.227703	−	0.820111i	−0.758091	−	0.652149i	$-0.773868\pi$
$641$	5.76497	−	20.7636i	0.227703	−	0.820111i	0.985793	−	0.167962i	$-0.0537186\pi$
$642$	0.879070	−	16.2135i	0.0346941	−	0.639895i
$643$	5.75730	−	0.626144i	0.227046	−	0.0246927i	0.00611116	−	0.999981i	$-0.498055\pi$
$643$	5.75730	−	0.626144i	0.227046	−	0.0246927i	0.220935	+	0.975289i	$0.429089\pi$
$644$	24.7715	+	14.9045i	0.976136	+	0.587321i
$645$	−15.1059	+	17.7840i	−0.594793	+	0.700245i
$646$	−0.547512	−	0.184478i	−0.0215416	−	0.00725820i
$647$	−40.8850	+	18.9154i	−1.60735	+	0.743641i	−0.998757	−	0.0498384i	$-0.984129\pi$
$647$	−40.8850	+	18.9154i	−1.60735	+	0.743641i	−0.608597	+	0.793480i	$0.708267\pi$
$648$	−1.00000			−0.0392837
$649$	−18.1548	+	3.53207i	−0.712640	+	0.138646i
$650$	−1.81229			−0.0710840
$651$	−9.25666	+	4.28259i	−0.362797	+	0.167848i
$652$	8.25274	+	2.78067i	0.323202	+	0.108900i
$653$	10.4532	−	12.3065i	0.409066	−	0.481590i	−0.518591	−	0.855022i	$-0.673543\pi$
$653$	10.4532	−	12.3065i	0.409066	−	0.481590i	0.927657	+	0.373433i	$0.121819\pi$
$654$	16.7912	+	10.1030i	0.656590	+	0.395057i
$655$	22.8118	−	2.48093i	0.891330	−	0.0969379i
$656$	−0.308960	+	5.69844i	−0.0120629	+	0.222487i
$657$	2.96684	−	10.6856i	0.115747	−	0.416884i
$658$	−23.4486	−	17.8252i	−0.914123	−	0.694898i
$659$	2.37957	+	0.258794i	0.0926948	+	0.0100812i	0.154349	−	0.988016i	$-0.450672\pi$
$659$	2.37957	+	0.258794i	0.0926948	+	0.0100812i	−0.0616540	+	0.998098i	$0.519638\pi$
$660$	0.828757	−	5.05519i	0.0322593	−	0.196773i
$661$	−14.6499	+	8.81456i	−0.569816	+	0.342847i	−0.771128	−	0.636680i	$-0.780307\pi$
$661$	−14.6499	+	8.81456i	−0.569816	+	0.342847i	0.201312	+	0.979527i	$0.435479\pi$
$662$	18.5593	−	14.1084i	0.721328	−	0.548339i
$663$	0.381607	+	0.957762i	0.0148204	+	0.0371964i
$664$	9.82769	+	11.5701i	0.381388	+	0.449005i
$665$	−2.62082	−	15.9863i	−0.101631	−	0.619922i
$666$	−0.0637298	−	1.17543i	−0.00246948	−	0.0455469i
$667$	−17.1164	−	3.76760i	−0.662748	−	0.145882i
$668$	−3.16659	+	2.99955i	−0.122519	+	0.116056i
$669$	24.3953	−	8.21972i	0.943176	−	0.317793i
$670$	−6.52499	+	16.3765i	−0.252082	+	0.632679i
$671$	−6.96162	−	25.0735i	−0.268750	−	0.967952i
$672$	−3.46991	+	0.763785i	−0.133855	+	0.0294637i
$673$	−22.5585	+	33.2713i	−0.869567	+	1.28251i	0.0885312	+	0.996073i	$0.471783\pi$
$673$	−22.5585	+	33.2713i	−0.869567	+	1.28251i	−0.958098	+	0.286441i	$0.907528\pi$
$674$	−2.69750	−	5.08803i	−0.103904	−	0.195983i
$675$	0.221970	−	0.418679i	0.00854361	−	0.0161150i
$676$	−0.912371	−	1.34565i	−0.0350912	−	0.0517556i
$677$	5.67230	+	5.37308i	0.218004	+	0.206504i	0.788906	−	0.614514i	$-0.210648\pi$
$677$	5.67230	+	5.37308i	0.218004	+	0.206504i	−0.570902	+	0.821018i	$0.693406\pi$
$678$	−1.01611	−	0.470103i	−0.0390235	−	0.0180542i
$679$	12.0065	+	5.55479i	0.460766	+	0.213173i
$680$	0.416380	+	0.394416i	0.0159675	+	0.0151252i
$681$	16.1036	+	23.7511i	0.617092	+	0.910143i
$682$	−3.23771	+	6.10696i	−0.123978	+	0.233848i
$683$	12.0339	+	22.6984i	0.460465	+	0.868530i	0.999653	+	0.0263442i	$0.00838660\pi$
$683$	12.0339	+	22.6984i	0.460465	+	0.868530i	−0.539187	+	0.842186i	$0.681269\pi$
$684$	−1.20270	+	1.77386i	−0.0459865	+	0.0678251i
$685$	−17.7286	+	3.90236i	−0.677374	+	0.149101i
$686$	−1.30824	−	4.71187i	−0.0499490	−	0.179900i
$687$	−6.15112	+	15.4381i	−0.234680	+	0.589002i
$688$	10.3937	−	3.50203i	0.396255	−	0.133514i
$689$	0.787796	−	0.746240i	0.0300126	−	0.0284295i
$690$	−16.9060	−	3.72129i	−0.643600	−	0.141667i
$691$	0.818140	+	15.0897i	0.0311235	+	0.574039i	0.971955	+	0.235165i	$0.0755632\pi$
$691$	0.818140	+	15.0897i	0.0311235	+	0.574039i	−0.940832	+	0.338874i	$0.889954\pi$
$692$	−3.20022	−	19.5205i	−0.121654	−	0.742058i
$693$	5.53847	+	6.52039i	0.210389	+	0.247689i
$694$	1.05490	+	2.64761i	0.0400436	+	0.100502i
$695$	−5.55940	+	4.22615i	−0.210880	+	0.160307i
$696$	1.84562	−	1.11047i	0.0699580	−	0.0420923i
$697$	−0.248895	+	1.51819i	−0.00942758	+	0.0575057i
$698$	−6.43348	−	0.699683i	−0.243511	−	0.0264834i
$699$	−13.1870	−	10.0245i	−0.498780	−	0.379163i
$700$	0.450434	−	1.62232i	0.0170248	−	0.0613178i
$701$	0.243460	−	4.49036i	0.00919536	−	0.169598i	−0.990328	−	0.138743i	$-0.955694\pi$
$701$	0.243460	−	4.49036i	0.00919536	−	0.169598i	0.999524	−	0.0308559i	$-0.00982330\pi$
$702$	3.80195	−	0.413487i	0.143495	−	0.0156061i
$703$	−2.16169	−	1.30064i	−0.0815296	−	0.0490547i
$704$	−1.55882	+	1.83519i	−0.0587504	+	0.0691663i
$705$	16.7137	+	5.63151i	0.629476	+	0.212095i
$706$	−6.87208	+	3.17936i	−0.258634	+	0.119657i
$707$	−13.5239			−0.508618
$708$	−5.99915	−	4.79689i	−0.225462	−	0.180278i
$709$	17.5093			0.657575			0.328788	−	0.944404i	$-0.393360\pi$
$709$	17.5093			0.657575			0.328788	+	0.944404i	$0.393360\pi$
$710$	−5.25583	+	2.43161i	−0.197248	+	0.0912565i
$711$	−2.68765	−	0.905576i	−0.100795	−	0.0339617i
$712$	5.59674	−	6.58899i	0.209747	−	0.246933i
$713$	20.0143	+	12.0422i	0.749540	+	0.450983i
$714$	−0.952209	+	0.103559i	−0.0356355	+	0.00387560i
$715$	−1.06064	+	19.5623i	−0.0396655	+	0.731587i
$716$	−5.39325	+	19.4247i	−0.201555	+	0.725937i
$717$	−9.36123	−	7.11622i	−0.349601	−	0.265760i
$718$	−17.9425	−	1.95137i	−0.669609	−	0.0728244i
$719$	2.53247	−	15.4474i	0.0944450	−	0.576089i	−0.896630	−	0.442781i	$-0.853992\pi$
$719$	2.53247	−	15.4474i	0.0944450	−	0.576089i	0.991075	−	0.133308i	$-0.0425599\pi$
$720$	1.82294	−	1.09682i	0.0679368	−	0.0408762i
$721$	15.5655	−	11.8326i	0.579690	−	0.440669i
$722$	−5.33256	−	13.3837i	−0.198457	−	0.498090i
$723$	−10.5063	−	12.3690i	−0.390734	−	0.460008i
$724$	1.23526	+	7.53473i	0.0459079	+	0.280026i
$725$	0.0552601	+	1.01921i	0.00205231	+	0.0378526i
$726$	−5.08052	−	1.11831i	−0.188556	−	0.0415042i
$727$	6.89888	−	6.53496i	0.255865	−	0.242368i	−0.549005	−	0.835819i	$-0.684993\pi$
$727$	6.89888	−	6.53496i	0.255865	−	0.242368i	0.804871	+	0.593450i	$0.202235\pi$
$728$	12.8766	−	4.33864i	0.477239	−	0.160801i
$729$	−0.370138	+	0.928977i	−0.0137088	+	0.0344065i
$730$	6.31185	+	22.7332i	0.233612	+	0.841395i
$731$	2.88761	−	0.635611i	0.106802	−	0.0235089i
$732$	6.06477	−	8.94487i	0.224160	−	0.330612i
$733$	−13.2245	−	24.9440i	−0.488456	−	0.921326i	−0.998140	−	0.0609644i	$-0.980582\pi$
$733$	−13.2245	−	24.9440i	−0.488456	−	0.921326i	0.509684	−	0.860362i	$-0.329762\pi$
$734$	−6.41696	+	12.1037i	−0.236854	+	0.446755i
$735$	−6.71413	−	9.90260i	−0.247654	−	0.365263i
$736$	5.90726	+	5.59565i	0.217744	+	0.206258i
$737$	−18.1080	−	8.37764i	−0.667016	−	0.308594i
$738$	5.17936	+	2.39623i	0.190655	+	0.0882063i
$739$	−18.9924	−	17.9905i	−0.698646	−	0.661793i	0.253535	−	0.967326i	$-0.418407\pi$
$739$	−18.9924	−	17.9905i	−0.698646	−	0.661793i	−0.952181	+	0.305533i	$0.901165\pi$
$740$	1.40541	+	2.07283i	0.0516640	+	0.0761987i
$741$	3.83915	−	7.24141i	0.141035	−	0.266020i
$742$	0.472212	+	0.890687i	0.0173355	+	0.0326982i
$743$	26.8290	−	39.5699i	0.984261	−	1.45168i	0.0943525	−	0.995539i	$-0.469922\pi$
$743$	26.8290	−	39.5699i	0.984261	−	1.45168i	0.889909	−	0.456138i	$-0.150768\pi$
$744$	−2.80353	+	0.617103i	−0.102782	+	0.0226241i
$745$	2.83448	+	10.2089i	0.103847	+	0.374024i
$746$	−0.102307	+	0.256772i	−0.00374573	+	0.00940108i
$747$	14.3859	−	4.84718i	0.526353	−	0.177349i
$748$	−0.471260	+	0.446402i	−0.0172310	+	0.0163221i
$749$	−56.3420	−	12.4018i	−2.05869	−	0.453152i
$750$	0.630475	+	11.6284i	0.0230217	+	0.424610i
$751$	−2.41398	−	14.7247i	−0.0880876	−	0.537310i	−0.993597	−	0.112984i	$-0.963959\pi$
$751$	−2.41398	−	14.7247i	−0.0880876	−	0.537310i	0.905509	−	0.424326i	$-0.139489\pi$
$752$	−5.36691	−	6.31842i	−0.195711	−	0.230409i
$753$	−6.39346	−	16.0464i	−0.232991	−	0.584762i
$754$	−6.55779	+	4.98510i	−0.238820	+	0.181547i
$755$	39.7644	−	23.9255i	1.44718	−	0.870737i
$756$	−0.574808	+	3.50617i	−0.0209056	+	0.127518i
$757$	36.2708	+	3.94468i	1.31828	+	0.143372i	0.740079	−	0.672520i	$-0.234788\pi$
$757$	36.2708	+	3.94468i	1.31828	+	0.143372i	0.578204	+	0.815892i	$0.303754\pi$
$758$	20.6175	+	15.6730i	0.748861	+	0.569269i
$759$	5.24150	−	18.8782i	0.190254	−	0.685234i
$760$	0.246845	−	4.55278i	0.00895400	−	0.165147i
$761$	27.3701	−	2.97668i	0.992165	−	0.107904i	0.402387	−	0.915470i	$-0.368181\pi$
$761$	27.3701	−	2.97668i	0.992165	−	0.107904i	0.589778	+	0.807565i	$0.299215\pi$
$762$	1.95138	+	1.17410i	0.0706909	+	0.0425333i
$763$	45.0745	−	53.0658i	1.63180	−	1.92111i
$764$	−1.07003	−	0.360537i	−0.0387125	−	0.0130438i
$765$	0.520522	−	0.240819i	0.0188195	−	0.00870683i
$766$	−14.2460			−0.514728
$767$	24.7919	+	15.7570i	0.895184	+	0.568951i
$768$	−1.00000			−0.0360844
$769$	44.7491	−	20.7031i	1.61369	−	0.746574i	0.614587	−	0.788849i	$-0.289323\pi$
$769$	44.7491	−	20.7031i	1.61369	−	0.746574i	0.999106	+	0.0422757i	$0.0134608\pi$
$770$	−17.2480	−	5.81153i	−0.621575	−	0.209433i
$771$	−2.60597	+	3.06799i	−0.0938518	+	0.110491i
$772$	0.400214	+	0.240801i	0.0144040	+	0.00866661i
$773$	−21.2756	+	2.31386i	−0.765231	+	0.0832239i	−0.482406	−	0.875948i	$-0.660237\pi$
$773$	−21.2756	+	2.31386i	−0.765231	+	0.0832239i	−0.282825	+	0.959172i	$0.591272\pi$
$774$	0.593785	−	10.9517i	0.0213431	−	0.393651i
$775$	0.363930	−	1.31076i	0.0130727	−	0.0470838i
$776$	2.96418	+	2.25331i	0.106408	+	0.0808891i
$777$	−4.15788	−	0.452197i	−0.149163	−	0.0162225i
$778$	1.03544	−	6.31593i	0.0371225	−	0.226437i
$779$	10.4798	−	6.30549i	0.375478	−	0.225917i
$780$	−6.47719	+	4.92383i	−0.231921	+	0.176301i
$781$	−2.42601	−	6.08883i	−0.0868096	−	0.217876i
$782$	1.42007	+	1.67183i	0.0507815	+	0.0597846i
$783$	−0.348469	−	2.12557i	−0.0124533	−	0.0759615i
$784$	0.304459	+	5.61541i	0.0108735	+	0.200550i
$785$	−48.8677	−	10.7566i	−1.74416	−	0.383920i
$786$	−7.83039	+	7.41734i	−0.279301	+	0.264568i
$787$	−23.8830	+	8.04713i	−0.851338	+	0.286849i	−0.710946	−	0.703247i	$-0.751733\pi$
$787$	−23.8830	+	8.04713i	−0.851338	+	0.286849i	−0.140392	+	0.990096i	$0.544836\pi$
$788$	−6.47516	+	16.2514i	−0.230668	+	0.578933i
$789$	−2.00201	−	7.21058i	−0.0712734	−	0.256704i
$790$	5.89268	−	1.29708i	0.209652	−	0.0461479i
$791$	−2.23233	+	3.29244i	−0.0793726	+	0.117066i
$792$	1.12787	+	2.12739i	0.0400771	+	0.0755934i
$793$	−19.3594	+	36.5156i	−0.687471	+	1.29671i
$794$	−19.8391	−	29.2605i	−0.704063	−	1.03842i
$795$	−0.438245	−	0.415128i	−0.0155430	−	0.0147231i
$796$	24.1905	+	11.1917i	0.857410	+	0.396680i
$797$	−16.1857	−	7.48829i	−0.573326	−	0.265249i	0.111731	−	0.993739i	$-0.464361\pi$
$797$	−16.1857	−	7.48829i	−0.573326	−	0.265249i	−0.685057	+	0.728490i	$0.740223\pi$
$798$	5.52812	+	5.23652i	0.195693	+	0.185371i
$799$	−1.25419	−	1.84979i	−0.0443699	−	0.0654407i
$800$	0.221970	−	0.418679i	0.00784781	−	0.0148025i
$801$	−4.04945	−	7.63808i	−0.143080	−	0.269878i
$802$	13.2174	−	19.4942i	0.466723	−	0.688365i
$803$	−26.0786	+	5.74033i	−0.920293	+	0.202572i
$804$	−2.21678	−	7.98413i	−0.0781799	−	0.281578i
$805$	−22.7652	+	57.1363i	−0.802368	+	2.01379i
$806$	10.4037	−	3.50542i	0.366455	−	0.123473i
$807$	11.4816	−	10.8759i	0.404171	−	0.382851i
$808$	−3.71736	−	0.818253i	−0.130776	−	0.0287860i
$809$	−0.314158	−	5.79431i	−0.0110452	−	0.203717i	−0.998847	−	0.0480020i	$-0.984715\pi$
$809$	−0.314158	−	5.79431i	−0.0110452	−	0.203717i	0.987802	−	0.155715i	$-0.0497681\pi$
$810$	−0.344186	−	2.09944i	−0.0120935	−	0.0737669i
$811$	−11.1841	−	13.1669i	−0.392725	−	0.462352i	0.529894	−	0.848064i	$-0.322232\pi$
$811$	−11.1841	−	13.1669i	−0.392725	−	0.462352i	−0.922619	+	0.385712i	$0.873956\pi$
$812$	−2.83263	−	7.10937i	−0.0994059	−	0.249490i
$813$	11.1524	−	8.47782i	0.391131	−	0.297330i
$814$	−2.42871	+	1.46131i	−0.0851262	+	0.0512187i
$815$	−2.99738	+	18.2832i	−0.104994	+	0.640433i
$816$	−0.268003	−	0.0291471i	−0.00938199	−	0.00102035i
$817$	−18.7126	−	14.2250i	−0.654671	−	0.497668i
$818$	3.38091	−	12.1769i	0.118211	−	0.425756i
$819$	0.735634	−	13.5680i	0.0257051	−	0.474103i
$820$	−12.0699	+	1.31268i	−0.421499	+	0.0458407i
$821$	−7.84938	−	4.72281i	−0.273945	−	0.164827i	0.371952	−	0.928252i	$-0.378689\pi$
$821$	−7.84938	−	4.72281i	−0.273945	−	0.164827i	−0.645897	+	0.763425i	$0.723516\pi$
$822$	5.52394	−	6.50328i	0.192669	−	0.226828i
$823$	−24.8826	−	8.38392i	−0.867352	−	0.292245i	−0.149772	−	0.988721i	$-0.547854\pi$
$823$	−24.8826	−	8.38392i	−0.867352	−	0.292245i	−0.717581	+	0.696476i	$0.754750\pi$
$824$	4.99447	−	2.31069i	0.173991	−	0.0804967i
$825$	−1.14104			−0.0397261
$826$	−20.2671	+	18.2768i	−0.705182	+	0.635930i
$827$	−5.26024			−0.182916			−0.0914582	−	0.995809i	$-0.529153\pi$
$827$	−5.26024			−0.182916			−0.0914582	+	0.995809i	$0.529153\pi$
$828$	7.38473	−	3.41654i	0.256637	−	0.118733i
$829$	−18.2294	−	6.14219i	−0.633132	−	0.213327i	−0.0156068	−	0.999878i	$-0.504968\pi$
$829$	−18.2294	−	6.14219i	−0.633132	−	0.213327i	−0.617525	+	0.786551i	$0.711865\pi$
$830$	−20.9081	+	24.6149i	−0.725731	+	0.854396i
$831$	0.985849	+	0.593165i	0.0341987	+	0.0205767i
$832$	3.80195	−	0.413487i	0.131809	−	0.0143351i
$833$	−0.0820770	+	1.51382i	−0.00284380	+	0.0524508i
$834$	0.878155	−	3.16283i	0.0304080	−	0.109520i
$835$	−7.38728	−	5.61567i	−0.255647	−	0.194338i
$836$	5.13017	+	0.557939i	0.177431	+	0.0192967i
$837$	−0.464418	+	2.83283i	−0.0160526	+	0.0979168i
$838$	23.6628	−	14.2374i	0.817417	−	0.491824i
$839$	32.6791	−	24.8420i	1.12821	−	0.857641i	0.137080	−	0.990560i	$-0.456228\pi$
$839$	32.6791	−	24.8420i	1.12821	−	0.857641i	0.991127	+	0.132919i	$0.0424352\pi$
$840$	−2.79782	−	7.02199i	−0.0965339	−	0.242282i
$841$	−15.7707	−	18.5667i	−0.543817	−	0.640230i
$842$	−3.24331	−	19.7833i	−0.111772	−	0.681778i
$843$	−0.724448	−	13.3617i	−0.0249513	−	0.460200i
$844$	22.2468	+	4.89689i	0.765767	+	0.168558i
$845$	2.51108	−	2.37862i	0.0863838	−	0.0818271i
$846$	−7.85616	+	2.64705i	−0.270100	+	0.0910074i
$847$	−6.84130	+	17.1704i	−0.235070	+	0.589981i
$848$	0.0759084	+	0.273397i	0.00260671	+	0.00938851i
$849$	−9.31294	+	2.04993i	−0.319619	+	0.0703536i
$850$	0.0716918	−	0.105737i	0.00245901	−	0.00362677i
$851$	4.48652	+	8.46248i	0.153796	+	0.290090i
$852$	1.27503	−	2.40496i	0.0436818	−	0.0823926i
$853$	−10.5192	−	15.5147i	−0.360171	−	0.531213i	0.603829	−	0.797114i	$-0.293641\pi$
$853$	−10.5192	−	15.5147i	−0.360171	−	0.531213i	−0.964000	+	0.265901i	$0.914331\pi$
$854$	−27.8762	−	26.4057i	−0.953903	−	0.903585i
$855$	−4.13806	−	1.91447i	−0.141519	−	0.0654735i
$856$	−14.7366	−	6.81787i	−0.503686	−	0.233030i
$857$	2.88177	+	2.72976i	0.0984395	+	0.0932468i	0.735337	−	0.677702i	$-0.237024\pi$
$857$	2.88177	+	2.72976i	0.0984395	+	0.0932468i	−0.636897	+	0.770949i	$0.719783\pi$
$858$	−5.16775	−	7.62185i	−0.176424	−	0.260206i
$859$	23.1548	−	43.6746i	0.790031	−	1.49016i	−0.0798024	−	0.996811i	$-0.525429\pi$
$859$	23.1548	−	43.6746i	0.790031	−	1.49016i	0.869833	−	0.493346i	$-0.164226\pi$
$860$	10.9297	+	20.6155i	0.372699	+	0.702984i
$861$	11.3787	−	16.7824i	0.387786	−	0.571942i
$862$	33.6048	−	7.39698i	1.14459	−	0.251942i
$863$	12.3282	+	44.4021i	0.419657	+	1.51147i	0.807571	+	0.589771i	$0.200782\pi$
$863$	12.3282	+	44.4021i	0.419657	+	1.51147i	−0.387914	+	0.921696i	$0.626804\pi$
$864$	−0.370138	+	0.928977i	−0.0125924	+	0.0316044i
$865$	39.8807	−	13.4374i	1.35598	−	0.456884i
$866$	−6.42581	+	6.08685i	−0.218358	+	0.206839i
$867$	16.5316	+	3.63887i	0.561442	+	0.123583i
$868$	0.552181	+	10.1844i	0.0187422	+	0.345680i
$869$	1.10481	+	6.73905i	0.0374781	+	0.228606i
$870$	2.96661	+	3.49256i	0.100577	+	0.118409i
$871$	11.7294	+	29.4386i	0.397436	+	0.997490i
$872$	15.6005	−	11.8592i	0.528299	−	0.401603i
$873$	3.19043	−	1.91962i	0.107980	−	0.0649691i
$874$	2.82120	−	17.2085i	0.0954284	−	0.582087i
$875$	41.1337	+	4.47356i	1.39057	+	0.151234i
$876$	−8.82852	−	6.71127i	−0.298288	−	0.226753i
$877$	−14.6234	+	52.6686i	−0.493796	+	1.77849i	0.124140	+	0.992265i	$0.460383\pi$
$877$	−14.6234	+	52.6686i	−0.493796	+	1.77849i	−0.617936	+	0.786228i	$0.712031\pi$
$878$	2.05726	−	37.9440i	0.0694293	−	1.28055i
$879$	5.50946	−	0.599189i	0.185829	−	0.0202102i
$880$	−4.38940	−	2.64102i	−0.147967	−	0.0890286i
$881$	−9.85060	+	11.5970i	−0.331875	+	0.390713i	−0.902637	−	0.430402i	$-0.858372\pi$
$881$	−9.85060	+	11.5970i	−0.331875	+	0.390713i	0.570762	+	0.821115i	$0.306648\pi$
$882$	5.32928	+	1.79564i	0.179446	+	0.0604624i
$883$	−19.6538	+	9.09283i	−0.661404	+	0.305998i	−0.721724	−	0.692181i	$-0.756650\pi$
$883$	−19.6538	+	9.09283i	−0.661404	+	0.305998i	0.0603198	+	0.998179i	$0.480788\pi$
$884$	1.03099			0.0346758
$885$	8.00597	−	14.2459i	0.269118	−	0.478870i
$886$	−2.87036			−0.0964315
$887$	17.4724	−	8.08360i	0.586666	−	0.271421i	−0.104020	−	0.994575i	$-0.533171\pi$
$887$	17.4724	−	8.08360i	0.586666	−	0.271421i	0.690686	+	0.723154i	$0.257309\pi$
$888$	−1.11553	−	0.375867i	−0.0374348	−	0.0126133i
$889$	5.23828	−	6.16698i	0.175686	−	0.206834i
$890$	15.7595	+	9.48219i	0.528261	+	0.317844i
$891$	2.39376	−	0.260337i	0.0801940	−	0.00872162i
$892$	1.39369	−	25.7051i	0.0466641	−	0.860669i
$893$	−4.75315	+	17.1193i	−0.159058	+	0.572876i
$894$	−3.96464	−	3.01384i	−0.132598	−	0.100798i
$895$	−42.6374	−	4.63710i	−1.42521	−	0.155001i
$896$	−0.574808	+	3.50617i	−0.0192030	+	0.117133i
$897$	−26.6637	+	16.0430i	−0.890274	+	0.535660i
$898$	7.46119	−	5.67185i	0.248983	−	0.189272i
$899$	−2.28864	−	5.74404i	−0.0763303	−	0.191575i
$900$	−0.306784	−	0.361174i	−0.0102261	−	0.0120391i
$901$	0.0123750	+	0.0754839i	0.000412269	+	0.00251473i
$902$	−0.743938	−	13.7211i	−0.0247704	−	0.456864i
$903$	−38.0573	−	8.37704i	−1.26647	−	0.278771i
$904$	−0.812816	+	0.769940i	−0.0270339	+	0.0256078i
$905$	−15.3936	+	5.18670i	−0.511699	+	0.172412i
$906$	−8.07397	+	20.2641i	−0.268240	+	0.673231i
$907$	−8.29439	−	29.8737i	−0.275411	−	0.991939i	−0.963806	−	0.266604i	$-0.914098\pi$
$907$	−8.29439	−	29.8737i	−0.275411	−	0.991939i	0.688396	−	0.725336i	$-0.258315\pi$
$908$	28.0248	−	6.16872i	0.930034	−	0.204716i
$909$	−2.13607	+	3.15047i	−0.0708491	+	0.104495i
$910$	13.5407	+	25.5404i	0.448869	+	0.846656i
$911$	−8.40720	+	15.8577i	−0.278543	+	0.525388i	−0.982827	−	0.184531i	$-0.940923\pi$
$911$	−8.40720	+	15.8577i	−0.278543	+	0.525388i	0.704284	+	0.709919i	$0.251268\pi$
$912$	1.20270	+	1.77386i	0.0398255	+	0.0587382i
$913$	−26.5372	−	25.1374i	−0.878255	−	0.831927i
$914$	34.5417	+	15.9807i	1.14254	+	0.528594i
$915$	20.8666	+	9.65394i	0.689830	+	0.319149i
$916$	12.0649	+	11.4285i	0.398636	+	0.377608i
$917$	21.5055	+	31.7182i	0.710174	+	1.04743i
$918$	−0.126275	+	0.238180i	−0.00416770	+	0.00786112i
$919$	−1.03226	−	1.94705i	−0.0340511	−	0.0642272i	0.865903	−	0.500212i	$-0.166745\pi$
$919$	−1.03226	−	1.94705i	−0.0340511	−	0.0642272i	−0.899954	+	0.435985i	$0.856400\pi$
$920$	−9.71455	+	14.3279i	−0.320279	+	0.472377i
$921$	17.1174	−	3.76783i	0.564038	−	0.124154i
$922$	9.60902	+	34.6086i	0.316456	+	1.13977i
$923$	−3.85318	+	9.67074i	−0.126829	+	0.318316i
$924$	8.10729	−	2.73167i	0.266710	−	0.0898652i
$925$	0.404982	−	0.383619i	0.0133157	−	0.0126133i
$926$	−7.31168	−	1.60942i	−0.240277	−	0.0528889i
$927$	−0.297931	−	5.49502i	−0.00978535	−	0.180480i
$928$	−0.348469	−	2.12557i	−0.0114390	−	0.0697751i
$929$	14.9954	+	17.6540i	0.491984	+	0.579209i	0.950989	−	0.309225i	$-0.100070\pi$
$929$	14.9954	+	17.6540i	0.491984	+	0.579209i	−0.459005	+	0.888434i	$0.651794\pi$
$930$	−2.26051	−	5.67345i	−0.0741250	−	0.186040i
$931$	9.59475	−	7.29374i	0.314455	−	0.239043i
$932$	−14.1936	+	8.54000i	−0.464926	+	0.279737i
$933$	0.245523	−	1.49762i	0.00803805	−	0.0490299i
$934$	33.8890	+	3.68565i	1.10888	+	0.120598i
$935$	−1.09940	−	0.835739i	−0.0359541	−	0.0273316i
$936$	1.02313	−	3.68497i	0.0334419	−	0.120447i
$937$	−1.75267	+	32.3261i	−0.0572572	+	1.05605i	0.818874	+	0.573974i	$0.194599\pi$
$937$	−1.75267	+	32.3261i	−0.0572572	+	1.05605i	−0.876131	+	0.482073i	$0.839884\pi$
$938$	−29.2680	+	3.18308i	−0.955633	+	0.103931i
$939$	10.3800	+	6.24545i	0.338739	+	0.203813i
$940$	11.4179	−	13.4422i	0.372412	−	0.438437i
$941$	22.2661	+	7.50234i	0.725856	+	0.244569i	0.657885	−	0.753118i	$-0.271451\pi$
$941$	22.2661	+	7.50234i	0.725856	+	0.244569i	0.0679703	+	0.997687i	$0.478348\pi$
$942$	21.3460	−	9.87570i	0.695489	−	0.321768i
$943$	−46.4350			−1.51213
$944$	−6.67672	+	3.79756i	−0.217309	+	0.123600i
$945$	−7.55885			−0.245889
$946$	−23.9682	+	11.0889i	−0.779274	+	0.360531i
$947$	23.7500	+	8.00230i	0.771771	+	0.260040i	0.677516	−	0.735508i	$-0.263057\pi$
$947$	23.7500	+	8.00230i	0.771771	+	0.260040i	0.0942550	+	0.995548i	$0.469953\pi$
$948$	−1.83606	+	2.16158i	−0.0596325	+	0.0702048i
$949$	36.3406	+	21.8654i	1.17967	+	0.709781i
$950$	−1.00964	+	0.109805i	−0.0327570	+	0.00356254i
$951$	−1.36605	+	25.1954i	−0.0442973	+	0.817016i
$952$	−0.256245	+	0.922911i	−0.00830495	+	0.0299117i
$953$	27.5353	+	20.9318i	0.891955	+	0.678047i	0.947275	−	0.320422i	$-0.103825\pi$
$953$	27.5353	+	20.9318i	0.891955	+	0.678047i	−0.0553195	+	0.998469i	$0.517618\pi$
$954$	0.282076	+	0.0306777i	0.00913256	+	0.000993226i
$955$	0.388635	−	2.37057i	0.0125759	−	0.0767097i
$956$	−10.0758	+	6.06238i	−0.325873	+	0.196071i
$957$	−4.12887	+	3.13869i	−0.133467	+	0.101459i
$958$	8.14423	+	20.4405i	0.263128	+	0.660402i
$959$	−19.6264	−	23.1060i	−0.633771	−	0.746132i
$960$	−0.344186	−	2.09944i	−0.0111086	−	0.0677592i
$961$	−1.23217	−	22.7260i	−0.0397474	−	0.733098i
$962$	4.39662	+	0.967769i	0.141753	+	0.0312021i
$963$	−11.7882	+	11.1664i	−0.379870	+	0.359832i
$964$	−15.3793	+	5.18189i	−0.495334	+	0.166897i
$965$	−0.367799	+	0.923106i	−0.0118399	+	0.0297158i
$966$	−7.73418	−	27.8560i	−0.248843	−	0.896252i
$967$	34.7022	−	7.63853i	1.11595	−	0.245638i	0.381543	−	0.924351i	$-0.375393\pi$
$967$	34.7022	−	7.63853i	1.11595	−	0.245638i	0.734404	+	0.678713i	$0.237462\pi$
$968$	−2.91937	+	4.30575i	−0.0938322	+	0.138392i
$969$	0.270626	+	0.510454i	0.00869375	+	0.0163982i
$970$	−3.71046	+	6.99867i	−0.119136	+	0.224714i
$971$	−21.6454	−	31.9246i	−0.694634	−	1.02451i	−0.997444	−	0.0714576i	$-0.977235\pi$
$971$	−21.6454	−	31.9246i	−0.694634	−	1.02451i	0.302810	−	0.953051i	$-0.402075\pi$
$972$	0.725995	+	0.687699i	0.0232863	+	0.0220580i
$973$	−10.5847	−	4.89698i	−0.339328	−	0.156990i
$974$	12.1924	+	5.64079i	0.390669	+	0.180743i
$975$	1.31572	+	1.24631i	0.0421366	+	0.0399139i
$976$	−6.06477	−	8.94487i	−0.194129	−	0.286318i
$977$	14.7071	−	27.7406i	0.470522	−	0.887499i	−0.528728	−	0.848791i	$-0.677331\pi$
$977$	14.7071	−	27.7406i	0.470522	−	0.887499i	0.999251	−	0.0387082i	$-0.0123243\pi$
$978$	−4.07919	−	7.69416i	−0.130438	−	0.246032i
$979$	−11.6819	+	17.2295i	−0.373355	+	0.550657i
$980$	−11.6844	+	2.57194i	−0.373246	+	0.0821576i
$981$	−5.24257	−	18.8820i	−0.167382	−	0.602857i
$982$	5.51494	−	13.8415i	0.175989	−	0.441699i
$983$	37.4410	−	12.6154i	1.19418	−	0.402367i	0.349143	−	0.937069i	$-0.386473\pi$
$983$	37.4410	−	12.6154i	1.19418	−	0.402367i	0.845041	+	0.534702i	$0.179576\pi$
$984$	4.14312	−	3.92457i	0.132078	−	0.125111i
$985$	−36.3476	−	8.00071i	−1.15813	−	0.254924i
$986$	−0.0314367	−	0.579815i	−0.00100115	−	0.0184651i
$987$	4.76523	+	29.0666i	0.151679	+	0.925200i
$988$	−5.30609	−	6.24681i	−0.168809	−	0.198737i
$989$	33.0320	+	82.9041i	1.05036	+	2.63620i
$990$	−4.07813	+	3.10011i	−0.129611	+	0.0985280i
$991$	21.9803	−	13.2251i	0.698227	−	0.420109i	−0.121708	−	0.992566i	$-0.538837\pi$
$991$	21.9803	−	13.2251i	0.698227	−	0.420109i	0.819935	+	0.572457i	$0.194009\pi$
$992$	−0.464418	+	2.83283i	−0.0147453	+	0.0899423i
$993$	−23.1763	−	2.52058i	−0.735478	−	0.0799881i
$994$	−7.69931	−	5.85286i	−0.244207	−	0.185642i
$995$	−15.1703	+	54.6386i	−0.480932	+	1.73216i
$996$	0.821859	−	15.1583i	0.0260416	−	0.480309i
$997$	16.4687	−	1.79108i	0.521570	−	0.0567241i	0.156452	−	0.987686i	$-0.449994\pi$
$997$	16.4687	−	1.79108i	0.521570	−	0.0567241i	0.365118	+	0.930961i	$0.381029\pi$
$998$	−25.7564	−	15.4971i	−0.815303	−	0.490552i
$999$	−0.762073	+	0.897182i	−0.0241109	+	0.0283856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.121.2	yes	56
59.20	even	29	inner	354.2.e.b.79.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.79.2	✓	56	59.20	even	29	inner
354.2.e.b.121.2	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(1.82294 + 1.09682i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(-0.192354 + 3.54777i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})\)	\(q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(1.82294 + 1.09682i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(-0.192354 + 3.54777i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(-2.11500 - 0.230020i) q^{10} +(0.389551 - 2.37615i) q^{11} +(0.856857 - 0.515554i) q^{12} +(-3.04455 + 2.31441i) q^{13} +(-1.31509 - 3.30063i) q^{14} +(1.37729 + 1.62148i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(-0.0145950 - 0.269188i) q^{17} +(-0.976621 - 0.214970i) q^{18} +(-1.55591 + 1.47384i) q^{19} +(2.01610 - 0.679304i) q^{20} +(-1.31509 + 3.30063i) q^{21} +(0.644175 + 2.32011i) q^{22} +(7.94654 - 1.74916i) q^{23} +(-0.561187 + 0.827689i) q^{24} +(-0.221970 - 0.418679i) q^{25} +(1.79137 - 3.37887i) q^{26} +(0.561187 + 0.827689i) q^{27} +(2.57945 + 2.44338i) q^{28} +(-1.95486 - 0.904416i) q^{29} +(-1.93084 - 0.893301i) q^{30} +(2.08407 + 1.97414i) q^{31} +(0.561187 + 0.827689i) q^{32} +(1.12787 - 2.12739i) q^{33} +(0.126275 + 0.238180i) q^{34} +(-4.24193 + 6.25638i) q^{35} +(0.976621 - 0.214970i) q^{36} +(0.314922 + 1.13425i) q^{37} +(0.793259 - 1.99093i) q^{38} +(-3.62417 + 1.22113i) q^{39} +(-1.54453 + 1.46306i) q^{40} +(-5.57339 - 1.22680i) q^{41} +(-0.192354 - 3.54777i) q^{42} +(1.77439 + 10.8233i) q^{43} +(-1.55882 - 1.83519i) q^{44} +(0.787457 + 1.97637i) q^{45} +(-6.47763 + 4.92416i) q^{46} +(7.10345 - 4.27401i) q^{47} +(0.161782 - 0.986827i) q^{48} +(-5.59069 - 0.608024i) q^{49} +(0.377253 + 0.286780i) q^{50} +(0.0721212 - 0.259757i) q^{51} +(-0.207047 + 3.81876i) q^{52} +(-0.282076 + 0.0306777i) q^{53} +(-0.856857 - 0.515554i) q^{54} +(3.31635 - 3.90431i) q^{55} +(-3.36699 - 1.13447i) q^{56} +(-1.94506 + 0.899882i) q^{57} +2.15394 q^{58} +(-2.66736 - 7.20314i) q^{59} +2.12747 q^{60} +(9.80821 - 4.53776i) q^{61} +(-2.72037 - 0.916600i) q^{62} +(-2.30015 + 2.70795i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(-8.08852 + 0.879680i) q^{65} +(-0.130360 + 2.40434i) q^{66} +(2.21678 - 7.98413i) q^{67} +(-0.214613 - 0.163145i) q^{68} +(8.08907 + 0.879740i) q^{69} +(1.22289 - 7.45927i) q^{70} +(2.33240 - 1.40336i) q^{71} +(-0.796093 + 0.605174i) q^{72} +(-4.10476 - 10.3022i) q^{73} +(-0.762073 - 0.897182i) q^{74} +(-0.0766653 - 0.467638i) q^{75} +(0.116027 + 2.14000i) q^{76} +(8.35511 + 1.83910i) q^{77} +(2.77647 - 2.63002i) q^{78} +(-2.68765 + 0.905576i) q^{79} +(0.787457 - 1.97637i) q^{80} +(0.267528 + 0.963550i) q^{81} +(5.57339 - 1.22680i) q^{82} +(8.51914 - 12.5648i) q^{83} +(1.66425 + 3.13910i) q^{84} +(0.268646 - 0.506721i) q^{85} +(-6.15499 - 9.07792i) q^{86} +(-1.56375 - 1.48126i) q^{87} +(2.18533 + 1.01104i) q^{88} +(-7.84611 - 3.63000i) q^{89} +(-1.54453 - 1.46306i) q^{90} +(-7.62535 - 11.2466i) q^{91} +(3.81133 - 7.18893i) q^{92} +(1.34463 + 2.53625i) q^{93} +(-4.65231 + 6.86164i) q^{94} +(-4.45287 + 0.980151i) q^{95} +(0.267528 + 0.963550i) q^{96} +(1.37817 - 3.45896i) q^{97} +(5.32928 - 1.79564i) q^{98} +(1.74811 - 1.65589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

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