LMFDB - Embedded newform 722.2.i.b.505.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			505.5
Character	$\chi$	$=$	722.505
Dual form			722.2.i.b.539.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.851919 - 0.523673i) q^{2} +(-0.600076 + 1.60273i) q^{3} +(0.451533 - 0.892254i) q^{4} +(2.07470 + 2.82274i) q^{5} +(0.328091 + 1.67964i) q^{6} +(-0.525734 + 0.804696i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(0.0536627 + 0.0467349i) q^{9} +O(q^{10})$	\(q+(0.851919 - 0.523673i) q^{2} +(-0.600076 + 1.60273i) q^{3} +(0.451533 - 0.892254i) q^{4} +(2.07470 + 2.82274i) q^{5} +(0.328091 + 1.67964i) q^{6} +(-0.525734 + 0.804696i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(0.0536627 + 0.0467349i) q^{9} +(3.24567 + 1.31828i) q^{10} +(2.51184 + 0.862315i) q^{11} +(1.15909 + 1.25911i) q^{12} +(-1.54581 - 1.87697i) q^{13} +(-0.0264856 + 0.960849i) q^{14} +(-5.76907 + 1.63134i) q^{15} +(-0.592235 - 0.805765i) q^{16} +(-0.259182 - 0.512158i) q^{17} +(0.0701901 + 0.0117127i) q^{18} +(-2.57658 + 3.51585i) q^{19} +(3.45540 - 0.576604i) q^{20} +(-0.974232 - 1.32549i) q^{21} +(2.59145 - 0.580758i) q^{22} +(-1.63959 - 4.37915i) q^{23} +(1.64681 + 0.465674i) q^{24} +(-2.17087 + 6.94066i) q^{25} +(-2.29983 - 0.789532i) q^{26} +(-4.62246 + 2.50155i) q^{27} +(0.480607 + 0.832436i) q^{28} +(1.21904 + 0.0672562i) q^{29} +(-4.06049 + 4.41087i) q^{30} +(4.00606 - 2.16797i) q^{31} +(-0.926494 - 0.376309i) q^{32} +(-2.88935 + 3.50835i) q^{33} +(-0.489006 - 0.300591i) q^{34} +(-3.36219 + 0.185497i) q^{35} +(0.0659299 - 0.0267784i) q^{36} +(8.59619 + 2.95108i) q^{37} +(-0.353886 + 4.34451i) q^{38} +(3.93589 - 1.35119i) q^{39} +(2.64177 - 2.30072i) q^{40} +(0.180157 + 0.175259i) q^{41} +(-1.52409 - 0.619032i) q^{42} +(-8.38690 + 3.40646i) q^{43} +(1.90358 - 1.85183i) q^{44} +(-0.0205861 + 0.248437i) q^{45} +(-3.69004 - 2.87207i) q^{46} +(0.0636976 + 0.326096i) q^{47} +(1.64681 - 0.465674i) q^{48} +(2.44073 + 5.56430i) q^{49} +(1.78523 + 7.04971i) q^{50} +(0.976381 - 0.108066i) q^{51} +(-2.37272 + 0.531740i) q^{52} +(-0.270019 - 1.38235i) q^{53} +(-2.62797 + 4.55178i) q^{54} +(2.77723 + 8.87930i) q^{55} +(0.845363 + 0.457487i) q^{56} +(-4.08882 - 6.23935i) q^{57} +(1.07374 - 0.581080i) q^{58} +(-7.67119 - 7.46264i) q^{59} +(-1.14936 + 5.88408i) q^{60} +(8.03591 - 3.79224i) q^{61} +(2.27753 - 3.94480i) q^{62} +(-0.0658197 + 0.0186121i) q^{63} +(-0.986361 + 0.164595i) q^{64} +(2.09110 - 8.25759i) q^{65} +(-0.624269 + 4.50190i) q^{66} +(11.4050 - 7.90804i) q^{67} -0.574005 q^{68} +8.00248 q^{69} +(-2.76717 + 1.91872i) q^{70} +(-1.75834 - 0.829781i) q^{71} +(0.0421438 - 0.0573388i) q^{72} +(-3.88744 - 7.68179i) q^{73} +(8.86866 - 1.98751i) q^{74} +(-9.82133 - 7.64425i) q^{75} +(1.97362 + 3.88649i) q^{76} +(-2.01446 + 1.56792i) q^{77} +(2.64548 - 3.21223i) q^{78} +(1.26900 - 0.515424i) q^{79} +(1.04575 - 3.34345i) q^{80} +(-1.20616 - 8.69822i) q^{81} +(0.245257 + 0.0549635i) q^{82} +(7.14147 + 16.2809i) q^{83} +(-1.62257 + 0.270759i) q^{84} +(0.907961 - 1.79418i) q^{85} +(-5.36109 + 7.29402i) q^{86} +(-0.839309 + 1.91343i) q^{87} +(0.651944 - 2.57447i) q^{88} +(4.60345 - 9.09667i) q^{89} +(0.112562 + 0.222428i) q^{90} +(2.32308 - 0.257119i) q^{91} +(-4.64765 - 0.514401i) q^{92} +(1.07074 + 7.72159i) q^{93} +(0.225033 + 0.244451i) q^{94} +(-15.2700 + 0.0213324i) q^{95} +(1.15909 - 1.25911i) q^{96} +(8.87539 + 6.15406i) q^{97} +(4.99318 + 3.46219i) q^{98} +(0.0944918 + 0.163665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{47}{57}\right)$

Coefficient data

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

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

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

$2$	0.851919	−	0.523673i	0.602398	−	0.370293i
$2$	0.851919	−	0.523673i	0.602398	−	0.370293i
$3$	−0.600076	+	1.60273i	−0.346454	+	0.925337i	0.641016	+	0.767528i	$0.278513\pi$
$3$	−0.600076	+	1.60273i	−0.346454	+	0.925337i	−0.987470	+	0.157810i	$0.949557\pi$
$4$	0.451533	−	0.892254i	0.225767	−	0.446127i
$5$	2.07470	+	2.82274i	0.927836	+	1.26237i	0.964783	+	0.263049i	$0.0847281\pi$
$5$	2.07470	+	2.82274i	0.927836	+	1.26237i	−0.0369467	+	0.999317i	$0.511763\pi$
$6$	0.328091	+	1.67964i	0.133942	+	0.685711i
$7$	−0.525734	+	0.804696i	−0.198709	+	0.304147i	−0.922593	−	0.385775i	$-0.873934\pi$
$7$	−0.525734	+	0.804696i	−0.198709	+	0.304147i	0.723884	+	0.689922i	$0.242355\pi$
$8$	−0.0825793	−	0.996584i	−0.0291962	−	0.352346i
$9$	0.0536627	+	0.0467349i	0.0178876	+	0.0155783i
$10$	3.24567	+	1.31828i	1.02637	+	0.416876i
$11$	2.51184	+	0.862315i	0.757348	+	0.259998i	0.676214	−	0.736705i	$-0.263620\pi$
$11$	2.51184	+	0.862315i	0.757348	+	0.259998i	0.0811338	+	0.996703i	$0.474146\pi$
$12$	1.15909	+	1.25911i	0.334600	+	0.363473i
$13$	−1.54581	−	1.87697i	−0.428731	−	0.520579i	0.512343	−	0.858781i	$-0.328778\pi$
$13$	−1.54581	−	1.87697i	−0.428731	−	0.520579i	−0.941074	+	0.338202i	$0.890181\pi$
$14$	−0.0264856	+	0.960849i	−0.00707858	+	0.256798i
$15$	−5.76907	+	1.63134i	−1.48957	+	0.421209i
$16$	−0.592235	−	0.805765i	−0.148059	−	0.201441i
$17$	−0.259182	−	0.512158i	−0.0628609	−	0.124217i	0.858660	−	0.512546i	$-0.171298\pi$
$17$	−0.259182	−	0.512158i	−0.0628609	−	0.124217i	−0.921520	+	0.388330i	$0.873052\pi$
$18$	0.0701901	+	0.0117127i	0.0165440	+	0.00276070i
$19$	−2.57658	+	3.51585i	−0.591109	+	0.806592i
$19$	−2.57658	+	3.51585i	−0.591109	+	0.806592i
$20$	3.45540	−	0.576604i	0.772650	−	0.128933i
$21$	−0.974232	−	1.32549i	−0.212595	−	0.289246i
$22$	2.59145	−	0.580758i	0.552500	−	0.123818i
$23$	−1.63959	−	4.37915i	−0.341878	−	0.913116i	−0.988624	−	0.150410i	$-0.951941\pi$
$23$	−1.63959	−	4.37915i	−0.341878	−	0.913116i	0.646746	−	0.762706i	$-0.276130\pi$
$24$	1.64681	+	0.465674i	0.336154	+	0.0950553i
$25$	−2.17087	+	6.94066i	−0.434174	+	1.38813i
$26$	−2.29983	−	0.789532i	−0.451033	−	0.154840i
$27$	−4.62246	+	2.50155i	−0.889593	+	0.481424i
$28$	0.480607	+	0.832436i	0.0908262	+	0.157316i
$29$	1.21904	+	0.0672562i	0.226370	+	0.0124892i	0.167918	−	0.985801i	$-0.446296\pi$
$29$	1.21904	+	0.0672562i	0.226370	+	0.0124892i	0.0584521	+	0.998290i	$0.481383\pi$
$30$	−4.06049	+	4.41087i	−0.741341	+	0.805311i
$31$	4.00606	−	2.16797i	0.719510	−	0.389379i	−0.0745511	−	0.997217i	$-0.523752\pi$
$31$	4.00606	−	2.16797i	0.719510	−	0.389379i	0.794061	+	0.607838i	$0.207963\pi$
$32$	−0.926494	−	0.376309i	−0.163783	−	0.0665227i
$33$	−2.88935	+	3.50835i	−0.502972	+	0.610725i
$34$	−0.489006	−	0.300591i	−0.0838638	−	0.0515509i
$35$	−3.36219	+	0.185497i	−0.568314	+	0.0313547i
$36$	0.0659299	−	0.0267784i	0.0109883	−	0.00446307i
$37$	8.59619	+	2.95108i	1.41320	+	0.485154i	0.922441	−	0.386139i	$-0.126191\pi$
$37$	8.59619	+	2.95108i	1.41320	+	0.485154i	0.490764	+	0.871292i	$0.336718\pi$
$38$	−0.353886	+	4.34451i	−0.0574079	+	0.704773i
$39$	3.93589	−	1.35119i	0.630247	−	0.216364i
$40$	2.64177	−	2.30072i	0.417700	−	0.363775i
$41$	0.180157	+	0.175259i	0.0281357	+	0.0273709i	0.711230	−	0.702959i	$-0.248138\pi$
$41$	0.180157	+	0.175259i	0.0281357	+	0.0273709i	−0.683095	+	0.730330i	$0.739366\pi$
$42$	−1.52409	−	0.619032i	−0.235172	−	0.0955187i
$43$	−8.38690	+	3.40646i	−1.27899	+	0.519481i	−0.911788	−	0.410661i	$-0.865298\pi$
$43$	−8.38690	+	3.40646i	−1.27899	+	0.519481i	−0.367202	+	0.930141i	$0.619684\pi$
$44$	1.90358	−	1.85183i	0.286976	−	0.279174i
$45$	−0.0205861	+	0.248437i	−0.00306879	+	0.0370348i
$46$	−3.69004	−	2.87207i	−0.544067	−	0.423464i
$47$	0.0636976	+	0.326096i	0.00929125	+	0.0475660i	0.985809	−	0.167871i	$-0.0536893\pi$
$47$	0.0636976	+	0.326096i	0.00929125	+	0.0475660i	−0.976518	+	0.215437i	$0.930882\pi$
$48$	1.64681	−	0.465674i	0.237697	−	0.0672142i
$49$	2.44073	+	5.56430i	0.348675	+	0.794900i
$50$	1.78523	+	7.04971i	0.252469	+	0.996979i
$51$	0.976381	−	0.108066i	0.136721	−	0.0151322i
$52$	−2.37272	+	0.531740i	−0.329038	+	0.0737391i
$53$	−0.270019	−	1.38235i	−0.0370900	−	0.189880i	0.958304	−	0.285752i	$-0.0922433\pi$
$53$	−0.270019	−	1.38235i	−0.0370900	−	0.189880i	−0.995394	+	0.0958714i	$0.969436\pi$
$54$	−2.62797	+	4.55178i	−0.357621	+	0.619418i
$55$	2.77723	+	8.87930i	0.374482	+	1.19729i
$56$	0.845363	+	0.457487i	0.112966	+	0.0611343i
$57$	−4.08882	−	6.23935i	−0.541577	−	0.826422i
$58$	1.07374	−	0.581080i	0.140989	−	0.0762996i
$59$	−7.67119	−	7.46264i	−0.998703	−	0.971554i	0.000892033	−	1.00000i	$-0.499716\pi$
$59$	−7.67119	−	7.46264i	−0.998703	−	0.971554i	−0.999595	+	0.0284460i	$0.990944\pi$
$60$	−1.14936	+	5.88408i	−0.148382	+	0.759631i
$61$	8.03591	−	3.79224i	1.02889	−	0.485546i	0.163449	−	0.986552i	$-0.447738\pi$
$61$	8.03591	−	3.79224i	1.02889	−	0.485546i	0.865444	+	0.501005i	$0.167036\pi$
$62$	2.27753	−	3.94480i	0.289247	−	0.500991i
$63$	−0.0658197	+	0.0186121i	−0.00829251	+	0.00234490i
$64$	−0.986361	+	0.164595i	−0.123295	+	0.0205743i
$65$	2.09110	−	8.25759i	0.259370	−	1.02423i
$66$	−0.624269	+	4.50190i	−0.0768422	+	0.554146i
$67$	11.4050	−	7.90804i	1.39334	−	0.966121i	0.394455	−	0.918915i	$-0.370933\pi$
$67$	11.4050	−	7.90804i	1.39334	−	0.966121i	0.998885	−	0.0472058i	$-0.0150317\pi$
$68$	−0.574005			−0.0696083
$69$	8.00248			0.963386
$70$	−2.76717	+	1.91872i	−0.330741	+	0.229330i
$71$	−1.75834	−	0.829781i	−0.208677	−	0.0984769i	0.319588	−	0.947557i	$-0.396455\pi$
$71$	−1.75834	−	0.829781i	−0.208677	−	0.0984769i	−0.528265	+	0.849080i	$0.677157\pi$
$72$	0.0421438	−	0.0573388i	0.00496670	−	0.00675744i
$73$	−3.88744	−	7.68179i	−0.454990	−	0.899085i	−0.998228	−	0.0595062i	$-0.981047\pi$
$73$	−3.88744	−	7.68179i	−0.454990	−	0.899085i	0.543238	−	0.839579i	$-0.317198\pi$
$74$	8.86866	−	1.98751i	1.03096	−	0.231044i
$75$	−9.82133	−	7.64425i	−1.13407	−	0.882681i
$76$	1.97362	+	3.88649i	0.226390	+	0.445811i
$77$	−2.01446	+	1.56792i	−0.229569	+	0.178681i
$78$	2.64548	−	3.21223i	0.299541	−	0.363713i
$79$	1.26900	−	0.515424i	0.142774	−	0.0579897i	−0.303804	−	0.952735i	$-0.598257\pi$
$79$	1.26900	−	0.515424i	0.142774	−	0.0579897i	0.446578	+	0.894745i	$0.352643\pi$
$80$	1.04575	−	3.34345i	0.116918	−	0.373809i
$81$	−1.20616	−	8.69822i	−0.134018	−	0.966469i
$82$	0.245257	+	0.0549635i	0.0270842	+	0.00606970i
$83$	7.14147	+	16.2809i	0.783879	+	1.78706i	0.592543	+	0.805539i	$0.298124\pi$
$83$	7.14147	+	16.2809i	0.783879	+	1.78706i	0.191336	+	0.981525i	$0.438718\pi$
$84$	−1.62257	+	0.270759i	−0.177037	+	0.0295423i
$85$	0.907961	−	1.79418i	0.0984822	−	0.194606i
$86$	−5.36109	+	7.29402i	−0.578101	+	0.786535i
$87$	−0.839309	+	1.91343i	−0.0899834	+	0.205141i
$88$	0.651944	−	2.57447i	0.0694974	−	0.274439i
$89$	4.60345	−	9.09667i	0.487965	−	0.964245i	−0.506801	−	0.862063i	$-0.669172\pi$
$89$	4.60345	−	9.09667i	0.487965	−	0.964245i	0.994766	−	0.102182i	$-0.0325823\pi$
$90$	0.112562	+	0.222428i	0.0118651	+	0.0234460i
$91$	2.32308	−	0.257119i	0.243525	−	0.0269533i
$92$	−4.64765	−	0.514401i	−0.484551	−	0.0536300i
$93$	1.07074	+	7.72159i	0.111030	+	0.800692i
$94$	0.225033	+	0.244451i	0.0232104	+	0.0252132i
$95$	−15.2700	+	0.0213324i	−1.56667	+	0.00218866i
$96$	1.15909	−	1.25911i	0.118299	−	0.128507i
$97$	8.87539	+	6.15406i	0.901159	+	0.624850i	0.927100	−	0.374813i	$-0.122293\pi$
$97$	8.87539	+	6.15406i	0.901159	+	0.624850i	−0.0259408	+	0.999663i	$0.508258\pi$
$98$	4.99318	+	3.46219i	0.504387	+	0.349734i
$99$	0.0944918	+	0.163665i	0.00949679	+	0.0164489i
$100$	5.21261	+	5.07091i	0.521261	+	0.507091i
$101$	3.30954	+	2.88228i	0.329312	+	0.286798i	0.805561	−	0.592512i	$-0.201864\pi$
$101$	3.30954	+	2.88228i	0.329312	+	0.286798i	−0.476250	+	0.879310i	$0.658004\pi$
$102$	0.775207	−	0.603368i	0.0767569	−	0.0597423i
$103$	−1.43532	−	2.19693i	−0.141427	−	0.216470i	0.759427	−	0.650593i	$-0.225479\pi$
$103$	−1.43532	−	2.19693i	−0.141427	−	0.216470i	−0.900854	+	0.434123i	$0.857058\pi$
$104$	−1.74291	+	1.69553i	−0.170907	+	0.166260i
$105$	1.72027	−	5.50000i	0.167881	−	0.536745i
$106$	−0.953934	−	1.03625i	−0.0926542	−	0.100649i
$107$	0.801717	+	0.433868i	0.0775049	+	0.0419436i	0.514238	−	0.857648i	$-0.328075\pi$
$107$	0.801717	+	0.433868i	0.0775049	+	0.0419436i	−0.436733	+	0.899591i	$0.643864\pi$
$108$	0.144824	+	5.25394i	0.0139357	+	0.505561i
$109$	0.328183	−	1.68012i	0.0314343	−	0.160926i	−0.962430	−	0.271528i	$-0.912471\pi$
$109$	0.328183	−	1.68012i	0.0314343	−	0.160926i	0.993865	+	0.110602i	$0.0352780\pi$
$110$	7.01583	+	6.11009i	0.668933	+	0.582574i
$111$	−9.88815	+	12.0065i	−0.938541	+	1.13961i
$112$	0.959755	−	0.0529511i	0.0906883	−	0.00500341i
$113$	−9.18289	−	14.0555i	−0.863853	−	1.32223i	−0.945519	−	0.325566i	$-0.894445\pi$
$113$	−9.18289	−	14.0555i	−0.863853	−	1.32223i	0.0816662	−	0.996660i	$-0.473976\pi$
$114$	−6.75072	−	3.17422i	−0.632263	−	0.297293i
$115$	8.95952	−	13.7136i	0.835480	−	1.27880i
$116$	0.610446	−	1.05732i	0.0566785	−	0.0981700i
$117$	0.00476780	−	0.172967i	0.000440783	−	0.0159908i
$118$	−10.4432	−	2.34038i	−0.961376	−	0.215449i
$119$	0.548393	+	0.0606961i	0.0502711	+	0.00556400i
$120$	2.10217	+	5.61465i	0.191901	+	0.512545i
$121$	−3.11480	−	2.42435i	−0.283164	−	0.220395i
$122$	4.86006	−	7.43887i	0.440009	−	0.673484i
$123$	−0.389001	+	0.183574i	−0.0350750	+	0.0165523i
$124$	−0.125512	−	4.55334i	−0.0112713	−	0.408902i
$125$	−7.52875	+	2.58462i	−0.673392	+	0.231176i
$126$	−0.0463265	+	0.0503240i	−0.00412709	+	0.00448322i
$127$	−4.03770	−	6.99350i	−0.358288	−	0.620573i	0.629387	−	0.777092i	$-0.283306\pi$
$127$	−4.03770	−	6.99350i	−0.358288	−	0.620573i	−0.987675	+	0.156519i	$0.949973\pi$
$128$	−0.754107	+	0.656752i	−0.0666542	+	0.0580492i
$129$	−0.426871	−	15.4861i	−0.0375839	−	1.36347i
$130$	−2.54282	−	8.12985i	−0.223020	−	0.713035i
$131$	−0.0286129	+	1.03802i	−0.00249992	+	0.0906924i	0.997341	+	0.0728722i	$0.0232165\pi$
$131$	−0.0286129	+	1.03802i	−0.00249992	+	0.0906924i	−0.999841	+	0.0178202i	$0.994327\pi$
$132$	1.82570	+	4.16217i	0.158907	+	0.362271i
$133$	−1.47459	−	3.92177i	−0.127864	−	0.340061i
$134$	5.57490	−	12.7095i	0.481598	−	1.09793i
$135$	−16.6515	−	7.85801i	−1.43313	−	0.676310i
$136$	−0.489006	+	0.300591i	−0.0419319	+	0.0257754i
$137$	6.16164	−	4.27239i	0.526425	−	0.365015i	−0.276577	−	0.960992i	$-0.589200\pi$
$137$	6.16164	−	4.27239i	0.526425	−	0.365015i	0.803002	+	0.595977i	$0.203235\pi$
$138$	6.81747	−	4.19068i	0.580341	−	0.356735i
$139$	0.969781	−	6.99355i	0.0822557	−	0.593185i	−0.903947	−	0.427644i	$-0.859344\pi$
$139$	0.969781	−	6.99355i	0.0822557	−	0.593185i	0.986203	−	0.165541i	$-0.0529370\pi$
$140$	−1.35263	+	3.08369i	−0.114318	+	0.260619i
$141$	−0.560868	−	0.0935923i	−0.0472336	−	0.00788190i
$142$	−1.93250	+	0.213889i	−0.162172	+	0.0179492i
$143$	−2.26428	−	6.04763i	−0.189349	−	0.505728i
$144$	0.00587640	−	0.0709176i	0.000489700	−	0.00590980i
$145$	2.33930	+	3.58056i	0.194268	+	0.297349i
$146$	−7.33453	−	4.50852i	−0.607010	−	0.373128i
$147$	−10.3827	+	0.572830i	−0.856351	+	0.0472462i
$148$	6.51458	−	6.33748i	0.535495	−	0.520937i
$149$	14.7866	+	4.18125i	1.21136	+	0.342541i	0.817122	−	0.576465i	$-0.195568\pi$
$149$	14.7866	+	4.18125i	1.21136	+	0.342541i	0.394242	+	0.919006i	$0.371007\pi$
$150$	−12.3701	−	1.36912i	−1.01001	−	0.111788i
$151$	−3.86833	−	15.2757i	−0.314801	−	1.24312i	−0.901309	−	0.433176i	$-0.857393\pi$
$151$	−3.86833	−	15.2757i	−0.314801	−	1.24312i	0.586509	−	0.809943i	$-0.300502\pi$
$152$	3.71662	+	2.27745i	0.301457	+	0.184725i
$153$	0.0100272	−	0.0395966i	0.000810654	−	0.00320120i
$154$	−0.895082	+	2.39066i	−0.0721278	+	0.192645i
$155$	14.4310	+	6.81016i	1.15913	+	0.547005i
$156$	0.571578	−	4.12192i	0.0457629	−	0.330018i
$157$	−4.64494	+	12.4061i	−0.370706	+	0.990113i	0.609614	+	0.792699i	$0.291325\pi$
$157$	−4.64494	+	12.4061i	−0.370706	+	0.990113i	−0.980320	+	0.197414i	$0.936746\pi$
$158$	0.811173	−	1.10364i	0.0645335	−	0.0878010i
$159$	2.37757	+	0.396746i	0.188553	+	0.0314640i
$160$	−0.859979	−	3.39598i	−0.0679873	−	0.268476i
$161$	4.38588	+	0.982898i	0.345655	+	0.0774632i
$162$	−5.58258	−	6.77855i	−0.438609	−	0.532573i
$163$	−18.5525	−	10.0401i	−1.45315	−	0.786403i	−0.458397	−	0.888748i	$-0.651576\pi$
$163$	−18.5525	−	10.0401i	−1.45315	−	0.786403i	−0.994749	+	0.102344i	$0.967366\pi$
$164$	0.237722	−	0.0816102i	0.0185630	−	0.00637269i
$165$	−15.8977	−	0.877100i	−1.23763	−	0.0682821i
$166$	14.6098	+	10.1302i	1.13394	+	0.786259i
$167$	−11.5287	−	0.636053i	−0.892114	−	0.0492193i	−0.396772	−	0.917917i	$-0.629870\pi$
$167$	−11.5287	−	0.636053i	−0.892114	−	0.0492193i	−0.495342	+	0.868698i	$0.664957\pi$
$168$	−1.24051	+	1.08036i	−0.0957075	+	0.0833518i
$169$	1.35874	−	6.95597i	0.104518	−	0.535075i
$170$	−0.166054	−	2.00397i	−0.0127357	−	0.153698i
$171$	−0.302580	+	0.0682537i	−0.0231388	+	0.00521949i
$172$	−0.747533	+	9.02138i	−0.0569988	+	0.687874i
$173$	−9.63259	−	2.72384i	−0.732352	−	0.207090i	−0.114544	−	0.993418i	$-0.536541\pi$
$173$	−9.63259	−	2.72384i	−0.732352	−	0.207090i	−0.617808	+	0.786329i	$0.711979\pi$
$174$	0.286989	+	2.06961i	0.0217566	+	0.156897i
$175$	−4.44382	−	5.39584i	−0.335921	−	0.407887i
$176$	−0.792775	−	2.53464i	−0.0597577	−	0.191056i
$177$	16.5639	−	7.81670i	1.24502	−	0.587539i
$178$	−0.841909	−	10.1603i	−0.0631037	−	0.761549i
$179$	6.58832	−	5.12789i	0.492434	−	0.383277i	−0.337334	−	0.941385i	$-0.609525\pi$
$179$	6.58832	−	5.12789i	0.492434	−	0.383277i	0.829768	+	0.558108i	$0.188473\pi$
$180$	0.212373	+	0.130546i	0.0158294	+	0.00973029i
$181$	9.47696	+	5.82546i	0.704417	+	0.433003i	0.829032	−	0.559202i	$-0.188892\pi$
$181$	9.47696	+	5.82546i	0.704417	+	0.433003i	−0.124615	+	0.992205i	$0.539770\pi$
$182$	1.84443	−	1.43558i	0.136718	−	0.106412i
$183$	1.25578	+	15.1550i	0.0928301	+	1.12029i
$184$	−4.22880	+	1.99562i	−0.311751	+	0.147119i
$185$	9.50444	+	30.3874i	0.698780	+	2.23413i
$186$	4.95577	+	6.01746i	0.363375	+	0.441221i
$187$	−0.209382	−	1.50995i	−0.0153115	−	0.110419i
$188$	0.319722	+	0.0904089i	0.0233181	+	0.00659374i
$189$	0.417198	−	5.03483i	0.0303467	−	0.366230i
$190$	−12.9976	+	8.01464i	−0.942946	+	0.581443i
$191$	0.635951	+	7.67479i	0.0460158	+	0.555328i	0.980130	+	0.198355i	$0.0635598\pi$
$191$	0.635951	+	7.67479i	0.0460158	+	0.555328i	−0.934114	+	0.356974i	$0.883809\pi$
$192$	0.328091	−	1.67964i	0.0236779	−	0.121218i
$193$	8.92022	−	7.76863i	0.642092	−	0.559198i	−0.273216	−	0.961953i	$-0.588087\pi$
$193$	8.92022	−	7.76863i	0.642092	−	0.559198i	0.915308	+	0.402754i	$0.131947\pi$
$194$	10.7838	+	0.594961i	0.774234	+	0.0427157i
$195$	11.9799	+	8.30666i	0.857896	+	0.594852i
$196$	6.06684	+	0.334717i	0.433346	+	0.0239084i
$197$	13.9980	−	4.80550i	0.997313	−	0.342378i	0.222751	−	0.974875i	$-0.428496\pi$
$197$	13.9980	−	4.80550i	0.997313	−	0.342378i	0.774562	+	0.632497i	$0.217970\pi$
$198$	0.166206	+	0.0899463i	0.0118118	+	0.00639220i
$199$	5.39810	+	6.55456i	0.382661	+	0.464640i	0.927458	−	0.373928i	$-0.121989\pi$
$199$	5.39810	+	6.55456i	0.382661	+	0.464640i	−0.544796	+	0.838569i	$0.683393\pi$
$200$	7.09622	+	1.59030i	0.501779	+	0.112451i
$201$	5.83061	+	23.0246i	0.411259	+	1.62403i
$202$	4.32883	+	0.722355i	0.304576	+	0.0508247i
$203$	−0.695011	+	0.945596i	−0.0487802	+	0.0663679i
$204$	0.344446	−	0.919975i	0.0241161	−	0.0644111i
$205$	−0.120939	+	0.872146i	−0.00844671	+	0.0609133i
$206$	−2.37325	−	1.11996i	−0.165352	−	0.0780316i
$207$	0.116674	−	0.311623i	0.00810942	−	0.0216593i
$208$	−0.596917	+	2.35717i	−0.0413887	+	0.163440i
$209$	−9.50373	+	6.60942i	−0.657387	+	0.457183i
$210$	−1.41467	−	5.58641i	−0.0976216	−	0.385499i
$211$	−13.9806	−	1.54737i	−0.962461	−	0.106525i	−0.384976	−	0.922926i	$-0.625790\pi$
$211$	−13.9806	−	1.54737i	−0.962461	−	0.106525i	−0.577485	+	0.816401i	$0.695966\pi$
$212$	−1.35533	−	0.383251i	−0.0930844	−	0.0263218i
$213$	2.38505	−	2.32022i	0.163421	−	0.158979i
$214$	0.910203	−	0.0502173i	0.0622202	−	0.00343279i
$215$	−27.0159	−	16.6066i	−1.84247	−	1.13256i
$216$	2.87473	+	4.40010i	0.195600	+	0.299389i
$217$	−0.361565	+	4.36344i	−0.0245446	+	0.296210i
$218$	−0.600245	−	1.60318i	−0.0406537	−	0.108581i
$219$	14.6446	−	1.62086i	0.989590	−	0.109528i
$220$	9.17661	+	1.53131i	0.618687	+	0.103241i
$221$	−0.560661	+	1.27818i	−0.0377141	+	0.0859796i
$222$	−2.13642	+	15.4067i	−0.143387	+	1.03403i
$223$	−2.41389	+	1.48381i	−0.161646	+	0.0993635i	−0.602134	−	0.798395i	$-0.705683\pi$
$223$	−2.41389	+	1.48381i	−0.161646	+	0.0993635i	0.440488	+	0.897759i	$0.354805\pi$
$224$	0.789905	−	0.547708i	0.0527777	−	0.0365953i
$225$	−0.440866	+	0.270999i	−0.0293911	+	0.0180666i
$226$	−15.1835	−	7.16528i	−1.00999	−	0.476628i
$227$	4.18217	−	9.53439i	0.277581	−	0.632820i	−0.720585	−	0.693367i	$-0.756127\pi$
$227$	4.18217	−	9.53439i	0.277581	−	0.632820i	0.998165	+	0.0605470i	$0.0192845\pi$
$228$	−7.41333	+	0.830992i	−0.490959	+	0.0550338i
$229$	−1.53434	−	3.49795i	−0.101392	−	0.231151i	0.857755	−	0.514059i	$-0.171859\pi$
$229$	−1.53434	−	3.49795i	−0.101392	−	0.231151i	−0.959147	+	0.282908i	$0.908701\pi$
$230$	0.451366	−	16.3747i	0.0297622	−	1.07972i
$231$	−1.30412	−	4.16951i	−0.0858049	−	0.274334i
$232$	−0.0336409	−	1.22043i	−0.00220863	−	0.0801250i
$233$	−5.18254	+	4.51348i	−0.339520	+	0.295688i	−0.809655	−	0.586907i	$-0.800346\pi$
$233$	−5.18254	+	4.51348i	−0.339520	+	0.295688i	0.470135	+	0.882595i	$0.344205\pi$
$234$	−0.0865163	−	0.149851i	−0.00565575	−	0.00979604i
$235$	−0.788330	+	0.856355i	−0.0514250	+	0.0558624i
$236$	−10.1224	+	3.47501i	−0.658910	+	0.226204i
$237$	0.0645888	+	2.34316i	0.00419549	+	0.152205i
$238$	0.498971	−	0.235470i	0.0323435	−	0.0152633i
$239$	−4.22651	+	6.46916i	−0.273390	+	0.418455i	−0.947295	−	0.320364i	$-0.896195\pi$
$239$	−4.22651	+	6.46916i	−0.273390	+	0.418455i	0.673904	+	0.738819i	$0.264616\pi$
$240$	4.73112	+	3.68238i	0.305393	+	0.237697i
$241$	9.48527	+	25.3340i	0.611000	+	1.63191i	0.765143	+	0.643860i	$0.222668\pi$
$241$	9.48527	+	25.3340i	0.611000	+	1.63191i	−0.154143	+	0.988049i	$0.549262\pi$
$242$	−3.92313	−	0.434212i	−0.252188	−	0.0279122i
$243$	−0.721471	−	0.161685i	−0.0462824	−	0.0103721i
$244$	0.244842	−	8.88240i	0.0156744	−	0.568637i
$245$	−10.6428	+	18.4338i	−0.679941	+	1.17769i
$246$	−0.235265	+	0.360100i	−0.0149999	+	0.0229591i
$247$	10.5821	−	0.598659i	0.673322	−	0.0380918i
$248$	−2.49139	−	3.81335i	−0.158203	−	0.242148i
$249$	−30.3794	+	1.67608i	−1.92521	+	0.106217i
$250$	−5.06039	+	6.14449i	−0.320047	+	0.388612i
$251$	18.0843	+	15.7496i	1.14147	+	0.994108i	0.999991	+	0.00416702i	$0.00132641\pi$
$251$	18.0843	+	15.7496i	1.14147	+	0.994108i	0.141480	+	0.989941i	$0.454814\pi$
$252$	−0.0131131	+	0.0671319i	−0.000826050	+	0.00422891i
$253$	−0.342177	−	12.4136i	−0.0215125	−	0.780434i
$254$	−7.10210	−	3.84347i	−0.445625	−	0.241160i
$255$	2.33074	+	2.53186i	0.145957	+	0.158551i
$256$	−0.298515	+	0.954405i	−0.0186572	+	0.0596503i
$257$	−0.393446	+	0.382751i	−0.0245425	+	0.0238753i	−0.709466	−	0.704740i	$-0.751064\pi$
$257$	−0.393446	+	0.382751i	−0.0245425	+	0.0238753i	0.684923	+	0.728615i	$0.259836\pi$
$258$	−8.47330	−	12.9694i	−0.527525	−	0.807437i
$259$	−6.89403	+	5.36584i	−0.428374	+	0.333417i
$260$	−6.42366	−	5.59437i	−0.398379	−	0.346948i
$261$	0.0622737	+	0.0605808i	0.00385464	+	0.00374986i
$262$	0.519208	+	0.899295i	0.0320768	+	0.0555586i
$263$	−17.1250	−	11.8742i	−1.05597	−	0.732196i	−0.0913482	−	0.995819i	$-0.529118\pi$
$263$	−17.1250	−	11.8742i	−1.05597	−	0.732196i	−0.964626	+	0.263623i	$0.915083\pi$
$264$	3.73496	+	2.58977i	0.229871	+	0.159389i
$265$	3.34180	−	3.63016i	0.205285	−	0.222999i
$266$	−3.30996	−	2.56883i	−0.202947	−	0.157505i
$267$	11.8171	+	12.8368i	0.723195	+	0.785599i
$268$	−1.90625	−	13.7469i	−0.116443	−	0.839725i
$269$	14.0611	+	1.55628i	0.857321	+	0.0948883i	0.527912	−	0.849299i	$-0.322975\pi$
$269$	14.0611	+	1.55628i	0.857321	+	0.0948883i	0.329409	+	0.944187i	$0.393151\pi$
$270$	−18.3007	+	2.02552i	−1.11375	+	0.123269i
$271$	11.6624	+	23.0455i	0.708441	+	1.39992i	0.907552	+	0.419940i	$0.137949\pi$
$271$	11.6624	+	23.0455i	0.708441	+	1.39992i	−0.199111	+	0.979977i	$0.563805\pi$
$272$	−0.259182	+	0.512158i	−0.0157152	+	0.0310541i
$273$	−0.981933	+	3.87757i	−0.0594293	+	0.234681i
$274$	3.01189	−	6.86642i	0.181955	−	0.414815i
$275$	−11.4379	+	15.5618i	−0.689732	+	0.938414i
$276$	3.61339	−	7.14025i	0.217500	−	0.429792i
$277$	−11.6340	+	1.94138i	−0.699021	+	0.116646i	−0.503425	−	0.864039i	$-0.667927\pi$
$277$	−11.6340	+	1.94138i	−0.699021	+	0.116646i	−0.195596	+	0.980685i	$0.562664\pi$
$278$	−2.83616	−	6.46579i	−0.170101	−	0.387792i
$279$	0.316296	+	0.0708836i	0.0189362	+	0.00424369i
$280$	0.462511	+	3.33539i	0.0276403	+	0.199328i
$281$	−2.16207	+	6.91251i	−0.128978	+	0.412366i	−0.996357	−	0.0852828i	$-0.972821\pi$
$281$	−2.16207	+	6.91251i	−0.128978	+	0.412366i	0.867379	+	0.497649i	$0.165803\pi$
$282$	−0.526826	+	0.213978i	−0.0313720	+	0.0127422i
$283$	9.68813	−	11.7636i	0.575900	−	0.699276i	−0.400242	−	0.916409i	$-0.631074\pi$
$283$	9.68813	−	11.7636i	0.575900	−	0.699276i	0.976142	+	0.217133i	$0.0696706\pi$
$284$	−1.53433	+	1.19421i	−0.0910454	+	0.0708635i
$285$	9.12895	−	24.4865i	0.540752	−	1.45045i
$286$	−5.09597	−	3.96635i	−0.301331	−	0.234535i
$287$	−0.235745	+	0.0528317i	−0.0139156	+	0.00311856i
$288$	−0.0321314	−	0.0634934i	−0.00189336	−	0.00374138i
$289$	9.87287	−	13.4325i	0.580757	−	0.790148i
$290$	3.86793	+	1.82532i	0.227133	+	0.107187i
$291$	−15.1892	+	10.5320i	−0.890408	+	0.617395i
$292$	−8.60941			−0.503828
$293$	13.6393			0.796817			0.398409	−	0.917208i	$-0.369563\pi$
$293$	13.6393			0.796817			0.398409	+	0.917208i	$0.369563\pi$
$294$	−8.54525	+	5.92514i	−0.498369	+	0.345561i
$295$	5.14964	−	37.1365i	0.299824	−	2.16217i
$296$	2.23113	−	8.81053i	0.129682	−	0.512101i
$297$	−13.7680	+	2.29747i	−0.798900	+	0.133313i
$298$	14.7866	−	4.18125i	0.856564	−	0.242213i
$299$	−5.68506	+	9.84681i	−0.328775	+	0.569456i
$300$	−11.2553	+	5.31149i	−0.649823	+	0.306659i
$301$	1.66811	−	8.53980i	0.0961484	−	0.492226i
$302$	−11.2950	−	10.9879i	−0.649953	−	0.632284i
$303$	−6.60550	+	3.57472i	−0.379476	+	0.205362i
$304$	4.35889	−	0.00608946i	0.250000	−	0.000349254i
$305$	27.3766	+	14.8155i	1.56758	+	0.848333i
$306$	−0.0121933	−	0.0389841i	−0.000697044	−	0.00222858i
$307$	9.95365	−	17.2402i	0.568085	−	0.983951i	−0.428671	−	0.903461i	$-0.641018\pi$
$307$	9.95365	−	17.2402i	0.568085	−	0.983951i	0.996755	−	0.0804905i	$-0.0256487\pi$
$308$	0.489385	+	2.50538i	0.0278853	+	0.142757i
$309$	4.38239	−	0.982116i	0.249305	−	0.0558706i
$310$	15.8604	−	1.75542i	0.900807	−	0.0997013i
$311$	7.06191	+	27.8868i	0.400444	+	1.58132i	0.761110	+	0.648623i	$0.224655\pi$
$311$	7.06191	+	27.8868i	0.400444	+	1.58132i	−0.360666	+	0.932695i	$0.617451\pi$
$312$	−1.67160	−	3.81087i	−0.0946358	−	0.215748i
$313$	−27.6197	+	7.81010i	−1.56116	+	0.441453i	−0.939701	−	0.341996i	$-0.888897\pi$
$313$	−27.6197	+	7.81010i	−1.56116	+	0.441453i	−0.621456	+	0.783449i	$0.713458\pi$
$314$	2.53961	+	13.0014i	0.143319	+	0.733712i
$315$	−0.189093	−	0.147177i	−0.0106542	−	0.00829250i
$316$	0.113107	−	1.36500i	0.00636279	−	0.0767874i
$317$	−16.9763	+	16.5148i	−0.953485	+	0.927565i	−0.997443	−	0.0714684i	$-0.977231\pi$
$317$	−16.9763	+	16.5148i	−0.953485	+	0.927565i	0.0439574	+	0.999033i	$0.486003\pi$
$318$	2.23326	−	0.907072i	0.125235	−	0.0508661i
$319$	3.00403	+	1.22013i	0.168193	+	0.0683142i
$320$	−2.51101	−	2.44275i	−0.140370	−	0.136554i
$321$	−1.17646	+	1.02458i	−0.0656639	+	0.0571867i
$322$	4.25113	−	1.45941i	0.236906	−	0.0813300i
$323$	2.46848	+	0.408372i	0.137350	+	0.0227224i
$324$	−8.30565	−	2.85133i	−0.461425	−	0.158407i
$325$	16.3832	−	6.65428i	0.908777	−	0.369113i
$326$	−21.0630	+	1.16208i	−1.16657	+	0.0643615i
$327$	2.49584	+	1.53419i	0.138020	+	0.0848407i
$328$	0.159783	−	0.194014i	0.00882256	−	0.0107126i
$329$	−0.295896	−	0.120183i	−0.0163133	−	0.00662589i
$330$	−14.0029	+	7.57797i	−0.770832	+	0.417154i
$331$	8.65590	−	9.40282i	0.475771	−	0.516826i	−0.450963	−	0.892543i	$-0.648919\pi$
$331$	8.65590	−	9.40282i	0.475771	−	0.516826i	0.926734	+	0.375717i	$0.122604\pi$
$332$	17.7513	+	0.979369i	0.974231	+	0.0537498i
$333$	0.323377	+	0.560105i	0.0177209	+	0.0306936i
$334$	−10.1546	+	5.49538i	−0.555633	+	0.300694i
$335$	45.9843	+	15.7864i	2.51239	+	0.862504i
$336$	−0.491059	+	1.57000i	−0.0267895	+	0.0856507i
$337$	−11.4159	−	3.22810i	−0.621863	−	0.175846i	−0.0534243	−	0.998572i	$-0.517014\pi$
$337$	−11.4159	−	3.22810i	−0.621863	−	0.175846i	−0.568438	+	0.822726i	$0.692452\pi$
$338$	−2.48512	−	6.63746i	−0.135173	−	0.361030i
$339$	28.0375	−	6.28336i	1.52279	−	0.341265i
$340$	−1.19089	−	1.62026i	−0.0645851	−	0.0878711i
$341$	11.9321	−	1.99111i	0.646157	−	0.107825i
$342$	−0.222031	+	0.216599i	−0.0120060	+	0.0117124i
$343$	−12.3975	−	2.06877i	−0.669401	−	0.111703i
$344$	4.08741	+	8.07695i	0.220379	+	0.435480i
$345$	16.6028	+	22.5889i	0.893864	+	1.21615i
$346$	−9.63259	+	2.72384i	−0.517851	+	0.146434i
$347$	−0.535629	+	19.4316i	−0.0287541	+	1.04314i	0.838385	+	0.545078i	$0.183500\pi$
$347$	−0.535629	+	19.4316i	−0.0287541	+	1.04314i	−0.867139	+	0.498066i	$0.834044\pi$
$348$	1.32829	+	1.61286i	0.0712039	+	0.0864581i
$349$	8.09550	+	8.79406i	0.433342	+	0.470735i	0.913731	−	0.406321i	$-0.133188\pi$
$349$	8.09550	+	8.79406i	0.433342	+	0.470735i	−0.480388	+	0.877056i	$0.659504\pi$
$350$	−6.61143	−	2.26971i	−0.353396	−	0.121321i
$351$	11.8408	+	4.80932i	0.632015	+	0.256702i
$352$	−2.00271	−	1.74416i	−0.106745	−	0.0929639i
$353$	0.0335405	+	0.404773i	0.00178518	+	0.0215439i	0.997419	−	0.0718026i	$-0.0228752\pi$
$353$	0.0335405	+	0.404773i	0.00178518	+	0.0215439i	−0.995634	+	0.0933465i	$0.970244\pi$
$354$	10.0177	−	15.3333i	0.532436	−	0.814954i
$355$	−1.30578	−	6.68488i	−0.0693038	−	0.354797i
$356$	−6.03793	−	8.21490i	−0.320010	−	0.435389i
$357$	−0.426357	+	0.842504i	−0.0225652	+	0.0445900i
$358$	2.92738	−	7.81867i	0.154717	−	0.413230i
$359$	−26.9308	+	16.5543i	−1.42135	+	0.873702i	−0.999457	−	0.0329421i	$-0.989512\pi$
$359$	−26.9308	+	16.5543i	−1.42135	+	0.873702i	−0.421896	+	0.906644i	$0.638635\pi$
$360$	0.249288			0.0131386
$361$	−5.72243	−	18.1178i	−0.301180	−	0.953567i
$362$	11.1242			0.584677
$363$	5.75470	−	3.53740i	0.302043	−	0.185665i
$364$	0.819534	−	2.18888i	0.0429552	−	0.114728i
$365$	13.6184	−	26.9106i	0.712818	−	1.40857i
$366$	9.00611	+	12.2533i	0.470757	+	0.640488i
$367$	−5.53524	−	28.3374i	−0.288937	−	1.47920i	−0.789635	−	0.613576i	$-0.789730\pi$
$367$	−5.53524	−	28.3374i	−0.288937	−	1.47920i	0.500698	−	0.865622i	$-0.333077\pi$
$368$	−2.55754	+	3.91461i	−0.133321	+	0.204063i
$369$	0.00147698	+	0.0178245i	7.68885e−5	+	0.000927906i
$370$	24.0101	+	20.9104i	1.24822	+	1.08708i
$371$	1.25433	+	0.509465i	0.0651216	+	0.0264501i
$372$	7.37310	+	2.53119i	0.382277	+	0.131236i
$373$	−3.28777	−	3.57147i	−0.170234	−	0.184924i	0.644774	−	0.764374i	$-0.276952\pi$
$373$	−3.28777	−	3.57147i	−0.170234	−	0.184924i	−0.815008	+	0.579450i	$0.803267\pi$
$374$	−0.969099	−	1.17671i	−0.0501109	−	0.0608463i
$375$	0.375365	−	13.6175i	0.0193838	−	0.703206i
$376$	0.319722	−	0.0904089i	0.0164884	−	0.00466248i
$377$	−1.75816	−	2.39207i	−0.0905501	−	0.123198i
$378$	−2.28118	−	4.50774i	−0.117331	−	0.231853i
$379$	6.71024	+	1.11974i	0.344682	+	0.0575173i	0.334404	−	0.942430i	$-0.391465\pi$
$379$	6.71024	+	1.11974i	0.344682	+	0.0575173i	0.0102783	+	0.999947i	$0.496728\pi$
$380$	−6.87587	+	13.6343i	−0.352725	+	0.699426i
$381$	13.6316	−	2.27472i	0.698370	−	0.116537i
$382$	4.56086	+	6.20527i	0.233354	+	0.317489i
$383$	19.2796	−	4.32067i	0.985144	−	0.220776i	0.303797	−	0.952737i	$-0.401746\pi$
$383$	19.2796	−	4.32067i	0.985144	−	0.220776i	0.681347	+	0.731961i	$0.261395\pi$
$384$	−0.600076	−	1.60273i	−0.0306225	−	0.0817890i
$385$	−8.60523	−	2.43333i	−0.438563	−	0.124014i
$386$	3.53109	−	11.2895i	0.179728	−	0.574622i
$387$	−0.609264	−	0.209161i	−0.0309707	−	0.0106322i
$388$	9.49852	−	5.14034i	0.482214	−	0.260961i
$389$	−5.19304	−	8.99461i	−0.263297	−	0.456045i	0.703819	−	0.710380i	$-0.251477\pi$
$389$	−5.19304	−	8.99461i	−0.263297	−	0.456045i	−0.967116	+	0.254335i	$0.918143\pi$
$390$	14.5559	+	0.803069i	0.737064	+	0.0406650i
$391$	−1.81786	+	1.97473i	−0.0919334	+	0.0998662i
$392$	5.34374	−	2.89189i	0.269900	−	0.146062i
$393$	−1.64650	−	0.668751i	−0.0830549	−	0.0337340i
$394$	9.40862	−	11.4243i	0.473999	−	0.575545i
$395$	4.08771	+	2.51270i	0.205675	+	0.126428i
$396$	0.188697	−	0.0104107i	0.00948237	−	0.000523157i
$397$	−13.0890	+	5.31631i	−0.656920	+	0.266818i	−0.680328	−	0.732908i	$-0.738163\pi$
$397$	−13.0890	+	5.31631i	−0.656920	+	0.266818i	0.0234074	+	0.999726i	$0.492548\pi$
$398$	8.03119	+	2.75711i	0.402567	+	0.138202i
$399$	7.17042	−	0.0100172i	0.358970	−	0.000501488i
$400$	6.87821	−	2.36129i	0.343910	−	0.118065i
$401$	−8.64292	+	7.52712i	−0.431607	+	0.375887i	−0.845089	−	0.534626i	$-0.820453\pi$
$401$	−8.64292	+	7.52712i	−0.431607	+	0.375887i	0.413482	+	0.910512i	$0.364312\pi$
$402$	17.0245	+	16.5617i	0.849107	+	0.826024i
$403$	−10.2618	−	4.16800i	−0.511179	−	0.207623i
$404$	4.06610	−	1.65151i	0.202296	−	0.0821655i
$405$	22.0504	−	21.4509i	1.09569	−	1.06590i
$406$	−0.0969101	+	1.16953i	−0.00480957	+	0.0580428i
$407$	19.0475	+	14.8252i	0.944148	+	0.734860i
$408$	−0.188326	−	0.964122i	−0.00932351	−	0.0477311i
$409$	−13.0506	+	3.69035i	−0.645309	+	0.182476i	−0.579006	−	0.815324i	$-0.696559\pi$
$409$	−13.0506	+	3.69035i	−0.645309	+	0.182476i	−0.0663033	+	0.997800i	$0.521121\pi$
$410$	0.353689	+	0.806330i	0.0174675	+	0.0398218i
$411$	3.15004	+	12.4392i	0.155380	+	0.613581i
$412$	−2.60831	+	0.288688i	−0.128502	+	0.0142226i
$413$	10.0382	−	2.24961i	0.493946	−	0.110696i
$414$	−0.0637915	−	0.326577i	−0.00313518	−	0.0160504i
$415$	−31.1403	+	53.9366i	−1.52862	+	2.64764i
$416$	0.725862	+	2.32071i	0.0355883	+	0.113782i
$417$	10.6268	+	5.75096i	0.520399	+	0.281626i
$418$	−4.63524	+	10.6075i	−0.226717	+	0.518832i
$419$	−18.3636	+	9.93788i	−0.897120	+	0.485497i	−0.857949	−	0.513735i	$-0.828261\pi$
$419$	−18.3636	+	9.93788i	−0.897120	+	0.485497i	−0.0391717	+	0.999232i	$0.512472\pi$
$420$	−4.13064	−	4.01835i	−0.201555	−	0.196075i
$421$	4.31466	−	22.0887i	0.210284	−	1.07654i	−0.715537	−	0.698574i	$-0.753818\pi$
$421$	4.31466	−	22.0887i	0.210284	−	1.07654i	0.925821	−	0.377962i	$-0.123375\pi$
$422$	−12.7206	+	6.00301i	−0.619230	+	0.292222i
$423$	−0.0118219	+	0.0204761i	−0.000574800	+	0.000995583i
$424$	−1.35533	+	0.383251i	−0.0658206	+	0.0186123i
$425$	4.11737	−	0.687067i	0.199722	−	0.0333276i
$426$	0.816839	−	3.22563i	0.0395760	−	0.156282i
$427$	−1.17315	+	8.46018i	−0.0567729	+	0.409417i
$428$	0.749122	−	0.519430i	0.0362102	−	0.0251076i
$429$	11.0515			0.533570
$430$	−31.7118			−1.52928
$431$	−13.3034	+	9.22434i	−0.640800	+	0.444321i	−0.845115	−	0.534584i	$-0.820468\pi$
$431$	−13.3034	+	9.22434i	−0.640800	+	0.444321i	0.204315	+	0.978905i	$0.434503\pi$
$432$	4.75325	+	2.24311i	0.228691	+	0.107922i
$433$	−16.2525	+	22.1124i	−0.781048	+	1.06265i	0.215240	+	0.976561i	$0.430947\pi$
$433$	−16.2525	+	22.1124i	−0.781048	+	1.06265i	−0.996287	+	0.0860923i	$0.972562\pi$
$434$	1.97699	+	3.90664i	0.0948987	+	0.187525i
$435$	−7.14243	+	1.60066i	−0.342453	+	0.0767456i
$436$	−1.35090	−	1.05145i	−0.0646966	−	0.0503554i
$437$	19.6210	+	5.51870i	0.938599	+	0.263995i
$438$	11.6272	−	9.04983i	0.555570	−	0.432417i
$439$	0.961077	−	1.16697i	0.0458697	−	0.0556965i	−0.748479	−	0.663158i	$-0.769216\pi$
$439$	0.961077	−	1.16697i	0.0458697	−	0.0556965i	0.794349	+	0.607462i	$0.207812\pi$
$440$	8.61963	−	3.50099i	0.410925	−	0.166903i
$441$	−0.129071	+	0.412663i	−0.00614623	+	0.0196506i
$442$	0.191709	+	1.38251i	0.00911868	+	0.0657592i
$443$	−13.0847	−	2.93235i	−0.621674	−	0.139320i	−0.103547	−	0.994625i	$-0.533019\pi$
$443$	−13.0847	−	2.93235i	−0.621674	−	0.139320i	−0.518126	+	0.855304i	$0.673370\pi$
$444$	6.24803	+	14.2441i	0.296519	+	0.675994i
$445$	35.2283	−	5.87856i	1.66998	−	0.278671i
$446$	−1.27941	+	2.52818i	−0.0605817	+	0.119713i
$447$	−15.5745	+	21.1899i	−0.736648	+	1.00225i
$448$	0.386115	−	0.880254i	0.0182422	−	0.0415881i
$449$	6.07914	−	24.0060i	0.286892	−	1.13291i	−0.643233	−	0.765671i	$-0.722407\pi$
$449$	6.07914	−	24.0060i	0.286892	−	1.13291i	0.930125	−	0.367242i	$-0.119698\pi$
$450$	−0.233667	+	0.461739i	−0.0110152	+	0.0217666i
$451$	0.301396	+	0.595574i	0.0141922	+	0.0280445i
$452$	−16.6874	+	1.84696i	−0.784910	+	0.0868738i
$453$	26.8042	+	2.96668i	1.25937	+	0.139387i
$454$	−1.43003	−	10.3126i	−0.0671146	−	0.483995i
$455$	5.54548	+	6.02400i	0.259976	+	0.282410i
$456$	−5.88039	+	4.59010i	−0.275374	+	0.214951i
$457$	−8.52239	+	9.25778i	−0.398660	+	0.433061i	−0.902469	−	0.430755i	$-0.858247\pi$
$457$	−8.52239	+	9.25778i	−0.398660	+	0.433061i	0.503809	+	0.863815i	$0.331932\pi$
$458$	−3.13891	−	2.17648i	−0.146672	−	0.101700i
$459$	2.47925	+	1.71907i	0.115721	+	0.0802394i
$460$	−8.19047	−	14.1863i	−0.381883	−	0.661440i
$461$	−19.4088	−	18.8811i	−0.903957	−	0.879383i	0.0892188	−	0.996012i	$-0.471563\pi$
$461$	−19.4088	−	18.8811i	−0.903957	−	0.879383i	−0.993176	+	0.116629i	$0.962791\pi$
$462$	−3.29447	−	2.86915i	−0.153272	−	0.133485i
$463$	−8.31929	+	6.47516i	−0.386630	+	0.300926i	−0.788813	−	0.614633i	$-0.789304\pi$
$463$	−8.31929	+	6.47516i	−0.386630	+	0.300926i	0.402183	+	0.915559i	$0.368252\pi$
$464$	−0.667764	−	1.02209i	−0.0310002	−	0.0474493i
$465$	−19.5746	+	19.0424i	−0.907748	+	0.883071i
$466$	−2.05152	+	6.55908i	−0.0950349	+	0.303844i
$467$	10.3304	+	11.2218i	0.478034	+	0.519283i	0.927403	−	0.374063i	$-0.122036\pi$
$467$	10.3304	+	11.2218i	0.478034	+	0.519283i	−0.449370	+	0.893346i	$0.648351\pi$
$468$	−0.152178	−	0.0823544i	−0.00703441	−	0.00380683i
$469$	0.367579	+	13.3351i	0.0169732	+	0.615757i
$470$	−0.223144	+	1.14237i	−0.0102929	+	0.0526937i
$471$	−17.0963	−	14.8892i	−0.787756	−	0.686057i
$472$	−6.80367	+	8.26124i	−0.313164	+	0.380255i
$473$	−24.0040	+	1.32434i	−1.10370	+	0.0608930i
$474$	1.28207	+	1.96236i	0.0588876	+	0.0901343i
$475$	−18.8089	−	25.5157i	−0.863011	−	1.17074i
$476$	0.301774	−	0.461899i	0.0138318	−	0.0211711i
$477$	0.0501140	−	0.0868000i	0.00229456	−	0.00397430i
$478$	−0.212925	+	7.72451i	−0.00973895	+	0.353311i
$479$	−18.6223	−	4.17336i	−0.850876	−	0.190686i	−0.228636	−	0.973512i	$-0.573427\pi$
$479$	−18.6223	−	4.17336i	−0.850876	−	0.190686i	−0.622240	+	0.782826i	$0.713777\pi$
$480$	5.95890	+	0.659530i	0.271985	+	0.0301033i
$481$	−7.74899	−	20.6966i	−0.353324	−	0.943685i
$482$	21.3474	+	16.6154i	0.972349	+	0.756810i
$483$	−4.20718	+	6.43957i	−0.191433	+	0.293010i
$484$	−3.56957	+	1.68452i	−0.162253	+	0.0765692i
$485$	1.04252	+	37.8207i	0.0473385	+	1.71735i
$486$	−0.699305	+	0.240072i	−0.0317211	+	0.0108899i
$487$	17.8267	−	19.3650i	0.807806	−	0.877511i	−0.186676	−	0.982422i	$-0.559771\pi$
$487$	17.8267	−	19.3650i	0.807806	−	0.877511i	0.994482	+	0.104910i	$0.0334555\pi$
$488$	−4.44289	−	7.69531i	−0.201120	−	0.348350i
$489$	27.2245	−	23.7099i	1.23114	−	1.07220i
$490$	0.586509	+	21.2774i	0.0264958	+	0.961217i
$491$	6.97718	+	22.3073i	0.314876	+	1.00671i	0.968314	+	0.249734i	$0.0803432\pi$
$491$	6.97718	+	22.3073i	0.314876	+	1.00671i	−0.653439	+	0.756979i	$0.726674\pi$
$492$	−0.0118522	+	0.429978i	−0.000534341	+	0.0193849i
$493$	−0.281507	−	0.641772i	−0.0126784	−	0.0289039i
$494$	8.70158	−	6.05156i	0.391502	−	0.272272i
$495$	−0.265940	+	0.606281i	−0.0119531	+	0.0272503i
$496$	−4.11941	−	1.94400i	−0.184967	−	0.0872880i
$497$	1.59214	−	0.978686i	0.0714173	−	0.0439001i
$498$	−25.0031	+	17.3367i	−1.12041	+	0.776878i
$499$	19.0397	−	11.7037i	0.852334	−	0.523928i	−0.0272732	−	0.999628i	$-0.508682\pi$
$499$	19.0397	−	11.7037i	0.852334	−	0.523928i	0.879608	+	0.475700i	$0.157805\pi$
$500$	−1.09334	+	7.88460i	−0.0488957	+	0.352610i
$501$	7.93749	−	18.0957i	0.354621	−	0.808454i
$502$	23.6540	+	3.94716i	1.05573	+	0.176170i
$503$	−18.4214	+	2.03888i	−0.821368	+	0.0909090i	−0.510863	−	0.859662i	$-0.670674\pi$
$503$	−18.4214	+	2.03888i	−0.821368	+	0.0909090i	−0.310506	+	0.950571i	$0.600498\pi$
$504$	0.0239838	+	0.0640580i	0.00106832	+	0.00285337i
$505$	−1.26960	+	15.3218i	−0.0564966	+	0.681813i
$506$	−6.79215	−	10.3962i	−0.301948	−	0.462166i
$507$	10.3332	+	6.35180i	0.458914	+	0.282093i
$508$	−8.06314	+	0.444856i	−0.357744	+	0.0197373i
$509$	−30.2103	+	29.3890i	−1.33905	+	1.30264i	−0.420522	+	0.907282i	$0.638153\pi$
$509$	−30.2103	+	29.3890i	−1.33905	+	1.30264i	−0.918525	+	0.395362i	$0.870619\pi$
$510$	3.31147	+	0.936395i	0.146634	+	0.0414643i
$511$	8.22527	+	0.910372i	0.363864	+	0.0402725i
$512$	0.245485	+	0.969400i	0.0108490	+	0.0428418i
$513$	3.11508	−	22.6973i	0.137534	−	1.00211i
$514$	−0.134748	+	0.532110i	−0.00594350	+	0.0234704i
$515$	3.22347	−	8.60951i	0.142043	−	0.379380i
$516$	−14.0103	−	6.61161i	−0.616768	−	0.291060i
$517$	−0.121200	+	0.874028i	−0.00533035	+	0.0384397i
$518$	−3.06321	+	8.18148i	−0.134590	+	0.359474i
$519$	10.1459	−	13.8039i	0.445354	−	0.605926i
$520$	−8.40206	−	1.40206i	−0.368455	−	0.0614842i
$521$	2.46393	+	9.72983i	0.107947	+	0.426272i	0.999653	−	0.0263428i	$-0.00838616\pi$
$521$	2.46393	+	9.72983i	0.107947	+	0.426272i	−0.891706	+	0.452614i	$0.850491\pi$
$522$	0.0847767	+	0.0189989i	0.00371057	+	0.000831559i
$523$	−2.63960	−	3.20509i	−0.115422	−	0.140149i	0.711019	−	0.703173i	$-0.248234\pi$
$523$	−2.63960	−	3.20509i	−0.115422	−	0.140149i	−0.826440	+	0.563024i	$0.809638\pi$
$524$	0.913260	+	0.494231i	0.0398959	+	0.0215906i
$525$	11.3147	−	3.88434i	0.493814	−	0.169527i
$526$	−20.8073	−	1.14797i	−0.907243	−	0.0500540i
$527$	−2.14864	−	1.48984i	−0.0935964	−	0.0648983i
$528$	4.53808	+	0.250373i	0.197495	+	0.0108961i
$529$	0.855749	−	0.745272i	0.0372065	−	0.0324031i
$530$	0.945926	−	4.84261i	0.0410884	−	0.210350i
$531$	−0.0628907	−	0.758978i	−0.00272922	−	0.0329368i
$532$	−4.16505	−	0.455098i	−0.180578	−	0.0197310i
$533$	0.0504687	−	0.609067i	0.00218604	−	0.0263816i
$534$	16.7895	+	4.74762i	0.726552	+	0.205449i
$535$	0.438632	+	3.16318i	0.0189637	+	0.136756i
$536$	−8.82285	−	10.7130i	−0.381089	−	0.462731i
$537$	4.26514	+	13.6364i	0.184055	+	0.588455i
$538$	12.7939	−	6.03759i	0.551585	−	0.260299i
$539$	1.33253	+	16.0813i	0.0573963	+	0.692670i
$540$	−14.5300	+	11.3092i	−0.625273	+	0.486669i
$541$	−8.41316	−	5.17155i	−0.361710	−	0.222342i	0.330881	−	0.943672i	$-0.392654\pi$
$541$	−8.41316	−	5.17155i	−0.361710	−	0.222342i	−0.692592	+	0.721330i	$0.743531\pi$
$542$	22.0038	+	13.5257i	0.945142	+	0.580977i
$543$	−15.0235	+	11.6933i	−0.644722	+	0.501807i
$544$	0.0474009	+	0.572044i	0.00203230	+	0.0245262i
$545$	5.42341	−	2.55937i	0.232313	−	0.109631i
$546$	1.19405	+	3.81759i	0.0511006	+	0.163378i
$547$	−12.7143	−	15.4381i	−0.543624	−	0.660086i	0.425990	−	0.904728i	$-0.359926\pi$
$547$	−12.7143	−	15.4381i	−0.543624	−	0.660086i	−0.969613	+	0.244642i	$0.921329\pi$
$548$	−1.02987	−	7.42688i	−0.0439938	−	0.317261i
$549$	0.608459	+	0.172056i	0.0259684	+	0.00734316i
$550$	−1.59486	+	19.2472i	−0.0680053	+	0.820701i
$551$	−3.37742	+	4.11266i	−0.143883	+	0.175205i
$552$	−0.660840	−	7.97515i	−0.0281272	−	0.339445i
$553$	−0.252398	+	1.29214i	−0.0107331	+	0.0549472i
$554$	−8.89461	+	7.74632i	−0.377896	+	0.329110i
$555$	−54.4062	−	3.00167i	−2.30941	−	0.127414i
$556$	−5.80214	−	4.02311i	−0.246065	−	0.170618i
$557$	−44.6881	−	2.46551i	−1.89350	−	0.104467i	−0.929246	−	0.369462i	$-0.879542\pi$
$557$	−44.6881	−	2.46551i	−1.89350	−	0.104467i	−0.964250	+	0.264995i	$0.914630\pi$
$558$	0.306579	−	0.105249i	0.0129785	−	0.00445553i
$559$	19.3584	+	10.4762i	0.818773	+	0.443098i
$560$	2.14067	+	2.59928i	0.0904600	+	0.109839i
$561$	2.54570	+	0.570504i	0.107479	+	0.0240867i
$562$	1.77799	+	7.02112i	0.0749999	+	0.296168i
$563$	−24.3175	−	4.05788i	−1.02486	−	0.171019i	−0.371791	−	0.928316i	$-0.621256\pi$
$563$	−24.3175	−	4.05788i	−1.02486	−	0.171019i	−0.653071	+	0.757297i	$0.726519\pi$
$564$	−0.336759	+	0.458177i	−0.0141801	+	0.0192927i
$565$	20.6231	−	55.0818i	0.867619	−	2.31731i
$566$	2.09320	−	15.0951i	0.0879839	−	0.634494i
$567$	7.63355	+	3.60236i	0.320579	+	0.151285i
$568$	−0.681744	+	1.82086i	−0.0286054	+	0.0764015i
$569$	−6.49884	+	25.6633i	−0.272445	+	1.07586i	0.670231	+	0.742153i	$0.266195\pi$
$569$	−6.49884	+	25.6633i	−0.272445	+	1.07586i	−0.942676	+	0.333710i	$0.891700\pi$
$570$	−5.04577	−	25.6411i	−0.211344	−	1.07399i
$571$	−1.18146	−	4.66548i	−0.0494425	−	0.195244i	0.939751	−	0.341860i	$-0.111057\pi$
$571$	−1.18146	−	4.66548i	−0.0494425	−	0.195244i	−0.989194	+	0.146615i	$0.953162\pi$
$572$	−6.41843	−	0.710391i	−0.268368	−	0.0297029i
$573$	−12.6823	−	3.58620i	−0.529809	−	0.149816i
$574$	−0.173169	+	0.168462i	−0.00722794	+	0.00703145i
$575$	33.9535	−	1.87327i	1.41596	−	0.0781207i
$576$	−0.0606231	−	0.0372649i	−0.00252596	−	0.00155270i
$577$	9.86146	+	15.0941i	0.410538	+	0.628375i	0.981242	−	0.192781i	$-0.0617506\pi$
$577$	9.86146	+	15.0941i	0.410538	+	0.628375i	−0.570704	+	0.821156i	$0.693330\pi$
$578$	1.37664	−	16.6136i	0.0572607	−	0.691034i
$579$	7.09822	+	18.9585i	0.294992	+	0.787888i
$580$	4.25104	−	0.470505i	0.176515	−	0.0195367i
$581$	−16.8557	−	2.81272i	−0.699293	−	0.116691i
$582$	−7.42468	+	16.9266i	−0.307763	+	0.701629i
$583$	0.513775	−	3.70508i	0.0212784	−	0.153449i
$584$	−7.33453	+	4.50852i	−0.303505	+	0.186564i
$585$	0.498132	−	0.345397i	0.0205952	−	0.0142804i
$586$	11.6196	−	7.14254i	0.480001	−	0.295056i
$587$	−34.1102	−	16.0970i	−1.40788	−	0.664394i	−0.436016	−	0.899939i	$-0.643611\pi$
$587$	−34.1102	−	16.0970i	−1.40788	−	0.664394i	−0.971864	+	0.235544i	$0.924313\pi$
$588$	−4.17703	+	9.52266i	−0.172258	+	0.392708i
$589$	−2.69969	+	19.6707i	−0.111239	+	0.810517i
$590$	−15.0603	−	34.3340i	−0.620023	−	1.41351i
$591$	−0.697903	+	25.3186i	−0.0287079	+	1.04147i
$592$	−2.71309	−	8.67424i	−0.111507	−	0.356509i
$593$	−1.32424	−	48.0408i	−0.0543798	−	1.97280i	−0.189228	−	0.981933i	$-0.560599\pi$
$593$	−1.32424	−	48.0408i	−0.0543798	−	1.97280i	0.134848	−	0.990866i	$-0.456945\pi$
$594$	−10.5261	+	9.16719i	−0.431891	+	0.376134i
$595$	0.966423	+	1.67389i	0.0396195	+	0.0686230i
$596$	10.4074	−	11.3054i	0.426303	−	0.463088i
$597$	−13.7445	+	4.71848i	−0.562524	+	0.193115i
$598$	0.313296	+	11.3658i	0.0128116	+	0.464782i
$599$	−37.0216	+	17.4709i	−1.51266	+	0.713843i	−0.990309	−	0.138885i	$-0.955648\pi$
$599$	−37.0216	+	17.4709i	−1.51266	+	0.713843i	−0.522355	+	0.852728i	$0.674946\pi$
$600$	−6.80710	+	10.4190i	−0.277899	+	0.425355i
$601$	−6.51855	−	5.07359i	−0.265897	−	0.206956i	0.472485	−	0.881339i	$-0.343357\pi$
$601$	−6.51855	−	5.07359i	−0.265897	−	0.206956i	−0.738382	+	0.674383i	$0.764410\pi$
$602$	−3.05097	−	8.14877i	−0.124348	−	0.332119i
$603$	0.981604	+	0.108644i	0.0399740	+	0.00442432i
$604$	−15.3765	−	3.44595i	−0.625661	−	0.140214i
$605$	0.381003	−	13.8221i	0.0154900	−	0.561947i
$606$	−3.75537	+	6.50449i	−0.152551	+	0.264227i
$607$	−16.4440	+	25.1694i	−0.667441	+	1.02160i	0.329554	+	0.944137i	$0.393102\pi$
$607$	−16.4440	+	25.1694i	−0.667441	+	1.02160i	−0.996996	+	0.0774585i	$0.975319\pi$
$608$	3.71024	−	2.28782i	0.150470	−	0.0927835i
$609$	−1.09848	−	1.68135i	−0.0445126	−	0.0681316i
$610$	31.0812	−	1.71480i	1.25844	−	0.0694300i
$611$	0.513610	−	0.623642i	0.0207784	−	0.0252299i
$612$	−0.0308026	−	0.0268260i	−0.00124512	−	0.00108438i
$613$	0.114812	−	0.587775i	0.00463723	−	0.0237400i	−0.979061	−	0.203567i	$-0.934747\pi$
$613$	0.114812	−	0.587775i	0.00463723	−	0.0237400i	0.983698	+	0.179827i	$0.0575537\pi$
$614$	−0.548532	−	19.8997i	−0.0221370	−	0.803088i
$615$	−1.32524	−	0.717186i	−0.0534390	−	0.0289197i
$616$	1.72892	+	1.87810i	0.0696600	+	0.0756709i
$617$	8.76983	−	28.0387i	0.353060	−	1.12880i	−0.593109	−	0.805123i	$-0.702100\pi$
$617$	8.76983	−	28.0387i	0.353060	−	1.12880i	0.946169	−	0.323674i	$-0.104918\pi$
$618$	3.21913	−	3.13162i	0.129492	−	0.125972i
$619$	−3.60458	−	5.51722i	−0.144880	−	0.221756i	0.757351	−	0.653008i	$-0.226493\pi$
$619$	−3.60458	−	5.51722i	−0.144880	−	0.221756i	−0.902232	+	0.431252i	$0.858072\pi$
$620$	12.5925	−	9.80112i	0.505726	−	0.393622i
$621$	18.5336	+	16.1409i	0.743728	+	0.647713i
$622$	20.6198	+	20.0592i	0.826777	+	0.804301i
$623$	4.89986	+	8.48681i	0.196309	+	0.340017i
$624$	−3.41972	−	2.37118i	−0.136898	−	0.0949231i
$625$	6.96518	+	4.82955i	0.278607	+	0.193182i
$626$	−19.4398	+	21.1173i	−0.776971	+	0.844016i
$627$	−4.89017	−	19.1981i	−0.195294	−	0.766698i
$628$	8.97203	+	9.74622i	0.358023	+	0.388917i
$629$	−0.716562	−	5.16747i	−0.0285712	−	0.206041i
$630$	−0.238165	−	0.0263601i	−0.00948872	−	0.00105021i
$631$	−0.917259	+	0.101522i	−0.0365155	+	0.00404153i	−0.128247	−	0.991742i	$-0.540935\pi$
$631$	−0.917259	+	0.101522i	−0.0365155	+	0.00404153i	0.0917319	+	0.995784i	$0.470760\pi$
$632$	−0.618457	−	1.22210i	−0.0246009	−	0.0486127i
$633$	10.8694	−	21.4785i	0.432020	−	0.853695i
$634$	−5.81409	+	22.9593i	−0.230907	+	0.911832i
$635$	11.3638	−	25.9068i	0.450958	−	1.02808i
$636$	1.42755	−	1.94225i	0.0566060	−	0.0770152i
$637$	6.67115	−	13.1825i	0.264320	−	0.522311i
$638$	3.19814	−	0.533675i	0.126616	−	0.0211284i
$639$	−0.0555776	−	0.126704i	−0.00219862	−	0.00501234i
$640$	−3.41839	−	0.766078i	−0.135124	−	0.0302819i
$641$	−1.06493	−	7.67972i	−0.0420622	−	0.303331i	−0.999873	−	0.0159315i	$-0.994929\pi$
$641$	−1.06493	−	7.67972i	−0.0420622	−	0.303331i	0.957811	−	0.287399i	$-0.0927907\pi$
$642$	−0.465706	+	1.48895i	−0.0183800	+	0.0587640i
$643$	39.4970	−	16.0423i	1.55761	−	0.632646i	0.574970	−	0.818175i	$-0.305014\pi$
$643$	39.4970	−	16.0423i	1.55761	−	0.632646i	0.982639	+	0.185529i	$0.0593998\pi$
$644$	2.85736	−	3.46950i	0.112596	−	0.136718i
$645$	42.8275	−	33.3340i	1.68633	−	1.31252i
$646$	2.31680	−	0.944774i	0.0911531	−	0.0371716i
$647$	18.5774	+	14.4594i	0.730353	+	0.568456i	0.909668	−	0.415335i	$-0.136336\pi$
$647$	18.5774	+	14.4594i	0.730353	+	0.568456i	−0.179316	+	0.983792i	$0.557388\pi$
$648$	−8.56891	+	1.92034i	−0.336619	+	0.0754380i
$649$	−12.8336	−	25.3599i	−0.503764	−	0.995464i
$650$	10.4725	−	14.2484i	0.410765	−	0.558866i
$651$	−6.77646	−	3.19789i	−0.265590	−	0.125335i
$652$	−17.3354	+	12.0201i	−0.678908	+	0.470744i
$653$	−36.1439			−1.41442			−0.707211	−	0.707003i	$-0.750047\pi$
$653$	−36.1439			−1.41442			−0.707211	+	0.707003i	$0.750047\pi$
$654$	2.92967			0.114559
$655$	−2.98942	+	2.07282i	−0.116806	+	0.0809918i
$656$	0.0345225	−	0.248959i	0.00134788	−	0.00972020i
$657$	0.150397	−	0.593905i	0.00586755	−	0.0231704i
$658$	−0.315016	+	0.0525669i	−0.0122806	+	0.00204927i
$659$	27.5205	−	7.78207i	1.07205	−	0.303146i	0.310047	−	0.950721i	$-0.399655\pi$
$659$	27.5205	−	7.78207i	1.07205	−	0.303146i	0.762002	+	0.647575i	$0.224217\pi$
$660$	−7.96093	+	13.7887i	−0.309879	+	0.536726i
$661$	−28.8614	+	13.6200i	−1.12258	+	0.529757i	−0.895919	−	0.444217i	$-0.853482\pi$
$661$	−28.8614	+	13.6200i	−1.12258	+	0.529757i	−0.226659	+	0.973974i	$0.572780\pi$
$662$	2.45013	−	12.5433i	0.0952270	−	0.487509i
$663$	−1.71214	−	1.66559i	−0.0664939	−	0.0646863i
$664$	15.6356	−	8.46155i	0.606778	−	0.328372i
$665$	8.01078	−	12.2989i	0.310645	−	0.476931i
$666$	0.568803	+	0.307821i	0.0220407	+	0.0119278i
$667$	−1.70420	−	5.44862i	−0.0659868	−	0.210972i
$668$	−5.77309	+	9.99929i	−0.223368	+	0.386884i
$669$	−0.929636	−	4.75922i	−0.0359418	−	0.184002i
$670$	47.4418	−	10.6320i	1.83284	−	0.410748i
$671$	23.4550	−	2.59600i	0.905471	−	0.100217i
$672$	0.403826	+	1.59467i	0.0155779	+	0.0615158i
$673$	−9.41087	−	21.4546i	−0.362762	−	0.827015i	−0.998481	−	0.0550942i	$-0.982454\pi$
$673$	−9.41087	−	21.4546i	−0.362762	−	0.827015i	0.635719	−	0.771921i	$-0.280704\pi$
$674$	−11.4159	+	3.22810i	−0.439723	+	0.124342i
$675$	−7.32765	−	37.5135i	−0.282041	−	1.44389i
$676$	−5.59298	−	4.35319i	−0.215115	−	0.167430i
$677$	0.979573	−	11.8217i	0.0376480	−	0.454344i	−0.951523	−	0.307577i	$-0.900482\pi$
$677$	0.979573	−	11.8217i	0.0376480	−	0.454344i	0.989171	−	0.146767i	$-0.0468867\pi$
$678$	20.5953	−	20.0354i	0.790958	−	0.769456i
$679$	−9.61825	+	3.90659i	−0.369114	+	0.149921i
$680$	−1.86303	−	0.756697i	−0.0714439	−	0.0290180i
$681$	12.7714	+	12.4243i	0.489403	+	0.476099i
$682$	9.12246	−	7.94476i	0.349317	−	0.304220i
$683$	−22.5607	+	7.74509i	−0.863260	+	0.296358i	−0.720547	−	0.693406i	$-0.756109\pi$
$683$	−22.5607	+	7.74509i	−0.863260	+	0.296358i	−0.142714	+	0.989764i	$0.545583\pi$
$684$	−0.0757251	+	0.300797i	−0.00289542	+	0.0115012i
$685$	24.8434	+	8.52876i	0.949218	+	0.325867i
$686$	−11.6450	+	4.72980i	−0.444609	+	0.180584i
$687$	6.52699	−	0.360104i	0.249020	−	0.0137388i
$688$	7.71183	+	4.74044i	0.294011	+	0.180728i
$689$	−2.17724	+	2.64367i	−0.0829461	+	0.100716i
$690$	25.9734	+	10.5495i	0.988791	+	0.401612i
$691$	42.0807	−	22.7729i	1.60082	−	0.866322i	0.603188	−	0.797599i	$-0.293897\pi$
$691$	42.0807	−	22.7729i	1.60082	−	0.866322i	0.997636	−	0.0687234i	$-0.0218926\pi$
$692$	−6.77979	+	7.36482i	−0.257729	+	0.279968i
$693$	−0.181378	−	0.0100069i	−0.00688998	−	0.000380131i
$694$	9.71950	+	16.8347i	0.368947	+	0.639035i
$695$	21.7530	−	11.7721i	0.825137	−	0.446542i
$696$	1.97621	+	0.678432i	0.0749079	+	0.0257159i
$697$	0.0430670	−	0.137693i	0.00163128	−	0.00521548i
$698$	11.5019	+	3.25243i	0.435354	+	0.123106i
$699$	−4.12398	−	11.0147i	−0.155983	−	0.416613i
$700$	−6.82099	+	1.52862i	−0.257809	+	0.0577764i
$701$	−3.34512	−	4.55120i	−0.126343	−	0.171896i	0.737996	−	0.674805i	$-0.235772\pi$
$701$	−3.34512	−	4.55120i	−0.126343	−	0.171896i	−0.864340	+	0.502908i	$0.832263\pi$
$702$	12.6059	−	2.10356i	0.475780	−	0.0793936i
$703$	−32.5244	+	22.6192i	−1.22668	+	0.853100i
$704$	−2.61951	−	0.437119i	−0.0987266	−	0.0164745i
$705$	−0.899449	−	1.77736i	−0.0338752	−	0.0669392i
$706$	0.240543	+	0.327270i	0.00905294	+	0.0123170i
$707$	−4.05930	+	1.14786i	−0.152666	+	0.0431698i
$708$	0.504676	−	18.3087i	0.0189669	−	0.688084i
$709$	19.3131	+	23.4506i	0.725317	+	0.880704i	0.996650	−	0.0817814i	$-0.0260609\pi$
$709$	19.3131	+	23.4506i	0.725317	+	0.880704i	−0.271333	+	0.962486i	$0.587464\pi$
$710$	−4.61311	−	5.01118i	−0.173127	−	0.188066i
$711$	0.0921863	+	0.0316476i	0.00345726	+	0.00118688i
$712$	−9.44575	−	3.83653i	−0.353994	−	0.143780i
$713$	−16.0622	−	13.9886i	−0.601533	−	0.523876i
$714$	0.0779749	+	0.941017i	0.00291814	+	0.0352167i
$715$	12.3732	−	18.9385i	0.462730	−	0.708261i
$716$	−1.60054	−	8.19387i	−0.0598150	−	0.306219i
$717$	−7.83210	−	10.6560i	−0.292495	−	0.397954i
$718$	−14.2738	+	28.2059i	−0.532695	+	1.05263i
$719$	6.54544	−	17.4821i	0.244104	−	0.651972i	−0.755892	−	0.654696i	$-0.772797\pi$
$719$	6.54544	−	17.4821i	0.244104	−	0.651972i	0.999996	+	0.00272340i	$0.000866885\pi$
$720$	0.212373	−	0.130546i	0.00791469	−	0.00486514i
$721$	2.52246			0.0939412
$722$	−14.3628	−	12.4382i	−0.534529	−	0.462902i
$723$	−46.2956			−1.72175
$724$	9.47696	−	5.82546i	0.352208	−	0.216502i
$725$	−3.11318	+	8.31492i	−0.115620	+	0.308808i
$726$	3.05010	−	6.02716i	0.113200	−	0.223689i
$727$	23.5755	+	32.0756i	0.874365	+	1.18962i	0.980745	+	0.195291i	$0.0625652\pi$
$727$	23.5755	+	32.0756i	0.874365	+	1.18962i	−0.106380	+	0.994326i	$0.533926\pi$
$728$	−0.448079	−	2.29391i	−0.0166069	−	0.0850181i
$729$	15.1011	−	23.1139i	0.559299	−	0.856071i
$730$	−2.49062	−	30.0573i	−0.0921819	−	1.11247i
$731$	3.91838	+	3.41252i	0.144927	+	0.126217i
$732$	14.0892	+	5.72253i	0.520751	+	0.211511i
$733$	−12.4736	−	4.28220i	−0.460724	−	0.158167i	0.0845595	−	0.996418i	$-0.473052\pi$
$733$	−12.4736	−	4.28220i	−0.460724	−	0.158167i	−0.545284	+	0.838252i	$0.683578\pi$
$734$	−19.5551	−	21.2425i	−0.721792	−	0.784075i
$735$	−23.1580	−	28.1192i	−0.854195	−	1.03719i
$736$	−0.128845	+	4.67425i	−0.00474928	+	0.172295i
$737$	35.4667	−	10.0290i	1.30643	−	0.369424i
$738$	0.0105925	+	0.0144116i	0.000389914	+	0.000530497i
$739$	−5.72238	−	11.3077i	−0.210501	−	0.415962i	0.762425	−	0.647076i	$-0.224008\pi$
$739$	−5.72238	−	11.3077i	−0.210501	−	0.415962i	−0.972927	+	0.231114i	$0.925763\pi$
$740$	31.4048	+	5.24054i	1.15447	+	0.192646i
$741$	−5.39056	+	17.3195i	−0.198027	+	0.636247i
$742$	1.33538	−	0.222836i	0.0490234	−	0.00818055i
$743$	12.5691	+	17.1009i	0.461116	+	0.627371i	0.972757	−	0.231829i	$-0.0744709\pi$
$743$	12.5691	+	17.1009i	0.461116	+	0.627371i	−0.511641	+	0.859199i	$0.670962\pi$
$744$	7.60680	−	1.70472i	0.278879	−	0.0624982i
$745$	18.8752	+	50.4135i	0.691535	+	1.84701i
$746$	−4.67119	−	1.32089i	−0.171025	−	0.0483611i
$747$	−0.377656	+	1.20743i	−0.0138177	+	0.0441777i
$748$	−1.44181	−	0.494973i	−0.0527177	−	0.0180980i
$749$	−0.770622	+	0.417040i	−0.0281579	+	0.0152383i
$750$	−6.81135	−	11.7976i	−0.248715	−	0.430788i
$751$	8.61831	+	0.475485i	0.314487	+	0.0173507i	0.211644	−	0.977347i	$-0.432118\pi$
$751$	8.61831	+	0.475485i	0.314487	+	0.0173507i	0.102843	+	0.994698i	$0.467206\pi$
$752$	0.225033	−	0.244451i	0.00820611	−	0.00891421i
$753$	−36.0944	+	19.5333i	−1.31535	+	0.711833i
$754$	−2.75048	−	1.11715i	−0.100166	−	0.0406841i
$755$	35.0936	−	42.6119i	1.27719	−	1.55080i
$756$	−4.30397	−	2.64564i	−0.156534	−	0.0962210i
$757$	28.8442	−	1.59138i	1.04836	−	0.0578396i	0.477294	−	0.878744i	$-0.341618\pi$
$757$	28.8442	−	1.59138i	1.04836	−	0.0578396i	0.571066	+	0.820904i	$0.306530\pi$
$758$	6.30297	−	2.56004i	0.228934	−	0.0929850i
$759$	20.1009	+	6.90066i	0.729618	+	0.250478i
$760$	1.28224	+	15.2161i	0.0465119	+	0.551944i
$761$	−34.1620	+	11.7278i	−1.23837	+	0.425133i	−0.864634	−	0.502402i	$-0.832450\pi$
$761$	−34.1620	+	11.7278i	−1.23837	+	0.425133i	−0.373736	+	0.927535i	$0.621923\pi$
$762$	10.4218	−	9.07639i	0.377544	−	0.328803i
$763$	1.17945	+	1.14738i	0.0426988	+	0.0415380i
$764$	7.13502	+	2.89799i	0.258136	+	0.104846i
$765$	0.132574	−	0.0538471i	0.00479324	−	0.00194685i
$766$	14.1621	−	13.7771i	0.511697	−	0.497786i
$767$	−2.14899	+	25.9345i	−0.0775956	+	0.936439i
$768$	−1.35052	−	1.05115i	−0.0487328	−	0.0379303i
$769$	−3.21001	−	16.4335i	−0.115756	−	0.592606i	−0.993534	−	0.113538i	$-0.963782\pi$
$769$	−3.21001	−	16.4335i	−0.115756	−	0.592606i	0.877778	−	0.479068i	$-0.159025\pi$
$770$	−8.60523	+	2.43333i	−0.310111	+	0.0876910i
$771$	−0.377349	−	0.860268i	−0.0135899	−	0.0309818i
$772$	−2.90381	−	11.4669i	−0.104511	−	0.412703i
$773$	−19.9800	+	2.21139i	−0.718631	+	0.0795381i	−0.461884	−	0.886940i	$-0.652826\pi$
$773$	−19.9800	+	2.21139i	−0.718631	+	0.0795381i	−0.256748	+	0.966479i	$0.582651\pi$
$774$	−0.628576	+	0.140867i	−0.0225937	+	0.00506337i
$775$	6.35052	+	32.5111i	0.228117	+	1.16783i
$776$	5.40012	−	9.35328i	0.193853	−	0.335763i
$777$	−4.46306	−	14.2692i	−0.160111	−	0.511904i
$778$	−9.13428	−	4.94323i	−0.327480	−	0.177223i
$779$	−1.08037	+	0.181834i	−0.0387084	+	0.00651489i
$780$	12.8210	−	6.93836i	0.459064	−	0.248433i
$781$	−3.70113	−	3.60052i	−0.132437	−	0.128837i
$782$	−0.514563	+	2.63427i	−0.0184007	+	0.0942015i
$783$	−5.80320	+	2.73860i	−0.207389	+	0.0978694i
$784$	3.03803	−	5.26203i	0.108501	−	0.187930i
$785$	−44.6560	+	12.6275i	−1.59384	+	0.450695i
$786$	−1.75289	+	0.292506i	−0.0625236	+	0.0104333i
$787$	11.2786	−	44.5380i	0.402037	−	1.58761i	−0.355409	−	0.934711i	$-0.615658\pi$
$787$	11.2786	−	44.5380i	0.402037	−	1.58761i	0.757446	−	0.652898i	$-0.226447\pi$
$788$	2.03281	−	14.6596i	0.0724159	−	0.522226i
$789$	29.3075	−	20.3214i	1.04337	−	0.723460i
$790$	4.79823			0.170713
$791$	16.1381			0.573806
$792$	0.155303	−	0.107684i	0.00551844	−	0.00382640i
$793$	−19.5399	−	9.22112i	−0.693884	−	0.327452i
$794$	−8.36680	+	11.3834i	−0.296927	+	0.403983i
$795$	3.81284	+	7.53437i	0.135227	+	0.267217i
$796$	8.28575	−	1.85688i	0.293681	−	0.0658154i
$797$	28.9465	+	22.5299i	1.02534	+	0.798052i	0.979611	−	0.200902i	$-0.0643874\pi$
$797$	28.9465	+	22.5299i	1.02534	+	0.798052i	0.0457255	+	0.998954i	$0.485440\pi$
$798$	6.10337	−	3.76349i	0.216057	−	0.133226i
$799$	0.150504	−	0.117142i	0.00532443	−	0.00414417i
$800$	4.62313	−	5.61356i	0.163452	−	0.198469i
$801$	0.672166	−	0.273010i	0.0237498	−	0.00964634i
$802$	−3.42132	+	10.9386i	−0.120811	+	0.386254i
$803$	−3.14049	−	22.6476i	−0.110826	−	0.799216i
$804$	23.1765	+	5.19397i	0.817371	+	0.183177i
$805$	6.32493	+	14.4194i	0.222925	+	0.508217i
$806$	−10.9249	+	1.82305i	−0.384814	+	0.0642142i
$807$	−10.9320	+	21.6023i	−0.384826	+	0.760437i
$808$	2.59914	−	3.53625i	0.0914373	−	0.124405i
$809$	−2.67687	+	6.10265i	−0.0941138	+	0.214558i	−0.956525	−	0.291651i	$-0.905796\pi$
$809$	−2.67687	+	6.10265i	−0.0941138	+	0.214558i	0.862411	+	0.506209i	$0.168953\pi$
$810$	7.55186	−	29.8216i	0.265345	−	1.04783i
$811$	−13.7428	+	27.1566i	−0.482576	+	0.953596i	0.512888	+	0.858456i	$0.328576\pi$
$811$	−13.7428	+	27.1566i	−0.482576	+	0.953596i	−0.995464	+	0.0951406i	$0.969670\pi$
$812$	0.529892	+	1.04709i	0.0185956	+	0.0367458i
$813$	−43.9341	+	4.86263i	−1.54084	+	0.170540i
$814$	23.9905	+	2.65527i	0.840866	+	0.0930671i
$815$	−10.1504	−	73.1992i	−0.355552	−	2.56406i
$816$	−0.665323	−	0.722733i	−0.0232910	−	0.0253007i
$817$	9.63293	−	38.2641i	0.337014	−	1.33869i
$818$	−9.18550	+	9.97811i	−0.321163	+	0.348876i
$819$	0.136679	+	0.0947713i	0.00477596	+	0.00331158i
$820$	0.723568	+	0.501711i	0.0252681	+	0.0175205i
$821$	−8.58244	−	14.8652i	−0.299529	−	0.518800i	0.676499	−	0.736443i	$-0.263496\pi$
$821$	−8.58244	−	14.8652i	−0.299529	−	0.518800i	−0.976028	+	0.217644i	$0.930163\pi$
$822$	9.19766	+	8.94762i	0.320805	+	0.312084i
$823$	12.6853	+	11.0476i	0.442180	+	0.385095i	0.848982	−	0.528421i	$-0.177216\pi$
$823$	12.6853	+	11.0476i	0.442180	+	0.385095i	−0.406802	+	0.913516i	$0.633356\pi$
$824$	−2.07089	+	1.61184i	−0.0721430	+	0.0561512i
$825$	−18.0778	−	27.6702i	−0.629389	−	0.963352i
$826$	7.37365	−	7.17320i	0.256562	−	0.249588i
$827$	−6.57963	+	21.0362i	−0.228796	+	0.731502i	0.767143	+	0.641476i	$0.221677\pi$
$827$	−6.57963	+	21.0362i	−0.228796	+	0.731502i	−0.995939	+	0.0900261i	$0.971305\pi$
$828$	−0.225365	−	0.244811i	−0.00783197	−	0.00850778i
$829$	−36.6213	−	19.8185i	−1.27191	−	0.688324i	−0.307203	−	0.951644i	$-0.599393\pi$
$829$	−36.6213	−	19.8185i	−1.27191	−	0.688324i	−0.964709	+	0.263320i	$0.915183\pi$
$830$	1.71610	+	62.2570i	0.0595668	+	2.16097i
$831$	3.86980	−	19.8112i	0.134242	−	0.687243i
$832$	1.83367	+	1.59694i	0.0635710	+	0.0553640i
$833$	2.21721	−	2.69221i	0.0768217	−	0.0932794i
$834$	12.0648	−	0.665635i	0.417771	−	0.0230491i
$835$	−22.1231	−	33.8620i	−0.765602	−	1.17184i
$836$	1.60603	+	11.4641i	0.0555458	+	0.396495i
$837$	−13.0946	+	20.0427i	−0.452615	+	0.692778i
$838$	−10.4401	+	18.0828i	−0.360647	+	0.624660i
$839$	−0.620735	+	22.5191i	−0.0214302	+	0.777447i	0.910227	+	0.414109i	$0.135907\pi$
$839$	−0.620735	+	22.5191i	−0.0214302	+	0.777447i	−0.931658	+	0.363338i	$0.881637\pi$
$840$	−5.62327	−	1.26020i	−0.194021	−	0.0434812i
$841$	−27.3425	−	3.02626i	−0.942843	−	0.104354i
$842$	−7.89149	−	21.0772i	−0.271959	−	0.726370i
$843$	−9.78149	−	7.61324i	−0.336893	−	0.262214i
$844$	−7.69333	+	11.7755i	−0.264815	+	0.405330i
$845$	22.4538	−	10.5962i	0.772436	−	0.364521i
$846$	0.000651489		0.0236348i	2.23986e−5		0.000812581i
$847$	3.58843	−	1.23191i	0.123300	−	0.0423289i
$848$	−0.953934	+	1.03625i	−0.0327582	+	0.0355849i
$849$	13.0404	+	22.5865i	0.447544	+	0.775168i
$850$	3.14787	−	2.74148i	0.107971	−	0.0940319i
$851$	−1.17102	−	42.4826i	−0.0401422	−	1.45628i
$852$	−0.993292	−	3.17573i	−0.0340296	−	0.108799i
$853$	−0.308203	+	11.1810i	−0.0105527	+	0.382831i	0.975846	+	0.218460i	$0.0701034\pi$
$853$	−0.308203	+	11.1810i	−0.0105527	+	0.382831i	−0.986399	+	0.164371i	$0.947440\pi$
$854$	3.43093	+	7.82174i	0.117404	+	0.267654i
$855$	−0.820425	−	0.712496i	−0.0280580	−	0.0243668i
$856$	0.366181	−	0.834808i	0.0125158	−	0.0285331i
$857$	−43.2829	−	20.4257i	−1.47852	−	0.697729i	−0.493430	−	0.869786i	$-0.664257\pi$
$857$	−43.2829	−	20.4257i	−1.47852	−	0.697729i	−0.985087	+	0.172057i	$0.944959\pi$
$858$	9.41496	−	5.78736i	0.321422	−	0.197577i
$859$	32.8927	−	22.8073i	1.12228	−	0.778175i	0.144858	−	0.989452i	$-0.453727\pi$
$859$	32.8927	−	22.8073i	1.12228	−	0.778175i	0.977426	+	0.211278i	$0.0677624\pi$
$860$	−27.0159	+	16.6066i	−0.921234	+	0.566280i
$861$	0.0567899	−	0.409539i	0.00193539	−	0.0139570i
$862$	−6.50285	+	14.8250i	−0.221488	+	0.504942i
$863$	2.05575	+	0.343044i	0.0699786	+	0.0116774i	0.199480	−	0.979902i	$-0.436075\pi$
$863$	2.05575	+	0.343044i	0.0699786	+	0.0116774i	−0.129502	+	0.991579i	$0.541338\pi$
$864$	5.22404	−	0.578196i	0.177725	−	0.0196706i
$865$	−12.2961	−	32.8414i	−0.418080	−	1.11664i
$866$	−2.26620	+	27.3490i	−0.0770087	+	0.929357i
$867$	15.6043	+	23.8841i	0.529948	+	0.811146i
$868$	3.73004	+	2.29285i	0.126606	+	0.0778243i
$869$	3.63198	−	0.200382i	0.123207	−	0.00679750i
$870$	−5.24655	+	5.10393i	−0.177875	+	0.173039i
$871$	−32.4731	−	9.18253i	−1.10031	−	0.311138i
$872$	−1.70148	−	0.188320i	−0.0576193	−	0.00637730i
$873$	0.188668	+	0.745034i	0.00638545	+	0.0252156i
$874$	19.6055	−	5.57350i	0.663166	−	0.188526i
$875$	1.87829	−	7.41718i	0.0634977	−	0.250747i
$876$	5.16630	−	13.7986i	0.174553	−	0.466211i
$877$	−42.0882	−	19.8619i	−1.42122	−	0.670689i	−0.446635	−	0.894716i	$-0.647378\pi$
$877$	−42.0882	−	19.8619i	−1.42122	−	0.670689i	−0.974583	+	0.224028i	$0.928079\pi$
$878$	0.207649	−	1.49746i	0.00700781	−	0.0505367i
$879$	−8.18463	+	21.8602i	−0.276061	+	0.737325i
$880$	5.50986	−	7.49643i	0.185737	−	0.252705i
$881$	−32.7619	−	5.46699i	−1.10378	−	0.184188i	−0.415469	−	0.909607i	$-0.636382\pi$
$881$	−32.7619	−	5.46699i	−1.10378	−	0.184188i	−0.688307	+	0.725420i	$0.741646\pi$
$882$	0.106142	+	0.419146i	0.00357400	+	0.0141134i
$883$	13.6835	+	3.06655i	0.460487	+	0.103197i	0.442750	−	0.896645i	$-0.354003\pi$
$883$	13.6835	+	3.06655i	0.460487	+	0.103197i	0.0177368	+	0.999843i	$0.494354\pi$
$884$	0.887303	+	1.07739i	0.0298432	+	0.0362366i
$885$	56.4297	+	30.5382i	1.89686	+	1.02653i
$886$	−12.6827	+	4.35398i	−0.426084	+	0.146275i
$887$	−22.8008	−	1.25795i	−0.765575	−	0.0422379i	−0.331909	−	0.943312i	$-0.607693\pi$
$887$	−22.8008	−	1.25795i	−0.765575	−	0.0422379i	−0.433666	+	0.901074i	$0.642780\pi$
$888$	12.7821	+	8.86288i	0.428938	+	0.297419i
$889$	7.75040	+	0.427602i	0.259940	+	0.0143413i
$890$	26.9332	−	23.4562i	0.902804	−	0.786252i
$891$	4.47092	−	22.8886i	0.149781	−	0.766798i
$892$	0.233986	+	2.82380i	0.00783444	+	0.0945477i
$893$	−1.31063	−	0.616263i	−0.0438585	−	0.0206225i
$894$	−2.17166	+	26.2080i	−0.0726310	+	0.876526i
$895$	28.1435	+	7.95822i	0.940733	+	0.266014i
$896$	−0.132026	−	0.952104i	−0.00441069	−	0.0318076i
$897$	−12.3703	−	15.0205i	−0.413033	−	0.501518i
$898$	−7.39235	−	23.6347i	−0.246686	−	0.788699i
$899$	5.02935	−	2.37341i	0.167738	−	0.0791576i
$900$	0.0427346	+	0.515730i	0.00142449	+	0.0171910i
$901$	−0.637997	+	0.496573i	−0.0212548	+	0.0165432i
$902$	0.568651	+	0.349548i	0.0189340	+	0.0116387i
$903$	12.6860	+	7.79806i	0.422164	+	0.259503i
$904$	−13.2491	+	10.3122i	−0.440659	+	0.342979i
$905$	3.21813	+	38.8371i	0.106974	+	1.29099i
$906$	24.3885	−	11.5092i	0.810255	−	0.382369i
$907$	−3.58607	−	11.4653i	−0.119074	−	0.380699i	0.875694	−	0.482867i	$-0.160405\pi$
$907$	−3.58607	−	11.4653i	−0.119074	−	0.380699i	−0.994767	+	0.102168i	$0.967422\pi$
$908$	−6.61871	−	8.03666i	−0.219650	−	0.266706i
$909$	0.0428958	+	0.309342i	0.00142276	+	0.0102602i
$910$	7.87891	+	2.22794i	0.261183	+	0.0738556i
$911$	1.35683	−	16.3745i	0.0449537	−	0.542510i	−0.936482	−	0.350717i	$-0.885938\pi$
$911$	1.35683	−	16.3745i	0.0449537	−	0.542510i	0.981435	−	0.191794i	$-0.0614304\pi$
$912$	−2.60591	+	6.98979i	−0.0862902	+	0.231455i
$913$	3.89894	+	47.0532i	0.129036	+	1.55723i
$914$	−2.41234	+	12.3498i	−0.0797930	+	0.408496i
$915$	−40.1733	+	34.9870i	−1.32809	+	1.15663i
$916$	−3.81386	−	0.210417i	−0.126014	−	0.00695236i
$917$	−0.820249	−	0.568748i	−0.0270870	−	0.0187817i
$918$	3.01235	+	0.166196i	0.0994224	+	0.00548529i
$919$	−7.33493	+	2.51808i	−0.241957	+	0.0830639i	−0.443011	−	0.896516i	$-0.646090\pi$
$919$	−7.33493	+	2.51808i	−0.241957	+	0.0830639i	0.201054	+	0.979580i	$0.435563\pi$
$920$	−14.4066	−	7.79646i	−0.474972	−	0.257042i
$921$	21.6585	+	26.2985i	0.713672	+	0.866564i
$922$	−26.4223	−	5.92137i	−0.870171	−	0.195010i
$923$	1.16059	+	4.58305i	0.0382011	+	0.150853i
$924$	−4.30912	−	0.719065i	−0.141760	−	0.0236555i
$925$	−39.1436	+	53.2568i	−1.28703	+	1.75107i
$926$	−3.69650	+	9.87290i	−0.121474	+	0.324444i
$927$	0.0256498	−	0.184973i	0.000842449	−	0.00607530i
$928$	−1.10412	−	0.521048i	−0.0362446	−	0.0171042i
$929$	−4.43162	+	11.8363i	−0.145397	+	0.388337i	−0.988860	−	0.148850i	$-0.952443\pi$
$929$	−4.43162	+	11.8363i	−0.145397	+	0.388337i	0.843463	+	0.537187i	$0.180513\pi$
$930$	−6.70394	+	26.4733i	−0.219831	+	0.868093i
$931$	−25.8520	−	5.75565i	−0.847265	−	0.188634i
$932$	1.68708	+	6.66213i	0.0552622	+	0.218225i
$933$	−48.9328	−	5.41588i	−1.60199	−	0.177308i
$934$	14.6772	+	4.15032i	0.480253	+	0.135803i
$935$	3.82780	−	3.72374i	0.125182	−	0.121779i
$936$	−0.172770	+	0.00953198i	−0.00564716	+	0.000311563i
$937$	6.22934	+	3.82916i	0.203504	+	0.125093i	0.621676	−	0.783274i	$-0.286452\pi$
$937$	6.22934	+	3.82916i	0.203504	+	0.125093i	−0.418172	+	0.908368i	$0.637329\pi$
$938$	7.29637	+	11.1679i	0.238235	+	0.364646i
$939$	4.05641	−	48.9536i	0.132376	−	1.59754i
$940$	0.408129	+	1.09006i	0.0133117	+	0.0355540i
$941$	−58.9951	+	6.52958i	−1.92319	+	0.212858i	−0.989426	−	0.145041i	$-0.953669\pi$
$941$	−58.9951	+	6.52958i	−1.92319	+	0.212858i	−0.933760	+	0.357899i	$0.883493\pi$
$942$	−22.3617	−	3.73151i	−0.728584	−	0.121579i
$943$	0.472103	−	1.07629i	0.0153738	−	0.0350487i
$944$	−1.46999	+	10.6008i	−0.0478442	+	0.345027i
$945$	15.0776	−	9.26814i	0.490473	−	0.301493i
$946$	−19.7559	+	13.6985i	−0.642321	+	0.445375i
$947$	17.3282	−	10.6516i	0.563092	−	0.346131i	−0.212702	−	0.977117i	$-0.568227\pi$
$947$	17.3282	−	10.6516i	0.563092	−	0.346131i	0.775795	+	0.630986i	$0.217349\pi$
$948$	2.11986	+	1.00039i	0.0688499	+	0.0324910i
$949$	−8.40928	+	19.1712i	−0.272977	+	0.622324i
$950$	−29.3855	−	11.8876i	−0.953392	−	0.385684i
$951$	−16.2817	−	37.1186i	−0.527972	−	1.20365i
$952$	0.0152029	−	0.551532i	0.000492728	−	0.0178753i
$953$	13.5856	+	43.4355i	0.440080	+	1.40701i	0.864995	+	0.501780i	$0.167321\pi$
$953$	13.5856	+	43.4355i	0.440080	+	1.40701i	−0.424916	+	0.905233i	$0.639696\pi$
$954$	−0.00276172	−	0.100190i	−8.94138e−5	−	0.00324377i
$955$	−20.3445	+	17.7180i	−0.658333	+	0.573342i
$956$	3.86372	+	6.69216i	0.124962	+	0.216440i
$957$	−3.75819	+	4.08248i	−0.121485	+	0.131968i
$958$	−18.0502	+	6.19664i	−0.583176	+	0.200204i
$959$	0.198588	+	7.20440i	0.00641273	+	0.232642i
$960$	5.42188	−	2.55865i	0.174990	−	0.0825799i
$961$	−5.60696	+	8.58209i	−0.180870	+	0.276842i
$962$	−17.4398	−	13.5739i	−0.562281	−	0.437641i
$963$	0.0227456	+	0.0607507i	0.000732966	+	0.00195766i
$964$	26.8873	+	2.97589i	0.865982	+	0.0958469i
$965$	40.4356	+	9.06183i	1.30167	+	0.291711i
$966$	−0.211951	+	7.68918i	−0.00681940	+	0.247395i
$967$	11.8052	−	20.4471i	0.379628	−	0.657536i	−0.611380	−	0.791337i	$-0.709385\pi$
$967$	11.8052	−	20.4471i	0.379628	−	0.657536i	0.991008	+	0.133802i	$0.0427185\pi$
$968$	−2.15885	+	3.30437i	−0.0693881	+	0.106206i
$969$	−2.13578	+	3.71125i	−0.0686113	+	0.119223i
$970$	20.6938	+	31.6743i	0.664439	+	1.01700i
$971$	−29.8382	+	1.64622i	−0.957555	+	0.0528298i	−0.527119	−	0.849791i	$-0.676728\pi$
$971$	−29.8382	+	1.64622i	−0.957555	+	0.0528298i	−0.430436	+	0.902621i	$0.641640\pi$
$972$	−0.470032	+	0.570729i	−0.0150763	+	0.0183061i
$973$	5.11784	+	4.45713i	0.164070	+	0.142889i
$974$	5.04602	−	25.8328i	0.161685	−	0.827736i
$975$	0.833862	+	30.2509i	0.0267049	+	0.968806i
$976$	−7.81480	−	4.22916i	−0.250146	−	0.135372i
$977$	25.8830	+	28.1164i	0.828071	+	0.899525i	0.996275	−	0.0862275i	$-0.0274812\pi$
$977$	25.8830	+	28.1164i	0.828071	+	0.899525i	−0.168205	+	0.985752i	$0.553797\pi$
$978$	10.7769	−	34.4557i	0.344607	−	1.10177i
$979$	19.4073	−	18.8797i	0.620260	−	0.603399i
$980$	11.6421	+	17.8195i	0.371893	+	0.569224i
$981$	0.0961312	−	0.0748219i	0.00306923	−	0.00238888i
$982$	17.6257	+	15.3502i	0.562459	+	0.489846i
$983$	12.7688	+	12.4217i	0.407261	+	0.396190i	0.872197	−	0.489154i	$-0.162695\pi$
$983$	12.7688	+	12.4217i	0.407261	+	0.396190i	−0.464936	+	0.885344i	$0.653923\pi$
$984$	0.215070	+	0.372513i	0.00685620	+	0.0118753i
$985$	42.6063	+	29.5425i	1.35755	+	0.941304i
$986$	−0.575900	−	0.399320i	−0.0183404	−	0.0127169i
$987$	0.370181	−	0.402124i	0.0117830	−	0.0127997i
$988$	4.24401	−	9.71222i	0.135020	−	0.308987i
$989$	28.6685	+	31.1423i	0.911605	+	0.990267i
$990$	0.0909339	+	0.655768i	0.00289007	+	0.0208417i
$991$	27.3125	+	3.02295i	0.867611	+	0.0960271i	0.532783	−	0.846252i	$-0.321146\pi$
$991$	27.3125	+	3.02295i	0.867611	+	0.0960271i	0.334828	+	0.942279i	$0.391322\pi$
$992$	−4.52742	+	0.501095i	−0.143746	+	0.0159098i
$993$	9.87599	+	19.5155i	0.313405	+	0.619305i
$994$	0.843865	−	1.66752i	0.0267658	−	0.0528906i
$995$	−7.30232	+	28.8362i	−0.231499	+	0.914169i
$996$	−12.2218	+	27.8629i	−0.387263	+	0.882871i
$997$	−0.910911	+	1.23934i	−0.0288488	+	0.0392503i	−0.819950	−	0.572434i	$-0.805999\pi$
$997$	−0.910911	+	1.23934i	−0.0288488	+	0.0392503i	0.791102	+	0.611685i	$0.209508\pi$
$998$	10.0914	−	19.9412i	0.319438	−	0.631226i
$999$	−47.1178	+	7.86257i	−1.49074	+	0.248761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.505.5	✓	612
361.178	even	57	inner	722.2.i.b.539.5	yes	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.505.5	✓	612	1.1	even	1	trivial
722.2.i.b.539.5	yes	612	361.178	even	57	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.851919 - 0.523673i) q^{2} +(-0.600076 + 1.60273i) q^{3} +(0.451533 - 0.892254i) q^{4} +(2.07470 + 2.82274i) q^{5} +(0.328091 + 1.67964i) q^{6} +(-0.525734 + 0.804696i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(0.0536627 + 0.0467349i) q^{9} +O(q^{10})\)	\(q+(0.851919 - 0.523673i) q^{2} +(-0.600076 + 1.60273i) q^{3} +(0.451533 - 0.892254i) q^{4} +(2.07470 + 2.82274i) q^{5} +(0.328091 + 1.67964i) q^{6} +(-0.525734 + 0.804696i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(0.0536627 + 0.0467349i) q^{9} +(3.24567 + 1.31828i) q^{10} +(2.51184 + 0.862315i) q^{11} +(1.15909 + 1.25911i) q^{12} +(-1.54581 - 1.87697i) q^{13} +(-0.0264856 + 0.960849i) q^{14} +(-5.76907 + 1.63134i) q^{15} +(-0.592235 - 0.805765i) q^{16} +(-0.259182 - 0.512158i) q^{17} +(0.0701901 + 0.0117127i) q^{18} +(-2.57658 + 3.51585i) q^{19} +(3.45540 - 0.576604i) q^{20} +(-0.974232 - 1.32549i) q^{21} +(2.59145 - 0.580758i) q^{22} +(-1.63959 - 4.37915i) q^{23} +(1.64681 + 0.465674i) q^{24} +(-2.17087 + 6.94066i) q^{25} +(-2.29983 - 0.789532i) q^{26} +(-4.62246 + 2.50155i) q^{27} +(0.480607 + 0.832436i) q^{28} +(1.21904 + 0.0672562i) q^{29} +(-4.06049 + 4.41087i) q^{30} +(4.00606 - 2.16797i) q^{31} +(-0.926494 - 0.376309i) q^{32} +(-2.88935 + 3.50835i) q^{33} +(-0.489006 - 0.300591i) q^{34} +(-3.36219 + 0.185497i) q^{35} +(0.0659299 - 0.0267784i) q^{36} +(8.59619 + 2.95108i) q^{37} +(-0.353886 + 4.34451i) q^{38} +(3.93589 - 1.35119i) q^{39} +(2.64177 - 2.30072i) q^{40} +(0.180157 + 0.175259i) q^{41} +(-1.52409 - 0.619032i) q^{42} +(-8.38690 + 3.40646i) q^{43} +(1.90358 - 1.85183i) q^{44} +(-0.0205861 + 0.248437i) q^{45} +(-3.69004 - 2.87207i) q^{46} +(0.0636976 + 0.326096i) q^{47} +(1.64681 - 0.465674i) q^{48} +(2.44073 + 5.56430i) q^{49} +(1.78523 + 7.04971i) q^{50} +(0.976381 - 0.108066i) q^{51} +(-2.37272 + 0.531740i) q^{52} +(-0.270019 - 1.38235i) q^{53} +(-2.62797 + 4.55178i) q^{54} +(2.77723 + 8.87930i) q^{55} +(0.845363 + 0.457487i) q^{56} +(-4.08882 - 6.23935i) q^{57} +(1.07374 - 0.581080i) q^{58} +(-7.67119 - 7.46264i) q^{59} +(-1.14936 + 5.88408i) q^{60} +(8.03591 - 3.79224i) q^{61} +(2.27753 - 3.94480i) q^{62} +(-0.0658197 + 0.0186121i) q^{63} +(-0.986361 + 0.164595i) q^{64} +(2.09110 - 8.25759i) q^{65} +(-0.624269 + 4.50190i) q^{66} +(11.4050 - 7.90804i) q^{67} -0.574005 q^{68} +8.00248 q^{69} +(-2.76717 + 1.91872i) q^{70} +(-1.75834 - 0.829781i) q^{71} +(0.0421438 - 0.0573388i) q^{72} +(-3.88744 - 7.68179i) q^{73} +(8.86866 - 1.98751i) q^{74} +(-9.82133 - 7.64425i) q^{75} +(1.97362 + 3.88649i) q^{76} +(-2.01446 + 1.56792i) q^{77} +(2.64548 - 3.21223i) q^{78} +(1.26900 - 0.515424i) q^{79} +(1.04575 - 3.34345i) q^{80} +(-1.20616 - 8.69822i) q^{81} +(0.245257 + 0.0549635i) q^{82} +(7.14147 + 16.2809i) q^{83} +(-1.62257 + 0.270759i) q^{84} +(0.907961 - 1.79418i) q^{85} +(-5.36109 + 7.29402i) q^{86} +(-0.839309 + 1.91343i) q^{87} +(0.651944 - 2.57447i) q^{88} +(4.60345 - 9.09667i) q^{89} +(0.112562 + 0.222428i) q^{90} +(2.32308 - 0.257119i) q^{91} +(-4.64765 - 0.514401i) q^{92} +(1.07074 + 7.72159i) q^{93} +(0.225033 + 0.244451i) q^{94} +(-15.2700 + 0.0213324i) q^{95} +(1.15909 - 1.25911i) q^{96} +(8.87539 + 6.15406i) q^{97} +(4.99318 + 3.46219i) q^{98} +(0.0944918 + 0.163665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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