LMFDB - Embedded newform 354.2.e.d.79.3

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:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			79.3
Character	$\chi$	$=$	354.79
Dual form			354.2.e.d.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.907575 - 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(2.39226 - 1.43938i) q^{5} +(0.994138 + 0.108119i) q^{6} +(0.142415 + 2.62669i) q^{7} +(-0.267528 - 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +O(q^{10})$	\(q+(-0.907575 - 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(2.39226 - 1.43938i) q^{5} +(0.994138 + 0.108119i) q^{6} +(0.142415 + 2.62669i) q^{7} +(-0.267528 - 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(-2.77554 + 0.301858i) q^{10} +(0.100607 + 0.613675i) q^{11} +(-0.856857 - 0.515554i) q^{12} +(0.0788257 + 0.0599217i) q^{13} +(0.973665 - 2.44371i) q^{14} +(-1.80744 + 2.12788i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(-0.0307196 + 0.566590i) q^{17} +(-0.976621 + 0.214970i) q^{18} +(0.984564 + 0.932629i) q^{19} +(2.64576 + 0.891459i) q^{20} +(-0.973665 - 2.44371i) q^{21} +(0.166367 - 0.599200i) q^{22} +(7.56750 + 1.66573i) q^{23} +(0.561187 + 0.827689i) q^{24} +(1.30907 - 2.46918i) q^{25} +(-0.0463798 - 0.0874815i) q^{26} +(-0.561187 + 0.827689i) q^{27} +(-1.90976 + 1.80902i) q^{28} +(8.13958 - 3.76577i) q^{29} +(2.53386 - 1.17229i) q^{30} +(-0.121473 + 0.115065i) q^{31} +(0.561187 - 0.827689i) q^{32} +(-0.291288 - 0.549427i) q^{33} +(0.265785 - 0.501325i) q^{34} +(4.12148 + 6.07873i) q^{35} +(0.976621 + 0.214970i) q^{36} +(0.263647 - 0.949572i) q^{37} +(-0.501966 - 1.25984i) q^{38} +(-0.0938325 - 0.0316158i) q^{39} +(-2.02691 - 1.91999i) q^{40} +(7.09597 - 1.56194i) q^{41} +(-0.142415 + 2.62669i) q^{42} +(-1.15344 + 7.03570i) q^{43} +(-0.402588 + 0.473963i) q^{44} +(1.03339 - 2.59361i) q^{45} +(-6.16866 - 4.68929i) q^{46} +(1.93266 + 1.16284i) q^{47} +(-0.161782 - 0.986827i) q^{48} +(0.0797706 - 0.00867558i) q^{49} +(-2.22486 + 1.69130i) q^{50} +(-0.151802 - 0.546740i) q^{51} +(0.00536060 + 0.0988704i) q^{52} +(-8.55702 - 0.930632i) q^{53} +(0.856857 - 0.515554i) q^{54} +(1.12399 + 1.32326i) q^{55} +(2.49284 - 0.839937i) q^{56} +(-1.23081 - 0.569436i) q^{57} -8.96849 q^{58} +(-6.77860 - 3.61255i) q^{59} -2.79190 q^{60} +(-7.78605 - 3.60221i) q^{61} +(0.158560 - 0.0534251i) q^{62} +(1.70298 + 2.00490i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(0.274822 + 0.0298887i) q^{65} +(0.0336672 + 0.620955i) q^{66} +(-1.01602 - 3.65937i) q^{67} +(-0.451721 + 0.343389i) q^{68} +(-7.70324 + 0.837778i) q^{69} +(-1.18816 - 7.24748i) q^{70} +(-8.04700 - 4.84172i) q^{71} +(-0.796093 - 0.605174i) q^{72} +(-1.90130 + 4.77190i) q^{73} +(-0.637995 + 0.751105i) q^{74} +(-0.452137 + 2.75791i) q^{75} +(-0.0734209 + 1.35417i) q^{76} +(-1.59760 + 0.351659i) q^{77} +(0.0718849 + 0.0680930i) q^{78} +(7.40741 + 2.49585i) q^{79} +(1.03339 + 2.59361i) q^{80} +(0.267528 - 0.963550i) q^{81} +(-7.09597 - 1.56194i) q^{82} +(-1.72389 - 2.54255i) q^{83} +(1.23217 - 2.32412i) q^{84} +(0.742048 + 1.39965i) q^{85} +(4.00105 - 5.90111i) q^{86} +(-6.51108 + 6.16762i) q^{87} +(0.564391 - 0.261115i) q^{88} +(-11.0055 + 5.09170i) q^{89} +(-2.02691 + 1.91999i) q^{90} +(-0.146170 + 0.215584i) q^{91} +(3.62954 + 6.84604i) q^{92} +(0.0783735 - 0.147828i) q^{93} +(-1.26577 - 1.86687i) q^{94} +(3.69774 + 0.813934i) q^{95} +(-0.267528 + 0.963550i) q^{96} +(1.39266 + 3.49532i) q^{97} +(-0.0760406 - 0.0256211i) q^{98} +(0.451472 + 0.427657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{4}{29}\right)$	$1$

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
$5$	2.39226	−	1.43938i	1.06985	−	0.643709i	0.132179	−	0.991226i	$-0.457803\pi$
$5$	2.39226	−	1.43938i	1.06985	−	0.643709i	0.937674	+	0.347517i	$0.112975\pi$
$6$	0.994138	+	0.108119i	0.405855	+	0.0441394i
$7$	0.142415	+	2.62669i	0.0538277	+	0.992794i	0.893320	+	0.449422i	$0.148370\pi$
$7$	0.142415	+	2.62669i	0.0538277	+	0.992794i	−0.839492	+	0.543372i	$0.817147\pi$
$8$	−0.267528	−	0.963550i	−0.0945856	−	0.340666i
$9$	0.796093	−	0.605174i	0.265364	−	0.201725i
$10$	−2.77554	+	0.301858i	−0.877702	+	0.0954559i
$11$	0.100607	+	0.613675i	0.0303341	+	0.185030i	0.997647	−	0.0685546i	$-0.0218387\pi$
$11$	0.100607	+	0.613675i	0.0303341	+	0.185030i	−0.967313	+	0.253584i	$0.918390\pi$
$12$	−0.856857	−	0.515554i	−0.247353	−	0.148828i
$13$	0.0788257	+	0.0599217i	0.0218623	+	0.0166193i	0.616048	−	0.787708i	$-0.288733\pi$
$13$	0.0788257	+	0.0599217i	0.0218623	+	0.0166193i	−0.594186	+	0.804328i	$0.702526\pi$
$14$	0.973665	−	2.44371i	0.260223	−	0.653110i
$15$	−1.80744	+	2.12788i	−0.466679	+	0.549417i
$16$	−0.161782	+	0.986827i	−0.0404455	+	0.246707i
$17$	−0.0307196	+	0.566590i	−0.00745061	+	0.137418i	0.992441	+	0.122720i	$0.0391616\pi$
$17$	−0.0307196	+	0.566590i	−0.00745061	+	0.137418i	−0.999892	+	0.0146986i	$0.995321\pi$
$18$	−0.976621	+	0.214970i	−0.230192	+	0.0506690i
$19$	0.984564	+	0.932629i	0.225874	+	0.213960i	0.792265	−	0.610177i	$-0.208902\pi$
$19$	0.984564	+	0.932629i	0.225874	+	0.213960i	−0.566390	+	0.824137i	$0.691660\pi$
$20$	2.64576	+	0.891459i	0.591609	+	0.199336i
$21$	−0.973665	−	2.44371i	−0.212471	−	0.533262i
$22$	0.166367	−	0.599200i	0.0354696	−	0.127750i
$23$	7.56750	+	1.66573i	1.57793	+	0.347330i	0.915667	−	0.401938i	$-0.131663\pi$
$23$	7.56750	+	1.66573i	1.57793	+	0.347330i	0.662267	+	0.749268i	$0.269594\pi$
$24$	0.561187	+	0.827689i	0.114552	+	0.168951i
$25$	1.30907	−	2.46918i	0.261815	−	0.493835i
$26$	−0.0463798	−	0.0874815i	−0.00909582	−	0.0171565i
$27$	−0.561187	+	0.827689i	−0.108001	+	0.159289i
$28$	−1.90976	+	1.80902i	−0.360911	+	0.341873i
$29$	8.13958	−	3.76577i	1.51148	−	0.699286i	0.523240	−	0.852185i	$-0.324723\pi$
$29$	8.13958	−	3.76577i	1.51148	−	0.699286i	0.988242	+	0.152899i	$0.0488610\pi$
$30$	2.53386	−	1.17229i	0.462618	−	0.214030i
$31$	−0.121473	+	0.115065i	−0.0218171	+	0.0206663i	−0.698530	−	0.715580i	$-0.746162\pi$
$31$	−0.121473	+	0.115065i	−0.0218171	+	0.0206663i	0.676713	+	0.736247i	$0.263404\pi$
$32$	0.561187	−	0.827689i	0.0992048	−	0.146316i
$33$	−0.291288	−	0.549427i	−0.0507067	−	0.0956429i
$34$	0.265785	−	0.501325i	0.0455818	−	0.0859765i
$35$	4.12148	+	6.07873i	0.696658	+	1.02749i
$36$	0.976621	+	0.214970i	0.162770	+	0.0358284i
$37$	0.263647	−	0.949572i	0.0433434	−	0.156109i	−0.938712	−	0.344703i	$-0.887979\pi$
$37$	0.263647	−	0.949572i	0.0433434	−	0.156109i	0.982055	+	0.188595i	$0.0603933\pi$
$38$	−0.501966	−	1.25984i	−0.0814296	−	0.204373i
$39$	−0.0938325	−	0.0316158i	−0.0150252	−	0.00506259i
$40$	−2.02691	−	1.91999i	−0.320483	−	0.303577i
$41$	7.09597	−	1.56194i	1.10820	−	0.243934i	0.377082	−	0.926180i	$-0.376928\pi$
$41$	7.09597	−	1.56194i	1.10820	−	0.243934i	0.731123	+	0.682246i	$0.238997\pi$
$42$	−0.142415	+	2.62669i	−0.0219751	+	0.405306i
$43$	−1.15344	+	7.03570i	−0.175899	+	1.07293i	0.740320	+	0.672255i	$0.234674\pi$
$43$	−1.15344	+	7.03570i	−0.175899	+	1.07293i	−0.916218	+	0.400679i	$0.868774\pi$
$44$	−0.402588	+	0.473963i	−0.0606924	+	0.0714526i
$45$	1.03339	−	2.59361i	0.154049	−	0.386633i
$46$	−6.16866	−	4.68929i	−0.909519	−	0.691398i
$47$	1.93266	+	1.16284i	0.281907	+	0.169618i	0.649484	−	0.760375i	$-0.274985\pi$
$47$	1.93266	+	1.16284i	0.281907	+	0.169618i	−0.367577	+	0.929993i	$0.619813\pi$
$48$	−0.161782	−	0.986827i	−0.0233512	−	0.142436i
$49$	0.0797706	−	0.00867558i	0.0113958	−	0.00123937i
$50$	−2.22486	+	1.69130i	−0.314643	+	0.239186i
$51$	−0.151802	−	0.546740i	−0.0212565	−	0.0765589i
$52$	0.00536060	+	0.0988704i	0.000743381	+	0.0137109i
$53$	−8.55702	−	0.930632i	−1.17540	−	0.127832i	−0.500495	−	0.865739i	$-0.666849\pi$
$53$	−8.55702	−	0.930632i	−1.17540	−	0.127832i	−0.674902	+	0.737907i	$0.735814\pi$
$54$	0.856857	−	0.515554i	0.116603	−	0.0701580i
$55$	1.12399	+	1.32326i	0.151558	+	0.178428i
$56$	2.49284	−	0.839937i	0.333120	−	0.112241i
$57$	−1.23081	−	0.569436i	−0.163025	−	0.0754236i
$58$	−8.96849			−1.17762
$59$	−6.77860	−	3.61255i	−0.882499	−	0.470314i
$59$	−6.77860	−	3.61255i	−0.882499	−	0.470314i
$60$	−2.79190			−0.360433
$61$	−7.78605	−	3.60221i	−0.996901	−	0.461216i	−0.147556	−	0.989054i	$-0.547141\pi$
$61$	−7.78605	−	3.60221i	−0.996901	−	0.461216i	−0.849345	+	0.527838i	$0.823003\pi$
$62$	0.158560	−	0.0534251i	0.0201372	−	0.00678500i
$63$	1.70298	+	2.00490i	0.214555	+	0.252594i
$64$	−0.856857	+	0.515554i	−0.107107	+	0.0644442i
$65$	0.274822	+	0.0298887i	0.0340874	+	0.00370723i
$66$	0.0336672	+	0.620955i	0.00414414	+	0.0764342i
$67$	−1.01602	−	3.65937i	−0.124126	−	0.447063i	0.875200	−	0.483761i	$-0.160730\pi$
$67$	−1.01602	−	3.65937i	−0.124126	−	0.447063i	−0.999326	+	0.0366982i	$0.988316\pi$
$68$	−0.451721	+	0.343389i	−0.0547792	+	0.0416421i
$69$	−7.70324	+	0.837778i	−0.927361	+	0.100857i
$70$	−1.18816	−	7.24748i	−0.142013	−	0.866239i
$71$	−8.04700	−	4.84172i	−0.955003	−	0.574606i	−0.0494212	−	0.998778i	$-0.515738\pi$
$71$	−8.04700	−	4.84172i	−0.955003	−	0.574606i	−0.905582	+	0.424172i	$0.860565\pi$
$72$	−0.796093	−	0.605174i	−0.0938205	−	0.0713205i
$73$	−1.90130	+	4.77190i	−0.222530	+	0.558508i	−0.997276	−	0.0737648i	$-0.976499\pi$
$73$	−1.90130	+	4.77190i	−0.222530	+	0.558508i	0.774746	+	0.632273i	$0.217878\pi$
$74$	−0.637995	+	0.751105i	−0.0741654	+	0.0873142i
$75$	−0.452137	+	2.75791i	−0.0522083	+	0.318456i
$76$	−0.0734209	+	1.35417i	−0.00842195	+	0.155334i
$77$	−1.59760	+	0.351659i	−0.182064	+	0.0400752i
$78$	0.0718849	+	0.0680930i	0.00813936	+	0.00771001i
$79$	7.40741	+	2.49585i	0.833399	+	0.280805i	0.703476	−	0.710719i	$-0.251630\pi$
$79$	7.40741	+	2.49585i	0.833399	+	0.280805i	0.129923	+	0.991524i	$0.458527\pi$
$80$	1.03339	+	2.59361i	0.115537	+	0.289975i
$81$	0.267528	−	0.963550i	0.0297254	−	0.107061i
$82$	−7.09597	−	1.56194i	−0.783619	−	0.172488i
$83$	−1.72389	−	2.54255i	−0.189222	−	0.279081i	0.721231	−	0.692695i	$-0.243577\pi$
$83$	−1.72389	−	2.54255i	−0.189222	−	0.279081i	−0.910453	+	0.413614i	$0.864266\pi$
$84$	1.23217	−	2.32412i	0.134441	−	0.253582i
$85$	0.742048	+	1.39965i	0.0804864	+	0.151813i
$86$	4.00105	−	5.90111i	0.431444	−	0.636333i
$87$	−6.51108	+	6.16762i	−0.698061	+	0.661239i
$88$	0.564391	−	0.261115i	0.0601643	−	0.0278350i
$89$	−11.0055	+	5.09170i	−1.16658	+	0.539719i	−0.904979	−	0.425456i	$-0.860114\pi$
$89$	−11.0055	+	5.09170i	−1.16658	+	0.539719i	−0.261604	+	0.965175i	$0.584252\pi$
$90$	−2.02691	+	1.91999i	−0.213655	+	0.202385i
$91$	−0.146170	+	0.215584i	−0.0153227	+	0.0225993i
$92$	3.62954	+	6.84604i	0.378406	+	0.713749i
$93$	0.0783735	−	0.147828i	0.00812695	−	0.0153291i
$94$	−1.26577	−	1.86687i	−0.130554	−	0.192553i
$95$	3.69774	+	0.813934i	0.379380	+	0.0835079i
$96$	−0.267528	+	0.963550i	−0.0273045	+	0.0983419i
$97$	1.39266	+	3.49532i	0.141403	+	0.354896i	0.982573	−	0.185875i	$-0.0595120\pi$
$97$	1.39266	+	3.49532i	0.141403	+	0.354896i	−0.841170	+	0.540771i	$0.818133\pi$
$98$	−0.0760406	−	0.0256211i	−0.00768126	−	0.00258812i
$99$	0.451472	+	0.427657i	0.0453747	+	0.0429812i
$100$	2.72939	−	0.600784i	0.272939	−	0.0600784i
$101$	0.814285	−	15.0186i	0.0810243	−	1.49441i	−0.621875	−	0.783117i	$-0.713629\pi$
$101$	0.814285	−	15.0186i	0.0810243	−	1.49441i	0.702899	−	0.711289i	$-0.251888\pi$
$102$	−0.0917987	+	0.559948i	−0.00908943	+	0.0554431i
$103$	−9.96697	+	11.7340i	−0.982075	+	1.15619i	0.00565009	+	0.999984i	$0.498202\pi$
$103$	−9.96697	+	11.7340i	−0.982075	+	1.15619i	−0.987725	+	0.156204i	$0.950074\pi$
$104$	0.0366495	−	0.0919832i	0.00359378	−	0.00901970i
$105$	−5.84669	−	4.44454i	−0.570578	−	0.433742i
$106$	7.37538	+	4.43762i	0.716360	+	0.431019i
$107$	0.106737	+	0.651069i	0.0103187	+	0.0629412i	0.991484	−	0.130229i	$-0.0415713\pi$
$107$	0.106737	+	0.651069i	0.0103187	+	0.0629412i	−0.981165	+	0.193170i	$0.938123\pi$
$108$	−0.994138	+	0.108119i	−0.0956610	+	0.0104038i
$109$	−1.17395	+	0.892414i	−0.112444	+	0.0854777i	−0.659885	−	0.751366i	$-0.729395\pi$
$109$	−1.17395	+	0.892414i	−0.112444	+	0.0854777i	0.547441	+	0.836844i	$0.315602\pi$
$110$	−0.464481	−	1.67291i	−0.0442865	−	0.159506i
$111$	0.0533535	+	0.984048i	0.00506409	+	0.0934017i
$112$	−2.61512	−	0.284412i	−0.247106	−	0.0268744i
$113$	−14.0746	+	8.46843i	−1.32403	+	0.796643i	−0.989332	−	0.145682i	$-0.953462\pi$
$113$	−14.0746	+	8.46843i	−1.32403	+	0.796643i	−0.334700	+	0.942325i	$0.608635\pi$
$114$	0.877958	+	1.03361i	0.0822283	+	0.0968066i
$115$	20.5011	−	6.90762i	1.91174	−	0.644139i
$116$	8.13958	+	3.76577i	0.755741	+	0.349643i
$117$	0.0990156			0.00915400
$118$	4.63522	+	6.12493i	0.426707	+	0.563845i
$119$	−1.49263			−0.136829
$120$	2.53386	+	1.17229i	0.231309	+	0.107015i
$121$	10.0577	−	3.38884i	0.914337	−	0.308076i
$122$	5.55390	+	6.53855i	0.502826	+	0.591973i
$123$	−6.22579	+	3.74593i	−0.561361	+	0.337759i
$124$	−0.166338	−	0.0180903i	−0.0149376	−	0.00162456i
$125$	0.333328	+	6.14788i	0.0298138	+	0.549883i
$126$	−0.703745	−	2.53466i	−0.0626946	−	0.225805i
$127$	5.50968	−	4.18835i	0.488905	−	0.371656i	−0.331485	−	0.943460i	$-0.607550\pi$
$127$	5.50968	−	4.18835i	0.488905	−	0.371656i	0.820390	+	0.571805i	$0.193757\pi$
$128$	0.994138	−	0.108119i	0.0878702	−	0.00955646i
$129$	−1.15344	−	7.03570i	−0.101555	−	0.619459i
$130$	−0.236871	−	0.142521i	−0.0207750	−	0.0124999i
$131$	1.33182	+	1.01242i	0.116362	+	0.0884558i	0.661737	−	0.749736i	$-0.269820\pi$
$131$	1.33182	+	1.01242i	0.116362	+	0.0884558i	−0.545375	+	0.838192i	$0.683613\pi$
$132$	0.230177	−	0.577700i	0.0200343	−	0.0502823i
$133$	−2.30951	+	2.71896i	−0.200260	+	0.235764i
$134$	−0.614416	+	3.74777i	−0.0530774	+	0.323758i
$135$	−0.151151	+	2.78781i	−0.0130090	+	0.239936i
$136$	0.554156	−	0.121979i	0.0475185	−	0.0104596i
$137$	−12.1646	−	11.5229i	−1.03929	−	0.984471i	−0.0394026	−	0.999223i	$-0.512545\pi$
$137$	−12.1646	−	11.5229i	−1.03929	−	0.984471i	−0.999891	+	0.0147520i	$0.995304\pi$
$138$	7.34305	+	2.47416i	0.625082	+	0.210615i
$139$	−2.96477	−	7.44102i	−0.251469	−	0.631139i	0.748001	−	0.663698i	$-0.231014\pi$
$139$	−2.96477	−	7.44102i	−0.251469	−	0.631139i	−0.999470	+	0.0325585i	$0.989634\pi$
$140$	−1.96479	+	7.07653i	−0.166055	+	0.598076i
$141$	−2.20279	−	0.484870i	−0.185508	−	0.0408334i
$142$	5.27027	+	7.77307i	0.442271	+	0.652302i
$143$	−0.0288420	+	0.0544018i	−0.00241189	+	0.00454931i
$144$	0.468408	+	0.883512i	0.0390340	+	0.0736260i
$145$	14.0517	−	20.7246i	1.16693	−	1.72109i
$146$	3.72924	−	3.53252i	0.308634	−	0.292354i
$147$	−0.0728248	+	0.0336923i	−0.00600648	+	0.00277890i
$148$	0.894409	−	0.413798i	0.0735200	−	0.0340140i
$149$	10.9807	−	10.4015i	0.899576	−	0.852124i	−0.0900285	−	0.995939i	$-0.528696\pi$
$149$	10.9807	−	10.4015i	0.899576	−	0.852124i	0.989605	+	0.143815i	$0.0459372\pi$
$150$	1.56837	−	2.31317i	0.128057	−	0.188869i
$151$	−10.7493	−	20.2754i	−0.874767	−	1.64999i	−0.753580	−	0.657356i	$-0.771675\pi$
$151$	−10.7493	−	20.2754i	−0.874767	−	1.64999i	−0.121187	−	0.992630i	$-0.538670\pi$
$152$	0.635235	−	1.19818i	0.0515244	−	0.0971853i
$153$	0.318430	+	0.469649i	0.0257436	+	0.0379689i
$154$	1.59760	+	0.351659i	0.128738	+	0.0283375i
$155$	−0.124973	+	0.450111i	−0.0100380	+	0.0361538i
$156$	−0.0366495	−	0.0919832i	−0.00293431	−	0.00736455i
$157$	−0.700859	−	0.236147i	−0.0559346	−	0.0188466i	0.291195	−	0.956664i	$-0.405947\pi$
$157$	−0.700859	−	0.236147i	−0.0559346	−	0.0188466i	−0.347130	+	0.937817i	$0.612844\pi$
$158$	−5.67480	−	5.37546i	−0.451463	−	0.427649i
$159$	8.40624	−	1.85035i	0.666658	−	0.146743i
$160$	0.151151	−	2.78781i	0.0119495	−	0.220396i
$161$	−3.29763	+	20.1147i	−0.259890	+	1.58526i
$162$	−0.647386	+	0.762162i	−0.0508635	+	0.0598811i
$163$	−0.212726	+	0.533901i	−0.0166619	+	0.0418183i	−0.937072	−	0.349135i	$-0.886475\pi$
$163$	−0.212726	+	0.533901i	−0.0166619	+	0.0418183i	0.920410	+	0.390954i	$0.127855\pi$
$164$	5.78429	+	4.39710i	0.451677	+	0.343356i
$165$	−1.48767	−	0.895101i	−0.115815	−	0.0696835i
$166$	0.496973	+	3.03140i	0.0385726	+	0.235282i
$167$	11.6270	−	1.26451i	0.899722	−	0.0978507i	0.353445	−	0.935455i	$-0.385010\pi$
$167$	11.6270	−	1.26451i	0.899722	−	0.0978507i	0.546277	+	0.837605i	$0.316045\pi$
$168$	−2.09416	+	1.59194i	−0.161568	+	0.122821i
$169$	−3.47525	−	12.5167i	−0.267327	−	0.962823i
$170$	−0.0857663	−	1.58187i	−0.00657797	−	0.121324i
$171$	1.34821	+	0.146626i	0.103100	+	0.0112128i
$172$	−6.10907	+	3.67570i	−0.465812	+	0.280270i
$173$	−6.95927	−	8.19309i	−0.529103	−	0.622909i	0.431068	−	0.902319i	$-0.358137\pi$
$173$	−6.95927	−	8.19309i	−0.529103	−	0.622909i	−0.960172	+	0.279411i	$0.909861\pi$
$174$	8.49902	−	2.86365i	0.644309	−	0.217093i
$175$	6.67218	+	3.08688i	0.504369	+	0.233346i
$176$	−0.621867			−0.0468750
$177$	7.57726	+	1.25903i	0.569542	+	0.0946344i
$178$	12.1263			0.908904
$179$	−22.1388	−	10.2425i	−1.65473	−	0.765560i	−0.999953	−	0.00973837i	$-0.996900\pi$
$179$	−22.1388	−	10.2425i	−1.65473	−	0.765560i	−0.654778	−	0.755821i	$-0.727238\pi$
$180$	2.64576	−	0.891459i	0.197203	−	0.0664454i
$181$	14.3736	+	16.9219i	1.06838	+	1.25779i	0.964747	+	0.263178i	$0.0847707\pi$
$181$	14.3736	+	16.9219i	1.06838	+	1.25779i	0.103632	+	0.994616i	$0.466953\pi$
$182$	0.223181	−	0.134284i	0.0165433	−	0.00995377i
$183$	8.52866	+	0.927548i	0.630457	+	0.0685663i
$184$	−0.419504	−	7.73730i	−0.0309263	−	0.570401i
$185$	−0.736078	−	2.65111i	−0.0541175	−	0.194914i
$186$	−0.133201	+	0.101257i	−0.00976679	+	0.00742452i
$187$	−0.350793	+	0.0381510i	−0.0256525	+	0.00278988i
$188$	0.364902	+	2.22580i	0.0266132	+	0.162334i
$189$	−2.25400	−	1.35619i	−0.163954	−	0.0986481i
$190$	−3.01422	−	2.29135i	−0.218674	−	0.166232i
$191$	−2.54168	+	6.37913i	−0.183909	+	0.461578i	−0.991807	−	0.127745i	$-0.959226\pi$
$191$	−2.54168	+	6.37913i	−0.183909	+	0.461578i	0.807898	+	0.589323i	$0.200605\pi$
$192$	0.647386	−	0.762162i	0.0467211	−	0.0550043i
$193$	−4.03136	+	24.5902i	−0.290184	+	1.77004i	0.291443	+	0.956588i	$0.405865\pi$
$193$	−4.03136	+	24.5902i	−0.290184	+	1.77004i	−0.581627	+	0.813455i	$0.697584\pi$
$194$	0.203700	−	3.75703i	0.0146248	−	0.269739i
$195$	−0.269979	+	0.0594269i	−0.0193336	+	0.00425565i
$196$	0.0582546	+	0.0551817i	0.00416104	+	0.00394155i
$197$	14.6709	+	4.94320i	1.04526	+	0.352188i	0.788982	−	0.614416i	$-0.210608\pi$
$197$	14.6709	+	4.94320i	1.04526	+	0.352188i	0.256275	+	0.966604i	$0.417505\pi$
$198$	−0.230177	−	0.577700i	−0.0163579	−	0.0410553i
$199$	−3.20247	+	11.5342i	−0.227017	+	0.817641i	0.759014	+	0.651075i	$0.225682\pi$
$199$	−3.20247	+	11.5342i	−0.227017	+	0.817641i	−0.986030	+	0.166566i	$0.946732\pi$
$200$	−2.72939	−	0.600784i	−0.192997	−	0.0424818i
$201$	2.13128	+	3.14340i	0.150329	+	0.221718i
$202$	−7.04517	+	13.2886i	−0.495696	+	0.934983i
$203$	11.0507	+	20.8438i	0.775606	+	1.46295i
$204$	0.318430	−	0.469649i	0.0222946	−	0.0328820i
$205$	14.7272	−	13.9504i	1.02859	−	0.974335i
$206$	13.9728	−	6.46449i	0.973529	−	0.450402i
$207$	7.03250	−	3.25358i	0.488792	−	0.226139i
$208$	−0.0718849	+	0.0680930i	−0.00498432	+	0.00472140i
$209$	−0.473277	+	0.698031i	−0.0327372	+	0.0482838i
$210$	3.44010	+	6.48871i	0.237389	+	0.447764i
$211$	−2.74298	+	5.17381i	−0.188835	+	0.356180i	−0.959794	−	0.280704i	$-0.909432\pi$
$211$	−2.74298	+	5.17381i	−0.188835	+	0.356180i	0.770960	+	0.636884i	$0.219777\pi$
$212$	−4.83040	−	7.12431i	−0.331754	−	0.489300i
$213$	9.17173	+	2.01885i	0.628437	+	0.138329i
$214$	0.176505	−	0.635712i	0.0120656	−	0.0434564i
$215$	7.36768	+	18.4915i	0.502472	+	1.26111i
$216$	0.947653	+	0.319302i	0.0644796	+	0.0217257i
$217$	−0.319539	−	0.302683i	−0.0216917	−	0.0205475i
$218$	1.44016	−	0.317004i	0.0975401	−	0.0214702i
$219$	0.278097	−	5.12919i	0.0187920	−	0.346599i
$220$	−0.280885	+	1.71332i	−0.0189372	+	0.115512i
$221$	−0.0363726	+	0.0428211i	−0.00244668	+	0.00288046i
$222$	0.364769	−	0.915500i	0.0244817	−	0.0614443i
$223$	−18.7574	−	14.2590i	−1.25609	−	0.954855i	−0.256160	−	0.966634i	$-0.582457\pi$
$223$	−18.7574	−	14.2590i	−1.25609	−	0.954855i	−0.999931	+	0.0117790i	$0.996251\pi$
$224$	2.25400	+	1.35619i	0.150602	+	0.0906140i
$225$	−0.452137	−	2.75791i	−0.0301425	−	0.183861i
$226$	16.3296	−	1.77595i	1.08623	−	0.118135i
$227$	9.25589	−	7.03614i	0.614335	−	0.467005i	−0.251145	−	0.967950i	$-0.580807\pi$
$227$	9.25589	−	7.03614i	0.614335	−	0.467005i	0.865479	+	0.500944i	$0.167014\pi$
$228$	−0.362810	−	1.30673i	−0.0240277	−	0.0865400i
$229$	0.626383	+	11.5530i	0.0413926	+	0.763441i	0.943387	+	0.331694i	$0.107620\pi$
$229$	0.626383	+	11.5530i	0.0413926	+	0.763441i	−0.901995	+	0.431747i	$0.857897\pi$
$230$	−21.5067	−	2.33900i	−1.41811	−	0.154229i
$231$	1.40169	−	0.843367i	0.0922243	−	0.0554895i
$232$	−5.80608	−	6.83544i	−0.381188	−	0.448769i
$233$	0.525609	−	0.177098i	0.0344338	−	0.0116021i	−0.302032	−	0.953298i	$-0.597665\pi$
$233$	0.525609	−	0.177098i	0.0344338	−	0.0116021i	0.336466	+	0.941696i	$0.390768\pi$
$234$	−0.0898642	−	0.0415756i	−0.00587460	−	0.00271788i
$235$	6.29719			0.410783
$236$	−1.63502	−	7.50511i	−0.106431	−	0.488541i
$237$	−7.81658			−0.507742
$238$	1.35467	+	0.626739i	0.0878105	+	0.0406254i
$239$	−15.3823	+	5.18289i	−0.994995	+	0.335253i	−0.769260	−	0.638936i	$-0.779375\pi$
$239$	−15.3823	+	5.18289i	−0.994995	+	0.335253i	−0.225735	+	0.974189i	$0.572478\pi$
$240$	−1.80744	−	2.12788i	−0.116670	−	0.137354i
$241$	−0.856760	+	0.515495i	−0.0551888	+	0.0332060i	−0.542881	−	0.839810i	$-0.682666\pi$
$241$	−0.856760	+	0.515495i	−0.0551888	+	0.0332060i	0.487692	+	0.873016i	$0.337839\pi$
$242$	−10.5511	−	1.14750i	−0.678248	−	0.0737639i
$243$	0.0541389	+	0.998533i	0.00347301	+	0.0640559i
$244$	−2.29511	−	8.26625i	−0.146930	−	0.529193i
$245$	0.178345	−	0.135574i	0.0113940	−	0.00866152i
$246$	7.22325	−	0.785576i	0.460538	−	0.0500865i
$247$	0.0217242	+	0.132512i	0.00138228	+	0.00843152i
$248$	0.143368	+	0.0862618i	0.00910389	+	0.00547763i
$249$	2.44549	+	1.85902i	0.154977	+	0.117810i
$250$	2.27891	−	5.71962i	0.144131	−	0.361741i
$251$	0.105576	−	0.124294i	0.00666393	−	0.00784538i	−0.758820	−	0.651300i	$-0.774224\pi$
$251$	0.105576	−	0.124294i	0.00666393	−	0.00784538i	0.765484	+	0.643455i	$0.222500\pi$
$252$	−0.425575	+	2.59589i	−0.0268087	+	0.163526i
$253$	−0.260876	+	4.81157i	−0.0164011	+	0.302501i
$254$	−6.75909	+	1.48779i	−0.424103	+	0.0933521i
$255$	−1.15011	−	1.08945i	−0.0720229	−	0.0682238i
$256$	−0.947653	−	0.319302i	−0.0592283	−	0.0199563i
$257$	−4.49521	−	11.2821i	−0.280403	−	0.703759i	−0.999957	−	0.00932191i	$-0.997033\pi$
$257$	−4.49521	−	11.2821i	−0.280403	−	0.703759i	0.719553	−	0.694437i	$-0.244347\pi$
$258$	−1.90738	+	6.86975i	−0.118748	+	0.427692i
$259$	2.53177	+	0.557286i	0.157317	+	0.0346280i
$260$	0.155136	+	0.228808i	0.00962111	+	0.0141901i
$261$	4.20092	−	7.92377i	0.260030	−	0.490469i
$262$	−0.783622	−	1.47807i	−0.0484123	−	0.0913153i
$263$	−8.10282	+	11.9508i	−0.499642	+	0.736916i	−0.990974	−	0.134056i	$-0.957200\pi$
$263$	−8.10282	+	11.9508i	−0.499642	+	0.736916i	0.491332	+	0.870972i	$0.336510\pi$
$264$	−0.451472	+	0.427657i	−0.0277862	+	0.0263205i
$265$	−21.8102	+	10.0905i	−1.33979	+	0.619852i
$266$	3.23771	−	1.49793i	0.198517	−	0.0918437i
$267$	8.80363	−	8.33924i	0.538774	−	0.510353i
$268$	2.13128	−	3.14340i	0.130188	−	0.192014i
$269$	−14.5513	−	27.4467i	−0.887211	−	1.67346i	−0.727294	−	0.686327i	$-0.759222\pi$
$269$	−14.5513	−	27.4467i	−0.887211	−	1.67346i	−0.159917	−	0.987130i	$-0.551123\pi$
$270$	1.30775	−	2.46668i	0.0795872	−	0.150117i
$271$	−1.71428	−	2.52838i	−0.104135	−	0.153588i	0.772051	−	0.635560i	$-0.219231\pi$
$271$	−1.71428	−	2.52838i	−0.104135	−	0.153588i	−0.876186	+	0.481972i	$0.839921\pi$
$272$	−0.554156	−	0.121979i	−0.0336007	−	0.00739607i
$273$	0.0696817	−	0.250971i	0.00421733	−	0.0151895i
$274$	6.20195	+	15.5657i	0.374674	+	0.940360i
$275$	1.64697	+	0.554930i	0.0993162	+	0.0334635i
$276$	−5.62550	−	5.32875i	−0.338615	−	0.320753i
$277$	17.9615	−	3.95363i	1.07920	−	0.237550i	0.360423	−	0.932789i	$-0.382632\pi$
$277$	17.9615	−	3.95363i	1.07920	−	0.237550i	0.718779	+	0.695239i	$0.244701\pi$
$278$	−0.433648	+	7.99816i	−0.0260085	+	0.479698i
$279$	−0.0270692	+	0.165115i	−0.00162059	+	0.00988515i
$280$	4.75455	−	5.59749i	0.284139	−	0.334514i
$281$	3.64226	−	9.14138i	0.217279	−	0.545329i	−0.779421	−	0.626500i	$-0.784487\pi$
$281$	3.64226	−	9.14138i	0.217279	−	0.545329i	0.996700	+	0.0811712i	$0.0258661\pi$
$282$	1.79560	+	1.36498i	0.106927	+	0.0812835i
$283$	−7.39095	−	4.44699i	−0.439347	−	0.264346i	0.278650	−	0.960393i	$-0.410113\pi$
$283$	−7.39095	−	4.44699i	−0.439347	−	0.264346i	−0.717997	+	0.696047i	$0.754941\pi$
$284$	−1.51934	−	9.26758i	−0.0901564	−	0.549930i
$285$	−3.76407	+	0.409367i	−0.222964	+	0.0242488i
$286$	0.0490191	−	0.0372633i	0.00289856	−	0.00220343i
$287$	5.11330	+	18.4164i	0.301829	+	1.08709i
$288$	−0.0541389	−	0.998533i	−0.00319017	−	0.0588391i
$289$	16.5803	+	1.80321i	0.975310	+	0.106071i
$290$	−21.4550	+	12.9090i	−1.25988	+	0.758045i
$291$	−2.43582	−	2.86767i	−0.142790	−	0.168106i
$292$	−4.86783	+	1.64016i	−0.284868	+	0.0959833i
$293$	−4.35344	−	2.01411i	−0.254330	−	0.117666i	0.288582	−	0.957455i	$-0.406816\pi$
$293$	−4.35344	−	2.01411i	−0.254330	−	0.117666i	−0.542912	+	0.839789i	$0.682678\pi$
$294$	0.0802410			0.00467975
$295$	−21.4160	+	1.11479i	−1.24689	+	0.0649054i
$296$	−0.985493			−0.0572806
$297$	−0.564391	−	0.261115i	−0.0327493	−	0.0151514i
$298$	−14.3333	+	4.82945i	−0.830306	+	0.279763i
$299$	0.496700	+	0.584760i	0.0287249	+	0.0338176i
$300$	−2.39468	+	1.44083i	−0.138257	+	0.0831865i
$301$	−18.6448	−	2.02775i	−1.07467	−	0.116877i
$302$	1.24241	+	22.9149i	0.0714928	+	1.31861i
$303$	4.02380	+	14.4924i	0.231161	+	0.832568i
$304$	−1.07963	+	0.820711i	−0.0619209	+	0.0470710i
$305$	−23.8112	+	2.58963i	−1.36343	+	0.148282i
$306$	−0.0917987	−	0.559948i	−0.00524778	−	0.0320101i
$307$	−18.0361	−	10.8519i	−1.02937	−	0.619353i	−0.102502	−	0.994733i	$-0.532685\pi$
$307$	−18.0361	−	10.8519i	−1.02937	−	0.619353i	−0.926871	+	0.375379i	$0.877512\pi$
$308$	−1.30229	−	0.989973i	−0.0742047	−	0.0564089i
$309$	5.69854	−	14.3023i	0.324179	−	0.813627i
$310$	0.302419	−	0.356035i	0.0171762	−	0.0202214i
$311$	−1.73129	+	10.5604i	−0.0981725	+	0.598826i	0.891221	+	0.453569i	$0.149849\pi$
$311$	−1.73129	+	10.5604i	−0.0981725	+	0.598826i	−0.989394	+	0.145257i	$0.953599\pi$
$312$	−0.00536060	+	0.0988704i	−0.000303484	+	0.00559744i
$313$	9.41673	−	2.07278i	0.532265	−	0.117160i	0.0592976	−	0.998240i	$-0.481114\pi$
$313$	9.41673	−	2.07278i	0.532265	−	0.117160i	0.472967	+	0.881080i	$0.343183\pi$
$314$	0.536927	+	0.508604i	0.0303005	+	0.0287022i
$315$	6.95978	+	2.34502i	0.392139	+	0.132127i
$316$	2.89322	+	7.26142i	0.162756	+	0.408487i
$317$	0.744568	−	2.68169i	0.0418191	−	0.150619i	−0.939693	−	0.342019i	$-0.888889\pi$
$317$	0.744568	−	2.68169i	0.0418191	−	0.150619i	0.981512	+	0.191401i	$0.0613029\pi$
$318$	−8.40624	−	1.85035i	−0.471398	−	0.103763i
$319$	3.12985	+	4.61619i	0.175238	+	0.258457i
$320$	−1.30775	+	2.46668i	−0.0731055	+	0.137892i
$321$	−0.309037	−	0.582906i	−0.0172488	−	0.0325346i
$322$	11.4388	−	16.8709i	0.637459	−	0.940181i
$323$	−0.558664	+	0.529194i	−0.0310849	+	0.0294452i
$324$	0.907575	−	0.419889i	0.0504209	−	0.0233272i
$325$	0.251146	−	0.116192i	0.0139311	−	0.00644520i
$326$	0.417244	−	0.395234i	0.0231090	−	0.0218900i
$327$	0.827548	−	1.22054i	0.0457635	−	0.0674962i
$328$	−3.40338	−	6.41946i	−0.187920	−	0.354455i
$329$	−2.77918	+	5.24209i	−0.153221	+	0.289006i
$330$	0.974329	+	1.43703i	0.0536350	+	0.0791057i
$331$	33.1874	+	7.30510i	1.82414	+	0.401525i	0.988928	−	0.148396i	$-0.0474111\pi$
$331$	33.1874	+	7.30510i	1.82414	+	0.401525i	0.835217	+	0.549921i	$0.185342\pi$
$332$	0.821812	−	2.95990i	0.0451028	−	0.162446i
$333$	−0.364769	−	0.915500i	−0.0199892	−	0.0501691i
$334$	−11.0833	−	3.73440i	−0.606452	−	0.204337i
$335$	−7.69780	−	7.29174i	−0.420576	−	0.398390i
$336$	2.56904	−	0.565489i	0.140153	−	0.0308500i
$337$	0.263683	−	4.86334i	0.0143637	−	0.264923i	−0.982527	−	0.186122i	$-0.940408\pi$
$337$	0.263683	−	4.86334i	0.0143637	−	0.264923i	0.996890	−	0.0788011i	$-0.0251092\pi$
$338$	−2.10158	+	12.8191i	−0.114311	+	0.697265i
$339$	10.6339	−	12.5192i	0.577554	−	0.679949i
$340$	−0.586369	+	1.47167i	−0.0318003	+	0.0798128i
$341$	−0.0828334	−	0.0629683i	−0.00448568	−	0.00340993i
$342$	−1.16203	−	0.699172i	−0.0628355	−	0.0378069i
$343$	3.01317	+	18.3795i	0.162696	+	0.992401i
$344$	7.08783	−	0.770848i	0.382150	−	0.0415613i
$345$	−17.2223	+	13.0921i	−0.927218	+	0.704852i
$346$	2.87587	+	10.3580i	0.154608	+	0.556848i
$347$	−0.787709	−	14.5284i	−0.0422864	−	0.779927i	−0.940381	−	0.340124i	$-0.889531\pi$
$347$	−0.787709	−	14.5284i	−0.0422864	−	0.779927i	0.898094	−	0.439803i	$-0.144952\pi$
$348$	−8.91591	−	0.969664i	−0.477943	−	0.0519795i
$349$	−13.4584	+	8.09764i	−0.720411	+	0.433457i	−0.827992	−	0.560739i	$-0.810517\pi$
$349$	−13.4584	+	8.09764i	−0.720411	+	0.433457i	0.107581	+	0.994196i	$0.465689\pi$
$350$	−4.75936	−	5.60315i	−0.254399	−	0.299501i
$351$	−0.0938325	+	0.0316158i	−0.00500841	+	0.00168753i
$352$	0.564391	+	0.261115i	0.0300821	+	0.0139175i
$353$	14.2159			0.756638			0.378319	−	0.925675i	$-0.376502\pi$
$353$	14.2159			0.756638			0.378319	+	0.925675i	$0.376502\pi$
$354$	−6.34828	−	4.32427i	−0.337407	−	0.229832i
$355$	−26.2196			−1.39159
$356$	−11.0055	−	5.09170i	−0.583292	−	0.269859i
$357$	1.41449	−	0.476599i	0.0748630	−	0.0252243i
$358$	15.7919	+	18.5917i	0.834628	+	0.982600i
$359$	−20.9663	+	12.6150i	−1.10656	+	0.665795i	−0.946949	−	0.321384i	$-0.895852\pi$
$359$	−20.9663	+	12.6150i	−1.10656	+	0.665795i	−0.159612	+	0.987180i	$0.551024\pi$
$360$	−2.77554	−	0.301858i	−0.146284	−	0.0159093i
$361$	−0.929069	−	17.1357i	−0.0488984	−	0.901877i
$362$	−5.93979	−	21.3932i	−0.312189	−	1.12440i
$363$	−8.44916	+	6.42288i	−0.443466	+	0.337114i
$364$	−0.258938	+	0.0281612i	−0.0135720	+	0.00147605i
$365$	2.32015	+	14.1523i	0.121442	+	0.740766i
$366$	−7.35094	−	4.42291i	−0.384240	−	0.231189i
$367$	−15.4196	−	11.7217i	−0.804897	−	0.611867i	0.119702	−	0.992810i	$-0.461806\pi$
$367$	−15.4196	−	11.7217i	−0.804897	−	0.611867i	−0.924598	+	0.380943i	$0.875599\pi$
$368$	−2.86808	+	7.19833i	−0.149509	+	0.375239i
$369$	4.70381	−	5.53775i	0.244870	−	0.288284i
$370$	−0.445127	+	2.71516i	−0.0231411	+	0.141154i
$371$	1.22583	−	22.6091i	0.0636420	−	1.17381i
$372$	0.163407	−	0.0359686i	0.00847225	−	0.00186488i
$373$	18.7350	+	17.7467i	0.970061	+	0.918891i	0.996734	−	0.0807533i	$-0.0257326\pi$
$373$	18.7350	+	17.7467i	0.970061	+	0.918891i	−0.0266728	+	0.999644i	$0.508491\pi$
$374$	0.334390	+	0.112669i	0.0172909	+	0.00582598i
$375$	−2.27891	−	5.71962i	−0.117682	−	0.295360i
$376$	0.603415	−	2.17330i	0.0311188	−	0.112080i
$377$	0.867259	+	0.190898i	0.0446661	+	0.00983176i
$378$	1.47623	+	2.17727i	0.0759289	+	0.111987i
$379$	13.5456	−	25.5497i	0.695789	−	1.31240i	−0.243711	−	0.969848i	$-0.578365\pi$
$379$	13.5456	−	25.5497i	0.695789	−	1.31240i	0.939500	−	0.342549i	$-0.111290\pi$
$380$	1.77352	+	3.34521i	0.0909795	+	0.171605i
$381$	−3.88392	+	5.72835i	−0.198979	+	0.293472i
$382$	4.98529	−	4.72232i	0.255070	−	0.241615i
$383$	1.21547	−	0.562338i	0.0621079	−	0.0287342i	−0.388589	−	0.921411i	$-0.627038\pi$
$383$	1.21547	−	0.562338i	0.0621079	−	0.0287342i	0.450697	+	0.892677i	$0.351175\pi$
$384$	−0.907575	+	0.419889i	−0.0463145	+	0.0214274i
$385$	−3.31572	+	3.14081i	−0.168984	+	0.160071i
$386$	13.9839	−	20.6248i	0.711764	−	1.04977i
$387$	3.33957	+	6.29911i	0.169760	+	0.320202i
$388$	−1.76241	+	3.32425i	−0.0894727	+	0.168763i
$389$	8.31890	+	12.2695i	0.421785	+	0.622086i	0.977913	−	0.209010i	$-0.0670241\pi$
$389$	8.31890	+	12.2695i	0.421785	+	0.622086i	−0.556129	+	0.831096i	$0.687714\pi$
$390$	0.269979	+	0.0594269i	0.0136709	+	0.00300920i
$391$	−1.17626	+	4.23650i	−0.0594860	+	0.214249i
$392$	−0.0297003	−	0.0745420i	−0.00150009	−	0.00376494i
$393$	−1.58537	−	0.534174i	−0.0799714	−	0.0269455i
$394$	−11.2393	−	10.6465i	−0.566230	−	0.536361i
$395$	21.3129	−	4.69133i	1.07237	−	0.236047i
$396$	−0.0336672	+	0.620955i	−0.00169184	+	0.0312041i
$397$	−4.93208	+	30.0843i	−0.247534	+	1.50989i	0.511753	+	0.859133i	$0.328996\pi$
$397$	−4.93208	+	30.0843i	−0.247534	+	1.50989i	−0.759286	+	0.650757i	$0.774452\pi$
$398$	7.74958	−	9.12351i	0.388451	−	0.457320i
$399$	1.32044	−	3.31406i	0.0661048	−	0.165911i
$400$	2.22486	+	1.69130i	0.111243	+	0.0845649i
$401$	−13.9432	−	8.38934i	−0.696290	−	0.418944i	0.122936	−	0.992415i	$-0.460769\pi$
$401$	−13.9432	−	8.38934i	−0.696290	−	0.418944i	−0.819226	+	0.573471i	$0.805597\pi$
$402$	−0.614416	−	3.74777i	−0.0306443	−	0.186922i
$403$	−0.0164701	+	0.00179123i	−0.000820432	+	8.92273e-5i
$404$	11.9738	−	9.10222i	0.595717	−	0.452852i
$405$	−0.746913	−	2.69014i	−0.0371144	−	0.133674i
$406$	−1.27725	−	23.5574i	−0.0633886	−	1.16913i
$407$	0.609253	+	0.0662602i	0.0301995	+	0.00328440i
$408$	−0.486200	+	0.292537i	−0.0240705	+	0.0144827i
$409$	12.0352	+	14.1689i	0.595100	+	0.700606i	0.974439	−	0.224652i	$-0.0721244\pi$
$409$	12.0352	+	14.1689i	0.595100	+	0.700606i	−0.379339	+	0.925258i	$0.623849\pi$
$410$	−19.2237	+	6.47720i	−0.949389	+	0.319886i
$411$	15.2071	+	7.03557i	0.750113	+	0.347039i
$412$	−15.3957			−0.758492
$413$	8.52367	−	18.3197i	0.419422	−	0.901455i
$414$	−7.74866			−0.380826
$415$	−7.78370	−	3.60112i	−0.382087	−	0.176772i
$416$	0.0938325	−	0.0316158i	0.00460052	−	0.00155009i
$417$	5.18550	+	6.10485i	0.253935	+	0.298956i
$418$	0.722630	−	0.434792i	0.0353450	−	0.0212664i
$419$	24.6019	+	2.67562i	1.20188	+	0.130713i	0.687070	−	0.726591i	$-0.258896\pi$
$419$	24.6019	+	2.67562i	1.20188	+	0.130713i	0.514811	+	0.857303i	$0.327862\pi$
$420$	−0.397608	−	7.33345i	−0.0194013	−	0.357836i
$421$	0.925219	+	3.33234i	0.0450924	+	0.162408i	0.982668	−	0.185372i	$-0.0593492\pi$
$421$	0.925219	+	3.33234i	0.0450924	+	0.162408i	−0.937576	+	0.347781i	$0.886935\pi$
$422$	4.66189	−	3.54387i	0.226937	−	0.172513i
$423$	2.24230	−	0.243864i	0.109024	−	0.0118571i
$424$	1.39253	+	8.49409i	0.0676275	+	0.412509i
$425$	1.35880	+	0.817561i	0.0659113	+	0.0396575i
$426$	−7.47634	−	5.68337i	−0.362230	−	0.275360i
$427$	8.35302	−	20.9645i	0.404231	−	1.01454i
$428$	−0.427120	+	0.502844i	−0.0206456	+	0.0243059i
$429$	0.00996165	−	0.0607634i	0.000480953	−	0.00293368i
$430$	1.07765	−	19.8760i	0.0519687	−	0.958507i
$431$	24.6847	−	5.43351i	1.18902	−	0.261723i	0.423959	−	0.905681i	$-0.360640\pi$
$431$	24.6847	−	5.43351i	1.18902	−	0.261723i	0.765060	+	0.643958i	$0.222709\pi$
$432$	−0.725995	−	0.687699i	−0.0349295	−	0.0330870i
$433$	−10.9257	−	3.68131i	−0.525058	−	0.176913i	0.0442754	−	0.999019i	$-0.485902\pi$
$433$	−10.9257	−	3.68131i	−0.525058	−	0.176913i	−0.569333	+	0.822107i	$0.692799\pi$
$434$	0.162912	+	0.408879i	0.00782004	+	0.0196268i
$435$	−6.69868	+	24.1265i	−0.321177	+	1.15678i
$436$	−1.44016	−	0.317004i	−0.0689713	−	0.0151817i
$437$	5.89718	+	8.69769i	0.282100	+	0.416067i
$438$	−2.40608	+	4.53836i	−0.114967	+	0.216851i
$439$	−10.2675	−	19.3665i	−0.490040	−	0.924314i	−0.998017	−	0.0629431i	$-0.979951\pi$
$439$	−10.2675	−	19.3665i	−0.490040	−	0.924314i	0.507977	−	0.861371i	$-0.330393\pi$
$440$	0.974329	−	1.43703i	0.0464493	−	0.0685076i
$441$	0.0582546	−	0.0551817i	0.00277403	−	0.00262770i
$442$	0.0509909	−	0.0235909i	0.00242539	−	0.00112211i
$443$	16.7294	−	7.73985i	0.794838	−	0.367731i	0.0199269	−	0.999801i	$-0.493657\pi$
$443$	16.7294	−	7.73985i	0.794838	−	0.367731i	0.774911	+	0.632070i	$0.217795\pi$
$444$	−0.715463	+	0.677723i	−0.0339544	+	0.0321633i
$445$	−18.9992	+	28.0218i	−0.900650	+	1.32836i
$446$	11.0366	+	20.8172i	0.522597	+	0.985722i
$447$	−7.08471	+	13.3632i	−0.335095	+	0.632056i
$448$	−1.47623	−	2.17727i	−0.0697452	−	0.102866i
$449$	20.9731	+	4.61654i	0.989783	+	0.217868i	0.680218	−	0.733010i	$-0.261885\pi$
$449$	20.9731	+	4.61654i	0.989783	+	0.217868i	0.309566	+	0.950878i	$0.399816\pi$
$450$	−0.747669	+	2.69286i	−0.0352455	+	0.126943i
$451$	1.67243	+	4.19748i	0.0787515	+	0.197651i
$452$	−15.5661	−	5.24481i	−0.732165	−	0.246695i
$453$	16.6606	+	15.7817i	0.782782	+	0.741491i
$454$	−11.3548	+	2.49938i	−0.532908	+	0.117302i
$455$	−0.0393694	+	0.726127i	−0.00184567	+	0.0340413i
$456$	−0.219402	+	1.33829i	−0.0102744	+	0.0626713i
$457$	13.4650	−	15.8522i	0.629865	−	0.741535i	−0.350967	−	0.936388i	$-0.614147\pi$
$457$	13.4650	−	15.8522i	0.629865	−	0.741535i	0.980832	+	0.194853i	$0.0624229\pi$
$458$	4.28247	−	10.7482i	0.200107	−	0.502230i
$459$	−0.451721	−	0.343389i	−0.0210845	−	0.0160280i
$460$	18.5368	+	11.1532i	0.864285	+	0.520023i
$461$	−1.03871	−	6.33587i	−0.0483777	−	0.295091i	0.951545	−	0.307509i	$-0.0994954\pi$
$461$	−1.03871	−	6.33587i	−0.0483777	−	0.295091i	−0.999923	+	0.0124180i	$0.996047\pi$
$462$	−1.62626	+	0.176866i	−0.0756604	+	0.00822856i
$463$	−32.4559	+	24.6723i	−1.50835	+	1.14662i	−0.560396	+	0.828225i	$0.689351\pi$
$463$	−32.4559	+	24.6723i	−1.50835	+	1.14662i	−0.947958	+	0.318396i	$0.896856\pi$
$464$	2.39932	+	8.64159i	0.111386	+	0.401176i
$465$	−0.0252903	−	0.466453i	−0.00117281	−	0.0216312i
$466$	−0.551391	−	0.0599674i	−0.0255427	−	0.00277794i
$467$	16.7462	−	10.0759i	0.774923	−	0.466255i	−0.0723727	−	0.997378i	$-0.523057\pi$
$467$	16.7462	−	10.0759i	0.774923	−	0.466255i	0.847295	+	0.531122i	$0.178230\pi$
$468$	0.0641014	+	0.0754660i	0.00296309	+	0.00348842i
$469$	9.46732	−	3.18991i	0.437160	−	0.147296i
$470$	−5.71517	−	2.64412i	−0.263621	−	0.121964i
$471$	0.739573			0.0340777
$472$	−1.66741	+	7.49798i	−0.0767486	+	0.345123i
$473$	−4.43367			−0.203861
$474$	7.09414	+	3.28210i	0.325845	+	0.150752i
$475$	3.59169	−	1.21018i	0.164798	−	0.0555270i
$476$	−0.966308	−	1.13763i	−0.0442906	−	0.0521430i
$477$	−7.37538	+	4.43762i	−0.337695	+	0.203185i
$478$	16.1368	+	1.75498i	0.738080	+	0.0802710i
$479$	1.76339	+	32.5238i	0.0805714	+	1.48605i	0.707355	+	0.706858i	$0.249888\pi$
$479$	1.76339	+	32.5238i	0.0805714	+	1.48605i	−0.626784	+	0.779193i	$0.715629\pi$
$480$	0.746913	+	2.69014i	0.0340918	+	0.122787i
$481$	0.0776821	−	0.0590524i	0.00354200	−	0.00269256i
$482$	0.994025	−	0.108107i	0.0452766	−	0.00492413i
$483$	−3.29763	−	20.1147i	−0.150048	−	0.915250i
$484$	9.09407	+	5.47172i	0.413367	+	0.248714i
$485$	8.36269	+	6.35715i	0.379730	+	0.288663i
$486$	0.370138	−	0.928977i	0.0167898	−	0.0421392i
$487$	15.7146	−	18.5006i	0.712095	−	0.838343i	−0.280495	−	0.959856i	$-0.590499\pi$
$487$	15.7146	−	18.5006i	0.712095	−	0.838343i	0.992590	+	0.121512i	$0.0387744\pi$
$488$	−1.38792	+	8.46594i	−0.0628282	+	0.383235i
$489$	0.0311147	−	0.573876i	0.00140705	−	0.0259516i
$490$	−0.218788	+	0.0481588i	−0.00988382	+	0.00217559i
$491$	−3.97235	−	3.76281i	−0.179270	−	0.169813i	0.592803	−	0.805348i	$-0.298021\pi$
$491$	−3.97235	−	3.76281i	−0.179270	−	0.169813i	−0.772073	+	0.635534i	$0.780780\pi$
$492$	−6.88550	−	2.31999i	−0.310422	−	0.104593i
$493$	1.88360	+	4.72749i	0.0848333	+	0.212915i
$494$	0.0359239	−	0.129386i	0.00161629	−	0.00582136i
$495$	1.69560	+	0.373230i	0.0762116	+	0.0167754i
$496$	−0.0938971	−	0.138488i	−0.00421610	−	0.00621829i
$497$	11.5717	−	21.8265i	0.519060	−	0.979051i
$498$	−1.43889	−	2.71403i	−0.0644782	−	0.121619i
$499$	17.4413	−	25.7239i	0.780778	−	1.15156i	−0.204209	−	0.978927i	$-0.565462\pi$
$499$	17.4413	−	25.7239i	0.780778	−	1.15156i	0.984986	−	0.172633i	$-0.0552276\pi$
$500$	−4.46989	+	4.23410i	−0.199899	+	0.189355i
$501$	−10.6146	+	4.91083i	−0.474224	+	0.219400i
$502$	−0.148008	+	0.0684760i	−0.00660594	+	0.00305623i
$503$	−11.6830	+	11.0667i	−0.520920	+	0.493442i	−0.902379	−	0.430944i	$-0.858181\pi$
$503$	−11.6830	+	11.0667i	−0.520920	+	0.493442i	0.381458	+	0.924386i	$0.375422\pi$
$504$	1.47623	−	2.17727i	0.0657564	−	0.0969834i
$505$	−19.6694	−	37.1005i	−0.875278	−	1.65095i
$506$	2.25709	−	4.25732i	0.100340	−	0.189261i
$507$	7.28993	+	10.7518i	0.323757	+	0.477506i
$508$	6.75909	+	1.48779i	0.299886	+	0.0660099i
$509$	8.08084	−	29.1046i	0.358177	−	1.29004i	−0.536719	−	0.843761i	$-0.680336\pi$
$509$	8.08084	−	29.1046i	0.358177	−	1.29004i	0.894896	−	0.446275i	$-0.147250\pi$
$510$	0.586369	+	1.47167i	0.0259648	+	0.0651669i
$511$	−12.8050	−	4.31452i	−0.566462	−	0.190863i
$512$	0.725995	+	0.687699i	0.0320848	+	0.0303923i
$513$	−1.32445	+	0.291534i	−0.0584759	+	0.0128715i
$514$	−0.657499	+	12.1269i	−0.0290010	+	0.534893i
$515$	−6.95393	+	42.4171i	−0.306427	+	1.86912i
$516$	4.61562	−	5.43393i	0.203191	−	0.239215i
$517$	−0.519167	+	1.30301i	−0.0228330	+	0.0573064i
$518$	−2.06378	−	1.56884i	−0.0906772	−	0.0689310i
$519$	9.21104	+	5.54210i	0.404320	+	0.243271i
$520$	−0.0447234	−	0.272800i	−0.00196125	−	0.0119631i
$521$	−7.01004	+	0.762388i	−0.307115	+	0.0334008i	−0.260379	−	0.965506i	$-0.583848\pi$
$521$	−7.01004	+	0.762388i	−0.307115	+	0.0334008i	−0.0467363	+	0.998907i	$0.514882\pi$
$522$	−7.13975	+	5.42750i	−0.312498	+	0.237555i
$523$	0.251251	+	0.904923i	0.0109864	+	0.0395695i	0.968840	−	0.247687i	$-0.0796705\pi$
$523$	0.251251	+	0.904923i	0.0109864	+	0.0395695i	−0.957854	+	0.287257i	$0.907257\pi$
$524$	0.0905714	+	1.67049i	0.00395663	+	0.0729758i
$525$	−7.30856	−	0.794854i	−0.318972	−	0.0346903i
$526$	12.3719	−	7.44394i	0.539441	−	0.324571i
$527$	−0.0614631	−	0.0723600i	−0.00267738	−	0.00315205i
$528$	0.589314	−	0.198563i	0.0256466	−	0.00864135i
$529$	33.6182	+	15.5534i	1.46166	+	0.676237i
$530$	24.0312			1.04385
$531$	−7.58262	+	1.22631i	−0.329058	+	0.0532172i
$532$	−3.56743			−0.154668
$533$	0.652939	+	0.302082i	0.0282819	+	0.0130846i
$534$	−11.4915	+	3.87194i	−0.497287	+	0.167555i
$535$	1.19248	+	1.40389i	0.0515553	+	0.0606956i
$536$	−3.25417	+	1.95797i	−0.140559	+	0.0845714i
$537$	24.2503	+	2.63738i	1.04648	+	0.113811i
$538$	1.68185	+	31.0199i	0.0725098	+	1.33736i
$539$	0.0133495	+	0.0480804i	0.000575002	+	0.00207097i
$540$	−2.22262	+	1.68959i	−0.0956461	+	0.0727083i
$541$	−13.3192	+	1.44855i	−0.572637	+	0.0622780i	−0.389856	−	0.920876i	$-0.627475\pi$
$541$	−13.3192	+	1.44855i	−0.572637	+	0.0622780i	−0.182781	+	0.983154i	$0.558510\pi$
$542$	0.494202	+	3.01450i	0.0212278	+	0.129484i
$543$	−19.0244	−	11.4466i	−0.816413	−	0.491219i
$544$	0.451721	+	0.343389i	0.0193674	+	0.0147227i
$545$	−1.52388	+	3.82464i	−0.0652757	+	0.163830i
$546$	−0.168621	+	0.198516i	−0.00721633	+	0.00849572i
$547$	7.24729	−	44.2065i	0.309872	−	1.89013i	−0.129097	−	0.991632i	$-0.541208\pi$
$547$	7.24729	−	44.2065i	0.309872	−	1.89013i	0.438969	−	0.898502i	$-0.355344\pi$
$548$	0.907140	−	16.7312i	0.0387511	−	0.714722i
$549$	−8.37838	+	1.84422i	−0.357581	+	0.0787095i
$550$	−1.26174	−	1.19519i	−0.0538009	−	0.0509629i
$551$	11.5260	+	3.88356i	0.491024	+	0.165445i
$552$	2.86808	+	7.19833i	0.122073	+	0.306381i
$553$	−5.50088	+	19.8124i	−0.233921	+	0.842508i
$554$	−17.9615	−	3.95363i	−0.763111	−	0.167973i
$555$	1.54405	+	2.27731i	0.0655413	+	0.0966662i
$556$	3.75191	−	7.07685i	0.159116	−	0.300125i
$557$	17.9918	+	33.9362i	0.762338	+	1.43792i	0.894675	+	0.446717i	$0.147407\pi$
$557$	17.9918	+	33.9362i	0.762338	+	1.43792i	−0.132337	+	0.991205i	$0.542248\pi$
$558$	0.0938971	−	0.138488i	0.00397498	−	0.00586266i
$559$	−0.512512	+	0.485477i	−0.0216770	+	0.0205335i
$560$	−6.66544	+	3.08376i	−0.281666	+	0.130313i
$561$	0.320248	−	0.148163i	0.0135209	−	0.00625543i
$562$	−7.14399	+	6.76715i	−0.301351	+	0.285455i
$563$	23.0210	−	33.9535i	0.970221	−	1.43097i	0.0689959	−	0.997617i	$-0.478020\pi$
$563$	23.0210	−	33.9535i	0.970221	−	1.43097i	0.901225	−	0.433352i	$-0.142669\pi$
$564$	−1.05650	−	1.99278i	−0.0444868	−	0.0839111i
$565$	−21.4810	+	40.5174i	−0.903712	+	1.70458i
$566$	4.84061	+	7.13936i	0.203466	+	0.300090i
$567$	2.56904	+	0.565489i	0.107890	+	0.0237483i
$568$	−2.51244	+	9.04898i	−0.105420	+	0.379687i
$569$	14.7257	+	36.9588i	0.617335	+	1.54939i	0.821349	+	0.570426i	$0.193222\pi$
$569$	14.7257	+	36.9588i	0.617335	+	1.54939i	−0.204014	+	0.978968i	$0.565399\pi$
$570$	3.58806	+	1.20896i	0.150287	+	0.0506377i
$571$	0.981650	+	0.929868i	0.0410808	+	0.0389138i	0.707965	−	0.706248i	$-0.249614\pi$
$571$	0.981650	+	0.929868i	0.0410808	+	0.0389138i	−0.666884	+	0.745162i	$0.732372\pi$
$572$	−0.0601349	+	0.0132367i	−0.00251437	+	0.000553454i
$573$	0.371763	−	6.85677i	0.0155306	−	0.286445i
$574$	3.09216	−	18.8613i	0.129064	−	0.787257i
$575$	14.0194	−	16.5049i	0.584650	−	0.688303i
$576$	−0.370138	+	0.928977i	−0.0154224	+	0.0387074i
$577$	−1.51101	−	1.14864i	−0.0629040	−	0.0478184i	0.573250	−	0.819381i	$-0.305682\pi$
$577$	−1.51101	−	1.14864i	−0.0629040	−	0.0478184i	−0.636154	+	0.771562i	$0.719476\pi$
$578$	−14.2907	−	8.59842i	−0.594414	−	0.357647i
$579$	−4.03136	−	24.5902i	−0.167538	−	1.02194i
$580$	24.8924	−	2.70721i	1.03360	−	0.112411i
$581$	6.43298	−	4.89022i	0.266885	−	0.202881i
$582$	1.00659	+	3.62540i	0.0417244	+	0.150278i
$583$	−0.289789	−	5.34485i	−0.0120019	−	0.221361i
$584$	5.10661	+	0.555377i	0.211313	+	0.0229817i
$585$	0.236871	−	0.142521i	0.00979343	−	0.00589251i
$586$	3.10537	+	3.65592i	0.128282	+	0.151025i
$587$	−28.2107	+	9.50531i	−1.16438	+	0.392326i	−0.834131	−	0.551567i	$-0.814030\pi$
$587$	−28.2107	+	9.50531i	−1.16438	+	0.392326i	−0.330252	+	0.943893i	$0.607134\pi$
$588$	−0.0728248	−	0.0336923i	−0.00300324	−	0.00138945i
$589$	−0.226911			−0.00934968
$590$	19.9047	+	7.98060i	0.819465	+	0.328556i
$591$	−15.4813			−0.636815
$592$	0.894409	+	0.413798i	0.0367600	+	0.0170070i
$593$	−30.5669	+	10.2992i	−1.25523	+	0.422937i	−0.866853	−	0.498564i	$-0.833861\pi$
$593$	−30.5669	+	10.2992i	−1.25523	+	0.422937i	−0.388378	+	0.921500i	$0.626965\pi$
$594$	0.402588	+	0.473963i	0.0165184	+	0.0194469i
$595$	−3.57076	+	2.14846i	−0.146387	+	0.0880781i
$596$	15.0364	+	1.63531i	0.615915	+	0.0669848i
$597$	−0.648074	−	11.9530i	−0.0265239	−	0.489204i
$598$	−0.205258	−	0.739273i	−0.00839363	−	0.0302311i
$599$	−13.8307	+	10.5138i	−0.565106	+	0.429583i	−0.848327	−	0.529472i	$-0.822390\pi$
$599$	−13.8307	+	10.5138i	−0.565106	+	0.429583i	0.283221	+	0.959055i	$0.408597\pi$
$600$	2.77835	−	0.302163i	0.113425	−	0.0123358i
$601$	1.09614	+	6.68614i	0.0447124	+	0.272733i	0.999715	−	0.0238632i	$-0.00759663\pi$
$601$	1.09614	+	6.68614i	0.0447124	+	0.272733i	−0.955003	+	0.296597i	$0.904148\pi$
$602$	16.0702	+	9.66910i	0.654971	+	0.394083i
$603$	−3.02340	−	2.29833i	−0.123122	−	0.0935953i
$604$	8.49415	−	21.3187i	0.345622	−	0.867446i
$605$	19.1829	−	22.5838i	0.779895	−	0.918163i
$606$	2.43331	−	14.8425i	0.0988463	−	0.602936i
$607$	2.29161	−	42.2663i	0.0930137	−	1.71554i	−0.464670	−	0.885484i	$-0.653827\pi$
$607$	2.29161	−	42.2663i	0.0930137	−	1.71554i	0.557684	−	0.830053i	$-0.311690\pi$
$608$	1.32445	−	0.291534i	0.0537136	−	0.0118233i
$609$	−17.1277	−	16.2242i	−0.694049	−	0.657438i
$610$	22.6978	+	7.64779i	0.919008	+	0.309650i
$611$	0.0826635	+	0.207470i	0.00334421	+	0.00839333i
$612$	−0.151802	+	0.546740i	−0.00613622	+	0.0221006i
$613$	−5.28387	−	1.16307i	−0.213414	−	0.0469759i	0.106977	−	0.994262i	$-0.465883\pi$
$613$	−5.28387	−	1.16307i	−0.213414	−	0.0469759i	−0.320390	+	0.947286i	$0.603814\pi$
$614$	11.8125	+	17.4221i	0.476713	+	0.703099i
$615$	−9.50192	+	17.9225i	−0.383154	+	0.722706i
$616$	0.766245	+	1.44529i	0.0308729	+	0.0582324i
$617$	5.40907	−	7.97779i	0.217761	−	0.321174i	−0.703081	−	0.711110i	$-0.748193\pi$
$617$	5.40907	−	7.97779i	0.217761	−	0.321174i	0.920842	+	0.389937i	$0.127503\pi$
$618$	−11.1772	+	10.5876i	−0.449614	+	0.425897i
$619$	−30.7855	+	14.2429i	−1.23737	+	0.572470i	−0.925894	−	0.377783i	$-0.876687\pi$
$619$	−30.7855	+	14.2429i	−1.23737	+	0.572470i	−0.311479	+	0.950253i	$0.600825\pi$
$620$	−0.423963	+	0.196146i	−0.0170268	+	0.00787742i
$621$	−5.62550	+	5.32875i	−0.225743	+	0.213835i
$622$	6.00548	−	8.85742i	0.240798	−	0.355150i
$623$	−14.9416	−	28.1829i	−0.598624	−	1.12912i
$624$	0.0463798	−	0.0874815i	0.00185668	−	0.00350206i
$625$	17.4883	+	25.7934i	0.699534	+	1.03174i
$626$	−9.41673	−	2.07278i	−0.376368	−	0.0828449i
$627$	0.225620	−	0.812609i	0.00901039	−	0.0324525i
$628$	−0.273744	−	0.687046i	−0.0109236	−	0.0274161i
$629$	0.529919	+	0.178550i	0.0211293	+	0.00711927i
$630$	−5.33187	−	5.05062i	−0.212427	−	0.201222i
$631$	−33.3911	+	7.34993i	−1.32928	+	0.292596i	−0.822148	−	0.569274i	$-0.807224\pi$
$631$	−33.3911	+	7.34993i	−1.32928	+	0.292596i	−0.507129	+	0.861870i	$0.669293\pi$
$632$	0.423181	−	7.80512i	0.0168332	−	0.310471i
$633$	0.947389	−	5.77881i	0.0376553	−	0.229687i
$634$	−1.80177	+	2.12120i	−0.0715573	+	0.0842437i
$635$	7.15198	−	17.9501i	0.283818	−	0.712329i
$636$	6.85235	+	5.20902i	0.271713	+	0.206551i
$637$	0.00680783	+	0.00409613i	0.000269736	+	0.000162295i
$638$	−0.902291	−	5.50373i	−0.0357221	−	0.217895i
$639$	−9.33624	+	1.01538i	−0.369336	+	0.0401677i
$640$	2.22262	−	1.68959i	0.0878566	−	0.0667868i
$641$	10.6619	+	38.4007i	0.421120	+	1.51674i	0.804956	+	0.593335i	$0.202189\pi$
$641$	10.6619	+	38.4007i	0.421120	+	1.51674i	−0.383836	+	0.923401i	$0.625397\pi$
$642$	0.0357187	+	0.658793i	0.00140970	+	0.0260005i
$643$	−35.7556	−	3.88866i	−1.41006	−	0.153354i	−0.628806	−	0.777562i	$-0.716456\pi$
$643$	−35.7556	−	3.88866i	−1.41006	−	0.153354i	−0.781258	+	0.624208i	$0.785422\pi$
$644$	−17.4655	+	10.5086i	−0.688237	+	0.414098i
$645$	−12.8864	−	15.1710i	−0.507400	−	0.597358i
$646$	0.729232	−	0.245707i	0.0286913	−	0.00966721i
$647$	−21.5673	−	9.97807i	−0.847896	−	0.392279i	−0.0526851	−	0.998611i	$-0.516778\pi$
$647$	−21.5673	−	9.97807i	−0.847896	−	0.392279i	−0.795211	+	0.606333i	$0.792640\pi$
$648$	−1.00000			−0.0392837
$649$	1.53496	−	4.52330i	0.0602524	−	0.177555i
$650$	−0.276722			−0.0108539
$651$	0.399460	+	0.184810i	0.0156561	+	0.00724326i
$652$	−0.544634	+	0.183509i	−0.0213295	+	0.00718676i
$653$	−11.1434	−	13.1190i	−0.436073	−	0.513385i	0.499598	−	0.866257i	$-0.333481\pi$
$653$	−11.1434	−	13.1190i	−0.436073	−	0.513385i	−0.935672	+	0.352872i	$0.885205\pi$
$654$	−1.26356	+	0.760256i	−0.0494089	+	0.0297284i
$655$	4.64332	+	0.504992i	0.181430	+	0.0197317i
$656$	0.393365	+	7.25519i	0.0153583	+	0.283267i
$657$	1.37422	+	4.94949i	0.0536134	+	0.193098i
$658$	4.72341	−	3.59064i	0.184138	−	0.139978i
$659$	22.9145	−	2.49210i	0.892622	−	0.0970785i	0.349700	−	0.936862i	$-0.386283\pi$
$659$	22.9145	−	2.49210i	0.892622	−	0.0970785i	0.542922	+	0.839783i	$0.317318\pi$
$660$	−0.280885	−	1.71332i	−0.0109334	−	0.0666909i
$661$	−1.45728	−	0.876815i	−0.0566815	−	0.0341041i	0.486931	−	0.873440i	$-0.338116\pi$
$661$	−1.45728	−	0.876815i	−0.0566815	−	0.0341041i	−0.543613	+	0.839336i	$0.682944\pi$
$662$	−27.0527	−	20.5650i	−1.05143	−	0.799280i
$663$	0.0207957	−	0.0521933i	0.000807639	−	0.00202702i
$664$	−1.98869	+	2.34126i	−0.0771760	+	0.0908586i
$665$	−1.61134	+	9.82872i	−0.0624849	+	0.381141i
$666$	−0.0533535	+	0.984048i	−0.00206741	+	0.0381311i
$667$	67.8691	−	14.9391i	2.62790	−	0.578445i
$668$	8.49091	+	8.04301i	0.328523	+	0.311194i
$669$	22.3285	+	7.52334i	0.863269	+	0.290869i
$670$	3.92461	+	9.85003i	0.151621	+	0.380540i
$671$	1.42725	−	5.14051i	0.0550986	−	0.198447i
$672$	−2.56904	−	0.565489i	−0.0991030	−	0.0218142i
$673$	10.8033	+	15.9337i	0.416438	+	0.614200i	0.976827	−	0.214029i	$-0.0686588\pi$
$673$	10.8033	+	15.9337i	0.416438	+	0.614200i	−0.560389	+	0.828229i	$0.689348\pi$
$674$	−2.28138	+	4.30313i	−0.0878753	+	0.165750i
$675$	1.30907	+	2.46918i	0.0503863	+	0.0950386i
$676$	7.28993	−	10.7518i	0.280382	−	0.413532i
$677$	28.2875	−	26.7953i	1.08718	−	1.02983i	0.0877441	−	0.996143i	$-0.472034\pi$
$677$	28.2875	−	26.7953i	1.08718	−	1.02983i	0.999432	−	0.0336854i	$-0.0107244\pi$
$678$	−14.9077	+	6.89705i	−0.572528	+	0.264880i
$679$	−8.98276	+	4.15587i	−0.344727	+	0.159488i
$680$	1.15011	−	1.08945i	0.0441049	−	0.0417783i
$681$	−6.52472	+	9.62324i	−0.250028	+	0.368763i
$682$	0.0487379	+	0.0919294i	0.00186627	+	0.00352016i
$683$	6.09353	−	11.4936i	0.233163	−	0.439791i	−0.739129	−	0.673564i	$-0.764762\pi$
$683$	6.09353	−	11.4936i	0.233163	−	0.439791i	0.972291	+	0.233773i	$0.0751073\pi$
$684$	0.761058	+	1.12248i	0.0290998	+	0.0429190i
$685$	−45.6868	−	10.0564i	−1.74560	−	0.384237i
$686$	4.98268	−	17.9460i	0.190240	−	0.685182i
$687$	−4.28247	−	10.7482i	−0.163387	−	0.410069i
$688$	−6.75641	−	2.27650i	−0.257586	−	0.0867907i
$689$	−0.618748	−	0.586109i	−0.0235724	−	0.0223290i
$690$	21.1277	−	4.65057i	0.804320	−	0.177044i
$691$	1.26307	−	23.2959i	0.0480494	−	0.886218i	−0.870807	−	0.491625i	$-0.836403\pi$
$691$	1.26307	−	23.2959i	0.0480494	−	0.886218i	0.918856	−	0.394593i	$-0.129114\pi$
$692$	1.73912	−	10.6082i	0.0661115	−	0.403263i
$693$	−1.05903	+	1.24678i	−0.0402290	+	0.0473613i
$694$	−5.38543	+	13.5164i	−0.204428	+	0.513075i
$695$	−17.8029	−	13.5334i	−0.675304	−	0.513353i
$696$	7.68471	+	4.62374i	0.291288	+	0.175262i
$697$	0.666995	+	4.06849i	0.0252642	+	0.154105i
$698$	15.6146	−	1.69819i	0.591022	−	0.0642775i
$699$	−0.441547	+	0.335655i	−0.0167008	+	0.0126957i
$700$	1.96678	+	7.08369i	0.0743371	+	0.267738i
$701$	0.379326	+	6.99626i	0.0143270	+	0.264245i	0.996917	+	0.0784597i	$0.0250002\pi$
$701$	0.379326	+	6.99626i	0.0143270	+	0.264245i	−0.982590	+	0.185785i	$0.940517\pi$
$702$	0.0984352	+	0.0107055i	0.00371520	+	0.000404052i
$703$	1.14518	−	0.689029i	0.0431911	−	0.0259872i
$704$	−0.402588	−	0.473963i	−0.0151731	−	0.0178632i
$705$	−5.96755	+	2.01070i	−0.224751	+	0.0757274i
$706$	−12.9020	−	5.96911i	−0.485574	−	0.224651i
$707$	39.5651			1.48800
$708$	3.94583	+	6.59018i	0.148293	+	0.247674i
$709$	41.3661			1.55354			0.776769	−	0.629786i	$-0.216857\pi$
$709$	41.3661			1.55354			0.776769	+	0.629786i	$0.216857\pi$
$710$	23.7963	+	11.0093i	0.893058	+	0.413172i
$711$	7.40741	−	2.49585i	0.277800	−	0.0936016i
$712$	7.85040	+	9.24220i	0.294206	+	0.346366i
$713$	−1.11091	+	0.668414i	−0.0416040	+	0.0250323i
$714$	−1.48388	−	0.161382i	−0.0555328	−	0.00603956i
$715$	0.00930703	+	0.171658i	0.000348063	+	0.00641965i
$716$	−6.52591	−	23.5042i	−0.243885	−	0.878393i
$717$	12.9221	−	9.82316i	0.482586	−	0.366852i
$718$	24.3254	−	2.64555i	0.907817	−	0.0987311i
$719$	6.20851	+	37.8702i	0.231538	+	1.41232i	0.805091	+	0.593152i	$0.202117\pi$
$719$	6.20851	+	37.8702i	0.231538	+	1.41232i	−0.573553	+	0.819169i	$0.694435\pi$
$720$	2.39226	+	1.43938i	0.0891544	+	0.0536424i
$721$	−32.2410	−	24.5090i	−1.20072	−	0.912763i
$722$	−6.35188	+	15.9420i	−0.236393	+	0.593301i
$723$	0.647313	−	0.762076i	0.0240738	−	0.0283419i
$724$	−3.59196	+	21.9100i	−0.133494	+	0.814278i
$725$	1.35696	−	25.0277i	0.0503964	−	0.929507i
$726$	10.3651	−	2.28154i	0.384687	−	0.0846760i
$727$	20.1660	+	19.1023i	0.747917	+	0.708465i	0.963407	−	0.268041i	$-0.0863764\pi$
$727$	20.1660	+	19.1023i	0.747917	+	0.708465i	−0.215490	+	0.976506i	$0.569135\pi$
$728$	0.246830	+	0.0831668i	0.00914814	+	0.00308237i
$729$	−0.370138	−	0.928977i	−0.0137088	−	0.0344065i
$730$	3.83669	−	13.8185i	0.142002	−	0.511446i
$731$	−3.95092	−	0.869664i	−0.146130	−	0.0321657i
$732$	4.81440	+	7.10071i	0.177945	+	0.262450i
$733$	−19.3070	+	36.4169i	−0.713122	+	1.34509i	0.216393	+	0.976306i	$0.430571\pi$
$733$	−19.3070	+	36.4169i	−0.713122	+	1.34509i	−0.929515	+	0.368784i	$0.879774\pi$
$734$	9.07265	+	17.1128i	0.334878	+	0.631646i
$735$	−0.125720	+	0.185423i	−0.00463725	+	0.00683944i
$736$	5.62550	−	5.32875i	0.207359	−	0.196420i
$737$	2.14344	−	0.991663i	0.0789548	−	0.0365284i
$738$	−6.59430	+	3.05085i	−0.242740	+	0.112303i
$739$	−35.4210	+	33.5525i	−1.30298	+	1.23425i	−0.348031	+	0.937483i	$0.613150\pi$
$739$	−35.4210	+	33.5525i	−1.30298	+	1.23425i	−0.954950	+	0.296766i	$0.904092\pi$
$740$	1.54405	−	2.27731i	0.0567605	−	0.0837154i
$741$	−0.0628982	−	0.118639i	−0.00231062	−	0.00435830i
$742$	−10.6059	+	20.0048i	−0.389353	+	0.734399i
$743$	5.18213	+	7.64307i	0.190114	+	0.280397i	0.910786	−	0.412879i	$-0.135477\pi$
$743$	5.18213	+	7.64307i	0.190114	+	0.280397i	−0.720672	+	0.693276i	$0.756167\pi$
$744$	−0.163407	−	0.0359686i	−0.00599079	−	0.00131867i
$745$	11.2971	−	40.6885i	0.413894	−	1.49071i
$746$	−9.55176	−	23.9731i	−0.349715	−	0.877718i
$747$	−2.91107	−	0.980853i	−0.106510	−	0.0358875i
$748$	−0.256176	−	0.242662i	−0.00936671	−	0.00887262i
$749$	−1.69495	+	0.373087i	−0.0619322	+	0.0136323i
$750$	−0.333328	+	6.14788i	−0.0121714	+	0.224489i
$751$	−4.97172	+	30.3261i	−0.181421	+	1.10662i	0.726405	+	0.687267i	$0.241190\pi$
$751$	−4.97172	+	30.3261i	−0.181421	+	1.10662i	−0.907825	+	0.419349i	$0.862258\pi$
$752$	−1.46019	+	1.71907i	−0.0532477	+	0.0626880i
$753$	−0.0603625	+	0.151499i	−0.00219973	+	0.00552091i
$754$	−0.706947	−	0.537407i	−0.0257455	−	0.0195712i
$755$	−54.8991	−	33.0317i	−1.99798	−	1.20215i
$756$	−0.425575	−	2.59589i	−0.0154780	−	0.0944116i
$757$	−46.4945	+	5.05658i	−1.68987	+	0.183784i	−0.901905	−	0.431935i	$-0.857831\pi$
$757$	−46.4945	+	5.05658i	−1.68987	+	0.183784i	−0.787965	+	0.615720i	$0.788865\pi$
$758$	−23.0216	+	17.5006i	−0.836184	+	0.635650i
$759$	−1.28912	−	4.64300i	−0.0467922	−	0.168530i
$760$	−0.204984	−	3.78071i	−0.00743555	−	0.137141i
$761$	5.89852	+	0.641503i	0.213821	+	0.0232545i	0.214403	−	0.976745i	$-0.431220\pi$
$761$	5.89852	+	0.641503i	0.213821	+	0.0232545i	−0.000581392		1.00000i	$0.500185\pi$
$762$	5.93022	−	3.56809i	0.214829	−	0.129258i
$763$	−2.51128	−	2.95650i	−0.0909144	−	0.107033i
$764$	−6.50738	+	2.19259i	−0.235429	+	0.0793252i
$765$	1.43777	+	0.665184i	0.0519827	+	0.0240498i
$766$	−1.33925			−0.0483892
$767$	−0.317857	−	0.690947i	−0.0114772	−	0.0249487i
$768$	1.00000			0.0360844
$769$	−11.8477	−	5.48133i	−0.427239	−	0.197662i	0.194473	−	0.980908i	$-0.437700\pi$
$769$	−11.8477	−	5.48133i	−0.427239	−	0.197662i	−0.621712	+	0.783246i	$0.713562\pi$
$770$	4.32805	−	1.45829i	0.155972	−	0.0525532i
$771$	7.86229	+	9.25621i	0.283154	+	0.333354i
$772$	−21.3516	+	12.8468i	−0.768461	+	0.462367i
$773$	−4.76745	−	0.518491i	−0.171473	−	0.0186488i	0.0219796	−	0.999758i	$-0.493003\pi$
$773$	−4.76745	−	0.518491i	−0.171473	−	0.0186488i	−0.193453	+	0.981110i	$0.561969\pi$
$774$	−0.385990	−	7.11916i	−0.0138741	−	0.255893i
$775$	0.125099	+	0.450566i	0.00449369	+	0.0161848i
$776$	2.99534	−	2.27700i	0.107526	−	0.0817394i
$777$	−2.57719	+	0.280286i	−0.0924560	+	0.0100552i
$778$	−2.39822	−	14.6285i	−0.0859802	−	0.524456i
$779$	8.44315	+	5.08007i	0.302507	+	0.182013i
$780$	−0.220074	−	0.167296i	−0.00787990	−	0.00599015i
$781$	2.16166	−	5.42535i	0.0773501	−	0.194134i
$782$	2.84641	−	3.35105i	0.101787	−	0.119833i
$783$	−1.45094	+	8.85034i	−0.0518524	+	0.316285i
$784$	−0.00434416	+	0.0801233i	−0.000155149	+	0.00286155i
$785$	−2.01654	+	0.443875i	−0.0719735	+	0.0158426i
$786$	1.21455	+	1.15048i	0.0433216	+	0.0410364i
$787$	−28.7767	−	9.69600i	−1.02578	−	0.345625i	−0.244395	−	0.969676i	$-0.578589\pi$
$787$	−28.7767	−	9.69600i	−1.02578	−	0.345625i	−0.781384	+	0.624051i	$0.785486\pi$
$788$	5.73021	+	14.3817i	0.204130	+	0.512328i
$789$	3.86277	−	13.9124i	0.137518	−	0.495296i
$790$	−21.3129	−	4.69133i	−0.758280	−	0.166910i
$791$	−24.2483	−	35.7636i	−0.862172	−	1.27161i
$792$	0.291288	−	0.549427i	0.0103505	−	0.0195230i
$793$	−0.397890	−	0.750500i	−0.0141295	−	0.0266510i
$794$	17.1083	−	25.2329i	0.607151	−	0.895481i
$795$	17.4466	−	16.5263i	0.618766	−	0.586127i
$796$	−10.8642	+	5.02631i	−0.385071	+	0.178153i
$797$	−45.6290	+	21.1102i	−1.61626	+	0.747762i	−0.999232	−	0.0391775i	$-0.987526\pi$
$797$	−45.6290	+	21.1102i	−1.61626	+	0.747762i	−0.617030	+	0.786940i	$0.711664\pi$
$798$	−2.58994	+	2.45332i	−0.0916828	+	0.0868466i
$799$	−0.718225	+	1.05930i	−0.0254090	+	0.0374754i
$800$	−1.30907	−	2.46918i	−0.0462828	−	0.0872986i
$801$	−5.68006	+	10.7137i	−0.200695	+	0.378551i
$802$	9.13190	+	13.4686i	0.322459	+	0.475591i
$803$	−3.11967	−	0.686692i	−0.110091	−	0.0242328i
$804$	−1.01602	+	3.65937i	−0.0358322	+	0.129056i
$805$	21.0638	+	52.8661i	0.742401	+	1.86329i
$806$	0.0156999	+	0.00528992i	0.000553007	+	0.000186330i
$807$	22.5534	+	21.3637i	0.793917	+	0.752039i
$808$	−14.6890	+	3.23330i	−0.516758	+	0.113747i
$809$	−2.44006	+	45.0042i	−0.0857878	+	1.58226i	0.566351	+	0.824164i	$0.308355\pi$
$809$	−2.44006	+	45.0042i	−0.0857878	+	1.58226i	−0.652139	+	0.758099i	$0.726128\pi$
$810$	−0.451680	+	2.75513i	−0.0158704	+	0.0968052i
$811$	13.2666	−	15.6186i	0.465852	−	0.548444i	−0.478195	−	0.878254i	$-0.658709\pi$
$811$	13.2666	−	15.6186i	0.465852	−	0.548444i	0.944047	+	0.329810i	$0.106985\pi$
$812$	−8.73230	+	21.9164i	−0.306444	+	0.769115i
$813$	2.43186	+	1.84865i	0.0852890	+	0.0648350i
$814$	−0.525121	−	0.315955i	−0.0184055	−	0.0110742i
$815$	0.259589	+	1.58342i	0.00909301	+	0.0554649i
$816$	0.564096	−	0.0613492i	0.0197473	−	0.00214765i
$817$	−7.69733	+	5.85136i	−0.269296	+	0.204713i
$818$	−4.97345	−	17.9128i	−0.173893	−	0.626305i
$819$	0.0141013	+	0.260083i	0.000492739	+	0.00908803i
$820$	20.1666	+	2.19325i	0.704249	+	0.0765917i
$821$	−15.9820	+	9.61605i	−0.557775	+	0.335602i	−0.766370	−	0.642400i	$-0.777939\pi$
$821$	−15.9820	+	9.61605i	−0.557775	+	0.335602i	0.208594	+	0.978002i	$0.433111\pi$
$822$	−10.8475	−	12.7706i	−0.378349	−	0.445427i
$823$	−26.5467	+	8.94462i	−0.925359	+	0.311790i	−0.741338	−	0.671132i	$-0.765808\pi$
$823$	−26.5467	+	8.94462i	−0.925359	+	0.311790i	−0.184022	+	0.982922i	$0.558912\pi$
$824$	13.9728	+	6.46449i	0.486764	+	0.225201i
$825$	−1.73795			−0.0605076
$826$	−15.4281	+	13.0476i	−0.536813	+	0.453982i
$827$	−1.54655			−0.0537788			−0.0268894	−	0.999638i	$-0.508560\pi$
$827$	−1.54655			−0.0537788			−0.0268894	+	0.999638i	$0.508560\pi$
$828$	7.03250	+	3.25358i	0.244396	+	0.113070i
$829$	−7.84515	+	2.64334i	−0.272473	+	0.0918070i	−0.452221	−	0.891906i	$-0.649368\pi$
$829$	−7.84515	+	2.64334i	−0.272473	+	0.0918070i	0.179748	+	0.983713i	$0.442472\pi$
$830$	5.55222	+	6.53658i	0.192720	+	0.226888i
$831$	−15.7589	+	9.48180i	−0.546669	+	0.328920i
$832$	−0.0984352	−	0.0107055i	−0.00341263	−	0.000371145i
$833$	0.00246497	+	0.0454638i	8.54063e−5	+	0.00157523i
$834$	−2.14288	−	7.71795i	−0.0742018	−	0.267251i
$835$	25.9947	−	19.7606i	0.899583	−	0.683845i
$836$	−0.838405	+	0.0911821i	−0.0289969	+	0.00315360i
$837$	−0.0270692	−	0.165115i	−0.000935647	−	0.00570719i
$838$	−21.2046	−	12.7584i	−0.732502	−	0.440732i
$839$	−36.2358	−	27.5458i	−1.25100	−	0.950985i	−0.251144	−	0.967950i	$-0.580807\pi$
$839$	−36.2358	−	27.5458i	−1.25100	−	0.950985i	−0.999856	+	0.0169643i	$0.994600\pi$
$840$	−2.71838	+	6.82261i	−0.0937929	+	0.235403i
$841$	33.2975	−	39.2009i	1.14819	−	1.35175i
$842$	0.559506	−	3.41284i	0.0192819	−	0.117614i
$843$	−0.532741	+	9.82584i	−0.0183486	+	0.338420i
$844$	−5.71905	+	1.25886i	−0.196858	+	0.0433317i
$845$	−26.3300	−	24.9411i	−0.905778	−	0.857998i
$846$	−2.13745	−	0.720190i	−0.0734870	−	0.0247607i
$847$	10.3338	+	25.9358i	0.355073	+	0.891165i
$848$	2.30274	−	8.29373i	0.0790765	−	0.284808i
$849$	8.42399	+	1.85426i	0.289111	+	0.0636381i
$850$	−0.889926	−	1.31254i	−0.0305242	−	0.0450198i
$851$	3.57689	−	6.74672i	0.122614	−	0.231275i
$852$	4.39896	+	8.29732i	0.150706	+	0.284262i
$853$	10.1004	−	14.8970i	0.345832	−	0.510064i	−0.614502	−	0.788915i	$-0.710643\pi$
$853$	10.1004	−	14.8970i	0.345832	−	0.510064i	0.960334	+	0.278851i	$0.0899534\pi$
$854$	−16.3838	+	15.5195i	−0.560641	+	0.531067i
$855$	3.43632	−	1.58981i	0.117520	−	0.0543703i
$856$	0.598782	−	0.277026i	0.0204660	−	0.00946856i
$857$	−26.0987	+	24.7220i	−0.891516	+	0.844489i	−0.988566	−	0.150791i	$-0.951818\pi$
$857$	−26.0987	+	24.7220i	−0.891516	+	0.844489i	0.0970495	+	0.995280i	$0.469059\pi$
$858$	−0.0345548	+	0.0509646i	−0.00117968	+	0.00173990i
$859$	−7.53208	−	14.2070i	−0.256991	−	0.484737i	0.721122	−	0.692808i	$-0.243626\pi$
$859$	−7.53208	−	14.2070i	−0.256991	−	0.484737i	−0.978114	+	0.208070i	$0.933282\pi$
$860$	−9.32377	+	17.5865i	−0.317938	+	0.599695i
$861$	−10.7260	−	15.8197i	−0.365542	−	0.539134i
$862$	−24.6847	−	5.43351i	−0.840764	−	0.185066i
$863$	8.05646	−	29.0168i	0.274245	−	0.987742i	−0.690235	−	0.723586i	$-0.742493\pi$
$863$	8.05646	−	29.0168i	0.274245	−	0.987742i	0.964480	−	0.264156i	$-0.0850935\pi$
$864$	0.370138	+	0.928977i	0.0125924	+	0.0316044i
$865$	−28.4413	−	9.58300i	−0.967035	−	0.325832i
$866$	8.37020	+	7.92867i	0.284431	+	0.269427i
$867$	−16.2881	+	3.58528i	−0.553173	+	0.121763i
$868$	0.0238287	−	0.439494i	0.000808797	−	0.0149174i
$869$	−0.786402	+	4.79684i	−0.0266769	+	0.162722i
$870$	16.2100	−	19.0839i	0.549571	−	0.647005i
$871$	0.139187	−	0.349334i	0.00471618	−	0.0118367i
$872$	1.17395	+	0.892414i	0.0397550	+	0.0302209i
$873$	3.22396	+	1.93979i	0.109115	+	0.0656521i
$874$	−1.70007	−	10.3700i	−0.0575058	−	0.350770i
$875$	−16.1011	+	1.75110i	−0.544315	+	0.0591979i
$876$	4.08931	−	3.10861i	0.138165	−	0.105030i
$877$	−5.89305	−	21.2249i	−0.198994	−	0.716713i	−0.993930	−	0.110018i	$-0.964909\pi$
$877$	−5.89305	−	21.2249i	−0.198994	−	0.716713i	0.794935	−	0.606694i	$-0.207505\pi$
$878$	1.18672	+	21.8878i	0.0400499	+	0.738677i
$879$	4.76866	+	0.518623i	0.160843	+	0.0174927i
$880$	−1.48767	+	0.895101i	−0.0501493	+	0.0301738i
$881$	−25.0852	−	29.5325i	−0.845141	−	0.994977i	−0.999975	−	0.00703632i	$-0.997760\pi$
$881$	−25.0852	−	29.5325i	−0.845141	−	0.994977i	0.154834	−	0.987940i	$-0.450516\pi$
$882$	−0.0760406	+	0.0256211i	−0.00256042	+	0.000862706i
$883$	14.4080	+	6.66587i	0.484869	+	0.224324i	0.647066	−	0.762434i	$-0.275996\pi$
$883$	14.4080	+	6.66587i	0.484869	+	0.224324i	−0.162197	+	0.986758i	$0.551858\pi$
$884$	−0.0561837			−0.00188966
$885$	19.9390	−	7.89460i	0.670243	−	0.265374i
$886$	−18.4331			−0.619271
$887$	−22.0134	−	10.1845i	−0.739136	−	0.341961i	0.0139322	−	0.999903i	$-0.495565\pi$
$887$	−22.0134	−	10.1845i	−0.739136	−	0.341961i	−0.753069	+	0.657942i	$0.771427\pi$
$888$	0.933906	−	0.314669i	0.0313398	−	0.0105596i
$889$	11.7861	+	13.8757i	0.395294	+	0.465376i
$890$	29.0093	−	17.4543i	0.972393	−	0.585070i
$891$	0.618221	+	0.0672356i	0.0207112	+	0.00225248i
$892$	−1.27561	−	23.5273i	−0.0427107	−	0.787752i
$893$	0.818326	+	2.94734i	0.0273842	+	0.0986290i
$894$	12.0410	−	9.15330i	0.402710	−	0.306132i
$895$	−67.7046	+	7.36332i	−2.26312	+	0.246129i
$896$	0.425575	+	2.59589i	0.0142174	+	0.0867226i
$897$	−0.657414	−	0.395553i	−0.0219504	−	0.0132071i
$898$	−17.0963	−	12.9962i	−0.570510	−	0.433690i
$899$	−0.555428	+	1.39402i	−0.0185246	+	0.0464931i
$900$	1.80927	−	2.13004i	0.0603090	−	0.0710012i
$901$	0.790155	−	4.81973i	0.0263239	−	0.160569i
$902$	0.244620	−	4.51176i	0.00814497	−	0.150225i
$903$	18.3163	−	4.03172i	0.609528	−	0.134167i
$904$	11.9251	+	11.2961i	0.396624	+	0.375702i
$905$	58.7424	+	19.7926i	1.95266	+	0.657928i
$906$	−8.49415	−	21.3187i	−0.282199	−	0.708267i
$907$	3.90115	−	14.0507i	0.129536	−	0.466545i	−0.870119	−	0.492842i	$-0.835958\pi$
$907$	3.90115	−	14.0507i	0.129536	−	0.466545i	0.999654	+	0.0262975i	$0.00837173\pi$
$908$	11.3548	+	2.49938i	0.376823	+	0.0829450i
$909$	−8.44062	−	12.4490i	−0.279958	−	0.412907i
$910$	0.340623	−	0.642484i	0.0112916	−	0.0212981i
$911$	22.5550	+	42.5432i	0.747279	+	1.40952i	0.906470	+	0.422270i	$0.138767\pi$
$911$	22.5550	+	42.5432i	0.747279	+	1.40952i	−0.159191	+	0.987248i	$0.550889\pi$
$912$	0.761058	−	1.12248i	0.0252011	−	0.0371689i
$913$	1.38686	−	1.31371i	0.0458985	−	0.0434774i
$914$	−18.8767	+	8.73327i	−0.624384	+	0.288871i
$915$	21.7379	−	10.0570i	0.718633	−	0.332475i
$916$	−8.39972	+	7.95663i	−0.277534	+	0.262895i
$917$	−2.46965	+	3.64246i	−0.0815549	+	0.120285i
$918$	0.265785	+	0.501325i	0.00877223	+	0.0165462i
$919$	1.40529	−	2.65065i	0.0463561	−	0.0874370i	−0.859252	−	0.511553i	$-0.829070\pi$
$919$	1.40529	−	2.65065i	0.0463561	−	0.0874370i	0.905608	+	0.424116i	$0.139415\pi$
$920$	−12.1405	−	17.9058i	−0.400259	−	0.590338i
$921$	20.5570	+	4.52494i	0.677376	+	0.149102i
$922$	−1.71765	+	6.18642i	−0.0565679	+	0.203739i
$923$	−0.344186	−	0.863841i	−0.0113290	−	0.0284337i
$924$	1.55022	+	0.522329i	0.0509984	+	0.0171833i
$925$	−1.99953	−	1.89405i	−0.0657440	−	0.0622760i
$926$	39.8158	−	8.76413i	1.30843	−	0.288007i
$927$	−0.833507	+	15.3731i	−0.0273760	+	0.504920i
$928$	1.45094	−	8.85034i	0.0476294	−	0.290527i
$929$	−0.0203130	+	0.0239143i	−0.000666449	+	0.000784604i	−0.762495	−	0.646994i	$-0.776026\pi$
$929$	−0.0203130	+	0.0239143i	−0.000666449	+	0.000784604i	0.761829	+	0.647779i	$0.224302\pi$
$930$	−0.172906	+	0.433960i	−0.00566980	+	0.0142301i
$931$	0.0866304	+	0.0658547i	0.00283920	+	0.00215830i
$932$	0.475249	+	0.285948i	0.0155673	+	0.00936654i
$933$	−1.73129	−	10.5604i	−0.0566799	−	0.345732i
$934$	−19.4292	+	2.11305i	−0.635743	+	0.0691412i
$935$	−0.784275	+	0.596190i	−0.0256485	+	0.0194975i
$936$	−0.0264895	−	0.0954065i	−0.000865836	−	0.00311846i
$937$	−0.140748	−	2.59594i	−0.00459804	−	0.0848058i	0.995334	−	0.0964930i	$-0.0307625\pi$
$937$	−0.140748	−	2.59594i	−0.00459804	−	0.0848058i	−0.999932	+	0.0116872i	$0.996280\pi$
$938$	−9.93171	−	1.08014i	−0.324282	−	0.0352678i
$939$	−8.26195	+	4.97105i	−0.269619	+	0.162224i
$940$	4.07671	+	4.79948i	0.132968	+	0.156542i
$941$	−27.1156	+	9.13630i	−0.883943	+	0.297835i	−0.724420	−	0.689359i	$-0.757892\pi$
$941$	−27.1156	+	9.13630i	−0.883943	+	0.297835i	−0.159523	+	0.987194i	$0.550996\pi$
$942$	−0.671218	−	0.310539i	−0.0218695	−	0.0101179i
$943$	56.3006			1.83340
$944$	4.66162	−	6.10486i	0.151723	−	0.198696i
$945$	−7.34423			−0.238908
$946$	4.02389	+	1.86165i	0.130828	+	0.0605275i
$947$	0.279667	−	0.0942309i	0.00908797	−	0.00306209i	−0.314754	−	0.949173i	$-0.601922\pi$
$947$	0.279667	−	0.0942309i	0.00908797	−	0.00306209i	0.323842	+	0.946111i	$0.395025\pi$
$948$	−5.06035	−	5.95750i	−0.164353	−	0.193491i
$949$	−0.435811	+	0.262219i	−0.0141470	+	0.00851198i
$950$	−3.76787	−	0.409781i	−0.122246	−	0.0132950i
$951$	0.150676	+	2.77906i	0.00488601	+	0.0901171i
$952$	0.399321	+	1.43822i	0.0129421	+	0.0466131i
$953$	15.5988	−	11.8579i	0.505294	−	0.384115i	−0.321243	−	0.946997i	$-0.604101\pi$
$953$	15.5988	−	11.8579i	0.505294	−	0.384115i	0.826537	+	0.562882i	$0.190307\pi$
$954$	8.55702	−	0.930632i	0.277044	−	0.0301303i
$955$	3.10161	+	18.9190i	0.100366	+	0.612204i
$956$	−13.9085	−	8.36844i	−0.449832	−	0.270655i
$957$	−4.43997	−	3.37518i	−0.143524	−	0.109104i
$958$	12.0560	−	30.2583i	0.389511	−	0.977600i
$959$	28.5347	−	33.5937i	0.921434	−	1.08480i
$960$	0.451680	−	2.75513i	0.0145779	−	0.0889213i
$961$	−1.67679	+	30.9266i	−0.0540900	+	0.997632i
$962$	−0.0952979	+	0.0209766i	−0.00307253	+	0.000676314i
$963$	0.478983	+	0.453717i	0.0154350	+	0.0146208i
$964$	−0.947546	−	0.319265i	−0.0305184	−	0.0102828i
$965$	25.7505	+	64.6290i	0.828939	+	2.08048i
$966$	−5.45308	+	19.6402i	−0.175450	+	0.631914i
$967$	35.3116	+	7.77267i	1.13554	+	0.249952i	0.742681	−	0.669645i	$-0.233554\pi$
$967$	35.3116	+	7.77267i	1.13554	+	0.249952i	0.392863	+	0.919597i	$0.371485\pi$
$968$	−5.95604	−	8.78450i	−0.191434	−	0.282344i
$969$	0.360447	−	0.679875i	0.0115792	−	0.0218407i
$970$	−4.92047	−	9.28100i	−0.157987	−	0.297995i
$971$	−24.2757	+	35.8040i	−0.779044	+	1.14900i	0.206310	+	0.978487i	$0.433854\pi$
$971$	−24.2757	+	35.8040i	−0.779044	+	1.14900i	−0.985355	+	0.170518i	$0.945456\pi$
$972$	−0.725995	+	0.687699i	−0.0232863	+	0.0220580i
$973$	19.1230	−	8.84724i	0.613055	−	0.283629i
$974$	−22.0304	+	10.1923i	−0.705898	+	0.326583i
$975$	−0.200899	+	0.190301i	−0.00643391	+	0.00609452i
$976$	4.81440	−	7.10071i	0.154105	−	0.227288i
$977$	−12.1010	−	22.8248i	−0.387144	−	0.730232i	0.610967	−	0.791656i	$-0.290781\pi$
$977$	−12.1010	−	22.8248i	−0.387144	−	0.730232i	−0.998112	+	0.0614241i	$0.980436\pi$
$978$	−0.269203	+	0.507771i	−0.00860817	+	0.0162367i
$979$	−4.23188	−	6.24155i	−0.135251	−	0.199481i
$980$	0.218788	+	0.0481588i	0.00698891	+	0.00153838i
$981$	−0.394508	+	1.42089i	−0.0125957	+	0.0453655i
$982$	2.02525	+	5.08299i	0.0646282	+	0.162205i
$983$	−32.0734	−	10.8068i	−1.02298	−	0.344683i	−0.242694	−	0.970103i	$-0.578031\pi$
$983$	−32.0734	−	10.8068i	−1.02298	−	0.344683i	−0.780288	+	0.625420i	$0.784928\pi$
$984$	5.27497	+	4.99672i	0.168160	+	0.159289i
$985$	42.2117	−	9.29150i	1.34498	−	0.296052i
$986$	0.275509	−	5.08146i	0.00877398	−	0.161827i
$987$	0.959891	−	5.85508i	0.0305537	−	0.186369i
$988$	−0.0869315	+	0.102344i	−0.00276566	+	0.00325599i
$989$	−20.4483	+	51.3214i	−0.650218	+	1.63192i
$990$	−1.38217	−	1.05070i	−0.0439283	−	0.0333934i
$991$	44.6647	+	26.8738i	1.41882	+	0.853675i	0.998556	−	0.0537264i	$-0.0171099\pi$
$991$	44.6647	+	26.8738i	1.41882	+	0.853675i	0.420264	+	0.907402i	$0.361937\pi$
$992$	0.0270692	+	0.165115i	0.000859447	+	0.00524239i
$993$	−33.7827	+	3.67409i	−1.07206	+	0.116594i
$994$	−19.6668	+	14.9503i	−0.623795	+	0.474196i
$995$	8.94098	+	32.2025i	0.283448	+	1.02089i
$996$	0.166308	+	3.06736i	0.00526966	+	0.0971932i
$997$	7.20012	+	0.783060i	0.228030	+	0.0247998i	0.221421	−	0.975178i	$-0.428931\pi$
$997$	7.20012	+	0.783060i	0.228030	+	0.0247998i	0.00660940	+	0.999978i	$0.497896\pi$
$998$	−26.6304	+	16.0230i	−0.842972	+	0.507199i
$999$	0.637995	+	0.751105i	0.0201853	+	0.0237639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.d.79.3	✓	84
59.3	even	29	inner	354.2.e.d.121.3	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.d.79.3	✓	84	1.1	even	1	trivial
354.2.e.d.121.3	yes	84	59.3	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.907575 - 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(2.39226 - 1.43938i) q^{5} +(0.994138 + 0.108119i) q^{6} +(0.142415 + 2.62669i) q^{7} +(-0.267528 - 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +O(q^{10})\)	\(q+(-0.907575 - 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(2.39226 - 1.43938i) q^{5} +(0.994138 + 0.108119i) q^{6} +(0.142415 + 2.62669i) q^{7} +(-0.267528 - 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(-2.77554 + 0.301858i) q^{10} +(0.100607 + 0.613675i) q^{11} +(-0.856857 - 0.515554i) q^{12} +(0.0788257 + 0.0599217i) q^{13} +(0.973665 - 2.44371i) q^{14} +(-1.80744 + 2.12788i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(-0.0307196 + 0.566590i) q^{17} +(-0.976621 + 0.214970i) q^{18} +(0.984564 + 0.932629i) q^{19} +(2.64576 + 0.891459i) q^{20} +(-0.973665 - 2.44371i) q^{21} +(0.166367 - 0.599200i) q^{22} +(7.56750 + 1.66573i) q^{23} +(0.561187 + 0.827689i) q^{24} +(1.30907 - 2.46918i) q^{25} +(-0.0463798 - 0.0874815i) q^{26} +(-0.561187 + 0.827689i) q^{27} +(-1.90976 + 1.80902i) q^{28} +(8.13958 - 3.76577i) q^{29} +(2.53386 - 1.17229i) q^{30} +(-0.121473 + 0.115065i) q^{31} +(0.561187 - 0.827689i) q^{32} +(-0.291288 - 0.549427i) q^{33} +(0.265785 - 0.501325i) q^{34} +(4.12148 + 6.07873i) q^{35} +(0.976621 + 0.214970i) q^{36} +(0.263647 - 0.949572i) q^{37} +(-0.501966 - 1.25984i) q^{38} +(-0.0938325 - 0.0316158i) q^{39} +(-2.02691 - 1.91999i) q^{40} +(7.09597 - 1.56194i) q^{41} +(-0.142415 + 2.62669i) q^{42} +(-1.15344 + 7.03570i) q^{43} +(-0.402588 + 0.473963i) q^{44} +(1.03339 - 2.59361i) q^{45} +(-6.16866 - 4.68929i) q^{46} +(1.93266 + 1.16284i) q^{47} +(-0.161782 - 0.986827i) q^{48} +(0.0797706 - 0.00867558i) q^{49} +(-2.22486 + 1.69130i) q^{50} +(-0.151802 - 0.546740i) q^{51} +(0.00536060 + 0.0988704i) q^{52} +(-8.55702 - 0.930632i) q^{53} +(0.856857 - 0.515554i) q^{54} +(1.12399 + 1.32326i) q^{55} +(2.49284 - 0.839937i) q^{56} +(-1.23081 - 0.569436i) q^{57} -8.96849 q^{58} +(-6.77860 - 3.61255i) q^{59} -2.79190 q^{60} +(-7.78605 - 3.60221i) q^{61} +(0.158560 - 0.0534251i) q^{62} +(1.70298 + 2.00490i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(0.274822 + 0.0298887i) q^{65} +(0.0336672 + 0.620955i) q^{66} +(-1.01602 - 3.65937i) q^{67} +(-0.451721 + 0.343389i) q^{68} +(-7.70324 + 0.837778i) q^{69} +(-1.18816 - 7.24748i) q^{70} +(-8.04700 - 4.84172i) q^{71} +(-0.796093 - 0.605174i) q^{72} +(-1.90130 + 4.77190i) q^{73} +(-0.637995 + 0.751105i) q^{74} +(-0.452137 + 2.75791i) q^{75} +(-0.0734209 + 1.35417i) q^{76} +(-1.59760 + 0.351659i) q^{77} +(0.0718849 + 0.0680930i) q^{78} +(7.40741 + 2.49585i) q^{79} +(1.03339 + 2.59361i) q^{80} +(0.267528 - 0.963550i) q^{81} +(-7.09597 - 1.56194i) q^{82} +(-1.72389 - 2.54255i) q^{83} +(1.23217 - 2.32412i) q^{84} +(0.742048 + 1.39965i) q^{85} +(4.00105 - 5.90111i) q^{86} +(-6.51108 + 6.16762i) q^{87} +(0.564391 - 0.261115i) q^{88} +(-11.0055 + 5.09170i) q^{89} +(-2.02691 + 1.91999i) q^{90} +(-0.146170 + 0.215584i) q^{91} +(3.62954 + 6.84604i) q^{92} +(0.0783735 - 0.147828i) q^{93} +(-1.26577 - 1.86687i) q^{94} +(3.69774 + 0.813934i) q^{95} +(-0.267528 + 0.963550i) q^{96} +(1.39266 + 3.49532i) q^{97} +(-0.0760406 - 0.0256211i) q^{98} +(0.451472 + 0.427657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Introduction

L-functions

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