LMFDB - Embedded newform 354.2.e.a.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	354.163
Dual form			354.2.e.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.856857 + 0.515554i) q^{2} +(-0.370138 - 0.928977i) q^{3} +(0.468408 - 0.883512i) q^{4} +(3.11390 - 0.338657i) q^{5} +(0.796093 + 0.605174i) q^{6} +(2.05914 - 0.693803i) q^{7} +(0.0541389 + 0.998533i) q^{8} +(-0.725995 + 0.687699i) q^{9} +O(q^{10})$	\(q+(-0.856857 + 0.515554i) q^{2} +(-0.370138 - 0.928977i) q^{3} +(0.468408 - 0.883512i) q^{4} +(3.11390 - 0.338657i) q^{5} +(0.796093 + 0.605174i) q^{6} +(2.05914 - 0.693803i) q^{7} +(0.0541389 + 0.998533i) q^{8} +(-0.725995 + 0.687699i) q^{9} +(-2.49357 + 1.89557i) q^{10} +(-0.557034 + 0.821564i) q^{11} +(-0.994138 - 0.108119i) q^{12} +(-1.28635 - 1.21850i) q^{13} +(-1.40669 + 1.65609i) q^{14} +(-1.46718 - 2.76739i) q^{15} +(-0.561187 - 0.827689i) q^{16} +(1.74059 + 0.586475i) q^{17} +(0.267528 - 0.963550i) q^{18} +(-0.606126 - 3.69721i) q^{19} +(1.15937 - 2.90980i) q^{20} +(-1.40669 - 1.65609i) q^{21} +(0.0537383 - 0.991144i) q^{22} +(0.574951 + 2.07079i) q^{23} +(0.907575 - 0.419889i) q^{24} +(4.69860 - 1.03424i) q^{25} +(1.73042 + 0.380895i) q^{26} +(0.907575 + 0.419889i) q^{27} +(0.351533 - 2.14425i) q^{28} +(6.78229 + 4.08077i) q^{29} +(2.68390 + 1.61485i) q^{30} +(0.950438 - 5.79742i) q^{31} +(0.907575 + 0.419889i) q^{32} +(0.969393 + 0.213380i) q^{33} +(-1.79380 + 0.394845i) q^{34} +(6.17699 - 2.85778i) q^{35} +(0.267528 + 0.963550i) q^{36} +(0.0190960 - 0.352205i) q^{37} +(2.42547 + 2.85549i) q^{38} +(-0.655829 + 1.64601i) q^{39} +(0.506744 + 3.09100i) q^{40} +(0.700608 - 2.52336i) q^{41} +(2.05914 + 0.693803i) q^{42} +(-1.72676 - 2.54679i) q^{43} +(0.464942 + 0.876974i) q^{44} +(-2.02779 + 2.38729i) q^{45} +(-1.56025 - 1.47795i) q^{46} +(-7.75183 - 0.843062i) q^{47} +(-0.561187 + 0.827689i) q^{48} +(-1.81398 + 1.37895i) q^{49} +(-3.49283 + 3.30858i) q^{50} +(-0.0994392 - 1.83405i) q^{51} +(-1.67910 + 0.565754i) q^{52} +(9.67245 + 7.35281i) q^{53} +(-0.994138 + 0.108119i) q^{54} +(-1.45632 + 2.74691i) q^{55} +(0.804265 + 2.01855i) q^{56} +(-3.21027 + 1.93155i) q^{57} -7.91531 q^{58} +(-7.65953 + 0.575876i) q^{59} -3.13227 q^{60} +(1.81807 - 1.09390i) q^{61} +(2.17449 + 5.45756i) q^{62} +(-1.01779 + 1.91976i) q^{63} +(-0.994138 + 0.108119i) q^{64} +(-4.41824 - 3.35866i) q^{65} +(-0.940640 + 0.316939i) q^{66} +(-0.708395 - 13.0656i) q^{67} +(1.33347 - 1.26313i) q^{68} +(1.71090 - 1.30059i) q^{69} +(-3.81946 + 5.63328i) q^{70} +(6.21527 + 0.675951i) q^{71} +(-0.725995 - 0.687699i) q^{72} +(-10.6342 + 12.5196i) q^{73} +(0.165218 + 0.311634i) q^{74} +(-2.69992 - 3.98208i) q^{75} +(-3.55044 - 1.19628i) q^{76} +(-0.577005 + 2.07818i) q^{77} +(-0.286653 - 1.74851i) q^{78} +(-2.39183 + 6.00303i) q^{79} +(-2.02779 - 2.38729i) q^{80} +(0.0541389 - 0.998533i) q^{81} +(0.700608 + 2.52336i) q^{82} +(-14.3587 + 6.64306i) q^{83} +(-2.12208 + 0.467105i) q^{84} +(5.61866 + 1.23676i) q^{85} +(2.79260 + 1.29199i) q^{86} +(1.28055 - 7.81103i) q^{87} +(-0.850516 - 0.511739i) q^{88} +(3.03286 + 1.82481i) q^{89} +(0.506744 - 3.09100i) q^{90} +(-3.49418 - 1.61658i) q^{91} +(2.09888 + 0.461998i) q^{92} +(-5.73746 + 1.26291i) q^{93} +(7.07686 - 3.27410i) q^{94} +(-3.13951 - 11.3075i) q^{95} +(0.0541389 - 0.998533i) q^{96} +(5.06980 + 5.96863i) q^{97} +(0.843397 - 2.11677i) q^{98} +(-0.160585 - 0.979524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{24}{29}\right)$	$1$

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 $

$2$	−0.856857	+	0.515554i	−0.605890	+	0.364552i
$2$	−0.856857	+	0.515554i	−0.605890	+	0.364552i
$3$	−0.370138	−	0.928977i	−0.213699	−	0.536345i
$3$	−0.370138	−	0.928977i	−0.213699	−	0.536345i
$4$	0.468408	−	0.883512i	0.234204	−	0.441756i
$5$	3.11390	−	0.338657i	1.39258	−	0.151452i	0.619120	−	0.785297i	$-0.287490\pi$
$5$	3.11390	−	0.338657i	1.39258	−	0.151452i	0.773460	+	0.633845i	$0.218524\pi$
$6$	0.796093	+	0.605174i	0.325004	+	0.247061i
$7$	2.05914	−	0.693803i	0.778280	−	0.262233i	0.0980009	−	0.995186i	$-0.468755\pi$
$7$	2.05914	−	0.693803i	0.778280	−	0.262233i	0.680279	+	0.732953i	$0.261859\pi$
$8$	0.0541389	+	0.998533i	0.0191410	+	0.353035i
$9$	−0.725995	+	0.687699i	−0.241998	+	0.229233i
$10$	−2.49357	+	1.89557i	−0.788537	+	0.599431i
$11$	−0.557034	+	0.821564i	−0.167952	+	0.247711i	−0.902346	−	0.431013i	$-0.858156\pi$
$11$	−0.557034	+	0.821564i	−0.167952	+	0.247711i	0.734394	+	0.678724i	$0.237467\pi$
$12$	−0.994138	−	0.108119i	−0.286983	−	0.0312113i
$13$	−1.28635	−	1.21850i	−0.356771	−	0.337951i	0.488231	−	0.872714i	$-0.337642\pi$
$13$	−1.28635	−	1.21850i	−0.356771	−	0.337951i	−0.845002	+	0.534763i	$0.820401\pi$
$14$	−1.40669	+	1.65609i	−0.375954	+	0.442607i
$15$	−1.46718	−	2.76739i	−0.378824	−	0.714538i
$16$	−0.561187	−	0.827689i	−0.140297	−	0.206922i
$17$	1.74059	+	0.586475i	0.422156	+	0.142241i	0.522358	−	0.852726i	$-0.325052\pi$
$17$	1.74059	+	0.586475i	0.422156	+	0.142241i	−0.100202	+	0.994967i	$0.531949\pi$
$18$	0.267528	−	0.963550i	0.0630570	−	0.227111i
$19$	−0.606126	−	3.69721i	−0.139055	−	0.848197i	−0.960576	−	0.278019i	$-0.910322\pi$
$19$	−0.606126	−	3.69721i	−0.139055	−	0.848197i	0.821521	−	0.570179i	$-0.193126\pi$
$20$	1.15937	−	2.90980i	0.259243	−	0.650651i
$21$	−1.40669	−	1.65609i	−0.306965	−	0.361387i
$22$	0.0537383	−	0.991144i	0.0114570	−	0.211313i
$23$	0.574951	+	2.07079i	0.119886	+	0.431789i	0.998995	−	0.0448320i	$-0.0142752\pi$
$23$	0.574951	+	2.07079i	0.119886	+	0.431789i	−0.879109	+	0.476621i	$0.841861\pi$
$24$	0.907575	−	0.419889i	0.185258	−	0.0857095i
$25$	4.69860	−	1.03424i	0.939721	−	0.206848i
$26$	1.73042	+	0.380895i	0.339364	+	0.0746997i
$27$	0.907575	+	0.419889i	0.174663	+	0.0808077i
$28$	0.351533	−	2.14425i	0.0664334	−	0.405226i
$29$	6.78229	+	4.08077i	1.25944	+	0.757779i	0.979346	−	0.202193i	$-0.0648070\pi$
$29$	6.78229	+	4.08077i	1.25944	+	0.757779i	0.280093	+	0.959973i	$0.409635\pi$
$30$	2.68390	+	1.61485i	0.490012	+	0.294830i
$31$	0.950438	−	5.79742i	0.170704	−	1.04125i	−0.752967	−	0.658059i	$-0.771378\pi$
$31$	0.950438	−	5.79742i	0.170704	−	1.04125i	0.923670	−	0.383188i	$-0.125174\pi$
$32$	0.907575	+	0.419889i	0.160438	+	0.0742266i
$33$	0.969393	+	0.213380i	0.168750	+	0.0371446i
$34$	−1.79380	+	0.394845i	−0.307634	+	0.0677154i
$35$	6.17699	−	2.85778i	1.04410	−	0.483053i
$36$	0.267528	+	0.963550i	0.0445881	+	0.160592i
$37$	0.0190960	−	0.352205i	0.00313936	−	0.0579021i	−0.996544	−	0.0830672i	$-0.973528\pi$
$37$	0.0190960	−	0.352205i	0.00313936	−	0.0579021i	0.999683	+	0.0251651i	$0.00801115\pi$
$38$	2.42547	+	2.85549i	0.393464	+	0.463221i
$39$	−0.655829	+	1.64601i	−0.105017	+	0.263572i
$40$	0.506744	+	3.09100i	0.0801233	+	0.488730i
$41$	0.700608	−	2.52336i	0.109417	−	0.394083i	−0.888480	−	0.458916i	$-0.848238\pi$
$41$	0.700608	−	2.52336i	0.109417	−	0.394083i	0.997896	+	0.0648334i	$0.0206516\pi$
$42$	2.05914	+	0.693803i	0.317731	+	0.107056i
$43$	−1.72676	−	2.54679i	−0.263329	−	0.388381i	0.672922	−	0.739714i	$-0.265039\pi$
$43$	−1.72676	−	2.54679i	−0.263329	−	0.388381i	−0.936251	+	0.351332i	$0.885729\pi$
$44$	0.464942	+	0.876974i	0.0700927	+	0.132209i
$45$	−2.02779	+	2.38729i	−0.302284	+	0.355877i
$46$	−1.56025	−	1.47795i	−0.230047	−	0.217912i
$47$	−7.75183	−	0.843062i	−1.13072	−	0.122973i	−0.476427	−	0.879214i	$-0.658068\pi$
$47$	−7.75183	−	0.843062i	−1.13072	−	0.122973i	−0.654294	+	0.756241i	$0.727034\pi$
$48$	−0.561187	+	0.827689i	−0.0810004	+	0.119467i
$49$	−1.81398	+	1.37895i	−0.259140	+	0.196993i
$50$	−3.49283	+	3.30858i	−0.493960	+	0.467904i
$51$	−0.0994392	−	1.83405i	−0.0139243	−	0.256818i
$52$	−1.67910	+	0.565754i	−0.232849	+	0.0784560i
$53$	9.67245	+	7.35281i	1.32861	+	1.00999i	0.997800	+	0.0662898i	$0.0211162\pi$
$53$	9.67245	+	7.35281i	1.32861	+	1.00999i	0.330813	+	0.943696i	$0.392677\pi$
$54$	−0.994138	+	0.108119i	−0.135285	+	0.0147131i
$55$	−1.45632	+	2.74691i	−0.196370	+	0.370394i
$56$	0.804265	+	2.01855i	0.107474	+	0.269741i
$57$	−3.21027	+	1.93155i	−0.425210	+	0.255841i
$58$	−7.91531			−1.03933
$59$	−7.65953	+	0.575876i	−0.997186	+	0.0749727i
$59$	−7.65953	+	0.575876i	−0.997186	+	0.0749727i
$60$	−3.13227			−0.404374
$61$	1.81807	−	1.09390i	0.232780	−	0.140059i	−0.394385	−	0.918945i	$-0.629042\pi$
$61$	1.81807	−	1.09390i	0.232780	−	0.140059i	0.627166	+	0.778886i	$0.284215\pi$
$62$	2.17449	+	5.45756i	0.276161	+	0.693111i
$63$	−1.01779	+	1.91976i	−0.128230	+	0.241868i
$64$	−0.994138	+	0.108119i	−0.124267	+	0.0135149i
$65$	−4.41824	−	3.35866i	−0.548015	−	0.416590i
$66$	−0.940640	+	0.316939i	−0.115785	+	0.0390124i
$67$	−0.708395	−	13.0656i	−0.0865443	−	1.59622i	−0.643350	−	0.765572i	$-0.722456\pi$
$67$	−0.708395	−	13.0656i	−0.0865443	−	1.59622i	0.556805	−	0.830643i	$-0.312027\pi$
$68$	1.33347	−	1.26313i	0.161707	−	0.153177i
$69$	1.71090	−	1.30059i	0.205968	−	0.156573i
$70$	−3.81946	+	5.63328i	−0.456512	+	0.673305i
$71$	6.21527	+	0.675951i	0.737616	+	0.0802206i	0.469212	−	0.883086i	$-0.344538\pi$
$71$	6.21527	+	0.675951i	0.737616	+	0.0802206i	0.268405	+	0.963306i	$0.413504\pi$
$72$	−0.725995	−	0.687699i	−0.0855594	−	0.0810462i
$73$	−10.6342	+	12.5196i	−1.24464	+	1.46530i	−0.412289	+	0.911053i	$0.635270\pi$
$73$	−10.6342	+	12.5196i	−1.24464	+	1.46530i	−0.832351	+	0.554249i	$0.813005\pi$
$74$	0.165218	+	0.311634i	0.0192062	+	0.0362267i
$75$	−2.69992	−	3.98208i	−0.311760	−	0.459811i
$76$	−3.55044	−	1.19628i	−0.407264	−	0.137223i
$77$	−0.577005	+	2.07818i	−0.0657558	+	0.236831i
$78$	−0.286653	−	1.74851i	−0.0324571	−	0.197980i
$79$	−2.39183	+	6.00303i	−0.269102	+	0.675394i	−0.999975	−	0.00711944i	$-0.997734\pi$
$79$	−2.39183	+	6.00303i	−0.269102	+	0.675394i	0.730873	+	0.682513i	$0.239113\pi$
$80$	−2.02779	−	2.38729i	−0.226713	−	0.266908i
$81$	0.0541389	−	0.998533i	0.00601543	−	0.110948i
$82$	0.700608	+	2.52336i	0.0773692	+	0.278659i
$83$	−14.3587	+	6.64306i	−1.57608	+	0.729170i	−0.996327	−	0.0856253i	$-0.972711\pi$
$83$	−14.3587	+	6.64306i	−1.57608	+	0.729170i	−0.579748	+	0.814796i	$0.696849\pi$
$84$	−2.12208	+	0.467105i	−0.231538	+	0.0509653i
$85$	5.61866	+	1.23676i	0.609429	+	0.134145i
$86$	2.79260	+	1.29199i	0.301133	+	0.139319i
$87$	1.28055	−	7.81103i	0.137290	−	0.837431i
$88$	−0.850516	−	0.511739i	−0.0906653	−	0.0545515i
$89$	3.03286	+	1.82481i	0.321482	+	0.193430i	0.667142	−	0.744930i	$-0.267517\pi$
$89$	3.03286	+	1.82481i	0.321482	+	0.193430i	−0.345660	+	0.938360i	$0.612345\pi$
$90$	0.506744	−	3.09100i	0.0534155	−	0.325820i
$91$	−3.49418	−	1.61658i	−0.366289	−	0.169463i
$92$	2.09888	+	0.461998i	0.218823	+	0.0481666i
$93$	−5.73746	+	1.26291i	−0.594947	+	0.130958i
$94$	7.07686	−	3.27410i	0.729922	−	0.337698i
$95$	−3.13951	−	11.3075i	−0.322106	−	1.16012i
$96$	0.0541389	−	0.998533i	0.00552553	−	0.101912i
$97$	5.06980	+	5.96863i	0.514760	+	0.606022i	0.956719	−	0.291013i	$-0.0939922\pi$
$97$	5.06980	+	5.96863i	0.514760	+	0.606022i	−0.441959	+	0.897035i	$0.645716\pi$
$98$	0.843397	−	2.11677i	0.0851959	−	0.213826i
$99$	−0.160585	−	0.979524i	−0.0161394	−	0.0984458i
$100$	1.28710	−	4.63572i	0.128710	−	0.463572i
$101$	−9.42406	−	3.17534i	−0.937729	−	0.315958i	−0.191383	−	0.981515i	$-0.561297\pi$
$101$	−9.42406	−	3.17534i	−0.937729	−	0.315958i	−0.746346	+	0.665558i	$0.768194\pi$
$102$	1.03076	+	1.52025i	0.102060	+	0.150527i
$103$	4.25593	+	8.02754i	0.419350	+	0.790977i	0.999727	−	0.0233704i	$-0.00743971\pi$
$103$	4.25593	+	8.02754i	0.419350	+	0.790977i	−0.580377	+	0.814348i	$0.697095\pi$
$104$	1.14707	−	1.35044i	0.112480	−	0.132421i
$105$	−4.94115	−	4.68050i	−0.482207	−	0.456770i
$106$	−12.0787	−	1.31364i	−1.17319	−	0.127592i
$107$	−4.43868	+	6.54657i	−0.429104	+	0.632880i	−0.979362	−	0.202114i	$-0.935219\pi$
$107$	−4.43868	+	6.54657i	−0.429104	+	0.632880i	0.550258	+	0.834994i	$0.314529\pi$
$108$	0.796093	−	0.605174i	0.0766041	−	0.0582329i
$109$	6.22711	−	5.89863i	0.596449	−	0.564987i	−0.328775	−	0.944408i	$-0.606636\pi$
$109$	6.22711	−	5.89863i	0.596449	−	0.564987i	0.925224	+	0.379422i	$0.123877\pi$
$110$	−0.168322	−	3.10453i	−0.0160489	−	0.296005i
$111$	−0.334258	+	0.112625i	−0.0317264	+	0.0106899i
$112$	−1.72981	−	1.31497i	−0.163452	−	0.124253i
$113$	−11.2608	+	1.22469i	−1.05933	+	0.115209i	−0.621160	−	0.783684i	$-0.713338\pi$
$113$	−11.2608	+	1.22469i	−1.05933	+	0.115209i	−0.438169	+	0.898893i	$0.644373\pi$
$114$	1.75492	−	3.31013i	0.164363	−	0.310022i
$115$	2.49163	+	6.25352i	0.232346	+	0.583144i
$116$	6.78229	−	4.08077i	0.629720	−	0.378890i
$117$	1.77185			0.163808
$118$	6.26623	−	4.44234i	0.576853	−	0.408951i
$119$	3.99102			0.365856
$120$	2.68390	−	1.61485i	0.245006	−	0.147415i
$121$	3.70684	+	9.30347i	0.336985	+	0.845770i
$122$	−0.993866	+	1.87463i	−0.0899804	+	0.169721i
$123$	−2.60347	+	0.283144i	−0.234747	+	0.0255302i
$124$	−4.67689	−	3.55528i	−0.419998	−	0.319274i
$125$	−0.560758	+	0.188941i	−0.0501557	+	0.0168994i
$126$	−0.117637	−	2.16969i	−0.0104800	−	0.193291i
$127$	−4.21098	+	3.98885i	−0.373664	+	0.353953i	−0.851369	−	0.524567i	$-0.824227\pi$
$127$	−4.21098	+	3.98885i	−0.373664	+	0.353953i	0.477705	+	0.878520i	$0.341469\pi$
$128$	0.796093	−	0.605174i	0.0703654	−	0.0534903i
$129$	−1.72676	+	2.54679i	−0.152033	+	0.224232i
$130$	5.51737	+	0.600050i	0.483905	+	0.0526279i
$131$	−0.305134	−	0.289038i	−0.0266596	−	0.0252534i	0.674254	−	0.738500i	$-0.264465\pi$
$131$	−0.305134	−	0.289038i	−0.0266596	−	0.0252534i	−0.700913	+	0.713246i	$0.747224\pi$
$132$	0.642595	−	0.756522i	0.0559308	−	0.0658468i
$133$	−3.81323	−	7.19252i	−0.330649	−	0.623670i
$134$	7.34301	+	10.8301i	0.634339	+	0.935580i
$135$	2.96830	+	1.00014i	0.255471	+	0.0860781i
$136$	−0.491381	+	1.76979i	−0.0421355	+	0.151759i
$137$	−1.63185	−	9.95381i	−0.139418	−	0.850412i	−0.960229	−	0.279212i	$-0.909927\pi$
$137$	−1.63185	−	9.95381i	−0.139418	−	0.850412i	0.820811	−	0.571199i	$-0.193522\pi$
$138$	−0.795472	+	1.99648i	−0.0677151	+	0.169952i
$139$	9.76676	+	11.4983i	0.828405	+	0.975274i	0.999951	−	0.00990186i	$-0.00315191\pi$
$139$	9.76676	+	11.4983i	0.828405	+	0.975274i	−0.171545	+	0.985176i	$0.554876\pi$
$140$	0.368471	−	6.79605i	0.0311415	−	0.574371i
$141$	2.08606	+	7.51332i	0.175678	+	0.632736i
$142$	−5.67408	+	2.62511i	−0.476159	+	0.220294i
$143$	1.71762	−	0.378077i	0.143635	−	0.0316163i
$144$	0.976621	+	0.214970i	0.0813850	+	0.0179142i
$145$	22.5014	+	10.4102i	1.86864	+	0.864524i
$146$	2.65749	−	16.2100i	0.219935	−	1.34155i
$147$	1.95243	+	1.17474i	0.161034	+	0.0968910i
$148$	−0.302232	−	0.181847i	−0.0248433	−	0.0149477i
$149$	−1.26982	+	7.74554i	−0.104028	+	0.634540i	0.882420	+	0.470463i	$0.155913\pi$
$149$	−1.26982	+	7.74554i	−0.104028	+	0.634540i	−0.986447	+	0.164077i	$0.947535\pi$
$150$	4.36642	+	2.02012i	0.356517	+	0.164942i
$151$	6.23628	+	1.37271i	0.507502	+	0.111710i	0.461338	−	0.887224i	$-0.347369\pi$
$151$	6.23628	+	1.37271i	0.507502	+	0.111710i	0.0461634	+	0.998934i	$0.485301\pi$
$152$	3.65897	−	0.805400i	0.296782	−	0.0653266i
$153$	−1.66698	+	0.771228i	−0.134768	+	0.0623501i
$154$	−0.577005	−	2.07818i	−0.0464964	−	0.167465i
$155$	0.996235	−	18.3745i	0.0800195	−	1.47587i
$156$	1.14707	+	1.35044i	0.0918392	+	0.108121i
$157$	−2.54233	+	6.38077i	−0.202900	+	0.509241i	−0.994852	−	0.101343i	$-0.967686\pi$
$157$	−2.54233	+	6.38077i	−0.202900	+	0.509241i	0.791951	+	0.610584i	$0.209065\pi$
$158$	−1.04543	−	6.37686i	−0.0831702	−	0.507315i
$159$	3.25044	−	11.7070i	0.257777	−	0.928429i
$160$	2.96830	+	1.00014i	0.234665	+	0.0790678i
$161$	2.62062	+	3.86513i	0.206534	+	0.304615i
$162$	0.468408	+	0.883512i	0.0368016	+	0.0694153i
$163$	−9.51086	+	11.1970i	−0.744948	+	0.877021i	−0.995852	−	0.0909914i	$-0.970996\pi$
$163$	−9.51086	+	11.1970i	−0.744948	+	0.877021i	0.250904	+	0.968012i	$0.419272\pi$
$164$	−1.90125	−	1.80096i	−0.148463	−	0.140631i
$165$	3.09086	+	0.336151i	0.240623	+	0.0261693i
$166$	8.87853	−	13.0949i	0.689108	−	1.01636i
$167$	−11.0037	+	8.36482i	−0.851494	+	0.647289i	−0.937108	−	0.349039i	$-0.886508\pi$
$167$	−11.0037	+	8.36482i	−0.851494	+	0.647289i	0.0856138	+	0.996328i	$0.472715\pi$
$168$	1.57750	−	1.49429i	0.121707	−	0.115287i
$169$	−0.533839	−	9.84609i	−0.0410646	−	0.757391i
$170$	−5.45200	+	1.83699i	−0.418150	+	0.140891i
$171$	2.98261	+	2.26732i	0.228086	+	0.173386i
$172$	−3.05895	+	0.332681i	−0.233243	+	0.0253667i
$173$	−7.12791	+	13.4447i	−0.541925	+	1.02218i	0.449718	+	0.893170i	$0.351524\pi$
$173$	−7.12791	+	13.4447i	−0.541925	+	1.02218i	−0.991643	+	0.129009i	$0.958821\pi$
$174$	2.92976	+	7.35314i	0.222104	+	0.557440i
$175$	8.95750	−	5.38955i	0.677123	−	0.407412i
$176$	0.992600			0.0748200
$177$	3.37006	+	6.90237i	0.253309	+	0.518814i
$178$	−3.53951			−0.265298
$179$	16.7771	−	10.0944i	1.25398	−	0.754494i	0.275591	−	0.961275i	$-0.411126\pi$
$179$	16.7771	−	10.0944i	1.25398	−	0.754494i	0.978387	+	0.206781i	$0.0662988\pi$
$180$	1.15937	+	2.90980i	0.0864144	+	0.216884i
$181$	4.03749	−	7.61550i	0.300104	−	0.566056i	−0.686900	−	0.726752i	$-0.741029\pi$
$181$	4.03749	−	7.61550i	0.300104	−	0.566056i	0.987004	+	0.160696i	$0.0513738\pi$
$182$	3.82744	−	0.416260i	0.283709	−	0.0308552i
$183$	−1.68914	−	1.28405i	−0.124865	−	0.0949200i
$184$	−2.03662	+	0.686218i	−0.150142	+	0.0505887i
$185$	−0.0598137	−	1.10320i	−0.00439759	−	0.0811087i
$186$	4.26508	−	4.04010i	0.312731	−	0.296235i
$187$	−1.45140	+	1.10332i	−0.106137	+	0.0806830i
$188$	−4.37588	+	6.45394i	−0.319144	+	0.470702i
$189$	2.16014	+	0.234929i	0.157127	+	0.0170886i
$190$	8.51972	+	8.07031i	0.618085	+	0.585482i
$191$	3.80882	−	4.48409i	0.275596	−	0.324457i	−0.606898	−	0.794779i	$-0.707587\pi$
$191$	3.80882	−	4.48409i	0.275596	−	0.324457i	0.882495	+	0.470322i	$0.155862\pi$
$192$	0.468408	+	0.883512i	0.0338045	+	0.0637620i
$193$	−5.66145	−	8.35001i	−0.407520	−	0.601047i	0.567444	−	0.823412i	$-0.307933\pi$
$193$	−5.66145	−	8.35001i	−0.407520	−	0.601047i	−0.974963	+	0.222366i	$0.928622\pi$
$194$	−7.42124	−	2.50051i	−0.532814	−	0.179526i
$195$	−1.48476	+	5.34761i	−0.106326	+	0.382950i
$196$	0.368636	+	2.24858i	0.0263312	+	0.160613i
$197$	5.01974	−	12.5986i	0.357642	−	0.897613i	−0.634549	−	0.772883i	$-0.718814\pi$
$197$	5.01974	−	12.5986i	0.357642	−	0.897613i	0.992191	−	0.124731i	$-0.0398066\pi$
$198$	0.642595	+	0.756522i	0.0456673	+	0.0537637i
$199$	−0.229243	+	4.22814i	−0.0162506	+	0.299725i	0.979098	+	0.203388i	$0.0651954\pi$
$199$	−0.229243	+	4.22814i	−0.0162506	+	0.299725i	−0.995349	+	0.0963369i	$0.969287\pi$
$200$	1.28710	+	4.63572i	0.0910118	+	0.327795i
$201$	−11.8754	+	5.49415i	−0.837628	+	0.387528i
$202$	9.71213	−	2.13780i	0.683343	−	0.150415i
$203$	16.7969	+	3.69728i	1.17891	+	0.259498i
$204$	−1.66698	−	0.771228i	−0.116712	−	0.0539968i
$205$	1.32707	−	8.09477i	0.0926866	−	0.565363i
$206$	−7.78536	−	4.68429i	−0.542432	−	0.326370i
$207$	−1.84149	−	1.10799i	−0.127992	−	0.0770105i
$208$	−0.286653	+	1.74851i	−0.0198758	+	0.121237i
$209$	3.37512	+	1.56150i	0.233462	+	0.108011i
$210$	6.64691	+	1.46310i	0.458680	+	0.100963i
$211$	12.8405	−	2.82641i	0.883976	−	0.194578i	0.250293	−	0.968170i	$-0.419473\pi$
$211$	12.8405	−	2.82641i	0.883976	−	0.194578i	0.633684	+	0.773592i	$0.281542\pi$
$212$	11.0270	−	5.10161i	0.757334	−	0.350380i
$213$	−1.67256	−	6.02403i	−0.114602	−	0.412760i
$214$	0.428209	−	7.89785i	0.0292718	−	0.539886i
$215$	−6.23947	−	7.34567i	−0.425528	−	0.500970i
$216$	−0.370138	+	0.928977i	−0.0251847	+	0.0632089i
$217$	−2.06519	−	12.5971i	−0.140194	−	0.855146i
$218$	−2.29468	+	8.26470i	−0.155415	+	0.559756i
$219$	15.5665	+	5.24496i	1.05189	+	0.354422i
$220$	1.74478	+	2.57336i	0.117633	+	0.173496i
$221$	−1.52440	−	2.87533i	−0.102542	−	0.193416i
$222$	0.228347	−	0.268831i	0.0153257	−	0.0180428i
$223$	−16.9128	−	16.0206i	−1.13256	−	1.07282i	−0.996624	−	0.0821029i	$-0.973836\pi$
$223$	−16.9128	−	16.0206i	−1.13256	−	1.07282i	−0.135939	−	0.990717i	$-0.543405\pi$
$224$	2.16014	+	0.234929i	0.144330	+	0.0156969i
$225$	−2.69992	+	3.98208i	−0.179995	+	0.265472i
$226$	9.01752	−	6.85494i	0.599837	−	0.455984i
$227$	6.46439	−	6.12340i	0.429057	−	0.406424i	−0.442461	−	0.896788i	$-0.645895\pi$
$227$	6.46439	−	6.12340i	0.429057	−	0.406424i	0.871518	+	0.490363i	$0.163136\pi$
$228$	0.202835	+	3.74107i	0.0134331	+	0.247758i
$229$	18.6128	−	6.27139i	1.22997	−	0.414425i	0.372051	−	0.928212i	$-0.378654\pi$
$229$	18.6128	−	6.27139i	1.22997	−	0.414425i	0.857918	+	0.513787i	$0.171758\pi$
$230$	−5.35900	−	4.07380i	−0.353362	−	0.268619i
$231$	2.14416	−	0.233191i	0.141075	−	0.0153428i
$232$	−3.70760	+	6.99327i	−0.243416	+	0.459131i
$233$	7.81978	+	19.6262i	0.512291	+	1.28575i	0.926748	+	0.375684i	$0.122592\pi$
$233$	7.81978	+	19.6262i	0.512291	+	1.28575i	−0.414457	+	0.910069i	$0.636029\pi$
$234$	−1.51822	+	0.913484i	−0.0992493	+	0.0597163i
$235$	−24.4240			−1.59324
$236$	−3.07899	+	7.03703i	−0.200425	+	0.458072i
$237$	6.46198			0.419751
$238$	−3.41973	+	2.05758i	−0.221668	+	0.133373i
$239$	6.53083	+	16.3912i	0.422445	+	1.06026i	0.974087	+	0.226175i	$0.0726221\pi$
$239$	6.53083	+	16.3912i	0.422445	+	1.06026i	−0.551642	+	0.834081i	$0.685999\pi$
$240$	−1.46718	+	2.76739i	−0.0947060	+	0.178635i
$241$	−12.1619	+	1.32269i	−0.783417	+	0.0852017i	−0.491081	−	0.871114i	$-0.663398\pi$
$241$	−12.1619	+	1.32269i	−0.783417	+	0.0852017i	−0.292336	+	0.956316i	$0.594433\pi$
$242$	−7.97267	−	6.06067i	−0.512503	−	0.389594i
$243$	−0.947653	+	0.319302i	−0.0607920	+	0.0204832i
$244$	−0.114872	−	2.11868i	−0.00735390	−	0.135635i
$245$	−5.18156	+	4.90823i	−0.331038	+	0.313576i
$246$	2.08482	−	1.58484i	0.132923	−	0.101046i
$247$	−3.72535	+	5.49448i	−0.237038	+	0.349606i
$248$	5.84037	+	0.635179i	0.370864	+	0.0403339i
$249$	11.4860	+	10.8801i	0.727893	+	0.689497i
$250$	0.383080	−	0.450997i	0.0242281	−	0.0285235i
$251$	−7.41939	−	13.9945i	−0.468308	−	0.883322i	−0.999353	−	0.0359783i	$-0.988545\pi$
$251$	−7.41939	−	13.9945i	−0.468308	−	0.883322i	0.531045	−	0.847344i	$-0.321800\pi$
$252$	1.21939	+	1.79847i	0.0768144	+	0.113293i
$253$	−2.02155	−	0.681140i	−0.127094	−	0.0428229i
$254$	1.55174	−	5.58886i	0.0973648	−	0.350676i
$255$	−0.930758	−	5.67738i	−0.0582864	−	0.355531i
$256$	−0.370138	+	0.928977i	−0.0231336	+	0.0580610i
$257$	−14.0546	−	16.5463i	−0.876700	−	1.03213i	−0.999213	−	0.0396637i	$-0.987371\pi$
$257$	−14.0546	−	16.5463i	−0.876700	−	1.03213i	0.122514	−	0.992467i	$-0.460905\pi$
$258$	0.166585	−	3.07247i	0.0103711	−	0.191284i
$259$	−0.205040	−	0.738486i	−0.0127405	−	0.0458873i
$260$	−5.03695	+	2.33034i	−0.312379	+	0.144522i
$261$	−7.73025	+	1.70156i	−0.478491	+	0.105324i
$262$	0.410470	+	0.0903514i	0.0253589	+	0.00558193i
$263$	−22.2144	−	10.2775i	−1.36980	−	0.633738i	−0.409399	−	0.912355i	$-0.634262\pi$
$263$	−22.2144	−	10.2775i	−1.36980	−	0.633738i	−0.960402	+	0.278618i	$0.910124\pi$
$264$	−0.160585	+	0.979524i	−0.00988331	+	0.0602855i
$265$	32.6092	+	19.6203i	2.00317	+	1.20526i
$266$	6.97552	+	4.19703i	0.427697	+	0.257337i
$267$	0.572630	−	3.49289i	0.0350444	−	0.213761i
$268$	−11.8754	−	5.49415i	−0.725407	−	0.335609i
$269$	−13.6884	−	3.01304i	−0.834596	−	0.183708i	−0.222940	−	0.974832i	$-0.571565\pi$
$269$	−13.6884	−	3.01304i	−0.834596	−	0.183708i	−0.611656	+	0.791124i	$0.709496\pi$
$270$	−3.05903	+	0.673344i	−0.186167	+	0.0409784i
$271$	−4.04332	+	1.87064i	−0.245614	+	0.113633i	−0.538834	−	0.842412i	$-0.681135\pi$
$271$	−4.04332	+	1.87064i	−0.245614	+	0.113633i	0.293220	+	0.956045i	$0.405273\pi$
$272$	−0.491381	−	1.76979i	−0.0297943	−	0.107309i
$273$	−0.208436	+	3.84437i	−0.0126151	+	0.232672i
$274$	6.52999	+	7.68769i	0.394491	+	0.464431i
$275$	−1.76759	+	4.43631i	−0.106590	+	0.267520i
$276$	−0.347689	−	2.12081i	−0.0209284	−	0.127658i
$277$	1.83719	−	6.61697i	0.110386	−	0.397575i	−0.887628	−	0.460561i	$-0.847648\pi$
$277$	1.83719	−	6.61697i	0.110386	−	0.397575i	0.998014	+	0.0629854i	$0.0200621\pi$
$278$	−14.2967	−	4.81712i	−0.857460	−	0.288912i
$279$	3.29687	+	4.86251i	0.197378	+	0.291111i
$280$	3.18800	+	6.01321i	0.190520	+	0.359358i
$281$	−8.69634	+	10.2381i	−0.518780	+	0.610755i	−0.957699	−	0.287771i	$-0.907086\pi$
$281$	−8.69634	+	10.2381i	−0.518780	+	0.610755i	0.438919	+	0.898527i	$0.355362\pi$
$282$	−5.66098	−	5.36236i	−0.337106	−	0.319324i
$283$	−23.0893	−	2.51112i	−1.37252	−	0.149270i	−0.608033	−	0.793911i	$-0.708041\pi$
$283$	−23.0893	−	2.51112i	−1.37252	−	0.149270i	−0.764485	+	0.644641i	$0.777007\pi$
$284$	3.50849	−	5.17464i	0.208191	−	0.307058i
$285$	−9.34233	+	7.10186i	−0.553392	+	0.420678i
$286$	−1.27684	+	1.20948i	−0.0755009	+	0.0715182i
$287$	−0.308070	−	5.68203i	−0.0181848	−	0.335399i
$288$	−0.947653	+	0.319302i	−0.0558410	+	0.0188150i
$289$	−10.8479	−	8.24633i	−0.638110	−	0.485078i
$290$	−24.6475	+	2.68058i	−1.44735	+	0.157409i
$291$	3.66819	−	6.91894i	0.215033	−	0.405596i
$292$	6.08002	+	15.2597i	0.355807	+	0.893007i
$293$	15.9404	−	9.59104i	0.931250	−	0.560314i	0.0328341	−	0.999461i	$-0.489547\pi$
$293$	15.9404	−	9.59104i	0.931250	−	0.560314i	0.898415	+	0.439147i	$0.144719\pi$
$294$	−2.27860			−0.132891
$295$	−23.6560	+	4.38718i	−1.37731	+	0.255431i
$296$	0.352722			0.0205015
$297$	−0.850516	+	0.511739i	−0.0493520	+	0.0296941i
$298$	−2.90519	−	7.29148i	−0.168293	−	0.422384i
$299$	1.78366	−	3.36434i	0.103152	−	0.194565i
$300$	−4.78288	+	0.520170i	−0.276140	+	0.0300320i
$301$	−5.32261	−	4.04614i	−0.306790	−	0.233216i
$302$	−6.05131	+	2.03892i	−0.348214	+	0.117327i
$303$	0.538391	+	9.93005i	0.0309298	+	0.570466i
$304$	−2.71999	+	2.57651i	−0.156002	+	0.147773i
$305$	5.29085	−	4.02200i	0.302953	−	0.230299i
$306$	1.03076	−	1.52025i	0.0589244	−	0.0869070i
$307$	26.5238	+	2.88464i	1.51380	+	0.164635i	0.826994	−	0.562210i	$-0.190049\pi$
$307$	26.5238	+	2.88464i	1.51380	+	0.164635i	0.686801	+	0.726845i	$0.259014\pi$
$308$	1.56583	+	1.48323i	0.0892212	+	0.0845148i
$309$	5.88212	−	6.92496i	0.334622	−	0.393947i
$310$	8.61940	+	16.2579i	0.489549	+	0.923387i
$311$	−5.84629	−	8.62263i	−0.331513	−	0.488944i	0.625004	−	0.780621i	$-0.285097\pi$
$311$	−5.84629	−	8.62263i	−0.331513	−	0.488944i	−0.956517	+	0.291677i	$0.905787\pi$
$312$	−1.67910	−	0.565754i	−0.0950602	−	0.0320295i
$313$	−5.98583	+	21.5590i	−0.338339	+	1.21859i	0.577281	+	0.816545i	$0.304114\pi$
$313$	−5.98583	+	21.5590i	−0.338339	+	1.21859i	−0.915621	+	0.402043i	$0.868300\pi$
$314$	−1.11122	−	6.77812i	−0.0627096	−	0.382511i
$315$	−2.51917	+	6.32264i	−0.141939	+	0.356241i
$316$	4.18340	+	4.92508i	0.235335	+	0.277057i
$317$	−1.42269	+	26.2400i	−0.0799064	+	1.47379i	0.633885	+	0.773428i	$0.281459\pi$
$317$	−1.42269	+	26.2400i	−0.0799064	+	1.47379i	−0.713791	+	0.700359i	$0.753023\pi$
$318$	3.25044	+	11.7070i	0.182276	+	0.656498i
$319$	−7.13058	+	3.29896i	−0.399236	+	0.184706i
$320$	−3.05903	+	0.673344i	−0.171005	+	0.0376411i
$321$	7.72453	+	1.70030i	0.431141	+	0.0949014i
$322$	−4.23818	−	1.96079i	−0.236184	−	0.109271i
$323$	1.11330	−	6.79082i	0.0619455	−	0.377851i
$324$	−0.856857	−	0.515554i	−0.0476032	−	0.0286419i
$325$	−7.30429	−	4.39485i	−0.405169	−	0.243782i
$326$	2.37677	−	14.4976i	0.131637	−	0.802950i
$327$	−7.78459	−	3.60153i	−0.430489	−	0.199165i
$328$	2.55759	+	0.562968i	0.141219	+	0.0310847i
$329$	−16.5470	+	3.64227i	−0.912265	+	0.200805i
$330$	−2.82173	+	1.30547i	−0.155331	+	0.0718638i
$331$	0.0533024	+	0.191978i	0.00292977	+	0.0105521i	0.965000	−	0.262248i	$-0.0844639\pi$
$331$	0.0533024	+	0.191978i	0.00292977	+	0.0105521i	−0.962071	+	0.272800i	$0.912050\pi$
$332$	−0.856531	+	15.7978i	−0.0470082	+	0.867016i
$333$	0.228347	+	0.268831i	0.0125134	+	0.0147319i
$334$	5.11611	−	12.8405i	0.279941	−	0.702599i
$335$	−6.63063	−	40.4451i	−0.362270	−	2.20975i
$336$	−0.581307	+	2.09368i	−0.0317129	+	0.114219i
$337$	25.5518	+	8.60940i	1.39190	+	0.468984i	0.912666	−	0.408706i	$-0.134020\pi$
$337$	25.5518	+	8.60940i	1.39190	+	0.468984i	0.479229	+	0.877690i	$0.340916\pi$
$338$	5.53361	+	8.16147i	0.300989	+	0.443925i
$339$	5.30577	+	10.0077i	0.288170	+	0.543546i
$340$	3.72452	−	4.38484i	0.201990	−	0.237802i
$341$	4.23352	+	4.01020i	0.229258	+	0.217165i
$342$	−3.72460	−	0.405075i	−0.201403	−	0.0219039i
$343$	−11.3142	+	16.6873i	−0.610912	+	0.901027i
$344$	2.44957	−	1.86211i	0.132072	−	0.100398i
$345$	4.88713	−	4.62933i	0.263114	−	0.249235i
$346$	−0.823848	−	15.1950i	−0.0442903	−	0.816887i
$347$	31.8785	−	10.7411i	1.71133	−	0.576613i	0.718430	−	0.695600i	$-0.244861\pi$
$347$	31.8785	−	10.7411i	1.71133	−	0.576613i	0.992896	+	0.118987i	$0.0379647\pi$
$348$	−6.30132	−	4.79014i	−0.337786	−	0.256778i
$349$	−15.1770	+	1.65060i	−0.812406	+	0.0883545i	−0.504885	−	0.863187i	$-0.668465\pi$
$349$	−15.1770	+	1.65060i	−0.812406	+	0.0883545i	−0.307521	+	0.951541i	$0.599500\pi$
$350$	−4.89670	+	9.23615i	−0.261739	+	0.493693i
$351$	−0.655829	−	1.64601i	−0.0350056	−	0.0878573i
$352$	−0.850516	+	0.511739i	−0.0453327	+	0.0272758i
$353$	−26.7582			−1.42420			−0.712098	−	0.702080i	$-0.752255\pi$
$353$	−26.7582			−1.42420			−0.712098	+	0.702080i	$0.752255\pi$
$354$	−6.44620	−	4.17690i	−0.342612	−	0.222000i
$355$	19.5827			1.03934
$356$	3.03286	−	1.82481i	0.160741	−	0.0967148i
$357$	−1.47723	−	3.70756i	−0.0781832	−	0.196225i
$358$	−9.17134	+	17.2990i	−0.484721	+	0.914280i
$359$	−3.22229	+	0.350445i	−0.170066	+	0.0184958i	−0.192756	−	0.981247i	$-0.561742\pi$
$359$	−3.22229	+	0.350445i	−0.170066	+	0.0184958i	0.0226899	+	0.999743i	$0.492777\pi$
$360$	−2.49357	−	1.89557i	−0.131423	−	0.0999051i
$361$	4.70346	−	1.58478i	0.247551	−	0.0834095i
$362$	0.466655	+	8.60694i	0.0245268	+	0.452371i
$363$	7.27066	−	6.88714i	0.381611	−	0.361481i
$364$	−3.06497	+	2.32993i	−0.160648	+	0.122121i
$365$	−28.8740	+	42.5860i	−1.51134	+	2.22905i
$366$	2.10935	+	0.229406i	0.110258	+	0.0119913i
$367$	−7.99992	−	7.57793i	−0.417593	−	0.395565i	0.449848	−	0.893105i	$-0.351478\pi$
$367$	−7.99992	−	7.57793i	−0.417593	−	0.395565i	−0.867441	+	0.497540i	$0.834237\pi$
$368$	1.39131	−	1.63798i	0.0725272	−	0.0853856i
$369$	1.22668	+	2.31376i	0.0638582	+	0.120449i
$370$	0.620010	+	0.914446i	0.0322328	+	0.0475398i
$371$	25.0183	+	8.42964i	1.29889	+	0.437645i
$372$	−1.57168	+	5.66067i	−0.0814877	+	0.293492i
$373$	−3.49308	−	21.3068i	−0.180865	−	1.10323i	−0.908693	−	0.417466i	$-0.862918\pi$
$373$	−3.49308	−	21.3068i	−0.180865	−	1.10323i	0.727828	−	0.685760i	$-0.240530\pi$
$374$	0.674817	−	1.69366i	0.0348940	−	0.0875773i
$375$	0.383080	+	0.450997i	0.0197822	+	0.0232894i
$376$	0.422150	−	7.78610i	0.0217707	−	0.401538i
$377$	−3.75201	−	13.5135i	−0.193238	−	0.695982i
$378$	−1.97205	+	0.912368i	−0.101431	+	0.0469271i
$379$	36.3446	−	8.00004i	1.86689	−	0.410934i	0.870237	−	0.492633i	$-0.163966\pi$
$379$	36.3446	−	8.00004i	1.86689	−	0.410934i	0.996657	+	0.0816986i	$0.0260345\pi$
$380$	−11.4609	−	2.52273i	−0.587930	−	0.129413i
$381$	5.26419	+	2.43548i	0.269693	+	0.124773i
$382$	−0.951824	+	5.80587i	−0.0486996	+	0.297054i
$383$	14.4103	+	8.67037i	0.736330	+	0.443035i	0.833703	−	0.552213i	$-0.186216\pi$
$383$	14.4103	+	8.67037i	0.736330	+	0.443035i	−0.0973732	+	0.995248i	$0.531044\pi$
$384$	−0.856857	−	0.515554i	−0.0437263	−	0.0263092i
$385$	−1.09294	+	6.66667i	−0.0557016	+	0.339765i
$386$	9.15593	+	4.23598i	0.466025	+	0.215606i
$387$	3.00505	+	0.661461i	0.152755	+	0.0336239i
$388$	7.64809	−	1.68347i	0.388273	−	0.0854654i
$389$	18.4313	−	8.52722i	0.934503	−	0.432347i	0.107285	−	0.994228i	$-0.465784\pi$
$389$	18.4313	−	8.52722i	0.934503	−	0.432347i	0.827218	+	0.561881i	$0.189922\pi$
$390$	−1.48476	−	5.34761i	−0.0751835	−	0.270787i
$391$	−0.213707	+	3.94160i	−0.0108076	+	0.199335i
$392$	−1.47513	−	1.73666i	−0.0745055	−	0.0877147i
$393$	−0.155568	+	0.390446i	−0.00784736	+	0.0196954i
$394$	2.19406	+	13.3832i	0.110535	+	0.674233i
$395$	−5.41495	+	19.5029i	−0.272456	+	0.981296i
$396$	−0.940640	−	0.316939i	−0.0472690	−	0.0159268i
$397$	2.75373	+	4.06146i	0.138206	+	0.203839i	0.890493	−	0.454997i	$-0.150360\pi$
$397$	2.75373	+	4.06146i	0.138206	+	0.203839i	−0.752287	+	0.658836i	$0.771049\pi$
$398$	−1.98341	−	3.74110i	−0.0994192	−	0.187525i
$399$	−5.27026	+	6.20463i	−0.263843	+	0.310620i
$400$	−3.49283	−	3.30858i	−0.174641	−	0.165429i
$401$	21.1932	+	2.30490i	1.05834	+	0.115101i	0.620698	−	0.784050i	$-0.286849\pi$
$401$	21.1932	+	2.30490i	1.05834	+	0.115101i	0.437639	+	0.899151i	$0.355815\pi$
$402$	7.34301	−	10.8301i	0.366236	−	0.540158i
$403$	−8.28675	+	6.29943i	−0.412793	+	0.313797i
$404$	−7.21976	+	6.83892i	−0.359196	+	0.340249i
$405$	−0.169577	−	3.12767i	−0.00842637	−	0.155415i
$406$	−16.2987	+	5.49167i	−0.808890	+	0.272547i
$407$	0.278721	+	0.211879i	0.0138157	+	0.0105024i
$408$	1.82598	−	0.198587i	0.0903993	−	0.00983151i
$409$	13.9390	−	26.2917i	0.689237	−	1.30004i	−0.253769	−	0.967265i	$-0.581670\pi$
$409$	13.9390	−	26.2917i	0.689237	−	1.30004i	0.943006	−	0.332774i	$-0.107985\pi$
$410$	3.03618	+	7.62024i	0.149946	+	0.376337i
$411$	−8.64285	+	5.20023i	−0.426321	+	0.256509i
$412$	9.08595			0.447632
$413$	−15.3725	+	6.50001i	−0.756429	+	0.319845i
$414$	2.14912			0.105624
$415$	−42.4620	+	25.5485i	−2.08438	+	1.25413i
$416$	−0.655829	−	1.64601i	−0.0321547	−	0.0807021i
$417$	7.06662	−	13.3291i	0.346054	−	0.652727i
$418$	−3.69704	+	0.402077i	−0.180828	+	0.0196662i
$419$	7.65625	+	5.82013i	0.374032	+	0.284332i	0.775255	−	0.631649i	$-0.217622\pi$
$419$	7.65625	+	5.82013i	0.374032	+	0.284332i	−0.401223	+	0.915981i	$0.631415\pi$
$420$	−6.44976	+	2.17318i	−0.314716	+	0.106040i
$421$	−2.00503	−	36.9807i	−0.0977194	−	1.80233i	−0.478944	−	0.877845i	$-0.658980\pi$
$421$	−2.00503	−	36.9807i	−0.0977194	−	1.80233i	0.381225	−	0.924482i	$-0.375502\pi$
$422$	−9.54531	+	9.04180i	−0.464658	+	0.440148i
$423$	6.20757	−	4.71887i	0.301822	−	0.229439i
$424$	−6.81837	+	10.0563i	−0.331129	+	0.488379i
$425$	8.78492	+	0.955418i	0.426131	+	0.0463446i
$426$	4.53886	+	4.29944i	0.219909	+	0.208308i
$427$	2.98471	−	3.51387i	0.144440	−	0.170048i
$428$	3.70485	+	6.98810i	0.179081	+	0.337782i
$429$	−0.986981	−	1.45569i	−0.0476519	−	0.0702813i
$430$	9.13342	+	3.07741i	0.440453	+	0.148406i
$431$	−5.78545	+	20.8373i	−0.278675	+	1.00370i	0.683205	+	0.730227i	$0.260586\pi$
$431$	−5.78545	+	20.8373i	−0.278675	+	1.00370i	−0.961880	+	0.273471i	$0.911828\pi$
$432$	−0.161782	−	0.986827i	−0.00778374	−	0.0474787i
$433$	6.27489	−	15.7488i	0.301552	−	0.756838i	−0.697632	−	0.716456i	$-0.745763\pi$
$433$	6.27489	−	15.7488i	0.301552	−	0.756838i	0.999184	−	0.0403823i	$-0.0128576\pi$
$434$	8.26404	+	9.72919i	0.396687	+	0.467016i
$435$	1.34226	−	24.7565i	0.0643563	−	1.18698i
$436$	−2.29468	−	8.26470i	−0.109895	−	0.395807i
$437$	7.30763	−	3.38087i	0.349572	−	0.161729i
$438$	−16.0423	+	3.53118i	−0.766532	+	0.168726i
$439$	−32.9140	−	7.24492i	−1.57090	−	0.345781i	−0.657696	−	0.753283i	$-0.728469\pi$
$439$	−32.9140	−	7.24492i	−1.57090	−	0.345781i	−0.913204	+	0.407502i	$0.866400\pi$
$440$	−2.82173	−	1.30547i	−0.134521	−	0.0622359i
$441$	0.368636	−	2.24858i	0.0175541	−	0.107075i
$442$	2.78858	+	1.67783i	0.132639	+	0.0798065i
$443$	9.50246	+	5.71744i	0.451476	+	0.271644i	0.723079	−	0.690765i	$-0.242726\pi$
$443$	9.50246	+	5.71744i	0.451476	+	0.271644i	−0.271603	+	0.962409i	$0.587554\pi$
$444$	−0.0570640	+	0.348075i	−0.00270814	+	0.0165189i
$445$	10.0620	+	4.65518i	0.476985	+	0.220677i
$446$	22.7513	+	5.00794i	1.07731	+	0.237133i
$447$	7.66544	−	1.68729i	0.362563	−	0.0798061i
$448$	−1.97205	+	0.912368i	−0.0931707	+	0.0431053i
$449$	−8.96196	−	32.2780i	−0.422941	−	1.52330i	−0.801658	−	0.597783i	$-0.796049\pi$
$449$	−8.96196	−	32.2780i	−0.422941	−	1.52330i	0.378717	−	0.925512i	$-0.376365\pi$
$450$	0.260467	−	4.80403i	0.0122785	−	0.226464i
$451$	1.68284	+	1.98119i	0.0792418	+	0.0932907i
$452$	−4.19264	+	10.5227i	−0.197205	+	0.494947i
$453$	−1.03307	−	6.30146i	−0.0485379	−	0.296068i
$454$	−2.38212	+	8.57962i	−0.111798	+	0.402662i
$455$	−11.4280	−	3.85054i	−0.535753	−	0.180516i
$456$	−2.10252	−	3.10099i	−0.0984596	−	0.145217i
$457$	7.70797	+	14.5388i	0.360564	+	0.680095i	0.995733	−	0.0922774i	$-0.0294147\pi$
$457$	7.70797	+	14.5388i	0.360564	+	0.680095i	−0.635170	+	0.772373i	$0.719070\pi$
$458$	−12.7153	+	14.9696i	−0.594146	+	0.699483i
$459$	1.33347	+	1.26313i	0.0622409	+	0.0589577i
$460$	6.69216	+	0.727816i	0.312024	+	0.0339346i
$461$	3.77740	−	5.57125i	0.175931	−	0.259479i	−0.729492	−	0.683989i	$-0.760243\pi$
$461$	3.77740	−	5.57125i	0.175931	−	0.259479i	0.905423	+	0.424511i	$0.139554\pi$
$462$	−1.71701	+	1.30524i	−0.0798826	+	0.0607252i
$463$	21.9730	−	20.8139i	1.02117	−	0.967305i	0.0216979	−	0.999765i	$-0.493093\pi$
$463$	21.9730	−	20.8139i	1.02117	−	0.967305i	0.999473	+	0.0324600i	$0.0103342\pi$
$464$	−0.428526	−	7.90370i	−0.0198938	−	0.366920i
$465$	−17.4382	+	5.87561i	−0.808677	+	0.272475i
$466$	−16.8188	−	12.7853i	−0.779115	−	0.592268i
$467$	18.6361	−	2.02679i	0.862374	−	0.0937888i	0.333767	−	0.942656i	$-0.391680\pi$
$467$	18.6361	−	2.02679i	0.862374	−	0.0937888i	0.528607	+	0.848867i	$0.322715\pi$
$468$	0.829949	−	1.56545i	0.0383644	−	0.0723630i
$469$	−10.5236	−	26.4123i	−0.485936	−	1.21961i
$470$	20.9278	−	12.5919i	0.965330	−	0.580820i
$471$	6.86860			0.316489
$472$	−0.989710	−	7.61712i	−0.0455551	−	0.350606i
$473$	3.05421			0.140433
$474$	−5.53700	+	3.33150i	−0.254323	+	0.153021i
$475$	−6.67175	−	16.7448i	−0.306121	−	0.768305i
$476$	1.86943	−	3.52611i	0.0856850	−	0.161619i
$477$	−12.0787	+	1.31364i	−0.553045	+	0.0601472i
$478$	−14.0465	−	10.6779i	−0.642473	−	0.488395i
$479$	−4.84317	+	1.63186i	−0.221290	+	0.0745614i	−0.427763	−	0.903891i	$-0.640698\pi$
$479$	−4.84317	+	1.63186i	−0.221290	+	0.0745614i	0.206473	+	0.978452i	$0.433802\pi$
$480$	−0.169577	−	3.12767i	−0.00774011	−	0.142758i
$481$	−0.453725	+	0.429792i	−0.0206881	+	0.0195968i
$482$	9.73909	−	7.40347i	0.443604	−	0.337219i
$483$	2.62062	−	3.86513i	0.119242	−	0.175869i
$484$	9.95604	+	1.08278i	0.452547	+	0.0492175i
$485$	17.8082	+	16.8688i	0.808628	+	0.765973i
$486$	0.647386	−	0.762162i	0.0293660	−	0.0345724i
$487$	1.51037	+	2.84886i	0.0684414	+	0.129094i	0.915372	−	0.402610i	$-0.131897\pi$
$487$	1.51037	+	2.84886i	0.0684414	+	0.129094i	−0.846930	+	0.531704i	$0.821552\pi$
$488$	1.19072	+	1.75618i	0.0539015	+	0.0794987i
$489$	13.9221	+	4.69091i	0.629581	+	0.212130i
$490$	1.90940	−	6.87703i	0.0862578	−	0.310672i
$491$	1.33071	+	8.11698i	0.0600542	+	0.366314i	0.999707	+	0.0241861i	$0.00769943\pi$
$491$	1.33071	+	8.11698i	0.0600542	+	0.366314i	−0.939653	+	0.342128i	$0.888852\pi$
$492$	−0.969324	+	2.43282i	−0.0437005	+	0.109680i
$493$	9.41195	+	11.0806i	0.423893	+	0.499045i
$494$	0.359393	−	6.62861i	0.0161698	−	0.298235i
$495$	−0.831768	−	2.99576i	−0.0373852	−	0.134649i
$496$	−5.33183	+	2.46677i	−0.239406	+	0.110761i
$497$	13.2670	−	2.92030i	0.595108	−	0.130993i
$498$	−15.4511	−	3.40104i	−0.692380	−	0.152404i
$499$	−11.4038	−	5.27598i	−0.510506	−	0.236185i	0.147688	−	0.989034i	$-0.452817\pi$
$499$	−11.4038	−	5.27598i	−0.510506	−	0.236185i	−0.658193	+	0.752849i	$0.728679\pi$
$500$	−0.0957318	+	0.583938i	−0.00428126	+	0.0261145i
$501$	11.8436	+	7.12607i	0.529134	+	0.318369i
$502$	13.5723	+	8.16615i	0.605759	+	0.364473i
$503$	−1.21958	+	7.43910i	−0.0543783	+	0.331693i	0.945601	+	0.325328i	$0.105475\pi$
$503$	−1.21958	+	7.43910i	−0.0543783	+	0.331693i	−0.999980	+	0.00636568i	$0.997974\pi$
$504$	−1.97205	−	0.912368i	−0.0878421	−	0.0406401i
$505$	−30.4210	−	6.69616i	−1.35372	−	0.297975i
$506$	2.08334	−	0.458579i	0.0926160	−	0.0203863i
$507$	−8.94919	+	4.14034i	−0.397448	+	0.183879i
$508$	1.55174	+	5.58886i	0.0688473	+	0.247966i
$509$	1.21377	−	22.3867i	0.0537996	−	0.992275i	−0.839655	−	0.543121i	$-0.817243\pi$
$509$	1.21377	−	22.3867i	0.0537996	−	0.992275i	0.893454	−	0.449154i	$-0.148275\pi$
$510$	3.72452	+	4.38484i	0.164925	+	0.194164i
$511$	−13.2112	+	33.1575i	−0.584427	+	1.46680i
$512$	−0.161782	−	0.986827i	−0.00714982	−	0.0436120i
$513$	1.00231	−	3.61000i	0.0442531	−	0.159385i
$514$	20.5733	+	6.93194i	0.907448	+	0.305755i
$515$	15.9712	+	23.5557i	0.703773	+	1.03799i
$516$	1.44129	+	2.71855i	0.0634491	+	0.119678i
$517$	5.01066	−	5.89901i	0.220369	−	0.259438i
$518$	0.556419	+	0.527068i	0.0244476	+	0.0231580i
$519$	15.1281	+	1.64528i	0.664050	+	0.0722197i
$520$	3.11453	−	4.59359i	0.136581	−	0.201442i
$521$	19.4756	−	14.8049i	0.853240	−	0.648616i	−0.0843207	−	0.996439i	$-0.526872\pi$
$521$	19.4756	−	14.8049i	0.853240	−	0.648616i	0.937560	+	0.347823i	$0.113079\pi$
$522$	5.74648	−	5.44335i	0.251516	−	0.238249i
$523$	0.679182	+	12.5268i	0.0296986	+	0.547758i	0.975088	+	0.221816i	$0.0711985\pi$
$523$	0.679182	+	12.5268i	0.0296986	+	0.547758i	−0.945390	+	0.325942i	$0.894319\pi$
$524$	−0.398296	+	0.134201i	−0.0173996	+	0.00586262i
$525$	−8.32228	−	6.32643i	−0.363214	−	0.276108i
$526$	24.3332	−	2.64640i	1.06098	−	0.115388i
$527$	5.05437	−	9.53355i	0.220172	−	0.415288i
$528$	−0.367399	−	0.922102i	−0.0159890	−	0.0401293i
$529$	15.7501	−	9.47654i	0.684788	−	0.412023i
$530$	−38.0567			−1.65308
$531$	5.16475	−	5.68554i	0.224131	−	0.246731i
$532$	−8.14082			−0.352949
$533$	−3.97595	+	2.39225i	−0.172217	+	0.103620i
$534$	1.31011	+	3.28813i	0.0566940	+	0.142291i
$535$	−11.6046	+	21.8886i	−0.501710	+	0.946325i
$536$	13.0081	−	1.41471i	0.561863	−	0.0611063i
$537$	−15.5873	−	11.8492i	−0.672643	−	0.511330i
$538$	13.2824	−	4.47535i	0.572644	−	0.192946i
$539$	−0.122448	−	2.25842i	−0.00527421	−	0.0972771i
$540$	2.27401	−	2.15406i	0.0978578	−	0.0926959i
$541$	16.2428	−	12.3475i	0.698333	−	0.530859i	−0.194693	−	0.980864i	$-0.562371\pi$
$541$	16.2428	−	12.3475i	0.698333	−	0.530859i	0.893026	+	0.450005i	$0.148578\pi$
$542$	2.50013	−	3.68742i	0.107390	−	0.158388i
$543$	−8.56905	−	0.931941i	−0.367733	−	0.0399934i
$544$	1.33347	+	1.26313i	0.0571719	+	0.0541561i
$545$	17.3930	−	20.4766i	0.745035	−	0.877123i
$546$	−1.80338	−	3.40153i	−0.0771775	−	0.145572i
$547$	4.46511	+	6.58554i	0.190914	+	0.281577i	0.911084	−	0.412220i	$-0.135247\pi$
$547$	4.46511	+	6.58554i	0.190914	+	0.281577i	−0.720170	+	0.693798i	$0.755936\pi$
$548$	−9.55868	−	3.22070i	−0.408327	−	0.137581i
$549$	−0.567640	+	2.04445i	−0.0242263	+	0.0872552i
$550$	−0.772587	−	4.71257i	−0.0329432	−	0.200945i
$551$	10.9765	−	27.5490i	0.467615	−	1.17363i
$552$	1.39131	+	1.63798i	0.0592182	+	0.0697170i
$553$	−0.760170	+	14.0205i	−0.0323257	+	0.596213i
$554$	1.83719	+	6.61697i	0.0780549	+	0.281128i
$555$	−1.00271	+	0.463901i	−0.0425625	+	0.0196915i
$556$	14.7337	−	3.24314i	0.624849	−	0.137540i
$557$	13.6158	+	2.99706i	0.576919	+	0.126989i	0.493839	−	0.869553i	$-0.335593\pi$
$557$	13.6158	+	2.99706i	0.576919	+	0.126989i	0.0830800	+	0.996543i	$0.473524\pi$
$558$	−5.33183	−	2.46677i	−0.225714	−	0.104427i
$559$	−0.882028	+	5.38013i	−0.0373058	+	0.227555i
$560$	−5.83180	−	3.50888i	−0.246438	−	0.148277i
$561$	1.56218	+	0.939932i	0.0659553	+	0.0396840i
$562$	2.17322	−	13.2560i	0.0916717	−	0.559172i
$563$	23.2574	+	10.7600i	0.980181	+	0.453480i	0.843497	−	0.537135i	$-0.180493\pi$
$563$	23.2574	+	10.7600i	0.980181	+	0.453480i	0.136684	+	0.990615i	$0.456355\pi$
$564$	7.61524	+	1.67624i	0.320659	+	0.0705825i
$565$	−34.6504	+	7.62712i	−1.45775	+	0.320875i
$566$	21.0789	−	9.75213i	0.886012	−	0.409913i
$567$	−0.581307	−	2.09368i	−0.0244126	−	0.0879262i
$568$	−0.338472	+	6.24275i	−0.0142020	+	0.261940i
$569$	−18.6178	−	21.9186i	−0.780498	−	0.918874i	0.217870	−	0.975978i	$-0.430089\pi$
$569$	−18.6178	−	21.9186i	−0.780498	−	0.918874i	−0.998368	+	0.0571041i	$0.981813\pi$
$570$	4.34365	−	10.9018i	0.181936	−	0.456624i
$571$	5.13905	+	31.3468i	0.215062	+	1.31182i	0.844828	+	0.535038i	$0.179703\pi$
$571$	5.13905	+	31.3468i	0.215062	+	1.31182i	−0.629766	+	0.776785i	$0.716849\pi$
$572$	0.470512	−	1.69463i	0.0196731	−	0.0708561i
$573$	−5.57540	−	1.87857i	−0.232916	−	0.0784784i
$574$	3.19336	+	4.70986i	0.133288	+	0.196586i
$575$	4.84316	+	9.13517i	0.201974	+	0.380963i
$576$	0.647386	−	0.762162i	0.0269744	−	0.0317568i
$577$	−29.9075	−	28.3299i	−1.24506	−	1.17939i	−0.976357	−	0.216166i	$-0.930645\pi$
$577$	−29.9075	−	28.3299i	−1.24506	−	1.17939i	−0.268708	−	0.963222i	$-0.586597\pi$
$578$	13.5465	+	1.47327i	0.563460	+	0.0612800i
$579$	−5.66145	+	8.35001i	−0.235282	+	0.347015i
$580$	19.7374	−	15.0040i	0.819551	−	0.623007i
$581$	−24.9576	+	23.6411i	−1.03542	+	0.980798i
$582$	0.423972	+	7.81969i	0.0175742	+	0.324137i
$583$	−11.4287	+	3.85077i	−0.473328	+	0.159483i
$584$	−13.0769	−	9.94081i	−0.541127	−	0.411354i
$585$	5.51737	−	0.600050i	0.228115	−	0.0248090i
$586$	−8.71397	+	16.4363i	−0.359971	+	0.678977i
$587$	−3.91079	−	9.81534i	−0.161416	−	0.405122i	0.825916	−	0.563793i	$-0.190658\pi$
$587$	−3.91079	−	9.81534i	−0.161416	−	0.405122i	−0.987332	+	0.158671i	$0.949279\pi$
$588$	1.95243	−	1.17474i	0.0805170	−	0.0484455i
$589$	−22.0103			−0.906920
$590$	18.0080	−	15.9551i	0.741377	−	0.656862i
$591$	−13.5618			−0.557858
$592$	−0.302232	+	0.181847i	−0.0124217	+	0.00747387i
$593$	5.40962	+	13.5771i	0.222147	+	0.557546i	0.997235	−	0.0743063i	$-0.0236743\pi$
$593$	5.40962	+	13.5771i	0.222147	+	0.557546i	−0.775089	+	0.631852i	$0.782295\pi$
$594$	0.464942	−	0.876974i	0.0190768	−	0.0359827i
$595$	12.4276	−	1.35159i	0.509484	−	0.0554097i
$596$	6.24849	+	4.74998i	0.255948	+	0.194567i
$597$	4.01270	−	1.35204i	0.164229	−	0.0553351i
$598$	0.206157	+	3.80234i	0.00843037	+	0.155489i
$599$	−28.2395	+	26.7498i	−1.15383	+	1.09297i	−0.159442	+	0.987207i	$0.550969\pi$
$599$	−28.2395	+	26.7498i	−1.15383	+	1.09297i	−0.994392	+	0.105762i	$0.966272\pi$
$600$	3.83007	−	2.91154i	0.156362	−	0.118863i
$601$	6.28467	−	9.26920i	0.256357	−	0.378098i	−0.677631	−	0.735402i	$-0.736993\pi$
$601$	6.28467	−	9.26920i	0.256357	−	0.378098i	0.933988	+	0.357303i	$0.116304\pi$
$602$	6.64672	+	0.722875i	0.270900	+	0.0294622i
$603$	9.49949	+	8.99839i	0.386849	+	0.366443i
$604$	4.13393	−	4.86684i	0.168207	−	0.198029i
$605$	14.6934	+	27.7147i	0.597373	+	1.12676i
$606$	−5.58080	−	8.23106i	−0.226704	−	0.334364i
$607$	1.53034	+	0.515632i	0.0621146	+	0.0209288i	0.350187	−	0.936680i	$-0.386118\pi$
$607$	1.53034	+	0.515632i	0.0621146	+	0.0209288i	−0.288073	+	0.957609i	$0.593014\pi$
$608$	1.00231	−	3.61000i	0.0406491	−	0.146405i
$609$	−2.78249	−	16.9724i	−0.112752	−	0.687757i
$610$	−2.45994	+	6.17400i	−0.0996003	+	0.249978i
$611$	8.94433	+	10.5301i	0.361849	+	0.426002i
$612$	−0.0994392	+	1.83405i	−0.00401959	+	0.0741370i
$613$	−7.01515	−	25.2663i	−0.283339	−	1.02050i	−0.959028	−	0.283310i	$-0.908568\pi$
$613$	−7.01515	−	25.2663i	−0.283339	−	1.02050i	0.675689	−	0.737187i	$-0.263846\pi$
$614$	−24.2143	+	11.2027i	−0.977211	+	0.452106i
$615$	−8.01105	+	1.76337i	−0.323037	+	0.0711058i
$616$	−2.10637	−	0.463648i	−0.0848682	−	0.0186809i
$617$	−26.5069	−	12.2634i	−1.06713	−	0.493706i	−0.193902	−	0.981021i	$-0.562114\pi$
$617$	−26.5069	−	12.2634i	−1.06713	−	0.493706i	−0.873226	+	0.487315i	$0.837976\pi$
$618$	−1.46994	+	8.96625i	−0.0591298	+	0.360676i
$619$	39.6883	+	23.8797i	1.59521	+	0.959804i	0.985991	+	0.166801i	$0.0533437\pi$
$619$	39.6883	+	23.8797i	1.59521	+	0.959804i	0.609217	+	0.793004i	$0.291484\pi$
$620$	−15.7674	−	9.48694i	−0.633235	−	0.381005i
$621$	−0.347689	+	2.12081i	−0.0139523	+	0.0851052i
$622$	9.45486	+	4.37429i	0.379105	+	0.175393i
$623$	7.51113	+	1.65332i	0.300927	+	0.0662390i
$624$	1.73042	−	0.380895i	0.0692724	−	0.0152480i
$625$	−23.5143	+	10.8789i	−0.940571	+	0.435154i
$626$	−5.98583	−	21.5590i	−0.239242	−	0.861672i
$627$	0.201334	−	3.71338i	0.00804049	−	0.148298i
$628$	4.44664	+	5.23499i	0.177440	+	0.208899i
$629$	0.239797	−	0.601846i	0.00956135	−	0.0239972i
$630$	−1.10109	−	6.71637i	−0.0438686	−	0.267587i
$631$	−5.02608	+	18.1023i	−0.200085	+	0.720642i	0.793600	+	0.608440i	$0.208204\pi$
$631$	−5.02608	+	18.1023i	−0.200085	+	0.720642i	−0.993685	+	0.112202i	$0.964210\pi$
$632$	−6.12372	−	2.06332i	−0.243588	−	0.0820745i
$633$	−7.37843	−	10.8824i	−0.293266	−	0.432535i
$634$	−12.3091	−	23.2174i	−0.488857	−	0.922082i
$635$	−11.7617	+	13.8470i	−0.466750	+	0.549501i
$636$	−8.82078	−	8.35548i	−0.349767	−	0.331316i
$637$	4.01367	+	0.436513i	0.159027	+	0.0172953i
$638$	4.40910	−	6.50293i	0.174558	−	0.257453i
$639$	−4.97711	+	3.78350i	−0.196891	+	0.149673i
$640$	2.27401	−	2.15406i	0.0898882	−	0.0851466i
$641$	2.63866	+	48.6672i	0.104221	+	1.92224i	0.322881	+	0.946440i	$0.395349\pi$
$641$	2.63866	+	48.6672i	0.104221	+	1.92224i	−0.218660	+	0.975801i	$0.570169\pi$
$642$	−7.49542	+	2.52550i	−0.295820	+	0.0996735i
$643$	0.233696	+	0.177651i	0.00921607	+	0.00700587i	0.609772	−	0.792577i	$-0.291261\pi$
$643$	0.233696	+	0.177651i	0.00921607	+	0.00700587i	−0.600556	+	0.799583i	$0.705054\pi$
$644$	4.64241	−	0.504892i	0.182936	−	0.0198955i
$645$	−4.51449	+	8.51523i	−0.177758	+	0.335287i
$646$	2.54709	+	6.39272i	0.100214	+	0.251518i
$647$	31.0054	−	18.6553i	1.21895	−	0.733417i	0.247092	−	0.968992i	$-0.420525\pi$
$647$	31.0054	−	18.6553i	1.21895	−	0.733417i	0.971856	+	0.235575i	$0.0756975\pi$
$648$	1.00000			0.0392837
$649$	3.79350	−	6.61357i	0.148908	−	0.259605i
$650$	8.52452			0.334359
$651$	−10.9380	+	6.58117i	−0.428694	+	0.257936i
$652$	5.43776	+	13.6478i	0.212959	+	0.534487i
$653$	−7.27745	+	13.7267i	−0.284789	+	0.537168i	−0.984093	−	0.177656i	$-0.943149\pi$
$653$	−7.27745	+	13.7267i	−0.284789	+	0.537168i	0.699304	+	0.714824i	$0.253493\pi$
$654$	8.52706	−	0.927374i	0.333435	−	0.0362632i
$655$	−1.04804	−	0.796700i	−0.0409504	−	0.0311297i
$656$	−2.48173	+	0.836192i	−0.0968953	+	0.0326478i
$657$	−0.889305	−	16.4023i	−0.0346951	−	0.639914i
$658$	12.3006	−	11.6518i	0.479528	−	0.454233i
$659$	−15.8602	+	12.0566i	−0.617827	+	0.469660i	−0.866669	−	0.498884i	$-0.833743\pi$
$659$	−15.8602	+	12.0566i	−0.617827	+	0.469660i	0.248841	+	0.968544i	$0.419950\pi$
$660$	1.74478	−	2.57336i	0.0679154	−	0.100168i
$661$	41.2816	+	4.48964i	1.60567	+	0.174627i	0.866600	−	0.499004i	$-0.166301\pi$
$661$	41.2816	+	4.48964i	1.60567	+	0.174627i	0.739068	+	0.673631i	$0.235266\pi$
$662$	−0.144648	−	0.137017i	−0.00562189	−	0.00532533i
$663$	−2.10687	+	2.48040i	−0.0818242	+	0.0963309i
$664$	−7.41068	−	13.9780i	−0.287590	−	0.542453i
$665$	−14.3098	−	21.1054i	−0.554911	−	0.818433i
$666$	−0.334258	−	0.112625i	−0.0129522	−	0.00436412i
$667$	−4.55091	+	16.3909i	−0.176212	+	0.634659i
$668$	2.23618	+	13.6401i	0.0865203	+	0.527751i
$669$	−8.62273	+	21.6414i	−0.333374	+	0.836705i
$670$	26.5331	+	31.2372i	1.02506	+	1.20680i
$671$	−0.114021	+	2.10300i	−0.00440175	+	0.0811855i
$672$	−0.581307	−	2.09368i	−0.0224244	−	0.0807653i
$673$	8.31465	−	3.84677i	0.320506	−	0.148282i	−0.253039	−	0.967456i	$-0.581430\pi$
$673$	8.31465	−	3.84677i	0.320506	−	0.148282i	0.573545	+	0.819174i	$0.305568\pi$
$674$	−26.3329	+	5.79630i	−1.01430	+	0.223265i
$675$	4.69860	+	1.03424i	0.180849	+	0.0398080i
$676$	−8.94919	−	4.14034i	−0.344200	−	0.159244i
$677$	2.21331	−	13.5006i	0.0850645	−	0.518870i	−0.909581	−	0.415526i	$-0.863597\pi$
$677$	2.21331	−	13.5006i	0.0850645	−	0.518870i	0.994646	−	0.103344i	$-0.0329543\pi$
$678$	−9.70581	−	5.83979i	−0.372749	−	0.224276i
$679$	14.5805	+	8.77277i	0.559546	+	0.336668i
$680$	−0.930758	+	5.67738i	−0.0356930	+	0.217717i
$681$	−8.08121	−	3.73877i	−0.309673	−	0.143270i
$682$	−5.69500	−	1.25356i	−0.218073	−	0.0480015i
$683$	29.6954	−	6.53645i	1.13626	−	0.250110i	0.393278	−	0.919419i	$-0.371341\pi$
$683$	29.6954	−	6.53645i	1.13626	−	0.250110i	0.742984	+	0.669309i	$0.233410\pi$
$684$	3.40029	−	1.57314i	0.130013	−	0.0601505i
$685$	−8.45234	−	30.4426i	−0.322947	−	1.16315i
$686$	1.09151	−	20.1317i	0.0416740	−	0.768632i
$687$	−12.7153	−	14.9696i	−0.485118	−	0.571125i
$688$	−1.13891	+	2.85845i	−0.0434205	+	0.108977i
$689$	−3.48281	−	21.2442i	−0.132685	−	0.809340i
$690$	−1.80090	+	6.48625i	−0.0685591	+	0.246927i
$691$	−9.37483	−	3.15875i	−0.356635	−	0.120164i	0.135280	−	0.990807i	$-0.456807\pi$
$691$	−9.37483	−	3.15875i	−0.356635	−	0.120164i	−0.491915	+	0.870643i	$0.663703\pi$
$692$	8.53975	+	12.5952i	0.324633	+	0.478797i
$693$	−1.01026	−	1.90556i	−0.0383767	−	0.0723861i
$694$	−21.7777	+	25.6387i	−0.826669	+	0.973230i
$695$	34.3067	+	32.4971i	1.30133	+	1.23268i
$696$	7.86891	+	0.855795i	0.298270	+	0.0324388i
$697$	2.69936	−	3.98126i	0.102246	−	0.150801i
$698$	12.1535	−	9.23889i	0.460019	−	0.349697i
$699$	15.3379	−	14.5288i	0.580131	−	0.549529i
$700$	−0.565963	−	10.4386i	−0.0213914	−	0.394541i
$701$	25.6249	−	8.63405i	0.967840	−	0.326103i	0.209389	−	0.977833i	$-0.432853\pi$
$701$	25.6249	−	8.63405i	0.967840	−	0.326103i	0.758452	+	0.651729i	$0.225956\pi$
$702$	1.41056	+	1.07228i	0.0532380	+	0.0404705i
$703$	−1.31375	+	0.142879i	−0.0495489	+	0.00538877i
$704$	0.464942	−	0.876974i	0.0175232	−	0.0330522i
$705$	9.04024	+	22.6893i	0.340475	+	0.854528i
$706$	22.9280	−	13.7953i	0.862906	−	0.519193i
$707$	−21.6085			−0.812670
$708$	7.67689	+	0.255641i	0.288515	+	0.00960756i
$709$	−40.5059			−1.52123			−0.760616	−	0.649202i	$-0.775103\pi$
$709$	−40.5059			−1.52123			−0.760616	+	0.649202i	$0.775103\pi$
$710$	−16.7795	+	10.0959i	−0.629725	+	0.378893i
$711$	−2.39183	−	6.00303i	−0.0897005	−	0.225131i
$712$	−1.65794	+	3.12720i	−0.0621339	+	0.117197i
$713$	12.5517	−	1.36508i	0.470064	−	0.0511225i
$714$	3.17722	+	2.41526i	0.118905	+	0.0903889i
$715$	5.22046	−	1.75898i	0.195234	−	0.0657821i
$716$	−1.06003	−	19.5511i	−0.0396151	−	0.730658i
$717$	12.8097	−	12.1340i	0.478387	−	0.453152i
$718$	2.58037	−	1.96154i	0.0962984	−	0.0732041i
$719$	−16.6529	+	24.5611i	−0.621047	+	0.915976i	−0.999955	−	0.00945834i	$-0.996989\pi$
$719$	−16.6529	+	24.5611i	−0.621047	+	0.915976i	0.378908	+	0.925434i	$0.376300\pi$
$720$	3.11390	+	0.338657i	0.116048	+	0.0126210i
$721$	14.3331	+	13.5770i	0.533792	+	0.505634i
$722$	−3.21316	+	3.78282i	−0.119581	+	0.140782i
$723$	5.73033	+	10.8085i	0.213113	+	0.401974i
$724$	−4.83720	−	7.13433i	−0.179773	−	0.265145i
$725$	36.0878	+	12.1594i	1.34027	+	0.451588i
$726$	−2.67923	+	9.64971i	−0.0994355	+	0.358134i
$727$	−5.85488	−	35.7132i	−0.217146	−	1.32453i	−0.840168	−	0.542326i	$-0.817544\pi$
$727$	−5.85488	−	35.7132i	−0.217146	−	1.32453i	0.623023	−	0.782204i	$-0.285904\pi$
$728$	1.42504	−	3.57657i	0.0528154	−	0.132557i
$729$	0.647386	+	0.762162i	0.0239773	+	0.0282282i
$730$	2.78554	−	51.3763i	0.103097	−	1.90152i
$731$	−1.51197	−	5.44563i	−0.0559223	−	0.201414i
$732$	−1.92569	+	0.890918i	−0.0711754	+	0.0329293i
$733$	−34.6270	+	7.62198i	−1.27898	+	0.281524i	−0.801964	−	0.597372i	$-0.796212\pi$
$733$	−34.6270	+	7.62198i	−1.27898	+	0.281524i	−0.477013	+	0.878896i	$0.658281\pi$
$734$	10.7616	+	2.36881i	0.397219	+	0.0874345i
$735$	6.47753	+	2.99682i	0.238927	+	0.110539i
$736$	−0.347689	+	2.12081i	−0.0128160	+	0.0781741i
$737$	11.1288	+	6.69599i	0.409935	+	0.246650i
$738$	−2.24395	−	1.35014i	−0.0826010	−	0.0496994i
$739$	−1.74423	+	10.6393i	−0.0641626	+	0.391375i	0.935148	+	0.354257i	$0.115266\pi$
$739$	−1.74423	+	10.6393i	−0.0641626	+	0.391375i	−0.999311	+	0.0371180i	$0.988182\pi$
$740$	−1.00271	−	0.463901i	−0.0368602	−	0.0170533i
$741$	6.48314	+	1.42705i	0.238164	+	0.0524239i
$742$	−25.7830	+	5.67528i	−0.946525	+	0.208346i
$743$	−16.5546	+	7.65897i	−0.607329	+	0.280980i	−0.699353	−	0.714776i	$-0.746528\pi$
$743$	−16.5546	+	7.65897i	−0.607329	+	0.280980i	0.0920238	+	0.995757i	$0.470666\pi$
$744$	−1.57168	−	5.66067i	−0.0576205	−	0.207530i
$745$	−1.33100	+	24.5489i	−0.0487642	+	0.899403i
$746$	13.9779	+	16.4560i	0.511767	+	0.602498i
$747$	5.85595	−	14.6973i	0.214258	−	0.537747i
$748$	0.294953	+	1.79913i	0.0107845	+	0.0657828i
$749$	−4.59782	+	16.5598i	−0.168001	+	0.605083i
$750$	−0.560758	−	0.188941i	−0.0204760	−	0.00689917i
$751$	−17.6366	−	26.0120i	−0.643569	−	0.949193i	−0.999890	−	0.0148293i	$-0.995280\pi$
$751$	−17.6366	−	26.0120i	−0.643569	−	0.949193i	0.356321	−	0.934363i	$-0.384031\pi$
$752$	3.65243	+	6.88922i	0.133191	+	0.251224i
$753$	−10.2543	+	12.0723i	−0.373688	+	0.439940i
$754$	10.1819	+	9.64480i	0.370803	+	0.351243i
$755$	19.8841	+	2.16252i	0.723655	+	0.0787023i
$756$	1.21939	−	1.79847i	0.0443488	−	0.0654096i
$757$	23.8915	−	18.1619i	0.868352	−	0.660104i	−0.0730733	−	0.997327i	$-0.523281\pi$
$757$	23.8915	−	18.1619i	0.868352	−	0.660104i	0.941425	+	0.337223i	$0.109488\pi$
$758$	−27.0176	+	25.5925i	−0.981325	+	0.929560i
$759$	0.115490	+	2.13009i	0.00419203	+	0.0773174i
$760$	11.1209	−	3.74708i	0.403398	−	0.135921i
$761$	−14.2998	−	10.8704i	−0.518367	−	0.394052i	0.313020	−	0.949747i	$-0.398659\pi$
$761$	−14.2998	−	10.8704i	−0.518367	−	0.394052i	−0.831387	+	0.555694i	$0.812453\pi$
$762$	−5.76628	+	0.627121i	−0.208890	+	0.0227182i
$763$	8.72997	−	16.4665i	0.316046	−	0.596126i
$764$	−2.17766	−	5.46552i	−0.0787850	−	0.197736i
$765$	−4.92964	+	2.96607i	−0.178232	+	0.107238i
$766$	−16.8176			−0.607644
$767$	10.5546	+	8.59235i	0.381104	+	0.310252i
$768$	1.00000			0.0360844
$769$	−29.7175	+	17.8804i	−1.07164	+	0.644784i	−0.938137	−	0.346265i	$-0.887450\pi$
$769$	−29.7175	+	17.8804i	−1.07164	+	0.644784i	−0.133502	+	0.991048i	$0.542622\pi$
$770$	−2.50053	−	6.27586i	−0.0901128	−	0.226166i
$771$	−10.1690	+	19.1808i	−0.366228	+	0.690779i
$772$	−10.0292	+	1.09074i	−0.360959	+	0.0392566i
$773$	−3.70186	−	2.81408i	−0.133147	−	0.101215i	0.536481	−	0.843912i	$-0.319753\pi$
$773$	−3.70186	−	2.81408i	−0.133147	−	0.101215i	−0.669628	+	0.742697i	$0.733546\pi$
$774$	−2.91591	+	0.982486i	−0.104810	+	0.0353147i
$775$	−1.53019	−	28.2227i	−0.0549662	−	1.01379i
$776$	−5.68540	+	5.38550i	−0.204094	+	0.193328i
$777$	−0.610143	+	0.463819i	−0.0218888	+	0.0166394i
$778$	−11.3967	+	16.8089i	−0.408593	+	0.602629i
$779$	−9.75404	−	1.06082i	−0.349475	−	0.0380077i
$780$	4.02920	+	3.81666i	0.144269	+	0.136659i
$781$	−4.01745	+	4.72971i	−0.143756	+	0.169242i
$782$	−1.84899	−	3.48756i	−0.0661197	−	0.124715i
$783$	4.44197	+	6.55141i	0.158743	+	0.234128i
$784$	2.15932	+	0.727560i	0.0771186	+	0.0259843i
$785$	−5.75568	+	20.7301i	−0.205429	+	0.739889i
$786$	−0.0679964	−	0.414760i	−0.00242535	−	0.0147940i
$787$	10.7708	−	27.0327i	0.383938	−	0.963613i	−0.602298	−	0.798271i	$-0.705748\pi$
$787$	10.7708	−	27.0327i	0.383938	−	0.963613i	0.986236	−	0.165342i	$-0.0528726\pi$
$788$	−8.77973	−	10.3363i	−0.312765	−	0.368215i
$789$	−1.32514	+	24.4408i	−0.0471763	+	0.870115i
$790$	−5.41495	−	19.5029i	−0.192655	−	0.693881i
$791$	−22.3379	+	10.3346i	−0.794243	+	0.367456i
$792$	0.969393	−	0.213380i	0.0344459	−	0.00758211i
$793$	−3.67160	−	0.808181i	−0.130382	−	0.0286993i
$794$	−4.45346	−	2.06039i	−0.158047	−	0.0731204i
$795$	6.15689	−	37.5554i	0.218362	−	1.33195i
$796$	3.62824	+	2.18304i	0.128599	+	0.0773757i
$797$	−21.3270	−	12.8320i	−0.755440	−	0.454533i	0.0850389	−	0.996378i	$-0.472899\pi$
$797$	−21.3270	−	12.8320i	−0.755440	−	0.454533i	−0.840479	+	0.541845i	$0.817726\pi$
$798$	1.31704	−	8.03358i	0.0466227	−	0.284386i
$799$	−12.9984	−	6.01368i	−0.459849	−	0.212749i
$800$	4.69860	+	1.03424i	0.166121	+	0.0365659i
$801$	−3.45676	+	0.760891i	−0.122139	+	0.0268848i
$802$	−19.3478	+	8.95126i	−0.683196	+	0.316080i
$803$	−4.36200	−	15.7105i	−0.153932	−	0.554411i
$804$	−0.708395	+	13.0656i	−0.0249832	+	0.460788i
$805$	9.46932	+	11.1481i	0.333750	+	0.392920i
$806$	3.85287	−	9.66998i	0.135712	−	0.340610i
$807$	2.26755	+	13.8314i	0.0798215	+	0.486890i
$808$	2.66047	−	9.58215i	0.0935950	−	0.337099i
$809$	−44.1485	−	14.8754i	−1.55218	−	0.522990i	−0.592858	−	0.805307i	$-0.702000\pi$
$809$	−44.1485	−	14.8754i	−1.55218	−	0.522990i	−0.959321	+	0.282317i	$0.908897\pi$
$810$	1.75779	+	2.59254i	0.0617623	+	0.0910926i
$811$	−1.82101	−	3.43479i	−0.0639444	−	0.120612i	0.849479	−	0.527622i	$-0.176916\pi$
$811$	−1.82101	−	3.43479i	−0.0639444	−	0.120612i	−0.913424	+	0.407010i	$0.866571\pi$
$812$	11.1344	−	13.1084i	0.390741	−	0.460015i
$813$	3.23437	+	3.06376i	0.113434	+	0.107451i
$814$	−0.348059	−	0.0378537i	−0.0121995	−	0.00132677i
$815$	−25.8239	+	38.0875i	−0.904573	+	1.33415i
$816$	−1.46222	+	1.11155i	−0.0511879	+	0.0389120i
$817$	−8.36936	+	7.92788i	−0.292807	+	0.277361i
$818$	1.61107	+	29.7145i	0.0563298	+	1.03894i
$819$	3.64848	−	1.22932i	0.127488	−	0.0429557i
$820$	−6.53022	−	4.96414i	−0.228045	−	0.173355i
$821$	−12.0710	+	1.31280i	−0.421280	+	0.0458170i	−0.316304	−	0.948658i	$-0.602442\pi$
$821$	−12.0710	+	1.31280i	−0.421280	+	0.0458170i	−0.104976	+	0.994475i	$0.533477\pi$
$822$	4.72469	−	8.91171i	0.164793	−	0.310832i
$823$	−12.6888	−	31.8465i	−0.442304	−	1.11010i	−0.966080	−	0.258243i	$-0.916856\pi$
$823$	−12.6888	−	31.8465i	−0.442304	−	1.11010i	0.523776	−	0.851856i	$-0.324523\pi$
$824$	−7.78536	+	4.68429i	−0.271216	+	0.163185i
$825$	4.77548			0.166261
$826$	9.82089	−	13.4949i	0.341713	−	0.469548i
$827$	−45.4289			−1.57972			−0.789859	−	0.613288i	$-0.789846\pi$
$827$	−45.4289			−1.57972			−0.789859	+	0.613288i	$0.789846\pi$
$828$	−1.84149	+	1.10799i	−0.0639962	+	0.0385053i
$829$	−13.0936	−	32.8626i	−0.454761	−	1.14136i	−0.960402	−	0.278619i	$-0.910123\pi$
$829$	−13.0936	−	32.8626i	−0.454761	−	1.14136i	0.505641	−	0.862744i	$-0.331256\pi$
$830$	23.2122	−	43.7829i	0.805708	−	1.51973i
$831$	−6.82703	+	0.742484i	−0.236827	+	0.0257565i
$832$	1.41056	+	1.07228i	0.0489023	+	0.0371745i
$833$	−3.96612	+	1.33634i	−0.137418	+	0.0463015i
$834$	0.816764	+	15.0643i	0.0282822	+	0.521635i
$835$	−31.4318	+	29.7737i	−1.08774	+	1.03036i
$836$	2.96054	−	2.25054i	0.102392	−	0.0778367i
$837$	3.29687	−	4.86251i	0.113956	−	0.168073i
$838$	−9.56090	−	1.03981i	−0.330276	−	0.0359197i
$839$	−15.3605	−	14.5503i	−0.530305	−	0.502331i	0.375040	−	0.927009i	$-0.377629\pi$
$839$	−15.3605	−	14.5503i	−0.530305	−	0.502331i	−0.905345	+	0.424677i	$0.860388\pi$
$840$	4.40613	−	5.18730i	0.152026	−	0.178979i
$841$	15.7629	+	29.7320i	0.543549	+	1.02524i
$842$	20.7836	+	30.6535i	0.716249	+	1.05639i
$843$	12.7298	+	4.28918i	0.438439	+	0.147727i
$844$	3.51743	−	12.6686i	0.121075	−	0.436073i
$845$	−4.99678	−	30.4790i	−0.171894	−	1.04851i
$846$	−2.88617	+	7.24373i	−0.0992285	+	0.249045i
$847$	14.0877	+	16.5853i	0.484058	+	0.569877i
$848$	0.657783	−	12.1321i	0.0225883	−	0.416618i
$849$	6.21348	+	22.3789i	0.213246	+	0.768043i
$850$	−8.01999	+	3.71044i	−0.275083	+	0.127267i
$851$	0.740320	−	0.162957i	0.0253778	−	0.00558608i
$852$	−6.10575	−	1.34398i	−0.209179	−	0.0460439i
$853$	−28.6177	−	13.2400i	−0.979851	−	0.453327i	−0.136471	−	0.990644i	$-0.543576\pi$
$853$	−28.6177	−	13.2400i	−0.979851	−	0.453327i	−0.843381	+	0.537317i	$0.819438\pi$
$854$	−0.745879	+	4.54966i	−0.0255235	+	0.155686i
$855$	10.0554	+	6.05014i	0.343888	+	0.206910i
$856$	−6.77727	−	4.07775i	−0.231642	−	0.139375i
$857$	−3.69149	+	22.5171i	−0.126099	+	0.769170i	0.845753	+	0.533575i	$0.179152\pi$
$857$	−3.69149	+	22.5171i	−0.126099	+	0.769170i	−0.971852	+	0.235594i	$0.924296\pi$
$858$	1.59619	+	0.738475i	0.0544929	+	0.0252111i
$859$	43.6316	+	9.60403i	1.48869	+	0.327685i	0.883513	−	0.468406i	$-0.155171\pi$
$859$	43.6316	+	9.60403i	1.48869	+	0.327685i	0.605177	+	0.796091i	$0.293103\pi$
$860$	−9.41260	+	2.07187i	−0.320967	+	0.0706502i
$861$	−5.16444	+	2.38932i	−0.176004	+	0.0814280i
$862$	−5.78545	−	20.8373i	−0.197053	−	0.709722i
$863$	0.550980	−	10.1622i	0.0187556	−	0.345926i	−0.974061	−	0.226284i	$-0.927342\pi$
$863$	0.550980	−	10.1622i	0.0187556	−	0.345926i	0.992817	−	0.119643i	$-0.0381749\pi$
$864$	0.647386	+	0.762162i	0.0220245	+	0.0259293i
$865$	−17.6425	+	44.2793i	−0.599863	+	1.50554i
$866$	2.74266	+	16.7295i	0.0931995	+	0.568492i
$867$	−3.64544	+	13.1297i	−0.123806	+	0.445908i
$868$	−12.0970	−	4.07596i	−0.410600	−	0.138347i
$869$	−3.59955	−	5.30893i	−0.122106	−	0.180093i
$870$	11.6132	+	21.9048i	0.393723	+	0.742641i
$871$	−15.0092	+	17.6702i	−0.508566	+	0.598730i
$872$	6.22711	+	5.89863i	0.210877	+	0.199753i
$873$	−7.78527	−	0.846699i	−0.263492	−	0.0286564i
$874$	−4.51858	+	6.66440i	−0.152843	+	0.225427i
$875$	−1.02359	+	0.778112i	−0.0346036	+	0.0263050i
$876$	11.9255	−	11.2964i	0.402924	−	0.381670i
$877$	2.18628	+	40.3236i	0.0738255	+	1.36163i	0.767364	+	0.641212i	$0.221568\pi$
$877$	2.18628	+	40.3236i	0.0738255	+	1.36163i	−0.693538	+	0.720420i	$0.743949\pi$
$878$	31.9378	−	10.7611i	1.07785	−	0.363169i
$879$	−14.8100	−	11.2583i	−0.499529	−	0.379732i
$880$	3.09086	−	0.336151i	0.104193	−	0.0113317i
$881$	7.51952	−	14.1833i	0.253339	−	0.477848i	−0.723924	−	0.689880i	$-0.757663\pi$
$881$	7.51952	−	14.1833i	0.253339	−	0.477848i	0.977263	+	0.212032i	$0.0680081\pi$
$882$	0.843397	+	2.11677i	0.0283986	+	0.0712752i
$883$	−21.4008	+	12.8764i	−0.720194	+	0.433326i	−0.827914	−	0.560855i	$-0.810472\pi$
$883$	−21.4008	+	12.8764i	−0.720194	+	0.433326i	0.107720	+	0.994181i	$0.465645\pi$
$884$	−3.25443			−0.109458
$885$	12.8316	+	20.3520i	0.431329	+	0.684126i
$886$	−11.0899			−0.372572
$887$	−49.5172	+	29.7935i	−1.66262	+	1.00037i	−0.706366	+	0.707847i	$0.749666\pi$
$887$	−49.5172	+	29.7935i	−1.66262	+	1.00037i	−0.956259	+	0.292521i	$0.905506\pi$
$888$	−0.130556	−	0.327670i	−0.00438117	−	0.0109959i
$889$	−5.90350	+	11.1352i	−0.197997	+	0.373462i
$890$	−11.0217	+	1.19868i	−0.369448	+	0.0401799i
$891$	0.790202	+	0.600696i	0.0264728	+	0.0201241i
$892$	−22.0765	+	7.43844i	−0.739176	+	0.249057i
$893$	1.58161	+	29.1711i	0.0529266	+	0.976174i
$894$	−5.69830	+	5.39771i	−0.190580	+	0.180527i
$895$	48.8237	−	37.1148i	1.63200	−	1.24061i
$896$	1.21939	−	1.79847i	0.0407370	−	0.0600826i
$897$	−3.78560	−	0.411709i	−0.126397	−	0.0137466i
$898$	24.3202	+	23.0373i	0.811575	+	0.768765i
$899$	30.1041	−	35.4412i	1.00403	−	1.18203i
$900$	2.25355	+	4.25065i	0.0751184	+	0.141688i
$901$	12.5236	+	18.4709i	0.417221	+	0.615355i
$902$	−2.46336	−	0.830004i	−0.0820211	−	0.0276361i
$903$	−1.78867	+	6.44221i	−0.0595233	+	0.214383i
$904$	−1.83254	−	11.1780i	−0.0609494	−	0.371775i
$905$	9.99329	−	25.0813i	0.332188	−	0.833730i
$906$	4.13393	+	4.86684i	0.137341	+	0.161690i
$907$	1.32716	−	24.4781i	0.0440678	−	0.812782i	−0.890060	−	0.455843i	$-0.849338\pi$
$907$	1.32716	−	24.4781i	0.0440678	−	0.812782i	0.934128	−	0.356939i	$-0.116179\pi$
$908$	−2.38212	−	8.57962i	−0.0790534	−	0.284725i
$909$	9.02550	−	4.17564i	0.299357	−	0.138497i
$910$	11.7773	−	2.59238i	0.390414	−	0.0859367i
$911$	−19.8574	−	4.37095i	−0.657906	−	0.144816i	−0.126544	−	0.991961i	$-0.540388\pi$
$911$	−19.8574	−	4.37095i	−0.657906	−	0.144816i	−0.531362	+	0.847145i	$0.678319\pi$
$912$	3.40029	+	1.57314i	0.112595	+	0.0520919i
$913$	2.54061	−	15.4970i	0.0840819	−	0.512877i
$914$	−14.1002	−	8.48378i	−0.466392	−	0.280618i
$915$	−5.69469	−	3.42638i	−0.188261	−	0.113273i
$916$	3.17755	−	19.3822i	0.104989	−	0.640406i
$917$	−0.828847	−	0.383465i	−0.0273709	−	0.0126631i
$918$	−1.79380	−	0.394845i	−0.0592042	−	0.0130318i
$919$	25.1669	−	5.53966i	0.830180	−	0.182736i	0.220503	−	0.975386i	$-0.429230\pi$
$919$	25.1669	−	5.53966i	0.830180	−	0.182736i	0.609677	+	0.792650i	$0.291299\pi$
$920$	−6.10945	+	2.82653i	−0.201423	+	0.0931881i
$921$	−7.13772	−	25.7077i	−0.235196	−	0.847099i
$922$	−0.364414	+	6.72121i	−0.0120013	+	0.221351i
$923$	−7.17139	−	8.44281i	−0.236049	−	0.277899i
$924$	0.798313	−	2.00362i	0.0262626	−	0.0659141i
$925$	−0.274540	−	1.67462i	−0.00902682	−	0.0550611i
$926$	−8.09701	+	29.1628i	−0.266084	+	0.958349i
$927$	−8.61033	−	2.90116i	−0.282800	−	0.0952865i
$928$	4.44197	+	6.55141i	0.145815	+	0.215061i
$929$	−1.57868	−	2.97770i	−0.0517947	−	0.0976951i	0.856263	−	0.516540i	$-0.172780\pi$
$929$	−1.57868	−	2.97770i	−0.0517947	−	0.0976951i	−0.908058	+	0.418844i	$0.862435\pi$
$930$	11.9129	−	14.0249i	0.390638	−	0.459894i
$931$	6.19776	+	5.87083i	0.203123	+	0.192409i
$932$	21.0028	+	2.28419i	0.687970	+	0.0748212i
$933$	−5.84629	+	8.62263i	−0.191399	+	0.282292i
$934$	−14.9235	+	11.3446i	−0.488312	+	0.371205i
$935$	−4.14586	+	3.92717i	−0.135584	+	0.128432i
$936$	0.0959260	+	1.76925i	0.00313544	+	0.0578298i
$937$	33.3020	−	11.2208i	1.08793	−	0.366566i	0.282506	−	0.959266i	$-0.408834\pi$
$937$	33.3020	−	11.2208i	1.08793	−	0.366566i	0.805424	+	0.592700i	$0.201938\pi$
$938$	22.6342	+	17.2061i	0.739034	+	0.561799i
$939$	22.2434	−	2.41912i	0.725887	−	0.0789449i
$940$	−11.4404	+	21.5789i	−0.373144	+	0.703825i
$941$	−5.94320	−	14.9163i	−0.193743	−	0.486257i	0.799726	−	0.600366i	$-0.204978\pi$
$941$	−5.94320	−	14.9163i	−0.193743	−	0.486257i	−0.993468	+	0.114108i	$0.963599\pi$
$942$	−5.88541	+	3.54114i	−0.191757	+	0.115376i
$943$	5.62816			0.183278
$944$	4.77507	+	6.01653i	0.155415	+	0.195821i
$945$	6.80603			0.221400
$946$	−2.61703	+	1.57461i	−0.0850869	+	0.0511951i
$947$	4.48544	+	11.2576i	0.145757	+	0.365823i	0.983670	−	0.179981i	$-0.0576036\pi$
$947$	4.48544	+	11.2576i	0.145757	+	0.365823i	−0.837913	+	0.545804i	$0.816224\pi$
$948$	3.02685	−	5.70924i	0.0983074	−	0.185428i
$949$	28.9344	−	3.14681i	0.939251	−	0.102150i
$950$	14.3496	+	10.9083i	0.465562	+	0.353911i
$951$	24.9030	−	8.39078i	0.807534	−	0.272090i
$952$	0.216069	+	3.98516i	0.00700285	+	0.129160i
$953$	20.8967	−	19.7944i	0.676909	−	0.641202i	−0.269941	−	0.962877i	$-0.587004\pi$
$953$	20.8967	−	19.7944i	0.676909	−	0.641202i	0.946850	+	0.321674i	$0.104246\pi$
$954$	9.67245	−	7.35281i	0.313157	−	0.238056i
$955$	10.3417	−	15.2529i	0.334650	−	0.493572i
$956$	17.5409	+	1.90769i	0.567313	+	0.0616990i
$957$	5.70395	+	5.40307i	0.184383	+	0.174656i
$958$	3.30860	−	3.89518i	0.106896	−	0.125848i
$959$	−10.2662	−	19.3641i	−0.331512	−	0.625298i
$960$	1.75779	+	2.59254i	0.0567323	+	0.0836739i
$961$	−3.32946	−	1.12183i	−0.107402	−	0.0361880i
$962$	0.167197	−	0.602190i	0.00539065	−	0.0194154i
$963$	−1.27961	−	7.80526i	−0.0412348	−	0.251521i
$964$	−4.52813	+	11.3647i	−0.145841	+	0.366034i
$965$	−20.4570	−	24.0838i	−0.658534	−	0.775286i
$966$	−0.252817	+	4.66293i	−0.00813425	+	0.150027i
$967$	9.64099	+	34.7237i	0.310033	+	1.11664i	0.940324	+	0.340280i	$0.110522\pi$
$967$	9.64099	+	34.7237i	0.310033	+	1.11664i	−0.630291	+	0.776359i	$0.717064\pi$
$968$	−9.08914	+	4.20508i	−0.292136	+	0.135156i
$969$	−6.72058	+	1.47931i	−0.215896	+	0.0475224i
$970$	−23.9558	−	5.27308i	−0.769176	−	0.169308i
$971$	−27.5537	−	12.7477i	−0.884242	−	0.409094i	−0.0754227	−	0.997152i	$-0.524031\pi$
$971$	−27.5537	−	12.7477i	−0.884242	−	0.409094i	−0.808819	+	0.588058i	$0.799893\pi$
$972$	−0.161782	+	0.986827i	−0.00518916	+	0.0316525i
$973$	28.0886	+	16.9004i	0.900480	+	0.541801i
$974$	−2.76291	−	1.66239i	−0.0885294	−	0.0532664i
$975$	−1.37911	+	8.41222i	−0.0441670	+	0.269407i
$976$	−1.92569	−	0.890918i	−0.0616397	−	0.0285176i
$977$	−7.24973	−	1.59579i	−0.231939	−	0.0510537i	0.0974797	−	0.995238i	$-0.468922\pi$
$977$	−7.24973	−	1.59579i	−0.231939	−	0.0510537i	−0.329419	+	0.944184i	$0.606853\pi$
$978$	−14.3477	+	3.15817i	−0.458789	+	0.100987i
$979$	−3.18860	+	1.47521i	−0.101908	+	0.0471478i
$980$	1.90940	+	6.87703i	0.0609935	+	0.219679i
$981$	−0.464368	+	8.56476i	−0.0148261	+	0.273452i
$982$	−5.32497	−	6.26904i	−0.169927	−	0.200053i
$983$	21.0693	−	52.8799i	0.672006	−	1.68661i	−0.0536590	−	0.998559i	$-0.517088\pi$
$983$	21.0693	−	52.8799i	0.672006	−	1.68661i	0.725665	−	0.688048i	$-0.241532\pi$
$984$	−0.423677	−	2.58432i	−0.0135063	−	0.0823851i
$985$	11.3644	−	40.9308i	0.362099	−	1.30416i
$986$	−13.7773	−	4.64213i	−0.438760	−	0.147835i
$987$	9.50825	+	14.0236i	0.302651	+	0.446377i
$988$	3.10946	+	5.86506i	0.0989250	+	0.186592i
$989$	4.28105	−	5.04004i	0.136129	−	0.160264i
$990$	2.25718	+	2.13812i	0.0717380	+	0.0679538i
$991$	22.6602	+	2.46444i	0.719824	+	0.0782856i	0.460697	−	0.887558i	$-0.347600\pi$
$991$	22.6602	+	2.46444i	0.719824	+	0.0782856i	0.259127	+	0.965843i	$0.416565\pi$
$992$	3.29687	−	4.86251i	0.104676	−	0.154385i
$993$	0.158614	−	0.120575i	0.00503346	−	0.00382634i
$994$	−9.86239	+	9.34216i	−0.312816	+	0.296315i
$995$	0.718051	+	13.2437i	0.0227637	+	0.419852i
$996$	14.9928	−	5.05166i	0.475065	−	0.160068i
$997$	4.35881	+	3.31348i	0.138045	+	0.104939i	0.671918	−	0.740626i	$-0.265471\pi$
$997$	4.35881	+	3.31348i	0.138045	+	0.104939i	−0.533873	+	0.845565i	$0.679264\pi$
$998$	12.4915	−	1.35853i	0.395412	−	0.0430036i
$999$	0.165218	−	0.311634i	0.00522726	−	0.00985966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.163.2	yes	56
59.21	even	29	inner	354.2.e.a.139.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.139.2	✓	56	59.21	even	29	inner
354.2.e.a.163.2	yes	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.856857 + 0.515554i) q^{2} +(-0.370138 - 0.928977i) q^{3} +(0.468408 - 0.883512i) q^{4} +(3.11390 - 0.338657i) q^{5} +(0.796093 + 0.605174i) q^{6} +(2.05914 - 0.693803i) q^{7} +(0.0541389 + 0.998533i) q^{8} +(-0.725995 + 0.687699i) q^{9} +O(q^{10})\)	\(q+(-0.856857 + 0.515554i) q^{2} +(-0.370138 - 0.928977i) q^{3} +(0.468408 - 0.883512i) q^{4} +(3.11390 - 0.338657i) q^{5} +(0.796093 + 0.605174i) q^{6} +(2.05914 - 0.693803i) q^{7} +(0.0541389 + 0.998533i) q^{8} +(-0.725995 + 0.687699i) q^{9} +(-2.49357 + 1.89557i) q^{10} +(-0.557034 + 0.821564i) q^{11} +(-0.994138 - 0.108119i) q^{12} +(-1.28635 - 1.21850i) q^{13} +(-1.40669 + 1.65609i) q^{14} +(-1.46718 - 2.76739i) q^{15} +(-0.561187 - 0.827689i) q^{16} +(1.74059 + 0.586475i) q^{17} +(0.267528 - 0.963550i) q^{18} +(-0.606126 - 3.69721i) q^{19} +(1.15937 - 2.90980i) q^{20} +(-1.40669 - 1.65609i) q^{21} +(0.0537383 - 0.991144i) q^{22} +(0.574951 + 2.07079i) q^{23} +(0.907575 - 0.419889i) q^{24} +(4.69860 - 1.03424i) q^{25} +(1.73042 + 0.380895i) q^{26} +(0.907575 + 0.419889i) q^{27} +(0.351533 - 2.14425i) q^{28} +(6.78229 + 4.08077i) q^{29} +(2.68390 + 1.61485i) q^{30} +(0.950438 - 5.79742i) q^{31} +(0.907575 + 0.419889i) q^{32} +(0.969393 + 0.213380i) q^{33} +(-1.79380 + 0.394845i) q^{34} +(6.17699 - 2.85778i) q^{35} +(0.267528 + 0.963550i) q^{36} +(0.0190960 - 0.352205i) q^{37} +(2.42547 + 2.85549i) q^{38} +(-0.655829 + 1.64601i) q^{39} +(0.506744 + 3.09100i) q^{40} +(0.700608 - 2.52336i) q^{41} +(2.05914 + 0.693803i) q^{42} +(-1.72676 - 2.54679i) q^{43} +(0.464942 + 0.876974i) q^{44} +(-2.02779 + 2.38729i) q^{45} +(-1.56025 - 1.47795i) q^{46} +(-7.75183 - 0.843062i) q^{47} +(-0.561187 + 0.827689i) q^{48} +(-1.81398 + 1.37895i) q^{49} +(-3.49283 + 3.30858i) q^{50} +(-0.0994392 - 1.83405i) q^{51} +(-1.67910 + 0.565754i) q^{52} +(9.67245 + 7.35281i) q^{53} +(-0.994138 + 0.108119i) q^{54} +(-1.45632 + 2.74691i) q^{55} +(0.804265 + 2.01855i) q^{56} +(-3.21027 + 1.93155i) q^{57} -7.91531 q^{58} +(-7.65953 + 0.575876i) q^{59} -3.13227 q^{60} +(1.81807 - 1.09390i) q^{61} +(2.17449 + 5.45756i) q^{62} +(-1.01779 + 1.91976i) q^{63} +(-0.994138 + 0.108119i) q^{64} +(-4.41824 - 3.35866i) q^{65} +(-0.940640 + 0.316939i) q^{66} +(-0.708395 - 13.0656i) q^{67} +(1.33347 - 1.26313i) q^{68} +(1.71090 - 1.30059i) q^{69} +(-3.81946 + 5.63328i) q^{70} +(6.21527 + 0.675951i) q^{71} +(-0.725995 - 0.687699i) q^{72} +(-10.6342 + 12.5196i) q^{73} +(0.165218 + 0.311634i) q^{74} +(-2.69992 - 3.98208i) q^{75} +(-3.55044 - 1.19628i) q^{76} +(-0.577005 + 2.07818i) q^{77} +(-0.286653 - 1.74851i) q^{78} +(-2.39183 + 6.00303i) q^{79} +(-2.02779 - 2.38729i) q^{80} +(0.0541389 - 0.998533i) q^{81} +(0.700608 + 2.52336i) q^{82} +(-14.3587 + 6.64306i) q^{83} +(-2.12208 + 0.467105i) q^{84} +(5.61866 + 1.23676i) q^{85} +(2.79260 + 1.29199i) q^{86} +(1.28055 - 7.81103i) q^{87} +(-0.850516 - 0.511739i) q^{88} +(3.03286 + 1.82481i) q^{89} +(0.506744 - 3.09100i) q^{90} +(-3.49418 - 1.61658i) q^{91} +(2.09888 + 0.461998i) q^{92} +(-5.73746 + 1.26291i) q^{93} +(7.07686 - 3.27410i) q^{94} +(-3.13951 - 11.3075i) q^{95} +(0.0541389 - 0.998533i) q^{96} +(5.06980 + 5.96863i) q^{97} +(0.843397 - 2.11677i) q^{98} +(-0.160585 - 0.979524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

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