LMFDB - Embedded newform 354.2.e.a.127.2

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			127.2
Character	$\chi$	$=$	354.127
Dual form			354.2.e.a.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.653953 + 1.23349i) q^{5} +(0.976621 - 0.214970i) q^{6} +(3.53789 + 0.384769i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +O(q^{10})$	\(q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.653953 + 1.23349i) q^{5} +(0.976621 - 0.214970i) q^{6} +(3.53789 + 0.384769i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +(1.36348 + 0.300124i) q^{10} +(-2.52267 - 0.849988i) q^{11} +(0.468408 - 0.883512i) q^{12} +(-0.888125 + 3.19874i) q^{13} +(2.58364 - 2.44735i) q^{14} +(-0.225867 + 1.37773i) q^{15} +(-0.947653 + 0.319302i) q^{16} +(-0.242929 + 0.0264202i) q^{17} +(0.907575 + 0.419889i) q^{18} +(0.163808 - 3.02126i) q^{19} +(1.11144 - 0.844894i) q^{20} +(2.58364 + 2.44735i) q^{21} +(-2.28097 + 1.37242i) q^{22} +(3.11613 - 1.44168i) q^{23} +(-0.370138 - 0.928977i) q^{24} +(1.71210 - 2.52516i) q^{25} +(1.86300 + 2.74771i) q^{26} +(-0.370138 + 0.928977i) q^{27} +(-0.192667 - 3.55354i) q^{28} +(-1.53428 - 1.80629i) q^{29} +(0.903827 + 1.06407i) q^{30} +(-0.0469407 - 0.865770i) q^{31} +(-0.370138 + 0.928977i) q^{32} +(-1.49389 - 2.20333i) q^{33} +(-0.137133 + 0.202256i) q^{34} +(1.83901 + 4.61556i) q^{35} +(0.907575 - 0.419889i) q^{36} +(4.24121 - 2.55185i) q^{37} +(-2.19665 - 2.08077i) q^{38} +(-2.64282 + 2.00902i) q^{39} +(0.0755842 - 1.39407i) q^{40} +(-11.3855 - 5.26749i) q^{41} +(3.53789 - 0.384769i) q^{42} +(-6.03277 + 2.03268i) q^{43} +(-0.430667 + 2.62695i) q^{44} +(-1.01357 + 0.960109i) q^{45} +(0.918550 - 3.30832i) q^{46} +(-4.23604 + 7.99002i) q^{47} +(-0.947653 - 0.319302i) q^{48} +(5.53230 + 1.21775i) q^{49} +(-0.816191 - 2.93965i) q^{50} +(-0.209383 - 0.125982i) q^{51} +(3.30028 + 0.358927i) q^{52} +(-5.69598 + 1.25378i) q^{53} +(0.468408 + 0.883512i) q^{54} +(-0.601262 - 3.66754i) q^{55} +(-2.83310 - 2.15367i) q^{56} +(1.95880 - 2.30607i) q^{57} -2.36995 q^{58} +(-7.01147 - 3.13677i) q^{59} +1.39612 q^{60} +(-8.36897 + 9.85272i) q^{61} +(-0.690245 - 0.524711i) q^{62} +(0.575742 + 3.51187i) q^{63} +(0.468408 + 0.883512i) q^{64} +(-4.52639 + 0.996334i) q^{65} +(-2.64642 - 0.287815i) q^{66} +(8.92508 + 5.37004i) q^{67} +(0.0653737 + 0.235455i) q^{68} +(3.35320 + 0.738094i) q^{69} +(4.70836 + 1.58643i) q^{70} +(3.50321 - 6.60776i) q^{71} +(0.267528 - 0.963550i) q^{72} +(2.70162 - 2.55911i) q^{73} +(0.800777 - 4.88453i) q^{74} +(2.89116 - 0.974144i) q^{75} +(-3.00796 + 0.327136i) q^{76} +(-8.59790 - 3.97781i) q^{77} +(-0.179727 + 3.31487i) q^{78} +(10.3845 - 7.89408i) q^{79} +(-1.01357 - 0.960109i) q^{80} +(-0.856857 + 0.515554i) q^{81} +(-11.3855 + 5.26749i) q^{82} +(3.67459 + 9.22253i) q^{83} +(1.99713 - 2.94554i) q^{84} +(-0.191453 - 0.282372i) q^{85} +(-2.35630 + 5.91387i) q^{86} +(-0.128307 - 2.36648i) q^{87} +(1.72336 + 2.02889i) q^{88} +(-2.19355 - 2.58245i) q^{89} +(0.0755842 + 1.39407i) q^{90} +(-4.37287 + 10.9751i) q^{91} +(-1.92682 - 2.84184i) q^{92} +(0.486572 - 0.717640i) q^{93} +(3.34734 + 8.40118i) q^{94} +(3.83381 - 1.77371i) q^{95} +(-0.856857 + 0.515554i) q^{96} +(-5.62283 - 5.32623i) q^{97} +(4.50966 - 3.42815i) q^{98} +(0.144119 - 2.65812i) 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 $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{21}{29}\right)$	$1$

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 $

$2$	0.647386	−	0.762162i	0.457771	−	0.538930i
$2$	0.647386	−	0.762162i	0.457771	−	0.538930i
$3$	0.796093	+	0.605174i	0.459625	+	0.349397i
$3$	0.796093	+	0.605174i	0.459625	+	0.349397i
$4$	−0.161782	−	0.986827i	−0.0808910	−	0.493413i
$5$	0.653953	+	1.23349i	0.292457	+	0.551632i	0.985585	−	0.169183i	$-0.0541128\pi$
$5$	0.653953	+	1.23349i	0.292457	+	0.551632i	−0.693128	+	0.720814i	$0.743768\pi$
$6$	0.976621	−	0.214970i	0.398704	−	0.0877613i
$7$	3.53789	+	0.384769i	1.33720	+	0.145429i	0.748613	−	0.663007i	$-0.230720\pi$
$7$	3.53789	+	0.384769i	1.33720	+	0.145429i	0.588584	+	0.808436i	$0.299685\pi$
$8$	−0.856857	−	0.515554i	−0.302945	−	0.182276i
$9$	0.267528	+	0.963550i	0.0891761	+	0.321183i
$10$	1.36348	+	0.300124i	0.431169	+	0.0949075i
$11$	−2.52267	−	0.849988i	−0.760615	−	0.256281i	−0.0878464	−	0.996134i	$-0.527998\pi$
$11$	−2.52267	−	0.849988i	−0.760615	−	0.256281i	−0.672769	+	0.739853i	$0.734895\pi$
$12$	0.468408	−	0.883512i	0.135218	−	0.255048i
$13$	−0.888125	+	3.19874i	−0.246322	+	0.887170i	0.732211	+	0.681078i	$0.238489\pi$
$13$	−0.888125	+	3.19874i	−0.246322	+	0.887170i	−0.978533	+	0.206092i	$0.933925\pi$
$14$	2.58364	−	2.44735i	0.690507	−	0.654083i
$15$	−0.225867	+	1.37773i	−0.0583185	+	0.355727i
$16$	−0.947653	+	0.319302i	−0.236913	+	0.0798254i
$17$	−0.242929	+	0.0264202i	−0.0589190	+	0.00640783i	−0.137531	−	0.990497i	$-0.543917\pi$
$17$	−0.242929	+	0.0264202i	−0.0589190	+	0.00640783i	0.0786120	+	0.996905i	$0.474951\pi$
$18$	0.907575	+	0.419889i	0.213918	+	0.0989688i
$19$	0.163808	−	3.02126i	0.0375802	−	0.693125i	−0.917673	−	0.397336i	$-0.869935\pi$
$19$	0.163808	−	3.02126i	0.0375802	−	0.693125i	0.955253	−	0.295789i	$-0.0955826\pi$
$20$	1.11144	−	0.844894i	0.248525	−	0.188924i
$21$	2.58364	+	2.44735i	0.563796	+	0.534056i
$22$	−2.28097	+	1.37242i	−0.486305	+	0.292600i
$23$	3.11613	−	1.44168i	0.649759	−	0.300610i	−0.0671860	−	0.997740i	$-0.521402\pi$
$23$	3.11613	−	1.44168i	0.649759	−	0.300610i	0.716945	+	0.697130i	$0.245540\pi$
$24$	−0.370138	−	0.928977i	−0.0755541	−	0.189627i
$25$	1.71210	−	2.52516i	0.342420	−	0.505032i
$26$	1.86300	+	2.74771i	0.365364	+	0.538871i
$27$	−0.370138	+	0.928977i	−0.0712331	+	0.178782i
$28$	−0.192667	−	3.55354i	−0.0364107	−	0.671555i
$29$	−1.53428	−	1.80629i	−0.284908	−	0.335419i	0.601027	−	0.799228i	$-0.294758\pi$
$29$	−1.53428	−	1.80629i	−0.284908	−	0.335419i	−0.885935	+	0.463809i	$0.846482\pi$
$30$	0.903827	+	1.06407i	0.165015	+	0.194271i
$31$	−0.0469407	−	0.865770i	−0.00843079	−	0.155497i	−0.999717	−	0.0237739i	$-0.992432\pi$
$31$	−0.0469407	−	0.865770i	−0.00843079	−	0.155497i	0.991287	−	0.131723i	$-0.0420509\pi$
$32$	−0.370138	+	0.928977i	−0.0654318	+	0.164221i
$33$	−1.49389	−	2.20333i	−0.260053	−	0.383550i
$34$	−0.137133	+	0.202256i	−0.0235181	+	0.0346865i
$35$	1.83901	+	4.61556i	0.310849	+	0.780172i
$36$	0.907575	−	0.419889i	0.151263	−	0.0699815i
$37$	4.24121	−	2.55185i	0.697251	−	0.419522i	−0.122327	−	0.992490i	$-0.539036\pi$
$37$	4.24121	−	2.55185i	0.697251	−	0.419522i	0.819578	+	0.572968i	$0.194208\pi$
$38$	−2.19665	−	2.08077i	−0.356343	−	0.337546i
$39$	−2.64282	+	2.00902i	−0.423191	+	0.321701i
$40$	0.0755842	−	1.39407i	0.0119509	−	0.220422i
$41$	−11.3855	−	5.26749i	−1.77812	−	0.822644i	−0.973444	−	0.228926i	$-0.926479\pi$
$41$	−11.3855	−	5.26749i	−1.77812	−	0.822644i	−0.804673	−	0.593718i	$-0.797659\pi$
$42$	3.53789	−	0.384769i	0.545909	−	0.0593712i
$43$	−6.03277	+	2.03268i	−0.919989	+	0.309980i	−0.739157	−	0.673534i	$-0.764776\pi$
$43$	−6.03277	+	2.03268i	−0.919989	+	0.309980i	−0.180832	+	0.983514i	$0.557879\pi$
$44$	−0.430667	+	2.62695i	−0.0649256	+	0.396028i
$45$	−1.01357	+	0.960109i	−0.151095	+	0.143125i
$46$	0.918550	−	3.30832i	0.135433	−	0.487785i
$47$	−4.23604	+	7.99002i	−0.617890	+	1.16546i	0.355146	+	0.934811i	$0.384431\pi$
$47$	−4.23604	+	7.99002i	−0.617890	+	1.16546i	−0.973036	+	0.230654i	$0.925914\pi$
$48$	−0.947653	−	0.319302i	−0.136782	−	0.0460872i
$49$	5.53230	+	1.21775i	0.790328	+	0.173964i
$50$	−0.816191	−	2.93965i	−0.115427	−	0.415730i
$51$	−0.209383	−	0.125982i	−0.0293195	−	0.0176410i
$52$	3.30028	+	0.358927i	0.457667	+	0.0497743i
$53$	−5.69598	+	1.25378i	−0.782402	+	0.172220i	−0.588172	−	0.808736i	$-0.700152\pi$
$53$	−5.69598	+	1.25378i	−0.782402	+	0.172220i	−0.194231	+	0.980956i	$0.562221\pi$
$54$	0.468408	+	0.883512i	0.0637423	+	0.120231i
$55$	−0.601262	−	3.66754i	−0.0810741	−	0.494530i
$56$	−2.83310	−	2.15367i	−0.378589	−	0.287796i
$57$	1.95880	−	2.30607i	0.259449	−	0.305447i
$58$	−2.36995			−0.311190
$59$	−7.01147	−	3.13677i	−0.912815	−	0.408373i
$59$	−7.01147	−	3.13677i	−0.912815	−	0.408373i
$60$	1.39612			0.180238
$61$	−8.36897	+	9.85272i	−1.07154	+	1.26151i	−0.107939	+	0.994158i	$0.534425\pi$
$61$	−8.36897	+	9.85272i	−1.07154	+	1.26151i	−0.963599	+	0.267353i	$0.913851\pi$
$62$	−0.690245	−	0.524711i	−0.0876613	−	0.0666384i
$63$	0.575742	+	3.51187i	0.0725367	+	0.442455i
$64$	0.468408	+	0.883512i	0.0585511	+	0.110439i
$65$	−4.52639	+	0.996334i	−0.561430	+	0.123580i
$66$	−2.64642	−	0.287815i	−0.325752	−	0.0354276i
$67$	8.92508	+	5.37004i	1.09037	+	0.656055i	0.942922	−	0.333015i	$-0.108066\pi$
$67$	8.92508	+	5.37004i	1.09037	+	0.656055i	0.147450	+	0.989069i	$0.452893\pi$
$68$	0.0653737	+	0.235455i	0.00792773	+	0.0285531i
$69$	3.35320	+	0.738094i	0.403677	+	0.0888561i
$70$	4.70836	+	1.58643i	0.562756	+	0.189615i
$71$	3.50321	−	6.60776i	0.415755	−	0.784197i	−0.583863	−	0.811852i	$-0.698459\pi$
$71$	3.50321	−	6.60776i	0.415755	−	0.784197i	0.999618	+	0.0276556i	$0.00880417\pi$
$72$	0.267528	−	0.963550i	0.0315285	−	0.113555i
$73$	2.70162	−	2.55911i	0.316201	−	0.299521i	−0.513094	−	0.858332i	$-0.671501\pi$
$73$	2.70162	−	2.55911i	0.316201	−	0.299521i	0.829295	+	0.558811i	$0.188742\pi$
$74$	0.800777	−	4.88453i	0.0930885	−	0.567815i
$75$	2.89116	−	0.974144i	0.333842	−	0.112484i
$76$	−3.00796	+	0.327136i	−0.345037	+	0.0375250i
$77$	−8.59790	−	3.97781i	−0.979822	−	0.453314i
$78$	−0.179727	+	3.31487i	−0.0203501	+	0.375336i
$79$	10.3845	−	7.89408i	1.16835	−	0.888154i	0.173039	−	0.984915i	$-0.444641\pi$
$79$	10.3845	−	7.89408i	1.16835	−	0.888154i	0.995308	+	0.0967613i	$0.0308483\pi$
$80$	−1.01357	−	0.960109i	−0.113321	−	0.107343i
$81$	−0.856857	+	0.515554i	−0.0952064	+	0.0572838i
$82$	−11.3855	+	5.26749i	−1.25732	+	0.581697i
$83$	3.67459	+	9.22253i	0.403339	+	1.01230i	0.980648	+	0.195778i	$0.0627233\pi$
$83$	3.67459	+	9.22253i	0.403339	+	1.01230i	−0.577309	+	0.816525i	$0.695897\pi$
$84$	1.99713	−	2.94554i	0.217904	−	0.321385i
$85$	−0.191453	−	0.282372i	−0.0207660	−	0.0306276i
$86$	−2.35630	+	5.91387i	−0.254087	+	0.637709i
$87$	−0.128307	−	2.36648i	−0.0137559	−	0.253713i
$88$	1.72336	+	2.02889i	0.183710	+	0.216281i
$89$	−2.19355	−	2.58245i	−0.232516	−	0.273739i	0.633514	−	0.773732i	$-0.281612\pi$
$89$	−2.19355	−	2.58245i	−0.232516	−	0.273739i	−0.866030	+	0.499992i	$0.833336\pi$
$90$	0.0755842	+	1.39407i	0.00796728	+	0.146948i
$91$	−4.37287	+	10.9751i	−0.458401	+	1.15050i
$92$	−1.92682	−	2.84184i	−0.200885	−	0.296283i
$93$	0.486572	−	0.717640i	0.0504552	−	0.0744158i
$94$	3.34734	+	8.40118i	0.345251	+	0.866516i
$95$	3.83381	−	1.77371i	0.393340	−	0.181979i
$96$	−0.856857	+	0.515554i	−0.0874526	+	0.0526185i
$97$	−5.62283	−	5.32623i	−0.570912	−	0.540797i	0.346853	−	0.937919i	$-0.387250\pi$
$97$	−5.62283	−	5.32623i	−0.570912	−	0.540797i	−0.917766	+	0.397123i	$0.870009\pi$
$98$	4.50966	−	3.42815i	0.455544	−	0.346296i
$99$	0.144119	−	2.65812i	0.0144845	−	0.267151i
$100$	−2.76888	−	1.28102i	−0.276888	−	0.128102i
$101$	−3.85463	+	0.419216i	−0.383550	+	0.0417136i	−0.297863	−	0.954609i	$-0.596274\pi$
$101$	−3.85463	+	0.419216i	−0.383550	+	0.0417136i	−0.0856868	+	0.996322i	$0.527308\pi$
$102$	−0.231570	+	0.0780251i	−0.0229289	+	0.00772564i
$103$	−1.19933	+	7.31558i	−0.118173	+	0.720825i	0.859570	+	0.511019i	$0.170732\pi$
$103$	−1.19933	+	7.31558i	−0.118173	+	0.720825i	−0.977743	+	0.209807i	$0.932717\pi$
$104$	2.41012	−	2.28299i	0.236332	−	0.223865i
$105$	−1.32920	+	4.78734i	−0.129716	+	0.467196i
$106$	−2.73191	+	5.15294i	−0.265347	+	0.500497i
$107$	−1.73729	−	0.585360i	−0.167950	−	0.0565889i	0.234071	−	0.972220i	$-0.424795\pi$
$107$	−1.73729	−	0.585360i	−0.167950	−	0.0565889i	−0.402020	+	0.915631i	$0.631692\pi$
$108$	0.976621	+	0.214970i	0.0939754	+	0.0206855i
$109$	−3.02241	−	10.8857i	−0.289494	−	1.04266i	−0.955081	−	0.296344i	$-0.904232\pi$
$109$	−3.02241	−	10.8857i	−0.289494	−	1.04266i	0.665587	−	0.746320i	$-0.268181\pi$
$110$	−3.18451	−	1.91605i	−0.303631	−	0.182689i
$111$	4.92072	+	0.535160i	0.467054	+	0.0507951i
$112$	−3.47555	+	0.765027i	−0.328409	+	0.0722883i
$113$	1.09951	+	2.07390i	0.103433	+	0.195096i	0.929827	−	0.367997i	$-0.119956\pi$
$113$	1.09951	+	2.07390i	0.103433	+	0.195096i	−0.826394	+	0.563093i	$0.809611\pi$
$114$	−0.489504	−	2.98584i	−0.0458462	−	0.279650i
$115$	3.81609	+	2.90092i	0.355852	+	0.270512i
$116$	−1.53428	+	1.80629i	−0.142454	+	0.167710i
$117$	−3.31974			−0.306910
$118$	−6.92985	+	3.31317i	−0.637945	+	0.305002i
$119$	−0.869624			−0.0797183
$120$	0.903827	−	1.06407i	0.0825077	−	0.0971356i
$121$	−3.11562	−	2.36843i	−0.283238	−	0.215312i
$122$	2.09141	+	12.7570i	0.189347	+	1.15497i
$123$	−5.87617	−	11.0836i	−0.529836	−	0.999377i
$124$	−0.846770	+	0.186388i	−0.0760422	+	0.0167382i
$125$	11.1740	+	1.21525i	0.999437	+	0.108695i
$126$	3.04934	+	1.83473i	0.271657	+	0.163451i
$127$	0.916115	+	3.29955i	0.0812920	+	0.292787i	0.993010	−	0.118029i	$-0.0376575\pi$
$127$	0.916115	+	3.29955i	0.0812920	+	0.292787i	−0.911718	+	0.410816i	$0.865244\pi$
$128$	0.976621	+	0.214970i	0.0863219	+	0.0190009i
$129$	−6.03277	−	2.03268i	−0.531156	−	0.178967i
$130$	−2.17096	+	4.09486i	−0.190405	+	0.359143i
$131$	0.901239	−	3.24597i	0.0787416	−	0.283602i	−0.913688	−	0.406416i	$-0.866778\pi$
$131$	0.901239	−	3.24597i	0.0787416	−	0.283602i	0.992430	+	0.122815i	$0.0391921\pi$
$132$	−1.93262	+	1.83067i	−0.168213	+	0.159340i
$133$	1.74202	−	10.6259i	0.151053	−	0.921381i
$134$	9.87081	−	3.32586i	0.852709	−	0.287311i
$135$	−1.38793	+	0.150947i	−0.119454	+	0.0129914i
$136$	0.221777	+	0.102605i	0.0190172	+	0.00879829i
$137$	−0.509044	+	9.38877i	−0.0434906	+	0.802137i	0.892702	+	0.450648i	$0.148807\pi$
$137$	−0.509044	+	9.38877i	−0.0434906	+	0.802137i	−0.936192	+	0.351489i	$0.885676\pi$
$138$	2.73336	−	2.07785i	0.232679	−	0.176878i
$139$	14.1909	+	13.4423i	1.20366	+	1.14016i	0.986454	+	0.164036i	$0.0524513\pi$
$139$	14.1909	+	13.4423i	1.20366	+	1.14016i	0.217201	+	0.976127i	$0.430307\pi$
$140$	4.25724	−	2.56150i	0.359803	−	0.216486i
$141$	−8.20764	+	3.79726i	−0.691208	+	0.319787i
$142$	−2.76825	−	6.94779i	−0.232307	−	0.583046i
$143$	4.95934	−	7.31448i	0.414721	−	0.611668i
$144$	−0.561187	−	0.827689i	−0.0467656	−	0.0689741i
$145$	1.22469	−	3.07374i	0.101705	−	0.255260i
$146$	−0.201465	−	3.71580i	−0.0166734	−	0.307522i
$147$	3.66727	+	4.31745i	0.302472	+	0.356097i
$148$	−3.20439	−	3.77250i	−0.263399	−	0.310097i
$149$	0.436480	+	8.05041i	0.0357579	+	0.659515i	0.960391	+	0.278656i	$0.0898890\pi$
$149$	0.436480	+	8.05041i	0.0357579	+	0.659515i	−0.924633	+	0.380859i	$0.875628\pi$
$150$	1.12924	−	2.83418i	0.0922020	−	0.231410i
$151$	2.90069	+	4.27819i	0.236054	+	0.348154i	0.927203	−	0.374558i	$-0.122206\pi$
$151$	2.90069	+	4.27819i	0.236054	+	0.348154i	−0.691149	+	0.722712i	$0.742895\pi$
$152$	−1.69798	+	2.50434i	−0.137725	+	0.203129i
$153$	−0.0904476	−	0.227006i	−0.00731226	−	0.0183524i
$154$	−8.59790	+	3.97781i	−0.692839	+	0.320541i
$155$	1.03722	−	0.624073i	0.0833113	−	0.0501268i
$156$	2.41012	+	2.28299i	0.192964	+	0.182785i
$157$	−4.01973	+	3.05572i	−0.320810	+	0.243873i	−0.753167	−	0.657829i	$-0.771475\pi$
$157$	−4.01973	+	3.05572i	−0.320810	+	0.243873i	0.432358	+	0.901702i	$0.357682\pi$
$158$	0.706205	−	13.0252i	0.0561827	−	1.03623i
$159$	−5.29328	−	2.44893i	−0.419784	−	0.194213i
$160$	−1.38793	+	0.150947i	−0.109726	+	0.0119334i
$161$	11.5793	−	3.90151i	0.912573	−	0.307482i
$162$	−0.161782	+	0.986827i	−0.0127108	+	0.0775324i
$163$	8.55302	−	8.10185i	0.669924	−	0.634586i	−0.275165	−	0.961397i	$-0.588733\pi$
$163$	8.55302	−	8.10185i	0.669924	−	0.634586i	0.945090	+	0.326811i	$0.105974\pi$
$164$	−3.35613	+	12.0877i	−0.262070	+	0.943891i
$165$	1.74084	−	3.28357i	0.135524	−	0.255625i
$166$	9.40794	+	3.16990i	0.730198	+	0.246032i
$167$	7.84621	+	1.72708i	0.607158	+	0.133646i	0.507900	−	0.861416i	$-0.330422\pi$
$167$	7.84621	+	1.72708i	0.607158	+	0.133646i	0.0992583	+	0.995062i	$0.468353\pi$
$168$	−0.952068	−	3.42904i	−0.0734536	−	0.264556i
$169$	1.69598	+	1.02044i	0.130460	+	0.0784953i
$170$	−0.339158	−	0.0368856i	−0.0260122	−	0.00282900i
$171$	2.95496	−	0.650436i	0.225972	−	0.0497401i
$172$	2.98189	+	5.62445i	0.227367	+	0.428860i
$173$	−3.24151	−	19.7723i	−0.246447	−	1.50326i	−0.762659	−	0.646801i	$-0.776107\pi$
$173$	−3.24151	−	19.7723i	−0.246447	−	1.50326i	0.516212	−	0.856461i	$-0.327342\pi$
$174$	−1.88670	−	1.43424i	−0.143031	−	0.108729i
$175$	7.02884	−	8.27499i	0.531330	−	0.625530i
$176$	2.66202			0.200658
$177$	−3.68349	−	6.74032i	−0.276868	−	0.506633i
$178$	−3.38832			−0.253966
$179$	14.1417	−	16.6489i	1.05700	−	1.24440i	0.0883163	−	0.996092i	$-0.471851\pi$
$179$	14.1417	−	16.6489i	1.05700	−	1.24440i	0.968682	−	0.248303i	$-0.0798728\pi$
$180$	1.11144	+	0.844894i	0.0828418	+	0.0629747i
$181$	−1.61896	−	9.87521i	−0.120336	−	0.734018i	−0.976209	−	0.216832i	$-0.930428\pi$
$181$	−1.61896	−	9.87521i	−0.120336	−	0.734018i	0.855873	−	0.517186i	$-0.173021\pi$
$182$	5.53385	+	10.4379i	0.410196	+	0.773712i
$183$	−12.6251	+	2.77899i	−0.933274	+	0.205429i
$184$	−3.41334	−	0.371223i	−0.251635	−	0.0273669i
$185$	5.92123	+	3.56268i	0.435337	+	0.261934i
$186$	−0.231958	−	0.835437i	−0.0170080	−	0.0612572i
$187$	0.635288	+	0.139838i	0.0464569	+	0.0102259i
$188$	8.57008	+	2.88760i	0.625037	+	0.210600i
$189$	−1.66695	+	3.14420i	−0.121253	+	0.228707i
$190$	1.13010	−	4.07026i	0.0819862	−	0.295288i
$191$	6.03145	−	5.71329i	0.436420	−	0.413399i	−0.437691	−	0.899126i	$-0.644204\pi$
$191$	6.03145	−	5.71329i	0.436420	−	0.413399i	0.874111	+	0.485727i	$0.161445\pi$
$192$	−0.161782	+	0.986827i	−0.0116756	+	0.0712181i
$193$	14.7796	−	4.97982i	1.06386	−	0.358455i	0.267673	−	0.963510i	$-0.413745\pi$
$193$	14.7796	−	4.97982i	1.06386	−	0.358455i	0.796184	+	0.605055i	$0.206849\pi$
$194$	−7.69960	+	0.837382i	−0.552799	+	0.0601205i
$195$	−4.20638	−	1.94608i	−0.301225	−	0.139362i
$196$	0.306683	−	5.65643i	0.0219059	−	0.404031i
$197$	−2.60778	+	1.98238i	−0.185796	+	0.141239i	−0.693938	−	0.720035i	$-0.744126\pi$
$197$	−2.60778	+	1.98238i	−0.185796	+	0.141239i	0.508142	+	0.861274i	$0.330333\pi$
$198$	−1.93262	−	1.83067i	−0.137345	−	0.130100i
$199$	7.21380	−	4.34040i	0.511373	−	0.307683i	−0.236379	−	0.971661i	$-0.575961\pi$
$199$	7.21380	−	4.34040i	0.511373	−	0.307683i	0.747752	+	0.663978i	$0.231133\pi$
$200$	−2.76888	+	1.28102i	−0.195790	+	0.0905819i
$201$	3.85538	+	9.67628i	0.271938	+	0.682512i
$202$	−2.17592	+	3.20925i	−0.153097	+	0.225802i
$203$	−4.73310	−	6.98080i	−0.332199	−	0.489956i
$204$	−0.0904476	+	0.227006i	−0.00633260	+	0.0158936i
$205$	−0.948202	−	17.4886i	−0.0662253	−	1.22145i
$206$	4.79923	+	5.65009i	0.334378	+	0.393660i
$207$	2.22278	+	2.61686i	0.154494	+	0.181884i
$208$	−0.179727	−	3.31487i	−0.0124618	−	0.229845i
$209$	−2.98127	+	7.48243i	−0.206219	+	0.517570i
$210$	2.78822	+	4.11232i	0.192406	+	0.283777i
$211$	−7.61504	+	11.2313i	−0.524241	+	0.773198i	−0.993975	−	0.109611i	$-0.965040\pi$
$211$	−7.61504	+	11.2313i	−0.524241	+	0.773198i	0.469734	+	0.882808i	$0.344350\pi$
$212$	2.15877	+	5.41810i	0.148265	+	0.372117i
$213$	6.78773	−	3.14034i	0.465088	−	0.215172i
$214$	−1.57083	+	0.945140i	−0.107380	+	0.0646084i
$215$	−6.45242	−	6.11206i	−0.440052	−	0.416839i
$216$	0.796093	−	0.605174i	0.0541673	−	0.0411769i
$217$	0.167050	−	3.08106i	0.0113401	−	0.209156i
$218$	−10.2534	−	4.74371i	−0.694445	−	0.321285i
$219$	3.69945	−	0.402339i	0.249985	−	0.0271876i
$220$	−3.52195	+	1.18668i	−0.237450	+	0.0800061i
$221$	0.131241	−	0.800532i	0.00882819	−	0.0538496i
$222$	3.59348	−	3.40393i	0.241179	−	0.228457i
$223$	5.08937	−	18.3303i	0.340810	−	1.22749i	−0.572393	−	0.819979i	$-0.693985\pi$
$223$	5.08937	−	18.3303i	0.340810	−	1.22749i	0.913203	−	0.407506i	$-0.133601\pi$
$224$	−1.66695	+	3.14420i	−0.111378	+	0.210081i
$225$	2.89116	+	0.974144i	0.192744	+	0.0649429i
$226$	2.29246	+	0.504608i	0.152492	+	0.0335660i
$227$	5.67566	+	20.4419i	0.376707	+	1.35677i	0.872619	+	0.488402i	$0.162420\pi$
$227$	5.67566	+	20.4419i	0.376707	+	1.35677i	−0.495912	+	0.868373i	$0.665166\pi$
$228$	−2.59259	−	1.55991i	−0.171699	−	0.103308i
$229$	−28.5539	−	3.10543i	−1.88690	−	0.205212i	−0.909365	−	0.415999i	$-0.863432\pi$
$229$	−28.5539	−	3.10543i	−1.88690	−	0.205212i	−0.977532	+	0.210787i	$0.932398\pi$
$230$	4.68145	−	1.03047i	0.308686	−	0.0679469i
$231$	−4.43746	−	8.36994i	−0.291964	−	0.550702i
$232$	0.383416	+	2.33873i	0.0251725	+	0.153545i
$233$	11.2706	+	8.56772i	0.738364	+	0.561290i	0.905348	−	0.424670i	$-0.139610\pi$
$233$	11.2706	+	8.56772i	0.738364	+	0.561290i	−0.166984	+	0.985960i	$0.553403\pi$
$234$	−2.14916	+	2.53018i	−0.140495	+	0.165403i
$235$	−12.6258			−0.823613
$236$	−1.96112	+	7.42657i	−0.127658	+	0.483429i
$237$	13.0443			0.847319
$238$	−0.562982	+	0.662794i	−0.0364927	+	0.0429626i
$239$	10.0167	+	7.61448i	0.647925	+	0.492540i	0.876762	−	0.480925i	$-0.159699\pi$
$239$	10.0167	+	7.61448i	0.647925	+	0.492540i	−0.228836	+	0.973465i	$0.573492\pi$
$240$	−0.225867	−	1.37773i	−0.0145796	−	0.0889318i
$241$	−0.0102763	−	0.0193831i	−0.000661953	−	0.00124858i	0.883181	−	0.469033i	$-0.155397\pi$
$241$	−0.0102763	−	0.0193831i	−0.000661953	−	0.00124858i	−0.883843	+	0.467784i	$0.845053\pi$
$242$	−3.82213	+	0.841316i	−0.245696	+	0.0540818i
$243$	−0.994138	−	0.108119i	−0.0637740	−	0.00693584i
$244$	11.0769	+	6.66473i	0.709124	+	0.426666i
$245$	2.11578	+	7.62036i	0.135172	+	0.486847i
$246$	−12.2517	−	2.69680i	−0.781138	−	0.171941i
$247$	9.51875	+	3.20724i	0.605663	+	0.204072i
$248$	−0.406129	+	0.766041i	−0.0257892	+	0.0486437i
$249$	−2.65592	+	9.56576i	−0.168312	+	0.606205i
$250$	8.16014	−	7.72970i	0.516093	−	0.488869i
$251$	−2.40606	+	14.6763i	−0.151869	+	0.926361i	0.795438	+	0.606035i	$0.207241\pi$
$251$	−2.40606	+	14.6763i	−0.151869	+	0.926361i	−0.947307	+	0.320326i	$0.896208\pi$
$252$	3.37247	−	1.13632i	0.212445	−	0.0715812i
$253$	−9.08640	+	0.988205i	−0.571257	+	0.0621279i
$254$	3.10787	+	1.43785i	0.195005	+	0.0902189i
$255$	0.0184699	−	0.340657i	0.00115663	−	0.0213328i
$256$	0.796093	−	0.605174i	0.0497558	−	0.0378234i
$257$	18.1052	+	17.1501i	1.12937	+	1.06980i	0.996906	+	0.0786090i	$0.0250479\pi$
$257$	18.1052	+	17.1501i	1.12937	+	1.06980i	0.132465	+	0.991188i	$0.457711\pi$
$258$	−5.45476	+	3.28202i	−0.339599	+	0.204330i
$259$	15.9868	−	7.39630i	0.993373	−	0.459583i
$260$	1.71550	+	4.30557i	0.106391	+	0.267020i
$261$	1.32999	−	1.96159i	0.0823242	−	0.121419i
$262$	−1.89051	−	2.78829i	−0.116796	−	0.172261i
$263$	1.69231	−	4.24739i	0.104353	−	0.261905i	−0.867524	−	0.497395i	$-0.834290\pi$
$263$	1.69231	−	4.24739i	0.104353	−	0.261905i	0.971877	+	0.235490i	$0.0756694\pi$
$264$	0.144119	+	2.65812i	0.00886991	+	0.163596i
$265$	−5.27142	−	6.20599i	−0.323821	−	0.381231i
$266$	−6.97088	−	8.20675i	−0.427412	−	0.503188i
$267$	−0.183440	−	3.38335i	−0.0112264	−	0.207058i
$268$	3.85538	−	9.67628i	0.235505	−	0.591073i
$269$	10.2697	+	15.1467i	0.626156	+	0.923511i	0.999992	−	0.00398344i	$-0.00126797\pi$
$269$	10.2697	+	15.1467i	0.626156	+	0.923511i	−0.373836	+	0.927495i	$0.621958\pi$
$270$	−0.783483	+	1.15555i	−0.0476812	+	0.0703246i
$271$	9.44280	+	23.6997i	0.573609	+	1.43965i	0.874043	+	0.485848i	$0.161489\pi$
$271$	9.44280	+	23.6997i	0.573609	+	1.43965i	−0.300434	+	0.953803i	$0.597131\pi$
$272$	0.221777	−	0.102605i	0.0134472	−	0.00622133i
$273$	−10.1230	+	6.09083i	−0.612674	+	0.368634i
$274$	6.82622	+	6.46614i	0.412387	+	0.390634i
$275$	−6.46543	+	4.91489i	−0.389880	+	0.296379i
$276$	0.185884	−	3.42843i	0.0111889	−	0.206367i
$277$	0.845702	+	0.391264i	0.0508133	+	0.0235087i	0.445131	−	0.895465i	$-0.353157\pi$
$277$	0.845702	+	0.391264i	0.0508133	+	0.0235087i	−0.394318	+	0.918974i	$0.629019\pi$
$278$	19.4322	−	2.11338i	1.16547	−	0.126752i
$279$	0.821654	−	0.276848i	0.0491912	−	0.0165744i
$280$	0.803804	−	4.90299i	0.0480365	−	0.293009i
$281$	−4.97157	+	4.70932i	−0.296579	+	0.280935i	−0.821490	−	0.570222i	$-0.806857\pi$
$281$	−4.97157	+	4.70932i	−0.296579	+	0.280935i	0.524911	+	0.851157i	$0.324098\pi$
$282$	−2.41939	+	8.71384i	−0.144072	+	0.518902i
$283$	−13.3543	+	25.1889i	−0.793832	+	1.49733i	0.0722290	+	0.997388i	$0.476989\pi$
$283$	−13.3543	+	25.1889i	−0.793832	+	1.49733i	−0.866061	+	0.499938i	$0.833356\pi$
$284$	−7.08747	−	2.38805i	−0.420564	−	0.141705i
$285$	4.12547	+	0.908085i	0.244372	+	0.0537903i
$286$	−2.36421	−	8.51512i	−0.139799	−	0.503509i
$287$	−38.2539	−	23.0166i	−2.25806	−	1.35863i
$288$	−0.994138	−	0.108119i	−0.0585801	−	0.00637097i
$289$	−16.5442	+	3.64166i	−0.973190	+	0.214215i
$290$	−1.54984	−	2.92331i	−0.0910096	−	0.171662i
$291$	−1.25300	−	7.64297i	−0.0734522	−	0.448039i
$292$	−2.96247	−	2.25201i	−0.173365	−	0.131789i
$293$	17.0244	−	20.0427i	0.994578	−	1.17091i	0.00929875	−	0.999957i	$-0.497040\pi$
$293$	17.0244	−	20.0427i	0.994578	−	1.17091i	0.985279	−	0.170951i	$-0.0546841\pi$
$294$	5.66474			0.330374
$295$	−0.716007	−	10.6998i	−0.0416876	−	0.622969i
$296$	−4.94973			−0.287697
$297$	1.72336	−	2.02889i	0.0999993	−	0.117728i
$298$	6.41829	+	4.87906i	0.371801	+	0.282636i
$299$	1.84403	+	11.2481i	0.106643	+	0.650493i
$300$	−1.42905	−	2.69547i	−0.0825061	−	0.155623i
$301$	−22.1254	+	4.87017i	−1.27529	+	0.280712i
$302$	5.13854	+	0.558850i	0.295690	+	0.0321582i
$303$	−3.32234	−	1.99899i	−0.190864	−	0.114839i
$304$	0.809461	+	2.91541i	0.0464258	+	0.167210i
$305$	−17.6261	−	3.87980i	−1.00927	−	0.222157i
$306$	−0.231570	−	0.0780251i	−0.0132380	−	0.00446040i
$307$	−7.12442	+	13.4381i	−0.406612	+	0.766952i	−0.999258	−	0.0385111i	$-0.987739\pi$
$307$	−7.12442	+	13.4381i	−0.406612	+	0.766952i	0.592646	+	0.805463i	$0.298083\pi$
$308$	−2.53443	+	9.12818i	−0.144412	+	0.520126i
$309$	−5.38198	+	5.09808i	−0.306170	+	0.290020i
$310$	0.195836	−	1.19454i	0.0111227	−	0.0678456i
$311$	17.2418	−	5.80944i	0.977692	−	0.329423i	0.215307	−	0.976546i	$-0.430925\pi$
$311$	17.2418	−	5.80944i	0.977692	−	0.329423i	0.762385	+	0.647123i	$0.224028\pi$
$312$	3.30028	−	0.358927i	0.186842	−	0.0203203i
$313$	−25.5045	−	11.7996i	−1.44160	−	0.666954i	−0.465652	−	0.884968i	$-0.654180\pi$
$313$	−25.5045	−	11.7996i	−1.44160	−	0.666954i	−0.975946	+	0.218014i	$0.930042\pi$
$314$	−0.273365	+	5.04192i	−0.0154269	+	0.284532i
$315$	−3.95534	+	3.00677i	−0.222858	+	0.169412i
$316$	−9.47011	−	8.97057i	−0.532736	−	0.504634i
$317$	12.1537	−	7.31266i	0.682622	−	0.410720i	−0.131577	−	0.991306i	$-0.542004\pi$
$317$	12.1537	−	7.31266i	0.682622	−	0.410720i	0.814199	+	0.580586i	$0.197177\pi$
$318$	−5.29328	+	2.44893i	−0.296832	+	0.137329i
$319$	2.33515	+	5.86080i	0.130744	+	0.328142i
$320$	−0.783483	+	1.15555i	−0.0437980	+	0.0645972i
$321$	−1.02880	−	1.51736i	−0.0574218	−	0.0846909i
$322$	4.52267	−	11.3511i	0.252039	−	0.632569i
$323$	0.0400284	+	0.738281i	0.00222724	+	0.0410791i
$324$	0.647386	+	0.762162i	0.0359659	+	0.0423423i
$325$	6.55677	+	7.71923i	0.363704	+	0.428186i
$326$	−0.637816	−	11.7638i	−0.0353253	−	0.651538i
$327$	4.18165	−	10.4951i	0.231246	−	0.580383i
$328$	7.04007	+	10.3833i	0.388723	+	0.573323i
$329$	−18.0610	+	26.6379i	−0.995734	+	1.46860i
$330$	−1.37562	−	3.45254i	−0.0757252	−	0.190056i
$331$	−29.6328	+	13.7096i	−1.62877	+	0.753548i	−0.999716	−	0.0238161i	$-0.992418\pi$
$331$	−29.6328	+	13.7096i	−1.62877	+	0.753548i	−0.629051	+	0.777364i	$0.716556\pi$
$332$	8.50655	−	5.11822i	0.466858	−	0.280899i
$333$	3.59348	+	3.40393i	0.196922	+	0.186534i
$334$	6.39585	−	4.86200i	0.349965	−	0.266037i
$335$	−0.787290	+	14.5207i	−0.0430143	+	0.793351i
$336$	−3.22984	−	1.49428i	−0.176202	−	0.0815198i
$337$	−21.7490	+	2.36534i	−1.18474	+	0.128848i	−0.679200	−	0.733954i	$-0.737673\pi$
$337$	−21.7490	+	2.36534i	−1.18474	+	0.128848i	−0.505542	+	0.862802i	$0.668707\pi$
$338$	1.87569	−	0.631995i	0.102024	−	0.0343760i
$339$	−0.379757	+	2.31642i	−0.0206256	+	0.125810i
$340$	−0.247679	+	0.234614i	−0.0134323	+	0.0127237i
$341$	−0.617478	+	2.22395i	−0.0334383	+	0.120434i
$342$	1.41726	−	2.67324i	0.0766368	−	0.144552i
$343$	−4.50313	−	1.51728i	−0.243146	−	0.0819255i
$344$	6.21718	+	1.36850i	0.335208	+	0.0737848i
$345$	1.28240	+	4.61880i	0.0690423	+	0.248668i
$346$	−17.1682	−	10.3298i	−0.922969	−	0.555332i
$347$	4.32914	+	0.470822i	0.232400	+	0.0252751i	0.223578	−	0.974686i	$-0.428226\pi$
$347$	4.32914	+	0.470822i	0.232400	+	0.0252751i	0.00882230	+	0.999961i	$0.497192\pi$
$348$	−2.31455	+	0.509470i	−0.124073	+	0.0273105i
$349$	−9.02371	−	17.0205i	−0.483028	−	0.911088i	−0.998530	−	0.0541996i	$-0.982739\pi$
$349$	−9.02371	−	17.0205i	−0.483028	−	0.911088i	0.515502	−	0.856889i	$-0.327606\pi$
$350$	−1.75651	−	10.7142i	−0.0938893	−	0.572700i
$351$	−2.64282	−	2.00902i	−0.141064	−	0.107234i
$352$	1.72336	−	2.02889i	0.0918552	−	0.108140i
$353$	18.4103			0.979884			0.489942	−	0.871755i	$-0.337018\pi$
$353$	18.4103			0.979884			0.489942	+	0.871755i	$0.337018\pi$
$354$	−7.52186	−	1.55618i	−0.399782	−	0.0827098i
$355$	10.4415			0.554178
$356$	−2.19355	+	2.58245i	−0.116258	+	0.136870i
$357$	−0.692301	−	0.526274i	−0.0366405	−	0.0278534i
$358$	−3.53401	−	21.5565i	−0.186778	−	1.13930i
$359$	−10.7847	−	20.3420i	−0.569193	−	1.07361i	−0.986332	−	0.164769i	$-0.947312\pi$
$359$	−10.7847	−	20.3420i	−0.569193	−	1.07361i	0.417139	−	0.908842i	$-0.363033\pi$
$360$	1.36348	−	0.300124i	0.0718615	−	0.0158179i
$361$	9.78742	+	1.06445i	0.515128	+	0.0560235i
$362$	−8.57460	−	5.15916i	−0.450671	−	0.271160i
$363$	−1.04701	−	3.77098i	−0.0549537	−	0.197925i
$364$	11.5379	+	2.53969i	0.604753	+	0.133116i
$365$	4.92336	+	1.65887i	0.257700	+	0.0868293i
$366$	−6.05527	+	11.4214i	−0.316514	+	0.597009i
$367$	5.71047	−	20.5673i	0.298084	−	1.07360i	−0.651129	−	0.758967i	$-0.725704\pi$
$367$	5.71047	−	20.5673i	0.298084	−	1.07360i	0.949213	−	0.314635i	$-0.101882\pi$
$368$	−2.49268	+	2.36120i	−0.129940	+	0.123086i
$369$	2.02955	−	12.3797i	0.105654	−	0.644462i
$370$	6.54866	−	2.20650i	0.340449	−	0.114711i
$371$	−20.6342	+	2.24410i	−1.07127	+	0.116508i
$372$	−0.786905	−	0.364061i	−0.0407991	−	0.0188757i
$373$	−0.640009	+	11.8043i	−0.0331384	+	0.611202i	0.934050	+	0.357142i	$0.116249\pi$
$373$	−0.640009	+	11.8043i	−0.0331384	+	0.611202i	−0.967188	+	0.254060i	$0.918234\pi$
$374$	0.517856	−	0.393664i	0.0267777	−	0.0203559i
$375$	8.16014	+	7.72970i	0.421388	+	0.399160i
$376$	7.74897	−	4.66240i	0.399623	−	0.240445i
$377$	7.14048	−	3.30354i	0.367753	−	0.170141i
$378$	1.31723	+	3.30600i	0.0677511	+	0.170042i
$379$	15.1379	−	22.3268i	0.777583	−	1.14685i	−0.208078	−	0.978112i	$-0.566721\pi$
$379$	15.1379	−	22.3268i	0.777583	−	1.14685i	0.985661	−	0.168737i	$-0.0539687\pi$
$380$	−2.37058	−	3.49635i	−0.121608	−	0.179359i
$381$	−1.26749	+	3.18116i	−0.0649354	+	0.162976i
$382$	−0.449777	−	8.29564i	−0.0230126	−	0.424442i
$383$	5.49879	+	6.47367i	0.280975	+	0.330789i	0.884487	−	0.466564i	$-0.154508\pi$
$383$	5.49879	+	6.47367i	0.280975	+	0.330789i	−0.603512	+	0.797354i	$0.706233\pi$
$384$	0.647386	+	0.762162i	0.0330368	+	0.0388939i
$385$	−0.716046	−	13.2067i	−0.0364931	−	0.673076i
$386$	5.77267	−	14.4883i	0.293821	−	0.737435i
$387$	−3.57252	−	5.26908i	−0.181602	−	0.267842i
$388$	−4.34639	+	6.41045i	−0.220655	+	0.325441i
$389$	−9.07216	−	22.7694i	−0.459977	−	1.15445i	−0.957866	−	0.287214i	$-0.907271\pi$
$389$	−9.07216	−	22.7694i	−0.459977	−	1.15445i	0.497889	−	0.867241i	$-0.334109\pi$
$390$	−4.20638	+	1.94608i	−0.212999	+	0.0985436i
$391$	−0.718911	+	0.432554i	−0.0363569	+	0.0218752i
$392$	−4.11257	−	3.89564i	−0.207716	−	0.196759i
$393$	2.68185	−	2.03869i	0.135281	−	0.102838i
$394$	−0.177344	+	3.27091i	−0.00893445	+	0.164786i
$395$	16.5282	+	7.64676i	0.831624	+	0.384750i
$396$	−2.64642	+	0.287815i	−0.132988	+	0.0144633i
$397$	−29.8159	+	10.0461i	−1.49642	+	0.504201i	−0.944164	−	0.329476i	$-0.893128\pi$
$397$	−29.8159	+	10.0461i	−1.49642	+	0.504201i	−0.552252	+	0.833677i	$0.686231\pi$
$398$	1.36203	−	8.30800i	0.0682723	−	0.416443i
$399$	7.81732	−	7.40496i	0.391356	−	0.370712i
$400$	−0.816191	+	2.93965i	−0.0408095	+	0.146983i
$401$	−12.8929	+	24.3186i	−0.643840	+	1.21441i	0.319870	+	0.947461i	$0.396361\pi$
$401$	−12.8929	+	24.3186i	−0.643840	+	1.21441i	−0.963710	+	0.266950i	$0.913984\pi$
$402$	9.87081	+	3.32586i	0.492311	+	0.165879i
$403$	2.81106	+	0.618761i	0.140029	+	0.0308227i
$404$	1.03730	+	3.73603i	0.0516078	+	0.185874i
$405$	−1.19627	−	0.719773i	−0.0594433	−	0.0357658i
$406$	−8.38465	−	0.911885i	−0.416123	−	0.0452561i
$407$	−12.8682	+	2.83251i	−0.637855	+	0.140403i
$408$	0.114461	+	0.215897i	0.00566667	+	0.0106885i
$409$	3.69196	+	22.5199i	0.182556	+	1.11354i	0.906038	+	0.423197i	$0.139092\pi$
$409$	3.69196	+	22.5199i	0.182556	+	1.11354i	−0.723482	+	0.690343i	$0.757460\pi$
$410$	−13.9430	−	10.5992i	−0.688594	−	0.523455i
$411$	−6.08709	+	7.16628i	−0.300254	+	0.353486i
$412$	7.41324			0.365224
$413$	−23.5989	−	13.7954i	−1.16123	−	0.678825i
$414$	3.43347			0.168746
$415$	−8.97285	+	10.5637i	−0.440460	+	0.518549i
$416$	−2.64282	−	2.00902i	−0.129575	−	0.0985005i
$417$	3.16232	+	19.2893i	0.154859	+	0.944601i
$418$	3.77279	+	7.11623i	0.184533	+	0.348066i
$419$	21.6927	−	4.77492i	1.05976	−	0.233270i	0.349300	−	0.937011i	$-0.386419\pi$
$419$	21.6927	−	4.77492i	1.05976	−	0.233270i	0.710457	+	0.703741i	$0.248488\pi$
$420$	4.93931	+	0.537183i	0.241014	+	0.0262118i
$421$	33.9152	+	20.4061i	1.65293	+	0.994533i	0.962558	+	0.271077i	$0.0873797\pi$
$421$	33.9152	+	20.4061i	1.65293	+	0.994533i	0.690370	+	0.723457i	$0.257448\pi$
$422$	3.63023	+	13.0749i	0.176717	+	0.636477i
$423$	−8.83205	−	1.94408i	−0.429429	−	0.0945244i
$424$	5.52703	+	1.86227i	0.268416	+	0.0904399i
$425$	−0.349205	+	0.658670i	−0.0169389	+	0.0319502i
$426$	2.00084	−	7.20636i	0.0969408	−	0.349149i
$427$	−33.3996	+	31.6377i	−1.61632	+	1.53106i
$428$	−0.296587	+	1.80910i	−0.0143361	+	0.0874462i
$429$	8.37463	−	2.82174i	0.404331	−	0.136235i
$430$	−8.83559	+	0.960929i	−0.426090	+	0.0463401i
$431$	10.2249	+	4.73056i	0.492518	+	0.227863i	0.650396	−	0.759596i	$-0.274603\pi$
$431$	10.2249	+	4.73056i	0.492518	+	0.227863i	−0.157878	+	0.987459i	$0.550465\pi$
$432$	0.0541389	−	0.998533i	0.00260476	−	0.0480420i
$433$	9.45329	−	7.18620i	0.454296	−	0.345347i	−0.352869	−	0.935673i	$-0.614794\pi$
$433$	9.45329	−	7.18620i	0.454296	−	0.345347i	0.807165	+	0.590326i	$0.201001\pi$
$434$	−2.24012	−	2.12196i	−0.107529	−	0.101857i
$435$	2.83511	−	1.70583i	0.135933	−	0.0817883i
$436$	−10.2534	+	4.74371i	−0.491047	+	0.227183i
$437$	−3.84524	−	9.65082i	−0.183943	−	0.461661i
$438$	2.08832	−	3.08005i	0.0997840	−	0.147170i
$439$	5.79875	+	8.55252i	0.276759	+	0.408189i	0.940511	−	0.339764i	$-0.110347\pi$
$439$	5.79875	+	8.55252i	0.276759	+	0.408189i	−0.663752	+	0.747953i	$0.731037\pi$
$440$	−1.37562	+	3.45254i	−0.0655799	+	0.164593i
$441$	0.306683	+	5.65643i	0.0146039	+	0.269354i
$442$	−0.525172	−	0.618280i	−0.0249799	−	0.0294086i
$443$	−20.8681	−	24.5679i	−0.991474	−	1.16725i	−0.985911	−	0.167269i	$-0.946505\pi$
$443$	−20.8681	−	24.5679i	−0.991474	−	1.16725i	−0.00556325	−	0.999985i	$-0.501771\pi$
$444$	−0.267973	−	4.94247i	−0.0127174	−	0.234559i
$445$	1.75094	−	4.39452i	0.0830024	−	0.208320i
$446$	−10.6758	−	15.7457i	−0.505516	−	0.745580i
$447$	−4.52442	+	6.67302i	−0.213998	+	0.315623i
$448$	1.31723	+	3.30600i	0.0622333	+	0.156194i
$449$	−29.5914	+	13.6904i	−1.39650	+	0.646091i	−0.966484	−	0.256728i	$-0.917355\pi$
$449$	−29.5914	+	13.6904i	−1.39650	+	0.646091i	−0.430020	+	0.902820i	$0.641493\pi$
$450$	2.61415	−	1.57288i	0.123232	−	0.0741463i
$451$	24.2446	+	22.9657i	1.14163	+	1.08141i
$452$	1.86870	−	1.42055i	0.0878962	−	0.0668170i
$453$	−0.279835	+	5.16126i	−0.0131478	+	0.242497i
$454$	19.2544	+	8.90802i	0.903652	+	0.418074i
$455$	−16.3972	+	1.78331i	−0.768715	+	0.0836028i
$456$	−2.86731	+	0.966111i	−0.134274	+	0.0452423i
$457$	5.31556	−	32.4235i	0.248651	−	1.51671i	−0.507122	−	0.861874i	$-0.669291\pi$
$457$	5.31556	−	32.4235i	0.248651	−	1.51671i	0.755774	−	0.654833i	$-0.227261\pi$
$458$	−20.8523	+	19.7523i	−0.974362	+	0.922965i
$459$	0.0653737	−	0.235455i	0.00305138	−	0.0109901i
$460$	2.24533	−	4.23514i	0.104689	−	0.197464i
$461$	17.3047	+	5.83064i	0.805961	+	0.271560i	0.691974	−	0.721922i	$-0.256741\pi$
$461$	17.3047	+	5.83064i	0.805961	+	0.271560i	0.113987	+	0.993482i	$0.463638\pi$
$462$	−9.25200	−	2.03652i	−0.430442	−	0.0947475i
$463$	1.21538	+	4.37741i	0.0564836	+	0.203436i	0.986408	−	0.164316i	$-0.0525416\pi$
$463$	1.21538	+	4.37741i	0.0564836	+	0.203436i	−0.929924	+	0.367751i	$0.880128\pi$
$464$	2.03071	+	1.22184i	0.0942735	+	0.0567225i
$465$	1.20339	+	0.130877i	0.0558061	+	0.00606928i
$466$	13.8264	−	3.04343i	0.640498	−	0.140984i
$467$	1.81537	+	3.42415i	0.0840053	+	0.158451i	0.921955	−	0.387296i	$-0.126591\pi$
$467$	1.81537	+	3.42415i	0.0840053	+	0.158451i	−0.837950	+	0.545747i	$0.816246\pi$
$468$	0.537075	+	3.27601i	0.0248263	+	0.151434i
$469$	29.5097	+	22.4327i	1.36263	+	1.03585i
$470$	−8.17374	+	9.62287i	−0.377026	+	0.443870i
$471$	−5.04932			−0.232661
$472$	4.39065	+	6.30255i	0.202096	+	0.290099i
$473$	16.9465			0.779199
$474$	8.44471	−	9.94188i	0.387878	−	0.456646i
$475$	−7.34872	−	5.58635i	−0.337182	−	0.256319i
$476$	0.140689	+	0.858168i	0.00644849	+	0.0393341i
$477$	−2.73191	−	5.15294i	−0.125086	−	0.235937i
$478$	12.2881	−	2.70482i	0.562046	−	0.123716i
$479$	−36.7804	−	4.00010i	−1.68054	−	0.182769i	−0.782488	−	0.622665i	$-0.786050\pi$
$479$	−36.7804	−	4.00010i	−1.68054	−	0.182769i	−0.898049	+	0.439896i	$0.855015\pi$
$480$	−1.19627	−	0.719773i	−0.0546021	−	0.0328530i
$481$	4.39598	+	15.8329i	0.200440	+	0.721918i
$482$	−0.0214258	−	0.00471617i	−0.000975918	−	0.000214816i
$483$	11.5793	+	3.90151i	0.526874	+	0.177525i
$484$	−1.83318	+	3.45774i	−0.0833263	+	0.157170i
$485$	2.89276	−	10.4188i	0.131354	−	0.473093i
$486$	−0.725995	+	0.687699i	−0.0329318	+	0.0311947i
$487$	2.60744	−	15.9047i	0.118154	−	0.720709i	−0.859602	−	0.510964i	$-0.829288\pi$
$487$	2.60744	−	15.9047i	0.118154	−	0.720709i	0.977756	−	0.209745i	$-0.0672632\pi$
$488$	12.2506	−	4.12771i	0.554560	−	0.186853i
$489$	11.7120	−	1.27376i	0.529637	−	0.0576014i
$490$	7.17768	+	3.32075i	0.324255	+	0.150016i
$491$	−0.651728	+	12.0204i	−0.0294121	+	0.542474i	0.946283	+	0.323340i	$0.104806\pi$
$491$	−0.651728	+	12.0204i	−0.0294121	+	0.542474i	−0.975695	+	0.219134i	$0.929677\pi$
$492$	−9.98696	+	7.59189i	−0.450247	+	0.342269i
$493$	0.420443	+	0.398265i	0.0189358	+	0.0179369i
$494$	8.60674	−	5.17851i	0.387236	−	0.232992i
$495$	3.37300	−	1.56052i	0.151605	−	0.0701400i
$496$	0.320925	+	0.805461i	0.0144100	+	0.0361663i
$497$	14.9365	−	22.0296i	0.669992	−	0.988164i
$498$	5.57125	+	8.21698i	0.249654	+	0.368212i
$499$	−0.906860	+	2.27605i	−0.0405966	+	0.101890i	−0.947877	−	0.318636i	$-0.896775\pi$
$499$	−0.906860	+	2.27605i	−0.0405966	+	0.101890i	0.907280	+	0.420526i	$0.138154\pi$
$500$	−0.608518	−	11.2235i	−0.0272138	−	0.501928i
$501$	5.20113	+	6.12324i	0.232369	+	0.273566i
$502$	9.62808	+	11.3351i	0.429722	+	0.505908i
$503$	−1.08680	−	20.0448i	−0.0484580	−	0.893755i	−0.917184	−	0.398463i	$-0.869544\pi$
$503$	−1.08680	−	20.0448i	−0.0484580	−	0.893755i	0.868726	−	0.495292i	$-0.164939\pi$
$504$	1.31723	−	3.30600i	0.0586741	−	0.147261i
$505$	−3.03784	−	4.48048i	−0.135182	−	0.199379i
$506$	−5.12924	+	7.56506i	−0.228022	+	0.336308i
$507$	0.732616	+	1.83873i	0.0325366	+	0.0816608i
$508$	3.10787	−	1.43785i	0.137889	−	0.0637944i
$509$	−6.34741	+	3.81911i	−0.281344	+	0.169279i	−0.649231	−	0.760592i	$-0.724909\pi$
$509$	−6.34741	+	3.81911i	−0.281344	+	0.169279i	0.367887	+	0.929871i	$0.380081\pi$
$510$	−0.247679	−	0.234614i	−0.0109674	−	0.0103889i
$511$	10.5427	−	8.01436i	0.466382	−	0.354534i
$512$	0.0541389	−	0.998533i	0.00239262	−	0.0441294i
$513$	2.74605	+	1.27046i	0.121241	+	0.0560921i
$514$	24.7922	−	2.69632i	1.09354	−	0.118930i
$515$	−9.80797	+	3.30469i	−0.432191	+	0.145622i
$516$	−1.02991	+	6.28215i	−0.0453391	+	0.276556i
$517$	17.4776	−	16.5556i	0.768663	−	0.728116i
$518$	4.71248	−	16.9728i	0.207054	−	0.745743i
$519$	9.38516	−	17.7023i	0.411963	−	0.777044i
$520$	4.39213	+	1.47988i	0.192608	+	0.0648971i
$521$	27.1572	+	5.97776i	1.18978	+	0.261890i	0.765377	−	0.643583i	$-0.222553\pi$
$521$	27.1572	+	5.97776i	1.18978	+	0.261890i	0.424404	+	0.905473i	$0.360484\pi$
$522$	−0.634030	−	2.28357i	−0.0277507	−	0.0999491i
$523$	7.78557	+	4.68442i	0.340439	+	0.204835i	0.675498	−	0.737362i	$-0.263929\pi$
$523$	7.78557	+	4.68442i	0.340439	+	0.204835i	−0.335059	+	0.942197i	$0.608756\pi$
$524$	−3.34901	−	0.364227i	−0.146302	−	0.0159113i
$525$	10.6034	−	2.33399i	0.462771	−	0.101864i
$526$	−2.14162	−	4.03952i	−0.0933790	−	0.176131i
$527$	0.0342770	+	0.209081i	0.00149313	+	0.00910770i
$528$	2.11922	+	1.61099i	0.0922271	+	0.0701092i
$529$	−7.25803	+	8.54482i	−0.315567	+	0.371514i
$530$	−8.14262			−0.353693
$531$	1.14667	−	7.59507i	0.0497612	−	0.329598i
$532$	−10.7677			−0.466840
$533$	26.9611	−	31.7410i	1.16781	−	1.37486i
$534$	−2.69742	−	2.05053i	−0.116729	−	0.0887349i
$535$	−0.414070	−	2.52572i	−0.0179018	−	0.109196i
$536$	−4.87897	−	9.20272i	−0.210739	−	0.397497i
$537$	21.3336	−	4.69587i	0.920611	−	0.202642i
$538$	18.1927	+	1.97858i	0.784344	+	0.0853026i
$539$	−12.9211	−	7.77438i	−0.556552	−	0.334866i
$540$	0.373501	+	1.34523i	0.0160729	+	0.0578894i
$541$	16.2894	+	3.58558i	0.700338	+	0.154156i	0.550846	−	0.834607i	$-0.314305\pi$
$541$	16.2894	+	3.58558i	0.700338	+	0.154156i	0.149492	+	0.988763i	$0.452236\pi$
$542$	24.1761	+	8.14588i	1.03845	+	0.349896i
$543$	4.68738	−	8.84133i	0.201155	−	0.379418i
$544$	0.0653737	−	0.235455i	0.00280287	−	0.0100950i
$545$	11.4509	−	10.8469i	0.490502	−	0.464628i
$546$	−1.91132	+	11.6585i	−0.0817968	+	0.498939i
$547$	−39.4665	+	13.2978i	−1.68747	+	0.568573i	−0.989110	−	0.147178i	$-0.952981\pi$
$547$	−39.4665	+	13.2978i	−1.68747	+	0.568573i	−0.698355	+	0.715751i	$0.746084\pi$
$548$	9.34744	−	1.01660i	0.399303	−	0.0434268i
$549$	−11.7325	−	5.42804i	−0.500732	−	0.231663i
$550$	−0.439687	+	8.10954i	−0.0187483	+	0.345792i
$551$	−5.70860	+	4.33957i	−0.243195	+	0.184872i
$552$	−2.49268	−	2.36120i	−0.106096	−	0.100499i
$553$	39.7766	−	23.9328i	1.69147	−	1.01773i
$554$	0.845702	−	0.391264i	0.0359304	−	0.0166232i
$555$	2.55780	+	6.41960i	0.108573	+	0.272497i
$556$	10.9694	−	16.1787i	0.465207	−	0.686128i
$557$	5.68530	+	8.38519i	0.240894	+	0.355292i	0.928847	−	0.370463i	$-0.120801\pi$
$557$	5.68530	+	8.38519i	0.240894	+	0.355292i	−0.687953	+	0.725755i	$0.741491\pi$
$558$	0.320925	−	0.805461i	0.0135858	−	0.0340979i
$559$	−1.14415	−	21.1025i	−0.0483922	−	0.892542i
$560$	−3.21650	−	3.78675i	−0.135922	−	0.160020i
$561$	0.421123	+	0.495784i	0.0177798	+	0.0209320i
$562$	0.370740	+	6.83789i	0.0156387	+	0.288439i
$563$	2.42936	−	6.09723i	0.102385	−	0.256968i	−0.868856	−	0.495065i	$-0.835144\pi$
$563$	2.42936	−	6.09723i	0.102385	−	0.256968i	0.971241	+	0.238097i	$0.0765237\pi$
$564$	5.07508	+	7.48519i	0.213700	+	0.315183i
$565$	−1.83910	+	2.71247i	−0.0773715	+	0.114114i
$566$	10.5526	+	26.4851i	0.443560	+	1.11325i
$567$	−3.22984	+	1.49428i	−0.135640	+	0.0627540i
$568$	−6.40841	+	3.85581i	−0.268891	+	0.161786i
$569$	15.6349	+	14.8101i	0.655447	+	0.620873i	0.941368	−	0.337380i	$-0.109541\pi$
$569$	15.6349	+	14.8101i	0.655447	+	0.620873i	−0.285921	+	0.958253i	$0.592299\pi$
$570$	3.36288	−	2.55640i	0.140856	−	0.107076i
$571$	−2.14849	+	39.6266i	−0.0899116	+	1.65832i	0.511426	+	0.859327i	$0.329117\pi$
$571$	−2.14849	+	39.6266i	−0.0899116	+	1.65832i	−0.601338	+	0.798995i	$0.705365\pi$
$572$	−8.02046	−	3.71066i	−0.335352	−	0.155150i
$573$	8.25913	−	0.898234i	0.345030	−	0.0375243i
$574$	−42.3075	+	14.2550i	−1.76588	+	0.594994i
$575$	1.69467	−	10.3370i	0.0706727	−	0.431084i
$576$	−0.725995	+	0.687699i	−0.0302498	+	0.0286541i
$577$	6.39933	−	23.0483i	0.266408	−	0.959514i	−0.702417	−	0.711766i	$-0.747896\pi$
$577$	6.39933	−	23.0483i	0.266408	−	0.959514i	0.968825	−	0.247748i	$-0.0796905\pi$
$578$	−7.93497	+	14.9669i	−0.330051	+	0.622543i
$579$	14.7796	+	4.97982i	0.614218	+	0.206954i
$580$	−3.23138	−	0.711280i	−0.134176	−	0.0295343i
$581$	9.45177	+	34.0422i	0.392125	+	1.41231i
$582$	−6.63636	−	3.99296i	−0.275086	−	0.165514i
$583$	15.4348	+	1.67863i	0.639244	+	0.0695219i
$584$	−3.63426	+	0.799961i	−0.150387	+	0.0331026i
$585$	−2.17096	−	4.09486i	−0.0897580	−	0.169301i
$586$	−4.25441	−	25.9508i	−0.175748	−	1.07202i
$587$	7.16264	+	5.44489i	0.295634	+	0.224735i	0.742467	−	0.669882i	$-0.233655\pi$
$587$	7.16264	+	5.44489i	0.295634	+	0.224735i	−0.446834	+	0.894617i	$0.647448\pi$
$588$	3.66727	−	4.31745i	0.151236	−	0.178049i
$589$	−2.62341			−0.108096
$590$	−8.61855	−	6.38122i	−0.354820	−	0.262711i
$591$	−3.27572			−0.134745
$592$	−3.20439	+	3.77250i	−0.131700	+	0.155049i
$593$	−27.5616	−	20.9518i	−1.13182	−	0.860387i	−0.140270	−	0.990113i	$-0.544797\pi$
$593$	−27.5616	−	20.9518i	−1.13182	−	0.860387i	−0.991550	+	0.129727i	$0.958590\pi$
$594$	−0.430667	−	2.62695i	−0.0176705	−	0.107785i
$595$	−0.568693	−	1.07267i	−0.0233141	−	0.0439751i
$596$	7.87374	−	1.73314i	0.322521	−	0.0709923i
$597$	8.36956	+	0.910244i	0.342543	+	0.0372538i
$598$	9.76666	+	5.87641i	0.399388	+	0.240304i
$599$	−5.92945	−	21.3560i	−0.242271	−	0.872581i	−0.980251	−	0.197758i	$-0.936634\pi$
$599$	−5.92945	−	21.3560i	−0.242271	−	0.872581i	0.737980	−	0.674823i	$-0.235780\pi$
$600$	−2.97953	−	0.655844i	−0.121639	−	0.0267747i
$601$	23.2714	+	7.84104i	0.949259	+	0.319843i	0.750996	−	0.660306i	$-0.229574\pi$
$601$	23.2714	+	7.84104i	0.949259	+	0.319843i	0.198263	+	0.980149i	$0.436470\pi$
$602$	−10.6118	+	20.0160i	−0.432506	+	0.815792i
$603$	−2.78659	+	10.0364i	−0.113479	+	0.408714i
$604$	3.75255	−	3.55461i	0.152689	−	0.144635i
$605$	0.883959	−	5.39191i	0.0359380	−	0.219212i
$606$	−3.67439	+	1.23805i	−0.149262	+	0.0502922i
$607$	−37.2895	+	4.05548i	−1.51354	+	0.164607i	−0.826881	−	0.562377i	$-0.809887\pi$
$607$	−37.2895	+	4.05548i	−1.51354	+	0.164607i	−0.686654	+	0.726984i	$0.740921\pi$
$608$	2.74605	+	1.27046i	0.111367	+	0.0515239i
$609$	0.456612	−	8.42172i	0.0185029	−	0.341265i
$610$	−14.3679	+	10.9222i	−0.581741	+	0.442228i
$611$	−21.7959	−	20.6461i	−0.881766	−	0.835253i
$612$	−0.209383	+	0.125982i	−0.00846381	+	0.00509251i
$613$	14.8488	−	6.86977i	0.599736	−	0.277467i	−0.0964399	−	0.995339i	$-0.530746\pi$
$613$	14.8488	−	6.86977i	0.599736	−	0.277467i	0.696176	+	0.717872i	$0.254883\pi$
$614$	5.62975	+	14.1296i	0.227198	+	0.570224i
$615$	9.82876	−	14.4963i	0.396334	−	0.584549i
$616$	5.31640	+	7.84110i	0.214204	+	0.315927i
$617$	5.83753	−	14.6511i	0.235010	−	0.589831i	−0.763416	−	0.645907i	$-0.776479\pi$
$617$	5.83753	−	14.6511i	0.235010	−	0.589831i	0.998427	+	0.0560757i	$0.0178588\pi$
$618$	0.401344	+	7.40236i	0.0161444	+	0.297767i
$619$	9.21978	+	10.8544i	0.370574	+	0.436274i	0.915566	−	0.402168i	$-0.131743\pi$
$619$	9.21978	+	10.8544i	0.370574	+	0.436274i	−0.544992	+	0.838441i	$0.683467\pi$
$620$	−0.783655	−	0.922590i	−0.0314723	−	0.0370521i
$621$	0.185884	+	3.42843i	0.00745928	+	0.137578i
$622$	6.73437	−	16.9020i	0.270024	−	0.677708i
$623$	−6.76691	−	9.98045i	−0.271111	−	0.399858i
$624$	1.86300	−	2.74771i	0.0745796	−	0.109997i
$625$	0.162112	+	0.406870i	0.00648447	+	0.0162748i
$626$	−25.5045	+	11.7996i	−1.01936	+	0.471608i
$627$	−6.90154	+	4.15252i	−0.275621	+	0.165836i
$628$	3.66579	+	3.47242i	0.146281	+	0.138565i
$629$	−0.962895	+	0.731973i	−0.0383931	+	0.0291857i
$630$	−0.268986	+	4.96115i	−0.0107167	+	0.197657i
$631$	−38.8666	−	17.9816i	−1.54725	−	0.715836i	−0.554079	−	0.832464i	$-0.686929\pi$
$631$	−38.8666	−	17.9816i	−1.54725	−	0.715836i	−0.993176	+	0.116628i	$0.962791\pi$
$632$	−12.9678	+	1.41034i	−0.515833	+	0.0561003i
$633$	−12.8592	+	4.33277i	−0.511107	+	0.172212i
$634$	2.29473	−	13.9972i	0.0911353	−	0.555901i
$635$	−3.47085	+	3.28776i	−0.137736	+	0.130471i
$636$	−1.56031	+	5.61974i	−0.0618705	+	0.222837i
$637$	−8.80864	+	16.6149i	−0.349011	+	0.658305i
$638$	5.97862	+	2.01443i	0.236696	+	0.0797522i
$639$	7.30412	+	1.60776i	0.288946	+	0.0636019i
$640$	0.373501	+	1.34523i	0.0147639	+	0.0531748i
$641$	8.05167	+	4.84453i	0.318022	+	0.191347i	0.665610	−	0.746300i	$-0.268172\pi$
$641$	8.05167	+	4.84453i	0.318022	+	0.191347i	−0.347588	+	0.937647i	$0.612999\pi$
$642$	−1.82250	−	0.198209i	−0.0719285	−	0.00782270i
$643$	−14.3978	+	3.16920i	−0.567795	+	0.124981i	−0.489585	−	0.871956i	$-0.662852\pi$
$643$	−14.3978	+	3.16920i	−0.567795	+	0.124981i	−0.0782101	+	0.996937i	$0.524921\pi$
$644$	−5.72342	−	10.7955i	−0.225535	−	0.425403i
$645$	−1.43787	−	8.77061i	−0.0566160	−	0.345342i
$646$	0.588604	+	0.447445i	0.0231583	+	0.0176045i
$647$	21.5265	−	25.3430i	0.846295	−	0.996335i	−0.153671	−	0.988122i	$-0.549110\pi$
$647$	21.5265	−	25.3430i	0.846295	−	0.996335i	0.999966	−	0.00821338i	$-0.00261443\pi$
$648$	1.00000			0.0392837
$649$	15.0214	+	13.8727i	0.589643	+	0.544552i
$650$	10.1281			0.397255
$651$	1.99757	−	2.35172i	0.0782908	−	0.0921711i
$652$	−9.37885	−	7.12962i	−0.367304	−	0.279217i
$653$	7.69242	+	46.9217i	0.301028	+	1.83619i	0.512358	+	0.858772i	$0.328772\pi$
$653$	7.69242	+	46.9217i	0.301028	+	1.83619i	−0.211330	+	0.977415i	$0.567779\pi$
$654$	−5.29186	−	9.98151i	−0.206928	−	0.390308i
$655$	4.59323	−	1.01105i	0.179472	−	0.0395048i
$656$	12.4714	+	1.35635i	0.486927	+	0.0529565i
$657$	3.18859	+	1.91851i	0.124399	+	0.0748482i
$658$	8.61000	+	31.0104i	0.335653	+	1.20891i
$659$	−18.2538	−	4.01797i	−0.711069	−	0.156518i	−0.155315	−	0.987865i	$-0.549639\pi$
$659$	−18.2538	−	4.01797i	−0.711069	−	0.156518i	−0.555754	+	0.831347i	$0.687570\pi$
$660$	−3.52195	−	1.18668i	−0.137092	−	0.0461916i
$661$	−13.8355	+	26.0965i	−0.538137	+	1.01503i	0.454132	+	0.890934i	$0.349949\pi$
$661$	−13.8355	+	26.0965i	−0.538137	+	1.01503i	−0.992270	+	0.124101i	$0.960395\pi$
$662$	−8.73494	+	31.4604i	−0.339493	+	1.22274i
$663$	0.588941	−	0.557874i	0.0228726	−	0.0216660i
$664$	1.60611	−	9.79684i	0.0623292	−	0.380191i
$665$	14.2461	−	4.80006i	0.552439	−	0.186138i
$666$	4.92072	−	0.535160i	0.190674	−	0.0207370i
$667$	−7.38509	−	3.41671i	−0.285952	−	0.132295i
$668$	0.434954	−	8.02226i	0.0168289	−	0.310391i
$669$	15.1446	−	11.5126i	0.585525	−	0.445104i
$670$	10.5575	+	10.0006i	0.407870	+	0.386355i
$671$	29.4869	−	17.7417i	1.13833	−	0.684910i
$672$	−3.22984	+	1.49428i	−0.124594	+	0.0576432i
$673$	−13.1211	−	32.9315i	−0.505782	−	1.26942i	−0.931229	−	0.364434i	$-0.881263\pi$
$673$	−13.1211	−	32.9315i	−0.505782	−	1.26942i	0.425448	−	0.904983i	$-0.360117\pi$
$674$	−12.2772	+	18.1075i	−0.472900	+	0.697476i
$675$	1.71210	+	2.52516i	0.0658988	+	0.0971935i
$676$	0.732616	−	1.83873i	0.0281776	−	0.0707203i
$677$	0.170502	+	3.14472i	0.00655291	+	0.120861i	0.999980	+	0.00639095i	$0.00203432\pi$
$677$	0.170502	+	3.14472i	0.00655291	+	0.120861i	−0.993427	+	0.114470i	$0.963483\pi$
$678$	1.51963	+	1.78905i	0.0583612	+	0.0687081i
$679$	−17.8436	−	21.0071i	−0.684775	−	0.806180i
$680$	0.0184699	+	0.340657i	0.000708288	+	0.0130636i
$681$	−7.85254	+	19.7084i	−0.300910	+	0.755227i
$682$	1.29527	+	1.91038i	0.0495983	+	0.0731521i
$683$	−3.44478	+	5.08067i	−0.131811	+	0.194406i	−0.887867	−	0.460101i	$-0.847813\pi$
$683$	−3.44478	+	5.08067i	−0.131811	+	0.194406i	0.756056	+	0.654507i	$0.227124\pi$
$684$	−1.11993	−	2.81081i	−0.0428215	−	0.107474i
$685$	−11.9138	+	5.51192i	−0.455203	+	0.210599i
$686$	−4.07168	+	2.44985i	−0.155457	+	0.0935356i
$687$	−20.8523	−	19.7523i	−0.795564	−	0.753598i
$688$	5.06794	−	3.85254i	0.193213	−	0.146877i
$689$	1.04823	−	19.3334i	0.0399343	−	0.736546i
$690$	4.35048	+	2.01275i	0.165620	+	0.0766240i
$691$	35.4820	−	3.85890i	1.34980	−	0.146799i	0.595513	−	0.803346i	$-0.296949\pi$
$691$	35.4820	−	3.85890i	1.34980	−	0.146799i	0.754286	+	0.656546i	$0.227983\pi$
$692$	−18.9874	+	6.39761i	−0.721794	+	0.243201i
$693$	1.53264	−	9.34869i	0.0582202	−	0.355127i
$694$	3.16147	−	2.99470i	0.120008	−	0.113677i
$695$	−7.30074	+	26.2949i	−0.276933	+	0.997423i
$696$	−1.11011	+	2.09388i	−0.0420785	+	0.0793684i
$697$	2.90504	+	0.978822i	0.110036	+	0.0370755i
$698$	−18.8142	−	4.14133i	−0.712129	−	0.156751i
$699$	3.78752	+	13.6414i	0.143257	+	0.515965i
$700$	−9.30312	−	5.59750i	−0.351625	−	0.211566i
$701$	−31.1286	−	3.38543i	−1.17571	−	0.127866i	−0.500664	−	0.865642i	$-0.666911\pi$
$701$	−31.1286	−	3.38543i	−1.17571	−	0.127866i	−0.675046	+	0.737776i	$0.735876\pi$
$702$	−3.24213	+	0.713647i	−0.122366	+	0.0269349i
$703$	−7.01507	−	13.2318i	−0.264579	−	0.499048i
$704$	−0.430667	−	2.62695i	−0.0162314	−	0.0990071i
$705$	−10.0513	−	7.64078i	−0.378553	−	0.287768i
$706$	11.9186	−	14.0317i	0.448563	−	0.528089i
$707$	−13.7986			−0.518949
$708$	−6.05560	+	4.72543i	−0.227584	+	0.177592i
$709$	27.1332			1.01901			0.509504	−	0.860468i	$-0.329829\pi$
$709$	27.1332			1.01901			0.509504	+	0.860468i	$0.329829\pi$
$710$	6.75969	−	7.95813i	0.253687	−	0.298663i
$711$	10.3845	+	7.89408i	0.389449	+	0.296051i
$712$	0.548170	+	3.34369i	0.0205435	+	0.125310i
$713$	−1.39443	−	2.63018i	−0.0522219	−	0.0985010i
$714$	−0.849292	+	0.186943i	−0.0317840	+	0.00699618i
$715$	12.2655	+	1.33395i	0.458703	+	0.0498870i
$716$	−18.7174	−	11.2619i	−0.699503	−	0.420877i
$717$	3.36612	+	12.1237i	0.125710	+	0.452767i
$718$	−22.4858	−	4.94949i	−0.839161	−	0.184713i
$719$	−28.6377	−	9.64917i	−1.06801	−	0.359853i	−0.270223	−	0.962798i	$-0.587098\pi$
$719$	−28.6377	−	9.64917i	−1.06801	−	0.359853i	−0.797783	+	0.602944i	$0.793994\pi$
$720$	0.653953	−	1.23349i	0.0243714	−	0.0459693i
$721$	−7.05790	+	25.4203i	−0.262850	+	0.946700i
$722$	7.14752	−	6.77049i	0.266003	−	0.251972i
$723$	0.00354929	−	0.0216497i	0.000131999	−	0.000805161i
$724$	−9.48320	+	3.19526i	−0.352440	+	0.118751i
$725$	−7.18801	+	0.781743i	−0.266956	+	0.0290332i
$726$	−3.55192	−	1.64329i	−0.131824	−	0.0609883i
$727$	−0.556677	+	10.2673i	−0.0206460	+	0.380793i	0.969890	+	0.243542i	$0.0783095\pi$
$727$	−0.556677	+	10.2673i	−0.0206460	+	0.380793i	−0.990536	+	0.137251i	$0.956173\pi$
$728$	9.40516	−	7.14962i	0.348579	−	0.264983i
$729$	−0.725995	−	0.687699i	−0.0268887	−	0.0254704i
$730$	4.45164	−	2.67846i	0.164763	−	0.0991344i
$731$	1.41183	−	0.653183i	0.0522185	−	0.0241589i
$732$	4.78490	+	12.0092i	0.176855	+	0.443872i
$733$	−26.1065	+	38.5042i	−0.964266	+	1.42219i	−0.0585571	+	0.998284i	$0.518650\pi$
$733$	−26.1065	+	38.5042i	−0.964266	+	1.42219i	−0.905708	+	0.423901i	$0.860660\pi$
$734$	−11.9787	−	17.6673i	−0.442142	−	0.652110i
$735$	−2.92729	+	7.34694i	−0.107975	+	0.270996i
$736$	0.185884	+	3.42843i	0.00685179	+	0.126374i
$737$	−17.9506	−	21.1331i	−0.661219	−	0.778447i
$738$	−8.12144	−	9.56130i	−0.298954	−	0.351956i
$739$	−0.837365	−	15.4443i	−0.0308030	−	0.568128i	−0.972677	−	0.232162i	$-0.925420\pi$
$739$	−0.837365	−	15.4443i	−0.0308030	−	0.568128i	0.941874	−	0.335966i	$-0.109063\pi$
$740$	2.55780	−	6.41960i	0.0940267	−	0.235989i
$741$	5.63687	+	8.31376i	0.207076	+	0.305414i
$742$	−11.6479	+	17.1794i	−0.427608	+	0.630675i
$743$	−0.328536	−	0.824564i	−0.0120528	−	0.0302503i	0.922827	−	0.385214i	$-0.125872\pi$
$743$	−0.328536	−	0.824564i	−0.0120528	−	0.0302503i	−0.934880	+	0.354964i	$0.884493\pi$
$744$	−0.786905	+	0.364061i	−0.0288493	+	0.0133471i
$745$	−9.64463	+	5.80298i	−0.353352	+	0.212605i
$746$	8.58244	+	8.12972i	0.314225	+	0.297650i
$747$	−7.90331	+	6.00794i	−0.289167	+	0.219819i
$748$	0.0352172	−	0.649543i	0.00128767	−	0.0237496i
$749$	−5.92111	−	2.73940i	−0.216353	−	0.100095i
$750$	11.1740	−	1.21525i	0.408019	−	0.0443747i
$751$	−20.0261	+	6.74757i	−0.730762	+	0.246222i	−0.659994	−	0.751271i	$-0.729441\pi$
$751$	−20.0261	+	6.74757i	−0.730762	+	0.246222i	−0.0707673	+	0.997493i	$0.522545\pi$
$752$	1.46307	−	8.92434i	0.0533527	−	0.325437i
$753$	−10.7972	+	10.2276i	−0.393471	+	0.372715i
$754$	2.10482	−	7.58086i	0.0766529	−	0.276079i
$755$	−3.38018	+	6.37569i	−0.123017	+	0.232035i
$756$	3.37247	+	1.13632i	0.122655	+	0.0413274i
$757$	−35.8311	−	7.88702i	−1.30230	−	0.286659i	−0.490936	−	0.871196i	$-0.663345\pi$
$757$	−35.8311	−	7.88702i	−1.30230	−	0.286659i	−0.811367	+	0.584537i	$0.801276\pi$
$758$	−7.21653	−	25.9916i	−0.262116	−	0.944057i
$759$	−7.83165	−	4.71215i	−0.284271	−	0.171040i
$760$	−4.19947	−	0.456720i	−0.152331	−	0.0165670i
$761$	−34.0153	+	7.48734i	−1.23306	+	0.271416i	−0.783248	−	0.621710i	$-0.786438\pi$
$761$	−34.0153	+	7.48734i	−1.23306	+	0.271416i	−0.449808	+	0.893126i	$0.648507\pi$
$762$	1.60400	+	3.02547i	0.0581068	+	0.109601i
$763$	−6.50447	−	39.6755i	−0.235478	−	1.43635i
$764$	−6.61380	−	5.02768i	−0.239279	−	0.181895i
$765$	0.220861	−	0.260017i	0.00798524	−	0.00940095i
$766$	8.49383			0.306895
$767$	16.2608	−	19.6420i	0.587142	−	0.709232i
$768$	1.00000			0.0360844
$769$	29.5805	−	34.8248i	1.06670	−	1.25581i	0.101350	−	0.994851i	$-0.467684\pi$
$769$	29.5805	−	34.8248i	1.06670	−	1.25581i	0.965349	−	0.260964i	$-0.0840403\pi$
$770$	−10.5292	−	8.00409i	−0.379446	−	0.288447i
$771$	4.03459	+	24.6099i	0.145302	+	0.886304i
$772$	−7.30529	−	13.7792i	−0.262923	−	0.495925i
$773$	40.9428	−	9.01220i	1.47261	−	0.324146i	0.595080	−	0.803666i	$-0.297120\pi$
$773$	40.9428	−	9.01220i	1.47261	−	0.324146i	0.877531	+	0.479520i	$0.159189\pi$
$774$	−6.32869	−	0.688287i	−0.227480	−	0.0247400i
$775$	−2.26658	−	1.36375i	−0.0814178	−	0.0489875i
$776$	2.07201	+	7.46269i	0.0743807	+	0.267895i
$777$	17.2031	+	3.78668i	0.617156	+	0.135846i
$778$	−23.2272	−	7.82615i	−0.832735	−	0.280581i
$779$	−17.7795	+	33.5357i	−0.637018	+	1.20154i
$780$	−1.23993	+	4.46581i	−0.0443965	+	0.159902i
$781$	−14.4540	+	13.6915i	−0.517204	+	0.489922i
$782$	−0.135737	+	0.827956i	−0.00485393	+	0.0296076i
$783$	2.24589	−	0.756730i	0.0802617	−	0.0270433i
$784$	−5.63153	+	0.612466i	−0.201126	+	0.0218738i
$785$	−6.39790	−	2.95999i	−0.228351	−	0.105646i
$786$	0.182381	−	3.36382i	0.00650532	−	0.119984i
$787$	25.6453	−	19.4951i	0.914156	−	0.694924i	−0.0384075	−	0.999262i	$-0.512228\pi$
$787$	25.6453	−	19.4951i	0.914156	−	0.694924i	0.952564	+	0.304338i	$0.0984354\pi$
$788$	2.37816	+	2.25271i	0.0847183	+	0.0802494i
$789$	3.91765	−	2.35717i	0.139472	−	0.0839175i
$790$	16.5282	−	7.64676i	0.588047	−	0.272060i
$791$	3.09199	+	7.76030i	0.109938	+	0.275925i
$792$	−1.49389	+	2.20333i	−0.0530832	+	0.0782918i
$793$	−24.0836	−	35.5206i	−0.855233	−	1.26137i
$794$	−11.6456	+	29.2283i	−0.413287	+	1.03727i
$795$	−0.440832	−	8.13067i	−0.0156347	−	0.288365i
$796$	−5.45029	−	6.41657i	−0.193180	−	0.227429i
$797$	18.1377	+	21.3533i	0.642470	+	0.756374i	0.982949	−	0.183878i	$-0.0588651\pi$
$797$	18.1377	+	21.3533i	0.642470	+	0.756374i	−0.340479	+	0.940252i	$0.610589\pi$
$798$	−0.582953	−	10.7519i	−0.0206363	−	0.380614i
$799$	0.817961	−	2.05293i	0.0289374	−	0.0726274i
$800$	1.71210	+	2.52516i	0.0605319	+	0.0892779i
$801$	1.90148	−	2.80448i	0.0671856	−	0.0990914i
$802$	10.1880	+	25.5700i	0.359751	+	0.902908i
$803$	−8.99052	+	4.15946i	−0.317268	+	0.146784i
$804$	8.92508	−	5.37004i	0.314763	−	0.189387i
$805$	12.3847	+	11.7315i	0.436505	+	0.413479i
$806$	2.29144	−	1.74191i	0.0807124	−	0.0613560i
$807$	−0.990742	+	18.2732i	−0.0348758	+	0.643246i
$808$	3.51900	+	1.62806i	0.123798	+	0.0572750i
$809$	−37.4177	+	4.06943i	−1.31554	+	0.143073i	−0.738838	−	0.673883i	$-0.764625\pi$
$809$	−37.4177	+	4.06943i	−1.31554	+	0.143073i	−0.576700	+	0.816956i	$0.695660\pi$
$810$	−1.32303	+	0.445782i	−0.0464867	+	0.0156632i
$811$	0.164616	−	1.00411i	0.00578044	−	0.0352591i	−0.983779	−	0.179386i	$-0.942589\pi$
$811$	0.164616	−	1.00411i	0.00578044	−	0.0352591i	0.989559	+	0.144127i	$0.0460373\pi$
$812$	−6.12311	+	5.80012i	−0.214879	+	0.203544i
$813$	−6.82507	+	24.5817i	−0.239366	+	0.862117i
$814$	−6.17189	+	11.6414i	−0.216325	+	0.408031i
$815$	15.5868	+	5.25180i	0.545982	+	0.183963i
$816$	0.238649	+	0.0525306i	0.00835438	+	0.00183894i
$817$	5.15303	+	18.5596i	0.180282	+	0.649317i
$818$	19.5540	+	11.7652i	0.683688	+	0.411362i
$819$	−11.7449	−	1.27733i	−0.410400	−	0.0446337i
$820$	−17.1048	+	3.76504i	−0.597324	+	0.131481i
$821$	0.352273	+	0.664457i	0.0122944	+	0.0231897i	0.889583	−	0.456773i	$-0.150995\pi$
$821$	0.352273	+	0.664457i	0.0122944	+	0.0231897i	−0.877289	+	0.479963i	$0.840650\pi$
$822$	1.52117	+	9.27870i	0.0530567	+	0.323632i
$823$	37.3672	+	28.4058i	1.30254	+	0.990165i	0.999306	+	0.0372485i	$0.0118593\pi$
$823$	37.3672	+	28.4058i	1.30254	+	0.990165i	0.303234	+	0.952916i	$0.401934\pi$
$824$	4.79923	−	5.65009i	0.167189	−	0.196830i
$825$	−8.12145			−0.282753
$826$	−25.7919	+	9.05526i	−0.897415	+	0.315073i
$827$	31.1862			1.08445			0.542225	−	0.840234i	$-0.317582\pi$
$827$	31.1862			1.08445			0.542225	+	0.840234i	$0.317582\pi$
$828$	2.22278	−	2.61686i	0.0772470	−	0.0909422i
$829$	−26.3143	−	20.0036i	−0.913934	−	0.694755i	0.0385780	−	0.999256i	$-0.487717\pi$
$829$	−26.3143	−	20.0036i	−0.913934	−	0.694755i	−0.952512	+	0.304501i	$0.901510\pi$
$830$	2.24232	+	13.6775i	0.0778320	+	0.474754i
$831$	0.436475	+	0.823279i	0.0151412	+	0.0285592i
$832$	−3.24213	+	0.713647i	−0.112401	+	0.0247412i
$833$	−1.37613	−	0.149663i	−0.0476801	−	0.00518552i
$834$	16.7488	+	10.0774i	0.579964	+	0.348953i
$835$	3.00072	+	10.8076i	0.103844	+	0.374013i
$836$	7.86618	+	1.73148i	0.272057	+	0.0598844i
$837$	0.821654	+	0.276848i	0.0284005	+	0.00956925i
$838$	10.4043	−	19.6246i	0.359410	−	0.677919i
$839$	−10.9678	+	39.5026i	−0.378652	+	1.36378i	0.491449	+	0.870906i	$0.336467\pi$
$839$	−10.9678	+	39.5026i	−0.378652	+	1.36378i	−0.870101	+	0.492874i	$0.835946\pi$
$840$	3.60706	−	3.41679i	0.124456	−	0.117891i
$841$	3.78300	−	23.0753i	0.130448	−	0.795699i
$842$	37.5090	−	12.6383i	1.29265	−	0.435543i
$843$	−6.80779	+	0.740392i	−0.234473	+	0.0255005i
$844$	12.3154	+	5.69769i	0.423912	+	0.196123i
$845$	−0.149604	+	2.75929i	−0.00514654	+	0.0949224i
$846$	−7.19945	+	5.47288i	−0.247522	+	0.188161i
$847$	−10.1114	−	9.57805i	−0.347433	−	0.329106i
$848$	4.99748	−	3.00688i	0.171614	−	0.103257i
$849$	−25.8750	+	11.9710i	−0.888027	+	0.410845i
$850$	0.275943	+	0.692564i	0.00946476	+	0.0237548i
$851$	9.53723	−	14.0664i	0.326932	−	0.482189i
$852$	−4.19710	−	6.19026i	−0.143790	−	0.212075i
$853$	2.65664	−	6.66766i	0.0909616	−	0.228296i	−0.876456	−	0.481482i	$-0.840099\pi$
$853$	2.65664	−	6.66766i	0.0909616	−	0.228296i	0.967418	+	0.253185i	$0.0814782\pi$
$854$	2.49067	+	45.9377i	0.0852290	+	1.57196i
$855$	2.73471	+	3.21955i	0.0935251	+	0.110106i
$856$	1.18682	+	1.39723i	0.0405647	+	0.0477565i
$857$	0.434365	+	8.01140i	0.0148376	+	0.273664i	0.996533	+	0.0832039i	$0.0265153\pi$
$857$	0.434365	+	8.01140i	0.0148376	+	0.273664i	−0.981695	+	0.190460i	$0.939002\pi$
$858$	3.27100	−	8.20958i	0.111670	−	0.280271i
$859$	−16.3965	−	24.1830i	−0.559441	−	0.825114i	0.437821	−	0.899062i	$-0.355750\pi$
$859$	−16.3965	−	24.1830i	−0.559441	−	0.825114i	−0.997262	+	0.0739485i	$0.976440\pi$
$860$	−4.98766	+	7.35625i	−0.170078	+	0.250846i
$861$	−16.5246	−	41.4737i	−0.563157	−	1.41342i
$862$	10.2249	−	4.73056i	0.348263	−	0.161124i
$863$	4.08459	−	2.45762i	0.139041	−	0.0836583i	−0.444334	−	0.895861i	$-0.646559\pi$
$863$	4.08459	−	2.45762i	0.139041	−	0.0836583i	0.583375	+	0.812203i	$0.301732\pi$
$864$	−0.725995	−	0.687699i	−0.0246989	−	0.0233960i
$865$	22.2691	−	16.9285i	0.757172	−	0.575587i
$866$	0.642878	−	11.8572i	0.0218459	−	0.402924i
$867$	−15.3746	−	7.11304i	−0.522148	−	0.241572i
$868$	−3.06750	+	0.333611i	−0.104118	+	0.0113235i
$869$	−32.9066	+	11.0875i	−1.11628	+	0.376118i
$870$	0.535293	−	3.26515i	0.0181481	−	0.110699i
$871$	−25.1039	+	23.7797i	−0.850615	+	0.805745i
$872$	−3.02241	+	10.8857i	−0.102352	+	0.368638i
$873$	3.62782	−	6.84280i	0.122783	−	0.231594i
$874$	−9.84484	−	3.31711i	−0.333007	−	0.112203i
$875$	39.0650	+	8.59886i	1.32064	+	0.290694i
$876$	−0.995543	−	3.58562i	−0.0336363	−	0.121147i
$877$	−18.7711	−	11.2942i	−0.633854	−	0.381377i	0.162065	−	0.986780i	$-0.448185\pi$
$877$	−18.7711	−	11.2942i	−0.633854	−	0.381377i	−0.795919	+	0.605403i	$0.793012\pi$
$878$	10.2724	+	1.11719i	0.346678	+	0.0377035i
$879$	25.6824	−	5.65312i	0.866245	−	0.190675i
$880$	1.74084	+	3.28357i	0.0586836	+	0.110689i
$881$	0.629003	+	3.83675i	0.0211917	+	0.129263i	0.995304	−	0.0968029i	$-0.0308617\pi$
$881$	0.629003	+	3.83675i	0.0211917	+	0.129263i	−0.974112	+	0.226066i	$0.927413\pi$
$882$	4.50966	+	3.42815i	0.151848	+	0.115432i
$883$	9.64414	−	11.3540i	0.324551	−	0.382091i	−0.575554	−	0.817764i	$-0.695214\pi$
$883$	9.64414	−	11.3540i	0.324551	−	0.382091i	0.900105	+	0.435673i	$0.143489\pi$
$884$	−0.811218			−0.0272842
$885$	5.90526	−	8.95138i	0.198503	−	0.300897i
$886$	−32.2344			−1.08294
$887$	23.5797	−	27.7601i	0.791728	−	0.932095i	−0.207204	−	0.978298i	$-0.566436\pi$
$887$	23.5797	−	27.7601i	0.791728	−	0.932095i	0.998932	+	0.0462033i	$0.0147122\pi$
$888$	−3.94045	−	2.99545i	−0.132233	−	0.100521i
$889$	1.97155	+	12.0259i	0.0661237	+	0.403337i
$890$	−2.21580	−	4.17945i	−0.0742739	−	0.140095i
$891$	2.59979	−	0.572256i	0.0870961	−	0.0191713i
$892$	−18.9122	−	2.05682i	−0.633226	−	0.0688675i
$893$	23.4461	+	14.1070i	0.784593	+	0.472074i
$894$	2.15688	+	7.76836i	0.0721367	+	0.259813i
$895$	29.7841	+	6.55599i	0.995574	+	0.219142i
$896$	3.37247	+	1.13632i	0.112666	+	0.0379616i
$897$	−5.33903	+	10.0705i	−0.178265	+	0.336244i
$898$	−8.72272	+	31.4164i	−0.291081	+	1.04838i
$899$	−1.49181	+	1.41312i	−0.0497547	+	0.0471301i
$900$	0.493574	−	3.01067i	0.0164525	−	0.100356i
$901$	1.35059	−	0.455068i	0.0449948	−	0.0151605i
$902$	33.1992	−	3.61063i	1.10541	−	0.120221i
$903$	−20.5612	−	9.51262i	−0.684233	−	0.316560i
$904$	0.127082	−	2.34390i	0.00422670	−	0.0779568i
$905$	11.1222	−	8.45488i	0.369715	−	0.281050i
$906$	3.75255	+	3.55461i	0.124670	+	0.118094i
$907$	41.3955	−	24.9068i	1.37452	−	0.827018i	0.379352	−	0.925253i	$-0.376147\pi$
$907$	41.3955	−	24.9068i	1.37452	−	0.827018i	0.995163	+	0.0982343i	$0.0313195\pi$
$908$	19.2544	−	8.90802i	0.638979	−	0.295623i
$909$	−1.43516	−	3.60198i	−0.0476012	−	0.119470i
$910$	−9.25618	+	13.6518i	−0.306840	+	0.452554i
$911$	20.8209	+	30.7086i	0.689828	+	1.01742i	0.997818	+	0.0660308i	$0.0210336\pi$
$911$	20.8209	+	30.7086i	0.689828	+	1.01742i	−0.307989	+	0.951390i	$0.599656\pi$
$912$	−1.11993	+	2.81081i	−0.0370845	+	0.0930751i
$913$	−1.43076	−	26.3888i	−0.0473512	−	0.873341i
$914$	−21.2707	−	25.0418i	−0.703573	−	0.828311i
$915$	−11.6841	−	13.7555i	−0.386263	−	0.454744i
$916$	1.55499	+	28.6802i	0.0513785	+	0.947620i
$917$	4.43744	−	11.1371i	0.146537	−	0.367780i
$918$	−0.137133	−	0.202256i	−0.00452605	−	0.00667543i
$919$	4.32068	−	6.37253i	0.142526	−	0.210210i	−0.749725	−	0.661749i	$-0.769814\pi$
$919$	4.32068	−	6.37253i	0.142526	−	0.210210i	0.892252	+	0.451539i	$0.149125\pi$
$920$	−1.77427	−	4.45307i	−0.0584958	−	0.146813i
$921$	−13.8041	+	6.38645i	−0.454860	+	0.210441i
$922$	15.6467	−	9.41432i	0.515298	−	0.310044i
$923$	18.0252	+	17.0744i	0.593307	+	0.562010i
$924$	−7.54178	+	5.73311i	−0.248106	+	0.188605i
$925$	0.817548	−	15.0788i	0.0268808	−	0.495787i
$926$	4.12312	+	1.90756i	0.135494	+	0.0626862i
$927$	−7.36978	+	0.801512i	−0.242055	+	0.0263251i
$928$	2.24589	−	0.756730i	0.0737251	−	0.0248409i
$929$	−0.621281	+	3.78965i	−0.0203836	+	0.124334i	−0.995058	−	0.0992935i	$-0.968342\pi$
$929$	−0.621281	+	3.78965i	−0.0203836	+	0.124334i	0.974675	+	0.223628i	$0.0717900\pi$
$930$	0.878811	−	0.832454i	0.0288173	−	0.0272972i
$931$	4.58538	−	16.5151i	0.150280	−	0.541259i
$932$	6.63146	−	12.5083i	0.217221	−	0.409722i
$933$	17.2418	+	5.80944i	0.564471	+	0.190192i
$934$	3.78500	+	0.833142i	0.123849	+	0.0272612i
$935$	0.242961	+	0.875067i	0.00794568	+	0.0286177i
$936$	2.84455	+	1.71151i	0.0929769	+	0.0559423i
$937$	−4.70340	−	0.511526i	−0.153653	−	0.0167108i	0.0309690	−	0.999520i	$-0.490141\pi$
$937$	−4.70340	−	0.511526i	−0.153653	−	0.0167108i	−0.184622	+	0.982810i	$0.559106\pi$
$938$	36.2016	−	7.96857i	1.18202	−	0.260183i
$939$	−13.1631	−	24.8282i	−0.429562	−	0.810239i
$940$	2.04262	+	12.4594i	0.0666229	+	0.406382i
$941$	19.1643	+	14.5683i	0.624737	+	0.474913i	0.869011	−	0.494794i	$-0.164756\pi$
$941$	19.1643	+	14.5683i	0.624737	+	0.474913i	−0.244273	+	0.969706i	$0.578549\pi$
$942$	−3.26886	+	3.84840i	−0.106505	+	0.125388i
$943$	−43.0728			−1.40264
$944$	7.64601	+	0.733798i	0.248857	+	0.0238831i
$945$	−4.96844			−0.161623
$946$	10.9709	−	12.9160i	0.356695	−	0.419934i
$947$	−35.6949	−	27.1345i	−1.15993	−	0.881754i	−0.165400	−	0.986227i	$-0.552892\pi$
$947$	−35.6949	−	27.1345i	−1.15993	−	0.881754i	−0.994528	+	0.104472i	$0.966685\pi$
$948$	−2.11034	−	12.8725i	−0.0685405	−	0.418079i
$949$	5.78654	+	10.9146i	0.187839	+	0.354302i
$950$	−9.01517	+	1.98439i	−0.292491	+	0.0643821i
$951$	14.1009	+	1.53357i	0.457254	+	0.0497294i
$952$	0.745143	+	0.448338i	0.0241502	+	0.0145307i
$953$	7.18209	+	25.8676i	0.232651	+	0.837932i	0.984021	+	0.178052i	$0.0569794\pi$
$953$	7.18209	+	25.8676i	0.232651	+	0.837932i	−0.751370	+	0.659881i	$0.770607\pi$
$954$	−5.69598	−	1.25378i	−0.184414	−	0.0405926i
$955$	10.9915	+	3.70348i	0.355678	+	0.119842i
$956$	5.89366	−	11.1166i	0.190614	−	0.359537i
$957$	−1.68780	+	6.07891i	−0.0545589	+	0.196503i
$958$	−26.8598	+	25.4430i	−0.867802	+	0.822025i
$959$	−5.41345	+	33.0206i	−0.174810	+	1.06629i
$960$	−1.32303	+	0.445782i	−0.0427008	+	0.0143876i
$961$	30.0709	−	3.27041i	0.970030	−	0.105497i
$962$	14.9131	+	6.89955i	0.480819	+	0.222450i
$963$	0.0992502	−	1.83056i	0.00319829	−	0.0589891i
$964$	−0.0174653	+	0.0132767i	−0.000562518	+	0.000427615i
$965$	15.8077	+	14.9738i	0.508867	+	0.482025i
$966$	10.4698	−	6.29949i	0.336861	−	0.202683i
$967$	−8.59905	+	3.97835i	−0.276527	+	0.127935i	−0.553251	−	0.833014i	$-0.686613\pi$
$967$	−8.59905	+	3.97835i	−0.276527	+	0.127935i	0.276725	+	0.960949i	$0.410751\pi$
$968$	1.44859	+	3.63567i	0.0465593	+	0.116855i
$969$	−0.414922	+	0.611965i	−0.0133292	+	0.0196591i
$970$	−6.06807	−	8.94974i	−0.194834	−	0.287359i
$971$	−9.41918	+	23.6404i	−0.302276	+	0.758655i	0.696865	+	0.717203i	$0.254578\pi$
$971$	−9.41918	+	23.6404i	−0.302276	+	0.758655i	−0.999140	+	0.0414525i	$0.986801\pi$
$972$	0.0541389	+	0.998533i	0.00173651	+	0.0320280i
$973$	45.0337	+	53.0177i	1.44371	+	1.69967i
$974$	−10.4339	−	12.2837i	−0.334324	−	0.393597i
$975$	0.548322	+	10.1132i	0.0175604	+	0.323882i
$976$	4.78490	−	12.0092i	0.153161	−	0.384405i
$977$	6.00356	+	8.85459i	0.192071	+	0.283284i	0.911515	−	0.411267i	$-0.134914\pi$
$977$	6.00356	+	8.85459i	0.192071	+	0.283284i	−0.719444	+	0.694551i	$0.755603\pi$
$978$	6.61140	−	9.75108i	0.211409	−	0.311805i
$979$	3.33857	+	8.37918i	0.106701	+	0.267800i
$980$	7.17768	−	3.32075i	0.229283	−	0.106077i
$981$	9.68037	−	5.82449i	0.309070	−	0.185962i
$982$	8.73958	+	8.27857i	0.278891	+	0.264180i
$983$	46.6753	−	35.4817i	1.48871	−	1.13169i	0.529750	−	0.848154i	$-0.322286\pi$
$983$	46.6753	−	35.4817i	1.48871	−	1.13169i	0.958962	−	0.283536i	$-0.0915074\pi$
$984$	−0.679171	+	12.5266i	−0.0216512	+	0.399332i
$985$	−4.15060	−	1.92027i	−0.132249	−	0.0611850i
$986$	0.575731	−	0.0626146i	0.0183350	−	0.00199405i
$987$	−30.4988	+	10.2762i	−0.970788	+	0.327097i
$988$	1.62503	−	9.91223i	0.0516990	−	0.315350i
$989$	−15.8684	+	15.0314i	−0.504587	+	0.477970i
$990$	0.994268	−	3.58103i	0.0315999	−	0.113813i
$991$	−4.03288	+	7.60681i	−0.128109	+	0.241638i	−0.939266	−	0.343189i	$-0.888493\pi$
$991$	−4.03288	+	7.60681i	−0.128109	+	0.241638i	0.811158	+	0.584827i	$0.198838\pi$
$992$	0.821654	+	0.276848i	0.0260875	+	0.00878992i
$993$	−31.8872	−	7.01890i	−1.01191	−	0.222738i
$994$	−7.12049	−	25.6457i	−0.225848	−	0.813431i
$995$	10.0713	+	6.05971i	0.319282	+	0.192106i
$996$	9.86942	+	1.07336i	0.312725	+	0.0340109i
$997$	−15.6165	+	3.43746i	−0.494580	+	0.108865i	−0.455255	−	0.890361i	$-0.650452\pi$
$997$	−15.6165	+	3.43746i	−0.494580	+	0.108865i	−0.0393252	+	0.999226i	$0.512521\pi$
$998$	1.14763	+	2.16466i	0.0363275	+	0.0685210i
$999$	0.800777	+	4.88453i	0.0253355	+	0.154540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.127.2	✓	56
59.46	even	29	inner	354.2.e.a.223.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.127.2	✓	56	1.1	even	1	trivial
354.2.e.a.223.2	yes	56	59.46	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)

\(f(q)\)	\(=\)	\(q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.653953 + 1.23349i) q^{5} +(0.976621 - 0.214970i) q^{6} +(3.53789 + 0.384769i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +O(q^{10})\)	\(q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.653953 + 1.23349i) q^{5} +(0.976621 - 0.214970i) q^{6} +(3.53789 + 0.384769i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +(1.36348 + 0.300124i) q^{10} +(-2.52267 - 0.849988i) q^{11} +(0.468408 - 0.883512i) q^{12} +(-0.888125 + 3.19874i) q^{13} +(2.58364 - 2.44735i) q^{14} +(-0.225867 + 1.37773i) q^{15} +(-0.947653 + 0.319302i) q^{16} +(-0.242929 + 0.0264202i) q^{17} +(0.907575 + 0.419889i) q^{18} +(0.163808 - 3.02126i) q^{19} +(1.11144 - 0.844894i) q^{20} +(2.58364 + 2.44735i) q^{21} +(-2.28097 + 1.37242i) q^{22} +(3.11613 - 1.44168i) q^{23} +(-0.370138 - 0.928977i) q^{24} +(1.71210 - 2.52516i) q^{25} +(1.86300 + 2.74771i) q^{26} +(-0.370138 + 0.928977i) q^{27} +(-0.192667 - 3.55354i) q^{28} +(-1.53428 - 1.80629i) q^{29} +(0.903827 + 1.06407i) q^{30} +(-0.0469407 - 0.865770i) q^{31} +(-0.370138 + 0.928977i) q^{32} +(-1.49389 - 2.20333i) q^{33} +(-0.137133 + 0.202256i) q^{34} +(1.83901 + 4.61556i) q^{35} +(0.907575 - 0.419889i) q^{36} +(4.24121 - 2.55185i) q^{37} +(-2.19665 - 2.08077i) q^{38} +(-2.64282 + 2.00902i) q^{39} +(0.0755842 - 1.39407i) q^{40} +(-11.3855 - 5.26749i) q^{41} +(3.53789 - 0.384769i) q^{42} +(-6.03277 + 2.03268i) q^{43} +(-0.430667 + 2.62695i) q^{44} +(-1.01357 + 0.960109i) q^{45} +(0.918550 - 3.30832i) q^{46} +(-4.23604 + 7.99002i) q^{47} +(-0.947653 - 0.319302i) q^{48} +(5.53230 + 1.21775i) q^{49} +(-0.816191 - 2.93965i) q^{50} +(-0.209383 - 0.125982i) q^{51} +(3.30028 + 0.358927i) q^{52} +(-5.69598 + 1.25378i) q^{53} +(0.468408 + 0.883512i) q^{54} +(-0.601262 - 3.66754i) q^{55} +(-2.83310 - 2.15367i) q^{56} +(1.95880 - 2.30607i) q^{57} -2.36995 q^{58} +(-7.01147 - 3.13677i) q^{59} +1.39612 q^{60} +(-8.36897 + 9.85272i) q^{61} +(-0.690245 - 0.524711i) q^{62} +(0.575742 + 3.51187i) q^{63} +(0.468408 + 0.883512i) q^{64} +(-4.52639 + 0.996334i) q^{65} +(-2.64642 - 0.287815i) q^{66} +(8.92508 + 5.37004i) q^{67} +(0.0653737 + 0.235455i) q^{68} +(3.35320 + 0.738094i) q^{69} +(4.70836 + 1.58643i) q^{70} +(3.50321 - 6.60776i) q^{71} +(0.267528 - 0.963550i) q^{72} +(2.70162 - 2.55911i) q^{73} +(0.800777 - 4.88453i) q^{74} +(2.89116 - 0.974144i) q^{75} +(-3.00796 + 0.327136i) q^{76} +(-8.59790 - 3.97781i) q^{77} +(-0.179727 + 3.31487i) q^{78} +(10.3845 - 7.89408i) q^{79} +(-1.01357 - 0.960109i) q^{80} +(-0.856857 + 0.515554i) q^{81} +(-11.3855 + 5.26749i) q^{82} +(3.67459 + 9.22253i) q^{83} +(1.99713 - 2.94554i) q^{84} +(-0.191453 - 0.282372i) q^{85} +(-2.35630 + 5.91387i) q^{86} +(-0.128307 - 2.36648i) q^{87} +(1.72336 + 2.02889i) q^{88} +(-2.19355 - 2.58245i) q^{89} +(0.0755842 + 1.39407i) q^{90} +(-4.37287 + 10.9751i) q^{91} +(-1.92682 - 2.84184i) q^{92} +(0.486572 - 0.717640i) q^{93} +(3.34734 + 8.40118i) q^{94} +(3.83381 - 1.77371i) q^{95} +(-0.856857 + 0.515554i) q^{96} +(-5.62283 - 5.32623i) q^{97} +(4.50966 - 3.42815i) q^{98} +(0.144119 - 2.65812i) 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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