LMFDB - Embedded newform 354.2.e.a.7.2

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			7.2
Character	$\chi$	$=$	354.7
Dual form			354.2.e.a.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561187 - 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(0.704657 - 0.326009i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(0.375788 - 1.35347i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})$	\(q+(-0.561187 - 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(0.704657 - 0.326009i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(0.375788 - 1.35347i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(-0.665279 - 0.400285i) q^{10} +(2.12101 - 2.00913i) q^{11} +(0.907575 + 0.419889i) q^{12} +(-0.0500012 + 0.00543796i) q^{13} +(-1.33114 + 0.448512i) q^{14} +(-0.287382 - 0.721273i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(-1.58122 - 5.69502i) q^{17} +(0.468408 + 0.883512i) q^{18} +(-0.852936 + 0.648385i) q^{19} +(0.0420344 + 0.775278i) q^{20} +(-1.33114 - 0.448512i) q^{21} +(-2.85322 - 0.628042i) q^{22} +(1.99495 - 3.76288i) q^{23} +(-0.161782 - 0.986827i) q^{24} +(-2.84667 + 3.35136i) q^{25} +(0.0325610 + 0.0383337i) q^{26} +(-0.161782 + 0.986827i) q^{27} +(1.11825 + 0.850068i) q^{28} +(1.58934 - 2.34410i) q^{29} +(-0.435715 + 0.642632i) q^{30} +(1.83097 + 1.39187i) q^{31} +(-0.161782 + 0.986827i) q^{32} +(-1.89136 - 2.22668i) q^{33} +(-3.82635 + 4.50473i) q^{34} +(-0.176441 - 1.07624i) q^{35} +(0.468408 - 0.883512i) q^{36} +(-9.59460 - 2.11193i) q^{37} +(1.01532 + 0.342100i) q^{38} +(0.00272297 + 0.0502223i) q^{39} +(0.618100 - 0.469868i) q^{40} +(-0.873055 - 1.64676i) q^{41} +(0.375788 + 1.35347i) q^{42} +(1.76058 + 1.66771i) q^{43} +(1.08137 + 2.71403i) q^{44} +(-0.735774 + 0.247911i) q^{45} +(-4.23404 + 0.460479i) q^{46} +(0.866451 + 0.400863i) q^{47} +(-0.725995 + 0.687699i) q^{48} +(4.30734 + 2.59164i) q^{49} +(4.37140 + 0.475418i) q^{50} +(-5.77228 + 1.27057i) q^{51} +(0.0134556 - 0.0484627i) q^{52} +(3.34449 - 2.01231i) q^{53} +(0.907575 - 0.419889i) q^{54} +(0.839593 - 2.10722i) q^{55} +(0.0760471 - 1.40261i) q^{56} +(0.601257 + 0.886788i) q^{57} -2.83210 q^{58} +(3.69108 + 6.73617i) q^{59} +0.776417 q^{60} +(1.84697 + 2.72407i) q^{61} +(0.124517 - 2.29657i) q^{62} +(-0.519921 + 1.30490i) q^{63} +(0.907575 - 0.419889i) q^{64} +(-0.0334609 + 0.0201327i) q^{65} +(-0.781591 + 2.81504i) q^{66} +(11.2337 - 2.47273i) q^{67} +(5.87581 + 0.639033i) q^{68} +(-3.64936 - 2.19575i) q^{69} +(-0.791776 + 0.750010i) q^{70} +(7.86560 + 3.63901i) q^{71} +(-0.994138 + 0.108119i) q^{72} +(2.07900 - 0.700498i) q^{73} +(3.63634 + 9.12654i) q^{74} +(3.19233 + 3.02394i) q^{75} +(-0.286630 - 1.03235i) q^{76} +(-1.92224 - 3.62573i) q^{77} +(0.0400403 - 0.0304379i) q^{78} +(0.301968 + 5.56948i) q^{79} +(-0.735774 - 0.247911i) q^{80} +(0.976621 + 0.214970i) q^{81} +(-0.873055 + 1.64676i) q^{82} +(1.15158 + 7.02431i) q^{83} +(0.909362 - 1.07058i) q^{84} +(-2.97084 - 3.49755i) q^{85} +(0.392330 - 2.39311i) q^{86} +(-2.25462 - 1.71391i) q^{87} +(1.63952 - 2.41812i) q^{88} +(1.53926 - 2.27023i) q^{89} +(0.618100 + 0.469868i) q^{90} +(-0.0114298 + 0.0697185i) q^{91} +(2.75722 + 3.24605i) q^{92} +(1.48895 - 1.75293i) q^{93} +(-0.154451 - 0.942111i) q^{94} +(-0.389648 + 0.734954i) q^{95} +(0.976621 + 0.214970i) q^{96} +(2.95033 + 0.994082i) q^{97} +(-0.272151 - 5.01954i) q^{98} +(-2.32581 + 1.76803i) 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 $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

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 $

$2$	−0.561187	−	0.827689i	−0.396819	−	0.585265i
$2$	−0.561187	−	0.827689i	−0.396819	−	0.585265i
$3$	0.0541389	−	0.998533i	0.0312571	−	0.576504i
$3$	0.0541389	−	0.998533i	0.0312571	−	0.576504i
$4$	−0.370138	+	0.928977i	−0.185069	+	0.464488i
$5$	0.704657	−	0.326009i	0.315132	−	0.145796i	−0.255947	−	0.966691i	$-0.582387\pi$
$5$	0.704657	−	0.326009i	0.315132	−	0.145796i	0.571079	+	0.820895i	$0.306525\pi$
$6$	−0.856857	+	0.515554i	−0.349810	+	0.210474i
$7$	0.375788	−	1.35347i	0.142035	−	0.511562i	−0.857963	−	0.513711i	$-0.828270\pi$
$7$	0.375788	−	1.35347i	0.142035	−	0.511562i	0.999998	+	0.00214897i	$0.000684039\pi$
$8$	0.976621	−	0.214970i	0.345288	−	0.0760035i
$9$	−0.994138	−	0.108119i	−0.331379	−	0.0360397i
$10$	−0.665279	−	0.400285i	−0.210380	−	0.126581i
$11$	2.12101	−	2.00913i	0.639510	−	0.605776i	−0.297650	−	0.954675i	$-0.596203\pi$
$11$	2.12101	−	2.00913i	0.639510	−	0.605776i	0.937160	+	0.348899i	$0.113444\pi$
$12$	0.907575	+	0.419889i	0.261994	+	0.121212i
$13$	−0.0500012	+	0.00543796i	−0.0138678	+	0.00150822i	−0.115050	−	0.993360i	$-0.536703\pi$
$13$	−0.0500012	+	0.00543796i	−0.0138678	+	0.00150822i	0.101182	+	0.994868i	$0.467737\pi$
$14$	−1.33114	+	0.448512i	−0.355761	+	0.119870i
$15$	−0.287382	−	0.721273i	−0.0742016	−	0.186232i
$16$	−0.725995	−	0.687699i	−0.181499	−	0.171925i
$17$	−1.58122	−	5.69502i	−0.383501	−	1.38125i	−0.863665	−	0.504067i	$-0.831836\pi$
$17$	−1.58122	−	5.69502i	−0.383501	−	1.38125i	0.480163	−	0.877179i	$-0.340577\pi$
$18$	0.468408	+	0.883512i	0.110405	+	0.208246i
$19$	−0.852936	+	0.648385i	−0.195677	+	0.148750i	−0.698425	−	0.715683i	$-0.746115\pi$
$19$	−0.852936	+	0.648385i	−0.195677	+	0.148750i	0.502748	+	0.864433i	$0.332322\pi$
$20$	0.0420344	+	0.775278i	0.00939917	+	0.173358i
$21$	−1.33114	−	0.448512i	−0.290478	−	0.0978734i
$22$	−2.85322	−	0.628042i	−0.608309	−	0.133899i
$23$	1.99495	−	3.76288i	0.415977	−	0.784615i	−0.583648	−	0.812007i	$-0.698375\pi$
$23$	1.99495	−	3.76288i	0.415977	−	0.784615i	0.999625	+	0.0273915i	$0.00872008\pi$
$24$	−0.161782	−	0.986827i	−0.0330236	−	0.201435i
$25$	−2.84667	+	3.35136i	−0.569334	+	0.670272i
$26$	0.0325610	+	0.0383337i	0.00638573	+	0.00751786i
$27$	−0.161782	+	0.986827i	−0.0311350	+	0.189915i
$28$	1.11825	+	0.850068i	0.211329	+	0.160648i
$29$	1.58934	−	2.34410i	0.295133	−	0.435288i	−0.650995	−	0.759082i	$-0.725648\pi$
$29$	1.58934	−	2.34410i	0.295133	−	0.435288i	0.946128	+	0.323794i	$0.104958\pi$
$30$	−0.435715	+	0.642632i	−0.0795503	+	0.117328i
$31$	1.83097	+	1.39187i	0.328852	+	0.249987i	0.756551	−	0.653934i	$-0.226883\pi$
$31$	1.83097	+	1.39187i	0.328852	+	0.249987i	−0.427699	+	0.903921i	$0.640676\pi$
$32$	−0.161782	+	0.986827i	−0.0285993	+	0.174448i
$33$	−1.89136	−	2.22668i	−0.329243	−	0.387615i
$34$	−3.82635	+	4.50473i	−0.656214	+	0.772555i
$35$	−0.176441	−	1.07624i	−0.0298239	−	0.181918i
$36$	0.468408	−	0.883512i	0.0780681	−	0.147252i
$37$	−9.59460	−	2.11193i	−1.57734	−	0.347199i	−0.661883	−	0.749607i	$-0.730242\pi$
$37$	−9.59460	−	2.11193i	−1.57734	−	0.347199i	−0.915460	+	0.402408i	$0.868173\pi$
$38$	1.01532	+	0.342100i	0.164706	+	0.0554960i
$39$	0.00272297	+	0.0502223i	0.000436024	+	0.00804200i
$40$	0.618100	−	0.469868i	0.0977302	−	0.0742926i
$41$	−0.873055	−	1.64676i	−0.136348	−	0.257180i	0.805930	−	0.592011i	$-0.201666\pi$
$41$	−0.873055	−	1.64676i	−0.136348	−	0.257180i	−0.942278	+	0.334831i	$0.891321\pi$
$42$	0.375788	+	1.35347i	0.0579854	+	0.208844i
$43$	1.76058	+	1.66771i	0.268486	+	0.254323i	0.810084	−	0.586315i	$-0.199422\pi$
$43$	1.76058	+	1.66771i	0.268486	+	0.254323i	−0.541598	+	0.840638i	$0.682180\pi$
$44$	1.08137	+	2.71403i	0.163022	+	0.409155i
$45$	−0.735774	+	0.247911i	−0.109683	+	0.0369564i
$46$	−4.23404	+	0.460479i	−0.624275	+	0.0678940i
$47$	0.866451	+	0.400863i	0.126385	+	0.0584718i	0.482062	−	0.876137i	$-0.339888\pi$
$47$	0.866451	+	0.400863i	0.126385	+	0.0584718i	−0.355678	+	0.934609i	$0.615750\pi$
$48$	−0.725995	+	0.687699i	−0.104788	+	0.0992609i
$49$	4.30734	+	2.59164i	0.615335	+	0.370235i
$50$	4.37140	+	0.475418i	0.618209	+	0.0672343i
$51$	−5.77228	+	1.27057i	−0.808280	+	0.177916i
$52$	0.0134556	−	0.0484627i	0.00186596	−	0.00672057i
$53$	3.34449	−	2.01231i	0.459401	−	0.276413i	−0.266983	−	0.963701i	$-0.586027\pi$
$53$	3.34449	−	2.01231i	0.459401	−	0.276413i	0.726384	+	0.687289i	$0.241199\pi$
$54$	0.907575	−	0.419889i	0.123505	−	0.0571397i
$55$	0.839593	−	2.10722i	0.113211	−	0.284137i
$56$	0.0760471	−	1.40261i	0.0101622	−	0.187431i
$57$	0.601257	+	0.886788i	0.0796384	+	0.117458i
$58$	−2.83210			−0.371873
$59$	3.69108	+	6.73617i	0.480537	+	0.876974i
$59$	3.69108	+	6.73617i	0.480537	+	0.876974i
$60$	0.776417			0.100235
$61$	1.84697	+	2.72407i	0.236480	+	0.348782i	0.927349	−	0.374198i	$-0.122082\pi$
$61$	1.84697	+	2.72407i	0.236480	+	0.348782i	−0.690869	+	0.722980i	$0.742772\pi$
$62$	0.124517	−	2.29657i	0.0158136	−	0.291665i
$63$	−0.519921	+	1.30490i	−0.0655039	+	0.164402i
$64$	0.907575	−	0.419889i	0.113447	−	0.0524861i
$65$	−0.0334609	+	0.0201327i	−0.00415031	+	0.00249716i
$66$	−0.781591	+	2.81504i	−0.0962072	+	0.346507i
$67$	11.2337	−	2.47273i	1.37242	−	0.302092i	0.533246	−	0.845960i	$-0.320972\pi$
$67$	11.2337	−	2.47273i	1.37242	−	0.302092i	0.839171	+	0.543868i	$0.183041\pi$
$68$	5.87581	+	0.639033i	0.712547	+	0.0774941i
$69$	−3.64936	−	2.19575i	−0.439331	−	0.264337i
$70$	−0.791776	+	0.750010i	−0.0946353	+	0.0896433i
$71$	7.86560	+	3.63901i	0.933475	+	0.431872i	0.826847	−	0.562427i	$-0.190132\pi$
$71$	7.86560	+	3.63901i	0.933475	+	0.431872i	0.106628	+	0.994299i	$0.465994\pi$
$72$	−0.994138	+	0.108119i	−0.117160	+	0.0127419i
$73$	2.07900	−	0.700498i	0.243329	−	0.0819870i	−0.194995	−	0.980804i	$-0.562469\pi$
$73$	2.07900	−	0.700498i	0.243329	−	0.0819870i	0.438324	+	0.898817i	$0.355572\pi$
$74$	3.63634	+	9.12654i	0.422716	+	1.06094i
$75$	3.19233	+	3.02394i	0.368619	+	0.349174i
$76$	−0.286630	−	1.03235i	−0.0328788	−	0.118419i
$77$	−1.92224	−	3.62573i	−0.219060	−	0.413190i
$78$	0.0400403	−	0.0304379i	0.00453367	−	0.00344641i
$79$	0.301968	+	5.56948i	0.0339741	+	0.626615i	0.965094	+	0.261903i	$0.0843500\pi$
$79$	0.301968	+	5.56948i	0.0339741	+	0.626615i	−0.931120	+	0.364712i	$0.881167\pi$
$80$	−0.735774	−	0.247911i	−0.0822620	−	0.0277173i
$81$	0.976621	+	0.214970i	0.108513	+	0.0238856i
$82$	−0.873055	+	1.64676i	−0.0964128	+	0.181854i
$83$	1.15158	+	7.02431i	0.126402	+	0.771018i	0.971611	+	0.236583i	$0.0760274\pi$
$83$	1.15158	+	7.02431i	0.126402	+	0.771018i	−0.845209	+	0.534435i	$0.820524\pi$
$84$	0.909362	−	1.07058i	0.0992195	−	0.116810i
$85$	−2.97084	−	3.49755i	−0.322233	−	0.379362i
$86$	0.392330	−	2.39311i	0.0423061	−	0.258056i
$87$	−2.25462	−	1.71391i	−0.241720	−	0.183751i
$88$	1.63952	−	2.41812i	0.174774	−	0.257772i
$89$	1.53926	−	2.27023i	0.163161	−	0.240644i	−0.737316	−	0.675548i	$-0.763907\pi$
$89$	1.53926	−	2.27023i	0.163161	−	0.240644i	0.900477	+	0.434904i	$0.143218\pi$
$90$	0.618100	+	0.469868i	0.0651535	+	0.0495284i
$91$	−0.0114298	+	0.0697185i	−0.00119816	+	0.00730848i
$92$	2.75722	+	3.24605i	0.287460	+	0.338424i
$93$	1.48895	−	1.75293i	0.154397	−	0.181771i
$94$	−0.154451	−	0.942111i	−0.0159304	−	0.0971713i
$95$	−0.389648	+	0.734954i	−0.0399770	+	0.0754047i
$96$	0.976621	+	0.214970i	0.0996759	+	0.0219403i
$97$	2.95033	+	0.994082i	0.299561	+	0.100934i	0.465068	−	0.885275i	$-0.346030\pi$
$97$	2.95033	+	0.994082i	0.299561	+	0.100934i	−0.165508	+	0.986208i	$0.552926\pi$
$98$	−0.272151	−	5.01954i	−0.0274915	−	0.507050i
$99$	−2.32581	+	1.76803i	−0.233752	+	0.177694i
$100$	−2.05967	−	3.88496i	−0.205967	−	0.388496i
$101$	2.15374	+	7.75709i	0.214306	+	0.771859i	0.990038	+	0.140798i	$0.0449667\pi$
$101$	2.15374	+	7.75709i	0.214306	+	0.771859i	−0.775733	+	0.631062i	$0.782620\pi$
$102$	4.29097	+	4.06462i	0.424869	+	0.402457i
$103$	5.17548	+	12.9895i	0.509956	+	1.27989i	0.928377	+	0.371639i	$0.121204\pi$
$103$	5.17548	+	12.9895i	0.509956	+	1.27989i	−0.418422	+	0.908253i	$0.637417\pi$
$104$	−0.0476632	+	0.0160596i	−0.00467376	+	0.00157477i
$105$	−1.08421	+	0.117915i	−0.105808	+	0.0115074i
$106$	−3.54246	−	1.63891i	−0.344074	−	0.159185i
$107$	5.98495	−	5.66924i	0.578587	−	0.548067i	−0.341449	−	0.939900i	$-0.610918\pi$
$107$	5.98495	−	5.66924i	0.578587	−	0.548067i	0.920036	+	0.391834i	$0.128159\pi$
$108$	−0.856857	−	0.515554i	−0.0824511	−	0.0496092i
$109$	0.487968	+	0.0530697i	0.0467388	+	0.00508315i	0.131459	−	0.991322i	$-0.458034\pi$
$109$	0.487968	+	0.0530697i	0.0467388	+	0.00508315i	−0.0847197	+	0.996405i	$0.526999\pi$
$110$	−2.21529	+	0.487622i	−0.211220	+	0.0464930i
$111$	−2.62828	+	9.46619i	−0.249465	+	0.898491i
$112$	−1.20360	+	0.724181i	−0.113729	+	0.0684287i
$113$	2.12127	−	0.981402i	0.199552	−	0.0923225i	−0.317568	−	0.948235i	$-0.602866\pi$
$113$	2.12127	−	0.981402i	0.199552	−	0.0923225i	0.517120	+	0.855913i	$0.327004\pi$
$114$	0.396567	−	0.995308i	0.0371419	−	0.0932191i
$115$	0.179025	−	3.30191i	0.0166941	−	0.307905i
$116$	1.58934	+	2.34410i	0.147566	+	0.217644i
$117$	0.0502960			0.00464987
$118$	3.50407	−	6.83531i	0.322576	−	0.629242i
$119$	−8.30223			−0.761064
$120$	−0.435715	−	0.642632i	−0.0397752	−	0.0586640i
$121$	−0.133435	+	2.46107i	−0.0121305	+	0.223734i
$122$	1.21819	−	3.05743i	0.110290	−	0.276807i
$123$	−1.69161	+	0.782621i	−0.152527	+	0.0705665i
$124$	−1.97073	+	1.18575i	−0.176976	+	0.106483i
$125$	−1.95192	+	7.03018i	−0.174585	+	0.628799i
$126$	1.37183	−	0.301962i	0.122212	−	0.0269009i
$127$	−6.37163	−	0.692957i	−0.565391	−	0.0614900i	−0.179040	−	0.983842i	$-0.557299\pi$
$127$	−6.37163	−	0.692957i	−0.565391	−	0.0614900i	−0.386351	+	0.922352i	$0.626265\pi$
$128$	−0.856857	−	0.515554i	−0.0757362	−	0.0455690i
$129$	1.76058	−	1.66771i	0.155010	−	0.146834i
$130$	0.0354414	+	0.0163970i	0.00310842	+	0.00143811i
$131$	−12.1109	+	1.31714i	−1.05814	+	0.115079i	−0.620605	−	0.784124i	$-0.713113\pi$
$131$	−12.1109	+	1.31714i	−1.05814	+	0.115079i	−0.437532	+	0.899203i	$0.644147\pi$
$132$	2.76859	−	0.932848i	0.240975	−	0.0811940i
$133$	0.557044	+	1.39808i	0.0483019	+	0.121229i
$134$	−8.35086	−	7.91036i	−0.721405	−	0.683351i
$135$	0.207714	+	0.748117i	0.0178771	+	0.0643876i
$136$	−2.76851	−	5.22196i	−0.237398	−	0.447780i
$137$	−15.9257	+	12.1064i	−1.36063	+	1.03432i	−0.366018	+	0.930608i	$0.619279\pi$
$137$	−15.9257	+	12.1064i	−1.36063	+	1.03432i	−0.994607	+	0.103713i	$0.966928\pi$
$138$	0.230578	+	4.25276i	0.0196281	+	0.362019i
$139$	8.60366	+	2.89891i	0.729753	+	0.245883i	0.659561	−	0.751651i	$-0.270742\pi$
$139$	8.60366	+	2.89891i	0.729753	+	0.245883i	0.0701922	+	0.997533i	$0.477639\pi$
$140$	1.06511	+	0.234448i	0.0900182	+	0.0198145i
$141$	0.447184	−	0.843478i	0.0376597	−	0.0710336i
$142$	−1.40210	−	8.55244i	−0.117662	−	0.717705i
$143$	−0.0951277	+	0.111993i	−0.00795498	+	0.00936532i
$144$	0.647386	+	0.762162i	0.0539489	+	0.0635135i
$145$	0.355741	−	2.16992i	0.0295427	−	0.180202i
$146$	−1.74650	−	1.32766i	−0.144542	−	0.109878i
$147$	2.82104	−	4.16072i	0.232675	−	0.343170i
$148$	5.51326	−	8.13146i	0.453188	−	0.668402i
$149$	−16.0586	−	12.2074i	−1.31557	−	1.00007i	−0.998667	−	0.0516107i	$-0.983565\pi$
$149$	−16.0586	−	12.2074i	−1.31557	−	1.00007i	−0.316901	−	0.948459i	$-0.602642\pi$
$150$	0.711384	−	4.33925i	0.0580843	−	0.354298i
$151$	−0.178521	−	0.210171i	−0.0145279	−	0.0171035i	0.754850	−	0.655897i	$-0.227710\pi$
$151$	−0.178521	−	0.210171i	−0.0145279	−	0.0171035i	−0.769378	+	0.638794i	$0.779434\pi$
$152$	−0.693611	+	0.816582i	−0.0562593	+	0.0662336i
$153$	0.956206	+	5.83260i	0.0773047	+	0.471538i
$154$	−1.92224	+	3.62573i	−0.154899	+	0.292170i
$155$	1.74397	+	0.383877i	0.140079	+	0.0308337i
$156$	−0.0476632	−	0.0160596i	−0.00381611	−	0.00128580i
$157$	−0.836169	−	15.4222i	−0.0667335	−	1.23083i	−0.819710	−	0.572779i	$-0.805865\pi$
$157$	−0.836169	−	15.4222i	−0.0667335	−	1.23083i	0.752976	−	0.658048i	$-0.228618\pi$
$158$	4.44033	−	3.37545i	0.353254	−	0.268537i
$159$	−1.82830	−	3.44853i	−0.144993	−	0.273486i
$160$	0.207714	+	0.748117i	0.0164212	+	0.0591438i
$161$	−4.34326	−	4.11415i	−0.342297	−	0.324240i
$162$	−0.370138	−	0.928977i	−0.0290808	−	0.0729873i
$163$	16.3205	−	5.49900i	1.27832	−	0.430715i	0.403416	−	0.915017i	$-0.367823\pi$
$163$	16.3205	−	5.49900i	1.27832	−	0.430715i	0.874901	+	0.484302i	$0.160926\pi$
$164$	1.85295	−	0.201520i	0.144691	−	0.0157361i
$165$	−2.05867	−	0.952444i	−0.160268	−	0.0741477i
$166$	5.16769	−	4.89510i	0.401091	−	0.379933i
$167$	−0.715466	−	0.430481i	−0.0553644	−	0.0333117i	0.487603	−	0.873066i	$-0.337872\pi$
$167$	−0.715466	−	0.430481i	−0.0553644	−	0.0333117i	−0.542967	+	0.839754i	$0.682699\pi$
$168$	−1.39643	−	0.151871i	−0.107737	−	0.0117171i
$169$	−12.6936	+	2.79407i	−0.976431	+	0.214929i
$170$	−1.22768	+	4.42171i	−0.0941590	+	0.339130i
$171$	0.918039	−	0.552366i	0.0702042	−	0.0422404i
$172$	−2.20092	+	1.01825i	−0.167819	+	0.0776412i
$173$	6.39075	−	16.0396i	0.485880	−	1.21947i	−0.457933	−	0.888987i	$-0.651410\pi$
$173$	6.39075	−	16.0396i	0.485880	−	1.21947i	0.943813	−	0.330480i	$-0.107211\pi$
$174$	−0.153327	+	2.82795i	−0.0116237	+	0.214386i
$175$	3.46621	+	5.11228i	0.262021	+	0.386452i
$176$	−2.92153			−0.220218
$177$	6.92612	−	3.32097i	0.520599	−	0.249620i
$178$	−2.74286			−0.205586
$179$	2.41703	+	3.56485i	0.180657	+	0.266450i	0.907225	−	0.420645i	$-0.138196\pi$
$179$	2.41703	+	3.56485i	0.180657	+	0.266450i	−0.726568	+	0.687095i	$0.758886\pi$
$180$	0.0420344	−	0.775278i	0.00313306	−	0.0577858i
$181$	−6.37277	+	15.9944i	−0.473684	+	1.18886i	0.477057	+	0.878872i	$0.341703\pi$
$181$	−6.37277	+	15.9944i	−0.473684	+	1.18886i	−0.950741	+	0.309985i	$0.899676\pi$
$182$	0.0641194	−	0.0296648i	0.00475285	−	0.00219890i
$183$	2.82007	−	1.69678i	0.208466	−	0.125430i
$184$	1.13940	−	4.10376i	0.0839980	−	0.302534i
$185$	−7.44941	+	1.63974i	−0.547692	+	0.120556i
$186$	−2.28646	−	0.248668i	−0.167652	−	0.0182332i
$187$	−14.7958	−	8.90236i	−1.08198	−	0.651005i
$188$	−0.693099	+	0.656538i	−0.0505494	+	0.0478829i
$189$	1.27484	+	0.589804i	0.0927310	+	0.0429019i
$190$	0.826979	−	0.0899393i	0.0599953	−	0.00652489i
$191$	−17.6575	+	5.94950i	−1.27765	+	0.430491i	−0.874671	−	0.484718i	$-0.838922\pi$
$191$	−17.6575	+	5.94950i	−1.27765	+	0.430491i	−0.402980	+	0.915209i	$0.632026\pi$
$192$	−0.370138	−	0.928977i	−0.0267124	−	0.0670431i
$193$	3.04617	+	2.88549i	0.219268	+	0.207702i	0.789447	−	0.613819i	$-0.210367\pi$
$193$	3.04617	+	2.88549i	0.219268	+	0.207702i	−0.570179	+	0.821521i	$0.693126\pi$
$194$	−0.832896	−	2.99982i	−0.0597985	−	0.215375i
$195$	0.0182917	+	0.0345018i	0.00130989	+	0.00247072i
$196$	−4.00189	+	3.04216i	−0.285849	+	0.217297i
$197$	0.300092	+	5.53488i	0.0213807	+	0.394344i	0.989563	+	0.144099i	$0.0460284\pi$
$197$	0.300092	+	5.53488i	0.0213807	+	0.394344i	−0.968183	+	0.250245i	$0.919489\pi$
$198$	2.76859	+	0.932848i	0.196755	+	0.0662946i
$199$	−6.36300	−	1.40060i	−0.451061	−	0.0992861i	−0.0163708	−	0.999866i	$-0.505211\pi$
$199$	−6.36300	−	1.40060i	−0.451061	−	0.0992861i	−0.434691	+	0.900580i	$0.643142\pi$
$200$	−2.05967	+	3.88496i	−0.145641	+	0.274708i
$201$	−1.86092	−	11.3511i	−0.131259	−	0.800646i
$202$	5.21180	−	6.13581i	0.366701	−	0.431714i
$203$	−2.57540	−	3.03200i	−0.180758	−	0.212805i
$204$	0.956206	−	5.83260i	0.0669478	−	0.408364i
$205$	−1.15206	−	0.875774i	−0.0804635	−	0.0611667i
$206$	7.84684	−	11.5732i	0.546715	−	0.806345i
$207$	−2.39010	+	3.52513i	−0.166123	+	0.245014i
$208$	0.0400403	+	0.0304379i	0.00277630	+	0.00211049i
$209$	−0.506399	+	3.08889i	−0.0350283	+	0.213663i
$210$	0.706044	+	0.831219i	0.0487217	+	0.0573596i
$211$	14.8309	−	17.4603i	1.02100	−	1.20202i	0.0418035	−	0.999126i	$-0.486690\pi$
$211$	14.8309	−	17.4603i	1.02100	−	1.20202i	0.979201	−	0.202893i	$-0.0650345\pi$
$212$	0.631469	+	3.85179i	0.0433695	+	0.264542i
$213$	4.05951	−	7.65705i	0.278153	−	0.524653i
$214$	−8.05105	−	1.77217i	−0.550358	−	0.121143i
$215$	1.78429	+	0.601199i	0.121688	+	0.0410014i
$216$	0.0541389	+	0.998533i	0.00368369	+	0.0679416i
$217$	2.57190	−	1.95511i	0.174592	−	0.132722i
$218$	−0.229916	−	0.433668i	−0.0155719	−	0.0293717i
$219$	−0.586915	−	2.11388i	−0.0396601	−	0.142843i
$220$	1.64679	+	1.55992i	0.111027	+	0.105170i
$221$	0.110032	+	0.276159i	0.00740155	+	0.0185765i
$222$	9.31002	−	3.13691i	0.624848	−	0.210536i
$223$	2.84591	−	0.309511i	0.190576	−	0.0207264i	−0.0123332	−	0.999924i	$-0.503926\pi$
$223$	2.84591	−	0.309511i	0.190576	−	0.0207264i	0.202909	+	0.979198i	$0.434960\pi$
$224$	1.27484	+	0.589804i	0.0851789	+	0.0394080i
$225$	3.19233	−	3.02394i	0.212822	−	0.201596i
$226$	−2.00272	−	1.20500i	−0.133219	−	0.0801553i
$227$	−12.1638	−	1.32289i	−0.807337	−	0.0878032i	−0.304864	−	0.952396i	$-0.598611\pi$
$227$	−12.1638	−	1.32289i	−0.807337	−	0.0878032i	−0.502473	+	0.864593i	$0.667577\pi$
$228$	−1.04635	+	0.230320i	−0.0692964	+	0.0152533i
$229$	2.00573	−	7.22397i	0.132542	−	0.477374i	−0.867248	−	0.497877i	$-0.834113\pi$
$229$	2.00573	−	7.22397i	0.132542	−	0.477374i	0.999790	+	0.0205034i	$0.00652688\pi$
$230$	−2.83342	+	1.70481i	−0.186830	+	0.112412i
$231$	−3.72448	+	1.72313i	−0.245053	+	0.113374i
$232$	1.04827	−	2.63096i	0.0688222	−	0.172731i
$233$	1.19152	−	21.9763i	0.0780591	−	1.43972i	−0.652978	−	0.757377i	$-0.726480\pi$
$233$	1.19152	−	21.9763i	0.0780591	−	1.43972i	0.731037	−	0.682338i	$-0.239037\pi$
$234$	−0.0282255	−	0.0416295i	−0.00184516	−	0.00272140i
$235$	0.741235			0.0483529
$236$	−7.62395	+	0.935611i	−0.496277	+	0.0609031i
$237$	5.57766			0.362308
$238$	4.65910	+	6.87166i	0.302005	+	0.445424i
$239$	−0.855022	+	15.7700i	−0.0553068	+	1.02007i	0.830794	+	0.556580i	$0.187887\pi$
$239$	−0.855022	+	15.7700i	−0.0553068	+	1.02007i	−0.886101	+	0.463493i	$0.846596\pi$
$240$	−0.287382	+	0.721273i	−0.0185504	+	0.0465580i
$241$	−17.6788	+	8.17906i	−1.13879	+	0.526860i	−0.896368	−	0.443311i	$-0.853804\pi$
$241$	−17.6788	+	8.17906i	−1.13879	+	0.526860i	−0.242421	+	0.970171i	$0.577942\pi$
$242$	2.11188	−	1.27068i	0.135757	−	0.0816823i
$243$	0.267528	−	0.963550i	0.0171620	−	0.0618118i
$244$	−3.21423	+	0.707506i	−0.205770	+	0.0452935i
$245$	3.88010	+	0.421986i	0.247890	+	0.0269597i
$246$	1.59707	+	0.960928i	0.101826	+	0.0612665i
$247$	0.0391219	−	0.0370582i	0.00248927	−	0.00235796i
$248$	2.08737	+	0.965722i	0.132548	+	0.0613234i
$249$	7.07635	−	0.769599i	0.448445	−	0.0487714i
$250$	6.91420	−	2.32966i	0.437292	−	0.147341i
$251$	7.03764	+	17.6632i	0.444212	+	1.11489i	0.965244	+	0.261351i	$0.0841681\pi$
$251$	7.03764	+	17.6632i	0.444212	+	1.11489i	−0.521032	+	0.853537i	$0.674453\pi$
$252$	−1.01978	−	0.965989i	−0.0642402	−	0.0608516i
$253$	−3.32880	−	11.9893i	−0.209280	−	0.753758i
$254$	3.00213	+	5.66261i	0.188370	+	0.355304i
$255$	−3.65326	+	2.77713i	−0.228776	+	0.173911i
$256$	0.0541389	+	0.998533i	0.00338368	+	0.0624083i
$257$	0.617655	+	0.208112i	0.0385283	+	0.0129817i	0.338500	−	0.940967i	$-0.390081\pi$
$257$	0.617655	+	0.208112i	0.0385283	+	0.0129817i	−0.299971	+	0.953948i	$0.596977\pi$
$258$	−2.36836	−	0.521315i	−0.147448	−	0.0324557i
$259$	−6.46397	+	12.1923i	−0.401651	+	0.757595i
$260$	−0.00631770	−	0.0385363i	−0.000391807	−	0.00238992i
$261$	−1.83346	+	2.15852i	−0.113489	+	0.133609i
$262$	7.88668	+	9.28492i	0.487241	+	0.573624i
$263$	−2.00603	+	12.2363i	−0.123697	+	0.754520i	0.850018	+	0.526753i	$0.176591\pi$
$263$	−2.00603	+	12.2363i	−0.123697	+	0.754520i	−0.973716	+	0.227767i	$0.926858\pi$
$264$	−2.32581	−	1.76803i	−0.143144	−	0.108815i
$265$	1.70069	−	2.50833i	0.104472	−	0.154085i
$266$	0.844566	−	1.24564i	0.0517837	−	0.0763752i
$267$	−2.18357	−	1.65991i	−0.133632	−	0.101585i
$268$	−1.86092	+	11.3511i	−0.113674	+	0.693379i
$269$	−2.23496	−	2.63120i	−0.136268	−	0.160427i	0.689795	−	0.724005i	$-0.257701\pi$
$269$	−2.23496	−	2.63120i	−0.136268	−	0.160427i	−0.826063	+	0.563577i	$0.809425\pi$
$270$	0.502642	−	0.591756i	0.0305898	−	0.0360131i
$271$	0.00195765	+	0.0119411i	0.000118919	+	0.000725371i	0.986886	−	0.161419i	$-0.0516072\pi$
$271$	0.00195765	+	0.0119411i	0.000118919	+	0.000725371i	−0.986767	+	0.162145i	$0.948159\pi$
$272$	−2.76851	+	5.22196i	−0.167866	+	0.316628i
$273$	0.0689974	+	0.0151875i	0.00417591	+	0.000919188i
$274$	18.9577	+	6.38758i	1.14527	+	0.385888i
$275$	0.695494	+	12.8276i	0.0419398	+	0.773535i
$276$	3.39056	−	2.57744i	0.204088	−	0.155144i
$277$	1.61413	+	3.04457i	0.0969837	+	0.182931i	0.927257	−	0.374426i	$-0.122160\pi$
$277$	1.61413	+	3.04457i	0.0969837	+	0.182931i	−0.830273	+	0.557357i	$0.811815\pi$
$278$	−2.42887	−	8.74799i	−0.145674	−	0.524670i
$279$	−1.66975	−	1.58167i	−0.0999654	−	0.0946922i
$280$	−0.403675	−	1.01315i	−0.0241242	−	0.0605472i
$281$	21.3509	−	7.19397i	1.27369	−	0.429156i	0.400393	−	0.916343i	$-0.368874\pi$
$281$	21.3509	−	7.19397i	1.27369	−	0.429156i	0.873298	+	0.487187i	$0.161977\pi$
$282$	−0.949091	+	0.103220i	−0.0565175	+	0.00614665i
$283$	23.7938	+	11.0082i	1.41439	+	0.654369i	0.970365	−	0.241644i	$-0.0776865\pi$
$283$	23.7938	+	11.0082i	1.41439	+	0.654369i	0.444029	+	0.896012i	$0.353549\pi$
$284$	−6.29192	+	5.96002i	−0.373357	+	0.353662i
$285$	0.712781	+	0.428866i	0.0422215	+	0.0254038i
$286$	0.146080	+	0.0158871i	0.00863788	+	0.000939426i
$287$	−2.55691	+	0.562819i	−0.150930	+	0.0332222i
$288$	0.267528	−	0.963550i	0.0157643	−	0.0567777i
$289$	−15.3665	+	9.24570i	−0.903911	+	0.543865i
$290$	−1.99566	+	0.923290i	−0.117189	+	0.0542175i
$291$	1.15235	−	2.89218i	0.0675520	−	0.169543i
$292$	−0.118772	+	2.19063i	−0.00695062	+	0.128197i
$293$	10.2432	+	15.1076i	0.598416	+	0.882598i	0.999440	−	0.0334701i	$-0.0106558\pi$
$293$	10.2432	+	15.1076i	0.598416	+	0.882598i	−0.401024	+	0.916068i	$0.631346\pi$
$294$	−5.02691			−0.293175
$295$	4.79699	+	3.54336i	0.279292	+	0.206303i
$296$	−9.82429			−0.571025
$297$	1.63952	+	2.41812i	0.0951348	+	0.140313i
$298$	−1.09207	+	20.1421i	−0.0632622	+	1.16680i
$299$	−0.0792877	+	0.198997i	−0.00458532	+	0.0115083i
$300$	−3.99077	+	1.84633i	−0.230407	+	0.106598i
$301$	2.91880	−	1.75618i	0.168237	−	0.101225i
$302$	−0.0737728	+	0.265706i	−0.00424515	+	0.0152896i
$303$	7.86231	−	1.73063i	0.451678	−	0.0994219i
$304$	1.06512	+	0.115839i	0.0610889	+	0.00664382i
$305$	2.18955	+	1.31741i	0.125373	+	0.0754346i
$306$	4.29097	−	4.06462i	0.245298	−	0.232359i
$307$	21.4118	+	9.90616i	1.22204	+	0.565375i	0.921494	−	0.388393i	$-0.126970\pi$
$307$	21.4118	+	9.90616i	1.22204	+	0.565375i	0.300544	+	0.953768i	$0.402832\pi$
$308$	4.07971	−	0.443696i	0.232463	−	0.0252819i
$309$	13.2506	−	4.46466i	0.753802	−	0.253986i
$310$	−0.660962	−	1.65889i	−0.0375401	−	0.0942186i
$311$	−10.0684	−	9.53729i	−0.570926	−	0.540810i	0.346843	−	0.937923i	$-0.387254\pi$
$311$	−10.0684	−	9.53729i	−0.570926	−	0.540810i	−0.917770	+	0.397113i	$0.870012\pi$
$312$	0.0134556	+	0.0484627i	0.000761774	+	0.00274366i
$313$	7.31311	+	13.7940i	0.413362	+	0.779683i	0.999535	−	0.0305031i	$-0.00971093\pi$
$313$	7.31311	+	13.7940i	0.413362	+	0.779683i	−0.586173	+	0.810186i	$0.699366\pi$
$314$	−12.2956	+	9.34684i	−0.693878	+	0.527473i
$315$	0.0590443	+	1.08901i	0.00332677	+	0.0613586i
$316$	−5.28569	−	1.78095i	−0.297343	−	0.100187i
$317$	−22.1808	−	4.88237i	−1.24580	−	0.274221i	−0.457331	−	0.889297i	$-0.651194\pi$
$317$	−22.1808	−	4.88237i	−1.24580	−	0.274221i	−0.788468	+	0.615076i	$0.789125\pi$
$318$	−1.82830	+	3.44853i	−0.102526	+	0.193384i
$319$	−1.33859	−	8.16506i	−0.0749468	−	0.457155i
$320$	0.502642	−	0.591756i	0.0280985	−	0.0330801i
$321$	−5.33691	−	6.28310i	−0.297877	−	0.350688i
$322$	−0.967858	+	5.90367i	−0.0539366	+	0.328999i
$323$	5.04124	+	3.83225i	0.280502	+	0.213232i
$324$	−0.561187	+	0.827689i	−0.0311771	+	0.0459827i
$325$	0.124112	−	0.183052i	0.00688452	−	0.0101539i
$326$	−13.7103	−	10.4223i	−0.759343	−	0.577237i
$327$	0.0794099	−	0.484379i	0.00439138	−	0.0267862i
$328$	−1.20665	−	1.42057i	−0.0666259	−	0.0784381i
$329$	0.868156	−	1.02207i	0.0478630	−	0.0563487i
$330$	0.366974	+	2.23844i	0.0202012	+	0.123222i
$331$	8.19858	−	15.4642i	0.450635	−	0.849987i	−0.549263	−	0.835650i	$-0.685091\pi$
$331$	8.19858	−	15.4642i	0.450635	−	0.849987i	0.999897	−	0.0143372i	$-0.00456383\pi$
$332$	−6.95166	−	1.53018i	−0.381522	−	0.0839793i
$333$	9.31002	+	3.13691i	0.510186	+	0.171902i
$334$	0.0452054	+	0.833764i	0.00247353	+	0.0456215i
$335$	7.10978	−	5.40472i	0.388449	−	0.295291i
$336$	0.657958	+	1.24104i	0.0358945	+	0.0677043i
$337$	−0.497137	−	1.79053i	−0.0270808	−	0.0975362i	0.948775	−	0.315954i	$-0.102324\pi$
$337$	−0.497137	−	1.79053i	−0.0270808	−	0.0975362i	−0.975855	+	0.218417i	$0.929911\pi$
$338$	9.43610	+	8.93835i	0.513256	+	0.486182i
$339$	−0.865120	−	2.17129i	−0.0469869	−	0.117928i
$340$	4.34876	−	1.46527i	0.235845	−	0.0794654i
$341$	6.67996	−	0.726490i	0.361740	−	0.0393416i
$342$	−0.972378	−	0.449870i	−0.0525802	−	0.0243262i
$343$	12.2648	−	11.6179i	0.662238	−	0.627305i
$344$	2.07793	+	1.25025i	0.112034	+	0.0674088i
$345$	−3.28738	−	0.357524i	−0.176987	−	0.0192484i
$346$	−16.8622	+	3.71165i	−0.906517	+	0.199540i
$347$	5.84145	−	21.0390i	0.313586	−	1.12943i	−0.623927	−	0.781483i	$-0.714464\pi$
$347$	5.84145	−	21.0390i	0.313586	−	1.12943i	0.937513	−	0.347951i	$-0.113122\pi$
$348$	2.42671	−	1.46010i	0.130085	−	0.0782696i
$349$	5.26257	−	2.43472i	0.281699	−	0.130328i	−0.273952	−	0.961743i	$-0.588331\pi$
$349$	5.26257	−	2.43472i	0.281699	−	0.130328i	0.555651	+	0.831416i	$0.312469\pi$
$350$	2.28618	−	5.73789i	0.122202	−	0.306703i
$351$	0.00272297	−	0.0502223i	0.000145341	−	0.00268067i
$352$	1.63952	+	2.41812i	0.0873869	+	0.128886i
$353$	19.8998			1.05916			0.529579	−	0.848261i	$-0.322350\pi$
$353$	19.8998			1.05916			0.529579	+	0.848261i	$0.322350\pi$
$354$	−6.63558	−	3.86898i	−0.352677	−	0.205634i
$355$	6.72890			0.357133
$356$	1.53926	+	2.27023i	0.0815804	+	0.120322i
$357$	−0.449474	+	8.29005i	−0.0237887	+	0.438756i
$358$	1.59418	−	4.00110i	0.0842552	−	0.211465i
$359$	−13.2897	+	6.14848i	−0.701405	+	0.324504i	−0.737976	−	0.674827i	$-0.764218\pi$
$359$	−13.2897	+	6.14848i	−0.701405	+	0.324504i	0.0365716	+	0.999331i	$0.488356\pi$
$360$	−0.665279	+	0.400285i	−0.0350633	+	0.0210969i
$361$	−4.77594	+	17.2014i	−0.251365	+	0.905336i
$362$	16.8147	−	3.70120i	0.883763	−	0.194531i
$363$	2.45024	+	0.266479i	0.128604	+	0.0139865i
$364$	−0.0605362	−	0.0364234i	−0.00317296	−	0.00190911i
$365$	1.23662	−	1.17138i	0.0647274	−	0.0613131i
$366$	−2.98699	−	1.38193i	−0.156133	−	0.0722347i
$367$	−32.4202	+	3.52591i	−1.69232	+	0.184051i	−0.902915	−	0.429820i	$-0.858577\pi$
$367$	−32.4202	+	3.52591i	−1.69232	+	0.184051i	−0.789406	+	0.613871i	$0.789612\pi$
$368$	−4.03606	+	1.35991i	−0.210394	+	0.0708900i
$369$	0.689891	+	1.73150i	0.0359143	+	0.0901381i
$370$	5.53771	+	5.24560i	0.287892	+	0.272706i
$371$	−1.46678	−	5.28286i	−0.0761514	−	0.274273i
$372$	1.07731	+	2.03203i	0.0558561	+	0.105356i
$373$	4.04004	−	3.07116i	0.209186	−	0.159019i	−0.495336	−	0.868702i	$-0.664955\pi$
$373$	4.04004	−	3.07116i	0.209186	−	0.159019i	0.704521	+	0.709683i	$0.251162\pi$
$374$	0.934847	+	17.2422i	0.0483398	+	0.891575i
$375$	6.91420	+	2.32966i	0.357048	+	0.120303i
$376$	0.932367	+	0.205230i	0.0480832	+	0.0105839i
$377$	−0.0667217	+	0.125850i	−0.00343634	+	0.00648163i
$378$	−0.227250	−	1.38616i	−0.0116885	−	0.0712965i
$379$	15.2488	−	17.9523i	0.783278	−	0.922146i	−0.215241	−	0.976561i	$-0.569054\pi$
$379$	15.2488	−	17.9523i	0.783278	−	0.922146i	0.998518	+	0.0544153i	$0.0173295\pi$
$380$	−0.538531	−	0.634008i	−0.0276261	−	0.0325239i
$381$	−1.03689	+	6.32477i	−0.0531217	+	0.324028i
$382$	14.8335	+	11.2761i	0.758947	+	0.576937i
$383$	11.5336	−	17.0108i	0.589338	−	0.869209i	−0.409737	−	0.912204i	$-0.634380\pi$
$383$	11.5336	−	17.0108i	0.589338	−	0.869209i	0.999075	+	0.0429948i	$0.0136899\pi$
$384$	−0.561187	+	0.827689i	−0.0286380	+	0.0422378i
$385$	−2.53654	−	1.92823i	−0.129274	−	0.0982716i
$386$	0.678814	−	4.14058i	0.0345507	−	0.210750i
$387$	−1.56995	−	1.84829i	−0.0798050	−	0.0939537i
$388$	−2.01551	+	2.37284i	−0.102322	+	0.120463i
$389$	4.80855	+	29.3308i	0.243803	+	1.48713i	0.770697	+	0.637202i	$0.219908\pi$
$389$	4.80855	+	29.3308i	0.243803	+	1.48713i	−0.526894	+	0.849931i	$0.676643\pi$
$390$	0.0182917	−	0.0345018i	0.000926235	−	0.00174706i
$391$	−24.5842	−	5.41138i	−1.24327	−	0.273665i
$392$	4.76377	+	1.60510i	0.240607	+	0.0810698i
$393$	0.659539	+	12.1645i	0.0332693	+	0.613616i
$394$	4.41275	−	3.35449i	0.222311	−	0.168997i
$395$	2.02848	+	3.82613i	0.102064	+	0.192513i
$396$	−0.781591	−	2.81504i	−0.0392764	−	0.141461i
$397$	−18.0462	−	17.0942i	−0.905711	−	0.857935i	0.0846552	−	0.996410i	$-0.473021\pi$
$397$	−18.0462	−	17.0942i	−0.905711	−	0.857935i	−0.990366	+	0.138476i	$0.955780\pi$
$398$	2.41157	+	6.05259i	0.120881	+	0.303389i
$399$	1.42618	−	0.480537i	0.0713985	−	0.0240569i
$400$	4.37140	−	0.475418i	0.218570	−	0.0237709i
$401$	−17.1490	−	7.93395i	−0.856378	−	0.396203i	−0.0579690	−	0.998318i	$-0.518462\pi$
$401$	−17.1490	−	7.93395i	−0.856378	−	0.396203i	−0.798409	+	0.602116i	$0.794325\pi$
$402$	−8.35086	+	7.91036i	−0.416503	+	0.394533i
$403$	−0.0991197	−	0.0596383i	−0.00493750	−	0.00297080i
$404$	−8.00334	−	0.870415i	−0.398181	−	0.0433048i
$405$	0.758265	−	0.166907i	0.0376785	−	0.00829366i
$406$	−1.06427	+	3.83315i	−0.0528188	+	0.190236i
$407$	−24.5934	+	14.7974i	−1.21905	+	0.733479i
$408$	−5.36419	+	2.48174i	−0.265567	+	0.122864i
$409$	3.85680	−	9.67985i	0.190707	−	0.478638i	−0.802268	−	0.596964i	$-0.796374\pi$
$409$	3.85680	−	9.67985i	0.190707	−	0.478638i	0.992975	+	0.118326i	$0.0377529\pi$
$410$	−0.0783468	+	1.44502i	−0.00386927	+	0.0713645i
$411$	11.2265	+	16.5578i	0.553760	+	0.816735i
$412$	−13.9826			−0.688872
$413$	10.5042	−	2.46438i	0.516880	−	0.121264i
$414$	4.25901			0.209319
$415$	3.10145	+	4.57430i	0.152244	+	0.224544i
$416$	0.00272297	−	0.0502223i	0.000133505	−	0.00246235i
$417$	3.36045	−	8.43410i	0.164562	−	0.413020i
$418$	2.84083	−	1.31431i	0.138949	−	0.0642849i
$419$	8.94780	−	5.38372i	0.437129	−	0.263012i	−0.279935	−	0.960019i	$-0.590313\pi$
$419$	8.94780	−	5.38372i	0.437129	−	0.263012i	0.717064	+	0.697007i	$0.245485\pi$
$420$	0.291768	−	1.05085i	0.0142368	−	0.0512765i
$421$	−32.3010	+	7.10998i	−1.57425	+	0.346519i	−0.914380	−	0.404858i	$-0.867321\pi$
$421$	−32.3010	+	7.10998i	−1.57425	+	0.346519i	−0.659873	+	0.751377i	$0.729390\pi$
$422$	−22.7747	−	2.47689i	−1.10865	−	0.120573i
$423$	−0.818031	−	0.492193i	−0.0397740	−	0.0239312i
$424$	2.83371	−	2.68423i	0.137617	−	0.130358i
$425$	23.5873	+	10.9126i	1.14415	+	0.529341i
$426$	−8.61580	+	0.937025i	−0.417437	+	0.0453990i
$427$	4.38101	−	1.47613i	0.212012	−	0.0714352i
$428$	3.05134	+	7.65828i	0.147492	+	0.370177i
$429$	0.106679	+	0.101051i	0.00515049	+	0.00487881i
$430$	−0.503717	−	1.81422i	−0.0242914	−	0.0874897i
$431$	−12.8599	−	24.2563i	−0.619437	−	1.16838i	−0.972526	−	0.232793i	$-0.925214\pi$
$431$	−12.8599	−	24.2563i	−0.619437	−	1.16838i	0.353089	−	0.935590i	$-0.385131\pi$
$432$	0.796093	−	0.605174i	0.0383020	−	0.0291165i
$433$	1.74603	+	32.2036i	0.0839087	+	1.54761i	0.673063	+	0.739585i	$0.264978\pi$
$433$	1.74603	+	32.2036i	0.0839087	+	1.54761i	−0.589154	+	0.808021i	$0.700539\pi$
$434$	−3.06154	−	1.03155i	−0.146959	−	0.0495162i
$435$	−2.14748	−	0.472697i	−0.102964	−	0.0226641i
$436$	−0.229916	+	0.433668i	−0.0110110	+	0.0207689i
$437$	0.738229	+	4.50300i	0.0353143	+	0.215407i
$438$	−1.42026	+	1.67206i	−0.0678628	+	0.0798943i
$439$	−10.5052	−	12.3677i	−0.501387	−	0.590278i	0.452004	−	0.892016i	$-0.350709\pi$
$439$	−10.5052	−	12.3677i	−0.501387	−	0.590278i	−0.953391	+	0.301738i	$0.902433\pi$
$440$	0.366974	−	2.23844i	0.0174948	−	0.106713i
$441$	−4.00189	−	3.04216i	−0.190566	−	0.144865i
$442$	0.166826	−	0.246049i	0.00793508	−	0.0117034i
$443$	3.64232	−	5.37202i	0.173052	−	0.255232i	−0.731266	−	0.682093i	$-0.761070\pi$
$443$	3.64232	−	5.37202i	0.173052	−	0.255232i	0.904318	+	0.426860i	$0.140380\pi$
$444$	−7.82105	−	5.94541i	−0.371171	−	0.282157i
$445$	0.344531	−	2.10155i	0.0163323	−	0.0996228i
$446$	−1.85327	−	2.18183i	−0.0877547	−	0.103313i
$447$	−13.0589	+	15.3741i	−0.617664	+	0.727171i
$448$	−0.227250	−	1.38616i	−0.0107365	−	0.0654900i
$449$	8.04419	−	15.1730i	0.379629	−	0.716056i	−0.617904	−	0.786253i	$-0.712018\pi$
$449$	8.04419	−	15.1730i	0.379629	−	0.716056i	0.997533	+	0.0701972i	$0.0223628\pi$
$450$	−4.29437	−	0.945263i	−0.202439	−	0.0445601i
$451$	−5.16031	−	1.73871i	−0.242990	−	0.0818727i
$452$	0.126538	+	2.33386i	0.00595186	+	0.109776i
$453$	−0.219528	+	0.166881i	−0.0103143	+	0.00784075i
$454$	5.73121	+	10.8102i	0.268979	+	0.507348i
$455$	0.0146748	+	0.0528538i	0.000687965	+	0.00247782i
$456$	0.777833	+	0.736803i	0.0364254	+	0.0345039i
$457$	6.89121	+	17.2956i	0.322357	+	0.809056i	0.997453	+	0.0713257i	$0.0227230\pi$
$457$	6.89121	+	17.2956i	0.322357	+	0.809056i	−0.675096	+	0.737730i	$0.735898\pi$
$458$	−7.10479	+	2.39388i	−0.331985	+	0.111859i
$459$	5.87581	−	0.639033i	0.274259	−	0.0298275i
$460$	3.00114	+	1.38847i	0.139929	+	0.0647379i
$461$	17.3267	−	16.4127i	0.806985	−	0.764417i	−0.168213	−	0.985751i	$-0.553800\pi$
$461$	17.3267	−	16.4127i	0.806985	−	0.764417i	0.975198	+	0.221334i	$0.0710410\pi$
$462$	3.51635	+	2.11571i	0.163595	+	0.0984320i
$463$	−5.85620	−	0.636900i	−0.272161	−	0.0295993i	−0.0289790	−	0.999580i	$-0.509226\pi$
$463$	−5.85620	−	0.636900i	−0.272161	−	0.0295993i	−0.243182	+	0.969981i	$0.578191\pi$
$464$	−2.76589	+	0.608818i	−0.128403	+	0.0282637i
$465$	0.477730	−	1.72063i	0.0221542	−	0.0797922i
$466$	−18.8582	+	11.3466i	−0.873590	+	0.525621i
$467$	−4.87783	+	2.25673i	−0.225719	+	0.104429i	−0.529490	−	0.848316i	$-0.677617\pi$
$467$	−4.87783	+	2.25673i	−0.225719	+	0.104429i	0.303770	+	0.952745i	$0.401754\pi$
$468$	−0.0186165	+	0.0467238i	−0.000860547	+	0.00215981i
$469$	0.874743	−	16.1337i	0.0403919	−	0.744984i
$470$	−0.415972	−	0.613512i	−0.0191873	−	0.0282992i
$471$	−15.4449			−0.711662
$472$	5.05286	+	5.78521i	0.232577	+	0.266286i
$473$	7.08487			0.325762
$474$	−3.13011	−	4.61657i	−0.143771	−	0.212046i
$475$	0.255056	−	4.70424i	0.0117028	−	0.215845i
$476$	3.07297	−	7.71258i	0.140849	−	0.353505i
$477$	−3.54246	+	1.63891i	−0.162198	+	0.0750407i
$478$	13.5324	−	8.14220i	0.618960	−	0.372416i
$479$	−1.62803	+	5.86362i	−0.0743864	+	0.267916i	−0.991386	−	0.130972i	$-0.958190\pi$
$479$	−1.62803	+	5.86362i	−0.0743864	+	0.267916i	0.917000	+	0.398888i	$0.130604\pi$
$480$	0.758265	−	0.166907i	0.0346099	−	0.00761821i
$481$	0.491226	+	0.0534241i	0.0223980	+	0.00243593i
$482$	16.6908	+	10.0425i	0.760246	+	0.457425i
$483$	−4.34326	+	4.11415i	−0.197625	+	0.187200i
$484$	−2.23689	−	1.03489i	−0.101677	−	0.0470407i
$485$	2.40305	−	0.261347i	0.109117	−	0.0118672i
$486$	−0.947653	+	0.319302i	−0.0429864	+	0.0144838i
$487$	−2.72318	−	6.83466i	−0.123399	−	0.309708i	0.854280	−	0.519814i	$-0.173999\pi$
$487$	−2.72318	−	6.83466i	−0.123399	−	0.309708i	−0.977679	+	0.210105i	$0.932619\pi$
$488$	2.38938	+	2.26334i	0.108162	+	0.102457i
$489$	−4.60737	−	16.5942i	−0.208352	−	0.750417i
$490$	−1.82819	−	3.44833i	−0.0825891	−	0.155780i
$491$	8.65433	−	6.57885i	0.390564	−	0.296899i	−0.391402	−	0.920220i	$-0.628010\pi$
$491$	8.65433	−	6.57885i	0.390564	−	0.296899i	0.781967	+	0.623320i	$0.214217\pi$
$492$	−0.100908	−	1.86114i	−0.00454929	−	0.0839067i
$493$	−15.8628	−	5.34479i	−0.714424	−	0.240717i
$494$	−0.0526274	−	0.0115842i	−0.00236782	−	0.000521196i
$495$	−1.06250	+	2.00409i	−0.0477559	+	0.0900772i
$496$	−0.372090	−	2.26965i	−0.0167073	−	0.101910i
$497$	7.88108	−	9.27833i	0.353515	−	0.416190i
$498$	−4.60814	−	5.42513i	−0.206496	−	0.243106i
$499$	6.00548	−	36.6318i	0.268842	−	1.63987i	−0.414702	−	0.909957i	$-0.636114\pi$
$499$	6.00548	−	36.6318i	0.268842	−	1.63987i	0.683545	−	0.729909i	$-0.260437\pi$
$500$	−5.80840	−	4.41543i	−0.259759	−	0.197464i
$501$	−0.468585	+	0.691111i	−0.0209348	+	0.0308765i
$502$	10.6702	−	15.7373i	0.476233	−	0.702391i
$503$	−11.4264	−	8.68616i	−0.509480	−	0.387297i	0.318615	−	0.947884i	$-0.396782\pi$
$503$	−11.4264	−	8.68616i	−0.509480	−	0.387297i	−0.828095	+	0.560587i	$0.810575\pi$
$504$	−0.227250	+	1.38616i	−0.0101225	+	0.0617446i
$505$	4.04653	+	4.76395i	0.180068	+	0.211993i
$506$	−8.05529	+	9.48343i	−0.358102	+	0.421590i
$507$	2.10276	+	12.8262i	0.0933867	+	0.569634i
$508$	3.00213	−	5.66261i	0.133198	−	0.251238i
$509$	−18.8341	−	4.14570i	−0.834807	−	0.183755i	−0.223056	−	0.974806i	$-0.571603\pi$
$509$	−18.8341	−	4.14570i	−0.834807	−	0.183755i	−0.611751	+	0.791051i	$0.709534\pi$
$510$	4.34876	+	1.46527i	0.192566	+	0.0648832i
$511$	−0.166835	−	3.07710i	−0.00738037	−	0.136123i
$512$	0.796093	−	0.605174i	0.0351827	−	0.0267452i
$513$	−0.501854	−	0.946597i	−0.0221574	−	0.0417933i
$514$	−0.174368	−	0.628016i	−0.00769104	−	0.0277006i
$515$	7.88163	+	7.46588i	0.347306	+	0.328986i
$516$	0.897606	+	2.25282i	0.0395149	+	0.0991749i
$517$	2.64314	−	0.890578i	0.116245	−	0.0391676i
$518$	13.7190	−	1.49203i	0.602776	−	0.0655559i
$519$	−15.6701	−	7.24975i	−0.687840	−	0.318229i
$520$	−0.0283506	+	0.0268551i	−0.00124326	+	0.00117768i
$521$	28.3945	+	17.0844i	1.24398	+	0.748481i	0.976591	−	0.215107i	$-0.0690099\pi$
$521$	28.3945	+	17.0844i	1.24398	+	0.748481i	0.267394	+	0.963587i	$0.413837\pi$
$522$	2.81550	+	0.306204i	0.123231	+	0.0134022i
$523$	−29.2301	+	6.43403i	−1.27814	+	0.281340i	−0.801626	−	0.597825i	$-0.796032\pi$
$523$	−29.2301	+	6.43403i	−1.27814	+	0.281340i	−0.476516	+	0.879166i	$0.658101\pi$
$524$	3.25912	−	11.7383i	0.142375	−	0.512790i
$525$	5.29244	−	3.18435i	0.230981	−	0.138977i
$526$	11.2536	−	5.20646i	0.490679	−	0.227012i
$527$	5.03156	−	12.6283i	0.219178	−	0.550096i
$528$	−0.158168	+	2.91724i	−0.00688339	+	0.126957i
$529$	2.72786	+	4.02329i	0.118603	+	0.174926i
$530$	−3.03052			−0.131637
$531$	−2.94113	−	7.09576i	−0.127634	−	0.307930i
$532$	−1.50496			−0.0652484
$533$	0.0526088	+	0.0775921i	0.00227874	+	0.00336089i
$534$	−0.148495	+	2.73883i	−0.00642602	+	0.118521i
$535$	2.36911	−	5.94602i	0.102426	−	0.257069i
$536$	10.4395	−	4.82983i	0.450918	−	0.208617i
$537$	3.69048	−	2.22049i	0.159256	−	0.0958212i
$538$	−0.923584	+	3.32645i	−0.0398185	+	0.143413i
$539$	14.3429	−	3.15711i	0.617792	−	0.135986i
$540$	−0.771866	−	0.0839454i	−0.0332158	−	0.00361244i
$541$	−23.8674	−	14.3605i	−1.02614	−	0.617408i	−0.100156	−	0.994972i	$-0.531934\pi$
$541$	−23.8674	−	14.3605i	−1.02614	−	0.617408i	−0.925983	+	0.377564i	$0.876762\pi$
$542$	0.00878492	−	0.00832152i	0.000377345	−	0.000357440i
$543$	15.6260	+	7.22934i	0.670574	+	0.310241i
$544$	5.87581	−	0.639033i	0.251923	−	0.0273983i
$545$	0.361151	−	0.121686i	0.0154700	−	0.00521245i
$546$	−0.0261499	−	0.0656314i	−0.00111911	−	0.00280877i
$547$	−26.6669	−	25.2602i	−1.14019	−	1.08005i	−0.995895	−	0.0905142i	$-0.971149\pi$
$547$	−26.6669	−	25.2602i	−1.14019	−	1.08005i	−0.144298	−	0.989534i	$-0.546092\pi$
$548$	−5.35186	−	19.2757i	−0.228620	−	0.823416i
$549$	−1.54162	−	2.90780i	−0.0657946	−	0.124102i
$550$	10.2270	−	7.77435i	0.436080	−	0.331499i
$551$	0.164275	+	3.02987i	0.00699834	+	0.129077i
$552$	−4.03606	−	1.35991i	−0.171786	−	0.0578815i
$553$	7.65158	+	1.68424i	0.325378	+	0.0716212i
$554$	1.61413	−	3.04457i	0.0685778	−	0.129352i
$555$	1.23403	+	7.52726i	0.0523817	+	0.319514i
$556$	−5.87757	+	6.91961i	−0.249264	+	0.293457i
$557$	17.9333	+	21.1128i	0.759860	+	0.894576i	0.997040	−	0.0768894i	$-0.0244988\pi$
$557$	17.9333	+	21.1128i	0.759860	+	0.894576i	−0.237180	+	0.971466i	$0.576223\pi$
$558$	−0.372090	+	2.26965i	−0.0157518	+	0.0960819i
$559$	−0.0971000	−	0.0738135i	−0.00410689	−	0.00312198i
$560$	−0.612035	+	0.902684i	−0.0258632	+	0.0381453i
$561$	−9.69033	+	14.2922i	−0.409126	+	0.603416i
$562$	−17.9362	−	13.6348i	−0.756595	−	0.575148i
$563$	5.99343	−	36.5583i	0.252593	−	1.54075i	−0.490429	−	0.871481i	$-0.663160\pi$
$563$	5.99343	−	36.5583i	0.252593	−	1.54075i	0.743022	−	0.669267i	$-0.233392\pi$
$564$	0.618051	+	0.727626i	0.0260247	+	0.0306386i
$565$	1.17482	−	1.38310i	0.0494250	−	0.0581876i
$566$	−4.24142	−	25.8715i	−0.178280	−	1.08746i
$567$	0.657958	−	1.24104i	0.0276316	−	0.0521188i
$568$	8.46399	+	1.86306i	0.355141	+	0.0781725i
$569$	14.1951	+	4.78290i	0.595091	+	0.200510i	0.600700	−	0.799475i	$-0.294889\pi$
$569$	14.1951	+	4.78290i	0.595091	+	0.200510i	−0.00560850	+	0.999984i	$0.501785\pi$
$570$	−0.0450357	−	0.830635i	−0.00188634	−	0.0347915i
$571$	28.5868	−	21.7311i	1.19632	−	0.909419i	0.198816	−	0.980037i	$-0.436290\pi$
$571$	28.5868	−	21.7311i	1.19632	−	0.909419i	0.997503	+	0.0706182i	$0.0224972\pi$
$572$	−0.0688285	−	0.129824i	−0.00287786	−	0.00542823i
$573$	4.98482	+	17.9537i	0.208244	+	0.750026i
$574$	1.90075	+	1.80048i	0.0793356	+	0.0751507i
$575$	6.93180	+	17.3975i	0.289076	+	0.725526i
$576$	−0.947653	+	0.319302i	−0.0394855	+	0.0133042i
$577$	−17.0267	+	1.85176i	−0.708831	+	0.0770900i	−0.455430	−	0.890272i	$-0.650515\pi$
$577$	−17.0267	+	1.85176i	−0.708831	+	0.0770900i	−0.253400	+	0.967361i	$0.581549\pi$
$578$	16.2760	+	7.53010i	0.676994	+	0.313211i
$579$	3.04617	−	2.88549i	0.126595	−	0.119917i
$580$	1.88414	+	1.13365i	0.0782345	+	0.0470721i
$581$	9.93991	+	1.08103i	0.412377	+	0.0448487i
$582$	−3.04051	+	0.669268i	−0.126033	+	0.0277420i
$583$	3.05071	−	10.9877i	0.126348	−	0.455063i
$584$	1.87981	−	1.13104i	0.0777871	−	0.0468030i
$585$	0.0354414	−	0.0163970i	0.00146532	−	0.000677931i
$586$	6.75606	−	16.9564i	0.279090	−	0.700463i
$587$	0.0341456	−	0.629778i	0.00140934	−	0.0259937i	−0.997744	−	0.0671312i	$-0.978615\pi$
$587$	0.0341456	−	0.629778i	0.00140934	−	0.0259937i	0.999153	+	0.0411375i	$0.0130982\pi$
$588$	2.82104	+	4.16072i	0.116338	+	0.171585i
$589$	−2.46417			−0.101534
$590$	0.240792	−	5.95891i	0.00991324	−	0.245324i
$591$	5.54301			0.228009
$592$	5.51326	+	8.13146i	0.226594	+	0.334201i
$593$	1.18490	−	21.8542i	0.0486580	−	0.897443i	−0.867701	−	0.497086i	$-0.834403\pi$
$593$	1.18490	−	21.8542i	0.0486580	−	0.897443i	0.916359	−	0.400357i	$-0.131114\pi$
$594$	1.08137	−	2.71403i	0.0443691	−	0.111358i
$595$	−5.85022	+	2.70660i	−0.239836	+	0.110960i
$596$	17.2843	−	10.3996i	0.707992	−	0.425984i
$597$	−1.74304	+	6.27785i	−0.0713377	+	0.256935i
$598$	0.209203	−	0.0460490i	0.00855494	−	0.00188309i
$599$	−31.6335	−	3.44035i	−1.29251	−	0.140569i	−0.564098	−	0.825708i	$-0.690776\pi$
$599$	−31.6335	−	3.44035i	−1.29251	−	0.140569i	−0.728413	+	0.685139i	$0.759742\pi$
$600$	3.76775	+	2.26698i	0.153818	+	0.0925491i
$601$	−29.4926	+	27.9369i	−1.20303	+	1.13957i	−0.216449	+	0.976294i	$0.569448\pi$
$601$	−29.4926	+	27.9369i	−1.20303	+	1.13957i	−0.986580	+	0.163276i	$0.947794\pi$
$602$	−3.09156	−	1.43031i	−0.126003	−	0.0582950i
$603$	−11.4352	+	1.24365i	−0.465678	+	0.0506455i
$604$	0.261322	−	0.0880496i	0.0106330	−	0.00358269i
$605$	0.708305	+	1.77771i	0.0287967	+	0.0722743i
$606$	−5.84465	−	5.53634i	−0.237423	−	0.224899i
$607$	−4.72876	−	17.0315i	−0.191934	−	0.691285i	−0.995389	−	0.0959194i	$-0.969421\pi$
$607$	−4.72876	−	17.0315i	−0.191934	−	0.691285i	0.803455	−	0.595366i	$-0.202993\pi$
$608$	−0.501854	−	0.946597i	−0.0203529	−	0.0383896i
$609$	−3.16698	+	2.40748i	−0.128333	+	0.0975560i
$610$	−0.138343	−	2.55158i	−0.00560133	−	0.103310i
$611$	−0.0455034	−	0.0153319i	−0.00184087	−	0.000620262i
$612$	−5.77228	−	1.27057i	−0.233330	−	0.0513599i
$613$	−15.5139	+	29.2623i	−0.626600	+	1.18189i	0.343492	+	0.939156i	$0.388390\pi$
$613$	−15.5139	+	29.2623i	−0.626600	+	1.18189i	−0.970092	+	0.242737i	$0.921955\pi$
$614$	−3.81682	−	23.2815i	−0.154034	−	0.939567i
$615$	−0.936861	+	1.10296i	−0.0377779	+	0.0444756i
$616$	−2.65672	−	3.12774i	−0.107042	−	0.126020i
$617$	−0.827695	+	5.04872i	−0.0333218	+	0.203254i	−0.998241	−	0.0592950i	$-0.981115\pi$
$617$	−0.827695	+	5.04872i	−0.0333218	+	0.203254i	0.964919	+	0.262549i	$0.0845630\pi$
$618$	−11.1314	−	8.46189i	−0.447772	−	0.340387i
$619$	−4.60055	+	6.78531i	−0.184912	+	0.272724i	−0.908835	−	0.417156i	$-0.863027\pi$
$619$	−4.60055	+	6.78531i	−0.184912	+	0.272724i	0.723923	+	0.689881i	$0.242337\pi$
$620$	−1.00212	+	1.47802i	−0.0402462	+	0.0593587i
$621$	3.39056	+	2.57744i	0.136059	+	0.103429i
$622$	−2.24366	+	13.6857i	−0.0899625	+	0.548747i
$623$	−2.49425	−	2.93646i	−0.0999300	−	0.117647i
$624$	0.0325610	−	0.0383337i	0.00130348	−	0.00153458i
$625$	−2.64045	−	16.1060i	−0.105618	−	0.644242i
$626$	7.31311	−	13.7940i	0.292291	−	0.551319i
$627$	3.05695	+	0.672885i	0.122083	+	0.0268725i
$628$	14.6364	+	4.93157i	0.584055	+	0.196791i
$629$	3.14363	+	57.9809i	0.125345	+	2.31185i
$630$	0.868225	−	0.660007i	0.0345909	−	0.0262953i
$631$	9.16642	+	17.2897i	0.364909	+	0.688292i	0.996185	−	0.0872665i	$-0.0278132\pi$
$631$	9.16642	+	17.2897i	0.364909	+	0.688292i	−0.631276	+	0.775559i	$0.717468\pi$
$632$	1.49218	+	5.37435i	0.0593558	+	0.213780i
$633$	−16.6318	−	15.7545i	−0.661055	−	0.626184i
$634$	8.40651	+	21.0987i	0.333865	+	0.837938i
$635$	−4.71573	+	1.58891i	−0.187138	+	0.0630541i
$636$	3.88033	−	0.422011i	0.153865	−	0.0167338i
$637$	−0.229466	−	0.106162i	−0.00909176	−	0.00420630i
$638$	−6.00693	+	5.69006i	−0.237817	+	0.225272i
$639$	−7.42605	−	4.46810i	−0.293770	−	0.176755i
$640$	−0.771866	−	0.0839454i	−0.0305107	−	0.00331824i
$641$	−40.5660	+	8.92924i	−1.60226	+	0.352684i	−0.924076	−	0.382209i	$-0.875163\pi$
$641$	−40.5660	+	8.92924i	−1.60226	+	0.352684i	−0.678183	+	0.734893i	$0.737232\pi$
$642$	−2.20545	+	7.94330i	−0.0870420	+	0.313497i
$643$	−17.9781	+	10.8171i	−0.708988	+	0.426584i	−0.823858	−	0.566797i	$-0.808183\pi$
$643$	−17.9781	+	10.8171i	−0.708988	+	0.426584i	0.114870	+	0.993381i	$0.463355\pi$
$644$	5.42955	−	2.51198i	0.213954	−	0.0989859i
$645$	0.696917	−	1.74913i	0.0274411	−	0.0688719i
$646$	0.342834	−	6.32319i	0.0134886	−	0.248783i
$647$	24.2577	+	35.7774i	0.953668	+	1.40655i	0.913263	+	0.407371i	$0.133554\pi$
$647$	24.2577	+	35.7774i	0.953668	+	1.40655i	0.0404049	+	0.999183i	$0.487135\pi$
$648$	1.00000			0.0392837
$649$	21.3627	+	6.87165i	0.838558	+	0.269736i
$650$	−0.221161			−0.00867463
$651$	−1.81300	−	2.67398i	−0.0710572	−	0.104802i
$652$	−0.932379	+	17.1967i	−0.0365148	+	0.673475i
$653$	6.91002	−	17.3428i	0.270410	−	0.678678i	−0.729576	−	0.683899i	$-0.760283\pi$
$653$	6.91002	−	17.3428i	0.270410	−	0.678678i	0.999986	+	0.00522150i	$0.00166206\pi$
$654$	−0.445479	+	0.206101i	−0.0174196	+	0.00805917i
$655$	−8.10465	+	4.87641i	−0.316675	+	0.190537i
$656$	−0.498639	+	1.79594i	−0.0194686	+	0.0701195i
$657$	−2.14255	+	0.471611i	−0.0835889	+	0.0183993i
$658$	−1.33316	−	0.144989i	−0.0519718	−	0.00565228i
$659$	−15.9378	−	9.58947i	−0.620850	−	0.373553i	0.170107	−	0.985426i	$-0.445589\pi$
$659$	−15.9378	−	9.58947i	−0.620850	−	0.373553i	−0.790956	+	0.611873i	$0.790416\pi$
$660$	1.64679	−	1.55992i	0.0641013	−	0.0607200i
$661$	41.0026	+	18.9698i	1.59481	+	0.737840i	0.997919	−	0.0644793i	$-0.0205386\pi$
$661$	41.0026	+	18.9698i	1.59481	+	0.737840i	0.596895	+	0.802319i	$0.296401\pi$
$662$	−17.4004	+	1.89241i	−0.676288	+	0.0735507i
$663$	0.281711	−	0.0949196i	0.0109408	−	0.00368637i
$664$	2.63467	+	6.61253i	0.102245	+	0.256616i
$665$	0.848311	+	0.803562i	0.0328961	+	0.0311608i
$666$	−2.62828	−	9.46619i	−0.101844	−	0.366808i
$667$	−5.64991	−	10.6569i	−0.218765	−	0.412635i
$668$	0.664728	−	0.505313i	0.0257191	−	0.0195512i
$669$	−0.154983	−	2.85849i	−0.00599198	−	0.110516i
$670$	−8.46334	−	2.85163i	−0.326968	−	0.110168i
$671$	9.39047	+	2.06700i	0.362515	+	0.0797956i
$672$	0.657958	−	1.24104i	0.0253813	−	0.0478742i
$673$	−1.83006	−	11.1629i	−0.0705438	−	0.430298i	−0.998359	−	0.0572589i	$-0.981764\pi$
$673$	−1.83006	−	11.1629i	−0.0705438	−	0.430298i	0.927816	−	0.373039i	$-0.121684\pi$
$674$	−1.20301	+	1.41630i	−0.0463383	+	0.0545537i
$675$	−2.84667	−	3.35136i	−0.109568	−	0.128994i
$676$	2.10276	−	12.8262i	0.0808753	−	0.493317i
$677$	−17.9989	−	13.6824i	−0.691753	−	0.525857i	0.199196	−	0.979960i	$-0.436167\pi$
$677$	−17.9989	−	13.6824i	−0.691753	−	0.525857i	−0.890949	+	0.454103i	$0.849960\pi$
$678$	−1.31166	+	1.93455i	−0.0503738	+	0.0742959i
$679$	2.45416	−	3.61961i	0.0941818	−	0.138908i
$680$	−3.65326	−	2.77713i	−0.140096	−	0.106498i
$681$	−1.97948	+	12.0743i	−0.0758539	+	0.462688i
$682$	−4.35002	−	5.12124i	−0.166571	−	0.196102i
$683$	23.0189	−	27.1000i	0.880794	−	1.03695i	−0.118239	−	0.992985i	$-0.537725\pi$
$683$	23.0189	−	27.1000i	0.880794	−	1.03695i	0.999033	−	0.0439661i	$-0.0139994\pi$
$684$	0.173334	+	1.05729i	0.00662758	+	0.0404264i
$685$	−7.27537	+	13.7228i	−0.277977	+	0.524321i
$686$	−16.4988	−	3.63167i	−0.629928	−	0.138658i
$687$	−7.10479	−	2.39388i	−0.271065	−	0.0913323i
$688$	−0.131290	−	2.42150i	−0.00500538	−	0.0923188i
$689$	−0.156286	+	0.118805i	−0.00595401	+	0.00452612i
$690$	1.54892	+	2.92157i	0.0589662	+	0.111222i
$691$	9.21696	+	33.1965i	0.350630	+	1.26285i	0.903140	+	0.429347i	$0.141256\pi$
$691$	9.21696	+	33.1965i	0.350630	+	1.26285i	−0.552510	+	0.833506i	$0.686330\pi$
$692$	12.5349	+	11.8737i	0.476507	+	0.451371i
$693$	1.51896	+	3.81231i	0.0577006	+	0.144818i
$694$	−20.6919	+	6.97192i	−0.785454	+	0.264650i
$695$	7.00770	−	0.762134i	0.265817	−	0.0289094i
$696$	−2.57035	−	1.18917i	−0.0974287	−	0.0450753i
$697$	−7.99783	+	7.57594i	−0.302939	+	0.286959i
$698$	−4.96848	−	2.98943i	−0.188060	−	0.113152i
$699$	−21.8796	−	2.37955i	−0.827561	−	0.0900027i
$700$	−6.03216	+	1.32778i	−0.227994	+	0.0501854i
$701$	−1.96575	+	7.07999i	−0.0742453	+	0.267407i	−0.991351	−	0.131237i	$-0.958105\pi$
$701$	−1.96575	+	7.07999i	−0.0742453	+	0.267407i	0.917106	+	0.398644i	$0.130519\pi$
$702$	−0.0430965	+	0.0259303i	−0.00162657	+	0.000978676i
$703$	9.55293	−	4.41965i	0.360295	−	0.166690i
$704$	1.08137	−	2.71403i	0.0407556	−	0.102289i
$705$	0.0401297	−	0.740148i	0.00151137	−	0.0278756i
$706$	−11.1675	−	16.4708i	−0.420294	−	0.619888i
$707$	11.3083			0.425293
$708$	0.521487	+	7.66342i	0.0195987	+	0.288009i
$709$	47.8329			1.79640			0.898200	−	0.439586i	$-0.144875\pi$
$709$	47.8329			1.79640			0.898200	+	0.439586i	$0.144875\pi$
$710$	−3.77617	−	5.56944i	−0.141717	−	0.209017i
$711$	0.301968	−	5.56948i	0.0113247	−	0.208872i
$712$	1.01524	−	2.54805i	0.0380476	−	0.0954922i
$713$	8.89014	−	4.11302i	0.332938	−	0.154034i
$714$	7.11382	−	4.28025i	0.266228	−	0.160184i
$715$	−0.0305217	+	0.109929i	−0.00114145	+	0.00411112i
$716$	−4.20630	+	0.925877i	−0.157197	+	0.0346017i
$717$	15.7005	+	1.70754i	0.586347	+	0.0637691i
$718$	12.5470	+	7.54931i	0.468252	+	0.281738i
$719$	−36.0343	+	34.1335i	−1.34385	+	1.27297i	−0.411503	+	0.911409i	$0.634996\pi$
$719$	−36.0343	+	34.1335i	−1.34385	+	1.27297i	−0.932350	+	0.361557i	$0.882245\pi$
$720$	0.704657	+	0.326009i	0.0262610	+	0.0121496i
$721$	19.5257	−	2.12355i	0.727176	−	0.0790852i
$722$	16.9176	−	5.70020i	0.629608	−	0.212140i
$723$	7.20996	+	18.0956i	0.268141	+	0.672984i
$724$	−12.4997	−	11.8403i	−0.464546	−	0.440041i
$725$	3.33160	+	11.9993i	0.123732	+	0.445644i
$726$	−1.15448	−	2.17758i	−0.0428467	−	0.0808175i
$727$	−24.9782	+	18.9879i	−0.926389	+	0.704222i	−0.955387	−	0.295357i	$-0.904561\pi$
$727$	−24.9782	+	18.9879i	−0.926389	+	0.704222i	0.0289984	+	0.999579i	$0.490768\pi$
$728$	0.00382487	+	0.0705455i	0.000141759	+	0.00261459i
$729$	−0.947653	−	0.319302i	−0.0350983	−	0.0118260i
$730$	−1.66351	−	0.366167i	−0.0615694	−	0.0135525i
$731$	6.71379	−	12.6636i	0.248319	−	0.468378i
$732$	0.532454	+	3.24782i	0.0196801	+	0.120043i
$733$	−24.5170	+	28.8637i	−0.905558	+	1.06610i	0.0919653	+	0.995762i	$0.470685\pi$
$733$	−24.5170	+	28.8637i	−0.905558	+	1.06610i	−0.997523	+	0.0703426i	$0.977591\pi$
$734$	21.1122	+	24.8552i	0.779264	+	0.917421i
$735$	0.631432	−	3.85156i	0.0232907	−	0.142067i
$736$	3.39056	+	2.57744i	0.124978	+	0.0950057i
$737$	18.8588	−	27.8147i	0.694674	−	1.02457i
$738$	1.04598	−	1.54271i	0.0385031	−	0.0567879i
$739$	0.689433	+	0.524094i	0.0253612	+	0.0192791i	0.617778	−	0.786353i	$-0.288033\pi$
$739$	0.689433	+	0.524094i	0.0253612	+	0.0192791i	−0.592417	+	0.805632i	$0.701826\pi$
$740$	1.23403	−	7.52726i	0.0453639	−	0.276708i
$741$	−0.0348859	−	0.0410708i	−0.00128156	−	0.00150877i
$742$	−3.54943	+	4.17871i	−0.130304	+	0.153405i
$743$	7.38443	+	45.0430i	0.270908	+	1.65247i	0.675050	+	0.737772i	$0.264122\pi$
$743$	7.38443	+	45.0430i	0.270908	+	1.65247i	−0.404142	+	0.914696i	$0.632430\pi$
$744$	1.07731	−	2.03203i	0.0394963	−	0.0744978i
$745$	−15.2955	−	3.36679i	−0.560384	−	0.123350i
$746$	−4.80919	−	1.62040i	−0.176077	−	0.0593272i
$747$	−0.385365	−	7.10764i	−0.0140998	−	0.260055i
$748$	13.7466	−	10.4499i	0.502625	−	0.382086i
$749$	−5.42406	−	10.2309i	−0.198191	−	0.373828i
$750$	−1.95192	−	7.03018i	−0.0712741	−	0.256706i
$751$	−8.31752	−	7.87877i	−0.303511	−	0.287501i	0.520752	−	0.853708i	$-0.325652\pi$
$751$	−8.31752	−	7.87877i	−0.303511	−	0.287501i	−0.824263	+	0.566207i	$0.808410\pi$
$752$	−0.353366	−	0.886882i	−0.0128859	−	0.0323413i
$753$	18.0183	−	6.07106i	0.656622	−	0.221242i
$754$	0.141608	−	0.0154008i	0.00515707	−	0.000560866i
$755$	−0.194314	−	0.0898993i	−0.00707181	−	0.00327177i
$756$	−1.01978	+	0.965989i	−0.0370891	+	0.0351327i
$757$	−15.5706	−	9.36854i	−0.565925	−	0.340506i	0.203669	−	0.979040i	$-0.434713\pi$
$757$	−15.5706	−	9.36854i	−0.565925	−	0.340506i	−0.769593	+	0.638534i	$0.779541\pi$
$758$	−23.4163	−	2.54668i	−0.850519	−	0.0924995i
$759$	−12.1519	+	2.67483i	−0.441086	+	0.0970903i
$760$	−0.222545	+	0.801534i	−0.00807255	+	0.0290747i
$761$	−35.2733	+	21.2232i	−1.27866	+	0.769342i	−0.982583	−	0.185824i	$-0.940505\pi$
$761$	−35.2733	+	21.2232i	−1.27866	+	0.769342i	−0.296073	+	0.955165i	$0.595677\pi$
$762$	5.81684	−	2.69116i	0.210722	−	0.0974903i
$763$	0.255201	−	0.640505i	0.00923888	−	0.0231878i
$764$	1.00876	−	18.6055i	0.0364958	−	0.673125i
$765$	2.57528	+	3.79825i	0.0931093	+	0.137326i
$766$	−20.5521			−0.742578
$767$	−0.221189	−	0.316744i	−0.00798668	−	0.0114370i
$768$	1.00000			0.0360844
$769$	23.3975	+	34.5088i	0.843736	+	1.24442i	0.967693	+	0.252130i	$0.0811311\pi$
$769$	23.3975	+	34.5088i	0.843736	+	1.24442i	−0.123957	+	0.992288i	$0.539559\pi$
$770$	−0.172499	+	3.18156i	−0.00621645	+	0.114656i
$771$	0.241246	−	0.605482i	0.00868827	−	0.0218059i
$772$	−3.80806	+	1.76179i	−0.137055	+	0.0634084i
$773$	−1.60899	+	0.968095i	−0.0578712	+	0.0348199i	−0.544195	−	0.838958i	$-0.683165\pi$
$773$	−1.60899	+	0.968095i	−0.0578712	+	0.0348199i	0.486324	+	0.873778i	$0.338337\pi$
$774$	−0.648771	+	2.33666i	−0.0233196	+	0.0839896i
$775$	−9.87683	+	2.17405i	−0.354786	+	0.0780943i
$776$	3.09505	+	0.336607i	0.111106	+	0.0120835i
$777$	11.8245	+	7.11457i	0.424202	+	0.255234i
$778$	21.5783	−	20.4401i	0.773620	−	0.732812i
$779$	1.81239	+	0.838502i	0.0649357	+	0.0300424i
$780$	−0.0388218	+	0.00422212i	−0.00139004	+	0.000151176i
$781$	23.9943	−	8.08463i	0.858584	−	0.289291i
$782$	9.31737	+	23.3848i	0.333188	+	0.836240i
$783$	2.05609	+	1.94763i	0.0734787	+	0.0696028i
$784$	−1.34484	−	4.84368i	−0.0480300	−	0.172989i
$785$	−5.61700	−	10.5948i	−0.200479	−	0.378144i
$786$	9.69828	−	7.37244i	0.345926	−	0.262966i
$787$	−0.171025	−	3.15438i	−0.00609639	−	0.112441i	−0.999998	−	0.00216764i	$-0.999310\pi$
$787$	−0.171025	−	3.15438i	−0.00609639	−	0.112441i	0.993901	−	0.110274i	$-0.0351727\pi$
$788$	−5.25285	−	1.76989i	−0.187125	−	0.0630498i
$789$	12.1097	+	2.66555i	0.431117	+	0.0948960i
$790$	2.02848	−	3.82613i	0.0721702	−	0.136127i
$791$	−0.531148	−	3.23986i	−0.0188855	−	0.115196i
$792$	−1.89136	+	2.22668i	−0.0672064	+	0.0791215i
$793$	−0.107164	−	0.126163i	−0.00380550	−	0.00448019i
$794$	−4.02143	+	24.5297i	−0.142715	+	0.870525i
$795$	−2.41257	−	1.83399i	−0.0855652	−	0.0650449i
$796$	3.65632	−	5.39267i	0.129595	−	0.191138i
$797$	−5.36312	+	7.91001i	−0.189971	+	0.280187i	−0.910733	−	0.412997i	$-0.864482\pi$
$797$	−5.36312	+	7.91001i	−0.189971	+	0.280187i	0.720761	+	0.693184i	$0.243792\pi$
$798$	−1.19809	−	0.910765i	−0.0424120	−	0.0322407i
$799$	0.912878	−	5.56831i	0.0322953	−	0.196993i
$800$	−2.84667	−	3.35136i	−0.100645	−	0.118489i
$801$	−1.77569	+	2.09050i	−0.0627408	+	0.0738642i
$802$	3.05693	+	18.6464i	0.107944	+	0.658428i
$803$	3.00220	−	5.66276i	0.105945	−	0.199834i
$804$	11.2337	+	2.47273i	0.396183	+	0.0872064i
$805$	−4.40176	−	1.48312i	−0.155142	−	0.0522733i
$806$	0.00626269	+	0.115509i	0.000220594	+	0.00406861i
$807$	−2.74834	+	2.08923i	−0.0967462	+	0.0735445i
$808$	3.77094	+	7.11274i	0.132661	+	0.250225i
$809$	1.45176	+	5.22878i	0.0510413	+	0.183834i	0.984676	−	0.174391i	$-0.0557957\pi$
$809$	1.45176	+	5.22878i	0.0510413	+	0.183834i	−0.933635	+	0.358225i	$0.883382\pi$
$810$	−0.563675	−	0.533942i	−0.0198055	−	0.0187608i
$811$	19.9454	+	50.0591i	0.700377	+	1.75781i	0.651056	+	0.759030i	$0.274326\pi$
$811$	19.9454	+	50.0591i	0.700377	+	1.75781i	0.0493212	+	0.998783i	$0.484294\pi$
$812$	3.76991	−	1.27023i	0.132298	−	0.0445764i
$813$	0.0120296	−	0.00130830i	0.000421896	−	4.58840e-5i
$814$	26.0492	+	12.0516i	0.913022	+	0.422409i
$815$	9.70760	−	9.19553i	0.340042	−	0.322105i
$816$	5.06442	+	3.04716i	0.177290	+	0.106672i
$817$	−2.58298	−	0.280916i	−0.0903670	−	0.00982801i
$818$	−10.1763	+	2.23997i	−0.355806	+	0.0783188i
$819$	0.0189007	−	0.0680740i	0.000660442	−	0.00237870i
$820$	1.24000	−	0.746081i	0.0433025	−	0.0260543i
$821$	41.7618	−	19.3211i	1.45750	−	0.674309i	0.478481	−	0.878098i	$-0.341188\pi$
$821$	41.7618	−	19.3211i	1.45750	−	0.674309i	0.979015	+	0.203788i	$0.0653255\pi$
$822$	7.40456	−	18.5840i	0.258264	−	0.648193i
$823$	−0.848942	+	15.6578i	−0.0295923	+	0.545797i	0.945722	+	0.324976i	$0.105356\pi$
$823$	−0.848942	+	15.6578i	−0.0295923	+	0.545797i	−0.975314	+	0.220821i	$0.929126\pi$
$824$	7.84684	+	11.5732i	0.273358	+	0.403172i
$825$	12.8465			0.447257
$826$	−7.93458	−	7.31127i	−0.276079	−	0.254392i
$827$	35.2992			1.22747			0.613737	−	0.789511i	$-0.289666\pi$
$827$	35.2992			1.22747			0.613737	+	0.789511i	$0.289666\pi$
$828$	−2.39010	−	3.52513i	−0.0830617	−	0.122507i
$829$	−1.73217	+	31.9480i	−0.0601607	+	1.10960i	0.800140	+	0.599813i	$0.204758\pi$
$829$	−1.73217	+	31.9480i	−0.0601607	+	1.10960i	−0.860301	+	0.509786i	$0.829724\pi$
$830$	2.04560	−	5.13408i	0.0710039	−	0.178206i
$831$	3.12750	−	1.44693i	0.108492	−	0.0501936i
$832$	−0.0430965	+	0.0259303i	−0.00149410	+	0.000898972i
$833$	7.94863	−	28.6284i	0.275404	−	0.991914i
$834$	−8.86666	+	1.95170i	−0.307027	+	0.0675818i
$835$	−0.644499	−	0.0700935i	−0.0223038	−	0.00242568i
$836$	−2.68207	−	1.61375i	−0.0927615	−	0.0558127i
$837$	−1.66975	+	1.58167i	−0.0577150	+	0.0546706i
$838$	−9.47743	−	4.38473i	−0.327393	−	0.151468i
$839$	−35.5594	+	3.86732i	−1.22765	+	0.133515i	−0.698871	−	0.715248i	$-0.746314\pi$
$839$	−35.5594	+	3.86732i	−1.22765	+	0.133515i	−0.528775	+	0.848762i	$0.677348\pi$
$840$	−1.03352	+	0.348233i	−0.0356597	+	0.0120152i
$841$	7.76520	+	19.4892i	0.267766	+	0.672041i
$842$	24.0117	+	22.7451i	0.827499	+	0.783849i
$843$	−6.02750	−	21.7091i	−0.207598	−	0.747701i
$844$	10.7307	+	20.2403i	0.369368	+	0.696701i
$845$	−8.03374	+	6.10709i	−0.276369	+	0.210090i
$846$	0.0516857	+	0.953287i	0.00177699	+	0.0327747i
$847$	3.28083	+	1.10544i	0.112731	+	0.0379834i
$848$	−3.81195	−	0.839074i	−0.130903	−	0.0288139i
$849$	12.2802	−	23.1629i	0.421456	−	0.794950i
$850$	−4.20461	−	25.6470i	−0.144217	−	0.879684i
$851$	−27.0877	+	31.8902i	−0.928556	+	1.09318i
$852$	5.61064	+	6.60536i	0.192217	+	0.226296i
$853$	−2.80865	+	17.1320i	−0.0961663	+	0.586588i	0.894151	+	0.447766i	$0.147780\pi$
$853$	−2.80865	+	17.1320i	−0.0961663	+	0.586588i	−0.990317	+	0.138823i	$0.955668\pi$
$854$	−3.68035	−	2.79773i	−0.125939	−	0.0957363i
$855$	0.466826	−	0.688517i	0.0159651	−	0.0235468i
$856$	4.62630	−	6.82329i	0.158124	−	0.233215i
$857$	−20.8975	−	15.8859i	−0.713845	−	0.542651i	0.184020	−	0.982923i	$-0.441089\pi$
$857$	−20.8975	−	15.8859i	−0.713845	−	0.542651i	−0.897865	+	0.440272i	$0.854882\pi$
$858$	0.0237724	−	0.145005i	0.000811577	−	0.00495040i
$859$	−11.3772	−	13.3942i	−0.388183	−	0.457005i	0.533010	−	0.846109i	$-0.321061\pi$
$859$	−11.3772	−	13.3942i	−0.388183	−	0.457005i	−0.921194	+	0.389104i	$0.872785\pi$
$860$	−1.21893	+	1.43504i	−0.0415653	+	0.0489345i
$861$	0.423565	+	2.58363i	0.0144351	+	0.0880500i
$862$	−12.8599	+	24.2563i	−0.438008	+	0.826171i
$863$	−2.17776	−	0.479361i	−0.0741318	−	0.0163176i	0.177750	−	0.984076i	$-0.443118\pi$
$863$	−2.17776	−	0.479361i	−0.0741318	−	0.0163176i	−0.251881	+	0.967758i	$0.581049\pi$
$864$	−0.947653	−	0.319302i	−0.0322398	−	0.0108629i
$865$	−0.725760	−	13.3858i	−0.0246766	−	0.455132i
$866$	25.6747	−	19.5174i	0.872462	−	0.663228i
$867$	8.40022	+	15.8445i	0.285286	+	0.538107i
$868$	0.864293	+	3.11290i	0.0293360	+	0.105659i
$869$	11.8303	+	11.2063i	0.401315	+	0.380146i
$870$	0.813894	+	2.04272i	0.0275936	+	0.0692547i
$871$	−0.548252	+	0.184728i	−0.0185768	+	0.00625926i
$872$	0.487968	−	0.0530697i	0.0165247	−	0.00179717i
$873$	−2.82556	−	1.30724i	−0.0956306	−	0.0442434i
$874$	3.31280	−	3.13805i	0.112057	−	0.106146i
$875$	8.78161	+	5.28372i	0.296873	+	0.178622i
$876$	2.18098	+	0.237196i	0.0736886	+	0.00801412i
$877$	52.2504	−	11.5012i	1.76437	−	0.388368i	0.789963	−	0.613154i	$-0.210099\pi$
$877$	52.2504	−	11.5012i	1.76437	−	0.388368i	0.974408	+	0.224786i	$0.0721685\pi$
$878$	−4.34122	+	15.6357i	−0.146509	+	0.527678i
$879$	15.6400	−	9.41030i	0.527525	−	0.317401i
$880$	−2.05867	+	0.952444i	−0.0693979	+	0.0321069i
$881$	−5.61846	+	14.1013i	−0.189291	+	0.475084i	−0.992739	−	0.120291i	$-0.961617\pi$
$881$	−5.61846	+	14.1013i	−0.189291	+	0.475084i	0.803448	+	0.595375i	$0.202997\pi$
$882$	−0.272151	+	5.01954i	−0.00916382	+	0.169017i
$883$	−1.16896	−	1.72408i	−0.0393386	−	0.0580201i	0.807511	−	0.589852i	$-0.200814\pi$
$883$	−1.16896	−	1.72408i	−0.0393386	−	0.0580201i	−0.846850	+	0.531832i	$0.821504\pi$
$884$	−0.297273			−0.00999836
$885$	3.79787	−	4.59813i	0.127664	−	0.154564i
$886$	−6.49038			−0.218049
$887$	−21.7257	−	32.0430i	−0.729478	−	1.07590i	−0.993769	−	0.111456i	$-0.964449\pi$
$887$	−21.7257	−	32.0430i	−0.729478	−	1.07590i	0.264292	−	0.964443i	$-0.414862\pi$
$888$	−0.531876	+	9.80988i	−0.0178486	+	0.329198i
$889$	−3.33228	+	8.36339i	−0.111761	+	0.280499i
$890$	−1.93277	+	0.894196i	−0.0647867	+	0.0299735i
$891$	2.50333	−	1.50620i	0.0838647	−	0.0504597i
$892$	−0.765850	+	2.75834i	−0.0256426	+	0.0923562i
$893$	−0.998940	+	0.219883i	−0.0334283	+	0.00735812i
$894$	20.0535	+	2.18095i	0.670688	+	0.0729417i
$895$	2.86535	+	1.72403i	0.0957782	+	0.0576278i
$896$	−1.01978	+	0.965989i	−0.0340685	+	0.0322714i
$897$	0.194413	+	0.0899449i	0.00649125	+	0.00300317i
$898$	−17.0728	+	1.85678i	−0.569726	+	0.0619615i
$899$	6.17271	−	2.07983i	0.205871	−	0.0693661i
$900$	1.62756	+	4.08487i	0.0542521	+	0.136162i
$901$	−16.7485	−	15.8651i	−0.557975	−	0.528542i
$902$	1.45679	+	5.24688i	0.0485057	+	0.174702i
$903$	−1.59558	−	3.00959i	−0.0530977	−	0.100153i
$904$	1.86070	−	1.41447i	0.0618859	−	0.0470445i
$905$	0.723717	+	13.3482i	0.0240572	+	0.443708i
$906$	0.261322	+	0.0880496i	0.00868184	+	0.00292525i
$907$	21.0375	+	4.63070i	0.698538	+	0.153760i	0.550022	−	0.835150i	$-0.314619\pi$
$907$	21.0375	+	4.63070i	0.698538	+	0.153760i	0.148516	+	0.988910i	$0.452550\pi$
$908$	5.73121	−	10.8102i	0.190197	−	0.358749i
$909$	−1.30243	−	7.94448i	−0.0431989	−	0.263502i
$910$	0.0355112	−	0.0418070i	0.00117719	−	0.00138589i
$911$	−27.1677	−	31.9843i	−0.900106	−	1.05969i	−0.997919	−	0.0644816i	$-0.979461\pi$
$911$	−27.1677	−	31.9843i	−0.900106	−	1.05969i	0.0978132	−	0.995205i	$-0.468815\pi$
$912$	0.173334	−	1.05729i	0.00573965	−	0.0350103i
$913$	16.5553	+	12.5850i	0.547899	+	0.416502i
$914$	10.4481	−	15.4099i	0.345594	−	0.509713i
$915$	1.43402	−	2.11502i	0.0474071	−	0.0699203i
$916$	5.96851	+	4.53714i	0.197205	+	0.149911i
$917$	−2.76843	+	16.8867i	−0.0914217	+	0.557648i
$918$	−3.82635	−	4.50473i	−0.126288	−	0.148678i
$919$	36.2813	−	42.7136i	1.19681	−	1.40899i	0.307584	−	0.951521i	$-0.400480\pi$
$919$	36.2813	−	42.7136i	1.19681	−	1.40899i	0.889225	−	0.457471i	$-0.151245\pi$
$920$	−0.534975	−	3.26320i	−0.0176376	−	0.107585i
$921$	11.0508	−	20.8441i	0.364138	−	0.686837i
$922$	−23.3082	−	5.13051i	−0.767613	−	0.168964i
$923$	−0.413078	−	0.139182i	−0.0135966	−	0.00458124i
$924$	−0.222174	−	4.09775i	−0.00730898	−	0.134806i
$925$	34.3905	−	26.1430i	1.13075	−	0.859577i
$926$	2.75927	+	5.20453i	0.0906752	+	0.171032i
$927$	−3.74074	−	13.4729i	−0.122862	−	0.442508i
$928$	2.05609	+	1.94763i	0.0674945	+	0.0639342i
$929$	−6.62393	−	16.6248i	−0.217324	−	0.545443i	0.779381	−	0.626550i	$-0.215534\pi$
$929$	−6.62393	−	16.6248i	−0.217324	−	0.545443i	−0.996705	+	0.0811074i	$0.974154\pi$
$930$	−1.69224	+	0.570182i	−0.0554908	+	0.0186970i
$931$	−5.35427	+	0.582312i	−0.175479	+	0.0190845i
$932$	19.9744	+	9.24116i	0.654285	+	0.302704i
$933$	−10.0684	+	9.53729i	−0.329624	+	0.312237i
$934$	4.60524	+	2.77088i	0.150688	+	0.0906661i
$935$	−13.3282	−	1.44953i	−0.435880	−	0.0474048i
$936$	0.0491201	−	0.0108122i	0.00160554	−	0.000353406i
$937$	13.4991	−	48.6194i	0.440997	−	1.58833i	−0.325151	−	0.945662i	$-0.605415\pi$
$937$	13.4991	−	48.6194i	0.440997	−	1.58833i	0.766148	−	0.642664i	$-0.222171\pi$
$938$	−13.8446	+	8.33000i	−0.452041	+	0.271984i
$939$	14.1697	−	6.55560i	0.462410	−	0.213934i
$940$	−0.274360	+	0.688590i	−0.00894862	+	0.0224593i
$941$	−1.18530	+	21.8615i	−0.0386395	+	0.712665i	0.913470	+	0.406907i	$0.133393\pi$
$941$	−1.18530	+	21.8615i	−0.0386395	+	0.712665i	−0.952109	+	0.305758i	$0.901090\pi$
$942$	8.66746	+	12.7836i	0.282401	+	0.416511i
$943$	−7.93825			−0.258505
$944$	1.95275	−	7.42878i	0.0635567	−	0.241786i
$945$	1.09061			0.0354775
$946$	−3.97593	−	5.86407i	−0.129269	−	0.190657i
$947$	−0.396642	+	7.31564i	−0.0128891	+	0.237726i	0.984989	+	0.172617i	$0.0552223\pi$
$947$	−0.396642	+	7.31564i	−0.0128891	+	0.237726i	−0.997878	+	0.0651092i	$0.979260\pi$
$948$	−2.06450	+	5.18151i	−0.0670520	+	0.168288i
$949$	−0.100143	+	0.0463312i	−0.00325079	+	0.00150398i
$950$	−4.03678	+	2.42885i	−0.130970	+	0.0788023i
$951$	−6.07605	+	21.8840i	−0.197030	+	0.709636i
$952$	−8.10813	+	1.78473i	−0.262786	+	0.0578435i
$953$	−44.8926	−	4.88236i	−1.45421	−	0.158155i	−0.653374	−	0.757035i	$-0.726647\pi$
$953$	−44.8926	−	4.88236i	−1.45421	−	0.158155i	−0.800839	+	0.598880i	$0.795613\pi$
$954$	3.34449	+	2.01231i	0.108282	+	0.0651511i
$955$	−10.5029	+	9.94886i	−0.339865	+	0.321938i
$956$	−14.3334	−	6.63136i	−0.463577	−	0.214473i
$957$	−8.22555	+	0.894583i	−0.265894	+	0.0289178i
$958$	5.76688	−	1.94309i	0.186320	−	0.0627784i
$959$	10.4009	+	26.1044i	0.335864	+	0.842954i
$960$	−0.563675	−	0.533942i	−0.0181925	−	0.0172329i
$961$	−6.87822	−	24.7731i	−0.221878	−	0.799133i
$962$	−0.231451	−	0.436563i	−0.00746229	−	0.0140754i
$963$	−6.56282	+	4.98892i	−0.211484	+	0.160766i
$964$	−1.05458	−	19.4505i	−0.0339657	−	0.626460i
$965$	3.08720	+	1.04020i	0.0993806	+	0.0334852i
$966$	5.84262	+	1.28606i	0.187983	+	0.0413782i
$967$	−15.2936	+	28.8468i	−0.491810	+	0.927652i	0.506065	+	0.862495i	$0.331099\pi$
$967$	−15.2936	+	28.8468i	−0.491810	+	0.927652i	−0.997875	+	0.0651564i	$0.979245\pi$
$968$	0.398742	+	2.43222i	0.0128160	+	0.0781744i
$969$	4.09956	−	4.82638i	0.131697	−	0.155046i
$970$	−1.56487	−	1.84231i	−0.0502451	−	0.0591531i
$971$	−1.58549	+	9.67108i	−0.0508809	+	0.310360i	−0.999989	−	0.00458927i	$-0.998539\pi$
$971$	−1.58549	+	9.67108i	−0.0508809	+	0.310360i	0.949109	+	0.314949i	$0.101987\pi$
$972$	0.796093	+	0.605174i	0.0255347	+	0.0194110i
$973$	7.15674	−	10.5554i	0.229434	−	0.338390i
$974$	−4.12876	+	6.08947i	−0.132294	+	0.195119i
$975$	−0.176064	−	0.133841i	−0.00563857	−	0.00428633i
$976$	0.532454	−	3.24782i	0.0170434	−	0.103960i
$977$	−36.4354	−	42.8950i	−1.16567	−	1.37233i	−0.914598	−	0.404365i	$-0.867492\pi$
$977$	−36.4354	−	42.8950i	−1.16567	−	1.37233i	−0.251073	−	0.967968i	$-0.580783\pi$
$978$	−11.1493	+	13.1259i	−0.356514	+	0.419721i
$979$	−1.29641	−	7.90776i	−0.0414335	−	0.252733i
$980$	−1.82819	+	3.44833i	−0.0583993	+	0.110153i
$981$	−0.479369	−	0.105517i	−0.0153051	−	0.00336890i
$982$	−10.3019	−	3.47113i	−0.328748	−	0.110768i
$983$	−0.129331	−	2.38537i	−0.00412502	−	0.0760816i	0.995746	−	0.0921404i	$-0.0293709\pi$
$983$	−0.129331	−	2.38537i	−0.00412502	−	0.0760816i	−0.999871	+	0.0160588i	$0.994888\pi$
$984$	−1.48382	+	1.12797i	−0.0473024	+	0.0359583i
$985$	2.01588	+	3.80236i	0.0642314	+	0.121153i
$986$	4.47816	+	16.1289i	0.142614	+	0.513648i
$987$	−0.973573	−	0.922217i	−0.0309892	−	0.0293545i
$988$	0.0199457	+	0.0500600i	0.000634558	+	0.00159262i
$989$	9.78767	−	3.29785i	0.311230	−	0.104866i
$990$	2.25503	−	0.245249i	0.0716694	−	0.00779452i
$991$	10.8502	+	5.01986i	0.344670	+	0.159461i	0.584585	−	0.811333i	$-0.301258\pi$
$991$	10.8502	+	5.01986i	0.344670	+	0.159461i	−0.239915	+	0.970794i	$0.577120\pi$
$992$	−1.66975	+	1.58167i	−0.0530146	+	0.0502181i
$993$	−14.9976	−	9.02377i	−0.475935	−	0.286361i
$994$	−12.1023	−	1.31621i	−0.383863	−	0.0417476i
$995$	−4.94035	+	1.08745i	−0.156619	+	0.0344746i
$996$	−1.90429	+	6.85862i	−0.0603396	+	0.217324i
$997$	−40.6708	+	24.4708i	−1.28806	+	0.774997i	−0.984087	−	0.177685i	$-0.943139\pi$
$997$	−40.6708	+	24.4708i	−1.28806	+	0.774997i	−0.303968	+	0.952682i	$0.598312\pi$
$998$	−33.6900	+	15.5866i	−1.06644	+	0.493386i
$999$	3.63634	−	9.12654i	0.115049	−	0.288751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.7.2	✓	56
59.17	even	29	inner	354.2.e.a.253.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.7.2	✓	56	1.1	even	1	trivial
354.2.e.a.253.2	yes	56	59.17	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)

\(f(q)\)	\(=\)	\(q+(-0.561187 - 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(0.704657 - 0.326009i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(0.375788 - 1.35347i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})\)	\(q+(-0.561187 - 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(0.704657 - 0.326009i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(0.375788 - 1.35347i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(-0.665279 - 0.400285i) q^{10} +(2.12101 - 2.00913i) q^{11} +(0.907575 + 0.419889i) q^{12} +(-0.0500012 + 0.00543796i) q^{13} +(-1.33114 + 0.448512i) q^{14} +(-0.287382 - 0.721273i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(-1.58122 - 5.69502i) q^{17} +(0.468408 + 0.883512i) q^{18} +(-0.852936 + 0.648385i) q^{19} +(0.0420344 + 0.775278i) q^{20} +(-1.33114 - 0.448512i) q^{21} +(-2.85322 - 0.628042i) q^{22} +(1.99495 - 3.76288i) q^{23} +(-0.161782 - 0.986827i) q^{24} +(-2.84667 + 3.35136i) q^{25} +(0.0325610 + 0.0383337i) q^{26} +(-0.161782 + 0.986827i) q^{27} +(1.11825 + 0.850068i) q^{28} +(1.58934 - 2.34410i) q^{29} +(-0.435715 + 0.642632i) q^{30} +(1.83097 + 1.39187i) q^{31} +(-0.161782 + 0.986827i) q^{32} +(-1.89136 - 2.22668i) q^{33} +(-3.82635 + 4.50473i) q^{34} +(-0.176441 - 1.07624i) q^{35} +(0.468408 - 0.883512i) q^{36} +(-9.59460 - 2.11193i) q^{37} +(1.01532 + 0.342100i) q^{38} +(0.00272297 + 0.0502223i) q^{39} +(0.618100 - 0.469868i) q^{40} +(-0.873055 - 1.64676i) q^{41} +(0.375788 + 1.35347i) q^{42} +(1.76058 + 1.66771i) q^{43} +(1.08137 + 2.71403i) q^{44} +(-0.735774 + 0.247911i) q^{45} +(-4.23404 + 0.460479i) q^{46} +(0.866451 + 0.400863i) q^{47} +(-0.725995 + 0.687699i) q^{48} +(4.30734 + 2.59164i) q^{49} +(4.37140 + 0.475418i) q^{50} +(-5.77228 + 1.27057i) q^{51} +(0.0134556 - 0.0484627i) q^{52} +(3.34449 - 2.01231i) q^{53} +(0.907575 - 0.419889i) q^{54} +(0.839593 - 2.10722i) q^{55} +(0.0760471 - 1.40261i) q^{56} +(0.601257 + 0.886788i) q^{57} -2.83210 q^{58} +(3.69108 + 6.73617i) q^{59} +0.776417 q^{60} +(1.84697 + 2.72407i) q^{61} +(0.124517 - 2.29657i) q^{62} +(-0.519921 + 1.30490i) q^{63} +(0.907575 - 0.419889i) q^{64} +(-0.0334609 + 0.0201327i) q^{65} +(-0.781591 + 2.81504i) q^{66} +(11.2337 - 2.47273i) q^{67} +(5.87581 + 0.639033i) q^{68} +(-3.64936 - 2.19575i) q^{69} +(-0.791776 + 0.750010i) q^{70} +(7.86560 + 3.63901i) q^{71} +(-0.994138 + 0.108119i) q^{72} +(2.07900 - 0.700498i) q^{73} +(3.63634 + 9.12654i) q^{74} +(3.19233 + 3.02394i) q^{75} +(-0.286630 - 1.03235i) q^{76} +(-1.92224 - 3.62573i) q^{77} +(0.0400403 - 0.0304379i) q^{78} +(0.301968 + 5.56948i) q^{79} +(-0.735774 - 0.247911i) q^{80} +(0.976621 + 0.214970i) q^{81} +(-0.873055 + 1.64676i) q^{82} +(1.15158 + 7.02431i) q^{83} +(0.909362 - 1.07058i) q^{84} +(-2.97084 - 3.49755i) q^{85} +(0.392330 - 2.39311i) q^{86} +(-2.25462 - 1.71391i) q^{87} +(1.63952 - 2.41812i) q^{88} +(1.53926 - 2.27023i) q^{89} +(0.618100 + 0.469868i) q^{90} +(-0.0114298 + 0.0697185i) q^{91} +(2.75722 + 3.24605i) q^{92} +(1.48895 - 1.75293i) q^{93} +(-0.154451 - 0.942111i) q^{94} +(-0.389648 + 0.734954i) q^{95} +(0.976621 + 0.214970i) q^{96} +(2.95033 + 0.994082i) q^{97} +(-0.272151 - 5.01954i) q^{98} +(-2.32581 + 1.76803i) 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

L-functions

Modular forms

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Database

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