LMFDB - Embedded newform 462.2.y.c.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	462.235
Dual form			462.2.y.c.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.04169 - 1.35425i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.194999 + 2.63856i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.04169 - 1.35425i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.194999 + 2.63856i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-1.66477 + 2.88347i) q^{10} +(-0.465221 + 3.28383i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(4.99010 + 3.62552i) q^{13} +(2.64448 + 0.0818733i) q^{14} +(-1.02889 - 3.16659i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.288432 + 2.74425i) q^{17} +(0.978148 + 0.207912i) q^{18} +(1.87203 - 0.397913i) q^{19} +(2.69366 + 1.95706i) q^{20} +(-1.83035 + 1.91045i) q^{21} +(3.21722 + 0.805927i) q^{22} +(-1.57878 - 2.73453i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(4.07225 + 4.52269i) q^{25} +(4.12726 - 4.58379i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.357849 - 2.62144i) q^{28} +(-0.159811 - 0.491849i) q^{29} +(-3.25679 + 0.692252i) q^{30} +(1.36217 - 0.606479i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.75166 + 1.85159i) q^{33} +2.75936 q^{34} +(2.98013 - 8.28975i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-1.86679 + 2.07328i) q^{37} +(-0.200052 - 1.90337i) q^{38} +(0.644742 + 6.13431i) q^{39} +(2.22790 - 2.47434i) q^{40} +(-3.61938 + 11.1393i) q^{41} +(1.70866 + 2.02002i) q^{42} -11.0713 q^{43} +(1.13780 - 3.11535i) q^{44} +(1.66477 - 2.88347i) q^{45} +(-2.88457 + 1.28430i) q^{46} +(-2.35383 + 0.500321i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-6.92395 + 1.02903i) q^{49} +(4.92358 - 3.57719i) q^{50} +(-1.84637 + 2.05061i) q^{51} +(-4.12726 - 4.58379i) q^{52} +(0.815559 - 0.363110i) q^{53} +(0.500000 + 0.866025i) q^{54} +(5.86219 - 9.35839i) q^{55} +(-2.56967 - 0.629903i) q^{56} +(1.54834 + 1.12494i) q^{57} +(-0.505859 + 0.107524i) q^{58} +(-1.54248 - 0.327864i) q^{59} +(0.348032 + 3.31131i) q^{60} +(13.6745 + 6.08828i) q^{61} +(-0.460770 - 1.41811i) q^{62} +(-2.64448 - 0.0818733i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-10.2685 - 17.7855i) q^{65} +(1.55382 + 2.93013i) q^{66} +(-0.0892859 + 0.154648i) q^{67} +(0.288432 - 2.74425i) q^{68} +(0.975740 - 3.00302i) q^{69} +(-7.93283 - 3.83032i) q^{70} +(8.96442 - 6.51303i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-3.59237 - 0.763582i) q^{73} +(1.86679 + 2.07328i) q^{74} +(-0.636148 + 6.05254i) q^{75} -1.91386 q^{76} +(-8.75530 - 0.587167i) q^{77} +6.16810 q^{78} +(0.932167 - 8.86898i) q^{79} +(-2.22790 - 2.47434i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(10.7000 + 4.76393i) q^{82} +(8.79297 - 6.38847i) q^{83} +(2.18756 - 1.48815i) q^{84} +(2.83907 - 8.73776i) q^{85} +(-1.15726 + 11.0106i) q^{86} +(0.258580 - 0.447874i) q^{87} +(-2.97935 - 1.45721i) q^{88} +(0.291418 + 0.504750i) q^{89} +(-2.69366 - 1.95706i) q^{90} +(-8.59306 + 13.8736i) q^{91} +(0.975740 + 3.00302i) q^{92} +(1.36217 + 0.606479i) q^{93} +(0.251539 + 2.39323i) q^{94} +(-6.23302 - 1.32487i) q^{95} +(0.978148 - 0.207912i) q^{96} +(9.88027 + 7.17844i) q^{97} +(0.299645 + 6.99358i) q^{98} +(-3.21722 - 0.805927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−3.04169	−	1.35425i	−1.36029	−	0.605638i	−0.408601	−	0.912713i	$-0.633983\pi$
$5$	−3.04169	−	1.35425i	−1.36029	−	0.605638i	−0.951685	+	0.307075i	$0.900650\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	0.194999	+	2.63856i	0.0737027	+	0.997280i
$7$	0.194999	+	2.63856i	0.0737027	+	0.997280i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−1.66477	+	2.88347i	−0.526448	+	0.911834i
$11$	−0.465221	+	3.28383i	−0.140269	+	0.990113i
$11$	−0.465221	+	3.28383i	−0.140269	+	0.990113i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	4.99010	+	3.62552i	1.38400	+	1.00554i	0.996493	+	0.0836722i	$0.0266649\pi$
$13$	4.99010	+	3.62552i	1.38400	+	1.00554i	0.387510	+	0.921865i	$0.373335\pi$
$14$	2.64448	+	0.0818733i	0.706768	+	0.0218815i
$15$	−1.02889	−	3.16659i	−0.265657	−	0.817609i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.288432	+	2.74425i	0.0699550	+	0.665577i	0.972168	+	0.234286i	$0.0752752\pi$
$17$	0.288432	+	2.74425i	0.0699550	+	0.665577i	−0.902213	+	0.431291i	$0.858058\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	1.87203	−	0.397913i	0.429474	−	0.0912875i	0.0118973	−	0.999929i	$-0.496213\pi$
$19$	1.87203	−	0.397913i	0.429474	−	0.0912875i	0.417577	+	0.908642i	$0.362880\pi$
$20$	2.69366	+	1.95706i	0.602321	+	0.437612i
$21$	−1.83035	+	1.91045i	−0.399415	+	0.416895i
$22$	3.21722	+	0.805927i	0.685913	+	0.171824i
$23$	−1.57878	−	2.73453i	−0.329198	−	0.570188i	0.653155	−	0.757225i	$-0.273445\pi$
$23$	−1.57878	−	2.73453i	−0.329198	−	0.570188i	−0.982353	+	0.187036i	$0.940112\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	4.07225	+	4.52269i	0.814450	+	0.904538i
$26$	4.12726	−	4.58379i	0.809423	−	0.898955i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.357849	−	2.62144i	0.0676270	−	0.495405i
$29$	−0.159811	−	0.491849i	−0.0296762	−	0.0913340i	0.935121	−	0.354328i	$-0.115290\pi$
$29$	−0.159811	−	0.491849i	−0.0296762	−	0.0913340i	−0.964798	+	0.262994i	$0.915290\pi$
$30$	−3.25679	+	0.692252i	−0.594605	+	0.126387i
$31$	1.36217	−	0.606479i	0.244654	−	0.108927i	−0.280747	−	0.959782i	$-0.590582\pi$
$31$	1.36217	−	0.606479i	0.244654	−	0.108927i	0.525401	+	0.850855i	$0.323916\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.75166	+	1.85159i	−0.479002	+	0.322320i
$34$	2.75936			0.473227
$35$	2.98013	−	8.28975i	0.503734	−	1.40122i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−1.86679	+	2.07328i	−0.306899	+	0.340845i	−0.876789	−	0.480875i	$-0.840319\pi$
$37$	−1.86679	+	2.07328i	−0.306899	+	0.340845i	0.569890	+	0.821721i	$0.306986\pi$
$38$	−0.200052	−	1.90337i	−0.0324528	−	0.308768i
$39$	0.644742	+	6.13431i	0.103241	+	0.982276i
$40$	2.22790	−	2.47434i	0.352262	−	0.391227i
$41$	−3.61938	+	11.1393i	−0.565253	+	1.73967i	0.101947	+	0.994790i	$0.467493\pi$
$41$	−3.61938	+	11.1393i	−0.565253	+	1.73967i	−0.667199	+	0.744879i	$0.732507\pi$
$42$	1.70866	+	2.02002i	0.263652	+	0.311696i
$43$	−11.0713			−1.68835			−0.844177	−	0.536064i	$-0.819911\pi$
$43$	−11.0713			−1.68835			−0.844177	+	0.536064i	$0.819911\pi$
$44$	1.13780	−	3.11535i	0.171530	−	0.469657i
$45$	1.66477	−	2.88347i	0.248170	−	0.429843i
$46$	−2.88457	+	1.28430i	−0.425307	+	0.189359i
$47$	−2.35383	+	0.500321i	−0.343341	+	0.0729794i	−0.376355	−	0.926476i	$-0.622823\pi$
$47$	−2.35383	+	0.500321i	−0.343341	+	0.0729794i	0.0330141	+	0.999455i	$0.489489\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−6.92395	+	1.02903i	−0.989136	+	0.147005i
$50$	4.92358	−	3.57719i	0.696299	−	0.505891i
$51$	−1.84637	+	2.05061i	−0.258544	+	0.287142i
$52$	−4.12726	−	4.58379i	−0.572348	−	0.635657i
$53$	0.815559	−	0.363110i	0.112026	−	0.0498770i	−0.349959	−	0.936765i	$-0.613804\pi$
$53$	0.815559	−	0.363110i	0.112026	−	0.0498770i	0.461984	+	0.886888i	$0.347138\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	5.86219	−	9.35839i	0.790457	−	1.26188i
$56$	−2.56967	−	0.629903i	−0.343387	−	0.0841744i
$57$	1.54834	+	1.12494i	0.205083	+	0.149001i
$58$	−0.505859	+	0.107524i	−0.0664226	+	0.0141186i
$59$	−1.54248	−	0.327864i	−0.200813	−	0.0426842i	0.106407	−	0.994323i	$-0.466065\pi$
$59$	−1.54248	−	0.327864i	−0.200813	−	0.0426842i	−0.307220	+	0.951638i	$0.599399\pi$
$60$	0.348032	+	3.31131i	0.0449308	+	0.427488i
$61$	13.6745	+	6.08828i	1.75084	+	0.779524i	0.991697	+	0.128600i	$0.0410484\pi$
$61$	13.6745	+	6.08828i	1.75084	+	0.779524i	0.759143	+	0.650924i	$0.225618\pi$
$62$	−0.460770	−	1.41811i	−0.0585179	−	0.180100i
$63$	−2.64448	−	0.0818733i	−0.333174	−	0.0103151i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−10.2685	−	17.7855i	−1.27365	−	2.20602i
$66$	1.55382	+	2.93013i	0.191262	+	0.360674i
$67$	−0.0892859	+	0.154648i	−0.0109080	+	0.0188932i	−0.871428	−	0.490524i	$-0.836806\pi$
$67$	−0.0892859	+	0.154648i	−0.0109080	+	0.0188932i	0.860520	+	0.509417i	$0.170139\pi$
$68$	0.288432	−	2.74425i	0.0349775	−	0.332789i
$69$	0.975740	−	3.00302i	0.117465	−	0.361521i
$70$	−7.93283	−	3.83032i	−0.948154	−	0.457811i
$71$	8.96442	−	6.51303i	1.06388	−	0.772955i	0.0890782	−	0.996025i	$-0.471608\pi$
$71$	8.96442	−	6.51303i	1.06388	−	0.772955i	0.974802	+	0.223070i	$0.0716079\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	−3.59237	−	0.763582i	−0.420455	−	0.0893705i	−0.00717461	−	0.999974i	$-0.502284\pi$
$73$	−3.59237	−	0.763582i	−0.420455	−	0.0893705i	−0.413281	+	0.910604i	$0.635617\pi$
$74$	1.86679	+	2.07328i	0.217010	+	0.241014i
$75$	−0.636148	+	6.05254i	−0.0734560	+	0.698887i
$76$	−1.91386			−0.219534
$77$	−8.75530	−	0.587167i	−0.997759	−	0.0669139i
$78$	6.16810			0.698400
$79$	0.932167	−	8.86898i	0.104877	−	0.997838i	−0.807883	−	0.589342i	$-0.799387\pi$
$79$	0.932167	−	8.86898i	0.104877	−	0.997838i	0.912760	−	0.408495i	$-0.133946\pi$
$80$	−2.22790	−	2.47434i	−0.249087	−	0.276639i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	10.7000	+	4.76393i	1.18161	+	0.526088i
$83$	8.79297	−	6.38847i	0.965154	−	0.701225i	0.0108120	−	0.999942i	$-0.496558\pi$
$83$	8.79297	−	6.38847i	0.965154	−	0.701225i	0.954342	+	0.298716i	$0.0965584\pi$
$84$	2.18756	−	1.48815i	0.238682	−	0.162371i
$85$	2.83907	−	8.73776i	0.307940	−	0.947743i
$86$	−1.15726	+	11.0106i	−0.124791	+	1.18731i
$87$	0.258580	−	0.447874i	0.0277227	−	0.0480171i
$88$	−2.97935	−	1.45721i	−0.317600	−	0.155339i
$89$	0.291418	+	0.504750i	0.0308902	+	0.0535034i	0.881057	−	0.473010i	$-0.156832\pi$
$89$	0.291418	+	0.504750i	0.0308902	+	0.0535034i	−0.850167	+	0.526513i	$0.823499\pi$
$90$	−2.69366	−	1.95706i	−0.283937	−	0.206292i
$91$	−8.59306	+	13.8736i	−0.900798	+	1.45435i
$92$	0.975740	+	3.00302i	0.101728	+	0.313086i
$93$	1.36217	+	0.606479i	0.141251	+	0.0628889i
$94$	0.251539	+	2.39323i	0.0259442	+	0.246843i
$95$	−6.23302	−	1.32487i	−0.639494	−	0.135929i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	9.88027	+	7.17844i	1.00319	+	0.728860i	0.962770	−	0.270323i	$-0.0871305\pi$
$97$	9.88027	+	7.17844i	1.00319	+	0.728860i	0.0404199	+	0.999183i	$0.487130\pi$
$98$	0.299645	+	6.99358i	0.0302687	+	0.706459i
$99$	−3.21722	−	0.805927i	−0.323342	−	0.0809987i
$100$	−3.04294	−	5.27053i	−0.304294	−	0.527053i
$101$	9.21485	−	4.10271i	0.916911	−	0.408235i	0.106645	−	0.994297i	$-0.465989\pi$
$101$	9.21485	−	4.10271i	0.916911	−	0.408235i	0.810266	+	0.586062i	$0.199322\pi$
$102$	1.84637	+	2.05061i	0.182818	+	0.203040i
$103$	−12.8194	+	14.2373i	−1.26313	+	1.40285i	−0.386065	+	0.922472i	$0.626166\pi$
$103$	−12.8194	+	14.2373i	−1.26313	+	1.40285i	−0.877063	+	0.480375i	$0.840501\pi$
$104$	−4.99010	+	3.62552i	−0.489319	+	0.355511i
$105$	8.15458	−	3.33226i	0.795806	−	0.325195i
$106$	−0.275872	−	0.849047i	−0.0267951	−	0.0824667i
$107$	2.29448	−	0.487707i	0.221816	−	0.0471484i	−0.0956629	−	0.995414i	$-0.530497\pi$
$107$	2.29448	−	0.487707i	0.221816	−	0.0471484i	0.317479	+	0.948265i	$0.397164\pi$
$108$	0.913545	−	0.406737i	0.0879060	−	0.0391383i
$109$	7.83983	−	13.5790i	0.750920	−	1.30063i	−0.196458	−	0.980512i	$-0.562944\pi$
$109$	7.83983	−	13.5790i	0.750920	−	1.30063i	0.947377	−	0.320119i	$-0.103723\pi$
$110$	−8.69436	−	6.80829i	−0.828974	−	0.649145i
$111$	−2.78988			−0.264803
$112$	−0.895057	+	2.48975i	−0.0845749	+	0.235260i
$113$	3.32333	−	10.2282i	0.312633	−	0.962185i	−0.664085	−	0.747657i	$-0.731179\pi$
$113$	3.32333	−	10.2282i	0.312633	−	0.962185i	0.976718	−	0.214528i	$-0.0688212\pi$
$114$	1.28062	−	1.42227i	0.119941	−	0.133208i
$115$	1.09893	+	10.4556i	0.102476	+	0.974994i
$116$	0.0540580	+	0.514327i	0.00501916	+	0.0477541i
$117$	−4.12726	+	4.58379i	−0.381566	+	0.423772i
$118$	−0.487300	+	1.49976i	−0.0448596	+	0.138064i
$119$	−7.18460	+	1.29617i	−0.658611	+	0.118820i
$120$	3.32955			0.303945
$121$	−10.5671	−	3.05542i	−0.960649	−	0.277765i
$122$	7.48430	−	12.9632i	0.677597	−	1.17363i
$123$	−10.7000	+	4.76393i	−0.964783	+	0.429549i
$124$	−1.45850	+	0.310014i	−0.130977	+	0.0278401i
$125$	−1.11725	−	3.43853i	−0.0999295	−	0.307551i
$126$	−0.357849	+	2.62144i	−0.0318797	+	0.233536i
$127$	0.500255	−	0.363457i	0.0443904	−	0.0322515i	−0.565369	−	0.824838i	$-0.691266\pi$
$127$	0.500255	−	0.363457i	0.0443904	−	0.0322515i	0.609759	+	0.792587i	$0.291266\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	−7.40813	−	8.22757i	−0.652250	−	0.724397i
$130$	−18.7615	+	8.35314i	−1.64549	+	0.732619i
$131$	3.63331	+	6.29307i	0.317444	+	0.549829i	0.979954	−	0.199224i	$-0.0638422\pi$
$131$	3.63331	+	6.29307i	0.317444	+	0.549829i	−0.662510	+	0.749053i	$0.730509\pi$
$132$	3.07649	−	1.23902i	0.267774	−	0.107843i
$133$	1.41496	+	4.86187i	0.122693	+	0.421578i
$134$	0.144468	+	0.104962i	0.0124801	+	0.00906732i
$135$	3.25679	−	0.692252i	0.280300	−	0.0595795i
$136$	−2.69906	−	0.573704i	−0.231443	−	0.0491947i
$137$	−1.22819	−	11.6854i	−0.104931	−	0.998352i	−0.912638	−	0.408768i	$-0.865958\pi$
$137$	−1.22819	−	11.6854i	−0.104931	−	0.998352i	0.807707	−	0.589584i	$-0.200708\pi$
$138$	−2.88457	−	1.28430i	−0.245551	−	0.109326i
$139$	−5.26087	−	16.1913i	−0.446221	−	1.37333i	−0.881139	−	0.472857i	$-0.843223\pi$
$139$	−5.26087	−	16.1913i	−0.446221	−	1.37333i	0.434918	−	0.900470i	$-0.356777\pi$
$140$	−4.63855	+	7.48900i	−0.392029	+	0.632936i
$141$	−1.94683	−	1.41445i	−0.163953	−	0.119118i
$142$	−5.54031	−	9.59611i	−0.464933	−	0.805287i
$143$	−14.2271	+	14.7000i	−1.18973	+	1.22927i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.179989	+	1.71248i	−0.0149472	+	0.142213i
$146$	−1.13490	+	3.49287i	−0.0939253	+	0.289072i
$147$	−5.39775	−	4.45694i	−0.445199	−	0.367602i
$148$	2.25706	−	1.63985i	0.185529	−	0.134795i
$149$	−11.7867	−	5.24777i	−0.965603	−	0.429914i	−0.137507	−	0.990501i	$-0.543909\pi$
$149$	−11.7867	−	5.24777i	−0.965603	−	0.429914i	−0.828096	+	0.560587i	$0.810576\pi$
$150$	5.95289	+	1.26533i	0.486051	+	0.103313i
$151$	0.871988	+	0.968441i	0.0709614	+	0.0788106i	0.777580	−	0.628784i	$-0.216447\pi$
$151$	0.871988	+	0.968441i	0.0709614	+	0.0788106i	−0.706619	+	0.707595i	$0.749780\pi$
$152$	−0.200052	+	1.90337i	−0.0162264	+	0.154384i
$153$	−2.75936			−0.223081
$154$	−1.49913	+	8.64596i	−0.120803	+	0.696711i
$155$	−4.96463			−0.398769
$156$	0.644742	−	6.13431i	0.0516207	−	0.491138i
$157$	2.19115	+	2.43352i	0.174873	+	0.194216i	0.824209	−	0.566285i	$-0.191620\pi$
$157$	2.19115	+	2.43352i	0.174873	+	0.194216i	−0.649337	+	0.760501i	$0.724953\pi$
$158$	−8.72295	−	1.85412i	−0.693961	−	0.147506i
$159$	0.815559	+	0.363110i	0.0646781	+	0.0287965i
$160$	−2.69366	+	1.95706i	−0.212952	+	0.154719i
$161$	6.90734	−	4.69893i	0.544375	−	0.370327i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	0.204069	−	1.94159i	0.0159839	−	0.152077i	−0.983619	−	0.180261i	$-0.942306\pi$
$163$	0.204069	−	1.94159i	0.0159839	−	0.152077i	0.999603	+	0.0281840i	$0.00897243\pi$
$164$	5.85629	−	10.1434i	0.457299	−	0.792065i
$165$	10.8772	−	1.90553i	0.846789	−	0.148345i
$166$	−5.43436	−	9.41258i	−0.421788	−	0.730558i
$167$	−2.62532	−	1.90741i	−0.203153	−	0.147600i	0.481557	−	0.876415i	$-0.340071\pi$
$167$	−2.62532	−	1.90741i	−0.203153	−	0.147600i	−0.684711	+	0.728815i	$0.740071\pi$
$168$	−1.25134	−	2.33113i	−0.0965428	−	0.179850i
$169$	7.73947	+	23.8196i	0.595343	+	1.83228i
$170$	−8.39313	−	3.73686i	−0.643724	−	0.286604i
$171$	0.200052	+	1.90337i	0.0152984	+	0.145554i
$172$	10.8293	+	2.30185i	0.825730	+	0.175514i
$173$	23.2696	−	4.94610i	1.76915	−	0.376045i	0.795837	−	0.605511i	$-0.207031\pi$
$173$	23.2696	−	4.94610i	1.76915	−	0.376045i	0.973317	+	0.229465i	$0.0736978\pi$
$174$	−0.418392	−	0.303979i	−0.0317182	−	0.0230446i
$175$	−11.1393	+	11.6268i	−0.842051	+	0.878901i
$176$	−1.76066	+	2.81071i	−0.132714	+	0.211865i
$177$	−0.788469	−	1.36567i	−0.0592649	−	0.102650i
$178$	0.532446	−	0.237060i	0.0399085	−	0.0177684i
$179$	12.8445	+	14.2653i	0.960043	+	1.06624i	0.997757	+	0.0669468i	$0.0213258\pi$
$179$	12.8445	+	14.2653i	0.960043	+	1.06624i	−0.0377139	+	0.999289i	$0.512008\pi$
$180$	−2.22790	+	2.47434i	−0.166058	+	0.184426i
$181$	12.3925	−	9.00371i	0.921131	−	0.669241i	−0.0226743	−	0.999743i	$-0.507218\pi$
$181$	12.3925	−	9.00371i	0.921131	−	0.669241i	0.943805	+	0.330502i	$0.107218\pi$
$182$	12.8994	+	9.99618i	0.956167	+	0.740966i
$183$	4.62555	+	14.2360i	0.341931	+	1.05235i
$184$	3.08856	−	0.656494i	0.227692	−	0.0483974i
$185$	8.48594	−	3.77818i	0.623899	−	0.277778i
$186$	0.745542	−	1.29132i	0.0546658	−	0.0946839i
$187$	−9.14583	−	0.329519i	−0.668810	−	0.0240968i
$188$	2.40641			0.175506
$189$	−1.70866	−	2.02002i	−0.124287	−	0.146935i
$190$	−1.96914	+	6.06039i	−0.142856	+	0.439667i
$191$	−17.2644	+	19.1740i	−1.24921	+	1.38738i	−0.358041	+	0.933706i	$0.616555\pi$
$191$	−17.2644	+	19.1740i	−1.24921	+	1.38738i	−0.891165	+	0.453679i	$0.850111\pi$
$192$	−0.104528	−	0.994522i	−0.00754369	−	0.0717734i
$193$	0.878145	+	8.35499i	0.0632102	+	0.601405i	0.979578	+	0.201067i	$0.0644408\pi$
$193$	0.878145	+	8.35499i	0.0632102	+	0.601405i	−0.916367	+	0.400339i	$0.868893\pi$
$194$	8.17188	−	9.07580i	0.586707	−	0.651604i
$195$	6.34627	−	19.5318i	0.454466	−	1.39870i
$196$	6.98659	+	0.433025i	0.499042	+	0.0309304i
$197$	12.2252			0.871007			0.435504	−	0.900187i	$-0.356570\pi$
$197$	12.2252			0.871007			0.435504	+	0.900187i	$0.356570\pi$
$198$	−1.13780	+	3.11535i	−0.0808601	+	0.221398i
$199$	12.2912	−	21.2890i	0.871302	−	1.50914i	0.0106517	−	0.999943i	$-0.496609\pi$
$199$	12.2912	−	21.2890i	0.871302	−	1.50914i	0.860650	−	0.509196i	$-0.170057\pi$
$200$	−5.55973	+	2.47535i	−0.393132	+	0.175034i
$201$	−0.174670	+	0.0371272i	−0.0123202	+	0.00261875i
$202$	−3.11702	−	9.59322i	−0.219313	−	0.674976i
$203$	1.26661	−	0.517581i	0.0888984	−	0.0363271i
$204$	2.23237	−	1.62191i	0.156297	−	0.113557i
$205$	26.0945	−	28.9808i	1.82252	−	2.02411i
$206$	12.8194	+	14.2373i	0.893167	+	0.991962i
$207$	2.88457	−	1.28430i	0.200492	−	0.0892647i
$208$	3.08405	+	5.34173i	0.213840	+	0.370382i
$209$	0.435771	+	6.33256i	0.0301429	+	0.438033i
$210$	−2.46162	−	8.45823i	−0.169868	−	0.583673i
$211$	−10.1027	−	7.34006i	−0.695500	−	0.505310i	0.182963	−	0.983120i	$-0.441431\pi$
$211$	−10.1027	−	7.34006i	−0.695500	−	0.505310i	−0.878464	+	0.477809i	$0.841431\pi$
$212$	−0.873232	+	0.185611i	−0.0599738	+	0.0127478i
$213$	10.8385	+	2.30379i	0.742641	+	0.157853i
$214$	−0.245197	−	2.33289i	−0.0167613	−	0.159473i
$215$	33.6754	+	14.9933i	2.29664	+	1.02253i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	1.86585	+	3.47591i	0.126662	+	0.235960i
$218$	−12.6851	−	9.21627i	−0.859144	−	0.624205i
$219$	−1.83631	−	3.18059i	−0.124087	−	0.214924i
$220$	−7.67980	+	7.93507i	−0.517772	+	0.534982i
$221$	−8.51001	+	14.7398i	−0.572445	+	0.991504i
$222$	−0.291621	+	2.77459i	−0.0195723	+	0.186218i
$223$	−4.20173	+	12.9316i	−0.281369	+	0.865964i	0.706095	+	0.708117i	$0.250455\pi$
$223$	−4.20173	+	12.9316i	−0.281369	+	0.865964i	−0.987464	+	0.157847i	$0.949545\pi$
$224$	2.38256	+	1.15040i	0.159191	+	0.0768646i
$225$	−4.92358	+	3.57719i	−0.328239	+	0.238479i
$226$	−9.82475	−	4.37426i	−0.653533	−	0.290971i
$227$	−6.04625	−	1.28517i	−0.401304	−	0.0852998i	0.00283820	−	0.999996i	$-0.499097\pi$
$227$	−6.04625	−	1.28517i	−0.401304	−	0.0852998i	−0.404142	+	0.914696i	$0.632430\pi$
$228$	−1.28062	−	1.42227i	−0.0848111	−	0.0941922i
$229$	1.25820	−	11.9710i	0.0831440	−	0.791063i	−0.870913	−	0.491437i	$-0.836472\pi$
$229$	1.25820	−	11.9710i	0.0831440	−	0.791063i	0.954057	−	0.299625i	$-0.0968617\pi$
$230$	10.5132			0.693223
$231$	−5.42209	−	6.89935i	−0.356747	−	0.453944i
$232$	0.517160			0.0339532
$233$	−2.21183	+	21.0441i	−0.144902	+	1.37865i	0.644422	+	0.764670i	$0.277098\pi$
$233$	−2.21183	+	21.0441i	−0.144902	+	1.37865i	−0.789323	+	0.613978i	$0.789568\pi$
$234$	4.12726	+	4.58379i	0.269808	+	0.299652i
$235$	7.83717	+	1.66584i	0.511241	+	0.108668i
$236$	1.44060	+	0.641398i	0.0937753	+	0.0417515i
$237$	7.21467	−	5.24177i	0.468643	−	0.340489i
$238$	0.538073	+	7.28073i	0.0348781	+	0.471940i
$239$	−0.164136	+	0.505157i	−0.0106171	+	0.0326759i	−0.956225	−	0.292633i	$-0.905468\pi$
$239$	−0.164136	+	0.505157i	−0.0106171	+	0.0326759i	0.945608	+	0.325309i	$0.105468\pi$
$240$	0.348032	−	3.31131i	0.0224654	−	0.213744i
$241$	−1.86136	+	3.22397i	−0.119901	+	0.207674i	−0.919728	−	0.392556i	$-0.871591\pi$
$241$	−1.86136	+	3.22397i	−0.119901	+	0.207674i	0.799827	+	0.600230i	$0.204924\pi$
$242$	−4.14325	+	10.1899i	−0.266338	+	0.655030i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−12.1098	−	8.79832i	−0.775254	−	0.563255i
$245$	22.4541	+	6.24675i	1.43454	+	0.399090i
$246$	3.61938	+	11.1393i	0.230763	+	0.710217i
$247$	10.7843	+	4.80146i	0.686186	+	0.305510i
$248$	0.155861	+	1.48292i	0.00989717	+	0.0941653i
$249$	10.6312	+	2.25973i	0.673725	+	0.143205i
$250$	−3.53648	+	0.751701i	−0.223666	+	0.0475418i
$251$	11.8300	+	8.59497i	0.746701	+	0.542510i	0.894802	−	0.446462i	$-0.147316\pi$
$251$	11.8300	+	8.59497i	0.746701	+	0.542510i	−0.148102	+	0.988972i	$0.547316\pi$
$252$	2.56967	+	0.629903i	0.161874	+	0.0396802i
$253$	9.71422	−	3.91229i	0.610728	−	0.245964i
$254$	−0.309175	−	0.535506i	−0.0193993	−	0.0336006i
$255$	8.39313	−	3.73686i	0.525598	−	0.234011i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−9.96177	+	11.0637i	−0.621398	+	0.690133i	−0.968873	−	0.247556i	$-0.920372\pi$
$257$	−9.96177	+	11.0637i	−0.621398	+	0.690133i	0.347475	+	0.937689i	$0.387039\pi$
$258$	−8.95685	+	6.50754i	−0.557629	+	0.405141i
$259$	−5.83449	−	4.52134i	−0.362538	−	0.280943i
$260$	6.34627	+	19.5318i	0.393579	+	1.21131i
$261$	0.505859	−	0.107524i	0.0313119	−	0.00665555i
$262$	6.63838	−	2.95560i	0.410121	−	0.182598i
$263$	9.45543	−	16.3773i	0.583047	−	1.00987i	−0.412069	−	0.911153i	$-0.635194\pi$
$263$	9.45543	−	16.3773i	0.583047	−	1.00987i	0.995116	−	0.0987142i	$-0.0314729\pi$
$264$	−0.910655	−	3.18915i	−0.0560470	−	0.196279i
$265$	−2.97242			−0.182594
$266$	4.98314	−	0.899005i	0.305536	−	0.0551215i
$267$	−0.180106	+	0.554309i	−0.0110223	+	0.0339232i
$268$	0.119488	−	0.132705i	0.00729888	−	0.00810623i
$269$	−1.61421	−	15.3582i	−0.0984200	−	0.936404i	−0.926627	−	0.375982i	$-0.877306\pi$
$269$	−1.61421	−	15.3582i	−0.0984200	−	0.936404i	0.828207	−	0.560422i	$-0.189361\pi$
$270$	−0.348032	−	3.31131i	−0.0211806	−	0.201520i
$271$	6.50807	−	7.22795i	0.395337	−	0.439066i	−0.512310	−	0.858801i	$-0.671210\pi$
$271$	6.50807	−	7.22795i	0.395337	−	0.439066i	0.907647	+	0.419734i	$0.137877\pi$
$272$	−0.852690	+	2.62431i	−0.0517019	+	0.159122i
$273$	−16.0600	+	2.89737i	−0.971995	+	0.175357i
$274$	−11.7498			−0.709830
$275$	−16.7463	+	11.2685i	−1.00984	+	0.679518i
$276$	−1.57878	+	2.73453i	−0.0950314	+	0.164599i
$277$	23.5773	−	10.4973i	1.41662	−	0.630721i	0.451441	−	0.892301i	$-0.350910\pi$
$277$	23.5773	−	10.4973i	1.41662	−	0.630721i	0.965182	+	0.261580i	$0.0842435\pi$
$278$	−16.6525	+	3.53960i	−0.998750	+	0.212291i
$279$	0.460770	+	1.41811i	0.0275856	+	0.0848997i
$280$	6.96311	+	5.39595i	0.416125	+	0.322470i
$281$	−14.8041	+	10.7558i	−0.883136	+	0.641636i	−0.934079	−	0.357066i	$-0.883777\pi$
$281$	−14.8041	+	10.7558i	−0.883136	+	0.641636i	0.0509433	+	0.998702i	$0.483777\pi$
$282$	−1.61020	+	1.78831i	−0.0958863	+	0.106492i
$283$	−17.9788	−	19.9675i	−1.06873	−	1.18694i	−0.981640	−	0.190742i	$-0.938911\pi$
$283$	−17.9788	−	19.9675i	−1.06873	−	1.18694i	−0.0870876	−	0.996201i	$-0.527756\pi$
$284$	−10.1227	+	4.50690i	−0.600669	+	0.267435i
$285$	−3.18613	−	5.51855i	−0.188730	−	0.326891i
$286$	13.1323	+	15.6857i	0.776530	+	0.927516i
$287$	−30.0975	−	7.37779i	−1.77660	−	0.435497i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	9.18082	−	1.95144i	0.540048	−	0.114791i
$290$	1.68428	+	0.358005i	0.0989044	+	0.0210228i
$291$	1.27657	+	12.1458i	0.0748341	+	0.711999i
$292$	3.35511	+	1.49379i	0.196343	+	0.0874175i
$293$	7.69269	+	23.6757i	0.449412	+	1.38315i	0.877572	+	0.479445i	$0.159162\pi$
$293$	7.69269	+	23.6757i	0.449412	+	1.38315i	−0.428160	+	0.903703i	$0.640838\pi$
$294$	−4.99674	+	4.90230i	−0.291416	+	0.285908i
$295$	4.24773	+	3.08616i	0.247313	+	0.179683i
$296$	−1.39494	−	2.41610i	−0.0810791	−	0.140433i
$297$	−1.55382	−	2.93013i	−0.0901616	−	0.170023i
$298$	−6.45107	+	11.1736i	−0.373700	+	0.647268i
$299$	2.03581	−	19.3694i	0.117734	−	1.12016i
$300$	1.88064	−	5.78801i	0.108579	−	0.334171i
$301$	−2.15889	−	29.2122i	−0.124436	−	1.68376i
$302$	1.05428	−	0.765982i	0.0606672	−	0.0440773i
$303$	9.21485	+	4.10271i	0.529379	+	0.235695i
$304$	1.87203	+	0.397913i	0.107368	+	0.0228219i
$305$	−33.3486	−	37.0373i	−1.90953	−	2.12075i
$306$	−0.288432	+	2.74425i	−0.0164885	+	0.156878i
$307$	29.9103			1.70707			0.853535	−	0.521035i	$-0.174454\pi$
$307$	29.9103			1.70707			0.853535	+	0.521035i	$0.174454\pi$
$308$	8.44189	+	2.39466i	0.481022	+	0.136449i
$309$	−19.1582			−1.08987
$310$	−0.518946	+	4.93744i	−0.0294741	+	0.280428i
$311$	−13.5279	−	15.0243i	−0.767099	−	0.851950i	0.225392	−	0.974268i	$-0.427634\pi$
$311$	−13.5279	−	15.0243i	−0.767099	−	0.851950i	−0.992491	+	0.122318i	$0.960967\pi$
$312$	−6.03331	−	1.28242i	−0.341569	−	0.0726027i
$313$	−11.4440	−	5.09518i	−0.646851	−	0.287996i	0.0569682	−	0.998376i	$-0.481857\pi$
$313$	−11.4440	−	5.09518i	−0.646851	−	0.287996i	−0.703819	+	0.710380i	$0.748523\pi$
$314$	2.64922	−	1.92477i	0.149504	−	0.108621i
$315$	7.93283	+	3.83032i	0.446964	+	0.215814i
$316$	−2.75576	+	8.48136i	−0.155024	+	0.477114i
$317$	−0.962292	+	9.15559i	−0.0540477	+	0.514229i	0.933687	+	0.358089i	$0.116572\pi$
$317$	−0.962292	+	9.15559i	−0.0540477	+	0.514229i	−0.987735	+	0.156140i	$0.950095\pi$
$318$	0.446370	−	0.773136i	0.0250312	−	0.0433553i
$319$	1.68950	−	0.295976i	0.0945937	−	0.0165715i
$320$	1.66477	+	2.88347i	0.0930636	+	0.161191i
$321$	1.89774	+	1.37879i	0.105922	+	0.0769567i
$322$	−3.95117	−	7.36067i	−0.220190	−	0.410194i
$323$	1.63192	+	5.02255i	0.0908027	+	0.279462i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	3.92382	+	37.3327i	0.217654	+	2.07084i
$326$	−1.90962	−	0.405903i	−0.105764	−	0.0224809i
$327$	15.3370	−	3.25998i	0.848139	−	0.180278i
$328$	−9.47567	−	6.88448i	−0.523206	−	0.380132i
$329$	−1.77912	−	6.11314i	−0.0980860	−	0.337028i
$330$	−0.758113	−	11.0168i	−0.0417328	−	0.606455i
$331$	7.58335	+	13.1348i	0.416819	+	0.721951i	0.995617	−	0.0935191i	$-0.0298116\pi$
$331$	7.58335	+	13.1348i	0.416819	+	0.721951i	−0.578799	+	0.815470i	$0.696478\pi$
$332$	−9.92906	+	4.42070i	−0.544928	+	0.242618i
$333$	−1.86679	−	2.07328i	−0.102300	−	0.113615i
$334$	−2.17138	+	2.41156i	−0.118813	+	0.131955i
$335$	0.481012	−	0.349475i	0.0262805	−	0.0190939i
$336$	−2.44916	+	1.00081i	−0.133612	+	0.0545989i
$337$	−8.05189	−	24.7812i	−0.438614	−	1.34992i	−0.889337	−	0.457252i	$-0.848834\pi$
$337$	−8.05189	−	24.7812i	−0.438614	−	1.34992i	0.450723	−	0.892664i	$-0.351166\pi$
$338$	24.4981	−	5.20724i	1.33252	−	0.283236i
$339$	9.82475	−	4.37426i	0.533607	−	0.237577i
$340$	−4.59371	+	7.95654i	−0.249129	+	0.431504i
$341$	1.35786	+	4.75530i	0.0735324	+	0.257514i
$342$	1.91386			0.103489
$343$	−4.06532	−	18.0686i	−0.219507	−	0.975611i
$344$	3.42121	−	10.5294i	0.184459	−	0.567708i
$345$	−7.03473	+	7.81286i	−0.378737	+	0.420630i
$346$	−2.48667	−	23.6591i	−0.133684	−	1.27192i
$347$	3.63187	+	34.5550i	0.194969	+	1.85501i	0.456386	+	0.889782i	$0.349144\pi$
$347$	3.63187	+	34.5550i	0.194969	+	1.85501i	−0.261417	+	0.965226i	$0.584190\pi$
$348$	−0.346048	+	0.384325i	−0.0185501	+	0.0206020i
$349$	−9.24039	+	28.4390i	−0.494627	+	1.52230i	0.322911	+	0.946429i	$0.395339\pi$
$349$	−9.24039	+	28.4390i	−0.494627	+	1.52230i	−0.817538	+	0.575875i	$0.804661\pi$
$350$	10.3987	+	12.2936i	0.555834	+	0.657120i
$351$	−6.16810			−0.329229
$352$	2.61127	+	2.04481i	0.139181	+	0.108989i
$353$	−2.09489	+	3.62846i	−0.111500	+	0.193124i	−0.916375	−	0.400320i	$-0.868899\pi$
$353$	−2.09489	+	3.62846i	−0.111500	+	0.193124i	0.804875	+	0.593444i	$0.202232\pi$
$354$	−1.44060	+	0.641398i	−0.0765672	+	0.0340899i
$355$	−36.0873	+	7.67058i	−1.91531	+	0.407112i
$356$	−0.180106	−	0.554309i	−0.00954560	−	0.0293783i
$357$	−5.77068	−	4.47189i	−0.305417	−	0.236678i
$358$	15.5297	−	11.2830i	0.820772	−	0.596325i
$359$	1.06189	−	1.17935i	0.0560446	−	0.0622438i	−0.714471	−	0.699665i	$-0.753332\pi$
$359$	1.06189	−	1.17935i	0.0560446	−	0.0622438i	0.770515	+	0.637422i	$0.219999\pi$
$360$	2.22790	+	2.47434i	0.117421	+	0.130409i
$361$	−14.0112	+	6.23818i	−0.737431	+	0.328325i
$362$	−7.65902	−	13.2658i	−0.402549	−	0.697235i
$363$	−4.80018	−	9.89739i	−0.251944	−	0.519478i
$364$	11.2898	−	11.7838i	0.591745	−	0.617641i
$365$	9.89280	+	7.18754i	0.517813	+	0.376213i
$366$	14.6415	−	3.11215i	0.765323	−	0.162675i
$367$	13.5930	+	2.88928i	0.709549	+	0.150819i	0.548528	−	0.836132i	$-0.315188\pi$
$367$	13.5930	+	2.88928i	0.709549	+	0.150819i	0.161020	+	0.986951i	$0.448522\pi$
$368$	−0.330055	−	3.14026i	−0.0172053	−	0.163697i
$369$	−10.7000	−	4.76393i	−0.557018	−	0.248000i
$370$	−2.87046	−	8.83438i	−0.149228	−	0.459278i
$371$	1.11712	+	2.08109i	0.0579980	+	0.108045i
$372$	−1.20631	−	0.876437i	−0.0625444	−	0.0454412i
$373$	4.54065	+	7.86464i	0.235106	+	0.407216i	0.959304	−	0.282377i	$-0.0911229\pi$
$373$	4.54065	+	7.86464i	0.235106	+	0.407216i	−0.724197	+	0.689593i	$0.757790\pi$
$374$	−1.28371	+	9.06129i	−0.0663792	+	0.468548i
$375$	1.80774	−	3.13110i	0.0933514	−	0.161689i
$376$	0.251539	−	2.39323i	0.0129721	−	0.123421i
$377$	0.985732	−	3.03377i	0.0507678	−	0.156247i
$378$	−2.18756	+	1.48815i	−0.112516	+	0.0765423i
$379$	−16.7203	+	12.1480i	−0.858863	+	0.624000i	−0.927575	−	0.373636i	$-0.878111\pi$
$379$	−16.7203	+	12.1480i	−0.858863	+	0.624000i	0.0687125	+	0.997637i	$0.478111\pi$
$380$	5.82136	+	2.59184i	0.298629	+	0.132958i
$381$	0.604837	+	0.128562i	0.0309867	+	0.00658643i
$382$	17.2644	+	19.1740i	0.883323	+	0.981029i
$383$	−0.673925	+	6.41197i	−0.0344360	+	0.327636i	0.963719	+	0.266919i	$0.0860056\pi$
$383$	−0.673925	+	6.41197i	−0.0344360	+	0.327636i	−0.998155	+	0.0607176i	$0.980661\pi$
$384$	−1.00000			−0.0510310
$385$	25.8357	+	13.6428i	1.31671	+	0.695303i
$386$	8.40101			0.427600
$387$	1.15726	−	11.0106i	0.0588270	−	0.559702i
$388$	−8.17188	−	9.07580i	−0.414864	−	0.460754i
$389$	−28.3403	−	6.02392i	−1.43691	−	0.305425i	−0.577367	−	0.816485i	$-0.695920\pi$
$389$	−28.3403	−	6.02392i	−1.43691	−	0.305425i	−0.859545	+	0.511060i	$0.829253\pi$
$390$	−18.7615	−	8.35314i	−0.950023	−	0.422978i
$391$	7.04884	−	5.12128i	0.356475	−	0.258994i
$392$	1.16095	−	6.90306i	0.0586369	−	0.348657i
$393$	−2.24551	+	6.91096i	−0.113271	+	0.348612i
$394$	1.27788	−	12.1582i	0.0643786	−	0.612521i
$395$	−14.8462	+	25.7143i	−0.746991	+	1.29383i
$396$	2.97935	+	1.45721i	0.149718	+	0.0732277i
$397$	8.35193	+	14.4660i	0.419172	+	0.726026i	0.995856	−	0.0909403i	$-0.0289872\pi$
$397$	8.35193	+	14.4660i	0.419172	+	0.726026i	−0.576685	+	0.816967i	$0.695654\pi$
$398$	−19.8876	−	14.4492i	−0.996877	−	0.724273i
$399$	−2.66628	+	4.30475i	−0.133481	+	0.215507i
$400$	1.88064	+	5.78801i	0.0940320	+	0.289401i
$401$	23.9693	+	10.6718i	1.19697	+	0.532925i	0.905783	−	0.423741i	$-0.139283\pi$
$401$	23.9693	+	10.6718i	1.19697	+	0.532925i	0.291187	+	0.956666i	$0.405950\pi$
$402$	0.0186658	+	0.177594i	0.000930967	+	0.00885756i
$403$	8.99617	+	1.91220i	0.448131	+	0.0952533i
$404$	−9.86648	+	2.09719i	−0.490876	+	0.104339i
$405$	2.69366	+	1.95706i	0.133849	+	0.0972470i
$406$	−0.382349	−	1.31377i	−0.0189757	−	0.0652013i
$407$	−5.93984	−	7.09477i	−0.294427	−	0.351675i
$408$	−1.37968	−	2.38968i	−0.0683044	−	0.118307i
$409$	−15.3782	+	6.84683i	−0.760405	+	0.338554i	−0.750040	−	0.661392i	$-0.769966\pi$
$409$	−15.3782	+	6.84683i	−0.760405	+	0.338554i	−0.0103645	+	0.999946i	$0.503299\pi$
$410$	−26.0945	−	28.9808i	−1.28871	−	1.43126i
$411$	7.86214	−	8.73179i	0.387811	−	0.430707i
$412$	15.4993	−	11.2609i	0.763597	−	0.554786i
$413$	0.564305	−	4.13385i	0.0277676	−	0.203413i
$414$	−0.975740	−	3.00302i	−0.0479550	−	0.147590i
$415$	−35.3971	+	7.52388i	−1.73757	+	0.369333i
$416$	5.63484	−	2.50879i	0.276271	−	0.123004i
$417$	8.51226	−	14.7437i	0.416847	−	0.722001i
$418$	6.34342	+	0.228550i	0.310267	+	0.0111787i
$419$	−7.79672			−0.380894			−0.190447	−	0.981697i	$-0.560994\pi$
$419$	−7.79672			−0.380894			−0.190447	+	0.981697i	$0.560994\pi$
$420$	−8.66920	+	1.56400i	−0.423014	+	0.0763156i
$421$	9.01550	−	27.7469i	0.439389	−	1.35230i	−0.449133	−	0.893465i	$-0.648267\pi$
$421$	9.01550	−	27.7469i	0.439389	−	1.35230i	0.888522	−	0.458835i	$-0.151733\pi$
$422$	−8.35587	+	9.28014i	−0.406757	+	0.451750i
$423$	−0.251539	−	2.39323i	−0.0122302	−	0.116363i
$424$	0.0933168	+	0.887850i	0.00453187	+	0.0431178i
$425$	−11.2368	+	12.4797i	−0.545065	+	0.605356i
$426$	3.42410	−	10.5383i	0.165898	−	0.510583i
$427$	−13.3977	+	37.2681i	−0.648362	+	1.80353i
$428$	−2.34574			−0.113386
$429$	−20.4440	−	0.736585i	−0.987046	−	0.0355626i
$430$	18.4312	−	31.9237i	0.888830	−	1.53950i
$431$	−23.3060	+	10.3765i	−1.12261	+	0.499818i	−0.882210	−	0.470857i	$-0.843945\pi$
$431$	−23.3060	+	10.3765i	−1.12261	+	0.499818i	−0.240399	+	0.970674i	$0.577278\pi$
$432$	−0.978148	+	0.207912i	−0.0470611	+	0.0100032i
$433$	−0.00422913	−	0.0130159i	−0.000203239	−	0.000625506i	0.950955	−	0.309330i	$-0.100105\pi$
$433$	−0.00422913	−	0.0130159i	−0.000203239	−	0.000625506i	−0.951158	+	0.308704i	$0.900105\pi$
$434$	3.65190	−	1.49230i	0.175297	−	0.0716326i
$435$	−1.39305	+	1.01211i	−0.0667918	+	0.0485271i
$436$	−10.4917	+	11.6523i	−0.502463	+	0.558042i
$437$	−4.04363	−	4.49091i	−0.193433	−	0.214829i
$438$	−3.35511	+	1.49379i	−0.160313	+	0.0713761i
$439$	−19.6988	−	34.1194i	−0.940174	−	1.62843i	−0.765136	−	0.643868i	$-0.777328\pi$
$439$	−19.6988	−	34.1194i	−0.940174	−	1.62843i	−0.175038	−	0.984562i	$-0.556005\pi$
$440$	7.08884	+	8.46717i	0.337947	+	0.403657i
$441$	−0.299645	−	6.99358i	−0.0142688	−	0.333028i
$442$	13.7695	+	10.0041i	0.654947	+	0.475847i
$443$	18.1620	−	3.86045i	0.862902	−	0.183416i	0.244858	−	0.969559i	$-0.421259\pi$
$443$	18.1620	−	3.86045i	0.862902	−	0.183416i	0.618044	+	0.786143i	$0.287925\pi$
$444$	2.72891	+	0.580048i	0.129508	+	0.0275278i
$445$	−0.202845	−	1.92995i	−0.00961580	−	0.0914882i
$446$	12.4216	+	5.53044i	0.588178	+	0.261874i
$447$	−3.98698	−	12.2707i	−0.188578	−	0.580382i
$448$	1.39315	−	2.24925i	0.0658200	−	0.106267i
$449$	−4.64331	−	3.37356i	−0.219131	−	0.159208i	0.472804	−	0.881167i	$-0.343242\pi$
$449$	−4.64331	−	3.37356i	−0.219131	−	0.159208i	−0.691936	+	0.721959i	$0.743242\pi$
$450$	3.04294	+	5.27053i	0.143446	+	0.248455i
$451$	−34.8959	−	17.0677i	−1.64318	−	0.803687i
$452$	−5.37726	+	9.31369i	−0.252925	+	0.438079i
$453$	−0.136218	+	1.29603i	−0.00640008	+	0.0608927i
$454$	−1.91014	+	5.87880i	−0.0896471	+	0.275906i
$455$	44.9258	−	30.5621i	2.10615	−	1.43277i
$456$	−1.54834	+	1.12494i	−0.0725077	+	0.0526800i
$457$	−0.238383	−	0.106135i	−0.0111511	−	0.00496479i	0.401154	−	0.916011i	$-0.368609\pi$
$457$	−0.238383	−	0.106135i	−0.0111511	−	0.00496479i	−0.412305	+	0.911046i	$0.635276\pi$
$458$	−11.7739	−	2.50261i	−0.550156	−	0.116939i
$459$	−1.84637	−	2.05061i	−0.0861813	−	0.0957141i
$460$	1.09893	−	10.4556i	0.0512380	−	0.487497i
$461$	15.7428			0.733215			0.366607	−	0.930376i	$-0.380519\pi$
$461$	15.7428			0.733215			0.366607	+	0.930376i	$0.380519\pi$
$462$	−7.42831	+	4.67121i	−0.345596	+	0.217324i
$463$	10.4942			0.487708			0.243854	−	0.969812i	$-0.421588\pi$
$463$	10.4942			0.487708			0.243854	+	0.969812i	$0.421588\pi$
$464$	0.0540580	−	0.514327i	0.00250958	−	0.0238770i
$465$	−3.32199	−	3.68944i	−0.154054	−	0.171094i
$466$	20.6977	+	4.39943i	0.958801	+	0.203799i
$467$	−0.863379	−	0.384401i	−0.0399524	−	0.0177880i	0.386663	−	0.922221i	$-0.373628\pi$
$467$	−0.863379	−	0.384401i	−0.0399524	−	0.0177880i	−0.426616	+	0.904433i	$0.640294\pi$
$468$	4.99010	−	3.62552i	0.230667	−	0.167590i
$469$	−0.425457	−	0.205430i	−0.0196458	−	0.00948586i
$470$	2.47593	−	7.62011i	0.114206	−	0.351490i
$471$	−0.342291	+	3.25668i	−0.0157719	+	0.150060i
$472$	0.788469	−	1.36567i	0.0362922	−	0.0628600i
$473$	5.15059	−	36.3563i	0.236825	−	1.67166i
$474$	−4.45891	−	7.72307i	−0.204805	−	0.354732i
$475$	9.42302	+	6.84622i	0.432358	+	0.314126i
$476$	7.29709	+	0.225918i	0.334461	+	0.0103549i
$477$	0.275872	+	0.849047i	0.0126313	+	0.0388752i
$478$	0.485233	+	0.216040i	0.0221941	+	0.00988143i
$479$	−1.54945	−	14.7421i	−0.0707963	−	0.673582i	−0.971158	−	0.238439i	$-0.923364\pi$
$479$	−1.54945	−	14.7421i	−0.0707963	−	0.673582i	0.900361	−	0.435143i	$-0.143302\pi$
$480$	−3.25679	−	0.692252i	−0.148651	−	0.0315968i
$481$	−16.8322	+	3.57779i	−0.767482	+	0.163133i
$482$	3.01175	+	2.18816i	0.137181	+	0.0996681i
$483$	8.11390	+	1.98896i	0.369195	+	0.0905007i
$484$	9.70096	+	5.18568i	0.440953	+	0.235713i
$485$	−20.3314	−	35.2149i	−0.923199	−	1.59903i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	7.63546	+	8.48004i	0.345996	+	0.384267i	0.890876	−	0.454247i	$-0.150092\pi$
$487$	7.63546	+	8.48004i	0.345996	+	0.384267i	−0.544880	+	0.838514i	$0.683425\pi$
$488$	−10.0159	+	11.1238i	−0.453401	+	0.503552i
$489$	1.57943	−	1.14752i	0.0714243	−	0.0518928i
$490$	8.55962	−	21.6781i	0.386684	−	0.979318i
$491$	−3.30384	−	10.1682i	−0.149100	−	0.458884i	0.848415	−	0.529332i	$-0.177557\pi$
$491$	−3.30384	−	10.1682i	−0.149100	−	0.458884i	−0.997515	+	0.0704477i	$0.977557\pi$
$492$	11.4566	−	2.43518i	0.516504	−	0.109786i
$493$	1.30366	−	0.580426i	0.0587138	−	0.0261411i
$494$	5.90242	−	10.2233i	0.265563	−	0.459968i
$495$	8.69436	+	6.80829i	0.390782	+	0.306010i
$496$	1.49108			0.0669517
$497$	18.9330	+	22.3831i	0.849263	+	1.00402i
$498$	3.35862	−	10.3368i	0.150503	−	0.463201i
$499$	9.15763	−	10.1706i	0.409952	−	0.455298i	−0.502442	−	0.864611i	$-0.667565\pi$
$499$	9.15763	−	10.1706i	0.409952	−	0.455298i	0.912394	+	0.409313i	$0.134232\pi$
$500$	0.377921	+	3.59568i	0.0169011	+	0.160804i
$501$	−0.339203	−	3.22730i	−0.0151545	−	0.144185i
$502$	9.78446	−	10.8667i	0.436702	−	0.485006i
$503$	−11.0470	+	33.9993i	−0.492563	+	1.51595i	0.328158	+	0.944623i	$0.393572\pi$
$503$	−11.0470	+	33.9993i	−0.492563	+	1.51595i	−0.820721	+	0.571329i	$0.806428\pi$
$504$	0.895057	−	2.48975i	0.0398690	−	0.110902i
$505$	−33.5848			−1.49450
$506$	−2.87545	−	10.0699i	−0.127829	−	0.447664i
$507$	−12.5227	+	21.6900i	−0.556153	+	0.963286i
$508$	−0.564890	+	0.251505i	−0.0250629	+	0.0111587i
$509$	41.0350	−	8.72226i	1.81884	−	0.386607i	0.832865	−	0.553476i	$-0.186699\pi$
$509$	41.0350	−	8.72226i	1.81884	−	0.386607i	0.985979	+	0.166869i	$0.0533656\pi$
$510$	−2.83907	−	8.73776i	−0.125716	−	0.386914i
$511$	1.31424	−	9.62757i	0.0581387	−	0.425898i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.28062	+	1.42227i	−0.0565407	+	0.0627948i
$514$	9.96177	+	11.0637i	0.439395	+	0.487998i
$515$	58.2734	−	25.9450i	2.56783	−	1.14327i
$516$	5.53564	+	9.58801i	0.243693	+	0.422089i
$517$	−0.547922	−	7.96234i	−0.0240976	−	0.350183i
$518$	−5.10645	+	5.32992i	−0.224364	+	0.234183i
$519$	19.2461	+	13.9831i	0.844808	+	0.613789i
$520$	20.0882	−	4.26988i	0.880925	−	0.187246i
$521$	−12.9416	−	2.75083i	−0.566983	−	0.120516i	−0.0845034	−	0.996423i	$-0.526930\pi$
$521$	−12.9416	−	2.75083i	−0.566983	−	0.120516i	−0.482480	+	0.875907i	$0.660264\pi$
$522$	−0.0540580	−	0.514327i	−0.00236605	−	0.0225115i
$523$	−3.84894	−	1.71366i	−0.168302	−	0.0749331i	0.320856	−	0.947128i	$-0.396029\pi$
$523$	−3.84894	−	1.71366i	−0.168302	−	0.0749331i	−0.489159	+	0.872195i	$0.662696\pi$
$524$	−2.24551	−	6.91096i	−0.0980955	−	0.301907i
$525$	−16.0940	−	0.498271i	−0.702400	−	0.0217463i
$526$	−15.2992	−	11.1155i	−0.667077	−	0.484660i
$527$	2.05722	+	3.56321i	0.0896139	+	0.155216i
$528$	−3.26687	+	0.572309i	−0.142172	+	0.0249066i
$529$	6.51491	−	11.2842i	0.283257	−	0.490615i
$530$	−0.310703	+	2.95614i	−0.0134961	+	0.128406i
$531$	0.487300	−	1.49976i	0.0211470	−	0.0650839i
$532$	−0.373200	−	5.04981i	−0.0161803	−	0.218937i
$533$	−58.4469	+	42.4641i	−2.53161	+	1.83933i
$534$	0.532446	+	0.237060i	0.0230412	+	0.0102586i
$535$	−7.63958	−	1.62384i	−0.330288	−	0.0702049i
$536$	−0.119488	−	0.132705i	−0.00516109	−	0.00573197i
$537$	−2.00651	+	19.0906i	−0.0865872	+	0.823822i
$538$	−15.4428			−0.665785
$539$	−0.158003	−	23.2158i	−0.00680566	−	0.999977i
$540$	−3.32955			−0.143281
$541$	−0.772650	+	7.35127i	−0.0332188	+	0.316056i	0.965277	+	0.261228i	$0.0841276\pi$
$541$	−0.772650	+	7.35127i	−0.0332188	+	0.316056i	−0.998496	+	0.0548275i	$0.982539\pi$
$542$	−6.50807	−	7.22795i	−0.279546	−	0.310467i
$543$	14.9833	+	3.18480i	0.642995	+	0.136673i
$544$	2.52080	+	1.12233i	0.108079	+	0.0481196i
$545$	−42.2357	+	30.6860i	−1.80918	+	1.31444i
$546$	1.20277	+	16.2749i	0.0514740	+	0.696500i
$547$	2.34254	−	7.20958i	0.100160	−	0.308260i	−0.888404	−	0.459062i	$-0.848186\pi$
$547$	2.34254	−	7.20958i	0.100160	−	0.308260i	0.988564	+	0.150802i	$0.0481857\pi$
$548$	−1.22819	+	11.6854i	−0.0524655	+	0.499176i
$549$	−7.48430	+	12.9632i	−0.319422	+	0.553255i
$550$	9.45635	+	17.8324i	0.403220	+	0.760376i
$551$	−0.494885	−	0.857166i	−0.0210828	−	0.0365165i
$552$	2.55452	+	1.85597i	0.108728	+	0.0789952i
$553$	23.5831	+	0.730132i	1.00285	+	0.0310484i
$554$	−7.97529	−	24.5454i	−0.338837	−	1.04283i
$555$	8.48594	+	3.77818i	0.360208	+	0.160375i
$556$	1.77955	+	16.9313i	0.0754696	+	0.718045i
$557$	−12.9639	−	2.75556i	−0.549297	−	0.116757i	−0.0751010	−	0.997176i	$-0.523928\pi$
$557$	−12.9639	−	2.75556i	−0.549297	−	0.116757i	−0.474196	+	0.880419i	$0.657261\pi$
$558$	1.45850	−	0.310014i	0.0617432	−	0.0131239i
$559$	−55.2468	−	40.1391i	−2.33669	−	1.69770i
$560$	6.09423	−	6.36093i	0.257528	−	0.268799i
$561$	−5.87488	−	7.01717i	−0.248037	−	0.296265i
$562$	9.14941	+	15.8472i	0.385945	+	0.668476i
$563$	17.1475	−	7.63456i	0.722681	−	0.321758i	−0.0122268	−	0.999925i	$-0.503892\pi$
$563$	17.1475	−	7.63456i	0.722681	−	0.321758i	0.734908	+	0.678167i	$0.237225\pi$
$564$	1.61020	+	1.78831i	0.0678018	+	0.0753016i
$565$	−23.9600	+	26.6103i	−1.00801	+	1.11950i
$566$	−21.7374	+	15.7931i	−0.913690	+	0.663835i
$567$	0.357849	−	2.62144i	0.0150282	−	0.110090i
$568$	3.42410	+	10.5383i	0.143672	+	0.442177i
$569$	31.5400	−	6.70404i	1.32223	−	0.281048i	0.507881	−	0.861427i	$-0.330429\pi$
$569$	31.5400	−	6.70404i	1.32223	−	0.281048i	0.814346	+	0.580379i	$0.197096\pi$
$570$	−5.82136	+	2.59184i	−0.243830	+	0.108560i
$571$	−2.85958	+	4.95293i	−0.119670	+	0.207274i	−0.919637	−	0.392770i	$-0.871517\pi$
$571$	−2.85958	+	4.95293i	−0.119670	+	0.207274i	0.799967	+	0.600044i	$0.204850\pi$
$572$	16.9725	−	11.4208i	0.709656	−	0.477527i
$573$	−25.8012			−1.07786
$574$	−10.4834	+	29.1614i	−0.437569	+	1.21717i
$575$	5.93823	−	18.2760i	0.247641	−	0.762162i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	0.0864058	+	0.822096i	0.00359712	+	0.0342243i	0.996173	−	0.0874008i	$-0.0278561\pi$
$577$	0.0864058	+	0.822096i	0.00359712	+	0.0342243i	−0.992576	+	0.121625i	$0.961189\pi$
$578$	−0.981096	−	9.33451i	−0.0408082	−	0.388264i
$579$	−5.62137	+	6.24317i	−0.233616	+	0.259457i
$580$	0.532099	−	1.63763i	0.0220942	−	0.0679990i
$581$	18.5709	+	21.9550i	0.770453	+	0.910847i
$582$	12.2127			0.506232
$583$	0.812979	+	2.84709i	0.0336701	+	0.117914i
$584$	1.83631	−	3.18059i	0.0759872	−	0.131614i
$585$	18.7615	−	8.35314i	0.775691	−	0.345360i
$586$	24.3501	−	5.17577i	1.00589	−	0.213809i
$587$	2.76848	+	8.52050i	0.114267	+	0.351679i	0.991793	−	0.127850i	$-0.0408077\pi$
$587$	2.76848	+	8.52050i	0.114267	+	0.351679i	−0.877526	+	0.479529i	$0.840808\pi$
$588$	4.35314	+	5.48180i	0.179521	+	0.226066i
$589$	2.30871	−	1.67737i	0.0951286	−	0.0691150i
$590$	3.51326	−	3.90187i	0.144639	−	0.160637i
$591$	8.18024	+	9.08507i	0.336490	+	0.373710i
$592$	−2.54868	+	1.13474i	−0.104750	+	0.0466377i
$593$	18.4196	+	31.9037i	0.756404	+	1.31013i	0.944673	+	0.328012i	$0.106379\pi$
$593$	18.4196	+	31.9037i	0.756404	+	1.31013i	−0.188270	+	0.982117i	$0.560288\pi$
$594$	−3.07649	+	1.23902i	−0.126230	+	0.0508378i
$595$	23.6087	+	5.78719i	0.967861	+	0.237252i
$596$	10.4380	+	7.58369i	0.427559	+	0.310640i
$597$	24.0453	−	5.11098i	0.984107	−	0.209179i
$598$	−19.0505	−	4.04932i	−0.779034	−	0.165589i
$599$	−2.14766	−	20.4336i	−0.0877509	−	0.834894i	−0.946545	−	0.322573i	$-0.895452\pi$
$599$	−2.14766	−	20.4336i	−0.0877509	−	0.834894i	0.858794	−	0.512321i	$-0.171214\pi$
$600$	−5.55973	−	2.47535i	−0.226975	−	0.101056i
$601$	−11.2845	−	34.7301i	−0.460304	−	1.41667i	−0.864794	−	0.502127i	$-0.832551\pi$
$601$	−11.2845	−	34.7301i	−0.460304	−	1.41667i	0.404490	−	0.914542i	$-0.367449\pi$
$602$	−29.2778	−	0.906442i	−1.19328	−	0.0369438i
$603$	−0.144468	−	0.104962i	−0.00588318	−	0.00427438i
$604$	−0.651583	−	1.12857i	−0.0265125	−	0.0459211i
$605$	28.0042	+	23.6042i	1.13853	+	0.959646i
$606$	5.04345	−	8.73551i	0.204876	−	0.354856i
$607$	0.0882570	−	0.839709i	0.00358224	−	0.0340827i	−0.992585	−	0.121554i	$-0.961212\pi$
$607$	0.0882570	−	0.839709i	0.00358224	−	0.0340827i	0.996167	+	0.0874717i	$0.0278788\pi$
$608$	0.591414	−	1.82018i	0.0239850	−	0.0738182i
$609$	1.23216	+	0.594943i	0.0499298	+	0.0241083i
$610$	−40.3203	+	29.2944i	−1.63252	+	1.18610i
$611$	−13.5597	−	6.03719i	−0.548569	−	0.244238i
$612$	2.69906	+	0.573704i	0.109103	+	0.0231906i
$613$	11.7181	+	13.0143i	0.473291	+	0.525643i	0.931764	−	0.363066i	$-0.118270\pi$
$613$	11.7181	+	13.0143i	0.473291	+	0.525643i	−0.458472	+	0.888709i	$0.651603\pi$
$614$	3.12648	−	29.7464i	0.126174	−	1.20047i
$615$	38.9975			1.57253
$616$	3.26396	−	8.14534i	0.131509	−	0.328185i
$617$	−2.96929			−0.119539			−0.0597697	−	0.998212i	$-0.519037\pi$
$617$	−2.96929			−0.119539			−0.0597697	+	0.998212i	$0.519037\pi$
$618$	−2.00258	+	19.0533i	−0.0805556	+	0.766435i
$619$	6.03396	+	6.70139i	0.242525	+	0.269352i	0.852102	−	0.523375i	$-0.175327\pi$
$619$	6.03396	+	6.70139i	0.242525	+	0.269352i	−0.609577	+	0.792727i	$0.708661\pi$
$620$	4.85614	+	1.03221i	0.195027	+	0.0414544i
$621$	2.88457	+	1.28430i	0.115754	+	0.0515370i
$622$	−16.3560	+	11.8834i	−0.655818	+	0.476479i
$623$	−1.27498	+	0.867347i	−0.0510812	+	0.0347495i
$624$	−1.90605	+	5.86621i	−0.0763030	+	0.234836i
$625$	1.92243	−	18.2907i	0.0768973	−	0.731629i
$626$	−6.26348	+	10.8487i	−0.250339	+	0.433600i
$627$	−4.41442	+	4.56115i	−0.176295	+	0.182155i
$628$	−1.63731	−	2.83591i	−0.0653358	−	0.113165i
$629$	−6.22803	−	4.52493i	−0.248328	−	0.180421i
$630$	4.63855	−	7.48900i	0.184804	−	0.298369i
$631$	3.91297	+	12.0429i	0.155773	+	0.479419i	0.998238	−	0.0593308i	$-0.0188967\pi$
$631$	3.91297	+	12.0429i	0.155773	+	0.479419i	−0.842466	+	0.538750i	$0.818897\pi$
$632$	8.14684	+	3.62721i	0.324064	+	0.144283i
$633$	−1.30532	−	12.4192i	−0.0518816	−	0.493621i
$634$	9.00485	+	1.91404i	0.357628	+	0.0760162i
$635$	−2.01383	+	0.428053i	−0.0799165	+	0.0169868i
$636$	−0.722242	−	0.524740i	−0.0286388	−	0.0208073i
$637$	−38.2820	−	19.9679i	−1.51679	−	0.791158i
$638$	−0.117754	−	1.71118i	−0.00466191	−	0.0677463i
$639$	5.54031	+	9.59611i	0.219171	+	0.379616i
$640$	3.04169	−	1.35425i	0.120233	−	0.0535314i
$641$	4.63048	+	5.14267i	0.182893	+	0.203123i	0.827619	−	0.561291i	$-0.189695\pi$
$641$	4.63048	+	5.14267i	0.182893	+	0.203123i	−0.644726	+	0.764414i	$0.723028\pi$
$642$	1.56961	−	1.74323i	0.0619475	−	0.0687996i
$643$	−5.52037	+	4.01078i	−0.217702	+	0.158170i	−0.691292	−	0.722576i	$-0.742958\pi$
$643$	−5.52037	+	4.01078i	−0.217702	+	0.158170i	0.473590	+	0.880746i	$0.342958\pi$
$644$	−7.73336	+	3.16013i	−0.304737	+	0.124527i
$645$	11.3911	+	35.0582i	0.448524	+	1.38041i
$646$	5.16562	−	1.09799i	0.203238	−	0.0431997i
$647$	38.8940	−	17.3167i	1.52908	−	0.680790i	0.541906	−	0.840439i	$-0.317703\pi$
$647$	38.8940	−	17.3167i	1.52908	−	0.680790i	0.987174	+	0.159649i	$0.0510364\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	1.79424	−	4.91271i	0.0704302	−	0.192841i
$650$	37.5383			1.47237
$651$	−1.33460	+	3.71243i	−0.0523073	+	0.145502i
$652$	−0.603289	+	1.85673i	−0.0236266	+	0.0727152i
$653$	13.2905	−	14.7606i	0.520098	−	0.577627i	−0.424678	−	0.905345i	$-0.639613\pi$
$653$	13.2905	−	14.7606i	0.520098	−	0.577627i	0.944776	+	0.327717i	$0.106279\pi$
$654$	−1.63897	−	15.5938i	−0.0640888	−	0.609765i
$655$	−2.52902	−	24.0620i	−0.0988169	−	0.940180i
$656$	−7.83724	+	8.70414i	−0.305993	+	0.339839i
$657$	1.13490	−	3.49287i	0.0442768	−	0.136270i
$658$	−6.26562	+	1.13038i	−0.244259	+	0.0440667i
$659$	−31.2817			−1.21856			−0.609280	−	0.792955i	$-0.708542\pi$
$659$	−31.2817			−1.21856			−0.609280	+	0.792955i	$0.708542\pi$
$660$	−11.0357	−	0.397609i	−0.429564	−	0.0154769i
$661$	−20.1978	+	34.9836i	−0.785604	+	1.36071i	0.143034	+	0.989718i	$0.454314\pi$
$661$	−20.1978	+	34.9836i	−0.785604	+	1.36071i	−0.928638	+	0.370988i	$0.879019\pi$
$662$	13.8555	−	6.16886i	0.538508	−	0.239759i
$663$	−16.6481	+	3.53866i	−0.646558	+	0.137430i
$664$	3.35862	+	10.3368i	0.130340	+	0.401144i
$665$	2.28031	−	16.7045i	0.0884266	−	0.647773i
$666$	−2.25706	+	1.63985i	−0.0874592	+	0.0635428i
$667$	−1.09267	+	1.21353i	−0.0423082	+	0.0469880i
$668$	2.17138	+	2.41156i	0.0840132	+	0.0933061i
$669$	−12.4216	+	5.53044i	−0.480245	+	0.213819i
$670$	−0.297282	−	0.514907i	−0.0114850	−	0.0198926i
$671$	−26.3546	+	42.0724i	−1.01741	+	1.62419i
$672$	0.739324	+	2.54035i	0.0285201	+	0.0979963i
$673$	19.7277	+	14.3330i	0.760447	+	0.552497i	0.899047	−	0.437851i	$-0.144260\pi$
$673$	19.7277	+	14.3330i	0.760447	+	0.552497i	−0.138600	+	0.990348i	$0.544260\pi$
$674$	−25.4871	+	5.41744i	−0.981725	+	0.208672i
$675$	−5.95289	−	1.26533i	−0.229127	−	0.0487024i
$676$	−2.61796	−	24.9082i	−0.100691	−	0.958009i
$677$	−30.6336	−	13.6389i	−1.17734	−	0.524187i	−0.277638	−	0.960686i	$-0.589552\pi$
$677$	−30.6336	−	13.6389i	−1.17734	−	0.524187i	−0.899705	+	0.436499i	$0.856218\pi$
$678$	−3.32333	−	10.2282i	−0.127632	−	0.392810i
$679$	−17.0141	+	27.4694i	−0.652940	+	1.05418i
$680$	7.43278	+	5.40023i	0.285034	+	0.207089i
$681$	−3.09067	−	5.35319i	−0.118435	−	0.205135i
$682$	4.87118	−	0.853361i	0.186527	−	0.0326769i
$683$	4.19189	−	7.26057i	0.160398	−	0.277818i	−0.774613	−	0.632435i	$-0.782055\pi$
$683$	4.19189	−	7.26057i	0.160398	−	0.277818i	0.935012	+	0.354617i	$0.115389\pi$
$684$	0.200052	−	1.90337i	0.00764919	−	0.0727772i
$685$	−12.0892	+	37.2067i	−0.461904	+	1.42159i
$686$	−18.3945	+	2.15437i	−0.702306	+	0.0822543i
$687$	9.73805	−	7.07511i	0.371530	−	0.269932i
$688$	−10.1141	−	4.50310i	−0.385597	−	0.171679i
$689$	5.38618	+	1.14487i	0.205197	+	0.0436160i
$690$	7.03473	+	7.81286i	0.267808	+	0.297431i
$691$	−1.85813	+	17.6789i	−0.0706865	+	0.672537i	0.900604	+	0.434641i	$0.143125\pi$
$691$	−1.85813	+	17.6789i	−0.0706865	+	0.672537i	−0.971290	+	0.237897i	$0.923542\pi$
$692$	−23.7894			−0.904339
$693$	1.49913	−	8.64596i	0.0569472	−	0.328433i
$694$	34.7453			1.31891
$695$	−5.92509	+	56.3734i	−0.224751	+	2.13837i
$696$	0.346048	+	0.384325i	0.0131169	+	0.0145678i
$697$	−31.6130	−	6.71954i	−1.19743	−	0.254521i
$698$	27.3173	+	12.1625i	1.03398	+	0.460356i
$699$	−17.1189	+	12.4376i	−0.647495	+	0.470432i
$700$	13.3132	−	9.05671i	0.503192	−	0.342312i
$701$	13.9129	−	42.8196i	0.525484	−	1.61727i	−0.237872	−	0.971297i	$-0.576450\pi$
$701$	13.9129	−	42.8196i	0.525484	−	1.61727i	0.763356	−	0.645978i	$-0.223550\pi$
$702$	−0.644742	+	6.13431i	−0.0243342	+	0.231525i
$703$	−2.66971	+	4.62407i	−0.100690	+	0.174400i
$704$	2.30656	−	2.38323i	0.0869318	−	0.0898213i
$705$	4.00613	+	6.93882i	0.150880	+	0.261331i
$706$	3.38961	+	2.46270i	0.127570	+	0.0926848i
$707$	12.6221	+	23.5139i	0.474704	+	0.884330i
$708$	0.487300	+	1.49976i	0.0183139	+	0.0563643i
$709$	44.0690	+	19.6208i	1.65505	+	0.736874i	0.999828	−	0.0185658i	$-0.00591002\pi$
$709$	44.0690	+	19.6208i	1.65505	+	0.736874i	0.655218	+	0.755440i	$0.272577\pi$
$710$	3.85642	+	36.6914i	0.144729	+	1.37700i
$711$	8.72295	+	1.85412i	0.327136	+	0.0695350i
$712$	−0.570099	+	0.121178i	−0.0213654	+	0.00454135i
$713$	−3.80900	−	2.76740i	−0.142648	−	0.103640i
$714$	−5.05059	+	5.27162i	−0.189014	+	0.197286i
$715$	63.1819	−	25.4458i	2.36287	−	0.951619i
$716$	−9.59790	−	16.6240i	−0.358690	−	0.621270i
$717$	−0.485233	+	0.216040i	−0.0181214	+	0.00806815i
$718$	−1.06189	−	1.17935i	−0.0396295	−	0.0440130i
$719$	19.9805	−	22.1905i	0.745145	−	0.827568i	−0.244718	−	0.969594i	$-0.578695\pi$
$719$	19.9805	−	22.1905i	0.745145	−	0.827568i	0.989863	+	0.142027i	$0.0453619\pi$
$720$	2.69366	−	1.95706i	0.100387	−	0.0729353i
$721$	−40.0658	−	31.0483i	−1.49213	−	1.15630i
$722$	4.73944	+	14.5865i	0.176384	+	0.542853i
$723$	−3.64137	+	0.773998i	−0.135424	+	0.0287853i
$724$	−13.9937	+	6.23041i	−0.520072	+	0.231551i
$725$	1.57369	−	2.72571i	0.0584453	−	0.101230i
$726$	−10.3449	+	3.73932i	−0.383936	+	0.138779i
$727$	−35.1823			−1.30484			−0.652421	−	0.757857i	$-0.726246\pi$
$727$	−35.1823			−1.30484			−0.652421	+	0.757857i	$0.726246\pi$
$728$	−10.5392	−	12.4597i	−0.390608	−	0.461786i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	8.18225	−	9.08731i	0.302839	−	0.336336i
$731$	−3.19331	−	30.3823i	−0.118109	−	1.12373i
$732$	−1.56464	−	14.8866i	−0.0578309	−	0.550224i
$733$	−6.99582	+	7.76964i	−0.258396	+	0.286978i	−0.858359	−	0.513050i	$-0.828516\pi$
$733$	−6.99582	+	7.76964i	−0.258396	+	0.286978i	0.599962	+	0.800028i	$0.295182\pi$
$734$	4.29431	−	13.2165i	0.158506	−	0.487831i
$735$	10.3825	+	20.8665i	0.382963	+	0.769674i
$736$	−3.15756			−0.116389
$737$	−0.466300	−	0.365146i	−0.0171764	−	0.0134503i
$738$	−5.85629	+	10.1434i	−0.215573	+	0.373383i
$739$	30.5529	−	13.6030i	1.12391	−	0.500396i	0.241273	−	0.970457i	$-0.422435\pi$
$739$	30.5529	−	13.6030i	1.12391	−	0.500396i	0.882634	+	0.470062i	$0.155768\pi$
$740$	−9.08603	+	1.93130i	−0.334009	+	0.0709958i
$741$	3.64790	+	11.2271i	0.134009	+	0.412437i
$742$	2.18646	−	0.893467i	0.0802676	−	0.0328002i
$743$	31.2314	−	22.6909i	1.14577	−	0.832450i	0.157857	−	0.987462i	$-0.449542\pi$
$743$	31.2314	−	22.6909i	1.14577	−	0.832450i	0.987913	+	0.155012i	$0.0495416\pi$
$744$	−0.997730	+	1.10809i	−0.0365786	+	0.0406246i
$745$	28.7447	+	31.9242i	1.05312	+	1.16961i
$746$	8.29619	−	3.69370i	0.303745	−	0.135236i
$747$	5.43436	+	9.41258i	0.198833	+	0.344388i
$748$	8.87746	+	2.22384i	0.324592	+	0.0813118i
$749$	1.73426	+	5.95901i	0.0633686	+	0.217738i
$750$	−2.92499	−	2.12513i	−0.106805	−	0.0775987i
$751$	−27.4999	+	5.84527i	−1.00348	+	0.213297i	−0.680217	−	0.733011i	$-0.738114\pi$
$751$	−27.4999	+	5.84527i	−1.00348	+	0.213297i	−0.323267	+	0.946308i	$0.604781\pi$
$752$	−2.35383	−	0.500321i	−0.0858352	−	0.0182448i
$753$	1.52848	+	14.5425i	0.0557010	+	0.529960i
$754$	−2.91411	−	1.29745i	−0.106126	−	0.0472503i
$755$	−1.34081	−	4.12659i	−0.0487971	−	0.150182i
$756$	1.25134	+	2.33113i	0.0455107	+	0.0847823i
$757$	−19.0089	−	13.8107i	−0.690889	−	0.501960i	0.186064	−	0.982538i	$-0.440427\pi$
$757$	−19.0089	−	13.8107i	−0.690889	−	0.501960i	−0.876952	+	0.480578i	$0.840427\pi$
$758$	10.3337	+	17.8985i	0.375337	+	0.650102i
$759$	9.40748	+	4.60124i	0.341470	+	0.167014i
$760$	3.18613	−	5.51855i	0.115573	−	0.200179i
$761$	3.42388	−	32.5761i	0.124116	−	1.18088i	−0.738226	−	0.674554i	$-0.764336\pi$
$761$	3.42388	−	32.5761i	0.124116	−	1.18088i	0.862341	−	0.506327i	$-0.168997\pi$
$762$	0.191080	−	0.588085i	0.00692211	−	0.0213041i
$763$	37.3577	+	18.0379i	1.35244	+	0.653017i
$764$	20.8736	−	15.1656i	0.755181	−	0.548671i
$765$	8.39313	+	3.73686i	0.303454	+	0.135107i
$766$	6.30640	+	1.34047i	0.227860	+	0.0484331i
$767$	−6.50844	−	7.22835i	−0.235006	−	0.261001i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	10.4813			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$769$	10.4813			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$770$	16.2687	−	24.2682i	0.586282	−	0.874564i
$771$	−14.8876			−0.536165
$772$	0.878145	−	8.35499i	0.0316051	−	0.300703i
$773$	6.92511	+	7.69112i	0.249079	+	0.276630i	0.854699	−	0.519124i	$-0.173742\pi$
$773$	6.92511	+	7.69112i	0.249079	+	0.276630i	−0.605620	+	0.795754i	$0.707075\pi$
$774$	−10.8293	−	2.30185i	−0.389253	−	0.0827382i
$775$	8.29002	+	3.69096i	0.297786	+	0.132583i
$776$	−9.88027	+	7.17844i	−0.354681	+	0.257691i
$777$	−0.544023	−	7.36124i	−0.0195167	−	0.264083i
$778$	−8.95330	+	27.5554i	−0.320991	+	0.987909i
$779$	−2.34313	+	22.2934i	−0.0839513	+	0.798743i
$780$	−10.2685	+	17.7855i	−0.367671	+	0.636824i
$781$	17.2173	+	32.4677i	0.616083	+	1.16178i
$782$	−4.35642	−	7.54555i	−0.155785	−	0.269828i
$783$	0.418392	+	0.303979i	0.0149521	+	0.0108633i
$784$	−6.74389	−	1.87616i	−0.240853	−	0.0670056i
$785$	−3.36921	−	10.3694i	−0.120252	−	0.370099i
$786$	6.63838	+	2.95560i	0.236783	+	0.105423i
$787$	2.85703	+	27.1829i	0.101842	+	0.968964i	0.919455	+	0.393195i	$0.128630\pi$
$787$	2.85703	+	27.1829i	0.101842	+	0.968964i	−0.817613	+	0.575769i	$0.804703\pi$
$788$	−11.9580	−	2.54176i	−0.425987	−	0.0905463i
$789$	18.4976	−	3.93179i	0.658533	−	0.139975i
$790$	24.0216	+	17.4527i	0.854650	+	0.620940i
$791$	27.6356	+	6.77431i	0.982610	+	0.240867i
$792$	1.76066	−	2.81071i	0.0625622	−	0.0998742i
$793$	46.1639	+	79.9582i	1.63933	+	2.83940i
$794$	15.2597	−	6.79408i	0.541548	−	0.241113i
$795$	−1.98894	−	2.20894i	−0.0705404	−	0.0783430i
$796$	−16.4489	+	18.2683i	−0.583015	+	0.647504i
$797$	−20.9567	+	15.2260i	−0.742325	+	0.539331i	−0.893438	−	0.449186i	$-0.851714\pi$
$797$	−20.9567	+	15.2260i	−0.742325	+	0.539331i	0.151113	+	0.988516i	$0.451714\pi$
$798$	4.00246	+	3.10164i	0.141686	+	0.109797i
$799$	−2.05192	−	6.31517i	−0.0725918	−	0.223415i
$800$	5.95289	−	1.26533i	0.210466	−	0.0447360i
$801$	−0.532446	+	0.237060i	−0.0188131	+	0.00837612i
$802$	13.1188	−	22.7225i	0.463242	−	0.802359i
$803$	4.17872	−	11.4415i	0.147464	−	0.403762i
$804$	0.178572			0.00629774
$805$	−27.3735	+	4.93844i	−0.964790	+	0.174057i
$806$	2.84208	−	8.74701i	0.100108	−	0.308100i
$807$	10.3332	−	11.4762i	0.363747	−	0.403982i
$808$	1.05437	+	10.0316i	0.0370926	+	0.352912i
$809$	−1.01075	−	9.61669i	−0.0355362	−	0.338105i	−0.997817	−	0.0660451i	$-0.978962\pi$
$809$	−1.01075	−	9.61669i	−0.0355362	−	0.338105i	0.962280	−	0.272060i	$-0.0877048\pi$
$810$	2.22790	−	2.47434i	0.0782805	−	0.0869393i
$811$	8.61970	−	26.5287i	0.302679	−	0.931549i	−0.677855	−	0.735196i	$-0.737090\pi$
$811$	8.61970	−	26.5287i	0.302679	−	0.931549i	0.980533	−	0.196353i	$-0.0629099\pi$
$812$	−1.34654	+	0.242928i	−0.0472543	+	0.00852511i
$813$	9.72616			0.341111
$814$	−7.67678	+	5.16570i	−0.269071	+	0.181058i
$815$	−3.25011	+	5.62936i	−0.113846	+	0.197188i
$816$	−2.52080	+	1.12233i	−0.0882457	+	0.0392895i
$817$	−20.7258	+	4.40541i	−0.725104	+	0.154126i
$818$	5.20186	+	16.0097i	0.181879	+	0.559765i
$819$	−12.8994	−	9.99618i	−0.450741	−	0.349295i
$820$	−31.5497	+	22.9222i	−1.10176	+	0.800477i
$821$	24.0188	−	26.6755i	0.838261	−	0.930983i	−0.160164	−	0.987090i	$-0.551202\pi$
$821$	24.0188	−	26.6755i	0.838261	−	0.930983i	0.998425	+	0.0561074i	$0.0178689\pi$
$822$	−7.86214	−	8.73179i	−0.274223	−	0.304556i
$823$	−28.0256	+	12.4778i	−0.976909	+	0.434948i	−0.832169	−	0.554522i	$-0.812901\pi$
$823$	−28.0256	+	12.4778i	−0.976909	+	0.434948i	−0.144740	+	0.989470i	$0.546235\pi$
$824$	−9.57911	−	16.5915i	−0.333704	−	0.577993i
$825$	−19.5796	−	4.90477i	−0.681674	−	0.170762i
$826$	−4.05221	−	0.993318i	−0.140995	−	0.0345620i
$827$	−13.8608	−	10.0704i	−0.481986	−	0.350183i	0.320108	−	0.947381i	$-0.396281\pi$
$827$	−13.8608	−	10.0704i	−0.481986	−	0.350183i	−0.802094	+	0.597198i	$0.796281\pi$
$828$	−3.08856	+	0.656494i	−0.107335	+	0.0228147i
$829$	26.7041	+	5.67613i	0.927472	+	0.197140i	0.646797	−	0.762663i	$-0.276108\pi$
$829$	26.7041	+	5.67613i	0.927472	+	0.197140i	0.280675	+	0.959803i	$0.409442\pi$
$830$	3.78266	+	35.9896i	0.131298	+	1.24922i
$831$	23.5773	+	10.4973i	0.817887	+	0.364147i
$832$	−1.90605	−	5.86621i	−0.0660803	−	0.203374i
$833$	−4.82100	−	18.7042i	−0.167038	−	0.648063i
$834$	−13.7731	−	10.0068i	−0.476924	−	0.346506i
$835$	5.40231	+	9.35708i	0.186955	+	0.323815i
$836$	0.890366	−	6.28478i	0.0307939	−	0.217364i
$837$	−0.745542	+	1.29132i	−0.0257697	+	0.0446344i
$838$	−0.814979	+	7.75400i	−0.0281530	+	0.267858i
$839$	11.0207	−	33.9184i	0.380478	−	1.17099i	−0.559229	−	0.829013i	$-0.688903\pi$
$839$	11.0207	−	33.9184i	0.380478	−	1.17099i	0.939708	−	0.341979i	$-0.111097\pi$
$840$	0.649259	+	8.78519i	0.0224016	+	0.303118i
$841$	23.2451	−	16.8886i	0.801556	−	0.582364i
$842$	−26.6525	−	11.8665i	−0.918505	−	0.408945i
$843$	−17.8989	−	3.80454i	−0.616473	−	0.131035i
$844$	8.35587	+	9.28014i	0.287621	+	0.319435i
$845$	8.71662	−	82.9331i	0.299861	−	2.85299i
$846$	−2.40641			−0.0827342
$847$	6.00131	−	28.4778i	0.206207	−	0.978508i
$848$	0.892741			0.0306568
$849$	2.80856	−	26.7217i	0.0963896	−	0.917086i
$850$	11.2368	+	12.4797i	0.385419	+	0.428051i
$851$	8.61670	+	1.83154i	0.295377	+	0.0627842i
$852$	−10.1227	−	4.50690i	−0.346797	−	0.154404i
$853$	17.9135	−	13.0149i	0.613346	−	0.445622i	−0.237245	−	0.971450i	$-0.576244\pi$
$853$	17.9135	−	13.0149i	0.613346	−	0.445622i	0.850591	+	0.525828i	$0.176244\pi$
$854$	35.6635	+	17.2199i	1.22038	+	0.589254i
$855$	1.96914	−	6.06039i	0.0673432	−	0.207261i
$856$	−0.245197	+	2.33289i	−0.00838065	+	0.0797366i
$857$	2.29084	−	3.96785i	0.0782535	−	0.135539i	−0.824243	−	0.566236i	$-0.808399\pi$
$857$	2.29084	−	3.96785i	0.0782535	−	0.135539i	0.902496	+	0.430697i	$0.141732\pi$
$858$	−2.86953	+	20.2550i	−0.0979641	+	0.691495i
$859$	4.98465	+	8.63366i	0.170074	+	0.294577i	0.938446	−	0.345427i	$-0.112266\pi$
$859$	4.98465	+	8.63366i	0.170074	+	0.294577i	−0.768372	+	0.640004i	$0.778933\pi$
$860$	−29.8223	−	21.6671i	−1.01693	−	0.738843i
$861$	−14.6564	−	27.3035i	−0.499488	−	0.930501i
$862$	7.88350	+	24.2629i	0.268513	+	0.826399i
$863$	−4.61803	−	2.05608i	−0.157199	−	0.0699897i	0.326629	−	0.945153i	$-0.394087\pi$
$863$	−4.61803	−	2.05608i	−0.157199	−	0.0699897i	−0.483828	+	0.875163i	$0.660754\pi$
$864$	0.104528	+	0.994522i	0.00355613	+	0.0338343i
$865$	−77.4772	−	16.4683i	−2.63430	−	0.559938i
$866$	−0.0133867	+	0.00284543i	−0.000454898	+	9.66916e-5i
$867$	7.59337	+	5.51691i	0.257884	+	0.187364i
$868$	−1.10240	−	3.78788i	−0.0374177	−	0.128569i
$869$	28.6906	+	7.18712i	0.973261	+	0.243806i
$870$	0.860955	+	1.49122i	0.0291891	+	0.0505570i
$871$	−1.00622	+	0.447999i	−0.0340946	+	0.0151799i
$872$	10.4917	+	11.6523i	0.355295	+	0.394595i
$873$	−8.17188	+	9.07580i	−0.276576	+	0.307169i
$874$	−4.88898	+	3.55205i	−0.165372	+	0.120150i
$875$	8.85489	−	3.61843i	0.299350	−	0.122325i
$876$	1.13490	+	3.49287i	0.0383448	+	0.118013i
$877$	8.56973	−	1.82155i	0.289379	−	0.0615094i	−0.0609349	−	0.998142i	$-0.519408\pi$
$877$	8.56973	−	1.82155i	0.289379	−	0.0615094i	0.350314	+	0.936632i	$0.386075\pi$
$878$	−35.9916	+	16.0245i	−1.21466	+	0.540800i
$879$	−12.4470	+	21.5589i	−0.419828	+	0.727164i
$880$	9.16177	−	6.16495i	0.308843	−	0.207820i
$881$	−0.712468			−0.0240037			−0.0120018	−	0.999928i	$-0.503820\pi$
$881$	−0.712468			−0.0240037			−0.0120018	+	0.999928i	$0.503820\pi$
$882$	−6.98659	−	0.433025i	−0.235251	−	0.0145807i
$883$	−10.7908	+	33.2105i	−0.363138	+	1.11762i	0.588001	+	0.808860i	$0.299915\pi$
$883$	−10.7908	+	33.2105i	−0.363138	+	1.11762i	−0.951139	+	0.308763i	$0.900085\pi$
$884$	11.3886	−	12.6483i	0.383040	−	0.425410i
$885$	0.548825	+	5.22172i	0.0184486	+	0.175526i
$886$	−1.94086	−	18.4660i	−0.0652044	−	0.620378i
$887$	−14.5619	+	16.1727i	−0.488942	+	0.543025i	−0.936240	−	0.351360i	$-0.885719\pi$
$887$	−14.5619	+	16.1727i	−0.488942	+	0.543025i	0.447299	+	0.894385i	$0.352386\pi$
$888$	0.862119	−	2.65333i	0.0289308	−	0.0890399i
$889$	1.05655	+	1.24908i	0.0354355	+	0.0418927i
$890$	−1.94058			−0.0650483
$891$	1.13780	−	3.11535i	0.0381178	−	0.104368i
$892$	6.79855	−	11.7754i	0.227632	−	0.394271i
$893$	−4.20736	+	1.87324i	−0.140794	+	0.0626855i
$894$	−12.6202	+	2.68250i	−0.422082	+	0.0897164i
$895$	−19.7503	−	60.7852i	−0.660180	−	2.03182i
$896$	−2.09131	−	1.62063i	−0.0698657	−	0.0541413i
$897$	15.7565	−	11.4478i	0.526095	−	0.382231i
$898$	−3.84044	+	4.26524i	−0.128157	+	0.142333i
$899$	−0.515986	−	0.573061i	−0.0172091	−	0.0191127i
$900$	5.55973	−	2.47535i	0.185324	−	0.0825117i
$901$	1.23170	+	2.13336i	0.0410338	+	0.0710726i
$902$	−20.6218	+	32.9206i	−0.686631	+	1.09614i
$903$	20.2643	−	21.1511i	0.674354	−	0.703866i
$904$	8.70060	+	6.32135i	0.289378	+	0.210245i
$905$	−49.8876	+	10.6039i	−1.65832	+	0.352487i
$906$	1.27469	+	0.270943i	0.0423487	+	0.00900149i
$907$	−5.32223	−	50.6377i	−0.176722	−	1.68140i	−0.619681	−	0.784854i	$-0.712738\pi$
$907$	−5.32223	−	50.6377i	−0.176722	−	1.68140i	0.442959	−	0.896542i	$-0.353929\pi$
$908$	5.64693	+	2.51417i	0.187400	+	0.0834358i
$909$	3.11702	+	9.59322i	0.103385	+	0.318187i
$910$	−25.6987	−	47.8743i	−0.851903	−	1.58702i
$911$	−33.1642	−	24.0952i	−1.09878	−	0.798310i	−0.117919	−	0.993023i	$-0.537622\pi$
$911$	−33.1642	−	24.0952i	−1.09878	−	0.798310i	−0.980860	+	0.194713i	$0.937622\pi$
$912$	0.956928	+	1.65745i	0.0316870	+	0.0548836i
$913$	16.8880	+	31.8467i	0.558911	+	1.05397i
$914$	−0.130471	+	0.225983i	−0.00431561	+	0.00747486i
$915$	5.20956	−	49.5656i	0.172223	−	1.63859i
$916$	−3.71960	+	11.4478i	−0.122899	+	0.378245i
$917$	−15.8961	+	10.8138i	−0.524937	+	0.357104i
$918$	−2.23237	+	1.62191i	−0.0736792	+	0.0535311i
$919$	−18.7172	−	8.33343i	−0.617423	−	0.274894i	0.0740979	−	0.997251i	$-0.476392\pi$
$919$	−18.7172	−	8.33343i	−0.617423	−	0.274894i	−0.691521	+	0.722357i	$0.743059\pi$
$920$	−10.2835	−	2.18583i	−0.339037	−	0.0720645i
$921$	20.0139	+	22.2277i	0.659480	+	0.732427i
$922$	1.64557	−	15.6566i	0.0541940	−	0.515621i
$923$	68.3464			2.24965
$924$	3.86915	+	7.87589i	0.127286	+	0.259098i
$925$	−16.9788			−0.558261
$926$	1.09694	−	10.4367i	0.0360478	−	0.342972i
$927$	−12.8194	−	14.2373i	−0.421043	−	0.467615i
$928$	−0.505859	−	0.107524i	−0.0166056	−	0.00352964i
$929$	−3.88007	−	1.72752i	−0.127301	−	0.0566780i	0.342098	−	0.939664i	$-0.388863\pi$
$929$	−3.88007	−	1.72752i	−0.127301	−	0.0566780i	−0.469399	+	0.882986i	$0.655529\pi$
$930$	−4.01647	+	2.91814i	−0.131705	+	0.0956895i
$931$	−12.5524	+	4.68151i	−0.411388	+	0.153430i
$932$	6.53882	−	20.1244i	0.214186	−	0.659197i
$933$	2.11327	−	20.1064i	0.0691854	−	0.658255i
$934$	−0.472543	+	0.818468i	−0.0154621	+	0.0267811i
$935$	27.3726	+	13.3880i	0.895178	+	0.437835i
$936$	−3.08405	−	5.34173i	−0.100805	−	0.174600i
$937$	25.5882	+	18.5909i	0.835929	+	0.607338i	0.921230	−	0.389017i	$-0.127185\pi$
$937$	25.5882	+	18.5909i	0.835929	+	0.607338i	−0.0853017	+	0.996355i	$0.527185\pi$
$938$	−0.248777	+	0.401653i	−0.00812285	+	0.0131144i
$939$	−3.87105	−	11.9139i	−0.126327	−	0.388794i
$940$	−7.31957	−	3.25888i	−0.238738	−	0.106293i
$941$	−2.00023	−	19.0309i	−0.0652056	−	0.620390i	−0.977512	−	0.210881i	$-0.932367\pi$
$941$	−2.00023	−	19.0309i	−0.0652056	−	0.620390i	0.912306	−	0.409509i	$-0.134300\pi$
$942$	3.20306	+	0.680832i	0.104361	+	0.0221827i
$943$	36.1750	−	7.68923i	1.17802	−	0.250396i
$944$	−1.27577	−	0.926900i	−0.0415227	−	0.0301680i
$945$	2.46162	+	8.45823i	0.0800763	+	0.275146i
$946$	−35.6187	−	8.92264i	−1.15806	−	0.290100i
$947$	−16.4713	−	28.5291i	−0.535245	−	0.927072i	−0.999151	−	0.0411878i	$-0.986886\pi$
$947$	−16.4713	−	28.5291i	−0.535245	−	0.927072i	0.463906	−	0.885884i	$-0.346448\pi$
$948$	−8.14684	+	3.62721i	−0.264597	+	0.117806i
$949$	−15.1579	−	16.8345i	−0.492046	−	0.546472i
$950$	7.79369	−	8.65577i	0.252861	−	0.280830i
$951$	−7.44783	+	5.41117i	−0.241512	+	0.175469i
$952$	0.987434	−	7.23350i	0.0320029	−	0.234439i
$953$	11.4130	+	35.1255i	0.369702	+	1.13783i	0.946984	+	0.321282i	$0.104114\pi$
$953$	11.4130	+	35.1255i	0.369702	+	1.13783i	−0.577281	+	0.816545i	$0.695886\pi$
$954$	0.873232	−	0.185611i	0.0282719	−	0.00600939i
$955$	78.4793	−	34.9413i	2.53953	−	1.13067i
$956$	0.265577	−	0.459993i	0.00858937	−	0.0148772i
$957$	1.35045	+	1.05749i	0.0436538	+	0.0341840i
$958$	−14.8233			−0.478918
$959$	30.5931	−	5.51928i	0.987903	−	0.178227i
$960$	−1.02889	+	3.16659i	−0.0332072	+	0.102201i
$961$	−19.2553	+	21.3852i	−0.621140	+	0.689846i
$962$	1.79875	+	17.1140i	0.0579940	+	0.551776i
$963$	0.245197	+	2.33289i	0.00790136	+	0.0751764i
$964$	2.49099	−	2.76652i	0.0802293	−	0.0891037i
$965$	8.64369	−	26.6025i	0.278250	−	0.856366i
$966$	2.82620	−	7.86155i	0.0909313	−	0.252941i
$967$	2.84229			0.0914020			0.0457010	−	0.998955i	$-0.485448\pi$
$967$	2.84229			0.0914020			0.0457010	+	0.998955i	$0.485448\pi$
$968$	6.17130	−	9.10577i	0.198353	−	0.292671i
$969$	−2.64051	+	4.57350i	−0.0848254	+	0.146922i
$970$	−37.1472	+	16.5390i	−1.19273	+	0.531036i
$971$	−10.8084	+	2.29740i	−0.346859	+	0.0737271i	−0.378047	−	0.925786i	$-0.623404\pi$
$971$	−10.8084	+	2.29740i	−0.346859	+	0.0737271i	0.0311881	+	0.999514i	$0.490071\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	41.6957	−	17.0384i	1.33670	−	0.546225i
$974$	9.23171	−	6.70723i	0.295803	−	0.214913i
$975$	−25.1180	+	27.8964i	−0.804421	+	0.893400i
$976$	10.0159	+	11.1238i	0.320603	+	0.356065i
$977$	−33.8770	+	15.0830i	−1.08382	+	0.482548i	−0.869357	−	0.494184i	$-0.835467\pi$
$977$	−33.8770	+	15.0830i	−1.08382	+	0.482548i	−0.214463	+	0.976732i	$0.568800\pi$
$978$	−0.976142	−	1.69073i	−0.0312136	−	0.0540635i
$979$	−1.79309	+	0.722147i	−0.0573074	+	0.0230799i
$980$	−20.6646	−	10.7787i	−0.660108	−	0.344313i
$981$	12.6851	+	9.21627i	0.405004	+	0.294253i
$982$	−10.4578	+	2.22288i	−0.333723	+	0.0709350i
$983$	−30.9717	−	6.58324i	−0.987843	−	0.209973i	−0.314464	−	0.949269i	$-0.601825\pi$
$983$	−30.9717	−	6.58324i	−0.987843	−	0.209973i	−0.673380	+	0.739297i	$0.735158\pi$
$984$	−1.22430	−	11.6484i	−0.0390292	−	0.371338i
$985$	−37.1852	−	16.5559i	−1.18482	−	0.527515i
$986$	−0.440977	−	1.35719i	−0.0140436	−	0.0432217i
$987$	3.35248	−	5.41263i	0.106711	−	0.172286i
$988$	−9.55032	−	6.93872i	−0.303836	−	0.220750i
$989$	17.4791	+	30.2747i	0.555804	+	0.962680i
$990$	7.67980	−	7.93507i	0.244080	−	0.252193i
$991$	17.5403	−	30.3808i	0.557187	−	0.965077i	−0.440542	−	0.897732i	$-0.645214\pi$
$991$	17.5403	−	30.3808i	0.557187	−	0.965077i	0.997730	−	0.0673450i	$-0.0214528\pi$
$992$	0.155861	−	1.48292i	0.00494858	−	0.0470826i
$993$	−4.68677	+	14.4244i	−0.148730	+	0.457744i
$994$	24.2395	−	16.4897i	0.768830	−	0.523020i
$995$	−66.2168	+	48.1093i	−2.09921	+	1.52517i
$996$	−9.92906	−	4.42070i	−0.314614	−	0.140075i
$997$	−56.3234	−	11.9719i	−1.78378	−	0.379154i	−0.806520	−	0.591206i	$-0.798652\pi$
$997$	−56.3234	−	11.9719i	−1.78378	−	0.379154i	−0.977258	+	0.212053i	$0.931985\pi$
$998$	−9.15763	−	10.1706i	−0.289880	−	0.321944i
$999$	0.291621	−	2.77459i	0.00922649	−	0.0877842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.c.235.1	yes	40
7.2	even	3	inner	462.2.y.c.37.5	yes	40
11.3	even	5	inner	462.2.y.c.25.5	✓	40
77.58	even	15	inner	462.2.y.c.289.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.c.25.5	✓	40	11.3	even	5	inner
462.2.y.c.37.5	yes	40	7.2	even	3	inner
462.2.y.c.235.1	yes	40	1.1	even	1	trivial
462.2.y.c.289.1	yes	40	77.58	even	15	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.04169 - 1.35425i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.194999 + 2.63856i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.04169 - 1.35425i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.194999 + 2.63856i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-1.66477 + 2.88347i) q^{10} +(-0.465221 + 3.28383i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(4.99010 + 3.62552i) q^{13} +(2.64448 + 0.0818733i) q^{14} +(-1.02889 - 3.16659i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.288432 + 2.74425i) q^{17} +(0.978148 + 0.207912i) q^{18} +(1.87203 - 0.397913i) q^{19} +(2.69366 + 1.95706i) q^{20} +(-1.83035 + 1.91045i) q^{21} +(3.21722 + 0.805927i) q^{22} +(-1.57878 - 2.73453i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(4.07225 + 4.52269i) q^{25} +(4.12726 - 4.58379i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.357849 - 2.62144i) q^{28} +(-0.159811 - 0.491849i) q^{29} +(-3.25679 + 0.692252i) q^{30} +(1.36217 - 0.606479i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.75166 + 1.85159i) q^{33} +2.75936 q^{34} +(2.98013 - 8.28975i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-1.86679 + 2.07328i) q^{37} +(-0.200052 - 1.90337i) q^{38} +(0.644742 + 6.13431i) q^{39} +(2.22790 - 2.47434i) q^{40} +(-3.61938 + 11.1393i) q^{41} +(1.70866 + 2.02002i) q^{42} -11.0713 q^{43} +(1.13780 - 3.11535i) q^{44} +(1.66477 - 2.88347i) q^{45} +(-2.88457 + 1.28430i) q^{46} +(-2.35383 + 0.500321i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-6.92395 + 1.02903i) q^{49} +(4.92358 - 3.57719i) q^{50} +(-1.84637 + 2.05061i) q^{51} +(-4.12726 - 4.58379i) q^{52} +(0.815559 - 0.363110i) q^{53} +(0.500000 + 0.866025i) q^{54} +(5.86219 - 9.35839i) q^{55} +(-2.56967 - 0.629903i) q^{56} +(1.54834 + 1.12494i) q^{57} +(-0.505859 + 0.107524i) q^{58} +(-1.54248 - 0.327864i) q^{59} +(0.348032 + 3.31131i) q^{60} +(13.6745 + 6.08828i) q^{61} +(-0.460770 - 1.41811i) q^{62} +(-2.64448 - 0.0818733i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-10.2685 - 17.7855i) q^{65} +(1.55382 + 2.93013i) q^{66} +(-0.0892859 + 0.154648i) q^{67} +(0.288432 - 2.74425i) q^{68} +(0.975740 - 3.00302i) q^{69} +(-7.93283 - 3.83032i) q^{70} +(8.96442 - 6.51303i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-3.59237 - 0.763582i) q^{73} +(1.86679 + 2.07328i) q^{74} +(-0.636148 + 6.05254i) q^{75} -1.91386 q^{76} +(-8.75530 - 0.587167i) q^{77} +6.16810 q^{78} +(0.932167 - 8.86898i) q^{79} +(-2.22790 - 2.47434i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(10.7000 + 4.76393i) q^{82} +(8.79297 - 6.38847i) q^{83} +(2.18756 - 1.48815i) q^{84} +(2.83907 - 8.73776i) q^{85} +(-1.15726 + 11.0106i) q^{86} +(0.258580 - 0.447874i) q^{87} +(-2.97935 - 1.45721i) q^{88} +(0.291418 + 0.504750i) q^{89} +(-2.69366 - 1.95706i) q^{90} +(-8.59306 + 13.8736i) q^{91} +(0.975740 + 3.00302i) q^{92} +(1.36217 + 0.606479i) q^{93} +(0.251539 + 2.39323i) q^{94} +(-6.23302 - 1.32487i) q^{95} +(0.978148 - 0.207912i) q^{96} +(9.88027 + 7.17844i) q^{97} +(0.299645 + 6.99358i) q^{98} +(-3.21722 - 0.805927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Introduction

L-functions

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