LMFDB - Embedded newform 546.2.z.a.131.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.14
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.48032 - 0.899243i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85844 + 3.21892i) q^{5} +(1.73162 - 0.0386050i) q^{6} +(-1.15681 + 2.37945i) q^{7} +1.00000i q^{8} +(1.38272 - 2.66234i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.48032 - 0.899243i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85844 + 3.21892i) q^{5} +(1.73162 - 0.0386050i) q^{6} +(-1.15681 + 2.37945i) q^{7} +1.00000i q^{8} +(1.38272 - 2.66234i) q^{9} +(-3.21892 + 1.85844i) q^{10} +(-1.05687 + 0.610184i) q^{11} +(1.51893 + 0.832377i) q^{12} -1.00000i q^{13} +(-2.19155 + 1.48226i) q^{14} +(0.143490 + 6.43624i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.08102 + 3.60444i) q^{17} +(2.52865 - 1.61430i) q^{18} +(3.91082 + 2.25792i) q^{19} -3.71689 q^{20} +(0.427259 + 4.56261i) q^{21} -1.22037 q^{22} +(-0.756604 - 0.436825i) q^{23} +(0.899243 + 1.48032i) q^{24} +(-4.40762 - 7.63423i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-0.347215 - 5.18454i) q^{27} +(-2.63907 + 0.187904i) q^{28} -4.39119i q^{29} +(-3.09385 + 5.64569i) q^{30} +(-2.49530 + 1.44066i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.01581 + 1.85365i) q^{33} +4.16205i q^{34} +(-5.50941 - 8.14574i) q^{35} +(2.99702 - 0.133698i) q^{36} +(-0.546406 + 0.946403i) q^{37} +(2.25792 + 3.91082i) q^{38} +(-0.899243 - 1.48032i) q^{39} +(-3.21892 - 1.85844i) q^{40} +11.9670 q^{41} +(-1.91129 + 4.16497i) q^{42} +11.9943 q^{43} +(-1.05687 - 0.610184i) q^{44} +(6.00015 + 9.39869i) q^{45} +(-0.436825 - 0.756604i) q^{46} +(4.05889 - 7.03021i) q^{47} +(0.0386050 + 1.73162i) q^{48} +(-4.32360 - 5.50513i) q^{49} -8.81525i q^{50} +(6.32186 + 3.46439i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-7.98565 + 4.61051i) q^{53} +(2.29157 - 4.66355i) q^{54} -4.53597i q^{55} +(-2.37945 - 1.15681i) q^{56} +(7.81971 - 0.174334i) q^{57} +(2.19559 - 3.80288i) q^{58} +(-2.97293 - 5.14927i) q^{59} +(-5.50220 + 3.34238i) q^{60} +(6.35777 + 3.67066i) q^{61} -2.88133 q^{62} +(4.73538 + 6.36994i) q^{63} -1.00000 q^{64} +(3.21892 + 1.85844i) q^{65} +(-1.80654 + 1.09741i) q^{66} +(-7.28275 - 12.6141i) q^{67} +(-2.08102 + 3.60444i) q^{68} +(-1.51283 + 0.0337273i) q^{69} +(-0.698417 - 9.80913i) q^{70} +1.92486i q^{71} +(2.66234 + 1.38272i) q^{72} +(-1.89964 + 1.09676i) q^{73} +(-0.946403 + 0.546406i) q^{74} +(-13.3897 - 7.33761i) q^{75} +4.51583i q^{76} +(-0.229312 - 3.22064i) q^{77} +(-0.0386050 - 1.73162i) q^{78} +(1.29925 - 2.25038i) q^{79} +(-1.85844 - 3.21892i) q^{80} +(-5.17615 - 7.36257i) q^{81} +(10.3637 + 5.98350i) q^{82} +8.05101 q^{83} +(-3.73771 + 2.65132i) q^{84} -15.4699 q^{85} +(10.3874 + 5.99717i) q^{86} +(-3.94874 - 6.50038i) q^{87} +(-0.610184 - 1.05687i) q^{88} +(1.01501 - 1.75806i) q^{89} +(0.496942 + 11.1396i) q^{90} +(2.37945 + 1.15681i) q^{91} -0.873651i q^{92} +(-2.39835 + 4.37654i) q^{93} +(7.03021 - 4.05889i) q^{94} +(-14.5361 + 8.39242i) q^{95} +(-0.832377 + 1.51893i) q^{96} +11.4288i q^{97} +(-0.991782 - 6.92938i) q^{98} +(0.163161 + 3.65747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.48032	−	0.899243i	0.854666	−	0.519178i
$3$	1.48032	−	0.899243i	0.854666	−	0.519178i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.85844	+	3.21892i	−0.831121	+	1.43954i	0.0660287	+	0.997818i	$0.478967\pi$
$5$	−1.85844	+	3.21892i	−0.831121	+	1.43954i	−0.897150	+	0.441726i	$0.854366\pi$
$6$	1.73162	−	0.0386050i	0.706931	−	0.0157604i
$7$	−1.15681	+	2.37945i	−0.437231	+	0.899349i
$7$	−1.15681	+	2.37945i	−0.437231	+	0.899349i
$8$			1.00000i			0.353553i
$9$	1.38272	−	2.66234i	0.460908	−	0.887448i
$10$	−3.21892	+	1.85844i	−1.01791	+	0.587691i
$11$	−1.05687	+	0.610184i	−0.318658	+	0.183977i	−0.650794	−	0.759254i	$-0.725564\pi$
$11$	−1.05687	+	0.610184i	−0.318658	+	0.183977i	0.332136	+	0.943231i	$0.392231\pi$
$12$	1.51893	+	0.832377i	0.438477	+	0.240287i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−2.19155	+	1.48226i	−0.585716	+	0.396152i
$15$	0.143490	+	6.43624i	0.0370491	+	1.66183i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.08102	+	3.60444i	0.504722	+	0.874205i	0.999985	+	0.00546150i	$0.00173846\pi$
$17$	2.08102	+	3.60444i	0.504722	+	0.874205i	−0.495263	+	0.868743i	$0.664928\pi$
$18$	2.52865	−	1.61430i	0.596007	−	0.380493i
$19$	3.91082	+	2.25792i	0.897205	+	0.518001i	0.876292	−	0.481780i	$-0.160010\pi$
$19$	3.91082	+	2.25792i	0.897205	+	0.518001i	0.0209124	+	0.999781i	$0.493343\pi$
$20$	−3.71689			−0.831121
$21$	0.427259	+	4.56261i	0.0932356	+	0.995644i
$22$	−1.22037			−0.260183
$23$	−0.756604	−	0.436825i	−0.157763	−	0.0910844i	0.419040	−	0.907968i	$-0.362367\pi$
$23$	−0.756604	−	0.436825i	−0.157763	−	0.0910844i	−0.576803	+	0.816883i	$0.695700\pi$
$24$	0.899243	+	1.48032i	0.183557	+	0.302170i
$25$	−4.40762	−	7.63423i	−0.881525	−	1.52685i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−0.347215	−	5.18454i	−0.0668215	−	0.997765i
$28$	−2.63907	+	0.187904i	−0.498737	+	0.0355105i
$29$		−	4.39119i		−	0.815423i	−0.913111	−	0.407711i	$-0.866327\pi$
$29$		−	4.39119i		−	0.815423i	0.913111	−	0.407711i	$-0.133673\pi$
$30$	−3.09385	+	5.64569i	−0.564858	+	1.03076i
$31$	−2.49530	+	1.44066i	−0.448170	+	0.258751i	−0.707057	−	0.707157i	$-0.749978\pi$
$31$	−2.49530	+	1.44066i	−0.448170	+	0.258751i	0.258887	+	0.965908i	$0.416644\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.01581	+	1.85365i	−0.176829	+	0.322680i
$34$			4.16205i			0.713785i
$35$	−5.50941	−	8.14574i	−0.931260	−	1.37688i
$36$	2.99702	−	0.133698i	0.499503	−	0.0222831i
$37$	−0.546406	+	0.946403i	−0.0898286	+	0.155588i	−0.907439	−	0.420185i	$-0.861965\pi$
$37$	−0.546406	+	0.946403i	−0.0898286	+	0.155588i	0.817610	+	0.575772i	$0.195299\pi$
$38$	2.25792	+	3.91082i	0.366282	+	0.634419i
$39$	−0.899243	−	1.48032i	−0.143994	−	0.237042i
$40$	−3.21892	−	1.85844i	−0.508956	−	0.293846i
$41$	11.9670			1.86893			0.934465	−	0.356054i	$-0.115878\pi$
$41$	11.9670			1.86893			0.934465	+	0.356054i	$0.115878\pi$
$42$	−1.91129	+	4.16497i	−0.294918	+	0.642669i
$43$	11.9943			1.82912			0.914559	−	0.404452i	$-0.132538\pi$
$43$	11.9943			1.82912			0.914559	+	0.404452i	$0.132538\pi$
$44$	−1.05687	−	0.610184i	−0.159329	−	0.0919887i
$45$	6.00015	+	9.39869i	0.894450	+	1.40107i
$46$	−0.436825	−	0.756604i	−0.0644064	−	0.111555i
$47$	4.05889	−	7.03021i	0.592050	−	1.02546i	−0.401906	−	0.915681i	$-0.631652\pi$
$47$	4.05889	−	7.03021i	0.592050	−	1.02546i	0.993956	−	0.109780i	$-0.0350147\pi$
$48$	0.0386050	+	1.73162i	0.00557215	+	0.249938i
$49$	−4.32360	−	5.50513i	−0.617657	−	0.786447i
$50$		−	8.81525i		−	1.24666i
$51$	6.32186	+	3.46439i	0.885237	+	0.485112i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	−7.98565	+	4.61051i	−1.09691	+	0.633303i	−0.935408	−	0.353569i	$-0.884968\pi$
$53$	−7.98565	+	4.61051i	−1.09691	+	0.633303i	−0.161504	+	0.986872i	$0.551635\pi$
$54$	2.29157	−	4.66355i	0.311844	−	0.634629i
$55$		−	4.53597i		−	0.611630i
$56$	−2.37945	−	1.15681i	−0.317968	−	0.154585i
$57$	7.81971	−	0.174334i	1.03575	−	0.0230911i
$58$	2.19559	−	3.80288i	0.288295	−	0.499342i
$59$	−2.97293	−	5.14927i	−0.387043	−	0.670377i	0.605008	−	0.796220i	$-0.293170\pi$
$59$	−2.97293	−	5.14927i	−0.387043	−	0.670377i	−0.992050	+	0.125842i	$0.959837\pi$
$60$	−5.50220	+	3.34238i	−0.710331	+	0.431500i
$61$	6.35777	+	3.67066i	0.814029	+	0.469980i	0.848353	−	0.529431i	$-0.177595\pi$
$61$	6.35777	+	3.67066i	0.814029	+	0.469980i	−0.0343242	+	0.999411i	$0.510928\pi$
$62$	−2.88133			−0.365929
$63$	4.73538	+	6.36994i	0.596602	+	0.802537i
$64$	−1.00000			−0.125000
$65$	3.21892	+	1.85844i	0.399258	+	0.230512i
$66$	−1.80654	+	1.09741i	−0.222370	+	0.135082i
$67$	−7.28275	−	12.6141i	−0.889729	−	1.54106i	−0.840196	−	0.542283i	$-0.817560\pi$
$67$	−7.28275	−	12.6141i	−0.889729	−	1.54106i	−0.0495332	−	0.998772i	$-0.515773\pi$
$68$	−2.08102	+	3.60444i	−0.252361	+	0.437102i
$69$	−1.51283	+	0.0337273i	−0.182123	+	0.00406029i
$70$	−0.698417	−	9.80913i	−0.0834768	−	1.17241i
$71$			1.92486i			0.228439i	0.993456	+	0.114219i	$0.0364366\pi$
$71$			1.92486i			0.228439i	−0.993456	+	0.114219i	$0.963563\pi$
$72$	2.66234	+	1.38272i	0.313760	+	0.162956i
$73$	−1.89964	+	1.09676i	−0.222336	+	0.128366i	−0.607031	−	0.794678i	$-0.707640\pi$
$73$	−1.89964	+	1.09676i	−0.222336	+	0.128366i	0.384696	+	0.923044i	$0.374306\pi$
$74$	−0.946403	+	0.546406i	−0.110017	+	0.0635184i
$75$	−13.3897	−	7.33761i	−1.54611	−	0.847274i
$76$			4.51583i			0.518001i
$77$	−0.229312	−	3.22064i	−0.0261325	−	0.367026i
$78$	−0.0386050	−	1.73162i	−0.00437115	−	0.196067i
$79$	1.29925	−	2.25038i	0.146178	−	0.253187i	−0.783634	−	0.621223i	$-0.786636\pi$
$79$	1.29925	−	2.25038i	0.146178	−	0.253187i	0.929812	+	0.368036i	$0.119970\pi$
$80$	−1.85844	−	3.21892i	−0.207780	−	0.359886i
$81$	−5.17615	−	7.36257i	−0.575128	−	0.818063i
$82$	10.3637	+	5.98350i	1.14448	+	0.660767i
$83$	8.05101			0.883713			0.441857	−	0.897086i	$-0.354320\pi$
$83$	8.05101			0.883713			0.441857	+	0.897086i	$0.354320\pi$
$84$	−3.73771	+	2.65132i	−0.407818	+	0.289283i
$85$	−15.4699			−1.67794
$86$	10.3874	+	5.99717i	1.12010	+	0.646691i
$87$	−3.94874	−	6.50038i	−0.423350	−	0.696914i
$88$	−0.610184	−	1.05687i	−0.0650458	−	0.112663i
$89$	1.01501	−	1.75806i	0.107591	−	0.186354i	−0.807203	−	0.590274i	$-0.799020\pi$
$89$	1.01501	−	1.75806i	0.107591	−	0.186354i	0.914794	+	0.403921i	$0.132353\pi$
$90$	0.496942	+	11.1396i	0.0523823	+	1.17421i
$91$	2.37945	+	1.15681i	0.249435	+	0.121266i
$92$		−	0.873651i		−	0.0910844i
$93$	−2.39835	+	4.37654i	−0.248698	+	0.453826i
$94$	7.03021	−	4.05889i	0.725111	−	0.418643i
$95$	−14.5361	+	8.39242i	−1.49137	+	0.861044i
$96$	−0.832377	+	1.51893i	−0.0849542	+	0.155025i
$97$			11.4288i			1.16042i	0.814467	+	0.580210i	$0.197029\pi$
$97$			11.4288i			1.16042i	−0.814467	+	0.580210i	$0.802971\pi$
$98$	−0.991782	−	6.92938i	−0.100185	−	0.699974i
$99$	0.163161	+	3.65747i	0.0163983	+	0.367589i
$100$	4.40762	−	7.63423i	0.440762	−	0.763423i
$101$	−0.958887	−	1.66084i	−0.0954128	−	0.165260i	0.814368	−	0.580349i	$-0.197084\pi$
$101$	−0.958887	−	1.66084i	−0.0954128	−	0.165260i	−0.909781	+	0.415089i	$0.863750\pi$
$102$	3.74269	+	6.16118i	0.370582	+	0.610048i
$103$	−1.18122	−	0.681975i	−0.116389	−	0.0671970i	0.440676	−	0.897666i	$-0.354739\pi$
$103$	−1.18122	−	0.681975i	−0.116389	−	0.0671970i	−0.557064	+	0.830469i	$0.688072\pi$
$104$	1.00000			0.0980581
$105$	−15.4807	−	7.10405i	−1.51076	−	0.693284i
$106$	−9.22103			−0.895626
$107$	−15.0435	−	8.68535i	−1.45431	−	0.839644i	−0.455585	−	0.890192i	$-0.650570\pi$
$107$	−15.0435	−	8.68535i	−1.45431	−	0.839644i	−0.998722	+	0.0505482i	$0.983903\pi$
$108$	4.31633	−	2.89297i	0.415340	−	0.278376i
$109$	8.20573	+	14.2127i	0.785966	+	1.36133i	0.928420	+	0.371532i	$0.121167\pi$
$109$	8.20573	+	14.2127i	0.785966	+	1.36133i	−0.142454	+	0.989801i	$0.545499\pi$
$110$	2.26798	−	3.92826i	0.216244	−	0.374545i
$111$	0.0421880	+	1.89234i	0.00400431	+	0.179613i
$112$	−1.48226	−	2.19155i	−0.140061	−	0.207082i
$113$		−	11.7885i		−	1.10897i	−0.832193	−	0.554485i	$-0.812915\pi$
$113$		−	11.7885i		−	1.10897i	0.832193	−	0.554485i	$-0.187085\pi$
$114$	6.85923	+	3.75888i	0.642426	+	0.352051i
$115$	2.81221	−	1.62363i	0.262240	−	0.151404i
$116$	3.80288	−	2.19559i	0.353088	−	0.203856i
$117$	−2.66234	−	1.38272i	−0.246134	−	0.127833i
$118$		−	5.94586i		−	0.547361i
$119$	−10.9839	+	0.782064i	−1.00690	+	0.0716917i
$120$	−6.43624	+	0.143490i	−0.587545	+	0.0130988i
$121$	−4.75535	+	8.23651i	−0.432305	+	0.748774i
$122$	3.67066	+	6.35777i	0.332326	+	0.575605i
$123$	17.7150	−	10.7612i	1.59731	−	0.970308i
$124$	−2.49530	−	1.44066i	−0.224085	−	0.129375i
$125$	14.1808			1.26837
$126$	0.915991	+	7.88422i	0.0816029	+	0.702382i
$127$	2.18809			0.194162			0.0970809	−	0.995276i	$-0.469049\pi$
$127$	2.18809			0.194162			0.0970809	+	0.995276i	$0.469049\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	17.7555	−	10.7858i	1.56329	−	0.949639i
$130$	1.85844	+	3.21892i	0.162996	+	0.282318i
$131$	1.88356	−	3.26242i	0.164567	−	0.285039i	−0.771934	−	0.635702i	$-0.780711\pi$
$131$	1.88356	−	3.26242i	0.164567	−	0.285039i	0.936502	+	0.350663i	$0.114044\pi$
$132$	−2.11321	+	0.0471123i	−0.183932	+	0.00410060i
$133$	−9.89667	+	6.69366i	−0.858150	+	0.580414i
$134$		−	14.5655i		−	1.25827i
$135$	17.3339	+	8.51752i	1.49186	+	0.733071i
$136$	−3.60444	+	2.08102i	−0.309078	+	0.178446i
$137$	−13.4830	+	7.78442i	−1.15193	+	0.665068i	−0.949357	−	0.314199i	$-0.898264\pi$
$137$	−13.4830	+	7.78442i	−1.15193	+	0.665068i	−0.202574	+	0.979267i	$0.564931\pi$
$138$	−1.32701	−	0.727207i	−0.112963	−	0.0619040i
$139$			8.48522i			0.719707i	0.933009	+	0.359853i	$0.117173\pi$
$139$			8.48522i			0.719707i	−0.933009	+	0.359853i	$0.882827\pi$
$140$	4.29972	−	8.84416i	0.363392	−	0.747468i
$141$	−0.313387	−	14.0569i	−0.0263920	−	1.18381i
$142$	−0.962429	+	1.66698i	−0.0807652	+	0.139889i
$143$	0.610184	+	1.05687i	0.0510261	+	0.0883799i
$144$	1.61430	+	2.52865i	0.134525	+	0.210720i
$145$	14.1349	+	8.16077i	1.17384	+	0.677715i
$146$	−2.19351			−0.181536
$147$	−11.3508	−	4.26142i	−0.936197	−	0.351476i
$148$	−1.09281			−0.0898286
$149$	−18.1499	−	10.4789i	−1.48690	−	0.858461i	−0.487010	−	0.873396i	$-0.661913\pi$
$149$	−18.1499	−	10.4789i	−1.48690	−	0.858461i	−0.999888	+	0.0149348i	$0.995246\pi$
$150$	−7.92705	−	13.0494i	−0.647241	−	1.06548i
$151$	7.43311	+	12.8745i	0.604898	+	1.04771i	0.992068	+	0.125705i	$0.0401193\pi$
$151$	7.43311	+	12.8745i	0.604898	+	1.04771i	−0.387170	+	0.922008i	$0.626547\pi$
$152$	−2.25792	+	3.91082i	−0.183141	+	0.317210i
$153$	12.4737	−	0.556459i	1.00844	−	0.0449870i
$154$	1.41173	−	2.90381i	0.113760	−	0.233996i
$155$		−	10.7096i		−	0.860213i
$156$	0.832377	−	1.51893i	0.0666435	−	0.121612i
$157$	1.21219	−	0.699858i	0.0967433	−	0.0558548i	−0.450848	−	0.892601i	$-0.648878\pi$
$157$	1.21219	−	0.699858i	0.0967433	−	0.0558548i	0.547591	+	0.836746i	$0.315545\pi$
$158$	2.25038	−	1.29925i	0.179030	−	0.103363i
$159$	−7.67538	+	14.0061i	−0.608697	+	1.11076i
$160$		−	3.71689i		−	0.293846i
$161$	1.91465	−	1.29498i	0.150895	−	0.102059i
$162$	−0.801393	−	8.96425i	−0.0629634	−	0.704298i
$163$	3.98169	−	6.89649i	0.311870	−	0.540175i	−0.666897	−	0.745150i	$-0.732378\pi$
$163$	3.98169	−	6.89649i	0.311870	−	0.540175i	0.978767	+	0.204975i	$0.0657113\pi$
$164$	5.98350	+	10.3637i	0.467233	+	0.809271i
$165$	−4.07894	−	6.71471i	−0.317545	−	0.522739i
$166$	6.97238	+	4.02550i	0.541162	+	0.312440i
$167$	2.41676			0.187015			0.0935074	−	0.995619i	$-0.470192\pi$
$167$	2.41676			0.187015			0.0935074	+	0.995619i	$0.470192\pi$
$168$	−4.56261	+	0.427259i	−0.352013	+	0.0329638i
$169$	−1.00000			−0.0769231
$170$	−13.3973	−	7.73493i	−1.02753	−	0.593242i
$171$	11.4189	−	7.28989i	0.873228	−	0.557472i
$172$	5.99717	+	10.3874i	0.457280	+	0.792032i
$173$	1.96748	−	3.40778i	0.149585	−	0.259089i	−0.781489	−	0.623919i	$-0.785540\pi$
$173$	1.96748	−	3.40778i	0.149585	−	0.259089i	0.931074	+	0.364830i	$0.118873\pi$
$174$	−0.169522	−	7.60387i	−0.0128514	−	0.576448i
$175$	23.2641	−	1.65642i	1.75860	−	0.125213i
$176$		−	1.22037i		−	0.0919887i
$177$	−9.03135	−	4.94920i	−0.678838	−	0.372005i
$178$	1.75806	−	1.01501i	0.131772	−	0.0760785i
$179$	18.1488	−	10.4782i	1.35651	−	0.783179i	0.367355	−	0.930081i	$-0.380263\pi$
$179$	18.1488	−	10.4782i	1.35651	−	0.783179i	0.989151	+	0.146902i	$0.0469301\pi$
$180$	−5.13943	+	9.89563i	−0.383070	+	0.737577i
$181$		−	1.62350i		−	0.120674i	−0.998178	−	0.0603370i	$-0.980782\pi$
$181$		−	1.62350i		−	0.120674i	0.998178	−	0.0603370i	$-0.0192175\pi$
$182$	1.48226	+	2.19155i	0.109873	+	0.162449i
$183$	12.7124	−	0.283412i	0.939726	−	0.0209504i
$184$	0.436825	−	0.756604i	0.0322032	−	0.0557776i
$185$	−2.03093	−	3.51767i	−0.149317	−	0.258624i
$186$	−4.26530	+	2.59101i	−0.312747	+	0.189982i
$187$	−4.39874	−	2.53961i	−0.321668	−	0.185715i
$188$	8.11779			0.592050
$189$	12.7380	+	5.17132i	0.926555	+	0.376158i
$190$	−16.7848			−1.21770
$191$	16.3128	+	9.41819i	1.18035	+	0.681477i	0.956096	−	0.293054i	$-0.0946714\pi$
$191$	16.3128	+	9.41819i	1.18035	+	0.681477i	0.224256	+	0.974530i	$0.428005\pi$
$192$	−1.48032	+	0.899243i	−0.106833	+	0.0648973i
$193$	−11.3267	−	19.6185i	−0.815316	−	1.41217i	−0.909101	−	0.416576i	$-0.863230\pi$
$193$	−11.3267	−	19.6185i	−0.815316	−	1.41217i	0.0937850	−	0.995592i	$-0.470103\pi$
$194$	−5.71440	+	9.89763i	−0.410270	+	0.710609i
$195$	6.43624	−	0.143490i	0.460909	−	0.0102756i
$196$	2.60578	−	6.49691i	0.186127	−	0.464065i
$197$		−	11.3239i		−	0.806795i	−0.915025	−	0.403398i	$-0.867829\pi$
$197$		−	11.3239i		−	0.806795i	0.915025	−	0.403398i	$-0.132171\pi$
$198$	−1.68743	+	3.24904i	−0.119921	+	0.230899i
$199$	14.1005	−	8.14094i	0.999560	−	0.577096i	0.0914416	−	0.995810i	$-0.470853\pi$
$199$	14.1005	−	8.14094i	0.999560	−	0.577096i	0.908118	+	0.418714i	$0.137519\pi$
$200$	7.63423	−	4.40762i	0.539821	−	0.311666i
$201$	−22.1240	−	12.1240i	−1.56050	−	0.855160i
$202$		−	1.91777i		−	0.134934i
$203$	10.4486	+	5.07975i	0.733350	+	0.356528i
$204$	0.160676	+	7.20709i	0.0112496	+	0.504597i
$205$	−22.2400	+	38.5208i	−1.55331	+	2.69041i
$206$	−0.681975	−	1.18122i	−0.0475155	−	0.0822992i
$207$	−2.20915	+	1.41033i	−0.153547	+	0.0980247i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	−5.51098			−0.381202
$210$	−9.85467	−	13.8926i	−0.680037	−	0.958684i
$211$	3.48656			0.240024			0.120012	−	0.992772i	$-0.461707\pi$
$211$	3.48656			0.240024			0.120012	+	0.992772i	$0.461707\pi$
$212$	−7.98565	−	4.61051i	−0.548456	−	0.316651i
$213$	1.73091	+	2.84941i	0.118600	+	0.195239i
$214$	−8.68535	−	15.0435i	−0.593718	−	1.02835i
$215$	−22.2908	+	38.6088i	−1.52022	+	2.63310i
$216$	5.18454	−	0.347215i	0.352763	−	0.0236250i
$217$	−0.541412	−	7.60403i	−0.0367535	−	0.516195i
$218$			16.4115i			1.11152i
$219$	−1.82583	+	3.33179i	−0.123378	+	0.225142i
$220$	3.92826	−	2.26798i	0.264844	−	0.152908i
$221$	3.60444	−	2.08102i	0.242461	−	0.139985i
$222$	−0.909632	+	1.65990i	−0.0610505	+	0.111406i
$223$			27.9701i			1.87301i	0.350650	+	0.936507i	$0.385961\pi$
$223$			27.9701i			1.87301i	−0.350650	+	0.936507i	$0.614039\pi$
$224$	−0.187904	−	2.63907i	−0.0125548	−	0.176330i
$225$	−26.4195	+	1.17858i	−1.76130	+	0.0785723i
$226$	5.89426	−	10.2092i	0.392080	−	0.679103i
$227$	10.2073	+	17.6795i	0.677480	+	1.17343i	0.975737	+	0.218944i	$0.0702613\pi$
$227$	10.2073	+	17.6795i	0.677480	+	1.17343i	−0.298257	+	0.954485i	$0.596405\pi$
$228$	4.06083	+	6.68490i	0.268935	+	0.442718i
$229$	−8.35971	−	4.82648i	−0.552425	−	0.318943i	0.197674	−	0.980268i	$-0.436661\pi$
$229$	−8.35971	−	4.82648i	−0.552425	−	0.318943i	−0.750100	+	0.661325i	$0.769994\pi$
$230$	3.24726			0.214118
$231$	−3.23559	−	4.56138i	−0.212886	−	0.300117i
$232$	4.39119			0.288295
$233$	14.6728	+	8.47134i	0.961247	+	0.554976i	0.896557	−	0.442929i	$-0.146061\pi$
$233$	14.6728	+	8.47134i	0.961247	+	0.554976i	0.0646902	+	0.997905i	$0.479394\pi$
$234$	−1.61430	−	2.52865i	−0.105530	−	0.165303i
$235$	15.0864	+	26.1305i	0.984131	+	1.70457i
$236$	2.97293	−	5.14927i	0.193521	−	0.335189i
$237$	−0.100315	−	4.49963i	−0.00651619	−	0.292283i
$238$	−9.90340	−	4.81468i	−0.641942	−	0.312089i
$239$		−	15.9914i		−	1.03440i	−0.855865	−	0.517199i	$-0.826975\pi$
$239$		−	15.9914i		−	1.03440i	0.855865	−	0.517199i	$-0.173025\pi$
$240$	−5.64569	−	3.09385i	−0.364428	−	0.199707i
$241$	−21.8829	+	12.6341i	−1.40960	+	0.813834i	−0.995350	−	0.0963274i	$-0.969290\pi$
$241$	−21.8829	+	12.6341i	−1.40960	+	0.813834i	−0.414253	+	0.910162i	$0.635957\pi$
$242$	−8.23651	+	4.75535i	−0.529463	+	0.305686i
$243$	−14.2831	−	6.24438i	−0.916263	−	0.400577i
$244$			7.34132i			0.469980i
$245$	25.7557	−	3.68634i	1.64547	−	0.235512i
$246$	20.7223	−	0.461986i	1.32121	−	0.0294551i
$247$	2.25792	−	3.91082i	0.143668	−	0.248840i
$248$	−1.44066	−	2.49530i	−0.0914823	−	0.158452i
$249$	11.9181	−	7.23982i	0.755280	−	0.458805i
$250$	12.2810	+	7.09042i	0.776717	+	0.448437i
$251$	−9.68074			−0.611043			−0.305522	−	0.952185i	$-0.598831\pi$
$251$	−9.68074			−0.611043			−0.305522	+	0.952185i	$0.598831\pi$
$252$	−3.14884	+	7.28593i	−0.198358	+	0.458971i
$253$	1.06618			0.0670299
$254$	1.89494	+	1.09405i	0.118899	+	0.0686466i
$255$	−22.9004	+	13.9112i	−1.43408	+	0.871151i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.2707	+	22.9856i	−0.827805	+	1.43380i	0.0719512	+	0.997408i	$0.477077\pi$
$257$	−13.2707	+	22.9856i	−0.827805	+	1.43380i	−0.899756	+	0.436392i	$0.856256\pi$
$258$	20.7696	−	0.463041i	1.29306	−	0.0288277i
$259$	−1.61984	−	2.39495i	−0.100652	−	0.148815i
$260$			3.71689i			0.230512i
$261$	−11.6908	−	6.07180i	−0.723645	−	0.375835i
$262$	3.26242	−	1.88356i	0.201553	−	0.116367i
$263$	−4.74191	+	2.73774i	−0.292399	+	0.168817i	−0.639023	−	0.769187i	$-0.720661\pi$
$263$	−4.74191	+	2.73774i	−0.292399	+	0.168817i	0.346624	+	0.938004i	$0.387328\pi$
$264$	−1.85365	−	1.01581i	−0.114084	−	0.0625186i
$265$		−	34.2735i		−	2.10541i
$266$	−11.9176	+	0.848541i	−0.730715	+	0.0520274i
$267$	−0.0783692	−	3.51524i	−0.00479612	−	0.215129i
$268$	7.28275	−	12.6141i	0.444864	−	0.770528i
$269$	12.2587	+	21.2327i	0.747426	+	1.29458i	0.949053	+	0.315117i	$0.102044\pi$
$269$	12.2587	+	21.2327i	0.747426	+	1.29458i	−0.201627	+	0.979462i	$0.564623\pi$
$270$	10.7528	+	16.0433i	0.654396	+	0.976366i
$271$	−8.05762	−	4.65207i	−0.489466	−	0.282593i	0.234887	−	0.972023i	$-0.424528\pi$
$271$	−8.05762	−	4.65207i	−0.489466	−	0.282593i	−0.724353	+	0.689430i	$0.757861\pi$
$272$	−4.16205			−0.252361
$273$	4.56261	−	0.427259i	0.276142	−	0.0258589i
$274$	−15.5688			−0.940548
$275$	9.31657	+	5.37892i	0.561810	+	0.324361i
$276$	−0.785624	−	1.29329i	−0.0472890	−	0.0778467i
$277$	−12.0135	−	20.8080i	−0.721823	−	1.25023i	−0.960268	−	0.279078i	$-0.909971\pi$
$277$	−12.0135	−	20.8080i	−0.721823	−	1.25023i	0.238445	−	0.971156i	$-0.423362\pi$
$278$	−4.24261	+	7.34841i	−0.254455	+	0.440729i
$279$	0.385229	+	8.63540i	0.0230631	+	0.516988i
$280$	8.14574	−	5.50941i	0.486801	−	0.329250i
$281$		−	15.0432i		−	0.897399i	−0.893683	−	0.448700i	$-0.851887\pi$
$281$		−	15.0432i		−	0.897399i	0.893683	−	0.448700i	$-0.148113\pi$
$282$	6.75706	−	12.3303i	0.402377	−	0.734261i
$283$	2.71318	−	1.56645i	0.161282	−	0.0931160i	−0.417187	−	0.908821i	$-0.636984\pi$
$283$	2.71318	−	1.56645i	0.161282	−	0.0931160i	0.578468	+	0.815705i	$0.303651\pi$
$284$	−1.66698	+	0.962429i	−0.0989168	+	0.0571096i
$285$	−13.9713	+	25.4950i	−0.827589	+	1.51019i
$286$			1.22037i			0.0721619i
$287$	−13.8435	+	28.4749i	−0.817155	+	1.68082i
$288$	0.133698	+	2.99702i	0.00787825	+	0.176601i
$289$	−0.161318	+	0.279411i	−0.00948928	+	0.0164359i
$290$	8.16077	+	14.1349i	0.479217	+	0.830028i
$291$	10.2773	+	16.9183i	0.602464	+	0.991771i
$292$	−1.89964	−	1.09676i	−0.111168	−	0.0641828i
$293$	−25.8944			−1.51277			−0.756384	−	0.654128i	$-0.773036\pi$
$293$	−25.8944			−1.51277			−0.756384	+	0.654128i	$0.773036\pi$
$294$	−7.69936	−	9.36589i	−0.449036	−	0.546230i
$295$	22.1001			1.28672
$296$	−0.946403	−	0.546406i	−0.0550086	−	0.0317592i
$297$	3.53048	+	5.26752i	0.204859	+	0.305652i
$298$	−10.4789	−	18.1499i	−0.607024	−	1.05140i
$299$	−0.436825	+	0.756604i	−0.0252623	+	0.0437555i
$300$	−0.340313	−	15.2647i	−0.0196480	−	0.881306i
$301$	−13.8751	+	28.5400i	−0.799748	+	1.64502i
$302$			14.8662i			0.855455i
$303$	−2.91296	−	1.59631i	−0.167345	−	0.0917057i
$304$	−3.91082	+	2.25792i	−0.224301	+	0.129500i
$305$	−23.6311	+	13.6434i	−1.35311	+	0.781220i
$306$	11.0808	+	5.75496i	0.633447	+	0.328989i
$307$		−	23.5533i		−	1.34426i	−0.740435	−	0.672128i	$-0.765380\pi$
$307$		−	23.5533i		−	1.34426i	0.740435	−	0.672128i	$-0.234620\pi$
$308$	2.67450	−	1.80891i	0.152394	−	0.103072i
$309$	−2.36185	+	0.0526553i	−0.134361	+	0.00299546i
$310$	5.35478	−	9.27476i	0.304131	−	0.526771i
$311$	−10.3713	−	17.9636i	−0.588103	−	1.01862i	−0.994481	−	0.104920i	$-0.966541\pi$
$311$	−10.3713	−	17.9636i	−0.588103	−	1.01862i	0.406377	−	0.913705i	$-0.366792\pi$
$312$	1.48032	−	0.899243i	0.0838069	−	0.0509096i
$313$	4.60413	+	2.65819i	0.260241	+	0.150250i	0.624444	−	0.781069i	$-0.285325\pi$
$313$	4.60413	+	2.65819i	0.260241	+	0.150250i	−0.364204	+	0.931319i	$0.618659\pi$
$314$	1.39972			0.0789906
$315$	−29.3048	+	3.40463i	−1.65114	+	0.191829i
$316$	2.59851			0.146178
$317$	12.7070	+	7.33636i	0.713694	+	0.412051i	0.812427	−	0.583063i	$-0.198146\pi$
$317$	12.7070	+	7.33636i	0.713694	+	0.412051i	−0.0987336	+	0.995114i	$0.531479\pi$
$318$	−13.6501	+	8.29195i	−0.765461	+	0.464989i
$319$	2.67943	+	4.64091i	0.150019	+	0.259841i
$320$	1.85844	−	3.21892i	0.103890	−	0.179943i
$321$	−30.0795	+	0.670596i	−1.67887	+	0.0374290i
$322$	2.30563	−	0.164162i	0.128487	−	0.00914840i
$323$			18.7951i			1.04579i
$324$	3.78810	−	8.16396i	0.210450	−	0.453554i
$325$	−7.63423	+	4.40762i	−0.423471	+	0.244491i
$326$	6.89649	−	3.98169i	0.381961	−	0.220525i
$327$	24.9278	+	13.6605i	1.37851	+	0.755429i
$328$			11.9670i			0.660767i
$329$	12.0327	+	17.7905i	0.663385	+	0.980824i
$330$	−0.175111	−	7.85458i	−0.00963955	−	0.432380i
$331$	−0.244509	+	0.423503i	−0.0134394	+	0.0232778i	−0.872667	−	0.488316i	$-0.837611\pi$
$331$	−0.244509	+	0.423503i	−0.0134394	+	0.0232778i	0.859227	+	0.511594i	$0.170945\pi$
$332$	4.02550	+	6.97238i	0.220928	+	0.382659i
$333$	1.76412	+	2.76333i	0.0966733	+	0.151430i
$334$	2.09298	+	1.20838i	0.114523	+	0.0661197i
$335$	54.1383			2.95789
$336$	−4.16497	−	1.91129i	−0.227218	−	0.104269i
$337$	9.20861			0.501625			0.250812	−	0.968036i	$-0.419302\pi$
$337$	9.20861			0.501625			0.250812	+	0.968036i	$0.419302\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	−10.6007	−	17.4508i	−0.575754	−	0.947800i
$340$	−7.73493	−	13.3973i	−0.419485	−	0.726570i
$341$	1.75814	−	3.04519i	0.0952086	−	0.164906i
$342$	13.5340	−	0.603759i	0.731837	−	0.0326476i
$343$	18.1008	−	3.91944i	0.977350	−	0.211630i
$344$			11.9943i			0.646691i
$345$	2.70295	−	4.93236i	0.145522	−	0.265549i
$346$	3.40778	−	1.96748i	0.183203	−	0.105773i
$347$	−6.70981	+	3.87391i	−0.360201	+	0.207962i	−0.669169	−	0.743110i	$-0.733350\pi$
$347$	−6.70981	+	3.87391i	−0.360201	+	0.207962i	0.308968	+	0.951073i	$0.400016\pi$
$348$	3.65512	−	6.66990i	0.195935	−	0.357544i
$349$		−	28.8702i		−	1.54539i	−0.634779	−	0.772693i	$-0.718909\pi$
$349$		−	28.8702i		−	1.54539i	0.634779	−	0.772693i	$-0.281091\pi$
$350$	20.9755	+	10.1975i	1.12119	+	0.545081i
$351$	−5.18454	+	0.347215i	−0.276730	+	0.0185330i
$352$	0.610184	−	1.05687i	0.0325229	−	0.0563313i
$353$	9.29510	+	16.0996i	0.494728	+	0.856894i	0.999982	−	0.00607690i	$-0.00193435\pi$
$353$	9.29510	+	16.0996i	0.494728	+	0.856894i	−0.505254	+	0.862971i	$0.668601\pi$
$354$	−5.34677	−	8.80181i	−0.284178	−	0.467811i
$355$	−6.19596	−	3.57724i	−0.328847	−	0.189860i
$356$	2.03003			0.107591
$357$	−15.5565	+	11.0349i	−0.823339	+	0.584031i
$358$	20.9564			1.10758
$359$	−20.8262	−	12.0240i	−1.09917	−	0.634604i	−0.163164	−	0.986599i	$-0.552170\pi$
$359$	−20.8262	−	12.0240i	−1.09917	−	0.634604i	−0.936002	+	0.351995i	$0.885503\pi$
$360$	−9.39869	+	6.00015i	−0.495354	+	0.316236i
$361$	0.696364	+	1.20614i	0.0366507	+	0.0634809i
$362$	0.811751	−	1.40599i	0.0426647	−	0.0738974i
$363$	0.367161	+	16.4689i	0.0192709	+	0.864394i
$364$	0.187904	+	2.63907i	0.00984883	+	0.138325i
$365$		−	8.15304i		−	0.426750i
$366$	11.1509	+	6.11075i	0.582869	+	0.319414i
$367$	3.41657	−	1.97256i	0.178343	−	0.102967i	−0.408171	−	0.912906i	$-0.633833\pi$
$367$	3.41657	−	1.97256i	0.178343	−	0.102967i	0.586514	+	0.809939i	$0.300500\pi$
$368$	0.756604	−	0.436825i	0.0394407	−	0.0227711i
$369$	16.5470	−	31.8603i	0.861405	−	1.65858i
$370$		−	4.06186i		−	0.211166i
$371$	−1.73267	−	24.3349i	−0.0899555	−	1.26341i
$372$	−4.98937	+	0.111234i	−0.258687	+	0.00576720i
$373$	−10.3207	+	17.8760i	−0.534385	+	0.925582i	0.464808	+	0.885412i	$0.346123\pi$
$373$	−10.3207	+	17.8760i	−0.534385	+	0.925582i	−0.999193	+	0.0401705i	$0.987210\pi$
$374$	−2.53961	−	4.39874i	−0.131320	−	0.227454i
$375$	20.9922	−	12.7520i	1.08404	−	0.658512i
$376$	7.03021	+	4.05889i	0.362555	+	0.209321i
$377$	−4.39119			−0.226158
$378$	8.44580	+	10.8475i	0.434405	+	0.557936i
$379$	11.2026			0.575440			0.287720	−	0.957715i	$-0.407103\pi$
$379$	11.2026			0.575440			0.287720	+	0.957715i	$0.407103\pi$
$380$	−14.5361	−	8.39242i	−0.745686	−	0.430522i
$381$	3.23909	−	1.96763i	0.165944	−	0.100805i
$382$	9.41819	+	16.3128i	0.481877	+	0.834635i
$383$	17.3973	−	30.1330i	0.888960	−	1.53972i	0.0478543	−	0.998854i	$-0.484762\pi$
$383$	17.3973	−	30.1330i	0.888960	−	1.53972i	0.841106	−	0.540870i	$-0.181905\pi$
$384$	−1.73162	+	0.0386050i	−0.0883664	+	0.00197005i
$385$	10.7931	+	5.24724i	0.550069	+	0.267424i
$386$		−	22.6535i		−	1.15303i
$387$	16.5848	−	31.9330i	0.843055	−	1.62325i
$388$	−9.89763	+	5.71440i	−0.502476	+	0.290105i
$389$	6.68011	−	3.85676i	0.338695	−	0.195546i	−0.321000	−	0.947079i	$-0.604019\pi$
$389$	6.68011	−	3.85676i	0.338695	−	0.195546i	0.659695	+	0.751534i	$0.270686\pi$
$390$	5.64569	+	3.09385i	0.285881	+	0.156663i
$391$		−	3.63617i		−	0.183889i
$392$	5.50513	−	4.32360i	0.278051	−	0.218375i
$393$	−0.145430	−	6.52322i	−0.00733595	−	0.329053i
$394$	5.66196	−	9.80679i	0.285245	−	0.494059i
$395$	4.82918	+	8.36439i	0.242983	+	0.420858i
$396$	−3.08588	+	1.97004i	−0.155071	+	0.0989980i
$397$	−17.5161	−	10.1129i	−0.879107	−	0.507553i	−0.00874317	−	0.999962i	$-0.502783\pi$
$397$	−17.5161	−	10.1129i	−0.879107	−	0.507553i	−0.870364	+	0.492409i	$0.836116\pi$
$398$	16.2819			0.816137
$399$	−8.63106	+	18.8083i	−0.432094	+	0.941593i
$400$	8.81525			0.440762
$401$	26.4495	+	15.2706i	1.32082	+	0.762578i	0.983860	−	0.178940i	$-0.0572669\pi$
$401$	26.4495	+	15.2706i	1.32082	+	0.762578i	0.336963	+	0.941518i	$0.390600\pi$
$402$	−13.0979	−	21.5617i	−0.653265	−	1.07540i
$403$	1.44066	+	2.49530i	0.0717646	+	0.124300i
$404$	0.958887	−	1.66084i	0.0477064	−	0.0826299i
$405$	33.3191	−	2.97869i	1.65564	−	0.148012i
$406$	6.50890	+	9.62350i	0.323031	+	0.477606i
$407$		−	1.33363i		−	0.0661057i
$408$	−3.46439	+	6.32186i	−0.171513	+	0.312979i
$409$	−14.4836	+	8.36208i	−0.716166	+	0.413478i	−0.813340	−	0.581789i	$-0.802353\pi$
$409$	−14.4836	+	8.36208i	−0.716166	+	0.413478i	0.0971741	+	0.995267i	$0.469020\pi$
$410$	−38.5208	+	22.2400i	−1.90241	+	1.09835i
$411$	−12.9591	+	23.6480i	−0.639228	+	1.16647i
$412$		−	1.36395i		−	0.0671970i
$413$	15.6915	−	1.11725i	0.772130	−	0.0549762i
$414$	−2.61835	+	0.116806i	−0.128685	+	0.00574069i
$415$	−14.9623	+	25.9155i	−0.734473	+	1.27214i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	7.63027	+	12.5609i	0.373656	+	0.615109i
$418$	−4.77264	−	2.75549i	−0.233438	−	0.134775i
$419$	−6.59270			−0.322075			−0.161037	−	0.986948i	$-0.551484\pi$
$419$	−6.59270			−0.322075			−0.161037	+	0.986948i	$0.551484\pi$
$420$	−1.58807	−	16.9587i	−0.0774901	−	0.827501i
$421$	−28.8501			−1.40607			−0.703034	−	0.711156i	$-0.748172\pi$
$421$	−28.8501			−1.40607			−0.703034	+	0.711156i	$0.748172\pi$
$422$	3.01945	+	1.74328i	0.146984	+	0.0848615i
$423$	−13.1045	−	20.5270i	−0.637163	−	0.998057i
$424$	−4.61051	−	7.98565i	−0.223906	−	0.387817i
$425$	18.3447	−	31.7740i	0.889850	−	1.54127i
$426$	0.0743091	+	3.33312i	0.00360029	+	0.161490i
$427$	−16.0889	+	10.8818i	−0.778595	+	0.526606i
$428$		−	17.3707i		−	0.839644i
$429$	1.85365	+	1.01581i	0.0894952	+	0.0490436i
$430$	−38.6088	+	22.2908i	−1.86188	+	1.07496i
$431$	−8.09598	+	4.67422i	−0.389970	+	0.225149i	−0.682147	−	0.731215i	$-0.738954\pi$
$431$	−8.09598	+	4.67422i	−0.389970	+	0.225149i	0.292177	+	0.956364i	$0.405620\pi$
$432$	4.66355	+	2.29157i	0.224375	+	0.110253i
$433$		−	0.818527i		−	0.0393359i	−0.999807	−	0.0196679i	$-0.993739\pi$
$433$		−	0.818527i		−	0.0393359i	0.999807	−	0.0196679i	$-0.00626091\pi$
$434$	3.33314	−	6.85599i	0.159996	−	0.329098i
$435$	28.2627	−	0.630093i	1.35509	−	0.0302106i
$436$	−8.20573	+	14.2127i	−0.392983	+	0.680667i
$437$	−1.97263	−	3.41669i	−0.0943636	−	0.163443i
$438$	−3.24711	+	1.97250i	−0.155153	+	0.0942498i
$439$	−6.38479	−	3.68626i	−0.304730	−	0.175936i	0.339836	−	0.940485i	$-0.389628\pi$
$439$	−6.38479	−	3.68626i	−0.304730	−	0.175936i	−0.644566	+	0.764549i	$0.722962\pi$
$440$	4.53597			0.216244
$441$	−20.6349	+	3.89884i	−0.982614	+	0.185659i
$442$	4.16205			0.197968
$443$	5.32501	+	3.07440i	0.252999	+	0.146069i	0.621137	−	0.783702i	$-0.286671\pi$
$443$	5.32501	+	3.07440i	0.252999	+	0.146069i	−0.368138	+	0.929771i	$0.620005\pi$
$444$	−1.61772	+	0.982704i	−0.0767735	+	0.0466371i
$445$	3.77269	+	6.53450i	0.178843	+	0.309765i
$446$	−13.9850	+	24.2228i	−0.662210	+	1.14698i
$447$	−36.2908	+	0.809072i	−1.71650	+	0.0382678i
$448$	1.15681	−	2.37945i	0.0546539	−	0.112419i
$449$			1.81833i			0.0858125i	0.999079	+	0.0429062i	$0.0136617\pi$
$449$			1.81833i			0.0858125i	−0.999079	+	0.0429062i	$0.986338\pi$
$450$	−23.4692	−	12.1890i	−1.10635	−	0.574597i
$451$	−12.6476	+	7.30207i	−0.595550	+	0.343841i
$452$	10.2092	−	5.89426i	0.480198	−	0.277243i
$453$	22.5807	+	12.3743i	1.06094	+	0.581395i
$454$			20.4145i			0.958101i
$455$	−8.14574	+	5.50941i	−0.381878	+	0.258285i
$456$	0.174334	+	7.81971i	0.00816392	+	0.366191i
$457$	−8.03000	+	13.9084i	−0.375628	+	0.650606i	−0.990421	−	0.138082i	$-0.955906\pi$
$457$	−8.03000	+	13.9084i	−0.375628	+	0.650606i	0.614793	+	0.788688i	$0.289239\pi$
$458$	−4.82648	−	8.35971i	−0.225527	−	0.390624i
$459$	17.9648	−	12.0407i	0.838525	−	0.562010i
$460$	2.81221	+	1.62363i	0.131120	+	0.0757021i
$461$	6.62737			0.308668			0.154334	−	0.988019i	$-0.450677\pi$
$461$	6.62737			0.308668			0.154334	+	0.988019i	$0.450677\pi$
$462$	−0.521413	−	5.56807i	−0.0242584	−	0.259050i
$463$	2.28593			0.106236			0.0531181	−	0.998588i	$-0.483084\pi$
$463$	2.28593			0.106236			0.0531181	+	0.998588i	$0.483084\pi$
$464$	3.80288	+	2.19559i	0.176544	+	0.101928i
$465$	−9.63051	−	15.8536i	−0.446604	−	0.735195i
$466$	8.47134	+	14.6728i	0.392427	+	0.679704i
$467$	3.00097	−	5.19783i	0.138868	−	0.240527i	−0.788200	−	0.615419i	$-0.788987\pi$
$467$	3.00097	−	5.19783i	0.138868	−	0.240527i	0.927068	+	0.374892i	$0.122320\pi$
$468$	−0.133698	−	2.99702i	−0.00618021	−	0.138537i
$469$	38.4394	−	2.73691i	1.77496	−	0.126379i
$470$			30.1729i			1.39177i
$471$	1.16509	−	2.12607i	0.0536846	−	0.0979642i
$472$	5.14927	−	2.97293i	0.237014	−	0.136840i
$473$	−12.6764	+	7.31875i	−0.582864	+	0.336516i
$474$	2.16294	−	3.94695i	0.0993471	−	0.181290i
$475$		−	39.8082i		−	1.82652i
$476$	−6.16925	−	9.12133i	−0.282767	−	0.418076i
$477$	1.23284	+	27.6356i	0.0564477	+	1.26535i
$478$	7.99570	−	13.8490i	0.365715	−	0.633437i
$479$	7.60960	+	13.1802i	0.347692	+	0.602220i	0.985839	−	0.167695i	$-0.0536323\pi$
$479$	7.60960	+	13.1802i	0.347692	+	0.602220i	−0.638147	+	0.769914i	$0.720299\pi$
$480$	−3.34238	−	5.50220i	−0.152558	−	0.251140i
$481$	0.946403	+	0.546406i	0.0431523	+	0.0249140i
$482$	−25.2682			−1.15094
$483$	1.66980	−	3.63873i	0.0759785	−	0.165568i
$484$	−9.51070			−0.432305
$485$	−36.7884	−	21.2398i	−1.67047	−	0.964449i
$486$	−9.24736	−	12.5494i	−0.419469	−	0.569250i
$487$	−7.18047	−	12.4369i	−0.325378	−	0.563571i	0.656211	−	0.754578i	$-0.272158\pi$
$487$	−7.18047	−	12.4369i	−0.325378	−	0.563571i	−0.981589	+	0.191006i	$0.938825\pi$
$488$	−3.67066	+	6.35777i	−0.166163	+	0.287803i
$489$	−0.307426	−	13.7896i	−0.0139023	−	0.623585i
$490$	24.1483	+	9.68540i	1.09091	+	0.437542i
$491$		−	16.2770i		−	0.734573i	−0.930108	−	0.367286i	$-0.880287\pi$
$491$		−	16.2770i		−	0.734573i	0.930108	−	0.367286i	$-0.119713\pi$
$492$	18.1770	+	9.96106i	0.819484	+	0.449079i
$493$	15.8278	−	9.13816i	0.712846	−	0.411562i
$494$	3.91082	−	2.25792i	0.175956	−	0.101588i
$495$	−12.0763	−	6.27199i	−0.542790	−	0.281905i
$496$		−	2.88133i		−	0.129375i
$497$	−4.58011	−	2.22669i	−0.205446	−	0.0998805i
$498$	13.9413	−	0.310809i	0.624724	−	0.0139277i
$499$	−10.9013	+	18.8817i	−0.488011	+	0.845260i	−0.999905	−	0.0137889i	$-0.995611\pi$
$499$	−10.9013	+	18.8817i	−0.488011	+	0.845260i	0.511894	+	0.859049i	$0.328944\pi$
$500$	7.09042	+	12.2810i	0.317093	+	0.549222i
$501$	3.57759	−	2.17326i	0.159835	−	0.0970940i
$502$	−8.38377	−	4.84037i	−0.374186	−	0.216036i
$503$	28.6550			1.27766			0.638831	−	0.769347i	$-0.279418\pi$
$503$	28.6550			1.27766			0.638831	+	0.769347i	$0.279418\pi$
$504$	−6.36994	+	4.73538i	−0.283740	+	0.210931i
$505$	7.12815			0.317199
$506$	0.923335	+	0.533088i	0.0410472	+	0.0236986i
$507$	−1.48032	+	0.899243i	−0.0657435	+	0.0399368i
$508$	1.09405	+	1.89494i	0.0485405	+	0.0840746i
$509$	−2.87948	+	4.98741i	−0.127631	+	0.221063i	−0.922758	−	0.385379i	$-0.874071\pi$
$509$	−2.87948	+	4.98741i	−0.127631	+	0.221063i	0.795127	+	0.606442i	$0.207404\pi$
$510$	−26.7879	+	0.597214i	−1.18619	+	0.0264451i
$511$	−0.412169	−	5.78884i	−0.0182333	−	0.256083i
$512$		−	1.00000i		−	0.0441942i
$513$	10.3484	−	21.0598i	0.456891	−	0.929813i
$514$	−22.9856	+	13.2707i	−1.01385	+	0.585347i
$515$	4.39045	−	2.53483i	0.193466	−	0.111698i
$516$	18.2185	+	9.98381i	0.802027	+	0.439513i
$517$			9.90669i			0.435696i
$518$	−0.205343	−	2.88401i	−0.00902227	−	0.126716i
$519$	−0.151909	−	6.81387i	−0.00666808	−	0.299096i
$520$	−1.85844	+	3.21892i	−0.0814981	+	0.141159i
$521$	18.5831	+	32.1868i	0.814140	+	1.41013i	0.909944	+	0.414731i	$0.136124\pi$
$521$	18.5831	+	32.1868i	0.814140	+	1.41013i	−0.0958044	+	0.995400i	$0.530542\pi$
$522$	−7.08867	−	11.1038i	−0.310263	−	0.485998i
$523$	−36.1899	−	20.8942i	−1.58247	−	0.913642i	−0.994497	−	0.104764i	$-0.966591\pi$
$523$	−36.1899	−	20.8942i	−1.58247	−	0.913642i	−0.587976	−	0.808878i	$-0.700075\pi$
$524$	3.76712			0.164567
$525$	32.9488	−	23.3721i	1.43801	−	1.02004i
$526$	−5.47549			−0.238743
$527$	−10.3856	−	5.99611i	−0.452402	−	0.261195i
$528$	−1.09741	−	1.80654i	−0.0477585	−	0.0786196i
$529$	−11.1184	−	19.2576i	−0.483407	−	0.837286i
$530$	17.1368	−	29.6817i	0.744373	−	1.28929i
$531$	−17.8199	+	0.794952i	−0.773316	+	0.0344980i
$532$	−10.7452	−	5.22394i	−0.465864	−	0.226486i
$533$		−	11.9670i		−	0.518348i
$534$	1.68975	−	3.08347i	0.0731226	−	0.133435i
$535$	55.9148	−	32.2825i	2.41741	−	1.39569i
$536$	12.6141	−	7.28275i	0.544845	−	0.314567i
$537$	17.4437	−	31.8314i	0.752750	−	1.37363i
$538$			24.5174i			1.05702i
$539$	7.92863	+	3.18001i	0.341510	+	0.136973i
$540$	1.29056	+	19.2703i	0.0555368	+	0.829264i
$541$	10.1507	−	17.5815i	0.436411	−	0.755886i	−0.560999	−	0.827817i	$-0.689583\pi$
$541$	10.1507	−	17.5815i	0.436411	−	0.755886i	0.997410	+	0.0719309i	$0.0229161\pi$
$542$	−4.65207	−	8.05762i	−0.199823	−	0.346104i
$543$	−1.45992	−	2.40331i	−0.0626513	−	0.103136i
$544$	−3.60444	−	2.08102i	−0.154539	−	0.0892231i
$545$	−60.9995			−2.61293
$546$	4.16497	+	1.91129i	0.178244	+	0.0817957i
$547$	9.62175			0.411396			0.205698	−	0.978615i	$-0.434053\pi$
$547$	9.62175			0.411396			0.205698	+	0.978615i	$0.434053\pi$
$548$	−13.4830	−	7.78442i	−0.575966	−	0.332534i
$549$	18.5636	−	11.8511i	0.792275	−	0.505791i
$550$	5.37892	+	9.31657i	0.229358	+	0.397260i
$551$	9.91493	−	17.1732i	0.422390	−	0.731601i
$552$	−0.0337273	−	1.51283i	−0.00143553	−	0.0643904i
$553$	3.85168	+	5.69476i	0.163790	+	0.242166i
$554$		−	24.0271i		−	1.02081i
$555$	−6.16968	−	3.38100i	−0.261888	−	0.143515i
$556$	−7.34841	+	4.24261i	−0.311642	+	0.179927i
$557$	10.2285	−	5.90542i	0.433395	−	0.250221i	−0.267397	−	0.963586i	$-0.586163\pi$
$557$	10.2285	−	5.90542i	0.433395	−	0.250221i	0.700792	+	0.713366i	$0.252830\pi$
$558$	−3.98408	+	7.67109i	−0.168660	+	0.324743i
$559$		−	11.9943i		−	0.507306i
$560$	9.80913	−	0.698417i	0.414511	−	0.0295135i
$561$	−8.79530	+	0.196084i	−0.371338	+	0.00827866i
$562$	7.52158	−	13.0278i	0.317279	−	0.549543i
$563$	−5.78437	−	10.0188i	−0.243782	−	0.422243i	0.718007	−	0.696036i	$-0.245055\pi$
$563$	−5.78437	−	10.0188i	−0.243782	−	0.422243i	−0.961788	+	0.273794i	$0.911721\pi$
$564$	12.0170	−	7.29986i	0.506005	−	0.307380i
$565$	37.9463	+	21.9083i	1.59641	+	0.921689i
$566$	3.13291			0.131686
$567$	23.5067	−	3.79935i	0.987189	−	0.159558i
$568$	−1.92486			−0.0807652
$569$	1.02111	+	0.589538i	0.0428071	+	0.0247147i	0.521251	−	0.853404i	$-0.325466\pi$
$569$	1.02111	+	0.589538i	0.0428071	+	0.0247147i	−0.478444	+	0.878118i	$0.658799\pi$
$570$	−24.8470	+	15.0936i	−1.04073	+	0.632203i
$571$	−12.2843	−	21.2771i	−0.514083	−	0.890417i	−0.999867	−	0.0163383i	$-0.994799\pi$
$571$	−12.2843	−	21.2771i	−0.514083	−	0.890417i	0.485784	−	0.874079i	$-0.338534\pi$
$572$	−0.610184	+	1.05687i	−0.0255131	+	0.0441899i
$573$	32.6175	−	0.727179i	1.36261	−	0.0303783i
$574$	−26.2263	+	17.7383i	−1.09466	+	0.740380i
$575$			7.70145i			0.321172i
$576$	−1.38272	+	2.66234i	−0.0576135	+	0.110931i
$577$	−6.46528	+	3.73273i	−0.269153	+	0.155396i	−0.628503	−	0.777807i	$-0.716332\pi$
$577$	−6.46528	+	3.73273i	−0.269153	+	0.155396i	0.359350	+	0.933203i	$0.382999\pi$
$578$	−0.279411	+	0.161318i	−0.0116219	+	0.00670993i
$579$	−34.4090	−	18.8562i	−1.42999	−	0.783638i
$580$			16.3215i			0.677715i
$581$	−9.31345	+	19.1570i	−0.386387	+	0.794767i
$582$	0.441209	+	19.7903i	0.0182887	+	0.820336i
$583$	5.62652	−	9.74543i	0.233027	−	0.403614i
$584$	−1.09676	−	1.89964i	−0.0453841	−	0.0786076i
$585$	9.39869	−	6.00015i	0.388588	−	0.248076i
$586$	−22.4252	−	12.9472i	−0.926377	−	0.534844i
$587$	−24.0213			−0.991467			−0.495734	−	0.868475i	$-0.665101\pi$
$587$	−24.0213			−0.991467			−0.495734	+	0.868475i	$0.665101\pi$
$588$	−1.98490	−	11.9608i	−0.0818559	−	0.493254i
$589$	−13.0116			−0.536133
$590$	19.1392	+	11.0500i	0.787950	+	0.454923i
$591$	−10.1829	−	16.7631i	−0.418871	−	0.689540i
$592$	−0.546406	−	0.946403i	−0.0224572	−	0.0388969i
$593$	7.53575	−	13.0523i	0.309456	−	0.535994i	−0.668787	−	0.743454i	$-0.733186\pi$
$593$	7.53575	−	13.0523i	0.309456	−	0.535994i	0.978244	+	0.207460i	$0.0665196\pi$
$594$	0.423730	+	6.32705i	0.0173858	+	0.259602i
$595$	17.8956	−	36.8098i	0.733649	−	1.50906i
$596$		−	20.9577i		−	0.858461i
$597$	13.5527	−	24.7310i	0.554674	−	1.01217i
$598$	−0.756604	+	0.436825i	−0.0309398	+	0.0178631i
$599$	21.7668	−	12.5670i	0.889365	−	0.513475i	0.0156306	−	0.999878i	$-0.495024\pi$
$599$	21.7668	−	12.5670i	0.889365	−	0.513475i	0.873735	+	0.486402i	$0.161691\pi$
$600$	7.33761	−	13.3897i	0.299557	−	0.546634i
$601$			11.0050i			0.448905i	0.974485	+	0.224453i	$0.0720594\pi$
$601$			11.0050i			0.448905i	−0.974485	+	0.224453i	$0.927941\pi$
$602$	−26.2862	+	17.7788i	−1.07134	+	0.724609i
$603$	−43.6531	+	1.94738i	−1.77769	+	0.0793036i
$604$	−7.43311	+	12.8745i	−0.302449	+	0.523857i
$605$	−17.6751	−	30.6142i	−0.718595	−	1.24464i
$606$	−1.72455	−	2.83893i	−0.0700549	−	0.115324i
$607$	−14.9747	−	8.64566i	−0.607805	−	0.350917i	0.164301	−	0.986410i	$-0.447463\pi$
$607$	−14.9747	−	8.64566i	−0.607805	−	0.350917i	−0.772106	+	0.635494i	$0.780797\pi$
$608$	−4.51583			−0.183141
$609$	20.0353	−	1.87617i	0.811871	−	0.0760264i
$610$	−27.2868			−1.10481
$611$	−7.03021	−	4.05889i	−0.284412	−	0.164205i
$612$	6.71878	+	10.5243i	0.271590	+	0.425421i
$613$	4.91200	+	8.50784i	0.198394	+	0.343628i	0.948008	−	0.318247i	$-0.103094\pi$
$613$	4.91200	+	8.50784i	0.198394	+	0.343628i	−0.749614	+	0.661875i	$0.769761\pi$
$614$	11.7766	−	20.3977i	0.475266	−	0.823185i
$615$	1.71715	+	77.0224i	0.0692421	+	3.10584i
$616$	3.22064	−	0.229312i	0.129763	−	0.00923923i
$617$			27.6373i			1.11264i	0.830969	+	0.556318i	$0.187786\pi$
$617$			27.6373i			1.11264i	−0.830969	+	0.556318i	$0.812214\pi$
$618$	−2.07175	−	1.13532i	−0.0833378	−	0.0456693i
$619$	27.2711	−	15.7450i	1.09612	−	0.632844i	0.160919	−	0.986968i	$-0.448554\pi$
$619$	27.2711	−	15.7450i	1.09612	−	0.632844i	0.935199	+	0.354124i	$0.115221\pi$
$620$	9.27476	−	5.35478i	0.372483	−	0.215053i
$621$	−2.00203	+	4.07431i	−0.0803388	+	0.163497i
$622$		−	20.7426i		−	0.831704i
$623$	3.00904	+	4.44891i	0.120555	+	0.178242i
$624$	1.73162	−	0.0386050i	0.0693203	−	0.00154544i
$625$	−4.31617	+	7.47582i	−0.172647	+	0.299033i
$626$	2.65819	+	4.60413i	0.106243	+	0.184018i
$627$	−8.15803	+	4.95571i	−0.325800	+	0.197912i
$628$	1.21219	+	0.699858i	0.0483716	+	0.0279274i
$629$	−4.54834			−0.181354
$630$	−27.0810	−	11.7039i	−1.07893	−	0.466294i
$631$	21.7241			0.864824			0.432412	−	0.901676i	$-0.357663\pi$
$631$	21.7241			0.864824			0.432412	+	0.901676i	$0.357663\pi$
$632$	2.25038	+	1.29925i	0.0895151	+	0.0516816i
$633$	5.16124	−	3.13526i	0.205141	−	0.124615i
$634$	7.33636	+	12.7070i	0.291364	+	0.504658i
$635$	−4.06645	+	7.04329i	−0.161372	+	0.279505i
$636$	−15.9673	+	0.355978i	−0.633146	+	0.0141154i
$637$	−5.50513	+	4.32360i	−0.218121	+	0.171307i
$638$			5.35886i			0.212159i
$639$	5.12463	+	2.66154i	0.202727	+	0.105289i
$640$	3.21892	−	1.85844i	0.127239	−	0.0734614i
$641$	−12.9010	+	7.44842i	−0.509561	+	0.294195i	−0.732653	−	0.680602i	$-0.761718\pi$
$641$	−12.9010	+	7.44842i	−0.509561	+	0.294195i	0.223092	+	0.974797i	$0.428385\pi$
$642$	−26.3849	−	14.4590i	−1.04133	−	0.570650i
$643$		−	18.3968i		−	0.725500i	−0.931886	−	0.362750i	$-0.881838\pi$
$643$		−	18.3968i		−	0.725500i	0.931886	−	0.362750i	$-0.118162\pi$
$644$	2.07881	+	1.01064i	0.0819166	+	0.0398250i
$645$	1.72107	+	77.1984i	0.0677671	+	3.03968i
$646$	−9.39755	+	16.2770i	−0.369742	+	0.640411i
$647$	7.08659	+	12.2743i	0.278603	+	0.482554i	0.971038	−	0.238926i	$-0.0767954\pi$
$647$	7.08659	+	12.2743i	0.278603	+	0.482554i	−0.692435	+	0.721480i	$0.743462\pi$
$648$	7.36257	−	5.17615i	0.289229	−	0.203338i
$649$	6.28400	+	3.62807i	0.246669	+	0.142414i
$650$	−8.81525			−0.345762
$651$	−7.63934	−	10.7696i	−0.299409	−	0.422093i
$652$	7.96338			0.311870
$653$	−14.7767	−	8.53130i	−0.578255	−	0.333856i	0.182185	−	0.983264i	$-0.441683\pi$
$653$	−14.7767	−	8.53130i	−0.578255	−	0.333856i	−0.760440	+	0.649409i	$0.775017\pi$
$654$	14.7579	+	24.2943i	0.577079	+	0.949982i
$655$	7.00098	+	12.1260i	0.273551	+	0.473804i
$656$	−5.98350	+	10.3637i	−0.233616	+	0.404635i
$657$	0.293269	+	6.57400i	0.0114415	+	0.256476i
$658$	1.52536	+	21.4234i	0.0594648	+	0.835171i
$659$			9.30977i			0.362657i	0.983423	+	0.181329i	$0.0580398\pi$
$659$			9.30977i			0.362657i	−0.983423	+	0.181329i	$0.941960\pi$
$660$	3.77564	−	6.88982i	0.146967	−	0.268186i
$661$	4.15509	−	2.39894i	0.161614	−	0.0933080i	−0.417012	−	0.908901i	$-0.636923\pi$
$661$	4.15509	−	2.39894i	0.161614	−	0.0933080i	0.578626	+	0.815593i	$0.303589\pi$
$662$	−0.423503	+	0.244509i	−0.0164599	+	0.00950313i
$663$	3.46439	−	6.32186i	0.134546	−	0.245521i
$664$			8.05101i			0.312440i
$665$	−3.15393	−	44.2963i	−0.122304	−	1.71774i
$666$	0.146107	+	3.27518i	0.00566154	+	0.126911i
$667$	−1.91818	+	3.32239i	−0.0742723	+	0.128643i
$668$	1.20838	+	2.09298i	0.0467537	+	0.0809798i
$669$	25.1519	+	41.4048i	0.972428	+	1.60080i
$670$	46.8851	+	27.0691i	1.81133	+	1.04577i
$671$	−8.95911			−0.345863
$672$	−2.65132	−	3.73771i	−0.102277	−	0.144185i
$673$	−37.9174			−1.46161			−0.730804	−	0.682587i	$-0.760855\pi$
$673$	−37.9174			−1.46161			−0.730804	+	0.682587i	$0.760855\pi$
$674$	7.97489	+	4.60430i	0.307181	+	0.177351i
$675$	−38.0496	+	25.5022i	−1.46453	+	0.981581i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−12.8874	+	22.3216i	−0.495302	+	0.857889i	−0.999985	−	0.00541581i	$-0.998276\pi$
$677$	−12.8874	+	22.3216i	−0.495302	+	0.857889i	0.504683	+	0.863305i	$0.331609\pi$
$678$	−0.455096	−	20.4132i	−0.0174778	−	0.783966i
$679$	−27.1943	−	13.2209i	−1.04362	−	0.507372i
$680$		−	15.4699i		−	0.593242i
$681$	31.0082	+	16.9926i	1.18824	+	0.651158i
$682$	3.04519	−	1.75814i	0.116606	−	0.0673227i
$683$	−31.1560	+	17.9879i	−1.19215	+	0.688288i	−0.958794	−	0.284103i	$-0.908304\pi$
$683$	−31.1560	+	17.9879i	−1.19215	+	0.688288i	−0.233356	+	0.972391i	$0.574971\pi$
$684$	12.0227	+	6.24415i	0.459699	+	0.238751i
$685$		−	57.8676i		−	2.21101i
$686$	17.6354	+	5.65605i	0.673325	+	0.215949i
$687$	−16.7153	+	0.372652i	−0.637727	+	0.0142176i
$688$	−5.99717	+	10.3874i	−0.228640	+	0.396016i
$689$	4.61051	+	7.98565i	0.175647	+	0.304229i
$690$	4.80700	−	2.92008i	0.182999	−	0.111165i
$691$	−39.1484	−	22.6024i	−1.48928	−	0.859834i	−0.489352	−	0.872086i	$-0.662767\pi$
$691$	−39.1484	−	22.6024i	−1.48928	−	0.859834i	−0.999925	+	0.0122518i	$0.996100\pi$
$692$	3.93497			0.149585
$693$	−8.89152	−	3.84274i	−0.337761	−	0.145974i
$694$	−7.74782			−0.294103
$695$	−27.3132	−	15.7693i	−1.03605	−	0.598164i
$696$	6.50038	−	3.94874i	0.246396	−	0.149677i
$697$	24.9036	+	43.1343i	0.943291	+	1.63383i
$698$	14.4351	−	25.0023i	0.546377	−	0.946352i
$699$	29.3383	−	0.654072i	1.10968	−	0.0247393i
$700$	13.0665	+	19.3191i	0.493868	+	0.730192i
$701$		−	33.5055i		−	1.26549i	−0.774362	−	0.632743i	$-0.781929\pi$
$701$		−	33.5055i		−	1.26549i	0.774362	−	0.632743i	$-0.218071\pi$
$702$	−4.66355	−	2.29157i	−0.176014	−	0.0864898i
$703$	−4.27380	+	2.46748i	−0.161189	+	0.0930627i
$704$	1.05687	−	0.610184i	0.0398323	−	0.0229972i
$705$	45.8305	+	25.1152i	1.72608	+	0.945894i
$706$			18.5902i			0.699651i
$707$	5.06114	−	0.360357i	0.190344	−	0.0135526i
$708$	−0.229540	−	10.2960i	−0.00862664	−	0.386946i
$709$	8.15654	−	14.1275i	0.306325	−	0.530571i	−0.671230	−	0.741249i	$-0.734234\pi$
$709$	8.15654	−	14.1275i	0.306325	−	0.530571i	0.977556	+	0.210678i	$0.0675672\pi$
$710$	−3.57724	−	6.19596i	−0.134251	−	0.232530i
$711$	−4.19476	−	6.57071i	−0.157316	−	0.246421i
$712$	1.75806	+	1.01501i	0.0658860	+	0.0380393i
$713$	2.51727			0.0942726
$714$	−18.9898	+	1.77827i	−0.710676	+	0.0665502i
$715$	−4.53597			−0.169636
$716$	18.1488	+	10.4782i	0.678253	+	0.391590i
$717$	−14.3802	−	23.6725i	−0.537037	−	0.884065i
$718$	−12.0240	−	20.8262i	−0.448732	−	0.777227i
$719$	24.2122	−	41.9367i	0.902962	−	1.56398i	0.0793322	−	0.996848i	$-0.474721\pi$
$719$	24.2122	−	41.9367i	0.902962	−	1.56398i	0.823630	−	0.567128i	$-0.191945\pi$
$720$	−11.1396	+	0.496942i	−0.415148	+	0.0185199i
$721$	2.98917	−	2.02174i	0.111322	−	0.0752934i
$722$			1.39273i			0.0518319i
$723$	−21.0327	+	38.3806i	−0.782214	+	1.42739i
$724$	1.40599	−	0.811751i	0.0522534	−	0.0301685i
$725$	−33.5233	+	19.3547i	−1.24502	+	0.718815i
$726$	−7.91649	+	14.4461i	−0.293809	+	0.536145i
$727$			20.2355i			0.750492i	0.926925	+	0.375246i	$0.122442\pi$
$727$			20.2355i			0.750492i	−0.926925	+	0.375246i	$0.877558\pi$
$728$	−1.15681	+	2.37945i	−0.0428741	+	0.0881884i
$729$	−26.7589	+	3.60030i	−0.991070	+	0.133344i
$730$	4.07652	−	7.06074i	0.150879	−	0.261330i
$731$	24.9605	+	43.2328i	0.923197	+	1.59902i
$732$	6.60163	+	10.8675i	0.244003	+	0.401676i
$733$	−29.6215	−	17.1020i	−1.09409	−	0.631675i	−0.159430	−	0.987209i	$-0.550966\pi$
$733$	−29.6215	−	17.1020i	−1.09409	−	0.631675i	−0.934663	+	0.355534i	$0.884299\pi$
$734$	3.94511			0.145617
$735$	34.8119	−	28.6177i	1.28406	−	1.05558i
$736$	0.873651			0.0322032
$737$	15.3938	+	8.88763i	0.567039	+	0.327380i
$738$	30.2603	−	19.3183i	1.11390	−	0.711115i
$739$	14.9143	+	25.8324i	0.548632	+	0.950259i	0.998369	+	0.0570974i	$0.0181845\pi$
$739$	14.9143	+	25.8324i	0.548632	+	0.950259i	−0.449737	+	0.893161i	$0.648482\pi$
$740$	2.03093	−	3.51767i	0.0746585	−	0.129312i
$741$	−0.174334	−	7.81971i	−0.00640431	−	0.287264i
$742$	10.6669	−	21.9410i	0.391596	−	0.805480i
$743$			13.3917i			0.491295i	0.969359	+	0.245647i	$0.0790005\pi$
$743$			13.3917i			0.491295i	−0.969359	+	0.245647i	$0.920999\pi$
$744$	−4.37654	−	2.39835i	−0.160452	−	0.0879279i
$745$	67.4612	−	38.9487i	2.47159	−	1.42697i
$746$	−17.8760	+	10.3207i	−0.654485	+	0.377867i
$747$	11.1323	−	21.4346i	0.407310	−	0.784249i
$748$		−	5.07923i		−	0.185715i
$749$	38.0687	−	25.7480i	1.39100	−	0.940810i
$750$	24.5558	−	0.547451i	0.896652	−	0.0199901i
$751$	2.29843	−	3.98099i	0.0838708	−	0.145268i	−0.821039	−	0.570873i	$-0.806605\pi$
$751$	2.29843	−	3.98099i	0.0838708	−	0.145268i	0.904909	+	0.425604i	$0.139938\pi$
$752$	4.05889	+	7.03021i	0.148013	+	0.256365i
$753$	−14.3306	+	8.70534i	−0.522238	+	0.317240i
$754$	−3.80288	−	2.19559i	−0.138493	−	0.0799588i
$755$	−55.2560			−2.01097
$756$	1.89052	+	13.6171i	0.0687575	+	0.495250i
$757$	−6.86874			−0.249649			−0.124824	−	0.992179i	$-0.539837\pi$
$757$	−6.86874			−0.249649			−0.124824	+	0.992179i	$0.539837\pi$
$758$	9.70175	+	5.60131i	0.352383	+	0.203449i
$759$	1.57829	−	0.958751i	0.0572881	−	0.0348004i
$760$	−8.39242	−	14.5361i	−0.304425	−	0.527279i
$761$	3.11852	−	5.40143i	0.113046	−	0.195802i	−0.803951	−	0.594696i	$-0.797273\pi$
$761$	3.11852	−	5.40143i	0.113046	−	0.195802i	0.916997	+	0.398894i	$0.130606\pi$
$762$	3.78895	−	0.0844713i	0.137259	−	0.00306007i
$763$	−43.3110	+	3.08377i	−1.56796	+	0.111640i
$764$			18.8364i			0.681477i
$765$	−21.3905	+	41.1861i	−0.773376	+	1.48909i
$766$	30.1330	−	17.3973i	1.08875	−	0.628590i
$767$	−5.14927	+	2.97293i	−0.185929	+	0.107346i
$768$	−1.51893	−	0.832377i	−0.0548097	−	0.0300358i
$769$			1.91906i			0.0692031i	0.999401	+	0.0346015i	$0.0110162\pi$
$769$			1.91906i			0.0692031i	−0.999401	+	0.0346015i	$0.988984\pi$
$770$	6.72351	+	9.94080i	0.242298	+	0.358242i
$771$	1.02463	+	45.9597i	0.0369012	+	1.65520i
$772$	11.3267	−	19.6185i	0.407658	−	0.706084i
$773$	−16.6221	−	28.7903i	−0.597855	−	1.03552i	−0.993137	−	0.116956i	$-0.962686\pi$
$773$	−16.6221	−	28.7903i	−0.597855	−	1.03552i	0.395282	−	0.918560i	$-0.370647\pi$
$774$	30.3294	−	19.3624i	1.09017	−	0.695967i
$775$	21.9967	+	12.6998i	0.790145	+	0.456191i
$776$	−11.4288			−0.410270
$777$	−4.55153	−	2.08868i	−0.163285	−	0.0749310i
$778$	7.71353			0.276543
$779$	46.8008	+	27.0205i	1.67681	+	0.968108i
$780$	3.34238	+	5.50220i	0.119677	+	0.197010i
$781$	−1.17452	−	2.03432i	−0.0420275	−	0.0727938i
$782$	1.81809	−	3.14902i	0.0650147	−	0.112609i
$783$	−22.7663	+	1.52468i	−0.813600	+	0.0544878i
$784$	6.92938	−	0.991782i	0.247478	−	0.0354208i
$785$			5.20259i			0.185688i
$786$	3.13566	−	5.72199i	0.111845	−	0.204097i
$787$	−2.86012	+	1.65129i	−0.101952	+	0.0588622i	−0.550109	−	0.835093i	$-0.685414\pi$
$787$	−2.86012	+	1.65129i	−0.101952	+	0.0588622i	0.448157	+	0.893955i	$0.352081\pi$
$788$	9.80679	−	5.66196i	0.349353	−	0.201699i
$789$	−4.55767	+	8.31688i	−0.162257	+	0.296089i
$790$			9.65837i			0.343629i
$791$	28.0502	+	13.6370i	0.997352	+	0.484877i
$792$	−3.65747	+	0.163161i	−0.129962	+	0.00579768i
$793$	3.67066	−	6.35777i	0.130349	−	0.225771i
$794$	−10.1129	−	17.5161i	−0.358894	−	0.621623i
$795$	−30.8202	−	50.7359i	−1.09308	−	1.79942i
$796$	14.1005	+	8.14094i	0.499780	+	0.288548i
$797$	−49.5495			−1.75513			−0.877566	−	0.479455i	$-0.840834\pi$
$797$	−49.5495			−1.75513			−0.877566	+	0.479455i	$0.840834\pi$
$798$	−16.8789	+	11.9729i	−0.597505	+	0.423837i
$799$	33.7866			1.19528
$800$	7.63423	+	4.40762i	0.269911	+	0.155833i
$801$	−3.27707	−	5.13322i	−0.115789	−	0.181374i
$802$	15.2706	+	26.4495i	0.539224	+	0.933963i
$803$	1.33845	−	2.31826i	0.0472328	−	0.0818096i
$804$	−0.562301	−	25.2219i	−0.0198308	−	0.889508i
$805$	0.610172	+	8.56975i	0.0215057	+	0.302044i
$806$			2.88133i			0.101490i
$807$	37.2402	+	20.4077i	1.31092	+	0.718386i
$808$	1.66084	−	0.958887i	0.0584282	−	0.0337335i
$809$	4.52101	−	2.61021i	0.158950	−	0.0917700i	−0.418415	−	0.908256i	$-0.637414\pi$
$809$	4.52101	−	2.61021i	0.158950	−	0.0917700i	0.577365	+	0.816486i	$0.304081\pi$
$810$	30.3445	+	14.0799i	1.06620	+	0.494718i
$811$			25.8302i			0.907021i	0.891251	+	0.453511i	$0.149829\pi$
$811$			25.8302i			0.907021i	−0.891251	+	0.453511i	$0.850171\pi$
$812$	0.825120	+	11.5886i	0.0289560	+	0.406682i
$813$	−16.1112	+	0.359186i	−0.565046	+	0.0125972i
$814$	0.666816	−	1.15496i	0.0233719	−	0.0404813i
$815$	14.7995	+	25.6335i	0.518404	+	0.897902i
$816$	−6.16118	+	3.74269i	−0.215685	+	0.131020i
$817$	46.9077	+	27.0822i	1.64109	+	0.947486i
$818$	−16.7242			−0.584747
$819$	6.36994	−	4.73538i	0.222584	−	0.165468i
$820$	−44.4800			−1.55331
$821$	−3.79440	−	2.19070i	−0.132425	−	0.0764558i	0.432324	−	0.901718i	$-0.357694\pi$
$821$	−3.79440	−	2.19070i	−0.132425	−	0.0764558i	−0.564749	+	0.825263i	$0.691027\pi$
$822$	−23.0469	+	14.0002i	−0.803854	+	0.488312i
$823$	10.7993	+	18.7050i	0.376441	+	0.652015i	0.990542	−	0.137213i	$-0.0438144\pi$
$823$	10.7993	+	18.7050i	0.376441	+	0.652015i	−0.614101	+	0.789228i	$0.710481\pi$
$824$	0.681975	−	1.18122i	0.0237577	−	0.0411496i
$825$	18.6285	−	0.415307i	0.648561	−	0.0144591i
$826$	14.1479	+	6.87821i	0.492268	+	0.239323i
$827$			54.7748i			1.90471i	0.304995	+	0.952354i	$0.401345\pi$
$827$			54.7748i			1.90471i	−0.304995	+	0.952354i	$0.598655\pi$
$828$	−2.32596	−	1.20802i	−0.0808326	−	0.0419815i
$829$	17.6572	−	10.1944i	0.613259	−	0.354065i	−0.160981	−	0.986958i	$-0.551466\pi$
$829$	17.6572	−	10.1944i	0.613259	−	0.354065i	0.774240	+	0.632892i	$0.218132\pi$
$830$	−25.9155	+	14.9623i	−0.899542	+	0.519351i
$831$	−36.4954	−	19.9996i	−1.26601	−	0.693778i
$832$			1.00000i			0.0346688i
$833$	10.8454	−	27.0405i	0.375771	−	0.936896i
$834$	0.327572	+	14.6932i	0.0113429	+	0.508783i
$835$	−4.49142	+	7.77936i	−0.155432	+	0.269216i
$836$	−2.75549	−	4.77264i	−0.0953005	−	0.165065i
$837$	8.33558	+	12.4368i	0.288120	+	0.429878i
$838$	−5.70945	−	3.29635i	−0.197230	−	0.113871i
$839$	16.3732			0.565265			0.282632	−	0.959228i	$-0.408792\pi$
$839$	16.3732			0.565265			0.282632	+	0.959228i	$0.408792\pi$
$840$	7.10405	−	15.4807i	0.245113	−	0.534136i
$841$	9.71749			0.335086
$842$	−24.9849	−	14.4251i	−0.861037	−	0.497120i
$843$	−13.5275	−	22.2688i	−0.465910	−	0.766977i
$844$	1.74328	+	3.01945i	0.0600061	+	0.103934i
$845$	1.85844	−	3.21892i	0.0639324	−	0.110734i
$846$	−1.08533	−	24.3292i	−0.0373146	−	0.836454i
$847$	−14.0974	−	20.8432i	−0.484392	−	0.716180i
$848$		−	9.22103i		−	0.316651i
$849$	2.60776	−	4.75867i	0.0894982	−	0.163317i
$850$	31.7740	−	18.3447i	1.08984	−	0.629219i
$851$	0.826826	−	0.477368i	0.0283432	−	0.0163640i
$852$	−1.60221	+	2.92372i	−0.0548907	+	0.100165i
$853$		−	30.0915i		−	1.03031i	−0.857096	−	0.515156i	$-0.827734\pi$
$853$		−	30.0915i		−	1.03031i	0.857096	−	0.515156i	$-0.172266\pi$
$854$	−19.3743	+	1.37946i	−0.662973	+	0.0472042i
$855$	2.24410	+	50.3045i	0.0767468	+	1.72038i
$856$	8.68535	−	15.0435i	0.296859	−	0.514175i
$857$	0.237765	+	0.411821i	0.00812190	+	0.0140676i	0.870058	−	0.492950i	$-0.164081\pi$
$857$	0.237765	+	0.411821i	0.00812190	+	0.0140676i	−0.861936	+	0.507017i	$0.830748\pi$
$858$	1.09741	+	1.80654i	0.0374649	+	0.0616743i
$859$	5.37339	+	3.10233i	0.183338	+	0.105850i	0.588860	−	0.808235i	$-0.299577\pi$
$859$	5.37339	+	3.10233i	0.183338	+	0.105850i	−0.405522	+	0.914085i	$0.632910\pi$
$860$	−44.5816			−1.52022
$861$	5.11301	+	54.6008i	0.174251	+	1.86079i
$862$	−9.34843			−0.318409
$863$	−5.70402	−	3.29322i	−0.194167	−	0.112103i	0.399765	−	0.916618i	$-0.369092\pi$
$863$	−5.70402	−	3.29322i	−0.194167	−	0.112103i	−0.593932	+	0.804515i	$0.702425\pi$
$864$	2.89297	+	4.31633i	0.0984207	+	0.146845i
$865$	7.31291	+	12.6663i	0.248646	+	0.430668i
$866$	0.409263	−	0.708865i	0.0139073	−	0.0240882i
$867$	0.0124553	+	0.558682i	0.000423006	+	0.0189738i
$868$	6.31457	−	4.27089i	0.214331	−	0.144963i
$869$			3.17114i			0.107573i
$870$	24.7913	+	13.5857i	0.840503	+	0.460598i
$871$	−12.6141	+	7.28275i	−0.427412	+	0.246766i
$872$	−14.2127	+	8.20573i	−0.481304	+	0.277881i
$873$	30.4274	+	15.8029i	1.02981	+	0.534846i
$874$		−	3.94526i		−	0.133450i
$875$	−16.4045	+	33.7427i	−0.554573	+	1.14071i
$876$	−3.79833	+	0.0846806i	−0.128334	+	0.00286109i
$877$	−7.64676	+	13.2446i	−0.258213	+	0.447237i	−0.965763	−	0.259425i	$-0.916467\pi$
$877$	−7.64676	+	13.2446i	−0.258213	+	0.447237i	0.707551	+	0.706663i	$0.249800\pi$
$878$	−3.68626	−	6.38479i	−0.124405	−	0.215476i
$879$	−38.3321	+	23.2854i	−1.29291	+	0.785396i
$880$	3.92826	+	2.26798i	0.132422	+	0.0764538i
$881$	−0.703966			−0.0237172			−0.0118586	−	0.999930i	$-0.503775\pi$
$881$	−0.703966			−0.0237172			−0.0118586	+	0.999930i	$0.503775\pi$
$882$	−19.8198	−	6.94096i	−0.667366	−	0.233714i
$883$	28.7350			0.967009			0.483505	−	0.875342i	$-0.339364\pi$
$883$	28.7350			0.967009			0.483505	+	0.875342i	$0.339364\pi$
$884$	3.60444	+	2.08102i	0.121230	+	0.0699924i
$885$	32.7153	−	19.8734i	1.09971	−	0.668036i
$886$	3.07440	+	5.32501i	0.103286	+	0.178897i
$887$	0.0613481	−	0.106258i	0.00205987	−	0.00356779i	−0.864994	−	0.501783i	$-0.832678\pi$
$887$	0.0613481	−	0.106258i	0.00205987	−	0.00356779i	0.867053	+	0.498215i	$0.166011\pi$
$888$	−1.89234	+	0.0421880i	−0.0635026	+	0.00141574i
$889$	−2.53120	+	5.20647i	−0.0848937	+	0.174619i
$890$			7.54539i			0.252922i
$891$	9.96304	+	4.62287i	0.333774	+	0.154872i
$892$	−24.2228	+	13.9850i	−0.811039	+	0.468253i
$893$	31.7472	−	18.3293i	1.06238	−	0.613366i
$894$	−31.8333	−	17.4447i	−1.06466	−	0.583439i
$895$			77.8927i			2.60367i
$896$	2.19155	−	1.48226i	0.0732145	−	0.0495190i
$897$	0.0337273	+	1.51283i	0.00112612	+	0.0505120i
$898$	−0.909167	+	1.57472i	−0.0303393	+	0.0525492i
$899$	6.32622	+	10.9573i	0.210991	+	0.365448i
$900$	−14.2304	−	22.2906i	−0.474347	−	0.743021i
$901$	−33.2366	−	19.1892i	−1.10727	−	0.639284i
$902$	−14.6041			−0.486265
$903$	5.12469	+	54.7255i	0.170539	+	1.82115i
$904$	11.7885			0.392080
$905$	5.22592	+	3.01719i	0.173715	+	0.100295i
$906$	13.3683	+	22.0068i	0.444133	+	0.731128i
$907$	−26.8229	−	46.4587i	−0.890641	−	1.54264i	−0.839108	−	0.543964i	$-0.816923\pi$
$907$	−26.8229	−	46.4587i	−0.890641	−	1.54264i	−0.0515328	−	0.998671i	$-0.516411\pi$
$908$	−10.2073	+	17.6795i	−0.338740	+	0.586715i
$909$	−5.74761	+	0.256403i	−0.190636	+	0.00850436i
$910$	−9.80913	+	0.698417i	−0.325169	+	0.0231523i
$911$		−	52.8400i		−	1.75067i	−0.483520	−	0.875333i	$-0.660642\pi$
$911$		−	52.8400i		−	1.75067i	0.483520	−	0.875333i	$-0.339358\pi$
$912$	−3.75888	+	6.85923i	−0.124469	+	0.227132i
$913$	−8.50887	+	4.91260i	−0.281602	+	0.162583i
$914$	−13.9084	+	8.03000i	−0.460048	+	0.265609i
$915$	−22.7130	+	41.4468i	−0.750867	+	1.37019i
$916$		−	9.65296i		−	0.318943i
$917$	5.58387	+	8.25583i	0.184396	+	0.272632i
$918$	21.5783	−	1.44512i	0.712190	−	0.0476962i
$919$	−16.9939	+	29.4343i	−0.560577	+	0.970948i	0.436869	+	0.899525i	$0.356087\pi$
$919$	−16.9939	+	29.4343i	−0.560577	+	0.970948i	−0.997446	+	0.0714232i	$0.977246\pi$
$920$	1.62363	+	2.81221i	0.0535295	+	0.0927158i
$921$	−21.1801	−	34.8665i	−0.697908	−	1.14889i
$922$	5.73947	+	3.31369i	0.189020	+	0.109130i
$923$	1.92486			0.0633574
$924$	2.33248	−	5.08280i	0.0767329	−	0.167212i
$925$	9.63341			0.316745
$926$	1.97967	+	1.14297i	0.0650561	+	0.0375602i
$927$	−3.44895	+	2.20182i	−0.113278	+	0.0723173i
$928$	2.19559	+	3.80288i	0.0720739	+	0.124836i
$929$	−0.222723	+	0.385768i	−0.00730731	+	0.0126566i	−0.869656	−	0.493658i	$-0.835659\pi$
$929$	−0.222723	+	0.385768i	−0.00730731	+	0.0126566i	0.862349	+	0.506315i	$0.168993\pi$
$930$	−0.413443	−	18.5449i	−0.0135573	−	0.608112i
$931$	−4.47872	−	31.2919i	−0.146784	−	1.02555i
$932$			16.9427i			0.554976i
$933$	−31.5066	−	17.2657i	−1.03148	−	0.565254i
$934$	5.19783	−	3.00097i	0.170078	−	0.0981946i
$935$	16.3496	−	9.43946i	0.534690	−	0.308703i
$936$	1.38272	−	2.66234i	0.0451957	−	0.0870214i
$937$			35.9320i			1.17385i	0.809642	+	0.586924i	$0.199661\pi$
$937$			35.9320i			1.17385i	−0.809642	+	0.586924i	$0.800339\pi$
$938$	34.6579	+	16.8494i	1.13162	+	0.550154i
$939$	9.20597	−	0.205239i	0.300425	−	0.00669772i
$940$	−15.0864	+	26.1305i	−0.492066	+	0.852283i
$941$	−17.2501	−	29.8780i	−0.562337	−	0.973996i	−0.997292	−	0.0735441i	$-0.976569\pi$
$941$	−17.2501	−	29.8780i	−0.562337	−	0.973996i	0.434955	−	0.900452i	$-0.356764\pi$
$942$	2.07203	−	1.25869i	0.0675105	−	0.0410102i
$943$	−9.05427	−	5.22749i	−0.294848	−	0.170230i
$944$	5.94586			0.193521
$945$	−40.3190	+	31.3921i	−1.31158	+	1.02118i
$946$	−14.6375			−0.475906
$947$	−29.2395	−	16.8815i	−0.950158	−	0.548574i	−0.0570278	−	0.998373i	$-0.518162\pi$
$947$	−29.2395	−	16.8815i	−0.950158	−	0.548574i	−0.893130	+	0.449799i	$0.851496\pi$
$948$	3.84664	−	2.33669i	0.124933	−	0.0758922i
$949$	1.09676	+	1.89964i	0.0356022	+	0.0616649i
$950$	19.9041	−	34.4749i	0.645774	−	1.11851i
$951$	25.4076	−	0.566440i	0.823898	−	0.0183681i
$952$	−0.782064	−	10.9839i	−0.0253468	−	0.355991i
$953$			45.1427i			1.46232i	0.682208	+	0.731158i	$0.261020\pi$
$953$			45.1427i			1.46232i	−0.682208	+	0.731158i	$0.738980\pi$
$954$	−12.7501	+	24.5496i	−0.412801	+	0.794821i
$955$	−60.6328	+	35.0064i	−1.96203	+	1.13278i
$956$	13.8490	−	7.99570i	0.447907	−	0.258599i
$957$	8.13974	+	4.46060i	0.263120	+	0.144191i
$958$			15.2192i			0.491710i
$959$	−2.92544	−	41.0873i	−0.0944675	−	1.32678i
$960$	−0.143490	−	6.43624i	−0.00463113	−	0.207729i
$961$	−11.3490	+	19.6570i	−0.366096	+	0.634097i
$962$	0.546406	+	0.946403i	0.0176168	+	0.0305133i
$963$	−43.9243	+	28.0414i	−1.41544	+	0.903623i
$964$	−21.8829	−	12.6341i	−0.704801	−	0.406917i
$965$	84.2003			2.71051
$966$	3.26545	−	2.31633i	0.105064	−	0.0745267i
$967$	−19.3858			−0.623406			−0.311703	−	0.950180i	$-0.600899\pi$
$967$	−19.3858			−0.623406			−0.311703	+	0.950180i	$0.600899\pi$
$968$	−8.23651	−	4.75535i	−0.264731	−	0.152843i
$969$	16.9014	+	27.8229i	0.542950	+	0.893799i
$970$	−21.2398	−	36.7884i	−0.681968	−	1.18120i
$971$	25.1987	−	43.6454i	0.808665	−	1.40065i	−0.105125	−	0.994459i	$-0.533524\pi$
$971$	25.1987	−	43.6454i	0.808665	−	1.40065i	0.913789	−	0.406189i	$-0.133143\pi$
$972$	−1.73377	−	15.4917i	−0.0556108	−	0.496898i
$973$	−20.1902	−	9.81575i	−0.647268	−	0.314678i
$974$		−	14.3609i		−	0.460154i
$975$	−7.33761	+	13.3897i	−0.234992	+	0.428815i
$976$	−6.35777	+	3.67066i	−0.203507	+	0.117495i
$977$	−21.9587	+	12.6779i	−0.702520	+	0.405600i	−0.808285	−	0.588791i	$-0.799604\pi$
$977$	−21.9587	+	12.6779i	−0.702520	+	0.405600i	0.105765	+	0.994391i	$0.466271\pi$
$978$	6.62854	−	12.0958i	0.211957	−	0.386782i
$979$			2.47738i			0.0791775i
$980$	16.0703	+	20.4620i	0.513348	+	0.653633i
$981$	49.1854	−	2.19418i	1.57037	−	0.0700549i
$982$	8.13852	−	14.0963i	0.259711	−	0.449832i
$983$	−21.0300	−	36.4249i	−0.670751	−	1.16178i	−0.977691	−	0.210046i	$-0.932638\pi$
$983$	−21.0300	−	36.4249i	−0.670751	−	1.16178i	0.306940	−	0.951729i	$-0.400695\pi$
$984$	10.7612	+	17.7150i	0.343056	+	0.564735i
$985$	36.4507	+	21.0448i	1.16142	+	0.670545i
$986$	18.2763			0.582037
$987$	33.8103	+	15.5154i	1.07619	+	0.493862i
$988$	4.51583			0.143668
$989$	−9.07496	−	5.23943i	−0.288567	−	0.166604i
$990$	−7.32240	−	11.4699i	−0.232721	−	0.364536i
$991$	18.4783	+	32.0054i	0.586983	+	1.01668i	0.994625	+	0.103542i	$0.0330177\pi$
$991$	18.4783	+	32.0054i	0.586983	+	1.01668i	−0.407642	+	0.913142i	$0.633649\pi$
$992$	1.44066	−	2.49530i	0.0457411	−	0.0792260i
$993$	0.0188786	+	0.846795i	0.000599093	+	0.0268722i
$994$	−2.85315	−	4.21842i	−0.0904963	−	0.133800i
$995$			60.5179i			1.91855i
$996$	12.2289	+	6.70148i	0.387488	+	0.212344i
$997$	−45.8507	+	26.4719i	−1.45211	+	0.838374i	−0.998601	−	0.0528789i	$-0.983160\pi$
$997$	−45.8507	+	26.4719i	−1.45211	+	0.838374i	−0.453506	+	0.891253i	$0.649827\pi$
$998$	−18.8817	+	10.9013i	−0.597689	+	0.345076i
$999$	5.09638	+	2.50426i	0.161242	+	0.0792312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.14	✓	32
3.2	odd	2		546.2.z.b.131.7	yes	32
7.3	odd	6		546.2.z.b.521.7	yes	32
21.17	even	6	inner	546.2.z.a.521.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.14	✓	32	1.1	even	1	trivial
546.2.z.a.521.14	yes	32	21.17	even	6	inner
546.2.z.b.131.7	yes	32	3.2	odd	2
546.2.z.b.521.7	yes	32	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.48032 - 0.899243i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85844 + 3.21892i) q^{5} +(1.73162 - 0.0386050i) q^{6} +(-1.15681 + 2.37945i) q^{7} +1.00000i q^{8} +(1.38272 - 2.66234i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.48032 - 0.899243i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85844 + 3.21892i) q^{5} +(1.73162 - 0.0386050i) q^{6} +(-1.15681 + 2.37945i) q^{7} +1.00000i q^{8} +(1.38272 - 2.66234i) q^{9} +(-3.21892 + 1.85844i) q^{10} +(-1.05687 + 0.610184i) q^{11} +(1.51893 + 0.832377i) q^{12} -1.00000i q^{13} +(-2.19155 + 1.48226i) q^{14} +(0.143490 + 6.43624i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.08102 + 3.60444i) q^{17} +(2.52865 - 1.61430i) q^{18} +(3.91082 + 2.25792i) q^{19} -3.71689 q^{20} +(0.427259 + 4.56261i) q^{21} -1.22037 q^{22} +(-0.756604 - 0.436825i) q^{23} +(0.899243 + 1.48032i) q^{24} +(-4.40762 - 7.63423i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-0.347215 - 5.18454i) q^{27} +(-2.63907 + 0.187904i) q^{28} -4.39119i q^{29} +(-3.09385 + 5.64569i) q^{30} +(-2.49530 + 1.44066i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.01581 + 1.85365i) q^{33} +4.16205i q^{34} +(-5.50941 - 8.14574i) q^{35} +(2.99702 - 0.133698i) q^{36} +(-0.546406 + 0.946403i) q^{37} +(2.25792 + 3.91082i) q^{38} +(-0.899243 - 1.48032i) q^{39} +(-3.21892 - 1.85844i) q^{40} +11.9670 q^{41} +(-1.91129 + 4.16497i) q^{42} +11.9943 q^{43} +(-1.05687 - 0.610184i) q^{44} +(6.00015 + 9.39869i) q^{45} +(-0.436825 - 0.756604i) q^{46} +(4.05889 - 7.03021i) q^{47} +(0.0386050 + 1.73162i) q^{48} +(-4.32360 - 5.50513i) q^{49} -8.81525i q^{50} +(6.32186 + 3.46439i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-7.98565 + 4.61051i) q^{53} +(2.29157 - 4.66355i) q^{54} -4.53597i q^{55} +(-2.37945 - 1.15681i) q^{56} +(7.81971 - 0.174334i) q^{57} +(2.19559 - 3.80288i) q^{58} +(-2.97293 - 5.14927i) q^{59} +(-5.50220 + 3.34238i) q^{60} +(6.35777 + 3.67066i) q^{61} -2.88133 q^{62} +(4.73538 + 6.36994i) q^{63} -1.00000 q^{64} +(3.21892 + 1.85844i) q^{65} +(-1.80654 + 1.09741i) q^{66} +(-7.28275 - 12.6141i) q^{67} +(-2.08102 + 3.60444i) q^{68} +(-1.51283 + 0.0337273i) q^{69} +(-0.698417 - 9.80913i) q^{70} +1.92486i q^{71} +(2.66234 + 1.38272i) q^{72} +(-1.89964 + 1.09676i) q^{73} +(-0.946403 + 0.546406i) q^{74} +(-13.3897 - 7.33761i) q^{75} +4.51583i q^{76} +(-0.229312 - 3.22064i) q^{77} +(-0.0386050 - 1.73162i) q^{78} +(1.29925 - 2.25038i) q^{79} +(-1.85844 - 3.21892i) q^{80} +(-5.17615 - 7.36257i) q^{81} +(10.3637 + 5.98350i) q^{82} +8.05101 q^{83} +(-3.73771 + 2.65132i) q^{84} -15.4699 q^{85} +(10.3874 + 5.99717i) q^{86} +(-3.94874 - 6.50038i) q^{87} +(-0.610184 - 1.05687i) q^{88} +(1.01501 - 1.75806i) q^{89} +(0.496942 + 11.1396i) q^{90} +(2.37945 + 1.15681i) q^{91} -0.873651i q^{92} +(-2.39835 + 4.37654i) q^{93} +(7.03021 - 4.05889i) q^{94} +(-14.5361 + 8.39242i) q^{95} +(-0.832377 + 1.51893i) q^{96} +11.4288i q^{97} +(-0.991782 - 6.92938i) q^{98} +(0.163161 + 3.65747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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