LMFDB - Embedded newform 930.2.bg.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 195x^{12} + 892x^{10} + 2229x^{8} + 2923x^{6} + 1685x^{4} + 213x^{2} + 1 $ x^16 + 22x^14 + 195x^12 + 892x^10 + 2229x^8 + 2923x^6 + 1685x^4 + 213*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.2
Root			$-2.47474i$ of defining polynomial
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.b.661.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.97142 - 0.844151i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.97142 - 0.844151i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.104528 - 0.994522i) q^{10} +(0.847048 + 0.940743i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(3.89934 - 1.73610i) q^{13} +(-2.71677 + 3.01727i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.30402 + 2.55887i) q^{17} +(0.913545 - 0.406737i) q^{18} +(0.106866 + 0.0475796i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.424400 - 4.03790i) q^{21} +(-1.23823 - 0.263194i) q^{22} +(-0.0893550 - 0.275006i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.13418 + 3.69650i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.424400 - 4.03790i) q^{28} +(1.57422 - 1.14373i) q^{29} -1.00000 q^{30} +(2.52416 + 4.96272i) q^{31} +1.00000 q^{32} +(1.02413 - 0.744074i) q^{33} +(0.359923 - 3.42444i) q^{34} +(-1.25465 + 3.86142i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.591458 + 1.02444i) q^{37} +(-0.114423 + 0.0243213i) q^{38} +(-1.31899 - 4.05945i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(-0.840828 - 7.99994i) q^{41} +(2.71677 + 3.01727i) q^{42} +(-5.44913 - 2.42611i) q^{43} +(1.15645 - 0.514885i) q^{44} +(0.669131 - 0.743145i) q^{45} +(0.233934 + 0.169963i) q^{46} +(6.60760 + 4.80070i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(8.66475 - 3.85780i) q^{49} +(0.913545 + 0.406737i) q^{50} +(2.30402 + 2.55887i) q^{51} +(-0.446165 - 4.24497i) q^{52} +(6.08501 + 1.29341i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-1.23823 + 0.263194i) q^{55} +(2.03007 + 3.51619i) q^{56} +(0.0584895 - 0.101307i) q^{57} +(-0.601297 + 1.85060i) q^{58} +(0.472912 - 4.49946i) q^{59} +(0.809017 - 0.587785i) q^{60} +14.5569 q^{61} +(-4.95910 - 2.53126i) q^{62} -4.06014 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.446165 + 4.24497i) q^{65} +(-0.391183 + 1.20394i) q^{66} +(-0.0802061 + 0.138921i) q^{67} +(1.72165 + 2.98199i) q^{68} +(-0.282840 + 0.0601195i) q^{69} +(-1.25465 - 3.86142i) q^{70} +(1.25559 + 0.266884i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-3.86087 - 4.28793i) q^{73} +(-1.08065 - 0.481136i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(0.0782742 - 0.0869323i) q^{76} +(4.15811 + 3.02105i) q^{77} +(3.45317 + 2.50888i) q^{78} +(6.35647 - 7.05957i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(5.38249 + 5.97786i) q^{82} +(-0.308955 - 2.93951i) q^{83} +(-3.97142 - 0.844151i) q^{84} +(-1.06404 - 3.27477i) q^{85} +(5.83447 - 1.24016i) q^{86} +(-0.972918 - 1.68514i) q^{87} +(-0.632947 + 1.09630i) q^{88} +(2.66900 - 8.21432i) q^{89} +(-0.104528 + 0.994522i) q^{90} +(14.0204 - 10.1864i) q^{91} -0.289159 q^{92} +(5.19938 - 1.99159i) q^{93} -8.16745 q^{94} +(-0.0946379 + 0.0687585i) q^{95} +(0.104528 - 0.994522i) q^{96} +(-3.84479 + 11.8330i) q^{97} +(-4.74238 + 8.21404i) q^{98} +(-0.632947 - 1.09630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	3.97142	−	0.844151i	1.50105	−	0.319059i	0.617195	−	0.786810i	$-0.288269\pi$
$7$	3.97142	−	0.844151i	1.50105	−	0.319059i	0.883860	+	0.467751i	$0.154936\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	−0.104528	−	0.994522i	−0.0330548	−	0.314495i
$11$	0.847048	+	0.940743i	0.255395	+	0.283645i	0.857184	−	0.515010i	$-0.172212\pi$
$11$	0.847048	+	0.940743i	0.255395	+	0.283645i	−0.601789	+	0.798655i	$0.705545\pi$
$12$	−0.913545	−	0.406737i	−0.263718	−	0.117415i
$13$	3.89934	−	1.73610i	1.08148	−	0.481507i	0.212911	−	0.977072i	$-0.431706\pi$
$13$	3.89934	−	1.73610i	1.08148	−	0.481507i	0.868571	+	0.495565i	$0.165039\pi$
$14$	−2.71677	+	3.01727i	−0.726086	+	0.806400i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.30402	+	2.55887i	−0.558806	+	0.620617i	−0.954661	−	0.297696i	$-0.903782\pi$
$17$	−2.30402	+	2.55887i	−0.558806	+	0.620617i	0.395854	+	0.918313i	$0.370448\pi$
$18$	0.913545	−	0.406737i	0.215325	−	0.0958687i
$19$	0.106866	+	0.0475796i	0.0245166	+	0.0109155i	0.418958	−	0.908005i	$-0.362395\pi$
$19$	0.106866	+	0.0475796i	0.0245166	+	0.0109155i	−0.394442	+	0.918921i	$0.629062\pi$
$20$	0.669131	+	0.743145i	0.149622	+	0.166172i
$21$	−0.424400	−	4.03790i	−0.0926118	−	0.881142i
$22$	−1.23823	−	0.263194i	−0.263992	−	0.0561132i
$23$	−0.0893550	−	0.275006i	−0.0186318	−	0.0573428i	0.941308	−	0.337548i	$-0.109598\pi$
$23$	−0.0893550	−	0.275006i	−0.0186318	−	0.0573428i	−0.959940	+	0.280205i	$0.909598\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.13418	+	3.69650i	−0.418547	+	0.724944i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.424400	−	4.03790i	0.0802041	−	0.763091i
$29$	1.57422	−	1.14373i	0.292324	−	0.212386i	−0.431951	−	0.901897i	$-0.642175\pi$
$29$	1.57422	−	1.14373i	0.292324	−	0.212386i	0.724275	+	0.689511i	$0.242175\pi$
$30$	−1.00000			−0.182574
$31$	2.52416	+	4.96272i	0.453353	+	0.891331i
$31$	2.52416	+	4.96272i	0.453353	+	0.891331i
$32$	1.00000			0.176777
$33$	1.02413	−	0.744074i	0.178278	−	0.129527i
$34$	0.359923	−	3.42444i	0.0617263	−	0.587286i
$35$	−1.25465	+	3.86142i	−0.212075	+	0.652700i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	0.591458	+	1.02444i	0.0972352	+	0.168416i	0.910539	−	0.413423i	$-0.135667\pi$
$37$	0.591458	+	1.02444i	0.0972352	+	0.168416i	−0.813304	+	0.581839i	$0.802333\pi$
$38$	−0.114423	+	0.0243213i	−0.0185618	+	0.00394543i
$39$	−1.31899	−	4.05945i	−0.211208	−	0.650032i
$40$	−0.978148	−	0.207912i	−0.154659	−	0.0328737i
$41$	−0.840828	−	7.99994i	−0.131315	−	1.24938i	−0.839502	−	0.543356i	$-0.817153\pi$
$41$	−0.840828	−	7.99994i	−0.131315	−	1.24938i	0.708187	−	0.706025i	$-0.249513\pi$
$42$	2.71677	+	3.01727i	0.419206	+	0.465575i
$43$	−5.44913	−	2.42611i	−0.830985	−	0.369978i	−0.0532582	−	0.998581i	$-0.516961\pi$
$43$	−5.44913	−	2.42611i	−0.830985	−	0.369978i	−0.777727	+	0.628602i	$0.783627\pi$
$44$	1.15645	−	0.514885i	0.174342	−	0.0776219i
$45$	0.669131	−	0.743145i	0.0997481	−	0.110781i
$46$	0.233934	+	0.169963i	0.0344917	+	0.0250597i
$47$	6.60760	+	4.80070i	0.963818	+	0.700255i	0.954034	−	0.299698i	$-0.0968858\pi$
$47$	6.60760	+	4.80070i	0.963818	+	0.700255i	0.00978352	+	0.999952i	$0.496886\pi$
$48$	−0.669131	+	0.743145i	−0.0965807	+	0.107264i
$49$	8.66475	−	3.85780i	1.23782	−	0.551114i
$50$	0.913545	+	0.406737i	0.129195	+	0.0575212i
$51$	2.30402	+	2.55887i	0.322627	+	0.358314i
$52$	−0.446165	−	4.24497i	−0.0618719	−	0.588672i
$53$	6.08501	+	1.29341i	0.835840	+	0.177663i	0.605899	−	0.795541i	$-0.292813\pi$
$53$	6.08501	+	1.29341i	0.835840	+	0.177663i	0.229941	+	0.973205i	$0.426147\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−1.23823	+	0.263194i	−0.166963	+	0.0354891i
$56$	2.03007	+	3.51619i	0.271280	+	0.469870i
$57$	0.0584895	−	0.101307i	0.00774712	−	0.0134184i
$58$	−0.601297	+	1.85060i	−0.0789541	+	0.242996i
$59$	0.472912	−	4.49946i	0.0615679	−	0.585780i	−0.919631	−	0.392782i	$-0.871513\pi$
$59$	0.472912	−	4.49946i	0.0615679	−	0.585780i	0.981199	−	0.192997i	$-0.0618208\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	14.5569			1.86382			0.931908	−	0.362694i	$-0.118143\pi$
$61$	14.5569			1.86382			0.931908	+	0.362694i	$0.118143\pi$
$62$	−4.95910	−	2.53126i	−0.629807	−	0.321470i
$63$	−4.06014			−0.511530
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.446165	+	4.24497i	−0.0553399	+	0.526524i
$66$	−0.391183	+	1.20394i	−0.0481513	+	0.148194i
$67$	−0.0802061	+	0.138921i	−0.00979874	+	0.0169719i	−0.870883	−	0.491490i	$-0.836452\pi$
$67$	−0.0802061	+	0.138921i	−0.00979874	+	0.0169719i	0.861084	+	0.508462i	$0.169786\pi$
$68$	1.72165	+	2.98199i	0.208781	+	0.361619i
$69$	−0.282840	+	0.0601195i	−0.0340499	+	0.00723754i
$70$	−1.25465	−	3.86142i	−0.149960	−	0.461528i
$71$	1.25559	+	0.266884i	0.149011	+	0.0316733i	0.281813	−	0.959469i	$-0.409064\pi$
$71$	1.25559	+	0.266884i	0.149011	+	0.0316733i	−0.132802	+	0.991143i	$0.542397\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	−3.86087	−	4.28793i	−0.451881	−	0.501865i	0.473557	−	0.880763i	$-0.342970\pi$
$73$	−3.86087	−	4.28793i	−0.451881	−	0.501865i	−0.925438	+	0.378898i	$0.876303\pi$
$74$	−1.08065	−	0.481136i	−0.125623	−	0.0559309i
$75$	−0.913545	+	0.406737i	−0.105487	+	0.0469659i
$76$	0.0782742	−	0.0869323i	0.00897866	−	0.00997182i
$77$	4.15811	+	3.02105i	0.473861	+	0.344280i
$78$	3.45317	+	2.50888i	0.390995	+	0.284074i
$79$	6.35647	−	7.05957i	0.715159	−	0.794264i	−0.270553	−	0.962705i	$-0.587207\pi$
$79$	6.35647	−	7.05957i	0.715159	−	0.794264i	0.985712	+	0.168441i	$0.0538733\pi$
$80$	0.913545	−	0.406737i	0.102137	−	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	5.38249	+	5.97786i	0.594397	+	0.660144i
$83$	−0.308955	−	2.93951i	−0.0339122	−	0.322653i	−0.998306	−	0.0581825i	$-0.981469\pi$
$83$	−0.308955	−	2.93951i	−0.0339122	−	0.322653i	0.964394	−	0.264471i	$-0.0851972\pi$
$84$	−3.97142	−	0.844151i	−0.433317	−	0.0921044i
$85$	−1.06404	−	3.27477i	−0.115411	−	0.355199i
$86$	5.83447	−	1.24016i	0.629147	−	0.133729i
$87$	−0.972918	−	1.68514i	−0.104308	−	0.180666i
$88$	−0.632947	+	1.09630i	−0.0674724	+	0.116866i
$89$	2.66900	−	8.21432i	0.282913	−	0.870717i	−0.704103	−	0.710097i	$-0.748651\pi$
$89$	2.66900	−	8.21432i	0.282913	−	0.870717i	0.987016	−	0.160619i	$-0.0513491\pi$
$90$	−0.104528	+	0.994522i	−0.0110183	+	0.104832i
$91$	14.0204	−	10.1864i	1.46973	−	1.06782i
$92$	−0.289159			−0.0301469
$93$	5.19938	−	1.99159i	0.539151	−	0.206518i
$94$	−8.16745			−0.842408
$95$	−0.0946379	+	0.0687585i	−0.00970965	+	0.00705447i
$96$	0.104528	−	0.994522i	0.0106684	−	0.101503i
$97$	−3.84479	+	11.8330i	−0.390379	+	1.20146i	0.542123	+	0.840299i	$0.317621\pi$
$97$	−3.84479	+	11.8330i	−0.390379	+	1.20146i	−0.932502	+	0.361164i	$0.882379\pi$
$98$	−4.74238	+	8.21404i	−0.479052	+	0.829743i
$99$	−0.632947	−	1.09630i	−0.0636136	−	0.110182i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	−1.65443	−	5.09180i	−0.164622	−	0.506653i	0.834387	−	0.551180i	$-0.185822\pi$
$101$	−1.65443	−	5.09180i	−0.164622	−	0.506653i	−0.999008	+	0.0445265i	$0.985822\pi$
$102$	−3.36806	−	0.715902i	−0.333487	−	0.0708849i
$103$	−0.761365	−	7.24391i	−0.0750195	−	0.713763i	−0.965793	−	0.259315i	$-0.916503\pi$
$103$	−0.761365	−	7.24391i	−0.0750195	−	0.713763i	0.890773	−	0.454448i	$-0.150163\pi$
$104$	2.85609	+	3.17201i	0.280062	+	0.311041i
$105$	3.70912	+	1.65141i	0.361973	+	0.161161i
$106$	−5.68312	+	2.53029i	−0.551993	+	0.245763i
$107$	−6.31682	+	7.01554i	−0.610670	+	0.678218i	−0.966598	−	0.256296i	$-0.917498\pi$
$107$	−6.31682	+	7.01554i	−0.610670	+	0.678218i	0.355929	+	0.934513i	$0.384165\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−0.00708792	−	0.00514967i	−0.000678900	−	0.000493249i	0.587446	−	0.809264i	$-0.300134\pi$
$109$	−0.00708792	−	0.00514967i	−0.000678900	−	0.000493249i	−0.588125	+	0.808770i	$0.700134\pi$
$110$	0.847048	−	0.940743i	0.0807629	−	0.0896963i
$111$	1.08065	−	0.481136i	0.102571	−	0.0456674i
$112$	−3.70912	−	1.65141i	−0.350479	−	0.156043i
$113$	9.78491	+	10.8672i	0.920487	+	1.02230i	0.999676	+	0.0254447i	$0.00810016\pi$
$113$	9.78491	+	10.8672i	0.920487	+	1.02230i	−0.0791893	+	0.996860i	$0.525233\pi$
$114$	0.0122276	+	0.116338i	0.00114522	+	0.0108961i
$115$	0.282840	+	0.0601195i	0.0263750	+	0.00560617i
$116$	−0.601297	−	1.85060i	−0.0558290	−	0.171824i
$117$	−4.17508	+	0.887441i	−0.385986	+	0.0820440i
$118$	2.26212	+	3.91811i	0.208245	+	0.360691i
$119$	−6.99014	+	12.1073i	−0.640785	+	1.10987i
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	0.982308	−	9.34603i	0.0893007	−	0.849639i
$122$	−11.7768	+	8.55632i	−1.06622	+	0.774652i
$123$	−8.04401			−0.725304
$124$	5.49984	−	0.867055i	0.493900	−	0.0778639i
$125$	1.00000			0.0894427
$126$	3.28472	−	2.38649i	0.292626	−	0.212606i
$127$	−1.64926	+	15.6917i	−0.146349	+	1.39241i	0.637016	+	0.770851i	$0.280169\pi$
$127$	−1.64926	+	15.6917i	−0.146349	+	1.39241i	−0.783364	+	0.621563i	$0.786498\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.98241	+	5.16568i	−0.262587	+	0.454813i
$130$	−2.13418	−	3.69650i	−0.187180	−	0.324205i
$131$	7.19498	−	1.52934i	0.628629	−	0.133619i	0.117429	−	0.993081i	$-0.462535\pi$
$131$	7.19498	−	1.52934i	0.628629	−	0.133619i	0.511199	+	0.859462i	$0.329201\pi$
$132$	−0.391183	−	1.20394i	−0.0340481	−	0.104789i
$133$	0.464572	+	0.0987479i	0.0402835	+	0.00856253i
$134$	−0.0167676	−	0.159534i	−0.00144850	−	0.0137816i
$135$	−0.669131	−	0.743145i	−0.0575896	−	0.0639597i
$136$	−3.14561	−	1.40052i	−0.269734	−	0.120093i
$137$	−15.6132	+	6.95143i	−1.33392	+	0.593900i	−0.944909	−	0.327332i	$-0.893850\pi$
$137$	−15.6132	+	6.95143i	−1.33392	+	0.593900i	−0.389013	+	0.921232i	$0.627184\pi$
$138$	0.193485	−	0.214887i	0.0164705	−	0.0182924i
$139$	−5.50864	−	4.00226i	−0.467237	−	0.339467i	0.329127	−	0.944286i	$-0.393246\pi$
$139$	−5.50864	−	4.00226i	−0.467237	−	0.339467i	−0.796363	+	0.604818i	$0.793246\pi$
$140$	3.28472	+	2.38649i	0.277610	+	0.201695i
$141$	5.46509	−	6.06959i	0.460243	−	0.511152i
$142$	−1.17266	+	0.522103i	−0.0984077	+	0.0438139i
$143$	4.93615	+	2.19771i	0.412781	+	0.183782i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	0.203395	+	1.93518i	0.0168911	+	0.160708i
$146$	5.64390	+	1.19965i	0.467092	+	0.0992835i
$147$	−2.93095	−	9.02053i	−0.241741	−	0.744001i
$148$	1.15707	−	0.245942i	0.0951104	−	0.0202163i
$149$	6.55261	+	11.3494i	0.536811	+	0.929783i	0.999073	+	0.0430401i	$0.0137043\pi$
$149$	6.55261	+	11.3494i	0.536811	+	0.929783i	−0.462263	+	0.886743i	$0.652962\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−4.28769	+	13.1962i	−0.348927	+	1.07389i	0.610520	+	0.792001i	$0.290960\pi$
$151$	−4.28769	+	13.1962i	−0.348927	+	1.07389i	−0.959447	+	0.281887i	$0.909040\pi$
$152$	−0.0122276	+	0.116338i	−0.000991791	+	0.00943627i
$153$	2.78569	−	2.02392i	0.225210	−	0.163624i
$154$	−5.13971			−0.414170
$155$	−5.55992	−	0.295373i	−0.446584	−	0.0237249i
$156$	−4.26836			−0.341742
$157$	−7.88966	+	5.73218i	−0.629664	+	0.457477i	−0.856284	−	0.516506i	$-0.827232\pi$
$157$	−7.88966	+	5.73218i	−0.629664	+	0.457477i	0.226620	+	0.973983i	$0.427232\pi$
$158$	−0.992978	+	9.44755i	−0.0789971	+	0.751607i
$159$	1.92238	−	5.91647i	0.152455	−	0.469207i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−0.587013	−	1.01674i	−0.0462631	−	0.0801300i
$162$	−0.978148	+	0.207912i	−0.0768505	+	0.0163351i
$163$	−3.70145	−	11.3919i	−0.289920	−	0.892281i	−0.984881	−	0.173234i	$-0.944578\pi$
$163$	−3.70145	−	11.3919i	−0.289920	−	0.892281i	0.694961	−	0.719047i	$-0.255422\pi$
$164$	−7.86823	−	1.67244i	−0.614405	−	0.130596i
$165$	0.132322	+	1.25896i	0.0103013	+	0.0980099i
$166$	1.97775	+	2.19651i	0.153503	+	0.170483i
$167$	−17.8895	−	7.96491i	−1.38433	−	0.616343i	−0.426712	−	0.904388i	$-0.640328\pi$
$167$	−17.8895	−	7.96491i	−1.38433	−	0.616343i	−0.957617	+	0.288044i	$0.906995\pi$
$168$	3.70912	−	1.65141i	0.286165	−	0.127409i
$169$	3.49210	−	3.87837i	0.268623	−	0.298336i
$170$	2.78569	+	2.02392i	0.213653	+	0.155228i
$171$	−0.0946379	−	0.0687585i	−0.00723714	−	0.00525809i
$172$	−3.99124	+	4.43272i	−0.304329	+	0.337992i
$173$	−1.83676	+	0.817778i	−0.139646	+	0.0621745i	−0.475370	−	0.879786i	$-0.657686\pi$
$173$	−1.83676	+	0.817778i	−0.139646	+	0.0621745i	0.335724	+	0.941960i	$0.391019\pi$
$174$	1.77761	+	0.791443i	0.134760	+	0.0599991i
$175$	−2.71677	−	3.01727i	−0.205368	−	0.228084i
$176$	−0.132322	−	1.25896i	−0.00997414	−	0.0948976i
$177$	−4.42538	−	0.940643i	−0.332632	−	0.0707030i
$178$	2.66900	+	8.21432i	0.200050	+	0.615690i
$179$	−1.68726	+	0.358639i	−0.126112	+	0.0268060i	−0.270535	−	0.962710i	$-0.587201\pi$
$179$	−1.68726	+	0.358639i	−0.126112	+	0.0268060i	0.144423	+	0.989516i	$0.453867\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−3.96566	+	6.86872i	−0.294765	+	0.510548i	−0.974930	−	0.222511i	$-0.928575\pi$
$181$	−3.96566	+	6.86872i	−0.294765	+	0.510548i	0.680165	+	0.733059i	$0.261908\pi$
$182$	−5.35530	+	16.4819i	−0.396962	+	1.22172i
$183$	1.52161	−	14.4771i	0.112480	−	1.07018i
$184$	0.233934	−	0.169963i	0.0172459	−	0.0125299i
$185$	−1.18292			−0.0869698
$186$	−3.03576	+	4.66735i	−0.222593	+	0.342227i
$187$	−4.35885			−0.318751
$188$	6.60760	−	4.80070i	0.481909	−	0.350127i
$189$	−0.424400	+	4.03790i	−0.0308706	+	0.293714i
$190$	0.0361485	−	0.111254i	0.00262249	−	0.00807118i
$191$	7.42394	−	12.8586i	0.537178	−	0.930419i	−0.461877	−	0.886944i	$-0.652824\pi$
$191$	7.42394	−	12.8586i	0.537178	−	0.930419i	0.999055	−	0.0434751i	$-0.0138429\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	1.52100	−	0.323298i	0.109484	−	0.0232715i	−0.152844	−	0.988250i	$-0.548843\pi$
$193$	1.52100	−	0.323298i	0.109484	−	0.0232715i	0.262328	+	0.964979i	$0.415510\pi$
$194$	−3.84479	−	11.8330i	−0.276040	−	0.849563i
$195$	4.17508	+	0.887441i	0.298984	+	0.0635510i
$196$	−0.991426	−	9.43279i	−0.0708162	−	0.673771i
$197$	−1.66372	−	1.84775i	−0.118535	−	0.131647i	0.680956	−	0.732324i	$-0.261564\pi$
$197$	−1.66372	−	1.84775i	−0.118535	−	0.131647i	−0.799491	+	0.600677i	$0.794898\pi$
$198$	1.15645	+	0.514885i	0.0821854	+	0.0365913i
$199$	−10.9187	+	4.86132i	−0.774007	+	0.344610i	−0.755440	−	0.655218i	$-0.772577\pi$
$199$	−10.9187	+	4.86132i	−0.774007	+	0.344610i	−0.0185665	+	0.999828i	$0.505910\pi$
$200$	0.669131	−	0.743145i	0.0473147	−	0.0525483i
$201$	0.129776	+	0.0942880i	0.00915371	+	0.00665056i
$202$	4.33134	+	3.14691i	0.304752	+	0.221415i
$203$	5.28638	−	5.87112i	0.371031	−	0.412072i
$204$	3.14561	−	1.40052i	0.220237	−	0.0980557i
$205$	7.34857	+	3.27179i	0.513246	+	0.228512i
$206$	4.87382	+	5.41292i	0.339575	+	0.377136i
$207$	0.0302253	+	0.287575i	0.00210081	+	0.0199878i
$208$	−4.17508	−	0.887441i	−0.289490	−	0.0615330i
$209$	0.0457601	+	0.140835i	0.00316529	+	0.00974178i
$210$	−3.97142	+	0.844151i	−0.274054	+	0.0582519i
$211$	−13.3629	−	23.1452i	−0.919937	−	1.59338i	−0.799507	−	0.600657i	$-0.794906\pi$
$211$	−13.3629	−	23.1452i	−0.919937	−	1.59338i	−0.120430	−	0.992722i	$-0.538427\pi$
$212$	3.11047	−	5.38750i	0.213628	−	0.370015i
$213$	0.396667	−	1.22081i	0.0271791	−	0.0836488i
$214$	0.986784	−	9.38862i	0.0674552	−	0.641793i
$215$	4.82564	−	3.50603i	0.329106	−	0.239109i
$216$	−1.00000			−0.0680414
$217$	14.2138	+	17.5783i	0.964895	+	1.19329i
$218$	0.00876115			0.000593380
$219$	−4.66802	+	3.39151i	−0.315435	+	0.229177i
$220$	−0.132322	+	1.25896i	−0.00892114	+	0.0848790i
$221$	−4.54169	+	13.9779i	−0.305507	+	0.940255i
$222$	−0.591458	+	1.02444i	−0.0396961	+	0.0687557i
$223$	−7.55705	−	13.0892i	−0.506057	−	0.876517i	−0.999975	−	0.00700859i	$-0.997769\pi$
$223$	−7.55705	−	13.0892i	−0.506057	−	0.876517i	0.493918	−	0.869508i	$-0.335564\pi$
$224$	3.97142	−	0.844151i	0.265352	−	0.0564022i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−14.3038	−	3.04036i	−0.951472	−	0.202242i
$227$	2.69400	+	25.6317i	0.178807	+	1.70123i	0.604694	+	0.796458i	$0.293295\pi$
$227$	2.69400	+	25.6317i	0.178807	+	1.70123i	−0.425887	+	0.904776i	$0.640038\pi$
$228$	−0.0782742	−	0.0869323i	−0.00518383	−	0.00575723i
$229$	5.97891	+	2.66198i	0.395097	+	0.175909i	0.594662	−	0.803976i	$-0.297286\pi$
$229$	5.97891	+	2.66198i	0.395097	+	0.175909i	−0.199564	+	0.979885i	$0.563953\pi$
$230$	−0.264160	+	0.117611i	−0.0174182	+	0.00775507i
$231$	3.43914	−	3.81955i	0.226279	−	0.251308i
$232$	1.57422	+	1.14373i	0.103352	+	0.0750898i
$233$	3.87459	+	2.81505i	0.253833	+	0.184420i	0.707424	−	0.706790i	$-0.249857\pi$
$233$	3.87459	+	2.81505i	0.253833	+	0.184420i	−0.453591	+	0.891210i	$0.649857\pi$
$234$	2.85609	−	3.17201i	0.186708	−	0.207361i
$235$	−7.46133	+	3.32200i	−0.486724	+	0.216703i
$236$	−4.13310	−	1.84018i	−0.269042	−	0.119785i
$237$	−6.35647	−	7.05957i	−0.412897	−	0.458569i
$238$	−1.46134	−	13.9037i	−0.0947245	−	0.901243i
$239$	−12.1699	−	2.58680i	−0.787208	−	0.167326i	−0.203268	−	0.979123i	$-0.565156\pi$
$239$	−12.1699	−	2.58680i	−0.787208	−	0.167326i	−0.583940	+	0.811797i	$0.698490\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	−19.3421	+	4.11130i	−1.24594	+	0.264832i	−0.783260	−	0.621695i	$-0.786444\pi$
$241$	−19.3421	+	4.11130i	−1.24594	+	0.264832i	−0.462677	+	0.886527i	$0.653111\pi$
$242$	4.69876	+	8.13848i	0.302047	+	0.523162i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.49832	−	13.8444i	0.287975	−	0.886297i
$245$	−0.991426	+	9.43279i	−0.0633399	+	0.602639i
$246$	6.50774	−	4.72815i	0.414918	−	0.301456i
$247$	0.499308			0.0317702
$248$	−3.93982	+	3.93419i	−0.250179	+	0.249821i
$249$	−2.95570			−0.187310
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	0.864940	−	8.22936i	0.0545945	−	0.519432i	−0.932714	−	0.360617i	$-0.882566\pi$
$251$	0.864940	−	8.22936i	0.0545945	−	0.519432i	0.987308	−	0.158815i	$-0.0507673\pi$
$252$	−1.25465	+	3.86142i	−0.0790357	+	0.243247i
$253$	0.183022	−	0.317004i	0.0115065	−	0.0199299i
$254$	−7.88907	−	13.6643i	−0.495004	−	0.857372i
$255$	−3.36806	+	0.715902i	−0.210916	+	0.0448315i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−14.2439	−	3.02764i	−0.888512	−	0.188859i	−0.259026	−	0.965870i	$-0.583401\pi$
$257$	−14.2439	−	3.02764i	−0.888512	−	0.188859i	−0.629487	+	0.777011i	$0.716735\pi$
$258$	−0.623493	−	5.93214i	−0.0388170	−	0.369319i
$259$	3.21371	+	3.56918i	0.199690	+	0.221778i
$260$	3.89934	+	1.73610i	0.241827	+	0.107668i
$261$	−1.77761	+	0.791443i	−0.110031	+	0.0489891i
$262$	−4.92194	+	5.46637i	−0.304078	+	0.337713i
$263$	−19.6754	−	14.2950i	−1.21324	−	0.881469i	−0.217717	−	0.976012i	$-0.569861\pi$
$263$	−19.6754	−	14.2950i	−1.21324	−	0.881469i	−0.995521	+	0.0945434i	$0.969861\pi$
$264$	1.02413	+	0.744074i	0.0630308	+	0.0457946i
$265$	−4.16263	+	4.62307i	−0.255708	+	0.283993i
$266$	−0.433889	+	0.193180i	−0.0266035	+	0.0118446i
$267$	−7.89034	−	3.51301i	−0.482881	−	0.214992i
$268$	0.107337	+	0.119210i	0.00655664	+	0.00728188i
$269$	−0.977603	−	9.30127i	−0.0596055	−	0.567108i	−0.983045	−	0.183364i	$-0.941301\pi$
$269$	−0.977603	−	9.30127i	−0.0596055	−	0.567108i	0.923440	−	0.383744i	$-0.125365\pi$
$270$	0.978148	+	0.207912i	0.0595282	+	0.0126531i
$271$	−2.84734	−	8.76320i	−0.172963	−	0.532326i	0.826571	−	0.562832i	$-0.190288\pi$
$271$	−2.84734	−	8.76320i	−0.172963	−	0.532326i	−0.999535	+	0.0305057i	$0.990288\pi$
$272$	3.36806	−	0.715902i	0.204218	−	0.0434080i
$273$	−8.66507	−	15.0083i	−0.524434	−	0.908346i
$274$	8.54537	−	14.8010i	0.516244	−	0.894162i
$275$	0.391183	−	1.20394i	0.0235892	−	0.0726001i
$276$	−0.0302253	+	0.287575i	−0.00181935	+	0.0173100i
$277$	19.1956	−	13.9464i	1.15335	−	0.837958i	0.164427	−	0.986389i	$-0.447422\pi$
$277$	19.1956	−	13.9464i	1.15335	−	0.837958i	0.988923	+	0.148432i	$0.0474225\pi$
$278$	6.80905			0.408380
$279$	−1.43719	−	5.37908i	−0.0860426	−	0.322037i
$280$	−4.06014			−0.242640
$281$	−24.7380	+	17.9732i	−1.47574	+	1.07219i	−0.496847	+	0.867838i	$0.665509\pi$
$281$	−24.7380	+	17.9732i	−1.47574	+	1.07219i	−0.978897	+	0.204352i	$0.934491\pi$
$282$	−0.853730	+	8.12270i	−0.0508389	+	0.483700i
$283$	−5.61869	+	17.2925i	−0.333996	+	1.02794i	0.633218	+	0.773974i	$0.281734\pi$
$283$	−5.61869	+	17.2925i	−0.333996	+	1.02794i	−0.967214	+	0.253962i	$0.918266\pi$
$284$	0.641820	−	1.11166i	0.0380850	−	0.0659652i
$285$	0.0584895	+	0.101307i	0.00346462	+	0.00600089i
$286$	−5.28521	+	1.12341i	−0.312521	+	0.0664284i
$287$	−10.0924	−	31.0613i	−0.595738	−	1.83349i
$288$	−0.978148	−	0.207912i	−0.0576379	−	0.0122513i
$289$	0.537662	+	5.11551i	0.0316272	+	0.300912i
$290$	−1.30202	−	1.44604i	−0.0764572	−	0.0849143i
$291$	11.3663	+	5.06062i	0.666306	+	0.296659i
$292$	−5.27114	+	2.34686i	−0.308470	+	0.137340i
$293$	−15.9987	+	17.7684i	−0.934654	+	1.03804i	0.0645405	+	0.997915i	$0.479442\pi$
$293$	−15.9987	+	17.7684i	−0.934654	+	1.03804i	−0.999195	+	0.0401236i	$0.987225\pi$
$294$	7.67333	+	5.57500i	0.447517	+	0.325140i
$295$	3.66019	+	2.65928i	0.213104	+	0.154829i
$296$	−0.791526	+	0.879079i	−0.0460065	+	0.0510954i
$297$	−1.15645	+	0.514885i	−0.0671041	+	0.0298767i
$298$	−11.9722	−	5.33037i	−0.693531	−	0.308780i
$299$	−0.825863	−	0.917214i	−0.0477609	−	0.0530438i
$300$	0.104528	+	0.994522i	0.00603495	+	0.0574187i
$301$	−23.6888	−	5.03521i	−1.36540	−	0.290225i
$302$	−4.28769	−	13.1962i	−0.246729	−	0.759354i
$303$	−5.23684	+	1.11312i	−0.300849	+	0.0639474i
$304$	−0.0584895	−	0.101307i	−0.00335460	−	0.00581034i
$305$	−7.27844	+	12.6066i	−0.416762	+	0.721853i
$306$	−1.06404	+	3.27477i	−0.0608270	+	0.187206i
$307$	1.28709	−	12.2459i	0.0734583	−	0.698909i	−0.894375	−	0.447317i	$-0.852379\pi$
$307$	1.28709	−	12.2459i	0.0734583	−	0.698909i	0.967834	−	0.251591i	$-0.0809539\pi$
$308$	4.15811	−	3.02105i	0.236930	−	0.172140i
$309$	−7.28381			−0.414361
$310$	4.67169	−	3.02908i	0.265334	−	0.172040i
$311$	−14.6469			−0.830548			−0.415274	−	0.909696i	$-0.636314\pi$
$311$	−14.6469			−0.830548			−0.415274	+	0.909696i	$0.636314\pi$
$312$	3.45317	−	2.50888i	0.195497	−	0.142037i
$313$	−0.909513	+	8.65344i	−0.0514087	+	0.489121i	0.938279	+	0.345879i	$0.112419\pi$
$313$	−0.909513	+	8.65344i	−0.0514087	+	0.489121i	−0.989688	+	0.143242i	$0.954247\pi$
$314$	3.01358	−	9.27485i	0.170066	−	0.523410i
$315$	2.03007	−	3.51619i	0.114382	−	0.198115i
$316$	−4.74980	−	8.22689i	−0.267197	−	0.462799i
$317$	15.0139	−	3.19131i	0.843266	−	0.179242i	0.234029	−	0.972230i	$-0.424809\pi$
$317$	15.0139	−	3.19131i	0.843266	−	0.179242i	0.609237	+	0.792988i	$0.291476\pi$
$318$	1.92238	+	5.91647i	0.107802	+	0.331779i
$319$	2.40940	+	0.512133i	0.134900	+	0.0286739i
$320$	−0.104528	−	0.994522i	−0.00584332	−	0.0555955i
$321$	6.31682	+	7.01554i	0.352570	+	0.391569i
$322$	1.07253	+	0.477519i	0.0597695	+	0.0266111i
$323$	−0.367970	+	0.163831i	−0.0204744	+	0.00911579i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	−3.45317	−	2.50888i	−0.191548	−	0.139167i
$326$	9.69052	+	7.04057i	0.536708	+	0.389941i
$327$	−0.00586235	+	0.00651080i	−0.000324189	+	0.000360048i
$328$	7.34857	−	3.27179i	0.405757	−	0.180655i
$329$	30.2941	+	13.4878i	1.67017	+	0.743606i
$330$	−0.847048	−	0.940743i	−0.0466285	−	0.0517862i
$331$	2.88379	+	27.4374i	0.158507	+	1.50810i	0.727702	+	0.685894i	$0.240589\pi$
$331$	2.88379	+	27.4374i	0.158507	+	1.50810i	−0.569194	+	0.822203i	$0.692745\pi$
$332$	−2.89111	−	0.614525i	−0.158670	−	0.0337264i
$333$	−0.365541	−	1.12502i	−0.0200315	−	0.0616508i
$334$	19.1545	−	4.07142i	1.04809	−	0.222778i
$335$	−0.0802061	−	0.138921i	−0.00438213	−	0.00759007i
$336$	−2.03007	+	3.51619i	−0.110749	+	0.191824i
$337$	−7.65719	+	23.5664i	−0.417114	+	1.28374i	0.493233	+	0.869897i	$0.335815\pi$
$337$	−7.65719	+	23.5664i	−0.417114	+	1.28374i	−0.910347	+	0.413847i	$0.864185\pi$
$338$	−0.545520	+	5.19027i	−0.0296724	+	0.282314i
$339$	11.8305	−	8.59537i	0.642545	−	0.466836i
$340$	−3.44330			−0.186739
$341$	−2.53056	+	6.57825i	−0.137037	+	0.356232i
$342$	0.116979			0.00632550
$343$	8.16172	−	5.92984i	0.440692	−	0.320181i
$344$	0.623493	−	5.93214i	0.0336165	−	0.319840i
$345$	0.0893550	−	0.275006i	0.00481071	−	0.0148058i
$346$	1.00529	−	1.74122i	0.0540448	−	0.0936084i
$347$	−11.1383	−	19.2920i	−0.597933	−	1.03565i	−0.993126	−	0.117052i	$-0.962656\pi$
$347$	−11.1383	−	19.2920i	−0.597933	−	1.03565i	0.395193	−	0.918598i	$-0.370678\pi$
$348$	−1.90332	+	0.404562i	−0.102028	+	0.0216868i
$349$	9.15000	+	28.1608i	0.489788	+	1.50741i	0.824924	+	0.565244i	$0.191218\pi$
$349$	9.15000	+	28.1608i	0.489788	+	1.50741i	−0.335135	+	0.942170i	$0.608782\pi$
$350$	3.97142	+	0.844151i	0.212281	+	0.0451218i
$351$	0.446165	+	4.24497i	0.0238145	+	0.226580i
$352$	0.847048	+	0.940743i	0.0451478	+	0.0501417i
$353$	14.7730	+	6.57738i	0.786290	+	0.350079i	0.760290	−	0.649583i	$-0.225057\pi$
$353$	14.7730	+	6.57738i	0.786290	+	0.350079i	0.0259991	+	0.999662i	$0.491723\pi$
$354$	4.13310	−	1.84018i	0.219672	−	0.0978042i
$355$	−0.858923	+	0.953930i	−0.0455869	+	0.0506294i
$356$	−6.98752	−	5.07673i	−0.370338	−	0.269066i
$357$	11.3103	+	8.21741i	0.598604	+	0.434911i
$358$	1.15422	−	1.28189i	0.0610026	−	0.0677502i
$359$	14.6202	−	6.50933i	0.771624	−	0.343549i	0.0171278	−	0.999853i	$-0.494548\pi$
$359$	14.6202	−	6.50933i	0.771624	−	0.343549i	0.754497	+	0.656304i	$0.227881\pi$
$360$	0.913545	+	0.406737i	0.0481481	+	0.0214369i
$361$	−12.7043	−	14.1096i	−0.668649	−	0.742610i
$362$	−0.829048	−	7.88787i	−0.0435738	−	0.414577i
$363$	−9.19215	−	1.95385i	−0.482463	−	0.102551i
$364$	−5.35530	−	16.4819i	−0.280694	−	0.863888i
$365$	5.64390	−	1.19965i	0.295415	−	0.0627924i
$366$	7.27844	+	12.6066i	0.380450	+	0.658959i
$367$	−6.90023	+	11.9516i	−0.360189	+	0.623866i	−0.987992	−	0.154507i	$-0.950621\pi$
$367$	−6.90023	+	11.9516i	−0.360189	+	0.623866i	0.627802	+	0.778373i	$0.283955\pi$
$368$	−0.0893550	+	0.275006i	−0.00465795	+	0.0143357i
$369$	−0.840828	+	7.99994i	−0.0437717	+	0.416460i
$370$	0.957000	−	0.695301i	0.0497521	−	0.0361470i
$371$	25.2579			1.31133
$372$	−0.287416	−	5.56034i	−0.0149018	−	0.288290i
$373$	15.5241			0.803806			0.401903	−	0.915682i	$-0.368349\pi$
$373$	15.5241			0.803806			0.401903	+	0.915682i	$0.368349\pi$
$374$	3.52639	−	2.56207i	0.182345	−	0.132481i
$375$	0.104528	−	0.994522i	0.00539783	−	0.0513569i
$376$	−2.52388	+	7.76770i	−0.130159	+	0.400589i
$377$	4.15276	−	7.19279i	0.213878	−	0.370448i
$378$	−2.03007	−	3.51619i	−0.104416	−	0.180853i
$379$	26.4425	−	5.62052i	1.35826	−	0.288707i	0.529498	−	0.848311i	$-0.322380\pi$
$379$	26.4425	−	5.62052i	1.35826	−	0.288707i	0.828760	+	0.559604i	$0.189047\pi$
$380$	0.0361485	+	0.111254i	0.00185438	+	0.00570719i
$381$	15.4333	+	3.28046i	0.790674	+	0.168063i
$382$	1.55203	+	14.7666i	0.0794086	+	0.755522i
$383$	−13.7916	−	15.3172i	−0.704719	−	0.782670i	0.279401	−	0.960175i	$-0.409864\pi$
$383$	−13.7916	−	15.3172i	−0.704719	−	0.782670i	−0.984120	+	0.177505i	$0.943197\pi$
$384$	−0.913545	−	0.406737i	−0.0466192	−	0.0207562i
$385$	−4.69536	+	2.09051i	−0.239298	+	0.106542i
$386$	−1.04048	+	1.15557i	−0.0529591	+	0.0588171i
$387$	4.82564	+	3.50603i	0.245301	+	0.178222i
$388$	10.0658	+	7.31322i	0.511013	+	0.371273i
$389$	18.0969	−	20.0986i	0.917547	−	1.01904i	−0.0822013	−	0.996616i	$-0.526195\pi$
$389$	18.0969	−	20.0986i	0.917547	−	1.01904i	0.999749	−	0.0224237i	$-0.00713829\pi$
$390$	−3.89934	+	1.73610i	−0.197451	+	0.0879107i
$391$	0.909581	+	0.404972i	0.0459995	+	0.0204803i
$392$	6.34654	+	7.04854i	0.320549	+	0.356005i
$393$	−0.768883	−	7.31543i	−0.0387850	−	0.369015i
$394$	2.43206	+	0.516949i	0.122525	+	0.0260435i
$395$	2.93554	+	9.03465i	0.147703	+	0.454583i
$396$	−1.23823	+	0.263194i	−0.0622235	+	0.0132260i
$397$	10.4464	+	18.0937i	0.524290	+	0.908097i	0.999600	+	0.0282789i	$0.00900266\pi$
$397$	10.4464	+	18.0937i	0.524290	+	0.908097i	−0.475310	+	0.879819i	$0.657664\pi$
$398$	5.97601	−	10.3507i	0.299550	−	0.518836i
$399$	0.146768	−	0.451705i	0.00734759	−	0.0226135i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	2.51778	−	1.82928i	0.125732	−	0.0913497i	−0.523142	−	0.852246i	$-0.675240\pi$
$401$	2.51778	−	1.82928i	0.125732	−	0.0913497i	0.648874	+	0.760896i	$0.275240\pi$
$402$	−0.160412			−0.00800064
$403$	18.4583	+	14.9691i	0.919475	+	0.745666i
$404$	−5.35384			−0.266363
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	−0.825814	+	7.85709i	−0.0409845	+	0.389941i
$407$	−0.462737	+	1.42416i	−0.0229370	+	0.0705929i
$408$	−1.72165	+	2.98199i	−0.0852344	+	0.147630i
$409$	12.0125	+	20.8062i	0.593979	+	1.02880i	0.993690	+	0.112160i	$0.0357769\pi$
$409$	12.0125	+	20.8062i	0.593979	+	1.02880i	−0.399712	+	0.916641i	$0.630890\pi$
$410$	−7.86823	+	1.67244i	−0.388584	+	0.0825961i
$411$	5.28133	+	16.2543i	0.260509	+	0.801763i
$412$	−7.12464	−	1.51439i	−0.351006	−	0.0746086i
$413$	−1.92009	−	18.2684i	−0.0944815	−	0.898931i
$414$	−0.193485	−	0.214887i	−0.00950927	−	0.0105611i
$415$	2.70017	+	1.20219i	0.132546	+	0.0590133i
$416$	3.89934	−	1.73610i	0.191181	−	0.0851191i
$417$	−4.55615	+	5.06011i	−0.223115	+	0.247795i
$418$	−0.119802	−	0.0870410i	−0.00585969	−	0.00425731i
$419$	28.9661	+	21.0451i	1.41509	+	1.02812i	0.992558	+	0.121770i	$0.0388571\pi$
$419$	28.9661	+	21.0451i	1.41509	+	1.02812i	0.422528	+	0.906350i	$0.361143\pi$
$420$	2.71677	−	3.01727i	0.132565	−	0.147228i
$421$	−26.1523	+	11.6437i	−1.27458	+	0.567481i	−0.928712	−	0.370801i	$-0.879083\pi$
$421$	−26.1523	+	11.6437i	−1.27458	+	0.567481i	−0.345871	+	0.938282i	$0.612416\pi$
$422$	24.4152	+	10.8703i	1.18851	+	0.529159i
$423$	−5.46509	−	6.06959i	−0.265722	−	0.295114i
$424$	0.650266	+	6.18687i	0.0315797	+	0.300461i
$425$	3.36806	+	0.715902i	0.163375	+	0.0347264i
$426$	0.396667	+	1.22081i	0.0192186	+	0.0591486i
$427$	57.8114	−	12.2882i	2.79769	−	0.594668i
$428$	4.72017	+	8.17557i	0.228158	+	0.395181i
$429$	2.70164	−	4.67938i	0.130437	−	0.225923i
$430$	−1.84323	+	5.67288i	−0.0888885	+	0.273571i
$431$	3.71746	−	35.3693i	0.179064	−	1.70368i	−0.423737	−	0.905785i	$-0.639282\pi$
$431$	3.71746	−	35.3693i	0.179064	−	1.70368i	0.602801	−	0.797892i	$-0.294051\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	19.1141			0.918565			0.459283	−	0.888290i	$-0.348107\pi$
$433$	19.1141			0.918565			0.459283	+	0.888290i	$0.348107\pi$
$434$	−21.8314	−	5.86646i	−1.04794	−	0.281599i
$435$	1.94584			0.0932957
$436$	−0.00708792	+	0.00514967i	−0.000339450	+	0.000246625i
$437$	0.00353573	−	0.0336402i	0.000169137	−	0.00160923i
$438$	1.78302	−	5.48758i	0.0851962	−	0.262207i
$439$	−16.3104	+	28.2504i	−0.778452	+	1.34832i	0.154381	+	0.988011i	$0.450662\pi$
$439$	−16.3104	+	28.2504i	−0.778452	+	1.34832i	−0.932834	+	0.360308i	$0.882672\pi$
$440$	−0.632947	−	1.09630i	−0.0301746	−	0.0522639i
$441$	−9.27749	+	1.97199i	−0.441785	+	0.0939043i
$442$	−4.54169	−	13.9779i	−0.216026	−	0.664861i
$443$	−0.994472	−	0.211381i	−0.0472488	−	0.0100430i	0.184227	−	0.982884i	$-0.441022\pi$
$443$	−0.994472	−	0.211381i	−0.0472488	−	0.0100430i	−0.231475	+	0.972841i	$0.574355\pi$
$444$	−0.123648	−	1.17644i	−0.00586810	−	0.0558312i
$445$	5.77932	+	6.41858i	0.273966	+	0.304270i
$446$	13.8074	+	6.14746i	0.653800	+	0.291090i
$447$	11.9722	−	5.33037i	0.566266	−	0.252118i
$448$	−2.71677	+	3.01727i	−0.128355	+	0.142553i
$449$	−17.8573	−	12.9741i	−0.842738	−	0.612285i	0.0803961	−	0.996763i	$-0.474381\pi$
$449$	−17.8573	−	12.9741i	−0.842738	−	0.612285i	−0.923134	+	0.384478i	$0.874381\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	6.81366	−	7.56734i	0.320843	−	0.356332i
$452$	13.3591	−	5.94784i	0.628358	−	0.279763i
$453$	12.6757	+	5.64358i	0.595556	+	0.265158i
$454$	−17.2454	−	19.1530i	−0.809367	−	0.898893i
$455$	1.81149	+	17.2352i	0.0849240	+	0.807998i
$456$	0.114423	+	0.0243213i	0.00535833	+	0.00113895i
$457$	4.03479	+	12.4178i	0.188739	+	0.580880i	0.999993	−	0.00381462i	$-0.00121424\pi$
$457$	4.03479	+	12.4178i	0.188739	+	0.580880i	−0.811253	+	0.584695i	$0.801214\pi$
$458$	−6.40171	+	1.36073i	−0.299132	+	0.0635825i
$459$	−1.72165	−	2.98199i	−0.0803597	−	0.139187i
$460$	0.144579	−	0.250419i	0.00674105	−	0.0116758i
$461$	1.97654	−	6.08317i	0.0920567	−	0.283321i	−0.894419	−	0.447230i	$-0.852410\pi$
$461$	1.97654	−	6.08317i	0.0920567	−	0.283321i	0.986475	+	0.163909i	$0.0524104\pi$
$462$	−0.537246	+	5.11155i	−0.0249949	+	0.237811i
$463$	−24.7214	+	17.9611i	−1.14890	+	0.834725i	−0.988334	−	0.152300i	$-0.951332\pi$
$463$	−24.7214	+	17.9611i	−1.14890	+	0.834725i	−0.160566	+	0.987025i	$0.551332\pi$
$464$	−1.94584			−0.0903332
$465$	−0.874925	+	5.49859i	−0.0405737	+	0.254991i
$466$	−4.78926			−0.221858
$467$	13.8724	−	10.0789i	0.641940	−	0.466397i	−0.218576	−	0.975820i	$-0.570141\pi$
$467$	13.8724	−	10.0789i	0.641940	−	0.466397i	0.860516	+	0.509423i	$0.170141\pi$
$468$	−0.446165	+	4.24497i	−0.0206240	+	0.196224i
$469$	−0.201262	+	0.619420i	−0.00929340	+	0.0286022i
$470$	4.08372	−	7.07321i	0.188368	−	0.326263i
$471$	4.87608	+	8.44562i	0.224678	+	0.389154i
$472$	4.42538	−	0.940643i	0.203694	−	0.0432966i
$473$	−2.33333	−	7.18126i	−0.107287	−	0.330195i
$474$	9.29200	+	1.97508i	0.426796	+	0.0907183i
$475$	−0.0122276	−	0.116338i	−0.000561042	−	0.00533796i
$476$	9.35464	+	10.3894i	0.428769	+	0.476196i
$477$	−5.68312	−	2.53029i	−0.260212	−	0.115854i
$478$	11.3662	−	5.06055i	0.519877	−	0.231464i
$479$	−6.87285	+	7.63307i	−0.314028	+	0.348764i	−0.879410	−	0.476066i	$-0.842062\pi$
$479$	−6.87285	+	7.63307i	−0.314028	+	0.348764i	0.565381	+	0.824830i	$0.308729\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	4.08482	+	2.96779i	0.186252	+	0.135320i
$482$	13.2316	−	14.6951i	0.602681	−	0.669345i
$483$	−1.07253	+	0.477519i	−0.0488016	+	0.0217279i
$484$	−8.58505	−	3.82231i	−0.390230	−	0.173741i
$485$	−8.32532	−	9.24621i	−0.378033	−	0.419849i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	−29.1548	−	6.19704i	−1.32113	−	0.280815i	−0.507225	−	0.861814i	$-0.669329\pi$
$487$	−29.1548	−	6.19704i	−1.32113	−	0.280815i	−0.813904	+	0.580999i	$0.802662\pi$
$488$	4.49832	+	13.8444i	0.203629	+	0.626707i
$489$	−11.7164	+	2.49039i	−0.529833	+	0.112620i
$490$	−4.74238	−	8.21404i	−0.214239	−	0.371072i
$491$	−1.98461	+	3.43745i	−0.0895643	+	0.155130i	−0.907327	−	0.420426i	$-0.861881\pi$
$491$	−1.98461	+	3.43745i	−0.0895643	+	0.155130i	0.817763	+	0.575555i	$0.195214\pi$
$492$	−2.48573	+	7.65031i	−0.112066	+	0.344902i
$493$	−0.700351	+	6.66340i	−0.0315422	+	0.300104i
$494$	−0.403948	+	0.293486i	−0.0181745	+	0.0132045i
$495$	1.26589			0.0568977
$496$	0.874925	−	5.49859i	0.0392853	−	0.246894i
$497$	5.21176			0.233779
$498$	2.39121	−	1.73732i	0.107153	−	0.0778511i
$499$	0.588660	−	5.60072i	0.0263520	−	0.250723i	−0.973413	−	0.229056i	$-0.926436\pi$
$499$	0.588660	−	5.60072i	0.0263520	−	0.250723i	0.999765	−	0.0216667i	$-0.00689725\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−9.79123	+	16.9589i	−0.437440	+	0.757668i
$502$	4.13734	+	7.16609i	0.184659	+	0.319838i
$503$	26.9406	−	5.72640i	1.20122	−	0.255328i	0.436509	−	0.899700i	$-0.356215\pi$
$503$	26.9406	−	5.72640i	1.20122	−	0.255328i	0.764712	+	0.644372i	$0.222881\pi$
$504$	−1.25465	−	3.86142i	−0.0558867	−	0.172002i
$505$	5.23684	+	1.11312i	0.233036	+	0.0495334i
$506$	0.0382621	+	0.364039i	0.00170096	+	0.0161835i
$507$	−3.49210	−	3.87837i	−0.155090	−	0.172244i
$508$	14.4140	+	6.41755i	0.639520	+	0.284733i
$509$	−4.99129	+	2.22227i	−0.221235	+	0.0985002i	−0.514361	−	0.857574i	$-0.671971\pi$
$509$	−4.99129	+	2.22227i	−0.221235	+	0.0985002i	0.293126	+	0.956074i	$0.405304\pi$
$510$	2.30402	−	2.55887i	0.102024	−	0.113309i
$511$	−18.9528	−	13.7700i	−0.838423	−	0.609150i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.0782742	+	0.0869323i	−0.00345589	+	0.00383815i
$514$	13.3032	−	5.92296i	0.586779	−	0.261251i
$515$	6.65409	+	2.96259i	0.293214	+	0.130547i
$516$	3.99124	+	4.43272i	0.175705	+	0.195140i
$517$	1.08073	+	10.2825i	0.0475306	+	0.452223i
$518$	−4.69786	−	0.998560i	−0.206412	−	0.0438742i
$519$	0.621305	+	1.91218i	0.0272722	+	0.0839353i
$520$	−4.17508	+	0.887441i	−0.183089	+	0.0389169i
$521$	−14.2832	−	24.7393i	−0.625760	−	1.08385i	−0.988393	−	0.151916i	$-0.951456\pi$
$521$	−14.2832	−	24.7393i	−0.625760	−	1.08385i	0.362634	−	0.931932i	$-0.381878\pi$
$522$	0.972918	−	1.68514i	0.0425835	−	0.0737568i
$523$	−3.34346	+	10.2901i	−0.146199	+	0.449955i	−0.997163	−	0.0752688i	$-0.976019\pi$
$523$	−3.34346	+	10.2901i	−0.146199	+	0.449955i	0.850964	+	0.525224i	$0.176019\pi$
$524$	0.768883	−	7.31543i	0.0335888	−	0.319576i
$525$	−3.28472	+	2.38649i	−0.143357	+	0.104155i
$526$	24.3201			1.06041
$527$	−18.5147	−	4.97519i	−0.806512	−	0.216723i
$528$	−1.26589			−0.0550910
$529$	18.5397	−	13.4699i	0.806076	−	0.585648i
$530$	0.650266	−	6.18687i	0.0282458	−	0.268740i
$531$	−1.39807	+	4.30281i	−0.0606710	+	0.186726i
$532$	0.237475	−	0.411320i	0.0102959	−	0.0178330i
$533$	−17.1673	−	29.7347i	−0.743600	−	1.28795i
$534$	8.44831	−	1.79574i	0.365594	−	0.0777094i
$535$	−2.91722	−	8.97829i	−0.126123	−	0.388166i
$536$	−0.156907	−	0.0333516i	−0.00677735	−	0.00144057i
$537$	0.180307	+	1.71551i	0.00778084	+	0.0740297i
$538$	6.25805	+	6.95026i	0.269804	+	0.299647i
$539$	10.9687	+	4.88356i	0.472454	+	0.210350i
$540$	−0.913545	+	0.406737i	−0.0393127	+	0.0175032i
$541$	13.7877	−	15.3128i	0.592778	−	0.658347i	−0.369876	−	0.929081i	$-0.620600\pi$
$541$	13.7877	−	15.3128i	0.592778	−	0.658347i	0.962654	+	0.270734i	$0.0872665\pi$
$542$	7.45442	+	5.41595i	0.320195	+	0.232635i
$543$	6.41657	+	4.66191i	0.275361	+	0.200062i
$544$	−2.30402	+	2.55887i	−0.0987839	+	0.109711i
$545$	0.00800371	−	0.00356348i	0.000342841	−	0.000152643i
$546$	15.8319	+	7.04880i	0.677541	+	0.301661i
$547$	1.55659	+	1.72876i	0.0665548	+	0.0739166i	0.775503	−	0.631344i	$-0.217497\pi$
$547$	1.55659	+	1.72876i	0.0665548	+	0.0739166i	−0.708948	+	0.705261i	$0.750830\pi$
$548$	1.78647	+	16.9971i	0.0763141	+	0.726080i
$549$	−14.2388	−	3.02654i	−0.607696	−	0.129170i
$550$	0.391183	+	1.20394i	0.0166801	+	0.0513360i
$551$	0.222648	−	0.0473252i	0.00948511	−	0.00201612i
$552$	−0.144579	−	0.250419i	−0.00615371	−	0.0106585i
$553$	19.2848	−	33.4023i	0.820075	−	1.42041i
$554$	−7.33205	+	22.5657i	−0.311509	+	0.958726i
$555$	−0.123648	+	1.17644i	−0.00524859	+	0.0499370i
$556$	−5.50864	+	4.00226i	−0.233618	+	0.169734i
$557$	−7.62815			−0.323215			−0.161608	−	0.986855i	$-0.551668\pi$
$557$	−7.62815			−0.323215			−0.161608	+	0.986855i	$0.551668\pi$
$558$	4.32446	+	3.50700i	0.183069	+	0.148463i
$559$	−25.4600			−1.07684
$560$	3.28472	−	2.38649i	0.138805	−	0.100848i
$561$	−0.455624	+	4.33497i	−0.0192365	+	0.183023i
$562$	9.44907	−	29.0812i	0.398585	−	1.22672i
$563$	3.36027	−	5.82015i	0.141618	−	0.245290i	−0.786488	−	0.617606i	$-0.788103\pi$
$563$	3.36027	−	5.82015i	0.141618	−	0.245290i	0.928106	+	0.372316i	$0.121436\pi$
$564$	−4.08372	−	7.07321i	−0.171956	−	0.297836i
$565$	−14.3038	+	3.04036i	−0.601764	+	0.127909i
$566$	−5.61869	−	17.2925i	−0.236171	−	0.726860i
$567$	3.97142	+	0.844151i	0.166784	+	0.0354510i
$568$	0.134177	+	1.27661i	0.00562994	+	0.0535653i
$569$	−21.3162	−	23.6740i	−0.893620	−	0.992466i	0.106378	−	0.994326i	$-0.466075\pi$
$569$	−21.3162	−	23.6740i	−0.893620	−	0.992466i	−0.999998	+	0.00185994i	$0.999408\pi$
$570$	−0.106866	−	0.0475796i	−0.00447611	−	0.00199289i
$571$	−40.9315	+	18.2239i	−1.71293	+	0.762646i	−0.714946	+	0.699180i	$0.753549\pi$
$571$	−40.9315	+	18.2239i	−1.71293	+	0.762646i	−0.997984	+	0.0634659i	$0.979785\pi$
$572$	3.61550	−	4.01542i	0.151172	−	0.167893i
$573$	−12.0122	−	8.72737i	−0.501817	−	0.364591i
$574$	26.4223	+	19.1970i	1.10285	+	0.801265i
$575$	−0.193485	+	0.214887i	−0.00806888	+	0.00896140i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	13.4602	+	5.99286i	0.560355	+	0.249486i	0.667313	−	0.744777i	$-0.267444\pi$
$577$	13.4602	+	5.99286i	0.560355	+	0.249486i	−0.106958	+	0.994264i	$0.534111\pi$
$578$	−3.44180	−	3.82250i	−0.143160	−	0.158995i
$579$	−0.162539	−	1.54646i	−0.00675490	−	0.0642686i
$580$	1.90332	+	0.404562i	0.0790309	+	0.0167985i
$581$	−3.70838	−	11.4132i	−0.153849	−	0.473500i
$582$	−12.1701	+	2.58684i	−0.504467	+	0.107228i
$583$	3.93753	+	6.82000i	0.163076	+	0.282456i
$584$	2.88499	−	4.99695i	0.119382	−	0.206775i
$585$	1.31899	−	4.05945i	0.0545337	−	0.167838i
$586$	2.49924	−	23.7787i	0.103243	−	0.982289i
$587$	−33.7375	+	24.5117i	−1.39249	+	1.01171i	−0.396908	+	0.917858i	$0.629917\pi$
$587$	−33.7375	+	24.5117i	−1.39249	+	1.01171i	−0.995587	+	0.0938479i	$0.970083\pi$
$588$	−9.48475			−0.391145
$589$	0.0336216	+	0.650443i	0.00138535	+	0.0268010i
$590$	−4.52424			−0.186260
$591$	−2.01153	+	1.46146i	−0.0827433	+	0.0601165i
$592$	0.123648	−	1.17644i	0.00508192	−	0.0483513i
$593$	−11.8369	+	36.4301i	−0.486082	+	1.49601i	0.344327	+	0.938850i	$0.388107\pi$
$593$	−11.8369	+	36.4301i	−0.486082	+	1.49601i	−0.830408	+	0.557155i	$0.811893\pi$
$594$	0.632947	−	1.09630i	0.0259701	−	0.0449816i
$595$	−6.99014	−	12.1073i	−0.286568	−	0.496350i
$596$	12.8188	−	2.72473i	0.525080	−	0.111609i
$597$	3.69338	+	11.3670i	0.151160	+	0.465222i
$598$	1.20726	+	0.256611i	0.0493686	+	0.0104936i
$599$	4.87756	+	46.4069i	0.199292	+	1.89613i	0.400050	+	0.916493i	$0.368993\pi$
$599$	4.87756	+	46.4069i	0.199292	+	1.89613i	−0.200759	+	0.979641i	$0.564341\pi$
$600$	−0.669131	−	0.743145i	−0.0273171	−	0.0303388i
$601$	25.0483	+	11.1522i	1.02174	+	0.454909i	0.848064	−	0.529893i	$-0.177768\pi$
$601$	25.0483	+	11.1522i	1.02174	+	0.454909i	0.173678	+	0.984802i	$0.444435\pi$
$602$	22.1243	−	9.85035i	0.901717	−	0.401470i
$603$	0.107337	−	0.119210i	0.00437109	−	0.00485459i
$604$	11.2253	+	8.15567i	0.456752	+	0.331850i
$605$	7.60275	+	5.52372i	0.309096	+	0.224571i
$606$	3.58242	−	3.97868i	0.145526	−	0.161623i
$607$	4.64470	−	2.06795i	0.188522	−	0.0839356i	−0.310305	−	0.950637i	$-0.600431\pi$
$607$	4.64470	−	2.06795i	0.188522	−	0.0839356i	0.498827	+	0.866702i	$0.333764\pi$
$608$	0.106866	+	0.0475796i	0.00433397	+	0.00192961i
$609$	−5.28638	−	5.87112i	−0.214215	−	0.237910i
$610$	−1.52161	−	14.4771i	−0.0616081	−	0.586162i
$611$	34.0998	+	7.24813i	1.37953	+	0.293228i
$612$	−1.06404	−	3.27477i	−0.0430112	−	0.132375i
$613$	−0.549610	+	0.116823i	−0.0221986	+	0.00471845i	−0.218998	−	0.975725i	$-0.570279\pi$
$613$	−0.549610	+	0.116823i	−0.0221986	+	0.00471845i	0.196799	+	0.980444i	$0.436945\pi$
$614$	6.15666	+	10.6637i	0.248463	+	0.430350i
$615$	4.02200	−	6.96631i	0.162183	−	0.280909i
$616$	−1.58826	+	4.88815i	−0.0639927	+	0.196949i
$617$	−1.76295	+	16.7733i	−0.0709736	+	0.675269i	0.899969	+	0.435955i	$0.143589\pi$
$617$	−1.76295	+	16.7733i	−0.0709736	+	0.675269i	−0.970942	+	0.239314i	$0.923077\pi$
$618$	5.89272	−	4.28131i	0.237040	−	0.172220i
$619$	−4.39164			−0.176515			−0.0882575	−	0.996098i	$-0.528130\pi$
$619$	−4.39164			−0.176515			−0.0882575	+	0.996098i	$0.528130\pi$
$620$	−1.99903	+	5.19653i	−0.0802829	+	0.208698i
$621$	0.289159			0.0116035
$622$	11.8496	−	8.60921i	0.475124	−	0.345198i
$623$	3.66557	−	34.8756i	0.146858	−	1.39726i
$624$	−1.31899	+	4.05945i	−0.0528020	+	0.162508i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.35055	−	7.53538i	−0.173883	−	0.301174i
$627$	0.144847	−	0.0307882i	0.00578463	−	0.00122956i
$628$	3.01358	+	9.27485i	0.120255	+	0.370107i
$629$	−3.98413	−	0.846853i	−0.158858	−	0.0337662i
$630$	0.424400	+	4.03790i	0.0169085	+	0.160874i
$631$	−20.7070	−	22.9974i	−0.824331	−	0.915513i	0.173260	−	0.984876i	$-0.444570\pi$
$631$	−20.7070	−	22.9974i	−0.824331	−	0.915513i	−0.997591	+	0.0693633i	$0.977903\pi$
$632$	8.67831	+	3.86383i	0.345205	+	0.153695i
$633$	−24.4152	+	10.8703i	−0.970416	+	0.432057i
$634$	−10.2707	+	11.4068i	−0.407902	+	0.453021i
$635$	−12.7648	−	9.27416i	−0.506555	−	0.368034i
$636$	−5.03285	−	3.65658i	−0.199566	−	0.144993i
$637$	27.0893	−	30.0857i	1.07332	−	1.19204i
$638$	−2.25027	+	1.00188i	−0.0890889	+	0.0396649i
$639$	−1.17266	−	0.522103i	−0.0463899	−	0.0206541i
$640$	0.669131	+	0.743145i	0.0264497	+	0.0293754i
$641$	2.40153	+	22.8491i	0.0948549	+	0.902484i	0.933686	+	0.358093i	$0.116573\pi$
$641$	2.40153	+	22.8491i	0.0948549	+	0.902484i	−0.838831	+	0.544392i	$0.816761\pi$
$642$	−9.23404	−	1.96276i	−0.364439	−	0.0774638i
$643$	−4.63949	−	14.2789i	−0.182963	−	0.563104i	0.816944	−	0.576717i	$-0.195667\pi$
$643$	−4.63949	−	14.2789i	−0.182963	−	0.563104i	−0.999907	+	0.0136136i	$0.995667\pi$
$644$	−1.14837	+	0.244094i	−0.0452521	+	0.00961864i
$645$	−2.98241	−	5.16568i	−0.117432	−	0.203399i
$646$	0.201397	−	0.348829i	0.00792385	−	0.0137245i
$647$	−1.81774	+	5.59442i	−0.0714627	+	0.219940i	−0.980409	−	0.196974i	$-0.936888\pi$
$647$	−1.81774	+	5.59442i	−0.0714627	+	0.219940i	0.908946	+	0.416914i	$0.136888\pi$
$648$	−0.104528	+	0.994522i	−0.00410627	+	0.0390685i
$649$	4.63341	−	3.36637i	0.181877	−	0.132142i
$650$	4.26836			0.167419
$651$	18.9677	−	12.2985i	0.743403	−	0.482016i
$652$	−11.9781			−0.469100
$653$	20.2539	−	14.7153i	0.792596	−	0.575855i	−0.116137	−	0.993233i	$-0.537051\pi$
$653$	20.2539	−	14.7153i	0.792596	−	0.575855i	0.908733	+	0.417379i	$0.137051\pi$
$654$	0.000915790	−	0.00871316i	3.58102e−5	−	0.000340711i
$655$	−2.27304	+	6.99571i	−0.0888152	+	0.273345i
$656$	−4.02200	+	6.96631i	−0.157033	+	0.271989i
$657$	2.88499	+	4.99695i	0.112554	+	0.194950i
$658$	−32.4363	+	6.89456i	−1.26450	+	0.268778i
$659$	−9.65015	−	29.7001i	−0.375917	−	1.15695i	−0.942858	−	0.333194i	$-0.891874\pi$
$659$	−9.65015	−	29.7001i	−0.375917	−	1.15695i	0.566942	−	0.823758i	$-0.308126\pi$
$660$	1.23823	+	0.263194i	0.0481981	+	0.0102448i
$661$	−3.61977	−	34.4398i	−0.140793	−	1.33955i	−0.805565	−	0.592508i	$-0.798138\pi$
$661$	−3.61977	−	34.4398i	−0.140793	−	1.33955i	0.664772	−	0.747047i	$-0.268529\pi$
$662$	−18.4603	−	20.5023i	−0.717482	−	0.796844i
$663$	13.4266	+	5.97790i	0.521445	+	0.232162i
$664$	2.70017	−	1.20219i	0.104787	−	0.0466541i
$665$	−0.317804	+	0.352957i	−0.0123239	+	0.0136871i
$666$	0.957000	+	0.695301i	0.0370830	+	0.0269424i
$667$	−0.455198	−	0.330721i	−0.0176253	−	0.0128056i
$668$	−13.1032	+	14.5526i	−0.506979	+	0.563057i
$669$	−13.8074	+	6.14746i	−0.533825	+	0.237674i
$670$	0.146544	+	0.0652456i	0.00566149	+	0.00252066i
$671$	12.3304	+	13.6943i	0.476009	+	0.528661i
$672$	−0.424400	−	4.03790i	−0.0163716	−	0.155765i
$673$	−8.61373	−	1.83090i	−0.332035	−	0.0705762i	0.0388778	−	0.999244i	$-0.487622\pi$
$673$	−8.61373	−	1.83090i	−0.332035	−	0.0705762i	−0.370913	+	0.928668i	$0.620955\pi$
$674$	−7.65719	−	23.5664i	−0.294944	−	0.907744i
$675$	0.978148	−	0.207912i	0.0376489	−	0.00800252i
$676$	−2.60943	−	4.51967i	−0.100363	−	0.173833i
$677$	7.64153	−	13.2355i	0.293688	−	0.508682i	−0.680991	−	0.732292i	$-0.738451\pi$
$677$	7.64153	−	13.2355i	0.293688	−	0.508682i	0.974679	+	0.223610i	$0.0717841\pi$
$678$	−4.51885	+	13.9076i	−0.173546	+	0.534118i
$679$	−5.28039	+	50.2395i	−0.202643	+	1.92802i
$680$	2.78569	−	2.02392i	0.106826	−	0.0776138i
$681$	25.7729			0.987618
$682$	−1.81934	−	6.80934i	−0.0696660	−	0.260743i
$683$	42.4521			1.62438			0.812192	−	0.583390i	$-0.198274\pi$
$683$	42.4521			1.62438			0.812192	+	0.583390i	$0.198274\pi$
$684$	−0.0946379	+	0.0687585i	−0.00361857	+	0.00262905i
$685$	1.78647	−	16.9971i	0.0682574	−	0.649426i
$686$	−3.11750	+	9.59468i	−0.119027	+	0.366327i
$687$	3.27237	−	5.66790i	0.124849	−	0.216244i
$688$	2.98241	+	5.16568i	0.113703	+	0.196940i
$689$	25.9730	−	5.52072i	0.989491	−	0.210323i
$690$	0.0893550	+	0.275006i	0.00340169	+	0.0104693i
$691$	5.69998	+	1.21157i	0.216838	+	0.0460903i	0.315049	−	0.949075i	$-0.397979\pi$
$691$	5.69998	+	1.21157i	0.216838	+	0.0460903i	−0.0982118	+	0.995166i	$0.531312\pi$
$692$	0.210163	+	1.99957i	0.00798921	+	0.0760122i
$693$	−3.43914	−	3.81955i	−0.130642	−	0.145093i
$694$	20.3506	+	9.06068i	0.772499	+	0.343939i
$695$	6.22038	−	2.76949i	0.235952	−	0.105053i
$696$	1.30202	−	1.44604i	0.0493529	−	0.0548119i
$697$	22.4081	+	16.2804i	0.848767	+	0.616665i
$698$	−23.9550	−	17.4043i	−0.906711	−	0.658764i
$699$	3.20464	−	3.55911i	0.121211	−	0.134618i
$700$	−3.70912	+	1.65141i	−0.140192	+	0.0624174i
$701$	−9.72666	−	4.33059i	−0.367371	−	0.163564i	0.214745	−	0.976670i	$-0.431108\pi$
$701$	−9.72666	−	4.33059i	−0.367371	−	0.163564i	−0.582115	+	0.813106i	$0.697775\pi$
$702$	−2.85609	−	3.17201i	−0.107796	−	0.119720i
$703$	0.0144643	+	0.137618i	0.000545530	+	0.00519037i
$704$	−1.23823	−	0.263194i	−0.0466676	−	0.00991950i
$705$	2.52388	+	7.76770i	0.0950548	+	0.292549i
$706$	−15.8177	+	3.36216i	−0.595308	+	0.126537i
$707$	−10.8687	−	18.8251i	−0.408758	−	0.707990i
$708$	−2.26212	+	3.91811i	−0.0850157	+	0.147252i
$709$	−12.3611	+	38.0436i	−0.464231	+	1.42876i	0.395716	+	0.918373i	$0.370496\pi$
$709$	−12.3611	+	38.0436i	−0.464231	+	1.42876i	−0.859947	+	0.510383i	$0.829504\pi$
$710$	0.134177	−	1.27661i	0.00503557	−	0.0479102i
$711$	−7.68533	+	5.58372i	−0.288222	+	0.209406i
$712$	8.63705			0.323687
$713$	1.13923	−	1.13760i	0.0426646	−	0.0426036i
$714$	−13.9803			−0.523199
$715$	−4.37135	+	3.17597i	−0.163479	+	0.118775i
$716$	−0.180307	+	1.71551i	−0.00673840	+	0.0641116i
$717$	−3.84474	+	11.8329i	−0.143584	+	0.441907i
$718$	−8.00190	+	13.8597i	−0.298628	+	0.517239i
$719$	−13.5972	−	23.5511i	−0.507091	−	0.878308i	−0.999966	−	0.00820783i	$-0.997387\pi$
$719$	−13.5972	−	23.5511i	−0.507091	−	0.878308i	0.492875	−	0.870100i	$-0.335946\pi$
$720$	−0.978148	+	0.207912i	−0.0364534	+	0.00774841i
$721$	−9.13865	−	28.1259i	−0.340341	−	1.04746i
$722$	18.5714	+	3.94748i	0.691157	+	0.146910i
$723$	2.06697	+	19.6659i	0.0768715	+	0.731384i
$724$	5.30709	+	5.89412i	0.197236	+	0.219053i
$725$	−1.77761	−	0.791443i	−0.0660188	−	0.0293935i
$726$	8.58505	−	3.82231i	0.318621	−	0.141859i
$727$	−24.7927	+	27.5351i	−0.919512	+	1.02122i	0.0801892	+	0.996780i	$0.474448\pi$
$727$	−24.7927	+	27.5351i	−0.919512	+	1.02122i	−0.999701	+	0.0244419i	$0.992219\pi$
$728$	14.0204	+	10.1864i	0.519629	+	0.377533i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−3.86087	+	4.28793i	−0.142897	+	0.158704i
$731$	18.7630	−	8.35383i	0.693975	−	0.308977i
$732$	−13.2984	−	5.92081i	−0.491522	−	0.218840i
$733$	−27.7695	−	30.8412i	−1.02569	−	1.13914i	−0.990183	−	0.139775i	$-0.955362\pi$
$733$	−27.7695	−	30.8412i	−1.02569	−	1.13914i	−0.0355068	−	0.999369i	$-0.511305\pi$
$734$	−1.44254	−	13.7249i	−0.0532452	−	0.506594i
$735$	9.27749	+	1.97199i	0.342205	+	0.0727380i
$736$	−0.0893550	−	0.275006i	−0.00329367	−	0.0101369i
$737$	−0.198627	+	0.0422196i	−0.00731654	+	0.00155518i
$738$	−4.02200	−	6.96631i	−0.148052	−	0.256434i
$739$	17.5608	−	30.4162i	0.645984	−	1.11888i	−0.338090	−	0.941114i	$-0.609781\pi$
$739$	17.5608	−	30.4162i	0.645984	−	1.11888i	0.984073	−	0.177762i	$-0.0568859\pi$
$740$	−0.365541	+	1.12502i	−0.0134376	+	0.0413566i
$741$	0.0521919	−	0.496572i	0.00191732	−	0.0182420i
$742$	−20.4341	+	14.8462i	−0.750159	+	0.545023i
$743$	−14.5164			−0.532554			−0.266277	−	0.963896i	$-0.585794\pi$
$743$	−14.5164			−0.532554			−0.266277	+	0.963896i	$0.585794\pi$
$744$	3.50081	+	4.32947i	0.128346	+	0.158726i
$745$	−13.1052			−0.480138
$746$	−12.5592	+	9.12482i	−0.459826	+	0.334083i
$747$	−0.308955	+	2.93951i	−0.0113041	+	0.107551i
$748$	−1.34696	+	4.14552i	−0.0492497	+	0.151575i
$749$	−19.1646	+	33.1940i	−0.700258	+	1.21288i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−24.8268	+	5.27710i	−0.905942	+	0.192564i	−0.637246	−	0.770661i	$-0.719926\pi$
$751$	−24.8268	+	5.27710i	−0.905942	+	0.192564i	−0.268697	+	0.963225i	$0.586593\pi$
$752$	−2.52388	−	7.76770i	−0.0920364	−	0.283259i
$753$	−8.09386	−	1.72040i	−0.294957	−	0.0626950i
$754$	0.868164	+	8.26003i	0.0316167	+	0.300812i
$755$	−9.28436	−	10.3113i	−0.337893	−	0.375268i
$756$	3.70912	+	1.65141i	0.134900	+	0.0600611i
$757$	49.2091	−	21.9093i	1.78854	−	0.796307i	0.811151	−	0.584836i	$-0.198841\pi$
$757$	49.2091	−	21.9093i	1.78854	−	0.796307i	0.977384	−	0.211471i	$-0.0678254\pi$
$758$	−18.0887	+	20.0896i	−0.657013	+	0.729687i
$759$	−0.296136	−	0.215155i	−0.0107491	−	0.00780965i
$760$	−0.0946379	−	0.0687585i	−0.00343288	−	0.00249413i
$761$	−12.5274	+	13.9131i	−0.454117	+	0.504348i	−0.926110	−	0.377255i	$-0.876868\pi$
$761$	−12.5274	+	13.9131i	−0.454117	+	0.504348i	0.471993	+	0.881602i	$0.343535\pi$
$762$	−14.4140	+	6.41755i	−0.522166	+	0.232483i
$763$	−0.0324962	−	0.0144682i	−0.00117644	−	0.000523785i
$764$	−9.93518	−	11.0341i	−0.359442	−	0.399201i
$765$	0.359923	+	3.42444i	0.0130130	+	0.123811i
$766$	20.1609	+	4.28532i	0.728441	+	0.154835i
$767$	−5.96745	−	18.3659i	−0.215472	−	0.663155i
$768$	0.978148	−	0.207912i	0.0352959	−	0.00750237i
$769$	1.18348	+	2.04985i	0.0426774	+	0.0739194i	0.886575	−	0.462585i	$-0.153078\pi$
$769$	1.18348	+	2.04985i	0.0426774	+	0.0739194i	−0.843898	+	0.536504i	$0.819745\pi$
$770$	2.56985	−	4.45112i	0.0926111	−	0.160407i
$771$	−4.49995	+	13.8494i	−0.162062	+	0.498775i
$772$	0.162539	−	1.54646i	0.00584991	−	0.0556582i
$773$	−36.0168	+	26.1677i	−1.29543	+	0.941188i	−0.999900	−	0.0141445i	$-0.995498\pi$
$773$	−36.0168	+	26.1677i	−1.29543	+	0.941188i	−0.295534	+	0.955332i	$0.595498\pi$
$774$	−5.96482			−0.214401
$775$	3.03576	−	4.66735i	0.109048	−	0.167656i
$776$	−12.4420			−0.446642
$777$	3.88556	−	2.82302i	0.139394	−	0.101275i
$778$	−2.82701	+	26.8972i	−0.101353	+	0.964310i
$779$	0.290779	−	0.894924i	0.0104182	−	0.0320640i
$780$	2.13418	−	3.69650i	0.0764158	−	0.132356i
$781$	0.812476	+	1.40725i	0.0290727	+	0.0503554i
$782$	−0.973903	+	0.207009i	−0.0348267	+	0.00740264i
$783$	0.601297	+	1.85060i	0.0214886	+	0.0661351i
$784$	−9.27749	−	1.97199i	−0.331339	−	0.0704282i
$785$	−1.01938	−	9.69874i	−0.0363832	−	0.346163i
$786$	4.92194	+	5.46637i	0.175560	+	0.194979i
$787$	−23.9386	−	10.6581i	−0.853318	−	0.379921i	−0.0670067	−	0.997753i	$-0.521345\pi$
$787$	−23.9386	−	10.6581i	−0.853318	−	0.379921i	−0.786311	+	0.617831i	$0.788012\pi$
$788$	−2.27143	+	1.01131i	−0.0809163	+	0.0360263i
$789$	−16.2733	+	18.0734i	−0.579347	+	0.643430i
$790$	−7.68533	−	5.58372i	−0.273432	−	0.198660i
$791$	48.0336	+	34.8984i	1.70788	+	1.24085i
$792$	0.847048	−	0.940743i	0.0300986	−	0.0334278i
$793$	56.7622	−	25.2721i	2.01568	−	0.897440i
$794$	−19.0865	−	8.49788i	−0.677356	−	0.301578i
$795$	4.16263	+	4.62307i	0.147633	+	0.163963i
$796$	1.24933	+	11.8865i	0.0442812	+	0.421307i
$797$	−18.8535	−	4.00744i	−0.667825	−	0.141951i	−0.138491	−	0.990364i	$-0.544225\pi$
$797$	−18.8535	−	4.00744i	−0.667825	−	0.141951i	−0.529335	+	0.848413i	$0.677558\pi$
$798$	0.146768	+	0.451705i	0.00519553	+	0.0159902i
$799$	−27.5084	+	5.84709i	−0.973178	+	0.206855i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−4.31853	+	7.47991i	−0.152588	+	0.264290i
$802$	−0.961708	+	2.95983i	−0.0339591	+	0.104515i
$803$	0.763496	−	7.26418i	0.0269432	−	0.256347i
$804$	0.129776	−	0.0942880i	0.00457686	−	0.00332528i
$805$	1.17403			0.0413790
$806$	−23.7317	−	1.26076i	−0.835915	−	0.0444082i
$807$	−9.35250			−0.329224
$808$	4.33134	−	3.14691i	0.152376	−	0.110708i
$809$	4.39303	−	41.7969i	0.154451	−	1.46950i	−0.593010	−	0.805195i	$-0.702060\pi$
$809$	4.39303	−	41.7969i	0.154451	−	1.46950i	0.747460	−	0.664306i	$-0.231273\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	12.1128	−	20.9799i	0.425337	−	0.736705i	−0.571115	−	0.820870i	$-0.693489\pi$
$811$	12.1128	−	20.9799i	0.425337	−	0.736705i	0.996452	+	0.0841651i	$0.0268223\pi$
$812$	−3.95019	−	6.84192i	−0.138624	−	0.240104i
$813$	−9.01282	+	1.91573i	−0.316093	+	0.0671877i
$814$	−0.462737	−	1.42416i	−0.0162189	−	0.0499167i
$815$	11.7164	+	2.49039i	0.410407	+	0.0872347i
$816$	−0.359923	−	3.42444i	−0.0125998	−	0.119879i
$817$	−0.466891	−	0.518535i	−0.0163345	−	0.0181413i
$818$	−21.9479	−	9.77183i	−0.767390	−	0.341664i
$819$	−15.8319	+	7.04880i	−0.553210	+	0.246305i
$820$	5.38249	−	5.97786i	0.187965	−	0.208756i
$821$	−16.2866	−	11.8329i	−0.568406	−	0.412971i	0.266120	−	0.963940i	$-0.414258\pi$
$821$	−16.2866	−	11.8329i	−0.568406	−	0.412971i	−0.834526	+	0.550969i	$0.814258\pi$
$822$	−13.8267	−	10.0457i	−0.482261	−	0.350383i
$823$	−24.2519	+	26.9344i	−0.845368	+	0.938876i	−0.998785	−	0.0492856i	$-0.984306\pi$
$823$	−24.2519	+	26.9344i	−0.845368	+	0.938876i	0.153417	+	0.988162i	$0.450972\pi$
$824$	6.65409	−	2.96259i	0.231806	−	0.103207i
$825$	−1.15645	−	0.514885i	−0.0402625	−	0.0179260i
$826$	12.2913	+	13.6509i	0.427669	+	0.474975i
$827$	−4.49572	−	42.7739i	−0.156332	−	1.48739i	−0.738460	−	0.674298i	$-0.764446\pi$
$827$	−4.49572	−	42.7739i	−0.156332	−	1.48739i	0.582128	−	0.813097i	$-0.302220\pi$
$828$	0.282840	+	0.0601195i	0.00982937	+	0.00208930i
$829$	−12.1341	−	37.3449i	−0.421435	−	1.29704i	−0.906367	−	0.422491i	$-0.861156\pi$
$829$	−12.1341	−	37.3449i	−0.421435	−	1.29704i	0.484932	−	0.874552i	$-0.338844\pi$
$830$	−2.89111	+	0.614525i	−0.100352	+	0.0213305i
$831$	−11.8635	−	20.5482i	−0.411541	−	0.712809i
$832$	−2.13418	+	3.69650i	−0.0739893	+	0.128153i
$833$	−10.0921	+	31.0604i	−0.349672	+	1.07618i
$834$	0.711740	−	6.77175i	0.0246455	−	0.234487i
$835$	15.8425	−	11.5103i	0.548254	−	0.398330i
$836$	0.148083			0.00512155
$837$	−5.49984	+	0.867055i	−0.190102	+	0.0299698i
$838$	−35.8041			−1.23683
$839$	13.6165	−	9.89300i	0.470095	−	0.341544i	−0.327383	−	0.944892i	$-0.606167\pi$
$839$	13.6165	−	9.89300i	0.470095	−	0.341544i	0.797478	+	0.603347i	$0.206167\pi$
$840$	−0.424400	+	4.03790i	−0.0146432	+	0.139321i
$841$	−7.79147	+	23.9797i	−0.268671	+	0.826885i
$842$	14.3136	−	24.7919i	0.493279	−	0.854385i
$843$	15.2889	+	26.4812i	0.526578	+	0.912060i
$844$	−26.1417	+	5.55659i	−0.899835	+	0.191266i
$845$	1.61272	+	4.96343i	0.0554792	+	0.170747i
$846$	7.98897	+	1.69811i	0.274666	+	0.0583821i
$847$	−3.98831	−	37.9462i	−0.137040	−	1.30385i
$848$	−4.16263	−	4.62307i	−0.142945	−	0.158757i
$849$	16.6105	+	7.39547i	0.570071	+	0.253812i
$850$	−3.14561	+	1.40052i	−0.107894	+	0.0480373i
$851$	0.228877	−	0.254193i	0.00784579	−	0.00871363i
$852$	−1.03849	−	0.754505i	−0.0355780	−	0.0258489i
$853$	6.08356	+	4.41997i	0.208297	+	0.151337i	0.687043	−	0.726617i	$-0.258908\pi$
$853$	6.08356	+	4.41997i	0.208297	+	0.151337i	−0.478746	+	0.877954i	$0.658908\pi$
$854$	−39.5476	+	43.9221i	−1.35329	+	1.50298i
$855$	0.106866	−	0.0475796i	0.00365472	−	0.00162719i
$856$	−8.62418	−	3.83973i	−0.294768	−	0.131239i
$857$	−16.6576	−	18.5002i	−0.569014	−	0.631954i	0.388117	−	0.921610i	$-0.373126\pi$
$857$	−16.6576	−	18.5002i	−0.569014	−	0.631954i	−0.957131	+	0.289656i	$0.906459\pi$
$858$	0.564797	+	5.37369i	0.0192819	+	0.183455i
$859$	−21.2602	−	4.51900i	−0.725389	−	0.154186i	−0.169604	−	0.985512i	$-0.554249\pi$
$859$	−21.2602	−	4.51900i	−0.725389	−	0.154186i	−0.555785	+	0.831326i	$0.687582\pi$
$860$	−1.84323	−	5.67288i	−0.0628536	−	0.193444i
$861$	−31.9461	+	6.79036i	−1.08872	+	0.231415i
$862$	17.7820	+	30.7994i	0.605659	+	1.04903i
$863$	21.2986	−	36.8903i	0.725013	−	1.25576i	−0.233955	−	0.972247i	$-0.575167\pi$
$863$	21.2986	−	36.8903i	0.725013	−	1.25576i	0.958969	−	0.283512i	$-0.0914997\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	0.210163	−	1.99957i	0.00714576	−	0.0679874i
$866$	−15.4636	+	11.2350i	−0.525476	+	0.381780i
$867$	5.14369			0.174689
$868$	21.1102	−	8.08613i	0.716528	−	0.274461i
$869$	12.0255			0.407936
$870$	−1.57422	+	1.14373i	−0.0533709	+	0.0387762i
$871$	−0.0715703	+	0.680946i	−0.00242507	+	0.0230730i
$872$	0.00270734	−	0.00833235i	9.16822e−5	−	0.000282169i
$873$	6.22100	−	10.7751i	0.210549	−	0.364681i
$874$	0.0169127	+	0.0292937i	0.000572082	+	0.000990875i
$875$	3.97142	−	0.844151i	0.134258	−	0.0285375i
$876$	1.78302	+	5.48758i	0.0602428	+	0.185408i
$877$	40.8656	+	8.68625i	1.37993	+	0.293314i	0.837340	−	0.546682i	$-0.184109\pi$
$877$	40.8656	+	8.68625i	1.37993	+	0.293314i	0.542593	+	0.839996i	$0.317443\pi$
$878$	−3.40980	−	32.4421i	−0.115075	−	1.09487i
$879$	15.9987	+	17.7684i	0.539623	+	0.599312i
$880$	1.15645	+	0.514885i	0.0389840	+	0.0173568i
$881$	−2.69477	+	1.19979i	−0.0907891	+	0.0404219i	−0.451629	−	0.892206i	$-0.649157\pi$
$881$	−2.69477	+	1.19979i	−0.0907891	+	0.0404219i	0.360840	+	0.932628i	$0.382490\pi$
$882$	6.34654	−	7.04854i	0.213699	−	0.237337i
$883$	−22.8150	−	16.5761i	−0.767785	−	0.557829i	0.133503	−	0.991048i	$-0.457377\pi$
$883$	−22.8150	−	16.5761i	−0.767785	−	0.557829i	−0.901288	+	0.433220i	$0.857377\pi$
$884$	11.8903	+	8.63881i	0.399914	+	0.290555i
$885$	3.02731	−	3.36217i	0.101762	−	0.113018i
$886$	0.928791	−	0.413525i	0.0312034	−	0.0138926i
$887$	−32.8173	−	14.6112i	−1.10190	−	0.490596i	−0.226504	−	0.974010i	$-0.572730\pi$
$887$	−32.8173	−	14.6112i	−1.10190	−	0.490596i	−0.875392	+	0.483415i	$0.839396\pi$
$888$	0.791526	+	0.879079i	0.0265619	+	0.0294999i
$889$	6.69625	+	63.7105i	0.224585	+	2.13678i
$890$	−8.44831	−	1.79574i	−0.283188	−	0.0601935i
$891$	0.391183	+	1.20394i	0.0131051	+	0.0403334i
$892$	−14.7838	+	3.14240i	−0.494999	+	0.105215i
$893$	0.477709	+	0.827417i	0.0159859	+	0.0276885i
$894$	−6.55261	+	11.3494i	−0.219152	+	0.379582i
$895$	0.533042	−	1.64053i	0.0178176	−	0.0548370i
$896$	0.424400	−	4.03790i	0.0141782	−	0.134897i
$897$	−0.998515	+	0.725464i	−0.0333394	+	0.0242225i
$898$	22.0728			0.736580
$899$	9.64961	+	4.92542i	0.321832	+	0.164272i
$900$	1.00000			0.0333333
$901$	−17.3296	+	12.5907i	−0.577333	+	0.419457i
$902$	−1.06440	+	10.1271i	−0.0354406	+	0.337195i
$903$	−7.48378	+	23.0327i	−0.249044	+	0.766480i
$904$	−7.31166	+	12.6642i	−0.243182	+	0.421204i
$905$	−3.96566	−	6.86872i	−0.131823	−	0.228324i
$906$	−13.5721	+	2.88483i	−0.450901	+	0.0958420i
$907$	−7.08273	−	21.7984i	−0.235178	−	0.723804i	−0.997098	−	0.0761321i	$-0.975743\pi$
$907$	−7.08273	−	21.7984i	−0.235178	−	0.723804i	0.761920	−	0.647672i	$-0.224257\pi$
$908$	25.2097	+	5.35848i	0.836612	+	0.177827i
$909$	0.559628	+	5.32451i	0.0185617	+	0.176603i
$910$	−11.5961	−	12.8788i	−0.384408	−	0.426928i
$911$	−6.37982	−	2.84048i	−0.211373	−	0.0941093i	0.298319	−	0.954466i	$-0.403574\pi$
$911$	−6.37982	−	2.84048i	−0.211373	−	0.0941093i	−0.509692	+	0.860357i	$0.670241\pi$
$912$	−0.106866	+	0.0475796i	−0.00353867	+	0.00157552i
$913$	2.50362	−	2.78055i	0.0828578	−	0.0920229i
$914$	−10.5632	−	7.67462i	−0.349400	−	0.253854i
$915$	11.7768	+	8.55632i	0.389328	+	0.282863i
$916$	4.37928	−	4.86368i	0.144695	−	0.160701i
$917$	27.2833	−	12.1473i	0.900974	−	0.401139i
$918$	3.14561	+	1.40052i	0.103821	+	0.0462239i
$919$	−14.8244	−	16.4642i	−0.489013	−	0.543103i	0.447248	−	0.894410i	$-0.352404\pi$
$919$	−14.8244	−	16.4642i	−0.489013	−	0.543103i	−0.936260	+	0.351307i	$0.885737\pi$
$920$	0.0302253	+	0.287575i	0.000996499	+	0.00948106i
$921$	−12.0443	−	2.56008i	−0.396872	−	0.0843577i
$922$	1.97654	+	6.08317i	0.0650939	+	0.200338i
$923$	5.35930	−	1.13915i	0.176404	−	0.0374957i
$924$	−2.56985	−	4.45112i	−0.0845420	−	0.146431i
$925$	0.591458	−	1.02444i	0.0194470	−	0.0336833i
$926$	9.44273	−	29.0617i	0.310307	−	0.955028i
$927$	−0.761365	+	7.24391i	−0.0250065	+	0.237921i
$928$	1.57422	−	1.14373i	0.0516761	−	0.0375449i
$929$	15.0872			0.494996			0.247498	−	0.968888i	$-0.420392\pi$
$929$	15.0872			0.494996			0.247498	+	0.968888i	$0.420392\pi$
$930$	−2.52416	−	4.96272i	−0.0827705	−	0.162734i
$931$	1.10952			0.0363629
$932$	3.87459	−	2.81505i	0.126916	−	0.0922101i
$933$	−1.53101	+	14.5666i	−0.0501232	+	0.476890i
$934$	−5.29880	+	16.3080i	−0.173382	+	0.533615i
$935$	2.17943	−	3.77488i	0.0712749	−	0.123452i
$936$	−2.13418	−	3.69650i	−0.0697578	−	0.120824i
$937$	42.8810	−	9.11464i	1.40086	−	0.297762i	0.555304	−	0.831647i	$-0.312602\pi$
$937$	42.8810	−	9.11464i	1.40086	−	0.297762i	0.845557	+	0.533885i	$0.179269\pi$
$938$	−0.201262	−	0.619420i	−0.00657143	−	0.0202248i
$939$	8.51096	+	1.80906i	0.277745	+	0.0590365i
$940$	0.853730	+	8.12270i	0.0278456	+	0.264933i
$941$	21.1991	+	23.5440i	0.691072	+	0.767514i	0.981928	−	0.189253i	$-0.0606067\pi$
$941$	21.1991	+	23.5440i	0.691072	+	0.767514i	−0.290856	+	0.956767i	$0.593940\pi$
$942$	−8.90904	−	3.96656i	−0.290272	−	0.129238i
$943$	−2.12490	+	0.946068i	−0.0691963	+	0.0308082i
$944$	−3.02731	+	3.36217i	−0.0985305	+	0.109429i
$945$	−3.28472	−	2.38649i	−0.106852	−	0.0776326i
$946$	6.10875	+	4.43827i	0.198613	+	0.144300i
$947$	0.705591	−	0.783638i	0.0229286	−	0.0254648i	−0.731571	−	0.681765i	$-0.761213\pi$
$947$	0.705591	−	0.783638i	0.0229286	−	0.0254648i	0.754500	+	0.656300i	$0.227879\pi$
$948$	−8.67831	+	3.86383i	−0.281858	+	0.125491i
$949$	−22.4991	−	10.0173i	−0.730352	−	0.325174i
$950$	0.0782742	+	0.0869323i	0.00253955	+	0.00282046i
$951$	−1.60444	−	15.2653i	−0.0520276	−	0.495010i
$952$	−13.6748	−	2.90666i	−0.443202	−	0.0942055i
$953$	5.40210	+	16.6260i	0.174991	+	0.538567i	0.999633	−	0.0270877i	$-0.00862333\pi$
$953$	5.40210	+	16.6260i	0.174991	+	0.538567i	−0.824642	+	0.565655i	$0.808623\pi$
$954$	6.08501	−	1.29341i	0.197009	−	0.0418756i
$955$	7.42394	+	12.8586i	0.240233	+	0.416096i
$956$	−6.22091	+	10.7749i	−0.201199	+	0.348486i
$957$	0.761178	−	2.34266i	0.0246054	−	0.0757276i
$958$	1.07364	−	10.2150i	0.0346879	−	0.330033i
$959$	−56.1383	+	40.7869i	−1.81280	+	1.31708i
$960$	−1.00000			−0.0322749
$961$	−18.2572	+	25.0534i	−0.588942	+	0.808175i
$962$	−5.04911			−0.162790
$963$	7.63739	−	5.54889i	0.246112	−	0.178811i
$964$	−2.06697	+	19.6659i	−0.0665727	+	0.633397i
$965$	−0.480514	+	1.47887i	−0.0154683	+	0.0476065i
$966$	0.587013	−	1.01674i	0.0188868	−	0.0327129i
$967$	9.32649	+	16.1539i	0.299920	+	0.519476i	0.976117	−	0.217244i	$-0.0697068\pi$
$967$	9.32649	+	16.1539i	0.299920	+	0.519476i	−0.676198	+	0.736720i	$0.736373\pi$
$968$	9.19215	−	1.95385i	0.295447	−	0.0627992i
$969$	0.124470	+	0.383079i	0.00399855	+	0.0123063i
$970$	12.1701	+	2.58684i	0.390759	+	0.0830583i
$971$	0.512895	+	4.87987i	0.0164596	+	0.156602i	0.999664	−	0.0259028i	$-0.00824604\pi$
$971$	0.512895	+	4.87987i	0.0164596	+	0.156602i	−0.983205	+	0.182505i	$0.941579\pi$
$972$	−0.669131	−	0.743145i	−0.0214624	−	0.0238364i
$973$	−25.2556	−	11.2445i	−0.809658	−	0.360483i
$974$	27.2293	−	12.1232i	0.872482	−	0.388454i
$975$	−2.85609	+	3.17201i	−0.0914680	+	0.101586i
$976$	−11.7768	−	8.55632i	−0.376965	−	0.273881i
$977$	13.7472	+	9.98791i	0.439811	+	0.319542i	0.785560	−	0.618786i	$-0.212375\pi$
$977$	13.7472	+	9.98791i	0.439811	+	0.319542i	−0.345749	+	0.938327i	$0.612375\pi$
$978$	8.01494	−	8.90149i	0.256289	−	0.284638i
$979$	9.98833	−	4.44709i	0.319229	−	0.142130i
$980$	8.66475	+	3.85780i	0.276785	+	0.123233i
$981$	0.00586235	+	0.00651080i	0.000187171	+	0.000207874i
$982$	−0.414897	−	3.94748i	−0.0132399	−	0.125969i
$983$	−24.1770	−	5.13897i	−0.771125	−	0.163908i	−0.194484	−	0.980906i	$-0.562303\pi$
$983$	−24.1770	−	5.13897i	−0.771125	−	0.163908i	−0.576641	+	0.816998i	$0.695637\pi$
$984$	−2.48573	−	7.65031i	−0.0792423	−	0.243883i
$985$	2.43206	−	0.516949i	0.0774917	−	0.0164714i
$986$	−3.35005	−	5.80246i	−0.106687	−	0.184788i
$987$	16.5805	−	28.7183i	0.527763	−	0.914112i
$988$	0.154295	−	0.474870i	0.00490876	−	0.0151076i
$989$	−0.180289	+	1.71533i	−0.00573284	+	0.0545444i
$990$	−1.02413	+	0.744074i	−0.0325490	+	0.0236482i
$991$	−24.0404			−0.763670			−0.381835	−	0.924231i	$-0.624708\pi$
$991$	−24.0404			−0.763670			−0.381835	+	0.924231i	$0.624708\pi$
$992$	2.52416	+	4.96272i	0.0801422	+	0.157567i
$993$	27.5886			0.875496
$994$	−4.21640	+	3.06340i	−0.133736	+	0.0971650i
$995$	1.24933	−	11.8865i	0.0396063	−	0.376829i
$996$	−0.913362	+	2.81104i	−0.0289410	+	0.0890712i
$997$	25.3068	−	43.8327i	0.801475	−	1.38819i	−0.117171	−	0.993112i	$-0.537382\pi$
$997$	25.3068	−	43.8327i	0.801475	−	1.38819i	0.918645	−	0.395083i	$-0.129284\pi$
$998$	2.81579	+	4.87708i	0.0891321	+	0.154381i
$999$	−1.15707	+	0.245942i	−0.0366080	+	0.00778127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.b.121.2	✓	16
31.10	even	15	inner	930.2.bg.b.661.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.b.121.2	✓	16	1.1	even	1	trivial
930.2.bg.b.661.2	yes	16	31.10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.97142 - 0.844151i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.97142 - 0.844151i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.104528 - 0.994522i) q^{10} +(0.847048 + 0.940743i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(3.89934 - 1.73610i) q^{13} +(-2.71677 + 3.01727i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.30402 + 2.55887i) q^{17} +(0.913545 - 0.406737i) q^{18} +(0.106866 + 0.0475796i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.424400 - 4.03790i) q^{21} +(-1.23823 - 0.263194i) q^{22} +(-0.0893550 - 0.275006i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.13418 + 3.69650i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.424400 - 4.03790i) q^{28} +(1.57422 - 1.14373i) q^{29} -1.00000 q^{30} +(2.52416 + 4.96272i) q^{31} +1.00000 q^{32} +(1.02413 - 0.744074i) q^{33} +(0.359923 - 3.42444i) q^{34} +(-1.25465 + 3.86142i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.591458 + 1.02444i) q^{37} +(-0.114423 + 0.0243213i) q^{38} +(-1.31899 - 4.05945i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(-0.840828 - 7.99994i) q^{41} +(2.71677 + 3.01727i) q^{42} +(-5.44913 - 2.42611i) q^{43} +(1.15645 - 0.514885i) q^{44} +(0.669131 - 0.743145i) q^{45} +(0.233934 + 0.169963i) q^{46} +(6.60760 + 4.80070i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(8.66475 - 3.85780i) q^{49} +(0.913545 + 0.406737i) q^{50} +(2.30402 + 2.55887i) q^{51} +(-0.446165 - 4.24497i) q^{52} +(6.08501 + 1.29341i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-1.23823 + 0.263194i) q^{55} +(2.03007 + 3.51619i) q^{56} +(0.0584895 - 0.101307i) q^{57} +(-0.601297 + 1.85060i) q^{58} +(0.472912 - 4.49946i) q^{59} +(0.809017 - 0.587785i) q^{60} +14.5569 q^{61} +(-4.95910 - 2.53126i) q^{62} -4.06014 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.446165 + 4.24497i) q^{65} +(-0.391183 + 1.20394i) q^{66} +(-0.0802061 + 0.138921i) q^{67} +(1.72165 + 2.98199i) q^{68} +(-0.282840 + 0.0601195i) q^{69} +(-1.25465 - 3.86142i) q^{70} +(1.25559 + 0.266884i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-3.86087 - 4.28793i) q^{73} +(-1.08065 - 0.481136i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(0.0782742 - 0.0869323i) q^{76} +(4.15811 + 3.02105i) q^{77} +(3.45317 + 2.50888i) q^{78} +(6.35647 - 7.05957i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(5.38249 + 5.97786i) q^{82} +(-0.308955 - 2.93951i) q^{83} +(-3.97142 - 0.844151i) q^{84} +(-1.06404 - 3.27477i) q^{85} +(5.83447 - 1.24016i) q^{86} +(-0.972918 - 1.68514i) q^{87} +(-0.632947 + 1.09630i) q^{88} +(2.66900 - 8.21432i) q^{89} +(-0.104528 + 0.994522i) q^{90} +(14.0204 - 10.1864i) q^{91} -0.289159 q^{92} +(5.19938 - 1.99159i) q^{93} -8.16745 q^{94} +(-0.0946379 + 0.0687585i) q^{95} +(0.104528 - 0.994522i) q^{96} +(-3.84479 + 11.8330i) q^{97} +(-4.74238 + 8.21404i) q^{98} +(-0.632947 - 1.09630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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